Excess adsorption analysis

The analysis of experimental excess adsorption isotherms using equation (2-50) had shown unusual results [22]. The adsorbed layer thickness of acetonitrile adsorbed from water on different types of reversed-phase adsorbents calculated as the ratio of adsorbed layer volume and adsorbent surface area appears to be on average equal to 14 A, which is equivalent to approximately five monolayers of acetonitrile molecules adsorbed on the hydrophobic surface. At the same time, the adsorbed layer thickness of methanol adsorbed from water on the same adsorbents is equal to only 2.5 A, which is equivalent to the monolayer-type adsorption. 

A. Dabrowskl, M. Jaronlec, Excess Adsorption Isotherms for Solid-Liquid Systems and Their Analysis to Determine the Surface Phase Capacity, Adv. Colloid Interface Set, 31 (1990) 155. (Essential an attempt to obtain and define surface areas by adsorption from binary mixtures.)... 

Parallel events in the field of in situ IR spectroscopy (for a review of sulfate IR studies, see Ref. 26) resulted in a coupled shift to molecular level bi-sulfate anion was recognized in sulfate adlayer even in solutions with predominating sulfate. It was com-pletey new situation, when chemical equilibrium is affected by adsoibate-surface interactioa In usual terms of solution equilibria, the effect corresponds to increase of pKa from its bulk value (ca. 2) to 3.3-4.7 (pKa is potential-dependent). To agree this situation with bulk thermodynamics, one should simply use electrochemical potential instead of chemical. The phenomena of adsorption-induced protonation is relative to UPD, when adsoibate-surface interaction shifts redox equihbria. In more molecular terms, the species determined as bi-sidfate ions are probably interfacial ion pairs, i.e., the phenomenon can be considered as coadsorptioa This situation is screened in purely thermodynamic analysis, as excess surface protonation is hidden in Gibbs adsorptions of sulfate and H. However it becomes important for any further model consideration, as it can affect lateral interactions and the order in the adlayer. The excess adsorption-induced protonation of various anions is a very attractive field. In particular it is the only chance to explain why multicharged oxoanions can form complete mono-layers on platinum. 

The isosteric heats of adsorption of methane in BPL activated carbon and ethane in MCM-41 were obtained by Monte Carlo simulation. The simulated absolute isosteric heats were converted into their experimental excess counterparts using a thermodynamie equation, which was derived by the thermodynamic analysis of the Clausius-Clqieyron equation for the isosteric heats. The difference between absolute and excess adsorption is small at low pressure in small pores but becomes bigger as the pressure increases, and is substantial in pores with a pore size bigger than 20 A even at low pressures. Excellent fits were obtained between experimental and simulated isosteric heats of adsorption of methane in BPL activated carbon and ethane in an MCM-41 sample. A pore size distribution model was used to relate simulation results for pores of different sizes to the experimental adsorbent. It is found that the isosteric heat is a more sensitive measure of the structure of activated carbon adsorbents than an adsorption isotherm. 

The fit in Fignre 10 is very good. There is some over prediction of the amount in the adsorption cell at lower pressure (pressure increases. The source of this difference in unclear at this time and requires further investigation. The final point of interest is the difference between the excess adsorption isotherm obtained by the new method (eq. 5 less the final term for the bulk contribution to the amount in the adsorption cell) and that obtained from a traditional analysis of volumetric adsorption experiments. Excess adsorption isotherms at 273.15K and 333.15K are plotted in Figure 11. 

The adsorption issue is of particular importance in surface analytical techniques as excessive adsorption during analysis will affect, in one form or another, the signals of interest. Indeed, this will introduce significant background levels to any secondary ions containing the same species. Note It is commonly stated that SIMS does not suffer from a background signal, which is one of the reasons for the extreme detection limits possible with SIMS. 

The first step of modeling is to formulate an expression for absolute adsorption. As elucidated in Section IVF, the experimental excess adsorption data are represented in the coordinates of ln[ln( )] versus l/ln(p), and a set of linear isotherms are obtained as shown in Fig. 14. To avoid numerical singularity, rf values (in mmol/g) are enlarged 10-fold and is in kdopascals. As shown in Fig. 14, the experimental points for the condition of low surface concentration are on the linear plots. Because the relationship is linear, the formulation for absolute adsorption contains only two parameters [refer to Eq. (46)], which are evaluated by nonlinear regression analysis and shown by Eqs. (46.2) and (46.3). These equations together with Eq. (46.1) can yield the corresponding data of absolute adsorption for any experimental conditions. 

