Chapter 3

Relaxation dynamics of orientationally disordered plastic crystals: Effect of dopants

Sometimes exceptional properties of some of the aromatic compounds are intimately

associated with the disorder or short-range order in them, i. e. their nanoscale structure. 1

Quantification of disorder in such materials may aid in the design of new functional molecular

materials. Hexasubstituted benzenes which belong to this class of materials have, thus, been

subjected to in depth study using x-ray scattering,2-9 solid-state NMR3,4,10 and dielectric

spectroscopy.11-13 In addition some of these materials have some practical applications, for

example in agriculture as a fungicide. 14 However, recently there is a growing interest among

researchers working on the glass transition phenomenon, to study the nature of the frozen

orientational disorder in these materials. 15- 17

Glass transition phenomena occur when a dynamically disordered system (e. g. liquid,

plastic crystal or paramagnet) freezes as a function of external temperature (or pressure)

devoid of long range order. In this freezing process, one or more degrees of freedom of

atoms or molecules continuously slow down, reaching the so-called glass transition. when

their dynamics has a characteristic time, generally chosen to be 102 sec. 18- 21 Since in the

liquid phase there are basically translational and orientational disorders of molecules, the

70

glass transition of canonical glass formers is associated with the freezing of these two de­

grees of freedom completely. But a mesophase can exist between the completely ordered

crystalline phase and the translationally and orientationally disordered liquid phase, the so

called plastic crystalline phase or orientationally disordered (OD) phase. 22- 31 In the plastic

phase, the centers of mass of the molecules have spatial long range order, forming a lattice

which generally has high symmetry (such as cubic, quasi-cubic or rhombohedra132) but only

short-range order with respect to the orientational degrees of freedom. It is well known that

the relaxation characteristics in supercooled plastically crystalline (PC) phase are very simi­

lar to that of supercooled liquids. 22,30,31,33-37 The main relaxation process (also called as the

a-process) in supercooled PC phase is found to be non-Debye in frequency dependence and

non-Arrhenius in temperature (T)-dependence with a step-like change in the specific heat

(Cp ) at the so-called glass transition temperature (Tg ).38-42 Therefore, a clear understand­

ing of the molecular relaxation in these substances, where only the orientational degrees of

freedom are involved, is considered to be important to understand the glass transition phe­

nomena in general. Among compounds forming orientational glasses, the hexa-substituted

benzenes exhibit molecular relaxation in the crystalline phase where the molecular rotation

is hindered43 to varying degrees,11-13 that is, free rotation of the molecules as in the true

liquid phase is not possible, and, hence the molecules exhibit limited rotational mobility.13,43

Most of the measurements3,4,9,10,12,13 reported so far measured dielectric relaxation over a

narrow frequency range, and the T -dependence of the relaxation rates is not very clear.

These substances also are attractive to the researchers of glass physics, as they are com­

posed of "rigid" non-H-bonded molE)cular systems and appear to lack a secondary (or (3-)

relaxation process,22 hitherto thought of as a characteristic feature of glass transition. A

recent study17 of the relaxation of one of these substances viz. pentachloronitrobenzene

(PCNB) indicated that the dielectric strength is very sensitive to the presence of dopants l

whereas this effect is not expected in a liquid glass. A recent report2 on the structure of

71

PCNB, reiterates its structure to be rhombohedral with equal probability of finding the

molecule in anyone of the six possible orientations. It is noted that such a distortion the

PCNB molecules must be very uncomfortable in the average structural geometry,2 the sys­

tem surprisingly chooses to pack this way rather than find an energy minimum defining a

different crystal structure. Therefore a critical examination of the effect of wide variety of

dopants on the dielectric relaxation in PCNB and other such systems is needed to find out

whether this phenomenon is of general occurrence or specific only to PCNB because of its

uncomfortable structural geometry. For this purpose, we have decided to study some "rigid"

non-H-bonded molecular systems with a wide variety of dopants. Here we report the results

of our measurements of dielectric relaxation and differential scanning calorimetry (DSC)

studies on these systems over a wide range of temperatures.

3.1: Experiment

The samples used in the study are pentachloronitrobenzene (PCNB), cyanoadamantane

(CNADM), chloroadamantane (CLADM), 1,2,3-trichlorobenzene (TCB) (all with the spec­

ified purity of ~ 99 %), and pentachlqrobenzene (PCB) (purity> 98 %) are obtained from

Aldrich Co., USA. The other samples studied here are: 1,2-dichloro-3,4,5,6-tetramethylbenzene

(DCTMB), its deuterated sample DCTMB-d12 , 1,2,3-trichloro-4,5,6-trimethylbenzene (TCTMB),

its deuterated sample TCTMB-dg and 1,2,3-trichlorobenzene (TCB). These four compounds

were synthesized by direct chlorination of the corresponding hydrocarbons and purified by

successive crystallization.3,4

The DSC measurements are performed using Perkin-Elmer Sapphire DSC equipped with

a quench cooling accessory. The DSC cell was calibrated for temperature using indium

(melting transition = 429.75 K) and cyclohexane (solid-solid transition = 186.09 K) as

standards. For the dielectric measurements, an HP 4284A precision LCR meter in the

72

frequency range of 20 Hz - 1 MHz is used. For frequencies in the range 20 Hz - 10-3 Hz,

we have sampled the dielectric absorption currents in the time window of 0.01 - 1000 secs.,

using a digital storage oscilloscope (DSO) card DSO-2200 (Link Instruments Inc. USA),

in combination with a Keithley Model No. 617 Programmable Electrometer. The complex

permittivity was calculated by taking Discrete Fourier Transform (DFT) of the discharging

current. But because of a limitation, set by the resolution of the DSO card in this type

of measurement, we are not able to determine the complete spectral characteristic at the

lower frequencies. However, the fm values measured with the help of this technique are

comparable as good as those measured by the LCR bridge. The sample PCNB was studied

using a concentric cylindrical capacitor whose empty cell capacitance, Co is about 214 pF and

the sample is melted in vacuum to fill the capacitor plates. While the sample CNADM was

studied using a cylindrical capacitor with an empty cell capacitance Co of ~ 20 pf and is filled

by the molten sample (in vacuum). Because of the method used in filling the capacitor there

may be an uncertainty of about 10 % in the absolute values of the dielectric parameters

which however will not alter the general inferences. In all the other cases because of the

constraints on the sample size, a disk of 2.5 cm in diameter and of about 0.1 cm in thickness

is made out of the sample by pressing the sample in a pressure die at a pressure of 10 kbar.

