6410
J. Phys. Chem. 1987, 91, 6410-6414
Effect of Quasi-Spherical, Chainlike, and Rodllke Solutes on Nematic-Isotropic and Smectic A-Nematlc Phase Equillbria in p-n -0ctyl-p’-cyanobiphenyl Liquid Crystal Samir Ghodbane and Daniel E. Martire* Department of Chemistry, Georgetown University, Washington, D.C. 20057 (Received: March 9, 1987; In Final Form: June 29, 1987)
The moduli of the slopes, p, and pi, of the nematic and isotropic boundary lines in reduced transition temperature ( P = T/TNI)vs solute mole fraction (0.01 =S x2 d 0.06) diagrams are determined for five quasi-spherical (Et4C, Me4Sn, Et,Sn, n-Pr4Sn,and n-Bu4Sn),five chainlike (n-C8HI8to n-C16H4(, even members), and four rodlike (benzene, 2,4-hexadiyne,biphenyl, and p-terphenyl) solutes in the liquid-crystalline solvent p-n-octyl-p’-cyanobiphenyl (8CB). These and earlier experimental results are interpreted and analyzed in terms of theoretical results from the lattice model described in the preceding article (Martire, D. E.; Ghodbane, S. J . Phys. Chem., accompanying article in this issue). It is seen that the agreement between theory and experiment is at least semiquantitative. The lattice model correctly describes the important features of the dependence of p, and pi on the molecular volume of the quasi-spherical, chainlike, and rodlike solutes and on the length of the end chain of the solvent molecule, as well as the trends in the neat-solvent and dilute-solutioncontributions to 0, and pi. Also presented and provisionally interpreted are the smectic A-nematic phase equilibrium results for the same solutes in 8CB.
Introduction Addition of a nonmesomurphic solute at low solute mole fraction, x2, to a liquid-crystalline solvent usually depresses, but sometimes elevates, the nematic-to-isotropic transition temperature of the neat solvent TNIand leads to the formation of a two-phase region. The solute’s ability to destabilize or, as the case may be, even stabilize the nematic phase is measured by the initial slope of the nematic and isotropic phase boundary lines in the reduced tempeature (P= T / TNI)vs x2 diagram, /3, and &, respectively (see Figure 1 in ref 1). As reviewed in the preceding article,’ this solute probe approach, whereby the response of the orientationally ordered nematic fluid to major or minor perturbations in molecular geometry is studied by thermodynamics and statistical mechanics, has yielded much useful information on the relationship between molecular structure and phase stability. Depending on the molecular volume, shape, and flexibility of the solute probe, pronounced differences in phase behavior have been found. Also, attention has been drawn to the effects of the length and flexibility of the end chain(s) or “tail(s)” attached to the rigid, rodlike core of the solvent molecule. Nematic-isotropic phase diagrams for series of quasi-spherical and chainlike solutes at low mole fraction in p-n-penty1-p’cyanobiphenyl (SCB) were reported and analyzed in a previous study.2 In the present paper we report the results (& and pi) of a systematic thermodynamic investigation of quasi-spherical, chainlike, and rodlike solutes in p-n-octyl-p’-cyanobiphenyl (8CB). These results are compared with those obtained in SCB, 7CB3 (quasi-spherical solutes), and p-(ethoxybenzy1idene)-p’-n-butylaniline (EBBA)4 (rodlike solutes) in order to examine more closely the role of the length of the solvent molecular tail. All of these results are viewed in light of recent predictions based on a hard-molecule lattice model of dilute binary mixtures of cubic, semiflexible-chain and rigid-rod solute molecules and solvent molecules consisting of rigid, rodlike cores and semiflexible end chains.] Also, since 8CB exhibits a smectic A mesophase, as a dividend the same experimental setup permits us to conduct, for the first time, a systematic study of the effect of solute molecular structure on smectic-nematic phase equilibrium. For reasons to be discussed, the corresponding destabilizing ability of the solute is ( 1 ) Martire, D. E.; Ghodbane, S.J . Phys. Chem., accompanying article in this issue, and references cited therein. (2) Oweimreen, G. A.; Martire, D. E. J . Chem. Phys. 1980, 72,2500, and references cited therein. (3) Oweimreen, G. A.; Hasan, M. Mol. Cryst. Liq. Crysr. 1983,100, 357. (4) Kronberg, B.;Bassignana, I.; Patterson, D. J . Phys. Chem. 1978, 82, 1714.
