Dutka F, Napiórkowski M, Dietrich S
Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, 00-681 Warszawa, Hoza 69, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 1):021602. doi: 10.1103/PhysRevE.78.021602. Epub 2008 Aug 11.
If the constituent particles of fluid phases interact via long-ranged van der Waals forces, the effective Hamiltonian for interfaces between such fluid phases contains--in lateral Fourier space--nonanalytic terms approximately q4ln q. Similar nonanalytic terms characterize the effective Hamiltonian for two interacting interfaces which can emerge between the three possible coexisting fluid phases in binary liquid mixtures. This is in contrast with the structure of the phenomenological Helfrich Hamiltonian for membranes, which does not contain such nonanalytic terms. We show that under favorable conditions for the bulk densities characterizing a binary liquid mixture and for the long-ranged interparticle interactions, the corresponding effective Hamiltonian for a model fluid membrane does not exhibit such nonanalytic contributions. We discuss the properties of the resulting effective Hamiltonian, with a particular emphasis on the influence of the long range of the interactions on the coefficient of the bending rigidity.
如果流体相的组成粒子通过长程范德华力相互作用，那么此类流体相之间界面的有效哈密顿量在横向傅里叶空间中包含近似为q4ln q的非解析项。类似的非解析项也表征了两个相互作用界面的有效哈密顿量，这两个界面可能出现在二元液体混合物的三种可能共存的流体相之间。这与膜的唯象赫尔弗里希哈密顿量的结构形成对比，后者不包含此类非解析项。我们表明，在表征二元液体混合物的体密度以及长程粒子间相互作用的有利条件下，模型流体膜的相应有效哈密顿量不会表现出此类非解析贡献。我们讨论了所得有效哈密顿量的性质，特别强调了相互作用的长程对弯曲刚度系数的影响。
