relaxation dynamics of orientationally disordered plastic crystals: effect of dopants

Relaxation Dynamics of Orientationally Disordered Plastic Crystals: Effect of Dopants

L. P. Singh,† S. S. N. Murthy,*,† T. Bra1uniger,‡ and H. Zimmermann§

School of Physical Sciences, Jawaharlal Nehru UniVersity, New Delhi - 110067, India, Institute of Physics,Martin-Luther-UniVersity, Halle-Wittenberg, Friedemann-Bach-Platz 6, 06108 Halle, Germany, andMax-Planck-Institut fu¨r Medizinische Forschung, Jahnstrasse 29, 69120 Heidelberg, Germany

ReceiVed: September 1, 2007; In Final Form: NoVember 13, 2007

We have examined the relaxation that occurs in the supercooled plastic crystalline phases of pentachloroni-trobenzene (PCNB), dichlorotetramethylbenzene (DCTMB), trichlorotrimethylbenzene (TCTMB) along withsome of their deuterated samples, and 1-cyanoadamantane (CNADM) in the presence of intentionally addeddopants. The experimental techniques used in the present study are dielectric spectroscopy and differentialscanning calorimetry (DSC). Only one relaxation process similar to that of the primary (orR-) relaxationcharacteristic of glass-forming materials is found, but there is no indication of any observable secondaryrelaxation within the resolution of our experimental setup. TheR-process can reasonably be described by aHavriliak-Negami (HN) shape function throughout the frequency range. However, in the case of PCNB thedielectric strength (∆ε) of the above saidR-process does not change appreciably with temperature, thoughinterestingly, a small addition of a dopant such as pentachlorobenzene (PCB), trichlorobenzene (TCB), andchloroadamantane (CLADM) to the molten state of PCNB drastically lowers the dielectric strength by afactor of 4 to 8. Powder X-ray diffraction measurements at room temperature and DSC data do not indicateany appreciable change in the crystalline structure. It is noticed that the effect of PCB as a dopant on themagnitude ofR-process of CNADM is moderate, whereas both PCB and TCB as dopants show a muchreduced effect on the relaxation in DCTMB and TCTMB. It is suggested that the drastic changes in thedielectric strength of theR-process is due to the rotational hindrance caused by the presence of a smallnumber of dopant molecules in the host crystalline lattice. In the above context, the possibility of a certaindegree of antiparallel ordering of dipoles is also discussed.

1. Introduction

Sometimes exceptional properties of some of the aromaticcompounds are intimately associated with the disorder or short-range order in them, i.e., their nanoscale structure.1 Quantifica-tion of disorder in such materials may aid in the design of newfunctional molecular materials. Hexasubstituted benzenes thatbelong to this class of materials have thus been subjected toin-depth study using X-ray scattering,2-9 solid-state NMR,3,4,10

and dielectric spectroscopy.11-13 In addition, some of thesematerials have some practical applications, for example, inagriculture as a fungicide.14 However, recently there is a growinginterest among researchers working on the glass transitionphenomenon to study the nature of the frozen orientationaldisorder in these materials.15-17

Glass transition phenomena occur when a dynamicallydisordered system (e.g. liquid, plastic crystal, or paramagnet)freezes as a function of external temperature (or pressure) devoidof long-range order. In this freezing process, one or moredegrees of freedom of atoms or molecules continuously slowdown, reaching the so-called glass transition when their dynam-ics has a characteristic time, generally chosen to be 102 s.18-21

Since in the liquid phase there are basically translational andorientational disorders of molecules, the glass transition ofcanonical glass formers is associated with the freezing of these

two degrees of freedom completely. However, a mesophase canexist between the completely ordered crystalline phase and thetranslationally and orientationally disordered liquid phase, theso-called plastic crystalline phase, or the orientationally disor-dered (OD) phase.22-31 In the plastic phase, the centers of massof the molecules have spatial long-range order, forming a latticethat generally has high symmetry (such as cubic, quasi-cubic,or rhombohedral32) but only short-range order with respect tothe orientational degrees of freedom. It is well-known that therelaxation characteristics in the supercooled plastically crystal-line (PC) phase are very similar to that of supercooledliquids.22,30,31,33-37 The main relaxation process (also called theR-process) in the supercooled PC phase is found to be non-Debye in frequency dependence and non-Arrhenius in temper-ature (T) dependence with a steplike change in the specific heat(Cp) at the so-called glass transition temperature (Tg).38-42

Therefore, a clear understanding of the molecular relaxation inthese substances, where only the orientational degrees offreedom are involved, is considered to be important to under-stand the glass transition phenomena in general. Amongcompounds forming orientational glasses, the hexasubstitutedbenzenes exhibit molecular relaxation in the crystalline phasewhere the molecular rotation is hindered43 to varying degrees,11-13

that is, free rotation of the molecules as in the true liquid phaseis not possible, and hence the molecules exhibit limited rotationalmobility.13,43 Most of the measurements3,4,9,10,12,13reported sofar measured dielectric relaxation over a narrow frequency range,and theT dependence of the relaxation rates is not very clear.

* Author for correspondence. E-mail: [email protected].† Jawaharlal Nehru University.‡ Martin-Luther-University.§ Max-Planck-Institut fu¨r Medizinische Forschung.

