Pulse injection method

The above example demonstrates that treatment of the basic data by different numerical methods can produce distinctly different results. The discrepancy between the results in this case is, in part, due to the inadequacy of the data provided the data points are too few in number and their precision is poor. A lesson to be drawn from this example is that tracer experiments set up with the intention of measuring dispersion coefficients accurately need to be very carefully designed. As an alternative to the pulse injection method considered here, it is possible to introduce the tracer as a continuous sinusoidal concentration wave (Fig. 2.2c), the amplitude and frequency of which can be adjusted. Also there is a variety of different ways of numerically treating the data from either pulse or sinusoidal injection so that more weight is given to the most accurate and reliable of the data points. There has been extensive research to determine the best experimental method to adopt in particular circumstances 7 " . 

The repeated pulse injection method was applied to determine the association rate constant of the antigen-immobilized monoclonal antibody reaction 124.25). These monoclonal antibodies differ by their specificity and affinity for HSA. The epitope recognized by the HA6 antibody is located between residues I and 128. The epitope of the commercial antibody (m-anti-HSA) is located between residues 124 and 298 of the HSA molecule. They differ by their affinity for HSA. with equilibrium binding constants of respectively 6.7 x 108 mol-dm and 1.6 x 10K dm3 mol-1 for the HSA/HA6 and the HSA/m-anti-HSA association in solution 25). Close binding rate constants are obtained on both immobilized monoclonal antibodies with Aa = 2.5 x I0 i dm -moC -s-1. 

Fig, 10.24. Simplified schematics illustrating some deposition techniques (a) thermal evaporation (b) stamping (c) liquid-solid interface (d) electro-chemistry set-up (e) Langmuir-Blodgett technique (f) electro-spray deposition (g) pulse injection method (h) solution casting (i) spin-coating. 

The pulse injection method (Fig. 10.24g) uses a fast valve (open only for milliseconds) to inject the solvent with the molecules directly into vacuum onto a sample mounted approximately 100 mm under the opening [136]. The molecules remain uncharged and the pressure in the chamber substantially increases during the deposition. This method is successful even for very large and fragile supramolecular assemblies (see discussion below). 

In a previous study [12], the pulse injection method allowed us to detect on a 1.9 wt % Pt /Ti02 catalyst, the presence of strongly and weakly poisoned sites, effective during the first pulse of CROALD and during all the following ones (reproducible state), respectively. The variations of activity and selectivity during time on stream are different in the initial and reproducible states. The experiments performed in this study occur on a catalyst in its reproducible state. So, the observed decrease of activity is due to the presence of these weakly poisoned sites, activity that is recovered at the beginning of each new pulse. 

In the pulse injection method, the response curve contains information about the various processes occurring inside the pellet. The moment method is applied to analyze the response curve. The zero-order moment gives the amount injected into the system. The first order moment contains information about the processes responsible directly to the through flux, while the second-order moment contains information about the secondary processes occurring in the pellet. Similar to the pulse injection method, the response curve of the step injection method also contains information about all processes occurring in the pellet. This curve is usually analyzed by matching the time domain solution to the experimental data. The steady state of the step-injection response contains only information about the through processes while the transient part of the curve contains information of all processes. 

Method of Moments The first step in the analysis of chromatographic systems is often a characterization of the column response to sm l pulse injections of a solute under trace conditions in the Henry s law limit. For such conditions, the statistical moments of the response peak are used to characterize the chromatographic behavior. Such an approach is generally preferable to other descriptions of peak properties which are specific to Gaussian behavior, since the statisfical moments are directly correlated to eqmlibrium and dispersion parameters. Useful references are Schneider and Smith [AJChP J., 14, 762 (1968)], Suzuki and Smith [Chem. Eng. ScL, 26, 221 (1971)], and Carbonell et al. [Chem. Eng. Sci., 9, 115 (1975) 16, 221 (1978)]. 

In the salt injection method(3l) a pulse of salt solution is injected into the line and the time is measured for it to travel between two electrode pairs situated a known distance apart, downstream from the injection point. 

In a recent study of the transport of coarse solids in a horizontal pipeline of 38 mrrt diameter, pressure drop, as a function not only of mixture velocity (determined by an electromagnetic flowmeter) but also of in-line concentration of solids and liquid velocity. The solids concentration was determined using a y-ray absorption technique, which depends on the difference in the attenuation of y-rays by solid and liquid. The liquid velocity was determined by a sail injection method,1"1 in which a pulse of salt solution was injected into the flowing mixture, and the time taken for the pulse to travel between two electrode pairs a fixed distance apart was measured, It was then possible, using equation 5.17, to calculate the relative velocity of the liquid to the solids. This relative velocity was found to increase with particle size and to be of the same order as the terminal falling velocity of the particles in the liquid. 

Comparison of Pulse and Step Methods. A brief summary of the advantages of the pulse and step injections methods is given below. 

The pulse reactor method is similar to semibatch in that all the ingredients except HCN are placed in a small, well-mixed vessel in a thermostated bath. Very small amounts of HCN are then rapidly injected into the reaction mixture with vigorous mixing and the exotherm is monitored. Repeated pulses are made only after the reaction mixture has come back to temperature equilibrium with the bath. In this manner, kinetic information may be obtained. 

