Dielectric and calorimetric study of phase transitions in mixed

J. Phys. Chem. 1992, 96, 4686-4691

4686

Dielectric and Calorimetric Study of Phase Transitions in Mixed Diacetylene Single Crystals Polymerizing in the Solid State Maciej E. Orczyk,+Juliusz Sworakowski,* Institute of Organic and Physical Chemistry, Technical University of Wrocluw, 50-370 Wrocluw, Poland

and Marcel Bertault Groupe M a t i k e CondensCe et Materiaux, UniversitC de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France (Received: November 25, 1991)

Dielectric and calorimetric experiments were performed on a series of pTS-pFBS mixed diacetylene single crystals. The electric permittivity measurements were carried out in the direction of growing polymer chains in the temperature range 80-333 K, as a function of the degree of polymerization of the samples. The specific heat measurements were performed on monomeric and fully polymerized samples in the temperature range 120-220 K. Phase transitions, already described in the literature for pure pTS crystals, were found to shift toward lower temperatures upon increasing the pFBS content in mixed crystals. In pFBS-rich and pure pFBS crystals, no evidence of any phase transition was found. A qualitative model employing an approach based on the Ising model was put forward to explain the observed shifts of the transition temperatures. A difference in the magnitude of the dipole moments associated with the polar side groups of pTS and pFBS diacetylene molecules is thought to be the main factor responsible for this phenomenon.

Introduction Substituted diacetylene crystals represent a unique class of solids capable of undergoing a topochemical reaction leading to the creation of single-crystalline polymers: nR1-C=C-CeL-R2 [R, (=C)-C=C-(C=)R,],

-

Dielectric m e a ~ u r e m e n t s proved ~ - ~ - ~ to ~ be useful in observation of the phase transitions in pTS crystals. The transition was found to manifest itself in anomalies of the electric permittivity measured in the direction of the 2-fold axis b (a) which is also the direction of growing polymer chains in this system. It is worthy of note that the anomaly can be observed at any stage of the polymerization, even within the conversion range where the temperature dependence of the specific heat is completely featureless. Much less information has been collected to date on the chemical analogue of pTS, the bis(p-fluorobenzenesulfonate)of hexadiynediol (pFBS; R, = R2 = -CH20S02PhF). Room-temperature crystallographic structures of monomers and polymers of pTS and pFBS are very similar, and the unit cells of the crystals of both compounds are isomorphous.20 However, despite such a close similarity, structural,20 spectroscopic,21and dielectric22

