Critical heat capacity of octylcyanobiphenyl (8CB) near the nematic-smectic A transition

Transcription

1 Critical heat capacity of octylcyanobiphenyl (8CB) near the nematicsmectic A transition G.B. Kasting, C.W. Garland, K.J. Lushington To cite this version: G.B. Kasting, C.W. Garland, K.J. Lushington. Critical heat capacity of octylcyanobiphenyl (8CB) near the nematicsmectic A transition. Journal de Physique, 1980, 41 (8), pp < /jphys: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1980 HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 La An There J. Physique 41 (1980) AOÛT 1980, 879 Classification Physics Abstracts E Critical heat capacity of octylcyanobiphenyl (8CB) near the nematicsmectic A transition G. B. Kasting, C. W. Garland and K. J. Lushington Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. (Reçu le 11 février 1980, accepté le 14 avril 1980) technique ac a été utilisée pour mesurer la capacité calorifique près de la transition nématique 2014 Résumé. smectique A (NSmA) du composé 8CB le long d isobars à 1, 750 et bar. La grandeur du pic Cp associé à cette transition décroît quand la pression augmente mais la forme du pic reste essentiellement inchangée. La capacité calorifique en excès à 1 atm. est conforme à une transition NSmA du second ordre, caractérisée par un exposant critique effectif 03B1 0,30 ± 0, Abstract. ac technique has been used to measure the heat capacity near the nematicsmectic A (NSmA) transition in 8CB along isobars at 1, 750 and bar. As the pressure is increased, the magnitude of the Cp peak associated with this transition decreases but the shape of the peak remains essentially unchanged. The excess heat capacity at 1 atm. is consistent with a secondorder NSmA transition characterized by an effective critical exponent 03B ± Introduction. has been considerable interest in the nematicsmectic A (NSmA) transition in liquid crystals, especially since McMillan s meanfield prediction [1] of possible secondorder character. A more realistic model proposed by de Gennes [2] placed this transition in the d 3, n 2 universality class (XY model in three dimensions) along with the superconductingnormal transition in metals and the lambda transition in He. Subsequent analysis of de Gennes hamiltonian showed that the NSmA transition should be weakly firstorder [3] and that the observed quasicritical behaviour could be much more complicated than that of the simple X Y model. In particular, anisotropic behaviour with correlationlength exponents v jj > vl is possible, as are crossover sequences from meanfield to anisotropic critical to isotropic critical (XY) and finally to a firstorder transition [4]. Several materials have been investigated in which the NSmA transition is secondorder to within the resolution of careful experiments [5, 8]. Among these materials are pcyanobenzilidenenoctyloxyaniline (CBOOA), its biphenyl analog octyloxycyanobiphenyl (80CB), and octylcyanobiphenyl (8CB) which is the subject of the present study. All three of these materials are bilayer smectics; i.e., each smectic layer is composed of pairs of oppositely oriented molecules with their aromatic portions overlapping [9]. CBOOA and 80CB show a reentrant nematic phase at high pressures [10], whereas 8CB does not (at least below 7 kbar) [10, 11]. The critical behaviour at the NSmA transition in these compounds is inconsistent with the simple XY interpretation of the de Gennes model. According to Xray scattering results in the nematic phase of all these materials [6], the divergence of the correlationlength parallel to the incipient smectic density wave is generally consistent with v Il VHe 0.67, but the corresponding exponent for the perpendicular correlationlength is somewhat smaller (v ). Light scattering measurements of the