关于开尔文公式推导的讨论

应用弯曲界面存在的气液平衡条件和界面热力学方法,分析讨论了物理化学教材中开尔文公式的推导方法和过程,指出了存在的一些容易产生误解的问题。明确指出:等温下小液滴饱和蒸气压相对于平面液体饱和蒸气压的增大是由弯曲液面下液体的附加压力引起的,而不是界面自由能变化所致。并提出了一些教学建议。     

关于等温循环方法推导开尔文公式的讨论

等温循环方法是物理化学教材中推导开尔文公式的一个经典方法。本文从热力学基本原理出发,明确指出其中小液滴可逆相变为气体的吉布斯自由能变化值应由吉布斯自由能判据求解,并对温度恒定、两相压强分别恒定时的判据进行了重新推导。同时,本文还提出了一种对推导开尔文公式的等温循环法的新理解方式,该方式在建立的"箱管模型"辅助下,意义明确,便于理解,更适宜教学使用。     

外压法推导开尔文公式的探究

液体的饱和蒸气压受外压的影响,根据外压对液体饱和蒸气压的影响公式可以推导出液滴、弯曲液面的开尔文公式。     

关于一些热力学公式使用条件的讨论

物理化学中的热力学公式在不同条件下有不同的衍变形式,极易诱导学生产生错误理解。通过实例分析,对热力学能和焓变化计算公式、赫姆霍兹自由能和吉布斯自由能判据、热力学基本方程等的使用和理解中存在的一些问题予以讨论。     

吉布斯自由能的多功能性质探讨

在物理化学常用的热力学函数中,吉布斯自由能是一个用途最为广泛、最具有明确意义的热力学函数,它除了在特定条件下可作为过程与方向的判据外,还具有狭义化学势、最大非膨胀功和狭义表面自由能等功能。本文就吉布斯自由能的多功能特性展开讨论,并通过两个实例说明实际体系中ΔG的计算方法及用途,以帮助学生在物理化学学习过程中深入理解吉布斯自由能。     

对球状液滴拉普拉斯公式热力学推导方法的讨论

本文针对球状液滴拉普拉斯公式热力学推导方法进行了讨论分析。首先从界面热力学基本方程的建立方法和界面热力学基本方程中作为偏微分的压强的数学定义两个角度进行分析,得出了液滴界面热力学基本方程中,压强为与之平衡的外界气体压强。另外,从实际发生的物理过程来看,本文所质疑的球状液滴拉普拉斯公式的热力学推导方法采用无外力做功时液滴体积增大d V的过程是明显违反热力学第一定律的。     

热力学方程在计算热力学函数中的应用

热力学方程是包含热力学基本方程、热力学状态方程以及吉布斯-亥姆霍兹方程在内的广泛的一组方程。文中对目前物理化学教材中很少提及的其他热力学状态方程进行了系统的总结和推导,同时强调理论的系统性和完整性在教学中的重要性,并在此基础上导出了物理化学教材中很少见到的吉布斯-亥姆霍兹第一方程及其在表面化学中的应用。在物理化学教学中需要特别强调特征变量的重要性,以及特征变量和化学反应条件之间的内在关系,并注意与交叉学科物理专业的热力学和统计物理学的衔接。     

关于球形小液滴热力学公式及其气液平衡条件的讨论

依据热力学第一和第二定律,从不同角度导出了球形小液滴的热力学基本公式。明确指出公式中的压力为液体相的压力,不是气相压力。分别用熵判据和Gibbs自由能判据证明了小液滴的气液相平衡条件为物质在两体相的化学势相等。强调指出:相平衡条件具有普适性,与是否为孤立体系或封闭体系及其类型无关,不仅适于球形液滴,对其他形状的液体也适用。对文献中存在的相关问题进行了较详细的讨论,澄清了一些容易模糊的认识。     

Cu-Zn原电池标准电动势测定实验的计算化学设计

基于量子化学计算软件Gaussian 16,对“电动势的测定”这一经典物理化学实验进行了计算化学设计。用密度泛函方法计算了Cu²⁺和Zn²⁺的溶剂化自由能,通过热力学循环计算得到电池反应的标准摩尔吉布斯自由能变,进而求出Cu-Zn原电池的标准电动势。该实验旨在帮助学生加深对标准摩尔吉布斯自由能、电极电势和能斯特方程等物理化学基本概念的理解,发挥学生的主观能动性,培养学生设计实验能力、动手实践能力以及科学思维。     

