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Phase Transitions: A Multinational
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Slow molecular processes in a nematic
liquid crystal confined to random
porous network formed by aerosil
particles
a

a

b

a

M. Rajeswari , S. Dhara , K. Venu , V.S.S. Sastry & R.
DabrowskicaSchool of Physics, University of Hyderabad, Hyderabad 500 046,
Andhra Pradesh, Indiab

Soctronics Technologies Pvt. Ltd, Hyderabad 500 034, Andhra
Pradesh, IndiacInstitute of Chemistry, Military University of Technology, 00-908
Warsaw, Poland
Available online: 16 Feb 2012

To cite this article: M. Rajeswari, S. Dhara, K. Venu, V.S.S. Sastry & R. Dabrowski (2012): Slow
molecular processes in a nematic liquid crystal confined to random porous network formed byaerosil particles, Phase Transitions: A Multinational Journal, 85:4, 322-336
To link to this article: http://dx.doi.org/10.1080/01411594.2011.646269

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Phase Transitions
Vol. 85, No. 4, April 2012, 322–336

Slow molecular processes in a nematic liquid crystal confined to random
porous network formed by aerosil particles

Downloaded by [Tata Institute of Fundamental Research] at 05:29 25 April 2012

M. Rajeswaria*, S. Dharaa, K. Venub, V.S.S. Sastrya and R. DabrowskicaSchool of Physics, University of Hyderabad, Hyderabad 500 046, Andhra Pradesh, India;
Soctronics Technologies Pvt. Ltd, Hyderabad 500 034, Andhra Pradesh, India; cInstitute ofChemistry, Military University of Technology, 00-908 Warsaw, Polandb(Received 20 November 2011; final version received 25 November 2011)
Frequency dispersion measurements of proton spin–lattice relaxation rates (R1) of
liquid crystal 4-propyl-40 -pentylazoxybenzene in bulk and confined samples (inrandom porous network of aerosil nano-particles) are reported in isotropic andnematic phases. Significant low-frequency increase in R1 in confined samples
indicates slow molecular reorientations mediated by translational displacements
near the adsorbing porous surface. The resulting dispersion behavior of R1(!p) reflects the nature of the random surface (p ¼ 0.5 for equi-partition of the
diffusive modes). The observed temperature-independent exponent in theisotropic phase (p ¼ 0.34) indicates the abundance of low-wavelength surface
modes. Its temperature-dependent higher values in the nematic phase (from0.59 to 0.65 on cooling), and increased spin–lattice coupling via this mechanism,show progressive onset of longer wavelength modes. A detailed analysis shows theeffect of confinement on the order director fluctuations, molecular reorientations,and translational diffusion of the molecules.
Keywords: liquid crystals; porous media; RMTD process; molecular dynamics;
NMR relaxometry

1. Introduction
Interest in liquid crystalline materials confined to various types of geometries expanded
greatly in the last two decades because of their important role in electro-optic devices andphysical properties, which require basic understanding of surface–fluid interactions.
Independent of the methods used to confine the liquid crystals (LCs), these systems have
one underlying common theme: a symmetry-breaking, non-planar confinement imposedby the surrounding matrix. In addition, confined LCs differ significantly frommacroscopic bulk systems because of their large surface-to-volume ratio. Their composite
nature profoundly affects the ordering of the LC molecules and their susceptibility toexternal fields, making them ideal for electro-optic applications [1].
Among the confined LC systems, LC-aerosil dispersions are demonstrated to beparticularly interesting to study through many distinct experimental and theoreticalmethodologies [2–17]. While porous matrices like nucleopore, anopore, millipore, andcontrolled porous glass (CPG) all have a well-defined geometry of the pores, aerosil, and*Corresponding author. Email: raji.hcu@gmail.com
ISSN 0141–1594 print/ISSN 1029–0338 online
ß 2012 Taylor & Francis
http://dx.doi.org/10.1080/01411594.2011.646269
http://www.tandfonline.com

