M. Badia et al., Determination of the amplitude of the repulsive-pair potential between particles clothed by end-grafted polymers, COLLOID P S, 279(8), 2001, pp. 763-770
We examine the problem of the determination of the repulsive potential betw
een spherical particles clothed by long end-grafted flexible polymers. This
potential varying with the distance according to a logarithmic law has a p
otential amplitude that depends on the number, L, of grafting chains per pa
rticle. The purpose of this work is to compute such a potential amplitude.
The clothed particles are first regarded as star polymers with small enough
diameter and the same number of arms. Then, the amplitude potential is ide
ntified to the critical exponent related to the contact probability between
cores of these stars, which allows us to find a universal function for the
expected potential amplitude depending on L and d-space dimension only. In
two-dimensional space, conformal invariance is used to extract the potenti
al amplitude as a function of L. For dimensions greater than 2, the potenti
al amplitude is obtained within the framework of renormalization theory to
third order in epsilon = 4 - d, where d is the critical dimension of the sy
stem. To determine the best three-dimensional expression for the potential
amplitude, A(L), use is made of the Pade-Borel transformation, which provid
es a closer form valid for small, intermediate and high values of L. This f
orm of potential amplitude, consistent with the exact scaling asymptotic va
lue of Witten and Pincus [(1986) Macromolecules 19:2509], allows us to find
the associated prefactor. The procedure is also extended to interacting st
ars of different numbers of arms.