1594 J. Phys. Chem. B2008,112,1594-1603

10.1021/jp077023l CCC: $40.75 © 2008 American Chemical SocietyPublished on Web 01/23/2008

These substances also are attractive to the researchers of glassphysics, as they are composed of “rigid” non-H-bonded mo-lecular systems and appear to lack a secondary (orâ-) relaxationprocess,22 hitherto thought of as a characteristic feature of glasstransition. A recent study17 of the relaxation of one of thesesubstances, viz. pentachloronitrobenzene (PCNB) indicated thatthe dielectric strength is very sensitive to the presence ofdopants, whereas this effect is not expected in a liquid glass. Arecent report2 on the structure of PCNB, reiterates its structureto be rhombohedral with equal probability of finding themolecule in any one of the six possible orientations. It is notedthat such a distortion of the PCNB molecules must be veryuncomfortable in the average structural geometry,2 and thesystem surprisingly chooses to pack this way rather than findan energy minimum defining a different crystal structure.Therefore, a critical examination of the effect of a wide varietyof dopants on the dielectric relaxation in PCNB and other suchsystems is needed to find out whether this phenomenon is ofgeneral occurrence or specific only to PCNB because of itsuncomfortable structural geometry. For this purpose, we havedecided to study some “rigid” non-H-bonded molecular systemswith a wide variety of dopants. Here we report the results ofour measurements of dielectric relaxation and differentialscanning calorimetry (DSC) studies on these systems over awide range of temperatures.

2. Experiment

The samples used in the study are pentachloronitrobenzene(PCNB), 1-cyanoadamantane (CNADM), chloroadamantane(CLADM), 1,2,3-trichlorobenzene (TCB) (all with the specifiedpurity of g99%), and pentachlorobenzene (PCB) (purity>98%)obtained from Aldrich Co., U.S.A. The other samples studiedhere are 1,2-dichloro-3,4,5,6-tetramethylbenzene (DCTMB), itsdeuterated sample DCTMB-d12, 1,2,3-trichloro-4,5,6-trimeth-ylbenzene (TCTMB), and its deuterated sample TCTMB-d9.These four compounds were synthesized by direct chlorinationof the corresponding hydrocarbons and purified by successivecrystallization.3,4

The DSC measurements were performed using a 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-solidtransition) 186.09 K) as standards. For the dielectric measure-ments, an HP 4284A precision LCR meter in the frequencyrange of 20 Hz to 1 MHz was used. For frequencies in the rangeof 20 Hz to 10-3 Hz, we sampled the dielectric absorptioncurrents in the time window of 0.01-1000 s, using a digitalstorage oscilloscope (DSO) card DSO-2200 (Link Instruments,Inc., U.S.A.), in combination with a Keithley model no. 617programmable electrometer. The complex permittivity wascalculated by taking discrete Fourier transform (DFT) of thedischarging current. But, because of a limitation set by theresolution of the DSO card in this type of measurement, we arenot able to determine the complete spectral characteristic at thelower frequencies. However, thefm values measured with thehelp of this technique are comparable to those measured by theLCR bridge. The sample PCNB was studied using a concentriccylindrical capacitor whose empty cell capacitance,C0, is about214 pF, and the sample is melted in vacuum to fill the capacitorplates. The sample CNADM was studied using a cylindricalcapacitor with an empty cell capacitanceC0 of ∼20 pF and isfilled by the molten sample (in vacuum). Because of the methodused in filling the capacitor, there may be an uncertainty ofabout 10% in the absolute values of the dielectric parameters,

which, however, will not alter the general inferences. In all theother cases, because of the constraints on the sample size, adisk 2.5 cm in diameter and about 0.1 cm in thickness was madeout of the sample by pressing the sample in a pressure die at apressure of 10 kbar. Two electrodes were made independentlyfrom silver powder pressed at the same pressure. The sampledisk was then pressed between the silver pallets at the samepressure to make the capacitor. This capacitor was held betweentwo chromium-plated electrodes with the aid of a light-weightspring. The sample temperature was measured with the help ofa thermocouple kept deep inside the bottom electrode. Thetemperature of the assembly was then controlled in the sameway as before. For further details of the experimental setup andfor accuracy in the measurements, the reader may consult anearlier article.17

3. Results

Among the materials chosen to be added as dopants, bothTCB [Tm (melting temperature)) 326.3 K,∆Hm (enthalpy ofmelting)) 3.3 kJ/mol)] and PCB (Tm ) 358.5 K,∆Hm ) 4.89kJ/mol) are rigid rotator phase crystalline solids, whereasCLADM (Tm ) 439.8 K, but∆Hm could not be measured withcertainty) crystallizes to a rotator phase solid, which undergoesa first-order transition to a rigid rotator phase at a temperatureof 245.4 K with an associated enthalpy (∆H) of 4.05 kJ/mol.The reason for choosing these materials is that, because of theirhigh melting and boiling temperatures, they can readily be mixedwith the samples under study in their molten state without theproblem of evaporation.