K2 and K3 elastic constants in the N phase yield v Il values that are generally consistent with the X Y model [6, 12] and vl values that are somewhat uncertain but smaller [8] ; furthermore, the elastic constants B and D in the SmA phase are both anpmalous [6]. Calorimetric studies of CBOOA and 80CB have shown that the specific heat divergence at the NSmA transition is best characterized with a fairly large positive exponent (in the range oc 0.15 for CBOOA [13] and a 0.25 for 80CB [7]) rather than the almost logarithmic (a 0.026) singularity of the XY model. We report here the results of an ac calorimetric investigation of the NSmA transition in 8CB over the range bar. The experimental method and the procedure for reducing the data to Cp values have been described elsewhere [7]. The results are Article published online by EDP Sciences and available at

3 We Heat Critical 880 similar to those reported for 80CB in that (1) a large positive exponent a a 0.30 ± 0.05 is required to represent the data at 1 atm. ; (2) the decrease in the magnitude of the Cp peak with increasing pressure has the same dependence on TNAI TNr in both cases; and (3) the shape of the Cp peak is not sensitive to the pressure. 2. Results. have measured the heat capacity of 8CB along isobars at 1, 750, and bar over the température ranges shown in figure 1. Two samples Fig. 2. capacity of 8CB (sample A) at 1 atm. and 750 bar. Background curves used to obtain ACp at the NSmA transition are shown. Fig. l. PT phase diagram for 8CB (MW ). The dashed lines indicate the range of our data, the triangles indicate the observed transition temperatures, and the crosses represent the melting point of the crystal on warming. The solid phase lines are from reference [10]. of material from BDH Chemicals were investigated [14]. The temperature dependence of Cp for sample A at 1 atm. and at 750 bar is shown in figure 2. As in 80CB, the magnitude of the Cp peak associated with the nematicisotropic (NI) transition is almost independent of pressure, while the magnitude of the NSmA peak is very sensitive to the pressure. This behaviour suggests that the energy fluctuations responsible for the excess heat capacity at the NSmA transition are largely associated with fluctuations in the nematic order parameter S, which are expected to decrease with increasing TNI TNA [15]. The excess heat capacity ACp in the vicinity of the NSmA transition at 1 atm. is shown in figure 3. The smooth background shown in figure 2 has been subtracted from the observed Cp values, and the resulting values of àc,irc,(obs)ircp(bkgd)ir have been plotted as a function of the reduced temperature t (T TNA)/TNA. The data shown in figure 3 have been corrected for a constant drift in the value of TNA ( mk per day) during the 18 days required Fig. 3. heat capacity near the NSmA transition in 8CB (sample A) at 1 atm. The data for N 3 and N 4 have been shifted upward by 10 and 20 units, respectively, for clarity. The arrows indicate the positions of 1 t Imin for the leastsquares fits reported in tables 1 and II. to obtain this set of data points. This drift rate was determined by observing the variation of Cp at constant temperature during three consecutive overnight ( 12 h) periods when the temperature was very close to TNA. The fact that TNA increased slowly with time suggests that this drift may have been caused by the segregation of an impurity from the bulk of the sample during the run. The heat capacity peak shown in figure 3 is also considerably more rounded close to TNA than that observed by Thoen et al. [16] in an adiabatic experiment or that observed by us in,80cb [7]. This roundoff region is much too broad to be explained as the result of finite ac temperature oscillations, which are 7 mk peaktopeak near TNA [17].

