Journal of Chemical Physics, Vol.118, No.10, 4759-4765, 2003
Effective force between confined colloids clothed by end-grafted polymer chains in solution
We consider colloidal particles clothed each by f end-grafted polymer chains, and immersed in a good solvent. The clothed particles are small enough to be regarded as star polymers. The purpose is a quantitative study of the influence of the confinement on the expression of the effective force between a pair of particles. Such a force originates from the swelling of grafted chains due to the presence of solvent. To simplify, we chose as confining geometry a thin space of thickness D delimited by two parallel plates. The problem depends on two natural lengths, which are the gyration radius, R(3)similar toaf(1/5)N(3/5), of an isolated star polymer and the thickness D. Thus, there exist two regimes depending on whether R-3 is smaller or greater than D. The system is confined only when D is below R-3. We first present a detailed study of conformations of a confined star polymer (R-3>D). The confinement imposes to the star polymer to adopt a configuration parallel to the plates, which is characterized by a parallel radius, denoted by R-parallel to. We show that the latter increases when D is decreased according to R(parallel to)similar toaf(1/4)D(-1/4)N(3/4). The main result is that the star polymer becomes two dimensional, and where the grafted chains have blobs of size D as new units. The second purpose is a quantitative investigation of the effective force between two confined star polymers. For the unconfined regime (R-3D), however, a drastic change of the force expression occurs. For this regime, we show that the force is similar to the one governing the interaction between two-dimensional star polymers, and is given by F-2(r)/k(B)Tsimilar or equal totheta(2)(f )/r, with the exact amplitude theta(2)(f )=(2+9f(2))/24. The two forces then decrease with distance according to the same decay, but with different amplitudes. As a conclusion, the effective force between two confined star polymers is theta(2)(f )/theta(3)(f )similar or equal to(3/20)(2+9f(2))/f(3/2) times more intense than that between unconfined ones. Finally, we say that the confinement may be a mechanism that reinforces the colloidal stabilization. (C) 2003 American Institute of Physics.