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Effect of confinement on molecular processes in the liquid crystal 8OCB:
application of NMR relaxometry
M. Rajeswari,*a S. Dhara,a K. Venu,b V. S. S. Sastrya and R. Dabrowskic
Received 20th March 2012, Accepted 14th June 2012
DOI: 10.1039/c2sm25643f
Dispersions of proton spin–lattice relaxation rates (R1) in the nematic and smectic phases of the liquid
crystal 40 -octyloxy-4-cyanobiphenyl (8OCB), embedded in a nano-porous medium formed by an aerosil
matrix, are investigated over a wide frequency (n) range (104 Hz to 5 ! 107 Hz) at two average poresizes. In the low frequency (sub-MHz) region we observe a significant increase of R1 in the confinedsamples, mediated by slow translational displacements (RMTD), arising from the formation ofadsorption layers near the porous surface. Dispersion in this region is well accounted for by a power law
behaviour (R1 " u#p), bracketed by low and high cutoff frequencies reflecting the limiting length scalesof such displacements in these layers. The exponent p increases from 0.45 to 0.6 with a decrease of thetemperature within the nematic phase, due to the progressive onset of longer wavelength diffusivemodes within these layers. This signifies the onset of order director fluctuation (ODF) modes within theadsorption layers. Confinement is also seen to place restrictions on the long wavelength ODF modes ofthe bulk-like region of the liquid crystal, thus weakening considerably their dispersive effects in the low
frequency region, relative to the bulk samples. In the smectic phase, p decreases appreciably signalling adepletion of such long range cooperative modes on layer formation. Analysis of the R1 data also showsthat individual dynamic processes like translational diffusion and reorientations of the molecules
within the voids are largely unaffected due to confinement.

1 Introduction
The importance of the effects of quenched random disorder on
the properties of liquid crystals (LCs) has been recognizedpreviously,1 and curious disorder-induced phenomena wereexperimentally investigated through, for example, calorimetry,2
X-ray scattering and intensity fluctuations,2,3 dielectric spectroscopy,4–7 Fourier-transform infrared spectroscopy,8 protonand deuteron nuclear magnetic resonance (DNMR)9–12 andoptical anisotropy measurements.13 In this context, LC–aerosil
systems were found to be particularly interesting because therandom disorder could be introduced in a controlled manner
unlike the cases with other random porous matrices like aerogels,14 CPG15–17 and anopore18 etc. These nano sized particles
embedded in the LC system on one hand provide an ordering
mechanism even in the isotropic phase through surface interactions, and on the other tend to interfere with the long rangeaSchool of Physics, University of Hyderabad, Hyderabad 500 046, India.
E-mail: raji.hcu@gmail.com; Fax: +91-40-23010227; Tel: +91-4023134318b
Soctronics Technologies Pvt. Ltd, Banjara Hills, Hyderabad 500 034,
IndiacInstitute of Chemistry, Military University of Technology, Warsaw 00908, Poland

10008 | Soft Matter, 2012, 8, 10008–10016

orientational order of the mesophases, due to the finite sizes of
the confining geometry.
Typically, the surface of the treated aerosil particles is covered
with hydroxyl groups that tend to form hydrogen bonds witheach other. At low densities rs (<0.01 g cm#3), the number ofparticles is too small to form a network and they act as impurities
added to the LC. As the concentration increases above thegelation threshold, with rs ranging from 0.01 to 0.1 (the relevant
units are implied hereafter), the silica spheres are able to form a
3-D network, referred to as soft gel, and beyond this concentration, the network becomes more rigid, forming a stiff gel. The
earlier proton NMR measurements in such confined LC systems(octylcyanobiphenyl (8CB) and octyloxycyanobiphenyl (8OCB))
were carried out in the isotropic phase.9,10 In the present work, we
extend these studies to mesophases in confined environments,
focusing on the possible changes in the orientational structure
factors, as effectively sensed by the diffusing LC molecules on
cooling due to the progressive enhancement of ordering in thesystem. This problem was addressed earlier in 8CB–aerosil
mixtures based on DNMR experiments,11,12 and on calorimetricstudies.19,20
Here we report on our proton spin–lattice relaxation rate (R1)measurements of 8OCB in its nematic and smectic phases, bothin the bulk state as well as under confinement by random
networks of the aerosil particles, at two different concentrations.
This journal is ª The Royal Society of Chemistry 2012

