Ideal adsorption from binary liquid mixtures on heterogeneous solid surfaces: Equations for excess isotherms and heats of immersion

Application of the Dubinin–Radushkevich Equation for Describing Adsorption from Solutions on to Various Carbons

Dozens of papers have been published recently describing adsorption processes from solutions on to solid surfaces, but a certain lack of understanding of this problem is still observed. This article deals with the description of adsorption from binary solutions of non-electrolytes on to solids. This description covers adsorption both on homogeneous and heterogeneous surfaces from ideal and non-ideal liquid mixtures. Some important factors determining the adsorption process, i.e. the heterogeneity of the solid surface, interactions between the species in the bulk and surface phases, differences in molecular sizes of the adsorbate molecules, etc., have been discussed. The main attention has been focused on the Dubinin–Radushkevich equation and its application in the description of adsorption from solutions on to energetically, heterogeneous adsorbents. Numerous model calculations have been reported for this equation and several experimental systems have been analyzed. The application of the Dubinin–Radushkevich equation in characterizing liquid adsorption on to various carbons has been demonstrated.

A fractal analysis of analyte-estrogen receptor binding and dissociation kinetics using biosensors: environmental effects

A fractal analysis is used to model the binding and dissociation kinetics between analytes in solution and estrogen receptors (ER) immobilized on a sensor chip of a surface plasmon resonance (SPR) biosensor. Both cases are analyzed: unliganded as well as liganded. The influence of different ligands is also analyzed. A better understanding of the kinetics provides physical insights into the interactions and suggests means by which appropriate interactions (to promote correct signaling) and inappropriate interactions such as with xenoestrogens (to minimize inappropriate signaling and signaling deleterious to health) may be better controlled. The fractal approach is applied to analyte-ER interaction data available in the literature. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor chip surface. In general, the binding and the dissociation rate coefficients are very sensitive to the degree of heterogeneity on the surface. For example, the binding rate coefficient, k, exhibits a 4.60 order of dependence on the fractal dimension, D(f), for the binding of unliganded and liganded VDR mixed with GST-RXR in solution to Spp-1 VDRE (1,25-dihydroxyvitamin D(3) receptor element) DNA immobilized on a sensor chip surface (Cheskis and Freedman, Biochemistry 35 (1996) 3300-3318). A single-fractal analysis is adequate in some cases. In others (that exhibit complexities in the binding or the dissociation curves) a dual-fractal analysis is required to obtain a better fit. A predictive relationship is also presented for the ratio K(A)(=k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). This has biomedical and environmental implications in that the dissociation and binding rate coefficients may be used to alleviate deleterious effects or enhance beneficial effects by selective modulation of the surface. The K(A) exhibits a 112-order dependence on the ratio of the fractal dimensions for the ligand effects on VDR-RXR interaction with specific DNA.

A mathematical analysis using fractals for binding interactions of nuclear estrogen receptors occurring on biosensor surfaces

A mathematical approach using fractal concepts is presented for modeling the binding and dissociation interactions between analytes and nuclear estrogen receptors (ER) occurring on surface plasmon resonance biosensor chip surfaces. A kinetic knowledge of the binding interactions mediated by ER would help in better understanding the carcinogenicity of these steroidogenic compounds and assist in modulating these reactions. The fractal approach is applied to analyte-ER interaction data obtained from literature. Numerical values obtained for the binding and dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor surface. For example, a single-fractal analysis is used to describe the binding and dissociation phases for the binding of estradiol and ERalpha in solution to clone 31 protein immobilized on a biosensor chip (C-S. Suen et al., 1998, J. Biol. Chem. 273(42), 27645-27653). The binding and the dissociation rate coefficients are 27.57 and 8.813, respectively, and the corresponding fractal dimensions are 1.986 and 2.268, respectively. In some examples dual-fractal models were employed to obtain a better fit of either the association or the dissociation phases or for both. Predictive relationships are developed for (a) the binding and the dissociation rate coefficients as a function of their respective fractal dimensions and (b) the ratio K(A) (= k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). The analysis should provide further physical insights into the ER-mediated interactions occurring on biosensor and other surfaces.