Two electrodes are made independently from silver powder pressed at the same pressure.

The sample disk is then pressed between the silver pallets at the same pressure to make the

capacitor. This capacitor is held between two chromium-plated electrodes with the aid of

light weight spring. The sample temperature is measured with the help of a thermocouple

kept deep inside the bottom electrode. The temperature of the assembly is then controlled

in the same way as before. For further details of the experimental setup and for accuracy in

the measurements the reader may consult earlier chapter 2.

73

3.2: Results

Among the materials chosen to be added as dopants, both TCB [Tm (melting temperature)

= 326.3 K, ~Hm(enthalpy of melting) = 3,3 kJ/mol)] and PCB (Tm = 358.5 K, ~Hm =

4.89 kJ/mol) are rigid rotator phase crystalline solids, whereas CLADM (Tm = 439.8 K,

but ~Hm could not be measured with certainty) crystallizes to a rotator phase solid which

undergoes a 1st order transition to rigi<.i rotator phase at a temperature of 245.4 K with an

associated enthalpy (~H) of 4.05 kJ/moL The reason for choosing these materials is that

because of their high melting and boiling temperatures, they can readily be mixed with the

samples under study in their molten state without the problem of evaporation.

3.2.1: Effect of dopants on the dielectric behavior of peNB

The first order transition temperatures and the associated enthalpies15 are; for PCNB,

Tm = 417.2 K, ~Hm = 18.55 kJ/mol, Tl (solid-solid transition) . 413.4 K, ~H = 0.57

kJ/mol. According to an earlier report,8 the solid phase for Tl < T < Tm (designated as Sf)

is triclinic in structure and is a rotator phase solid; and that for T < Tl designated as SII is

rhombohedral which is also a rotator (plastic) phase crystalline.7,8 This plastic phase exhibits

a well defined dielectric relaxation similar to the so called a- (or primary) relaxation process

found in supercooled liquids & plastic phases and exhibits a well defined glass transition

in specific heat data at a temperature of 201 K. 15,16 The spectral dependence of the a-

relaxation in PCNB was reported previously.15 We have analyzed the relaxation data using

the Havriliak-Negami (HN) shape function44 (eq. 1.46). The temperature dependence of

peak loss frequency Um) is then calculated from the parameters of eq. 1.4645 The peakloss

frequency Um) is analyzed with the critical power law15,46 eq. 1.59. Alternatively, the data

can also be described equally well by the Vogel-Fulcher-Tammann equation47 (eq. 1.58). Eq . . 1.58 reduces to the Arrhenius equation,48 for To = 0 [eq. 1.42]. Since the deviation of 1m values from eq. 1.42 are not strong in some of the substances ofthis group, we have analyzed

74

3.5

o

2.5

2.0

2

-0.5

-1.0

= w C) -1.5 0

-2.0

-2.5 .."

2

• PCNB-Pure, T = 281.7 K o PCNB-PCB, xm = 0.003, T = 281.8 K & PCNB-PCB, xm = 0.007, T = 281.4 K 'iT PCNB-PCB, xm = 0.012, T = 281.7 K .." PCNB-TCB, xm = 0.024, T = 281.6 K c. PCNB-CLADM, xm = 0.012, T = 281.4 K ® PCNB-DCTMB, xm = 0.010, T = 281.8 K

3 4

log f (Hz)

• PCNB-Pure, T = 281.7 K o PCNB-PCB, xm = 0.903, T = 281.8 K & PCNB-PCB, xm = 0.007, T = 281.4 K 'iT PCNB-PCB, xm = 0.012, T = 281.7 K .." PCNB-TCB, xm = 0.024, T = 281.6 K t:. PCNB-CLADM, xm = 0.012, T = 281.4 K

, ® PCNB-DCTMB, x = 0.010, T = 281.8 K

3 4

log f (Hz)

•

5

5

6

6

Figure 3.1: Variation of (a) real and (b) imaginary parts of complex dielectric co~stant of a-relaxation with frequency at a fixed temperature of ~ 281.5 K, in peNB for various dopants (whose concentration is expressed as mole fraction Xm). The thick lines correspond to fits to eq. 1.46 as given in Table 3.1.

75

Table 3.1 : Details of a-process as described by Eq. 1.46 for samples shown in Figure 3.1.

Sample Temp UHN PHN fo(Hz) fm(Hz) M:

PCNB 281.8 0.075 0.684 6.12 x 102 0.86 x 103 1.22 PCNB-PCB 281.8 0.085 0.693 8.38 x 10": . 1.17 x 10

j 0.91 Xm = 0.003 PCNB-PCB 281.4 0.066 0.663 6.92 x 10": 0.99 x 10j 0.64 Xm = 0.007 PCNB-PCB 281.7 0.044 0.632 8.85 x 10": 1.30 x lO j 0.20 Xm= 0.012

PCNB-TCB 281.6 0.067 0.669 7.96 x 10": 1.13 x lOj

0.21 Xm = 0.024

PCNB-CLADM 281.4 0.098 0.724 9.37 x 102 1.26 X 103 0.43 Xm= 0.012

PCNB-DCTMB 281.8 0.080 0.666 9.36 x 102 1.35 x 103 0.65 Xm= 0.0101

the data in terms of both the equations viz. eq. 1.59 & 1.42. Addition of a small amount

of PCB, TCB, CLADM and DCTMB as dopant brings in a drastic drop in the relaxation

strength of PCNB (Figure 3.1). However, there is no appreciable change either in the shape

of the relaxation spectra (Figure 3.1, where the corresponding HN parameters are given in

Table 3.1) nor in the peak loss frequency (Figure 3.2).

