Mol. Cryst. Liq. Cryst., Vol. 546: pp. 45=[1515]–56=[1526], 2011
Copyright # Taylor & Francis Group, LLC
ISSN: 1542-1406 print=1563-5287 online
DOI: 10.1080/15421406.2011.571607

Slow Molecular Processes in a Liquid Crystal
Embedded in Aerosil Matrix: Nuclear Magnetic
Relaxometric Study
M. RAJESWARI,1 SURAJIT DHARA,1 K. VENU,1
V. S. S. SASTRY,1 AND R. DABROWSKI2
1

School of Physics, University of Hyderabad, Hyderabad, India
Institute of Chemistry, Military University of Technology, Warsaw,
Poland2Frequency dispersion studies on proton spin-lattice relaxation rates of a liquid crysal(4’-octyloxy-4-cyanobiphenyl) embedded in Aerosil matrix show significant
increase at low frequencies (sub-MHz regime) relative to the bulk sample, andare interpreted as primarily due to slow reorientations near the surface orderedlayers mediated by translation displacements. The computed exponent in the powerlaw behavior of the dispersion profiles at different temperatures in the isotropic
phase indicates an enhanced role of the low-wavelength diffusion modes during thisprocess. The data also show critical contribution near the isotropic-nematic transition to the length scales relevant to adsorption kinetics.
Keywords Liquid crystal; molecular dynamics; nuclear magnetic relaxometry;porous media

1. Introduction
Dynamical behavior of liquid crystals immersed into various porous matrices has
been attracting considerable attention over the recent years [1]. Typical examples
of such matrices are anopore [2], aerogel [3], controlled porous glass (CPG) [4,5],
vycor glass [6], millipore [7,8], nucleopore [9] and Aerosil [10–15]. LC-Aerosil mixtures are particularly interesting because the random disorder can be introduced into
the system in a controlled manner by changing the concentration of the silica particles. At very low concentrations (less than 0.01 g=cm3), the few silica particles added
to the LC act as just impurities in the LC medium, as their number is too small toform a 3-d network. In the density range of 0.01 to 0.1 g=cm3, these particles tend
to form a 3-d network due to the inter-particle hydrogen bonds [16] referred as softPresent address: Soctronics Technologies Pvt. Ltd., Banjanra Hills, Hyderabad 500 034,
India.
Address correspondence to M. Rajeswari, School of Physics, University of Hyderabad,
Hyderabad 500 046, India. Tel.: þ91-40 23011033; Fax: þ91-40 23010227; E-mail:raji.hcu@gmail.com

45=[1515]

46=[1516]

M. Rajeswari et al.

gel. When the concentration is further increased, the network becomes more rigid
and the resulting dispersion becomes a stiff-gel.
Interestingly changes in the physical properties of liquid crystals confined tosuch Aerosil matrices were studied by various experimental techniques [10–18].
The DNMR [16,17] results in the nematic and smectic phases showed how the fieldanneals the random disorder introduced by the Aerosil particles upto a certain concentration, beyond which, i.e., in the so called stiff-gel regime, disordering effects
completely dominate. Previous proton NMR studies [18] in LC-Aerosil systems
showed a clear evidence of an increase in the spin-lattice relaxation rate at very
low frequencies (below MHz), and this was explained qualitatively in terms of an
extra relaxation mechanism mediated by slow molecular processes near the surfaceof the porous medium arising from LC-surface interactions.
In the present work, we report our NMR results on 8OCB-Aerosil systems at
two concentrations of Aerosil particles (section-2). The appropriate analytical models to account for the observed relaxation rate are discussed in section-3. We analyze
the data based on a random walk model which takes into account the LC-surface
interaction and the resulting slow time scales as seen by the NMR experiment(section-4). The results are discussed in the light of pretransitional effects near thetransition temperature.

