Grishina Vera, Vikhrenko Vyacheslav, Ciach Alina
Department of Mechanics and Engineering, Belarusian State Technological University, 13a Sverdlova Str., 220006 Minsk, Belarus.
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland.
Entropy (Basel). 2020 Oct 26;22(11):1215. doi: 10.3390/e22111215.
A triangular lattice model for pattern formation by core-shell particles at fluid interfaces is introduced and studied for the particle to core diameter ratio equal to 3. Repulsion for overlapping shells and attraction at larger distances due to capillary forces are assumed. Ground states and thermodynamic properties are determined analytically and by Monte Carlo simulations for soft outer- and stiffer inner shells, with different decay rates of the interparticle repulsion. We find that thermodynamic properties are qualitatively the same for slow and for fast decay of the repulsive potential, but the ordered phases are stable for temperature ranges, depending strongly on the shape of the repulsive potential. More importantly, there are two types of patterns formed for fixed chemical potential-one for a slow and another one for a fast decay of the repulsion at small distances. In the first case, two different patterns-for example clusters or stripes-occur with the same probability for some range of the chemical potential. For a fixed concentration, an interface is formed between two ordered phases with the closest concentration, and the surface tension takes the same value for all stable interfaces. In the case of degeneracy, a stable interface cannot be formed for one out of four combinations of the coexisting phases, because of a larger surface tension. Our results show that by tuning the architecture of a thick polymeric shell, many different patterns can be obtained for a sufficiently low temperature.
介绍并研究了一种用于描述流体界面处核壳颗粒图案形成的三角晶格模型，其中颗粒与核直径之比等于3。假定存在重叠壳层间的排斥力以及由于毛细力在较大距离处产生的吸引力。对于软质外层和硬质内层壳，通过解析方法以及蒙特卡罗模拟确定了基态和热力学性质，颗粒间排斥力具有不同的衰减率。我们发现，对于排斥势的缓慢衰减和快速衰减，热力学性质在定性上是相同的，但有序相在一定温度范围内是稳定的，这强烈依赖于排斥势的形状。更重要的是，对于固定的化学势，会形成两种类型的图案——一种是排斥力在小距离处缓慢衰减时形成的，另一种是排斥力快速衰减时形成的。在第一种情况下，对于某些化学势范围，两种不同的图案（例如团簇或条纹）出现的概率相同。对于固定浓度，在具有最接近浓度的两个有序相之间会形成一个界面，并且所有稳定界面的表面张力都取相同的值。在简并情况下，由于表面张力较大，共存相的四种组合中的一种无法形成稳定界面。我们的结果表明，通过调整厚聚合物壳的结构，在足够低的温度下可以获得许多不同的图案。
