Confined in two dimensional planes, polymer chains comprising dense monolayer solution are segregated from each other due to topological interaction. Although the segregation is inherent in two dimensions (2D), the solution may display different properties depending on the solvent quality. Among others, it is well known in both theory and experiment that the osmotic pressure ($\Pi$) in the semi-dilute regime displays solvent quality-dependent increases with the area fraction ($\phi$) (or monomer concentration, $\rho$), that is, $\Pi\sim \phi^3$ for good solvent and $\Pi\sim \phi^8$ for $\Theta$ solvent. The osmotic pressure can be associated with the Flory exponent (or the correlation length exponent) for the chain size and the pair distribution function of monomers; however, they do not necessarily offer a detailed microscopic picture leading to the difference. To gain microscopic understanding into the different surface pressure isotherms of polymer solution under the two distinct solvent conditions, we study the chain configurations of polymer solution based on our numerical simulations that semi-quantitatively reproduce the expected scaling behaviors. Notably, at the same value of $\phi$, polymer chains in $\Theta$ solvent occupy the surface in a more \emph{inhomogeneous} manner than the chains in good solvent, yielding on average a greater and more heterogeneous interstitial void size, which is related to the fact that the polymer in $\Theta$ solvent has a greater correlation length. The polymer configurations and interstitial voids visualized and quantitatively analyzed in this study offer microscopic understanding to the origin of the solvent quality dependent osmotic pressure of 2D polymer solutions.

中文翻译：

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二维聚合物溶液的溶剂质量依赖渗透压

受限于二维平面，包含致密单层溶液的聚合物链由于拓扑相互作用而彼此分离。尽管分离是二维 (2D) 固有的，但溶液可能会根据溶剂质量显示不同的特性。其中，在理论和实验中众所周知的是，半稀状态下的渗透压 ($\Pi$) 会随着面积分数 ($\phi$)（或单体浓度，$ \rho$)，即 $\Pi\sim \phi^3$ 为良好的溶剂，$\Pi\sim \phi^8$ 为 $\Theta$ 溶剂。渗透压可以与单体链大小和对分布函数的 Flory 指数（或相关长度指数）相关联；然而，它们不一定提供导致差异的详细微观图像。为了从微观上了解聚合物溶液在两种不同溶剂条件下的不同表面压力等温线，我们基于半定量再现预期缩放行为的数值模拟研究了聚合物溶液的链构型。值得注意的是，在相同的 $\phi$ 值下，$\Theta$ 溶剂中的聚合物链比良溶剂中的链以更不均匀的方式占据表面，平均产生更大和更不均匀的间隙空隙尺寸，这与$\Theta$溶剂中的聚合物具有更大的相关长度有关。