3.1. Effect of Dopants on the Dielectric Behavior of PCNB.The first-order transition temperatures and the associatedenthalpies15 are, for PCNB,Tm ) 417.2 K,∆Hm ) 18.55 kJ/mol, T1 (solid-solid transition)) 413.4 K, and∆H ) 0.57kJ/mol. According to an earlier report,8 the solid phase forT1

< T < Tm (designated asSI) is triclinic in structure and is arotator phase solid, and that forT < T1, designated asSII , isrhombohedral, which is also a rotator (plastic) phase crystal-line.7,8 This plastic phase exhibits a well-defined dielectricrelaxation similar to the so-calledR- (or primary) relaxationprocess found in supercooled liquids and plastic phases andexhibits a well-defined glass transition in specific heat data ata temperature of 201 K.15,16

The spectral dependence of theR-relaxation in PCNB wasreported previously.15 We have analyzed the relaxation datausing the Havriliak-Negami (HN) shape function44 given by

wheref0 is the mean relaxation frequency,RHN andâHN are thespectral shape parameters, andε0 and ε∞ are the limitingdielectric constants for the process under consideration. Thetemperature dependence of peak loss frequency (fm) is thencalculated from the parameters of eq 1.45 The peak lossfrequency (fm) is analyzed with the critical power law (PL)15,46

equation,

wheref0,R is a constant,T′g is the glass transition temperature atwhich fm,R ) 0, andr is the dynamic exponent, which can berelated to the size of the cooperatively rearranging region.46

Alternatively, the data can also be described equally well by

ε*( f) - ε∞

ε0 - ε∞) (1 + i( f

f0)1-RHN)-âHN

(1)

fm,R ) f0,R(T - T′gT′g )r

(2)

Relaxation Dynamics of Plastic Crystals J. Phys. Chem. B, Vol. 112, No. 6, 20081595

the Vogel-Fulcher-Tammann equation47 given by

whereT0 is the limiting temperature, andf0,R andB are constants.The above equation reduces to the Arrhenius equation,48

for T0 ) 0. Since the deviation offm values from eq 4 are notstrong in some of the substances of this group, we have analyzedthe data in terms of both of the equations, viz. eqs 2 and 4.

The addition of a small amount of PCB, TCB, CLADM, andDCTMB as dopants brings in a drastic drop in the relaxationstrength of PCNB (Figure 1). However, there is no appreciablechange either in the shape of the relaxation spectra (Figure 1,where the corresponding HN parameters are given in Table 1)or in the peak loss frequency (Figure 2).

We have examined the∆ε (ε0 - ε∞) of the R-process ofPCNB with PCB, TCB, CLADM, and DCTMB as dopants. Inall cases,∆ε values of PCNB are lowered, interestingly evenupon addition of other hexasubstituted benzenes such asDCTMB. The amount of dopant to cause the same amount ofdecrease varies with the nature of the dopant. For example, a1% mole fraction of PCB, which is a pentasubstituted benzeneand hence asymmetric in shape, causes a 6-fold reduction in

the ∆ε value, whereas the same mole fraction of DCTMB (amore symmetric molecule) effects a 2-fold reduction only. Inorder to understand the actual phase behavior of the sample,we have closely monitored the dielectric behavior of the sampleduring very slow heating, and the behavior is noted in smallsteps of temperature variation. The correspondingT variationof ∆ε of the R-process is shown in Figure 3a. DSC measure-ments on these samples are plotted in Figure 3b.

3.2. Effect of Dopants on the Dielectric Behavior of OtherHexasubstituted Benzenes.To test whether the phenomenafound in PCNB in the presence of dopants is also present amongthe other members in the group of hexasubstituted benzenes,we have examined two samples, viz. DCTMB and TCTMB,and their deuterated samples in the presence of dopants. Thedeuterated samples were originally synthesized for NMR,3,4 andas such there is some genuine interest in comparing the behaviorof the purely protonated samples to that of the deuteratedsamples. By substituting protons for deuterons at the outerperiphery of the molecule, the moment of inertia of themolecules increases slightly, which may affect the relaxationrate.

Before taking the dielectric measurements, we have examinedthese samples for the existence of various equilibrium andnonequilibrium phases using DSC. In Figure 4, we have shownthe DSC scans of both of the samples obtained at a heatingrate of 10°/min, where the different transition temperatures areindicated by vertical arrows. The details of various first-orderphase transition temperatures and the associated enthalpies are

Figure 1. Variation of (a) real and (b) imaginary parts of complexdielectric constant ofR-relaxation with frequency at a fixed temperatureof ∼281.5 K, in PCNB for various dopants (whose concentration isexpressed as a mole fractionxm). The thick lines correspond to fits toeq 1 as given in Table 1.

fm,R ) f0,Re(-B/(T-T0)) (3)

fm ) f0e-(E/RT) (4)

Figure 2. Arrhenius plot offm of R-relaxation of PCNB with variousdopants (whose concentration is expressed as a mole fractionxm). Thethick line corresponds to the PL equation (eq 2) for the followingparameters: logf0,R(Hz) ) 4.92, r ) 12.66, andT′g ) 166.7 K.

TABLE 1: Details of r-Process as Described by Eq 1 forSamples Shown in Figure 1

sample temp RHN âHN f0 (Hz) fm(Hz) ∆ε

PCNB 281.8 0.075 0.684 6.12× 102 0.86× 103 1.22PCNB-PCB

xm ) 0.003281.8 0.085 0.693 8.38× 102 1.17× 103 0.91

PCNB-PCBxm ) 0.007

281.4 0.066 0.663 6.92× 102 0.99× 103 0.64

PCNB-PCBxm ) 0.012

281.7 0.044 0.632 8.85× 102 1.30× 103 0.20

PCNB-TCBxm ) 0.024

281.6 0.067 0.669 7.96× 102 1.13× 103 0.21

PCNB-CLADMxm ) 0.012

281.4 0.098 0.724 9.37× 102 1.26× 103 0.43

PCNB-DCTMBxm ) 0.0101

281.8 0.080 0.666 9.36× 102 1.35× 103 0.65

1596 J. Phys. Chem. B, Vol. 112, No. 6, 2008 Singh et al.

given in Table 2. The values reported in Table 2 are an averageof four runs. To give some idea of the deviations of thesetransition temperatures from the data of others, we have alsoentered the corresponding values reported in the literature. We

