Effective dimensions of oligomers in size exclusion chromatography. A molecular dynamics simulation study

Size exclusion chromatography (SEC) is a widely used method for determining the molecular weights of polymer molecules. SEC calibration is often achieved using the ''universal calibration'' technique, which assumes hydrodynamic volume is the sole determinate of retention time. Recent work has demonstrated the failure of this approach when molecular weights are small (< 5000) and particularly in the oligomer range. In order to explore the theoretical reasons for this failure, molecular dynamics (MD) simulations have been used to compute the partition coefficients as a function of pore size for oligomeric series of three polymers: polyethylene(PE), polyisobutylene (PIE), and polystyrene(PS). The molecular weight ranges studied were from dimers up to 500 g/mol for PE and up to 1000 g/mol for PIE and PS. MD simulation was used to generate a large number of configurations of the various oligomers. These configurations were then used to compute the partition coefficients of the species in cylindrical pores of varying diameters. The MD model of the oligomers included all atoms explicitly and all internal degrees of freedom. Solvent was not included specifically but the configurations were generated under phantom chain conditions for longer range interactions that are appropriate to the theta solvent conditions that prevail for short molecules. The variation of partition coefficient with pore size for a given oligomer could be described well by assigning an effective hard-sphere radius, called here the retention radius, to the molecule. The retention radii for an oligomer series were found to correlate well with the radii of gyration. There were however significant differences in the retention radii vs radii of gyration correlations among the three series studied. At the same radius of gyration, the retention radii order is found to be PS > PIB > PE. This order agrees with experimental SEC data for retention times for these oligomer series. The differences are attributed to asphericity of individual configurations enhancing the effects of substituent size. The approach of the mean-square radius of gyration and mean-square end-to-end distance dependence on chain length to limiting long-chain behavior is discussed. It is found that the limiting proportionality to chain length has not been reached in the molecular weight ranges studied. A comparison of the use of the intrinsic viscosity-molecular weight product ([eta]M) as a measure of radius of gyration, the radius of gyration determined independently, and the retention radius from simulation as criteria for equal retention times is made. The errors in molecular weight determination resulting from the use of each of the three criteria are discussed. The retention radius from simulation is found to be a significantly better criterion for retention time than the [eta]M product or directly determined radius of gyration.