4 Critical 3.1 We a 881 Highpressure data near the NSmA transition are shown in detail in figure 4. These data are less reliable than those obtained at 1 atm. for several reasons : (1) Hnhole leaks in the silver cells for both samples allowed argon gas to slowly dissolve in the liquid crystà during the course of the pressure runs ; (2) Poor pressure stability during the 750 bar run caused TNA to drcp 90 mk in the 18 h period during which the data very close to the transition (j t 1 103) were obtained, leading to a large correction in the AT values; (3) Several abrupt changes in the Cp values (see Ref. [7]) led to slightly different results for each of four separate passes through the NSmA transition at 750 bar ; (4) The bar data were quite scattered due to problems with the highpressure electrical leads during this run. The dissolving of argon into the samples at high pressures was our principal experimental difficulty. The présence of dissolved argon was detected in two ways. First, the value of TNI was observed to drop by several degrees between the beginning and the end of each high pressure run (a period of approximately 30 days). The corresponding drop in ÎNA was only 0.2 K. Second, the sample cells blew up upon depressurization from bar due to the release of dissolved gas. The cell containing sample A was repaired and studied again at 1 atm. The Cp peaks were very similar to those observed in the initial 1 atm. run (Fig. 2), and TNI was lower by only 0.3 K. Hence, the large shifts in TNI observed at high pressures were a reversible consequence of dissolved argon rather than a result of thermal decomposition or some other chemical reaction. We believe that the highpressure I1Cp values shown in figure 4 are not greatly influenced by dissolved gas since these data were taken near the beginning of the first pressure run on each sample. In particular, the decrease in the magnitude of ACp with pressure cannot be caused by dissolved gas. When sample A was definitely influenced by dissolved argon after being held at 750 bar for 35 days and bar for 15 days more, it gave a ACp peak at bar that was considerably larger than the sample B peak shown in figure 4. Furthermore, the trend of decreasing ACp peaks was also observed in 80CB samples sealed in cells that were free of leaks [7]. Thus the major features ACp peak that preserves its shape but diminishes in magnitude upôn increasing the pressure are felt to be intrinsic properties of 8CB. Nonetheless, it likely that the linear Cp variation between seems Fil. 4. heat capacity near the NSmA transition in 8C3 at 750 bar and bar, multiplied by the scale factors z 2.18 and 5.45, respectively, to allow direct comparison with the 1 atm. data (solid line, z 1). The data for N 3 has been shifted upward by 30 units for clarity. at 750 bar corresponds to a twophase region induced by dissolved argon and is not a property of pure 8CB [18]. 3. Discussion. critical enthalpy ÔHNA ACP our 1 atm. Cp NSmA ENTHALPY. The dt obtained from data near the NSmA transition is 228 J. mol1. This value may be compared with total enthalpy values of 126 [11], 130 [19], and 200 [20] J. mol1 determined by means of differential scanning calorimetry. It is common practice to report such DSC results as the latent heat AH, although the rapid sweep rates used in this technique do not allow one to distinguish between a true latent heat and a rapid but continuous variation of enthalpy through the transition. The ac method does not give reliable latent heats either, but it does give an accurate measure of the equilibrium pretransitional enthalpy associated with a transition. Thus a comparison between our value for ÔHNA and the DSC results indicates that the latent heat at this transition must be very small. An estimate of I1H 0 10 J. mol1 is supported by a recent adiabatic study of 8CB [16]. Thus, the best calorimetric data are consistent with a secondorder NSmA transition in 8CB. Leadbetter et al. [20] reported a volume change (i.e., AV/V 5 x 104) over a 0.1 K range near this transition. Although they interpreted this result as indicating a very weak firstorder transition, it seems quite possible in light of our data that the volume change at the transition could also occur continuously. We therefore feel that there is no convincing experimental evidence of firstorder character at this transition. 3.2 CRITICAL EXPONENTS. have used the to fit the 1 atm. data at the Marquardt algorithm

5 Results Critical 882 NSmA transition to simple power laws of the form In view of the very small error in the temperature measurements, the data points have been given equal weights [7] (constant standard deviation ui 0.12). The first step was to determine the minimum reduced temperature at which these data still followed a the data powerlaw divergence. To do this we fit above and below TNA separately over the range for values of 1 t Imin between 1 x 105 and 3 x 104. TNA and TNA were fixed at Tm C, the temperature of the Cp maximum [21]. The results of these fits are summarized in figure 5. The inclusion of data at t values less than those indicated by the arrows led to a marked deterioration in the quality of the fits and introduced a systematic pattern of deviations. Above TNA these deviations could possibly be associated with the finite Tac amplitude [17], but the deviations below TNA extend too far away from the transition to be explained as finite amplitude effects. We believe that positive deviations at small 1 t in the SmA phase