The results of two independent experiments in the vicinity of the “transition” from the third blue phase ( BPIII) to isotropic phase ( I) are reported for a highly chiral liquid crystal. Heat capacity measurements using a high-resolution calorimeter and dynamic light-scattering measurements using circularly polarized light have been performed. The data show a continuous evolution of BPIII into I with no critical fluctuations. This is strong evidence that the BPIII-I transition in this compound is supercritical, indicating that the BPIII and I phases possess the same macroscopic symmetry

Collings, Peter J.

Garland, C. W.

Kutnjak, Z.

Passmore, J. Loren

English

Works

Swarthmore College Works Physics & Astronomy Faculty Works Physics & Astronomy 6-12-1995 Supercritical Conversion Of The 3rd Blue Phase To The Isotropic-Phase In A Highly Chiral Liquid-Crystal Z. Kutnjak C. W. Garland J. Loren Passmore Peter J. Collings Swarthmore College, pcollin1@swarthmore.edu This work is brought to you for free and open access by . It has been accepted for inclusion in Physics & Astronomy Faculty Works by an authorized administrator of Works. For more information, please contact myworks@swarthmore.edu. Follow this and additional works at: https://works.swarthmore.edu/fac-physics  Part of the Physics Commons Let us know how access to these works benefits you  Recommended Citation Z. Kutnjak, C. W. Garland, J. Loren Passmore, and Peter J. Collings. (1995). "Supercritical Conversion Of The 3rd Blue Phase To The Isotropic-Phase In A Highly Chiral Liquid-Crystal". Physical Review Letters. Volume 74, Issue 24. 4859-4862. DOI: 10.1103/PhysRevLett.74.4859 https://works.swarthmore.edu/fac-physics/91 VOLUME 74, NUMBER 24 PHYSICAL REVIEW LETTERS 12 JUNE 1995Supercritical Conversion of the Third Blue Phase to the Isotropic Phase in a Highly ChiralLiquid CrystalZdravko Kutnjak and Carl W. GarlandDepartment of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139J. Loren Passmore and Peter J. CollingsDepartment of Physics and Astronomy, Swarthmore College, Swarthmore, Pennsylvania 19081(Received 28 October 1994)The results of two independent experiments in the vicinity of the "transition" from the third bluephase (BP«&) to isotropic phase (I) are reported for a highly chiral liquid crystal. Heat capacitymeasurements using a high-resolution calorimeter and dynamic light-scattering measurements usingcircularly polarized light have been performed. The data show a continuous evolution of BP»& intoI with no critical fluctuations. This is strong evidence that the BPill-I transition in this compound issupercritical, indicating that the BP«& and I phases possess the same macroscopic symmetry.PACS numbers: 61.30.—v, 64.70.Md, 65.20+w, 78.20.DjThe effect of chirality on liquid crystal phases andtheir transitions has been a subject of intense interest andsurprising results. New liquid crystal phases that possessa regular array of "defects" become stable if the chiralityis high. These include the blue phases between the chiralnematic (N*) and isotropic (I) phases; two of the bluephases have cubic lattices of defects and one blue phasehas a seemingly amorphous array of defects [1]. Thesedefects are lines between double-twist cylinders wherethe orientational order goes to zero and the direction ofpreferred orientation is undefined. Other examples arethe twist-grain-boundary phases in chiral systems withsmectic phases [2]. The defects in these phases are grainboundaries between smectic blocks. The amorphous bluephase (BPttt), which exists at temperatures just belowthe isotropic phase in highly chiral liquid crystals, is notwell understood. Suggestions have been made that it isa "melted" version of the cubic blue phases [3], or thatit is a phase possessing random double-twist cylinders[4], icosahedral or quasicrystalline order [5], or bondorientational order [6].The effect that chirality has on liquid crystal phasetransitions is more subtle. While fluctuations play animportant role in the weakly discontinuous transition froma