Sun Sufang, Yang Gengliang, Wang  Dexian, Sun Hanwen
(College of Chemistry and Environmental Science, Hebei University, Baoding, 071002,   China)

Received on Mar.16, 2001; Supported by the Natural Science Foundation of China (Grant No. 20075005) and the Natural Science Foundation of Hebei Province (Grant No. 200077).

Abstract The frontal velocity analysis is a new method to be used to determine the competitive adsorption isotherms for 2-phenylethanol and 3-phenylpropanol on ODS-silica with 50:50 methanol-water as the mobile phase. The data obtained are fitted to competitive Langmuir isotherm and the best coefficients are acquired. Under the same conditions, a classical method, the rectangular pulse method is also used to determine the isotherms for the same binary mixture. The results show that the competitive isotherms obtained by the frontal velocity analysis method are in well agreement with those obtained by the rectangular pulse method. This shows that the frontal velocity analysis method, which is much simpler, easier and faster than the classical methods, can be used for the determination of binary competitive isotherms accurately.
Keywords: Competitive isotherms, Frontal velocity analysis method, Rectangular pulse method, Liquid chromatography

The determination of an isotherm equation that describes the distribution between mobile and stationary phase has fundamental importance in the study of an adsorption-based separation process ^[1]. Although it is commonly realized that the use of the models and the computing facilities now available can allow considerable savings in the optimization of new separations, potential users are still reluctant because of the experimental difficulties encountered in the accurate determination of competitive equilibrium isotherms. Therefore, a considerable attention is devoted to the development of new methods, which should be much more practical and easier than the existed ones while achieving the same level of accuracy.
    Several traditional methods have been used to measure competitive isotherms, such as the static method ^[2], the pulse method ^[3-7] and the wave method ^[1,8,9]. Because those methods themselves have many drawbacks, they are not often used.
    The most widely used method is the frontal analysis method ^[1,10-14] rather than the above ones. There are two main variants of this method, the staircase frontal analysis ^[1,10-12] and the rectangular pulse ^[1,13,14]. Both methods are well suited to measure competitive isotherms of any type, but only work if the intermediate plateau is well formed for the determination of the two concentrations on the intermediate plateau ^[12,13].
    In our previous papers ^[14,15], a new simple method of competitive isotherm determination, the frontal velocity analysis method is presented and used for the determination of competitive isotherms of oxazepam. The purpose of this paper is to deal with this method for the measurement of competitive isotherms of 2-phenylethanol and 3-phenylpropanol, and compare the results with those obtained by the classical rectangular pulse method, in order to validate the new one's applicability in more general cases.

1 THEORETICAL
1.1 Rectangular pulse method  
This method consists of injecting a single step, washing the solution off from the column with pure mobile phase after the elution of the first step is completed, and starting again with a new, higher step. For the binary mixture of A and B, two plateaus are observed in the elution profiles. The first one is pure A (the less retained), and the second one is composed of A and B, and their concentrations are the same as that of the sample injected. The schematic is shown in Fig.1 (j=1).
    According to our precious studies ^[14,15], the following equations can be inferred straightforward.
Component A (the less retained):
=                     (1)
Component B (the more retained):
=                                               (2)
Where and are the concentrations of M (A or B) in the stationary phase and in the mobile phase at equilibrium respectively. and are the elution volumes of the two elution plateaus; is the hold-up volume of the column and is the volume of stationary phase in the column.
    Since only the first component is present during the elution of the intermediate plateau, can be directly derived from the height of this plateau and no analysis of the effluent is required.
1.2 Frontal velocity analysis method     
A new method called frontal velocity analysis for determining competitive isotherm is described in the previous paper ^[14]. For each concentration step of the binary solution entering the column, two concentration steps are obtained in the elution profiles. A concentration plateau follows each step. The schematic is shown in Fig.1.

Fig.1 Schematic depiction of a binary mixture breakthrough profiles. Where and are the frontal velocities of the first and the second fronts of the j^th step injection concentration; and are the elution volumes of the first front and the second front; , and, are the concentrations of A and B in the mobile phase before and after the j^th concentration increase, respectively; and are the concentrations of A and B on the intermediate plateau after j^th injection.

    When the injection concentration step is not very high, according to reference ^[14], the following expressions can be inferred directly,

                     (3)
                   (4)
Where j is the rank of the concentration step; (M=A or B) is the amount of component M adsorbed at equilibrium with the new mobile phase concentration, ; is the amount adsorbed at equilibrium with the preceding concentration, ; is the phase ratio (, is the packing porosity); and are the retention volumes of the two fronts of every step increase.
    As shown in Eqs.(3) and (4), for the frontal velocity analysis method, the competitive isotherms can be obtained by determining the retention volumes of the two fronts for every concentration step, and .
    The only practical limitation of the method is that the concentration steps achieved should not be too high ^[14], and this can easily be realized in the experiment. The advantage of the frontal velocity analysis method over the classical, staircase frontal analysis method is that a second HPLC system is no longer necessary ^[15]. Thus, the new method is simpler and faster than conventional frontal analysis although using the same principle. Its advantage over the rectangular pulse method is to demand smaller amount of chemicals and to need less time to perform the experiments.