The frequency dispersion of R1 is a measure of the cumulative
power spectrum arising from the time modulation of the dominant spin–spin interactions effected by a variety of molecular
processes. The confinement such as discussed above is known to
introduce slow processes in the LC system near the porous
surfaces, taking place typically in a low frequency regime("kHz). For this purpose, we extend the dynamic range of the R1
measurements to encompass slow time scales by adopting a
recent technique based on the fast field cycling NMR(FFCNMR) principle.21,22 This interesting method has proved tobe particularly useful to study ultra slow processes in many soft
materials, like polymers, protein dynamics, macromolecular
processes, confined fluids, etc.21 Dielectric measurements also
give complementary information on molecular reorientational
processes in liquid crystals and the earlier investigations on
cyanobiphenyls with a wide range of aerosil concentrations
confirm the presence of slow relaxation processes in confinedsystems and their temperature dependence shows a behavior
typical for glass-forming liquids.6,7
The present paper is organized as follows. Experimental details
related to the sample preparation and NMR measurements are
given in Section 2. Relaxation mechanisms interpreting theexperimental observations are discussed in Section 3, while aquantitative analysis of the data in terms of bulk and surfaceinduced relaxation mechanisms is presented in Section 4. The
conclusions are summarized in the last Section.

and non-polarized pulse sequences were used21,22 to measure R1
on the FCNMR instrument, while an inversion recovery
sequence was used at higher frequencies. The decay of magnetization was found to be exponential in all the experiments
requiring a single relaxation time constant. Relative errors in the
R1 measurements were within 3% and the temperature of thesample was controlled to within $0.1 K.
Fig. 1 shows the frequency dependence of the relaxation rates
in bulk and confined LC samples in different mesophases, andthe differences in the bulk profiles at different temperaturesindicate very different underlying slow molecular processes

2 Experimental details
The liquid crystal 8OCB, synthesized in our laboratory(Warsaw), has the phase sequence: I 353K N 340K SmA 327.5K
Cr. The LC–aerosil mixtures were prepared using the solvent
method.2 Aerosil A300 consists of small silica spheres of diameter
7 nm and specific surface area 300 m2 g#1. The small angle x-ray
scattering (SAXS) investigation by Iannacchione et al. on theseparticles gives a hierarchical structure of different length scales.
Their results suggested that the individual 7 nm particles fuse
together during the manufacturing process to form a larger
primary particle of size 21 nm. At higher concentrations theseprimary particles form aggregates of size 440 nm and theseaggregates form further agglomerates.2 These silica spheres weredried under vacuum at 473 K for over 15 hours, before being
added to the LC diluted with pure acetone. The mixture wassonicated for about 2 hours to achieve a homogeneous dispersion
and the solvent was then slowly evaporated over a long time ("10hours) at 333 K. The surfaces of the spheres are covered withhydroxyl groups and interactions among them lead to a 3-D
network within the LC medium. Because of the hydrophilic
nature of the aerosil particles, the polar 8OCB molecules orient
homeotropically at the surface. The densities of silica (rs) in our
two samples were 0.05 and 0.07 g cm#3. The average void sizes
formed by these networks were estimated to be 133 nm and90 nm, respectively.17 The shifts in the transition temperature dueto the addition of these particles were within $1 K.
Proton spin–lattice relaxation rates (R1) were measured at
different Larmor frequencies ranging from 10 kHz to 10 MHz
using the field-cycling NMR Relaxometer (FCNMR, Stelar
Spinmaster FFC 2000) and with a home-built pulsed field-variable spectrometer covering 10 MHz to 50 MHz. Pre-polarizedThis journal is ª The Royal Society of Chemistry 2012

Fig. 1 The frequency dependence of the proton spin–lattice relaxation
rate R1 for 8OCB in the bulk (a), 8OCB + aerosil, at rs ¼ 0.05 (b), and
8OCB + aerosil, at rs ¼ 0.07 (c), at three temperatures: 352 K (just below
the clearing temperature), 346 K (deep in the nematic phase), and 334 K(in the smectic phase).

Soft Matter, 2012, 8, 10008–10016 | 10009

effective at low frequencies. Progressive confinement with thetwo porous structures is seen to modify the bulk behaviour
qualitatively. Fig. 2 exhibits the temperature dependence of these
rates at different Larmor frequencies, bringing out contrasting
features of the different phases in the bulk as well as in theconfined systems.

