Static Light scattering and electric field-induced Kerr measurements were performed above the nematic-isotropic phase transition of a terminal-lateral-lateral-terminal negative Poisson ratio trimer. Far both measurements the inverse susceptibility was observed to be nearly linear with temperature, a result inconsistent with our previously reported Kerr data [Phys. Rev. E 58, 2041 (1998)]. [S1063-651X(99)11010-9]

Griffin, A.C.

He, Chaobin

Kang, Daeseung

Lu, Puwei

Mahajan, Milind P.

Petschek, Rolfe G.

Rosenblatt, Charles

Zhang, Shiyong

English

Aquila Digital Community

The University of Southern Mississippi The Aquila Digital Community Faculty Publications 10-1-1999 Pretransitional Behavior Above the Nematic-Isotropic Phase Transition of an Auxetic Trimer Liquid Crystal Daeseung Kang Case Western Reserve University Milind P. Mahajan Case Western Reserve University Shiyong Zhang Case Western Reserve University Rolfe G. Petschek Case Western Reserve University Charles Rosenblatt Case Western Reserve University See next page for additional authors Follow this and additional works at: https://aquila.usm.edu/fac_pubs  Part of the Chemistry Commons Recommended Citation Kang, D., Mahajan, M. P., Zhang, S., Petschek, R. G., Rosenblatt, C., He, C., Lu, P., Griffin, A. (1999). Pretransitional Behavior Above the Nematic-Isotropic Phase Transition of an Auxetic Trimer Liquid Crystal. Physical Review E, 60(4), 4980-4982. Available at: https://aquila.usm.edu/fac_pubs/9262 This Article is brought to you for free and open access by The Aquila Digital Community. It has been accepted for inclusion in Faculty Publications by an authorized administrator of The Aquila Digital Community. For more information, please contact Joshua.Cromwell@usm.edu. Authors Daeseung Kang, Milind P. Mahajan, Shiyong Zhang, Rolfe G. Petschek, Charles Rosenblatt, Chaobin He, Puwei Lu, and A.C. Griffin This article is available at The Aquila Digital Community: https://aquila.usm.edu/fac_pubs/9262 Pretransitional behavior above the nematic-isotropic phase transitionof an auxetic trimer liquid crystalDaeseung Kang,1 Milind P. Mahajan,1 Shiyong Zhang,1 Rolfe G. Petschek,1 Charles Rosenblatt,1 Chaobin He,2Puwei Liu,2 and A. C. Griffin2,31Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-70792Department of Chemistry & Biochemistry, University of Southern Mississippi, Hattiesburg, Mississippi 394063Department of Polymer Science, University of Southern Mississippi, Hattiesburg, Mississippi 39406~Received 12 February 1999!Static light scattering and electric field-induced Kerr measurements were performed above the nematic-isotropic phase transition of a terminal-lateral-lateral-terminal negative Poisson ratio trimer. For both measure-ments the inverse susceptibility was observed to be nearly linear with temperature, a result inconsistent withour previously reported Kerr data @Phys. Rev. E 58, 2041 ~1998!#. @S1063-651X~99!11010-9#PACS number~s!: 61.30.Gd, 64.70.MdAlthough most polymers exhibit a positive Poisson ratio,one can imagine cases where the Poisson ratio is negative,i.e., the polymer expands laterally when stretched @1,2#. Thisso-called ‘‘auxetic’’ behavior has been found in several poly-mers @2–6# and metal foams @5#, and may be based onatomic scale mechanisms @7,8# or an inverted honeycomb~reentrant cell! molecular structure @1,3,9#. He et al. havesynthesized a new class of auxetic materials based upon site-connectivity driven rod reorientation in main chain liquidcrystalline polymers @10#, which is schematically illustratedin Fig. 1 for the model trimer. For this class of molecules theterminal mesogens are connected at their ends, and the cen-tral mesogen at its core. In the nematic phase the moleculesinteract via a combination of anisotropic van der Waals andsteric interactions, giving rise to a molecular arrangement inwhich the mesogenic axes are approximately parallel to eachother @Fig. 1~a!#. For conformations in which the ends of themolecule are far apart, i.e., the spacer groups are fully ex-tended, the central mesogen orients at a large angle, or evenperpendicular, to the main chain direction @Fig. 1~b!