DYNAMICS AT THE GAS LIQUID INTERFACE:
QUANTUM STATE RESOLVED STUDIES OF DCL, CO AND OCS
by
TIMOTHY ANDREW LIVINGSTON LARGE
B.S., University of Washington, 2013

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirement for the degree ofDoctor of Philosophy
Department of Physics
2021
Committee Members:
David Nesbitt
Heather Lewandowski
Eric Cornell
J. Mathias Weber
Carl Lineberger

Livingston Large, Timothy Andrew (Ph.D., Physics)
Dynamics at the Gas Liquid Interface: Quantum State Resolved Studies of DCl, CO and OCS
Thesis directed by Professor David J. Nesbitt

The gas-liquid interface is explored via quantum state resolve direct absorption molecularbeam scattering. Both rovibrational populations and Doppler profiles are measured in order toelucidate the dynamics at the gas-liquid interface. This work explores the collisional dynamics
between several different molecules (DCl, CO and OCS) and the liquid surface of the three
prototypical liquid scattering surfaces (PFPE, glycerol and squalane) as function of both theincident collisional energy and the temperature of the surface. Each of these molecules has had aninteresting story to tell.
The scattering of deuterium chloride (DCl) was shown to follow the known empiricalscattering pathways. These can be split up into two distinct paradigms, thermal desorption (TD)where molecules collide with the surface, trap in the surfaces bound well, thermalize with thesurface and then desorb at the temperature of the surface, and impulsive scattering (IS) wheremolecules hits the surface hard, undergoes a few collisions and then scatters from the surface. In
this IS pathway, empirically it has been seen that the molecules scatter with a rotational distributionthat is temperature-like but hotter than the surface. It was shown that a simple impulsive scatteringmodel of DCl, when convolved with gaussian distributed surface roughness, can predict atemperature like rotational distribution. Carbon monoxide scattering from these prototypicalliquids showed behavior that did not follow the two temperature model. At low collision energies,
a sub thermal scattering pathway was discovered. By comparing molecular dynamics between
molecules that undergo TD dynamics and CO, it was proposed that due to the shallow attractive
interaction CO undergoes with the surface is not deep enough for CO to promote the TD pathway
and thus a low energy IS pathway is probably seen. Due to the low energy vibrations of OCS,
populated vibrational states can be observed in both the incident and the outgoing molecules. Lowiienergy collisional studies showed that vibrational energy transfer does not occur for TD
trajectories. At high collisional energies, the same behavior was seen for the IS pathway.
Remarkably, at these high energies, it was shown the vibrational energy transfer occurs along theTD pathway.

iii

To Oscar,iv

Acknowledgements

I could not have earned a Ph.D. without the generous support of those around me. I havethe sincerest gratitude to my research advisor, David J. Nesbitt. Through his gifts of time andmentorship, he has help shape me into the scientist I am today. He has taught me the importanceof clear communication and I shall always strive to be a clearer communicator. I would also liketo thank him for his kindness and support during some of the difficult life events that have
happened during graduate school.
My work at JILA could not have occurred without the help and support of all the staff at
JILA. They make it a wonderful place to work. I would especially like to thank Hans Green of themachine shop and Terry Brown and Carl Sauer of the electronics shop. Through years of my nearconstant questions, some of their extensive knowledge of the practical world has rubbed off on
me. Without their help, my experiment would be a much poorer version of itself.
I would like to thank the Nesbitt group members, past and present, for the years of good
discussions, friendship, and support. You guys have made this time I have spent here quite fun.
And finally, I would like to thank my family and friends for all their support over the years. I could
not do this alone and I am so glad I had you guys.

v

CONTENTS

CHAPTERI.

Introduction ........................................................................................................1
i. References for Chapter 1 .......................................................................7

II.

Experimental ......................................................................................................9i. Quantum Cascade Lasers .......................................................................9ii. Spectrometer ........................................................................................14iii. Scattering Chamber ..............................................................................17iv. Liquids of Study...................................................................................17
v. Thermal Control of Liquid Surfaces ....................................................18
vi. LN2 Trap ..............................................................................................19vii. References to Chapter 2 .......................................................................20

III. Quantum State and Doppler Resolved Scattering of Thermal/Hyperthermal
DCl at the Gas-Liquid Interface: Support for a Simple
Lever Arm” Model of the Energy Transfer .....................................21
i. Introduction .......................................................................................21
ii. Experimental/Methods ......................................................................25
iii. Results and Analysis .........................................................................29
a. Low energy DCl scattering yields fully TD distributions invi

equilibrium with the liquid......................................................29b. IS Scattering Model ..............................................................34c.

IS Dynamics of DCl scattering at High Einc.........................38

iv. Discussion .........................................................................................42a. A simple lever-arm model ....................................................42b. Averaging over capillary waves predicts hot yet Boltzmann-likerotational distributions ..........................................................48
v. Conclusion ........................................................................................52
vi. References to Chapter 3 ....................................................................54

IV. Low Energy CO Scattering at the Gas-Liquid Interface: Experimental/Theoretical
Evidence for a Novel Sub-Thermal Impulsive Scattering (STIS) Channel .....59
i. Introduction ................................................................................................59
ii. Experimental/Methods ............................................................................64iii. Results and Analysis ...............................................................................67
iv. Molecular Dynamics Simulations ...........................................................73
a. CO, DCl, and CO2 + FSAMs Potential Energy Surface ...................73b.Trajectories: Low Energy Collisions of CO, DCl, CO2
with FSAMs ..........................................................................78c. Theoretical Results and Analysis: CO with FSAMs.........................79
d.Theoretical Results and Analysis: DCl and CO2 with FSAMs .........82
e. Interaction Time Analysis: CO, DCl, CO2 with FSAMs ..................83
v.Discussion .................................................................................................89vii

vi. Conclusion ..............................................................................................92
vii. References to Chapter 4 ..........................................................................94

IV. Low Energy OCS Scattering: A study of Vibrational Energy
Transfer at the Gas-Liquid Interface ....................................................97
i. Introduction .............................................................................................97
ii. Experimental/Method ........................................................................101
iii. Results and Analysis ..........................................................................108
iv. Discussion ..........................................................................................115
v.Conclusion ............................................................................................121
vi. References to Chapter 5 .....................................................................122

V. Quantum State Resolved Scattering of Polyatomics
at the Gas-Liquid Interface: Hyperthermal vs.
Thermal Vibrational Equilibrium Dynamics .....................................124
i. Introduction ...........................................................................................124
ii. Experimental/Methods .......................................................................129
iii. Results and Analysis ..........................................................................132
iv. Discussion ..........................................................................................139
v. Conclusion ..........................................................................................140
vi. References to Chapter 6 .....................................................................142
vii.
VI. Cumulative Bibliography ..................................................................................144

viii

VII.

APPENDIX

A.

Gassuan Distribution of Surface Roughness.........................................152ix

TABLES

Table 3.1 Liquid Properties................................................................................................27
Table 3.2 Summary of Least Squares DCl parameters ......................................................40
Table 4.1 Fit Parameters for CO-FSAM ............................................................................77
Table 4.2 Fit Parameters for DCl-FSAM ...........................................................................77x

FIGURES

1.1 Snapshot of Liquid Squalane

3

1.2 Diagrammatic Representation of the TD and IS Pathways

4

2.1 Interband Quantum Cascade Laser Structure

10

2.2 Laser Frequency Noise Spectral Density

12

2.3 Optics Table and Vacuum Chamber

15

2.4 Absorbance Noise Spectral Density

16

3.1 Cartoon Depiction of DCl Scattering Pathways

23

3.2 Gas-Liquid Scattering Chamber

25

3.3 Sample DCl Boltzmann Plots30

3.4 Summary of low energy scattering as a function of surface temperature32

3.5 DCl Doppler Profiles as a Function of J36

3.6 DCl Scattered Populations

37

3.7 Summary of DCl Fitting Parameters

39

3.8 DCl “lever arm” model

44

3.9 Simulated PFPE Surface Scattering

49

4.1 A schematic of the TD/IS gas-liquid scattering paradigm.

61

4.2 Sample CO Scattering Data

69

4.3 CO Doppler Profiles as a function of J70

4.4 Temperature Dependence of Low Energy CO Scattering72

4.5 Sample CO and DCl ab intio Potential Energy Slices

76

4.6 Comparison of MD and experimental temperature dependence.

80xi

4.7 Histograms of surface FSAM interaction times

85

4.8 Surface Height Probability Distributions

86

4.9 Potential of Mean Force88

5.1 Layout of Experiment101

5.2 Full Low Energy Spectrum of OCS

104

5.3 Experimental Diagnostics

107

5.4 OCS Spectrum Blowups

108

5.5 Low Energy OCS Scattering Populations

110

5.6 OCS Rotational Boltzmann Plot111

5.7 OCS Vibrational Boltzmann Plot112

5.8 OCS Summary of Multiple Liquids

113

5.9 Surface Temperature Dependence of Rotational and Vibrational Degrees of Freedom 115
5.10 OCS Example PES approaches

118

5.11 Landau-Teller Probabilities120

6.1 High Energy OCS Full Spectrum

132

6.2 OCS Population Plot

133

6.3 Rotational Energy Boltzmann Plot

135

6.4 Summary of Fit Parameters

136

6.5 Scattering Parameters Dependence of Surface Temperature137

6.6 Vibrational temperatures of the TD and IS channels

138

xii

Chapter 1
Introduction
Dynamics at the gas-liquid interface play a crucial role in many important chemical
environments, from atmospheric chemistry and environmental science, to catalysis and otherengineering fields.1-6 Interfaces play a particularly crucial role in heterogeneous chemistry, often
providing reagents with lower barrier pathways toward chemical reactions that might be kineticallyunfavorable in the gas phase. Due to the complexity of the liquids surface, the dynamics of thesesystems is not well known, and thus are a worthwhile system to study.
To understand the interface between the liquid and gas phases, we must first have someunderstanding of what the liquid interface looks like on its own. When one looks at the surface ofa lake or pond on a windless day, you will see a pristine flat surface. However, any perturbationof the surface will generate waves that travel across the surface. These ripples are a form ofcapillary waves. These are waves on a liquid surface whose dynamics are significantly dominatedby the effects of surface tension. However, even on a perfectly still day, the liquid surface will not
be perfectly flat. Thermal fluctuations constantly perturb and roughen the surface. For the lengthscales of these experiments, the dynamics of capillary waves can be broken up into two ranges,
gravity-capillary waves and proper capillary waves. These both behave very similarly with the
only difference being that at longer length scales, the restoring force of gravity compared to surface
tension become comparable thus the dispersion relationship of the gravity-capillary waves depends
on both of these forces. The only importance of this is that without any directional restoring force(like gravity), there would be no well defined flat surface. As has been seen in many a space station

1

video in microgravity, a liquid without any restoring force will curl up in a ball due to the surface
tension relaxing the liquid into the lowest energy shape with the ratio of surface area to volume
being maximized. This restoring force does not have to be gravity. Since the key importance of
this regime for us is that a directional force defines the plane of the surface, any force that preventsthe liquid from balling up will work. For our vertical liquid surfaces, the self adhesion of the liquid
to itself and the adhesion to the rotating glass wheel helps define the plane of the liquid interface.
This continuum model of capillary waves is quite good at describing the physics of theliquid interface. However, because it is a continuum model, there is going to be some short lengthscale at which it fails. To understand where this occurs, a more complete model of the surface isneeded.7-8 To achieve this, viscous damping can be added, which primarily affects the model atshort length and time scales (which will be defined below). When one treats this problem
completely, the damping coefficient grows with increasing momentum until the system moves
from an underdamped regime, where damping is only a minor perturbation, to an overdamped
regime, where the viscous damping damps out all frequencies that are too high or the length scales
are too short. By setting both the characteristic pressures and characteristic timescales for both
capillary and viscous forces to be equal, we can calculate the viscocapillary (vc) length and time
𝜇2

𝜇3

scales. The vc length scale is 𝑙𝑣𝑐 = 𝜎 𝜌 and the time scale is 𝑡𝑣𝑐 = 𝜎2 𝜌 where 𝜇 is the dynamical
viscosity, 𝜎 is the surface tension and 𝜌 is the mass density of the liquid. These length and timescales vary wildly, with water having one of the fastest timescales and the shortest lengths scales.
For water, this damping length scale is 74 nm with an upper allowed frequency of 2.5 GHz. On
the other side of the viscosity scale, glycerol has a transition length scale of 14 cm with an upper
frequency of 0.9 Hz. As we can see, these scales vary all over the range of interest. Since even the
shortest length scales for water are much larger than the size of the molecules and atoms that make2

Figure 1.1 :Snapshot of the liquid squalane surface at 298. Dark blue spheres areprimary carbon atoms, red spheres are secondary, and green spheres are tertiary carbon
atoms. Hydrogen atoms, inserted retrospectively, are represented in the respective lighter
color. (a) Plan view along z-axis and (b) side view along y-axis. "Reprinted with permission
from J. Phys. Chem. B 2006, 110, 24, 11717-11724. Copyright 2006 American Chemical
Society.
up the surface, this length scale allows for a clear demarcation between these continuum models
and a full molecular representation at the shortest of length scales. At this time, there is no complete
theory of the liquid surface which included all details of the local molecular motion due to theextreme complexity with many degrees of freedom and low symmetry preventing simplification.
One way around this is to simulate a small part of the liquid surface using molecular dynamics9-13.
The Minton group has run some molecular dynamics simulations of a squalane surface where
figure 1.1 shows a vertical slice through this surface12 and shows visually how complicated the
local surface structure is. Unlike solid surfaces where, generally, surface reorganization happens
quite slowly, locking the surface into a fixed configuration, liquid surfaces have a much faster3

reorganization time, which means that a set static configuration for a liquid surface is not possible
to generate. All thermodynamically allowed surface configurations would appear with thermal
weighting in the measurement region of most experiments. Thus, we can see that understanding
the liquid interface requires both understanding the local structure of the surface but also themacroscopic properties of the liquid.
Gas-liquid surface scattering is a relatively young field at least in comparison to the rest of
surface science. Since isolating bare liquid surfaces has required cleverness and improvements in
vacuum technology, it only has been in the last 20-30 years that this problem has received
appreciable attention from the research community. To understand how atoms and moleculesinteract with the liquid surface, a two pathway empirical paradigm has been used by thecommunity14. These two pathways have been summarized in figure 1.2. Early work with atomicliquid interface scattering detected by time of flight mass spectroscopy has shown that the velocity

Figure 1.2 a diagrammatic representation of both the TD and IS pathways.
"Reprinted with permission from J. Phys. Chem. C 2019, 123, 6, 3449–3460. Copyright2019 American Chemical Society."4

distribution can be broken up into a fast component with peaked velocity distribution and a slower
component that matches with a thermal Maxwell-Boltzmann distribution15-18. As the collisionenergy decreases, this fast component both slows down and decreases in intensity implying that at
low enough energies, only the thermal component will survive. When Perkins from the Nesbitt
group extended these studies to molecules, it was seen that this two pathway paradigm survives.9,
14, 19-26

Using the molecule CO2, Perkins saw that the lower energy pathway is thermal in both thetranslational and rotational degrees of freedom. This pathway has been given the name thermal
desorption (TD). This is where a molecule collides with the surface, dissipating enough of thecollisional translational energy to be trapped in the local van der Waals surface well. In this well,it interacts with the surface long enough to exchange energy and become thermalized to thesurface. It then goes through a barrierless exit channel and appears as thermal rotational andtranslational distributions effectively evaporating from the surface. Typically, everything else that
does not scatter via the TD pathway is considered part of the impulsive scattering (IS) pathway.
Even though this is a less rigorous scattering pathway, it does have some well defined
characteristics. Translationally, one expects a non-thermal translational distribution whose central
velocity scales with the beam energy. Rotationally, one sees a thermal-like rotational distribution.
However, this “temperature” is not necessarily a rigorous temperature a priori but more a measureof average rotational energy. This pathway generally retains more energy than kTs and thus clearly
does not have sufficient time to come to equilibrium with the surface. This pathway is for all themolecules that do not trap and thermalize. They collide with the surface and exchange energy but
they do not interact long enough with the surface to lose all “memory” of their initial conditions.
By understanding this empirical model and where it fails, we can develop a better understandingof collision dynamics at the gas-liquid interface.

5

The structure of the rest of the thesis is as follows. Chapter 2 will discuss some of the
improvements and changes that have been made to the experimental apparatus. Chapter 3 will
explore the dynamics of DCl scattering and how thermal averaging of simple impulsive collisionalmodels can generate temperature-like rotational distributions. Chapter 4 discusses the curious caseof CO. In this chapter, it is shown that the weak attractive forces between the surface and the COmolecule turn off the trapping part of the TD channel, leaving only a single sub-thermal IS channel.
Chapter 5 explores low energy collision of OCS with the liquid surface and how little to novibrational energy transfer occurs even though thermalization was seen with respect to therotational degrees of freedom. Chapter 6 explores higher energy scattering of OCS. Like the TD
channel of the lower energy studies, the IS channel does not exchange vibrational energy with thesurface. However, TD pathway shows markedly different behavior, with the vibrational degrees
of freedom nearly completely thermalizing with the surface. The dynamical behavior of the TD
pathway appears to conflict with the “memoryless” behavior that has been previously seen andassumed, thus implying that there is more to understand about the dynamics of this simple
pathway.

6

Chapter 1 References
1.
Kolb, C. E., et al., An Overview of Current Issues in the Uptake of Atmospheric Trace
Gases by Aerosols and Clouds. Atmos. Chem. Phys. 2010, 10, 10561-10605.
2.
Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E.; Vandoren, J.; Davidovits, P., Uptake of
Gaseous HNO3, N2O5, and HCl into Sulfuric-Acid Droplets. Abstr. Pap. Am. Chem. S. 1990,
200, 122-Phys.
3.
Watson, L. R.; Vandoren, J. M.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb,
C. E., Uptake of HCl Molecules by Aqueous Sulfuric-Acid Droplets as a Function of Acid
Concentration. J. Geophys. Res.-Atmos. 1990, 95, 5631-5638.
4.
Vandoren, J. M.; Watson, L. R.; Davidovits, P.; Worsnop, D. R.; Zahniser, M. S.; Kolb,
C. E., Temperature-Dependence of the Uptake Coefficients of HNO3, HCl, and N2O5 by Water
Droplets. J. Phys. Chem. 1990, 94, 3265-3269.
5.
Hammerich, A. D.; Finlayson-Pitts, B. J.; Gerber, R. B., Mechanism for Formation of
Atmospheric Cl Atom Precursors in the Reaction of Dinitrogen Oxides with HCl/Cl- on Aqueous
Films. Phys. Chem. Chem. Phys. 2015, 17, 19360-19370.
6.
Hammerich, A. D.; Finlayson-Pitts, B. J.; Gerber, R. B., NOx Reactions on Aqueous
Surfaces with Gaseous HCl: Formation of a Potential Precursor to Atmospheric Cl Atoms. J.
Phys. Chem. Lett. 2012, 3, 3405-3410.
7.
Denner, F.; Pare, G.; Zaleski, S., Dispersion and Viscous Attenuation of Capillary Waves
with Finite Amplitude. Eur. Phys. J.-Spec. Top. 2017, 226, 1229-1238.
8.
Denner, F., Frequency Dispersion of Small-Amplitude Capillary Waves in Viscous
Fluids. Phys. Rev. E 2016, 94.
9.
Nogueira, J. J.; Vazquez, S. A.; Mazyar, O. A.; Hase, W. L.; Perkins, B. G.; Nesbitt, D.
J.; Martinez-Nunez, E., Dynamics of CO2 Scattering Off a Perfluorinated Self-Assembled
Monolayer. Influence of the Incident Collision Energy, Mass Effects, and Use of Different
Surface Models. J. Phys. Chem. A 2009, 113, 3850-3865.
10.
Martinez-Nunez, E.; Rahaman, A.; Hase, W. L., Chemical Dynamics Simulations of CO2
Scattering Off a Fluorinated Self-Assembled Monolayer Surface. J. Phys. Chem. C 2007, 111,354-364.
11.
Zhang, J. M.; Upadhyaya, H. P.; Brunsvold, A. L.; Minton, T. K., Hyperthermal
Reactions of O and O2 with a Hydrocarbon Surface: Direct C-C Bond Breakage by O and HAtom Abstraction by O2. J. Phys. Chem. B 2006, 110, 12500-12511.
12.
Kohler, S. P. K.; Reed, S. K.; Westacott, R. E.; McKendrick, K. G., Molecular Dynamics
Study to Identify the Reactive Sites of a Liquid Squalane Surface. J. Phys. Chem. B 2006, 110,11717-11724.
13.
Wiens, J. P.; Nathanson, G. M.; Alexander, W. A.; Minton, T. K.; Lakshmi, S.; Schatz,
G. C., Collisions of Sodium Atoms with Liquid Glycerol: Insights into Solvation and Ionization.
J. Am. Chem. Soc. 2014, 136, 3065-3074.
14.
Perkins, B. G.; Haber, T.; Nesbitt, D. J., Quantum State-Resolved Energy Transfer
Dynamics at Gas-Liquid Interfaces: IR Laser Studies of CO2 Scattering from PerfluorinatedLiquids. J. Phys. Chem. B 2005, 109, 16396-16405.
15.
King, M. E.; Nathanson, G. M.; Hanninglee, M. A.; Minton, T. K., Probing theMicroscopic Corrugation of Liquid Surfaces with Gas-Liquid Collisions. Phys. Rev. Lett. 1993,
70, 1026-1029.

7

16.
Saecker, M. E.; Nathanson, G. M., Collisions of Protic and Aprotic Gases with
Hydrogen-Bonding and Hydrocarbon Liquids. J. Chem. Phys. 1993, 99, 7056-7075.
17.
Saecker, M. E.; Nathanson, G. M., Collisions of Protic and Aprotic Gases with a
Perfluorinated Liquid. J. Chem. Phys. 1994, 100, 3999-4005.
18.
King, M. E.; Fiehrer, K. M.; Nathanson, G. M.; Minton, T. K., Effects of Thermal
Roughening on the Angular Distributions of Trapping and Scattering in Gas-Liquid Collisions. J.
Phys. Chem. A 1997, 101, 6556-6561.
19.
Perkins, B. G.; Nesbitt, D. J., Quantum-State-Resolved CO2 Scattering Dynamics at theGas-Liquid Interface: Incident Collision Energy and Liquid Dependence. J. Phys. Chem. B 2006,
110, 17126-17137.
20.
Perkins, B. G.; Nesbitt, D. J., Quantum-State-Resolved CO2 Scattering Dynamics at theGas-Liquid Interface: Dependence on Incident Angle. J. Phys. Chem. A 2007, 111, 7420-7430.
21.
Perkins, B. G.; Nesbitt, D. J., Correlated Angular and Quantum State-Resolved CO2
Scattering Dynamics at the Gas-Liquid Interface. J. Phys. Chem. A 2008, 112, 9324-9335.
22.
Perkins, B. G.; Nesbitt, D. J., Stereodynamics in State-Resolved Scattering at the GasLiquid Interface. P. Natl. Acad. Sci. USA 2008, 105, 12684-12689.
23.
Perkins, B. G.; Nesbitt, D. J., Quantum State-Resolved CO2 Collisions at the Gas-LiquidInterface: Surface Temperature-Dependent Scattering Dynamics. J. Phys. Chem. B 2008, 112,507-519.
24.
Perkins, B. G.; Nesbitt, D. J., Toward Three-Dimensional Quantum State-Resolved
Collision Dynamics at the Gas-Liquid Interface: Theoretical Investigation of Incident Angle. J.
Phys. Chem. A 2009, 113, 4613-4625.
25.
Perkins, B. G.; Nesbitt, D. J., Stereodynamics at the Gas-Liquid Interface: Orientation
and Alignment of CO2 Scattered from Perfluorinated Liquid Surfaces. J. Phys. Chem. A 2010,
114, 1398-1410.
26.
Perkins, B. G.; Nesbitt, D. J., High Resolution Dopplerimetry of Correlated Angular andQuantum State-Resolved CO2 Scattering Dynamics at the Gas-Liquid Interface. Phys. Chem.
Chem. Phys. 2010, 12, 14294-14308.