have also examined the DSC curves in the glass transition (Tg)region of both of the samples used in this study, but we couldnot find any clear evidence of steplike change characteristic ofglass transition within the resolution of the DSC. The samplesDCTMB and TCTMB are rotator (plastic) phases at roomtemperature.3-6,9,10,13 The various phases present in thesesamples do not supercool much, and readily undergo transitionto the more ordered states. The dielectric measurements aremade on the compressed sample (in the form of pellet) becauseof the problem in filling a cylindrical capacitor associated withthe high melting temperature and subsequent sublimation.However, this method gives less reliable values for the emptycell capacitanceC0, and hence the corresponding dielectricparameters estimated using thisC0 are approximate. Only onelarge dispersion is found in these samples at temperatures above77 K, which is shown in Figure 5. It may be identified as theR-process of the plastic phase, and there is no evidence of theâ-process in the sub-Tg region (or it may exist below ourexperimental resolution). We have analyzed the relaxation datausing the HN equation, which is also demonstrated in Figure5, and the corresponding parameters are given in Table 3. Incontrast to the observations of Brot and Darmon9 (on puresamples of DCTMB and TCTMB), a clear deviation from theDebye behavior is seen in all the cases studied here, and thespectral shape is clearly non-Debye in nature. However, ourfmand∆ε values are more or less in agreement with those reportedby Brot and Darmon.9

The temperature dependence of the relaxation rate corre-sponding to the primary (R-) relaxation process is examined.The Arrhenius plots of theR-process are shown in Figure 6. Inall these cases, we could not measure the dielectric lossaccurately on the lower frequency range (for frequencies lessthan 100 Hz) because of the presence of noise. The solid linesgiven in Figure 6 are the critical PL fits derived from eq 2 andare not distinguishable from an Arrhenius fit for the range offm values shown in the figure for a given phase.

From the Arrhenius plot, we have found in all cases a slightshift in the T dependence of thefm value at the transitiontemperatureT2, which corresponds to the SIIIf SII phasepresent in these samples (see inset of Figure 6). The solid linestherein are the Arrhenius fits (eq 4) for the temperature rangeT2 e T e T1 andT < T2, respectively. These fitting parametersare given in Table 4. From Figure 6 and Table 4, it appearsthat theT dependence of the relaxation rate is Arrhenius, but aslight deviation is seen on the lower temperature side, whichneeds to be probed further. Shown in Figure 7 is the frequencyvariation of the real and imaginary parts of the dielectric constantof DCTMB with added dopant TCB. Note that the reduction indielectric strength (∆ε) of the R-process is not as pronouncedas that in the case of PCNB. The relaxation can be welldescribed by the HN fit, the details of which are given in Table5. The presence of small amounts of TCB (xm e 0.02) has nodetectable effect on the relaxation in either the protonated ordeuterated TCTMB samples, and the results are similar to thoseshown in Figure 7. Depicted in Figure 8 is the temperaturevariation of the dielectric strength (∆ε) of theR-process in (a)DCTMB, DCTMB-d12, and DCTMB-TCB with xm ) 0.02 and0.05, and (b) TCTMB, TCTMB-d12, and TCTMB-TCB, xm )0.02. From this plot, a change in theT dependence of the∆ε

value at the transition temperatures,T1 andT2, is observed. Thus,as we decrease the temperature belowT2, the dielectric strength(∆ε) decreases continuously in all cases, which suggests aprogressive antiparallel ordering of molecular dipoles in thecrystal. According to Brot and Darmon,9 the more polar the

Figure 3. Effect of the dopants on the behavior of PCNB. (a) TheTvariation of∆ε. The vertical dashed lines correspond to the temperaturesT1 andTm of the pure PCNB sample. (b) The DSC curves above roomtemperature up to the melting temperature for a heating rate of 2 deg/min in some of the samples shown in panel a. The curves are shiftedvertically for the sake of clarity. (The sample size corresponding tothe curves in order from top to bottom are 11.72 mg, 11.66 mg, 14.12mg, and 14.40 mg.)

Figure 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 of10 deg/min. The arrows indicates the various first-order phase transitiontemperatures (see Table 2). Parts of the DSC curves are magnified inthe inset to show the highly diffuse transitions ending atT1 andT2.


compound, the higher the ordering temperature. It is felt that acomparison of the spectral half-width (i.e., the bandwidth athalf of the maximum loss) of different hexasubstituted benzenesmay be of some use to relate the departure from Arrheniusbehavior with the spectral half width, and hence they are shownat different temperatures in Figure 9.

3.3. Effect of Dopants on the Dielectric Behavior ofCNADM. This material (CNADM), because of its large dipolemomentµ ) 3.83 D, is one of the most widely studied materialsin its supercooled plastic crystalline state using the dielectricrelaxation technique.16,32,49-52 The first-order transition tem-peratures and the associated enthalpies32 are Tm (meltingtemperature)) 458 K (∆H ) 15 kJ/mol) andT1 (solid-solidtransition)) 280 K (∆H ) 5.5 kJ/mol). According to an earlierreport,53 the solid phase stable forT1 < T < Tm, designated asSI, is a face-centered cubic witha ) 9.81 Å (at 293 K), and isa rotator phase solid; the stable phase forT < T1, designated asSII , is monoclinic witha ) 11.278 Å,b ) 6.874 Å, andc )12.092 Å, and the angleâ ) 101°37′ (at 240 K) is a(dielectrically) rigid rotator phase. TheS1 phase can besupercooled, which exhibits53,54 a glass transition temperatureTg at 170( 3 K and is associated with this transition, and is awell-defined dielectric relaxation aboveTg, which is similar totheR- (or primary) relaxation process found in PCNB describedin the previous sections. ThisR- relaxation in the presence ofa dopant is the subject of study here.

