Adsorption parameter

The adsorption transition can be discussed best when looking at the distance of the mean center-of-mass distance (zcm) of the polymer from the surface [Figs. 13.11(a) and (b)] 

One clearly identifies a quite sharp adsorption transition that divides the projection of (zcm) in Fig. 13.11 (a) into an adsorbed (bright) regime and a desorbed (dark) regime. This transition appears as a straight line in the phase diagram and is parametrized by a T. Intuitively, this makes sense since at higher T the stronger Brownian fluctuation is more likely to overcome the surface attraction. 

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The adsorption isotherm in the form (7) should be considered as a reasonable approximation, the more so, as our aim here is not to obtain faithful values of the adsorption parameters but to describe as completely as possible the qualitative behaviour of the NA-water system. It is worth to note here that the use of a polynomial of the form ... 

Having chosen a suitable refrigerant, the best adsorbent must be found. Zeolites, silica gels and chemical adsorbents have been used as well as carbons, but this chapter will concentrate on the carbon adsorbents. An indication as to the range of cop s that can be expected and the influence of the type of carbon used can be obtained by modelling the perfonnance of carbons with a range of adsorption parameters. For this purpose it is preferable to use the Dubinin-Raduschkevich... 

The adsorption behavior of homologous sodium alcohol sulfates at the interface can be characterized by the adsorption isotherms. However, the adsorption parameters of these isotherms are very sensitive to impurities present in the surfactant. Wiinstneck et al. [145] determined the equilibrium values of... 

Figure 4. Modeled U-series date profiles across a 10 ky bone according to the D-A model under constant conditions. The dates are calculated using the closed system assumption. The parameter D/R is the diffusion-adsorption parameter and is related to the water content of the soil, the state of preservation of the bone and aspects of the geochemistry of the burial environment. After Pike et al. (2002). [Used by permission of Elsevier Science, from Pike et al. (2002), Geochim Cosmochim Acta, Vol. 66, Fig. 2, p. 4275.]...

Basically, three types of experiments are carried out for measurement of the adsorption parameters of a given rock sample. 

A comprehensive kinetic model addressing all the findings has not been developed. Some of the reported rate equations consider the self-poisoning effect of the reactant compounds, some other that effect of ammonia, and so on so forth. The reported data is dispersed with a variety of non-comparable conditions and results. The adsorption of the poisoning compounds has been modeled assuming one or two-sites on the catalyst surface however, the applicability of these expressions also needs to be addressed to other reacting systems to verity its reliability. The model also needs of validated adsorption parameters, difficult to measure under the operating conditions. 

Figure 11. Contour plot of the dimensionless time (DMr/>o) needed for Jm to reach l.l/ f in terms of the logarithm of the dimensionless adsorption parameter (Kn/ro), in abscissas, and the logarithm of the dimensionless internalisation parameter (kr /Du), in ordinates. The number on each curve indicates the value of log(Z>Mt/ro). The diagonal (dashed line) corresponds with kAHr0 — DM...

J. Cunningham, G. Al-Sayyed, Factors influencing efficiencies of Ti02-sensitised photodegradation. Part 1. Substituted benzoic adds Discrepancies with dark-adsorption parameters,... 

Adsorption equilibrium constant for species i Estimate of a parameter after ith iteration of nonlinear estimation program Vector of estimated rate and adsorption parameters Vector of initial estimates of K for use in nonlinear least squares... 

Though thermodynamics cannot provide direct insight into the metal/so-lution interface on a microscale, it generates important information about the energies of interaction of metals with the solvent and the solute. Adsorption parameters are of great value to understanding mutual interactions of the system components at the interface. 

The study of thiourea adsorption on an Hg electrode from ethanolic solutions shows that different supporting electrolytes can make a comparison of the adsorption parameters more difficult. The data obtained for various electrolytes (KF, KPFe, LiCl, NH4NO3, and KCNS) suggest that coadsorption, size, and polarizability of ions strongly influence the interfacial behavior of TU, at high concentration of the ions in particular. The effect of the electrolyte on AG° and parameter A in the Frumkin isotherm is illustrated in Table 6. 

Various adsorption parameters for the effective removal of Pb + and ions by using new synthesized resin as an adsorbent from aqueous solutions were studied and optimized. Time-dependent behavior of Pb + and ions adsorption was measured by varying the equilibrium time between in the range of 30-300 min. The percentage adsorption of Pb + plotted in Fig. 26.2 as a function of contact time... 