3 Relaxation mechanisms
The spin–lattice relaxation of protons in these systems is
predominantly mediated by the time modulation of dipole–
dipole interactions between the spins, caused by processes suchas molecular reorientations, translational diffusion and collectivemodes like order parameter fluctuations (OPF), order director
fluctuations (ODF) or layer undulations (LU). Significant
interactions of the LC molecules with the confining surfaces
could lead to surface diffusion modes with constrained molecularorientations, leading to slow processes relevant to the present
experiment. The molecular dynamic models of interest to ourstudy are briefly presented here.23–26
3.1 Rotational dynamics (R)Molecular reorientations and conformational changes modulate
the dipolar interaction, providing a relaxation pathway.
However within the frequency range of the experiment limited by
the largest Larmor frequency, all processes faster than "10#9 are
white-noise like, and do not contribute to observable dispersion.
Only reorientations about the short axes of the molecules (R)typically lead to slight dispersion at the high frequency end. This
contribution is well-accounted for by the BPP theory,24,27 as
R1R ¼ AR

2
X

p2 sR

p¼1 1 þ ðpusR Þ

2

:

(1)

Here AR quantifies the contribution from the reorientations.
3.2 Molecular translational self-diffusion (SD)Intermolecular spin interactions are modulated by (random)
molecular translational displacements. Their contribution to therelaxation rate (R1SD) was calculated analytically for viscous
isotropic liquids,28 and was subsequently extended to the nematicand smectic A phases.29,30 Its contribution was shown to beeffectively given by
R1SD ¼

1
ðR1 ÞTorrey :
1:4

(2)

This model in turn implies28 specification of the (average)
diffusion constant D and the coupling strength AD of the spins to
the lattice modes through this mechanism.
3.3 Order parameter fluctuations (OPF)
At the onset of the nematic phase, i.e., just below the isotropic–
nematic transition temperature TNI, fluctuations in the magnitudeof the nematic order parameter S are effective in relaxing thenuclear spins, i.e. the fluctuations in the long-range orientational
order modulates the dipole–dipole interactions between the nuclear
spins providing additional mechanisms for spin–lattice relaxation.
Within the small temperature region where these order parameter
fluctuations (OPF) are dominant (typically within a few degrees
below the clearing point), these processes contribute appreciably tothe relaxation rate through their spectral density given by23
2

Fig. 2 The temperature dependence of the proton spin–lattice relaxation
rate R1 at three Larmor frequencies for 8OCB in the bulk (a), 8OCB +aerosil, at rs ¼ 0.05 (b), and 8OCB + aerosil, at rs ¼ 0.07 (c). The phasetransition temperatures are indicated by vertical dotted lines.

10010 | Soft Matter, 2012, 8, 10008–10016

6JðmL uÞ ¼ AOPF 4

31
2

sOPF
7
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi5
1 þ 1 þ ðmL usOPF Þ2

ðmL ¼ 1; 2Þ:(3)

Here sOPF is the characteristic time associated with the fluctuation of the long-range order, and AOPF is a measure of thelattice coupling that this mechanism provides to the spin system.
This journal is ª The Royal Society of Chemistry 2012

3.4 Order director fluctuations (ODF)
Order director fluctuations are characteristic collective (hydrodynamic) modes in the nematic phase, and provide distinct slow
modulations of spin interactions. Their wave-vector dependent
life times in principle relate to the three elastic distortions (splay,
twist and bend with constants K1, K2, and K3, respectively), andassociated viscosities.31 Under the assumption of equal values forthese constants (one constant approximation, i.e. K1 ¼ K2 ¼
K3 ¼ K), a simplified expression for the spectral density of thefluctuations arising from these processes results as an integral
over an interval of wave vectors defined by the limiting scales inthe system23
ð qmaxV
kB T
sðqÞ
4pq2 dq:
J1 ðuÞODF ¼!
ð2pÞ3 qmin VKq2 1 þ u2 s2 ðqÞHere qmin and qmax are determined by the largest and smallest
sustainable wavelengths dictated by the visco-elastic characteristics of the LC phase and the geometry of the sample. These aretranslated as the corresponding limiting frequencies uODFmin anduODFmax of the dispersion profile (u ¼ Kq2/h). For small enoughamplitudes of these fluctuations, the corresponding contribution
to R1 is expressed as23#
$u%&
AODF $uODFmax %ODFmin#f(4)
R1ODF ¼ 1=2 f
u
u
u
where
f ð yÞ ¼#$pffiffiffiffiffi%$pffiffiffiffiffi%
1
arctan2y þ 1 þ arctan
2y # 1p' pffiffiffiffiffi (&2y:# arctanyþ1

qmin

Here S(q) is the orientational structure factor. Thus thederived spectral density Jk(u)RMTD contains Lorentzian-type
contributions of all the q-modes, weighted by the orientational
structure factor S(q), and is written asð qmax2sq
Jk ðuÞRMTD ¼
SðqÞ
dq
1
þ
u2 sq 2
qmin
where
sq ¼