The spectral dependence of the dielectric constant and lossare shown in Figure 10 for three concentrations of PCB asdopant. The spectral dependence of the dielectric constant andloss can be reasonably described by eq 1, and the correspondingparameters are given in Table 6. Although this reduction in∆ε

value upon the addition of PCB is not as pronounced as in the

TABLE 2: Details of Various First-Order Phase Transition Temperatures and Associated Enthalpies in DCTMB and TCTMB

transition temperature (K) enthalpya (∆H) kJ/mol

samplenature oftransitionb our work

literature(refs 3, 4, 9) our work

1,2- DCTMB (C10H12Cl2) SI f L Tm 472.5 466.2 13.19SII f SI T1 380.8( 2 383.0 1.21SIII f SII T2 164.2( 2 170.0 0.11

1,2- DCTMB-d12 (C10D12Cl2) SI f L Tm 471.9 470.0 15.29SIIfSI T1 379.6( 2 381.0 0.85SIIIfSII T2 163.7( 2 170.0 0.10

1,2-DCTMB-TCB,xm ) 0.02 SIfL Tm 470.4 13.66SIIfSI T1 378.6( 2 0.82SIIIfSII T2 162.2( 2 0.26

1,2,3-TCTMB (C9H9Cl3) SIfL Tm 501.9 498.2, 500 20.07SIIfSI T1 398.9( 2 401( 3 1.65SIIIfSII T2 264.5( 2 260( 3 0.38

1,2,3-TCTMB-d9 (C9D9Cl3) SIfL Tm 501.9 17.80SIIfSI T1 400.6( 2 1.23SIIIfSII T2 266.3( 2 0.23

1,2,3-TCTMB-TCB, xm ) 0.02 SIfL Tm 500.2 15.34SIIfSI T1 398.6( 2 1.34SIIIfSII T2 264.0( 2 0.18

a The ∆H values associated with transitions atT1 and T2 are approximate based on the assumption that they are first-order transitions.b S:crystalline solid; L: liquid.

Figure 5. Double logarithmic plot ofε′′ vs frequency forT e T1 ofpure (a) DCTMB and (b) TCTMB, at different temperatures. The thickline corresponds to the HN parameters shown in Table 3.

TABLE 3: Details of HN Parameters for Samples Shown inFigure 5

samples T (K) RHN âHN fo (Hz) fm (Hz) ∆ε

1,2-DCTMB 170.3 0.288 1.00 5.70× 102 6.92× 102 5.40(T2 < T < T1) (SII) 180.0 0.223 0.910 2.79× 103 3.10× 103 5.46

189.3 0.193 0.878 7.96× 103 9.14× 103 5.45199.3 0.156 0.825 2.21× 104 2.68× 104 5.43209.4 0.129 0.784 6.15× 104 7.78× 104 5.43219.4 0.102 0.717 1.58× 105 2.15× 105 5.49231.9 0.076 0.631 3.91× 105 5.88× 105 5.68

1,2,3-TCTMB 193.2 0.223 0.703 9.95× 102 1.48× 103 0.69(T < T2) (SIII ) 200.8 0.279 0.859 3.98× 103 4.80× 103 0.91

208.2 0.190 0.742 1.86× 104 1.09× 104 1.08216.5 0.150 0.689 2.42× 104 3.51× 104 1.32225.0 0.120 0.611 5.71× 104 9.12× 104 1.56235.1 0.122 0.598 1.57× 105 2.57× 105 1.81244.5 0.116 0.557 3.57× 105 6.22× 105 2.13


case of PCNB discussed in section 3.1, still the∆ε valuedecreases by a factor of about 2 for a small addition of abouta 5% mole fraction of PCB with some change in relaxationrate. Depicted in Figure 11 is the variation of the∆ε valueduring cooling and subsequent heating. These CNADM sampleswith PCB demonstrate considerable supercooling, which, uponsubsequent heating, crystallize partially to theSII phase that meltsat T1 (as shown in the corresponding DSC curves) upon furtherheating. However, during cooling or heating cycles, we havenoticed some amount of change in the magnitude offm valueas shown in Figure 12.

4. Discussion

For the sake of convenience, the results are discussed in thefollowing sections.

4.1. Dielectric Spectra and Thermal Behavior of NeatSamples. It is observed that the behavior of the deuteratedsamples is essentially the same as those of the isotopicallynormal compound, and hence, whatever inferences we makefor the neat samples is also valid for the deuterated samples,unless specified otherwise. The normal and deuterated samplesof DCTMB and TCTMB show very diffuse transitions below

Tm, especially the one atT1 that is spread out by about 50°(Figure 4). The dielectric relaxation could not be studied forTg T1, as the corresponding relaxation occurs at frequencies wellabove the range used in the present study. The corresponding∆ε variation withT (Figure 8) also does not show any drasticchange atT ) T1. Moreover, no X-ray studies on Phase I havebeen published so far, and hence, we are not in a position tocomment on the nature of Phase I.

