Intramolecular association within the SAFT framework

Abstract

A general theory for modelling intramolecular association within the SAFT framework is proposed. Sear and Jackson [Phys. Rev. E. 50 (1), 386 (1994)] and Chapman [J. Chem. Phys. 102 (6), 2585 (1995)] have previously extended SAFT to include intramolecular association for chains with two sites. We show that the resulting equations from the two approaches are equivalent, and use their work as a basis for developing a new general theory. The approach used by Ghonasgi and Chapman is based on mass balances and an infinite dilution result and provides the equations needed to determine the contribution to the Helmholtz free energy from association (inter-as well as intramolecularly) at equilibrium. Sear and Jackson rederived the contribution to the Helmholtz free energy from association from the theory by Wertheim [J. Stat. Phys. 42 (3-4), 459 (1986)] with inclusion of intramolecular association, and using this approach we obtain an expression for the Helmholtz free energy that is valid also at non-equilibrium states (with respect to hydrogen bonds), which is very useful when calculating derivatives.

Self-Assembly in Chains, Rings, and Branches: A Single Component System with Two Critical Points

“…Extensions of the theory to include the effects of ring formation have been limited to the cases of particles with two patches [27][28][29][30][31] (i.e. to the competition between chain and ring formation, but no branching) or with one patch, but allowing the formation of rings with 3 particles by double bonding of the patches [32].…”

Application of Simplified PC-SAFT to Glycol Ethers

“…This Appendix will present expressions for the derivatives of the Helmholtz free energy needed to calculate pressure and chemical potential for the theory for intramolecular association presented by Avlund et al 5 Michelsen and Hendriks 36 presented a simple way to calculate these derivatives when only intermolecular association is considered, and the same approach is used here. The derivatives are given for the case where only two sites on a molecule can associate intramolecularly.…”

“…A general theory for intramolecular association in the framework of SAFT was presented in a recently published paper by Avlund et al 5 and in the Ph.D. thesis by Avlund. 4 This theory was developed on the basis of previous work by Sear and Jackson 14 and Ghonasgi and Chapman, 15 who have developed intramolecular association theories for two associating sites.…”

“…Two parameter sets have been estimated for each of the three glycol ethers: one set for regular sPC-SAFT, 12 and one for sPC-SAFT plus intramolecular association. Industrial & Engineering Chemistry Research ARTICLE sPC-SAFT plus intramolecular association means that the new association term presented by Avlund et al 5 (eq 1), where intramolecular association is included, is used instead of the usual association term from sPC-SAFT, while the remaining terms are the same for the two models. Using the expression for the intramolecular association strength in eq 6 from Sear and Jackson 14 enables us to use identical values of the association parameters for inter-and intramolecular association (ε inter = ε intra and k inter = k intra ).…”

“…Glycol ethers are therefore interesting candidates for testing the new theory for intramolecular association for SAFT type equations of state 1À3 (EoS) presented in the Ph.D. thesis by Avlund 4 and in a recently published paper. 5 A lattice theory, which accounts for both inter-and intramolecular association for polyethoxyalcohols, was presented in 1999 by Missopolinou and Panayiotou, 6 and the theory has been applied for glycol ethers in a number of papers.…”