Adsorption isotherms applications

The equation can be fitted to a wide range of isotherms with quite small residual errors over the entire range of concentrations of interest. It is a liquid liquid analogue of the Langmuir adsorption isotherm applicable to... 

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

Brunauer, Emmett, and Teller (1938) successfully extended the Langmuir adsorption isotherm applicable to monolayer adsorption to multilayer adsorption. While the assumptions made contain some serious deficiencies, the reproducibility of the BET method has made it the standard procedure for determining total surface area. In addition to the assumptions involved in the Langmuir adsorption, the BET method assumes that heats of adsorption for the multilayer adsorption are the same for the second and subsequent layers and are equal to the heat of liquefaction of the adsorbate. Adsorption and desorption rate constants are assumed to be the same for all layers except for the first layer, which is in contact with the... 

In this seetion, we intend to present some simple and straightforward aspects of adsorption of nonelectrolytes from binary liquid solutions on to mineral surfaces. Owing to the vast literature on this subject, we limit the presentation to a description of some frequently observed adsorption isotherms applicable to experimental data represented by the adsorption of polar molecules on to mineral oxide surfaces from dilute nonaqueous solutions. 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

When the film thickens beyond two or three molecular layers, the effect of surface structure is largely smoothed out. It should therefore be possible, as Hill and Halsey have argued, to analyse the isotherm in the multilayer region by reference to surface forces (Chapter 1), the partial molar entropy of the adsorbed film being taken as equal to that of the liquid adsorptive. By application of the 6-12 relation of Chapter 1 (with omission of the r" term as being negligible except at short distances) Hill was able to arrive at the isotherm equation... 

At the upper end of the pore size range there is no theoretical limit to the applicability of the Kelvin equation to adsorption isotherms so long as 9 < 90°. There is however a practical limitation, the nature of which may be gathered from Table 3.8 which gives the relative pressures corresponding to... 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

The major surfactant in the foam may usually be considered to be present at the bubble surfaces in the form of an adsorbed monolayer with a substantially constant F, often of the order of 3 X 10" (g mol)/ cm", for a molecular weight of several hundred. On the other hand, trace materials follow the linear-adsorption isotherm Tj = KiCj if their concentration is low enough. For a wider range of concentration a Langmuir or other type of isotherm may be applicable (Davies and Rideal, loc. cit.). 

Nieoud R. M., Seidel-Morgenstem A. (1993) Adsorption Isotherms Experimental Determination and Applieation to Preparative Chromatography Simulated Moving Bed Basics and Applications, R. M Nieoud (ed.), Institut National Polyteehnique de Lorraine, Naney, Pranee, p. 4-34. 

Such a model should be as simple as possible, without however missing any of the underlying thermodynamic and physicochemical factors which cause electrochemical promotion. In particular it will be shown that even the use of Langmuir-type adsorption isotherms, appropriately modified due to the application of potential (or equivalently by the presense of promoters) suffice to describe all the experimentally observed rules G1 to G7 as well as practically all other observations regarding electrochemical promotion including the effect of potential on heats of adsorption as well as on kinetics and reaction orders. 

Adsorption phenomena from solutions onto sohd surfaces have been one of the important subjects in colloid and surface chemistry. Sophisticated application of adsorption has been demonstrated recently in the formation of self-assembhng monolayers and multilayers on various substrates [4,7], However, only a limited number of researchers have been devoted to the study of adsorption in binary hquid systems. The adsorption isotherm and colloidal stabihty measmement have been the main tools for these studies. The molecular level of characterization is needed to elucidate the phenomenon. We have employed the combination of smface forces measmement and Fomier transform infrared spectroscopy in attenuated total reflection (FTIR-ATR) to study the preferential (selective) adsorption of alcohol (methanol, ethanol, and propanol) onto glass surfaces from their binary mixtures with cyclohexane. Om studies have demonstrated the cluster formation of alcohol adsorbed on the surfaces and the long-range attraction associated with such adsorption. We may call these clusters macroclusters, because the thickness of the adsorbed alcohol layer is about 15 mn, which is quite large compared to the size of the alcohol. The following describes the results for the ethanol-cycohexane mixtures [10],... 

The main difference between the chromatographic process carried out in the linear and the nonlinear range of the adsorption isotherm is the fact that in the latter case, due to the skewed shapes of the concentration profiles of the analytes involved, separation performance of a chromatographic system considerably drops, i.e., the number of theoretical plates (N) of a chromatographic system indisputably lowers. In these circumstances, all quantitative models, along with semiquantitative and nonquantitative rules, successfully applied to optimization of the linear adsorption TLC show a considerably worse applicability. 