We have exa~ined the D.E (EO - Eoo) of 0:- process of PCNB with PCB, TCB, CLADM

and DCTMB as dopants. In all cases D.E values of PCNB are lowered, interestingly even on

addition of other hexasubstituted benzene such as DCTMB. The amount of dopant to cause

the same amount of decrease varies with the nature of the dopant. For example, 1% mole

fraction of PCB which is a pentasubstituted benzene and hence asymmetric in shape, causes

a reduction in D.E value by about six times whereas the same mole fraction of DCTMB (a

more symmetric molecule) effects a reduction by a factor of two only. In order to understand

the actual phase behavior of the sample, we have closely monitored the dielectric behavior of

76

6

-N ::c 3 -

o

o PCNB (pure)

CJ PCNB - PCB, Xm = 0.0030

A PCNB - PCB, Xm = 0.0071

• PCNB - PCB, Xm = 0.0118

a PCNB - CLADM, Xm = 0.0114

® PCNB - CLADM, Xm = 0.0501

"fI PCNB -1,2,3-TCB, Xm = 0.024

.t. PCNB - 1,2,3-TCB, Xm = 0.0502

o PCNB - DCTMB, Xm = 0.0101

-3 ~--~--------~--------~---------r--------~----~--~ 3 4 5

1000/T(K)

Figure 3.2: Arrhenius plot of fm of a-relaxation of PCNB with various dopants (whose concentration is expressed as mole fraction Xm). The thick line corresponds to the PL equation (eq. 1.59) for the parameters: log fo,a(H z) = 4.92, r = 12.66, T~ = 166.7 K.

the sample during very slo~ heating, and the behavior is noted in small steps of temperature

variation. The corresponding T-variation of ~€ of the a-process is shown in Figure 3.3(a).

DSC measurements on these samples are plotted in Figure 3.3(b).

3.2.2: Effect of dopants on the dielectric behavior of other hexasubstituted ben-

zenes.

To test whether the phenomena found in PCNB in the presence of dopants is also present

among the other members in the group of hexasubstituted benzenes, we have examined two

samples viz. DCTMB & TCTMB and their deuterated samples in the presence of dopants.

The deuterated samples were originally synthesized for NMR3,4 and as such there is some

genuine interest in comparing the behaviour of the purely protonated to the deuterated

77

3.0...-----------------------rr---,

2.5

2.0

8 to) 1.5 <l

1.0

0.5

0.0

-0.5

:§ ~ -1.0 ~ 0 u: -ro Q)

J: -1.5

-2.0

(a)o PCNB(pure) o PCNB - PCB. x,., = 0.0030 11 PCNB - PCB. x", = 0.0071 • PCNB - PCB. Xm = 0.0118 a PCNB - CLAOM. Xm = 0.0114 <1> PCNB - CLADM. x", = 0.0501 Y PCNB - 1.2.3- TCB. Xm = 0.0240 • PCNB - 1.2.3- TCB. x", = 0.0502 o PCNB - DCTMB. Xm = 0.0101

8 88

Oe oe III ,g 0

D D

250

(b)PCNB (Pure)

PCNB-PCB, Xm - 0.01

PCNB-TCB, Xm = 0.02

PCNB-CLADM, Xm = 0.02

,

360 380

•

8 8 8 8 8 8 8 • 0IA 0 .0 II 0

II " A A

300 T (K) 350 400

~1 T r V"-i

y---l "\,/\ Or--

,

Tllq.

T (K) 400 420

Figure 3.3: Effect of the dopants upon behavior of PCNB. (a) The T- variation of t::,.€. The vertical dashed lines correspond to the temperatures Tl and Tm of the pure PCNB sample. (b) The DSC curves above room temperature up to the melting temperature for a heating rate of 2 deg./min. in some of the samples shown in (a). The curves are shifted vertically for the sake of clarity. (The sample size corresponding to the curves in the order from top to bottom are 11.72 mg., 11.66 mg., 14.12 mg., and 14.40 mg

78

0.0

-0.2

-0.4 -0> - -0.6 S '-"

3: -0.8 .Q LL +-' CO -1.0 Q)

::c -1.2

0 "0 c:

-1.4 W

-1.6

----- DCTMB

TCTMB -----

r----~-"'--=--==---==---:.:.:----- ..... I' ---..... Ttm ~ m

~~------------~--------------~~~ ..... I T2 T2 I " I '\ I ,I

,VI \ \ I \ I I I I I I I

.a.25

·0.30

.Ql ~ .a.35

T2 ~ ~ .a.40

m :1:.

.a.45

.a.50 150 200

150 200

250 T (K) 300 350

250 300 350

T (K)

400

400 450

I II II 1/ I

500

Figure 3.4: DSC curves for DCTMB (solid line, sample size 15.6 mg) and TCTMB (dotted line, sample size 16.2 mg) for a heating rate of 10 deg./min. The arrows indicates the various first order phase transition temperatures (see Table 3.2). Parts of the DSC curves are magnified in the inset to show the highly diffuse transitions ending at Tl and T2.

samples. By substituting protons for deuterons at the outer periphery of the molecule,

the moment of inertia of the molecules increases slightly, which may affect the relaxation

rate. Before taking the dielectric measurements, we have examined these samples for

the existence of various equilibrium and nonequilibrium phases using differential scanning

calorimetry (DSC). In Figure 3.4, we have shown the DSC scans of both the samples obtained

for a heating rate of lao/min, where the different transition temperatures are indicated by

vertical arrows. The details of various first order phase transition temperatures and the

associated enthalpies are given in Table 3.2. The values reported in Table 3.2 are an average

of four runs. To give some idea of the deviations of these transition temperatures from the

79

Table. 3.2: Details of various first order phase transition temperatures and associated enthalpies in DCTMB and TCTMB.