nonchiral nematic liquid crystal to the isotropic liquidphase, chirality introduces modes that fluctuate morestrongly [7]. There is considerable evidence that chiralitytends to drive the system toward a continuous transition[8—11], but there is only a small amount of indirectevidence that the BP»&-I transition actually is continuousin any liquid crystal system [11—13.]To be more specific, Voets and Van Dael have shownthrough adiabatic scanning calorimetry experiments thatthe BP«&-I transition in S-(+)-4-(2-methylbutyl)phenyl-4-decyloxybenoate (CE6) is discontinuous with a latentheat that decreases from 1627 mJ/g in the racemicmixture (an N* Itransition) to 785-mJ/g in the chiralenantiomer [10]. An even smaller BPtt~-I latent heat(but still a discontinuous transition) was observed in thepure chiral material S-(+)-4-(2-methylbutyl)phenyl-4-hexyloxybenzoate (CE4), where the latent heat decreasedfrom 957 mJ/g in the racemic mixture (an N* Itransi--tion) to 147 mJ/g in the chiral enantiomer [13]. Beckerand Collings confirmed these CE4 measurements opticallyby showing that the discontinuity in the intensity of staticlight scattering decreased with increasing chiral fractionbut was still discontinuous for the pure chiral isomer [11].A similar static light scattering experiment on the morechiral compound S,S-(+)-4"-(methylbutylphenyl)-4'-(methylbutyl)-4-biphenylcarboxylate (S,S-MBBPC [14])showed no discontinuity at all [11].In this Letter we report the results of two differ-ent types of experiments performed in the vicinity ofthe BP~t~-I transition in S,S-MBBPC: (1) heat capacitymeasurements using a new high-resolution calorimeter,and (2) improved static and new dynamic light-scatteringmeasurements. The heat capacity and the light-scatteringdata evolve continuously in the BP»&-I region for thiscompound with no evidence for critical fluctuations.As discussed below, our results indicate a supercriti-cal BP»i-I evolution in S,S-MBBPC, i.e., a continuousbut nonsingular variation in properties analogous to whatoccurs in a simple fluid at pressures above the liquid-gas critical pressure. The implication of this is that themacroscopic symmetry of the BP»& and isotropic phasesis the same.The calorimeter is capable of measuring the heatcapacity C~ using an ac technique with-excellent signal-to-noise ratio and very high resolution. In addition, a newnonadiabatic scanning technique can be used to measureC„ in the absence of two-phase coexistence and alsoquantitative latent heats at first-order transitions [15]. Theinvestigated temperature range (388—393 K) includes thechiral nematic to first blue phase (BPt) transition, the BP&to BP»i transition, as well as the supercritical evolutionfrom BPi I I to the isotropic phase, as shown in Fig. 1.0031-9007/95/74(24)/4859(4)$06. 00 1995 The American Physical Society 4859VOLUME 74, NUMBER 24 PHYSICAL REVIEW LETTERS 12 JUNE 1995latent heat L is then given by4.0— & nonadiabatie seae»eg C (T) +ta0—ae C (T) dataT2[C~(eff) —C„(coex)]dT, (2)3.5—CaP~3.0—I BPI I388 389 390 39i 392T (Kj393 394FIG. 1. The specific heat-capacity variation in the N"-BP&-BP»&-I transition region for S,S-MBBPC. The heat peaks forthe scanning data at the N'-BP& and BP&-BP»I are artificialC„(eff) values due to two phase coexistence and latent heateffects. Note the absence of latent heat peak at the BP»&-Itransition. The heating rate for the nonadiabatic scanning run(open circles) was 4 K/h, while the heating or cooling ratesfor the ac calorimetry run at ~e = 0.196 s ' (solid line) were50 mK/h.where I' is the dc power input, T is the time-dependenttemperature of the sample, Tb is the time-independenttemperature of the heat bath, and R is the thermalresistance between the sample and bath. Thus (T-Tb)/R represents the rate of heat leak between sampleand bath. For a one-phase system, this method yieldsthe true C~ value. However, if two coexisting phases areinterconverting at a first-order transition, Eq. (1) yields anapparent value C„(eff) refiecting latent heat effects. The4860Data from an ac calorimetry