Faraday Discuss. Chem. Soc., 1985, 79, 133-140 Phase Studies of Binary Mesogenic Systems BY WILLIAM R. KRIGBAUM Department of Chemistry, Duke University, Durham, North Carolina 27706, U.S.A. Received 26th November, 1984 Although several theories exist for rod-like nematogens, our understanding of thermotropic mesomorphism in semiflexible chain polymers is less well developed. Flory observed that the nematic behaviour of Kuhn chain polymers is governed by the axial ratio of the Kuhn link and is nearly independent of the contour length of the chain. Following this lead, we attempted to fit binary phase diagrams of two polymer + diluent systems using the Warner- Flory treatment of rod-like nematogens. The only modification involved replacement of the axial ratio of the rod by that of the Kuhn link.This theory assumes the nematic phase i s stabilized by orientation-dependent interactions and that the axial ratio of the rod is indepen- dent of temperature. Poor agreement with the experimental phase diagrams suggests some other factor is important. We then took into account the temperature dependence of the unperturbed dimensions through appropriate modification of Flory’s treatment of Kuhn chain polymers. This predicts a thermotropic nematic-isotropic transition, even in the absence of orientation-dependent interactions: at the temperature which reduces the axial ratio of the Kuhn link to the critical value. Persistence lengths measured for two polymers at different temperatures, when extrapolated to their isotropization temperatures, produce axial ratios very near the critical value.This treatment predicts that all semiflexible polymers that behave as Kuhn chains should be in corresponding states at their isotropization temperatures. The application of this concept is illustrated by examining the thermal behaviour of a number of substituted poly(p-phenylene terephthalates). According to current theory of rod-like mesogens, thermotropic behaviour requires orientation-dependent interactions and an axial ratio less than the critical value. Orientation-dependent forces are required to provide an enthalpic contribu- tion to the stabilization of the nematic phase. If the axial ratio exceeds the critical value, the entropic contribution provides ample stabilization, and no thermotropic transition to the isotropic phase is possible.Flory and Ronca,’ in seeking an experimental system for comparison with theoretical predictions, emphasized the requirement that the nematogen be a rigid rod with nearly cylindrical symmetry. They proposed the p-phenylene oligomers as ideal candidates. This system has been extensively studied,*-’ but it presents serious experimental difficulties because the transition temperatures increase rapidly, accompanied by a corresponding decrease in solubility, as the size of the oligomer increases. Similar problems can be anticipated6 for other rod-like mesogens owing to the small entropy change accompanying their crystal-nematic transitions. An extension of the Flory-Ronca theory by Warner and Flory7 accounts for the effect of diluent in diminishing the orientation-dependent interactions between nematogenic molecules.This affords predictions for binary systems which are much more amenable to experimental study. Our theoretical understanding of semiflexible polymers which exhibit a ther- motropic nematic phase is currently in a more rudimentary state. Flory,* in his treatment of Kuhn chain polymers, observed that their nematic behaviour is governed by the axial ratio of the Kuhn link and is almost independent of the contour length 133134 PHASE STUDIES OF BINARY MESOGENIC SYSTEMS N I I I I I I I I 1 I 0 2 Fig. 1. ( a ) Variation of the nematic-isotropic transition temperature of PHIC in toluene (open circles and dotted curve) compared with the temperature dependence of the biphasic region predicted according to the Warner-Flory treatment with axial ratio 40.