EnthalpyT Transition Temperature (~H)

Sample Nature of (K) kllmole transition •

Our work Literature Our work (Refs. 3, 4, 9)

SI~L Tm 472.5 466.2 13.19 1,2- DCTMB SII~ SI TJ 380.8 ± 2 383.0 1.21 (CIOH12 Ch) SIII~ SII T2 164.2 ± 2 170.0 0.11 , 1,2- DCTMB-d12 SI~L Tm 471.9 470.0 15.29

(CIOD12 Ch) SII~ SI TJ 379.6 ± 2 381.0 0.85 SIII~ SII T2 163.7 ± 2 170.0 0.10

1 ,2-DCTMB-TCB, SI~L Tm 470.4 13.66 Xm = 0.02 SII~ SI TJ 378.6 ± 2 -------------- 0.82

SIII~ SII T2 162.2 ± 2 0.26

1,2,3-TCTMB SI~L Tm 501.9 498.2,500 20.07 (C9 H9Ch) SII~ SI TJ 398.9 ± 2 401 ± 3 . 1.65

SIII~ SII T2 264.5 ± 2 260 ± 3 0.38 1,2,3-TCTMB-d9 SI~L Tm 501.9 17.80 (C9D9Ch) SII~ SI TJ 400.6 ± 2 -------------- 1.23

SIII~ SII T2 266.3 ± 2 0.23

1,2,3-TCTMB-TCB, SI~L Tm 500.2 15.34 Xm = 0.02 SII~ SI TJ 398.6 ± 2 -- .. ----------- 1.34

SIII~ SII T2 264.0 ± 2 0.18

• S: crystalline solid, L: liquid. t The ilH values associated with transitions at T 1 and T 2 are approximate based on the

assumption that they are 1 st order transitions.

data of others, we have also entered the corresponding values reported in the literature. We

have also examined the DSC curves in the glass transition (Tg) region of both the samples

used in this study but we could not find any clear evidence of step like change characteristic

of glass transition within the resolution of the DSC. The samples DCTMB and TCTMB

are rotator (plas~ic) phases at room temperature.3- 6,9,lO,13 The various phases present in

these samples do not supercool much, and readily undergo transition to the more ordered

80

0.5 (a) DCTMB 0231.92K .. 219.38 K v 209.44 K

0.0 " 199.32 K 6189.27 K • 180.02 K

-0.5 o 170.25 K • 162.95 K - 0154.98 K --- 0149.35 K -tA;)

-1.0 I!I 145.57 K 0> 6141.13 K .Q

" 135.05 K

-1.5

-2.0

-2.5 2 3 4 5 6 7

log f (Hz)

0.0 (b) TCTMB .. 244.51 K

v 235.11 K " 224.99 K

-0.5 6 216.48 K • 208.22 K o 200.81 K • 193.21 K

C -1.0 o 182.62 K -- D 177.32 K -tA;) III 170.20 K 0> 6 166.33 K 0

-1.5 '" 160.01 K

-2.0

-2.5 +---''--'---4.--r-----'---,----''----r---'----+--~-_l 2 3 4 5 6 7

log f (Hz)

Figure 3.5: Double logarithmic plot of E" vs. frequency for T :::; Tl of pure (a) DCTMB, (b) TCTMB, at different. temperatures. The thick line corresponds to the HN parameters shown in Table 3.3.

81

Table 3.3. Details of HN-parameters for samples shown in Figure 3.5.

Samples T(K) aHN ~HN fo (Hz) fm (Hz) 8S

170.3 0.288 1.00 5.70 x 102 6.92 X 102 5.40 180.0 0.223 0.910 2.79 x 103 3.10 X 103 5.46 189.3 0.193 0.878 7.96 x 103 9.14 X 103 5.45

1,2-DCTMB 199.3 0.156 0.825 2.21 x 104 2.68 X 104 5.43 (T2 < T < T1) 209.4 0.129 0.784 6.15 x 104 7.78 X 104 5.43

(SII) 219.4 0.102 0.717 1.58 x 105 2.15 X 105 5.49 231.9 0.076 0.631 3.91 x 105 5.88 x 105 5.68

193.2 0.223 0.703 9.95 x 102 1.48 X 103 0.69 200.8 0.279 0.859 3.98 x 103 4.80 x 103 0.91

1,2,3-TCTMB 208.2 0.190 0.742 1.86 x 104 1.09 X 104 1.08 (T < T2) 216.5 0.150 0.689 2.42 x 104 3.51 X 104 1.32 (Sm) 225.0 0.120 0.611 5.71 x 104 9.12 X 104 1.56

235.1 0.122 0.598 1.57 x 105 2.57 X 105 1.81 244.5 0.116 0.557 3.57 x 105 6.22 X 105 2.13

states. The dielectric measurements are made on the compressed sample (in the form of

pellet) because of the problem in filling a cylindrical capacitor associated with the high

melting temperature and subsequent sublimation. However, this method gives less reliable

values for the empty cell capacitance Co and hence the corresponding dielectric parameters

estimated using this Co are approximate. Only one large dispersion is found in these samples

at temperatures above 77 K which is shown in Figure 3.5. It may be identified as (X-- process

of the plastic phase and there is no evidence of the {3- process in the sub-Tg region (or may

exist below our experimental resolution). We have analyzed the relaxation data using the

Havriliak-Negami (HN) shape function (eq. 1.46) which is' also demonstrated in Figure 3.5,

and the corresponding parameters are given in Table 3.3. In contrast to the observations ,

of Brot and Darmon9 (on pure samples of DCTMB & TCTMB), a clear deviation from

the Debye behaviour is seen in all the cases studied here and the spectral shape is clearly

82

non-Debye in nature. However, our fm and ~E values more or less are in agreement with

those reported by Brot and Darmon.9'

The temperature dependence of the relaxation rate corresponding to the primary (a-)

relaxation process is examined. The Arrhenius plots of the a-process are shown in Figure

3.6. In all these cases we could not measure the dielectric loss accurately on the lower

frequency range (for frequencies less than 100 Hz) due to the presence of noise. The solid

lines given in Figure 3.6 are the critical power law fits derived from eq. 1.59 and are not

distinguishable from an Arrhenius fit (eq. 1.42) for the ran,ge of fm values shown in the

figure for a given phase. From the Arrhenius plot, we have found in all cases a slight

shift in the T - dependence of fm value at the transition temperature T2 , which corresponds

to the SIII-tSII phase present in these samples (see inset of Figure 3.6). The solid lines

therein are the Arrhenius fits [eq. 1.42] for the temperature range T2 :::; T :::; Tl and T

< T2 respectively. These fitting parameters are given in Table 3.4. From Figure 3.6 &

Table 3.4, it appears that the T-dependence of the relaxation rate is Arrhenius, but a slight

deviation is seen on the lower temperature side which needs to be probed further. Shown

in Figure 3.7 is the frequency variation of the real and imaginary parts of the dielectric

constant of DCTMB with added dopant TCB. Note that the reduction in dielectric strength