0022-3654/87/209 1-6410$01.50/0
TABLE I: Solutes Used in Visual Experiments solute n-octane n-decane n-dodecane n-tetradecane n-hexadecane tetramethyltin 3,3-diethylpentane tetraethyltin tetra-n-propyltin tetra-n-butyltin benzene 2,4-hexadiyne biphenyl
p-terphenyl p-quaterphenylc
v2*
symbol n-Cs
109.1 129.7 150.1 170.6 80.2 98.9 121.0 162.0 202.9
n-C10 4
2
n G 4
0-C16 Me4Sn Et& Et,Sn Pr4Sn Bu4Sn Bz
48.4
HD BP TP QP
68.9 91.7 135.0 178.3
In milliliters per mole; from ref 5.
DZ)b
88.7
1.92 2.36 2.89 3.87 4.85
D2 is a reduced diameter; Le.,
it is relative to the diameter of the short axis of the solvent molecule
which is taken to be spherocylindrical in shape.2.6cNot studied here, but studied in ref 4. reported as an average value,
&’.
Experimental Section 8CB, with a quoted purity of 99.5%, was purchased from BDH, handled according to the producer’s recommendations, and used without further purification. The quoted purity was confirmed by analysis of the crystal-to-smectic A endotherm obtained from DSC measurements. The five chainlike, five quasi-spherical, and four rodlike solutes studied are listed in Table I, along with their van der Waals volumes5 and estimated values of the relative diameters of the quasispherical solutes.6 Attempts to study the solute p-quaterpheny14 were unsuccessful due to its very limited solubility in 8CB. All solutes were at least 98% pure, as established by gas-chromatographic analysis,2 and were thus used without further purification. The “simple apparatus” and the procedure used in the direct “visual” determination of the phase diagrams are described elsewhere.6 The only notable refinement is an intangible oneexperience, which has enabled us to improve the reproducibility and precision of the measurements. To construct the phase diagrams, at least five solute mole fractions in the range 0.01 Q x2 S0.06 were studied through successive addition of solute to 8CB. (5) Bondi, A. J . Phys. Chem. 1964, 68, 441. (6) Martire, D. E.; Oweimreen, G. A,; Agren, G.I.; Ryan, S. G.; Peterson, H. T. J . Chem. Phys. 1976, 64, 1456.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 25, 1987 6411
Phase Equilibria in 8CB Liquid Crystal TABLE 11: Transition Temperatures and Enthalpies of 8CB
-
transition crystal smectic
temp, OC enthalpy, cal mol-' lit."*b this work lit."J 21.2 21.0-21.1 5900 f 150 5500-610OC
this work
A (c-sA) smectic A
33.4d
32.0-33.5
16 f 2
OC-48
nematic (SA-N) nematic isotropic (N-I)
40.6d
39.4-40.5
187 f 9
146'-210
"Ref 8-10. bRef 11. 'Ref 12. dDeterminedby DSC and thermal microscopy. For about half of the systems studied, duplicate sets of experiments were conducted to ensure the reproducibility of the results. A differential scanning calorimeter (Perkin-Elmer Corp.; Model DSC-2 with an Intracooler I1 intermediate-range accessory) was used to determine the transition temperatures and enthalpies of 8CB. Before each run, the DSC cell was cooled to -50 OC and programmed at the desired scanning rate from at least 20 OC below the lowest transition temperature. The temperature axis was carefully calibrated in the range 243.5-429.8 K by using the known melting points of seven ultrapure (99.999%) standards. Each calibrant (and sample) was run at four different scanning rates (10.0, 5.0, 2.5, and 1.25 K/min), and the static transition temperature was determined by extrapolation to zero scanning rate. The transition enthalpies (AH) were determined by using an ultrapure indium standard and the Guttman-Flynn procedure.' In all, six samples of 8CB, ranging in weight from 5 to 10 mg, were studied. The nature of the mesophases (by examining their textures) and transition temperatures were verified by thermal microscopy of samples heated between crossed polarizers. A Leitz-Wetzlar Dialux-Pol coupled with a Mettler FP52 microfurnace for sample temperature control was the apparatus used.