The results of Renard et al. 23 show that the effective adsorption rate constant can be determined either from the analysis of the breakthrough curves or from the repeated pulse injection mode. The advantage with the latter method is simplicity, because it is based on peak area measurements, with minute amounts of protein consumed. Another advantage is the standard HPLC instrumentation used for such experiments. 

The experimental method used in TEOM for diffusion measurements in zeolites is similar to the uptake and chromatographic methods (i.e., a step change or a pulse injection in the feed is made and the response curve is recorded). It is recommended to operate with dilute systems and low zeolite loadings. For an isothermal system when the uptake rate is influenced by intracrystalline diffusion, with only a small concentration gradient in the adsorbed phase (constant diffusivity), solutions of the transient diffusion equation for various geometries have been given (ii). Adsorption and diffusion of o-xylene, / -xylene, and toluene in HZSM-5 were found to be described well by a one-dimensional model for diffusion in a slab geometry, represented by Eq. (7) (72) ... 

Since the charge is injected in a very short time (< 1 Jts), measurement often can be completed before diffusion limitation hn ij become significant. In this respect the charge-injection (coulostatfc) ii method is similar to the double-pulse galvanostatic method, except lh< f one has more freedom in the choice of the parameters of the pulse, sinot there is no need to match it to the second pulse. 

The dependence of HETP upon solution flow rate when exchanging the H -Na pair of ions between 0.2 M chloride solution and cation exchanger, KU-2 x 8, with beads 0.25-0.50 mm in diameter, has been compared in the literature for columns of different types [76,84]. The pulse method which has been used possesses the advantage that with the pulsed injection of a small amount of substance all physicochemical and hydrodynamic characteristics of the system remain invariably determined by the primary substance, Na" " ion in this case. Dynamic parameters obtained characterize the process when the concentration range of impurity is low. 

A possibility to reduce the influence of column efficiency on the results obtained by the ECP method is to detect the position of the peak maximum only, which is called the peak-maximum or retention-time method. Graphs like Fig. 6.23 are then achieved by a series of pulse injections with different sample concentrations. The concentration and position of the maximum is strongly influenced by the adsorption equilibrium due to the compressive nature of either the front or the rear of the peak (Chapter 2.2.3). Thus, the obtained values are less sensitive to kinetic effects than in the case of the ECP method. The isotherm parameters can be evaluated in the same way as described in Section 6.5.7.6, but the same limitations have to be kept in mind. For some isotherm equations, analytical solutions of the ideal model can be used to replace the concentration at the maximum (Golshan-Shirazi and Guiochon, 1989 and Guiochon et al., 1994b). Thus, only retention times must be considered and detector calibration can be omitted in these cases. 

The minor disturbance or perturbation method relies on equilibrium theory too and was first suggested by Reilley et al. (1962). As known from linear chromatography, the retention time of a small pulse injected into a column filled with pure eluent can be used to obtain the initial slope of the isotherm. This approach is expanded to cover the whole isotherm range. For the example of a single-component system (Fig. 6.24) the procedure is as follows The column is equilibrated with a concentration ca and, once the plateau is established, a small pulse is injected at a time fstart a and a pulse of a different concentration is detected at the corresponding retention time tR a. 

Figure 3.38 Typical chromatograms obtained in the determination of equilibrium isotherms by pulse chromatographic methods, (a) Injection on a concentration plateau, and response of a selective detector for a tracer, (b) Response of a nonselective detector for the tracer injection made in (a), (c) Individual profiles of the labeled tracer (gray line) and the unlabeled component (black line).

The principle of this pulse method and its general equations are easily extended to the case of several components in a mixture. The method was used by Lindholm et al. [24] to determine the quaternary isotherms of the enantiomers of methyl- and ethyl-mandelate on the chiral phase Chiral AGP. One of the serious roadblocks encountered in the use of the pulse tracer method is that the amplitudes of most of the system peaks decrease rapidly when the plateau concentration increases. Since the signal noise increases in the same time, it becomes rapidly impossible to make any accurate measurements of the retention time of these peaks. On the basis of fundamental work by Tondeur et al. [114], the origin of this variation of the relative intensity of the system peaks was explained by Forss n et al. [47], who then derived an effective rule to determine the composition of a perturbation pulse that generates system peaks that are detected easily. The concentrations of the components in the injected perturbation pulse should... 

In most cases, chromatography is performed with a simple initial condition, C(f = 0,z) = q t = 0,z) = 0. TTie column is empty of solute and the stationary and mobile phases are under equilibrium. There are some cases, however, in which pulses of solute are injected on top of a concentration plateau (see Chapter 3, Section 3.5.4). The behavior of positive concentration pulses injected xmder such conditions is similar to that of the same pulses injected in a column empty of solute and they exhibit similar profiles. Even imder nonlinear conditions (high plateau concentration), a pulse that is sufficiently small can exhibit a quasi-linear behavior and give a Gaussian elution profile. Its retention time is linearly related to the slope of the isotherm at the plateau concentration. Measuring this slope is the purpose of the pulse method of measurement of isotherm data. Large pulses may also be injected and they will give overloaded elution profiles similar to those obtained with a column empty of solute. 

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