8

Chapter 2
Experimental
The experiments in this thesis were performed with the same direct absorption
spectroscopy apparatus. Dr. Brad Perkins originally designed and developed the apparatus and adetailed description of the spectrometer and scattering chamber can be found in his thesis.1 The
sample holder was upgraded by Andrew Gisler and a description of this lazy Susan sample holder
can be found in the following paper2. Several major upgrades have been performed in pursuit ofthis thesis and shall be discussed in this chapter.
2.1 Quantum Cascade Lasers
Quantum cascade laser (QCL) diodes are modern bandgap engineered diodes3-4. They arestill fairly new devices with many kinks to be worked out, but they open the possibilities of easier
single frequency access to midinfrared light. Unlike cryogenic lead salt diode lasers, these diodes
can be operated at room temperature, making them more practical and robust. When several thinlayers (<10’s of nanometers) of different semiconductors with differing bandgaps are layered next
to each other, a set of “particle-in-a-finite-well” states are created in both the conduction andvalence band of this semiconductor system. These are called quantum wells. By varying the
thickness of both the wells and the barriers, a coupled system of finite wells can be engineered.
Because this system’s properties are only weakly dependent on the semiconductor material
properties and strongly on the organization of these thin layers, many of the important properties
can be designed to specifications rather than having to rely on material properties found in nature.
A standard diode laser emits light when an electron is driven across the bandgap from theconduction band to the valence band, emitting a single photon of light. This is quite different from9Figure 2.1 An example QCL diode interband structure. Solid black lines show the upperlasing levels while the dotted line show the lower lasing levels. Other allowed states in thesystem are shown in red. This figure is used under GNU Free Documentation License and is
attributed to Evans82 at English Wikipedia
how a quantum cascade laser works, which use subband transitions between the engineered levelsin the semiconductor device. When one applies a strong enough voltage to one of these patterned
quantum well devices, these particle in a well states get shifted by a strong linear voltage gradientacross the device. This can be seen in figure 2.1. If designed properly, this can create a quantum
well that has an optical transition across a predefined energy gap. If multiple of these wells are put
next to each other, an electron can undergo an optical transition, be captured in the lower state andbe injected into the next well’s lasing level. This allows for one electron to generate multiple
photons of a designed wavelength. This has the added benefit of allowing these devices togenerally be operated at room temperature. With a normal midinfrared laser diode, the thermalenergy at room temperature would populate the conduction band enough to turn off the population
10

inversion and quench the lasing. With a QCL, the bottom couple of rungs of the staircase will bethermally populated, but because there are multiple wells on top of each other, there are still lasinglevels that can generate light.
For our specific laser systems, we use a QCL diode inside of an external cavity laser(ECQCL). The specific lasers that are used are Daylight Solution’s single frequency mode hop
free tuning laser. These laser diodes are broadband emitting laser diodes whose frequency isnarrowed by using a grating to feedback the light. These lasers are in a double Littrow cavity
configuration. A Littrow cavity feeds the first order diffraction peak from the grating back into thediode to create a cavity. Unlike the normal Littrow cavity where the output coupler is the zerothorder diffraction peak from the grating, the light is taken out of the backside of the diode. This
preserves many of the advantageous tuning properties of a Littrow cavity, while removing thebeam steering that occurs due to turning the grating to tune the laser. An important part of ourspectroscopic data collection is the ability to scan over a frequency range without hopping to adifferent laser mode at a different frequency. This can be minimized by tuning all the laser’s cavity
conditions at the same rate. This is called mode hop free tuning. In an ideal world, a Littrow cavity
diode laser can be designed to support only one laser mode over its entire tuning range. In practice,
this is difficult. With proper design, Daylight Solutions has been able to provide a laser that cancontinuously tune for around 1 cm-1 before it undergoes a mode hop. This is done this by balancing
the two important cavity conditions while tuning, the optical length of the cavity and the angle atwhich the laser light diffracts off the tuning grating. In practice, there are other engineering
concerns that must be balanced when building a laser, but the general idea is that the rotational

11

pivot point of the grating needs to be along the plane of the grating and slightly past the back faceteof the diode (optical length of the cavity from the grating surface along the optical axis of laser).
This reliance on the grating for frequency selection has some downsides. One of the major
downsides is that the laser frequency acquires sensitivities to mechanical noise and vibrations. Thisis made even worse by the fact that the grating plus its tuning mechanism has an underdamped
response function with a Q of at least 10 and a resonant frequency at ~ 240 Hz. This low frequency
mechanical resonance means that the mechanical vibrations and external noise can couple directly
into the frequency of the laser. This has been mitigated by several strategies, which boil down tomechanically isolating the laser system from the rest of the experiment. To eliminate couplingfrom the optics table and all other devices on the optics table, the laser is supported on sorbethane
feet with the correct amount of additional weight to damp most low frequency vibrations between

Figure 2.2 Laser Frequency noise spectral density. Three major features can be seen. i.) the
mechanical resonance of the grating tuning mechanism at 240 Hz, ii.) 60 Hz line noise
through from the current controller, and iii.) 1/f pickup noise.

12the laser and the table. This isolation was enhanced by damping all vibrations that travel along thepower and cooling cables by securing them in vibrationally dampening foam secured to the optics
table. The final step was to reduce the noise that travelled through the cooling water itself. This isaccomplished by turning down cooling pump speed to the minimal value that achieves the required
cooling of the laser, while imparting the least amount of turbulence on the water itself. Figure 2.2
shows the frequency noise spectral density. There are several noise sources that are identified. As
mentioned above, the noise around 240 Hz comes from the mechanical resonance of the grating.
It has the characteristic form of a mechanical resonance and matches well with the sensitivity plotmeasured from the PZT tuning of the laser. Another identified source of noise is bleed through of
60 Hz line noise and its harmonics (120, 180, 240, 300, 360, etc.) from the laser current controller.
The final source of noise that has been identified is 1/f noise that is picked up by the grating. A
significate proportion of this noise comes from the turbulence of the water cooling system. Though
this has been reduced, it can be reduced further by turning off the cooling pump. This is not asolution to this problem because the laser absolutely needs water cooling to prevent thermal
overload of the system. If one only considers the noise above a KHz, the laser has a linewidth onorder only a couple of MHz but due to the low frequency noise, this fairly narrow laser wanders
over ~5-15 MHz depending on the stability of the cavity at a frequency and how well the isolation
is working. Without isolation, linewidths of 25-75 MHz were seen.
Two different QCL diode are used for the experiments in this thesis. The original diode isused for the DCl work in chapter 3, with the newer diode for the CO and OCS work in chapter 46. The original diode tuning range is from 2075 to 2275 cm-1 with ~ 100 mW of infrared light
across the spectrum. In the summer of 2015, the laser cavity was sent off to Daylight Solutions totune up the laser cavity, since the tuning range was creeping in from the edges of the spectrum.

13

After realignment during their normal thermal cycling tests, the diode underwent thermal overload
and was destroyed. They could not replace this diode and after 6 months or more of negotiations,a new diode was chosen. This diode covers a range of 1980 – 2200 cm-1 with an average power of~300 mW. However, this laser is significantly red shifted from the previous laser preventing accessto all DCl’s states above R(13). Thus, with the new laser, the target molecules of choice shifted to
CO and OCS, which have redshifted band origins compared to DCl. One must be careful when
operating in the lower part of the frequency range of the new diode. The antireflection coating of
the diode is not perfect in this region thus the laser frequency can get caught on diode modes andmode hop quite frequently between two modes 10 cm-1 apart. This can be mitigated by shiftingaround the temperatures of either the diode (by controlling the TEC setpoint) and/or the base of
the laser cavity (by changing the temperature setpoint of the cooling water). This can shift aroundthe alignment enough to prevent mode hops in the region of interest at the cost of moving them toother frequency regions.

2.2 Spectrometer
A simplified schematic of the optical table can be seen in figure 2.3a. Since the light
generated in the ECQCL is several orders of magnitude more powerful than what is usable in theseexperiments, the power is cut by a factor of ~50 by a weak reflection from a tilted BaF window
and then adjustably by crossed Rochon polarizers. This leaves, after transmission through the restof the system, ~10-50 uW on each of our LN2 cooled InSb photodetectors. This power level ischosen to maximize the power on the detectors while minimizing the nonlinearity of thephotodetectors. Our frequency diagnostics comes in three pieces. We use a commercial wavemeteras rough calibration of our spectrum. This traveling Michelson interferometer, similar to others

14

Figure 2.3 a) A schematic layout of the optics table used for these experiments. PD = Infrared
Photodiodes b) An image of the internals of the vacuum chamber. Traced out in red is thepath of the Harriot cell light.
used in lab, gives a frequency measurement several times a second, allowing for real time
diagnostics of the laser frequency. During a scan, signals from both a bowtie etalon and a gas cellare recorded. The dry air purged bowtie etalon has a finesse of ~20-30 and a FSR of 249.566(30)MHz. Thus, by interpolating between the etalon fringes, the relative tuning of the laser can be

15

Figure 2.4 Absorbance noise spectral density. The reference detector signal is scaled to thesignal detector signal and then they are subtracted from each other, removing common modenoise and leave us with the subtracted signal, whose noise has been reduced by 20-40 db
depending on the frequency. The shot noise noise floor for these powers is ~1*10-7 per rootHz.
calculated. With an appropriate choice of reference gas (often the gas under study), the absolute
frequencies of the measured reference lines can be used to calibrate the starting frequency of eachscan. The scattering signal is measured in a shot-noise limited spectrometer. This is achieved via
a balance detection scheme, with one of the two arms containing the scattering system in thevacuum chamber. The signal from the reference detector is scaled to DC value of the signal
detector and then, the two channels are subtracted, leaving only the differential signal, whichcontained the absorbance from the scattered molecules. This setup achieves absorbancesensitivities of around 1.0*10-5 in the bandwidth of the experiment. An absorbance spectral noise
density plot can be seen in Fig 2.4. Due to practical limitations on electronic, the reduction incommon mode noise is between ~20-40 db.
16

2.3 Scattering Chamber
The 60 L square vacuum chamber contains the scattering system. This chamber is pumped
by a liquid N2 cooled 6-inch diffusion pump that maintains an operating pressure below 1*10-4 torr
during full operation, which means the minimum mean free path is several times the length of thevacuum chamber. This prevents any collisions with background gasses while the scatterer
molecules travel from the beam sources to the surface and then from the surface to themeasurement region. The scattering system is made up of the molecular beam source, the scatteringtarget and the multipass cell. Fig. 2.3b shows an image of the vacuum system with the path of theinfrared light traced out by a HeNe laser. Our beam source is of Proch and Trickl design5. The
molecular beams used in this thesis were prepared generally as directed in the Perkins thesis1. CO
and OCS behave much like CO2 in a supersonic expansion. However, DCl is a much “stickier”
molecule and thus, special effort must be made to prevent clustering. Since the flux of the beamsources is proportional to the source pressure and the area of the orifice and the collisional rate(~”clustering” rate) is proportional to the square of the source pressure and the diameter of theorifice, one should use a large diameter orifice with a low source pressure to minimize the totalclustering of the molecular beam. The molecule’s rovibrational populations are characterized bymeasuring the incident beam 1-2 cm downstream from the molecular beam skimmer and theincident beam energy is measure using a time of flight microphone setup that is described in detailelsewhere.6 The scattered signal is measured in a 16 pass concentric Herriot cell highlighted inFig. 2.3b. The single pass cell length is ~40 cm. This beam path lies parallel to the plane of liquidsurface and perpendicular to the molecular beam. This means that the Doppler broadening reportson the velocity perpendicular to the scattering plane defined by the liquid surface normal and themolecular beam.

17

2.4 Liquids of study
This thesis involve three different classes of liquids that sample different scattering
dynamical regimes: 1) perfluorinated polyether, (PFPE, Krytox 1506, F-[CF(CF3)CF2O)]14(avg)CF2CF3), as prototype for a rough but chemically inert liquid surface, 2) squalane (2,6,10,15,19,23hexamethyltetracosane, C30H62), as prototype for strongly hydrophobic surface, and 3) glycerol(1,2,3-propanetriol, C3H8O3), as prototype for a highly hydrophilic surface due to multiple
protruding OH groups. Each liquid is degassed under ~1 mTorr vacuum at room temperature forseveral hours to remove dissolved atmospheric gases, or at slightly elevated temperatures (~ 350K) for the glycerol liquid samples to allow for more complete degassing within a reasonable timeframe.
2.5 Thermal control of liquid surface
For the studies that involve different surface temperatures, a temperature regulation system
was added. In the studies of DCl in chapter 3, the copper liquid trough was directly cooled by acold plate connected to a recirculating ethanol chiller. This allowed for temperature stabilization
between -20C to 40C. For the studies of CO in chapter 4, efforts were put forth to reduce thermal
gradients and increase temperature stability and accuracy. The liquid trough was better thermallyisolated with Teflon spacers and the glass wheel was replaced with a bead blasted steel wheel.
Since the thermal conductivity of the metal parts is much larger than the Teflon spacers, the liquid+ metal system will be held a constant temperature. Temperature stabilization was achieved byadding a thermoelectric cooler (TEC) between the cold plate of the ethanol chiller. This TEC wascontrolled by a Thorlabs QCL controller (ITC4002QCL) with an integrated TEC controller. It
stabilized the temperature to a thermistor (RC44008) epoxied to the front of the copper trough.
Accounting for the thermistor’s accuracy and the systematic errors introduced through the TEC
18

controller, the combined systematic and probabilistic errors in the temperature stabilization givean absolute error of under .5 kelvin over the entire operating range of the thermal system. Thissystem as also used for the temperature dependent work on OCS in chapter 5 and 6.
2.6 LN2 trap
For the work in chapter 5 and 6, a LN2 cooled cold plate was added at the top of the vacuum
chamber and achieves a temperature of 90 K when cooled. This was implemented to reduce thebackground OCS in the vacuum chamber. Since the FWHM of a room temperature OCS transitionis ~100 MHz and the laser’s linewidth is ~10 MHz, there is no appreciable frequency noise fromthe scattered signal. However, since the frequency noise on the background gas in the chamber is
not common mode on both the signal and reference detectors, it passes straight through thecommon mode subtraction circuit and appears as extra noise. This noise is reduced by the
cryopumping by a factor of ~10-100, due to an equivalent reduction of background OCS.

19

Chapter 2 References
1.
Perkins, B. G., Jr. Quantum State-Resolved Energy Transfer Dynamics at the Gas -LiquidInterface. Ph.D., University of Colorado at Boulder, Boulder, 2009.
2.
Gisler, A. W.; Nesbitt, D. J., On Probing Ions at the Gas-Liquid Interface by Quantum
State-Resolved Molecular Beam Scattering: The Curious Incident of the Cation in the NightTime. Faraday Discuss. 2012, 157, 297-305.
3.
Curl, R. F.; Capasso, F.; Gmachl, C.; Kosterev, A. A.; McManus, B.; Lewicki, R.;
Pusharsky, M.; Wysocki, G.; Tittel, F. K., Quantum Cascade Lasers in Chemical Physics. Chem.
Phys. Lett. 2010, 487, 1-18.
4.
Weida, M. J.; Caffey, D.; Rowlette, J. A.; Arnone, D. F.; Day, T., Utilizing Broad Gain
Bandwidth in Quantum Cascade Devices. Opt. Eng. 2010, 49.
5.
Proch, D.; Trickl, T., A High-Intensity Multi-Purpose Piezoelectric Pulsed MolecularBeam Source. Rev. Sci. Instrum. 1989, 60, 713-716.
6.
Nizkorodov, S. A.; Harper, W. W.; Chapman, W. B.; Blackmon, B. W.; Nesbitt, D. J.,
Energy-Dependent Cross Sections and Nonadiabatic Reaction Dynamics in F(2P3/2), 2P1/2)+n-H2 > HF(V,J)+H. J. Chem. Phys. 1999, 111, 8404-8416.

20

Chapter 3
Quantum State and Doppler Resolved Scattering of Thermal/Hyperthermal DCl at theGas-Liquid Interface: Support for a Simple “Lever Arm” Model of the Energy Transfer
Dynamics*

3.1 Introduction
The dynamics of collisions at the gas liquid interface are essential to many aspects ofatmospheric and environmental chemistry.1

Interfaces play a particularly crucial role inheterogeneous chemistry, often providing reagents with lower barrier pathways toward chemical
reactions that might be kinetically unfavorable in the gas phase.2-3 The interaction of gas
molecules with aerosol droplets is of special importance to atmospheric chemistry;4 one example
of key impact being the depletion of ozone in the upper atmosphere catalyzed by chlorine atoms(Cl) and chlorine generated hydrocarbon radicals.5-6 For example, it has been shown that an
important pathway to generating highly active Cl radicals is oxidation of hydrogen chloride by
N2O5 on water droplets, for which the reagents HCl and N2O5 must first physisorb and thermallyaccommodate on the gas-liquid interface. As a result, an understanding of energy transfer
dynamics in molecular collisions with liquid surfaces rises to considerable significance.
One direction in which the atmospheric community has made considerable progress is inmeasuring the temperature dependent equilibrium properties at the gas-liquid interface, for which
both enthalpy and entropy of solvation can be extracted from gas-droplet absorption
measurements. For example, from ~100 µm water droplets moving through a low-pressure gas,Davidovits and coworkers have been able to measure uptake of gas molecules into the liquid as afunction of interaction time and droplet temperature.7-8 In experiments with hydrogen chloride
21*Published in J Phys. Chem. C, 123, 3449, (2019)on water droplets, for example, it has been proposed that the rate-limiting step to solvation is
physical adsorption of HCl onto the liquid surface. Despite the considerable power of thesedroplet-train techniques, the uptake processes are detected by total loss of reagent HCl andcannot be easily decoupled into more fundamental reaction steps. One critical limitation of theabove methods is that they sample an equilibrium state and therefore do not provide kinetic
information on molecular interactions with gas liquid interface.
An alternative approach to probing such kinetics at the gas liquid interface is byscattering a cold, monoenergetic molecular beam from a surface of interest and measuring theresulting fluxes under low pressure, collision free conditions. This allows for the extraction of
more dynamical information about both i) the gas-liquid interfacial properties and ii) the
molecule-specific interactions with the surface. By way of example, previous studies by several
groups using molecular beam scattering have revealed compelling evidence for microscopic
branching into two dynamical scattering pathways.9-16 Specifically, incident molecules caneither i) collide with the surface and thermally accommodate through a sequence of collisional
interactions, trapping on the surface, and then undergoing a final desorption step (trappingdesorption (TD)) or ii) impulsively scatter (IS) into an energized rotational/translational state
distribution through one or a few collisional interactions with the interface (see Fig. 3.1). On the
one hand, earlier quantum state resolved studies with CO2 reported that both rotationally andtranslationally scattered molecules from the thermal desorption (TD) pathway emerged in a
Boltzmann-like distribution characteristic of the surface temperature (TS).17 On the other hand, it
was also noted, in NO gas-liquid scattering studies, that this same fully accommodated TD
pathway resulted in asymptotic rotational and electronic temperatures that were out of
equilibrium with and cooler than the surface.18-21 By detailed balance, it was suggested that NO22

Figure 3.1: Cartoon depiction of the dominant DCl scattering pathways: Microscopic
branching between i) trapping desorption (TD) processes, based on multiple collisions with
the interface and leading to complete thermalization, vs. ii) impulsive scattering (IS)processes, which involve only a relatively few collisions with the surface and thereby
allowing for scattering into much hotter internal (rovibrational) and external (translational)
channels.

might experience rotational and/or electronic state dependent dynamical barriers while leaving
the surface, asymptotically causing the flux to fall out of equilibrium with TS.
By way of contrast, the impulsive scattering (IS) pathway is not required to lose memoryof its original collision dynamics and, as a result, often results in flux distributions forward
peaked in the scattering plane.16, 22 In CO2, the Doppler velocity distributions perpendicular tothe scattering plane were also effectively described as a Maxwell Boltzmann temperature
distribution23 and in equilibrium with the rotational distributions. Most relevantly, rotational
distributions in the IS component of such scattered NO and CO2 have been routinely found to bewell described by a “temperature” (TIS(rot) >>TS),17-26 despite the lack of any dynamical picture
for “equilibration” within the IS quantum state manifolds.

23

Pioneering studies on DCl scattering at the gas-glycerol interface have been performed
with time of flight methods by the Nathanson group.27-37 As noted in previous gas-liquidinterfacial studies, their methods again reveal two distinct scattering pathways, one achieving
complete thermalization with the surface (TD) and the other scattering impulsively (IS) with anaverage energy content often much higher than the surface thermal energy (kTS). Furthermore,
Nathanson’s powerful combination of mass spectroscopy and time of flight methods revealed
that proton exchange between DCl → HCl at the surface of liquid glycerol requires trapping andthermalization of the incident DCl.27-28, 30, 34 Indeed, as one plausible model, it was proposed thatthese DCl molecules must first dissociate into the liquid and recombine with other solvated ions(such as H3O+ or OH-) in the glycerol. The present work nicely complements these studies, inwhich we focus on quantum state resolved scattering dynamics of DCl at the gas-liquid interface,
using direct infrared laser absorption and high resolution ( 10 MHz) laser Dopplerimetry
methods to probe the internal rotational and out-of-plane translational velocity distributions inthe scattered molecules.
The chapter is organized as follows. In Sec. 3.2, we briefly summarize the quantum state
resolved experimental techniques. This is followed in Sec. 3.3 by presenting results fromthermal (Einc = 1.5(1) kcal/mol) and hyperthermal (Einc = 11.5(5) kcal/mol) DCl scatteringstudies from a series of prototypical liquids, which successfully explore both TD and IS
components in the energy transfer collision dynamics. These rotational distributions are thenanalyzed in Sec. 3.4, appealing to the simple but physically motivated “lever arm” models of
McCaffery and coworkers38-43 (e.g., angular momentum transfer via hard sphere scattering fromthe liquid surface) to help interpret the observed trends. One unexpected success is the
combination of these “lever arm” scattering models with capillary wave theory44 to provide a24

first analytical framework for rationalizing the Boltzmann temperature-like behavior observed
empirically in present and previous studies.17-26 The chapter concludes with summarizing
comments and directions for future experiments in Sec. 3.5.

3.2 Experimental/Methods
A detailed overview of the experimental apparatus has been given elsewhere, thus only
essential details and modifications17, 24, 45 specific to the present work need to be considered. A
schematic diagram of the scattering chamber is shown in Fig. 3.2. The instrument consists of asupersonic molecular beam, a freshly cleaned liquid surface and a near quantum shot noise
limited infrared laser direct absorption spectrometer. To help deconstruct contributions fromtrapping desorption (TD) and impulsive scattering (IS) pathways, both thermal and hyperthermal

Figure 3.2. Gas-liquid scattering chamber with a skimmed molecular beam impinging on a
Fenn-type rotating wheel assembly. Also shown is a visualization of the infrared multipass
Herriott cell geometry for quantum state and high resolution Doppler resolved detection of
the scattered DCl (v,J,v⊥) molecular density.
25

molecular beams are explored. The thermal molecular beam is generated from a 10% DCl/Ar
mixture supersonically expanded through a piezoelectric 300 m pinhole valve with a pulse
length of 400 sec and collimated with a 3 mm skimmer situated 1.5 cm from the nozzle orifice.
The hyperthermal molecular beam is generated by reverse seeding DCl in a 6.7% mixture with
H2, expanded through a slightly larger 500 m pinhole nozzle but with the same 400 sec pulse
length and skimmer geometry.

The translationally thermal and hyperthermal beams haveenergies of 1.5(1) kcal per mol and 11.5(5) kcal per mol, respectively, as measured with a fast in
vacuo hearing aid microphone/time of flight setup.46 Both molecular beams are rotationally cold
(Trot = 9.5(1) K), which translates into more than 75% of the DCl population in the J = 0 or 1
rotational state. The thermal and hyperthermal studies have been performed at incident angles of
45o (5) and 65o (8), respectively, with scattered DCl species detected in the corresponding near
specular angular direction. Due to the geometry of the scattering chamber, the 45o beam collects
scattered signal from -25o to 70o and the 65o beam collects signal -40o to 75o. However, both ofthese beam collection efficiencies are peaked around 60o-70o. The hyperthermal energy
scattering results exhibit negligible contamination from DCl (J = 0, 1) in the incident beam, due
to the more glancing scattering geometry and therefore a greater degree of angular/spatial
separation in the scattered flux.
The liquid surface is prepared in the method of Lednovich and Fenn,47 using a rotating(  0.2 Hz) frosted glass wheel (12.7 cm diameter) half-submerged in the liquid reservoir andscrapped with a stationary razor blade to present a clean, thin ( 500 m) gas-liquid surface tothe impinging molecular beam. These studies have examined three prototypical liquids tosample three broad classes of gas-liquid scattering dynamics (see Table 1): 1) Perfluorinatedpolyether, (PFPE, Krytox 1506, F-[CF(CF3)CF2O)]14(avg)-CF2CF3) as a chemically inert liquid26

dominated by CF functional groups, thus imparting the interface with partially negatively
charged F atoms and a strongly dipolar character, 2) Squalane (2,6,10,15,19,23hexamethyltetracosane, C30H62) as a prototypical hydrophobic hydrocarbon with predominantly
CH surface groups and thus only a weakly positive dipolar interfacial character, and 3) Glycerol(1,2,3-propanetriol, C3H8O3) as a small hydrophilic hydrocarbon chain, with multiple OH groups
giving it a mixed positive and negative dipolar character depending on bond orientation at thegas-liquid interface. Each liquid is degassed under ~1 mtorr vacuum at room temperature forseveral hours to remove dissolved gases (H2O, O2, N2, CO2), with elevated temperatures for theglycerol liquid samples to allow for complete degassing within a reasonable time frame.

Table 3.1: Liquid properties
Surface Tension (dyne/cm)
Density (g/cc)
Molar Mass (amu)
Molecular Size (nm)
Vapor Pressure (Torr, 25 Celsius)

PFPE
17
1.87
2400
1.29

Squalane
30
0.81
422
0.95

-7

Glycerol
63
1.26
92
0.49

-8

-4

Surface Groups

7 x 10CF and CF

2 x 10CH and CH

1.7 x 10
Bonded OH,
CH

Estimated Surface Roughness (Å)*

8.0

6.2

4.4

2

3

2

3

2

*Root mean square (rms) width of the surface region (δ) is approximately [(kTliq/2πγ)× ln(2π1/2Lc/d)] where γ is the surface tension, Lc = [γ/(g ρ)]
the molecular size ((molecular mass/density)1/3).