(~E) of a-process is not as pronounced as in the case of PCNB. The relaxation can well be

described by HN fit the details of which are given in Table 3.5. Presence of small amounts

of TCB (xm :::; 0.02) has no detectable effect on the relaxation in the either protonated

or deuterated TCTMB samples, and the results are similar to those shown in Depicted

in Figure 3.8 is the temperature variation of dielectric strength (~E) of a-process in (a)

DCTMB, DCTMB-d12 and DCTMB-TCB with Xm = 0.02 & 0.05; (b) TCTMB, TCTMB­

d12 and TCTMB-TCB, Xm = 0.02. From this plot, a change in the T-dependence of the

~E value at the transition temperatures, Tl and T2, is observed. Thus as we decrease the

temperature below T2 , the dieleCtric strength (~E) decreases continuously in all cases, which

83

6

N

5 e. .! ~

- 4 N :c -_E 5.' 5.1 6.0 6.3 6.6 6.9

Ol 3 1000fT(K)

.Q

2 • DCTMB o DCTMB-d12 v DCTMB-TCB, Xm = 0.02

,

® DCTMB-TCB, Xm = 0.05

0 4 5 6 7 8

10001T(K) .7

6,90

6.60

6 N e. 6.30

T2 _E

~ 5 6.00

-N 5.10 :c -_E 4 3.1 3 .• 3.9 '.0 '.1 Ol 1000fT (K) .Q

3

ATCTMB

2 eTCTMB-d 9

/)" TCTMB-TCB, X = 0.02 m

4 5 6 7 8

10001T(K)

Figure 3.6: Arrhenius plots for (a) DCTMB, DCTMB-d12 and DCTMB - TCB (Xm = 0.02) (b) TCTMB, TCTMB-dg, TCTMB - TCB (xm = 0.02). The thick line corresponds to PL equation (eqn. 1.59) for the parameters: log 10,0: (Hz") = 2.37, r = 12. 73, T~ = 81.3 K for pure DCTMB, and log 10,0: (Hz) = 3.81, r = 13.14, T~ = 101.6 K for pure TCTMB. Also shown in the inset of both (a) & (b), are the expended portion of the Arrhenius curve to show the diffuse discontinuity of 1m at transition T2, where the thick lines correspond to Arrhenius - fit (see Table 3.4).

84

Table 3.4. Details bf a-process for samples shown in Figure 3.6.

HN parameters

Sample Range of temp UHN

(K) 1,2-DCTMB 152-248 0.312-

0.072 1,2-DCTMB-d12 150-244 0.327-

0.079 1,2-DCTMB-TCB, 150-245 0.325-

Xm = 0.02 0.l06

1,2,3-TCTMB T 177-263 0.280-0.001

1,2,3-TCTMB-d9 t 179-258 0.352-0.068

1,2,3-TCTMB-TCB T 175-261 0.332-Xm = 0.02 0.002

* The parameters for T < T 2 are approximate. t The parameters for T > T 2 are approximate.

~HN

1.00-0.64 1.00-0.428 l.00-0.733

0.859-0.427 1.00-0.438

l.00-0.564

Arrhenius parameters

T2<T<TJ T<T2 log fo(Hz) E log fo(Hz)

JkJ/moll 13.85 .35.91 12.74

13.96 35.85 1l.84

14.32 37.01 12.14

14.89 42.52 15.38

14.94 43.51 15.20

15.28 44.56 15.45

E (kJ/mol) 32.40

29.03

30.36

45.00

44.77

45.l9

suggests a progressive antiparallel ordering of mole~"ular dipoles in the crystal. According to . I

Brot & Darmon,9 the more polar the compound, the'higher the ordering temperature. It is

felt that a comparison of spectral-half width (i.e. the band-width at half of the maximum

loss) of different hexasubstituted benzenes may be of some use to relate the departure from

Arrhenius behaviour with the spectral half width, and hence, they are shown at different

temperatures in Figure 3.9.

3.2.3: Effect of dopants on the dielectric behavior of cyanoadamantane.

This material (CNADM), because of its large dipole moment J1, = 3.83 D, is one of the

most widely studied materials in its supercooled plastic crystalline state using dielectric

relaxation technique. 16,32,49-52 The first order transition temperatures and the associated

enthalpies32 are: Tm (melting temperature) = 458 K, (.6.H = 15 kJ/mol), Tl (solid-solid

transition) = 280 K, (.6.H = 5.5 kJ Imol). According to an earlier report,53 the solid phase

85

9 (a)

8

7

C 6 -·w

5

4

3

0.5 (b)

0.0

·w g> -0.5

-1.0

2

• Xm = 0.00, T = 190.2 K • Xm = 0.02, T = 190.7 K ... Xm = 0.05, T = 190.3 K

2 3

3

4

log f (Hz)

• xm = 0.00, T = 190.2 K • Xm = 0.02, T = 190.7 K ... Xm = 0.05, T = 190.3 K

4

log f (Hz)

DCTMB-TCB

5 6

DCTMB·TCB

5 6

Figure 3.7: Variation of real and imaginary parts of relaxation in DCTMB at a fixed temperature for various concentra.tions of the dopant TCB. The thick line corresponds to eq. 1.46, the details of which are given in Table 3.5.

86

Table 3.5: Details of a-process as described by Eq. 1.46 for samples shown in Figure 3.7.

Sample Temp (lHN ~HN fo (Hz) fm(Hz) At

DCTMB 190.2 0.167 0.831 1.27 x 104 1.54 X 104 5.82

DCTMB-TCB 190.7 0.148 0.815 1.92 x 10'+ 2.35 X 10" 5.69 Xm = 0.02 DCTMB-TCB 190.3 0.226 0.999 2.43 x 10'+ 2.44 X 10'+ 4.04 Xm= 0.05

stable for T1 < T < Tm designated as S1 is a face centered cubic with a = 9.81 AO (at 293 K),

and is a rotator phase solid; and the stable phase for T < T1 designated as S II is monocliniv with a = 11.278 AO, b = 6.874 AO, c = 12.092 AO and the ahgle j3 = 101°37' (at 240 K) is

a (dielectrically) rigid rotator phase. The 81 phase can be supercooled which exhibits53,54

a glass transition temperature Tg at 170 ± 3 K and associated with this transition is a

well defined dielectric relaxation above Tg which is similar to the a-(or primary) relaxation

process found in PCNB described in the previous sections. This a-relaxation in the presence

of a dopant is, the subject Qf study here.

