Measurements of the surface tension of aqueous solutions of polysorbates (Tween 20, Tween 60 and Tween 80) at 293, 303 and 313 K were made. On the basis of the obtained results the Gibbs surface excess concentration of the Tweens at the water–air interface and critical micelle concentrations were determined. Knowing the Gibbs surface excess concentration and taking into account the difference between the limiting area occupied by water and Tween molecules at the water–air interface, the fraction occupied by Tween molecules was established. The limiting area occupied by the Tween molecule was calculated by applying the Joos equation. The area determined in such a way was confirmed by the calculations of cross section of Tween molecules based on the bond lengths and the angles between them as well as the average distance between the molecules, taking into account their different conformations. This area was used for calculation of the standard Gibbs energy of adsorption using the Langmuir equation. The standard Gibbs energy of Tweens adsorption at the water–air interface was also calculated from the hydrophobic part of Tween molecule–water interface tension and that of hydrophobic part. Using the determined values of standard Gibbs energy of adsorption at different temperatures, the standard enthalpy and entropy values were deduced. The standard thermodynamic functions of micellization were also determined and compared to the Gibbs energy of Tween molecules interactions through the water phase.

中文翻译：

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一些聚山梨醇酯在不同温度下的吸附和聚集特性

对聚山梨醇酯水溶液（吐温 20、吐温 60 和吐温 80）在 293、303 和 313 K 下的表面张力进行了测量。根据获得的结果，确定了水-空气界面处吐温的 Gibbs 表面过量浓度和临界胶束浓度。已知吉布斯表面过量浓度并考虑水和吐温分子在水-空气界面占据的极限面积之间的差异，建立吐温分子占据的分数。通过应用 Joos 方程计算吐温分子占据的极限面积。以这种方式确定的面积通过基于键长和它们之间的角度以及分子之间的平均距离计算吐温分子的横截面来确认，考虑到它们的不同构象。该面积用于使用朗缪尔方程计算标准吉布斯吸附能。水-空气界面处吐温吸附的标准吉布斯能也由吐温分子-水界面张力的疏水部分和疏水部分的疏水部分计算得出。使用不同温度下标准吉布斯吸附能的测定值，推导出标准焓值和熵值。还确定了胶束化的标准热力学函数，并将其与通过水相的吐温分子相互作用的吉布斯能量进行了比较。水-空气界面处吐温吸附的标准吉布斯能也由吐温分子-水界面张力的疏水部分和疏水部分的疏水部分计算得出。使用不同温度下标准吉布斯吸附能的测定值，推导出标准焓值和熵值。还确定了胶束化的标准热力学函数，并将其与通过水相的吐温分子相互作用的吉布斯能量进行了比较。水-空气界面处吐温吸附的标准吉布斯能也由吐温分子-水界面张力的疏水部分和疏水部分的疏水部分计算得出。使用不同温度下标准吉布斯吸附能的测定值，推导出标准焓值和熵值。还确定了胶束化的标准热力学函数，并将其与通过水相的吐温分子相互作用的吉布斯能进行了比较。