Thermodynamic parameters of adsorption

Very often thermodynamic parameters of adsorption, calculated from different isotherms and reported in the literature, can scarcely be compared because the standard-state conditions used in the calculation are not specified. 

In contrast to this, there is little information available (11) on the thermodynamics of adsorption of alkyl betaines and no data on the thermodynamic parameters of adsorption or micellization for sulfobetaines. 

Standard Thermodynamic Parameters of Adsorption. Table IV lists the standard thermodynamic parameters of adsorption. Values have been... 

TABLE 2-3 Standard Thermodynamic Parameters of Adsorption for Surfactants at the Aqueous Solution-Air Interface or Aqueous Solution-Hydrocarbon Interface"... 

When minute amounts of solute are adsorbed, the adsorption process can be described by the initial part of the adsorption isotherm, which is practically linear. Under these conditions Henry s law applies. It is then possible to relate the thermodynamic parameters of adsorption, such as the variation in free energy upon adsorption of the solute at zero coverage (AG°), to the retention volume of the probe (Vn) ... 

J. He, S. Hong, L. Zhang, E Gan, Y.-S. Ho, Equilibrium and thermodynamic parameters of adsorption of methylene blue onto rectorite. Fresenius Environ Bull 2010,19,2651-2656. 

The thermodynamic parameters of adsorption of nitrophenols on highly purified graphite from buffered aqueous solution have been tabulated by Kozlov and Glushchenko. The adsorption isotherms were determined at 293, 308, and 323 K by a chromatographic technique. AG ds. is the quantity defined in equation (56), and the differential enthalpy was calculated from [3 In C2/3(1/T)]r = q/R (see ref. 3 p. 68). It is not stated how c was calculated from the observed adsorption. They argue that because nitrophenols are essentially dissociated when they adsorb at pH 6.5 the entropy of adsorption includes contributions arising from an entropy of ionization and entropy of hydration. In another paper Avramenko, Glushchenko, and Kozlov have studied adsorption at two pH s (1.60 and 6.50) of a series of nitrophenols from... 

The equation has been found to apply for the adsorption of nitrogen, saturated hydrocarbons, benzene and cyclohexane over the relative pressure range 10- to 10-f on a range of microporous samples [57]. However, the equation needs correction for adsorbate compressibility [58,59]. It has also been used for determining the micropore volume of carbons [60-66] and the thermodynamic parameters of adsorption [67-70]. 

Obviously, thermodynamic quantities AHdes, ASdes and AGdes) for the activated process such as desorption can be extracted from the data obtained from desorption experiments. Importantly, since the adsorption is spontaneous process (it does not need the energy of activation), the heat of adsorption equals, in general, the activation energy for desorption. Hence, desorption experiments provide also thermodynamic parameters of adsorption. 

Recent studies describe the use of cyclic voltammetry in conjunction with controlled-potential coulometry to study the oxidative reaction mechanisms of benzofuran derivatives [115] and bamipine hydrochloride [116]. The use of fast-scan cyclic voltammetry and linear sweep voltammetry to study the reduction kinetic and thermodynamic parameters of cefazolin and cefmetazole has also been described [117]. Determinations of vitamins have been studied with voltammetric techniques, such as differential pulse voltammetry for vitamin D3 with a rotating glassy carbon electrode [118,119], and cyclic voltammetry and square-wave adsorptive stripping voltammetry for vitamin K3 (menadione) [120]. 

Lin and Yang (1987) also calculated the thermodynamic parameters of diazepam for micellar solubilization in Pluronic surfactant solutions at different temperatures (Table 13.4). For all systems, AG was negative, indicating micellar solubilization was spontaneous. The sign of entropy has been associated with the location of solubilized molecules within the micelles. Positive values have been observed for molecules embedded in the micelle center and negative values for adsorption of the molecules on the micelle surface. The results in this paper indicate that in the F-108 and F-88 Pluronics, diazepam molecules can penetrate into the micelle interior, whereas for F-68 and lower concentrations of F-88, diazepam is adsorbed on the micelle surface without penetration into the micellar core. 

Once the thermodynamic parameters of stable structures and TSs are determined from quantum-chemical calculations, the next step is to find theoretically the rate constants of all elementary reactions or elementary physical processes (say, diffusion) relevant to a particular overall process (film growth, deposition, etc.). Processes that proceed at a surface active site are most important for modeling various epitaxial processes. Quantum-chemical calculations show that many gas-surface reactions proceed via a surface complex (precursor) between an incident gas-phase molecule and a surface active site. Such precursors mostly have a substantial adsorption energy and play an important role in the processes of dielectric film growth. They give rise to competition among subsequent processes of desorption, stabilization, surface diffusion, and chemical transformations of the surface complex. 

On the basis of those discussed here, we can say that the thermodynamic parameters of ion exchange determined by linear isotherm equations are not correct. We determine the mechanism of sorption (ion exchange and/or adsorption) and then choose the isotherm equation. When simultaneous interfacial processes take place, the dominant process, if any, has to be selected or experimentally separated, or Equation 1.119 should be used. 

A further advantage of an SCM approach is that thermodynamic parameters for adsorption reactions can be compared with the thermodynamic properties of other types of reactions, to assess correlative relations that may be used to predict the behaviour of chemical species for which experimental data are currently lacking. In Fein et al. (1997) the authors compared model results for equilibrium constants of metal-bacteria adsorption reactions, and found a strong correlative relationship between these values and corresponding equilibrium constants for metal-oxalate and metal-tiron (4,5-dihydroxy-m-benzenedisulphonic acid) aqueous... 

Comparison of adsorption thermodynamic parameters of the test compounds benzene - on the studied adsorbents... 

In order to better understand the equilibria in the interfacial layer, it is desirable to obtain the thermodynamic parameters of the reactions involved in the surface charging processes. It is not a simple task to determine the enthalpy of specified surface reactions. At first the mechanisms of the reactions are not always clear, and secondly the situation is often so complicated that several contributions can hardly be distinguished. In the most simple case, when association of counterions does not take place (low ionic strength), one can use measurements of the temperature dependency of the point of zero charge [48-56]. The slope of the pHp c vs. reciprocal thermodynamic temperature yields the enthalpy value dependent on the assumed stoichiometry of the processes. Application of the adsorption or amphotheric or coordination concept yield [22]... 

In Table 5.4 we summarize the expressions for the surface free energy, F, and chemical potential pij, for several thermodynamic models of adsorption. We recall that the parameter F is defined in different ways for the different models. On the other hand, the parameter K is defined in the same way for all models, specifically by Equation 5.3. The expressions in Tables 5.2 through 5.4 can be generalized for multicomponent adsorption layers. - ... 

Thermodynamic parameters of catalysts are highly relevant for practical applications. In particular, surface energies and acid-base properties of catalysts are of high interest since they reflect properties of active sites involved in the catalytic process and the initial adsorption step. 

The use of temperature as a variable yields information on the thermodynamics of the adsorption-desorption process. A thermodynamic parameter of great importance measurable by GC techniques is the heat of adsorption. It provides a quantitative measure of the interactions occurring between the adsorbate and the adsorbent. The solute heat of adsorption at zero surface coverage (AH°)is related to the retention data via... 

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