Finite concentration adsorption

Bogillo, V.I. Shkilev, V.P., and Voelkel, A., Chemical heterogeneity of metal oxide surfaces as studied by inverse gas chromatography at finite concentrations, Adsorpt. Sci. Technol. 14(3), 189-198 (1996). 

In the biomedical literature (e.g. solute = enzyme, drug, etc.), values of kf and kr are often estimated from kinetic experiments that do not distinguish between diffusive transport in the external medium and chemical reaction effects. In that case, reaction kinetics are generally assumed to be rate-limiting with respect to mass transport. This assumption is typically confirmed by comparing the adsorption transient to maximum rates of diffusive flux to the cell surface. Values of kf and kr are then determined from the start of short-term experiments with either no (determination of kf) or a finite concentration (determination of kT) of initial surface bound solute [189]. If the rate constant for the reaction at the cell surface is near or equal to (cf. equation (16)), then... 

It is clear from equation (7) that the addition of a second surfactant results in further decrease in y the essential requirements being a not too small adsorption of the second surfactant. Whether it replaces the first surfactant or is adsorbed in addition to it is immaterial, just as it is not essential for the two surfactants to form a complex. If the two surfactants are of the same type e.g. both water soluble anionic surfactants, they will form mixed micelles and this will lower the activity of the second surfactant added and decrease both its Fand dp. However, if the two surfactants are different in nature, e.g. one predominantly water soluble and the other oil soluble, they will only slightly affect each other s activity and their combined effect on the interfactial tension may be large enough to bring y to zero at finite concentrations. 

Finite concentration IGC is a useful tool to investigate surface and pore properties. A novel combination of finite concentration IGC and thermal desorption provides the possibility to separate micropore adsorption from surface and mesopore adsorption. This allows the calculation of BET values with physical relevance for highly microporous materials and the consideration of molecular sieve effects. 

The first observation suggests that the results derived from the infinite dilution state are related to the most active adsorption sites which leads to a high surface free energy value. It is then not evident that a relationship exists between the results at infinite dilution and those of the classical liquid contact angle measurement as one of the wetting methods or the results at finite concentration. 

According to second and third observations, it is difficult to appreciate the maximum value of the surface free energy and surface enthalpy of a solid, especially in the case of microporous materials which are widely efficient adsorption properties of the surface (sample V). Therefore, for this material, more works may be needed on the adsorption isotherm, spreading pressure, isosteric heat of adsorption, and even heterogeneities of solid surfaces. They are concerned with the finite concentration technique with increasing amount adsorbed, which will be dealt to some extent in the next section. 

When the surface energy is forced on the interface of two adherents, the surface energy can be also studied by the adsorption isotherm as a function of the amount adsorbed at finite dilution (or concentration). The theoretical and applied studies on adsorption isotherm of the solid surfaces have been widely carried out with the finite concentration, since Thomas Young described the three-phase equilibrium in 1805 [71]. 

Adsorption site energy, pre-exponential factor of Henry s constant and correlation between infinite and finite concentration... 

The relationships of Equations 5 and 2 are unquestionably valid for unlimited surface coverage on ideal external open (flat, planar, accessible) surfaces ranging from nil at E to infinity at E=0. All of the inherent assumptions (tabulated above) are equally valid as models for physical adsorption in internal constricted regions. These are classically denoted as ultramicropores ( 2 nm), micropores(<2 nm), mesopores (2<1000nm) and macropores (very large and difficult to define with adsorption isotherm). In these instances there are finite concentration limits corresponding to the volume (space, void) size domain(s). Although caution is needed to deduce models from thermodynamic data, we can expect to observe linear relationships over the respective domains. The results will be consistent with, albeit not absolute proof of the models. 

Extensive neutron reflectivity studies on surfactant adsorption at the air-water interface show that a surfactant monolayer is formed at the interface. Even for concentration cmc, where complex sub-surface ordering of micelles may exist,the interfacial layer remains a monolayer. This is in marked contrast to the situation for amphiphilic block copolymers, where recent measurements by Richards et al. on polystyrene polyethylene oxide block copolymers (PS-b-PEO) and by Thomas et al. on poly(2-(dimethyl-amino)ethylmethacrylamide-b-methyl methacrylate) (DMAEMA-b-MMA) show the formation of surface micelles at a concentration block copolymer, where an abrupt change in thickness is observed at a finite concentration, and signals the onset of surface micellisation. 

Inverse Gas Chromatography at finite concentration conditions (IGC-FC) offers another possibility to perform such determinations. Furthermore, IGC readily provides the data required for the calculation of adsorption energy distribution functions. The aim of the present study was to... 

This study demonstrates the ability of IGC, at finite concentration conditions, to determine quickly (within one or two days depending on the desired accuracy) water adsorption isotherms, with relative pressures ranging from 0 to 0.85. Moreover, IGC provides isotherms made up of several hundreds of experimental points. This permits the computation of meaningful adsorption energy distribution functions. 