and the region of rounding (negative deviations) at even smaller 1 t in both phases are related to impurities. For all subsequent fits, the values Of 1 t Im;n are those indicated by the arrows in figures 3 and 5. Having established 1 t Lin. we then fit the data above and below TNA over the ranges shown in table I. These fits are very stable and there is no evidence that TNA 1 TNA However, the effective critical exponent in the N phase does not equal that in the SmA phase. The fits listed in table 1 are all Fig. 5. exponents and reduced chisquares for leatsquares fits of eq. (1) to the 1 atm. data in 8CB near the NSnA transition over the range 1 t Imin 1 t 3 x The arrcws indicate the values ouf 1 t Imin used in the fits reported in tabijs I and II. based on ACp values determined from the smooth background shown in figure 2. In order to test the effect of a different choice of background, we idded a term Et to eq. (1 a) and E t to eq. (1b) and refit the data with TNA TNA Tm. The maximum change in a(a ) resulting from this procédure was 0.01 and the largest improvement in xÿ was 10 %. Hence the background shown in figure 2, which seems very reasonable on physical grounds, is also close to the optimum choice. To test the compatibility of the data witk scaling (a a, B B ) and allow for a possible confluent singularity, we have fit the data in both phases simul Table 1. of leastsquares fits» ith eq. (1) to the 1 atm. data near the NSmA transition in 8CB over the range 1 t Imin 1 t t max A bracket indicates that the parameter was fixed at the indicated value. Error bounds are 95 % confidence limits based on the F test.

6 Results The 883 taneously with the equation The values of 1 t Imin were taken to be the same as those in table 1 and TNA was set equal to T NA. (Allowing TNA # T NA led to no improvement in X,.) The results of these fits are shown in table II. It is evident that a simple power law (D D 0) is inadequate to explain the data except over a very restricted range (approx. one decade of reduced temperature). The correctionstoscaling form, on the other hand, allows a good fit all the way out to 1 t max 1 x 102. It is interesting to note that the values a obtained in these fits agree well with those obtained in similar fits on 80CB, but the coefficients D and D have the opposite sign [7]. The latter fact raises some questions about their physical significance. Due to the experimental problems discussed in section 2 we have refrained from fitting the highpressure data at the NSmA transition. Instead, figure 4 is presented as an indication that the shape of the Cp peak is not affected by pressure or by the ratio TNA/TNI. This conclusion agrees with our result for 80CB [7] but does not agree with the interpretation of Cp measurements near the NSmA transition in the homologous series ns. 5 [22]. 3.3 INTERPRETATION. critical exponents obtained from scaling fits of the heatcapacity data near the NSmA transitions in 80CB and 8CB (a 0.25 ± 0.05 and a 0.30 ± 0.05, respectively) present certain problems in terms of our current understanding of critical phenomena. These results strongly rule out the nearly logarithmic (a 0.026) singularity expected for a simple XY model. Moreover, they do not agree with any of the familiar exponents for nvector models or multicritical points. It is possible that they represent effective exponents resulting from the anisotropic fixed point or one of the complex crossover sequences described by Lubensky and Chen [4] or from crossover from tricritical to X Y behaviour [22]. If such crossover explanations are correct, however, the insensitivity of the a values to range shrinking and to changes in pressure is quite surprising. A feature of the NSmA transition which may complicate the observed quasicritical behaviour is the fact that the lower marginal dimensionality d is 3 for the SmA phase [23]. For spatial dimensionalities below d thermal fluctuations are sufficiently strong to destroy the phase transition and prevent the establishment of longrange order. Although the divergent phase fluctuations in the SmA order parameter associated with marginal dimensionality effects are effectively removed in the LubenskyChen analysis, they are still expected to destroy longrange order in a real SmA phase. This feature has been invoked to explain the unusual temperature dependence of the SmA elastic constants B and D [6, 23] and could possibly lead to some unexpected Cp effects. One way to assess the role of the anisotropic fixed point in the LubenskyChen model [4] is to consider their modified version of hyperscaling : This equation enables us to relate the calorimetric results with experimental measurements of the longitudinal and transverse correlationlengths near the NSmA transition. The Xray scattering results for 80CB, 8CB and CBOOA are ail consistent with while the best values of vl are 0.58 ± 0.04 for 80CB, 0.51 ± 0.03 for 8CB, and 0.62 ± 0.05 for CBOOA [6]. Using v 0.67 together with the a values for these materials [7, 13], one obtains from eq. (3) for 80CB, ± for 8CB and 0.59 for CBOOA, in good agreement with the measured values. Another comparison of our data with the scattering results may be made in terms of the concept of twoscalefactor universality [24]. This hypothesis (allowing for correlationlength anisotropy) predicts Table II. of simultaneous fits with eq. (2) to the 1 atm. data above and below the NSmA transition in 8CB. The minimum values of 1 tiare shown by the arrom S in figures 3 and 5.