run and a nonadiabaticscanning run are both given in this figure.The heat capacity data obtained in the ac calorimetryrun show very little scatter, and the 450 data points arerepresented by a smooth curve C„(T). It must be stressedthat the ac calorimetry technique does not measureenthalpy and cannot provide a quantitative measure oflatent heats. However, characteristic changes in the phaseshift @ between the input ac power Pp exp[iver] and theobserved oscillatory sample temperature T„ex[pi(cut +P —~/2)] do provide qualitative indications of two-phase coexistence at discontinuous transitions [15,16]. Inthe present study, an ac phase shift anomaly was seenat the BP]-BP]~~ transition but was not present in thetemperature range 391—393 K (note that no ac C„datawere taken below 390.2 K).The nonadiabatic scanning technique measures an ef-fective heat capacity C~ defined bydH/dt P —(T Tb)/RdT/dt dT/dtwhere C„(coex) is the heat capacity that a two-phasecoexisting mixture would have in the absence of pha se.conversion. Thus C„(coex) accounts for the heat effectsassociated with raising the temperature of a two-phasemixture over the narrow coexistence range from T~ to T2and is well represented by the ac C„(T) data. Note thatthe coexistence range T2 —T~ is only 88 mK for N*-BP)and 40 mK for BP]-BP~~~. The nonadiabatic scanningtechnique is completely analogous to the well-establishedadiabatic scanning method [17] and is closely related tothe relaxation method described in Ref. [16].Figure 1 clearly shows the excess C„(eff) peaks at389.20 ~ 0.05 and 390.34 ~ 0.02 K which are associatedwith latent heat effects at the N'-BPI and BP~-BP~~ ~tran-sitions. No such latent heat peak is observed at the BP~~I—I transition (C„maximum at 392.12 ~ 0.08 K). Thelatent heats were determined to be 56.4 and 11.3 mJ/gfor the N"-BP& and BP&-BP»& transitions, respectively,which agree well with values reported for other chiralliquid crystals. The N'-BP& latent heat is 34 mJ/g forcholesteryl nonanoate (CN) [18] and 87 mJ/g for CE6[10]. The sum of the latent heats for the BP~-BP~~and BPqq-BPqqq transitions is 14.6 mJ/g for CN [18] and71 mJ/g for CE6 [10]. The essential new feature for S,S-MBBPC is the absence of any indication of a BP~~~-I la-tent heat. This is in contrast to the reported BP~~~-I latentheat values in less chiral materials: 323 ~ 50 mJ/g forCN [18],785 mJ/g for CE6 [10], and 147 mJ/g for CE4[13]. The value for CE4 is the smallest BP~~~-I latent heatever reported.Static and dynamic light-scattering measurements wereperformed on S,S-MBBPC using 488 nm light and a 90scattering angle for an 8 K interval that included theBPj, BP~I], and I phases. Two polarization arrangementswere used: (1) right circular polarized (RCP) incidentlight and right circular polarized detected light, and(2) left circular polarized (LCP) incident light and leftcircular polarized detected light. The first polarizationarrangement is sensitive to the most strongly fluctuatingmode (a chiral mode) in S,S-MBBPC, and the secondarrangement is sensitive to the most weakly fluctuatingmode (a chiral mode) in S,S-MBBPC [7]. In each case,a nonchiral fluctuating mode contributes to the detectedlight at the 2% level and another chiral fluctuating modecontributes at less than the 0.1% level. In this temperatureregion, S,S-MBBPC has some of the shortest relaxationtimes measured in liquid crystals. In order to measurethese submicrosecond times, a cross-correlation techniqueemploying a beam splitter and two photomultiplier tubes(PMTs) was used to eliminate the effects of afterpulsingin the PMTs. The correlator was a Malvern 7032ES setto a 50 ns sample time. Exponential fits to the correlationVOLUME 74, NUMBER 24 PH YSICAL REVIEW LETTERS 12 JvNE 1995function allowed the relaxation times to be measured withan uncertainty of between 10 and 30 ns.The thermistor used for temperature control in theselight-scattering experiments was not individually cali-brated. Instead, parameters supplied by the manufacturerwere used. This is probably the reason why all the