2. Experimental Methods
Pure sample of 8OCB was synthesized in our laboratory (Warsaw), and has thephase sequence: I 80 C N 67 C SmA 54.5 C Cr. The liquid crystal-Aerosil mixtures
were prepared using solvent method [11]. A hydrophilic Aerosil (type A300),
obtained from Degussa Corp., was first dried under vacuum at 200 C overnight,
before adding it to the liquid crystal dissolved in pure acetone. After sonicating
the mixture for about 2 hours to achieve homogeneous dispersion, the solvent wasremoved through evaporation at 60 C for a long time, and was sealed in the
NMR sample tube under vacuum. Aerosil (A300) consists of small silica spheresof 7 nm in diameter and has a specific surface area of 300 m2=g. The surface of thespheres is covered with hydroxyl groups that interact with each other and formhydrogen bonding between the spheres, leading to a three dimensional network
within the liquid crystal environment. The density of silica in our samples is 0.05
and 0.07 g=cm3 (sample-A and sample-B, respectively). The interaction of thehydroxyl groups on the surface of the Aerosil particles with the polar liquid crystal
is known to lead to a homeotropic alignment of LC molecules near the surfaces. The
shift of the nematic-isotropic transition temperature in both the mixtures is less than
1 K as compared to the bulk sample. The mean void size in these systems is calculated [19] to be 133 nm and 95 nm in samples A and B, respectively.
Proton spin-lattice relaxation times T1 at different Larmor frequencies n (x ¼ 2pn)
were measured covering the range 10 kHz to 50 MHz, on a commercial fast field cycling
NMR relaxometer (Stelar Spinmaster FFC 2000) and a homemade pulsed field NMR
spectrometer. At higher frequencies (MHz regime) an inversion-recovery pulse sequence
was used. On the field-cycling relaxometer (covering the range 10 kHz to 10 MHz), a different sequence (BH!L-si-BL!H-P) leading to a free induction decay was employed.
Here si is the evolution time, BH and BL are high and low magnetic fields respectively,
and P is the radio-frequency pulse causing the magnetization rotation by p=2 underresonant condition. The time dependence of magnetization recovery was found to be

Slow Molecular Processes in a Liquid Crystal

47=[1517]

Figure 1. Frequency dispersion of the proton spin-lattice relaxation rate profiles in the isotropic phase at different temperatures (a) Bulk 8OCB, (b) Sample-A, (c) Sample-B.

exponential over the observation time scale. T1 measurements are accurate to within 3%,
while the temperature of the sample was controlled through Stelar unit to within 0.2 K.
Figures 1 and 2 show the frequency and temperature dependences of proton
relaxation rate R1 ¼ T1
1 in the isotropic phase of the bulk and confined 8OCB at
the two different concentrations, clearly bringing out the low frequency enhancement of the relaxation rate due to confinement. The temperature dependence ofR1, measured at two frequencies, 0.4 MHz and 12 kHz, shows an enhancement in
the relaxation rate even 15 K above TNI.

3. Relaxation Mechanisms in Bulk and Confined Systems
Proton spin-lattice relaxation occurs via the time modulation of dipole-dipole interactions of spin pairs, and in the isotropic phase it is effectively mediated by bothinter- and intra-molecular dipolar interactions arising from individual molecular
processes [20,21]. These typically occur in the nano second (ns) range, leading toobservable dispersion features in the range 107–108 Hz. Close to TNI, short-range
nematic order develops in the isotropic phase, and the life times of this orderincreases as the clearing point is reach from above. This reflects in the critical

48=[1518]

M. Rajeswari et al.

Figure 2. Temperature dependence of proton spin-lattice relaxation rate at two Latmor
frequencies for 8OCB in the bulk and Samples A and B.

dependence of the associated correlation times among molecular reorientations. The
total spin-lattice relaxation rate R1 in the bulk isotropic system is thus expressed as [21]R1B ¼ R1SD þ R1R þ R1CF

ð1ÞThe first term takes into account the contribution from molecular translational
self-diffusion, as it modulates in time the dipole-dipole interaction among spins, particularly via inter-molecular spin interactions. Its contribution in viscous isotropic
liquids was computed earlier [22], needing two fitting parameters: the coupling constant B and the diffusion coefficient D. This can be expressed as
R1SD ¼

pﬃﬃﬃ
B½f ða; xÞ þ f ða; 2xÞ:x

Slow Molecular Processes in a Liquid Crystal

49=[1519]