#. X-rayresults on a polymer that is based on this model trimer in-deed show increased lateral separation between chains whenthe polymer fiber is stretched @10#.In a previous paper we examined the trimer shown in Fig.2 @11#. In the nematic phase we measured the splay, twist,and bend elastic constants, finding values similar to that oftypical monomers @12#. However, the ratio K33 /K11 wasslightly enhanced and the ratio K11 /K22 was slightly reducedfrom that of typical monomers, especially near the nematic-isotropic ~NI! phase transition temperature TNI . We also ex-amined the temperature dependence of the susceptibility x inthe isotropic phase via an electric-field-induced birefringence~Kerr! experiment. For most liquid crystalline materials theinverse susceptibility x21 is linear in temperature @12#. Forthe auxetic trimer, however, x21 was found to rise rapidlyjust above the transition, with its slope decreasing with in-creasing temperature. This behavior is shown in the inset ofFig. 3. The results were explained in terms of a Landaumodel based on separate but coupled order parameters, oneorder parameter for the two terminal mesogens and anotherorder parameter for the core mesogen. In this paper we re-visit the pretransitional behavior above the nematic-isotropicphase transition using two mutually independent probes, viz.,light scattering and Kerr measurements. Our central result isthat both measurements exhibit mean-field-like behavior,i.e., x21 is linear in temperature. These results are not con-sistent with our previously reported Kerr measurements, re-sults that we believe were compromised by faulty tempera-ture control.The trimeric liquid crystal was prepared by a multistepsynthetic route @13#. The compound was subjected to thestandard chromatographic and spectroscopic techniques forpurity and structure determination. Unlike the polymer, thetrimer flows easily, with a relatively low viscosity that is notmuch different from that of typical low molecular weightnematics @12#.We first reexamined the susceptibility using the electric-field-induced birefringence ~Kerr! technique. Because of therelatively high phase transition temperature TNI , we suspectthat there may have been a systematic artifact that affectedour previously reported measurements @11#. In those mea-surements the temperature went well beyond the desirableoperating region of the temperature controller and sensingthermistor. For these experiments we modified the thermalapparatus to handle temperatures between 150 °C and200 °C, and repeated our earlier measurements. A pair ofclean, untreated, indium-tin-oxide-coated glass slides wasseparated by a 6-mm Mylar spacer and cemented togetherwith high temperature epoxy ~rigid to 220 °C!. The thicknessof the cell was measured by an interference method @14# anddetermined to be 6.560.2 mm. The cell was placed into anFIG. 1. Schematic representation of auxetic trimer. ~a! Nematicphase. ~b! Stretched molecule with extended spacer groups.PHYSICAL REVIEW E OCTOBER 1999VOLUME 60, NUMBER 4PRE 601063-651X/99/60~4!/4980~3!/$15.00 4980 © 1999 The American Physical Societyimproved temperature controlled oven, stable to 10 mK. Theoptical arrangement and method of data analysis are de-scribed in detail in Ref. @11#. The liquid crystal was drivenwith an a.c. voltage at frequency f 51000 Hz and the result-ing 2 f component of birefringence Dn was measured as afunction of electric field E. Figure 3 shows (dDn/dE2)21 vstemperature. Unlike the previously reported data ~shown inthe inset of Fig. 3!, the new data are nearly linear in E2. Thesmall deviations of x21 from linearity at high temperatureare most likely due to conformational changes of the mol-ecule, as well as experimental noise when measuring smallvalues of x in the region well above TNI . Finally, note thatthe temperatures of the phase transition for the new data andold data ~inset! are offset by approximately 5 °C, a conse-quence of our faulty temperature control in the earlier experi-ment.Given the nearly linear behavior of x21 vs