超疏水表面上冷凝液滴发生弹跳的机制与条件分析

使用液滴合并前后的体积和表面自由能守恒作为两个限制条件,确定了合并液滴的初始形状,即为偏离平衡态的亚稳态液滴,具有缩小其底半径而向平衡态液滴转变的推动力.进而分析了液滴变形过程中的推动力和三相线(TPCL)上的滞后阻力,建立了液滴变形的动态方程并进行了差分求解.如果液滴能够变形至底半径为0mm的状态,则根据该状态下液滴重心上移的速度确定液滴的弹跳高度.不同表面上冷凝液滴合并后的变形行为的计算结果表明,光滑表面上的液滴合并后,液滴只能发生有限的变形,一般都在达到平衡态之前就停止了变形,因此冷凝液滴不会发生弹跳;粗糙表面上的Wenzel态液滴的三相线上的滞后阻力更大,因而液滴更难以变形和弹跳;具有微纳二级结构表面上只润湿微米结构,但不润湿纳米结构的部分Wenzel态液滴能够变形至Cassie态,但没有明显的弹跳;只有在纳米或微纳二级结构表面上的较小Cassie态液滴合并后,液滴易于变形至底半径为0mm的状态并发生弹跳.因此,Cassie态合并液滴处于亚稳态,并且其三相线上的移动阻力很小,是导致冷凝液滴弹跳的关键因素.     

Kelvin方程的一种理论推导

从液滴平衡条件推导出严格意义的Kelvin方程, 验证了其在宏观尺度可以转化为经典形式. 利用Tolman方程, 在考虑表面张力与曲率半径关系的条件下, 给出在液体压缩性可忽略时, 饱和蒸气压、蒸气密度、蒸气摩尔体积和曲率半径等关系; 液体压缩性不可忽略时, 得出以等温压缩系数和Tolman长度表示的饱和蒸气压与液滴半径的关系.     

Experimental studies on the applicability of the Kelvin equation to highly curved concave menisci

The thermodynamic properties of liquids trapped in microscopic pores are described in theory by the Kelvin equation, which relates the equilibrium meniscus curvature to the relative vapor pressure. We report here two series of experiments designed to test the validity of the Kelvin equation by direct measurement of the mean radius of curvature of the surface of cyclohexane condensed between crossed mica cylinders. In one series of experiments, the relative vapor pressure of the volatile cyclohexane was controlled by mixing it with a relatively involatile solute (n-dodecane or n-hexadecane). We found that the mean radius of curvature rapidly reached that predicted by the Kelvin equation at each relative vapor pressure of the volatile liquid, but that there was also a slow, but continuous, accumulation of the “involatile” solute at the point of condensation as the system approached true equilibrium. Such accumulation of very low vapor pressure materials may be one factor responsible for the discordant results reported by earlier workers. We find that the process of impurity buildup is complex, and suggest that studies of real porous systems may be affected by accumulation of “involatile” impurities through the vapor phase and by surface diffusion. The other series of experiments was designed to eliminate the impurity problem by maintaining the vapor pressure by temperature control of the pure liquid. The results from this series of experiments were not time dependent, and no evidence of contamination was found. The measured radii were within ±6% of those predicted by the Kelvin equation, for radii in the range 4–20 nm. We conclude that the thermodynamic basis of the Kelvin equation is valid in principle for menisci with radii as low as 4 nm.     

The Kelvin equation

The capillary condensation/evaporation process is studied in conjunction with small angle X-ray scattering measurements. The scattering data are analyzed with the indirect Fourier transformation technique and the results are compared with the predictions of the Kelvin equation. It is found that the Kelvin equation is obeyed by menisci with mean radius of curvature as low as 40 A. For smaller radii, in particular from 40 to 30 A, the two methods differ by approximately 25%. Broekhoff and de Boer analysis may improve the prediction. The hysteresis region of an adsorption step is presented schematically.     

Generalized Kelvin equation and pseudospinodal in nucleation theory

The classical Kelvin equation, relating the size of the critical cluster to the supersaturation, is inadequate for very small, molecular-sized clusters emerging at deep quenches observed in recent nucleation experiments. Using statistical mechanical considerations, we propose a generalization of the Kelvin equation applicable up to the vicinity of the pseudospinodal, where the nucleation barrier is approximately k(B)T. The supersaturation at the pseudospinodal is expressed in terms of the second virial coefficient. It is shown that near the pseudospinodal the critical cluster size is close to the coordination number in the liquid phase. Comparisons with computer simulations are presented.     