2 EXPERIMENTAL
2.1 Instrumentation
The schematic of the HPLC system used by the frontal velocity analysis method sees reference^[15] except that it is unnecessary to use another on-line HPLC. The sample introduction in the frontal velocity analysis is achieved by simultaneously switching the two valves 1 and 2, interconnected in such a way that when loop A is flushed into the column, loop B can be filled with the solution at the next higher concentration. The pump is Waters 510, loop A and loop B are of 2 mL volume and the injection valves are Rheodyne 7125. The column (2.0mmi.d.×200mm) is packed with 5µm spherical ODS-silica particles from Hypersil and it is thermostated at 35^oC. The variable wavelength UV detector is Shimadzu SPD-6AV and it is set at 275 nm in order to determine the steps even at high concentrations. The flow rate is 0.3 mL.min^-1. The signals of the detector are recorded on a PC computer and evaluated with JS-3030 workstation.
2.2 Chemicals
2-Phenylethanol, 3-phenylpropanol and methanol are all of analytical grades from Beijing Chemical Reagent Plant (Beijing, China). All the reagents are applied without further purification. Doubly distilled water is used. The mobile phase is methanol-water (50:50). Concentrations are reported in mg.mL^-1: a concentration of 1mg.mL^-1 is 8.2mM for 2-phenylethanol and 7.45mM for 3-phenylpropanol.
2.3 Chromatographic measurements   
The column hold-up volume is measured with methanol as the unretained marker. The volume of the stationary phase is calculated from the column volume and the dead volume. The stability of the volume flow rate of the effluent is checked periodically by measuring the volume of column effluent collected over a measured time. The retention volumes of the steps are calculated from the inflection points of the breakthrough curves recorded in the two different methods. In frontal velocity analysis, first, loop A is filled with the lowest concentration planned in the run, then injected onto the column by simultaneously switching valves 1 and 2. Meanwhile, loop B is filled with the solution at the next higher concentration. The corresponding new concentration step is injected at the proper time, by turning both valves simultaneously again. Other injections required are performed in the same way.

3 RESULTS AND DISCUSSION
3.1 Experimental data     
Competitive isotherm data are obtained under conditions of increasing total sample concentration at constant mass ratios of the two components with the frontal velocity analysis and the rectangular pulse method. The mass ratios of 2-phenylethanol (PE) to 3-phenylpropanol (PP) concentration investigated are 3:1, 1:1, and 1:3. The experimental data are shown in Figs.2-4 (symbols) respectively. The circles represent the data obtained from the new method and the crosses are the data from the classical method. As can be seen in Figs.2-4 (symbols), the experimental data obtained from the frontal velocity analysis method and the rectangular pulse method are in good agreement.

Fig.2 Competitive isotherms for 2-phenylethanol (PE) and 3-phenylpropanol (PP) (the mass ratio of PE to PP is 3:1) on ODS-silica, which are calculated by two different methods. Crosses (×) represent the data obtained from rectangular pulse method, and circles (·) are the data from frontal velocity analysis method.

Fig.3 The same as in Fig.2, but the mass ratio of PE to PP is 1:1

Fig.4 The same as in Fig.2, but the mass ratio of PE to PP is 1:3.

3.2 Determination of the isotherms and Coefficients of the isotherms      
The experimental values obtained for the two homologues, with either method mentioned above, are fitted to the equations of the competitive Langmuir isotherms.
                (5)
                 (6)
Where is the maximum column loadability and is numerical coefficient. When the ratios of are constant, equations (5) and (6) are simplified and become the following expressions
                               (7)
                               (8)
Here is the total concentration in the mobile phase; and are apparent parameters, and they are simply related to the coefficients in Eqs.(5) and (6) and the ratio of the two concentrations in the corresponding feed.
    For the investigated ratios of 2-phenylethanol and 3-phenylpropanol, the experimental data obtained from the two different methods are fitted to Eqs.(7) and (8). Figs.2-4 show the competitive isotherms for PE and PP (3:1, 1:1, 1:3) on ODS-silica respectively (solid line). As can be seen in the three Figures, there is an excellent agreement between the experimental data got from the two different methods and the best Langmuir isotherms obtained from the regression. Meanwhile, the values of the four coefficients , , and are also obtained from the nonlinear regression, and the results are reported in Table 1. As shown in Table 1, the Langmuir constants obtained from the rectangular pulse method and the frontal velocity analysis method are close.

Table 1. Langmuir constants determined by both methods.

* a_i , b_i in mL.mg^-1.

3.3 Comparison of the two methods
Both the rectangular pulse and the frontal velocity analysis method are all suitable for the measurement of any kind of isotherm if there are discontinuities in the fronts and the same accurate results can be obtained in the experiments with different economic effects. For the rectangular pulse method, before each individual concentration step increases, the column must be eluted to emptiness. This is a time-consuming and solvent-wasting process. As to the new method, the process is realized by continuous injection, i.e. the lower concentration sample is eluted by the higher concentration sample, the solvent does not go into the column during the whole process until the last injection is finished. Thus, the frontal velocity analysis method is much faster and more economic than the rectangular pulse method.
    On the other hand, for the rectangular pulse method, the concentration of the intermediate plateau can be calculated from the absorption curve of the less retained component, this is superior to the staircase frontal analysis method, where the concentration of the intermediate plateau is determined by another analytical HPLC system. However, because the width of the intermediate plateau decreases with the increase of the concentration of the two components in the mobile phase^[12], when the injection concentration is much higher, the intermediate plateau almost disappears, it is very difficult to calculate the concentration of the component on it. While in the frontal velocity analysis method, as seen from Eqs.(3) and (4), the only parameter needed to determine the isotherm is the retention volume of the elution front, only does the front shock associated with the intermediate plateau appear, the isotherms can be calculated by the new method.

4. CONCLUSIONS
The experimental data characterizing the equilibrium adsorption for 2-phenylethanol and 3-phenylpropanol on ODS-silica are acquired by two different methods, the rectangular pulse method and the frontal velocity analysis method. The results show that the competitive isotherms obtained with both methods are in well agreement. This means that the frontal velocity analysis method not only has the advantages of greater experimental simplicity, fastness, and smaller amount of materials but also can be used to determine binary competitive isotherms accurately.

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