渗透压是施加在溶液上以防止溶剂经半透膜内流的最低压力，其在生命科学、医药、工业、环境与能源等领域中发挥着极其重要的作用。例如，人体内稳定的渗透压环境为人体各器官执行正常生理功能提供了必要条件，渗透压环境失稳会直接引起溶血性贫血、肾与颅脑损伤等疾病；同时，基于渗透压的相关技术也已经被用于物质高效纯化与清洁能源开发。因此，对渗透压的研究不仅具有重要的理论意义，而且具有广泛的实际应用价值。由于渗透压与溶质浓度、溶剂化作用、溶质分子间相互作用等众多因素密切相关，从而难以建立溶液渗透压与溶液性质之间准确的定量关系，这也导致与渗透压相关的科学实践缺乏理论指导，阻碍了渗透压理论的推广应用以及相关技术的发展。针对这一研究热点与挑战，本文基于分子间相互作用理论与Virial定理，开展了深入系统的研究，定量描述了溶剂化作用、溶液渗透压以及非理想溶液渗透压的性质，具体研究成果如下：

1、基于分子间相互作用基本理论建立了溶质-溶剂相互作用模型，定量描述了溶液中水合结构与水合作用的性质，给出了初级水合层和次级水合层的半径、厚度、静电屏蔽因子以及水合层中的介电常数与水分子数密度，理论结果与实验结果十分吻合；进一步，证明了水合层结构及其性质主要受溶质晶体半径与带电量的影响。更重要的是，本文发现并确定了新的特征长度，将其用于区分离子的强弱水合、判断水合离子的电性以及反映离子水合半径与晶体半径相关性的变化；同时，证明了该长度对应于溶剂化作用指数衰减的特征长度。在此基础上，基于溶质分子的溶剂化结构与性质，利用溶质数密度准确界定了理想溶液、稀溶液以及浓溶液；并确定了溶质分子的Stokes半径，进而准确表征了溶质分子在溶液中的有效占据空间。

2、基于Virial定理建立了渗透平衡方程，建立了电解质、胶体溶液等常见溶液的渗透压与各项物性参数之间的定量关系。确立了渗透压的毫渗量单位与压力单位之间的精准换算关系，打破了以往实际应用中仅能以毫渗量为单位描述渗透压的局限，理论结果与实验结果相一致。进一步，统一了包括Van’t Hoff定律、Morse理论在内的多个渗透压经典理论。在此基础上，首次提出并确立了溶液的结构参数，将其用于表征溶质-溶质相互作用以及溶液的结构。

3、定量描述了非理想溶液渗透压的性质，并界定了理想溶液渗透压理论的适用范围。同时，发现了稀溶液中溶液渗透压对溶液性质仍具有强依赖性，从而纠正了关于“溶液渗透压仅与溶质数密度相关”这一渗透压依数性的传统认知。进一步，计算得出多种不同浓度的等渗溶液具有相同的渗透压，并确定了生理状态下等渗溶液的渗透压为773.1 kPa。在此基础上，给出了生理状态下渗透浓度维持在固定值的根本原因，即在生理渗透浓度下溶质分子的平均能量最低。此外，本文提出了一种通过稀溶液渗透压获得溶液结构参数的方法，为浓溶液渗透压的计算提供了新的途径。

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane, which plays a crucial role in various fields such as life sciences, medicine, industry, environment, and energy. For instance, the homeostasis of osmotic pressure within the human body is indispensable for enabling the proper physiological functioning of various organs. Destabilization of osmotic pressure can directly lead to diseases such as hemolytic anemia, renal impairment, and cerebral damage. Simultaneously, technologies based on osmotic pressure have also been applied to the efficient purification and the development of clean energy. Therefore, the investigation into osmotic pressure bears not only substantial theoretical significance but also encompasses a wide array of practical applications. Given the intricate interplay between osmotic pressure and factors such as solute concentration, solvent-solute interactions, and intermolecular interactions among solute molecules, the precise establishment of quantitative relationships between solution osmotic pressure and solution properties has proven challenging. Consequently, a dearth of theoretical guidance in scientific practices pertaining to osmotic pressure has impeded the widespread adoption of osmotic pressure theory and the advancement of associated technologies. To tackle this focal point and challenge, this dissertation conducts an in-depth and systematic study based on the theories of intermolecular interactions and the virial theorem. It provides a quantitative delineation of solvent-solute interactions, solution osmotic pressure, and the characteristics of non-ideal solution osmotic pressure. The specific research findings are outlined as follows:

(1) By drawing upon the basic theory of intermolecular interactions, a model for solute-solvent interactions was established, allowing for a quantitative depiction of hydration structures and hydration phenomena within solutions. This model provides detailed descriptions of the properties of hydration shells, including the radii, thicknesses, electrostatic screening factors of the primary and secondary hydration layers, as well as the dielectric constants and water molecule density within these shells. The theoretical results closely align with experimental data, further demonstrating that the structure and properties of hydration layers are primarily influenced by the solute crystal radius and charge. Moreover, novel characteristic lengths were discovered and identified to distinguish the strength of ion hydration, assess the electrical properties of hydrated ions, and reflect the correlation between ion hydration radii and crystal radii changes. Simultaneously, it was proven that this length corresponds to the characteristic length of the exponential decay of solvention. Building upon these findings, based on the solvation structure and properties of solute molecules, ideal solutions, dilute solutions, and concentrated solutions were accurately defined using solute number density. Additionally, the Stokes radius of solute molecules was determined to precisely describe the effective occupied space of solute molecules within the solution.

(2) Based on the virial theorem, an osmotic equilibrium equation was established, which provides a quantitative relationship between osmotic pressure and various physical parameters for common solutions like electrolytes and colloidal solutions. A precise conversion relationship was established between the osmotic pressure units in milliosmolarity and pascals, thereby breaking the constraints in previous practical applications, where osmotic pressure was solely described in milliosmolarity. The theoretical findings align with experimental results. Furthermore, multiple classical theories of osmotic pressure, including Van’t Hoff's law and Morse theory, were unified. Based on these foundations, we have introduced and established, for the first time, the structural parameters of solutions. These parameters serve as a means to characterize both solute-solute interactions and the structural arrangement within the solution.

(3) Quantitative descriptions of the properties of osmotic pressure in non-ideal solution were provided, along with the delineation of the applicable range of the theory of osmotic pressure in ideal solution. Additionally, it was discovered that in dilute solutions, osmotic pressure still exhibits a strong dependence on solution properties, thereby correcting the traditional understanding that “Osmotic pressure is colligative”. Furthermore, calculations revealed that solutions of various concentrations may exhibit identical osmotic pressure, with the osmotic pressure of isotonic solutions in physiological states determined to be 773.1 kPa. Building upon this, the fundamental reason for maintaining osmotic concentration at a fixed value under physiological conditions was elucidated, namely, at physiological osmotic concentrations, solute molecules attain their lowest average energy. Moreover, a method was proposed for obtaining solution structural parameters via osmotic pressure in dilute solutions, thus providing a new avenue for calculating osmotic pressure in concentrated solutions.