RAPID COMMUNICATION

Analysis of Transitions of Liquid Crystals and Conformationally DisorderedCrystals by Temperature-Modulated Calorimetry

WEI CHEN,1 AKIHIKO TODA,2 IL-KWON MOON,1 BERNHARD WUNDERLICH1

1 Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996-1600; Division of Analytical andChemical Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6197

2 Faculty of Arts and Sciences, Hiroshima University, 1-7-1 Kagamiyama, Higashi-Hiroshima 739, Japan

Received 30 November 1998; revised 8 February 1999; accepted 10 February 1999

Keywords: liquid crystal; conformationally disordered crystal (condis crystal); re-versible phase transition; irreversible phase transition; temperature-modulated calo-rimetry

INTRODUCTION

In the system of phases of linear, flexible macromole-cules, there are two types of thermotropic mesophases,namely, liquid crystals (LC, with positional, dynamicdisorder and some long-range orientational order), andcondis crystals (short for conformationally disorderedcrystals, CDC, with dynamic conformational disorderand long-range positional and orientational order).1

Due to the intrinsically high viscosity of macromole-cules and only partial crystallinity in macromolecularCDCs, the main differences between the two me-sophases, the liquid-like behavior of the LC and thehigher entropy of isotropization of the CD, become am-biguous. This is particularly true for the cases of mac-romolecules with rigid aromatic segments (mesogens)which are separated by flexible, aliphatic segments.2

Certain superficial similarities in the morphologicalstructures of liquid crystals and condis crystals furtherincrease the chance of improper assignments of the twomesophases. Based on structure-consideration alone,both mesophases have even erroneously been consid-ered to be identical.3 Often, the detailed informationwith respect to molecular mobility and ordering needsto be assessed by NMR and X-ray analysis, respec-tively, before a correct mesophase assignment is possi-

ble. The thermodynamic behavior of liquid crystals andcondis crystals is, however, distinct: The LCs, resem-bling liquids, show reversible phase-transition behav-ior (i.e., no supercooling or superheating is observed).The CDCs, on the other hand, show in their orderingtransitions a more than 15 K supercooling, typical ofmacromolecular crystals.1,2

In this paper, temperature-modulated calorimetry isused to investigate a known LC and a well-character-ized CDC. Both consist of a rigid, aromatic segment anda flexible, aliphatic spacer. The results of this workprovide conclusive experimental evidence for the ther-modynamic reversibility of the isotropization transitionof a polymeric LCs over their full transition range, andthe irreversibility of the isotropization of CDCs of mac-romolecules.

DATA TREATMENT AND EXPERIMENTAL DETAIL

The measurements were carried out with temperature-modulated differential scanning calorimetry (TMDSC),well documented in.4–9 Briefly, an oscillation of ATs

sin(vt 2 «) is added to the average sample tempera-ture ,Ts. that, in steady state, would otherwise haveincreased linearly:

Ts 2 To 5 , q . t 2, q . Cs

K 1 ATssin~vt 2 «! (1)Correspondence to: B. Wunderlich (E-mail: athas@utk.edu)

Journal of Polymer Science: Part B: Polymer Physics, Vol. 37, 1539–1544 (1999)© 1999 John Wiley & Sons, Inc. CCC 0887-6266/99/131539-06

1539

The average ,. in TMDSC is always taken over onemodulation cycle so that the modulation effect becomeszero. In eq. (1), To is the temperature at time t 5 0;,q., the underlying, constant scanning rate; Cs, theheat capacity of the sample calorimeter (sample1 pan); K, the Newton’s law constant; ATs

, the ampli-tude of temperature modulation; v, the modulation fre-quency in rad s21 (52p/p where p is the length of themodulation period in seconds); and « the phase lagrelative to a reference oscillation. A similar expressioncan be written for the reference calorimeter with tem-perature Tr, heat capacity Cr, and phase lag f. Thedifferential heat flow Q 5 dQ/dt is then proportional toDT 5 Tr 2 Ts with a phase lag of d, and can be derivedfrom the general DSC equation7:

Tr 2 Ts 5~Cs 2 Cr!