The spectral dependence of the dielectric constant and loss are shown in Figure 3.10 for three

concentrations of PCB as dopant. The spectral dependence of the dielectric constant and

loss can be reasonably described by eq. 1.46 and the corresponding parameters are given in

Table 3.6. Although this reduction in ~E value on addition of PCB is not as pronounced as in

the case of PCNB discussed in section 3.2.1, still the ~E value decreases by a factor of about

2 for a small addition of about 5 % mole fraction of PCB with some change in relaxation

rate. Depicted in Figure 3.11 is the variation of the b.E value during cooling and subsequent

heating. These CNADM samples with PCB demonstrate considerable supercooling, which

on subsequent heating crystallize partially to S II phase that melts at T1 (as shown in the

corresponding D8C curves) on further heating. However, during cooling or heating cycles

87

6 (a)

5

4

--E-< '-" 3 tI)

<::I

2 T2 Tl

• DCTMB o DCTMB-d12 I!. DCTMB-TCB. xm = 0.02 ® DCTMB-TCB. x~ = 0.05

0 T

150 200 250 300 350 400 T (K)

5~------------------------------~----------------~ (b~ TCTMB

o TCTMB-dg

4 I!. TCTMB-TCB. xm = 0.02

2

200 250 300 350 400

T (K).

Figure 3.8: T- variation of total dielectric strength (.6.E) for the samples shown in Tables 3.4 & 3.5 (and Figures 3.5 & 3.7J. (For the purpose of calculation of AE·= EO -'Eoo • the too from the high frequency limit of a-process is extrapolated linearly towards higher temperatures). Also indicated are the different transition temperatures (shown by arrows at Tl and T2) as obtained from DSC experiment (Figure 3.4) and Table 3.2.

88

2.3~---------------------------.------------------~

- 2.1 ~ --.r:::. ..... "0 .~ -CO 1.9 :c ~ U Q) 0.

C/) 1.7 ... DCTMB \l DCTMB-dg

• TCTMB o TCTMB-d12

a PCNB

150 200 250 300 350

T (K)

Figure 3.9: Variation of spectral half-width with temperature in the pure samples of hexasubstituted benzenes.

we have noticed some amount of change in the magnitude of 1m value as shown in Figure

3.12.

3.3: Discussion

For the sake of convenience, the results are discussed under the following sections.

3.3.1: Dielectric spectra and thermal behavior of neat samples.

It is observed that the behaviour of the deuterated samples is essentially the same as those

of the isotopically normal compound, and hence, what ever inferences we make for the neat

samples is also valid for the deuterated samples, unless specified otherwise. The normal and

deuterated samples of DCTMB, TCTMB show very diffuse transitions below Tm , especially

the one at Tl that is spread,out by about fifty degrees (Figure 3.4). The dielectric relaxation

89

7 (a) CNADM·PCB • xm = 0.00, T = 234.7 K • Xm = 0.02, T = 234.2 K • Xm = 0.05, T = 234.8 K

2 3 4 5 6

log f (Hz)

O,5~------------------------------------------------~ (b) CNADM·PCB

0.0

-0.5

-1.0

-1.5

2 3

• Xm = 0.00, T = 234.7 K • ><m = 0.02, T = 234.2 K ... ><m = 0.05, T = 234.6 K

4

log f (Hz) 5 6

Figure 3.10: Variation of (a) real and (b) imaginary parts of the complex dielectric constant of a- relaxation with frequency at a fixed temperature of R:: 234.5 K, in the supercooled phase SI of CNADM for various concentration of the dopant PCB, where the data are taken during cooling at a rate of about 0.2 deg/min. The thick lines are fits to eq. 1.46 whose parameters are shown in Table 3.6.

90

Table 3.6: Details of a.-process as described by Eq. 1.46 for samples shown in Figure 3.10.

Sample Temp aHN PHN fo(Hz) fm(Hz) AE

CNADM 234.7 0.067 0.897 9.09 x 10j

9.99 x lO j 4.35

CNADM-PCB 234.2 0.121 0.891 1.11 x 104 1.24 X 104 3.12 Xm= 0.02 CNADM-PCB 234.8 0.123 0.901 7.14 x 10

j 7.88 x lO j 2.04 "

Xm = 0.05

could not be studied for T ~ Tl as the corresponding relaxation occurs at frequencies much

above the range used in the present study. The corresponding D..E variation with T (Figure

3.8) too, does not show any drastic change at T = T1. Moreover, no X- ray studies on phase

I have been published so far, and hence, we are not in a position to comment on the nature

of Phase I.

However, the dielectric characteristics change at T2: the T-dependence of D..E & fm show

changes as revealed in Figures 3.6 and 3.8. More importantly, the D..E value falls on lowering

the temperature and do not change on annealing, indicating it to be an equilibrium property.

This clearly testifies to the onset of ordering at T2 which continues to the lower temperature

side. However, on examination ofthe corresponding dielectric loss curves shown in Figure 3.5,

it is clear that the relaxation process which reflects the orientational disorder is present even

at temperatures much below T2• On lowering the temperature, however there is an increase

in ordering and hence a decrease in D..E and a shift of peak loss frequency to lower and lower

values until the T reaches Tg , where the relaxation gets arrested kinetically. Fourme and

Renaud5,6 studied the X-ray structure of TCTMB at 173 K and found it to be triclinic, . ,

belonging to the space group PI/c. The transition from Phase I to this phase (III) involves

almost no change in position of the molecules or in the orientation of their planes, rather,

the transition involves, predominantly, the setting in of orientational order. Brauniger et al.4

observed by single-crystal NMR experiments that during heating the transformation from

triclinic to monoclinic phase is rather gradual, spanning a wide temperature range. The

91

-C\l Q)