To date, much effort has been devoted to the studies of these systems, special attention being paid to studies of the electrical and optical properties of fully polymerized diacetylene crystals (for reviews see, e.&, refs 1-3), much less interest being focused on dielectric investigations (refs 4 and 5 and references therein). A significant part of the work on polymerizable diacetylenes has been carried out on the bis(p-toluenesulfonate) of hexadiynediol (pTS, the side groups being R I = R2 += -CH20S02PhCH3). Crystals of the pTS monomer exhibit two structural phase transitions at ca. 160 and ca. 200 K.6 These transitions, although (1) Cantow, H.-J., Ed. Polydiacetylenes; Springer: Berlin, 1984. slightly shifted in temperature, are also present in monomer-rich (2) Bloor, D., Chance, R. R., Eds. Polydiacetylenes: Synthesis, Structure crystals. The phase between the two temperatures was found to and Electronic Properties; Nijhoff Dordrecht, 1985. In polymer-rich and in fully polymerized be incommen~urate.~,~ (3) Schott, M.; Wegner, G. In Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D. S., Zyss, J., Eds.; Academic Press: New crystals the transition proceeds directly from the low-T to the York, 1987; Vol. 2, p 3. high-T phasee-10 (in poly-pTS a t ca. 190 K). In both the low-T (4) Nowak, R.; Sworakowski, J.; Kuchta, B.; Bertault, M.; Schott, M.; and the high-T phases the monomer and polymer unit cells are Jakubas. R.: Kolcdziei, H. A. Chem. Phys. 1986, 104,467. monoclinic (space group P2,/c), the diacetylene stacks (polydi( 5 ) Orczyk, M. E. b e m . Phys. 1990; 142, 485. acetylene chains in polymer) extending along the 2-fold axis (6) Robin, P.; Pouget, J. P.; Comes, R.; Moradpour, A. Chem. Phys. Lett. 1 9 ~ n7. -. 1 . -217. The low-T phase of pTS crystals at any stage of conversion to (7) Patillon, J. N.; Robin, P.; Albouy, P. A.; Pouget, J. P.; Comes, R. Mol. polymer contains two pairs of molecules per unit cell differing Crysr. Liq. Crysr. 1981, 76, 297. in conformations of the side groups R , and R2,9910312-14 whereas (8) Bertault, M.; Collet, A.; Schott, M. J. Phys. (Paris) Lett. 1981, 42, the unit cell in the high-T phase contains only one pair of identical, 131. (9) Enkelmann, V.; Wegner, G. Makromol. Chem. 1977, 178, 635. but crystallographically inequivalent, pTS molecules. 11,13 (10) Bloor, D.; Kennedy, R. J. Chem. Phys. 1980, 47, 1. The observation of enlarged ellipsoids of thermal motion de(1 1) Kobelt, D.; Paulus, E. F. Acta Crystallogr. 1974, B30, 232. termined for the atoms constituting pTS side groups in the high-T (1 2) Enkelmann, V. Acta Crystallogr. 1977, 833, 2842. (13) Aim$, J. P.; Lefebvre, J.; Bertault, M.; Schott, M.; Williams, J. 0. was one of the reasons for which this phase is often J . Phys. (Paris) 1982, 43, 307. described as a disordered one, the transition in poly-pTS crystals Enkelmann, V.; Leyrer, R. J.; Wegner, G. Makromol. Chem. 1979, beiig discussed in terms of an order-disorder t r a n s f ~ r m a t i o n . l ~ , ~ ~180, ~ ~(14) 1787. Calorimetric measurements carried out on pTS single crystals (15) Bloor, D.; Fischer, D. A,; Batchelder, D. N.; Kennedy, R.; Cottle, A. showed that the anomalies associated with the phase transitions C.; Lewis, W. F.; Hursthouse, M. B. Mol. Crysr. Liq. Cryst. 1979, 52, 83. (16) Robin, P. ThEse, Universitt de Paris Sud, Paris, 1980. clearly visible in pure monomer shift toward lower temperatures (17) Williams, R. L.; Bloor, D.; Batchelder, D. N.; Hursthouse, M. B.; and become smeared as the polymerization proceeds. Any sigDaniels, W. B. Discuss. Faraday SOC.1980, 69, 49. nature of the transitions disappears when the amount of polymer (18) Bara, M. These, Universitt Paris VII, Paris, 1985. exceeds ca. 7% to reappear close to the completion of the po(19) Zielinski, R.; Kalinowski, J. J. Phys. C 1987, 20, 177. (20) Aim& J. P.; Schott, M.; Bertault, M.; Toupet, L. Acta Crystallogr. lymerization (x 2 0.97).8 - - - - /

Present address: Photonics Research Laboratory, State University of New York at Buffalo, Buffalo, NY 14214. *To whom correspondence should be addressed

1988, 844, 617. (21) Chance, R. R.; Yee, K. C.; Baughman, R. H.; Eckhardt, H.; Eckhardt, C. J. J. Polym. Sci., Polym. Phys. Ed. 1980, 18, 1651. (22) Orczyk, M.; Sworakowski, J.; Bertault, M.; Faria, R. M. Synth. Met. 1990, 35, 77.

