Sorption isotherms computing

Nitrogen sorption isotherms of the three parent silica supports are presented in Figure 1, and computed textural properties are reported in Table 1. Pore radii were determined by means of Barrett-Joyner-Halenda (BJH) and Broekhoff-De-Boer (BdB) calculations. Chain loadings ng are reported in Table 2. 

Wide pressure range for data acquisition to allow more complete description of the system of interest. It all to easy to overlook important trends and construet an incomplete or inaccurate paradigm. One should avoid limiting the analyses to restricted data regimes such as the traditional BET region of the sorption isotherm. Maximum number of data points should be acquired to further elucidate trends or show the absence of thermodynamic and/or kinetic trends. Modem automated computer driven equipment has permitted the efficient use of operator time and equipment. ... 

Vapor sorption isotherms in a polymer as computed from Flory-Huggins theory by using interaction parameters shown. 

Ihe empirical isotherm method considers equilibrium distribution of only one component and requires the experimental determination of its sorption isotherms in specific conditions. However, ground water contains multiple ions, which compete for the location in the exchange capacity. For this reason, ion exchange equilibrium directly correlates with the ground water composition and adsorption capacity of its components. This effect of ions on one another may be identified only computational methods based on exchange coefficients. 

By a combined gravimetric and i.r. technique, spectra of lysozyme protein films have been recorded during sorption isotherms at constant water content h (mg per mg dry protein) in the range 0Computer-aided differential analysis shows the effect of progressive hydration on some significant sites of the protein such as the ionizable acidic side-chains and the backbone amide carbonyls, as well as the spectrum of the absorbed water itself. In order to derive thermodynamic properties of these sites, the... 

Numerous sorption isotherm equations (of approximately 80 available) cannot be analytically converted to the explicit form. In this case they have to be solved numerically for

drying rate calculation. This slows down computations considerably. 

Sorption isotherms based on macroscopic observations are not capable of providing detailed molecular-level insight into the chemical mechanisms underlying the sorption behavior. In order to obtain this type of information, spectroscopic, structural, and computational data and methods are required. X-ray diffraction methods were combined with sorption and spectroscopic data to study the interaction of DNOC with smectite (11). The /-spacing of the DNOC-smectite complex in the presence and absence of water and varying amounts of adsorbed DNOC are shown in Eigure 7. In the air-dried DNOC-smectite complex, the d-... 

For the sorption isotherm, the Gibbs energy of water sorption AG is computed from the thermodynamic relation... 

The Freundlich isotherm (or Freundlich model) is an empirical description of species sorption similar to the K, approach, but differing in how the ratio of sorbed to dissolved mass is computed. In the model, dissolved mass, the denominator in the ratio, is raised to an exponent less than one. The ratio, represented by the Freundlich coefficient Kf, is taken to be constant, as is the exponent, denoted f, where 0< f <1. As before, the masses of dissolved and sorbed species are entered, respectively, in units such as moles per gram of dry sediment and moles per cm3 fluid. Since the denominator is raised to an arbitrary exponent rif, the units for Kf are not commonly reported, and care must be taken to note the units in which the ratio was determined. 

Modern N2 sorption porosimeters are very sophisticated and generally reliable. Typically they come supplied with customized user-friendly software which enables the experimental data to be readily computed using the above models and mathematical expressions. Usually the raw isotherm data is displayed graphically along with various forms of the derived pore size distribution curve and tabulated data for surface area, pore volume and average pore diameter. 

Perrone et al. (2001) modelled Ni(II) adsorp-tion to synthetic carbonate fluoroapatite (CaI0 ((P04)5(C03))(0H,F). The solid phase had a pHIEP of 6.3 and a ZPC of 6.4 with an SSA of 8.8m2/g, an estimated sorption site density of 3.1 sites/nm2. They conducted 8-day isotherms in closed vessels at Ni concentrations of 5 x 10-10 to 1 x 10 8 M, constant I (0.05, 0.1 or 0.5 M), constant solid phase concentrations of 10 g/dm3 at pH values of 4 to 12. As Ni sorption occurred, no significant release of Ca was seen. Sorption was reversible. Rather than precisely characterize surface functional groups, they elected to describe their sorbent surfaces using acid-base reactions for the average behaviour of all sites involved in protonation and deprotonation. Potentiametric titration data were used to estimate the constants with the FTTEQL computer code ... 

Equilibrium Results. Table V shows all of the isotherm parameters computed for the sorption of methanol on the acetylated and unaltered coals. These values are on a moisture-free basis. 

The satisfactory s eement between the experimental and the calculated (theoretical) kinetic curves and concentration profiles suggests that the values of D = 10" cmVs, = 10 cmVs, and = 1.5 10 cm /s adopted for the calculations do indeed characterize the mobility of and Ag+ ions in ampholyte VPC. By using these values and the above ratio, Dji/D = 7, it was possible to evaluate the rate of the Ag/Na exchange. A rectangular isotherm characterizes the sorption of Ag" " ions by the VPC ampholyte and this warrants the use of the approximate analytical solution (11, Sec. II) [26,27] for the above computations. 

As presented above, and in most of the published literature, the isotherm model equations are expressed in terms of total sorbate concentrations. In MINTEQA2, however, aqueous species activities are used rather than their concentrations. This is preferable in that reactions are written in terms of activities. Also, so that the concentrations of sorption sites, sorbed species, and dissolved species are computationally equivalent, the former are entered in MINTEQA2 as moles of sites per liter of solution. Activity coefficients of sorption sites and sorbed species are generally taken to be equal to unity by most authors and in MINTEQA2. 

Finite-difference techniques were used to compute numerical solutions as column-breakthrough curves because of the nonlinear Freundlich isotherm in each transport model. Along the column, 100 nodes were used, and 10 nodes were used in the side-pore direction for the profile model. A predictor-corrector calculation was used at each time step to account for nonlinearity. An iterative solver was used for the profile model whereas, a direct solution was used for the mixed side-pore and the rate-controlled sorption models. 

The surface complex formation constants and the protolysis constants were optimized by using the experimentally obtained data sets and the computer code FITEQL (Herbelin and Westall, 1996). Surface site densities were evaluated from adsorption isotherms at pH 6.5 and a total uranium concentration of 1x10" M. The formation of ferrihydrite during the batch sorption experiment was identified by Mossbauer spec-... 

Manderscheid et al. [39] determined Langmuir parameters for SO sorption in soils from two forested catchments in Germany. These parameters were included in the chemical equilibrium model. Model of Acidification of Groundwater in Catchments (MAGIC), in order to study the effect of isotherm variability on the prediction of SO fluxes with seepage. Langmuir isotherms are not commonly used in transport models because of the computational burden they introduce due to their nonlinearity and also because many researchers, perhaps unjustifiably, often report just the K. ... 

Abstract A dynamic model of protein adsorption on solid surfaces is presented. It is based on the assumption that a protein molecule may change conformation after adsorption. The computed adsorption isotherms are similar in form to experimentally observed isotherms. A model for the experimentally observed reversible potential changes at a metal electrode upon protein adsorption/de-sorption is also discussed. It is thus suggested that a second loosely bound protein layer may be present on several metal surfaces. Some notes are also made about the significance of the time scale and detailed method of performing an adsorption experiment. 

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