Apolar, Polar, and Electrostatic Interactions of Spherical Particles in Cylindrical Pores

A new Surface Element Integration (SEI) technique is developed for determination of the interaction energy of a spherical particle in a cylindrical pore based on the knowledge of the corresponding interaction energy per unit area between plane-parallel half spaces. Like the celebrated Deryaguin's approximation, the SEI can be used for any component of the interaction energy (e.g., apolar Lifshitz-van der Waals, electrostatic, polar) whenever interaction between corresponding half-spaces is known theoretically or experimentally. Accuracy of the SEI is assessed based on its comparison with the exact results for the van der Waals interaction energy. Results of the SEI are also compared with the approximate series solution for the electrostatic interaction in the Debye-Huckel approximation. While Deryaguin's approximation fails for the particle-pore geometry for small pores (<10 nm), the SEI is accurate for all realistic combinations of particle and pore radii, radial position of the particle, and decay length of interactions. Based on the SEI, the role of polar repulsion (hydration pressure) on the partitioning behavior of macromolecules across small pores is also studied. The hydration force in aqueous hydrophilic systems can lead to a significant lowering of the distribution coefficient in small pores characteristic of ultrafiltration.