Heats of Mixing and the Solid-state Transition in [(C,H,)3PCH3],-~[(C,H,),AsCH3I~(TCNQ)i, (0 X I), Anion Radical Salts BY Y~ICHI IIDA* Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, Japan Received 4th March, 1977 The phase transitions of solid solutions were investigated with the anion radical salts of [(C6H5)3PCH3]1-i [(C~H&ASCH~]; (TCNQ):, (0 < x < 1). The behaviour of the phase transi- tions with respect to the composition parameter (x) was studied by using a regular binary solid solution model. It was found that the difference in the heats of mixing between the low-temperature (ccy) and high-temperature (&) phases of the solid solutions was very important in theexplanation of the line shape of the observed phase diagram. Much attention has been paid to the solid anion radical salts of 7,7,8,8-tetra- cyanoquinodimethane (TCNQ) because of their prominent electronic properties. 1-9 In particular, the anion radical salts containing mixed cations represented by [(C6H5)3PCH3]1-: [(C,H,),AsCH,]; (TCNQ);, (0 < x < l), are known to under- go phase transitions at 1 atm pressure in the solid state, and show discontinuities in 440 I I I 700 600 500 rl 400 % E CI 300 Q 200 100 0 0.0 0.2 0.4 0.6 0.8 1.0 composition parameter, x FIG.1 .-The experimental relations (a) of transition temperature (Tc) to composition parameter (x), and (6) of heat of the phase transition (AH) to x in[ (C6H5)3PCH3]+-: [(C6H5)3hCH3]+z (TCNQ)T, (0 Q x =+G l), anion radical salts at 1 atm pressure. The solid h e of (a) shows the theoretical relation between Tc and x , as predicted by eqn (4), see ref.(6) and text. 190Y. IIDA 191 the temperature dependence of the electrical conductivity and magnetic susceptibility at the transition temperat~re.~” The phase transition of pure methyltriphenyl- phosphonium salt, where x = 0.00, takes place at 315.7 K. Heat-capacity measure- ments of this phase transition have been made by Kosaki et d3 The transition has thus been found to be of the first order. The enthalpy and the total entropy change associated with the phase transition were experimentally determined to be 485.18 cal mol-1 and 1.7206 cal deg-l mol-l, re~pectively.~ For the mixed crystals, we earlier found that the transition temperature (Tc) increased, while the magnitude of the heat of transition (AH) decreased, progressively with an increase in the composition parameter (x), and that pure methyltriphenylarsonium salt, where x = 1.00, has no such phase transition up to a decomposition temperature of ~ 4 8 0 K at 1 atm pressure.2-6 The experimental results of this thermodynamic behaviour plotted against the composition parameter are illustrated in fig.1. In this paper, we have attempted to understand the mechanism of the phase transitions of [(C,H,),PCH,],-~ [(C6H5)&CH3]: (TCNQ)?, (0 < x < l), anion radical salts and to explain their experimental phase diagram in fig. 1 by the use of a regular binary solid solution model. The difference in the heat of mixing between the high- and low-temperature phases of those solid solutions was derived from the experimental relation between AH and x and also by analysing the phase diagram in terms of such a model.THEORETICAL In a previous paper,6 we proposed a thermodynamical theory of an ideal solid solution model for [(C,H,),PCH,],-~ [(C,H,),AsCH,]f; (TCNQ)?, (0 < x < l), anion radical salts. This model assumes that the phase transition of a solid solution does not change the manner of ideal mixing of the two components, because the methyltriphenylphosphonium and methyltriphenylarsonium cations are so bulky that we cannot expect cation exchange in the phase transition. In this respect, we have to note that the phase transition of our system is not the usual order-disorder type with respect to the mixing of the. two components.Moreover, we could assign the low- and high-temperature phases of the solid solutions at 1 atm pressure as ccy and phases, respectively.6 Their Gibbs free energies per mol were expressed by G’Y(T,p, X) = (1-X) G:(T,p)+xG$ (T,p)+ RT ((1 -x) In (1 --x)+x In x], (i = a, p), (1) where (1 - x ) and x are the mole fractions of the component [(C6H5),PCH3]+ (TCNQ)? and [(C,H5)3AsCH3]+ (TCNQ);, respectively. G;((T, p ) and Gf(T, p ) are