At different types of adsorption isotherms plotted for adsorption of donor particles on oxides (see section 1.5) expressions (1.112) - (1.115) provide the rise in and decrease in with the growth of partial pressure of gas P, the functions themselves being different. Thus, in case of applicability of the Henry isotherm at small P we have the function oi - exp const-P becoming a power function <7s P with the rise in P which is often observed in experiments [154, 155, 169]. 

In a separate study, Igwe and Abia46 determined the equilibrium adsorption isotherms of Cd(II), Pb(II), and Zn(II) ions and detoxification of wastewater using unmodified and ethylenediamine tetraacetic acid (EDTA)-modified maize husks as a biosorbent. This study established that maize husks are excellent adsorbents for the removal of these metal ions, with the amount of metal ions adsorbed increasing as the initial concentrations increased. The study further established that EDTA modification of maize husks enhances the adsorption capacity of maize husks, which is attributed to the chelating ability of EDTA. Therefore, this study demonstrates that maize husks, which are generally considered as biomass waste, may be used as adsorbents for heavy metal removal from wastewater streams from various industries and would therefore find application in various parts of the world where development is closely tied to affordable cost as well as environmental cleanliness.46... 

Polymer adsorption is important in the flocculation and stabilization of colloidal sols and has been reviewed by Vincent et al. (1) and Tadros (2). Polyvinyl alcohol (PVA) has been used in these studies because of its practical application in textiles, adhesives, and coatings. The adsorption of PVA has been studied on silver iodide by Fleer (3) and Koopal (4), and on polystyrene (PS) latex particles by Garvey (5). The adsorption isotherms reported by these workers extend up to 600 ppm PVA. The adsorption at... 

From an isotherm test it can be determined whether a particular organic material can be removed effectively. It will also show the approximate capacity of the carbon for the application and provide a rough estimate of the carbon dosage required. Isotherm tests also afford a convenient means of studying the effects of pH and temperature on adsorption. Isotherms put a large amount of data into concise form for ready evaluation and interpretation. Isotherms obtained under identical conditions using the same contaminated groundwater for two or more carbons can be quickly and conveniently compared to determine the relative merits of the carbons. 

Adsorption from liquids is less well understood than adsorption from gases. In principle the equations derived for gases ought to be applicable to liquid systems, except when capillary condensation is occurring. In practice, some offer an empirical fit of the equilibrium data. One of the most popular adsorption isotherm equations used for liquids was proposed by Freundlich 21-1 in 1926. Arising from a study of the adsorption of organic compounds from aqueous solutions on to charcoal, it was shown that the data could be correlated by an equation of the form ... 

Multicomponent pollutants in an aqueous environment and/or leachate of SWMs, which are COMs, usually consist of more than one pollutant in the exposed environment [1, 66-70]. Multicomponent adsorption involves competition among pollutants to occupy the limited adsorbent surface available and the interactions between different adsorbates. A number of models have been developed to predict multicomponent adsorption equilibria using data from SCS adsorption isotherms. For simple systems considerable success has been achieved but there is still no established method with universal proven applicability, and this problem remains as one of the more challenging obstacles to the development of improved methods of process design [34,71 - 76]. 

Porous texture characterization of all the samples was performed by physical adsorption of N2 at 77K. and CO2 at 273K, using an automatic adsorption system (Autosorb-6, Quantachrome). The micropore volume, Vpp (N2), was determined by application of Dubinin-Radushkevich equation to the N2 adsorption isotherm at 77K up to P/Po< 0.1. The volume of narrow micropores, Vnpp (DR,C02>, (mean pore size lower than 0.7 nm) was calculated from CO2 adsorption at 273 K. 

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

In analytical applications where the concentrations of analytes in mobile phase are very small the adsorption isotherm is usually considered to be linear, i.e., for each component involved in the separation the relationship between mobile (C) and stationary phase (q) concentrations is linear ... 

The quantitative relationship between the degree of adsorption at a solution interface (7), G—L or L—L, and the lowering of the free-surface eneigy can be deduced by using an approximate form of the Gibbs adsorption isotherm (eq. 9), which is applicable to dilute binary solutions where the activity coefficient is unity and the radius of curvature of the surface is not too great ... 

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