Equilibrium phase compositions of heterogeneous copolymers

Bauer, Barry J.

doi:10.1002/pen.760251706

Cited by 25 publications

(56 citation statements)

References 23 publications

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“…which shows quite transparently the mechanism of phase separation in this system: Phases that contain a spread of different σ can always lower their excess free energy by fractionation; as temperature is lowered, this effect dominates the corresponding loss of entropy of mixing in the ideal part of the free energy, and one expects separation into an ever-increasing number of phases § . This remarkable behaviour has indeed been found in numerical calculations [39,40,41]; an example is shown in Fig. 7(top).…”

Section: Polymers Ii: Random Copolymerssupporting

confidence: 71%

Predicting phase equilibria in polydisperse systems

Sollich

2001

J. Phys.: Condens. Matter

199

263

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Many materials containing colloids or polymers are polydisperse: They comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review focusses on the theoretical prediction of phase equilibria in polydisperse systems; the presence of an effectively infinite number of distinguishable particle species makes this a highly nontrivial task. I first describe qualitatively some of the novel features of polydisperse phase behaviour, and outline a theoretical framework within which they can be explored. Current techniques for predicting polydisperse phase equilibria are then reviewed. I also discuss applications to some simple model systems including homopolymers and random copolymers, spherical colloids and colloid-polymer mixtures, and liquid crystals formed from rod-and plate-like colloidal particles; the results surveyed give an idea of the rich phenomenology of polydisperse phase behaviour. Extensions to the study of polydispersity effects on interfacial behaviour and phase separation kinetics are outlined briefly.

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Section: Polymers Ii: Random Copolymerssupporting

confidence: 71%

Predicting phase equilibria in polydisperse systems

Sollich

2001

J. Phys.: Condens. Matter

199

263

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“…In other cases (see e.g. [2][3][4][5]) σ is instead a parameter distinguishing species of continuously varying chemical properties. In the most general case, several attributes may be required to distinguish the various particle species in the system (such as length and chemical composition in length-polydisperse random copolymers) and σ is then a collection of parameters [6].…”

Section: Introductionmentioning

confidence: 99%

Moment Free Energies for Polydisperse Systems

Sollich

Warren

Cates

2001

Advances in Chemical Physics

109

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A polydisperse system contains particles with at least one attribute σ (such as particle size in colloids or chain length in polymers) which takes values in a continuous range. It therefore has an infinite number of conserved densities, described by a density distribution ρ(σ). The free energy depends on all details of ρ(σ), making the analysis of phase equilibria in such systems intractable. However, in many (especially mean-field) models the excess free energy only depends on a finite number of (generalized) moments of ρ(σ); we call these models truncatable. We show, for these models, how to derive approximate expressions for the total free energy which only depend on such moment densities. Our treatment unifies and explores in detail two recent separate proposals by the authors for the construction of such moment free energies. We show that even though the moment free energy only depends on a finite number of density variables, it gives the same spinodals and critical points as the original free energy and also correctly locates the onset of phase coexistence. Results from the moment free energy for the coexistence of two or more phases occupying comparable volumes are only approximate, but can be refined arbitrarily by retaining additional moment densities. Applications to Flory-Huggins theory for length-polydisperse homopolymers, and for chemically polydisperse copolymers, show that the moment free energy approach is computationally robust and gives new geometrical insights into the thermodynamics of polydispersity.

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“…In this research we have attempted to improve the mechanical properties of the PAr–PS–PAr by modifying the miscibility between PS and PAr segments. The miscibility between two different polymers can be modified by an adequate random copolymerization, which is interpreted by recent idea of “repulsion” in random copolymers in relation to “miscibility window” 8–11. This idea has been applied to the miscibility modification of various immiscible polymer blend systems.…”

Section: Introductionmentioning

confidence: 99%

“…In the binary blend of homopolymer A and random copolymer BC comprised of monomeric unit B and C, the Flory–Huggins interaction parameter χ between homopolymer A and random copolymer BC is formulated by eq 1:8–11 where χ i / j and ϕ B are the Flory–Huggins interaction parameter between resins i and j , and volume fraction of unit B in the random copolymer BC, respectively. In eq 1, the first two terms arise from the interaction between polymers A and BC, and the last term arises from the interaction between units B and C within the copolymer BC.…”

Section: Introductionmentioning

confidence: 99%