(243d) Calculation of Thermodynamic Properties of Pure Components and Mixtures At Vapor-Liquid Interfaces Using Classical Density Functional Theory

Authors: 
Gross, J., Delft University of Technology



The accurate prediction of thermodynamic properties such as surface tension or transport resistivities across an interface is a challenging task in molecular thermodynamics especially for pure dipolar components or mixtures.

As a versatile and successful tool to describe interfaces we use the classical density functional theory in combination with the PC-SAFT equation of state. With this approach we are able to calculate a continuous density profile across the interface. All other thermodynamic properties can be calculated as derivatives of the density profile.
Based on a previous study [1] for pure non-polar or weakly dipolar inhomogeneous fluids the approach is here extended to pure strongly dipolar fluids and mixtures of non-associating components. Polar fluids show a non-isotropic orientation across interfaces. The orientation of molecules at the interface is a degree of freedom that is used to minimize the free energy of the system. It is therefore important to account for the orientational distribution for calculating thermodynamic properties.
We formulate and analyze a Helmholtz energy functional that properly accounts for the orientational distribution of molecules across vapor-liquid interfaces. The theory reduces to the PCP-SAFT equation of state for bulk phases. Our approach goes beyond previous work [2] that was based on a mean-field approximation in that we do not rely on a low-density limit and do not introduce approximations in solving the orientational distribution function.
For calculating mixtures it is necessary to reformulate the Helmholtz energy functional for both, the repulsive and attractive interactions. The repulsive contribution to the Helmholtz energy functional is formulated according to the fundamental measure theory [3,4] and the SAFT-chain term [5]. The functional for dispersive attractions is based on a non-mean field first order perturbation approach. This approach requires no adjustable parameters beyond the binary parameter kij that was independently adjusted to bulk-phase vapor-liquid data.
The mass- and heat-transport across interfaces requires the interfacial resistivities. Recent studies [6,7] show results of the resistivities for heat transfer, for mass transfer and for the coupling of heat and mass transfer for Lenard-Jones-fluids with different pair potentials. Our approach is not only capable of calculating model fluids as proposed but also of calculating real components and mixtures.

[1] Gross J., J. Chem. Phys. 131, 204705 (2009)

[2] Frodl P., Dietrich S., Phys. Rev. A 45, 7330 (1992)

[3] Roth R. et al., J. Phy.: Condens. Matter 14, 12063 (2002)

[4] Yu Y., Wu J., J. Chem. Phys. 117, 10156 (2002)

[5] Tripathi S., Chapman W. G., J. Chem. Phys. 122, 094506 (2005).

[6] Johannessen E. et al., J. Chem. Phys. 129, 184703 (2008)

[7] Glavatskiy K. S., Bedeaux D., Phys. Rev. E 77, 061101 (2008)