Towards an understanding of the heat capacity of liquids. A simple two-state model for molecular association

Abstract

A model for the temperature dependence of the isobaric heat capacity of associated pure liquids C(p,m)(o)(T) is proposed. Taking the ideal gas as a reference state, the residual heat capacity is divided into nonspecific C(p) (res,ns) and associational C(p) (res,ass) contributions. Statistical mechanics is used to obtain C(p)(res,ass) by means of a two-state model. All the experimentally observed C(p,m)(o)(T) types of curves in the literature are qualitatively described from the combination of the ideal gas heat capacity C(p)(id)(T) and C(p)(res,ass)(T). The existence of C(p,m)(o)(T) curves with a maximum is predicted and experimentally observed, for the first time, through the measurement of C(p,m)(o)(T) for highly sterically hindered alcohols. A detailed quantitative analysis of C(p,m)(o)(T) for several series of substances (n-alkanes, linear and branched alcohols, and thiols) is made. All the basic features of C(p,m)(o)(T) at atmospheric and high pressures are successfully described, the model parameters being physically meaningful. In particular, the molecular association energies and the C(p)(res,ns) values from the proposed model are found to be in agreement with those obtained through quantum mechanical ab initio calculations and the Flory model, respectively. It is concluded that C(p,m)(o)(T) is governed by the association energy between molecules, their self-association capability and molecular size.

Study of the volumetric properties of weakly associated alcohols by means of high-pressure speed of sound measurements

“…Moreover, by comparing the average and absolute average deviations it is found that the equation does not introduce any systematic error. As can be seen in figures 1 and 2, the behaviour of the speed of sound against pressure and temperature shows regular tendencies and there are not any remarkable unusual tendencies for the three alcohols in contrast with the observed behaviour of the heat capacity for two of the studied alcohols [5].…”

“…It has been shown that to this weaker association can affect to their thermodynamic properties in a unusual way. A recent work [5] has shown that the isobaric heat capacity at atmospheric pressure presents a maximum against temperature for the 3-methyl-3-pentanol and 3-ethyl-3-pentanol. Then, the determination of thermodynamic properties for these kinds of alcohols is interesting since they could give information about the nature of the association phenomena.…”

Second-order thermodynamic derivative properties of binary mixtures of n-alkanes through the SAFT-CP equation of state

“…A detailed quantitative analysis of heat capacities for several series of substances, including n-alkanes, linear and branched alcohols and thiols is reported by Delgado and co-workers [28]. It should be mentioned that our results for the binary mixtures between n-alkane fluids are obtained without introducing any binary interaction parameter in the combining rules.…”

Dependence on molecular parameters of the heat capacity critical behaviour for nitroalkane+alcohol binary systems

“…It is well-known [14] that association capability between alcohol molecules decreases with carbon number due to the lower probability of making a hydrogen bond as the alkyl chain is longer. In addition, primary alcohols present higher association ability than non-primary ones, due to the lower steric hindrance over the hydroxyl group, which is higher as the hydroxyl is in positions distant from the end of the alkyl chain.…”

“…Thus, the influence on critical behaviour of the alkyl chain of both nitroalkane and alcohol seemed to be an interesting molecular parameter, fact which motivated the selection of the critical mixtures of nitromethane and nitroethane with the series of 1-alcohols, from 1-propanol to 1-decanol. Moreover, it was assumed that other significant parameter could be the position of the hydroxyl group, which strongly affects to the self-association capability of the alcohol [14]; therefore four non-primary alcohols were also selected (2-propanol, 2-pentanol, 3-pentanol and 5-nonanol). From the obtained C p V À1 experimental data, the critical amplitudes A + and the critical temperature T c are determined for all studied systems and n þ 0 are calculated by means of the two-scale factor universality, in order to obtain microscopic information about the processes involved in the phase transition.…”