We reviewed eight commonly used equilibrium adsorption models and examined their underlying assumptions, fitting qualities, and parameter stabilities. We compared several objective functions that have been applied to curve fitting analysis and a few statistics tests that have been performed to evaluate regression quality. The iteratively reweighted least squares algorithm was selected as the most suitable regression method for adsorption models in the presence of heteroscedasticity. The fraction of unexplained variance was selected to indicate the model fitting quality. Two sources of parameter instability were identified: residue instability and function instability. While the definition of the instability caused by residue is well established, we are the first to consider the instability caused by an adsorption model. The models discussed in this article can be applied to many surfactants, such as normal alcohols, polyglycol ethers, and sodium dodecyl sulfate at different salt concentrations. Our results show that both the model fitting quality and parameter instability increase with the number of parameters subject to curve fitting. For the Frumkin-type of reorientation model, the parameter instability can be as high as 25%. The high degree of instability in some complicated adsorption models may invalidate the estimated parameters. Therefore, additional measurements or simulations are required for complicated models to extract reliable model parameters.

我们回顾了八个常用的平衡吸附模型，并检查了它们的基本假设，拟合质量和参数稳定性。我们比较了已应用于曲线拟合分析的一些目标函数和已进行的一些用于评估回归质量的统计测试。在存在异方差的情况下，迭代加权最小二乘算法被选为最适合吸附模型的回归方法。选择无法解释的方差分数来表示模型拟合质量。确定了两个参数不稳定的来源：残基不稳定和功能不稳定。虽然已经很好地确定了由残留物引起的不稳定性的定义，但我们是第一个考虑由吸附模型引起的不稳定性的人。本文讨论的模型可以应用于许多表面活性剂，例如不同盐浓度的正构醇，聚乙二醇醚和十二烷基硫酸钠。我们的结果表明，模型拟合的质量和参数的不稳定性都随着受曲线拟合的参数数量的增加而增加。对于Frumkin型重定向模型，参数不稳定性可能高达25％。在某些复杂的吸附模型中，高度的不稳定性可能会使估计的参数无效。因此，复杂模型需要额外的测量或模拟以提取可靠的模型参数。我们的结果表明，模型拟合的质量和参数的不稳定性都随着受曲线拟合的参数数量的增加而增加。对于Frumkin型重定向模型，参数不稳定性可能高达25％。在某些复杂的吸附模型中，高度的不稳定性可能会使估计的参数无效。因此，复杂模型需要额外的测量或模拟以提取可靠的模型参数。我们的结果表明，模型拟合的质量和参数的不稳定性都随着受曲线拟合的参数数量的增加而增加。对于Frumkin型重定向模型，参数不稳定性可能高达25％。在某些复杂的吸附模型中，高度的不稳定性可能会使估计的参数无效。因此，复杂模型需要额外的测量或模拟以提取可靠的模型参数。