7 884 a single value for the quantity X AÇllo çlolkb in a given (d, n) universality class, where A is the amplitude of the Cp power law in the disordered phase and Çllo are the bare correlationlengths defined by j II ç" 0 t VII, ç.l ç.lo tv 1. By fitting the data for 8CB and 80CB presented here and in references [6] and [7] with exponents a, vll and vl fixed at identical values for the two systems, internally consistent values of X may be computed. The results of such fits over the range 104 t with the choices a 0.27, v jj 0.67 and VL 0.53 [which are consistent both with the experimental results and with eq. (3)] are 100 X 10.5 for 8CB and 100 X 8.8 for 80CB [25]. It would be interesting to further test this apparent success of the twoscalefactor concept by making highpressure correlationlength measurements in these materials. This work was supported by NSF grant DMR A02, an NSF Predoctoral Fellowship to G. B. K and a NATO Postdoctoral Fellowship to K. J. L. References [1] MCMILLAN, W. L., Phys. Rev. A 4 (1971) [2] DE GENNES, P. G., Solid State Commun. 10 (1972) 753 ; Mol. Cryst. Liq. Cryst. 21 (1973) 49. [3] HALPERIN, B. I., LUBENSKY, T. C. and MA, S.K., Phys. Rev. Lett. 32 (1974) 292. [4] LUBENSKY, T. C. and CHEN, J.H., Phys. Rev. B 17 (1978) 366. [5] ARMITAGE, D. and PRICE, F. P., Mol. Cryst. Liq. Cryst. 38 (1977) 229 ; DELAYE, M., J. Physique Colloq. 37 (1976) C399 ; LIM, K.C. and Ho, J. T., Phys. Rev. Lett. 40 (1978) 944. [6] LITSTER, J. D., ALSNIELSEN, J., BIRGENEAU, R. J., DANA, S. S., DAVIDOV, D., GARCIAGOLDING, F., KAPLAN, M., SAFINYA, C. R. and SCHAETZING, R., J. Physique Colloq. 40 (1979) C3339 ; DAVIDOV, D., SAFINYA, C. R., KAPLAN, M., SCHAETZING, R., BIRGENEAU, R. J. and LITSTER, J. D., Phys. Rev. B 19 (1979) 1657 ; LITSTER, J. D., BIRGENEAU, R. J., KAPLAN, M., SAFINYA, C. R. and ALSNIELSEN, J., Ordering in StronglyFluctuating Condensed Matter Systems (NATO Advanced Study Institute, April, 1979), to be published. [7] KASTING, G. B., LUSHINGTON, K. J. and GARLAND, C. W., Phys. Rev. B (in press) ; GARLAND, C. W., KASTING, G. B. and LUSHINGTON, K. J., Phys. Rev. Lett. 43 (1979) [8] CHU, K. C. and MCMILLAN, W. L., Phys. Rev. A 11 (1975) [9] LEADBETTER, A. J., FROST, J. C., GAUGHAN, J. P., GRAY, C. W. and MOSLEY, A., J. Physique 40 (1979) 375. [10] CLADIS, P. E., BOGARDUS, R. K. and AADSEN, D., Phys. Rev. A 18 (1978) [11] LIEBERT, L. and DANIELS, W. B., J. Physique Lett. 38 (1977) L333. [12] CHEUNG, L., MEYER, R. B. and GRULER, H., Phys. Rev. Lett. 31 (1973) 349 ; HUANG, C. C., PINDAK, R. S. and Ho, J. T., SolidState Commun. 