However, the dielectric characteristics change atT2: theT-dependence of∆ε andfm show changes, as revealed in Figures6 and 8. More importantly, the∆ε value falls upon loweringthe temperature and does not change upon annealing, indicatingthat it is an equilibrium property. This clearly testifies to theonset of ordering atT2, which continues to the lower temperatureside. However, upon examination of the corresponding dielectricloss curves shown in Figure 5, it is clear that the relaxationprocess that reflects the orientational disorder is present evenat temperatures well belowT2. Upon lowering the temperature,however, there is an increase in ordering and hence a decreasein ∆ε and a shift of peak loss frequency to lower and lowervalues until theT reachesTg, where the relaxation gets arrestedkinetically. Fourme and Renaud5,6 studied the X-ray structureof TCTMB at 173 K and found it to be triclinic, belonging tothe space groupP1/c. The transition from Phase I to this phase(III) involves almost no change in the position of the moleculesor in the orientation of their planes; rather, the transitioninvolves, predominantly, the setting in of orientational order.Brauniger et al.4 observed by single-crystal NMR experimentsthat, during heating, the transformation from triclinic to mono-clinic phase is rather gradual, spanning a wide temperaturerange. The transition is in fact between two partially orderedphases and is consequently only weakly first order. It does notinvolve any major structural change of the lattice but merely arelatively small, discontinuous change in the molecular polariza-tion. Our results shown in Figures 4, 6, and 8 testify to this. Inthe case of DCTMB, Bra¨uniger et al.3 performed X-raydiffraction and deuterium NMR on DCTMB and its deuteratedsample (DCTMB-d12) in Phases II and III (at 110 K) andobserved that both Phase II and Phase III are monoclinic (spacegroup P21/c), with very similar unit cell dimensions andmolecular coordinates, but they differ in the nature of disorder.Phase III is “right-left” disordered, with molecular para axesthat are well ordered in the crystal. Our thermal and dielectricstudies shown in Figures 4, 6, and 8 support the view that thereis a lot of disorder present in Phase II, that in Phase III someordering sets in, and that this ordering increases upon loweringthe temperature. However, even at temperatures well belowT2,some amount of disorder is still present, as can be seen fromthe dielectric relaxation with peak loss frequencies at lowerfrequencies, whose high-frequency tail can be noticed in Figure5a. The fact that the∆ε and fm values do not change veryabruptly atT2 indicates that the corresponding transition is aweak first-order transition, as also testified from the X-raymeasurements presented by Bra¨uniger et al.3 Despite thesimilarity in the dipole moments55 (µ ) 2.94 D for DCTMBand 3.15 D for TCTMB) and lattice parameters of the phasespresent in these two systems, the∆ε value of TCTMB in PhaseII is considerably lower than that of DCTMB, probably becauseof the greater degree of disorder in the latter sample. This isalso evident from the deuterium NMR and X-ray results ofBrauniger et al.4 on deuterated TCTMB, where a considerabledegree of order is retained even in Phase II, reflected by a non-equal population distribution of the molecular orientation in thecrystal lattice sites. Compared to this, the Phase II of DCTMB

Figure 6. Arrhenius plots for (a) DCTMB, DCTMB-d12, and DCTMB-TCB (xm ) 0.02) and (b) TCTMB, TCTMB-d9, and TCTMB-TCB(xm ) 0.02). The thick line corresponds to the PL equation (eq 2) forthe following parameters: logf0,R(Hz) ) 2.37,r ) 12.73,T′g ) 81.3 Kfor pure DCTMB, and logf0,R(Hz) ) 3.81, r ) 13.14,T′g ) 101.6 Kfor pure TCTMB. Also shown in the inset of both panels a and b arethe expended portion of the Arrhenius curve to show the diffusediscontinuity offm at transitionT2, where the thick lines correspond toArrhenius fit (see Table 4).


is much more mobile and disordered, with the molecular paraaxes distributed over all six local crystallographic orientations.

Phases II and III do not supercool much, and hence the resultspresented in Figures 5-8 correspond to the equilibrium phases.

Thefm values for Phase II in DCTMB and Phase III in TCTMBcover about four decades of frequency (Figure 6) in which thebehavior is Arrhenius. Interestingly, the correspondingf0 valuesshown in Table 4 are about 1-3 orders greater than the latticevibrational frequencies, indicating some amount of cooperativityamong the molecules. Upon extrapolation of the Arrheniuscurves of Figure 8 to lower temperatures, we expect thefm valueto be 10-3 Hz atTg(dielectric) or Tg(D). This value is 109.5(1 K in DCTMB (and its deuterated sample) and is 127.7( 1 Kin TCTMB (and its deuterated sample). Going by the trend

TABLE 4: Details of r-Process for Samples Shown in Figure 6

Arrhenius parameters

HN parameters T2 < T < T1 T < T2

samplerange oftemp (K) RHN âHN

log f0(Hz)

E(kJ/mol)

log f0(Hz)

E(kJ/mol)

1,2-DCTMBa 152-248 0.312-0.072 1.00-0.64 13.85 35.91 12.74 32.401,2-DCTMB-d12

a 150-244 0.327-0.079 1.00-0.428 13.96 35.85 11.84 29.031,2-DCTMB-TCBa

xm ) 0.02150-245 0.325-0.106 1.00-0.733 14.32 37.01 12.14 30.36

1,2,3-TCTMBb 177-263 0.280-0.001 0.859-0.427 14.89 42.52 15.38 45.001,2,3-TCTMB-d9b 179-258 0.352-0.068 1.00-0.438 14.94 43.51 15.20 44.771,2,3-TCTMB-TCBb

xm ) 0.02175-261 0.332-0.002 1.00-0.564 15.28 44.56 15.45 45.19

a The parameters forT < T2 are approximate.b The parameters forT > T2 are approximate.