Results and Discussion
it follows that @,"/Pi" = y2,n"/y2,i" and that the width of the two-phase region (in terms of x2) at a given P'and its thermal "length" (in terms of P)at a given x i are respectively x2,i
- XZ,, = [(pi")-'
-
(0,")-'I
= (AS,i/R)(l -
Ti* - T,* = (p,"
[ 1 - T*' 1
(3a)
P')
- Pi")X2'
(4)
as illustrated in Figure 1 of the preceding article.' For the nematic-isotropic phase equilibria, which is the primary focus of the present study, there is clear evidence that ASJR > 0 and y2,nm/y2jm > for 8CB. Accordingly, the N-I transition is depressed and a well-defined thermal length is found for all solutes except p-terphenyl (vide infra). For example, with typical values of 0,"= 0.500 and x2' = 0.04, values of pi" = 0.435 and a thermal length of 0.82 OC are calculated from eq 3 and 4. This permits distinction between p, and pi in our experiments. Our discussion will concentrate mostly on p,, which reflects the upper limit of thermal stability for a homogeneous nematic phase. Also, for clarity, we shall continue to distinguish between the low-solute-concentration values from the visual experiments (p, and pi) and the infinite-dilution values from theory' or an alternative (but more restrictive) experimental methodI4 (p," and p,"), even though the two sets should be equivalent2 (vide infra). Equations 1-4 with the subscripts n and i replaced by the subscripts s and n, respectively, are also applicable to smectic A-nematic phase equilibria, provided that AS,,/R > 0 and certain approximations continue to hold.'6J7 However, taking ASSn/R = 0.026 f 0.003 for 8CB (from Table 11), the smectic-nematic counterparts of eq 3 and 4 yield the following values: (a) p," = 0.199 and a thermal length of merely 0.01 OC, when typical values of 0,"= 0.200 and x i = 0.04 are used; and, under the most favorable of present circumstances, (b) p," = 0.376 and a thermal length of 0.07 "C, when p," = 0.400 and x i = 0.06. Indeed, since the error in the determination of the phase-boundary temperature was usually comparable to the thermal length, it was generally not possible to define the two-phase region accurately. This led us to rely on the mean of the determined values, &' = (0,' P,,')/2, as a measure of the ability of a solute to destabilize the smectic A phase and induce the onset of the nematic phase.I7 Linear least-squares analysis of the primary data on T* as a function of x2 yields the p, and pi values and the corresponding standard deviations listed in Table 111. The linear correlation coefficients of these fits are all in excess of 0.995. Also, the reproducibility of these measurements is very good, as can be seen from the results on duplicate sets of measurements. With the exception of p-terphenyl, which may be considered a "latent"
Shown in Table I1 are the results of the DSC and thermal microscopy studies. The observed transition temperatures are consistent with literature values:-" and the determined transition fall in the range of other reported values.s-10J2 enthalpies Of particular note is the value we obtain for the SA-N transition, A H = 16 f 2 cal mol-', indicating a very weakly first-order phase transition. However, the highest AH for the C-SA transition and the lowest A H for the SA-N and N-I transitions are those from high-precision adiabatic calorimetry,I2 from which an upper limit of AH 6 0.1 cal