Equilibrium adsorption density

Adsorption and electrokinetic effects of amino acids, solid-aqueous interface, 311-26 Adsorption density, equilibrium PAA at various pH values, 299f PAA on hematite, 304f SDS with and without polymer, 298f,303f... 

The trapping efficiency of polymeric, microporous adsorbents [e.g., polystyrene, polyurethane foam (PUF), Tenax] for compound vapors will be affected by compound vapor density (i. e., equilibrium vapor pressure). The free energy change required in the transition from the vapor state to the condensed state (e.g., on an adsorbent) is known as the adsorption potential (calories per mole), and this potential is proportional to the ratio of saturation to equilibrium vapor pressure. This means that changes in vapor density (equilibrium vapor pressure) for very volatile compounds, or for compounds that are gases under ambient conditions, can have a dramatic effect on the trapping efficiency for polymeric microporous adsorbents. 

Figure 4. Equilibrium adsorption densities of polyacrylic acid on hematite at various pH values. Reproduced with permission from Ref. 22. Copyright 1983, Colloids and Surfaces.

At equilibrium surfactant concentrations of less than 0.0003 M SDS where the hematite surface is still positively charged, adsorption of surfactant follows its normal pattern due to the electrostatic forces which provide the driving force for adsorption. Sufficient effective surface area must be available for this level of SDS adsorption density. As surfactant adsorption... 

Figure 7. Equilibrium adsorption densities of polyacrylamide on hematite at pH 4.1 and 0.001 M NaCl.

Adsorption and ElectroKlnetic Behavior of Rutile. Isotherms for the adsorption of lysine, prollne and glutamic acid on rutile (1102) are given in Figure 1. There is no simple relationship between the adsorption density and the equilibrium concentration. The adsorption does not obey the Langmiur, Freundllch or Stern-Grahame relationships. The leveling-off of the adsorption... 

Fig. 34 Plot of equilibrium concentration of NP-10 versus adsorption density, J3/J1 of pyrene in bulk and at sUica-water interface (pH = 5.0 0.2, J = 0.01 M NaCl, Temp = (23 0.2°C), S/L = 0.01)...

This is the important Gibbs adsorption isotherm. (Note that for concentrated solutions the activity should be used in this equation.) Experimental measurements of y over a range of concentrations allows us to plot y against Inci and hence obtain Ti, the adsorption density at the surface. The validity of this fundamental equation of adsorption has been proven by comparison with direct adsorption measurements. The method is best applied to liquid/vapour and liquid/liquid interfaces, where surface energies can easily be measured. However, care must be taken to allow equilibrium adsorption of the solute (which may be slow) during measurement. 

We saw in connection with the discussion of Figure 9.5 that measurable gas adsorption occurs even at gas pressures as low as 10 10 torr. As a matter of fact, the two-dimensional density of the adsorbed molecules is not low enough to conform to the two-dimensional ideal gas law even when the pressure is on the order of 10 10 torr. A question of considerable practical importance, then, is how low the pressure must be for an initially clean surface to remain that way for a reasonable period of time. The above reference to adsorption cites equilibrium data that are not useful for answering questions of rate. 

Fuerstenau") was the first who used the Stern-Grahame model of EDL to describe the adsorption of long-chain surfactants for the equilibrium in heterogeneous systems. The adsorption density in the Stem plane is given by the equation... 

The study of adsorption kinetics of a surfactant on the mineral surface can help to clarify the adsorption mechanism in a number of cases. In the literature we found few communications of this kind though the adsorption kinetics has an important role in flotation. Somasundaran et al.133,134 found that the adsorption of Na dodecylsulfonate on alumina and of K oleate on hematite at pH 8.0 is relatively fast (the adsorption equilibrium is reached within a few minutes) as expected for physical adsorption of minerals with PDI H+ and OH". However, the system K oleate-hematite exhibits a markedly different type of kinetics at pH 4.8 where the equilibrium is not reached even after several hours of adsorption. Similarly, the effect of temperature on adsorption density varies. The adsorption density of K oleate at pH 8 and 25 °C is greater than at 75 °C whereas the opposite is true at pH 4.8. Evidently the adsorption of oleic acid on hematite involves a mechanism that is different from that of oleate or acid soaps. 

The adsorption kinetics was examined according to the change of adsorption density in the time for the equilibrium concentration < CMC. The validity of the proposed adsorption mechanism was verified by using the general kinetic equation ... 