1/2

and d is simple density based estimate ofDuring pulsed valve operation (11 Hz repetition rate), the chamber is maintained at < 1 x
10-4 Torr with a liquid N2 cooled 6” diffusion pump, even for relatively high vapor pressureliquids such as glycerol. This translates into mean free path conditions (  100 cm)

27

comfortably longer than the chamber dimensions and guarantees that nascently scattered DCl (v= 0, J) can travel collision free from the surface to the laser probe region. For the hyperthermal
collision energy studies, the liquids reside in one of three Teflon reservoirs mounted on a rotatingplate, providing convenient interchangeable access to the molecular beam in vacuo with only anominal time delay. For the temperature-dependent studies, the liquids are housed in a copper
reservoir in contact with an aluminum block, whose temperature is controlled by a circulating
ethanol flow. Temperatures can be varied from -20 to 40 Celsius, with the lower and upper
values constrained by the liquid melting points and excessive vapor pressure in the chamber,respectively.
The scattered DCl number densities are measured via high resolution Beers law
absorption spectroscopy, with light generated by an external cavity quantum cascade laser 48-50(ECQCL, Daylight Solutions MHF-QCL, 4.6 um laser chip) directed through a 16 pass Herriot
cell parallel to the wetted wheel surface. Light intensities are measured differentially before andafter the Herriot cell on liquid N2 cooled Indium Antimony (InSb) photodetectors in a fast servo
loop subtraction circuit to yield high bandwidth (60 MHz) rejection of common mode laser
noise. The resulting absorbance spectral sensitivities (2-3x10-7 per Hz1/2 for 10 W on eachdetector) are within a factor of two of the fundamental quantum shot noise limit.
The infrared laser is scanned across each Doppler broadened transition in 2 MHz steps,
with signals integrated over the rising edge (300 sec) for every gas pulse (11 Hz rep rate) toeliminate collisionally relaxed DCl molecules recrossing the laser multipass region. The infraredlaser is calibrated by combination of a low pressure (< 1 Torr) DCl reference gas cell for
absolute frequencies and 249.566(33) MHz fringe spacings from a Fabry-Perot cavity tofacilitate precision least squares fits to the Doppler profiles. The laser tunes from R(0) (2101.63

28

cm-1) through R(18) (2249.49 cm-1) in DCl, which, for a rotational constant of BDCl  5.4 cm-1,
provides access to lower states from Erot = 0 up to 1800 cm-1. The frequency noise of the
ECQCL is < 10 MHz FWHM over a single scan, which is 10-20 fold narrower than typicalscattered Doppler velocity contributions of 140 MHz. The laser polarization is normal to theliquid surface. The use of a few mW and frequency stable quantum cascade lasers allows for adramatically reduced absorbance noise floor as well as a decrease in frequency noise comparedto our previous Pb-Salt diode laser capabilities operating with only a few W power levels. Thishas greatly expanded the flexibility of our experimental apparatus and allows gas-liquid
scattering dynamics with much weaker oscillator strength projectiles such as DCl (S0 = 16.4
km/mol, compared to CO2 with S0= 665 km/mol) to be studied with quantum state resolved,
direct absorption laser methods.51-52

3.3 Results and Analysis
3.3.1 Low energy DCl scattering yields fully TD distributions in equilibrium with the liquid
The natural metric to consider in a pulsed scattering experiment is the scattered flux (𝐹,#/cm2/s), since particle number is rigorously conserved among all possible scattering pathways.
However, high resolution direct absorption methods measure column integrated density ( #/cm2),
arising from integration of the number density (N(l)) along the laser path and equivalent to theflux of molecules passing through the probe laser divided by the transit time velocity. This yields
a differential absorbance𝑡𝑑𝐴 = 𝑆𝐽′ ,𝑣′ ,𝐽,𝑣 𝑁(𝑙) 𝑑𝑙 = 𝑆𝐽′ ,𝑣′ ,𝐽,𝑣 𝐹(𝑙) ∗ (𝑑𝑡𝑟𝑎𝑛𝑠𝑖𝑡 ) 𝑑𝑙 = 𝑆𝐽′ ,𝑣′ ,𝐽,𝑣 〈𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝐹(𝑣𝑡𝑟𝑎𝑛𝑠𝑖𝑡 ,𝑙)𝑣𝑡𝑟𝑎𝑛𝑠𝑖𝑡

〉 𝑑𝑙

Eq. 1

where 𝑆𝐽′ ,𝑣′ ,𝐽,𝑣 is the rovibrational line strength and can be calculated from the integrated crosssection, the Hönl-London factors and Herman-Wallis rovibrational coupling terms.52 The angle
29brackets imply an averaging over the transit time velocities (𝑣𝑡𝑟𝑎𝑛𝑠𝑖𝑡 ). For the present geometry(laser perpendicular to the scattering plane), Eq. (1) integrates to yield:
𝐴(𝑗, 𝑣,v⊥)
𝐹(𝑣𝑡𝑟𝑎𝑛𝑠𝑖𝑡 )〉 ∗ 𝑙𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒=〈
𝑆𝐽′ ,𝑣′ ,𝐽,𝑣
𝑣𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝐹∗𝑃(𝑣𝑡𝑟𝑎𝑛𝑠𝑖𝑡 )≈ 〈 𝑡𝑜𝑡𝑎𝑙𝑣

𝑡𝑟𝑎𝑛𝑠𝑖𝑡〉 ∗ 𝑙𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 ∗ 𝑃(𝑗, 𝑣, 𝑣⊥ ) = 𝑁 ∗ 𝑃(𝑗, 𝑣, 𝑣⊥ )Eq. 2

Since the laser linewidth is much narrower than Doppler shifts for the scattered DCl, theabsorption is directly proportional to the quantum state probabilities P(j,v) times the Doppler
distribution along the probe laser beam ( v⊥ ).

The flux distribution can approximately beseparated into the transit velocity scattering distribution and the scattering distribution of the restof the resolved parameters and thus the unresolved factors can be collapsed into a single

Figure 3.3: Sample Boltzmann plots (Einc = 1.5(1) kcal/mol) for scattering of DCl from thegas-perfluoropolyether (PFPE) interface as a function of surface temperature. Note that good
agreement between TS and Trot, consistent with fully equilibrated TD dynamics at low
incident energies.
30

normalization factor (N). The validity of this approximation is discussed elsewhere, but whenused in the context of a two temperature model, this separation is found to slightly overpredict
the branching ratio into the TD component but accurately capture the TD and IS rotationaltemperatures.22
Time of flight mass spectroscopy studies by Nathanson and coworkers27-30 suggest thatthe trapping desorption (TD) fraction of the scattered molecules completely thermalize, lose all
memory of the incident collision dynamics, and eventually desorb in equilibrium with the surface
temperature, TS. Though explicitly confirmed in quantum state resolved studies in our group26, 53
for CO2 (BCO2  0.40 cm-1) with respect to rotational, vibrational and translational degrees of
freedom, the expected behavior for a light hydride such as DCl (BDCl  5.45 cm-1) is perhaps lessobvious. By way of due diligence, therefore, we have performed a series of DCl scatteringstudies at thermal collision energies as a function of the liquid surface temperature TS. Fig. 3.3
displays sample Boltzmann plots (ln [Pop/(2J+1)] vs. Erot) for DCl populations scattered fromPFPE at low collision energies (Einc ≈ 1.5(1) Kcal/mol), for which single temperature fits to thedata recapitulate the surface temperatures (TS) to within measurement uncertainty. A
confounding effect that must be acknowledged is the possibility of non-isotropic mJ
distributions.

31

Figure 3.4. Summary of low energy (Einc = 1.5(1) kcal/mol) scattering as a function of
surface temperature (TS) for three different liquids. (a) The upper panel displays thedependence of the DCl rotational temperature on TS, with (b) the lower panel highlighting thedependence of the perpendicular Doppler distributions on surface temperature. Both plots arein agreement with a simple T  TS prediction (solid line), which would imply fullthermalization and equilibration of the scattered DCl with the surface prior to desorption.
32

The polarization of the laser and the geometry of the detection system used leads to acorrection of the absorption strength that is proportional to <Jy>, which is the degree of forwards
or backwards end over end tumbling of the scattered molecule. The size of the effect has beenmeasured at high collision energies (10.6 kcal per mol) for CO2 and it has been seen to be on theorder of about 2.5% decrease in the strength of the absorption at ~1000 cm-1 rotational energy
with decreasing magnitude as the rotational energy decreases.54 At rotational energies where the
TD scattering dominates, the effect is weak enough to be considered zero with the detection
sensitivities determined by shot noise. In this current experiment at low collision energies, we
expect the effect to be much smaller than the error bars on the data being presented thus it can be
entirely ignored for this analysis. Fig. 3.4a presents a summary of results for all the liquid
temperatures explored for each of the three different liquids. By microscopic reversibility anddetailed balance considerations, this has clear implications.55-59 Specifically, this requires thatover a range of collision energies consistent with TS, DCl must exhibit unity sticking probability
independent of initial rotational quantum state. In other words, DCl at near thermal energies must
undergo purely trapping desorption (TD) dynamics on each of the three gas-liquid interfaces in a
J-independent fashion.
We can test this further by also probing the Doppler velocity components along the laser
probe direction, for which a Gaussian velocity distribution can be used as a physically motivatedmodel for the transverse DCl velocities desorbing from the surface. Fig. 3.4b summarizes thecorresponding Doppler velocity based temperature (TDopp) as a function of TS. Consistent withthe above expectations, the TD component sampled via low collision energy scattering
thermalizes for all three test liquids in both rotational and transverse translational degrees of33

freedom, yielding TDopp  Trot  TS over an appreciable range of liquid temperatures. Although
our current detection geometry does not permit us to sample translational distributions in the
scattering plane, time of flight studies by the Nathanson group directly probe the velocities in the
scattering plane and they see the signatures of DCl thermalizing with the surface.27 Along withthe data measured in this chapter, this leads us to conclude that DCl truly does thermalize withthe surface in both the translational and rotational degrees of freedom at low collision energies.

3.3.2 IS scattering model
The fully equilibrated behavior observed in Sec 3.3.1 for near thermal (Einc  1.5(1)kcal/mol) scattering provides the necessary backdrop for both distinguishing and analyzing
contributions from the non-equilibrium IS component of the collision dynamics under
hyperthermal (Einc  11.5(5) kcal/mol) conditions. To establish a context, it has been routinely
noted in previous quantum state resolved studies with CO2 and NO scattering from similar
liquids that the IS component of the flux scatters into rotational and translational distributions
characteristically much hotter than the surface temperature, yet modeled surprisingly well by ahot Boltzmann distribution in internal rotation and velocity components perpendicular to thescattering plane.17-18, 25-26

However, it is important to stress the absence of any a priori

dynamical basis for why the IS component should emerge in a hyperthermal yet temperature-like
distribution. This is particularly so, as the IS angular distributions in the scattering plane
observed in TOF studies by Nathanson, Minton, and others15, 39, 60 are strongly anisotropic, with aclear propensity for a broadened but “lobular” forward scattering into more nearly specular
directions.

Indeed, the fact that i) rotational quantum state and ii) transverse velocity

distributions in the IS channel can be so well characterized by a “temperature” should be34

recognized as an entirely unexpected and fundamentally surprising result. Indeed, upon closer
inspection with improved experimental tools, analysis techniques, and signal-to-noise, one
should expect this simple “dual temperature” microscopic branching picture into thermalized TD
and IS channels to fail. As illustrated herein (vide infra), DCl scattering from these three test
liquids provides first indications of the breakdown of such “two–temperature” models.
The experimental tool which most clearly highlights this breakdown is high resolution
Dopplerimetry on the transverse velocity distributions for the scattered DCl. As the simplest
model that incorporates non-equilibration dynamics in the DCl IS distributions, we allow thetransverse velocity Doppler profiles to be characterized by a different temperature (TIS,trans) thanfor end-over-end rotation (TIS,rot). Such a model predicts the Doppler absorption profiles to be
described by:𝐴(𝐽,𝑣⊥ )𝑆𝐽′ ,𝑣′ ,𝐽,𝑣

∝ {𝛼 𝑃𝑟𝑜𝑡 (𝐽, 𝑇𝑇𝐷 )𝑃𝑡𝑟𝑎𝑛𝑠 (𝑣⊥ , 𝑇𝑇𝐷 ) + (1 − 𝛼)𝑃𝑟𝑜𝑡 (𝐽, 𝑇𝐼𝑆,𝑟𝑜𝑡 )𝑃𝑡𝑟𝑎𝑛𝑠 (𝑣⊥ , 𝑇𝐼𝑆,𝑡𝑟𝑎𝑛𝑠 )} Eq. 3

where Prot(J,TTD), Prot(J,TIS, rot) and Ptrans(v⊥,TIS,trans) are the rotational (TD, IS) and transverse
velocity (IS) distributions, respectively. If we fix TTD at the surface temperature (as consistent
with the data in Fig. 3.4), Eq. 3 permits a global fit of the complete set of DCl(J) absorption
profiles to i) the TD vs IS branching ratio (𝛼), ii) the two IS temperatures (TIS,trans, TIS,rot), and iii)
one overall normalization constant. The results of such a fit for a sample set of absorption
profiles are illustrated in Figure 3.5, for which the model captures the data quite well. The
central frequency region of the profiles is dominated by the TD channel, while the wings reflect
the strongly Doppler shifted IS components in the scattered signal. This use of global fitting
parameters for the full set of DCl (v=1 0, J’J”) transitions greatly reduces parametercorrelation and permits teasing apart the IS/TD pathways far more robustly than from thevelocity integrated column integrated densities themselves. Indeed, the importance of such a
35

Figure 3.5: Doppler resolved data for sample DCl (v = 0, J) rotational states, providing
support for a global fit to transverse Doppler (TDopp) and rotational (TIS,rot) temperatures. The
blue and red lines reflect the trapping-desorption (TD) component and the impulsively
scattered (IS) components, respectively. See text for details.
approach can be most clearly appreciated in Fig. 3.6, which reveals the deconstruction of TD, IS
and total rotational components in the fit as a function of J state. Specifically, the TD and IS
subcomponents are quite similarly shaped (though, notably, with the fits always yielding TIS
 TTD). This similarity adds in (destabilizing) linear dependence to the data, which makes it
essential to also combine the transverse Doppler profile information in order to deconvolve the
distributions stably and successfully.

36

Figure 3.6: Scattered DCl(J) populations for the three different liquids at Einc =11.5(5)kcal/mol. (top panel: PFPE, middle panel: squalane and lower panel: glycerol. As in
Fig. 5, the blue and red lines reflect the TD and IS components, respectively, from a leastsquares fit (see text for details).

37

3.3.3 IS Dynamics of DCl scattering at high EincOne surprising result immediately evident in the hyperthermal (11.5(5) kcal/mol) DCl
scattering data is that the average rotational state only increases to J~5-6 from the averagethermally populated state of J  4. This corresponds to a very modest ( 0.3 kcal/mol) increasein rotational energy, i.e., only a small fraction (3%) of the ~11 kcal/mol incident translationalenergy. This differs qualitatively from previous IS scattering studies for both CO2 and NO
projectiles, in which a substantial fraction (10-20%) of the incident translational energy isfunneled into rotational degrees of freedom.17-18, 25 Specifically, DCl undergoes far less efficienttranslational to rotational (T to R) energy transfer at the liquid surface, as further elucidated witha simple “lever arm” collision model in Sec 3.4. This weak rotational excitation of hydrides has
been seen before in the scattering of OH done by McKendrick and coworkers.13 In summary,with both the rotational populations and transverse Doppler distributions fit simultaneously, all
the data can be robustly deconstructed into two well defined pathways, i) a thermallyaccommodated (TD) component emerging fully in equilibrium with TS and ii) a non-equilibrium,
hyperthermal DCl scattering distribution characterized by rotational temperatures (400 K) only
slightly hotter than and yet translational temperatures (1000 K) very much hotter than the gasliquid interface.
The data also reveal that the propensity to transfer incident hyperthermal energy differs
dramatically for out-of-plane translational vs. rotational degrees of freedom. In contrast with anexceedingly modest excitation of DCl rotation, the liquid interface proves to be far more efficientat transferring the incident in-plane momentum into the out-of-plane component. These results
are summarized in Fig. 3.7b, which displays the DCl rotational (Trot) and transverse velocity(TDopp) temperatures observed for each of the three liquids. Specifically, the fitted temperatures

38

Figure 3.7: Summary of fit parameters for hyperthermal (Einc = 11.5(5) kcal/mol) scattering
conditions. (a) Top panel reflects the fractional trapping desorption coefficient ( = NTD/(NIS+ NTD), where N is the total population in that channel. Lower panel displays the rotational(blue) and out-of-plane (green) temperatures from combined Boltzmann fits to the integrated
absorption and high resolution Doppler profile data. Note the 3-4 fold differences between
TIS,trans, and TIS,rot, indicating a lack of equilibration between these degrees of freedom for the
IS channel.
39

for (and thus collisional energy transfer into) translational degrees of freedom transverse to thescattering plane are 300%-400% larger than transferred into DCl rotation. Even for elastic
scattering (not a good approximation), this would correspond to outgoing speeds requiring
angular spreads of 25o RMS in the scattered flux to achieve the 250-300 MHz Doppler
linewidths (FWHM) in the IS scattered component, with a correspondingly broader angularrange if translational energy is lost to the surface.
Along with lower rotational excitation efficiencies, a larger fraction of DCl thermallyaccommodates on the surface than observed previously for CO2 (see Table 3.2 and Fig. 3.7a).
For DCl scattering from PFPE, 40% of the collisions can be attributed to a long-lived TD
interaction with the liquid vs. only a 30% for CO2.25 Such an increase in the trapping fraction for
DCl vs. CO2 certainly can be partially attributed to the much deeper well depths at the gas-liquidinterface for DCl. This is perhaps not surprising since DCl has a strong dipole moment  =1.080 D61 vs.  = 0 D for centrosymmetric CO2, while having comparable polarizabilities andquadrupole moments.61-62

Table 3.2: Summary of least squares DCl scattering parameters

LiquidAlpha

TIS Rotational (K)TIS Doppler (K)PFPE

0.398(24)508(15)1612(28)

Squalane

0.540(16)412(10)1054(13)Glycerol

0.556(9)397(13)1191(27)40

It might at first seem to be a simple task to use the trapping desorption ratios () fromthese fits as a metric for absolute branching between various scattering pathways. As noted
previously, however, the multipass absorption geometry samples only the transverse velocity
component from Dopplerimetry and thus is not able to extract relative fluxes (i.e. velocityweighted densities) from the measured J-state distributions. This geometry also samples a broad
distribution of scattering angles, which can confound the separation of the pathways in an
absolute fashion thus making  useful for comparing trends among similar experimental setups.
Additionally, DCl can undergo signal loss via i) proton exchange to form HCl or ii) temporary
solvation into the bulk liquid, the latter of which would result in signal loss due to residence
times in excess of the integration window. Interestingly, in work by Nathanson et al on H/Dproton exchange of hydrogen halides at the glycerol surface, nearly all of the proton exchange
signal was shown to result from a TD pathway, i.e. the H/D exchanged product species comes
off with a Maxwell-Boltzmann velocity distribution at TS.27-28, 30-32

Thus, the lack ofincorporation of such loss channels in our model translates into a lower limit for the measured
fraction of molecules that thermalize with the surface. Finally, we note that one can circumventthese flux vs density issues for DCl projectiles with resonant multiphoton ionization (REMPI)
and 3D velocity map imaging methods, as recently demonstrated for HCl scattering from selfassembled monolayers (SAMs) of alkane thiols on Au films.53
We next turn to the dependence of the collision dynamics on the nature of the liquidsurface (see Fig. 3.7). Most noticeable in Fig. 3.7b is that hyperthermal DCl systematicallyscatters from PFPE with considerably more energy in both rotational and translational degrees of
freedom compared with the other liquids studied. This is in good agreement with both time-offlight CO2 studies by the Nathanson group and infrared based studies from our group.17, 63-65

41

Indeed, these studies show in general that the heavy, rough, and fluorinated surface leads toincreased rotational excitation and less overall energy deposition into the surface. Secondly,
glycerol and squalane liquids exhibit similar levels of T→R excitation for DCl. This behavior
has also been noted previously in molecular beam CO2 scattering studies from these liquids andhas been used to argue that the presence of hydroxyl groups do not play a strong role inrotational excitation for impulsive scattering (IS) collision events17. In terms of transverse
velocity distributions, however, a statistically greater momentum is transferred into the out ofplane degree of freedom for glycerol than for squalane. This is in contrast to what was reported
in previous CO2 scattering studies, for which all three liquids were shown to produce
perpendicular velocity distributions within experimental error.17 If the OH groups were oriented
parallel to the surface, this might offer a possible explanation for the differences between DCl
and CO2 scattering from glycerol. Such planar OH groups generate electric fields pointed along
the surface, which would couple more strongly to the DCl dipole than to the vanishing dipole
moment in CO2, rationalizing stronger forces perpendicular to the scattering plane than for a
non-polar hydrocarbon surface. The sum frequency generation studies of Oh-e et al.66 provide
additional support for this picture, with no free OH stretch and only a small amount hydrogenbonded OH groups detected, which implies OH groups lying predominantly parallel to interfacial
plane or pointing down into the bulk.

3.4 Discussion
3.4.1 A simple lever-arm model
Although quantum state resolved molecular scattering from the gas-liquid interface
represents an extremely complex dynamical event, it is a challenging but worthwhile exercise to42

explore simple, physically motivated models to reproduce the basic scattering phenomena.
Indeed, there has been an extensive literature on quantum state resolved scattering of moleculesin the gas phase and on single crystal surfaces, for which there have been many major theoreticaladvances.40-43, 56, 58-59, 67-69 As a starting point, we can build intuition for molecular scatteringfrom a liquid surface by considering the much simpler problem of diatomic scattering from ahard potential wall. This choice maps onto a long-studied problem in the gas and gas-solid phaseenergy transfer community,67, 69-79 specifically tapping into the impulsive atom + diatom, “hardcube” and effective mass models by McCaffery, Tully, Minton and coworkers.38-43 The essential
physics captured in each of these treatments is that angular momentum transfer is dominated by
impulsive collisions exerted on the atom or molecular rotor at the classical turning point, forwhich simple analytic expressions can be derived based on conservation of linear momentum,
angular momentum and energy. Based on these pioneering efforts, we extend impulsive models
for energy transfer on a wavy but locally flat surface (see Fig. 3.8a), as a simple entry point forincorporating stochastic capillary wave structure at the gas-liquid interface.
For the origin at the center of mass of a non-rotating diatomic (AB) colliding with alocally flat surface, conservation of angular momentum requires that
𝐿 = 𝐿’ + 𝐽

Eq. 4

where J is the asymptotic rotational angular momentum of AB and L and L’ represent the initialand final orbital angular momenta before and after an impulsive collision. The initial orbital
angular momentum (L) is given by

43

Figure 3.8: (a) Schematic “lever arm” model for impulsive scattering of a diatomic
molecule from the gas-liquid interface. This diagram shows the two van der waal radii
spheres with the black bar fixing the bond length of the molecule. The red arrow is
the force normal to the surface of the liquid and the yellow bar represents the impact
parameter of the surface collision. (b) Angular momentum (units of ħ) transferred due
to torque of as a function of DCl orientation at the point of impulsive contact ( = 0
corresponds to the D atom directed antiparallel to the local surface normal).

44

𝐿 = 𝜇 𝑣𝑟 𝑏

Eq. 5

where 𝑣𝑟 represents the relative speed of the molecule + liquid surface system of reduced mass
. The impact parameter 𝑏 with which the torque on AB is generated is determined by theperpendicular distance between the AB center of mass and the force vector F originating at theimpulsive classical turning point. From conservation of energy and momentum tangential to thesurface, one can easily show for impulsive scattering that the final rotational angular momentum
must be:2𝐼𝜇𝑣 𝑏𝑟
𝐽 = 𝜇 𝑏2+𝐼

Eq. 6

where I is the AB moment of inertia. If we further assume the surface mass to be much heavier
than the scattering molecule,  becomes the mass of AB. Due to limited degrees of freedom
measured in this experiment, this assumption is made to simplify the model and not out of apriori scientific fact. Most of the analysis will be done with an infinite surface mass to avoid ad
hoc parameters. All the terms in Eq. 6 are known except for the “lever arm” b, which will be afunction of the locus of classical turning points for a given intermolecular potential energy
surface and collision energy. Indeed, McCaffery et al. developed and used this exact scatteringmodel to describe gas phase rotational excitation of CO by H atom collisions in the gas phase,treating the H-CO intermolecular potential as a hard wall ellipsoid38 and averaging over all
possible lever arm values of b weighted by the probability P(b) that such a lever arm would
occur. For the present diatom-liquid surface scattering model, further simplification can be
invoked since a locally flat surface makes explicit calculation of P(b) from the gas-surface
potential even easier.