the Gibbs free energies per mol for the low-temperature (a) and high-temperature (p) phases of pure phosphonium salt, respectively, while G;(T,p) is that for the (y) phase of pure arsonium salt at 1 atm pressure. In order to explain the experimental relation between T , and x of fig. 1, this kind of ideal solid solution model is not sufficient,’ because the phase transition is related to the cooperative interaction between the two components of methyltriphenyl- phosphonium and methyltriphenylarsonium salts.Therefore, we introduce into eqn (1) a heat of mixing effect between the two components and consider a regular solid solution model, as expressed by GiY(T, p , x) = (1 -x) Gi(T, p ) + xG,Y(T, p ) +Hz(l - X ) * X + RT ((I -x) In (1 - x ) + x In x}, (i = a, p), (2) where Hz is the heat of mixing per mol for each phase, and is assumed to be independent of temperature.192 PHASE TRANSITIONS I N TCNQ SALTS First, we examine how the effect of heat of mixing may influence the heat of transition for the ay 4 By phase transition of the solid solutions. If we do not consider any heat of mixing effect, as expressed by eqn (I), the heat of transition per mol, AH, against x of the solid solution is simply given by AH = (1 -x).(Hf - H;"), where H: and Hf are the enthalpies per mol for the a and /? phases of pure phss- phonium salt, respectively.6 Therefore, if the (Hf -H;) value remains constant, the heat of transition AH of the solid solutions will have a maximum value of 485.18 cal mol-1 for the salt with x = 0.00,3 decrease linearly with increase in x, converging to zero at x = 1 .OO.However, fig. 1 shows that, although the AH value is 485.18 cal mol-1 for x = 0.00 and converges to zero at x = 1.00, the experimental relation between AH and x is different from the predicted linear relation, having a broad hump over the region of 0.00 < x -= 1.00. This deviation in the heat of transition may arise from the difference in the heats of mixing between the ay and /?y phases, that is, (HB,'-H;)-(l - x ) - x .If this term is fitted to the experimental hump of the deviated heat, the ( H g - H z ) value is estimated to be 180+ 60 cal mol-I. Next, we consider the phase diagram of the solid solutions at 1 atm pressure. For the ay + B y phase transition, the phase equilibrium condition at the transition point is GaY(T,p, x) = GBY(T,p, x ) . If the temperature and the composition para- meter vary as T 4 T+ dT and x -+ x+ dx under a constant pressure of p = 1 atm, then GaY+dGar = GB"+dG@Y. In this case, from eqn (2), dGaY and dGBY can be expressed by eqn (3) dG" = - ( l - ~ ) S i dT-Gi dx-xSi dT+G,Y dx+H2(1-2x)dx+ R((1 -x) In (1-x)+x In x) dT+RT In - (1 ") dx, where i = a or j?, and where Si or S2y is the entropy per mol for each phase.There- fore, the condition dGaY = dG@Y leads to a theoretical relation between the transition temperature (Tc) and the composition parameter (x), as expressed by eqn (4) dTc - (GY-G~)+(HE-HZ)(~-~X) - - !dx (SE -s;)(l -x) (4) For pure phosphonium salt, where x = 0.00, the experimental values of Tc and Sf-ST are 315.7 K and 1.7206 cal deg-l mol-l, re~pectively,~ but since G4 - Gf = 0, the slope value of eqn (4) is reduced to (dTc/dx) = (HE-Hky)/(Sf-S;) at T, = 315.7 K. From fig. 1, the experimental slope value of (dTJdx) at x = 0.00 is found to be 82.5 & 2.5 K per composition unit, so that the value of f12 - HZ is estimated to be 142 5 cal mol-1 by putting Sf - S; = 1.7206 cal deg-l mol-1 value into the reduced equation.The (HF-HZY) value thus estimated is found to agree, within experimental error, with the 180 +_ 60 cal mol-1 value which was previously derived from the relation between the heat of transition and composition parameters of the solid solutions. We consider the phase diagram of the solid solutions. As the value of x increases, the denominator value of (Sf- Sq).(l -x) in eqn (4) will be positive and decrease linearly, while the (G;--G!) value of the numerator will be positive and increase progressively, because the a phase of pure phosphonium salt is the unstable phase in the temperature range above 315.7 K. On the other hand, the (Hg--HkY)*(l-2x) term of the numerator is greatest (i.e., Hg-HzY) at x = 0.00, decreases linearly with the increase in x, and is zero at x = 0.50.In the range 0.50 < x < 1.00, this (HE - Hz).