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Phase Transitions

323

aerogel systems in contrast provide random porous structures. Aerosil gels are partly
similar to silica aerogel, a different type of fractal silica gel used to confine LC. Aerosil andaerogel systems are nearly identical in several aspects: fractal-like nature of the gel
structure, surface composition, chemical properties, as well as density. The crucial
difference between the two systems is their differing response to elastic strains since
aerogels possess much larger shear modulus than aerosil gels. In LC-aerogel systems, thesilica network is fixed in space and the elastic strains imposed by the random anchoring
surfaces are fully quenched. The disorder introduced by even the low-density aerogels is so
severe that the features of phase transitions are dramatically smeared [16]. In contrast, inaerosil gels, a weaker, better-controlled random disorder can be introduced: elastic strains
can be partially annealed, thus reducing some of the disordering effects. In addition, theability to grow a network directly within the LC permits the formation of structures ofhigher porosity [17,18]. Indeed, a distinct advantage of aerosil systems is the ease of
producing nearly arbitrary silica densities.
Nuclear magnetic relaxation methods, widely used to probe molecular dynamics inmany condensed systems, are extremely sensitive to the orientational order of molecules
and have the potential to report on the dynamic processes over a wide time scale [19]. The
random network confining the LC induces ordering near the surface, which decreases
exponentially with a correlation length depending on the disordering density. For example,
the deuterium NMR studies on the LC 8CB confined to aerosil matrix [6,9] revealed thedetails of the director configuration and the orientational order in the voids, supporting
this scenario. The proton NMR relaxometry in this context provides a valuablesupplementing technique, which throws further light on the degree of surface-inducedorder and on the changes in the molecular dynamics induced upon confinement [14,15].
In this article, we present a detailed dispersion study of proton spin–lattice relaxation
rates in bulk 4-propyl-40 -pentylazoxybenzene (PPA) and PPA confined to aerosil matrix at
two different concentrations. These relaxation rates of confined systems are found to bevery sensitive in the presence of the silica network, and show qualitatively different
frequency dependence compared to the bulk sample. We analyze the additional
contribution to the relaxation rate on confinement, in terms of slow reorientation ofmolecules very near the porous surfaces due to adsorption kinetics. This article isorganized as follows: the experimental details are given in Section 2. The relaxation models
and the analysis of the experimental data are discussed in Sections 3 and 4. The last section
summarizes the results of this work.

2. Experimental details
The LC PPA was synthesized in the laboratories in Warsaw, Poland. The molecular
structure and its phase sequence are shown in Figure 1. The LC–aerosil mixtures wereprepared by the solvent method [3]. Aerosil (type A300 from Degussa Corp.) was initiallydried over-night at 200 C under vacuum before adding to a dilute solution of the LC inpure acetone. This solution was kept in the sonicator for over 2 h to achieve ahomogeneous dispersion. The solvent was then evaporated by keeping the sample at 60 C
for over 15 h. The mixture was then transferred into an NMR tube and was sealed undervacuum. Aerosil A300 consists of small silica spheres of diameter 7 nm and a specificsurface area of 300 m2 g1. The surface of these spheres is covered with hydroxyl groups
that interact with each other via hydrogen bonding, and the resulting system thus forms a
3-D random network. Due to the hydrophilic nature of the spheres and the polar nature of

324

M. Rajeswari et al.
4-propyl-4'-pentylazoxybenzene (PPA)

C3H7

N

N

C5H11

O
Cr 0 oC N 61.8 oC I

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Figure 1. Molecular structure and phase sequence of the liquid crystal PPA.

the LC, the alignment of the molecules at the silica surfaces is homeotropic. The density ofsilica particles in our samples was 0.05 (Sample A) and 0.07 g cm3 (Sample B). The shiftof the isotropic-to-nematic transition temperature (TNI) is within 1 K at both the aerosil
concentrations.
Proton spin–lattice relaxation rates (R1) were measured over a range of Larmor
frequencies using the field-cycling NMR relaxometry (Stelar Spinmaster FFC 2000) from
10 kHz to 10 MHz and a pulsed variable field spectrometer at 20 MHz. The decay of theobserved magnetization was exponential over several decades of the observation time,
indicating single relaxation time constant. The errors in the R1 measurements were within
3% and the temperature of the sample was controlled to 0.1 K. The frequency
dependence of these rates in bulk and confined PPA systems (at two different
concentrations) in the isotropic and nematic phases are shown in Figure 2(a–c). Theirtemperature dependences at different Larmor frequencies (in bulk and confined samples)
are shown in Figure 3(a–c). These plots bring out clearly the pre-transitional behavior near
the nematic–isotropic point, and also portray specific features of the different phases in thebulk as well as in confined LC systems.