mol-' is found for the SA-N transition. Other evidence from X-ray scattering and DSC experimentsI3 supports the view that the SA-N transition is second order. As discussed in the preceding article,' the limiting slopes, 0," (14) Oweimreen, G . A,; Lin, G. C.; Martire, D. E. J . Phys. Chem. 1979, and PI", are related to the ratio of the infinite-dilution solute 83, 211. activity coefficients in the nematic and isotropic phases, yz,nm/y2,im (15) Ghodbane, S.; Oweimreen, G. A.; Martire, D. E., to be submitted for publication. (a dilute-solution property), and AS,,/R (a neat-solvent property (16) Peterson, H. T.; Martire, D. E. Mol. Cryst. Liq. Cryst. 1974, 25, 89, only), through and references cited therein. (17) Despite the small values (60.07 "C) predicted for the thermal length, Pn" = lim H d T * / d x ~ ) n l = [(~2,n"/~2,i") - I l [ R / ~ n i l (1)
+
(m
x2-0
where ASni is the nematic-isotropic transition entropy, R is the gas constant, and, from Table 11, ASni/R = 0.300 f 0.014 for is accessible from 8CB. For sufficiently volatile solutes, yz gas-liquid chromatography (GLC).14J5 Also, from eq 1 and 2, (7) Guttman, C. M.; Flynn, J. H. Anal. Chem. 1973, 45, 407. (8) Leadbetter, A. J.; Durant, J. L. A.; Rugman, M. Mol. Cryst. Liq. Cryst. Lett. 1977, 34, 231. (9) Coles, H. J.; Strazielle, C. Mol. Cryst. Liq. Cryst. 1979, 55, 237. (10) Liebert, L.; Daniels, W. B. J . Phys. Letr. (Paris) 1977, 38, L-333. ( 1 1) Dalmolen, L. G. P.; Picken, S. J.; de Jong, A. F.; de Jeu, W. H. J . Phys. (Paris) 1985, 46, 1443. (12) Marynissen, H.; Thoen, J.; van Dael, W. Mol. Cryst. Liq. Cryst. 1983, 97, 149. (13) Navard, P.; Cox, R. Mol. Cryst. Liq. Cryst. Lett. 1984, 202, 261, and references cited therein.
it was possible in many cases to observe and measure with fair precision a two-phase region. This suggests that eq 1-4 may not be applicable to the present smectic-nematic equilibria. In their derivation the solute contribution toward the total entropy difference between the two phases of the dilute solution ( x 2 < 0.06) is neglected relative to the solvent contribution.I6 The former contribution depends on - S2,n, where s denotes the partial molar entropy, and the latter on SI," - S',,$, which is assumed to be equal to .Is,, of the pure solvent. Also neglected are other terms involving x2. Strictly, one would need to derive expressions for 8,' and p,' of the actual dilute solution, for which the smectic A-nematic transition in these 8CB mixtures is apparently first order, albeit weakly so. The situation becomes more complicated if the SA-N transition in pure 8CB is truly second order (AS,, = 0), as recent evidence12s13indicates. Since there is also evidence15 that y2,s-/y2n- is quite close to unity for some solutes in 8CB, the counterparts of eq 1 and 2 (based on first-order transitions) would result in &" and p', being undefined for these systems. A-more elaborate thermodynamics analysis16 taking into account the actual S,'s in the two phases, terms in x 2 , and second-order transition effects would then be required. However, given the extensive information that would be needed to apply the resulting equations, it is unlikely that such an analysis would prove useful in practice. These concerns a b u t the applicability of eq 1-4 notwithstanding, Psn'can still serve a measure of the destabilizing ability of a solute.