Where
hr2 i
a¼
;
12a2


x¼

xa2
D



 
  


2
1
1
f ða; xÞ ¼ 2 v 1  2
þ v 1þ 2
þ 2 e2v cos2uxðu þ v2 Þðu þ v2 Þ



1
2v
þu 1  2e sin2uðu þ v2 Þ
(
)1=2
 
u
ðxa2 =2DÞ1=2
xs
1
:
¼
v
ð4 þ x2 s2 Þ1=4
ð4 þ x2 s2 Þ1=2
The second term represents the contribution from molecular reorientations characterized by the correlation time sR, and is given by [23]R1R ¼ AR2X

p2 s Rp¼1 1 þ ðpxsR Þ

2:

Here AR is the coupling constant quantifying the contribution from reorientations. In
the limit of fast reorientations, xsR << 1, the above contribution becomes essentiallyfrequency independent and is constant over the frequency region of our experiment at
a given temperature.
The third term comes from the time-modulation of dipolar interactions due toshort-range nematic order fluctuations. This contribution is expressed as [21,24]:
2

31=2

sCF
6
7
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ5
R1CF ¼ ACF 422
1 þ 1 þ x sCF:

pﬃﬃﬃ
Here ACF ¼ AT g is a temperature dependent parameter, providing a measure of thecontribution of short-range nematic order fluctuations. sCF is the average correlation
time of the short-range nematic order fluctuations and g is the effective viscosity. The
correlation time sCF is further written in terms of the correlation length n as
sCF ¼

gn2
L

Where
sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
L
n¼
 Þc
aðT  TNI
L is related to the elastic constants, a is the temperature independent coefficient in theLandau expansion of the relevant free energy, and c is the associated exponent (whichis unity in the mean field approximation).

50=[1520]

M. Rajeswari et al.

The confinement of liquid crystals introduces a new relaxation mechanism
contributing to the total relaxation rate. The interaction of the liquid crystal
molecules with the surfaces induces local order relative to the surface. In thiscontext, it is convenient to view a confined LC system to consist of two phases:
a bulk like phase away from the surface where the orientational order parameteris zero, and a surface ordered phase close to the surfaces where fast molecularreorientations are spatially restricted and the orientational order parameter takes
a finite value. The surface ordered phase has a finite thickness determined by
the relative strengths of the two ordering mechanisms. Thus a confining nanoporous system presents a more complex scenario of molecular processes, withliquid crystal molecules exchanging between these two dynamically different
organizations. A simplification is usually made by assuming that a fast molecular exchange takes place between the two phases. The reorientations of themolecules occurring due to translational diffusion near the ordering surface(RMTD) have a different time scale, and slower relative to bulk medium,
because of the surface induced preferred orientation and relatively smooth (atmolecular level) surface of the pores (providing topologically a two dimensionalsurface). This mechanism has been explored in detail earlier [25,26].
Within the two-phase fast exchange regime, the RMTD process describes molecular reorientations caused by the diffusional displacement of LC molecules on
the surface of the pore. The time correlation function for the RMTD process consequently contains dynamic as well as geometrical information on the system. The
dynamical part refers to the translational diffusion and the geometrical part refers
to the surface topology of the pores in the matrix. The general correlation function
for RMTD is given byGðtÞ ¼

Z 1

2SðkÞeDtk dk

0

Where S(k) is the orientational structure factor: k refers to the wave vector. The corresponding spectral density is given byJðxÞ ¼

Z 1GðtÞ cosðxtÞdt ¼

Z 1

0

SðkÞ
0

2sk
dk
1 þ x2 s2k

Where

sk ¼

1
:
Dk2

The relaxation rate R1RMTD ¼ (T11 )RMTD in confined liquid crystals above TNI canbe expressed as [27,30]