Adsorption--from theory to practice

Adsorption at various interfaces has concerned scientists since the beginning of this century. This phenomenon underlies a number of extremely important processes of utilitarian significance. The technological, environmental and biological importance of adsorption can never be in doubt. Its practical applications in industry and environmental protection are of paramount importance. The adsorption of substrates is the first stage in many catalytic processes. The methods for separation of mixtures on a laboratory and on an industrial scale are increasingly based on utilising the change in concentration of components at the interface. Moreover, such vital problems as purification of water, sewages, air and soil are involved here too. On the other hand, many areas in which technological innovation has covered adsorption phenomena have been expanded more through art and craft than through science. A basic understanding of the scientific principles is far behind; in part because the study of interfaces requires extremely careful experimentation if meaningful and reproducible results are to be obtained. In recent years, however, considerable effort has been increasingly directed toward closing the gap between theory and practice. Crucial progress in theoretical description of the adsorption has been achieved, mainly through the development of new theoretical approaches formulated on a molecular level, by means of computer simulation methods and owing to new techniques which examine surface layers or interfacial regions. Moreover, during the last 15 years new classes of solid adsorbents have been developed, such as activated carbon fibres and carbon molecular sieves, fullerenes and heterofullerenes, microporous glasses and nanoporous--both carbonaceous and inorganic--materials. Nanostructured solids are very popular in science and technology and have gained extreme interest due to their sorption, catalytic, magnetic, optical and thermal properties. Although the development of adsorption up to the 1918s has been following rather a zig-zag path, this arm of surface science is now generally considered to have become a well-defined branch of physical science representing an intrinsically interdisciplinary area between chemistry, physics, biology and engineering. This review presents in brief the history of adsorption and highlights the progress in theoretical description of the phenomenon under consideration. The paper deals with the above problems critically, showing the development of adsorption, presenting some of the latest important results and giving a source of up-to-date literature on it. Moreover, in this paper the most important aspects are overviewed referring to today's trends and visions in application of adsorption science in industry, environmental protection and in environmental analysis. The relationship between development of adsorption theory and adsorption practice is pointed out. Current understanding and perspectives pertaining to applications of adsorption phenomena on laboratory and on industrial scale as well as environmental protection are discussed and illustrated by means of a few spectacular examples.

Analyte-receptor binding and dissociation kinetics for biosensor applications: a fractal analysis

A fractal analysis of confirmative nature only is presented for analyte-receptor binding and dissociation kinetics for biosensor applications. Data taken from the literature may be modeled, in the case of binding using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. Relationships are presented for the binding and dissociation rate coefficients as a function of their corresponding fractal dimension, Df or the degree of heterogeneity that exists on the surface. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in Df) leads to an increase in the binding and in the dissociation rate coefficient. It is suggested that an increase in the degree of heterogeneity on the surface leads to an increase in the turbulence on the surface owing to the irregularities on the surface. This turbulence promotes mixing, minimizes diffusional limitations, and leads subsequently to an increase in the binding and in the dissociation rate coefficient (Martin S.J., Granstaff, V.E., Frye, G.C., Anal. Chem., 65, (1991) 2910). The binding and the dissociation rate coefficient are rather sensitive to the degree of heterogeneity, Df,bind and Df,diss respectively, that exists on the biosensor surface. For example, the order of dependence on Df,bind is 19.2 for the binding rate coefficient, kbind for the binding of 0.03-1.0 microM SH-2Ld in solution to 2C TCR immobilized on a surface plasmon resonance (SPR) biosensor (Corr, M., Salnetz, A.E., Boyd, L.F., Jelonek, M.T., Khilko, S., Al-Ramadi, B.K., Kim, Y.S., Maher, S.E., Bothwell, A.L.M., Margulies, D.H., Science, 265, (1994) 946). The order of dependence on Df,diss is -6.22 for the dissociation rate coefficient, kdiss for the dissociation of 250-1000 nM Sophora japonica agglutinin (SJA)-lactose complex from the SPR surface. In general, the technique is applicable to other reactions occurring on different types of surfaces, such as cell-surface reactions.