(5)

Here AODF depends upon, amongst others, the degree of theorientational order ("S2), and provides a measure of the efficacyof the ODF mechanism in mediating the spin–lattice relaxation.
3.5 Layer undulations (LU)
At the onset of the smectic A phase, layer undulations provide
another class of slow modulations, arising from the splay
deformations sustained over long length scales. The twist andbend distortions are not energetically feasible in the layered
structures and hence are expelled. The corresponding relaxation
rate is given by23
$u
%
$u
%i
ALU h
LU maxLU minarctan# arctan:(6)
R1LU ¼upuuHere ALU measures the strength of this mechanism. uLUmax
and uLUmin provide the two bracketing high and low frequency
cutoff values for this dispersion, arising from considerations
similar to the ODF modes.
3.6 Reorientations mediated by translational displacements(RMTD)The enhancement of the relaxation rates observed in the confinedsamples in the low frequency regime of the dispersion profiles(Fig. 1) is indicative of the onset of slow processes arising from
This journal is ª The Royal Society of Chemistry 2012

the anchoring interaction between the LC molecules and thesurface. Translational displacements in the presence of surfaceinduced ordering within the adsorption layer leads to relatively
long correlation times among the (short-axes) molecular reorientations, and hence to significant additional contributions tothe spectral densities at lower frequencies. The time scales of the
RMTD mechanism are determined both by the translational
mobility of the probe molecules specified by the diffusion coefficient D, as well as the relatively larger length scales of theroughness of the porous surface (compared to moleculardisplacements) quantified by the wave-vector dependent orientational surface structure factor. The corresponding orientational time correlation function of the probe molecule between
the limits, say, qmin and qmax of the RMTD process, isexpressed as25
ð qmax2GðtÞ ¼SðqÞe#Dtq dq:

1
:
Dq2

Within the assumption of the isotropic distribution of pores in
the random porous media,26 J2(u)RMTD ¼ 4J1(u)RMTD.
For a constant orientational structure factor, the corresponding relaxation rate induced by the RMTD process isexpressed as21,26,32
)
# $
$u
%&
1
uRMTD max %RMTD min#f
R1RMTD ¼ ARMTD 1=2 f
u
u
u
)
# $
(7)
$u
%&
4
uRMTD max %RMTD min
#
f
;
f
þ
2u
2u
ð2uÞ1=2%$u%$u
RMTD max
RMTD minand f
are given by eqn (5).
where fuu
The prefactor ARMTD depends on the diffusion coefficient,geometrical features of the confined matrix and residual dipole–
dipole interactions among the proton spins. Such effects of the
RMTDmechanismonthespin–lattice
relaxation
dispersion were observed previously in other porous systems
like liquid crystals in random porous glass,26,32 in polymers21
and water as well as polar and non-polar liquids in
different random porous matrices.25,33,34 In real systems thesurface structure factor is indeed dependent on the amplitude of
the wave-vector (q), and the expression for relaxation rateneeds to be derived suitably. For a specific q dependence, viz
S(q) ¼ cq#c + e,26 the relaxation rate assumes a simple andinteresting frequency dependence with a power law dependence
on q between its minimum and maximum realizable values(R1RMTD " u#p).
Soft Matter, 2012, 8, 10008–10016 | 10011

4 Analysis and discussion
Analysis of the frequency dispersion of the spin–lattice relaxation
rate (R1B) of bulk liquid crystal just below TNI requires theinvoking of the following relaxation mechanisms: reorientations
about the short axes (R), translational self-diffusion (SD) andorder parameter fluctuations (OPF). In confined systems anadditional mechanism arising from the RMTD dynamics also
contributes to the corresponding total relaxation (R1C). Thus
these two total relaxation rates are expressed as
R1B ¼ R1R + R1SD + R1OPF(8)

R1C ¼ R1R + R1SD + R1OPF + R1RMTD.

