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 ¿, which for better than ¿ conditions reads 1/¿2 = 1/¿02 + 1/¿2. Here ¿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 ¿ 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¿/D) and gives an upper bound for the narrow-pore regime. In fact, the simple form K = 1 - 2¿ID for 2¿/D <1 and K = 0 for 2¿/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 ¿i (the "interaction distance") enters, which in semidilute solutions is somewhat higher than ¿, leading to a smaller K than that obtained with the wide-pore length scale ¿. 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.
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