# Presentation: 499933

## The Influence of Environment on Polymer Mobility: Quasielastic Neutron Scattering on PEO/PMMA Blends

**Janna K. Maranas**
**Department of Chemical Engineering**
**The Pennsylvania State University**
***ACNS June 2004, College Park, MD***

## Acknowledgements

_**The Maranas Group:**_** **
**	****Chunxia Chen**
**	****Jiahong Liu**
**	****Susan Fullerton **
**	****Praveen Depa**
**	****Andrew May**
**	****Victoria García Sakai**
**	****David Asay **
**	****Erin Boland**
**    ****Matthew Eggert**
**	****Arun Neelakantan 2003**

**Collaborators:**** **
**Zema Chowdhuri**** – backscattering at NIST**
**Nick Rosov**** – NSE at NIST**
**Inma Peral, John Copley**** – time of flight at NIST**
**Jeff Lynn – Triple Axis at NIST**
**Funding:****  ****NSF-CAREER Polymers Program **
**	****DMR 0134910**
**Beam Time:**** ****NIST Center for Neutron Research**

## Structural dynamics of pure amorphous polymers

- _Important temperatures:_
**Tg**: -relaxation frozen;     **Tc**:  merge

## Origin of distinct component mobility

- Effective local concentration different from Xbulk

- Xbulk = 0.5

- How does this arise?

- _Concentration fluctuations_
-   & MW, Tg
- Length scale:  varies ~10 nm?, different for high Tg, low Tg components.

- _Chain connectivity_
- eff = s + (1-s)Xbulk
- Length scale: Kuhn length temp & comp independent.

- Lodge & McLeish, Macromolecules, 33, 5278 (2000)

- Kumar, et al J. Chem. Phys. 105, 3777 (1996).

## Concentration fluctuations

- Probability distribution of local compositions

- Local composition, 

- 

- high Tg comp

- low Tg comp

- Large “cooperative” volume, 

- Small 

## Bimodal distributions

**Bimodal distributions**

- eg. Dielectric Spectroscopy

- Quasi-Elastic Neutron Scattering: “in the green”

******1****: low Tg component-rich regions, small P(********), small ******** **
******2****: regions of ********≈ ********bulk****, high P(********), large ******** **

- Kumar, et al J. Chem. Phys. 105, 3777 (1996).

**Notes:**
No spatial scale: each has its own copperative volume which would define the length scale

## Target System: PEO/PMMA

**Large ********Tg and ******** ≈ 0**
**Interactions independent of T**
**Different component behavior**

**PEO**  “poly ethylene oxide”
- Tg ~ 220 K, more mobile

**     ****PMMA **
- “poly methyl methacrylate”

- Tg ~ 400 K, less mobile

**Concentration fluctuations**

**Distribution of local concentrations a constant**

**Highlight concentration fluctuations**

## measurements

**hPMMA – HFBS at NIST**
**	****	*****“******self”***** *****motion of PMMA ***
**hPMMA/dPEO – HFBS at NIST**
**	****	*****self motion of PMMA in blend***
**hPEO – DCS at NIST**
**	****	*****self motion of PEO***
**dPMMA/hPEO – DCS at NIST**
**	****	*****self motion of PEO in blend***
**dPMMA/DPEO – NSE at NIST**
**	****	*****collective motion of blend***
**MD simulations – pure PEO, pure PMMA, blend underway...**

*backscattering*

*Time-of-flight*

*Neutron spin echo*

## Data treatment

**KWW Equation**

****

## Verification: PMMA

- Q = 1.7 Å-1

- Q = 0.9 Å-1

- dielectric

- Dielectric + neutrons for pure PMMA

- PMMA in blend – no other measurements available.

**Notes:**
Dark colours are data from dielectric for pure PMMA
Light colours are our data for pure PMMA alpha at Q=0.991; beta at Q=1.676; 
Dashed lines are fits (to our data) with the VF equation and the arrhenius equation for alpha and beta relaxations 
Relaxation times obtained using beta values from dielectric 

## Verification:  PEO

**Lutz et al., Macromolecules (2003)*

- NMR + neutrons for PEO in blend

## Comparison of component mobilities

- Q = 0.9 A-1

**Notes:**
Figure 8. Intermediate scattering function for dPEO /dPMMA from NSE at several temperatures.  Plotted for comparison are DCS data for PEO in the blend at T = 440 K and q = 1.05 Å-1 (circles) and HFBS data for PMMA in the blend at T = 440 K and q = 0.99 Å-1 (diamonds).