0022-3654/92/2096-4686%03.00/0 0 1992 American Chemical Society

Mixed Diacetylene Single Crystals

The Journal of Physical Chemistry, Vol. 96, No. 1 1 , 1992 4687

experiments showed no evidence of any phase transition in crystals of both monomer and polymer of pFBS. The close similarity of shapes and sizes of pTS and pFBS molecules and identical symmetries of unit cells of their crystals enable one to obtain mixed pTS-pFBS crystals throughout the entire composition Thus it seemed interesting to raise a question concerning the existence of phase transitions in mixed pTS-pFBS crystals. In this paper we report on results of measurements of the temperatures of phase transitions in function of the composition of mixed pTS-pFBS crystals and for various degrees of polymerization of the samples, employing both the calorimetric and dielectric methods. The experiments reported here cover the temperature range down to 80 K.

Experimental Section The syntheses of pTS and pFBS, purification of the material, and growth of the diacetylene single crystals were performed according to the procedures described in detail in ref 25. Only crystals with a well-defined habit were retained for further use. The mixed crystals used in the experiments reported in this paper cover the entire range of compositions from pure pTS to pure pFBS. The compositions of mixed crystals were determined as described in detail in ref 24. Plane-parallel samples were cut from monomer crystals and subsequently polished on acetone-soaked tissues for use in the dielectric measurements. The largest planes of the samples were always perpendicular to the crystallographic direction 6. Silver paste painted electrodes were used in the experiments reported in this paper. During all stages of purification, crystal growth, sample preparation, and measurements, the samples were kept in darkness or handled under weak red light and at possibly low temperature to reduce an uncontrolled light-induced or thermal polymerization. Typically, thicknesses of the samples used for measurements of electric permittivities were about 0.5 mm, and their electroded area was of the order of 20 mm2. Because of uncertainty in the determination of the electroded areas and the thicknesses of the samples, the values of electric permittivity calculated from capacitance measurements are uncertain to within ca. 10%. We must emphasize, however, that relative changes of permittivity measured on a given sample were determined with about 0.1% accuracy. The dielectric experiments were performed in the dark, under nitrogen atmosphere at ambient pressure, within the temperature range 8&333 K. The rate of temperature changes was about f l K/min. The capacitance measurements were carried out a t a frequency of 1 kHz employing an autobalance C-bridge, the ac field applied to the samples amounting to ca. 5 X lo4 V/m. The thermal polymerization of the measured diacetylene samples was performed in situ at 333 K. Only the real part of electric permittivity was measured in the experiments. Nevertheless, the loss tangent was continuously monitored, being always of the order of 10-3-10-2. The calorimetric experiments reported in this paper were carried out employing a Perkin-Elmer DSC7 scanning calorimeter, the measurements being carried out in the temperature range 120-220 K. Single-crystalline samples were preferentially used for the measurements. The samples were encapsulated in aluminum pans, allowing for a good heat exchange between them and the calorimeter. The rates of temperature changes in most experiments amounted to f5 or f 1 0 K/min.

e

1 dt-

C

-4 50 100 150 200 250 300 350

1 I

h

9 f e

dC

ba

50 100 150 200 250 300 350

T

j i h-

9f e

d C

b a1

(A)Dielectric Measurements. Figure 1 shows the temperature dependences of the electric permittivity measured in the direction of growing polymer chains, eb, in mixed crystals of various compitions. Far from the region of the phase transitions, the electric permittivities were found almost independent of the sample compositions, depending mainly on the polymer contents. In this (23) Enkelmann, V. Mukromol. Chem. 1983, 184, 1945. (24) Orczyk, M.; Pater, E.; Sworakowski, J. Mukromol. Chem., in press. (25) Bertault, M., Thhe, Universit6 Paris VI, Paris, 1983.

[KI

I

I

I

I

I

I

50 100 150 200 250 300 350

T

[KI

Figure 1. e,,(?'') dependences in pTS-pFBS mixed crystals of various compositions (expressed in mol % of pFBS: (a) 0 (pure pTS), (b) 3, (c) 5 , (dl 10, (e) 15, (0 17, (g) 20, (h) 39, (i) 54, Ci) 87, (k) 100 (pure pFBS)), and at various stages of polymerization ((A) crystals of monomers, (B) crystals polymerized in SO%, (C) fully polymerized crystals). For the sake of clarity subsequent curves are vertically shifted by 0.5 c unit in parts A and B and by one t unit in part C.

