Extension of the associated perturbed anisotropic chain theory to mixtures with more than one associating component

Ikonomou, George D.; Donohue, Marc D.

doi:10.1016/0378-3812(88)85002-7

Cited by 69 publications

(47 citation statements)

References 6 publications

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“…[19][20][21][22] Of additional relevance are theoretical studies by Asakura and Oosawa 23 of the self-assembly of actin and other protein fibers and the more recent investigations of protein self-assembly by Minton and co-workers, [24][25][26][27][28] who emphasize the influence of crowding and constraints due to geometrical confinement that are characteristic of in vivo assembly and that can substantially alter self-assembly processes from their solution counterparts. More recent theoretical developments [29][30][31][32][33][34][35] in modeling selfassembly employ the liquid state based Wertheim theory 36 which is essentially equivalent 37 to the equilibrium association approach of Tobolsky and Eisenberg [5][6][7] and others [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] following them. a) Author to whom correspondence should be addressed.…”

Section: A Theories Of Self-assemblymentioning

confidence: 99%

Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains

Dudowicz

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2012

The Journal of Chemical Physics

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The lattice cluster theory (LCT) for the thermodynamics of a wide array of polymer systems has been developed by using an analogy to Mayer's virial expansions for non-ideal gases. However, the high-temperature expansion inherent to the LCT has heretofore precluded its application to systems exhibiting strong, specific "sticky" interactions. The present paper describes a reformulation of the LCT necessary to treat systems with both weak and strong, "sticky" interactions. This initial study concerns solutions of linear telechelic chains (with stickers at the chain ends) as the self-assembling system. The main idea behind this extension of the LCT lies in the extraction of terms associated with the strong interactions from the cluster expansion. The generalized LCT for sticky systems reduces to the quasi-chemical theory of hydrogen bonding of Panyioutou and Sanchez when correlation corrections are neglected in the LCT. A diagrammatic representation is employed to facilitate the evaluation of the corrections to the zeroth-order approximation from short range correlations.

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Section: A Theories Of Self-assemblymentioning

confidence: 99%

Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains

Dudowicz

Freed

2012

The Journal of Chemical Physics

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“…Heidemann and Prausnitz (1976) showed that it is possible to solve analytically for the chemical equilibria within the equation of state so that the conditions of the phase equilibria can be solved directly; this has led to the development of several new equations of state for hydrogen-bonding systems. Ikonomou and Donohue (1986Donohue ( , 1988 applied this approach using the perturbed-anisotropic-chain theory (PACT) and obtained a closed form equation of state, the associated-PACT (APACT). Because of the assumptions made in the development of APACT, the resulting hydrogen bonding terms are very simple mathematically.…”

Section: Introductionmentioning

confidence: 99%

Chemical, quasi‐chemical and perturbation theories for associating fluids

1991

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“…The equations presented here are general and can be applied to any type of mixture that contains species that hydrogenbond. In addition, these equations reduce to all those derived previously by Ikonomou and Donohue (1988) and Economou et al (1990) for specific cases including a binary mixture of an amphoteric and an acidic component, a binary mixture of an amphoteric and a basic component, a binary mixture of an acidic and a basic component, and a binary mixture of an amphoteric and a diluent component. Further, calculations obtained from the equations presented here give exactly the same results as the equations derived by Economou et al (1990).…”

Section: Theorymentioning

confidence: 93%

Closed‐form expressions for “chemical theory” of associating mixtures

1992

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Various thermodynamic models have been proposed for systems containing hydrogen bonding compounds (Economou and Donohue, 1991b). The most widely used theory is based on the assumption that hydrogen bonding results in the formation of new species in the system and is referred to as chemical theory. The associated-perturbed-anisotropic-chain theory (APACT) (Ikonomou and Donohue, 1986), an equation of state that accounts for hydrogen bonding using chemical theory, was recently generalized to treat compounds that can self-associate and solvate with other compounds in the mixture (Economou et al., 1990). The resulting equations for hydrogenbonding interactions were solved analytically for three types of binary mixtures. The first one contains an amphoteric component, which is both acidic and basic (that is, an alcohol), and a component that is only acidic (that is, chloroform) or only basic (that is, a ketone). The second type of binary mixtures contains an amphoteric component and a component that does not self-associate nor solvate (a diluent). The third type of binary mixtures contains one basic and one acidic component. However, for the general case of two or more self-associating components, the resulting expressions contained coupled infinite series so that these expressions could not be written in a closed form and were not solved analytically. Thus, approximate or numerical solutions have been proposed (Economou et al., 1990;Panayiotou, 1990;Anderko, 1991;Economou and Donohue, 1991a).In this work, we derive expressions for the mole fraction of the monomeric species and the ratio n,/no, that is a measure of the extent of the association, using an approach introduced by Nagata and Ohtsubo (1986). This approach accounts explicitly for all the different configurations of the association species of the system. We present here the closed-form equations for the general case of an associating binary mixture. These expressions are believed to be general and reduce to the analytic equations for the special cases described above. However, the need of an approximate or numerical solution for Correspondence concerning this work should be addressed to M. D. Donohue. the general case of a multicomponent associating system remains. TheoryIn the ABPACT (acid-base-perturbed-anisotropic-chain theory) equation of state and in many other theories for associating systems (Economou and Donohue, 1991b), the assumption is made that hydrogen bonding results in the formation of new species. For the specific case of two bonding sites per molecule, linear chains (such as dimers and trimers) are formed. For systems where more than one associating compound is present, linear chains can contain monomer molecules from only one of the compounds or from different compounds. Specifically, for a binary mixture of components M and N where both components have one acidic (electron acceptor) site and one basic (electron donor) site, hydrogen bonding is described through the following chemical equilibria:The first two equilibria account for the self-...

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Extension of the associated perturbed anisotropic chain theory to mixtures with more than one associating component

Cited by 69 publications

References 6 publications

Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains

Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains

Chemical, quasi‐chemical and perturbation theories for associating fluids

Closed‐form expressions for “chemical theory” of associating mixtures

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