45

As the simplest representation of the AB + surface potential, we consider a dumbbell
model of two hard spheres separated by a bond length R. Depending on which atom experiences
the impulsive collision event, the lever arm length is given geometrically by:
𝑚𝐶𝑙 𝑅
𝑚𝐶𝑙 +𝑚𝐷𝑏(𝜃) = { 𝑚𝐷𝑅

sin 𝜃 , 𝜃 < 𝜃0sin 𝜃 , 𝜃 ≥ 𝜃0
𝑚 +𝑚
𝐶𝑙

Eq. 7

𝐷

where R = 1.275 Å is the DCl bond length, 𝜃 is the angle of the DCl bond axis with respect tothe surface normal (𝜃 = 0 corresponds to the D atom pointing towards the surface), and 𝜃0 is theangle at which the impulsively colliding atom switches from D to Cl. For hard sphere radii rCl,
rD, this angle can be determined from:cos 𝜃0 =(𝑟𝐶𝑙 −𝑟𝐷 )(𝑚𝐶𝑙 +𝑚𝐷 )𝑅(𝑚𝐶𝑙 −𝑚𝐷 )Eq. 8

These hard sphere radii can be estimated from the van der Waals radii of the respective atoms(1.75 Å for Cl and 1.20 Å for D), for which Eq. 8 predicts 0  61o. With 0 determined, Eqs. 68 permit one to calculate J as a function of cos() for a given velocity component (v⊥) normal tothe average surface plane, which under the current hyperthermal beam conditions (Einc = 11.5(5)kcal/mol, inc = 65o) is v⊥  6.8(1)𝑥 104 𝑐𝑚/𝑠.
The resulting plot of J() vs. cos() for DCl scattering impulsively from a locally flat
surface is displayed in Fig. 3.8b, revealing a particularly strong dependence of angularmomentum transfer on orientation of the incident DCl. Orientations with either the D ( = 0o) orCl ( = 180o) atom pointing exactly toward the surface obviously generate zero angularmomentum. However, the angular momentum transfer grows quite steeply with tilt away fromthe cos() = 1.0 and -1.0 limits, with maximal transfer occurring for striking with the D end withcos()   (  13.8o), but also with a smaller but much broader maximum for the Cl end

46

near cos(0)  0.0724 (  85.8o). This is consistent with simple physical observation thatstriking the lighter of the two atoms generates the larger “lever arm” for torqueing on the diatom.
If at the moment of impact, the DCl angular orientation is assumed to be isotropic ( = [0o, 180o],φ = [0o, 360o]), we can simply average over Eq. 6 to predict a mean final angular momentum of<J>  5.1. Considering the extreme simplicity of such a model treatment, we wish to emphasizethat this is already in excellent qualitative agreement with the only modest levels of DClrotational excitation (<Jexp>  5.8-6.6) observed for all three liquids (see Fig. 3.6).
The actual quantum state distributions can be predicted from this “lever arm” model byusing Monte Carlo methods to sample orientation of the molecular bond axis with respect to the
local surface normal. For an isotropic distribution of   sampled from the usual sin()dd
Jacobian, we can therefore histogram J() into integer values and thus predict rotational quantum
state distribution for impulsive collisions with a static flat liquid surface. The resulting histogramfrom such a calculation is shown in Fig. 3.9a, which reveals a highly peaked rotational
distribution with a pronounced maximum near J  5. This peaking is of course simply an
example of “rotational rainbow” structure, both predicted and observed in crossed molecularbeam and gas-single crystal scattering studies.80-82 This sharp rainbow peak is clearly the resultof the broad maximum in J() around J  5, cos()  -0.1, which is the essential ingredient for aclassical rainbow (see Fig. 3.8b).80-82 Interestingly, this rainbow feature clearly identifies thatthe reduced levels of DCl rotational excitation observed experimentally arise from the higher
probability of scattering with the Cl vs. D atom end first, which results in correspondingly
smaller impact parameters for rotationally exciting the DCl subunit. However, it is also
important to note that Fig. 3.8b predicts dramatic enhancement of the rotational excitation
efficiency for non-isotropic sampling of the D atom orientation prior to the collisional event, as
47

could be achieved for a light dipolar hydride such as DCl by strongly charged species ormolecular ions in the interfacial region.83

3.4.2 Averaging over capillary waves predicts hot yet Boltzmann-like rotational
distributions
We can push this “lever arm” analysis further to capture even more of the trends
observed in gas-liquid interfacial collisions. Specifically, the angular momentum predictions
from our simple “lever arm” model (e.g., see Fig. 3.9a) may be correct on average but greatly
overestimate the degree of sharp “rainbow” structure in the J distributions. This is due to ourassumption of impulsive collisions on a locally flat collision surface, whereas any gas-liquidinterface of course exhibits substantial roughness due to capillary wave excitation. As the nextstage of treatment, therefore, we empirically incorporate surface roughness in our gas-liquid
collision model, the major source of which is from thermal activated capillary waves. From thetheoretical analysis by Phillips,44 the root mean square angle for surface deviation from normal isfound to be:𝜋𝑘 𝑇tan 𝜃𝑟𝑚𝑠 = √ 8𝛾𝜎𝑏2

Eq. 10where 𝛾 is the surface tension and 𝜎 is the molecular diameter of the liquid. This model ofsurface roughness predicts a range of rms  18.2o (PFPE) to 13.7o (squalane) to 18.1o (glycerol)
for the capillary wave angular deviations, with values of the input parameters found in Table 1.

48

Figure 3.9: Simulated PFPE surface scattering using parameters found in table 1. (a)Distribution of DCl (J) populations predicted from a simple “lever arm” model. (b)Predicted populations thermally averaged over the distribution of local surface tilt
angles (s) due to capillary waves at the gas-liquid interface. (c) Blue data corresponds
to Boltzmann plot of data in (b) and green data is for a finite mass of 120 amu, whose
linearity reflects a “near temperature-like” behavior (T  400-500 K) consistent withobservations from many quantum state resolved gas-liquid experiments.
49

The obvious next step is to combine these lever arm model predictions with the above capillary
wave estimates of surface roughness. A simple way to incorporate surface roughness would be
to assume the surface to be locally flat at the point of impact, but to allow the direction of thesurface normal to fluctuate according to predictions of capillary wave theory in Eq. 10. The only
difference is that we must now also additionally average over fluctuations in the normal velocity
component,‖𝑣𝑟 ‖ = 𝑣⃑ ∙ 𝑛⃗ = ‖𝑣‖ ∗ (cos 𝜃𝑠 ∗ cos 𝜃𝑖𝑛𝑐 + cos 𝜙𝑠 ∗ sin 𝜃𝑠 ∗ sin 𝜃𝑖𝑛𝑐 )Eq. 11

where (s, s) are the instantaneous spherical polar angles associated with the local surface
normal (with s = 0 pointing in the forward scattering direction) and inc is the incident molecularbeam angle measured with respect to the global surface normal.

Most importantly, suchaveraging will contribute to a blurring of the sharp rotational rainbow-like structure in Fig. 3.9a.
We can perform such an angular average explicitly. If there is no preferential azimuthal
direction in the liquid surface, 𝜙𝑠 will be evenly distributed over [0, 360𝑜 ] . However, thedistribution in the local tilt angle 𝜃𝑠 is not uniform, with 𝜃𝑠 distributed as a Gaussian around s 
0 weighted by usual the sin(s) Jacobian for a spherical polar coordinate system:
𝑃(𝜃𝑠 ) ∝ sin 𝜃𝑠 ∗ 𝑒

1 𝜃
2 𝜃0

− ( 𝑠 )2≈ 𝜃𝑠 ∗ 𝑒−𝜃21𝑠
2 (𝜋𝑘𝑠 𝑇𝑠 /8𝛾𝜎2 ),Eq. 12where 𝜃0 is the rms angular roughness from capillary wave theory (𝜃𝑟𝑚𝑠 in Eq. 10) and sin(𝜃𝑠 ) 𝜃𝑠 can be taken in the small angle limit. The gaussian angular distribution naturally follows from
Phillips’ work. See appendix A for a clear derivation of this fact. The predicted J distribution
from Eqs. 10-12 is plotted in Fig. 3.9b, where we have taken values for  and  consistent withPFPE (i.e., 0 = 18.1o, see Table 3.1).

Most importantly, averaging over capillary wave

distributions at the gas-liquid interface has smoothed over the strongly peaked rainbow-like50

features predicted for a static, locally flat surface (Fig. 3.9a), resulting in quantum state
distributions much more visually consistent with experimental observation (e.g., Fig. 3.6).
As a final observation, we can take this analysis one step further by recasting the above J
distributions in terms of a Boltzmann plot, i.e., ln[Pop/(2J+1)] vs Erot (see Fig. 3.9c). The
resulting plots are remarkably linear, indeed quite characteristic of a “temperature-like” behavior
at T  400 - 500 K. Figure 3.9c also contains the data for a finite surface mass of 120 amu, whichshows a slightly colder but still linear “temperature-like” behavior. This is a particularly striking
result, specifically that thermal averaging of an impulsive, classical rotational excitation modelover surface capillary wave roughness recapitulates the “hot-but-Boltzmann-like” distributions
experimentally observed in many quantum state resolved scattering studies to date.17-20, 22-26 To
the best of our knowledge, this is the first theoretical justification for the appearance of such“dual temperature” (i.e., TTD and TIS) behavior in rotational gas-liquid scattering dynamics,
despite the ubiquitous evidence for such behavior in the literature.
This, however, is not a complete explanation of IS scattering. Several major assumptions
were made in this model for the sake of simplicity. Finite surface mass has been shown toaccurately explain angular distributions in atom-liquid scattering and it is completely possiblethat variations in surface mass can add to the averaging over the rotational rainbow structure.39
Also MD studies have shown that surface interactions often undergo multiple collisions and eachof these collisions cannot be categorized as a truly impulsive collision.84 This does not weaken
the fact that impulsive molecular scattering produces rotational rainbows and that gaussian
averaging over such rotational rainbows gives temperature-like rotational behavior. The largest
source of gaussian broadening is most likely from surface capillary waves but there are many51

sources that can have strong contributions to this averaging. A more accurate model should be
developed and it would encompass all of these effects.
Given these level arm model results, it would appear that characterization of the IS
component with some effective “temperature” does not require any true equilibration taking
place during the gas-liquid surface interaction. This is in agreement with experiment as well as
the identification of IS scattering as arising from gas-liquid scattering dynamics with insufficient
time to lose all memory of the incident collision conditions. This is also particularly noteworthy
in light of the fact that the in-plane velocity distributions for the IS scattering component havebeen routinely determined from time-of-flight studies by Nathanson, Minton, and others to be i)lobularly peaked toward the near specular angle and ii) with velocities poorly represented by atranslational temperature.10, 15-16, 39 It is our hope that future theoretical and experimental efforts
will permit further developments in this direction to provide a simple, quasi-predictive model for
quantum state resolved impulsive scattering of molecules from the gas-liquid interface.

3.5 Conclusions and Summary
Jet cooled DCl(J = 0, 1) has been scattered at thermal (1.5(1) kcal/mol) and hyperthermal(11.5(5) kcal/mol) collision energies from surfaces of three prototypical liquids (PFPE, squalene,
and glycerol), with the data revealing several key ideas. First of all, the TD component of DCldesorbing in equilibrium (in both rotationally and transverse velocity distributions) with theliquid (TDopp  Trot  TS) implies by detailed balance that the sticking coefficient for DCl in thereverse direction must be unity over a similar range of thermal collision energies.55-59
Secondly, impulsive scattering of hyperthermal DCl molecules proves to be far lessefficient at channeling incident translational energy into rotational degrees of freedom (<J>  

52

TIS,rot  400-500 K) than for CO2 or NO. We interpret this as simply arising from the much larger
rotational constant (BDCl  5.4 cm-1 vs. BCO2  .5 cm-1) larger rotational spacings, and thus thecorrespondingly larger changes in rotational energy required for a light hydride rotor. In contrast,
however, DCl transfers its incident momentum very strongly into the out-of-plane velocity
component, achieving Boltzmann temperatures (TIS,trans  − ) from fits to the highresolution Doppler profiles 3-4 fold higher than the corresponding rotational temperatures (TIS,rot
 400-500 K).
Thirdly, we present a simple physical “lever arm” model based on early gas andinterfacial phase collisional energy transfer studies by McCaffery, Tully and Minton andcoworkers,38-43 that successfully rationalizes both the low levels of average DCl rotational
excitation observed but also makes clear predictions for how angular orientation of the incident
projectile can strongly impact the degree of rotational excitation. Viewed from this perspective,
such a “lever arm” model provides an intriguing potential route to probing the degree ofanisotropic orientation of impulsively scattered molecules (especially light and strongly polar
hydrides) as they collide with a gas-liquid surface. Finally and most importantly, appropriately
averaging such “level arm” model predictions over capillary wave surface roughness yields
rotational distributions for hyperthermal collision energies that recapitulate the ubiquitous patternof “hot-but-Boltzmann-like” temperatures reported empirically in the literature for over a decade.
More comprehensive theory will clearly be needed to make these connections more quantitative,
but the current results leave us hopeful that the prospects for understanding the essential
underlying physics of quantum state resolved energy transfer of molecules at the gas-liquidinterface are improving.

53

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58

Chapter 4
Low Energy CO Scattering at the Gas-Liquid Interface: Experimental/Theoretical
Evidence for a Novel Sub-Thermal Impulsive Scattering (STIS) Channel*

4.1 Introduction
Ever since the earliest experimental attempts to probe fundamental scattering at the gas-liquidinterface, compelling evidence has been reported for two physically distinct pathways.1-4 The firstis the thermal desorption pathway (TD), whereby the incident molecular projectile traps transiently
on the liquid surface and undergoes multiple collisional interactions, which causes it to lose all
memory of the incident collision conditions (e.g., speed, direction, quantum state), and desorb in
perfect equilibrium with the liquid temperature (TS). This TD pathway has been presumed todominate at collision energies comparable to the surface temperature (Einc  kTS), as confirmed bymultiple energy-dependent studies of the final external (i.e., translational) and internal (i.e.,rovibrational) quantum state distributions.5,6 To help minimize further potential confusion in theliterature, we note that such TD dynamics (i.e., “complete loss of incident quantum state memory”)
is consistent with but does not strictly require the final distribution to be in perfect equilibriumwith TS. As one specific example, non-equilibrium distributions are in fact rigorously predictedby detailed balance considerations if there is some potential energy barrier (e.g., in projectilesurface displacement or angle) serving as a transition state bottleneck along the desorption
coordinate. This is known to be the case, for example, for H2 molecules scattering from Ni, Pt, andFe, for which a potential barrier in the adsorption coordinate results in high pz momentum
distributions and narrower than cos() angular distributions in the corresponding desorption
dynamics.7 This behavior has also been seen in a multitude of systems8 such as the oxidation of59*Published in J Phys. Chem. C, 124, 28006, (2020)

CO on Rh(111), which has an exit channel barrier for the product (CO2) leaving the surface.9
Evidence for such transition state barrier complications in quantum state resolved scatteringstudies at the gas-liquid interface has not been reported to date. However, given the rapid progressin this field, it is likely only a matter of time, apparatus sophistication, and experimental sensitivity
before such evidence will emerge.
As the familiar counterpart to TD, a second dynamical pathway emerges as a function ofincreasing collision energy dubbed impulsive scattering (IS), whereby the molecules retain apartial memory of the incident collision conditions. One of the earliest papers to identify and label
this channel was published by Hurst et al. As noted by Hase and coworkers, this molecular memory
is not an experimental observable, and thus such a “catch-all” pathway has no a priori rigorous
definition.10 For example, were the IS dynamical pathway to result in distributions thatcoincidentally matched those of pure TD scattering, these would be indistinguishable from (andby definition subsumed into) the TD pathway. Experimentally, however, distinguishable IS andTD pathways are routinely observed in numerous quantum state-resolved and time-of-flight (TOF)
gas-liquid scattering studies.1,5,11-14 Particularly under glancing incident scattering conditions, such
IS deviations from pure cos() TD thermalization dynamics have been empirically well describedby an additive, near specular component with translational distributions often hotter than thesurface (though not necessarily Boltzmann) and with an average energy content scaling with theincident collision energy. A schematic cartoon of these two pathways is illustrated in Fig. 4.1,
which portrays the two limits of i) pure cos() and ii) quasi-specular angular distributions for the
TD and IS pathways, respectively.
Although no predictive theory currently exists that successfully recapitulates all observed
gas-liquid scattering behavior, there have been several heuristic models that capture much of the60

Fig. 4.1 A schematic of the TD/IS gas-liquid scattering paradigm.
essential physics. For example, pioneering work by Tully and coworkers on the IS pathway for
gas-single crystal scattering has been based on an inertial (“hard cube”) description of the local
surface response.15 Minton and coworkers extended these ideas into a simple but elegant kinematic
collision model that succeeds in reproducing in-plane angular distributions for IS scattering basedon the effective mass of such a cube.16 One recurring conundrum, particularly evident for
projectiles with internal (e.g., rotational/vibrational) degrees of freedom, is that the IS scattering
distributions have often appeared hot but Boltzmann, i.e., well described by a hyperthermal IS“temperature,” despite the absence of any reason why such a pathway should appear thermal. Freshinsight into this long-standing puzzle has been provided by recent work (“lever arm model”) which
reveals that averaging over the collision dynamics (e.g., capillary wave spatial fluctuations of the61gas-liquid interface) can convert highly structured impulsive rainbow-like scattering distributions
into a remarkably thermal-like distribution without invoking any equilibration.17 However, nomodel has yet been forwarded that can predict these effective IS temperatures a priori and/or
branching ratios () into IS/TD channels.
Thermal desorption, conceptually the simpler of the two IS/TD pathways, is the more
universal process in gas-liquid scattering.18 For gas-liquid systems studied with internal quantum
state resolution, the standard paradigm has been that atoms/molecules undergo complete TD
scattering behavior (  1) at low collision energies (Einc  kTS) with finite branching ratios ( <1) into IS vs. TD pathways appearing only at hyperthermal energies.5 As one of many systems,
CO2 gas-liquid scattering has been studied with full rovibrational quantum state and Doppler
velocity resolution,1 which for multiple liquids, surface temperatures, and incident angles
demonstrate pure TD (  1) at low collision energies and mixed TD/IS behavior ( < 1) only athigher energies.5,19 Indeed, it was largely based on this early work that such “dual temperature”
models (TTD  TS, with TIS treated as an empirical parameter) were originally postulated formolecular systems probed with both internal and external degrees of freedom.
The most robust empirical support for a dual temperature TD/IS pathway has been foundin scattering studies with HCl/DCl. From time of flight studies by Nathanson and coworkers in theforward scattering direction, it was established that HCl/DCl undergo complete thermalization andcos() desorption from several liquid surfaces.20-22 This was subsequently reinvestigated with both
IR direct absorption and REMPI/VMI measurements, which confirmed that HCl/DCl at low
energies equilibrates and undergoes thermal desorption in both external (translational) and internal(rotational) degrees of freedom (Ttrans  Trot  TS).17,23 The REMPI/VMI studies at higher collisionenergies took this one step farther and showed that, due to extreme glancing incident angles (75o),62J state populations from both TD and IS pathways could be extracted by separate analysis of the
backward and forward velocity components, respectively. This permitted a novel and completely
independent test of the dual temperature TD/IS paradigm, demonstrating that the IS distributions
still appear Boltzmann-like but with TIS >> TTD and TD distributions with TTD  TS Evidence forsuch thermal equilibration of the TD fraction to the surface temperature TS has been seen in manyother gas-liquid scattering experiments, for example, McKendrick, Minton, and coworkers report
this for OH24 + hydrocarbon surfaces and O2 + Squalane.16 The one notable exception for thisparadigm has been NO,25-27 which, at low collision energies, has been reported to scatter withrotational temperatures colder than the liquid surface. Specifically, Trot was found to increase
monotonically with surface temperature but with an incremental slope (dTrot/dTS) less than unity.2527

Sub-thermal behavior at low collision energies has been also seen in NO scattering from single-

crystal metals and attributed to a combination of dynamical barriers and further rationalized by thecomplicated open shell rovibronic structure of NO.28-30 Work by Polanyi et al., however, has
shown that even the related closed shell CO exhibits a lack of equilibration with respect to TS in
scattering from single-crystal LiF (001).31 Based on these results, one might therefore anticipate
similar anomalies in low energy CO scattering of supersonic beams from gas-liquid interfaces.
In this paper, we explore the concept of thermal desorption in scattering experiments
through both low energy quantum state resolved scattering and molecular dynamics studies. The
paper is organized as follows. First, we describe the experimental methodology in Sec 4.2,
followed in Sec. 4.3 by low energy scattering results as a function of liquid type (perfluorinatedpolyethers (PFPE), non-polar hydrocarbons, and polar glycerol) and liquid surface temperature (TS= 253-303 K), for each of which the final quantum state distributions are notably cooler than TS.
To help interpret these experimental results, we present molecular dynamics calculations in Sec.

63

4.4, based on atom-atom intermolecular potentials for CO, DCl and CO2 colliding with afluorinated self-assembled monolayer surface (FSAMs), which prove to be in remarkably
quantitative agreement with experiment. We exploit these simulations to examine projectile
dependent interaction times at the gas-liquid interface and extend the MD results over a larger
temperature footprint (TS = 50 - 450 K), to elucidate the TS-dependence on the collision dynamics.
Finally, a discussion of possible reasons for this “sub-thermal impulsive scattering” (STIS)
behavior for CO vs HCl, CO2 is presented in Sec. 4.5, with conclusions summarized in Sec. 4.6.

4.2 Experimental
A detailed overview of the experimental apparatus has been presented elsewhere and thus
only essential details and modifications for the current studies need be described.5,17,32 This
experiment consists of three key components: i) a temperature-stabilized liquid scattering target,ii) a supersonic molecular beam, and iii) a narrow linewidth, shot noise limited infrared absorption
spectrometer. The temperature-stabilized scattering target is a modified version of the “lazy Susan”
apparatus described in previous studies.32 The liquid surface is prepared according to the methodof Lednovich and Fenn,18 using a rotating (~ 0.2 Hz) wheel (12.7 cm diameter) half-submerged in
the liquid reservoir and scraped with a stationary razor blade to present a thin (~500 um), freshly
prepared gas-liquid surface to the impinging molecular beam. To facilitate the temperaturedependent studies, we have replaced the Teflon liquid reservoir with a copper reservoir and theglass wheel by a bead-blasted stainless steel wheel to promote adhesion, with the liquid interfacial
temperature-stabilized by a two-stage thermoelectric cooling system. A recirculating ethanol
chiller (Lauda K-4/R) is used to regulate the temperature of a cold plate in the vacuum chamberfrom –TS  20C to 30C. (Companies are named in the interest of completeness and not intended64as commercial product support.) One side of this plate is attached to the lazy Susan apparatus andthe other side to a thermoelectric cooler (TEC) attached to the fluid-filled copper reservoir. A
thermistor attached directly to the copper vessel permits the TEC to servo-loop stabilize thereservoir to a primary target Tres, with the wheel temperature maintained within 1o C of the desired
setpoint. This reduces temperature gradients across all elements in thermal contact with thescattering fluid, which strengthens confidence that the liquid wheel surface is maintained at a welldetermined temperature limited by thermistor uncertainty ( 0.5 K).
These studies involve three different classes of liquids that sample different scattering
dynamical regimes: 1) perfluorinated polyether, (PFPE, Krytox 1506, F-[CF(CF3)CF2O)]14(avg)CF2CF3), as a rough but chemically inert liquid surface, 2) squalane (2,6,10,15,19,23hexamethyltetracosane, C30H62), as a strongly hydrophobic surface, and 3) glycerol (1,2,3propanetriol, C3H8O3), as a strongly hydrophilic surface due to multiple protruding OH groups.33
Each liquid is degassed under ~1 mTorr vacuum (1 Torr = 133 Pascal) at room temperature forseveral hours to remove dissolved gases (H2O, O2, N2, CO2), or at slightly elevated temperatures(~ 350 K) for the glycerol liquid samples to allow for more complete degassing within a reasonable
time frame.
A low collision energy molecular beam is generated through a Proch and Trickl34 stylepinhole valve, with 5% CO in Argon expanded through a 500 um diameter pinhole at 100 Torrbacking pressure. These low stagnation pressures are chosen intentionally to maximize CO signals
while minimizing Ar-CO clustering in the incident beam. This 5% beam composition leads to an
on-axis mean velocity of 550(30) m/sec measured with a time of flight microphone setup35 yielding
an average beam energy of Einc = 1.0(1) kcal/mol. The resulting molecular beam is collimated witha 3 mm diameter skimmer (Beam Dynamics) 2.25 cm from the pinhole orifice for a HWHM beam65

divergence of   3.82o, with rotational temperatures of 10(2) K measured along the beam
expansion axis using the infrared spectrometer described below. The pulse valve is aligned so thecenter of the molecular beam strikes the surface at inc  -65o away from normal incidence, withthis highly glancing incident angle geometry chosen to maximize positively scattered COabsorption signals ( > 0) while minimizing CO(low J) contamination from the incident beam.
Signals are collected in an angular wedge from   -40o to 75o, with the peak collection efficiency
around the specular direction (spec  + 65 o) and 2/3 of the collected molecules coming fromgreater than 45 o. For rotational states J  5 (Erot  60 cm-1), the CO background (Abackground  3 x
10-5) due to incident beam contamination are an order of magnitude smaller than typical peakabsorbance signals (A > 4 x 10-4) due to scattering.
The scattered populations are measured with a tunable laser direct absorption spectrometer
operating near the quantum shot-noise limit. This spectrometer consists of i) a narrow linewidth
external cavity quantum cascade laser (ECQCL, Daylight Solutions, 21047-MHF-013-D0724)36,ii) frequency calibration/diagnostics, and iii) an in vacuo multipass cell with quantum shot-noise
limited balanced detection. The ECQCL provides CW output greater than 250 mW over afrequency range of 1960 to 2200 cm -1 with an optical linewidth  < 10 MHz in the experimental
detection bandwidth (10 KHz). The laser frequency is calibrated with the combination of a fixed
Fabry Perot etalon (FSR = 249.566(33) MHz) and a 5 cm gas transmission cell (500 mTorr of CO),which allows for both absolute (~5 MHz) and relative (~100 ppm) frequency diagnostics. The IR
laser beam makes 16 passes through the scattering region in the vacuum chamber, with the lightdetected on two balanced InSb photodiodes (one before/after the multipass cell) in a fast servo
subtraction circuit, removing common-mode technical noise down to the quantum shot-noise limit.

66

The net absorption sensitivity of the system is approximately 7 x 10-8 per Hz1/2, which translates
into a CO number density detection sensitivity of order 3 x 108 #/cm3/quantum state.