4688 The Journal of Physical Chemistry, Vol. 96, No. 11, 1992

Orczyk et al.

CP [J/qKl n

I50

Y

1

a

U

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e a

0.8 200

J

0.7

0.6 140

160

180

200

-1

220

0.00

0.05

0.10

0.15

0.20

Y

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3. Temperatures of phase transitions as determined from the a(r)

(filled symbols) and cp( T ) (empty symbols) dependences in pTS-pFBS mixed crystals of various compositions and polymer contents: triangles and squares, low-T and high-T transitions in monomer, respectively; spades, samples polymerized in 50%;circles, fully polymerized samples.

0 . 5 ! . ,. , . , . , . , 1 120 140 160 180 200 220 T [KI Figure 2. cp(T) dependences in (A) monomers and (B) polymers of pTS-pFBS mixed crystals of various compositions (expressed in mol % of pFBS). A: (a) 0 (pure pTS), (b) 0.8, (c) 1.5, (d) 3 , (e) 4.5; xB: (a) 0 (pure PTS), (b) 3, (c) 5, (dl 10, (e) 15, (0 17, (9) 20, (h) 39, (i) 54, (j)87. For the sake of clarity, the curves are vertically shifted by 0.05 J g-' K-I.

temperature range t b was found to increase linearly with the amount of polymer. This property may be used to determine the polymer fraction, as was shown in ref 24. The composition of mixed pTS-pFBS crystals crucially influences the positions (and even the existence) of the anomalies observed on the t b ( T ) dependences (see Figure 1). In pure pTS (both in monomer and in polymer) these anomalies are associated with the phase transition^.“^^^^ By analogy, we shall attribute the anomalies observed in pTS-rich mixed crystals to the same processes. The temperatures of the low-T phase transition (appearing as a delicate hump on tb( T ) curves measured in samples of monomers containing 0 and 3 mol % of pFBS) were determined from the positions of the local maxima of the &b(7')/aT derivative, and the temperatures of the high-T phase transition were determined directly from maxima of the eb( T ) dependences. Only in crystals containing 3 mol % of pFBS can one still find both phase transitions characteristic of pure pTS although at slightly different temperatures (cf. Figure 1A). In the crystals of monomers richer in pFBS, no signature of the low-T phase transition can be found (or, at best, the transition temperature can be determined quite arbitrarily-cf. curves c and d in Figure 1A). The high-T transition shifts downward with increasing pFBS contents in the samples, and crystals containing over 17 mol %

pFBS exhibit only an increase of permittivity on decreasing the temperature, possibly indicating the existence of a phase transition below the nitrogen temperatures. The eb( 7')curves obtained for samples containing over 39 mol % pFBS exhibit no signature of any phase transition in the temperature range under investigation. In fully polymerized pTS-rich mixed crystals one may observe, in analogy to poly-pTS, only one phase transition. Similarly as in the crystals of monomers, the phase transition temperature decreases on increasing the pFBS contents in the samples (see Figure 1C). In pure pTS the transition is observed at ca. 190 K, whereas in samples containing 20 mol % of pFBS the transition is shifted to ca. 83 K. The maxima of c b ( T ) curves in samples richer in pFBS apparently shift beyond the temperature range under investigation. pFBS-rich samples (over 54 mol 7%) exhibit no signatures of a phase transition, their eb( 7') dependences being completely flat within the temperature range covered by our experiments. Partly polymerized samples behave similarly to fully polymerized ones (cf. Figure 1B). (B)Calorimetric Measurements. We have also performed calorimetric experiments carried out on monomers and fully polymerized samples. Figure 2 presents temperature dependences of the specific heat, cp(7'). In the case of polymer samples (Figure 2B) the data collected cover the entire composition range, whereas for monomeric samples we show only the results obtained on pTS-rich compositions for which the positions of anomalies are best pronounced. Similarly to the dielectric measurements, one can clearly observe a downward shift of the temperatures of maxima associated with the phase transition (compare also Figure 3). The maxima on the c,(T) curves may be found only for the samples containing less than 15 mol 9% pFBS. The c,(T) curves determined for pFBS-rich samples do not show any signature of a phase transition within the temperature range under study. Discussion The results reported in this paper confirm earlier findings that pure pFBS, despite a close structural similarity to pTS, does not