(9)

The bulk liquid crystal dispersion data just below the clearing
temperature at 352 K (i.e. DTNI ¼ T # TNI ¼ #1 K), are analysedbased on eqn (8) using the suitable non-linear least squares
method35 and the resulting fit is shown in Fig. 3a. The experimental value of the diffusion coefficient D36,37 was used in our
analysis, as an input parameter. The free parameters in the fitting
procedure are thus the coupling constant associated with diffusionAD, the coupling strength of the reorientations AR, the reorientational correlation time around the short axes sR, and the
prefactor AOPF characterizing the contribution from orderparameter fluctuations along with their correlation time sOPF. The
results of the analysis are summarized in Table 1. We find that AD
decreases from 25 s#2 at 353.6 K (isotropic phase)10 to 19.7 s#2 inthe nematic phase, while AR remains essentially the same (seeTable 1). The slight change in the extracted reorientationalcorrelation time sR from 7.6 to 8.2 ns on cooling across the transition is within the error of estimation. Major change however isseen in the time scale of the order parameter fluctuations sOPF
from 183 ns in the isotropic phase at 353.6 K to 433 ns at 352 K,
and in the AOPF values as the nematic phase forms.10
The confined LC dispersion profiles at the two concentrationsof the aerosil particles were analysed based on eqn (9), and thefits are shown in Fig. 3b and c. The confinement of the LC to therandom porous matrix is seen clearly inducing slow dynamic
components near the surface, originating from the relatively
more persistent time correlations among the molecular reorientations brought about by molecular diffusion very near the
locally ordering porous surface (RMTD). Comparing the valuesof the model parameters extracted in the bulk system at thistemperature with the corresponding data of the confined systems(Table 1), we find that AD decreases at both the concentrations.
The observed decrease in the reorientational correlation time sRon the confinement from its bulk value, i.e. from 8 to 6 ns at rs ¼
0.05 and to 5.4 ns at rs ¼ 0.07, seems to be a clear manifestationof the surface ordering on the local individual molecular
processes. The exponent associated with the RMTD mechanism(R1 " u#p)26 changes from 0.38 in the isotropic phase to 0.45($0.05) just below the transition.10 The so-called equipartition
value of this exponent (0.5), which would have resulted byassuming an orientational structure factor with no wave-vector
dependence, is comparable to the value just below the transition(0.45) within estimation error. The degree of the coupling of thespin system to the lattice via the RMTD mechanism ARMTD alsochanges significantly across the transition.
10012 | Soft Matter, 2012, 8, 10008–10016

Fig. 3 Frequency dispersion of the proton spin–lattice relaxation rate of
8OCB at 352 K (DTNI ¼ #1 K): (a) bulk, (b) 8OCB + aerosil, at rs ¼ 0.05,(c) and 8OCB + aerosil, at rs ¼ 0.07. The dotted color lines represent thecontributions from the different molecular processes.

In the mid-nematic phase and just above the smectic–nematic
phase transition temperature TAN (at T ¼ 346 and 341 K,
respectively) the relaxation rates in the bulk sample (R1B) profiles
were analysed based on the following relevant mechanisms:
molecular reorientations (R), translational diffusion (SD) andorder director fluctuations (ODF). Those in confined LC profiles(R1C) were analysed by including the additional RMTD mechanism. The corresponding relaxation rates in this temperature
region are then expressed as
R1B ¼ R1R + R1SD + R1ODF(10)This journal is ª The Royal Society of Chemistry 2012

Table 1 The best fit parameters obtained from the experimental data in the nematic and smectic phases, based on the contributions explained in Section
3
SamplePure 8OCB

T (K)AD 108 s#2
D 10#11 m2 s#1
AR 109 s#2
sR 10#9 s
AOPF 103 s#3/2
sOPF 10#9 s
AODF 103 s#3/2
uODFmin/2p kHz
uODFmax/2p MHz
ALU 103s#3/2
uLU min/2p kHz
uLUmax/2p MHz
ARMTD 102s#(1+p)
uRMTDmin/2p kHz
uRMTDmax/2p MHz
p

352
19.73
9.8
0.24
8.15
12.31
422.9
—
—
—
—
—
—
—
—
—
—

346
9.42
7.5
1.5
0.75
—
—
5.84
1
100
—
—
—
—
—
—
—

8OCB + aerosil, rs ¼ 0.05
341
8.55
6.3
1.5
0.7
—
—
7.2
1
100
—
—
—
—
—
—
—

334
1.33
0.36
4.46
0.75
—
—

395.9
0.1
100
—
—
—
—

R1C ¼ R1R + R1SD + R1ODF + R1RMTD.