s',"
6412 The Journal of Physical Chemistry, Vol. 91, No. 25, 1987
Ghodbane and Martire
TABLE III: Results from Analysis of Nematic-Isotropic Phase Diamams with 8CB as the Solvent
solute n-Ca n-c;, n-C12 n-C14 n-C16
BZ
HD BP TP Me,Sn Et4C Et,Sn Pr,Sn Bu4Sn
Pn
Pi
0.359 f 0.004 0.397 f 0.003 0.418 f 0.007 0.434 f 0.012 0.440 f 0.005 0.272 f 0.005 0.258 f 0.006 0.324 f 0.012 0.372 f 0.005 0.379 f 0.010 -0.021 i 0.001 -0.019 f 0.001 0.352 f 0.005 0.365 f 0.01 1 0.499 f 0.01 3 0.472 f 0.019 0.634 f 0.004 0.635 f 0.008 0.692 f 0.003 0.687 f 0.009 0.760 f 0.012 0.778 f 0.006
0.313 f 0.003 0.343 f 0.003 0.353 f 0.005 0.368 f 0.001 0.369 f 0.007 0.251 f 0.009 0.241 f 0.007 0.293 f 0.002 0.320 f 0.005 0.331 f 0.004 -0.026 f 0.003 -0.018 f 0.001 0.314 f 0.006 0.311 f 0.003 0.385 f 0.022 0.393 f 0.022 0.497 f 0.006 0.520 0.016 0.539 f 0.01 1 0.531 0.010 0.565 f 0.006 0.567 f 0.016
G
O
n-C12 n-C14
n-C I6 BZ
HD BP TP Me,Sn Et4C Et,Sn Pr4Sn Bu4Sn
0.132 0.184 0.243 0.307 0.287 0.35 1 0.173 0.192 0.332 0.380 0.362 0.235 0.121 0.183 0.203 0.238 0.276 0.256
TABLE V Results from GLC
solutes
I
I
I
I
* *
TABLE I V Results from Analysis of Smectic A-Nematic Phase Diagrams with 8CB as the Solvent solute R., 13.' 8"'
n-C8
.' I
0.125 0.172 0.217 0.257 0.283 0.305 0.160 0.151 0.322 0.332 0.339 0.227 0.121 0.143 0.155 0.186 0.199 0.197
0.129 0.178 0.231 0.28 1 0.285 0.328 0.167 0.173 0.327 0.363 0.350 0.23 1 0.121 0.163 0.178 0.212 0.242 0.226
n
Figure 1. Dependence of on solute carbon number, n2, for n-alkanes in 8CB: (a) Pn (e), (b) Pi (A),A,' (W.
0.0
I
0.7 -
0.6-
P
0.5
-
0.40.3-
+ DSC Determination of &" and &"
~ 2 . n ~ 1 ~ 2 ~ F Pn"
8,
n-alkanes branched heptanes
Solvent: 5CBb 1.15 f 0.02c 0.61 f 0.08 0.53 f 0.07 1.20 f 0.0lC 0.80 f 0.05 0.67 f 0.04
n-alkanes branched heptanes
Solvent: 8CBd 1.12, f 0.003e 0.41 0.02 0.36 f 0.02 0.48 f 0.05 0.42 f 0.04 1.15 f 0.01'
*
(lCalculated from eq 1 and 2. bASn,/R= 0.253 f 0.009, from ref 14. cDetermined by GLC; from ref 14. dASn,/R = 0.300 f 0.014, from Table 11. 'Determined by GLC; from ref 15. nematogen, all of the nonmesomorphic solutes studied depressed the N-I transition and exhibited healthy thermal lengths. Listed in Table IV are the results for the smectic A-nematic equilibria, including &,' = ((3; + @,')/2. Without exception, all of the solutes studied depressed the SA-N transition. An indirect (and less precise) method of determining p," and p,", which combines GLC and DSC data via eq 1 and 2,14produces the results reported in Table V for chainlike (n-alkane) and globular (branched-heptane) solutes in both 5CB14and 8CB.lS Note that the (3," and pi" values in Table V for the n-alkane solutes in 8CB, which are virtually independent of solute chain length (mC6 to n-Clo). are quite close to the mean values for the n-alkane solutes listed in Table 111, (3, = 0.41 i 0.03 and (3, = 0.35 i 0.02 (showing a slight dependence on solute chain length). This provides addition confi-
O'O
u 1
2
3
4
5
6
0:
Figure 2. Dependence of on solute relative diameter to th_ethird power, D Z 3 ,for quasi-spherical solutes in 8CB: 6, ( O ) , P, (A),Ps: (H).
