Langmuir determination

Using the method of Devaux, Langmuir determined the maximum area (point Q) for a molecule of various substances all of which possess an active group," such as —COaH or —CHaOH, together with a long hydrocarbon chain. His results are given in the table. 

In the case of Langmuir monolayers, film thickness and index of refraction have not been given much attention. While several groups have measured A versus a, [143-145], calculations by Knoll and co-workers [146] call into question the ability of ellipsometry to unambiguously determine thickness and refractive index of a Langmuir monolayer. A small error in the chosen index of refraction produces a large error in thickness. A new microscopic imaging technique described in section IV-3E uses ellipsometric contrast but does not require absolute determination of thickness and refractive index. Ellipsometry is routinely used to successfully characterize thin films on solid supports as described in Sections X-7, XI-2, and XV-7. 

The rate of physical adsorption may be determined by the gas kinetic surface collision frequency as modified by the variation of sticking probability with surface coverage—as in the kinetic derivation of the Langmuir equation (Section XVII-3A)—and should then be very large unless the gas pressure is small. Alternatively, the rate may be governed by boundary layer diffusion, a slower process in general. Such aspects are mentioned in Ref. 146. 

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

Some early observations on the catalytic oxidation of SO2 to SO3 on platinized asbestos catalysts led to the following observations (1) the rate was proportional to the SO2 pressure and was inversely proportional to the SO3 pressure (2) the apparent activation energy was 30 kcal/mol (3) the heats of adsorption for SO2, SO3, and O2 were 20, 25, and 30 kcal/mol, respectively. By using appropriate Langmuir equations, show that a possible explanation of the rate data is that there are two kinds of surfaces present, 5 and S2, and that the rate-determining step is... 

Allara D L and Nuzzo R G 1985 Spontaneously organized molecular assemblies. 2. Quantitative infrared spectroscopic determination of equilibrium structures of solution-adsorbed normal-alkanoic acids on an oxidized aluminum surface Langmuir 1 52-66... 

Consider a binary adsorbed mixture for which each pure component obeys the Langmuir equation, Eq. (16-13). Let n = 4 mol/kg, nl =. 3 mol/kg, Kipi = K2P2 = 1. Use the ideal adsorbed-solution theory to determine ni and n. Substituting the pure component Langmuir isotherm... 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

The knowledge of these adsorption isotherms allows quantification of the respective affinity for the stationary phase with respect to the different solutes. Many different isotherm equations have been described in the literature, and experimental methods allowing their determination are reviewed by [58]. As a first approximation, modified competitive Langmuir isotherms can often he used ... 

The curves were determined from Eqs. 24"—26" in order to apply these in a numerical calculation one first has to know the values of the following functions at — 3°C Afz, the difference in chemical potential between the "empty Structure II lattice and ice Cpg. the Langmuir constant for propane in the larger cavities of Structure II (Cpi = 0 for geometrical reasons) Cmi> Cm2> the Langmuir constants for methane in the two types of cavities of Structure II. 

They varied only the values of the adsorption and desorption rate constants of the reaction intermediate B, and by using the simplest Langmuir kinetics, they calculated time-concentration curves of compounds A, B, and C shown in Fig. 5. Also from this example, which does not consider any step as clearly rate determining, it is evident how very different concentration versus time plots can be obtained for the same sequence of surface reactions if adsorption and desorption of the intermediate B proceed by different rates, which are, however, comparable with the rate of surface reactions. In particular, the curves in the first and second columns of Fig. 5 simulate the parallel formation of substances B and C, at least... 

The preferred kinetic model for the metathesis of acyclic alkenes is a Langmuir type model, with a rate-determining reaction between two adsorbed (complexed) molecules. For the metathesis of cycloalkenes, the kinetic model of Calderon as depicted in Fig. 4 agrees well with the experimental results. A scheme involving carbene complexes (Fig. 5) is less likely, which is consistent with the conclusion drawn from mechanistic considerations (Section III). However, Calderon s model might also fit the experimental data in the case of acyclic alkenes. If, for instance, the concentration of the dialkene complex is independent of the concentration of free alkene, the reaction will be first order with respect to the alkene. This has in fact been observed (Section IV.C.2) but, within certain limits, a first-order relationship can also be obtained from many hyperbolic models. Moreover, it seems unreasonable to assume that one single kinetic model could represent the experimental results of all systems under consideration. Clearly, further experimental work is needed to arrive at more definite conclusions. Especially, it is necessary to investigate whether conclusions derived for a particular system are valid for all catalyst systems. 

The area of colloids, surfactants, and fluid interfaces is large in scope. It encompasses all fluid-fluid and fluid-solid systems in which interfacial properties play a dominant role in determining the behavior of the overall system. Such systems are often characterized by large surface-to-volume ratios (e.g., thin films, sols, and foams) and by the formation of macroscopic assembhes of molecules (e.g., colloids, micelles, vesicles, and Langmuir-Blodgett films). The peculiar properties of the interfaces in such media give rise to these otherwise unlikely (and often inherently unstable) structures. 

FIG. 14 Measurements on monolayers and LB films of CdSe nanoparticles of narrow size distribution (a) II-A isotherms for Langmuir monolayers of CdSe nanoparticles of diameter 2.5 run (curve a), 3.0 mn (curve b), 3.6 mn (curve c), 4.3 mn (curve d), and 5.3 mn (curve e). The area per nanoparticle was determined by dividing the trough area by the estimated number of particles deposited on the surface, (b) Absorbance and photoluminescence spectra of the nanoparticles in solution (A, B) and in monolayers on sulfonated polystyrene-coated glass sbdes (C. D). The nanoparticle diameters are 2.5 nm (curves labeled a), 3.6 nm (curves labeled b), and 5.3 nm (curves labeled c). The excitation wavelengths are (a) 430 nm, (b) 490 nm, and (c) 540 nm. (Reproduced with permission from Ref. 158. Copyright 1994 American Chemical Society.)... 

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