Giesy Timothy J, Chou Alan S, McFeeters Robert L, Baird James K, Barlow Douglas A
Department of Chemical Engineering, University of Alabama in Huntsville, Huntsville, Alabama 35899, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061201. doi: 10.1103/PhysRevE.83.061201. Epub 2011 Jun 16.
The mixture of isobutyric acid and water has a consolute point at a temperature of 25.75 °C and mole fraction 0.1148 isobutyric acid. When charcoal is added to this mixture, the concentration of isobutyric acid is reduced by adsorption. We have measured the action of charcoal on solutions of isobutyric acid and water as a function of isobutyric acid mole fraction at temperatures of 25.85 and 32.50 °C. At the higher temperature, the specific adsorption density (y(2)(α)/m) satisfies the Freundlich equation (y(2)(α)/m)=KX(2)(1/n), where y(2)(α) is the mass of isobutyric acid adsorbed, m is the mass of charcoal, X(2) is the equilibrium mole fraction of isobutyric acid, n is the Freundlich index, and K=K(T) is an amplitude that depends upon the temperature T. At 25.85 °C, a critical endpoint is located at an isobutyric acid mole fraction X(2)(ce)=0.09. When compared with the Freundlich equation at this temperature, a plot of the specific adsorption density as a function of X(2) in the vicinity of the critical-endpoint composition assumes a shape which is reminiscent of the derivative of a Dirac delta function. Using critical-point scaling theory, we show that this divergent pattern is consistent with the principle of critical point universality.
异丁酸和水的混合物在温度为25.75℃、异丁酸摩尔分数为0.1148时具有共溶点。当向该混合物中加入木炭时，异丁酸的浓度会因吸附作用而降低。我们测量了在25.85℃和32.50℃温度下，木炭对异丁酸和水溶液的作用随异丁酸摩尔分数的变化。在较高温度下，比吸附密度（y(2)(α)/m）满足弗伦德利希方程（y(2)(α)/m）=KX(2)(1/n)，其中y(2)(α)是吸附的异丁酸质量，m是木炭质量，X(2)是异丁酸的平衡摩尔分数，n是弗伦德利希指数，且K = K(T)是一个取决于温度T的幅度。在25.85℃时，一个临界端点位于异丁酸摩尔分数X(2)(ce)=0.09处。与该温度下的弗伦德利希方程相比，在临界端点组成附近，比吸附密度随X(2)变化的曲线呈现出一种让人联想到狄拉克δ函数导数的形状。利用临界点标度理论，我们表明这种发散模式与临界点普适性原理是一致的。
