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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100.
The indices κ, λ, and k in all expressions are summarized in Tables I–III of Ref. 71 and reduce to unity for one-component systems. Consequently, we obtain the simplifications N(i, κ) ≡ N(i), N(i, j; κ) ≡ N(i, j), N(i, λ) ≡ N(i), and N(i, j; λ) ≡ N(i, i). In addition, the relations (Ref. 105) 2!N(1, 1) = N(1)2M − N(1) − 2N(2), N(1, 2) = N(1)N(2)M − 2N(2) − 2N(3), and 2!N(2, 2) = N(2)2M − N(2) − 2N(3) − 2N(4), derived in Ref. 105, are used in Eqs. (6)–(8).
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2012
American Institute of Physics
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