Adsorption prediction

Like the James and Healy ( ) model, the VSC-VSP model also requires an estimate of the magnitude of chemical interactions, which usually must be determined by comparison of experimental data with adsorption predicted at various values of AGpi. ... 

One method of checking whether a model (e.g., molecular adsorption versus dissociative adsorption) predicts the behavior of the experimental data is to linearize the model s equation and then plot the indicated variables against one another. For example. Equation (10-7) may be arranged in the form... 

Theories of macromolecular adsorption predict that film thickness should increase as the square root of the molecular weight (Frisch and Simha, 1957), and this has frequently been verified (Stromberg et al., 1965 Rowland and Eirich, 1966). The sparse data for proteins do not permit conclusions regarding molecular weight dependence of film thickness although the limited results in Table VIII indicate that the capacities do appear to be greater for the larger proteins. 

Pan, H., Ritter, J.A., andBalbuena, P.B. (1999). Binary isosteric heats of adsorption predicted from density functional theory. Langmuir, 15, 4570-78. 

Several theoretical studies of natural gas storage on activated carbons have been undertaken. A molecular simulation of CH4 adsorption predicts that the maximum storage capacity by a palletized and a monolith activated carbon will be 146 and 209m /m, respectively [43]. Nonisothermal fiU-discharge and dynamics of CFI4 ad(de)sorption in ANG systems have also been evaluated [44]. 

The data presented in columns (3) and (4) of Figure 6 illustrate the effea of lithium and fluoride Kd mass action equations on the simulation of system equilibrium. In colunrn (3) of Thble ly where the Li-Kd constant was used to simulate adsorption, predicted and observed concentrations of lithium match quite closely. However, fluoride levels are overestimated. In column (4), where the F-Kd constant was used to simulate adsorption, the match between predicted and observed fluoride in solution is improved. In this case, however, the predicted concentration of lithium in the leachate is overestimated. 

Although different definitions and names for this phenomenon have been proposed, the most general definition (accepted by lUPAC as well) is an operative one defining specific adsorption as the deviation from the extent of the adsorption predicted by GC theory. 

Hwang et al. synthesized poly(vinylphosphonic acid-co-methaciylic acid) microbeads by suspension polymerization, and they investigated the adsorption properties with indium. The maximum adsorption predicted by the Langmuir adsorption isotherm model was greatest at a 0.5 mol ratio of vinylphosphonic acid. The adsorption capacity of indium was... 

To examine flic monovalent cation adsorption equation behavior we will begin by comparing adsorption predicted by the quadratic adsorption equation (111) and approximate linear solution equation (113). In both cases we will assume ideal adsorption behavior by setting activity coefficient quotients to unity, = 1. 

Having derived the cation adsorption equations, it will now be of interest to examine how adsorption varies with the variables and constants in those equations. As a first example, the role of three variables and constants on cation adsorption predicted by Eq. (114) can be examined for ideal adsorption where the activity coefficient quotients have been set to unity. The role of activity coefficient quotients on adsorption will be examined later and in Chapter 4. 

Because the polymer adsorption is close to the particle deposition time (cf. Equations 1.2 and 1.8), both processes take place simultaneously. However, colloids can only deposit on polymer patches on the fibers, that is, after polymer adsorption has occurred. Notice that Equation 1.7, combined with Equation 1.1 for polymer adsorption predicts that at short times the deposition increases quadrati-cally (0 oc f ). When polymers are added before the fillers, 6p and thus the deposition efficiency is constant and does not depend on time in such cases the initial kinetics are linear in time. 

Equation X-S3 has been found to fit data on the adsorption of various vapors on low-energy solids, the parameters a and a being such as to predict the observed d [135, 148]. 

Figure A3.10.25 Arrhenius plots of CO oxidation by O2 over Rli single crystals and supported Rli/Al203 at PCO = PO2 = 0.01 atm [43]. The dashed line in the figure is the predicted behaviour based on the rate constants for CO and O2 adsorption and desorption on Rli under UHV conditions.

The partition coefficient and aqueous solubility are properties important for the study of the adsorption, distribution, metabolism, excretion, and toxicity (ADME-Tox) of drugs. The prediction of the ADME-Tox properties of drug candidates has recently attracted much interest because these properties account for the failure of about 60 % of all drug candidates in the clinical phases. The prediction of these properties in an early phase of the drug development process could therefore lead to significant savings in research and development costs. 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

An example of using one predicted property to predict another is predicting the adsorption of chemicals in soil. This is usually done by first predicting an octanol water partition coelficient and then using an equation that relates this to soil adsorption. This type of property-property relationship is most reliable for monofunctional compounds. Structure-property relationships, and to a lesser extent group additivity methods, are more reliable for multifunctional compounds than this type of relationship. 

If the region FGH of the isotherm represents the filling of all the pores with liquid adsorbate, then the amount adsorbed along to plateau FGH, when expressed as a volume of liquid (by use of the normal liquid density) should be the same for all adsorptives on a given porous solid. This prediction is embodied in a generalization put forward many years ago by Gurvitsch and usually known as the Gurvitsch rule. 

A major difficulty in testing the validity of predictions from the DR equation is that independent estimates of the relevant parameters—the total micropore volume and the pore size distribution—are so often lacking. However, Marsh and Rand compared the extrapolated value for from DR plots of CO2 on a series of activated carbons, with the micropore volume estimated by the pre-adsorption of nonane. They found that except in one case, the value from the DR plot was below, often much below, the nonane figure (Table 4.9). 

When the values of the BET monolayer capacity calculated from Type III isotherms are compared with independent estimates (e.g. from nitrogen adsorption) considerable discrepancies are frequently found. A number of typical examples are collected in Table 5.1. Comparison of the value of the monolayer capacity predicted by the BET equation with the corresponding value determined independently (columns (iv) and (v)) show that occasionally, as in line 6, the two agree reasonably well, but that in the majority... 

A PVDF membrane filter has been shown to remove >10 particles of vims for vimses >50 nm independent of fluid type (8). Vimses smaller than 50 nm are not removed as efficientiy but are removed in a predictable manner which correlates to the vims particle size. The chemistry of the suspending fluid affects titer reduction for vimses <50 nm owing to other removal mechanisms, such as adsorption, coming into play. The effects of these other mechanisms can be minimized by using filtration conditions that minimize adsorption. 

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

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