Multilayer kinetics

M.C. Bartelt and J.W. Evans, Transition to multilayer kinetic roughening for metal (100)... 

In considering isotherm models for chemisorption, it is important to remember the types of systems that are involved. As pointed out, conditions are generally such that physical adsorption is not important, nor is multilayer adsorption, in determining the equilibrium state, although the former especially can play a role in the kinetics of chemisorption. 

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

Additional applications of the transfer matrix method to adsorption and desorption kinetics deal with other molecules on low index metal surfaces [40-46], multilayers [47-49], multi-site stepped surfaces [50], and co-adsorbates [51-55]. A similar approach has been used to study electrochemical systems. 

The first-order and second-order kinetics of desorption are by far the most common and practically considered cases. Less than first-order desorption kinetics indicates multilayer adsorption or transport limited desorption (101). An actual significance of the third-order kinetics in desorption has been found recently by Goymour and King (102, 103). 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

In zone R, all three phenomena that take place in the film are fast compared to the diffusion of the substrate from the bulk of the solution to the film-solution interface. The concentrations of both Q and A are constant through the film. The RDEV response is similar to that of a monolayer coating (Section 4.3.2), except that more catalytic material is present on the surface of the electrode (it is multiplied by the number of layers in the multilayered coating). A linear Koutecky-Levich plot is obtained from the intercept, from which the kinetics of the catalytic reaction can be characterized. 

Immobilizing the catalyst on the electrode surface is useful for both synthetic and sensors applications. Monomolecular coatings do not allow redox catalysis, but multilayered coatings do. The catalytic responses are then functions of three main factors in addition to transport of the reactant from the bulk of the solution to the film surface transport of electrons through the film, transport of the reactant in the reverse direction, and catalytic reaction. The interplay of these factors is described with the help of characteristic currents and kinetic zone diagrams. In several systems the mediator plays the role of an electron shuttle and of a catalyst. More interesting are the systems in which the two roles are assigned to two different molecules chosen to fulfill these two different functions, as illustrated by a typical experimental example. 

Application of CBS extrapolations to the A5-ketosteroid isomerase-catalyzed conversion of A5-androstene-3,17-dione to the A4 isomer (Fig. 4.10) provides a test case for extensions to enzyme kinetics. This task requires integration of CBS extrapolations into multilayer ONIOM calculations [56, 57] of the steroid and the active site combined with a polarizable continuum model (PCM) treatment of bulk dielectric effects [58-60], The goal is to reliably predict absolute rates of enzyme-catalyzed reactions within an order of magnitude, in order to verify or disprove a proposed mechanism. 

A wide range of reversible adsorption kinetic rates was also found by TIR/FRAP for another protein, lysozyme, on a substrate with a different surface charge, alkylated silicon oxide.(61) It is possible that the wide range of rates results from a spectrum of surface binding site types and/or formation of multilayers of adsorbed protein. 

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. 

Equations 2.26 and 2.27 carmot be solved analytically except for a series of limiting cases considered by Bartlett and Pratt [147,192]. Since fine control of film thickness and organization can be achieved with LbL self-assembled enzyme polyelectrolyte multilayers, these different cases of the kinetic case-diagram for amperometric enzyme electrodes could be tested [147]. For the enzyme multilayer with entrapped mediator in the mediator-limited kinetics (enzyme-mediator reaction rate-determining step), two kinetic cases deserve consideration in this system in both cases I and II, there is no substrate dependence since the kinetics are mediator limited and the current is potential dependent, since the mediator concentration is potential dependent. Since diffusion is fast as compared to enzyme kinetics, mediator and substrate are both approximately at their bulk concentrations throughout the film in case I. The current is first order in both mediator and enzyme concentration and k, the enzyme reoxidation rate. It increases linearly with film thickness since there is no... 

Auer et al. [134] presented an example for multilayer formation and controlled deposition of functionalized nanoparticles on SAM of mercaptohexadecanoic acid (MHA) using electrostatic interactions. As a pH-sensitive switchable linker between the SAM of MHA and negatively charged gold nanoparticles, bis-benzami-dine bolaamphiphiles having different alkyl spacers were used [135]. This strategy resulted in a potentially tunable and switchable property of the entire assembly. For example, the kinetics of adsorption as well as the final particle layer thickness can be controlled by the kind of bis-benzamidine used as the linker (Fig. 9.16). 

Brunauer, Emmett and Teller, in 1938, extended Langmuir s kinetic theory to multilayer adsorption. The BET theory assumes that the uppermost molecules in adsorbed stacks are in dynamic equilibrium with the vapor. This means that, where the surface is covered with only one layer of adsorbate, an equilibrium exists between that layer and the vapor, and where two layers are adsorbed, the upper layer is in equilibrium with the vapor, and so forth. Since the equilibrium is dynamic, the actual location of the surface sites covered by one, two or more layers may vary but the number of molecules in each layer will remain constant. 

Until now, we have focused our attention on those adsorption isotherms that show a saturation limit, an effect usually associated with monolayer coverage. We have seen two ways of arriving at equations that describe such adsorption from the two-dimensional equation of state via the Gibbs equation or from the partition function via statistical thermodynamics. Before we turn our attention to multilayer adsorption, we introduce a third method for the derivation of isotherms, a kinetic approach, since this is the approach adopted in the derivation of the multilayer, BET adsorption isotherm discussed in Section 9.5. We introduce this approach using the Langmuir isotherm as this would be useful in appreciating the common features of (and the differences between) the Langmuir and BET isotherms. 

Most surface-reaction kinetics involves submonolayer coverages of adsorbed species. However, multilayer adsorption can occur. The standard description of multilayer adsorption is... 

Mixtures of gaseous HC1 and 1,3-butadiene at 294-334 K and <1 atm of total pressure give mixtures of 3-chloro-l-butene and (E)- and (Z)-l-chloro-2-butene with the ratio of 1,2- to 1,4-addition products being approximately unity. Kinetic measurements in pyrex cells, using FT IR spectroscopy, revealed that surface catalysis is required and that the reaction most probably occurs between a multilayer of adsorbed HC1 and gaseous or weakly adsorbed butadiene. This highly structured process is believed to proceed with nearly simultaneous proton and chloride transfer77,78. 

A novel capillary electrophoresis method using solutions of non-crosslinked PDADMAC is reported to be effective in the separation of biomolecules [211]. Soil studies conducted with PDADMAC report the minimization of run-off and erosion of selected types of soils [212]. In similar studies, PDADMAC has found to be a good soil conditioner [213]. The use of PDADMAC for the simultaneous determination of inorganic ions and chelates in the kinetic differentiation-mode capillary electrophoresis is reported by Krokhin [214]. Protein multilayer assemblies have been reported with the alternate adsorption of oppositely charged polyions including PDADMAC. Temperature-sensitive flocculants have been prepared based on n-isopropylacrylamide and DADMAC copolymers [215]. A potentiometric titration method for the determination of anionic polyelectrolytes has been developed with the use of PDADMAC, a marker ion and a plastic membrane. The end-point is detected as a sharp potential change due to the rapid decrease in the concentration of the marker due to its association with PDADMAC [216]. 

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