Examples of anisotropic polymeric materials. In bulk systems, anisotropy is induced by varying thermodynamic state (liquid-crystalline polymers) or introduction of an external field (rubber networks). Anisotropy in confined films and brushes arises from geometrical constraints imposed on the polymer chains which results in changes in the components of the radius of gyration , segment lengths, and an induced nonzero orientational order parameter, .
A schematic representation of different anisotropic polymeric materials in the two-dimensional space of the parallel and perpendicular components of the statistical segment lengths.
Variation of the critical coupling constant in oriented or liquid-crystalline polymer fluids with segmental orientational order parameter. Inset: deviation of the critical coupling constant from its isotropic value (filled circles) as a function of the degree of segmental alignment. The curve is a parabolic fit.
Relative shift of the crossover temperature as a function of the degree of segmental alignment for three systems: polystyrene (PS), poly-butadiene (PBD), and polyethylene (PE). Inset shows the variation of the dimensionless compressibility [computed using Eq. (4.4)] with orientational order parameter.
Critical value of the dimensionless compressibility of a rubber network as a function of strain for a segmental density of and . Inset shows the dimensionless compressibility as a function of strain as calculated from anisotropic PRISM (Ref. 40) theory for polyisoprene and .
Relative shift of the crossover temperature with strain for rubber networks of variable strand degree of polymerizations for material parameters corresponding to polyisoprene (PI) and polyethylene (PE).
Variation of the dimensionless compressibility, normalized by its isotropic value, with for the one-parameter model of locally deformed anisotropic polymers. Inset shows the corresponding critical coupling constant as function of .
Relative shift of the crossover temperature as a function of the parallel component of the statistical segmental length for parameters appropriate for polystyrene. Inset: ratio of the corresponding localization length (normalized by its isotropic value) as a function of (filled circles). The solid line is a power-law fit .
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