comprise of a steric (hard core) part and a long-ranged A new Surface Element Integration (SEI) technique is devel-(soft tail) part (1). The long-ranged part of the interactions oped for determination of the interaction energy of a spherical usually consists of three types of interactions, namely (5, particle in a cylindrical pore based on the knowledge of the corre-8-14): (i) the apolar Lifshitz-van der Waals (LW) interacsponding interaction energy per unit area between plane-parallel tion, (ii) the electrostatic double layer (EL) interaction, and half spaces. Like the celebrated Deryaguin's approximation, the (iii) the polar or acid-base (AB) interactions in aqueous SEI can be used for any component of the interaction energy systems. While the first two types of the DLVO interactions (e.g., apolar Lifshitz-van der Waals, electrostatic, polar) whenever (LW and EL) have been extensively studied (3,7,(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), interaction between corresponding half-spaces is known theoretithe polar interactions, described variously as acid-base (AB) cally or experimentally. Accuracy of the SEI is assessed based on its comparison with the exact results for the van der Waals interactions, hydration pressure, hydrophobic interaction, interaction energy. Results of the SEI are also compared with the hydrogen bonding, etc., are usually of foremost importance approximate series solution for the electrostatic interaction in the in aqueous media (11,12,(18)(19)(20)(21)(22)(23)(24)(25)(26).
Debye-Hu ยจckel approximation. While Deryaguin's approximation
The LW interactions for the sphere in cylindrical pore fails for the particle-pore geometry for small pores (รต10 nm), the geometry can be exactly calculated following Hamaker's SEI is accurate for all realistic combinations of particle and pore microscopic approach (10) by numerical integration of two radii, radial position of the particle, and decay length of interacnested volume integrals (3,14,15). It was recently shown tions. Based on the SEI, the role of polar repulsion (hydration that a proper choice of the volume elements for the pair wise pressure) on the partitioning behavior of macromolecules across summation of the energy leads to a simplified expression small pores is also studied. The hydration force in aqueous hydrofor the exact LW interaction energy between a spherical philic systems can lead to a significant lowering of the distribution particle and a cylindrical pore (14). Closed form expressions coefficient in small pores characteristic of ultrafiltration. แญง 1997