tran-sition temperatures measured via light scattering are 2 Klower than those meausured in the heat-capacity experi-ments. The widths of the BPi and BP«i phases measuredwith the uncalibrated thermistor (1.0 and 1.5 K, respec-tively) correspond nicely to those measured previously inoptical activity experiments (1.1 and 1.6 K, respectively)[12] and to those measured in the heat-capacity measure-ments reported here (1.14 and 1.78 K, respectively).The intensity of the scattered light I, as a function oftemperature for both polarization arrangements is shownin Fig. 2. Because of a combination of stray light reach-ing the detector and impurity scattering from the sample,there is a background intensity of about 20000 counts/s.When this background intensity is subtracted from I„the inverse intensity in the isotropic phase is linear,which is the mean-field result and has been verified pre-viously [9]. A discontinuity in the scattering for bothchiral modes is apparent at the BPi-BP»i phase transi-tion at 388.2 ~ 0.1 K, but only a change in temperaturedependence is observed at the BPi i i -I transition around389.7 ~ 0.2 K. The N*-BPi transition is easily measured(387.2 ~ 0.1 K), since the 1 cm thick sample is opaque inthe N* phase. The lack of a discontinuity in the BP«i-Itransition in the high-quality data of Fig. 2 confirms pre-vious optical results on this compound [11,12]. In fact,the temperature over which the data changes from mean-field behavior to a more or less linear dependence is about0.5 K, which is roughly the width of the heat-capacitypeak in Fig. 1. Similar measurements on CE6 reveal aclear discontinuity at the BP»i-I transition, with mean-field behavior followed right up to the discontinuity [19].The relaxation time of the fluctuations for both chiralmodes is displayed in Fig. 3. Again, a discontinuity isevident at the BPi-BPi» transition but not at the BP»i-Itransition. Graphing the inverse of the relaxation timevs temperature for the data in the isotropic phase yieldsa linear relationship as expected from mean-field theory.However, the divergent behavior in the isotropic phaseshown in Figs. 2 and ' 3 is no stronger than is seenin similar experiments on CE6 [19], indicating that thefiuctuations in the neighborhood of the BP»i-I transitionare not critical. This also suggests the evolution of onephase to another typical of a supercritical region.We feel that the evidence supporting a supercritical(continuous but nonsingular) evolution of BPiti to Iin S,S-MBBPC is very strong. There is no indicationof two-phase coexistence or latent heat in the thermalstudies of the BPiii-I transition. There is the continuousevolution of both intensity and relaxation time in theoptical studies. One possible concern is that our thermalresults are artificial due to rate effects if the BP«i-Itransition is kinetically very sluggish compared to theN -BP& and BP&-BP» i transitions. This possibility hasbeen tested in three ways. First, as shown in Fig. 1, thenonadiabatic scanning results and ac calorimetry data arein excellent agreement, even though the scanning rates300g) 250o200C)C)C)450't 0050S,S-MBBPC~ 5RCP-RCPLCP-LCP~0BP,388I I390 392T (K)394II~~~ 0I~~ I~ I~I~I'~~I ~~I ~Ig ~II8Pg) I IsotropicI1.2M 0.8I~EI—cocdXCd0.4CC0.2ilIIIgS,S-MBBPCRCP-RCPLCP-LCPi394IIBp BP„, i IsotropicI I I388 390 392FIG. 2. Light-scattering intensity I, for both polarizationsin the BP&-BP&» -I transition region for S,S-MBBPC. Thewavelength was 488 nm and the scattering angle was 90 . Notethe discontinuity in I, at the first-order BP&-BP»& transitionand the continuous change in temperature dependence with nodiscontinuity at the BP»l-I transition.F)G. 3. Relaxation time 7. of the scattered light for bothpolarizations in the BP& -BP&1&-I transition region for S,S-MBBPC. The wavelength was 488 nm and the scattering anglewas 90 . Note the discontinuity in ~ at the first-order BP&-BP»Itransition and the continuous change in temperature dependencewith no discontinuity at the BP»1-I transition.4861VOLUME 74, NUMBER 24 PHYSICAL REVIEW LETTERS 