SCALING THEORY OF MOLTEN POLYMERS IN SMALL PORES

One long, flexible coil (N monomers) is dissolved in a melt of shorter, chemically identical chains (P monomers per chain). (1) For bulk melts, two regimes are known to exist, (a) N < NC3 = P2: The monomer-monomer interactions of the N chain are screened out and the size R is ideal R = R0 = aN1/2. (b) N > NC3: The coil is partially swollen and behaves like a string of subunits, each of NC3 monomers. Within one subunit the behavior is ideal, and the subunit size is aNC31/2 = aP. Different subunits repel each other and the size is R3= (N/NC3)3/5aP. (2) For a melt confined in a slit of width D < R3 we find two regimes, (a) D > aP: We expect to find a two-dimensional swollen chain, made of superunits of size D; at scales r < D each superunit is a self-avoiding walk as described in (1b), (b) D < aP: The behavior at scales r < D is ideal. If N < NC2 = PD/a the whole N chain is ideal. If N > NC2 we find a two-dimensional self-avoiding behavior, based on ideal “pancakes” of size aNC21/2 that are mutually self-avoiding. (3) For a melt in a tube of diameter D < R3 we expect three regimes, (a) D > aP: We expect a one-dimensional (1d) swollen chain, again made of superunits, each of which is a 3d self-avoiding walk, (b) ap1/4 < D < aP: If Ν < CC1 = P2/3(D/a)4/3 the whole chain should be ideal. If N > NC1 we expect a Id sequence of mutually avoiding “sausages” of length aNC11/2. Inside each sausage the behavior should be ideal, (c) D < aP1/4: Here all chains segregate and the N chain completely fills a portion of the tube of length L ≃ Na3/D2. Our analysis is restricted to scaling laws; the exact prefactors in all our formulas remain unknown. © 1990, American Chemical Society. All rights reserved.