25 (1978) [13] DJUREK, D., BATURICRUBCIC, J. and FRANULOVIC, K., Phys. Rev. Lett. 33 (1974) [14] The 8CB samples were obtained from Prof. R. J. Birgeneau, who has carried out Xray scattering experiments on this material. A total of four runs (1 atm., 750 bar, bar, and then 1 atm. again) were carried out on sample A over a period of 120 days. The results at bar were suspect due to dissolved argon that entered through a pinhole leak. Sample B was then studied briefly (5 days) at 1 atm. and carefully at bar (15day run). The heat capacity values near the NSmA transition at 1 atm. were very similar for the two samples. The bar data reported here are those obtained on sample B. [15] DE GENNES, P. G., The Physics of Liquid Crystals (Wiley, Oxford) 1974, p [16] THOEN, J., MARYNISSEN, H. and VAN DAEL, W., private communication. The Cp peak at the NSmA transition in this experiment is reported to be virtually as sharp as that obtained in 8OCB (see Ref. [7]). [17] Numerical calculations show that the effect of a finite Tac amplitude on a powerlaw Cp peak is to introduce at first positive deviations from the powerlaw behaviour as the critical temperature is approached before causing the data to round off (negative deviations). Under the conditions prevailing in the present experiment, negative deviations are expected only when t The systematic positive deviations expected at larger t become equal to the random error in the data ( ~ 0.12 %) at t and three times the random error at t 4.5 x 105. [18] The data in this region are reminiscent of the twophase region in 8OCB at 1 atm. reported in JOHNSON, D., HAYES, C. F., DEHOFF, R. J. and SCHANTZ, C. A., Phys. Rev. B 18 (1978) [19] SMITH, G. W., Mol. Cryst. Liq. Cryst. 41 (1977) 89. [20] LEADBETTER, A. J., DURRANT, J. L. A. and RUGMAN, M., Mol. Cryst. Liq. Cryst. 34 (1977) 231. [21] Allowing TNA and TNA to be adjustable parameters produced no appreciable change in the results. [22] BRISBIN, D., DEHOFF, R., LOCKHART, T. E. and JOHNSON, D. L., Phys. Rev. Lett. 43 (1979) [23] SCHAETZING, R. and LITSTER, J. D., «Light Scattering Studies of Liquid Crystals», in Advances in Liquid Crystals, Vol. 4 ed. G. Brown (Academic Press, N.Y.), in press. [24] THOEN, J., BLOEMEN, E. and VAN DAEL, W., J. Chem. Phys. 68 (1978) 735 ; HOHENBERG, P. C., AHARONY, A., HALPERIN, B. I. and SIGGIA, E. D., Phys. Rev. B 13 (1976) [25] 03BE ~0 and 03BE~0 (in cm) were determined graphically from the data in ref. [6], A was determined by leastsquares fits of our data to eq. (2) with 03B The units of A were converted to J.K1.cm3 by assuming a density of 1.0 g.cm3 for both materials. In some cases (e.g., see ref. [24]), the amplitude of the singular term in 0394Cp is written as A/03B1 rather than A. In that convention, 100 X 2.83 for 8CB and 2.38 for 8OCB.