Diffusion Of Entangled Linear Polymer Chains In Semidilute/concentrated Solutions Through A Porous Membrane

The diffusion of linear polymer chains through a porous membrane is important for gel permeation chromatography, ultrafiltration, controlled releasing and translocation of biological macromolecules. We have synthesized small spherical core-shell particles with a core made of linear non-cross-linked polystyrene (PS) chains and a cross-linked polystyrene shell by the seeded emulsion polymerization. These particles can be redispersed and swollen in an athemal solvent and used as novel system to study the diffusion of polymer chains through a porous membrane. Using a combination of static and dynamic laser light scattering to monitor the change of the average molar mass of these particles via the scattering intensity, we have examined the diffusion out of linear PS chains from the core through the porous shell. Our main findings are as follows.Using a combination of different emulsion polymerization methods (micro-emulsion polymerization, surfactant-free emulsion polymerization and normal emulsion polymerization), we have synthesized different narrowly distributed PS particles with a diameter in the range 0.05-1.0μm. Their size distributions in water and in dry state have been characterized by laser light scattering (LLS) and transmission electron microscopy (TEM). The distributions of these PS particles are so narrow that they can be used as particle standards.Using these narrowly distributed PS particles as the seeds (core), we were able to encapsulate long linear PS chains (core) inside a thin layer of cross-linked PS chains (shell) by the seeded emulsion polymerization in water under starved-condition. Such core-shell particles can be dried and redispersed/swollen in an athermal solvent (toluene). Using these small core-shell particles to study the diffusion, we gain two advantages: namely, 1) they have a huge surface area so that the diffusion can reach its equilibrium within a reasonable time, and 2) we can use LLS to follow the diffusion out of linear PS chains inside the core through the porous shell without any interference.We have synthesized small spherical core-shell particles with different shell thicknesses, but the same core, to study the effect of shell thickness on the diffusion. Our results reveal that the diffusion has three stages, which can be attributed to a relative difference between the correlation length (ζ) of the polymer solution inside the core and the average pore size (d_pore) in the porous shell; namely, 1)ζ_c＜d_pore; 2) R_g＞ζ_c＞d_pore; and 3)ζ_c～R_g＞＞d_pore. We have, for the first time, observed that the diffusion of linear chains from a concentrated/semidilute solution through a porous membrane is even faster than their translational diffusion in a dilute solution as long asζ_c＜d_pore. In the third stage, the diffusion becomes slower as the shell thickness increases. This is because the polymer solution inside the core becomes dilute and the correlation length is equal to the chains size, a constant for a given solution. So that a thicker shell with longer pores slows down the diffusion.On the other hand, we have synthesized small spherical core-shell particles with the same core and the shell thicknesses, but different cross-linking densities so that we can study the effect of cross-linking density on the diffusion. Our results show that the diffusion process also has three stages. Again, the diffusion of linear PS chains in the first stage is faster than their translational diffusion in a dilute solution. The previous discussion is also valid here. Moreover, in the first stage, the effective diffusion coefficients are similar in spite of different cross-linking densities. In comparison with the particles with different shell thicknesses, we find that the effective diffusion coefficient in the first stage is independent of both the shell thickness and the cross-liking density as long asζ_c＜d_pore. In the third stage, the diffusion slows down as the cross-linking density increases. This is because the polymer solution inside the core becomes dilution and the correlation length remains a constant. A higher cross-linking density means small pores so that it is more difficult for linear PS chains to diffuse in.