The Journal of Physical Chemistry, Vol. 96, No. 11, 1992 4689

Mixed Diacetylene Single Crystals

a

b

C

L

tP

Figure 4. View of the arrangements of the side groups in poly-pTS (a) and simplified schemes of the orientations of side group dipoles in unit cells of the low-temperature phase (b) and high-temperture phase (c). The vectors below each scheme show in a simplified way a possible construction of two polar sublattices (after ref 4).

exhibit any phase transition. Moreover, the temperatures of phase transitions in mixed crystals decrease with increasing amount of pFBS. It seems difficult to link this fact with a difference in the size of the side groups of both diacetylenes. van der Waals volume increments of the fluorine atom and methylene group differ and 23.5 X nm3, respectively26)but substantially (9.6 X one should realize that fluorine and CH3 are only small fragments of the bulky side groups. Hence it does not seem reasonable to regard this difference as a factor controlling the temperature (or even the existence) of the phase transitions. On the other hand, it seems more feasible to associate the shift of the temperatures of the phase transitions in mixed pTS-pFBS crystals of various compositions (and its absence in pure pFBS samples) with differences in dipole-dipole interactions between the side groups. In the case of pTS the dipole moment of the tosyle group amounts to ca. 4 D2' (ca. 1.3 X C m). Replacing the methyl group with the highly electronegative fluorine atom results in a nearly 50% decrease of this value.2* Such a significant reduction of the dipole moment of the side groups should substantially alter their interactions, being a possible factor influencing structural transitions. Results of measurements carried out on mixed pTS-pFBS crystals, in which the constituent molecules (and hence the dipolar side groups) should be randomly d i ~ t r i b u t e d apparently ,~~ point out to the importance of the dipole-dipole interactions. One may clearly see a downward shift of T, on the eb(T) dependences measured in the monomer mixed crystals (Figure 1A) with increasing pFBS content in the samples. This tendency is much better pronounced in partly and fully polymerized crystals (Figure lB,C), where the position of T, is much easier to determine. The same trend is observed in the calorimetric experiments (cf. Figure 2A). As is clearly demonstrated in Figure 3, the transition temperatures determined from c ( T ) dependences are in a good agreement with those found in t i e dielectric measurements. As indicated earlier in this paper, the transitions in pTS possess some features characteristic of order-disorder phase transitions.1°J6'18 Hence our attempt to explain the dependence of T, on the pFBS content in the crystal employs a description of an order-disorder transitions based on the Ising model.29 Such (26) Kitaigorodsky,A. I. Molecular Crystals and Molecules; Academic Press: New York, 1973. (27) Eucken, A., Ed.Lundolt-Bdrnstein Zahlenwerte und Funktionen, 6th ed.; Springer: Berlin, 1951; Vol. 1, Part 111, p 446. (28) Minkin, V. I.; Osipov, 0. A.; Zhdanov, Y . A. Dipolnye Momenty u Organicheskoi Khimiyi (Dipole Moments in Organic Chemistry); Izdatel'stvo Khimiya: Leningrad, 1968. (29) Cusack, N. E. The Physics of Structurally Disordered Matter; Hilger: Bristol, 1988.

