Department of Physics, North Dakota State University, Fargo, ND 58108-6050, USA.
Department of Physics, Institute of Biosciences, Humanities and Exact Sciences, São Paulo State University (UNESP), São José do Rio Preto 15054-000, SP, Brazil.
Molecules. 2021 Jul 20;26(14):4372. doi: 10.3390/molecules26144372.
Langmuir monolayers can be assembled from molecules that change from a low-energy orientation occupying a large cross-sectional area to a high-energy orientation of small cross-sectional area as the lateral pressure grows. Examples include cyclosporin A, amphotericin B, nystatin, certain alpha-helical peptides, cholesterol oxydation products, dumbbell-shaped amphiphiles, organic-inorganic nanoparticles and hybrid molecular films. The transition between the two orientations leads to a shoulder in the surface pressure-area isotherm. We propose a theoretical model that describes the shoulder and can be used to extract the energy cost per molecule for the reorientation. Our two-state model is based on a lattice-sublattice approximation that hosts the two orientations and a corresponding free energy expression which we minimize with respect to the orientational distribution. Inter-molecular interactions other than steric repulsion are ignored. We provide an analysis of the model, including an analytic solution for one specific lateral pressure near a point of inflection in the surface pressure-area isotherm, and an approximate solution for the entire range of the lateral pressures. We also use our model to estimate energy costs associated with orientational transitions from previously reported experimental surface pressure-area isotherms.
可以从低能量取向的分子组装成 Langmuir 单分子层，这些分子的横截面积较大，随着侧向压力的增加，它们会变成高能量取向的小横截面积。例如环孢菌素 A、两性霉素 B、制霉菌素、某些α-螺旋肽、胆固醇氧化产物、哑铃形两亲分子、有机-无机纳米粒子和混合分子膜。这两种取向之间的转变导致表面压-面积等温线出现肩部。我们提出了一个理论模型来描述肩部，并可用于提取分子重新取向的能量成本。我们的两态模型基于一种晶格亚晶格近似，它包含了两种取向和相应的自由能表达式，我们通过最小化取向分布来最小化自由能表达式。除了位阻排斥之外，我们忽略了分子间的相互作用。我们对该模型进行了分析，包括在表面压-面积等温线拐点附近的特定侧向压力下的解析解，以及整个侧向压力范围内的近似解。我们还使用我们的模型来估计与之前报道的实验表面压-面积等温线相关的取向转变的能量成本。