ðR1 ÞRMTD ¼

xi
ARMTD h xRMTD max
RMTD min
f

f
xp
x
x
x
i
4ARMTD h xRMTD max
RMTD minþ 1=2 p f
f
2x
2x
2 x

Slow Molecular Processes in a Liquid Crystal

51=[1521]

where pﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃ
pﬃﬃﬃﬃﬃ
12yarctan ð 2y þ 1Þ þ arctan ð 2y  1Þ  arctan hf ðyÞ ¼pyþ1
22
and xRMTDmax ¼ Dkmax
are the minimum and maximum
Here xRMTDmin ¼ Dkmin
cutoff frequencies, which are in turn related to the corresponding length scales
Lmax ¼ (xRMTDmin)1 and Lmin ¼ (xRMTDmax)1. The relaxation rate in the confinedsystems now includes additional RMTD mechanism, and hence the observed relaxation rate is expressed as

R1C ¼ R1SD þ R1R þ R1CF þ RIRMTDð2Þ

Figure 3. Frequency dependence of proton spin-lattice relaxation rate of 8OCB at
DTNI ¼ 10 C (a) Bulk 8OCB, (b) Sample-A, (c) Sample-B. The black line is the calculated total
relaxation rate obtained by using Eqs. 1 & 2. Color lines are the corresponding relaxation rate
contributions from different mechanisms as shown in the figures.

52=[1522]

M. Rajeswari et al.

4. Results and Discussion
The dispersion data at different temperatures were fit to Eq. (1) in the case of bulk
sample and Eq. (2) for confined system. Non-linear least squares method was used to
get the best fit parameters consistent with frequency and temperature dependences.
Diffusion data were available from other experiments [28,29] and so D was not avariable in the analysis. We find that the coupling constant B is fairly insensitive
to temperature and so we took the average value and used the same at all temperatures. The prefactor AR and the reorientational correlation time sR showtemperature dependences as expected in liquid crystals. As we approach thenematic-isotropic transition, the contribution from critical fluctuation becomes significant, and is reflected in the plots showing relative contributions of different
mechanisms (Figure 4). We find that the sCF values (obtained from bulk sample
data) are comparable to those in other LC systems, like 6CHBT [31]. The fitted
curves and parameters are shown in Figures 3 and 4 and Table 1.
While analyzing the dispersion profiles of the confined system using Eq. (2), we
take advantage of the knowledge of the dynamic behavior in the bulk sample andFigure 4. Frequency dependence of proton spin-lattice relaxation rate of 8OCB at DTNI ¼ 1.5 C(a) Bulk 8OCB, (b) Sample-A, (c) Sample-B. The black line is the calculated total relaxation rate
obtained by using Eqs. 1 & 2. Color lines are the corresponding relaxation rate contributions fromdifferent mechanisms as shown in the figures.

53=[1523]

DTNI ( C)
B (1010) s2
D (1010) m2=s
AR (109) s2sR (109) s
ACF (103) s3=2
sCF (109) sp
ARMTD (102 s(1 þ p))
xRMTDmin=2p (103 Hz)
xRMTDmax=2p (107) Hz

Parameter

1.91
0.95
0.91
–
–

15
1.61
0.75
1.77
–
–

10

6
0.25
1.41
0.33
2.81
7
35
–
–
–
–

1.5
1.23
0.27
6.86
8.3
77

Bulk 8OCB

1.19
0.25
7.86
9.6
183

0.6

0.6
15
6.5

1.91
0.95
0.78
–
–

15

Table 1. Best fit parameters for the bulk and confined 8OCB systems

0.67
14
4.5

1.61
0.75
1.77
–
–

10

6
0.25
1.41
0.33
2.81
6.13
35
0.38
0.82
12
2.8

Sample-A

0.9
9
0.6

1.23
0.27
5.97
7.89
77

1.5

0.95
8
0.1

1.19
0.25
6.72
8.59
183

0.6

0.81
15
6.5

1.91
0.95
0.78
–
–

15

1.07
14
4.5

1.61
0.75
1.77
–
–

10

6
0.25
1.41
0.33
2.75
5.19
35
0.38
1.1
12
2.8

Sample-B

1.35
9
0.6

1.23
0.27
5.84
7.52
77

1.5

1.5
8
0.1

1.19
0.25
6.55
8.4
183

0.6

54=[1524]