temperature,we next examined orientational fluctuations in the isotropicphase by means of light scattering. Although the fluctuationsmay be characterized by measuring either the intensity of thescattered light or the relaxation time t of the intensity auto-correlation function, we opted for the static measurementbecause t is of order 1 ms, which is near the limit of ourinstrument. A glass capillary tube of inner diameter 1.5 mmwas filled with the liquid crystal and its end was sealed byflame heating. The tube was then inserted into a rectangularcuvette filled with Dow Corning 550 silicon oil. The oilserved as an index matching fluid to avoid scattering thatwould otherwise occur from a capillary—air interface. Boththe liquid crystal and the silicon oil were filtered to removedust using a 0.22-mm Millipore filter. The cuvette was trans-ferred to an oven that was temperature controlled to 10 mK,and the scattering apparatus is described in Ref. @15#. Thedepolarized intensity at a scattering angle of 90° was mea-sured by inputting the signal from the photomultiplier into apulse amplifier-discriminator, whose output was fed into adigital autocorrelator. The temperature of the oven was firststabilized at 175 °C, and electronically ramped downward atthe rate of 0.2 °C min21. The intensity of the scattered light@proportional to the count rate# was recorded by the cor-relator in the raw intensity mode, and the inverse of theintensity vs temperature is plotted in Fig. 4.According to the Landau theory @16#, the mean squareorder parameter fluctuation at a given wave vector qW is givenFIG. 2. The structure of the auxetic trimer.FIG. 3. Inverse Kerr coefficient (dDn/dE2)21 vs temperature.The dotted line represents the linear fit, and the dashed and solidlines represents behavior predicted by a two-order-parameter modelwith different sets of parameters ~see text!. The inset corresponds todata from Ref. @11#. Note that the two temperature scales differbecause of a faulty temperature control in Ref. @11#.FIG. 4. Inverse intensity vs temperature from light scatteringmeasurement. The solid line is meant as a guide for the eye.PRE 60 4981BRIEF REPORTSby ^QJ 2(qW )&5(kT/VA)(11j2q2), where QJ is the tensor or-der parameter of the nematic phase, A5a(T2T*) is thecoefficient of the term quadratic in QJ of the free energyexpansion, T* is the supercooling temperature of the isotro-pic phase, V is the volume, and j is the correlation length fornematic fluctuations. For visible light and 90° scattering, thequantity j2q2!1, and thus the inverse of intensity is ex-pected to be approximately proportional to (T2T*)/T . Thedata in Fig. 4 are clearly consistent with this mean-field be-havior and with the new Kerr data in Fig. 3. A line is drawnthrough the data to guide the eye and to emphasize its tradi-tional mean-field-like character. Three caveats are in order.First, at higher temperatures there is a small downward cur-vature to the data that comes about because of unavoidableminute quantities of dust in the scattering cell. Second, in theregion just above TNI there is also a small amount of curva-ture; this behavior is due to correlation effects and is wellknown @17#. Finally, we note that the rounding that occursover 200 mK near the phase transition is likely due to acombination of a small, impurity-driven biphasic region and,more importantly, to steady-state temperature gradients inthe cell that occur at these very high temperatures.In our earlier paper we speculated that the highly nonlin-ear behavior of (dDn/dE2)21 vs temperature could be de-scribed by a Landau model involving ~for simplicity! scalarorder parameters that are coupled @11#. We supposed that S1corresponds to the order parameter of the two end mesogensand S2 to the order parameter of the central mesogen, andwrote the most general phenomenological Landau free en-ergy for a scalar order parameters asF5aS121bS1S21cS222e1S12e2S2 ,where a, b, and c may each have a unique temperature de-pendence and e1 and e2 are electric field factors. After somealgebra, we obtained the inverse Kerr coefficient in the formS