352
18.27
9.8
0.3
6.04
12.65
422.9
—
—
—
—
—
—
2.08
6.5
0.5
0.45

346
13.0
7.5
1.5
0.75
—
—
5.84
4.7 ! 103
100
—
—
—
88.8
1
150
0.55

(11)

The results of the analysis of the bulk data (eqn (10)) aredepicted in Fig. 4. The data show a power law behavior of therelaxation rate (R1 " u#1/2) arising from the classical ODF
mechanism (within the single elastic constant approximation andthe assumption of the wave-vector independent viscosities),
between two cutoff frequencies. The lower cutoff frequency ineffect marks the upper bound of the long wavelength ODF
modes sustained in the nematic medium, and the ODF contribution below this cutoff frequency levels off leading a plateau in
the dispersion profile. But such an observation may not be
always accessible in the FCNMR experiment due to its inherent
limitations. The interpretation of the observed magnetization
recovery in terms of the well defined spin–lattice relaxation time
constant T1 is constrained in a field-cycling experiment at very
low Zeeman fields due to the presence of comparable local fields.
This requirement on the lowest accessible Zeeman field (to behigher than typical dipolar fields) thus restricts the profile toabout "104 Hz. The absence of a cutoff in the experimental data
(Fig. 4) is understood in this context, and the value used in theFig. 4 Frequency dispersion of the proton spin–lattice relaxation rate of
the bulk 8OCB at T ¼ 346 K. The dotted color lines represent thecontributions from the different molecular processes.

This journal is ª The Royal Society of Chemistry 2012

341
10.85
6.3
1.5
0.7
—
—
7.2
6.7 ! 103
100
—
—
—
93.8
1
50.5
0.55

8OCB + aerosil, rs ¼ 0.07
334
1.41
0.36
4.32
0.79
—
—

395.9
0.1
100
17.9
0.1
3.5
0.50

352
17.88
9.8
0.25
5.44
15.33
422.9
—
—
—
—
—
—
3.07
6.5
0.5
0.45

346
13.86
7.5
1.5
0.75
—
—
5.84
5.9 ! 103100———
161.58
1
65.1
0.58

341
10.59
6.3
1.5
0.7
—
—
7.2
7 ! 103100———
204.71
1
46.2
0.59

334
1.27
0.36
4.26
0.80
—
—

395.9
0.1
100
49.9
0.1
3.5
0.54

fitting procedure is only indicative that such a frequency is well
below the lowest accessible frequency of the experiment. The
higher cutoff frequency in these systems falls typically well above
the highest frequency of such experiments, and the value washence fixed at 100 MHz as is the case in such experiments.26 Thus
the ODF contribution to the bulk data in the mid-nematic region
has the typical u#1/2-type dependence of the relaxation rate overthe entire frequency region covered by the present experiment,
practically unhindered by the limitations on the lower and upper
wavelengths of these modes.
Analysis of the confined system, based on eqn (11), was carriedout utilizing the model parameters extracted from the bulk data
as useful inputs. An interesting aspect of this profile is that there
could in principle be power law type contributions (R1 " u#p) to
the dispersion profile both from the ODF mechanism as well asfrom the RMTD process. To resolve this issue, we first analysed
this data with a simple power law, say (R1)x " u#p, without
assigning a specific underlying mechanism, bracketed of courseby the two limiting frequencies. The exponent p for this fit was
found to be 0.52 and 0.56 at 346 K at the two concentrations,
respectively (Fig. 5). This exponent could in principle be assigned
entirely as being due to the ODF mechanism, and viewed as aconsequence of an increase in the relaxation rate upon confinement, arising from the fractal nature of the director fluctuationsin the cavities, as suggested by Leon et al.38 However counter
arguments against this interpretation,26 based on the consequence of fractional dimensionality on the calculation of theassociated length scales which then would tend to be unrealistic,favour our interpretation of the confined data both in terms of(the known) ODF and confinement-induced RMTD process.
Thus, we preferred to analyse the data with the additional
RMTD mechanism along with the ODF mechanism (details of
which are already known from the bulk data), while fullyrecognizing their competing nature in the mid-frequency region(above uODFmin). However, under these circumstances specificassignment of the relative contributions of the two processes
cannot be said to be unique. Frequency dispersion of the relaxation rate below uODFmin, if any, can however be reasonably
attributed to the RMTD process, and the corresponding
Soft Matter, 2012, 8, 10008–10016 | 10013

Fig. 5 Frequency dispersion of the proton spin–lattice relaxation rate at
T ¼ 346 K: (a) 8OCB + aerosil, at rs ¼ 0.05, (b) 8OCB + aerosil, at rs ¼
0.07. The color dotted lines are the contributions from the different
molecular processes.