dence that the theoretically determined] "infinite-dilution'' values, p," and pi", are relevant to the results of the present experiments. For a duplicate set of measurements the average of the two determined values of fin, (3,, or &,,' has been plotted in all of the figures. Shown in Figure 1 are plots of (3 vs solute carbon number, n2, for the n-alkane solute 8CB systems. Given in Figure 2 are plots of (3 vs DZ3for the quasi-spherical solutes in 8CB, where D2 is the estimated diameter of the solute molecule relative to that of the short axis of the solvent molecule which is taken to be spherccylindricalin shape.2,6Plots of (3 vs m2 for the rodlike solutes in 8CB are shown in Figure 3, where a value of m2 = 1 has been assigned to benzene, which may be regarded as quasi-spherical or as a rodlike solute with a length-to-breadth ratio of unity. The estimated m2 values (or length-to-breadth ratios) of the other rodlike solutes are then determined by the ratio of their van der Waals volumes (V2*)to that of benzene (Table I). Summarized in Figure 4 are the (3, results for all of the solutes in 8CB and for quasi-spherical solutes in 5CB,2where, again, m2 = V2*/VBz*.
+
The Journal of Physical Chemistry, Vol. 91, No. 25, 1987
Phase Equilibria in 8CB Liquid Crystal 0.41
2.0
1
1
Figure 3. Dependence of @ on solute molecular velum: relative to benzene, m2, for rodlike solutes in 8CB: 0, ( O ) , pi (A),&' (m).
1.4
I
0,416 \ 0.2
1
2
3
4
5
m2
p , on solute molecular volume relative to benzene, m2;quasi-spherical solutes in 5CB2( O ) , quasi-spherical solutes in 8CB ( O ) , n-alkanes in 8CB (m), rodlike solutes in 8CB (A). Figure 4. Dependence of
For clarity, the @, values of quasi-spherical solutes in 7CB3 and n-alkane solutes in 5CB2 are not displayed. The curve through the data points of the former would fall between the 5CB and 8CB ones, while the curve for the latter would lie approximately 0.15 unit higher than that for 8CB and show the same tendency to level-off with increasing m2. Referring to eq 1 and 2, and the extensive discussion of the pure-solvent and dilute-solution contributions to p," and @," in the preceding article,' let us consider the effect of the quasispherical and chainlike (n-alkane) solutes on nematic phase stability, as measured by @,, and the effect of increasing the length of the end chain of the solvent molecule. Note that the spherical-solute series spans a 2.5-fold range in molecular volume and the chain-solute series a 2-fold range. The observed behavior may be summarized as follows: (a) In both 8CB and 5CB the quasi-spherical solutes are clearly more destabilizing (larger @,) than the chainlike solutes, even more so as m2 increases (Figure 4). In each solvent this follows the trend in the relative preference of the solute for the two phases, 72,nm/72,1m (>l), which shows little dependence on m2 (or nz) for the n-alkane solutes (Table V). That a globular solute has a larger
2
3
4
5
m2
Figure 5. Dependence of 8," on the number of solute segments, m2, from lattice-model calculations.' (a) Cubic solutes with the solvent: ml = 5 , f l = 1, &,/k = 400 K. (b) Cubic, (c) semiflexible-chain ( E b , / k = 400 K), and (d) rigid-rod solutes with the solvent: ml = 6,f1= 2, &,/k = 400
L2t
6413
K.