A kinetic study of analyte-receptor binding and dissociation, and dissociation alone, for biosensor applications: a fractal analysis

A fractal analysis is presented for (a) analyte-receptor binding and dissociation kinetics and (b) dissociation kinetics alone for biosensor applications. Emphasis is placed on dissociation kinetics. Data taken from the literature may be modeled, in the case of binding, using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. A single-fractal analysis is adequate to model the dissociation kinetics in the examples presented. Predictive relationships developed for the dissociation rate coefficient(s) as a function of the analyte concentration are of particular value since they provide a means by which the dissociation rate coefficients may be manipulated. Relationships are also presented for the binding and dissociation rate coefficients as a function of their corresponding fractal dimension, D(f), or the degree of heterogeneity that exists on the surface. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in D(f)) leads to an increase in the binding and in the dissociation rate coefficient.

A Fractal Analysis Approach for the Evaluation of Hybridization Kinetics in Biosensors

The diffusion-limited hybridization kinetics of analyte in solution to a receptor immobilized on a biosensor or immunosensor surface is analyzed within a fractal framework. The data may be analyzed by a single- or a dual-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (Sigmaplot, Scientific Graphing Software, User's Manual, Jandel Scientific, CA, 1993). It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes, in general, in the same direction for both the single-fractal and the dual-fractal analysis examples presented. The binding rate coefficient expression developed as a function of the analyte concentration in solution and the fractal dimension is of particular value since it provides a means to better control biosensor or immunosensor performance. Copyright 2001 Academic Press.

A single-fractal analysis of cellular analyte-receptor binding kinetics utilizing biosensors

A fractal analysis of a confirmative nature only is presented for cellular analyte-receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using a single-fractal analysis. Relationships are presented for the binding rate coefficient as a function of the fractal dimension and for the analyte concentration in solution. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the biosensor surface. It is of interest to note that examples are presented where the binding coefficient, k exhibits an increase as the fractal dimension (D(f)) or the degree of heterogeneity increases on the surface. The predictive relationships presented provide further physical insights into the binding reactions occurring on the surface. These should assist in understanding the cellular binding reaction occurring on surfaces, even though the analysis presented is for the cases where the cellular "receptor" is actually immobilized on a biosensor or other surface. The analysis suggests possible modulations of cell surfaces in desired directions to help manipulate the binding rate coefficient (or affinity). In general, the technique presented is applicable for the most part to other reactions occurring on different types of biosensor or other surfaces.

An Evaluation of Cellular Analyte-Receptor Binding Kinetics Utilizing Biosensors: A Fractal Analysis

A fractal analysis is presented for cellular analyte-receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using (a) a single-fractal analysis and (b) a single- and a dual-fractal analysis. Case (b) represents a change in the binding mechanism as the reaction progresses on the biosensor surface. Relationships are presented for the binding rate coefficient(s) as a function of the fractal dimension for the single-fractal analysis examples. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the biosensor surface. For example, for the binding of mutagenized and back-mutagenized forms of peptide E1037 in solution to salivary agglutinin immobilized on a sensor chip, the order of dependence of the binding rate coefficient, k, on the fractal dimension, D(f), is 13.2. It is of interest to note that examples are presented where the binding coefficient (k) exhibits an increase as the fractal dimension (D(f)) or the degree of heterogeneity increases on the surface. The predictive relationships presented provide further physical insights into the binding reactions occurring on the surface. These should assist us in understanding the cellular binding reaction occurring on surfaces, even though the analysis presented is for the cases where the cellular "receptor" is actually immobilized on a biosensor or other surface. The analysis suggests possible modulations of cell surfaces in desired directions to help manipulate the binding rate coefficients (or affinities). In general, the technique presented is applicable for the most part to other reactions occurring on different types of biosensors or other surfaces. Copyright 2000 Academic Press.