(b) A similar comparison of the data of Conio et af." for hydroxypropylcellulose in dimethylacetamide (dotted curves) with the Warner-Flory predictions for axial ratios 6 (full curves) and 2 (dashed curves). of the chain. This suggests that the Warner-Flory treatment' might be applicable to binary semiflexible polymer + diluent systems simply by replacing the axial ratio of the rod by that of the Kuhn link. RESULTS AND DISCUSSION Krigbaum et aL9 collected data for the binary system poly(n-hexyl isocyanate), PHIC, in toluene to provide a test of this procedure. They also utilized the data of Conio et al. l o for hydroxypropylcellulose, HPC, in dimethylacetamide. The experi- mental observations are represented by the open circles and dotted curves in fig.1.W. R. KRIGBAUM 135 PHIC undergoes a thermotropic nematic-isotropic transition, and the transition temperature is depressed by the addition of toluene. We have assigned the axial ratio of the Kuhn link as l=40, which is approximately the value deduced from experimental data at 25 "C. Because this is larger than the critical value, 6.42, theory predicts no thermotropic transition for the bulk polymer. The binary system is predicted to exhibit a narrow biphasic region, as indicated by the two vertical lines in fig. l ( a ) . H ydroxypropylcellulose exhibits a thermotropic cholesteric-isotropic transition, and the transition temperature is again depressed by the addition of diluent, dimethylacetamide.For this system we have assigned the value of the axial ratio, l= 6, obtained by extrapolation to the isotropization temperature, Tf. Since this is less than the critical value, a thermotropic transition is predicted for the bulk polymer. The parameter T", a measure of the strength of the orientation-dependent interactions, can be evaluated from a knowledge of Tf. The cholesteric phase is designated as Ch in fig. 1 (6). The predicted biphasic region is indicated by the two full lines labelled l= 6 in the figure. The predicted depressions of the biphasic temperatures are much too steep, and remain so even when the calculations are repeated for a much smaller axial ratio, 5 = 2 [as shown by the pair of dashed curves in fig. l(b)]. It is evident that the observed transition temperatures for both systems span a much broader range of compositions than can be accommodated by the Warner- Flory treatment.In fact, the discrepancies between the theoretical predictions and observation are large enough to suggest that some other factor must play a significant role in the isotropization transition. In the foregoing treatment the axial ratio was assumed to be independent of temperature. It is well recognized that the unperturbed dimensions of coiling macromolecules (and the axial ratio of the Kuhn link) vary with temperature. We suggest that this temperature dependence is the missing factor which can provide an alternative mechanism for the nematic-isotropic transition. Even if the axial ratio exceeds the critical value at some particular temperature, this does not imply that the isotropization temperature of the polymer, Tf, is infinite.On the contrary, Tf will coincide with the temperature at which the axial ratio has decreased to the critical value. As a test of this proposal, Krigbaum et aL9 have measured the persistence length of PHIC in toluene and tetrahydrofuran over a range of temperatures. These data are represented by the open and filled circles in fig. 2, where In 5 is plotted against the reduced temperature, T / Tf. Fig. 2 also includes data collected by Aden et al." for HPC in dimethylacetamide. The critical value of the axial ratio of the Kuhn link given by Flory's treatment, Ccrit = 6.70, is represented by the small cross on the right-hand side of the figure. Extrapolation of the data for both polymers to Tf produces axial ratios very near the critical value, as expected from the foregoing argument.We would anticipate that the orientation-dependent interactions are minimal for PHIC owing to the shielding effect of the long sidechains. The lower extrapolated value for HPC may indicate that these interactions play a small role in stabilizing the nematic phase for this polymer. In order to test further the importance of the temperature dependence of the axial ratio we9 have modified the treatment of Kuhn chain polymers given by Flory* through introduction of a temperature-dependent axial ratio. Values of 6 = -d In l / d T for these two polymers can be obtained from the slopes of the lines in fig. 2. The predictions of this treatment are compared with the experimental data in fig.3. The full curves were calculated using the experimentally determined values,136 PHASE STUDIES OF BINARY MESOGENIC SYSTEMS 0.6 0.7 0.8 0.9 1.0 TR= T/TP Fig. 2. Temperature dependence of the axial ratio of PHIC in toluene (open circles) and tetrahydrofuran (filled circles) plotted as In 6 against the reduced temperature, T / r. The triangles and lower line represent the data of Aden et al" for hydroxypropylcellulose in dimethylacetamide. 