72n"/72Jm than a chainlike solute of comparable molecular volume is confirmed by the entries in Table V. Also, from the ratio @,/PI ( = ~ ~ , , " / 7 ~for , : the ) quasi-spherical solutes in 8CB (Table 111), it is seen that these solutes become increasingly more incompatible with the nematic phase (relative to the isotropic phase) as m2 (or D23)increases. In contrast to the quasi-spherical solutes where the biggest molecule (Bu4Sn) is roughly twice as destabilizing as the smallest one (Me4Sn) in both 8CB and SCB, for the chainlike solutes @, increases by about 20% over the entire n2 range (n-Cs to n-CI6) with 8CB and by about 10% (going from n-Cs to n-C,,) with 5CB. These trends in and @, (as well as @,)are wholly consistent with the theoretically predicted trends for the cubic and semiflexible-chain solutes of the lattice model.' (b) Comparing the results for 8CB and SCB, it is seen that both R/A& and y2,nm/72,10 are larger with 5CB (Table V). These complementary trends both promote the larger @, (and (3,) values found for the 5CB systems. For the n-alkane solutes @, is larger by 0.13-0.17 unit (3040% higher). For the quasi-spherical solutes @, is larger by 0.22-0.53 unit (35-80% higher), with the 7CB values3falling in between the 5CB and 8CB results. The behavior of these solutes is also fully consistent with the lattice-model @,,;and , @,are smaller for predictions' that RlAS,,,~ ~ , , " / 7 ~ the solvent molecule having the longer end chain. Figure 5 , based on our lattice-model results,' shows the dependence of @", on the number of solute segments, m2, for cubic, semiflexible-chain, and rodlike solutes and on the number of segments in the solvent tail, f l , for the cubic solutes only. Its resemblance to Figure 4 is striking. The experimental and theoretical values have the same magnitude, with the former ones being slightly higher (typically, by 0.2-0.3 unit). Therefore, despite certain limitations of the model,2 the approximate treatment of molecular flexibility,' the neglect of attractive interactions, the lack of any "fine-tuning" of the model molecular parameters, and differences in scaling and actual molecular shape, the agreement between theory and experiment is at least semiquantitative. Additional confirmation that the lattice model provides a viable predictive and interpretive framework for different types of solutes is seen in Figure 6 , which summarizes the p, results for rodlike solutes. Shown are the curves through the experimental points for the solvents 8CB and EBBA4 and the theoretical curves for the two model solvents of Figure 5 , all as a function of the solute-to-solvent molecular volume ratio, V2*/V1*.(The V2*'sare
The Journal of Physical Chemistry, Vol. 91, No. 25, 1987
6414
0.81
O'b: 0.4
P" o.20-
- 0.2-
0,41 02
0
0.4
0.6
1.o
0.8
v:/v; Figure 6. Dependence of &" and p, for rigid, rodlike solutes on the solute-to-solvent molecular volume ratio, V,*/V,*. (a) p," From lattice-model calculations' for the solvent: m, = 5,h = 1, E b , / k = 400 K. (b) j3," from lattice-model calculations' for the solvent: m 1= 6,J = 2, Ebl/k= 400 K. (c) 6, for the solvent EBBA.' (d) 0, for the solvent 8CB.
O0.6I
I
0.01
-0.4 I
I 1 1
I
I
I
2
3
4
I
m2
Figure 7. Dependence of &,' on solute molecular volume relative to benzene, m2,in 8CB: quasi-spherical solutes (a),n-alkane solutes (m),
rodlike solutes (A). listed in Table I; VI* is 186.6 and 172.9 m L mol-' for 8CB and EBBA, r~pectively.~) As predicted (and interpreted earlier') (a) each of the experimental curves exhibits a maximum and, for the range of m2's studied ( m 2 = V2*/VBz*), the p, values are lower for the solvent molecule with the longer end chain (8CB); (b) the maximum m u r s at a larger V2*(or m2)and with a lower /3, value for the solvent molecule with the longer end chain. Again, the overall agreement between theory and experiment is quite satisfactory. Finally, we examine the effect of solute structure on smectic A-nematic phase equilibrium in the 8CB systems (Table IV). Shown in Figure 7 are plots of &' against m2 (relative to m2 = 1 for benzene) for the three solute classes. The following unexpected trends are observed: (a) referring to Figures 1-3, both the chainlike and quasi-spherical solutes have a smaller effect on SA-Nthan on N-I relative stability, while the rodlike solutes have a smaller effect at lower m2 and a greater effect at higher m2 (offered without explanation); (b) for m2 6 2, the rodlike solutes, which again exhibit a maximum, are more destabilizing than either chainlike or quasi-spherical solutes with the same m2, and the latter two solutes are roughly comparable in their destabilizing ability (Figure 7); (c) as m2 increases, chainlike solutes become increasingly more disruptive than quasi-spherical solutes having the same m2 (with &,' increasing for both solute types), while the rodlike solutes continue to decline in their destabilizing ability, become comparable to the chainlike solutes at m2 2.7 (TP and n-C12),and tend toward being the least disruptive at even larger m2 (>3), as seen in Figure 7 .