Fig. 6 Frequency dispersion of the proton spin–lattice relaxation rate of
8OCB at 346 K: (a) 8OCB + aerosil, at rs ¼ 0.05, (b) and 8OCB + aerosil,
at rs ¼ 0.07. The color dotted lines are the contributions from thedifferent molecular processes.

parameters could be usefully considered with some confidence
for appreciating the effects of the surface interactions. With thiscaveat, we analysed the low-frequency data in terms of R1ODF +R1RMTD, obtaining quantitative contributions from both the
ODF and RMTD processes. For this purpose, the low frequency
cutoff of ODF is left as a free parameter and AODF is fixed at thebulk value. The results of these fits at 346 K are shown in Fig. 6,
and the fitted parameters at all temperatures are shown in Table
1. The lower cutoff frequencies of the ODF mechanism in theconfined samples are now found to have shifted to much higher
frequencies relative to the bulk values ("kHz), and are 4.7 MHz
for rs ¼ 0.05 and 5.9 MHz for rs ¼ 0.07, at 346 K. Their values
further increase with the decrease of temperature in the nematic
phase. This increasing restriction on the upper bound of the longwavelength ODF modes (on cooling) seems to be a directconsequence of the confinement on the ODF process in the bulk
region of the confined sample. This also has the welcome
consequence of allowing the observed dispersion below this cutoff value to be interpreted as essentially due to the RMTD,
facilitating its quantitative analysis.
The fits shown in Fig. 6 clearly bring out the importance of the
RMTD mechanism at low frequencies, with exponent values
0.55 $ 0.007 and 0.58 $ 0.01. The increase in the exponent
associated with this mechanism, from 0.45 near the transition to
0.55 in the mid-nematic phase, is interesting evidence of the onsetof the longer wavelength ODF modes within the adsorption
layers imparting relatively more significant weight to these lengthscales in the surface orientational structure factor. The exponent
value also shows a marginal increase with the concentration ofaerosil particles, hinting at its, though weaker, dependence on thevoid/pore size. Also, the RMTD interaction strength ARMTD wasfound to increase by an order of magnitude in the nematic phase.
Further, the decrease of the higher frequency cutoff value of theuRMTD with the decrease of temperature is a pointer to theenhancement of the surface-induced order in the voids. The
lower cutoff frequency for RMTD could not be estimated since
the data did not taper off to a low frequency plateau within theexperimental range. Thus the effect of the confinement on anematic system with fairly well-developed orientational ordercould be inferred by both the ODF effects on the bulk-like regionof the sample, as well as by the modified orientational structure
factor of the porous surfaces as reported by the RMTD
contribution.
The best-fit low frequency cutoff values of the collective
processes such as the RMTD and ODF mechanisms are related
to the largest diffusion time of RMTD during which the orientational correlation is lost sRMTDmax ¼ (uRMTDmin)#1 and the
decay time of the slowest director fluctuations, sODFmax ¼(uODFmin)#1. These values at 346 K are found to be 16 ! 10#5
and 27 ! 10#9 s. The decay time of the director fluctuations are

10014 | Soft Matter, 2012, 8, 10008–10016

This journal is ª The Royal Society of Chemistry 2012

shorter by four orders of magnitude than the RMTD process andthis clearly suggests that these two mechanism are distinctly
separable in the frequency range of our study. The maximum
distance thatpa ffimolecule
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficould
ffiffiffiffiffiffiffiffiffiffiffi travel in the voids is estimated aslRMTD max ¼ 2Dk ðsRMTD max Þ ¼ 154 nm and the maximum
wavelength pofffiffiffiffiffiffithe
ffiffiffiffiffiffiffiffiffidirector
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifluctuations is calculated to belODF max ¼ 4p2 K=huODF min " 20 nm: This shows that the
spatial confinement imposes restrictions on the ODF modes. The
length and time scales of the collective processes further indicate
strong surface anchoring of the LC in the aerosil matrix.
In the smectic phase of the bulk system, the high frequency
dispersion is usually expected from reorientations and selfdiffusion process, while the low frequency dispersion is expectedprimarily from the slow layer undulations (LU).23 The ODF
process is not expected to be as significant as in the nematic phaseon general arguments: the bend and twist distortions are known
to be energetically costly on layer formation and hence theircontribution to the ODF dynamics should be decreased significantly. It is then reasonable to attempt to fit the bulk data with
only the R, SD and LU mechanisms.39,40 Thus we write the total
relaxation rate in the bulk smectic phase at T ¼ 334 K (R1B) as,
R1B ¼ R1R + R1SD + R1LU.

(12)

For the confined smectic system, we introduce the additional
RMTD mechanism to account for the observed enhancement on
the confinement, and write the corresponding relaxation rate R1C
as,
R1C ¼ R1R + R1SD + R1LU + R1RMTD.