6 = 0.01 1 for PHIC and 0.005 for HPC. The predicted depressions are too steep for both systems. For HPC + dimethylacetamide we can achieve nearly quantitative agreement by increasing 5 to 0.0073. For HPIC+toluene an increase of 6 to 0.013 gives a better fit, but the experimental and predicted curves have a different shape.Despite the failure to achieve quantitative agreement, comparison with the results in fig. 1 clearly indicates that the predictions appearing in fig. 3 are significantly better than those based upon the Warner-Flory treatment. An important outcome of this treatment is the concept that all semiflexible polymers which can be represented by the Kuhn chain model should be in corre- sponding states at their respective isotropization temperatures. The application of this concept will be illustrated by considering data for substituted poly(p-phenylene terephthalates). Poly(ppheny1ene terephthalate) is a rigid macromolecule with a high crystal melting temperature. The persistence length of this polymer has not been determined experimentally, but Erman et aL12 have calculated a value of 784 A.This is substan- tially larger that the experimental value, cu. 200 for the corresponding aromatic polyamide. Jackson14 reported the crystal melting temperature of the aromatic polyester to be 600°C. As disclosed by the early patent of Goodman et u1.,l5 the melting temperature of the parent polyester can be lowered by placing a substituent on one or both of the aromatic rings. We16 have investigated the thermal behaviour of a number of substituents. The repeating unit will be represented by X Y so monosubstituted polymers will be symbolized by X/H or H/Y and disubstituted polymers by X/Y. The results of this study are summarized in table 1.W. R. KRIGBAUM 137 450 k4 2400 350 v2 Fig.3. Comparison of the phase diagram of ( a ) PHIC in toluene and ( b ) hydroxypropyl- cellulose in dimethylacetamide with predictions based upon a temperature-dependent axial ratio. The full and dashed curves for PHIC were calculated using ( = O . O l l and 0.013, respectively. The full and dashed curves for HPC represent predictions for (=0.005 and 0.0073, respectively. As shown in column three, a substituent such as a methyl group or a halogen atom lowers tKN into the range 370-405 "C owing to positional isomerism of the substituent. Larger depressions are obtained with phenyl or hexyl substituents which provide additional rotational or conformational degrees of freedom per repeating unit. As claimed by Harris,I7 the H/C6H5 polyester has a lower melting temperature than the C6H5/H polymer, the values being ca.290 and 345 "C, respectively. Substitu- tion on both aromatic rings affords still lower melting temperatures. With one exception, the range of tKN values for the disubstituted polymers is ca. 205-235 "C. The one exception is the C6H5/C6HS polymer, which is amorphous because the melting temperature has been lowered into the vicinity of the glass transition temperature.138 PHASE STUDIES OF BINARY MESOGENIC SYSTEMS Table 1. Transition temperatures (in "C) of substituted poly(p-pheny- lene terephthalates) substituent t G ~ K N tNI ( tNI - tKN) unsubstituted H/H 26718 66014 - - monosubstituted X/ H C1/ H 220 372 5 10 138 C6H5/ 170 346 475 129 C6H13/H - 330 462 132 Br/ H - 353 475 122 monosubstituted H/Y H/ C1 220 402 490 88 H/ Br - 405 490 85 H/C6H5 130 287 369 82 disubstituted X/Y C1/ Br 120 213 362 149 ClIC6H5 113 233 3 60 127 C6H5/Br 120 222 376 154 C6H5/C1 108 206 368 162 C6H 13/ Br 121 208 365 157 C6H5/C6H5 122 - 23 1 - We initially anticipated that the substituted poly(p-phenylene terephthalates) would retain the high chain extension of the parent polyester.It was therefore surprising to find that the substituted polymers exhibit a thermotropic transition to the isotropic phase. If all these polymers are in corresponding states at their isotropization temperatures, this implies that substitution on one or both aromatic rings reduces the unperturbed molecular dimensions (and the axial ratio of the Kuhn link). Column four lists the isotropization temperatures, tNI, while column five gives the temperature range of the nematic phase, ( tNI - tKN).Except for H/C6H5, the tNI values for the monosubstituted polymers fall in the range 460-5 10 "C, and (except for C ~ H ~ / C ~ H S ) those