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Some theoretical results of swelling in fiber or particle filled polymers
Author(s) -
Wu WenLi,
Prahinski John R.
Publication year - 1989
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760290408
Subject(s) - swelling , solvent , polymer , materials science , flory–huggins solution theory , thermodynamics , gaussian , nonlinear system , polymer chemistry , displacement (psychology) , physics , chemistry , composite material , organic chemistry , quantum mechanics , psychology , psychotherapist
The problem of inhomogeneous swelling of polymers around particles or fibers is treated analytically within the context of Gaussian statistics for polymer chains and the Flory‐Huggins approximation for the interaction between polymer and solvent. The resulting differential equation for the displacement field around the inclusions is quite simple; it contains a homogeneous part and a nonlinear part. The nonlinear part of the differential equation is preceded by a parameter n (1 − 2 χ ), where n is the molecular weight between crosslinks and χ is the Flory‐Huggins interaction parameter. Accordingly, the displacement field for the case of theta solvent, i.e. χ equals 0.5, can be solved exactly. In good solvents, the problem can be treated as a perturbation of the theta solvent condition. The amount of deviation from the theta solvent solution is obtained through a numerical technique and the results are tabulated as a function of n (1 − 2 χ ).