4.3 Experimental Results and Analysis
CO scattering from a series of liquids has been performed as a function of liquid surface
temperature (TS) to characterize the scattering pathways under low energy collision conditions(Einc = 1.0(1) kcal/mol). The absorption signals reflect column integrated densities (v,J) whichcannot be deconvolved into fluxes without prior knowledge of the coupled angular/speed
scattering distribution (f(v,,)).5,17 We can, however, express the experimental absorbance at agiven Doppler detuning (Doppler) as the double integral
(v, J, Doppler) = d’dl[v,J(l,’)( Doppler-’)]Eq. 1

where v,J(l,’) is the quantum state resolved density of absorbers at position l along the absorption
path and (Doppler-’) is the homogeneous absorption cross section per molecule (cm2/#). Since
(Doppler-’) is much narrower than the Doppler widths, the integral over ’ can be performed toyield
(v, J, Doppler) = S0J’,v’,J,v dl v,J(l,Doppler) = S0J’,v’,J,v Pscatter CID

Eq. 2

where S0 is the integrated absorption cross section (cm2cm-1/#) for the v’v, J’J rovibrationaltransition, CID is the column integrated density (#/cm2), and Pscatter is the total probability of
scattering into the v, J quantum state. The experimental absorption profiles are therefore a functionof three variables, J, v and vDoppler, where vDoppler is the velocity component along the laser beam67

axis and probed by Doppler tuning over the rovibrational transition. The laser beam isperpendicular to both the liquid surface normal and molecular beam. The Doppler velocity
measured is the velocity perpendicular to the scattering plane created by the surface and themolecular beam, which will be refer to as the out-of-plane velocity/speed. At low incident energies,
the expectation is that the CO projectile traps in the surface van der Waals well, undergoes many“memory destroying” collisional interactions, and then desorbs with its internal (rotational) andexternal (translational) degrees of freedom in equilibrium with the surface temperature (Trot  Ttrans TS). In our model, the scattering probability (Pscatter) is expressed as a product of an out-of-plane(vy = vDoppler) Maxwell-Boltzmann (MB) distribution times a thermalized rotational distribution:
Pscatter (J,vDoppler) = PMB(vDoppler, Ttrans) Prot(J, Trot)

Eq. 3

which allows us to characterize independent transverse Doppler and rotational distributions bydifferent temperatures (Ttrans  Trot). If these two temperatures are both experimentallyindistinguishable from the surface temperature (Ttrans  Trot  TS), detailed balance considerations7
imply that the incident CO undergoes complete thermalization and desorbs without any barrier
restricting the exit channel dynamics.
However, this is decidedly not what is observed, as evident in Fig. 4.2A from a Boltzmann
plot of the rotational state populations for CO scattering from PFPE at room68

Fig. 4.2 Sample data for CO scattering from room temperature squalane at Einc = 1.0
kcal/mol. A) Boltzmann plot of the rotational states. The blue dot-dash line represent a room
temperature rotational distribution while the red solid line is the fit that predict subthermal
behavior. Rotational states 5 through 18 are plotted. B) Same as in A) but for the translational
degree of freedom for J =8.
69

Fig. 4.3 Sample least squares fits (black line) to high resolution CO(J) Doppler velocity
profiles obtained from scattering of CO + squalane at room temperature. To avoid visualcongestion, only the odd rotational states from J = 5 -17 are shown out of the total J < 20
states detected.
temperature. Instead, the CO rotational distributions exhibit thermal Boltzmann-like behavior butwith a “temperature” (solid red line) that is significantly colder (T  -45(3) K) than the surface(TS = 293.1(1) K, blue dashed line). This absence of complete equilibration with the surface isfurther corroborated by high-resolution Doppler profile data in Fig. 4.2B, for which distinctly subthermal scattering “temperatures” are also noted in least squares Gaussian fits to the out-of-plane
velocity distributions, with comparison of the model fit with sample data summarized in Fig. 4.3.
Also worth noting is that, although both the translational and rotational “temperatures” are clearlyout of equilibrium with the liquid, they are indistinguishable from each other within experimental
uncertainty (Trot  Ttrans < TS). Thus, one simple physical picture for such behavior would be that70

the CO has enough interaction time with the liquid surface to equilibrate among its own
internal/external (rotation/translation) degrees of freedom, but still not enough time to equilibrate
completely with the surface itself. It is important to note that the translational “temperature” datain these studies probe only velocity components perpendicular to the scattering plane, with thecorresponding parallel velocity components inaccessible to laser Dopplerimetry in the current
experimental probe geometry.
We next explore the low energy CO gas-liquid scattering dynamics as a function of both i)the liquid and ii) the liquid temperature, with results summarized in Fig. 4.4. First of all, the dataconsistently indicate significant negative deviations (T = Trot/trans - TS  -45(15) K) from full CO
equilibration with the liquid surface, with both rotational and translational degrees of freedom
indistinguishable and yet colder than TS (Ttrans  Trot < TS). Secondly, despite such deviations, thereis nevertheless a clear sensitivity in the Trot and Ttrans values to the liquid temperature itself.
Specifically, the Ttrans  Trot values vary quasilinearly with changes in TS, but with a subunity
differential growth(dTrot/trans/dTS  0.50(8)) over the range of experimentally accessible

temperatures. Thirdly, such deviations from full TD equilibrium behavior are only weakly
dependent on the nature of the liquid, with a greater equilibration toward TS demonstrated for softhydrophobic hydrocarbon (squalane) vs. the more strongly interacting (glycerol or PFPE) gasliquid interfaces. In summary, the rotational quantum state and Doppler resolved experimental data
provide evidence for non-equilibrium scattering dynamics at the gas-liquid interface, even at low
collision energies (Einc  kTS) for which conventional wisdom would predict complete trapping
desorption (TD) equilibrium behavior. To help provide physical insight into such non-equilibrium
behavior, we turn next to molecular dynamics simulations in Sec. 3,4, specifically attempting to71

Fig. 4.4 Temperature dependence of low energy CO scattering for a series of liquids. The top
panel shows the scattered rotational temperature (Trot) as a function of TS. The black line
represents complete equilibration between rotational and surface temperatures. The bottom
panel displays similar data and analysis with respect to the Doppler translational degree of
freedom (Ttrans). Error bars represent 1 standard deviations of the mean. These
measurements contain data from J=5-18

model low energy experimental scattering behavior for three projectiles (CO, DCl, CO2) at aperfluorinated, hydrophobic, and hydrophilic gas-liquid interface.

72

4.4 Molecular Dynamics Simulations
In order to probe the nature of “TD” equilibration (or lack thereof) with the surface, threedifferent molecular projectiles have been explored: CO2, CO, and DCl/HCl. Experimentally, allthree molecules have been extensively characterized in gas-liquid scattering studies at low
collision energies. As mentioned in the introduction, CO2 and DCl/HCl thermalize with the gasliquid surface at low Einc while the present results clearly demonstrates that CO does not. By
comparing the trajectory results from these three projectiles, a mechanism for why CO (vs.
DCl/HCl, CO2) does not equilibrate and thermally desorb from the surface can be developed. To
these ends, two series of molecular dynamics studies have been explored. The first series focuseson the temperature dependence (TS) of CO surface scattering, which provides access to a muchwider range of temperatures as well as permits direct comparison to experimental data. A second
series looks at differences in scattering dynamics between the three probe molecules (non-polar(CO) vs. strongly dipolar (DCl) vs. quadrupolar CO2 projectiles) with scattering from a model
perfluorinated liquid interface.

4.4.1 CO, DCl, and CO2 + FSAMs Potential Energy Surface
Molecular dynamics calculations from our group in collaboration with the Hase group havebeen previously described. 37 In the interest of simplicity, we direct these efforts first toward
scattering of molecules from a perfluorinated interface, building on previous successes fortheoretical modeling of quantum state resolved scattering. The simulated surface is a fluorinatedself-assembled monolayer (FSAM), which has been shown to be an accurate yet computationallyfeasible proxy for the liquid, PFPE.38,39 As implemented previously, a sample surface is73

constructed from 48 fluorinated thiol radicals, CF3(CF2)7S, chemisorbed onto a slab of Au(111)by a harmonic Au–S stretch potential. This slab of gold atoms is fixed in space and used to define
the surface and its unit cell. Motions for the other atoms in the chain are governed by additional
potentials that involve two-atom stretches, three-atom bends, and four-atom torsions. Atoms in the
chains interact with each other through atom-atom non-bonding potentials that are constructedfrom the sum of an exponential repulsion and C/rn attraction term, with published parameters foreach of these expressions.37
The CO2-PFPE potential energy surface (PES) has been generated by Hase and coworkers
and utilized extensively by Perkins et al. New surfaces for the CO and H/DCl gas-SAM potentials
have been developed for the present study according to the same principles. Briefly, ab initio radial
1D scans have been calculated for both CO and HCl approaching CF4 from a series of Euler
approach (  ) angles, with the CF4 molecule serving as proxy for a CF head group at the gaspolyfluorinated liquid (PFPE) interface. For each intermolecular geometry, high level ab initio
calculations are performed with explicitly correlated (f12) electron methods at the CCSD(T)-f12
level of theory (MOLPRO software platform)40 with f12 correlation consistent Dunning basis sets
(AVnZ-f12; n=2,3,4), counterpoise correction for basis set superposition error (BSSE), andextrapolation to the complete basis set limit (CBS).41-46 This set of ab initio energy values is thenfit to a two-body atom-atom expression utilizing Lennard-Jones type exponential repulsion/inverse
power law attraction/repulsion terms:−𝑛𝑖

𝑉𝑗 (𝑟𝑗 ) = ∑𝑖 𝐴𝑖 𝑒 −𝑘𝑖 𝑟𝑗 + ∑𝑖 𝐵𝑖 𝑟𝑗

Eq. 4

where 𝑟𝑗 is the two-body spacing for the jth pair of atoms. Such a PES construction protocol has
been used in the generation of the corresponding potential for CO2-FSAMs scattering dynamics,
which demonstrates remarkably quantitative agreement with experiment.39

74

We note that such gas-SAMs PES data have distinct repulsive/attractive regions on very
different energy/length scales. Thus, any non-weighted least squares fit over a uniform grid
spacing will yield results sensitive to the ad hoc choice of grid range sampled, typicallyoversampling the repulsive hard wall (high E) and underweighting both the van der Waals well
region and long range attractive parts (low E) of the potential. This is especially relevant for
scattering at low incident energies, for which the trajectories do not sample high up on the repulsive
wall. To counterbalance these effects, we implement a weighted least-square fit which moredemocratically samples the three dynamically relevant regions (repulsive wall, van der Waals well,and attractive long range) of the potential. The empirical weighting function used is of the form:𝑊(𝐸𝑖𝑛𝑐 ) = (𝐸𝑖𝑛𝑐 + 𝐸𝑜𝑓𝑓 )

−2

Eq. 5

with the offset energy (Eoff > 0) chosen to prevent divergence at low Einc and regulate how quickly
the weights decrease with increasing energy. For a given CF4 – molecular projectile combination,
Eoff is chosen empirically such that the weight at the bottom of the van der Waals well isapproximately 16-fold larger than at Einc = 0. By way of example, Fig. 4.5 displays sample cuts ofthe calculated and least squares fitted PES for both CF4-CO and CF4-H/DCl potentials at Einc < 3kcal, as well as insets showing this good agreement extending to higher incident energies. The
optimized least squares fitted coefficients (Ai, ki, Bi, ni) for both CO-CF4 and H/DCl-CF4 potential
energy surfaces are summarized in Tables 4.1&4.2. Within the context of the Born Oppenheimer
approximation, the potentials are identical for both CF4-HCl and CF4-DCl.

75

Fig. 4.5 Sample ab initio CCSD(T)-f12/AVnZ (n = 2,3,4 CBS) potential slices for OC-CF4(C-C distance, top) and DCl-CF4 (C-Cl distance, bottom), with the analytic least squares
atom-atom fit to the full potential energy surface (PES) shown in red. See text for details.
The insets show the PES over a larger energy scale.

76

Table 4.1. Least squares fitted parameters for the CO-FSAMs atom-atom potential, as
obtained from least squares fits to high level ab initio CCSD(T)-f12/AVnZ-f12 (n=2,3,4,CBS)
calculations for a systematic series of CO approaches to CF4. See text for details.

Table 4.2. Least squares fitted parameters for the HCl-FSAMs atom-atom potential, as
obtained from least squares fits to high level ab initio CCSD(T)-f12/AVnZ-f12 (n=2,3,4,CBS)basis set superposition error (BSSE) corrected calculations for a systematic series of HClapproaches to CF4. See text for details.

77

The CO2 Van der Waals complex has been discussed in great detail by Hase and coworkers.
The lowest energy configuration for this complex is C2v symmetry with the carbon from the CO2
approaching between two of the fluorine’s with a carbon-carbon distance of 3.76 angstroms and awell depth of -.82 kcal/mol. For H/DCl, the bound state has was not captured along the trajectories
calculated. The lowest energy configuration calculated is with the chlorine centered between threeof the CF4’s fluorines with the hydrogen pointing perpendicular to this axis eclipsing the a fluorine
when looking down the symmetry axis, with a carbon-chlorine distance of 3.8 angstroms and a
depth of -.83 kcals/mol. Naively, we thought the bound state would be of C3v symmetry with thehydrogen pointing towards the central carbon but due to the large polarizability of the chlorine andthe large size of the fluorines, the hydrogen is pushed out of the way leading to a bound state ofCs symmetry. The final molecule, CO, is quite interesting since it has two near identical wells.
The lower energy configuration is where the carbon of the CO is facing the carbon of the CF4 witha carbon-carbon distance of 3.65 angstroms and a well depth of -.667 kcals/mol. The other boundwell is with the oxygen of the CO facing the CF4’s central carbon. This has a carbon-carbon
distance of 4.55 angstroms (with a carbon-oxygen distance of 3.42 angstroms) and a well depth of-.665 kcals/mol.

4.4.2 Trajectories: Low Energy Collisions of CO, DCl, CO2 with FSAMs
Scattering trajectories are calculated using the package VENUS05 developed by Hase andcoworkers,47 propagated with sufficiently small timesteps (t  0.2 fs) to ensure energy
conservation (E/E < 50 x 10-9) over the time scale of a typical 10,000 fs trajectory. To permit
temperature control of the gas-liquid interface, each trajectory is initiated with FSAM momenta

78

sampled from a Boltzmann distribution at TS. The FSAM simulation is then propagated for 2000
fs, with the atomic velocities uniformly rescaled after every 100 fs to equilibrate the atom ensemble
to a well-defined temperature and average kinetic energy (i.e., <E> = 3/2kTS). The CO, DCl, andCO2 projectiles are prepared asymptotically (zinit = 30 Å from the surface) in an initial statecorresponding to uniform 2D angular sampling of the molecular orientation and zero rotationalenergy (J = 0). The total incident linear momentum of the projectile is kept constant from trajectory
to trajectory, with the first point of contact randomized by 2D translation over an area equivalent
to a single FSAM unit cell. The trajectory is then propagated such that the projectile collides withand rebounds sufficiently far from the surface for any residual projectile-surface interaction to be
negligible, either by final height (zfinal > zinit = 30 Å) or total time interval (Tfinal > 100,000 fs). The
final projectile velocity components and kinetic energies are taken directly from the last simulation
point, for which the angular momentum J is sorted into bins of ħ width from the final simulation
value of <J2>  J(J+1) ħ2.

4.4.2 Theoretical Results and Analysis: CO with FSAMs
We are now in a position to analyze the molecular dynamics (MD) trajectories on the samefooting as the original quantum state resolved experimental data. The first and simplest comparison
to make is between experimental and theoretical “temperatures” for low energy (Einc = 1.0(1)kcal/mol) scattering of CO molecules from liquid PFPE (experiment, Fig 4.4, red symbols)) and
FSAMs (MD simulation, Fig. 4.6, black symbols). To extract a temperature (Trot) from therotational degree of freedom, we least squares fit the final CO(J) states to a single temperature
Boltzmann distribution, a sample log plot of which for CO scattering from FSAMs is reported (TS= 350 K) in the upper right panel of Fig. 4.6. Noteworthy is the remarkable agreement between theexperimental Trot values extracted from CO scattering data (as summarized in Fig. 4.4) with the79

Fig. 4.6 Comparison of MD and experimental temperature dependence. The left panels show
the rotational (top) and translational (bottom) temperature dependence. The right panels show
example fits to the MD data at a surface temperature of 350 K. Both the black and the blue
data points are simulated data while the red data points are experimental.

theoretical Trot values in Fig. 4.6A obtained from analysis of the low energy MD trajectory data,
although now accessible over a much broader dynamic range (TS  50-450K vs. TS  275-325K).
Also worth noting is that such good agreement between experiment and theory is largely
insensitive to incident energy, with MD trajectory data at an order of magnitude lower Einc  0.1
kcal/mol yielding only slightly cooler (blue symbols, Fig. 4.6A) but essentially indistinguishable

80results from the Einc  1.0(1) kcal/mol scattering data (black symbols, Fig. 4.6A). Furthermore, thetheoretical Trot data exhibit the same quasilinear incremental dependence on FSAM temperature.
Specifically, differential slopes (m  dTrot/dTS  0.42(3)) from the MD simulations are in
reasonable agreement with the values (m  dTrot/dTS  0.49(5)) determined experimentally for
CO + PFPE (see Fig. 4.4). Simply summarized, the CO(J) distributions for low energy collisions(Einc  1.0 kcal/mol) at the gas-PFPE liquid interface scatter with a rotational temperature colder
than (T  -53K at TS =300K) and differential slopes (m  0.49(5)) indicating sensitivity to thesurface temperature (TS). These trends are in close agreement with theoretical trajectory data for
CO + FSAMs over a much wider temperature window (see Fig. 4.6A) than is experimentally
accessible in the liquid phase.
In a similar fashion, we next analyze the trajectory calculations for translational
distributions in the scattered CO flux at low incident energies. We find that fits to a normal flux
weighted probability distribution (F(vx,vy, vz)  vz exp(-m(vx2+vy2+vz2)/2kTtrans) and temperature(Ttrans) already yield satisfactory agreement with the data. We thus report global fits to a single
translational temperature (Fig. 4.6, lower left panel), which yield statistics with low scatter for thefull set of N = 1000 trajectories (see Fig. 4.6B right panel for a sample speed distribution) thaneach degree of freedom fit independently. The MD scattering data for CO + FSAMs again yieldtranslational temperatures varying linearly with TS and in remarkably good agreement with theexperimental CO + PFPE results. Analysis of the translational data provides additional
experimental/theoretical support for CO scattering from a FSAMs surface in a temperature
distribution that is both i) colder than (T  -45(15)K) and ii) differentially proportional to(dTtrans/dTS  m  0.50(8)) the liquid temperature over our experimentally accessible window ofobservation. The combined experimental and theoretical results for CO are in fundamental
81

disagreement with a conventional picture of 100% trapping desorption (TD) dynamics dominating
at low collision energies, which in the absence of transition state barrier would predict complete
equilibration (Trot  Ttrans  TS) with the liquid surface temperature at all values of TS.
The trajectory data obtained over this more expanded temperature range in Fig 4.5 reveal
additional insight into the scattering dynamics. Specifically, the theoretical plots for Einc  1.0(1)kcal/mol intersect the T = TS line, and are therefore predicted to cross from a regime of sub-thermal
scattering (T < TS) at near room temperatures into a nominally “hyperthermal” scattering regime(T> TS) at sufficiently low surface temperatures. Indeed, this stimulated a parallel set of trajectorystudies at 10-fold lower collision energies (Einc = 0.1 kcal/mol, see Fig. 4.5), which clearly reiterate
the same sub-thermal to hyperthermal crossover near TS  200K. This non-physical result isinconsistent with full TD equilibrium predictions, for which one would expect Trot, Ttrans toasymptotically approach but never cross TS. This provides first unambiguous evidence that theenergy transfer dynamics are still far from the TD scattering regime even down at Einc = 0.1 – 1.0
kcal/mol. Instead, with CO–FSAMs well depths of  0.5 kcal/mol, these collision dynamics
sample an incident energy window competitive with long range interactions between the projectile
and the liquid surface atoms. One final note on the MD simulations at .1 kcal/mol, the point at Ts= 50 K was run but none of the trajectories finished within the 100 ps window. This could beindicative that the sticking coefficient goes to 1 around this surface temperature and collisionenergy for CO.

4.4.4 Theoretical Results and Analysis: DCl and CO2 with FSAMs
Although the MD results empirically match experimental observations quite well, they do
not yet provide an answer why CO molecules desorb from the surface at temperatures below TS.

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To achieve a further insight, we have extended these MD simulations to all three projectiles (CO,DCl and CO2) colliding with a FSAM model surface, each of which have been experimentallystudied with PFPE liquid in quantum state resolved experiments. These three molecules are quite
different in terms of their interactions with surface CF bonds, corresponding to van der Waals
dipole induced dipole (CO-CF), dipole-dipole (D/HCl-CF)48 vs dipole-quadrupole (OCO-CF)49.
Since DCl and CO2 have been shown to experimentally equilibrate with PFPE at low collisionenergies, we thus anticipate nearly full thermalization in the MD simulations to TS  300K.
The final quantum state populations from these additional molecular trajectories areanalyzed in identical fashion to the previous CO + FSAM data in Sec. IVB, with TS = 300K. As
expected, CO2 and DCl do scatter from FSAM with near thermal rotational temperatures,
specifically Trot  305(10) K and Trot  287(12) K, respectively. Similarly, we also observe fully
equilibrated results in the DCl and CO2 translational degrees of freedom, with temperatures fromleast squares fits to out-of-plane velocity profiles of Ttrans(DCl ) = 309(7) K and Ttrans (CO2)=304(7) K. This is in clear contrast with the CO trajectory behavior, which consistently scattersfrom an FSAM interface (TS = 300) with sub thermal rotational (Trot = 266(9) K) and translational(Ttrans = 264(6) K) temperatures. In summary, the MD theoretical predictions for each of thesethree projectile + gas-liquid interfacial trajectory simulations match closely what has been
experimentally observed from actual quantum state resolved scattering studies.

4.4.5 Interaction Time Analysis: CO, DCl, CO2 with FSAMs
The excellent agreement between MD simulations and experimental results motivates a
deeper statistical analysis into the trajectories themselves. One crucial observable is the interaction
time () of the molecule on the surface, which can be determined from durations over which the83gas-surface forces exceed some threshold. This threshold is chosen to be 10x the root mean square
force magnitude (fRMS) over the first 3 ps of the simulation, during which the molecule is 30
angstroms away from and does not interact appreciably with the surface. This gives us the level ofthe machine precision noise (the noise floor), and when the force exceeds that, the molecule isdetectably interacting with the surface. The level chosen is high enough to be clear of machine
precision noise but is low enough that every molecule only crossed this level twice, once when it
starts to interact with the surface and once when it leaves the surface. If the desorption were a 1storder kinetic process, we would expect the gas-liquid collisional durations to be exponentiallydistributed, with a slope reflecting the lifetime of the molecule-surface complex. The level chosen
above is ~ 1 nm above the surface and thus there will be a contribution to this extracted value fromthe flight time of the leaving molecules. This, however, is ~1-3 picoseconds on average and thus
does not appreciable change the extracted lifetimes.
Semilinear plots of the corresponding exponential decays are exhibited in Fig. 4.7, alongwith linear least squares fits to extract the corresponding projectile-surface residence lifetimes. As
expected, the residence times on this surface are indeed well characterized by single exponential
decay, with lifetimes on the 10-30 ps range. Interestingly, there is a clear 2-3 fold increase insurface residence lifetimes for the more strongly (CO2 = 28(1) ps and DCl = 19(1) ps) vs. lessstrongly (CO = 9(1) ps) interacting projectiles. Only a very small fraction of events are observedwith lifetimes in excess of the maximum cutoff trajectory duration (tcutoff = 100 ps), specifically,
0%, 1% and 5% for CO, DCl, and CO2 respectively. As expected, this is in the same order as the84

Fig. 4.7 Histograms of surface FSAM interaction times in MD simulations for low energy
scattering with each of the three projectiles. The fractions of trajectories that do not result inescape from the surface after 100 ps trajectories for CO2, DCl, and CO are 5%, 1% and 0%,
respectively.