Figure 7. Variation of real and imaginary parts of relaxation inDCTMB at a fixed temperature for various concentrations of the dopantTCB. The thick line corresponds to eq 1, the details of which are givenin Table 5.


sample temp RHN âHN f0 (Hz) fm (Hz) ∆ε

DCTMB 190.2 0.167 0.831 1.27× 104 1.54× 104 5.82DCTMB-TCB

xm ) 0.02190.7 0.148 0.815 1.92× 104 2.35× 104 5.69

DCTMB-TCBxm ) 0.05

190.3 0.226 0.999 2.43× 104 2.44× 104 4.04

Figure 8. T variation of total dielectric strength (∆ε) for the samplesshown in Tables 4 and 5 (and Figures 5 and 7). (For the purpose ofcalculation of∆ε ) ε0 - ε∞, the ε∞ from the high-frequency limit oftheR-process is extrapolated linearly toward higher temperatures). Alsoindicated are the different transition temperatures (shown by arrows atT1 andT2), as obtained from the DSC experiment (Figure 4) and Table2.


shown in Figures 5 and 8, the dielectric relaxation would existeven at Tg(D), but its strength∆ε must be too small inmagnitude. In view of the discussion in the previous paragraph,the Tg in these systems should correspond to the kinetic onsetof the order-disorder transition that is completed atT2.Regarding the dielectric spectra, Brot and Darmon9 havereported a symmetric Cole-Cole type of behavior, i.e.,âHN )

1 in eq 1. As shown by us in Figures 5 and 7 and Table 3 ofthis study, clear deviations from this type of behavior occur,where the relaxation characteristic is highly asymmetric (i.e.,âHN * 1), indicating some amount of cooperativity among themolecules. In Figure 5, the loss data of some representativeexample of neat samples at selected temperatures are comparedwith the HN fits, and the respective parameters are given inTables 3 and 4. To compare different substances, it is better toconsider the half-widths, which are well above the correspondingDebye value of 1.14 decades (Figure 9). Interestingly, we donot see a correlation between Arrhenius (or non-Arrhenius)behavior and spectral dependence. According to the “strong andfragile classification” of the glass-forming systems,33,47 devia-

Figure 9. Variation of spectral half-width with temperature in the puresamples of hexasubstituted benzenes.

Figure 10. Variation of (a) real and (b) imaginary parts of the complexdielectric constant ofR-relaxation with frequency at a fixed temperatureof ∼234.5 K, in the supercooled phaseSI of CNADM for variousconcentrations of the dopant PCB, where the data are taken duringcooling at a rate of about 0.2 deg/min. The thick lines are fits to eq 1,whose parameters are shown Table 6.

Figure 11. Dielectric and thermal behavior of CNADM for variousconcentrations of the dopant (PCB). (a)T variation of∆ε for the samplesduring cooling and heating cycles. The data are taken during coolingat a rate of about 0.2 deg/min down to a temperature of 77 K and thenheated at the same rate. Note that the samples crystallized to a largerextent during heating to rigid rotator phase solids that subsequentlyundergo transformation to a rotator phase solid at the correspondingT1. (b) The corresponding DSC scans aroundT1 taken during heatingafter an initial cooling at an approximate rate of 5 deg/min down to110 K. It may be borne in mind that the endotherm atT1 is a functionof annealing time and also depends on the concentration of PCB.


sample temp RHN âHN f0 (Hz) fm (Hz) ∆ε

CNADM 234.7 0.067 0.897 9.09× 103 9.99× 103 4.35CNADM-PCB

xm ) 0.02234.2 0.121 0.891 1.11× 104 1.24× 104 3.12

CNADM-PCBxm ) 0.05

234.8 0.123 0.901 7.14× 103 7.88× 103 2.04


tions from Debye behavior is accompanied by non-Arrheniusdependence of the relaxation rate, which does not appear to bethe case here, especially in DCTMB and TCTMB. However,we wish to mention in this context that, the difference betweeneq 2 (or 3) and eq 4 is not noticeable within the experimentaldata given in Figure 6 (also see Table 4). Presently, it is difficultto attribute any significance to this observation.

As opposed to the above two cases, in the PCNB phase II,the molecules populate equally well at all six available sites,2

resulting in high disorder, which continues to the lowertemperature side. However, the∆ε values do not changeappreciably upon lowering the temperature, indicating that theantiparallel ordering upon lowering the temperature, if any, isnot pronounced. The dipole moment of this molecule is 2.33D55 and is much lower than that of DCTMB and TCTMB, andthis partially explains the lower∆ε value in Phase II (since,∆ε

∝ µ2). The -NO2 group in PCNB is expected to give a largesteric hindrance to the rotation of the molecule about the hexadaxis, leading to hindered rotation and an increase in theactivation energy of rotation, which is 67 kJ/mol17 and is muchlarger than that of both DCTMB and TCTMB, which are givenin Table 5. The activation energies obtained from the Arrheniusequation (eq 4) forT < T2 (Phase III) andT2 < T < T1 (PhaseII) in the 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 Tables 3 and 5), which correspond closely withthe values from NMR measurements for DCTMB, i.e., 33 kJ/mol3 at 260 K, and for TCTMB.4