KdTs

dt 2Cr

Kd~Tr 2 Ts!

dt (2)

For the solution of eq. (2), the oscillating part of Ts andDT can be represented by:

Ts 5 ATsie2i~vt2«! (3)

DT 5 ADe2i~vt2d! (4)

The solution of eq. (2) for its real and imaginary partsthat result from insertion of eqs. (3) and (4) leads to thetwo basic TMDSC equations for the reversing part ofthe experiment7:

cos~« 2 d! 5KAD

ATsv~Cs 2 Cr!(5)

u~Cs 2 Cr!u 5AD

ATsÎSK

vD2

1 Cr2 (6)

where AD is the amplitude of the response of the tem-perature difference DT to the modulation of the sampletemperature Ts. The reversible heat capacity measuredin this fashion represents the thermodynamic heat ca-pacity as long as the sample response is fast relative tothe frequency of modulation, v. For a slow sampleresponse, as is possible during phase transitions, anadditional phase lag a may arise:

a 5 ~« 2 d! 2 ~«o 2 do! (7)

where «o and do are the extrapolated phase lags fromoutside of the transition region. The measured heatcapacity, in turn, will then become an apparent, fre-quency-dependent heat capacity, describable as a com-plex quantity. Typical examples of transitions thathave been treated in this fashion are the glass transi-tion,10 crystallization,11–15 and melting.16–18

In the present work, a commercial TMDSC wasused, the Thermal Analyst 2910 MDSC™ system witha liquid-nitrogen cooling accessory from TA Instru-

ments Inc. In this TMDSC, the modulation is controlledat the sample thermocouple. Dry nitrogen gas with aflow rate of 20 mL min21 was purged through the DSCcell. The temperature of the TMDSC equipment wasinitially calibrated in the standard DSC mode at 10 Kmin21 by using the onsets of the transition peaks forcyclohexane (186.09 and 297.7 K), octane (216.15 K),water (273.15 K), and indium (429.75 K). The heat flowwas calibrated with the heat of fusion of indium (28.45J g21).

Three series of experiments were performed: (1)Standard TMDSC runs were carried out with underly-ing scanning rates ,q. 5 1.0 K min21 and a temper-ature-modulation amplitude ATs

5 0.05 K. Modulationperiods from p 5 20–100 s were chosen as detailed inthe corresponding experiments. The modulation pa-rameters with underlying heating and cooling werechosen such that the runs showed only heating or cool-ing during the oscillations [i.e., ATs

, (u,q.u/v)]. Un-der these conditions, one avoids complications causedby cyclic disordering and ordering. (2) Quasi-isother-mal TMDSC (,q. 5 0) was carried out with a mod-ulation amplitude ATs

5 0.1 K, coupled with a modu-lation period p 5 100, 60, and 30 s and stepwisetemperature increments of 1.0 K between the runs. Thequasi-isothermal runs lasted 20 min for each tempera-ture. The last 10 min of these runs were used for datacollection. (3) Standard DSC runs were made withoutmodulation at the indicated heating rates. As long asthe response of the sample is reversible, the heat flowin standard DSC equals the total heat flow of theTMDSC, which is obtained by forming the sliding av-erage over one modulation cycle ,DT..

The liquid crystal-forming polymer sample underthe investigation is a polyether. It was synthesized bycoupling 4,49-dihydroxy-a-methylstilbene (DHMS)with a 1 : 1 molar mixture of 1,7-dibromoheptane and1,9-dibromononane. The name of this random copoly-mer is abbreviated as DHMS-7,9. The molar mass ofthe DHMS-7,9 was 36,000 Da. It forms a nematic liquidcrystalline phase between 400 and 470 K.19,20 The mo-lecular structures of the two repeating units are givenby the following formula with n 5 7 and 9:

The condis crystal forming polymer is poly(4,49-phtha-loimidobenzoyl-dodecamethyleneoxycarbonyl) (PEIM-12) with the following repeating unit:

The sample was synthesized as described in Refs. 21 and22. The sample had an inherent viscosity of 0.91 dL g21

1540 J. POLYM. SCI. PART B: POLYM. PHYS.: VOL. 37 (1999)

(measured in CH2Cl2/TFA of 4 : 1 volume ratio at 293 K).Both samples were analyzed as received. The detailedinvestigation of PEIM-12 by solid state NMR, Wide-angleX-ray, as well as standard DSC proved that below theisotropization temperature, the PEIM-12 is in a semicrys-talline condis state and its “smectic-like” layer structureis due to nanophase separation of the polar mesogenicgroups and the nonpolar methylene groups.23

The samples were pressed into thin films (ca. 0.015mm in thickness) for optimum thermal conduction withthe sample pan. The sample weights for DHMS-7,9 andPEIM-12 were 2.900 and 1.960 mg, respectively.

