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。     

Kelvin公式适用于微小气泡吗？

考虑到气泡要在液体中稳定地存在,必须充入其他气体,据此导得液体在气泡中的饱和蒸气压与在平面液体中相同,仅随温度而变,而与气泡的曲率半径无关。因此,Kelvin公式不适用于微小气泡。     

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。     

函数的单调性和导数在物理化学教学中的运用

分析了函数的单调性在阿伦尼乌斯方程、吸附热力学、范特霍夫方程和克拉佩龙方程中的运用;介绍了利用导数推导开尔文微小液滴饱和蒸气压公式,并介绍了导数在物理化学中的一些证明题和计算题中的巧妙运用。从而把物理化学抽象的内容通过数学知识具体化,使深奥的物理化学理论变成简单的数学知识。     

外压与凝聚态物质饱和蒸气压关系的讨论

应用外压与饱和蒸气压的关系公式,推导了范霍夫公式和开尔文公式。温度一定时,平液面的饱和蒸气压只会大于或等于真空密闭系统中纯物质气液平衡时的饱和蒸气压。毛细管的凹液面还会出现比平液面的饱和蒸气压小的情况。该关系公式称为"凝聚相表面的压力与饱和蒸气压的关系公式"更为合理。     

基于室温离子液体的电导型气体传感器

本文利用室温离子液体对水或有机蒸气吸收后其离子导电性的改变,研制了以离子液体BmimPF6为敏感材料的电导型气体传感器.考查了BmimPF6用量对传感器响应的影响,测定了传感器对不同浓度的水蒸汽及乙醇、二氯甲烷等饱和有机蒸气的响应.实验结果显示,该传感器具有制作方便、结构简单、稳定性高及线性范围宽等优点,可被用于不同浓度的水或有机蒸气/氮气混合气氛中,水蒸汽或有机蒸气浓度的测定.此外,还针对该传感器对乙醇等不同饱和有机蒸气响应信号与这些有机溶剂的理化性质参数间的定量关系,采用化学计量学方法进行了建模分析.     

完全不互溶双液系的蒸气压*

对完全不互溶双液系的饱和蒸气压进行了实验研究与理论讨论,认为完全不互溶双液系的平衡蒸气压随两组分相互溶解度减小而趋于但总是小于两纯组分的饱和蒸气压之和;当完全不互溶两液相一起静置时,上层液体能有效但不能完全阻止下层液体的挥发,这种阻止作用源于缓慢溶解、扩散和挥发这些动力学过程;提出了阻止下层液体挥发的方法,即用与之完全不互溶且密度小的液体来覆盖,并且2种液体充满容器,阴凉处密闭静置保存。     

化学势在解决相平衡类问题中的应用探究

采用微元法对有关平衡类问题中化学势变化进行了集中分析和讨论,将克劳修斯-克拉贝龙方程、液体的饱和蒸气压与外压的关系式、开尔文公式以及稀溶液的依数性公式等知识点有机的关联起来,显著降低了相关知识内容的学习难度,并对培养学生创新思维起到了有效锻炼和促进作用。     

顺丁烯二酸酐与邻苯二甲酸二甲酯二元体系在4.00, 8.00和12.00 kPa下的等压气液平衡

采用沸点仪测定了顺丁烯二酸酐和邻苯二甲酸二甲酯二元体系在4.00, 8.00和12.00 kPa下的等压气液平衡数据以及纯DMP组分饱和蒸气压数据, 将实验数据回归得到了纯DMP在417~525 K范围内的Antoine方程. 根据实验平衡温度、 压力和组成数据进一步回归得到NRTL方程参数, 推算出平衡气液相组成, 并利用UNIFAC方程对实验数据进行了预测, 其结果与沸点仪测定结果及NRTL拟合的结果基本相符.     

反应活化能的Tolman解释

修正的Arrhenius方程k=BTnexp(-E/RT)中的E,是化学反应名副其实的活化能。它与Arrhenius活化能E a有相同的物理意义,也服从Tolman解释。     

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.     

On the applicability of Young–Laplace equation for nanoscale liquid drops

Debates continue on the applicability of the Young–Laplace equation for droplets, vapor bubbles and gas bubbles in nanoscale. It is more meaningful to find the error range of the Young–Laplace equation in nanoscale instead of making the judgement of its applicability. To do this, for seven liquid argon drops (containing 800, 1000, 1200, 1400, 1600, 1800, or 2000 particles, respectively) at T = 78 K we determined the radius of surface of tension R_s and the corresponding surface tension γ_s by molecular dynamics simulation based on the expressions of R_s and γ_s in terms of the pressure distribution for droplets. Compared with the two-phase pressure difference directly obtained by MD simulation, the results show that the absolute values of relative error of two-phase pressure difference given by the Young–Laplace equation are between 0.0008 and 0.027, and the surface tension of the argon droplet increases with increasing radius of surface of tension, which supports that the Tolman length of Lennard-Jones droplets is positive and that Lennard-Jones vapor bubbles is negative. Besides, the logic error in the deduction of the expressions of the radius and the surface tension of surface of tension, and in terms of the pressure distribution for liquid drops in a certain literature is corrected.     

Vapor and liquid equilibria in porous media

The alteration of the vapor–liquid equilibrium (VLE) of volatile organic mixtures by placing porous media at the liquid–vapor interface was studied. Kelvin, assuming ideal behavior of fluids, first introduced the vapor pressure of liquid over a meniscus as a function of its surface tension and the radius of the curvature. A thermodynamic model (SS_mod model) predicting the VLE of non-ideal organic mixtures in porous media was developed as a function of pore sizes. The model was used to predict the VLE of two aqueous alcohol solutions, ethanol–water and propanol–water, and two binary solutions, methanol–isopropanol and ethanol–n-octane. Experiments were conducted using sintered metal and fritted glass plates as porous media, and the results were compared with the model predictions. Using the actual diameter of the porous media, the model prediction showed good agreement with the experimental results.     

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

On the derivation of Young's equation for sessile drops: nonequilibrium effects due to evaporation

Sessile liquid drops have a higher vapor pressure than planar liquid surfaces, as quantified by Kelvin's equation. In classical derivations of Young's equation, this fact is often not taken into account. For an open system, a sessile liquid drop is never in thermodynamic equilibrium and will eventually evaporate. Practically, for macroscopic drops the time of evaporation is so long that nonequilibrium effects are negligible. For microscopic drops evaporation cannot be neglected. When a liquid is confined to a closed system, real equilibrium can be established. Experiments on the evaporation of water drops confirm the calculations.     

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     

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.     

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.     

A New Understanding of the Relationship Between Solubility and Particle Size

Most discussions of the relationships between crystal solubility and particle size have hitherto been concerned with vapor condensation and have led to the prediction that the vapor pressure increases with curvature. Here, thermodynamic arguments are presented to show that such relationships, describing crystal solubility as a function of particle size, originally put forward by Ostwald and later corrected by Freundlich, may be unjustified for determining interfacial tension at solid–liquid interfaces. The Kelvin or Gibbs–Thomson equations are valid for liquid–vapor systems, but not for solid–liquid interfaces. Recent experimental observations have demonstrated that interfacial tension data obtained by the solubility–size approach are unreasonable. This leads to the conclusion that Ostwald ripening may not be due to a higher solubility of smaller crystals, but rather to a net negative interfacial tension between solid and solution.