### Abstract

Several association modeling approaches have been developed to accurately describe the properties of polar solutions. Chemical theory and Wertheim's perturbation theory are among the most popular of these and they have been shown to yield similar functional forms for the contributions of association to Helmholtz energy and activity coefficients. In this paper, we study Flory polymerization theory through the work of Campbell and elucidate its correlation to Wertheim's theory. A simple key relationship between the concentration-based equilibrium constant and Wertheim's association constant is developed for systems in which all associating components have one acceptor and one donor site. Algebraic and numerical proofs are given for the equivalence of Flory's polymerization theory and Wertheim's perturbation theory for pure fluids and mixtures. Additionally, a new generalized activity expression is developed for Wertheim's theory.

Original language | English (US) |
---|---|

Pages (from-to) | 47-56 |

Number of pages | 10 |

Journal | Fluid Phase Equilibria |

Volume | 430 |

DOIs | |

State | Published - Dec 25 2016 |

### Profile

### Keywords

- Association
- Chemical theory
- Perturbation theory
- Wertheim theory

### ASJC Scopus subject areas

- Chemical Engineering(all)
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

**Relation of Wertheim association constants to concentration-based equilibrium constants for mixtures with chain-forming components.** / Bala, Aseel M.; Lira, Carl T.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Relation of Wertheim association constants to concentration-based equilibrium constants for mixtures with chain-forming components

AU - Bala,Aseel M.

AU - Lira,Carl T.

PY - 2016/12/25

Y1 - 2016/12/25

N2 - Several association modeling approaches have been developed to accurately describe the properties of polar solutions. Chemical theory and Wertheim's perturbation theory are among the most popular of these and they have been shown to yield similar functional forms for the contributions of association to Helmholtz energy and activity coefficients. In this paper, we study Flory polymerization theory through the work of Campbell and elucidate its correlation to Wertheim's theory. A simple key relationship between the concentration-based equilibrium constant and Wertheim's association constant is developed for systems in which all associating components have one acceptor and one donor site. Algebraic and numerical proofs are given for the equivalence of Flory's polymerization theory and Wertheim's perturbation theory for pure fluids and mixtures. Additionally, a new generalized activity expression is developed for Wertheim's theory.

AB - Several association modeling approaches have been developed to accurately describe the properties of polar solutions. Chemical theory and Wertheim's perturbation theory are among the most popular of these and they have been shown to yield similar functional forms for the contributions of association to Helmholtz energy and activity coefficients. In this paper, we study Flory polymerization theory through the work of Campbell and elucidate its correlation to Wertheim's theory. A simple key relationship between the concentration-based equilibrium constant and Wertheim's association constant is developed for systems in which all associating components have one acceptor and one donor site. Algebraic and numerical proofs are given for the equivalence of Flory's polymerization theory and Wertheim's perturbation theory for pure fluids and mixtures. Additionally, a new generalized activity expression is developed for Wertheim's theory.

KW - Association

KW - Chemical theory

KW - Perturbation theory

KW - Wertheim theory

UR - http://www.scopus.com/inward/record.url?scp=84988664698&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988664698&partnerID=8YFLogxK

U2 - 10.1016/j.fluid.2016.09.015

DO - 10.1016/j.fluid.2016.09.015

M3 - Article

VL - 430

SP - 47

EP - 56

JO - Fluid Phase Equilibria

T2 - Fluid Phase Equilibria

JF - Fluid Phase Equilibria

SN - 0378-3812

ER -