Heat capacity singularity of binary liquid mixtures at the liquid-liquid critical point.

The critical anomaly of the isobaric molar heat capacity for the liquid-liquid phase transition in binary nonionic mixtures is explained through a theory based on the general assumption that their partition function can be exactly mapped into that of the Ising three-dimensional model. Under this approximation, it is found that the heat capacity singularity is directly linked to molar excess enthalpy. In order to check this prediction and complete the available data for such systems, isobaric molar heat capacity and molar excess enthalpy near the liquid-liquid critical point were experimentally determined for a large set of binary liquid mixtures. Agreement between theory and experimental results-both from literature and from present work-is good for most cases. This fact opens a way for explaining and predicting the heat capacity divergence at the liquid-liquid critical point through basically the same microscopic arguments as for molar excess enthalpy, widely used in the frame of solution thermodynamics.

Association effects in the {methanol + inert solvent} system via Monte Carlo simulations. I. Structure.

In this work, the clusters residing in the {methanol + inert solvent} binary system have been characterized using a specific methodology in the framework of Monte Carlo molecular simulations. The cluster classification scheme considered distinguishes into five types: linear chains, cyclic clusters or isolated rings, branched linear chains, branched cyclic clusters, and composite rings. The procedure allows one to compute the next rich structural information: the fraction of molecules in the monomer or associated state, the fraction of each type of aggregate with a given size (and of molecules belonging to them), and the most probable and average cluster size for each type; likewise, the degree of branching in branched linear chains and the size distribution of the inner ring in branched cyclic clusters can be quantified. Specifically, all these properties were obtained for the {Optimized Potential for Liquid Simulation methanol + Lennard-Jones spheres} system at 298.15 K and 1 bar throughout the composition range. The results have provided a complete structural picture of this mixture describing comprehensively the effect of dilution into the hydrogen-bonded network of the pure associated fluid.

Association effects in the {methanol + inert solvent} system via Monte Carlo simulations. II. Thermodynamics.

Mixtures containing associated substances show a singular thermodynamic behaviour that has attracted to scientific community during the last century. Particularly, binary systems composed of an associating fluid and an inert solvent, where association occurs only between molecules of the same kind, have been extensively studied. A number of theoretical approaches were used in order to gain insights into the effect of the association on the macroscopic behaviour, especially on the second-order thermodynamic derivatives (or response functions). Curiously, to our knowledge, molecular simulations have not been used to that end despite describing the molecules and their interactions in a more complete and realistic way than theoretical models. With this in mind, a simple methodology developed in the framework of Monte Carlo molecular simulation is used in this work to quantify the association contribution to a wide set of thermodynamic properties for the {methanol + Lennard Jones} specific system under room conditions and throughout the composition range. Special attention was paid to the response functions and their respective excess properties, for which a detailed comparison with selected previous works in the field has been established.

Association effects in pure methanol via Monte Carlo simulations. I. Structure.

A methodology for the determination of the oligomers residing in a pure associated fluid was developed in the framework of the molecular simulation technique. First, the number of hydrogen bonds between each pair of molecules of the fluid is computed by using a specific criterion to define the hydrogen bonding formation. Secondly, sets of molecules linked by hydrogen bonds are identified and classified as linear chains, cyclic aggregates, branched linear chains, branched cyclic aggregates, and the rest of clustering. The procedure is applied over all the configurations produced in usual Monte Carlo simulations and allows the computation of the following properties characterizing the structure of the fluid: the fraction of molecules in the monomer or associated state, the fraction of each type of aggregate with a given size (and of molecules belonging to them), and the most probable and the average cluster size for each type. In addition, the degree of branching in branched linear chains and the type of ring in branched cyclic clusters can be obtained. In this work, all these quantities were computed for OPLS methanol using NpT Monte Carlo simulations at atmospheric pressure for 298.15 K (room conditions) and from 800 K to 350 K (gas phase), and along several supercritical isobars: 25, 50, 100, 200, and 500 MPa from 250 K to 1000 K. An analysis of the results has provided a comprehensive structural picture of methanol over the whole thermodynamic state space.

