Coefficient, 451 Langmuir

SULFATE ADENYLYLTRANSFERASE (ADP) ADRENODOXIN ADSORPTION ABSORPTION BIOMINERALIZATION MICELLAR CATALYSIS LANGMIUR ISOTHERM Adsorption coefficient LANGMUIR ISOTHERM Adsorption of gases,... 

Spilhaus 8P) treats the shape of falling drops and the variation of the drag coefficient. Langmuir and Blodgett 6P) present a mathematical investigation of water droplet trajectories. 

Michaelis Menten constant (2) mass transport coefficient Langmuir-Blodgett... 

Eads, C.D., Robosky, L.C. NMR studies of binary surfactant mixture thermodynamics molecular size model for asymmetric activity coefficients. Langmuir 1999, 75(8), 2661-2668. 

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

L exposure would produce 1 ML of adsorbates if the sticking coefficient were unity. Note that a quantitative calculation of the exposure per surface atom depends on the molecular weight of the gas molecules and on the actual density of surface atoms, but the approximations inlierent in the definition of tire Langmuir are often inconsequential. 

Another limitation of tire Langmuir model is that it does not account for multilayer adsorption. The Braunauer, Ennnett and Teller (BET) model is a refinement of Langmuir adsorption in which multiple layers of adsorbates are allowed [29, 31]. In the BET model, the particles in each layer act as the adsorption sites for the subsequent layers. There are many refinements to this approach, in which parameters such as sticking coefficient, activation energy, etc, are considered to be different for each layer. 

At low values of the bulk concentration Bcy surface coverage is proportional to this concentration, but at high values it tends toward a limit of unity. This equation was derived by Irving Langmuir in 1918 with four basic assumptions (1) the adsorption is reversible (2) the number of adsorption sites is limited, and the value of adsorption cannot exceed A° (3) the surface is homogeneous aU adsorption sites have the same heat of adsorption and hence, the same coefficient B and (4) no interaction forces exist between the adsorbed particles. The rate of adsorption is proportional to the bulk concentration and to the fraction 1-9 of vacant sites on the surface = kjil - 9), while the rate of desorption is proportional to the fraction of sites occupied Vj = kjd. In the steady state these two rates are equal. With the notation kjk = B, we obtain Eq. (10.14). 

The distribution coefficient assumes that adsorption is linear (i.e., the amount of adsorption is directly proportional to the concentration of the compound in solution) and is actually a special case of the Langmuir and Freundlich isotherms, which are nonlinear.31 32... 

The Langmuir equation has a strong theoretical basis, whereas the Freundlich equation is an almost purely empirical formulation because the coefficient N has embedded in it a number of thermodynamic parameters that cannot easily be measured independently.120 These two nonlinear isotherm equations have most of the same problems discussed earlier in relation to the distribution-coefficient equation. All parameters except adsorbent concentration C must be held constant when measuring Freundlich isotherms, and significant changes in environmental parameters, which would be expected at different times and locations in the deep-well environment, are very likely to result in large changes in the empirical constants. 

Sorption. Capture of neutral organics by non-living particulates depends on the organic carbon content of the solids (9). Equilibrium sorption of such "hydrophobic" compounds can be described by a carbon-normalized partition coefficient on both a whole-sediment basis and by particle size classes. The success of the whole-sediment approach derives from the fact that most natural sediment organic matter falls in the "silt" or "fine" particle size fractions. So long as dissolved concentrations do not exceed 0.01 mM, linear isotherms (partition coefficients) can be used. At higher concentrations, the sorptive capacity of the solid can be exceeded, and a nonlinear Freundlich or Langmuir isotherm must be invoked. 

In this chapter, we consider several simple models of ion sorption and exchange that can be applied within the context of a geochemical model. These models include distribution coefficients, Freundlich and Langmuir isotherms, and ion exchange theory. In the following chapter (Chapter 10), we consider surface com-plexation theory, which is more complicated but in some ways more robust than the models presented here. 

Figure 9.10 (a) and (b) Example of a circular-difference effect from an isotropic Langmuir-Blodgett film composed of enantiomerically pure chiral molecules. Experimental data points are fitted to Eq. (42) (solid curve), (a) The -polarized second-harmonic signal, fit coefficients fs = 0.87 + 0.39z and hs = —0.38. (b) The / -polarized second-harmonic signal, fit coefficients fp = 0.63 — 0.20i, gp = 0.12 + 0.003z, and hp = 1.24. The right- and left-hand circular polarization are indicated by open and filled circles. 

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