Relevant information may be obtained by determining CH2CI2 adsorption isotherms using inverse gas chromatography at finite concentration conditions. The adsorption isotherms, in fact desorption isotherms, are readily acquired when applying IGC. The principle of this procedure is given in this book[l]. 

Since IGC is able to generate adsorption isotherms and to evaluate acid/base interactions for specified adsorbate-adsorbent pairs, it follows that the technique is able to develop a detailed picture of surface properties for non-volatile stationary phases. This is illustrated, again for carbon fibers, by Vukov and Gray (48). They combine IGC information at essentially zero coverage of the injected probes with finite concentration data to obtain heat of adsorption values ranging from zero to multi-layer coverage. Their meticulous study shows the effects of thermal pretreatment on fiber surface characteristics, and underscores the convenience and power of IGC to generate information otherwise far more difficult to obtain. 

Finite Concentration. In this concentration range, surface adsorption results in nonlinear isotherms in which partition coefficients and retention volumes are dependent upon the adsorbate concentration in the gas phase. This means that a single partition coefficient, Ks (= T/c), is insufficient to characterize the process and the differential (3r/3c)T is required. Here, T is the surface excess of adsorbate expressed in mol m z, c Is the gas phase adsorbate concentration, and T is the column temperature. Nonlinear Isotherms give asymmetric peaks, whose shapes and retention volumes depend on the concentration of the probe. 

The carbon fiber surface areas were previously determined by BET krypton adsorption to be 0.62 0.01 m g-1 and 0.74 0.01 n g-1 for T-300 and P-55, respectively. The molecular area of krypton was taken as 0.195 nm2. Prior to these measurements, the fibers were degassed at 300°C for 15 h. The elution of a characteristic point method of finite concentration IGC was used to determine the Isotherms for a series of n-alkanes. Approximately 15 to 20 Injections were used for each Isotherm. The hand-drawn curve through the peak maxima was digitized for Integration and subsequent data handling. 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

Salame, 1.1. and Bandosz, T.J. (2001). Study of diethyl ether adsorption on activated carbons using IGC at finite concentration. Langmuir, 17, 4967—72. 

Water adsorption studies are obviously indicated for the evaluation of the hydrophilic character of silica. Besides, according to our earlier studies, methylene chloride (CH2CI2), used as a probe for Inverse Gas Chromatography (IGC) measurements at finite concentration conditions, appears to be an alternative choice for determining the hydrophobicity of silica surfaces. Indeed, earlier indications suggest that this probe, when used under appropriate conditions, is not interacting with the hydrophilic silanol groups. The present work is complementary to file study of water adsorption on fumed silica samples, described in this book [1]. 

Moreover, the intermediate can either be a species which is relatively stable in solution, so as to exist at a finite concentration, as, e.g., in the case of Cu ion, or it can be so strongly adsorbed at the surface that, although present there at kinetically significant concentration, its concentration in solution, even at x = 0, is negligible. This can be taken care of by assuming an adsorption equilibrium... 

El-Sayed and Bandosz used three activated carbon samples of different origin, namely BPL from Calgon and MVP from Norit, both prepared from bituminous coal, and BAX from Westvaco, made from wood, using chemical activation with phosphoric acid for the adsorption of acetaldelyde. These carbons were washed in a soxhlet apparatus to remove water-soluble impurities and then oxidized with nitric acid. The adsorption of acetaldehyde was determined by inverse gas chromatography at infinite dilution and finite concentration. The heats of acetaldehyde adsorption at... 

It was emphasized in Section 4.2 that GSC is the only method of studying adsorption characteristics of surfaces at very low coverage. At the same time the methods apply at higher concentrations if chromatographic techniques are used for finite concentrations (e.g. elution on a plateau, which was described in Section 5.1.3). Thus a range of concentrations of the adsorbed substance may be covered and hence the adsorption isotherms can be determined [112, 113]. 

Other gas-chromatographic techniques besides frontal analysis were also utilized at finite concentration to determine the adsorption isotherms frontal analysis through characteristic points [145], elution through characteristic points [146—148] and, elutipn on a plateau [149, 150]. 

Here we give the elements of a calculation (Conway, 1975) for evaluating the change of electrostatic hydration energy due to an ion as the ion is transferred from the bulk solvent medium to a position near the interface of the solvent with another dielectric medium (vacuum or vapor). It is convenient to evaluate the hydration effects in ion adsorption at infinite dilution to eliminate complications due to ionic atmosphere effects which screen the ion/ion-image repulsion at finite concentrations. 

In a foam where the films ate iaterconnected the related time-dependent Marangoni effect is mote relevant. A similar restoring force to expansion results because of transient decreases ia surface concentration (iacteases ia surface tension) caused by the finite rate of surfactant adsorption at the surface. 

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