4.2. Effect of Dopants on the r-Process. Antiparallelalignment of dipoles is not uncommon in the supercooled liquidstates of alcohols where the-OH group is sterically hinderedby a neighboring radical on the same molecule. Typical is theexample of 4-methyl-3-heptanol, which, upon approachingTg

from a high temperature, increasingly prefers antiparallelarrangement of the molecules in the H-bonded structure.56 Thecorresponding Fuoss-Kirkwood correlation factor “g” ap-proaches zero upon lowering the temperature, which can be seenas a drastic fall in the∆ε value, and the dielectric signal isnearly absent nearTg.56 The discussion on the∆ε of DCTMBand TCTMB and the X-ray scattering studies of the same inthe previous sections clearly point to a possibility of antiparallelalignment of the dipoles in a crystalline lattice without affectingthe positional ordering in the crystal structure. Therefore, PCNB

was studied with dopants whose molecules are not too differentin size and shape from those of the host PCNB and, hence, areexpected to occupy the regular lattice site to form a solidsolution, at least for smaller concentrations of the dopant.Interestingly, the magnitude of∆ε decreases drastically withan initial increase in the concentration of the dopant, as shownin Figures 1a and 3a, without an appreciable change in thecorresponding spectral shape (Figure 1b) or relaxation rate(Figure 2) from that of the pure PCNB. This behavior isindependent of the dopant, namely, PCB, TCB, CLADM, andDCTMB, although the amount of dopant added to bring aboutthe same effect varies. Our preliminary study with DCTMB asthe dopant shows that a more symmetric molecular substancemay result in a smaller change in∆ε.

The change in∆ε also depends on the solid solubility of thedopant, which are not shown in this paper for the purpose ofclarity. However, the corresponding dielectric spectra wereexamined at a few concentrations. Thus, this study, along withthat of the PCNB-PCB system reported in one of our previouspublications,17 clearly proves that the fall in∆ε values of PCNBshown in Figures 1a and 3a is effected by solid solubility (evenif it is very little). This point is for smaller values of thexm ofPCB in CNADM; the∆ε values change (Figures 10 and 11),although not to the extent as seen in the case of PCNB withoutaffecting the relaxation rates (Figure 12). Somewhat similar isthe case with DCTMB and TCTMB, which, in the presence ofTCB, show a reduction in∆ε values (Figure 7), but not to theextent as seen in the case of PCNB or CNADM.

Our dielectric measurements shown in Figure 3a for temper-aturesT1 < T < Tm along with the DSC results of the sameshown in Figure 3b clearly reveal that, for temperaturesT1 < T< Tm, the sample PCNB may consist of freely rotating moleculesthat get hindered belowT1, and the degree of hindrance dependson the nature of the doped molecule present in the PCNB lattice.The structure above this temperature is probably triclinic withfreely rotating molecules.8 According to the X-ray measure-ments7,8 of Phase II at room temperature, the structure isrhombohedral (space groupR3h), with cell dimensionsahex )8.7512 Å,chex ) 11.1115 Å (from ref 7) andahex ) 8.769 Å,chex ) 11.209 Å (from ref 8; the reader may also see the morerecent ref 2). The molecular orientation is disordered in the sensethat the six substituent positions around the benzene ring areindistinguishable, but free rotation of the molecules is excluded.8

A more recent study by Thomas et al.2 reveals a lack of short-range orientational order in this phase, and the same trend isseen even at temperatures as low as 5 K. The idea that there isno structural change due to the addition of a small amount ofPCB is also confirmed by us using X-ray diffractograms in oneof our recent reports.17 Our preliminary X-ray diffraction studyof some of the samples examined here reveal some extra linesand differing intensity. Our analysis using Cryssfire software57

of this data gives many possible structures, whereas our DSCstudies presented in Figure 3b do not indicate a large structuralchange. Since conventional crystallography gives the averagestructure of the material, the orientational disorder is difficultto characterize. For this purpose, we need more sensitive X-raystudies than that used here with variable temperature arrange-ment.

5. Conclusions

The hexasubstituted benzenes used in the study appear to lackan observableâ-process within the resolution of our experi-mental setup, and the relaxation process in the supercooled PCphase is found to be non-Debye in frequency dependence. The

Figure 12. Arrhenius plot offm of R-relaxation of CNADM for variousconcentrations of the dopant (PCB) during heating. The thick linecorresponds to the PL equation (eq 2) for the following parameters:log f0,R(Hz) ) 5.736,r ) 10.16,T′g ) 147.7 K.


relaxation rate in DCTMB and TCTMB and their deuteratedsamples, although appearing to be Arrhenius in temperaturedependence, requires further investigation at lower frequenciesthan those used here to classify them as “strictly Arrhenius” innature. Our dielectric investigation of these materials andsubsequent analysis confirms the transitions atT1 andT2 to beof weak first-order in nature and are related to the antiparallelordering.

The interesting part of our study is that the lowering of∆ε

of theR-process of plastic crystal is linked to the solid solubilityof the dopant with the host matrix and appears to be a generalfeature of the non-hydrogen-bonded plastic crystals. It appearsthat this solid solution need not be structurally different fromthat of the host, but may differ in short-range orientationalordering from that of the corresponding pure phase. At thisjuncture, it appears that steric hindrance and antiparallelalignment of the dipoles may be interlinked. It requires detailedX-ray studies to clarify these points.

Acknowledgment. L.P.S. wishes to thank CSIR, India, forSenior Research fellowship (SRF).

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relaxation dynamics of orientationally disordered plastic crystals: effect of dopants

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