Desorption coefficient, calculation

The desorption and termination constants were calculated for a copolymer from the corresponding homopolymer constants as discussed in Nomura and Fujita (12.) The homopolymer desorption coefficients were calculated from the appropriate chain transfer constants and radical diffusivities in the aqueous and polymer phases using an extension of the desorption theory developed by Nomura and Fujita (12.). The homopolymer termination constants were corrected for the Trommsdorff effect by using the Friis and Hamielec (12) correlation. 

Arve and Liapis [34] suggest estimating the parameters characterizing the intraparticle diffusion and the adsorption-desorption step mechanisms of affinity chromatography from the experimental data obtained in a batch system. The numerical simulations of the chromatographic process will use the values of the parameters of the adsorption isotherm and those of the effective pore diffusion as determined from stirred tank experiments together with the film mass transfer coefficients calculated from chemical engineering expressions found in the literature. 

If absorption measurements are made on samples, which initially contain no water, by immersing them in salt solutions of different concentrations, the effective absorption diffusion coefficient can be calculated. These measurements are followed by desorption experiments in which the samples are dried by blowing air across both major surfaces and the effective desorption coefficient is calculated. The diffusion coefficients obtained from such absorption and desorption measurements are shown in Table II. It is evident that the ratio of the diffusion coefficient obtained from desorption to that from absorption measurements increases as the concentration of water in the rubber, C, Increases. The diffusion coefficient obtained from a desorption experiment can only be expected to be greater than that from an absorption experiment if D decreases with increasing liquid concentration (3). 

For sorption/desorption rate curves, a good estimation of integral diffusion coefficient can be obtained by taking the average of the diffusion coefficients calculated from first slope for the integral sorption (DJ and desorption (D ) cycle, [8]... 

Figure 6 shows the pressure dependence of diffusion coefficients calculated from permeation, sorption, and desorption rate curves for CO2 in PI2080. The average values of diffusion coefficients from sorption and desorption rate curves D y are in fair agreement with that from permeation rate curve D. The solid line in Figure 6 was computed from Equation 14... 

Table 6.3 collects the computed values of crit well as the activation energies and preexponential factors for the dissociation and desorption of CH4 and CD4 on the nickel atom. The activation energy has been computed from the rate constants using expression (4.131b). Table 6.4 gives the sticking coefficients, calculated using the hard sphere preexponential... 

Having estimated the sticking coefficient of nitrogen on the Fe(lll) surface above, we now consider the desorption of nitrogen, for which the kinetic parameters are readily derived from a TPD experiment. Combining adsorption and desorption enables us to calculate the equilibrium constant of dissociative nitrogen adsorption from... 

The reaction is carried out in close-loop reactor connected to a mass spectrometer for 1S02, 180160 and 1602 analyses as a function of time [38], The gases should be in equilibrium with the metallic surface (fast adsorption/desorption steps 1 and f ) If the bulk diffusion is slow (step 6) and the direct exchange (step 5) does occur at a negligible rate, coefficients of surface diffusion Ds can be calculated from the simple relationship between the number of exchanged atoms Ne and given by the model of circular sources developed by Kramer and Andre [41] ... 

The strength of the Bronsted (BAS) and Lewis (LAS) acid sites of the pure and synthesized materials was measured by Fourier transformed infrared spectroscopy (ATI Mattson FTIR) by using pyridine as a probe molecule. Spectral bands at 1545 cm 1 and 1450 cm 1 were used to indentify BAS and LAS, respectively. Quantitative determination of BAS and LAS was calculated with the coefficients reported by Emeis [5], The measurements were performed by pressing the catalyst into self supported wafers. Thereafter, the cell with the catalyst wafer was outgassed and heated to 450°C for lh. Background spectra were recorded at 100°C. Pyridine was then adsorbed onto the catalyst for 30 min followed by desorption at 250, 350 and 450°C. Spectra were recorded at 100°C in between every temperature ramp. 

The diffusion parameter calculated by the root time method is an average parameter, and is generally considered to be operative over the range of time from initial diffusion flux to near steady state flux conditions. The method is applicable for the situation where adsorption and desorption occur, and for various pH values of the influent. The closer (DE) is to (DB) in Fig. 5 d, the greater is the accuracy of the D coefficient. It is important to note that in the case of low pH values of the influent, desorption of cations from a clay soil could produce conditions where C2 > C1. Accordingly, the experimental values for relative change in concentration would then become negative. 

