Equilibrium, adsorption and

If we divide equation (2.31) by the term (1 + KiPb/e), we can see that all convective and diffusive transport is retarded by equilibrium adsorption and desorption. Thus, a retardation coefficient is defined ... 

A sharp separation results in two high purity, high recovery product streams. No restrictions are placed on the mole fractions of the components to be separated. A separation is considered to be sharp if the ratio of flow rates of a key component in the two products is >10. The separation methods that can potentially obtain a sharp separation in a single step are physical absorption, molecular sieve adsorption, equilibrium adsorption, and cryogenic distillation. Chemical absorption is often used to achieve sharp separations, but is generally limited to situations in which the components to be removed are present in low concentrations. 

The theory of equilibrium adsorption and kinetics of adsorption upon the surface of adsorbents have been thoroughly treated in the Russian literature since experimental results were obtained which did not agree with Langmuir s initial assumptions (1) that the surface of the adsorbent is energetically uniform (2) that the adsorbed particles do not interact with one another (3) that the surface is covered by only a monolayer of the adsorbate. If the third assumption is retained then three alternative possibilities are offered (a) assumption (1) is rejected and assumption (2)... 

The two types of surface, GB and PVPyr, differ in the effect of electrolyte on heparin adsorption. On GB, the heparin adsorption is unchanged between 0.15M and 0.5M NaCl, but drops by half at 1.0M on PVPyr the adsorption is unchanged between 0.05M and 0.15M, but drops to close to zero at 0.5M. These results were all obtained in adsorption sacks. Autoradiographs indicated that we had not found the conditions for uniform adsorption, although logically adsorption can be expected to be more uniform under conditions in which initial strike can be prevented, or leveled by equilibrium adsorption and desorption during longer exposure. 

TABLE 15 Equilibrium Adsorption and Desorption Results for Substituted Phenols on a Commercial Activated Carbon"... 

FIG. 12 Adsorption of a poly electrolyte (zp = — 1) on an uncharged surface as a function of time for various 1-1 electrolyte concentrations (indicated as volume fractions Balt). In (a) the adsorption is given for short times, in (b) for long times (on a logarithmic scale). Endpoints in (b) are for equilibrium adsorption and a polymer concentration of 300 mg L 4 (poiymer = 1CT4). (Calculated data from Ref. 14.)... 

To estimate x, the decrease in equilibrium adsorption and the actual adsorption rate according to the electrostatic phenomena, have to be considered. The application of Boltzmann s law assumes equilibrium condition of the DL and neglects any transport within the diffuse layer. Thus, the classic Boltzmann law cannot be used to describe the distribution of adsorbing ions within the double layer in non-equilibrium systems. The presence of any ionic flux is connected with a non-equilibrium state of the DL and the approach given by Overbeek (1943) in his theory of electrophoresis has to be considered. In that theory, the non-equilibrium of the DL causes non-linear dependencies of electrophoresis on the electrokinetic potential, in contrast to the theory of Smoluchowski where this effect is not allocated for. The importance of the non-equilibrium state of the DL for many other surface phenomena was emphasised by Dukhin Deijaguin (1974), Dukhin Shilov (1974), and Dukhin (1993). 

The interface between two immiscible liquids is used as a characteristic boundary for study of charge equilibrium, adsorption, and transport. Interfacial potential differences across the liquid-liquid boundary are explained theoretically and documented in experimental studies with fluorescent, potential-sensitive dyes. The results show that the presence of an inert salt or a physiological electrolyte is essential for the function of the dyes. Impedance measurements are used for studies of bovine serum albumin (BSA) adsorption on the interface. Methods for determination of liquid-liquid capacitance influenced by the presence of BSA are shown. The potential of zero charge of the interface was obtained for 0-200 ppm of BSA. The impedance behavior is also discussed as a function of pH. A recent new approach, using a microinterface for interfacial ion transport, is outlined. 

J. Blakely and J. Shelton. Equilibrium Adsorption and Segregation. In J. Blakely, editor. Surface Physics of Materials, Volume 1. Academic Press, New York, 1975. 

While many theoretical studies and models consider the general case of adsorption at a liquid-air interface, the vast majority of experimental work has been carried out with aqueous solutions. Data for other air-solvent interfaces are sparse, with most results being related to crude-oil systems. Some equilibrium adsorption and aggregation studies have involved nonaqueous solvents, but kinetic data are lacking. 

A non-equilibrium adsorption and desorption isotherm at 250, 300, 350, 400, 450 or 500 °C was measured by taking differential pressure steps of 20 + 5 torr between 65 and 300 torr and 50 + 5 torr between 300 and 980 torr (27 steps up and 27 steps down), waiting 45 min at each step, and proceeding in this manner until periodic behavior was realized. This produced Langmuirian-shaped isotherms under non-equilibrium conditions. The absolute and the dynamic working capacities of CO2 on K-promoted HTlc were extracted from these non-equilibrium isotherms. 

Figure 1. Dynamic non-equilibrium adsorption and desorption isotherms at 250, 300, 350, 400, 450 and 500 °C for CO2 on K-promoted HTlc at the periodic state and non-equilibrium absolute capacity for CO2 on K-promoted HTlc obtained from these results at 980 torr.

With two polymers of different chemical type, kinetic studies have shown that equilibrium adsorption and desorption are reached more rapidly than normally associated with polymer adsorption. Botham and Thies found that poly(vinyl acetate) (molecular weight 28000) could displace polystyrene (molecular weight 105 000) within one hour. This displacement study confirms the expected greater energy of the carbonyl group s interaction with silica compared with that of styrene. It is also demonstrated by the results of the competitive adsorption of polystyrene and poly(methyl methacrylate) on to silica. Here it was shown that the latter polymer was adsorbed in strong preference to the former indeed, no polystyrene was adsorbed until the poly(methyl methacrylate) had been completely removed from the solution. 

For the chemisorption of hydrogen on the catalyst, Emmett et al found a complex behavior [163, 380, 381]. Adsorption of H2 on the catalyst was detected at — 90°C and above + 100 °C [381]. Transients in the adsorption when the temperature is suddenly changed in the range 0-210 °C has also been observed by others [382]. Presumably this behavior is caused by two reactions where the low temperature reaction is a weakly exothermic equilibrium adsorption and the high temperature reaction is a reaction limited by a high activation energy. 

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