RESULTS

Figure 1 shows the isotropization/ordering transition ofthe nematic LC of DHMS-7,9. The heavy lines repre-sent the apparent heat capacity of a standard DSCmeasurement. The continuous and dotted thin linesrepresent the TMDSC results on heating and cooling,respectively. The calculations were carried out with eq.(6) by inserting the first-harmonic of the heat-flow andtemperature amplitudes, AD and ATs

. The solid circles

stand for the quasi-isothermal mode, similarly com-puted from eq. (6). Figure 2 shows the correspondingphase lags a, evaluated from eq. (7).

The experimental results from PEIM-12 on heatingand cooling are shown in Figures 3 and 4, respectively.In both figures, plots (a) represent the total heat flowsfor all TMDSC data. All heating curves in Figure 3(a)are identical, except for baseline shifts due to instru-ment drift between the runs of the experiment. Thesame is true for the cooling curves of Figure 4(a), whichindicate, however, a strong supercooling of about 27 K.The curves in Figure 3(b) are the apparent heat capac-ities calculated from the total heat flow (thick line) andthe reversible heat flow at different frequencies (thinlines). The latter were calculated from eq. (6) and showa strong frequency dependence. The analogous curveson cooling in Figure 4(b), on the other hand, show noreversible heat flow during the transition. The solidsymbols represent the quasi-isothermal TMDSC withstepwise increasing and decreasing temperatures be-tween the 20-min runs. No change occurs throughoutthe transitions. Plots (c) shows the change of the phaseangle a of eq. (7) as a function of frequency. Again, thethin lines represent the TMDSC measurements withunderlying heating and cooling. A clear difference ex-ists between heating (Fig. 3) and cooling (Fig. 4), whilethe solid symbols which depict the quasi-isothermalmeasurements show no difference.

Figure 2. The phase angle a in the N 7 I transitionrange for DHMS-7,9 for the experiments of Figure 1.

Figure 1. Apparent heat capacity of DHMS-7,9 in theN 7 I transition region. The experimental modes arelisted in the figures (STDSC 5 standard DSC, similarto the total heat flow).

RAPID COMMUNICATION 1541

Figure 5, finally shows a series of standard DSCtraces at different heating rates of samples that wereprior cooled at 10 K min21. The curves, when viewedwith increasing heating rates, are indicative of consid-erable reorganization on heating.24 When heatedslowly, reorganization starts at low temperature wherereorganization is slow and leads to only a limitingincrease in melting temperature. Speeding up the ex-periment produces better crystals because the highertemperature of reorganization is more effective for an-nealing of poor crystals. The fastest experiments, fi-nally, outrun the annealing kinetics and the sampleapproaches its zero-entropy-production isotropizationat lower temperature.24

DISCUSSION

Since the isotropization of a liquid crystal occurs atequilibrium, the transition can be seen at the sametemperature on heating and cooling and no nucleation

is required for the I3 LC transition.1 One would thusexpect the TMDSC to be frequency independent, as is,indeed, found for the DHMS-7,9 in all experiments:standard DSC, TMDSC with underlying heating andcooling rates, as well as in the quasi-isothermal mode.Furthermore, because of the limited molecular order-ing in the liquid crystalline state, the heat of transitionis small, which, in turn, ensures that steady state ismaintained during the entire measurement. Therefore,a liquid crystal actually provides an ideal system toevaluate the validity of the applications of TMDSC inthe study of thermal transitions as well as the instru-ment-effects in this type of measurements.

At higher temperatures, the TMDSC data decreaseslightly with increasing frequency relative to the stan-dard DSC data. Most likely this is due to a sharpertransition edge at high temperature. Larger changes inthe apparent heat capacity produce a poor representa-tion of the modulation amplitudes by their first har-monic in eq. (6). Condition of a precise representation isan approximately constant apparent heat capacity overthe whole modulation cycle (61

2p). Another possible

cause of this observation is that excessive temperature

Figure 4. Total heat flow, apparent heat capacity andphase angle a of PEIM-12 on cooling. The symbols F, ■,Œ, which practically coincide, represent the quasi-iso-thermal measurements with modulation period p 5 30s, 60 s and 100 s, respectively. The thin lines representTMDSC with p 5 44, 56, 100 s.