( 1 - 2x) term becomes negative, decreases linearly with increase in x and has the most negative value of -(HE--Hky) at x = 1.00. These situations areY. IIDA 193 demonstrated schematically in fig. 2, where the (a) line shows the relation of (G; - Gf) to x, while the (b) line, that of (H:--H:Y)*(1-2x) to x. Then, as is shown by the (c) line of fig. 2, the net value of the numerator, (G: - Gf) + (H:-H27)*(1-2~), in eqn (4) will be greatest at x = 0.00, gradually decrease with the increase in x and have a finite positive value at x = 1.00. As has been mentioned, the denominator value of eqn (4) will be positive and decrease linearly with increase in x, converging to zero at x = 1 .OO.Therefore, the value of the slope (dTc.dx) in eqn (4) will be 82.5 & 2.5 K per composition unit at x = 0.00 and gradually increase with increase in x, diverging to infinity for the salt with x = 1.00. This theoretical relation between Tc and x is schematically demonstrated in the solid (a) line of fig. 1. composition parameter, x FIG. 2.-A schematic energy diagram for the components of the numerator of eqn (4) against the composition parameter ( x ) in the solid solutions of [(C6H5),PCH3I1-~ [(C6H5)3A~CH3]: (TCNQ)i, (0 < x < l), anion radical salts (see text). (a), G;- Gf ; (b), (Hg-H&”) (1 -2x) ; (c), (a)+@). On the other hand, the experimental relation between Tc and x of the solid solutions at 1 atm pressure, as given in fig.1, shows that the Tc value is lowest (i.e., 315.7 K) at x = 0.00 and that the slope value of (dTc/dx) has a finite positive value at this point. Moreover, this slope value increases gradually with increase in x, and the T, value reaches very high temperatures (presumably up to infinity) for the salt with x = 1.00. Therefore, the above-mentioned theoretical phase diagram for the solid solutions can explain well the experimental relation between Tc and x. of [(C6H5),PcH3],-z [(C6H5),ASCH3]z (TCNQ);, (0 < x < l), anion radical salts DISCUSSION In this section, we consider the meaning of the estimated (HE-HZY) value on the basis of eqn (2). As for the phosphonium and arsonium components of the low-temperature (ay) phase of the solid solutions, the crystal and molecular structures as well as the chemical properties of the a phase of the phosphonium salt are known to be very similar to those of the y phase of the arsonium salt.8 This implies a very low value of H z in eqn (2) for the ay phase.However, as for the phosphonium and arsonium components of the high-temperature (By) phase of the solid solutions, only the structural change of the a phase into the phase takes place in the phosphonium component, while there is no change in the arsonium part.6 The crystal and molecular structures of the /? phase differ from the a phase, in that remarkable internal rotation of the phenyl substituents takes place in the methyltriphenylphosphonium cation, while no significant difference was observed in the TCNQ parts.9 This fact means that there exists appreciable structural difference between the /? phase of the 1-7194 PHASE TRANSITIONS I N TCNQ SALTS phosphonium salt and the y phase of the arsonium salt. This situation will lead to, in eqn (2), a large value of HZ for the B y phase of the solid solutions. The difference in the heat of mixing between the ay and j3y phases then makes an important contribu- tion, not only to the heat of transition, but also to the line shape of the phase diagram of those solid solutions. L. R. Melby, R. J. Harder, W R. Hertler, W. Mahler, R. E. Benson and W. E. Mochel, J. Amer. Chem. SOC., 1962, 84, 3374. W. J. Siemons, P. E. Bierstedt and R. G. Kepler, J. Chem. Phys., 1963,39,3523 ; R. G. Kepler, J. Chem. Phys., 1963,39,3528. A. Kosaki, Y . Iida, M. Sorai, H. Suga and S. Seki, Bull. Chern. SOC. Japan, 1970, 43, 2280. Y. Iida, J. Chem. Phys., 1973, 59, 1607, and the references therein. Y . Iida, Bull. Chem. SOC. Japan, 1970, 43, 3685. Y . Tida, J. Phys. Chem., 1976,80,2944. ’ Y . Iida, Mol. Cryst. and Liq. Cryst., 1977, 39,195. A. T. McPhail, G. M. Semeniuk and D. B. Chesnut, J. Chem. SOC. A, 1971, 2174. M. Konno and Y . Saito, Actu Cryst., 1973, B29,2815. (PAPER 7/387)