Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies.
Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies.
复制标题
应用非最佳频率的非线性频率响应方法估计单一溶质吸附等温线。
DOI：
10.1016/j.chroma.2008.05.063
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
A. Seidel
中科院分区：
文献类型：
--
作者：
M. Ilic;M. Petkovska;A. Seidel
为了估计单溶质吸附等温线，利用基于Volterra级数和广义傅里叶变换的高阶频响函数的概念，对色谱柱的非线性频响进行了实验分析和评价。在本案例研究中，研究了以甲醇和水（60:40）的混合物为溶剂，苯甲酸乙酯在十八烷基硅上的吸附。实验采用标准梯度高效液相色谱装置进行。用非线性FR法估计吸附等温线时，柱入口浓度在几个稳态浓度附近以近正弦波形变化。利用该方法，从对应函数的低频渐近线，即frf的相和一阶导数，估计出单个溶质吸附等温线的前三个局部导数。为了准确地估计等温线系数，应定期对低于某一临界频率的频率进行实验。这是足够接近相应函数的低频渐近行为所需的频率，因此由于零频率实验的不可行的误差可以忽略不计。不幸的是，根据系统的特性，可能会发生（就像这里研究的系统一样）临界频率的实验时间太长而无法实现。为了研究非线性频响法应用于非最优频率时的精度损失，在比评估频响相位所需的临界频率高约一个数量级的频率上进行了实验。将所得的等温线模型系数与常规锋面分析方法进行了比较。两种方法确定的等温线是相似的，但是仔细观察就会发现，在过载条件下预测的峰值是不同的。
In order to estimate single solute adsorption isotherms, the nonlinear frequency response (FR) of a chromatographic column is analyzed experimentally and evaluated using the concept of higher order frequency response functions (FRFs) based on the Volterra series and generalized Fourier transform. In this case study, it has been investigated the adsorption of ethyl benzoate on octadecyl silica from a mixture of methanol and water (60:40) as a solvent. Experiments are performed using a standard gradient HPLC unit. For estimation of adsorption isotherms by the nonlinear FR method the column inlet concentration is changed in a nearly sine waveform around several steady-state concentrations. Using this method the first three local derivatives of a single solute adsorption isotherm are estimated from the low frequency asymptotes of the corresponding functions, i.e. the phase and first order derivative of the FRFs. For an accurate estimation of isotherm coefficients periodical experiments should be preformed for frequencies below a certain critical frequency. This is the frequency needed for approaching the low frequency asymptotic behaviour of the corresponding functions close enough, so that errors due to the non-feasibility of experiments with zero frequency can be neglected. Unfortunately, depending on the properties of the system, it can happen (as for the system investigated here) that experiments for the critical frequency would be too long and cannot be realized. In order to study the loss of accuracy of the nonlinear FR method, when it is applied for non-optimal frequencies, experiments are performed for frequencies approximately one order of magnitude higher than the critical frequency required to evaluate the FRF phases. The obtained isotherm model coefficients are compared with the ones estimated using conventional frontal analysis as a reference method. The isotherms determined by two methods are similar, however a closer look reveals that peaks predicted under overloading conditions differ.