Theory of Polydisperse Inhomogeneous Polymers

Fredrickson, Glenn H.; Sides, Scott

doi:10.1021/ma034082y

Cited by 49 publications

(44 citation statements)

References 40 publications

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“…Polydispersity enriches the phase behavior at equilibrium [21] and decreases the free energy barrier of nucleation in meta-stable state of polymer blends [22]. The effort of polydispersity on the profile of the interface at equilibrium are studied by Fredrickson and Sides [23] in polydisperse polymer blends. In the present work, we studied the dynamics of interfaces in polydisperse blends.…”

Section: Introductionmentioning

confidence: 99%

External potential dynamic studies on the formation of interface in polydisperse polymer blends

Zhang

Yan

2010

The Journal of Chemical Physics

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The formation of interface from an initial sharp interface in polydisperse A/B blends is studied using the external potential dynamic method. The present model is a nonlocal coupling model as we take into account the correlation between segments in a single chain. The correlation is approximately expressed by Debye function and the diffusion dynamics are based on the Rouse chain model. The chain length distribution is described by the continuous Schulz distribution. Our numerical calculation indicates that for a wide range of the Flory-Huggins parameter the broadening of interface with respect to time obeys a power law at early time, and the power indices are the same for both monodisperse and polydisperse blends. The power index is larger than that in the local coupling model. However, there is no unified scaling form of the broadening of the interface width if only the interfacial width at equilibrium is taken into account as the characteristic length of the system, because the correlation makes an extra characteristic length in the system, and the polydispersity is related to this length.

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Section: Introductionmentioning

confidence: 99%

External potential dynamic studies on the formation of interface in polydisperse polymer blends

Zhang

Yan

2010

The Journal of Chemical Physics

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“…We use Simpson's rule to evaluate the quadratures over l, rather than the Gauss-Laguerre quadrature over the interval [0,∞) employed in previous studies of polydispersity. 13 Another quantity of interest is the ratio of the average density between the plates and the bulk density.…”

Section: Numerical Methods For Confined Systemmentioning

confidence: 99%

Confinement of Equilibrium Polymers: A Field-Theoretic Model and Mean-Field Solution

Feng

Fredrickson

2006

Macromolecules

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We develop a field-theoretic model for equilibrium polymers in good solvent. Using the Gaussian chain model, we present a derivation in the grand canonical ensemble in which the parameters are the monomer chemical potential µ M , the excluded volume parameter u 0 , and the energy decrease for forming a bond 2h. Only the quantity Γ, which is proportional to u 0 e -2h , matters in determining the mean-field solution. For a bulk system, the homogeneous mean-field solution gives an exponential polymer length distribution with a characteristic length that decreases with increasing Γ. Moreover, the extent of polymer overlap in a semi-dilute solution decreases with increasing density in the mean-field approximation. We study the inhomogeneous properties of equilibrium polymers confined between two parallel repulsive plates with numerical self-consistent field theory. The polymer length distribution is exponential for all L, the dimensionless distance between the plates. For small L, the characteristic polymer length of the exponential distribution scales as L 2 , which is ideal equilibrium polymer behavior. For any fixed L, the characteristic length approaches the bulk characteristic length as Γ increases. We also find that R, the ratio of the volume-averaged confined density to the bulk density, decreases monotonically with decreasing Γ and L. As u 0 f 0, our data converge to previous analytic results for ideal equilibrium polymers.

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“…The method is available as part of commercial software packages, which has been used to perform the simulation in this paper 13. In the past the compatibilizing properties of various chain architectures and composition have been investigated theoretically: The effect of adding block copolymers,14 effect of size polydispersity,15 also the distribution in composition has been subject of investigation. However, in the latter case the variations in chemical composition from chain‐to‐chain are limited and the compositional polydispersity is considered small compared to the average composition 16, 17.…”

Section: Introductionmentioning

confidence: 99%

Size‐Dependent Interfacial Tension of Polymer Blends with Broad Composition Polydispersity

Groenewold

Remerie

2010

Macro Theory & Simulations

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The surface tension as a function of system size of a pure blend with chemically polydisperse compatibilizer is investigated by simulation. The main finding is that such compatibilizers adsorb readily at the interface between the bulk phases giving rise to very broad interfacial zones. This phenomenon leads to a marked size dependence of the interfacial tension. However the adsorption only leads to a decrease of 40% of the interfacial tension of the blend without compatibilizer. The limited effect on interfacial tension is explained by the observation that a considerable fraction of the compatibilizing chains do not contribute to the interfacial tension, instead these chains become part of an inhomogeneous phase with extensive thermodynamic properties.magnified image

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Theory of Polydisperse Inhomogeneous Polymers

Cited by 49 publications

References 40 publications

External potential dynamic studies on the formation of interface in polydisperse polymer blends

External potential dynamic studies on the formation of interface in polydisperse polymer blends

Confinement of Equilibrium Polymers: A Field-Theoretic Model and Mean-Field Solution

Size‐Dependent Interfacial Tension of Polymer Blends with Broad Composition Polydispersity

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