dDndE2 D215F AT2T11 1 BT2T12G21, ~1!where A, B, T11 , and T12 are constants. This form success-fully fitted our earlier data ~cf. Fig. 3 inset!. Because theenvironments felt by the core and terminal mesogens arequite different, we believe that it is still reasonable to fit thepresent data with this form. In addition to the traditionallinear fit ~dotted line! in Fig. 3, we show two possible fits toEq. ~1!: The solid line represents the inverse Kerr coefficientusing the two-order-parameter model with parameters A55.431029 cgs, B51.031029 cgs, T115159.7 °C, andT125130.0 °C; and the dashed line using A55.731029 cgs, B520.431029 cgs, T115159.7 °C, and T125130.0 °C. It is important to recognize that with a four-parameter fit, the x-square surface has many shallowminima, and the parameters are extremely sensitive to smallvariations in the data. We thus conclude that despite the ap-parent ‘‘traditional’’ single-order parameter mean-field-likeKerr results, the terminal mesogens and core mesogen mayactually be best modeled by two distinct ~but coupled! orderparameters. In fact, one of the order parameters—this wouldbe S2 of course—may even be slightly negative ~cf. dashedline!, consistent with the molecular architecture. It is clear,however, that optical experiments are not completely suit-able to elucidate this conjecture, and the multiple order pa-rameter approach would be better investigated by, e.g., anuclear magnetic resonance probe. This work is planned inthe near future.To summarize, we have experimentally observed that thepretransitional behavior above TNI of the auxetic trimershown in Fig. 2 is apparently similar to that of typical mo-nomeric liquid crystals. We have also shown, however, thatwithin experimental error the Kerr data may be described bythe two-order-parameter model introduced in another publi-cation @11#. As the spacer groups may be made shorter orlonger, it is conceivable that qualitatively different behaviormay be observed, especially for shorter ~and therefore lessflexible! spacer groups.This work was supported by the National Science Foun-dation under Grant Nos. DMR-9502825 and DMR-9420843,by NSF’s Advanced Liquid Crystalline Optical MaterialsScience and Technology Center under Grant No. DMR-8920147, and by the U.S. Air Force Office of Scientific Re-search under Contract No. F49620-94-1-0454.@1# K. E. Evans, I. J. Hutchinson, and S. C. Rogers, Nature ~Lon-don! 353, 124 ~1991!.@2# R. S. Lakes, Science 235, 1038 ~1988!.@3# L. J. Gibson and M. F. Ashby, Cellular Solids: Structure andProperties ~Pergamon, Oxford, 1988!, pp. 70–82.@4# K. E. Evans, Endeavour 15, 170 ~1991!.@5# E. A. Friis, R. S. Lakes, and J. B. Park, J. Mater. Sci. 23, 4406~1988!.@6# K. L. Alderson and K. E. Evans, Polymer 33, 4435 ~1992!.@7# A. E. H. Love, A Treaty on the Mathematical Theory of Elas-ticity, 4th ed. ~Dover, New York, 1944!.@8# D. J. Gunton and G. A. Saunders, J. Mater. Sci. 7, 1061~1972!.@9# G. Wei and S. F. Edwards, Comput. Polym. Sci. 2, 44~1992!.@10# C. He, P. Liu, and A. C. Griffin, Macromolecules 31, 3145~1998!.@11# D. Kang, M. P. Mahajan, R. G. Petschek, C. Rosenblatt, C. He,P. Liu, and A. C. Griffin, Phys. Rev. E 58, 2041 ~1998!.@12# See, e.g., S. Chandrasekhar, Liquid Crystals ~Cambridge Uni-versity Press, Cambridge 1992!.@13# P. Liu, C. He, C. J. Booth, and A. C. Griffin, Abstr. Pop. Am.Chem. Soc. 216, U108 ~Part 3! ~1998!.@14# C. Rosenblatt, J. Phys. ~Paris! 45, 1087 ~1984!.@15# G. A. DiLisi, C. Rosenblatt, A. C. Griffin, and U. Hari, Phys.Rev. A 45, 5738 ~1992!.@16# L. D. Landau, and E. M. Lifshitz, Statistical Physics ~Addison-Wesley, Reading, MA, 1958!.@17# T. W. Stinson, J. D. Litster, and N. A. Clark, J. Phys. Colloq.33, C1-69 ~1972!.4982 PRE 60BRIEF REPORTS

Pretransitional Behavior Above the Nematic-Isotropic Phase Transition of an Auxetic Trimer Liquid Crystal

https://aquila.usm.edu/cgi/viewcontent.cgi?article=10435&context=fac_pubs

Pretransitional Behavior Above the Nematic-Isotropic Phase Transition of an Auxetic Trimer Liquid Crystal

Abstract

Similar works

Full text

Available Versions

Aquila Digital Community