1/e lifetimes of collisional durations, and in reverse order with respect to potential well depths forthe gas-liquid binding interactions (see Fig. 4.5). Similarly, instead of looking at the length of timethe molecule interacts with the surface, we can look at the number of classical turning points themolecule undergoes during its trajectory. This reports on the number of times the normal
momentum reverses and thus can be seen to be approximately twice the number of times themolecule attempts to leave the surface. For the three scatterers, we see a similar trend to the surface
residence times. CO undergoes an average of ~6 classical turning points meaning that it on average
85takes only three attempts to leave the surface before it is successful. This is in contrast to the twoother molecules with DCl undergoing ~19 classical turning points and CO2 undergoing ~35. Thus,
it can be seen that it requires many fewer attempts for CO to leave the surface than the other two
molecules.
An even more insightful metric can be obtained from the distribution of gas-liquid surface
heights P(z) over a full time dependent scattering trajectory. This is extracted by sampling thecenter of mass for each projectile (CO, DCl, CO2) every 2 fs (10 time steps) and recording theheight (z) above the gas-liquid interface. The three sets of data from all N = 1000 trajectories arethen histogrammed (z = 0.1 Å bins), normalized to unit incident flux, and displayed on the same
scale in Fig. 4.8. The surface height (z=0) was determined by looking at the distribution of thesurface fluorines and finding their time averaged 50% density position above the Au surface, from

Fig. 4.8 The probability distribution of the three molecules probed as a function of height
above the surface. The dotted lines show each of the peaks of the distributions in relation to
the surface height at z = 0 (black line).
86which the whole surface is anchored. The resulting plots exhibit a qualitatively similar topology
for each projectile, with i) a flat asymptotic approach probability (z > 5 Å), ii) strong peaking in
the adsorption well region (0 Å < z < 5 Å), and iii) rapid probability decay as the projectile
penetrates into the FSAM surface. However, there are also important differences between the plots
for CO vs. DCl/CO2 projectiles, which in turn inform critical differences in the collision dynamics.
For example, CO exhibits a much weaker statistical presence in the well region, with a maximum
relative probability density (Pwell ~ 1.7) two to three-fold smaller than for DCl (Pwell ~3.3) or CO2(Pwell ~5.5). As expected for a 1st order exponential process, these values are in excellent agreementwith ratios of observed residence lifetimes (see Fig. 4.7). Furthermore, if we look more closely at
the well region, the CO probability density peaks at zmax ~ 2.50(10) Å from the surface while themaxima for DCl and CO2 occur at ~2.00(10) and ~1.25(10) Å respectively. Simply summarized,
histogram analysis of the trajectories indicates that CO is i) trapped substantially more shallowly
than DCl or CO2 and ii) spends more of its residence time further away from the FSAMs surface.
Finally, an even subtler but more quantitative tool with which to represent such statistical
data is the potential of mean force (POMF), represented by
VPOMF(z) = -kTB ln[P(z)]Eq. 6

Under equilibrium conditions, VPOMF characterizes the relative probability for a projectile a
distance z above the gas-liquid interface in terms of a distance dependent free energy, i.e., G(z)~ VPOMF(z). However, it provides an equally meaningful probability distribution under nonequilibrium conditions, as obtained from calculations of the force normal to the surface for eachof the bin heights and integrating the reversible work from infinity back to the gas-liquid interface.
The values of this non-equilibrium potential of mean force (VPOMF(z)) have been calculated fromthe trajectories (Fig. 4.8) and are plotted in Fig. 4.9. As noted previously for the surface height87

distributions (Fig 4.8), there are three characteristic domains labelled as i) asymptotic, ii) van der
Waals well, and iii) repulsive wall regions, where we have chosen z = 0 as the point at which theaverage fluorine density has decayed to 50% of its bulk value. Of particular importance, both CO2
and DCl projectiles exhibit minima penetrating into the liquid (z < 0), whereas the well for CO ismore nearly centered on the gas-liquid interface itself. Profound differences can be seen in the
VPOMF well depths for these three projectiles, with the CO POMF well depth (0.3 kcal/mol) 3-4
times shallower than either DCl (0.8 kcal/mol) or CO2 (1.1 kcal/mol). Additionally, VPOMF for CO
in the repulsive region (left side of Fig.4.9) increases with a slope of m  0.6 kcal/mol/Å, while

Fig. 4.9 Calculated potentials of mean force, VPOMF(z), for CO, CO2, and DCl projectiles withrespect to distance from the FSAMs surface

88both CO2 and DCl exhibit notably shallower slopes of m  0.4 kcal/mol/Å. In summary, CO +PFPE thus clearly exhibits i) a weaker attractive well, ii) a VPOMF(z) minimum shifted notably
outward, and iii) more steeply repulsive interactions with the surface than experienced by either
DCl or CO2 projectiles, respectively.

4.5 Discussion
The combined experimental and theoretical results in this paper reveal anomalous behavior for
supersonically cooled CO(J = 0) scattering at low energies (Einc  0.1 – 1.0 kcal/mol ) from thegas-liquid interface, specifically CO desorbing at rotational and translational temperatures i) out
of equilibrium with and ii) colder than the surface (TS). This is fundamentally at odds withconventional detailed balance considerations, for which trapping desorption (TD) events might be
expected to dominate in the limit of low collision energies and unity sticking coefficients ( = 1).
A simple mechano-kinetic view of the TD process is summarized by three stages. 1) The projectile
approaches the surface at sufficiently low energy for all incoming molecular states to become
transiently bound in a physisorption well. 2) The molecule undergoes extended collisional
interactions with the surface sufficient to thermalize with the liquid (TS) and lose all residual
memory of the incident collision. 3) The thermalized molecule eventually leaves the surface
through a barrierless exit channel, which by detailed balance requires the asymptotic scattering
state distributions to be accurately described by the surface liquid temperature, TS. Experimental
evidence in this work argues that CO does not leave the surface at TS and thus clearly diverges
from this putative TD pathway. The question of interest is where?
A first place to look would be final desorption from the liquid interface, for which the
crucial assumption is that a molecule leaves along a monotonic and barrierless pathway. From

89

atom-atom modeling of the gas-liquid potential, this assumption seems secure - the potential
energy surface for all three projectiles rises monotonically from the bound well to infinite
separation. This is true not only for the static atom-atom PES but also for the thermodynamicallyaveraged potential of mean force (POMF). We can therefore be reasonably confident that themolecules do not experience transition state barriers and thus complex desorption dynamics (step3) cannot explain why CO comes off the surface both translationally and rotationally colder thanTS.
We next consider the thermalization step 2, for which a TD event requires the projectile toundergo many interactions before leaving the surface. For a molecule trapped in a well andinteracting with a thermal bath, the average residence time of the molecules should be describedby Arrhenius behavior, with the first order rates decreasing (exponentially) with surface cooling.
At sufficiently low temperatures, the slow rate constant for desorption is swamped by energy
transfer to/from the surface, and thus the projectile has ample time to thermalize. But withincreasing TS, the Arrhenius desorption rate increases more rapidly than the molecule-surface
equilibration rate. For initially jet cooled projectiles (Trot  10K << TS) at low incident energies,
as a result, one expects deviation in the desorption temperature below TS (as observed),
corresponding to a “roll off regime” as energy equilibration with the surface fails to compete withdecreasing residence times. Experimentally, we see such suppression of equilibration dynamics(i.e., Trot/trans < TS) over the entire range of liquid temperatures accessible. Due to freezing pointsof the three (PFPE, squalane, and glycerol) liquids investigated, we are not able to reach lower
temperatures experimentally, but the MD trajectory analysis empirically reveals that we are i)already in this roll off regime for CO scattering under near room temperature conditions and thatthese distributions become hyperthermal (Trot = Ttrans > TS) at slightly lower temperatures. In

90summary, there is ample evidence in the MD simulations for non-thermalization and profounddeviation from the TD dynamical paradigm. This is required for the scattered CO flux at low
incident energies to exhibit a final translational/rotational quantum state distribution temperature
lower than TS, as experimentally observed.
As a parting comment, we note that step 2 may not be the only weak link in violation of
the TD scattering paradigm. We consider the initial trapping event (step 1), which for a true TD
event would rigorously require CO to become trapped in the well long enough to lose all memoryof the incident collision conditions. Looking back at the MD simulations in Sec IV, one could
argue equally strongly that CO never “traps” on the surface long enough to lose complete memory.
Indeed, the key difference we see between (non-thermalizing) CO and the (thermalizing) DCl/CO2
projectiles is that CO spends a 2-3 fold shorter time in the vicinity of the surface, clearly
uncharacteristic with trapping desorption (TD) but rather an impulsive scattering (IS) pathway.
Although unconventional to think of low energy inelastic gas-liquid scattering in this context, one
simple physical interpretation could be that CO never interacts strongly enough with the liquidinterface to either trap or equilibrate on the time scale of the collision event. Such novel collision
dynamics might therefore best be characterized as a novel “sub-thermal impulsive scattering”(STIS) channel opening up at collision energies on the order of the well depth. Although further
experimental and theoretical work will be required to support or refute such an interpretation, theexistence of short lived, impulsive scattering at low energies serves to highlight the greater
dynamical richness of collision pathways than previously considered in the early TD/IS models
for quantum state resolved scattering dynamics at the gas-liquid interface.

91

4.6 Summary and Conclusion
Low energy scattering (Einc = 1.0(1) kcal/mol) of CO has been studied from a systematicseries of gas-liquid interfaces, exploiting high resolution infrared absorption methods to probe thefinal translational (out to plane vDoppler) and rotational (J) quantum state distributions. The
experimental studies reveal that CO scatters into a distribution characterized by distinctly subthermal (but nearly equivalent) rotational (Trot) and Doppler translational (Ttrans) temperatures (Trot Ttrans < TS). The results are fundamentally inconsistent with a traditional picture of complete
accommodation (trapping-desorption, TD) at low incident energy of molecular scattering eventsfrom the gas-liquid surface.
To explore the physical origins of such phenomena, molecular dynamics simulations ofCO, DCl, and CO2 projectile scattering from a fluorinated self-assembled monolayer (FSAM)
interface have been implemented, with atom-atom potentials modeled on high level ab initio
MOLPRO calculations (CCSD(T)-f12/AVnZ-f12 (n=2,3,CBS)) as a function of CF4 –projectile
distance/approach angle and corrected for basis set superposition error (BSSE). These potential
energy surfaces have then been implanted in the framework of the Venus molecular dynamics
program to probe energy transfer and accommodation dynamics over an expanded range ofcollision energies and liquid temperatures, revealing remarkably quantitative agreement withexperimental results. Detailed statistical analysis of the molecular dynamics permits comparison
between CO2, DCl and CO trajectories to elucidate mechanisms for projectile equilibration (orlack thereof) at the gas-liquid interface. Specifically, CO spends less time in the vicinity of theliquid interface and penetrate less deeply into the fluorinated surface compared to DCl and CO2
projectiles. This difference in behavior has been statistically reiterated by potential of mean force(VPOMF(z)) calculations, which highlight a 2-3 fold weaker well depth and 2-3 times steeper

92

repulsive wall for an CO-FSAM vs DCl-/CO2-FSAMs potential energy surfaces. The experimental
and theoretical quantum state resolved data reveal that CO does not trap long enough at low
energies on the gas-liquid interface to result in complete energy equilibration with the liquid TS.
Instead, we argue that the experimental CO distributions violate the conventional paradigm of low
energy scattering through complete equilibration with the liquid and are indeed more consistent
with a novel “sub-thermal impulsive scattering” (STIS) pathway rather than a trapping-desorption(TD) event. The data provide mounting evidence for a greater richness of collision pathways thanconsidered in the early TD/IS models for quantum state resolved scattering dynamics at the gasliquid interface.

93

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96Chapter 5
Low Energy OCS Scattering:
A study of Vibrational Energy Transfer at the Gas-Liquid Interface

5.1 Introduction
A detailed understanding of chemical dynamics at the gas-liquid interface requires aequally detailed understanding of collisional molecular energy transfer, in principle, into each of
the electronic, vibrational, rotational, and translational degrees of freedom. Through a multitudeof elegant molecular beam techniques, including direct absorption laser spectroscopy1-2, time offlight mass spectroscopy3-5 and REMPI+VMI6, collisional energy transfer between the scattering
projectile and the surface has been explored extensively in translational and rotational degrees of
freedom. In striking contrast to the potential complexity of such systems, it has been empiricallyfound that these scattering pathways appear to “bifurcate” into two rather remarkably simpler
channels. The first of the two is referred to as thermal desorption (TD), whereby an incident
molecule traps transiently on the surface, achieves complete thermalization, and then desorbs fromthe surface from initial conditions sampling a near thermal equilibrium distribution. In colloquial
language, such a subset of trajectories has “lost all memory” of the incident scattering conditions,and are found to occur on a > 10-100 ps time scale. We note that this does not require the final
state distributions to remain in thermal equilibrium with the liquid, as there can still be dynamicalbarriers to successful desorption that are favored/disfavored by some fractional subset of theinternal quantum and/or translational energy states.

97

The second pathway is denoted as impulsive scattering (IS), which corresponds tomolecular scattering from the interface while still maintaining some residual “memory” of its
initial scattering condition. In essence, this channel comprises all molecular flux that does not
represent trapping desorption (TD), though unambiguous separation into one of these two channels
is meaningful only statistically and rarely possible by inspection for a given trajectory. In general,
contributions to this IS channel occur on a much faster time scale (< 1-10 ps) and contain all nonequilibrium dynamical information on the gas-liquid scattering event. In our molecular beamstudies for non-orthogonal angles of incidence, this channel often appears as a lobular forward
scattering peak with a hot yet remarkably “temperature-like” internal rotational quantum state
distribution2, 7-8. It is worth noting that the existence of such “hyperthermal” rotational distributionsin the IS channel is far from obvious and indeed quite surprising, though simple models based onsmoothing of rainbow features by thermal roughening at the gas-liquid interface have been
proposed that begin to capture this behavior for rotational degrees of freedom. Rather remarkably,
however, there have been no studies reported of any such effects in IS scattering that include
vibrational degrees of freedom, specifically vibrational excitation, deexcitation, and/or
equilibration in molecular collisions at the gas-liquid interface. It is this inclusion of vibrational
degrees of freedom in the gas-liquid scattering dynamics that represents the major focus of thiswork.
Vibrational energy transfer via collisions in the gas phase has been extensively studied.
One essential trend observed is that vibrational energy transfer does not result from low energy
collisions but rather from a smaller number of very large energy transfer collisions.9 These generaltrends are well captured in Landau-Teller theory10, which predicts that the vibrational energy
transfer to be relatively inefficient and occurs only when the time dependent force f(t) between

98

oscillator and the collider/perturber contains Fourier components that resonantly match thevibration frequency of interest.
A similar trend in the predissociation dynamics11 of Van der Waals cluster was noted by
Ewing and coworker, where large changes in vibrational quanta during the dissociation event are
exponentially inhibited. For V → T transfer, this “exponential gap” penalty arises from a FranckCondon type perspective through the vanishingly small overlap between the van der Waals
repulsive wall potential and a rapidly oscillating translational wavefunction in the exit channel. In
general, the kinetic acceleration of vibrational excitation or relaxation arises from thepresence/absence of near resonant vibrational modes into which excess energy can be transferredfrom or into.
Investigation of vibrational energy transfer at the gas-condensed phase interface is aparticularly challenging process. Of special note are the early pioneering studies by Wodtke andcoworkers probing deexcitation of vibrationally prepared molecules on single crystal interfaces1215, which reveal two classic paradigms. If there is strong interaction/coupling with a single crystal

metallic surface, for example with significant anionic character due to electron transfer from themetal to the molecule, the vibrational lifetimes are short and multiquantum (v >>1) vibrationalenergy transfer quite efficient16. For insulating single crystal materials, on the other hand,vibrational energy transfer efficiencies are found to decrease by several orders of magnitude,
revealing only perturbative, harmonic oscillator like changes (v1) in the molecular vibrational
quantum state. However, it is not simply a matter of conductive versus insulating materials, as
there are single crystal metal-absorbate systems (Au + CO(v=1)) where molecular vibrations havebeen shown to survive for 100’s of picoseconds.17 The vibrational metastability in such systems
have been attributed to anomalously weak adsorbate-surface interactions, due to minimal electron99

transfer to/from the metal and leaving the molecule only weakly physiabsorbed. How these simple
gas-surface intuitions might transfer from the long-range order of a single crystal to the far moredisordered environment of a liquid remains largely unexplored and represents the major focus of
this work.
This study takes special advantage of polyatomic molecules as projectiles for study ofvibrational energy transfer dynamics at the gas-liquid interface. Carbonyl sulfide (OCS) is aparticularly suitable molecular probe for such energy transfer dynamics, as a linear triatomic
molecule with the right balance between small rotational constant (B = 0.203 cm-1) and a strong
infrared fundamental (590 km/mol) in the CO stretch region (2050 cm-1) accessible to our quantum
cascade laser. This combination allows for a large number of final scattered rotational states to be
detected within the signal to noise of our experiment, with some 70 rotational J states below 1000
cm-1 and readily generated in collisions at the gas-liquid interface . Most importantly, polyatomic
OCS also has two low lying vibrational modes below 1000 cm-1, specifically the OCS bend at 520
cm-1 and the predominantly CS stretch at 860 cm-1. As a result, both the OCS bend (0110) and CS
stretch (0001) excited states are therefore already populated in the incident beam and can besensitively observed via CO stretch “hot bands” (e.g., (1110  0110) and (1001)  (0001)) in ourlaser spectrometer. Consequently, this offers the novel opportunity to study energy transfer i) fromvibrationally excited OCS into the liquid as well as ii) excitation of these same polyatomic modes
by thermal vs. hyperthermal collisions at the gas-liquid interface. Under the low energy conditionsof the present studies, we find remarkably inefficient collisional energy transfer and equilibration
dynamics, which
The organization of this chapter is as follows. A brief overview of the experimental
spectrometer apparatus is described in section 5.2, with particular emphasis on the modifications
100

to the laser frequency diagnostics and scattering apparatus required for working with such small
rotational constant and polyatomic species. In Section 5.3, results are reported which explore
vibrational, rotational, and transverse translational collisional energy transfer in OCS with several
prototypical liquids under low energy beam conditions. The data highlight rapid equilibration
dynamics in rotational/translational degrees of freedom, which stands in stark contrast with theextreme inefficiency and highly adiabatic nature of vibrational excitation/deexcitation dynamics.
Section 5.4 explores these results in the context of simple dynamical theories and high level ab
initio potentials for the collision events, with conclusions and directions for future study
summarized in Section 5.5.

5.2 Experimental
The gas liquid scattering apparatus can be broken down into two major pieces, i) the midinfrared shot-noise limited direct absorption spectrometer and ii) the scattering vacuum chamber.
Many details of this experimental apparatus have been described elsewhere and can be briefly

Figure 5.1: Layout of experiment101

summarized, to which we include greater focus on specific apparatus modifications relevant to thepresent experiments18-23.
A schematic diagram of the laser optical system is shown in Fig. 5.1. The light source isan external cavity single mode quantum cascade laser (Daylight Solutions), which generates asmuch as ~300 mW of single mode infrared light from ~2000-2200 cm-1 with a linewidth of ~10
MHz. This is far more than can be used for linear detection; thus the IR power is first reduced 50x
by weak reflection from a BaF window and then adjustably trimmed to the desired level by a pairof crossed Rochon polarizers. After transmission through the rest of the optical system and vacuum
scattering chamber, this results in ~10-30 uW on each of two LN2 cooled InSb photodetectors. Our
frequency diagnostics offer three stages of dynamic range. First we use a Michelson wavemeter(Bristol wavemeter 621b) to obtain an initial estimate (0.1 cm-1) of the spectral scan startfrequency. Secondly, transmission signals from a room temperature gas cell (500 mT OCS, 1-5
cm path length) are also recorded, which in conjunction with the wavemeter reading permits
unambiguous determination of the absolute frequencies from an OCS atlas. Thirdly, in order toprovide a linear scan axis, we monitor the transmission fringes through an off-axis Fabry-Perot(bowtie) etalon with a moderate finesse of ~20-30 and 250 MHz FSR. Sample spectral diagnostics
through the transmission cell and Fabry-Perot etalon are represented in Fig. 5.3, which indicate
the presence of a strongly optically saturated absorption line on the CO stretch fundamental ((1000) (0000), R(17)), with additional much weaker lines corresponding to hot band transitions out ofthe doubly degenerate OCS bend ((1110)  (0110), R(Y)), split into a e/f parity doublets by ldoubling in the 1 = 0 and 1 lower/upper level.
Finally, the reduced IR light is split into signal and reference beams, with the distributionof final OCS rovibrational quantum states in the vacuum chamber probed by transient absorption102

of the quantum cascade laser signal light in a 16 pass Herriot cell, with the multipass axis oriented
perpendicular to the scattering plane and at 65° from normal and 1 cm away from the point on theliquid surface struck by the skimmed molecular beam. The transmitted IR light is measured on our
shot-noise limited spectrometer. This is achieved via a balanced detection scheme with one of thetwo arms contains the multipass cell in our vacuum chamber. This setup achieves absorbancesensitivities of around 1x10-5 in the bandwidth of the experiment.
The gas liquid scattering events occur in a 60 L Al vacuum chamber, evacuated by a 6-inch
diffusion/roughing pump combination. In the presence of the molecular beam gas pulse, thechamber pressure is maintained < 10-4 Torr, which ensures minimum mean free path lengths
several times the dimensions of the vacuum chamber. The scattering system is made up of amolecular beam source, the scattering target and the multipass cell. The beam source is of Prochand Trickl design24, with a mixture of 5% OCS/95% argon expanded through a 0.508 mm orifice
at a stagnation pressure of Pstag ~ 80 torr, where the choice of low stagnation pressure achieves
reasonably low rotational temperatures yet prevents clustering of OCS into dimers, trimers, etc.,
as verified by linear curves of growth vs. pressure for OCS transitions observed in the incident
beam. The average speed in the molecular beam pulse is measured to be 550(50) m/sec, as
measured by a simple time of flight setup as a function of microphone displacement. This translates
into an incident OCS energy of 2.2(4) kcal/mol for collisions with the liquid surface, with themolecular beam entering from below and oriented 65o from the liquid surface normal.

103

Figure 5.2: This is an example of a complete scan of OCS scattering from PFPE at low
collision energies. The downward spectrum is of the incident molecular beam
By way of assessment of OCS rotational/vibrational cooling in the supersonic expansion,
we monitor the CO stretch spectrum of the incident molecular beam. As shown in Fig. 5.2, there
are clearly contributions from the ground (0000) as well as both the low-lying OCS bend (0110)
and CS stretch (0001) excited states. From Boltzmann analysis of rotational populations in each of
the lower vibrational states, we obtain a rotational temperature of 10K. However, an equivalentBoltzmann analysis of populations in each manifold (summed over all J states) yields a vibrationaltemperature of Tvib = 240(5) K, which is clearly much hotter than the Trot = 10K rotationaltemperatures in the supersonic expansion. Such highly non-equilibrium behavior between rotationand vibration arises from the much larger number of collisions required to cool vibrations in a104

supersonic pinhole expansion, essentially due to the much larger vibrational (102-103 cm-1) vsrotational (100-101 cm-1) energy spacings to be collisionally removed. Indeed, this provides
another indication of “frustrated” vibrational energy transfer dynamics already in the throat of apinhole supersonic expansion, which provides a crucially important baseline for interpreting thesubsequent collision dynamics at the gas-liquid interface.
The liquid target for these scattering studies is based on a temperature dependent rotating
wheel setup described in reference18. The liquid scattering surface is prepared according to themethod of Lednovich and Fenn25, using a rotating (~ 0.2 Hz) bead blasted stainless steel wheel(12.7 cm diameter) half-submerged in the copper liquid reservoir and scraped with a stationary
razor blade to present a thin (~500 um), freshly prepared gas-liquid surface to the impinging
molecular beam. The liquid reservoir and gas-liquid surface are thermally isolated from the rest of
the vacuum chamber by Teflon spacers, with the liquid surface temperatures stabilized by a twostage servo loop cooling apparatus. The majority of the thermal cooling/heating is achieved bymeans of an ethanol recirculating chiller, which incrementally cools/heats the backplate athermoelectric element that servo loop stabilizes the temperature of a thermistor epoxied to thefront of the copper trough.
This study investigates three different classes of liquids that sample different scattering
dynamical regimes: 1) perfluorinated polyether, (PFPE, Krytox 1506, F-[CF(CF3)CF2O)]14(avg)CF2CF3), as a prototype for a rough but chemically inert liquid surface, 2) squalane(2,6,10,15,19,23-hexamethyltetracosane, C30H62), as a prototype for fully aliphatic, stronglyhydrophobic surface, and 3) glycerol (1,2,3-propanetriol, C3H8O3), as a prototype for a much morehydrophilic surface due to multiple protruding OH groups. Each liquid is degassed under ~1 mTorr
vacuum at room temperature for several hours to remove dissolved atmospheric gases, or at105

slightly elevated temperatures (~ 350 K) for the glycerol liquid samples to allow for complete
degassing within a reasonable (overnight) time frame.
Our quantum-state and Doppler-resolved scattered OCS signals are measured in a 16 passconcentric Herriot cell with a single pass cell length of ~40 cm. As can be seen in Fig. 5.1, thismultiple beam path lies along the plane of liquid surface and perpendicular to the molecular beam.
This means that the Doppler broadening reports on the velocity perpendicular to the scattering
plane made by the liquid surface normal and the molecular beam. A crucial addition to thescattering setup is a LN2 cooled cold plate at the top of the vacuum chamber, which helps us
achieve surface liquid operating temperatures of 90 K when cooled and implemented to reduce thebackground OCS in the vacuum chamber. Since the FWHM of a room temperature OCS transition
is typically ~100 MHz and the QC laser linewidth is ~10 MHz, this results in virtually noappreciable frequency noise contribution from the scattered signal. However, since frequency
noise on the background gas in our chamber is not common mode on both the signal and reference
detectors, it passes straight through our subtraction circuit and appears as extra noise. This noise
can be effectively removed by cryopumping to reduce the background OCS signal by ~10-100fold, which in turn reduces frequency noise by an equivalent amount.
The experiment consists of computer controlled recording time domain traces (2 ms) of thescattered OCS gas pulse at each laser frequency (step  = 3 to 7 MHz) over the 2054.5 to ~2090
cm-1 frequency window. This scan range is broken into smaller computer controlled “continuous”
step scans of ~0.8 cm-1, with approximately 0.1 cm-1 overlap between each scan to eliminate any
gaps in the spectrum. The time traces at each laser frequency step are converted into absorbanceFigure 5.3: Experimental diagnostics: the etalon trace and the thermal OCS reference gas cellallow for precise frequency alignment (* marked lines are isotope OCS lines)
106A() by integrating over the rising edge (300 s) of the gas pulse, subtracting an equivalent
integrated baseline (300 s window before the gas pulse), scaling the transmitted signal by incident
light level, and expressing as a base e logarithm. The relative frequency axis for each scan is
calculated by linear interpolation between etalon peaks, with zeroth order absolute frequency
estimates from the Bristol wavemeter. Such wavemeter readings contain small systematic offsets
but are sufficiently precise to unambiguously match to our reference cell OCS spectrum, which
therefore provides absolute frequencies by comparison with a high precision Hitran database.26 An
example of the reference cell and etalon traces are displayed in Fig. 5.3 The net result is an
information dense spectral scan with 150,000 – 350,000 elements covering the entire R branch

107

Figure 5.4: These are blowups of spectrum of Fig 5.2 compared with the fit model spectrum.
region (and much of the P branch region) for the fundamental ((1000) (0000)) and hot bands((1110)  (0110), (1001) (0001)) out of the ground (0000) and lowest two vibrationally excitedstates ((0110), (0001)).