3. Relaxation models
The proton spin–lattice relaxation is mediated via the time modulation of dipole–dipole
interactions between the neighboring spins [19,20], effected through various molecular
processes characteristic of the liquid crystalline systems. It is customary to assume theirstatistical independence, and hence express the observed relaxation rate R1T as a sum of
individual contributions {R1}i, asX
fR1 gi , i ¼ R, SD, CF, OPF, ODF, and RMTD
ð1Þ
R1T ¼
i
where the summation index i covers different molecular mechanisms, like: local molecularreorientations (R), translational self-diffusion (SD), orientational order critical fluctuations (CF), order parameter fluctuations (OPF), order director fluctuations (ODF), androtations/reorientations mediated by translational displacements (RMTD).
In the case of LC molecules, the molecular reorientations about their long and shortaxes can be distinguished due to separated time scales: reorientations around the long axes
are fast on the typical NMR experimental time scale and hence give a frequencyindependent contribution. On the other hand, dynamics about the short axes are slow, andcould fall in the time window of the experiment. The relaxation rate contribution due toPhase Transitions

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(a)

325

(b)

(c)

Figure 2. Frequency dispersions of proton spin–lattice relaxation rate R1 for PPA in the bulk (a),in Sample A (b), and in Sample B (c) in the isotropic and nematic phases.

these reorientations is given by the well-known BPP expression [21], which depends on acorrelation time  R and a pre-factor AR. The translational self-diffusion modulates theintermolecular spin interactions and its contribution to the total relaxation rate in theisotropic phase was calculated analytically [22] and later extended to the liquid crystalline
phases [23,24]. This contribution primarily depends on the diffusion coefficient D and a
related pre-factor AD.
The collective processes observed in LC systems are critical fluctuations of theorientational order just above the nematic–isotropic transition (TNI), order parameter
fluctuations just below this transition, and order director fluctuations in the nematic
phase. The first of these contributions arises from the time-modulation of the dipolarinteractions due to short-range nematic order fluctuations [19], and is quantified by acorrelation time  CF and a pre-factor ACF. In contrast to short-range nematic orderfluctuations in the isotropic phase, fluctuations in the magnitude of the nematic orderparameter S are effective in relaxing the nuclear spins just below nematic–isotropictransition [19]. Order director fluctuations observed in the nematic phase are typicallycharacterized by a spin–lattice relaxation rate that depends on frequency as R1  !1/2.
However, this characteristic frequency dependence is modified in the limiting cases of both
high- and low-frequency cut-off values. The relaxation rate becomes independent below a
lower cut-off frequency and it varies as R1  !2 above an upper cut-off frequency.

326

M. Rajeswari et al.
(b)

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(a)

(c)

Figure 3. Temperature dependences of proton spin–lattice relaxation rate R1 for PPA in the bulk (a),in Sample A (b), and in Sample B (c) in the isotropic and nematic phases.

The pre-factor AODF and the cut-off frequencies associated with ODF depend on thetemperature, nematic order parameter S, and visco-elastic properties of the liquid
crystalline medium [19].
In the case of LCs confined to nanometer size cavities, the molecular rotations andtranslational displacements close to the cavity surfaces are restricted, and are affected by
the influence of the surface. Such constrained dynamics was observed in many LC systems
confined to different types of random porous matrices [14,15,25–28], and the underlying
rotational processes are referred to as RMTD. The translational displacements close to thesurface is analyzed in terms of diffusion modes with different wave numbers q, decaying intime with damping constant  q ¼ 1/Dq2. The relaxation rate for this mechanism is the sumof all diffusion modes taking into account that each mode might contribute with adifferent weight. The weights depend on the structure of the confined porous matrix, andin general the orientational structure factor quantifying their relative importance is acomplex function of the wave number. But in some cases, it can be approximated by apower law with an exponent p. Therefore the spin–lattice relaxation rate associated withthis mechanism for an arbitrary value of the exponent p was calculated as [28]
 Z zmax 3
Z z pﬃ 3zp )max = 2 z
1z  zp1dzþdz
ð2ÞðR1 ÞRMTD ¼ ARMTD pp4! zmin 1 þ z
ð2!Þ zmin =pﬃ2 1 þ z4

Phase Transitions

327

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where zmin ¼ (!RMTDmin/!)1/2 and zmax ¼ (!RMTDmax/!)1/2. ARMTD is a pre-factor
depending on the diffusion coefficient, geometrical features of the confined matrix, andresidual dipole–dipole proton–spin interaction. The frequencies !RMTDmin and !RMTDmax
are the lower and higher cut-off limits, and are related to the largest and smallest
molecular displacements lmax and lmin of a molecule through the following relation:!RMTDmin ¼ l2max /4D and !RMTDmax ¼ l2min /4D. Apart from the additional RMTD contribution in the nano-confined samples, all the other relaxation mechanisms are common forboth the bulk and confined systems.