Ghodbane and Martire Given the absence of a detailed theoretical model and uncertainty about the appropriate thermodynamic relations" for describing smectic A-nematic phase equilibrium in these systems, it is possible to offer only a tentative, qualitative interpretation of trends b and c above. There is experimental evidence that rigid, rodlike aromatic molecules seem to prefer the rigid-core sublayer of smectic A phases, whereas more flexible n-alkane molecules tend to favor the sublayer defined by the more flexible solvent end chains.lsJ9 Consistent with this picture and based on results from a purely steric (hard repulsions only) lattice model, which reveals how molecular packing differences alone give rise to the smectic A phase and govern SA-N equilibrium in a single-component system, DowellZ0suggested a reasonable interpretation of Figure 7, which we adopt and refine here. The smectic A phase of the pure solvent exhibits both long-range orientational order, with the solvent cores being more aligned than the solvent tails, and positional order via the formation of layers, with the solvent cores aggregating with other solvent cores and similarly with the solvent tails, giving rise to two types of sublayers. Perturbing solutes in the more ordered solvent-coresublayer would be expected to be more effective in disrupting the smectic A phase than perturbing solutes in the solvent-tail sublayer. The chainlike solutes should concentrate in the latter sublayer and the rodlike solutes in the former one. Since the free solute chains are likely to be less aligned than the solvent end chains, they would be expected to be destabilizing (&' > 0). If the solute chain is long enough, it is conceivable that it could penetrate into the more sensitive solvent-core sublayer, leading to increased destabilization with increasing solute chain length, as is observed. Since the rodlike solutes should favor the more vulnerable solvent-core sublayer, they would be expected to be more disruptive than the chainlike solutes at low m2, where their alignment is wanting. Their tendency to destabilize the smectic A phase should continue to increase with increasing m2 until they become sufficiently aligned relative to the solvent cores, at which point (the observed maximum) they should begin to become less destabilizing (and still more aligned) with further increases in their molecular length-to-breadth ratio. The quasi-spherical molecules, on the other hand, cannot align and would be expected to pack with the less sensitive solvent-tail sublayer in order to minimize the disruption of the orientational and positional order of the smectic A phase. Similar to their effect on N-I equilibria, quasi-spherical and chainlike solutes having the same m2 value should be comparable in their destabilizing ability at low m2,where alignment of the latter solutes should be small. As the molecular diameter of the quasi-spherical solutes increases, they should become progressively more destabilizing. However, since they could remain accommodated by and, hence, concentrated in the solvent-tail sublayer, this increase in ',p with increasing m2 would be expected to be less pronounced than that of the chainlike solutes. A more definitive and quantitative interpretation of these and future &' data must await suitable extension of existing lattice-model treatments20,21and more detailed molecular-level information, especially from spectroscopic and X-ray diffraction studies.
Acknowledgment. This material is based upon work supported by the National Science Foundation under Grant CHE-8305045. We are also grateful to G. A. Oweimreen for advice on the phase-diagram experiments and to K. L. Churney for advice on the DSC measurements. Registry No. p-n-Octyl-p'-cyanobiphenyl, 52709-84-9; n-octane, 11 1-65-9; n-decane, 124-18-5; n-dodecane, 112-40-3; n-tetradecane, 629-59-4; n-hexadecane, 544-76-3; tetramethyltin, 594-27-4; 3,3-diethylpentane, 1067-20-5; tetraethyltin, 597-64-8; tetra-n-propyltin, 21 76-98-9; tetra-n-butyltin, 1461-25-2;benzene, 7 1-43-2; 2,4-hexadiyne, 2809-69-0; biphenyl, 92-52-4; p-terphenyl, 92-94-4. (18) Guillon, D.; Poeti, G.; Skoulios, A.; Fanelli, E. J . Phys. Leu. (Paris) 1983, 44, L-491. (19) Guillon, D., Skoulios, A. Mol. Cryst. Liq. Cryst. 1983, 91, 341. (20) Dowell, F. Phys. Reo. A 1983, 28, 3520, 3526. (21) Cotter, M. A. Mol. Crysr. Liq. Cryst. 1976, 35, 33.