Figure 3. Total heat flow, apparent heat capacity andphase angle a of PEIM-12 on heating. The symbols F,■, Œ, which practically coincide, represent the quasi-isothermal measurements with modulation period p5 30 s, 60 s, and 100 s, respectively. The thin linesrepresent TMDSC with p 5 20, 24, 28, 36, 44, 56, 68,84, 100 s.

1542 J. POLYM. SCI. PART B: POLYM. PHYS.: VOL. 37 (1999)

gradients build up inside of the sample as the modula-tion frequency increases. In order to exclude the latterargument, the same TMDSC measurements were per-formed on 6.00 mg of DHMS-7,9 instead of the 2.90 mg.The reversible heat flow traces of TMDSC with allfrequencies were, however, identical within the exper-imental errors. Only when increasing the sampleweight to 16.00 mg could one see a larger frequencydependence, indicative of an unacceptable temperaturegradient within the sample. Obviously, a sufficientlysmall sample mass is of importance for TMDSC, but inthe present case the maximum acceptable mass isabout 6–10 mg. The small difference between TMDSCwith underlying heating (dotted thin line) and cooling(solid thin line) is linked to the change of the instru-ment lag between sample and sample-thermocoupleand has been well documented.25

The changes of the phase angle a with modulationfrequency, shown in Figure 2, indicate almost nochange in the transition range (changes of less than 2°).This is also evidence that the transition is thermody-namically reversible over the whole temperature range.The big spike of the phase lag at the high-temperatureend of the transition on cooling (continuous line in Fig.2), is again due to the sharp beginning of the I 3 Ntransition. It may well be possible to extract finer de-tails about the high-temperature end of the isotro-pizarion transition from the differences between stan-dard DSC and TMDSC carried out with heating andcooling, and under quasi-isothermal conditions.

In contrast to the LC, the formation of a CDC nor-mally requires nucleation, which results in the 27 Ksupercooling [compare Figs. 3(a) to 4(a)]. Similarly, thecrystallization of a macromolecule is always irrevers-ible.24 As illustrated in Figure 3(b) in the TMDSCmeasurements with underlying heating rates, the ap-parent, reversing heat capacity decreases quickly asthe frequency v 5 2p/p increases. The phase angledecreases similarly [Fig. 3(c)]. The TMDSC measure-ments on cooling, illustrated in Figure 4(b) and (c) showpractically no response to the transition, indicating theordering is insensitive to the modulation (i.e., the su-percooling is so large that there is no change in the rateof ordering over the amplitude of modulation). Thequasi-isothermal measurements in the transitionrange also show no response to the heat of transition,neither on heating, nor on cooling. Therefore, plots (b)and (c) illustrate the thermally irreversible nature ofthe isotropization transition.

The strong frequency dependence of the apparentheat capacity based on the reversing heat flow in Fig-ure 3(b) and (c) was linked for macromolecules to thekinetics of irreversible melting for crystals of polyeth-ylene and poly(ethylene terephthalate).17,18 In princi-ple, the time scale of the temperature modulation of theTMDSC can be related to the scanning rate in a con-ventional DSC. Fast modulation corresponds to a highscanning rate. Therefore, in the case where the melting

kinetics is the controlling rate of the transition, super-heating should be observable (i.e., on faster heating,the transition peak should shift to higher tempera-tures).24 In the case of PEIM-12, Figure 5 illustrates,however, that the transition consists of a superpositionof annealing and isotropization, and the strong fre-quency dependence of the reversing, apparent heat ca-pacity and the phase angle a shown in Figure 3 can notbe linked exclusively to the irreversible melting kinet-ics of the condis crystals. In addition, earlier researchhas shown that crystals of flexible polymers superheatonly when their chains are extended or are re-strained,24 neither are likely in the present case.

CONCLUSIONS

A detailed analysis of the transitions for two polymers ofdifferent mesophase type revealed completely differentreversibility of the isotropization transition. The liquid-crystal-forming mainchain LC copolymer DHMS-7,9 isclose to fully reversible over the broad transition range ofalmost 25 K. The conformationally disordered homopoly-mer PEIM-12 consisting similarly of stiff, aromatic seg-ments and flexible, aliphatic spacers is completely irre-versible in its isotropization. The results provide for thefirst time an easy and direct approach to distinguishcondis crystals from liquid crystals for the case where thetwo thermotropic mesophases show superficially similarphase structures. The frequency-dependence of the heat-ing curves of the condis crystals give an indication of a

Figure 5. Standard DSC traces of PEIM-12 (withoutmodulation) with different heating rates. The sampleswere always cooled with 10 K min21 to keep the samethermal history of the sample.

