Strong Adsorption Theoretical Model

In the limit of strong adsorption, the polyelectrolyte adsorption energy is large compared to the thermal fluctuations of the polymer chain. Hence, the structural properties of adsorbed chains are essentially governed by maximization of polyelectrolyte-surface electrostatic interactions and minimization of polyelectrolyte-polyelectrolyte repulsion [59]. Therefore, we consider a polyelectrolyte chain 

The electrostatic energy of a polyelectrolyte with the charge density p(r) in the electrostatic potential is given by  

The electrostatic potential above the surface follows from the Poisson-Boltzmann equation. We apply the linearized Poisson-Boltzmann equation  

The mechanical bending energy is associated with the rigidity of the polyelectrolyte I = 2lp and is therefore given by the Kratky-Porod energy [180]  

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The measured electronic structure, occupied or unoccupied, provides the fullest information when also combined with theory. Electronic structure calculations in surface chemistry have advanced immensely in the past decades and have now reached a level of accuracy and predictive power so as to provide a very strong complement to experiment. Indeed, the type of theoretical modeling that will be employed and presented here can be likened to computer experiments, where it can be assumed that spectra can be computed reliably and thus computed spectra for different models of the surface adsorption used to determine which structural model is the most likely. In the present chapter, we will thus consistently use the interplay between experiment and theory in our analysis of the interaction between adsorbate and substrate. Before discussing what quantities are of interest to compute in the analysis of the surface chemical bond, we will briefly discuss and justify our choice of Density Functional Theory (DFT) as approach to spectrum and chemisorption calculations. 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

We turn to the more complicated but important problem of ionic surfactant adsorption, and start with the salt-free case where strong electrostatic interactions are present. In Fig. 3 we have reproduced experimental results published by Bonfillon-Colin et al. for SDS solutions with (open circles) and without (full circles) added salt [13]. The salt-free ionic case exhibits a much longer process with a peculiar intermediate plateau. Similar results were presented by Hua and Rosen for DESS solutions [21]. A few theoretical models were suggested for the problem of ionic surfactant adsorption [22-24], yet none of them could produce such dynamic surface tension curves. It is also rather clear that a theoretical scheme such as the one discussed in the previous section cannot fit these experimental results. On the other hand, addition of salt to the solution screens the electrostatic interactions and leads to a behavior very similar to the non-ionic one. We shall return to this issue in Section 4. We thus infer that strong electrostatic interactions affect drastically the adsorption kinetics. Let us now study this effect in more detail. We follow the same lines presented in the previous section while adding appropriate terms to account for the additional interactions. 

Based on crystallographical analysis a new mechanism of adsorbate phase transition is discussed and theoretically modeled. Qualitative comparisons between the model isotherm and its experimental counterpart are carried out. It C2m be concluded that the hysteresis loop in the p-xylene/ZSM-5 isotherms is caused by a strong crystal lattice mediated interaction between adsorbate molecules, while the intermediate plateau is the result of this interaction and the large energetic difference between two types of adsorption sites. 

The results confirm that the adsorption of ammonia is very fast and that ammonia is strongly adsorbed on the catalyst surface. The data were analyzed by a dynamic isothermal plug flow reactor model and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over the entire set of runs. The influences of both intra-particle and external mass transfer limitations were estimated to be negligible, on the basis of theoretical diagnostic criteria. 

The first two examples both involved the creation of cationic species on an acidic zeolite. In both cases we did not need to model the interaction of the cation with the zeolite framework good agreement was obtained with just calculation of the isolated cation. Apparently, the cation is not strongly perturbed by the presence of the zeolite. Such fortunate circumstances are rare. Here we show an example of how theoretical NMR calculations can help elucidate chemistry on a basic metal oxide surface, in particular, the adsorption of acetylene on MgO (26). For this study we needed to model the active sites of the catalyst, for which there are many possibilities. It is assumed the reactive sites are those in which Mg and O are substantially less coordinated than in the bulk. Comer sites are those in which Mg or O are three-coordinate, whereas Edge sites have four-fold coordination. These sites are where the strongest binding of the adsorbates are obtained. 

In analogy with the results of theoretical calculations on the dissociation path of CO on rhodium by De Koster and Van Santen [53], we visualize the rupture of the N-O bond as sketched in Fig. 5.12. Starting from a threefold position, the adsorbed NO molecule bends across a rhodium atom to the next threefold site. By stretching over the central rhodium atom, the antibonding NO orbitals have a strong interaction with the Rh d-orbitals, and the N-O bond is efficiently weakened. The picture implies that NO requires an ensemble of at least five atoms on the (111) surface of an fee transition metal in order to dissociate. This is in fair agreement with kinetic modelling, which indicates that three to four NO adsorption sites must be invoked to obtain realistic kinetic parameters [52]. 

Scheutjens-Fleer (SF) Theory. A conceptual model for the effects of NOM on colloidal stability can be developed by using existing theoretical and experimental investigations of polymer and polyelectrolyte adsorption on solid surfaces and of the effects of macromolecules on colloidal stability. The modeling approach begins with the work of Scheutjens and Fleer for uncharged macromolecules, termed here the SF theory (3-5). This approach has been extended to the adsorption of linear flexible strong polyelectrolytes by van der Schee and Lyldema (6), adapted to weak polyelectrolytes (7-9), and applied to particle-particle interactions (8, 10). 

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