I

5

4

3 -. f-o '-" w <I

2

-0.2

-0.4

-0.6

-0.8

-1.0

-1.2

.-1.4

(a) CNADM • PCB

oeXm = 0.00 o. Xm= 0.02 6. Xm = 0.05

200 220 240

(b) CNADM • PCB

- Xm =0.00 ....... Xm = 0.02. - - - - Xm = 0.05

11 0

" c W

200 220 240

260 280 300

T (K)

260 280 300

T (K)

Figure 3.11: Dielectric and thermal behaviour of CNADM for various concentration of the dopant (PCB). (a) T- variation of ~€ for the samples during cooling and heating cycles. The data are taken during cooling at a rate of about 0.2 deg/min. down to a temperature of 77 K and then heated at the same rate. Note that the samples crystallized to a larger extent during heating to rigid rotator phase solids which subsequently undergo transformation to a rotator phase solid at the corresponding Tl. (b) The corresponding DSC scans around Tl taken during heating after an initial cooling at an approximate rate of 5 deg/min. down to 110 K . It may be borne in mind that the endotherm at Tl is a function of annealing time and also depends on the concentration of PCB.

92

~ -.... E 0)

.2

7

o CNADM (pure) o CNADM - PCB, Xm = 0.02

6 A CNADM - PCB, Xm = 0.05

5

4

3

2'

1 +-~~~~~~~~--~~-r~--~~~-.~~~~~~

3.0 3.5 4.0

1000 IT (K)

4.5 5.0

Figure 3.12: Arrhenius plot of 1m of a- relaxation of CNADM for various concentration of the dopant (PCB) during heating. The thick line corresponds to the PL equation (eq. 1.59) for the parameters: log lo,,,,(Hz) = 5.736, r = 10.16, T~ = 147.7 K.

transition is in fact between two partially ordered phases and is consequently only weakly

first order. It does not involve any major structural change of the lattice but merely a

relatively small, discontinuous change in the molecular polarization. Our results shown in

Figures 3.4, 3.6 and 3.8 testify this. In the case of DCTMB, Brauniger et al. 3 performed

X-ray diffraction and deuterium NMR on DCTMB and its deuterated sample (DCTMB-d12 )

in Phase II, and III (at 110 K) and observed that both Phase II & phase III are monoclinic,

space group P2I/ C, with very similar unit cell dimensions and molecular coordinates, but

they differ in the nature of disorder. Phase III is "right-left" disordered, with molecular

para axes well order~d in the crystal. Our thermal and dielectric studies shown in Figures

3.4, 3.6 and 3.8 support the view that there is a lot of disorder present in Phase II and in

93

Phase III some ordering sets in and that this ordering increases on lowering the temperature.

However, even at temperatures much below T2 , some amount of disorder is still present as

can be seen from the dielectric relaxation with peak loss frequencies at lower frequencies,

whose high frequency tail can be noticed in Figure 3.5(a). That the ~E & 1m values do

not change very abruptly at T2 indicates that the corresponding transition is a weak first

order transition as also testified from the X-ray measurements presented by Brauniger et

al.3 . Despite the similarity in the dipdle moments55 (Jl =2.94 D for DCTMB and 3.15 D for

TCTMB) and lattice parameters of the phases present in these two ,systems, the ~E value

of TCTMB in Phase II are considerably lower than that of DCTMB probably because of

greater degree of disorder in the latter sample. This is also evident from the deuterium NMR

& X-ray results of Brauniger et al.4 on deuterated TCTMB, where a considerable degree of

order is retained even in Phase II, reflected by a non-equal population distribution of the

molecular orientation in the crystal lattice sites. Compared to this the Phase II of DCTMB

is much more mobile and disordered, with the molecular para axes distributed over all six

local crystallographic orientations.

The Phases II & III do not supercool much and hence, the results presented in Figures

3.5-3.8 correspond to the equilibrium phases. The 1m values for Phase II in DCTMB and

Phase III in TCTMB cover about four decades of frequency (Figure 3.6) in which the behav­

ior is Arrhenius. Interestingly, the corresponding 10 values shown in Table 3.4 are about 1 to

3 orders greater than the lattice vibrational frequencies, indicating some amount of coopera­

tivity among the molecules. On extrapolation of the Arrhenius curves of Figure 3.8 to lower

temperatures, we expect the 1m value to be 10-3 Hz at Tg(dielectric) or Tg(D). This value is

109.5 ± 1 Kin DCTMB (and its deuterated sample) and is 127.7 ± 1 K in TCTMB (and its

deuterated sample). Going by the trend shown in Figures 3.5 & 3.8, the dielectric relaxation

would exist even at Tg(D), but its strength ~E must be too small in magnitude. In view of

the discussion in the previous paragraph, the Tg in these systems should correspond to the

94 -

kinetic onset of order-disorder transition that is completed at T2• Regarding the dielectric

spectra, Brot and Darmon9 have reported symmetric Cole-Cole type of behaviour i.e. {3HN

= 1 in eq. 1.46. As shown by us in Figures 3.5 & 3.7, and Table 3.3 of this study show

clear deviations from this type of behaviour, where the relaxation characteristic is highly

asymmetric (i. e. (3 H N f:. 1) indicating some amount of cooperativity among the molecules.

In Figure 3.5, the loss data of some representative example of neat samples at selected tem­

peratures are compared with the H N-fits and the respective parameters are given in Tables

3.3 & 3.4. To compare different substances it is better to consider the half-widths, which are

much above the corresponding Debye value of 1.14 decades (Figure 3.9). Interestingly, we do

not see a correlation between Arrhenius (or non-Arrhenius) behaviour and spectral depen­

dence. According to the "strong and fragile classification" 6f the glass forming systems,33,47

deviations from Debye behaviour is accompanied by non-Arrhenius dependence of the re­

laxation rate which does not appear to be the case here, especially in DCTMB & TCTMB.

However, we wish to mention in this context that, the difference between eq. 1.59 (or 1.58)

and eq. 1.42 is not noticeable within the experimental data given in Figure 3.6 [also see

Table 3.4]. Presently, it is difficult to attribute any significance to this observation.