4. Analysis and discussion
The spin–lattice relaxation rate profiles in different phases of the LCs are analyzed interms of the above-mentioned different relaxation mechanisms. The parameters quantifying these processes were evaluated by employing a non-linear least square fitting
procedure based on the Levenberg–Marquardt (LM) algorithm [29]. The broad objectiveof this regression analysis is to locate efficiently the region of parameter space which is best
suited to account for the experimental data according to the chosen model, and thenminimize the deviation (mean square error, 2) between the experimental and computed
results, based on maximum likelihood criterion. The LM algorithm combines the gradientsearch method with parabolic approximation by modifying exclusively the diagonalcomponents of the Jacobian (curvature) matrix associated with the model during thegradient search, and asymptotically withdrawing these modifications in the immediateneighborhood of the 2 minimum, to recover the parabolic approximation. Further
simplification results by considering only the linearized version of the Jacobian matrix.
This analysis is carried out under these conditions, and the errors in the fitted parameters
thus obtained are to be taken as indicative (particularly if there are significant correlations
among some of them). To reduce the complexity of the fitting procedure, we used
experimentally measured values, wherever available, as inputs for the model parameters.

4.1. Isotropic phase
The relaxation rate dispersions of the bulk PPA at higher temperatures(DTNI ¼ T  TNI ¼ 10 C and 15 C) in the isotropic phase are well described by a superposition of the two relevant relaxation mechanisms: molecular reorientations (R) andtranslational self-diffusion (SD). We made use of the reported value of diffusion constant
D of a related azoxybenzene [30] in analyzing the present data, noting that bulk propertiesof diffusion in the isotropic phase of such similar systems are very much comparable.
We found that the coupling constant AD has not varied significantly over the temperature
range (within the estimated errors) in the isotropic phase; so its average value was used at
all temperatures in this phase. The reorientational correlation time  R has been found toincrease with the decrease of temperature, while its strength AR decreased. Close to thephase transition, i.e., at DTNI ¼ 0.6 C, 2 C, and 6 C, a better fit to the experimental data
was obtained with an additional mechanism, taking into account the critical fluctuationsof the orientational order (CF) in addition to the R and SD. The correlation time  CF andthe strength of the interaction ACF were found to increase on approaching the transition
from above. The observed behavior of all these parameters (with respect to frequency andtemperature) is very much comparable to the earlier observations reported in typical bulk
LC samples. The fitted experimental data at 10 C and 0.6 C away from TNI are shown in328

M. Rajeswari et al.
(b)

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(a)

(c)

Figure 4. (color online) Frequency dispersion of the proton spin–lattice relaxation rate R1 of PPA at
DTNI ¼ 10 C: in the bulk (a), Sample A (b), and Sample B (c). The solid line represents the calculated
total relaxation rate obtained by fitting the experimental data to the theoretical models explained in
Section 3. The dashed (color lines) lines represent the corresponding relaxation mechanisms. The fit
parameters are given in Table 1.

Figures 4 and 5, respectively, and the associated parameters at different temperatures arepresented in Table 1.
The relative increase in the relaxation rate in the confined systems (particularly in the
low-frequency region) can be consistently explained by invoking the RMTD mechanism,and the corresponding dispersion data were fitted by including this process also. The
analysis clearly indicates the dominant role of RMTD below 1 MHz. It exhibits acharacteristic power law frequency dependence between the two cut-off regimes,(R1)RMTD / !p, with p ¼ 0.34  0.05, which is different from the other reported confinedsystems [27,28]. The deviation of p from its equi-partition value (0.5) signals the important
contribution of low wavelength diffusion modes in this phase of the system. It may be
noted that our recent work on 8OCB confined to identical environment also yieldedalmost the same value of p within errors of estimation [15]. It appears that practically
identical confining environment provided for two different LCs is leading to a very similar
distribution of diffusive modes, thereby clearly alluding to the strong possibility that theobserved power law is essentially arising from the underlying structure factor of the(random) porous surfaces. Changes in the cut-off frequencies of the RMTD mechanism

Phase Transitions
(b)

(a)

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329

(c)