The value of Qst can be determined from the slope of the plot (log c)r against T. Measurements in the system N-dodecylammonium acetate-quartz showed that -AG increased with increasing temperature over the whole concentration range whereas the adsorption density against temperature showed a minimum over the greatest part of the concentration range. In the range of equilibrium surfactant concentrations of 1 - 9 x 10"4 mol 1" the values of - AG 12.55 to 17.58 kJ/mol were found for temperatures between 5 and 45 °C. 

The characteristic effect of surfactants is their ability to adsorb onto surfaces and to modify the surface properties. Both at gas/liquid and at liquid/liquid interfaces, this leads to a reduction of the surface tension and the interfacial tension, respectively. Generally, nonionic surfactants have a lower surface tension than ionic surfactants for the same alkyl chain length and concentration. The reason for this is the repulsive interaction of ionic surfactants within the charged adsorption layer which leads to a lower surface coverage than for the non-ionic surfactants. In detergent formulations, this repulsive interaction can be reduced by the presence of electrolytes which compress the electrical double layer and therefore increase the adsorption density of the anionic surfactants. Beyond a certain concentration, termed the critical micelle concentration (cmc), the formation of thermodynamically stable micellar aggregates can be observed in the bulk phase. These micelles are thermodynamically stable and in equilibrium with the monomers in the solution. They are characteristic of the ability of surfactants to solubilise hydrophobic substances. 

Fig. 38. (a, b) SFG spectra of CO adsorbed on Rh(l 11) at 300K at pressures between 10 and 1000 mbar. (c) Analysis of the on-top CO intensity (surface density), resonance position, and CO coverage as a function of the CO pressure. The open symbols indicate the pressure range of irreversible CO adsorption. The equilibrium CO surface coverage in (c) was calculated from adsorption/desorption kinetics adapted from Pery et al. (314). Copyright (2002) The Combustion Institute. 

Direct measurements of adsorption densities of the labelled anions, performed in dilute aqueous solutions of the corresponding acids, enabled to establish the following order of preferential adsorption H2PO4 > HSO4 > Cl" > CIO4. This sequence, based upon the results of co-adsorption experiments, refers to equilibrium adsorption conditions in the range of pH lower than the PZC of Ti02-... 

No direct adsorption data were available for Na and CL on corundum. Fuerstenau and Modi (18), however, computed the zeta potential, as a function of pH from experimental measurements of streaming potential in NaCl solutions. The value of Pp computed by the triple layer model in HYDRAQL is an approximation of (H). Because C, depends on H, Na, and CF adsorption densities, it was possible to use these data to constrain the equilibrium constants and Cj. The value of pK " was adjusted to force pH zc = 9.1 as observed by Fuerstenau and Modi (18), and p K " + was adjusted to fit the zeta-potential for pH < pH zc Results are shown in Figure 2. 

Chandar et al. (15) measured the adsorption density of dodecylsulfate on corundum at pH = 6.5 in 0.1 M NaCl. The experimental data are adequately described by a model closely analogous to that used for dodecylamine on quartz. In addition to the surface ionization and NaCl binding reactions (Table I), the reactions and equilibrium constants used were ... 

Where represents phthalate ion, which are considered here as potential determining ions. Khl and Kl, are the equilibrium constants, obtained by fit to adsorption data. The adsorption density as a function of phthalate aqueous concentration is illustrated in Figure 2, where the solid line shows SCF/DLM model calculation with log A // , = 16.45, log/i , = 11.28, in addition to the constants for hematite surface hydroxyl species. The model yields a good estimation at higher adsorption densities, but it overestimates the adsorbed organics at lower solution concentration. 

E vs. Aa seems to be most sensitive to product concentrations near the external surface of the catalyst and adsorption/desorption equilibrium constants. I c.surf. I d, surf, and 6>, directly affect the vacant-site fraction on the interior catalytic surface and the rate of reactant consumption. In the previous simulations, product molar densities near the external surface of the catalyst were varied by a factor of 50 (i.e., from 0.1 to 5), and 0, was varied by a factor of 20 (i.e., from 0.05 to 1). The effectiveness factor increases significantly when either 4 c,surf, I d. surf or 6i is larger. E vs. Aa is marginally sensitive to a stoichiometric imbalance between reactants A2 and B, but I B.sur ce was only varied by a factor of 4 (i.e., from 0.5 to 2). A four-fold decrease in the molecular weight of reactant B, which produces two-fold changes in 30b, effective and 5b, does not affect E. 

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