5.3 Results and Analysis

108Extraction of the quantum state resolved column integrated molecular densities is obtainedby global fit of the high resolution scattering spectra,27 with a sample fit region displayed in Fig.
5.4. The analysis is based on least squares adjusting a population model based on Hitran transition
frequencies to fit the entire spectrum, which includes MHz level of the reference etalon FSR toaccount for long term drift ( ~10 ppm day to day variation). The spectral model is based on several
reasonable assumptions. First, each upper state of the spectroscopic transition is completely
unpopulated, with the probing vibrational transition ~2000 cm-1 above the ground state andinaccessible at the collision energies explored. Secondly, the high resolution lineshapes for eachtransition are Doppler limited and arise from a common Gaussian distribution of velocities. This
experimental spectrum can be expressed as the following linear model:𝐴(𝑓𝑗 ) = ∑𝑖 𝑆𝑖 (𝑓𝑗 ) ∗ 𝑃𝑖

Eq. 1

where Pi are the quantum state populations and 𝑆𝑖 (𝑓𝑗 ) is the calculated spectrum from state i at
frequency point 𝑓𝑗 . The list of integrated cross-sections are obtained from the Hitran library, where
only transitions from the common isotopomers 16O12C32S (94%) and 16O12C34S (4%) areconsidered. From fitting this model spectrum (𝐴(𝑓𝑗 )) to the experimentally collected spectrum, thecolumn integrated molecular densities (Pi) can be extracted in a linear least squares fit. The highquality of spectral alignment is evident in both Fig, 5.3 and 5.4, with the quality of line shapemodelling seen in the spectral blowup in Fig. 5.4.
The extracted populations from such a linear least squares model for scattering of OCS at
Einc = 2.2(4) kcal/mol from PFPE at TS = 293 K are summarized in Fig. 5.5. In addition to extensive
collisional energy transfer into a large number of rotational levels (up to J = 67 at Erot = 1095 cm1), the data clearly also signal significant populations in both the ground and the two lowest

109

Figure 5.5: Extracted populations from the model fit.

vibrational manifolds. In the construction of these linear population fits, we have restricted therotational states to >100 cm-1 due to residual incident beam contamination along the laser
absorption path.
Closer inspection of the rotational distributions (Fig. 5.6) reveals that each of thevibrational manifolds looks “temperature-like” and can be well fit with a simple rotational
Boltzmann distribution. Indeed, each manifold of states exhibits rotational temperatures within
experimental error, with slopes corresponding to TR,gnd state =290(7) K TR, OCS bend = 297(20) K and
TR, CS stretch = 310(100) K for the ground, OCS bend, and CS stretch excited modes, respectively.
These three distributions are experimentally indistinguishable, which from an Occam’s razor
110

Figure 5.6: Rotational Boltzmann plot

perspective motivates analysis as a single equilibrated manifold. By way of additional support, Trot
= 298(5) K results from a fit to a common rotational temperature, matching well with the liquidsurface temperature of TS = 294(1) K. Simply stated, the data in each of the three vibrational
manifolds suggest complete rotational thermalization with the surface, at least at the molecularbeam collision energies (Einc = 2.2(4) kcal/mol) explored herein. From detailed balance
considerations, such behavior would be consistent with unity sticking coefficients into a longer
lived trapping-desorption (TD) channel from any rotational states populated in the incident beam,
as indeed has been confirmed previously in a number of gas-liquid molecular projectile scatteringsystems.
111

Figure 5.7: Vibrational Boltzmann plot of both the incident beam and the scattered molecules
Of particular dynamical interest and explicit focus of the present work is a first glimpse at
the distribution of final vibrational states in the scattered polyatomic projectile. Specifically, we
can sum over all rotational states and look at total populations in each of the vibrational manifolds.
Despite a limited number of data points, these vibrational populations (in red) fall quite nicely ona linear Boltzmann plot and are consistent with a vibrational temperature of Tvib = 240(5) K.
However, particularly noteworthy in Fig. 5.7 is the comparison plot (in blue) for relative
vibrational populations in the incident molecular beam, which is remarkably parallel to thecorresponding Boltzmann plot for the scattered populations (in red). This striking degree ofparallelism makes clear that there is little if any change in the OCS vibrational populations, before
and after a collision with the gas-liquid interface. Therefore, the highly non-equilibrium

112

rovibrational cooling dynamics in the supersonic expansion (i.e., Trot  10K << Tvib  240(5)K) is
recapitulated in the scattered flux, but now with i) the rotations warming rapidly up to and ii)
vibrations in our polyatomic OCS projectile remaining substantially colder than the liquid surface
temperature, TS (i.e., Trot  298(5)K > Tvib  250(5)K). Simply stated, the vibrational degrees of
freedom in the OCS projectile remain weakly coupled with the liquid interface, which speaks to ahigh degree of vibrational adiabaticity in the gas-liquid collision dynamics. Though such apropensity for vibrational adiabaticity is well appreciated for gas phase collisions, thecorresponding trend for collisions at the gas-liquid interface is far less evident, with the present
data on OCS scattering representing, to the best of our knowledge, the first such direct evidence
for weak vibrational state inelastic collision dynamics.

Figure 5.8: Summary of scattering parameters of multiple liquids

113

One could reasonably argue that this behavior depends sensitively on the nature of themolecule-liquid intermolecular potential. In the interest of completeness, we have supplemented
our current data with OCS scattering (Einc = 2.2(4) Kcal/mol) on the surfaces of two other low
pressure liquids commonly studied in the gas-liquid scattering literature, specifically squalane andglycerol. Spectral fits and population analysis for these additional liquids proceeds identically tothat of PFPE scattering, yielding fully thermalized rotations and yet highly non-equilibrium
vibrational distributions. The fitted temperature results of these studies for all three liquids are
summarized in Fig. 5.8. Within experimental uncertainty, all three liquid systems show
qualitatively identical behavior with respect to rotational thermalization (Trot) to the surface
temperature (TS). Of greater relevance to the current study, however, there is no change in thevibrational temperature (Tvib) of the scattered OCS with respect to the incident beam.
This striking nonequilibration of OCS vibrations at the gas-liquid interface despite clear
evidence for full equilibration of rotational and translational degrees of freedom deserves to befurther tested. As an ancillary set of experiments, low energy scattering studies have been repeatedfor OCS scattering from PFPE liquid under a wide variety of liquid interfacial temperature
conditions. Specifically, OCS rotational populations in each of the three vibrational manifolds((0000), (0110), (1000)) have been subjected to Boltzmann analysis to yield Trot, with the total
populations summed in each manifold to yield vibrational distributions and fitted to yield valuesof Tvib. The resulting dependence of Tvib and Trot on liquid PFPE temperature (TS = 263.15-303.15
K) is summarized in Fig 5.9.

114

Figure 5.9: Surface temperature dependence of the rotational and vibrational degrees of
freedom
There are several things that are immediately noticeable. 1.OCS clearly rotationallythermalizes with the surface and 2. Vibrationally, OCS does not seem to undergo any interaction
at all, leaving the vibrational degrees of freedom as spectators in this scattering event. By thecurrent understanding of the TD channel, this rotational thermalization is a characteristic of theTD pathway. However, the vibrations undergo this same dynamical pathway and show different
behavior, thus, it is clear that vibrations must be considered separately from the other degrees of
freedom.

5.4 Discussion
The current study presents first results for vibrationally quantum state resolved scatteringof a polyatomic molecule (OCS) at the gas-liquid interface, which has permitted probing of thermal
115accommodation dynamics with both i) rotational and ii) multiple vibrational degrees of freedom.
The essential results at Einc = 2.2(4) kcal/mol are readily summarized. 1) Rotational degrees of
freedom in the OCS/Ar molecular beam are strongly cooled by virtue of the supersonic expansion(Trot  10K) and yet rapidly thermalize (Trot  TS) in single low energy collisional interactions witheach of three gas-liquid interfaces. 2) By way of clear contrast, distributions in the lowest threethermally populated vibrational states (0000, 1000, 0110) are only very weakly cooled in the
supersonic expansion (Tvib  230K) and yet continue to remain completely unequilibrated insubsequent collisions with the corresponding three liquid surfaces. In order to explore thedynamics of such non-equilibrium effects, we consider predictions from simple analytic modelsof collisional energy transfer.
We first note that such behavior can be qualitatively rationalized by simple expectations
from collisional perturbation theory. In the framework of such perturbation theories, the collisional
mixing between asymptotic rovibrational quantum states I and j is proportional to the squareof the off diagonal matrix element of the interaction Hamiltonian scaled to energy difference
between the states, i.e., = |<i|Vint|j>|2/Eij.

Eq. 2

For the case of pure rotational transfer where energy differences are relatively small (Eij = BOCS
J(J+1) << Einc), it takes only weak collisional interactions to mix these states, therefore correctlypredicting facile thermal equilibration at the gas-liquid interface, as indeed experimentallyobserved.
This is fundamentally different from the dynamical behavior anticipated for vibrational
degrees of freedom in OCS, which exhibit 2-3 orders of magnitude larger spacings, e.g., OCS bend116

= 520 cm-1, CS stretch 860 cm-1, which therefore requires a much stronger collisional couplinginteraction to excite/deexcite or thermalize the vibrational state distribution. In particular, sincethese vibrational spacings are only comparable to the incident collision energy (Einc = 2.2(4)kcal/mol), this would rationalize quite inefficient energy transfer into/out of the polyatomic
vibrational degrees of freedom. Indeed, due to the finite number of collisions (perhaps 100-300)
in a supersonic jet (Pstag = 100 Torr, Ncoll = 100-200), this simple model motivates both i) poor
vibrational cooling down from Tstag in the pinhole supersonic expansion, as well as ii) a highly
constrained thermal equilibration of these high frequency polyatomic vibrational modes insubsequent collisions with the gas-liquid interface.
We can put these non-equilibrium predictions on a more quantitative footing by calculating
the ab initio interaction potential for OCS collisions with the PFPE surface. To keep things simple,
we have obtained 1D potential energy curves for each of seven different approach geometries for
OCS colliding with a carbon-tetrafluoride molecule (CF4). For each intermolecular geometry anddistance, high level ab initio calculations have been performed (MOLPRO platform), using
explicitly correlated (f12) electron methods at the CCSD(T)-f12 level with f12 correlationconsistent Dunning basis sets (AVnZ-f12; n=2,3,4). Additionally, we perform standard
counterpoise corrections for basis set superposition error (BSSE) and perform an extrapolation to
the complete basis set limit (CBS). The seven 1D geometries are chosen corresponding to strongest
possible interactions between our effective liquid surface and scatterer, with sample results fromtwo such 1D approach geometries (top panel, OCS coplanar with the FCF moiety; bottom panel,
OCS colinear with the CF bond) captured in Fig. 5.10. Least squares fits of these 1D potentials to117

a simple Morse potential function predict well depths that vary from 0-1 kcal/mol, withcharacteristic exponential repulsive wall parameters of roughly  = 2/Å.
A near analytical quantum model for vibrational energy transfer was developed by Landau
and Teller, whereby a structureless atom collisionally interacts with a collinear diatomic via an
exponentially repulsive potential V1D(x) = V0 exp(-x). The three key model assumptions are i)
harmonic vibrations, ii) linearized coupling in differential displacement of the proximate atom,
and iii) collisional time scales much longer than the vibrational period. Based on these

Figure 5.10: Examples of calculated approaches. The top is an example an approach for the
OCS bend and the bottom is an example an approach for the CS stretch
118

assumptions, Landau and Teller were able to derive perturbative collision excitation probabilities
from v = 0 → 1 of the form:28
2𝜋𝜔

𝑃0→1 ~𝑒𝑥𝑝 (− 𝛼𝑣 )

Eq. 3

0

where  is the angular frequency (radians/sec) of the vibration under study,  the exponential
repulsion potential parameter, and v0 the asymptotic approach velocity. While the prefactor in Eq
X proves difficult to calculate quantum mechanically, one can estimate it from a closely related
semiclassical derivation by Rapp for collinear A+ BC(v”) → A + BC(v’) collisional excitation.29
Specifically, the v = 0 → 1 semiclassical transition probability can be analytically written as:
𝜔

𝜇2

𝑀2

−

2𝜋𝜔

𝐶
𝑃0→1 = 8 𝜋 2 ℏ 𝑎2 𝜇𝐴,𝐵𝐶 (𝑀 +𝑀
𝑒 𝑣0 𝑎
)2
𝐵𝐶

𝐵

𝐶

Eq. 4

for which A,BC and BC represent the reduced masses of A + BC and BC, and 𝑚𝐵 , 𝑚𝑐 as the nearand far diatomic atoms, respectively. To apply such a simple diatomic model to our more complex
polyatomic OCS projectile requires additional modification of Eq (4) to take into account i)
effective normal mode mass and ii) overlap of the proximate atom B displacement onto thevibration coordinate of interest. For our present purposes, it suffices to treat the 3 mode as a“local” CS stretch with effective diatomic masses MB = MS (32 amu) and MC = MC + MO (28 amu)
and similar considerations for the “local” 2 bending mode dominated by motion of the central C
atom resulting in MB = 12 amu and MC = 48 amu. Furthermore, we can expand the Morse potential
as locally linear in atom B displacement and replace the exponential repulsion parameter by thelogarithmic derivative  =  ln{VMorse}/r , evaluated at the classical turning point of closest
approach, i.e., VMorse(r) = Einc. From Morse potential fits to both of the approach geometries shownin Fig. 5.10, one finds   6(1)/Å at Einc  2.2(4) kcal/mol.

119

The resulting theoretical predictions for the P0→1 inelastic collision probability vs. thedimensionless exponent 2v0 are plotted in Fig. Z for both (v1) CS stretch and (v2) OCS bend
excitation. Although not immediately interpretable in terms of a rate constant for thermal
accommodation at the gas-liquid interface, the reciprocal probability (1/ P0→1 = Z) does represent
a plausible estimate for the number of such low energy collisional interactions Z required toachieve significant equilibration of a given vibrational degree of freedom in OCS with TS. For Einc 2.2(4) kcal/mol, these predictions are of order Z = 1012 and 1023 for the v2 (0110) OCS bend andv1 (1000) CS stretch, respectively. Though such simple predictions from inelastic Landau Teller
theory plus semiclassical extensions by Rapp are likely to fail quantitatively at these longer
interaction times, the above calculations in Fig. 5.11 certainly drive home the self consistentmessage that i) even relatively low energy vibrations in polyatomic projectiles remain largely in

Figure 5.11: Examples of Landow-Teller probabilities vs. the velocity dependent exponent
term.
120

the adiabatic limit and do not equilibrate with the surface temperature and ii) there can be easily 6orders of magnitude difference between excitation probabilities for two low lying vibrations in thepolyatomic.

5.5 Summary and Conclusion
In this paper, quantum state resolved collisional energy transfer of carbonyl sulfide (OCS)at the gas-liquid interface has been studied via molecular beam scattering and high resolution IR
spectroscopy, which has permitted identification of rotational, vibrational and transverse Doppler
excitation/accommodation of the projectile under low incident energy (Einc = 2.2(4) kcal/mol)collision conditions. The results are found to be consistent with complete rotational andtranslational equilibration of the jet cooled OCS (Trot = 10K) with the liquid surface over a varietyof liquids (PFPE, squalene, and glycerol) and liquid temperatures (TS = 263 K – 303K). By wayof dramatic contrast, however, vibrational populations in the ground (0000), v2 OCS bend (0110)
and v1 CS stretch (1000) modes for the scattered OCS species remain far out of equilibrium withthe liquid surface, indeed remaining within experimental uncertainty at the exact same relative
populations and vibrational temperatures observed in the incident OCS molecular beam. Clearly,
the spectator nature of the vibrations requires that they be treated separately from the other degrees
of freedom scatter along the TD pathway. This dynamically observed variation on the TD channel
matches the expectations generated from simple physical intuition and the well known LandauTeller vibrational energy transfer model. To understand this further, more work must be done
exploring the vibrational dynamic at the gas liquid surface.

121Chapter 5 References
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Perkins, B. G.; Nesbitt, D. J., Quantum State-Resolved CO2 Collisions at the Gas-LiquidInterface: Surface Temperature-Dependent Scattering Dynamics. J. Phys. Chem. B 2008, 112,507-519.
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Perkins, B. G.; Nesbitt, D. J., Stereodynamics at the Gas-Liquid Interface: Orientation
and Alignment of CO2 Scattered from Perfluorinated Liquid Surfaces. J. Phys. Chem. A 2010,
114, 1398-1410.
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Faust, J. A.; Nathanson, G. M., Microjets and Coated Wheels: Versatile Tools for
Exploring Collisions and Reactions at Gas-Liquid Interfaces. Chem. Soc. Rev. 2016, 45, 36093620.
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Tesa-Serrate, M. A.; Smoll, E. J.; Minton, T. K.; McKendrick, K. G., Atomic andMolecular Collisions at Liquid Surfaces. Annu. Rev. Phys. Chem. 2016, 67, 515-540.
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Waring, C.; King, K. L.; Bagot, P. A. J.; Costen, M. L.; McKendrick, K. G., Collision
Dynamics and Reactive Uptake of OH Radicals at Liquid Surfaces of Atmospheric Interest.
Phys. Chem. Chem. Phys. 2011, 13, 8457-8469.
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Hoffman, C. H.; Nesbitt, D. J., Quantum State Resolved 3D Velocity Map Imaging ofSurface Scattered Molecules: Incident Energy Effects in HCl Plus Self-Assembled Monolayer
Collisions. J. Phys. Chem. C 2016, 120, 16687-16698.
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Perkins, B. G.; Nesbitt, D. J., High Resolution Dopplerimetry of Correlated Angular andQuantum State-Resolved CO2 Scattering Dynamics at the Gas-Liquid Interface. Phys. Chem.
Chem. Phys. 2010, 12, 14294-14308.
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Perkins, B. G.; Nesbitt, D. J., Toward Three-Dimensional Quantum State-Resolved
Collision Dynamics at the Gas-Liquid Interface: Theoretical Investigation of Incident Angle. J.
Phys. Chem. A 2009, 113, 4613-4625.
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Flynn, G. W.; Parmenter, C. S.; Wodtke, A. M., Vibrational Energy Transfer. J. Phys.
Chem. 1996, 100, 12817-12838.
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Nikitin, E. E.; Troe, J., 70 Years of Landau-Teller Theory for Collisional Energy
Transfer. Semiclassical Three-Dimensional Generalizations of the Classical Collinear Model.
Phys. Chem. Chem. Phys. 2008, 10, 1483-1501.
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Ewing, G. E., Selection-Rules for Vibrational-Energy Transfer - Vibrational
Predissociation of Vanderwaals Molecules. J. Phys. Chem. 1987, 91, 4662-4671.
12.
Lau, J. A.; Schonemann, A. M.; Schwarzer, D.; Wodtke, A. M., The Coverage
Dependence of the Infrared Absorption of Co Adsorbed to NaCl(100). J. Chem. Phys. 2020, 153.
13.
Steinsiek, C.; Shirhattii, P. R.; Geweke, J.; Lau, J. A.; Altschaffel, J.; Kandratsenka, A.;
Bartels, C.; Wodtke, A. M., Translational Inelasticity of NO and CO in Scattering from Ultrathin
Metallic Films of Ag/Au(111). J. Phys. Chem. C 2018, 122, 18942-18948.
14.
Wagner, R. J. V.; Henning, N.; Kruger, B. C.; Park, G. B.; Altschaffel, J.; Kandratsenka,
A.; Wodtke, A. M.; Schafer, T., Vibrational Relaxation of Highly Vibrationally Excited Co
Scattered from Au(111): Evidence for CO- Formation. J. Phys. Chem. Lett. 2017, 8, 4887-4892.
15.
Kruger, B. C.; Meyer, S.; Kandratsenka, A.; Wodtke, A. M.; Schafer, T., Vibrational
Inelasticity of Highly Vibrationally Excited NO on Ag(111). J. Phys. Chem. Lett. 2016, 7, 441446.
16.
Golibrzuch, K.; Shirhatti, P. R.; Altschaffel, J.; Rahinov, I.; Auerbach, D. J.; Wodtke, A.
M.; Bartels, C., State-to-State Time-of-Flight Measurements of NO Scattering from Au(111):

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Direct Observation of Translation-to-Vibration Coupling in Electronically Nonadiabatic Energy
Transfer. J. Phys. Chem. A 2013, 117, 8750-8760.
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Shirhatti, P. R.; Rahinov, I.; Golibrzuch, K.; Werdecker, J.; Geweke, J.; Altschaffel, J.;
Kumar, S.; Auerbach, D. J.; Bartels, C.; Wodtke, A. M., Observation of the Adsorption andDesorption of Vibrationally Excited Molecules on a Metal Surface. Nat. Chem. 2018, 10, 592598.
18.
Livingston Large, T. A.; Nesbitt, D. J., Low-Energy Co Scattering at the Gas-LiquidInterface: Experimental/Theoretical Evidence for a Novel Subthermal Impulsive Scattering(STIS) Channel. J. Phys. Chem. C 2020, 124, 28006-28017.
19.
Livingston Large, T. A.; Nesbitt, D. J., Quantum State and Doppler-Resolved Scatteringof Thermal/Hyperthermal Dci at the Gas-Liquid Interface: Support for a Simple "Lever Arm"
Model of the Energy-Transfer Dynamics (Vol 123, Pg 3449, 2019). J. Phys. Chem. C 2019, 123,
14104-14104.
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Perkins, B. G.; Nesbitt, D. J., Correlated Angular and Quantum State-Resolved CO2
Scattering Dynamics at the Gas-Liquid Interface. J. Phys. Chem. A 2008, 112, 9324-9335.
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Perkins, B. G.; Nesbitt, D. J., Quantum-State-Resolved CO2 Scattering Dynamics at theGas-Liquid Interface: Incident Collision Energy and Liquid Dependence. J. Phys. Chem. B 2006,
110, 17126-17137.
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Perkins, B. G.; Haber, T.; Nesbitt, D. J., Quantum State-Resolved Energy Transfer
Dynamics at Gas-Liquid Interfaces: IR Laser Studies of CO2 Scattering from PerfluorinatedLiquids. J. Phys. Chem. B 2005, 109, 16396-16405.
23.
Gisler, A. W.; Nesbitt, D. J., On Probing Ions at the Gas-Liquid Interface by Quantum
State-Resolved Molecular Beam Scattering: The Curious Incident of the Cation in the NightTime. Faraday Discuss. 2012, 157, 297-305.
24.
Proch, D.; Trickl, T., A High-Intensity Multi-Purpose Piezoelectric Pulsed MolecularBeam Source. Rev. Sci. Instrum. 1989, 60, 713-716.
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Lednovich, S. L.; Fenn, J. B., Absolute Evaporation Rates for Some Polar and Nonpolar
Liquids. AIChE. J. 1977, 23, 454-459.
26.
Rothman, L. S., et al., The Hitran Database - 1986 Edition. Appl. Optics. 1987, 26, 40584097.
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Ryazanov, M.; Nesbitt, D. J., Quantum-State-Resolved Studies of Aqueous Evaporation
Dynamics: NO Ejection from a Liquid Water Microjet. J. Chem. Phys. 2019, 150.
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Landau, L.; Teller, E., Theory of Sound Dispersion. Phys. Z. Sowjetunio 1936, 10, 34-43.
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Rapp, D., Complete Classical Theory of Vibrational Energy Exchange. J. Chem. Phys.
1960, 32, 735-737.