of the disubstituted derivatives range from 360 to 376 "C. We can infer from these data that the unperturbed molecular dimensions are reduced by substitution, and the reduction is larger for the disubstituted polymers. The unusually low tKN values for H/C6H5 and C ~ H ~ / C ~ H S suggest that a phenyl sub- stituent on the terephthalate ring probably forces the nearest carbonyl group out of the plane of the ring, creating a flexible link. The relatively smaller nematic temperature range, ( tNI- fKN), for the H/Y polymers may indicate that any substituent on terephthalic acid tends to destabilize the nematic phase more than when it is located on hydroquinone. Further support for these conclusions is provided by the glass-transition tem- peratures listed in column two.The glass-transition temperature, tG, of the parent polymer, 267 "C,'* is reduced to ca. 220 "C by a single substituent, to 170 "C for C6H5/H and to 130 "C for H/C&,. The tc values for the disubstituted polyestersW. R. KRIGBAUM 139 fall in the range 100-122 "C. Since the glass-transition temperature decreases as the chain becomes more flexible, these observations lead to the same conclusions as those reached from the tNI values. CONCLUSIONS We believe the results presented above strongly support our contention that the decrease in unperturbed dimensions with increasing temperature plays a significant role in bringing about the nematic-isotropic transition in semiflexible polymers.The observation that the axial ratios for two different polymers, when extrapolated to their isotropization temperatures, are very close to the critical value is particularly persuasive. The predicted binary phase diagrams, while not providing a quantitative fit to the experimental observations, nevertheless represent a significant improvement over the results obtained using the Warner-Flory treatment. Our predictions are based upon Flory's theory' for Kuhn chain polymers. Unfortunately that treatment does not predict the orientation distribution of the Kuhn links in the nematic phase, so that orientation-dependent interactions cannot be taken into account.Both ten Bosh et U L ' ~ and Ronca and Yoon20 have recently developed theories for the nematic behaviour of a thread-like model chain. The partition function used by the former workers does not include a factor for the number of degrees of conformational freedom accessible to a system of chains in the nematic phase, while the latter workers have not yet incorporated orientation-dependent interactions into their treatment. We anticipate that further improvements in the treatment of the mesomor- phic behaviour of semiflexible chain polymers will appear shortly. Consideration of the temperature dependence of the unperturbed dimensions and its influence upon the transition to the isotropic phase leads to the conclusion that all polymers meeting the requirements of a Kuhn chain will be in corresponding states at their isotropization temperatures.This conclusion has far reaching implica- tions. One possible practical application of thermotropic polymers is to produce ultra-high-modulus fibres by melt spinning. We, in collaboration with Acierno,2' 322 as well as Simoff and have spun semiflexible polymers from the nematic phase and obtained poor mechanical properties. In view of these results, we turned our attention to the class of rigid-chain polymers. As exemplified by poly(p- phenylene terephthalate) these have melting temperatures which are too high to permit melt spinning. By introducing randomness along the chain through substitu- tion one might hope to reduce the melting temperature while retaining the high chain rigidity.This proved not to be possible for the poly(p-phenylene terephtha- lates), as indicated above. Instead, both tKN and tNI are reduced simultaneously, which implies that those polymers having lower melting temperatures also have a more semiflexible chain character. Based upon our spinning experience cited above, we would expect the fibre modulus to be reduced in parallel with the isotropization temperature. One piece of confirmatory evidence is obtained upon comparing the literature values of the modulus for heat-treated fibres of H/C& and C&/H. These are 352 l7 and 910 l4 g denier-', respectively. As expected, the polymer having the lower isotropization temperature exhibits the lower fibre modulus. 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