Powder Apparent activation energy of desorption, (kJ/mol) Coefficient of fit in the Arrhenius equation Kinetic curves at temperatures taken for calculation (°C) Activation... 

As shown in Fig. 2.43b, the enthalpy of absorption and desorption calculated from the Van t Hoff plots using the mid-plateau pressures of PCT curves in Fig. 2.43a, which are listed in Table 2.18, is equal to -72 and 83 kJ/mol, respectively. The value of entropy is 138 and 151 J/mol K for absorption and desorption, respectively. The enthalpy value for absorption is very close to the values found in the literature for MgHj as discussed in Sect. 2.1.2 and 2.1.3. Surprisingly, however, the enthalpy of desorption at 83 kJ/mol is much greater than the former and also greater than the enthalpy of desorption of the as-received and activated MgH as shown in Fig. 2.11. The coefficients of fit are excellent and give good credibility to the obtained values. 

A C.P.D. method was adopted by Bosworth and Rideal (95, 119) to investigate the evaporation of Na from a W filament. Desorption was accompanied by a negative drift in the S.P. when the coated filament was held at a temperature in the range 610° to 795° K., and the resulting S.P.-time curves were converted into coverage-time curves by the use of calibration data previously obtained. The results represent the mutual effect of adsorption and desorption processes on the W filament. Hence, the heat of evaporation E wav iiaay be calculated from the temperature coefficient of... 

The rate of H2Oz consumption and the OH production were directly related to total iron concentration. The concentrations of hydroxyl radical produced were controlled by the rate of reaction with dissolved constituents. Rate constants for adsorption (ka) and desorption (kd) of PCBs from particles were calculated by regression of data from 1.5 to 5 hr. Adsorption rate constants were estimated from Equation (6.130) assuming that the partitioning rate constants between 2 and 5 hr without OH could be used for calculation of equilibrium partition coefficients Ky)... 

Calculations by the author and Kiperman (18) have shown that both interpretations of z are limiting cases and for z to possess the usual meaning of the relative adsorption coefficient, it is necessary that the desorption rate constant ke of the unchanged reactant molecules exceed the rate constant k of the dehydrogenation. 

Figure 5.8 (Bunzl et al., 1976) shows the initial rates of sorption and desorption during the first 10 s of exchange and corresponding half times for Pb2+, Cu2+, Cd2+, Zn2+, and Ca2+ by H-saturated peat using the same concentrations of metal and H30+ added for the experiments shown in Fig. 5.7. The absolute initial rates of sorption decreased in the order Pb > Cu > Cd > Zn > Ca, which is the order observed for the calculated distribution coefficients. This indicates that the higher the selectivity of peat for a given metal ion, the faster the initial rate of sorption. The relative rates of sorption, as shown by half-times (Fig. 5.8), shows that Ca2+ was sorbed the fastest, followed by Zn2+ > Cd2+ > Pb2+ > Cu2+. Thus, even though the absolute rate of Ca2+ adsorption by peat was low, the relative rate was comparatively high, since the total amount of Ca2+ adsorbed was small. The relative rates of desorption, as illustrated by the half-times, show longer times for Pb2+, Cu2+, and Ca2+ but shorter ones for Cd2+ and Zn2+.

Geochemical models of sorption and desorption must be developed from this work and incorporated into transport models that predict radionuclide migration. A frequently used, simple sorption (or desorption) model is the empirical distribution coefficient, Kj. This quantity is simply the equilibrium concentration of sorbed radionuclide divided by the equilibrium concentration of radionuclide in solution. Values of Kd can be used to calculate a retardation factor, R, which is used in solute transport equations to predict radionuclide migration in groundwater. The calculations assume instantaneous sorption, a linear sorption isotherm, and single-valued adsorption-desorption isotherms. These assumptions have been shown to be erroneous for solute sorption in several groundwater-soil systems (1-2). A more accurate description of radionuclide sorption is an isothermal equation such as the Freundlich equation ... 

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