Macromolecules, Vol.38, No.6, 2492-2505, 2005
Theory for concentration and solvency effects in size-exclusion chromatography of polymers
A simple analytical equation for the distribution coefficient K in size-exclusion chromatography (SEC) as a function of molar mass, concentration, and solvent quality is presented. The theory is based upon a modified Casassa equation, using a recently proposed mean-field relation for the depletion thickness delta, which for better than Theta conditions reads 1/delta(2) = 1/delta(0)(2) + 1/xi(2). Here delta(0) is the well-known (chain-length-dependent) depletion thickness at infinite dilution, and is the (concentration- and solvency-dependent) correlation length in the solution. Numerical lattice calculations for mean-field chains in slitlike pores of width D as a function of concentration are in quantitative agreement with our analytical equation, both for good solvents and in a Theta solvent. Comparison of our mean-field theory with Monte Carlo data for the concentration dependence of K for self-avoiding chains shows qualitatively the same trends; moreover, our model can also be adjusted to obtain nearly quantitative agreement. The modified Casassa equation works excellently in the wide-pore regime (where K = 1 - 2 delta/D) and gives an upper bound for the narrow-pore regime. In fact, the simple form K = 1 - 2 delta/D for 2 delta/D < 1 and K = 0 for 2 delta/D > 1 gives a first estimate of concentration effects even in the narrow-pore regime. A more detailed analysis of interacting depletion layers in narrow pores shows that a different length scale delta(i) (the "interaction distance") enters, which in semidilute solutions is somewhat higher than delta, leading to a smaller K than that obtained with the wide-pore length scale delta. Predictions for the effects of chain length, solvency, and chain stiffness on the basis of our analytical equation are in accordance with Monte Carlo simulations.