RAPID COMMUNICATION 1543

kinetic process that could be linked to the annealing cou-pled with isotropization.

The authors are grateful to Prof. M. Dadmun of UT,who provided the DHMS-7,9, and Prof. H. R. Krichel-dorf of the University of Hamburg who supplied thePEIM-12. This work was supported by the Div. of Ma-terials Res., NSF, Polymers Program, GrantDMR-9703692 and the Division of Materials Science,Office of Basic Energy Sciences, DOE at Oak RidgeNational Laboratory, managed by Lockheed MartinEnergy Res. Corp. for DOE, under contract DE-AC05-96OR22464.

REFERENCES AND NOTES

1. Wunderlich, B.; Grebowicz, J. Adv Polym Sci 1984,60/61, 1.

2. Wunderlich, B.; Chen, W. In A. I. Isayev, T. Kyu,and S. Z. D. Cheng, Eds., Liquid Crystalline Poly-mer Systems; ACS Symp Ser 1996, 632, 232.

3. Ungar, G. Polymer 1993, 34, 2050.4. Gill, P. S.; Sauerbrunn, S. R.; Reading, M. J Therm

Anal 1993, 40, 931.5. Reading, M.; Elliott, D.; Hill, V. L. J Therm Anal

1993, 40, 949.6. Reading, M.; Luget, A.; Wilson, R. Thermochim

Acta 1994, 238, 295.7. Wunderlich, B.; Jin, Y.; Boller, A. Thermochim

Acta 1994, 238, 277.8. Boller, A.; Jin, Y.; Wunderlich, B. J Therm Anal

1994, 42, 307.9. Hatta, I. Jpn J Appl Phys 1994, 33, L686.

10. Hensel, A.; Dobbertin, J.; Schawe, J. E. K.; Boller,A.; Schick, C. J Therm Anal 1996, 46, 935.

11. Schawe, J. E. K.; Hohne, G. W. H. J Therm Anal1996, 46, 893.

12. Toda, A.; Oda, T.; Hikosaka, M.; Saruyama, Y.Polymer 1997, 38, 231.

13. Toda, A.; Oda, T.; Hikosaka, M.; Saruyama, Y.Thermochim Acta 1997, 293, 47.

14. Toda, A.; Tomita, C.; Hikosaka, M.; Saruyama, Y.Polymer 1997, 38, 2849.

15. Toda, A.; Tomita, C.; Hikosaka, M.; Saruyama, Y.Polymer 1997, 39, 1439.

16. Schawe, J. E. K. Thermochim Acta 1996, 271, 127.17. Toda, A.; Tomita, C.; Hikosaka, M.; Saruyama, Y.

Polymer 1997, 39, 5093.18. Toda, A.; Tomita, C.; Hikosaka, M.; Saruyama, Y.

Personal communication.19. Gilmore, J. R.; Colby, R. H.; Hall, E.; Ober, C. K.

J Rheol 1994, 38, 1623.20. Hall, E.; Ober, C. K.; Kramer, E. J.; Colby, R. H.;

Gilmore, J. R. Macromolecules 1993, 26, 3764.21. de Abajo, J.; de la Campa, J.; Kricheldorf, H. R.;

Schwarz, G. Makromol Chem 1991, 191, 537.22. Kricheldorf, H. R.; Schwarz, G.; de Abajo, J. de la

Campa, J. J Polym 1991, 32, 942.23. Chen, W.; Pyda, M.; Habenschuss, A.; London,

J. D.; Wunderlich, B. Polym Adv Technol 1997, 8,747.

24. Wunderlich, B. Macromolecular Physics, Vol. 1:Crystal Structure, Morphology, Defects; Vol. 2:Crystal Nucleation, Growth, Annealing; Vol. 3:Crystal Melting; Academic Press: New York, 1973,1976, 1980.

25. Chen, W.; Dadmun, M.; Zhang, G.; Boller, A.;Wunderlich, B. Thermochim Acta 1998, 324, 87.

1544 J. POLYM. SCI. PART B: POLYM. PHYS.: VOL. 37 (1999)