Figure 5. (color online) Frequency dispersion of the proton spin–lattice relaxation rate R1 of PPA at
DTNI ¼ 0.6 C: in the bulk (a), Sample A (b), and Sample B (c). The solid line represents thecalculated total relaxation rate obtained by fitting the experimental data to the theoretical models
explained in Section 3. The dashed (color lines) lines represent the corresponding relaxation
mechanisms. The fit parameters are given in Table 1.

with the decrease in temperature are manifestations of the decrease in the diffusion
coefficient on cooling, and are in turn associated with the largest and smallest moleculardisplacements near the surface (lmax and lmin) that could cause significant loss in thecorrelation of molecular orientations. The experimental data on PPA report rather anominal change in lmin, steadily increasing from about 1.5 nm to 2 nm over 15 C(Figure 6). In comparison, in the case of 8OCB, for a similar variation of temperature
above its TNI value, it is observed that lmin is comparable (1.5 nm) at DTNI ¼ 15 C, but
increases to about 9 nm very close to TNI. Further, its variation with temperature in 8OCB
appears to approximate to a power law, unlike PPA. This contrasting variation of lmin inthese two LC systems, with a confining matrix having very similar structure factor (i.e.,very close p values), brings about an interesting point for discussion. The larger value oflmin near the transition, and its apparent pre-transitional behavior, in the case of 8OCB are
indicative of the presence of significant ordering near the surface, relative to PPA [15].
In addition, this length scale is fairly insensitive to temperature in the present system.
Taking into account the fact that both the systems seem to need RMTD mechanism forinterpretation of their data in the isotropic phase (thus confirming observable adsorption

–

–

–

!RMTDmin/2 kHz!RMTDmax/2 MHz

P

15
1.22
(0.03)
2.16(0.06)

10
12.5
0.94
(0.04)
2.27(0.14)
7(0.08)
57.2(4.41)

6
10

Bulk PPA

Note: Error estimates are given in parentheses.

–

18
1.20
(0.02)
1.71(0.01)

15

ARMTD 102 s(1þp)

 CF/OPF 109 s

ACF 103 s3/2

 R 109 s

D 1011 m2 s1
AR 109 s2

DTNI ( C)
AD 108 s2

Sample10.5
0.8(0.01)
3.0(0.1)
11(0.47)
68.1(1.82)

2
9.6
0.54(0.02)
3.4(0.23)
18(0.75)
75.3(3.37)

0.6

20(1.19)
49
(5.6)

0.32

1.24
(0.22)

15
18.5
(3.8)
18
1.2

18.1
(1.37)
40
(4.8)

0.42

1.97
(0.01)

10
15
(2.9)
15
1.22

0.49
(0.01)
16.9(1.28)
30(3.79)
0.34(0.04)

57.2

2.19(0.11)
7

6
13.9
(1)
12.5
0.94

Sample A

15.46(1.46)
20
(3.1)

0.56

68.1

3.26
(0.03)
11

2
10(0.78)
10.5
0.8

15.24
(1.58)
17(2.89)

0.57

75.3

3.72
(0.09)
18

0.6
9.2
(0.3)
9.6
0.54

20
(1.19)
49
(5.6)

0.72

1.29
(0.01)

15
18
(2)
18
1.2

Table 1. Best fit parameters in the bulk and confined PPA at two different concentrations in the isotropic phase.

Downloaded by [Tata Institute of Fundamental Research] at 05:29 25 April 201218
(1.37)
40
(4.8)

0.83

2.2
(0.1)

10
13.2
(1.1)
15
1.22

0.86
(0.01)
17(1.28)
30(3.79)
0.34(0.04)

57.2

2.27(0.06)
7

6
12.9
(0.2)
12.5
0.94

Sample B

16(1.46)
20
(3.1)

1.07

68.1

3.27
(0.1)
11

2
9.4
(0.5)
10.5
0.8

15.2
(1.58)
17(2.89)

1.13

75.3

3.49
(0.09)
18

0.6
9
(0.3)
9.6
0.54

330
M. Rajeswari et al.

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Phase Transitions

331

Figure 6. Variation of lmin with the temperature in the isotropic phase.

effects in both the cases), we attribute this dissimilar behavior with respect to lmin to thedifference in the orientations of the dipoles on the two molecules vis-à-vis the aligning
direction preferred by the local structure due to the anchoring interactions. The strength of
this interaction ARMTD shows an Arrhenius behavior with temperature in both the LCs,
the associated activation energy with this process being about 35 kJ mole1 for both thesamples. This seems to provide another pointer to the qualitative difference in the surface
interactions of the two LC systems.