There are three parameters in Eq. (60) q, b, and q. Their values are evaluated in fitting the model to the experimental excess adsorption data by nonlinear regression analysis. Each parameter is a fimction of temperature, as shown in Figs. 18-20. The amount adsorbed as predicted by the model is shown by the curves in Fig. 5. The model fits the experimental isotherms very well, even for the one near the critical temperature. The fitness of the model is measured by the total disagreement defined as the following ... 

The equlibrium between the bulk fluid and fluid adsorbed in disordered porous media must be discussed at fixed chemical potential. Evaluation of the chemical potential for adsorbed fluid is a key issue for the adsorption isotherms, in studying the phase diagram of adsorbed fluid, and for performing comparisons of the structure of a fluid in media of different microporosity. At present, one of the popular tools to obtain the chemical potentials is an approach proposed by Ford and Glandt [23]. From the detailed analysis of the cluster expansions, these authors have concluded that the derivative of the excess chemical potential with respect to the fluid density equals the connected part of the fluid-fluid direct correlation function (dcf). Then, it follows that the chemical potential of a fluid adsorbed in a disordered matrix, p ), is... 

The low molecular diffusion coefficients of proteins and other biopolymers reduces the efficiency of mass transfer and compromises efficiency as flow rate is increased. Therefore, high-performance SEC columns are usually operated at modest flow rates, e.g., 1 ml/min or less. However, operation at very low flow rates is undesirable due to excessive analysis times, loss of efficiency due to axial analyte diffusion, and the risk of poor recovery due to analyte adsorption. 

That this was known in industry at least 15 years earlier is one of the unfortunate discrepancies between academic research and commercial industrial research and development. Not all that is known is necessarily published. This realization subsequently lead to the development of both solid phase and gas phase linear driving force models that each provide very good representations of measured data without the excess labor involved with the diffusion-based models. For trace systems there are quite a few analytical solutions that are available and quite tractable for both design work and the analysis of adsorption column performance. 

The capacitance-potential dependences of Cd(OOOl) in dilute solutions of Cl04, N02, and NOs" were also studied [6]. A weak specific adsorption of anions increasing in the order Cl04 < N02 < N03 was observed. The adsorption of halides on the Cd(OOOl) single crystal electrode was studied [7], and was found to increase in the sequence Cl < Br < 1 [8]. Analysis of the impedance data does not point to the specific adsorption of Cl ions, and shows that the surface excess (T) of halide ions changes with potential and increases from Br to 1 (Fig. 1) [7]... 

Fortunately, this is the case in many environmental applications where the gas species to be removed are in such low concentrations (large excess of inerts) that the expansion factor is practically zero. As pointed out in the introduction of this section, the basic principles of the analysis are also applicable in the case of adsorption of solutes from the gaseous phase. Again, for environmental applications, the concentration of solutes is so low that the pressure drop is only due to the flow of the gas. Here, the expansion factor has the same meaning, i.e. it measures the change of the volume of the gas phase, which is negligible in the case of low concentrations of the removed gas species. 

The competitive adsorption of a short symmetric PS-PI diblocks or a long asymmetric PS-PI diblock to the surface of a PS homopolymer was examined by Budkowski etal. (1995).They used nuclear reaction analysis (Section 1.4.18) with labelled diblocks to determine the concentration of deuterium atoms as a function of depth, and hence the volume fraction of labelled chains. It was thus found that the shorter diblock tends to adsorb preferentially to the interface. The surface excess of PS and its interfacial density were compared to a theory for bidisperse brushes, a generalization of the model due to Leibler (1988). Excellent quantitative agreement was found, with no adjustable parameters. 

In serum replacement (6), the latex is confined in a cell with a semi-permeable membrane, e.g., Nuclepore filtration membrane, and water is pumped through the latex to literally replace the serum. The removal of adsorbed ions is quantitative provided the adsorption-desorption equilibrium is maintained. The Na+ and K+ ions are replaced by IT " ions by pumping dilute hydrochloric acid through the latex followed by water to remove the excess acid. Serum replacement takes longer than ion exchange, but avoids the arduous resin purification step moreover, the serum is recovered quantitatively in a form suitable for analysis. 

Roginskif suggested a simplified method of analysis for processes occurring on a nonuniform surface which made it possible to surmount these mathematical difficulties without excessive distortion of the physical model. The method has general applicability to statistical processes however, its application to adsorption equilibrium only will be discussed here. 

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