Jacek Dudowicz

Ionic association in model 2-2 electrolyte solutions

A detailed study has been made of the structural consequences of a charged soft sphere model for aqueous 2–2 electrolytes. The HNC approximation for this model gives structural features as well as thermodynamic functions that agree closely with the reported HNC results for a charged hard sphere model provided that R, the distance at which the pair potential u+−(r) is a minimum, is the same in both models. In both cases there is a strong enhancement of the like‐charge correlation function g++(r) [equals g−−(r) in these models] in the range where r?2R. The trends in the HNC results are generally confirmed by Monte Carlo (MC) results for the same model, but the enhancement of g++ is greatly reduced compared to HNC. The MC results confirm earlier interpretation of the enhancement as due to larger than pairwise clusters even at concentrations below 0.005 M. Analysis of the discrepancy between the MC and HNC results leads to a revised form of the latter, BHNC, which incorporates a simple approximation for the s...

Communication: Cosolvency and cononsolvency explained in terms of a Flory-Huggins type theory

Standard Flory-Huggins (FH) theory is utilized to describe the enigmatic cosolvency and cononsolvency phenomena for systems of polymers dissolved in mixed solvents. In particular, phase boundaries (specifically upper critical solution temperature spinodals) are calculated for solutions of homopolymers B in pure solvents and in binary mixtures of small molecule liquids A and C. The miscibility (or immiscibility) patterns for the ternary systems are classified in terms of the FH binary interaction parameters {χαβ} and the ratio r = ϕ A /ϕ C of the concentrations ϕ A and ϕ C of the two solvents. The trends in miscibility are compared to those observed for blends of random copolymers (AxC1-x) with homopolymers (B) and to those deduced for A/B/C solutions of polymers B in liquid mixtures of small molecules A and C that associate into polymeric clusters {ApCq}i, (i = 1, 2, …, ∞). Although the classic FH theory is able to explain cosolvency and cononsolvency phenomena, the theory does not include a consideration of the mutual association of the solvent molecules and the competitive association between the solvent molecules and the polymer. These interactions can be incorporated in refinements of the FH theory, and the present paper provides a foundation for such extensions for modeling the rich thermodynamics of polymers in mixed solvents.

Solvation of polymers as mutual association. II. Basic thermodynamic properties

The theory of equilibrium solvation of polymers B by a relatively low molar mass solvent A, developed in the simplest form in Paper I, is used to explore some essential trends in basic thermodynamic properties of solvated polymer solutions, such as the equilibrium concentrations of solvated polymers AiB and free solvent molecules A, the mass distribution φ(AiB)(i) of solvated clusters, the extent of solvation of the polymer Φ(solv), the solvation transition lines T(solv)(φB(o)), the specific heat C(V), the osmotic second virial coefficient B2, phase stability boundaries, and the critical temperatures associated with closed loop phase diagrams. We discuss the differences between the basic thermodynamic properties of solvated polymers and those derived previously for hierarchical mutual association processes involving the association of two different species A and B into AB complexes and the subsequent polymerization of these AB complexes into linear polymeric structures. The properties of solvated polymer solutions are also compared to those for solutions of polymers in a self-associating solvent. Closed loop phase diagrams for solvated polymer solutions arise in the theory from the competition between the associative and van der Waals interactions, a behavior also typical for dispersed molecular and nanoparticle species that strongly associate with the host fluid. Our analysis of the temperature dependence of the second osmotic virial coefficient reveals that the theory must be generalized to describe the association of multiple solvent molecules with each chain monomer, and this complex extension of the present model will be developed in subsequent papers aimed at a quantitative rather than qualitative treatment of solvated polymer solutions.

Concentration fluctuations in miscible polymer blends: Influence of temperature and chain rigidity

In contrast to binary mixtures of small molecule fluids, homogeneous polymer blends exhibit relatively large concentration fluctuations that can strongly affect the transport properties of these complex fluids over wide ranges of temperatures and compositions. The spatial scale and intensity of these compositional fluctuations are studied by applying Kirkwood-Buff theory to model blends of linear semiflexible polymer chains with upper critical solution temperatures. The requisite quantities for determining the Kirkwood-Buff integrals are generated from the lattice cluster theory for the thermodynamics of the blend and from the generalization of the random phase approximation to compressible polymer mixtures. We explore how the scale and intensity of composition fluctuations in binary blends vary with the reduced temperature τ ≡ (T - T(c))/T (where T(c) is the critical temperature) and with the asymmetry in the rigidities of the components. Knowledge of these variations is crucial for understanding the dynamics of materials fabricated from polymer blends, and evidence supporting these expectations is briefly discussed.

Relation Between Solvent Quality and Phase Behavior of Ternary Mixtures of Polymers and Two Solvents that Exhibit Cononsolvency

The phase boundaries of polymer solutions in mixed solvents can be extremely complex due to the many competing van der Waals and associative interactions that can arise in these ubiquitous and technologically important complex fluids. The present paper focuses specific attention on ternary solutions of polymers (B) dissolved in a mixture of two solvents (A, C) that competitively associate with the polymer. We are particularly concerned with explaining the origin of the peculiar phenomenon of cononsolvency in mixed solvents, where a mixture of two individually good solvents behaves effectively as a poor solvent. Our computations are based on a recently developed generalization of Flory-Huggins theory that incorporates the competitive solvation of a polymer by two associating solvents. On the basis of this framework, we evaluate the limit of polymer phase stability (spinodal curves) and the second osmotic virial coefficient [Formula: see text] as a function of temperature and the composition of the pure solvent mixture that is maintained in osmotic equilibrium with the ternary solution. The calculations provide new insights into the miscibility patterns of ternary A/B/C polymer solutions exhibiting cononsolvency.

Lattice cluster theory of associating polymers. IV. Phase behavior of telechelic polymer solutions.

The newly developed lattice cluster theory (in Paper I) for the thermodynamics of solutions of telechelic polymers is used to examine the phase behavior of these complex fluids when effective polymer-solvent interactions are unfavorable. The telechelics are modeled as linear, fully flexible, polymer chains with mono-functional stickers at the two chain ends, and these chains are assumed to self-assemble upon cooling. Phase separation is generated through the interplay of self-assembly and polymer/solvent interactions that leads to an upper critical solution temperature phase separation. The variations of the boundaries for phase stability and the critical temperature and composition are analyzed in detail as functions of the number M of united atom groups in a telechelic chain and the microscopic nearest neighbor interaction energy ε(s) driving the self-assembly. The coupling between self-assembly and unfavorable polymer/solvent interactions produces a wide variety of nontrivial patterns of phase behavior, including an enhancement of miscibility accompanying the increase of the molar mass of the telechelics under certain circumstances. Special attention is devoted to understanding this unusual trend in miscibility.