4.2. Nematic phase
The dispersion profiles in the nematic phase of PPA in bulk as well as in confined samples
are discussed in this section, focusing first on the nematic phase, very near to the transition
temperature (DTNI ¼ T  TNI ¼ 1 C), where order parameter fluctuations are known
to provide the dominant mechanism for relaxation in the bulk samples (Figure 7).
By analyzing the data based on this mechanism [19], the characteristic time associated withthese fluctuations  OPF is estimated to be about 134 ns. The effect of confinement at thistemperature, relative to the bulk sample, is interesting. There is practically no change in  R
due to confinement in PPA remaining at about 3 ns, while it changes from 8.14 to 5.4 ns in
8OCB.This observation seems to be interestingly correlated to the exponent p in the powerlaw governing the frequency dependence between the corresponding frequency limits,!RMTDmin and !RMTDmax. The exponent in the nematic phase of the confined PPA systemremains the same (at 0.34) as in the isotropic phase for PPA, while it shows a perceptible
increase in the confined 8OCB on the onset of the nematic phase (from 0.39 in the isotropic
phase to 0.45 just below the transition). Common to 8OCB and PPA is the observationthat progressive confinement (i.e., from Sample A to Sample B) leads in both the systems,
an increased coupling to the lattice via the RMTD mechanism (namely, ARMTD increases
with network density in these samples) [31].
We now discuss the results of our analysis at three temperatures deep in the nematic
phase (DTNI ¼ 3 C, 7 C, and 10 C). In the bulk sample (Table 2),  R decreases
progressively on cooling due to the gradual increase in the orientational order in thesample. Within the frequency range of the experiment, no leveling of the relaxation rate

332

M. Rajeswari et al.

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(a)

(b)

(c)

Figure 7. (Color online) Frequency dispersion of the proton spin–lattice relaxation rate R1 of PPA
at DTNI ¼ 1 C: in the bulk (a), Sample A (b), and Sample B (c). The solid line represents thecalculated total relaxation rate obtained by fitting the experimental data to the theoretical models
explained in Section 3. The dashed (color lines) lines represent the corresponding relaxation
mechanisms. The fit parameters are given in Table 2.

(i.e., reaching a plateau) at low-frequency end could be observed, indicating that !ODFminshould be significantly below the lowest frequency studied. AODF, representing thecoupling of the spin system to the lattice via ODF, marginally increases initially on coolingand saturates at DTNI ¼ 10 C (Table 2).
Effect due to confinement on the dynamic parameters of the PPA at these temperaturesof the nematic phase is summarized in Table 2, and Figure 8 shows the contribution ofdifferent relaxation mechanisms at DTNI ¼ 7 C. One immediate discernible effect ofconfinement is the significant increase of !ODFmin to the range of MHz. The confinement
due to the aerosil 3-D network seems to be placing a severe restriction on the longwavelength ODF modes, pushing the value of the corresponding cut-off frequency by anorder of magnitude. This circumstance leaves room for other slow mechanisms, like
RMTD, to play their visible role at much lower frequencies. An interesting consequence ofconfinement on PPA system is that the exponent p changes from 0.34 (within the vicinityof the transition DTNI ¼ 1 C) to 0.63. This is of course an indication of the qualitativechanges in the effective structure factor probed by the diffusing molecules, signaling achange, on cooling, to a regime where long wavelength diffusive modes are more probable.

–
–

–

!RMTDmin/2 kHz!RMTDmax/2 MHz

P

100

6.49
(0.04)
1

6.8
0.38(0.01)
3.23(0.16)

100

6.98(0.03)
1

5.5
0.5(0.04)
2.52(0.04)

Note: Error estimates are given in parentheses.