关于弯曲界面气液两相相平衡化学势相等热力学判据的讨论

Thermodynamic criterion of equal chemical potential for phase equilibrium between gas and liquid in curved interface has been introduced in many textbooks and papers. In this paper, the process of the derivation of the criterion is proved to be wrong with analysis. In order to solve the problem, a proof procedure for the thermodynamic criterion of equal chemical potential is provided based on the definition of chemical potential. At the same time, a new thermodynamic criterion of two-phase equilibrium in curved interface is established using Gibbs interface thermodynamics and a new method for derivation of Kelvin equation is put forward based on the thermodynamic criterion of two-phase equilibrium. The new criterion which is derived directly from the second law of thermodynamics has a specific thermodynamic significance and clear physical model.     

Validity of the Kelvin equation in estimation of small pore size by nitrogen adsorption

 We have investigated a practical lower limit of a pore-size estimation by the nitrogen desorption isotherms at 77 K using the Kelvin equation. Changes in pore size of porous silica glasses before and after the monolayer preadsorption of n-propylalcohol were estimated by measuring the nitrogen adsorption and desorption isotherms. These changes should correspond to the thickness of monolayer of adsorbed n-propylalcohol. The thickness of monolayers obtained for the samples whose pore sizes are below ca. 2 nm were underestimated, when the Kelvin equation was applied to the nitrogen desorption isotherms using the values of surface tension and molar volume of bulk liquid nitrogen at 77 K. Below ca. 2 nm pore radius a careful application of the Kelvin equation is required to estimate a pore size. These results suggest that a change in the physical properties of liquid nitrogen in such a small pore occurs. It is supposed that the interaction between the solid surface and adsorbate molecules causes the changes in the surface tension and density of liquid nitrogen in such a narrow pore. Received: 21 March 1997 Accepted: 18 July 1997     

基于PC-SAFT方程研究多孔介质中水合物相平衡的预测模型

对多孔介质中水合物的形成条件预测模型进行了研究.利用微扰链-统计缔合流体理论状态方程(PC-SAFT)结合van der Waals-Platteuw模型和毛细管Kelvin模型,建立了用于多孔介质水合物体系的相平衡预测模型.在此模型基础上,针对甲烷水合物和CO2水合物对界面张力作了进一步的研究.根据多孔介质水合物相平...     

Generalization of Kelvin's equation for compressible liquids in nanoconfinement

The Kelvin equation for a compressible liquid in nanoconfinement is written in a form that takes into account not only Laplace's pressure, but also the oscillatory compression pressure. This leads to a simple analytical equation for pressure in nanocapillaries. The corrected equation is used to analyze properties of aqueous systems, including the oscillatory structural forces between attractive surfaces and inert surfaces, repulsive "hydration" forces between hydrophilic surfaces, and attractive "hydrophobic" forces between hydrophobic surfaces. Relative vapor pressure in a nanocapillary also is discussed.     

基于吉布斯弯曲界面相平衡判据的开尔文方程推导

对两种界面热力学处理方法(古根海姆法与吉布斯法)进行了介绍。采用吉布斯界面热力学方法建立了存在界面相时两相平衡的热力学判据,并以此为基础提出了一种新的开尔文方程推导方法。     

Effect of surface area on equilibrium pressure. Adsorption approach

Changing droplet radii in a liquid-vapor system is due to the phase transition on the droplet surface. As a variation of the internal energy does not depend on the way the change occurs, we can imagine that a gas condenses on a droplet surface in two stages: in the first stage, autoadsorption occurs on the liquid surface, and in the second stage, adsorbed molecules transfer into the volume by diffusion. Assuming that the energetic effects of the diffusion are independent of the surface curvature, one may conclude that if two liquid bodies differ only with respect to their geometry, the difference of enthalpies of condensation on their surfaces, DeltaH(bd), is equal to the variation of energies of autoadsorption. An estimation of DeltaH(bd) for the simple bodies is presented, and the relationship between the saturation pressure and droplet radii is derived. In the range of micrometer dimensions, the new equation and the Kelvin model lead to close results; for nanocapillaries, the Kelvin equation predicts a divergence of hysteresis loops, whereas the new equation adequately describes the observations. The classical model presumes that a surface area, A, affects the free energy, while the new approach is based on the assumption that A is the repository for the internal energy.