M. Rajeswari et al.

hence focus primarily on the RMTD mechanism. Thus the fit parameters in this casepertain to the lower and upper cutoff frequencies (xRMTDmin and xRMTDmax) and theexponent p in the assumed power law behavior for the frequency dispersion between
these two frequency limits [27]. We find that the data in this region fit to (T1
1 )
p
/
x
,
with
p
¼
0.38

0.04.
Deviation
of
p
from
the
equipartition
value
of
RMTD
0.5 [27,30] point out to the relatively higher weight accorded to lower wavelength
modes of diffusion in this confined system, arising from the surface topology. The
cutoff frequencies xRMTDmin and xRMTDmax are related to the largest and smallest
molecular displacements, needed to cause appreciable loss of correlation among
the orientation of molecules, Lmax and Lmin, respectively [30]. The estimated valueof Lmax ¼ 91  6 nm does not show significant variation with the temperature, whilethat of Lmin shows a substantial change with temperature, particularly near the transition temperature indicating the role of pretransitional effects on the surface diffusion characteristics of the molecules. This points to enhanced ordering near thesurface over extended regions as the system approaches the transition region. This
pretransitional effect on Lmin is shown in Figure 5.
The strength of the RMTD interaction ARMTD shows an Arrhenius behavior
with temperature at both the concentrations (sample-A and sample-B) as shown in
Figure 6, and it is enhanced in sample-B, relative to sample-A, due to its dependence
on the diffusion coefficient, surface order parameter and the fraction of molecules inthe surface layer. The corresponding activation energies at the two concentrations
are: Ea ¼ 35 kJ=mole for sample-A and 41.5 kJ=mole for sample-B. The slightincrease in the activation energy at higher concentration might be due to anincreased attractive interaction between Aerosil matrix and the liquid crystal molecules at the surface. We did not find observable variation in the two cutoff frequencies for the two samples. It may also be noted that the values of sR (related tomolecular reorientation mechanism) in the two samples differ slightly, especiallynear the transition temperature, indicating corresponding changes in the

Figure 5. Temperature variation of Lmin (see the text).

Slow Molecular Processes in a Liquid Crystal

55=[1525]

Figure 6. Temperature variation of ARMTD at different Aerosil concentrations. The solid line
shows the best Arrhenius fit of the experimental data.

orientational ordering in the system. In comparison, there have been only very marginal changes in AR in the confined samples relative to its values in the corresponding
bulk systems, and keeping the errors of analysis in view its bulk values are used incomputing the contributions from this mechanism (Table 1).

5. Conclusions
In this paper we report proton spin-lattice relaxation rate measurements in the isotropic phase of bulk 8OCB and 8OCB confined to Aerosil matrix at two different concentrations. We found a notable increase in the relaxation rates in the sub-MHz
regime. This observed significant increase is quantitatively explained in terms of anadditional slow relaxation mechanism of molecular reorientations mediated by translational displacements (RMTD), and it is characterized by power-law dispersion in thefrequency range between low and high frequency cutoff values. The analysis of theexperimental data shows that the major increase in the relaxation rate is due to thisprocess. The low and high frequency cutoffs of the RMTD mechanism provide someinsight into how the molecules are reorienting at the surface. The exponent value indicates that the relative importance of low wavelength modes has increased compared to
expectation from equipartition distribution, and it is different from the other confinedsystems studied in the isotropic phase [27,30]. The increased interaction strength of
this mechanism on increasing the concentration of Aerosil particles shows that thefraction of molecules in the ordered layer has correspondingly increased.

Acknowledgment
MR would like to thank the University Grants Commission, New Delhi for providing RFSMS fellowship.

56=[1526]

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