非均相溶剂情况下Derjaguin近似的推导
Derivation of the Derjaguin approximation for the case of inhomogeneous solvents
摘要：
Derjaguin近似（DA）将曲面之间的力与平行平面之间的相互作用自由能联系起来。它通常是通过考虑所涉及的机构之间的直接相互作用而得出的，因此通过重新调整相应的Hamaker常数来隐含地处理干预溶剂的影响。在这里，我们提供了一个一般化的DA的情况下的分子介质之间的机构，在大多数应用程序中的情况下。推导是基于一个明确的物理机械处理的贡献，从分子溶剂的相互作用力，使用分子间和分子-表面相互作用的一般表达式。从力的精确表达式出发，DA由一系列定义明确的近似值得出。我们的结果表明，DA仍然有效，在分子溶剂中，只要（i）表面分子相互作用的范围是远远短于半径R的球和（ii）在溶剂中的密度相关长度小于R。然后，我们扩展我们的分析的情况下，发生相变的表面之间，这不能很容易地被覆盖使用的压缩力学形式主义由于介质的密度的不连续变化。相反，使用一个连续的热力学描述，我们表明，这种相变引起的机构之间的吸引力，弯曲表面之间的力可以与自由能在相应的平面的情况下，根据DA。
英文摘要：
The Derjaguin approximation (DA) relates the force between curved surfaces to the interaction free energy between parallel planes. It is typically derived by considering the direct interaction between the bodies involved, thus treating the effect of an intervening solvent implicitly by a rescaling of the corresponding Hamaker constant. Here, we provide a generalization of DA to the case of a molecular medium between the bodies, as is the case in most applications. The derivation is based on an explicit statistical-mechanical treatment of the contribution to the interaction force from a molecular solvent using a general expression for intermolecular and molecule-surface interactions. Starting from an exact expression for the force, DA is arrived at by a series of well-defined approximations. Our results show that DA remains valid in a molecular solvent as long as (i) the surface-molecule interactions are of much shorter range than the radius R of the sphere and (ii) the density correlation length in the solvent is smaller than R. We then extend our analysis to the case where a phase transition occurs between the surfaces, which cannot easily be covered using a statistical-mechanical formalism due to the discontinuous change in the density of the medium. Instead using a continuum thermodynamic description, we show that this phase transformation induces an attractive force between the bodies, and that the force between curved surfaces can be related to the free energy in the corresponding planar case, in accordance with DA.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