Association effects in pure methanol via Monte Carlo simulations. II. Thermodynamics.

A simple methodology [P. Gómez-Álvarez, A. Dopazo-Paz, L. Romani, and D. González-Salgado, J. Chem. Phys. 134, 014512 (2011)] recently developed in the light of the Monte Carlo molecular simulation technique was used in this work to study the association effects on the response functions of methanol over the whole thermodynamic state space. It consists basically on evaluating the first order properties of the fluid (energy and volume) in terms of those for two hypothetical fluids living in the bulk composed by monomers and associated molecules, respectively. In this context, the second order thermodynamic derivatives can be expressed in a perturbative way as the sum of the monomer term (reference term) and the association contribution. Specifically, both contributions to the residual isobaric heat capacity, and to the pressure and temperature derivatives of the volume were determined for the optimized potential for liquid simulation (OPLS) of methanol through NPT Monte Carlo simulations from 250 K to 1000 K along the supercritical isobars 25, 100, 200, 500 MPa, and from 800 K to 350 K at 0.1 MPa. Results showed that both terms are relevant for the residual isobaric heat capacity and that their influence depends considerably on the thermodynamic conditions; however, the volumetric response functions were found mainly affected by the monomer contribution, especially the pressure derivative of the volume.

Thermal properties of ionic systems near the liquid-liquid critical point.

Isobaric heat capacity per unit volume, C(p), and excess molar enthalpy, h(E), were determined in the vicinity of the critical point for a set of binary systems formed by an ionic liquid and a molecular solvent. Moreover, and, since critical composition had to be accurately determined, liquid-liquid equilibrium curves were also obtained using a calorimetric method. The systems were selected with a view on representing, near room temperature, examples from clearly solvophobic to clearly coulombic behavior, which traditionally was related with the electric permittivity of the solvent. The chosen molecular compounds are: ethanol, 1-butanol, 1-hexanol, 1,3-dichloropropane, and diethylcarbonate, whereas ionic liquids are formed by imidazolium-based cations and tetrafluoroborate or bis-(trifluromethylsulfonyl)amide anions. The results reveal that solvophobic critical behavior-systems with molecular solvents of high dielectric permittivity-is very similar to that found for molecular binary systems. However, coulombic systems-those with low permittivity molecular solvents-show strong deviations from the results usually found for these magnitudes near the liquid-liquid phase transition. They present an extremely small critical anomaly in C(p)-several orders of magnitude lower than those typically obtained for binary mixtures-and extremely low h(E)-for one system even negative, fact not observed, up to date, for any liquid-liquid transition in the nearness of an upper critical solution temperature.

On the isobaric thermal expansivity of liquids.

The temperature and pressure dependence of isobaric thermal expansivity, α(p), in liquids is discussed in this paper. Reported literature data allow general trends in this property that are consistent with experimental evidence to be established. Thus, a negative pressure dependence is to be expected except around the critical point. On the other hand, α(p) exhibits broad regions of negative and positive temperature dependence in the (T, p) plane depending on the nature of the particular liquid. These trends are rationalized here in terms of various molecular-based equations of state. The analysis of the Lennard-Jones, hard sphere square well and restricted primitive model equations allows understanding the differences in the α(p) behavior between liquids of diverse chemical nature (polar, nonpolar, and ionic): broader regions of negative temperature and positive pressure dependencies are obtained for liquids characterized by larger ranges of the interparticle potential. Also, using the statistical associating fluid theory (SAFT) allowed the behavior of more complex systems (basically, those potentially involving chain and association effects) to be described. The effect of chain length is rather simple: increasing it is apparently equivalent to raise the interaction range. By contrast, association presents a quite complex effect on α(p), which comes from a balance between the dispersive and associative parts of the interaction potential. Thus, if SAFT parameters are adjusted to obtain low association ability, α(p) is affected by each mechanism at clearly separate regions, one at low temperature, due to association, and the other to dispersive forces, which has its origin in fluctuations related with vapor-liquid transition.