Leaves of Sumac were used for removal of ions in aqueous solution. Tannins were extracted from the leaves of sumac by extracting with 70% (v/v) acetone-water solution. For the total tarmin determination Folin-Ciocalteu method was used and tannin content was found 27%. Various adsorption parameters for the effective removal of Cu + ions by using sumac leaves as an adsorbent from aqueous solutions were studied and optimized. 

The most critical parameter of reaction (2.144) is the adsorption parameter... 

The physical meaning of the kinetic parameter m is identical as for surface electrode reaction (Chap. 2.5.1). The electrochemical reversibility is primarily controlled by 03 (Fig. 2.71). The reaction is totally irreversible for log(m) < —3 and electrochemically reversible for log(fo) > 1. Between these intervals, the reaction appears quasireversible, attributed with a quasireversible maximum. Though the absolute net peak current value depends on the adsorption parameter. Fig. 2.71 reveals that the quasireversible interval, together with the position of the maximum, is independent of the adsorption strength. Similar to the surface reactions, the position of the maximum varies with the electron transfer coefficient and the amphtude of the potential modrrlation [92]. 

Here, Po = is the dimensionless adsorption parameter representing the adsorption of the O form. The integration factor (Ro)m is defined as ... 

The response of a reversible reaction (2.146) depends on two dimensionless adsorption parameters, Pr and po. When pR = po the adsorbed species accomplish instantaneously a redox equilibrium after application of each potential pulse, thus no current remains to be sampled at the end of the potential pulses. The only current measured is due to the flux of the dissolved forms of both reactant and product of the reaction. For these reasons, the response of a reversible reaction of an adsorbed redox couple is identical to the response of the simple reaction of a dissolved redox couple (2.157), provided Pr = po- As a consequence, the real net peak current depends linearly on /J, and the peak potential is independent of the frequency. If the adsorption strength of the product decreases, i.e., the ratio increases, the net peak current starts to increase (Fig. 2.73). Under these conditions, the establishment of equilibrium between the adsorbed redox forms is prevented by the mass transfer of the product from the electrode surface. Thus, the redox reaction of adsorbed species contributes to the overall response, causing an increase of the current. In the hmiting case, when ]8o —0, the reaction (2.146) simplifies to reaction (2.144). 

Voltammetric features of adsorption coupled EC mechanisms (2.177) [128] and (2.178) [129] are rather unpredictable and deviate strongly from the EQ mechanism of a dissolved redox couple. Their voltammetric behaviour is mainly controlled by the adsorption parameter p, and the dimensionless chemical parameters k"s = j and... 

The edl parameters and adsorption parameters for various electrodes are presented by Lust et al. [24]. 

Adsorption of a condensed 1-hydroxy-adamantane layer at the Hg elec-trode/(Na2S04 or NaF) solution interface has been studied as a function of temperature by Stenina et al. [174]. Later, Stenina etal. [175] have determined adsorption parameters and their temperature dependence for a two-dimensional condensation of adamantanol-1 at a mercury electrode in Na2S04 solutions. They have also studied coadsorption of halide (F , Cl , Br ) anions and 1-adamantanol molecules on Hg electrode [176]. More recently, Stenina etal. [177] have described a new type of an adsorption layer comprising organic molecules of a cage structure condensed at the electrode/solution interface. This phenomenon was discovered for adsorption of cubane derivatives at mercury electrode. 

The interfacial admittance applied to the study of adsorption parameters... 

The determination of the adsorption parameter (Vg) at three temperatures permits the calculation of the free energy, enthalpy, and entropy of adsorption. A plot of log Vg versus 1/T has a slope of -AHa(js/2.3R. AGacjs is obtained by... 

Although reductive dechlorination is modelled either based on an empirical approach or a single site model, TCE dechlorination in the presence of cysteine apparently requires the use of a two-site model. The simulation as shown in Figure 3b indicates that quantitatively, the two-site model proposed here is sufficient for the interpretation of the experimental results. To enhance the predictive capability of the model, further research is needed to determine adsorption parameters independently. 

Heats of reactions were estimated from heats of formations and chemical compositions of feed and product using standard procedures. For REY catalysts, we estimated approximately 130 Btu/lb heat of reaction. The heat of reaction was close to 200 Btu/lb for USY catalysts. These values are in close agreement with reported data (21)- The activation energies for different catalyst types were estimated from our extensive pilot plant data base, and found to be a weak function of catalyst type. The adsorption constants and other kinetic parameters used in these simulations were fitted to a large in-house data base. Typical parameter values are reported in Tables III and V. The kinetic parameters (k-, and Aj) are a strong function of catalyst used, whereas the adsorption parameters were found to be relatively insensitive. One could estimate these parameters even from a limited data base as illustrated below for Catalyst D. 

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