an approach has been known in the thermodynamics of disordered systems, e.g., solid solutions.3o For the purpose of our description, in addition to a possible orientational disorder of the side groups (as in the case of the high-T phase of pTS), one should also take into account the fact that the crystals under consideration are two-component, i.e., one should introduce a chemical disorder. The phase transition in pTS crystals may be understood as a reorientation of the polar side groups of the diacetylene molecules. Hence, in our discussion we shall describe the structure of mixed pTS-pFBS crystals as a network of dipoles being capable of changing their orientations. It was already mentioned in the Introduction that the ordered phases (low-temperature phases) of both polymer and monomer of pTS are characterized by the presence of two molecules in the unit cell differing in the orientations of their polar side groups in centrosymmetric mole~ u l e s ? J ~ J ~The - ' ~nonpolar lattice of pTS can also be divided into two polar sub lattice^,^ as is schematically shown in Figure 4. Hereafter, we shall label the sublattices A and B, and the orientations of side groups in two inequivalent molecules L (leftoriented) and R (right-oriented). Obviously, after interchanging the orientation of the dipoles in both sublattices, one also obtains the ordered structure. In the high-T phase the long-distance correlation of the orientations of the dipoles of both sublattices disappears; thus, the sublattices become undistinguishable and translationally equivalent. In our two-state model the disordered phase is represented by a totally stochastic distribution of the two allowed orientations of the dipoles. Let us consider the network composed of N dipoles equally distributed between the sublattices A and B. Furthermore, let nA,L ( I ) ~ , ~be ) the fraction of dipoles in the sublattice A which are left-oriented (right-oriented). Similarly, nB,R (nB,L) stands for the fraction of the right-oriented (left-oriented) dipoles in the sublattice B. It follows that ~ A . L+ ~ A . R= ~ B , L+ ~ B , R 1 (1) We may introduce an order parameter, 6, defined by the equation At low temperatures, nAL = 1 (or nllR = 1) and hence 6 = 1, while in the high-T phase nA,L = nA,R = and 6 = 0. Since the lattice remains centrosymmetric at both low-temperature and hightemperature phases, the same order parameter should describe the ordering of both sublattices. Let us consider interactions of the neighboring dipoles belonging to different sublattices. Crystallographic data11J3*20 for pTS and pFBS indicate that each dipole of a given sublattice is surrounded by three pairs of dipoles belonging to the other sublattice. Strictly (30) Swalin, R. A. Thermodynamics of Solids; Wiley: New York, 1962.

4690 The Journal of Physical Chemistry, Vol. 96, No. 11, 1992

speaking, these pairs are not equivalent, but for the purpose of a qualitative description it will be assumed that each dipole belonging to a given sublattice has six nearest neighbors belonging to the other sublattice. One may show (see the Appendix) that the total energy of interactions of all pairs of dipoles in the system is U = 3/2N[(I + 6’)Uo (1 - 6’)UD] (3)

Orczyk et a1 0-

-

1

. Y

+

where Uo and UD stand for the energies of interactions of an ordered and a disordered pair of dipoles, respectively. The Boltzmann configurational entropy of the system may be expressed (see the Appendix) as Smnf = kN[ln 2 - &[(I + 6) In (1 6) + (1 - 6) In (1 -a)]] (4) One should note at this point that the entropy of phase transition in pTS calculated employing the data from ref 25 amounts to ca. 0.29 J mol-‘ K-* for monomer of pTS and ca. 0.66 J mol-‘ K-‘ for poly-pTS, both values being significantly smaller than that expected of an order-disorder transition, where AS = R In 2 = 5.76 J m o l l 1 K-I. One should realize, however, tfat the latter value should be found only in the case of a total lack of coherence between reorienting species. Another possible way of rationalizing this discrepancy is to assume an incomplete ordering of the low-T phase caused, e.&, by pinning at imperfections of the crystal structure. It is easy to show that the entropy of such an “incomplete” order-disorder transition can be expressed as

