Adsorption equation parameters

Determination of the segmental adsorption energy. The determina-tion of x ° is also possible. Since x d can be found from Equation 5 if Xsc an the solvency terms are known, we can add xf° and find x ° by Equation 1. The determination of xf° calls for a separate experiment, e.g., an adsorption isotherm of the displacer from solvent, in the absence of polymer. Following such a scheme we used the values of cr obtained from the displacement isotherms of Figure 3 and 4 to determine segmental adsorption energy parameters Xg° for PVP on silica. The required additional information on xdo was obtained from the initial slopes of dis-... 

Wilson and co-workers developed a statistical mechanical model for single component surfactant adsorption (29-31) and expanded it to a binary system (2,3). Different adsorption curves were generated by varying the Van der Waals interaction parameters. The mixed adsorption equations that were developed were very complex and were not applied to experimental data. 

The methods depend on the theoretical treatment which is used. A majority of them are based on the Generalised Adsorption Isotherm (GAI) also called the Integral Adsorption Equation (LAE). The more recent approaches use the Monte Carlo simulations or the density functional theory to calculate the local adsorption isotherm. The analytical form of the pore size distribution function (PSD) is not a priori assumed. It is determined using the regularization method [1,2,3]. Older methods use the Dubinin-Radushkevich or the Dubinin-Astakhov models as kernel with a gaussian or a gamma-type function for the pore size distribution. In some cases, the generalised adsorption equation can be solved analytically and the parameters of the PSD appear directly in the isotherm equation [4,5,6]. Other methods which do not rely on the GAI concept are sometimes used the MP and the Horvath-Kawazoe (H-K) methods are the most well known [7,8]. 

Where W is the equilibrium adsorption capacity. Wo is the total volume of the micropores aecessible to the given adsorbate, k is a characteristic constant related to the pore structure of the adsorbent, P is an affinity coefficient, Csai is the saturation concentration in the gas phase of liquid adsorbate at the adsorption temperature T, and C is the eoncentration of adsorbate vapor in equilibrium. Plotting ln(W) versus [RTln(Csai/C)] the parameters K/p and Wo in the DR equation were determined by the slope and the intercept of the linear lines respeetively. The obtained results and correlation coefficients are eompiled in Table 2. This Table shows the DR equation parameters and the... 

The method of elution on a plateau was first suggested by Helfferich in Science more than forty years ago [126], In the PP method, the chromatographic column is equilibrated with a constant stream of molecules in the mobile phase and a concentration plateau is established. A perturbation is then accomplished by injecting a sample containing an excess or a deficiency of the molecules as compared to the concentration at the plateau. [118-120, 127], The response at the column outlet will be small peaks, known as perturbation peaks, and their retention times are used to determine the adsorption isotherm parameters. The retention time of the perturbation peak is related to the isotherm through the equation ... 

After the adsorption isotherm experiments have been completed, an isotherm equation must be chosen. This equation should fit the experimental data. Often are the experimental data (the experimental adsorption data acquired by the FA method or the perturbation retention times acquired by the PP method) only compared with the ones calculated using the adsorption isotherm parameters acquired from some adsorption isotherm models [131], This is sometimes the only validation done in this field [131], However, the adsorption isotherm parameters should preferably be validated in two step (1) the different isotherm models should be compared using statistical calculations, e.g., an F-test, and (2) by using the parameters to computer simulate elution profiles and then compare them with experimental ones. 

The apparent binding constants determined for the mass-law adsorption equations are empirical parameters related to thermodynamic constants (so-called intrinsic constants) via activity coefficients of the surface species. 

The important assumptions for the pesticide model are instantaneous, linear, reversible adsorption described by an adsorption partition coefficient, K, and first-order decay described by an overall decay rate, k. Parameters for the pesticide model include universal soil loss equation parameters (if erosion loss is to be modeled), pesticide application information (rate, date, and method of application), K, k, and a dispersion coefficient. 

The present study reports the measurements of intracrystalline diffusion and adsorption equilibrium for ethanol, propanols and butanols from aqueous solution in silicalite using a modified HPLC technique. The unique feature of the present work is the use of a mathematical model with a nonlinear adsorption isotherm equation to obtain the intracrystalline diffusivity and adsorption isotherm parameters. The adsorption equilibrium data for alcohols from aqueous solution in silicalite measured by the conventional batch method are also reported and compared with the results measured by the HPLC technique. 

Another frequently used adsorption model that allows for adsorption in multilayers where gas atoms or molecules adsorb on top of already adsorbed molecules was proposed by Brunauer, Emmett, and Teller [44] (the BET model). With the exception of the assumption that the adsorption process terminates at monolayer coverage, the BET model retains all other assumptions made in deriving the Langmuir adsorption isotherm. The BET model leads to a two-parameter adsorption equation of the form... 

The adsorptive and catalytic properties of zeolites HY, HZSM-5 and HM (natural and synthetic) subjected to dealumination, ion exchange with rare-earth and transition elements have been studied.The changes in conversion and selectivity for w-xylene and n-pentane are shown to be connected with the changes of the zeolites microporous structure.These changes are in conformity with DR equation parameters. The DR equation could be applied to the simple test method elaboration of the starting and modified zeolites microporous structure through their adsorptive properties. 

The second approach starts with an idea of possible mechanism, leading to a theoretical kinetic equation formulated in terms of concenhations of adsorbed reactants and intermediate species use of the steady-state principle then leads to an expression for the rate of product formation. Concentrations of adsorbed reactants are related to the gas-phase pressures by adsorption equations of the Langmuir type, in a way to be developed shortly the final equation, the form of which depends on the location of the slowest step, is then compared to the Power Rate Law expression, which if a possibly correct mechanism has been selected, will be an approximation to it. A further test is to try to fit the results to the theoretical equation by adjusting the variable parameters, mainly the adsorption coefficients (see below). If this does not work another mechanism has to be tried. 

As mentioned in the discussion around Eqs. (21)-(24), we need values of the five parameters listed in Eqs. (53) and of the surfactant concentration, Csa, to be able to calculate values of various properties of microemulsions (O/W + O or W/O-fW). Of these five parameters the area per surfactant molecule, (t.,., can be determined accurately from the Gibbs adsorption equation, Eq. (1), and there is only a small uncertainty regarding the values of / and c. 

The parameter n = 2 was first suggested by Dubinin and Radushkevich (1947), and hence the resulted adsorption equation is called the DR equation... 

This adsorption isotherm equation has three parameters, W°, q and n, with the last two being the structural parameters (hence will be independent from adsorbate and temperature). By fitting this adsorption equation with the experimental data, preferably with different adsorbates and temperatures, the three parameters can be obtained. 

The main parameters describing the system, in addition to suspension concentration and specific surface area, are the concentration of adsorption sites on the solid surface and the equilibrium constants in the adsorption equations, provided Langmuir-type adsorption, i.e., only one type of adsorption centers with constant adsorption enthalpy, is assumed ... 

The pAf) vector corresponds to the maximum entropy principle of the j-order (Muniz et al. 2000). This procedure was used to modify the CONTIN algorithm (CONTIN/MEM-y where j denotes the order of pKf)). A self-consistent regularization procedure (starting calculations were done without application of MEM) with an unfixed regularization parameter (for better fitting) was used on CONTIN/MEM-y calculations. This procedure was also applied to the nitrogen adsorption data with the overall adsorption equations described later. 

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