Surface adsorption equilibrium

The foregoing is an equilibrium analysis, yet some transient effects are probably important to film resilience. Rayleigh [182] noted that surface freshly formed by some insult to the film would have a greater than equilibrium surface tension (note Fig. 11-15). A recent analysis [222] of the effect of surface elasticity on foam stability relates the nonequilibrium surfactant surface coverage to the foam retention time or time for a bubble to pass through a wet foam. The adsorption process is important in a new means of obtaining a foam by supplying vapor phase surfactants [223]. 

Adsorption The separation achieved depends in part on the selectivity of adsorption at the bubble surface. At equilibrium, the adsorption of dissolved material follows the Gibbs equation (Gibbs, Collected Works, Longmans Green, New York, 1928). 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

Two important parameters, a and pf arise which depend on the equilibrium and kinetic properties of the surfactant. First, a measures the fractional change in equilibrium surface tension with a fractional change in surfactant adsorption ... 

Pigna M, Colombo C, Violante A (2003) Competitive sorption of arsenate and phosphate on synthetic hematites (in Italian). Proceedings XXI Congress of Societa Italiana Chimica Agraria SICA (Ancona), pp 70-76 Quirk JP (1955) Significance of surface area calculated from water vapour sorption isotherms by use of the B. E. T. equation. Soil Sci 80 423-430 Rancourt DG, Fortin D, Pichler T, Lamarche G (2001) Mineralogical characterization of a natural As-rich hydrous ferric oxide coprecipitate formed by mining hydrothermal fluids and seawater. Am Mineral 86 834-851 Raven K, Jain A, Loeppert, RH (1998) Arsenite and arsenate adsorption on ferrihydrite kinetics, equilibrium, and adsorption envelopes. Environ Sci Technol 32 344-349... 

The differences in time-dependent adsorption behavior between 99% PVAC at 25° and 50°C demonstrate the influence of intra- and intermolecular hydrogen bonding in the adsorption process. The limiting surface pressure of the hydrophobic water-soluble polymer appears to be 33 mN/m, approximately 7 mN/m below that of commonly used surfactants. The rate of attainment of equilibrium surface pressure values is faster if there is uniformity of the hydrophobic segments among the repeating units of the macromolecule. 

Westall, J., 1980, Chemical equilibrium including adsorption on charged surfaces. In M. C. Kavanaugh and J. O. Leckie (eds.), Advances in Chemistry Series 189, American Chemical Society, Washington, DC, pp. 33 14. 

EXTRACT and O-METHYLATED EXTRACT. The sorption of benzene by the extract and the O-methylated extract is characterized by a rapid, initial uptake followed by a very slow approach to equilibrium. Such sorption behavior is very similar to that of glassy polymers. Thus we have chosen to interpret the sorption curves shown in Figures 2 and 3 in terms of the Berens-Hopfenberg model developed for the sorption of organic vapors into glassy polymers.(lS) By doing so, we attempt to correct the total sorption values for surface adsorption in order to calculate x parameters. 

Rau, M. Rieck, D. Evans, J.W. (1987) Investigation of iron oxide reduction by TEM. Metallurgical Transactions 188 257-278 Raven, K.P. Jain, A. Loeppert, R.H. (1998) Ar-senite and arsenate adsorption on ferrihy-drite Kinetics, equilibrium, and adsorption envelopes. Environ. Sci. Techn. 32 344-349 Rea, B.A. Davis, J.A. Waychunas, G.A. (1994) Studies of the reactivity of the ferrihydrite surface by iron isotopic exchange and Moss-bauer spectroscopy. Clays Clay Min. 42 23-34... 

Poskus and Agafonovas [483] have applied radioactive Tl-204 to study its UPD on a polycrystalline gold electrode in alkaline solutions. The potential dependence of the equilibrium surface concentration obtained from the radiometric method has been compared to that calculated from CV. Surface concentration of Tl decreased monotonically as the potential was changed from the more positive Nern-stian values. This dependence exhibited a minimum without reaching zero. At more positive potentials (with respect to the minimum), adsorption of T1+ induced by specifically adsorbed hydroxyl anions occurred. 

The surface of a colloid dispersed in aqueous salt solution was found to have an equilibrium surface electrostatic potential of +80 mV, due to the specific adsorption of Na ions. What is the (chemical) free energy of adsorption of Na ions to this surface ... 

The equilibrium constants for the adsorption of the aldehyde and Schiff s base are Ka = kai/ka-i and Kb = kbi/kb-i respectively. Product C may adsorb but is less competitive than the surface adsorption of the Schiff s base B and aldehyde A. The total surface coverages are expressed as the sum of the adsorbed species and empty sites A -I- B -I- ° = 1. 

The monomolecular conversion of three components has also been considered in some detail by Kallo (30). Rate equations based on Langmuir adsorption were developed assuming a number of different mechanistic schemes including steps in which surface adsorption was not at equilibrium. Since the rate equations developed became complicated, practical application was devoted to cases in which only initial reaction rates were observed, so... 

A multi-component gas solubility model and a multi-component surface adsorption model are generally required to estimate the monomer concentration at active sites. If the latter equilibrium can be neglected then the gas-solubility in the suspending agent determines the monomer concentration near the active site, which changes significantly with temperature and pressure. 

Equilibrium of Adsorption, (a) The Soap Films. The isotherms of adsorption of the organic cations of the soaps are reproduced on the Figure 2. Classical methods (20) are used to obtain the surface densities of the soaps I and IV. 

According to the assumption made, c is identical for all surface sites. Thus, adsorption coefficients of gases A and A are mutually proportional. Equilibrium surface coverage by gas A is... 

Equations D3.5.30 and D3.5.32 are both very valuable. They state that the rate of adsorption can be obtained from plots of the interfacial tension versus either tA- (for t—>0) or lth (for the long-term solution f— >). With these two equations the tool to extract the adsorption rate from experimentally obtained surface tension-time curves is at hand. It should be noted that instead of the Gibbs model, one could use one of the previously mentioned adsorption isotherms such as the Langmuir adsorption isotherm to convert interfacial tension to interfacial coverage data. The adsorption isotherms may be obtained by fitting equilibrium surface tension data versus surfactant concentration. 

When fine powders of vitreous silica, quartz, tridymite, cristobalite, coesite, and stishovite of known particle-size distribution and specific surface area are investigated for their solubility in aqueous suspensions, final concentrations at and below the level of the saturated concentration of molybdate-active silicic acid are established. Experimental evidence indicates that all final concentrations are influenced by surface adsorption of silicic acid. Thus, the true solubility, in the sense of a saturated concentration of silicic acid in dynamic equilibrium with the suspended silica modification, is obscured. Regarding this solubility, the experimental final concentration represents a more or less supersaturated state. Through adsorption, the normally slow dissolution rates of silica decrease further with increasing silicic acid concentrations. Great differences exist between the dissolution rates of the individual samples. 

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