12 JUNE 1995differ by a factor of 80. Second, the ac calorimetryexperiment was repeated with an oscillation frequency9 times smaller and a scanning rate half as large, yieldingidentical results. Third, there is no change in the acheat capacity at the peak of the BP»&-I transition whenthe temperature is held constant for 2 X 105 s. Thus theidea of a discontinuous transition but very slow BP»~-Iconversion is not consistent with our data.The existence of a first-order BP»~-I coexistence linethat terminates at an isolated critical point is confirmedby preliminary Cp measurements on mixtures of S,S-MBBPC and its racemate. Two-phase coexistence anda latent heat are observed at low concentrations of S,S-MBBPC, and both these features disappear for highconcentrations of S,S-MBBPC. Further work to locateand characterize the critical mixture is in progress.The existence of a critical point for the BP»~-I transi-tion has extremely important implications for the struc-ture of BP»~. Any structure proposed for BP»~ mustpossess isotropic symmetry macroscopically, since onlythen could a critical point be present. Yet the existenceof optical activity in both BP»& and I indicates that thesymmetry of neither phase is completely isotropic [11,12].Obviously, some order parameter is discontinuous at theBP», -I transition in low chirality compounds but continu-ous in the more highly chiral S,S-MBBPC.Lubensky and Stark have introduced a scalar order pa-rameter (P) to describe both BPt~~ and I This model, i.nwhich (P) = ((V x Q) Q) with Q(r) being the alignmenttensor, predicts that the BP~~ ~-I transition is in the sameIsing universality class as the liquid-gas transition [20].These results are based upon work supported by theNational Science Foundation under Grants No. DMR-9224617 and No. DMR-9311853. One of the authors(Z. K.) wishes to acknowledge support from the Mini-stry of Science of Slovenia. We wish to acknowledgethe experimental assistance and advice of T. Chan andB. Zhou and useful discussions with P. H. Keyes and T. C.Lubensky.[1] Recent reviews include D. C. Wright and N. D. Mermin,Rev. Mod. Phys. 61, 385 (1989); P. P. Crooker, Liq. Cryst.[2][4][5][7][8][10][11][12][13][14][15][16][18][19][20]5, 751 (1989); R. M. Hornreich and S. Shtrikman, Mol.Cryst. Liq. Cryst. 165, 183 (1989); V. A. Belyakov andV. E. Dmitrienko, Usp. Fiz. Nauk 146, 369 (1986) [Sov.Phys. Usp. 28, 535 (1985)].G. Srajer, R. Pindak, M. A. Waugh, and J.W. Goodby,Phys. Rev. Lett. 64, 1545 (1990)S.R. Renn and T. C.Lubensky, Phys. Rev. A 38, 2132 (1988); .P. H. Keyes, Phys. Rev. Lett. 65, 436 (1990).R. M. Hornreich, M. Kugler, and S. Shtrikman, Phys. Rev.Lett. 48, 1404 (1982).L. Longa, W. Fink, and H. R. Trebin, Phys. Rev. E 48,2296 (1993)R.M. Hornreich and S. Shtrikman, Phys. Rev.Lett. 56, 1723 (1986); D. S. Rokhsar and J.P. Sethna, ibid56, 1727 (1986); .L. Longa and H. R. Trebin, Phys. Rev. Lett. 71, 2757(1993).For a recent review, see P. J. Collings, Mod. Phys. Lett. B6, 425 (1992).P. R. Battle, J. D. Miller, and P. J. Collings, Phys. Rev. A36, 369 (1987).J.E. Wyse and P. J. Collings, Phys. Rev. A 45, 2449(1992).G. Voets and W. Van Dael, Liq. Cryst. 14, 617 (1993).J.B. Becker and P. J. Collings, Mol. Cryst. Liq. Cryst. (tobe published).J. Ennis, J.E. Wyse, and P. J. Collings, Liq. Cryst. 5, 861(1989).G. Voets, Ph. D. thesis, University of Leuven, Belgium(1992).S,S-MBBPC is sold by BDH under the name CE2. Sinceit is not part of the same homologous series as CE4 andCE6 (also sold by BDH), we prefer to use a differentdesignation.H. Yao, T. Chan, and C. W. Garland, Phys. Rev. E 51,4585 (1995).K. Ema, H. Yao, I. Kawamura, T. Chan, and C. W.Garland, Phys. Rev. E 47, 1203 (1993); see, also,C. W. Garland, Thermochim. Acta 88, 127 (1985), andreferences therein.J. Thoen, E. Bloemen, and W. Van Dael, J. Chem. Phys.68, 735 (1978).J. Thoen, Phys. Rev. A 37, 1754 (1988).J.L. Passmore and P. J. Collings, in Proceedings of the15th International Liquid Crystal Conference, Budapest,1994 (unpublished).T. Lubensky and H. Stark (private communication).4862