123

Chapter 6
Quantum State Resolved Scattering of Polyatomics at the Gas-LiquidInterface:
Hyperthermal vs. Thermal Vibrational Equilibrium Dynamics

6.1 Introduction
Due to high number densities, strong intermolecular interactions, and the rapid decay ofshort-range spatial order, the chemical physics of liquids remains extremely challenging, indeed
arguably representing the most complex and least well understood of the three conventional phasesof matter. As yet an even higher level of challenge and complexity has been the gas-liquidinterface, which comprises a nanoscopically thin (a few Å) region between the liquid and thesurrounding gas or vacuum. Though only a vanishingly small fraction of total molecules in any
macroscopic liquid sample, this exceedingly thin interfacial region plays a crucial “gatekeeper”
role, from thermal accommodation of gaseous projectiles colliding with the interface, to thefundamental physics of molecular solvation and subsequent chemical reaction in the bulk. It isagainst this massive level of dynamical complexity that the powerful laser spectroscopy andmolecular beams tools of chemical physics can hope to push, in order to obtain hard-won new
insights into (and ultimately molecular control over) the interfacial dynamics.
The past several decades have witnessed enormous experimental and theoretical progressin these directions. In particular, simple scattering of supersonic molecule beams at the gas-liquidinterface and probing translational energies and angular distributions in the recoilingatoms/molecules by time-of flight (TOF) methods have proven extremely informative, as
124

originally pioneered by Fenn and coworkers and elegantly exploited by the Nathanson, Morris,and Minton groups. Though such measurements are sensitive to the 3D translational degrees of
freedom in the scattered molecular species, these studies revealed a remarkable and unexpected
simplicity in the collision dynamics. Specifically, TOF distributions for projectiles scattered at theliquid interface exhibit what appear to be a clear bifurcation into two simple dynamical pathways.15

One such pathway (trapping desorption, TD) is where the incident molecules/atoms aretransiently trapped and thermally accommodate with the gas-liquid interface. By way ofanthropomorphic analogy, the TD scattered projectile “loses all memory” of its initial conditions,such as internal quantum states (rotation, vibration, electronic, nuclear…), scalar translationalenergy Einc, and vector velocity vinc. This TD pathway comprises molecules that eventually desorb
back into the gas phase in a Boltzmann distribution, typically maintaining perfect translational
equilibrium with bulk liquid temperature (TS).
By way of contrast, these studies also clearly reveal a second component in the TOF
distributions that comprise all non-equilibrium collision dynamics, often referred to as impulsive
scattering (IS). In general, this represents a complementary pathway whereby molecules scatterfrom the gas-liquid interface while still maintaining some “memory” of its initial scattering
conditions. Though simple enough to describe in words, this pathway can be operationally hard to
define a priori, and therefore becomes measurable only in the context of a certain set of dynamical
assumptions. In TOF studies, for example, the IS channel is characterized as the difference
between i) experimentally observed fluxes and ii) the flux predicted for velocity distributions
moving away from the interface and fully equilibrated to the liquid temperature (TS), i.e.
IIS = Iexp - ITS.

125

Eq. 1

Alternatively, in angle resolved studies with oblique angles of incidence, an azimuthally
symmetric TD component can potentially be deconvolved from IS scattering distributions whichmight be more strongly forward peaked. To the extent that there is clean separation(“orthogonality”) between such TD and IS components in the TOF distributions, thisdeconstruction is well-defined.
The fundamental challenge in studying gas-liquid interfacial dynamics with molecules isthat diatomic and polyatomic scattering exhibits a much greater dynamical richness beyond thatobserved via simple translational TOF spectroscopy, specifically with additional opportunities forenergy deposition/redistribution into quantum state resolved rotational, vibrational, and electronic
degrees of freedom. Such experiments require probing with internal quantum state resolution, as
offered by high resolution IR direct absorption spectroscopy, laser induced fluorescence, and/or
resonance enhanced multiphoton ionization spectroscopy.
However, nature appears to have again offered another remarkable and unsuspected
simplification. Specifically, measurements of rotational distributions for molecules scattered froma liquid interface at hyperthermal energies reveal a similar bifurcation into two dynamical
pathways, i) the usual TD channel corresponding to linear Boltzmann plots and complete
equilibration with the surface (TTD = TS), particularly at low collision energies and ii) a second
channel (IS) associated with non-equilibrium rotational excitation dynamics. Both TD and IS
pathways from hyperthermal scattering experiments have been successfully studied by a multitudeof different techniques including direct absorption spectroscopy2-3, 6-12, time of flight mass
spectroscopy4, 13-14 and REMPI+VMI15, with studies mostly focused on the translational androtational energy transfer with the surface. The existence of such a TD rotational channel can be126

additionally confirmed by temperature dependent studies of TTD for a number of liquids, which
often exhibit continuous equilibration between TTD and TS.
Interestingly, there is quite often (though until more systems have been studied, one can
not claim this to be universal) an additional dynamical simplification, specifically that the IS
rotations appear as hot but nevertheless thermal “Boltzmannesque” distributions at a hyperthermal
temperature (TIS >> TS). Furthermore, for liquid-like self-assembled monolayer (SAMs) surfaces
and molecular projectiles (HCl/DCl) amendable to REMPI detection via velocity map imaging(VMI) methods, there is also compelling agreement between temperatures measured via rotationaland velocity distributions (perpendicular to the scattering plane) in each of the TD and IS channels.
Indeed, the studies thus far would seem to suggest an even simpler physical picture of i) a
collisional bifurcation into short-lived impulsive scattering (IS) and longer-lived trappingdesorption (TD) pathways, with ii) nearly complete equilibration in each of the TD/IS channels
between rotation and translation degrees of freedom perpendicular to the scattering plane.
Although these results represent an extremely attractive characterization of collision
dynamics at the gas-liquid interface, one should be indeed expect such simple pictures to break
down under sufficiently detailed experimental scrutiny. We have seen, for example, that low
energy scattering (Einc = 2 kcal/mol) of very weakly interacting molecules such as CO or NO withliquids can exhibit interaction times too short to achieve full “rotational warming” up to TS, achannel which might therefore be better described as “sub-thermal IS” rather than conventional
equilibrium TD dynamics. We also have presented simple theoretical models that the hot yet
Boltzmann-like IS rotational distributions of CO or NO observed at higher incident energies (Einc= 20 kcal/mol) may reflect residual rainbow scattering dynamics that have been blurred due toaveraging over, e.g., thermal roughness at the gas-liquid interface. These examples and exceptions
127

obviously indicate the crucial need for testing such models for gas-liquid scattering into new anddifferent dynamical regimes.
One such area which has remained relatively unexplored has been the dynamics ofpolyatomic vibrational energy transfer in collisions at the gas-liquid interface. Pioneering work on
vibrational energy transfer of diatomics with surfaces has been achieved by the Wodke group16-17,
for which they report drastically different behavior between NO(v) and CO(v) projectiles on
conducting vs. insulating surfaces. In particular, NO(v) is found to deposit multiple quanta ofvibrational energy into Au(111) metal surfaces quite readily (v > 10), with only perturbativechanges (v = 0, 1) observed for collisions from single crystal insulators such as NaCl. By way ofcontrast, vibrational energy transfer from CO(v) is found to be dramatically weaker for both metals
and insulating materials (v <<1). Such disparities in vibrational energy transfer for NO(v) withmetals vs. insulators have been rationalized by fundamental differences in chemical coupling withelectrons inside the bulk metal. Specifically, by electron transfer from the metal, NO collisions canaccess a bound anionic state (3+, NO-), stabilized by Coulomb attraction to an (+) image charge
in the metal surface, a pathway not available for either insulating single crystal surfaces or CO
molecular projectiles. An alternate description proposed by Tully and coworkers is that vibrational
spacings in the projectile can be perfectly resonant with a continuum of thermal electron hold pairexcitations present in the metal. Conversely, this continuum of electron-hole pair excitations are
not present in collisions with insulating species, thus greatly diminishing the efficiency ofvibrational energy transfer. Thus it can be inferred from these studies that only molecules thatinteract strongly with the surface will undergo vibrational energy transfer.
Of particular relevance to the present study, work by the authors has shown that OCS
interacting with the liquid surface at low collision energies does not undergo vibrational energy128transfer. The vibrations act as spectators in the dynamics of the collision. This paper extends theseprevious studies into a high (~20 Kcal/mol) collision energy regime.
The remainder of this chapter is organized as follows. Sec. 6.2 provides some backgroundexperimental details on the polyatomic molecular beam spectrometer, with Sec. 6.3 presenting
results and analysis for jet cooled OCS scattering from PFPE liquid at high incident energies (Einc= 20(1) kcal/mol) and as a function of liquid temperature. Most importantly, the high energy results
indicate strong vibrational adiabaticity in the collision dynamics, similar to what is seen at low
collision energies, but now with an unexpected sensitivity to the temperature of the liquid. This isfollowed in Sec. 6.4 by discussion of the underlying vibrational collision dynamics as well as
preliminary efforts to reproduce the observed experimental trends with molecular dynamics
trajectory calculations based on high level ab initio scattering potentials. Sec. 6.5 completes thepaper with a summary of the key results and identifies possible directions for further investigation.

6.2 Experimental
The gas-liquid scattering laser spectrometer apparatus used in this work for quantum state
resolved scattering has been described elsewhere.1, 18-19 It therefore suffices to offer a brief
overview summary, with major focus on changes relevant to the present study. Our light source isan external cavity quantum cascade laser (Daylight Solutions), which can generate ~300 mW ofsingle mode infrared light scanned under computer control over the 2000-2200 cm-1 spectral
window with a linewidth of ~10 MHz. The studies take advantage of a cascading series offrequency measurements for spectral calibration, from a fizeau wavemeter (Bristol) for roughcalibration, with signals transmitted through both an off-axis confocal Fabry Perot etalon (FSR =250 MHz, finesse ~20-30) and a gas cell (0.5 Torr OCS, 5 cm path length) to measure relative129frequency tuning during a scan as well as the absolute frequency from absorption lines in thereference gas cell. The internal quantum state (rovibrational) and translational Doppler profiles of
the incident and scattered OCS are measured by shot-noise limited absorption methods, achieved
via differential signal and reference beams on matched InSb detectors and with the signal beam
executing a 16-fold multipass in the Harriot cell in the scattering vacuum chamber. By virtue of
carefully balanced subtraction with fast analog electronics, the spectrometer achieves minimum
absorbance sensitivities of order 1 x 10-5 in the bandwidth of the experiment for ~20 W laser
power on each detector, which is near the quantum limit.
The scattering system is made up of the molecular beam source, the scattering target andthe multipass cell. Our beam source is of Proch and Trickl design20. A 5% OCS in a balance ofhydrogen is expanded through a .508 mm orifice at a stagnation pressure of ~70 torr. Using asimple time of flight microphone setup, the average speed of the molecular beam pulse is measured
to be 1700(70) m/sec. This gives the OCS an incident energy in the collision with the surface of21(2) kcal/mol. Our molecular beam is oriented 65 degrees from the liquid surface normal. The
rotational temperature of the beam is 10 K, and the vibrational temperature is 220(5) K fit fromthe ratio of the ground state to the two vibrational states.
Our scattering target is the temperature dependence setup described in reference. The liquidsurface is prepared according to the method of Lednovich and Fenn21, using a rotating (~ 0.2 Hz)
bead blasted stainless steel wheel (12.7 cm diameter) half-submerged in the copper liquid reservoir
and scraped with a stationary razor blade to present a thin (~500 um), freshly prepared gas-liquidsurface to the impinging molecular beam. It is thermally isolated from the rest of the system using
Teflon spacers. Its temperature is stabilized by a two-stage cooling apparatus. The bulk of the130cooling/heating is done by an ethanol recirculating chiller. This backs a thermoelectric cooler thatstabilizes the temperature of a thermistor epoxied to the front of the copper trough.
This study involve three different classes of liquids that sample different scattering
dynamical regimes: 1) perfluorinated polyether, (PFPE, Krytox 1506, F-[CF(CF3)CF2O)]14(avg)CF2CF3), as prototype for a rough but chemically inert liquid surface, 2) squalane (2,6,10,15,19,23hexamethyltetracosane, C30H62), as prototype for strongly hydrophobic surface, and 3) glycerol(1,2,3-propanetriol, C3H8O3), as prototype for a highly hydrophilic surface due to multiple
protruding OH groups. Each liquid is degassed under ~1 mTorr vacuum at room temperature forseveral hours to remove dissolved atmospheric gases, or at slightly elevated temperatures (~ 350K) for the glycerol liquid samples to allow for more complete degassing within a reasonable timeframe.
Each experiment consists of recording a 2 ms timetrace of the scattered gas pulse for eachfrequency step (3-7 MHz) over the appropriate frequency range for OCS of 2054.5 to ~2090 cm-1
where the scan is stopped when the signal drops below detectable limits. This scan range is broken
up into smaller “continuous” step scans which are ~0.8 cm-1. Each scan start is 0.7 cm-1 apart,
leaving approximately .1 cm-1 overlap between each scan preventing gaps in the spectrum. Eachtime trace is turned into an absorbance by integrating over the rising edge of the gas pulse (300 us)
and then subtracting the integrated baseline (300 us long taken 400 us before the start of the signal
integration). The relative frequency axis of each scan is calculated from interpolating between theetalon peak maxima. This relative frequency is roughly calibrated by estimating the start frequency
from measurements from the Bristol wavemeter. This absolute frequency is enhanced in precisionby shifting the offset frequency to match our recorded reference thermal OCS spectrum to athermal spectrum calculated from the Hitran database.22
1316.3 Results and Analysis
To align each individual scan and to extract the quantum state resolved column integrated
molecular densities, a global fit to all the scattering spectra is performed following a similar
method to reference 2323. An example of this alignment can be seen in Fig 6.1. This fit has two
key components, 1) a final adjustment of the frequency axis and 2) a model fit to the entire
spectrum. The final adjustment to the frequency axis is a simple linear transformation where a
global slope is varied to adjust for minute day to day changes is the etalon FSR ( ~10 ppb day to

Figure 6.1 A full spectrum figure of OCS off PFPE at 20(1) kcal/mol with blowups showing
more of the detailed spectrum. The largest blowup shows the spectral fit of the entire
spectrum.
132

day variation). Each individual scan is also given a linear term to adjust for inaccuracies in theearlier rough calibrations.
The spectrum model assumes several things. First, each upper state of the spectroscopictransition is empty. This is a quite good approximation since the probing vibrational transition is~2000 cm-1 above the ground state, which is inaccessible at the energies used in gas-liquid
scattering. Secondly, the transition lineshape comes from a common gaussian velocity distribution.
This model can be expressed as the following:𝐴(𝑓𝑗 ) = ∑𝑖 𝑆𝑖 (𝑓𝑗 ) ∗ 𝑃𝑖

Eq. 2

Where 𝑆𝑖 (𝑓𝑗 ) is the calculated spectrum from state i at frequency point 𝑓𝑗 . The list oftransitions and integrated cross-sections were obtained from the Hitran library. Only transitions

Figure 6.2 OCS population plot133

from 16O12C32S (94%) and 16O12C34S (4%) are considered. From fitting this model spectrum(𝐴(𝑓𝑗 )) to the experimentally collected spectrum, the column integrated molecular densities (Pi)can be extracted. An example population distribution is seen in Fig 6.2. It is clear to see that wehave a two temperature rotational distribution that has become expected from these type
experiments. However, before we delve too deeply into these populations, we must acknowledge
that these populations are only approximate since we fit a single width gaussian to a Doppler
distribution made up of two different gaussian velocity distributions that have a varying weights
across the spectrum, with the narrower distribution being concentrated at low rotational energies
while a wider width dominates at higher rotational energies. Thus to truly understand thisspectrum, we must generate a model of the scattering distributions and fit that to the entire
spectrum. Our classic model used in several other gas-liquid scattering papers is as follows:A(j,f,v)
Sj,v (2j+1)N= α Prot (j, Ttd𝑟𝑜𝑡 )Ptrans (f, Ttd𝑣𝑒𝑙 ) + (1 − α)Prot (j, Tisrot )Ptrans (f, Tis𝑣𝑒𝑙 ) Eq. 3

Where Prot and Ptrans are respectively a Boltzmann distribution for the rotational degrees of
freedom and Ptrans is a Maxwell-Boltzmann distribution describing the out of scatter plane speed
distribution. This, however, does not cover the vibrational degrees of freedom. To understand thisdegree of freedom, let us look to Fig 6.3. In this figure, we see that the crossing point between the
TD and IS components changes for each of the vibrational states (though this is mostly only visible
for the difference between the ground state and the bend excited state). This is indicative of adifferent effective alpha for each vibrational state. Another way to view this is that instead of an

134

Figure 6.3 Rotational energy Boltzmann plot. The TD and IS lines intersect at different
energies implying that there is an effective branching ratio difference in each vibrational state
individual alpha for each vibrational states, there is only one global branching ratio and that the
TD and IS components have their own vibrational temperature. This is model is displayed below:
A(j,f,v)= αProt (j, Ttd𝑟𝑜𝑡 )Ptrans (f, Ttd𝑣𝑒𝑙 )P𝑣𝑖𝑏 (v, T𝑡𝑑𝑣𝑖𝑏 ) +Sj,v (2j+1)N(1 − α)Prot (j, Tisrot )Ptrans (f, Tis𝑣𝑒𝑙 )P𝑣𝑖𝑏 (v, T𝑖𝑠𝑣𝑖𝑏 )Eq. 4

To use this model to extract information on the scattering, a fit is performed on theregistered spectrum generated from the previous fitting method. This model can be fit to thespectrum floating all 8 parameter, but this leads to parameter correlation between alpha and therotational and translation temperatures. In our previously published paper on low energy OCS
135

scattering, it was seen that OCS rotationally accommodates with the surface. Thus to reduceparameter correlation, we fix the TD rotational and translational temperatures to the temperatureof the surface. This does not change the fit vibrational temperatures by any statistical margin. A
spectrum fit to this mode can be seen in Fig 6.1. The blowup highlights both the two temperaturedoppler profile but also the relative differences in signal to noise of the differing vibrational states.
To explore OCS’s scattering dynamics, three difference liquids were used as scatteringtargets, PFPE, squalene, and glycerol. These scattering results are displayed in Fig 6.4. Ignoring
the vibrational data, the scattering data agree with what has been seen before. Both the translations
and rotations in the IS channel are much hotter than the surface temperature, with the translations
scattering hotter than the rotational degrees of freedom. This is the same trend that has been seen
with CO, H/DCl and CO2 and to be expected for a molecular beam with translational energies ~30
times larger than kT.

Figure 6.4 Summary of full spectrum fit parameters.
136

Figure 6.5 Scattering parameters as a function of surface temperature.
The most interesting part of this data is the vibrational temperatures. For the IS channel,
we see what we have seen previously at the low collision energies. The vibrational temperaturedoes not change from the incident conditions, showing us that no vibrational energy is transferedduring the IS channel collisions. This is in stark contrast to what we see in the TD channel. We see
the vibrational temperature rises from the much colder incident beam temperature to close to thesurface temperature.
To explore this unexpected effect in greater detail, scattering data from pfpe was collected
at a variety of surface temperatures. Fig 6.5a plots the temperature dependence of rotational andtranslational IS temperatures and the temperature dependence of the branching ratio. We can see
from this figure that IS scattering temperature is quite insensitive to the surface temperature. This
physically makes sense the total center of mass energy in the collision does not change by muchwhile changing the surface temperature thus the outgoing average energy (i.e. the scattered“temperature”) does not change by much. Another observation that can be made for Fig 6.5b isthat the branching ratio grows as the surface temperature increases. This has been seen previously

137with CO2 and has been attributed to the increase in roughness of the surface as the temperature
increases causing molecules to become trapped on the surface more easily.
The most remarkable piece of information from these temperature dependence studies isthe dependence of the vibration scattered temperature on the surface temperature. Both the TD and
IS vibrational temperatures are plotted in Fig 6.6. From this figure, we can see that the TD and IS
components of the vibrational temperature behave very differently. We can see that the TD
temperature rises from the incident beam temperature to near the temperature of the surface while
tracking with the changes in the surface temperature. The IS component behaves as we saw in theenergy scattering; it does not warm from the incident beams vibrational temperature. This is at
first glance a surprising result. With high energy collisions, the impulsively scattered molecules

Figure 6.6 Vibrational temperatures of the TD and IS channels as a function of surface
temperature.
138

behave more similarly to the low energy scattered TD channel, thus leaving the high energy
scattered TD channel as the only channel that allows the possibility of vibrational energy transfer.

6.4 Discussion
One of the assumptions that has been made about the TD channel can be said colloquiallyas “molecules lose all memory of their initial conditions” when scattering via the TD channel. Thishas held true for many of the molecules studied especially for the translational and rotational
degrees of freedom. For the vibrational degrees of freedom, this does not apply to scattering by
OCS. As the beam energy changes, so too does the vibrational accommodation with the surface.
Thus casting the TD channel into a static scattering channel underestimates the dynamics that goon and can clearly effect the scattering outcome.
To try and understand this, let us think about this physically. The only difference between
the molecules that vibrational thermalize in the TD channel is the collision energy and thus thechange in thermalization must be directly or indirectly resulting from this change. The general
simplified mechanism of TD can be view as a three step mechanism of trap, thermalize and thendesorb. Generally, by the time the molecules are trapped in the well and are thermalizing, there
should be very little memory of the initial conditions of the molecule. Thus it must be that thechange occurs as the molecule traps. This is not an outlandish idea. The difference in dissipatinga kcal/mol or two of translational energy into the surface to trap the molecule is quite different
from dissipating 20 kcal/mol into the surface. Arguably, this would lead to closer approaches tothe molecules of the surface with the possibility of an increased chance of penetration into thesurface. This would allow for very many secondary interactions with molecules that would notappear in the averaged interaction. All of these changes in the collision would increase the strength139

of the interaction and thus allowing for the OCS molecules to exchange vibrational energy withthe surface.
Because we do not see vibrational energy transfer in the IS channel, we can be confident
that it is not just the collision at these high energies that cause the vibrational energy transfer.
Collisions at these energies still need to hit the system with specific “impact parameters” to allow
these vibrations to exchange quanta. This highlights the discrete nature of the TD channel. Yetagain we see this distinct two channel scattering with no continuum in between. A molecule either
scatters from the surface impulsively, leaving the surface translationally and rotationally hot while
no vibrational energy transfer occurs, or it can undergo a strong collision with the surface,dissipating enough of its translational energy to trap in the local van der Waals bound well andthen thermalize with the surface (including the vibrational degrees of freedom).
To get to the bottom of this problem, more theory is necessary. Analysis similar to ourprevious work done with CO, except as a function of collision energy instead of surface
temperature, should give deeper answers to what is occurring. However, that is for future workand not covered here.

6.5 Summary and Conclusions
In this paper, we have explored OCS scattering off liquids at energies many times kT. In
this, both the rotational and translation degrees of freedom followed the empirical two temperaturemodel. However, the vibrational degrees of freedom do not follow this behavior. It was seen that
unlike the low energy studies, the TD channel of the scattering allowed the vibrations to approach
thermalization while the hard hitting IS channel showed no vibrational energy transfer at all. Thisimplies that the TD channel is not memoryless like previously thought but actually does have some140

dependence on the collision energy. This means that the in the future, one must also consider notjust the thermal behavior of the TD channel, but also the possible dynamics for the degrees of
freedom that do not so readily exchange energy with the surface.

141

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Appendix A
Quantum State and Doppler Resolved Scattering of Thermal/Hyperthermal DCl at theGas-Liquid Interface: Support for a Simple “Lever Arm” Model of the Energy Transfer
Dynamics
Supporting Information
This derivation follows the general form as presented in the Phillips work. Changes have been
made to add clarity and rigor to the derivation. As can be seen in the previous work done on
thermal capillary waves, the surface height (h) can be described approximately as a being boundedwith periodic boundary conditions in a box with side lengths of L which is half the wavelength inwhich capillary waves are superseded by gravity waves. Solving the standard thermal capillary
Hamiltonian gives the following solution for the thermally averaged height of the interface.
ℎ(𝑥, 𝑦) = ∑𝑁𝑛,𝑚=1 √ 2

2 𝑘𝑏 𝑇

2 +𝑘 2 )𝐿 𝛾 (𝑘𝑥,𝑛𝑦,𝑚cos(𝑘𝑥,𝑛 𝑥 + 𝜙𝑛 ) cos(𝑘𝑦,𝑚 𝑦 + 𝜙𝑚 )Eq. 1

where gamma is the surface tension and phi is a uniformly distributed random phase. The sum isfrom 1 to N where 1 is equivalent to the smallest allowed momentum and N is the largest. Since
the momentum in both the x and y direction can be considered an integer multiple of the smallest
momentum allowed in our box, we can make the following substitution.
𝑘𝑥,𝑛 =

2𝜋
𝐿

Eq. 2

𝑛

Thus:
2𝑘 𝑇

2𝜋

2𝜋

𝑏
𝑁
ℎ(𝑥, 𝑦) = ∑𝑁𝑛,𝑚=1 √(2 𝜋)2 𝛾 (𝑛2 +𝑚2 ) cos(𝑛 𝐿 𝑥 + 𝜙𝑛 ) cos(𝑚 𝐿 𝑦 + 𝜙𝑚 ) = ∑𝑛,𝑚=1 ℎ𝑛,𝑚 Eq. 3152

N now can be seen as 𝐿/𝜎 where sigma is the smallest allowed distance which in this case is themolecular diameter of the surface molecules. Let us now look at the derivatives of each of theindividual mode of this sum.
2 𝑘 𝑇 𝑛22𝜋2𝜋𝑏𝜕𝑥 ℎ𝑛,𝑚 = −√ 𝐿2 𝛾 (𝑛2 +𝑚2 ) sin(𝑛 𝐿 𝑥 + 𝜙𝑛 ) cos(𝑚 𝐿 𝑦 + 𝜙𝑚 )Eq. 4

Averaging over both x and y, we see that:Eq.5〈𝜕𝑥 ℎ𝑛,𝑚 〉 = 0
𝑛2

𝑘𝑏 𝑇

𝑛2 +𝑚2𝐿2 𝛾

2〈(𝜕𝑥 ℎ𝑛,𝑚 ) 〉 =Eq. 6

This can be restated as the mean of each of these modes is zero and the variance is finite andknown. Since each surface mode has a know and finite mean and a known and finite variance,
when they are add together with a randomly distributed phase, the central limit theorem says thatthe sum of these randomly distributed variables tends to a gaussian distribution. This gaussian has
a zero mean and a variance defined as:
𝑛2

𝑘 𝑇

𝑁 𝑘 𝑇

𝑏
𝑏
𝜎 2 = ∑√𝑁𝑛,𝑚=1 𝑛2 +𝑚2 𝐿2 𝛾 = 2 𝐿2 𝛾

Eq. 7

Which is the same as the variance derived in the Phillips’ work. Notice the change of the sum fromN to √𝑁. This was done to keep in line with Phillips’ paper, which defined N as the total numberof modes in a L x L box.

153

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