## Potential advantages of neutrons for this problem

- Macroscopic sample

- “Relevant length scale....”

- “Importance of concentration fluctuations”

## Mobility of a “local” volume

***CONCENTRATION FLUCTUATIONS:***** ****different local**** ****compositions ******
****** ≈ ********bulk**
****** ≈ ****1**
**distribution = f(Q)**

***DYNAMIC HETEROGENEITY*****: **
**	****same ******** ****- different mobility **

*Only local compositions mobile within the QENS timescale contribute to the average!*

## Impact of Concentration Fluctuations

_**Dynamic heterogeneity**_

**Stretching exponent from KWW equation**

_**Concentration fluctuations**_

**Notes:**
Stretching exponent from KWW equation: 
measures distribution of local environments
function of temperature & length scale 

## “Slow” component - PMMA

**20% blend**

**“****Slow” component - PMMA**

_**Dynamic heterogeneity**_

**Stretching exponent from KWW equation**

**Notes:**
Stretching exponent from KWW equation: 
measures distribution of local environments
function of temperature & length scale 

## Temperature dependence

- Result is a simple temperature scaling......

- Same behavior at same distance above Tg.....

## “Fast” component - PEO

**“****Fast” component - PEO**

**slow**

**fast**

*T =345K, q=1.5Å**-1*

**Bimodal?**

**slow**

**fast**

## Mobility distribution - PEO

- q=2.3Å-1

- q=1.5Å-1

- q=0.9Å-1

** ****concentration fluctuation driven dynamics **

**Pure PEO**

**20% blend**

## Relevant length scale for local compositions

**Relevant length scale for local compositions**

- T=348K

**Pure PEO**

**20% blend**

- T=343K

- More local environments in blend through peak in S(Q)

## Relaxation Times

- q=0.9Å-1

- q=1.5Å-1

- q=2.3Å-1

## PMMA: dynamics not sensitive to variations in local composition.

PEO: concentration fluctuations important.
Spatial scales less than peak in S(Q) bias towards PEO.

**PMMA: dynamics not sensitive to variations in local composition.**
**PEO: concentration fluctuations important.**
**Spatial scales less than peak in S(Q) bias towards PEO.**

- q=2.3Å-1

## Time & Spatial Scales of Neutrons

**Time & Spatial Scales of Neutrons**

- 0	0.5	1.0	1.5	2.0	2.5	3.0
- 		         Q (Å-1)

**whole chain**
***Rg~100Å***** **

**intermolecular *****~ 5Å***

**intramolecular *****~ 1-4Å***

- Neutron spin-echo** **

- MD simulation

## Issues in miscible blend dynamics

**Importance of concentration fluctuations....**
**Relevant length scale for local compositions...**
**Asymmetry of changes...**
**Other contributions to local compositions....**
**Temperature dependence....**

## Techniques to Explore Dynamics

## Experimental Probe: QENS

**Self-motion**

**hPEO**

**dPMMA**

**+**

## KWW fit parameters - Q dependence of   Q-n

- T=387K

- T=405K

- T=420K

**Stretching Exponent, ******

- Q=0.62Å-1

- DS -process

**KWW fit parameters - Q dependence of  ************ **Q-n

-  At T ≥ 1.17 Tg : n = 2 (non-Gaussian*, heterogeneous**)
-  At T < 1.17 Tg : n = 2/ (Gaussian*, homogeneous**)

- * Colmenero et al., Phys.Rev.Lett. 1992
- ** Colmenero et al., J.Phys.:Cond. Matt. 1999

## Static Structure

- Triple-axis spectrometer BT7 at NIST
**Ein = Eout measures S(Q,0)**
**accessible Q-range= 0.5-4.0 Å****-1**

- d8PMMA and d8PMMA/ d4PEO blends

- d4PEO