–

8.2
0.26
(0.07)
3.03(0.59)
23.9(2.11)
134.1(11.22)!ODFmax/2 MHz
ARMTD 102 s(1þp)!ODFmin/2 kHz

AODF 103 s3/2

 OPF 109 s

AOPF 103 s3/2

 R 109 s

D 1011 m2/s
AR 109 s2

7
5

3
10

DTNI ( C)
AD 108 s2

1
10Bulk PPA

Sample100

6.98(0.04)
1

4.6
0.56(0.03)
2.23(0.16)

10
4

0.6(0.01)
13
15
(0.6)
0.34
(0.05)

134.1

26.2

2.98

1
9.1
(0.4)
8.2
0.26

913.7
(200.2)100
159.1(21.77)1
8.43(0.69)
0.6(0.01)

6.49

3.23

3
17.1
(0.1)
6.8
0.38

900
(183.2)
100
284.6(21.11)1
6.35(0.46)
0.63(0.006)

6.98

2.52

7
11.7
(0.08)
5.5
0.5

Sample A

1114(116.9)100
301(1.77)
1
6.82(0.31)
0.63(0.01)

6.98

2.23

10
9.9
(0.1)
4.6
0.56

1.18
(0.02)
13
15
(0.6)
0.34
(0.05)

134.1

24.98

2.95

1
9.1
(0.4)
8.2
0.26

Table 2. Best fit parameters in the bulk and confined PPA at two different concentrations in the nematic phase.

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900
(203.5)100
161(0.89)
1
13
(1.2)
0.6
(0.01)

6.49

3.23

3
19
(0.1)
6.8
0.38

2676.1(314.6)100548(3.72)
1
6
(0.6)
0.65
(0.01)

6.98

2.52

7
14.5
(0.02)
5.5
0.5

Sample B

2714(224.1)
100
669.8
(4)
1
6.5
(0.5)
0.66
(0.02)

6.98

2.23

10
12.4
(0.1)
4.6
0.56

Phase Transitions
333

334

M. Rajeswari et al.

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(a)

(b)

(c)

Figure 8. (Color online) Frequency dispersion of the proton spin–lattice relaxation rate R1 of PPA
at DTNI ¼ 7 C: in the bulk (a), Sample A (b), and Sample B (c). The solid line represents thecalculated total relaxation rate obtained by fitting the experimental data to the theoretical models
explained in Section 3. The dashed (color lines) lines represent the corresponding relaxation
mechanisms. The fit parameters are given in Table 2.

A similar change was observed in the case of 8OCB on confinement (p ¼ 0.58) [31], and inother such systems. In the case of CPG matrix, however, with confining lengths in therange of 15 nm, the distinguishing features of the phase transition were smeared out andthe exponent was observed to increase continuously [28]. In this case, the exponent
however increases marginally in the deep nematic phase. The difference between these twocases suggests that the exponent value in the present system is limited by pore size. Finally,
the progressive onset of the orientational order on cooling into the nematic phase has
profound effect in the confined samples. The effect, for example, on !ODFmin and ARMTD
is seen in both the samples (A and B), correspondingly more in Sample B.

5. Conclusions
We present the frequency dispersions of spin–lattice relaxation rates at various
temperatures covering the isotropic and nematic phases of LC PPA, and compare theresults obtained in the bulk sample with two confined systems with different average poresizes. In the isotropic phase, PPA exhibits pre-transitional effects on the relaxation profiles

Downloaded by [Tata Institute of Fundamental Research] at 05:29 25 April 2012

Phase Transitions

335

within a range of about 6–7 C above TNI, like in the case of a typical LC. Surface
interactions of the LC medium as a result of confinement induce RMTD mechanism,
which provides an insight into the surface topology (in terms of its orientational structure
factor) and adsorption kinetics (!RMTD cut-off values). We find that the exponent
p obtained from confined PPA samples is lower than the equi-partition value (0.5), and isessentially the same as was reported by 8OCB under essentially identical random
environment. The observed value (0.34–0.38) is indicative of the relative abundance of
low-wavelength diffusion modes, reflecting the nature of the surface formed by the 3-D
network of the chosen aerosil particles. Temperature variation of lmin in the isotropic
phase of PPA is compared with confined 8OCB. The observed qualitative difference seems
to be related to the difference in the direction of the dipoles located on the two molecules(relative to the respective long axis) and hence the observed differing sensitivity todecoherence effects on diffusion. The effect of increasing orientational order on coolingthe nematic PPA, and confinement related effects at each of the temperatures in this phase,are qualitatively analyzed. The lower cut-off frequency of the ODF mechanism is observed
to shift to higher frequencies, yielding to RMTD mechanism to play a dominant role at
low frequencies even in this phase. This mechanism has been observed to be more effectivein the nematic phase (by an order of magnitude) relative to its isotropic phase.

Acknowledgments
M. Rajeswari would like to thank the University Grants Commission (UGC), New Delhi, forproviding financial support under the RFSMS scheme.

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