Langmuir principle

Using Langmuir s principle of independent surface action, make qualitative calculations and decide whether the polar or the nonpolar end of ethanol should be oriented toward the mercury phase at the ethanol-mercury interface. 

Film pressure is often measured directly by means of a film balance. The principle of the method involves the direct measurement of the horizontal force on a float separating the film from clean solvent surface. The film balance has been considerably refined since the crude model used by Langmuir and in many... 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

Hyperbolic, based on the Langmuir adsorption principle for instance,... 

The second step, Figure 32b, consists of the covering of the styli with cadmium arachidate LB films. Monolayers of arachidic acid (in principle, it is also possible to use stearic or behenic acids with practically the same results) were spread over the surface of 10 " M CdCli water subphase in a Langmuir trough. The monolayer was compressed to a surface pressure of 27 mN/m and transfered onto styli by a vertical dipping technique. Up to six monolayers were deposited. 

There are several isotherm models for which the isotherm shapes and peak prohles are very similar to that for the anti-Langmuir case. One of these models was devised by Fowler and Guggenheim [2], and it assumes ideal adsorption on a set of localized active sites with weak interactions among the molecules adsorbed on the neighboring active sites. It also assumes that the energy of interactions between the two adsorbed molecules is so small that the principle of random distribution of the adsorbed molecules on the adsorbent surface is not significandy affected. For the liquid-solid equilibria, the Fowler-Guggenheim isotherm has been empirically extended, and it is written as ... 

In principle, the FIAM does not imply that the measured flux. / s should be linear with the metal ion concentration. The linear relationship holds under submodels assuming a linear (Henry) isotherm and first-order internalisation kinetics [2,5,66], but other nonlinear functional dependencies with for adsorption (e.g. Langmuir isotherm [11,52,79]) and internalisation (e.g. second-order kinetics) are compatible with the fact that the resulting uptake is a function (not necessarily linear) of the bulk free ion concentration cjjjj, as long as these functional dependencies do not include parameters corresponding with the speciation of the medium (such as or K [11]). 

The Langmuir equation is derived here from application of the mass law, in a similar way as the surface complex formation equilibria were derived in Chapter 2. In principle at a constant pH there is no difference between a Langmuir constant and a surface complex formation constant. 

This equation, containing the Langmuir expression for the adsorption (surface complex formation) of phenol on the Mn(III)(hydr)oxide, is similar to the principles discussed for reductive dissolution of Fe(IH)(hydr)oxide. 

Niels Bohr s 1913 hydrogen atom paper demonstrates the traditional interest of some physicists in placing the facts and laws of chemistry within a broader framework of foundational principles laid out by physicists. During the course of the next two decades, a number of physicists who became known as quantum physicists developed physical theories and mathematical techniques that they claimed would create a mathematical and theoretical chemistry. However, few of them had much chemical knowledge beyond a general understanding of the periodic table of the elements and familiarity with the Lewis-Langmuir theory of the electron duplet and octet. 

This approach may also be applied to racemic bilayers built up from homo-chiral Langmuir-Blodgett monolayers. By measuring the two-dimensional diffraction pattern from such a bilayer it is possible to deduce the molecular chirality of each of the two monolayers in the order they were inserted to construct the bilayer. This approach can be extended to multilayers. Thus, in principle, we close the circle started in Section IV-G-1. It is possible to assign the absolute configuration of chiral molecules in centrosymmetric crystals provided that one can construct the crystal (in this case the multilayer) by adding homochiral layers one by one. 

McClements DJ. Principles of ultrasonic droplet size determination in emulsions. Langmuir 1996 12 3454-3461. 

The form of the isotherm need not be Langmuir in nature, but in any event, must be experimentally determined in order to identify the true profile of the overloaded peak. In practice, the determination of the adsorption isotherm of each compound to be separated by a preparative chromatographic procedure can be arduous and time consuming. A better alternative might be to design the fully optimized column from basic principles in the manner previously described. 

It should be apparent — since an adsorption isotherm can be derived from a two-dimensional equation of state —that an isotherm can also be derived from the partition function since the equation of state is implicitly contained in the partition function. The use of partition functions is very general, but it is also rather abstract, and the mathematical difficulties are often formidable (note the cautious in principle in the preceding paragraph). We shall not attempt any comprehensive discussion of the adsorption isotherms that have been derived by the methods of statistical thermodynamics instead, we derive only the Langmuir equation for adsorption from the gas phase by this method. The interested reader will find other examples of this approach discussed by Broeckhoff and van Dongen (1970). 

In principle it is possible to write down the rate equation for any rate determining chemical step assuming any particular mechanism. To take a specific example, the overall rate may be controlled by the adsorption of A and the reaction may involve the dissociative adsorption of A, only half of which then reacts with adsorbed B by a Langmuir-Hinshelwood mechanism. The basic rate equation which represents such a process can be transposed into an equivalent expression in terms of partial... 

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