+

-1 00

i J

0.00

e e

0.05

0.10

0.20

0.15

Y Figure 5. CQ) dependences (see eq 8) plotted for different values of the

ratio gLTs/gFBs (indicated near the curves). The points give the experimental values of the shift of the transition temperatures in pTS-pFBS mixed crystals of various compositions and degrees of polymerization determined by the dielectric and the calorimetric measurements. The meaning of the symbols is the same as in Figure 3. of pTS is (1 - y)’, the probability that both are pFBS amounts to yz, and the dipoles belong to different molecules with the probability 2y(l - y ) . The energy of interactions of a pair of neighboring dipoles in the lattice can thus be expressed as

a,f= f/2[(1 + 6,)

In (1 + ~ L T )+ (1 - ~ L T )In (1 - 6LT)I (5) where 6LT is the order parameter in the low-T phase (6LT < 1). Employing eq 5 , one may infer that in order to meet the results obtained in ref 24 we should put ~ L TN 0.26 for monomer and 6LT N 0.4 for poly-pTS. Employing eqs 3 and 4 to express the free energy of the system and finding the stability conditions (see the Appendix), one may show that the critical temperature, T,, is T, = ~ ( U D U - o ) / k = 3AU/k (6)

In the above equations, the subscripts TS and FBS label the dipoles associated with the pTS and pFBS side groups, respectively. The function C(y) = [( 1 - y)pm + ypFaS]’is a function of the crystal composition and parametrically depends on pm and pFBsvalues. Making use of eqs 6-8, one arrives at the equation

The critical temperature is thus, in our approximation, a linear function of the difference of interaction energies of the dipoles Equation 9 describes the dependence of the temperature of an order-disorder transition on the composition of a mixed diacetylene in the disordered and ordered phases. Moreover, it comes from crystal. The coefficients fo and fD in our approximation are eq 6 that a long distance order (characterized by 6 > 0) may be independent of y; hence, the function C(y) should describe the achieved by the system only if the energy of interactions of the ordered dipoles be lower than that of the disordered ones. changes of T, on varying the pFBS content in the samples. Since pFBS< pm (cf. refs 27 and 28), C(y) and, consequently, The energy of interactions of two dipoles (hereafter labeled i and j) may be expressed in the form U = p i p ~ r i , r j , ~ i , ~ j , ~ i , ~ ,T, ) , should decrease on increasing the mole fraction of pFBS. Moreover, as the polymerization does not substantially change where p stands for the magnitude of the dipole moment andftor the magnitudes and orientations of the side groups, one should a function describing the interaction which is dependent on the expect C(y) being almost independent of the polymer content. positions and orientations of the dipoles in the lattice. Assuming Therefore the shift of the transition temperature itself should that the phase transition does not substantially influence the values primarily depend on y, irrespective of the amount of the polymer. of pi and pj, we may write Such a behavior was indeed observed in the experiments described (7) Au = PipjCfD - f0) in this paper. The results of Figure 3 replotted on a common diagram (Figure 5 ) demonstrate that, to within a reasonable where the subscripts 0 and D refer to the interactions of ordered accuracy, all transition temperatures determined for diluted dipoles and disordered dipoles, respectively. In our simple two-state systems 0, < 0.1 5 ) fall onto a common master curve best fitted modelfo describes a conformation in which the neighboring dipoles are rotated in the opposite directions, and fD describes a conby pTS/pFeSratio amounting to 2 f 0.5, in a good agreement with independently available data.27.28 In the crystals containing more formation where the dipoles are rotated in the same direction. In than 15 mol 5% of pFBS we observed a rapid decrease of T, which fact, the function fD should be taken as a correlation-sensitive cannot be accounted for by the simple model put forward in this average,fD = weighed with respect to all mutual orienpaper. This behavior may indicate that the faster decrease of T, tations of the dipoles in the high-T phase. For our purpose, above y 0.15 is due to the activation of a mechanism different however, it is only necessary to note that if Uo < UD thenfo < from the one considered here. fD must be satisfied. Describing the process responsible for the appearance of the To rationalize the composition-dependent shift of the temanomalies observed on the cb(T) and C,