(13)

Analysis of the bulk smectic data (eqn (12)) leads to theassignment of the relative contributions as shown in Fig. 7a. It
appears that the layer undulations are very effective below
100 kHz, while the SD is generally dominant in the sub-MHz
regime. Individual molecular reorientations are effective at higher
frequencies as expected. Fig. 7b and c show the results of theanalysis of the confined smectic phase data based on eqn (13). We
immediately observe that it is not possible to uniquely distinguishbetween the contributions of LU and RMTD mechanisms at low
frequencies as they compete in the same frequency regime, unlike
the case of the ODF mechanism in the nematic phase. The exponent value of RMTD marginally decreases to 0.53 and below,
depending on the aerosil density, indicating the somewhat lowered importance of the longer wavelength diffusion modes to the
RMTD at the onset of the smectic phase. These findings areinteresting, particularly in contrast with similar relaxometricresults on another related LC (octylcyanobiphenyl—8CB),
confined to random porous glass (CPG of diameter 15 nm). In thelatter system there was no specific signature of the onset of thesmectic phase, nor evidence of the diminished role of the longwavelength diffusive modes on the surface. In fact the corresponding exponent was reported to increase continually as one
cools the system in the smectic phase.26
Thus, the present system confined to a 3-D porous structurewith comparable lateral dimensions in all directions seems to besensitive to the onset of layer formation, as evidenced by thechanges in the data across the N–Sm A transition. For example,
Fig. 2 shows (say, data at 12 kHz in these figures across the N–Sm
This journal is ª The Royal Society of Chemistry 2012

Fig. 7 Frequency dispersion of the proton spin–lattice relaxation rate of
8OCB at 334 K: (a) bulk, (b) 8OCB + aerosil, at rs ¼ 0.05, and (c)8OCB + aerosil, at rs ¼ 0.07. The color dotted lines are the contributions
from the different molecular processes.

A transition) that the onset of the smectic phase leads to adiscernible decrease of the relaxation rate corresponding to low
frequency modes, both in the bulk as well as in confined systems.
This loss becomes progressively smaller with enhanced confinement. This is to be compared with results reported earlier acrossthe same transition in 8CB but with a cylindrical confinement(CPG) under much more severe geometric restrictions.26 It
appears that this transition was wiped out in the previous case due
to a high degree of confinement, while the present work could
bring out the effect of such a layering transition on the dynamics ofthe confined system. We conclude that within the limits to which
we could restrict the system in our experiments, the smectic phase
is effectively inhibiting the long wavelength modes, resulting in acorresponding decrease in the exponent of the RMTD.
Soft Matter, 2012, 8, 10008–10016 | 10015

5 Conclusions
We measured the frequency dispersion of proton spin–lattice
relaxation rates of 8OCB in bulk form and in two samples
embedded in random porous 3-D networks formed by aerosil
nano-particles, at two different average pore sizes. The observed
increase in the relaxation rate in the low frequency regime isinterpreted as due to the slow reorientational correlations of the
LC molecules undergoing diffusion processes within theadsorption layers near the porous surfaces. We find that as
the thermodynamic phase of the LC medium undergoes
progressive changes with a decrease in temperature, the characteristics of the slow dynamics also correspondingly change. These
are reflected in two ways: the change in the power law behaviourof the relaxation rate between the two cutoff frequency limits of
the RMTD process, and the efficacy of the RMTD mechanism incontributing to R1. The variation of this power law exponent, fora given topology of the embedding network, is thus an indicationof the subtle changes in the characteristics of the adsorption layer
induced by changes in the ordering of the LC medium on cooling.
We find that this exponent increases from 0.45 to 0.6 as theconfined system is cooled in its nematic range. This is interpreted
as a progressive onset of order director fluctuations within these
adsorption layers, promoting correlated nematic regions overlonger length scales, consistent with the behaviour of the central
core region. This is further supported by a corresponding
increase (by an order of magnitude) in the coupling strength of
the spin–lattice relaxation to the RMTD mechanism. The onsetof the smectic phase dramatically changes this exponent value
from 0.6 to 0.5, interpreted as due to the relative losses of thecontribution from the long wavelength modes on the formationof smectic layers, and results on the bulk sample in the corresponding phase also support this interesting scenario. We also
report in this process dynamic parameters connected with individual processes (molecular reorientations and translational
diffusion). This work also shows the sensitivity of a 3-D confined
LC system to layer formation, in contrast to the system earlier
investigated under severe CPG confinement.

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