As opposed to the above two cases, in the PCNB phase II the molecules populate equally

well all the six available sites,2 resulting in high disorder which continues to the lower temper­

ature side. However the .6.E values do not change appreciably on lowering the temperature,

indicating that the antiparallel ordering on lowering the temperature if any, is not pro­

nounced. The dipole moment of this molecule is 2.33 D55 and is. much lower than DCTMB

& TCTMB and this explains partially the lower .6.E value in phase II (since, DoE 0( Jl2).

The -N02 group in PCNB is expected to give a large steric hindrance to the rotation of

the molecule about the hexad axis leading to hindered rotation, and an increase in the

activation energy of rotation which is 67 kJ/mol17 and is much larger than that of both

DCTMB & TCTMB which are given in Table 3.5. The activation energies obtained from

95

Arrhenius equation (eq. 1.42) for T < T2 (Phase III) and T2 < T < Tl (Phase II) in case of

DCTMB are around 32.4 and 35.9 kJ/mol and in case of TCTMB are around 45.0 and 42.5

kJ/mol respectively (see Table 3.3 & 3.5), which correspond closely with the values from

NMR-measurements for DCTMB i.e. 33 kJ/mol3 at 260 K; and for TCTMB.4

3.3.2: Effect of dopants on the a-process

Antiparallel alignment of dipoles is not uncommon in the supercooled liquid states of

alcohols where the -OH group is sterically hindered by a neighbouring radical on the same

molecule. Typical is the example of 4-methyl-3-heptanol which on approaching Tg from a

high temperature increasingly prefers antiparallel arrangement of the molecules in the H­

bonded structure. 56 The corresponding Fuoss-Kirkwood correlation factor "g" approaches

zero on lowering the temperature which can be seen as a drastic fall in D.E value, and the

dielectric signal is nearly absent near Tg •56 The discussion on D.E of DCTMB & TCTMB

and the X-ray scattering studies of the same in the previous sections clearly point to a

possibility of antiparallel alignment of the dipoles in a crystalline lattice without affecting

the positional ordering in the crystal structure. Therefore, PCNB was studied with dopants,

whose molecules are not too different in size and shape from those of the host PCNB, and

hence, are expected to occupy the regular lattice site to form a solid solution, at least, for

smaller concentrations of the dopant. Interestingly, the magnitude of D.E decreases drastically

with an initial increase in the concentration of the dopant as shown in Figures 3.1(a) &

3.3(a), without an appreciable change in the corresponding spectral shape [Figure 3.1(b)] or

relaxation rate (Figure 3.2) from that of the pure PCNE. This behavior is independent of

the dopant, namely PCB, TCB, CLADM & DCTMB although, the amount of dopant added

to bring about the same effect varies. Our preliminary study with DCTMB as dopant shows

that a more symmetric molecular substance may result in a smaller change in D.E.

The change in D.E also depends on the solid solubility of the dopant. Which are not shown

in this paper for the purpose of clarity. However, the corresponding dielectric spectra were

96

examined at a few concentrations. Thus this study along with that of PCNB-PCB system

reported in one of our previous publications,17 clearly proves that the fall in ~E values of

PCNB shown in Figures 3.1(a) & 3.3(a) is effected by solid solubility (even if it is very little). o

This point is for smaller values of Xm of PCB in CNADM, the ~E values change [Figures

3.10 and 3.11] although not to the extent as seen in the case of PCNB without affecting

the relaxation rates (Figure 3.12). Somewhat similar is the case with DCTMB & TCTMB,

which in the presence of TCB show a reduction in ~E values (Figure 3.7), but not to the

extent as seen in the case of PCNB or CNADM.

Our dielectric measurements shown in Figure 3.3{a) for temperatures T1 < T < Tm along

with the DSC results of the same shown in Figure 3.3{b) clearly reveal that for temperatures

T1 < T < Tm, the sample PCNB may consist offreely rotating molecules which get hindered

below T1 and the degree of hindrance depends on the nature of the doped molecule present

in the PCNB lattice. The structure above this temperature is probably triclinic with freely

rotating molecules.s According to the X-ray measurements7,8 of Phase II at room tempera­

ture, the structure is rhombohedral, space group R3, with cell dimensions: ahex = 8.7512 AO,

Chex = 11.1115 AO (from Ref. 7); and ahex = 8.769 AO, Chex = 11.209 AO (from Ref. 8 - the

reader may also see the more recent reference 2). The molecular orientation is disordered

in the sense that the six substituent positions around the benzene ring are indistinguish­

able, but free rotation of the molecules is excluded.s A more recent study by Thomas et

al. 2 reveal lack of short range orientational order in this phase and the same trend is seen

even at temperatures as low as 5 K. That there is no structural change due to addition of

a small amount of PCB, is also confirmed by us using X-ray diffractograms in one of our

recent reportsY Our preliminary X-ray diffraction study of some of the samples examined

here, reveal some extra lines and differing intensity. Our analysis using Crysfire software57

of this data gives many possible structures, whereas our DSC studies presented in Figure

3.3{b) do not indicate a large structural change. Since conventional crystallography gives

97

average structure of the material, the orientational disorder is difficult to characterize. For

this purpose, we need more sensitive X-ray studies than used here with variable temperature

arrangement.

3.4: Conclusions

The hexasubstituted benzenes used in the study appear to lack an observable ,B-process

within the resolution of our experimental setup and the relaxation process in the supercooled

PC phase is found to be non-Debye in frequency dependence. The relaxation rate in DCTMB

& TCTMB and their deuterated samples although appears to be Arrhenius in temperature

dependence, requires further investigation at lower frequencies than used here to classify

them as "strictly Arrhenius" in nature. Our dielectric investigation of these materials and

subsequent analysis confirms the transitions at Tl and T2~O be of weak first order in nature

and are related to the anti-parallel ordering.

The interesting part of ~ur study is that the lowering of ~€ of the a-process of plastic

crystal is linked to solid solubility of the dopant with the host matrix and appears to be

a general feature of the non-hydrogen bonded plastic crystals. It appears that this solid

solution need not be structurally different from that of the host, but may differ in short

range orientational ordering from that of the corresponding pure phase. At this juncture, it

appears that steric hindrance and anti-parallel alignment of the dipoles may be interlinked.

It requires detailed X-ray studies to clarify these points.

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101

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102