Thermodynamic consistency near the liquid-liquid critical point.

The thermodynamic consistency of the isobaric heat capacity per unit volume at constant composition C(p,x) and the density rho near the liquid-liquid critical point is studied in detail. To this end, C(p,x)(T), rho(T), and the slope of the critical line (dT/dp)(c) for five binary mixtures composed by 1-nitropropane and an alkane were analyzed. Both C(p,x)(T) and rho(T) data were measured along various quasicritical isopleths with a view to evaluate the effect of the uncertainty in the critical composition value on the corresponding critical amplitudes. By adopting the traditionally employed strategies for data treatment, consistency within 0.01 K MPa(-1) (or 8%) is attained, thereby largely improving the majority of previous results. From temperature range shrinking fits and fits in which higher-order terms in the theoretical expressions for C(p,x)(T) and rho(T) are included, we conclude that discrepancies come mainly from inherent difficulties in determining the critical anomaly of rho accurately: specifically, to get full consistency, higher-order terms in rho(T) are needed; however, the various contributions at play cannot be separated unambiguously. As a consequence, the use of C(p,x)(T) and (dT/dp)(c) for predicting the behavior of rho(T) at near criticality appears to be the best choice at the actual experimental resolution levels. Furthermore, the reasonably good thermodynamic consistency being encountered confirms that previous arguments appealing to the inadequacy of the theoretical expression relating C(p,x) and rho for describing data in the experimentally accessible region must be fairly rejected.

Heat capacity of associated systems. Experimental data and application of a two-state model to pure liquids and mixtures.

The predictions from a recently reported (J. Chem. Phys. 2004, 120, 6648) two-state association model (TSAM) have been tested against experimental data. The temperature, T, and pressure, p, dependence of the isobaric heat capacity, C(p), for three pure alcohols and the temperature dependence at atmospheric pressure of the excess heat capacity, C(p)(E), for four alcohol + ester mixtures have been measured. The branched alcohols were 3-pentanol, 3-methyl-3-pentanol, and 3-ethyl-3-pentanol, and the mixtures were 1-butanol and 3-methyl-3-pentanol mixed with propyl acetate and with butyl formate. These data, together with literature data for alcohol + n-alkane and alcohol + toluene mixtures, have been analyzed using the TSAM. The model, originally formulated for the C(p) of pure liquids, has been extended here to account for the C(p)(E) of mixtures. To evaluate its performance, quantum mechanical ab initio calculations for the H-bond energy, which is one of the model parameters, were performed. The effect of pressure on C(p) for pure liquids was elucidated, and the variety of C(p)(E)(T) behaviors was rationalized. Furthermore, from the C(p) data at various pressures, the behavior of the volume temperature derivative, (deltaV/deltaT)(p), was inferred, with the existence of a (deltaV/deltaT)(p) versus T maximum for pure associated liquids such as the branched alcohols being predicted. It is concluded that the TSAM captures the essential elements determining the behavior of the heat capacity for pure liquids and mixtures, providing insight into the macroscopic manifestation of the association phenomena occurring at the molecular level.

Griffiths-Wheeler geometrical picture of critical phenomena: experimental testing for liquid-liquid critical points.

An experimental approach to the verification of specific relations between thermodynamic properties as predicted from the Griffiths-Wheeler theory of critical phenomena in multicomponent systems is developed for the particular case of ordinary liquid-liquid critical points of binary mixtures. Densities rho(T) , isobaric heat capacities per unit volume C(p)(T) , and previously reported values of the slope of the critical line (dT/dp)c for five critical mixtures are used to check the thermodynamic consistency of C(p) and rho near the critical point. An appropriate treatment of rho (T) data is found to provide the key solution to this issue. In addition, various alternative treatments for C(p)(T) data provide values for both the critical exponent alpha and the ratio between the critical amplitudes of the heat capacity A+/A- that are in agreement with their widely accepted counterparts, whereas two-scale-factor universality is successfully verified in one of the systems studied.

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

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.