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Hindered interdiffusion in asymmetric polymer‐polymer junctions
Author(s) -
BrochardWyart F.,
De Gennes P. G.
Publication year - 1990
Publication title -
makromolekulare chemie. macromolecular symposia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.257
H-Index - 76
eISSN - 1521-3900
pISSN - 0258-0322
DOI - 10.1002/masy.19900400117
Subject(s) - reptation , polymer , monomer , degree of polymerization , diffusion , volume fraction , materials science , polymer chemistry , polymerization , thermodynamics , physics , composite material
Abstract We discuss theoretically the diffuse interface formed when a long (L) polymer is put into contact with shorter chains (S) of the same material (all chains being entangled). At time t shorter than the reptation time T L of the long chains, the L chains behave like a gel swollen by the S chains. The “penetration factor” ψ (i.e. the volume fraction of S near the gel surface) is controled by a balance between the osmotic pressure of the swollen L chains, and the elastic tension ψ due to swelling. If t is larger than T S (the reptation time of the short chains), ψ is of order N e /N S (where N e is the number of monomers between entanglement points, and N S is the degree of polymerisation of the short chains). On the other hand, if t < T S , N S must be replaced by the average number s (t) of monomers of an S chain which have entered the L region, and ψ ∼ N e / s (t) ∼t −1/2 . The width of the mixed region e(t) increases like s 1/2 (t) at T S , and like (D S t) 1/2 (where D S is the reptation diffusion constant of the S chains) at t>T S .