Contributions to the statistical theory of adsorption. II

1938 ◽  
Vol 34 (4) ◽  
pp. 587-598 ◽  
Author(s):  
G. P. Dube
Keyword(s):  
Statistical Theory ◽  
Partition Function ◽  
Adsorption Isotherm ◽  
Critical Phenomena ◽  
General Problem ◽  
Arbitrary Number ◽  
Solid Surfaces ◽  
Attractive Force ◽  
Adsorbed Molecules ◽  
Number Of Layers

The adsorption of gaseous molecules in a monolayer on solid surfaces has been studied theoretically by several workers, namely Fowler, Peierls and Wang. They have shown that the adsorption isotherm exhibits critical phenomena if there is assumed to be an attractive force between the neighbouring adsorbed molecules, and this has provided an explanation of the critical condensation phenomena observed in deposition experiments, for example those of Cockcroft on the deposition of cadmium on copper. The actual critical phenomena observed consist in the deposition of many layers which are formed if the first layer has fairly started. It is of interest, therefore, to consider if there are other ways in which critical phenomena can arise than through interactions in the first layer. The general problem of adsorption of an arbitrary number of layers is too complicated to study because of the mathematical difficulty in constructing the partition function. We therefore confine ourselves to the consideration of adsorption in two layers only.

Contributions to the statistical theory of adsorption

1938 ◽  
Vol 34 (3) ◽  
pp. 392-398 ◽  
Author(s):  
F. Cernuschi
Keyword(s):  
Statistical Theory ◽  
Partition Function ◽  
Adsorption Isotherm ◽  
Critical Phenomena ◽  
Solid Surface ◽  
Adsorbed Layer ◽  
Single Layer ◽  
Considerable Progress ◽  
Adsorbed Molecules

Considerable progress has been made recently in the study of the adsorption of gaseous molecules in a monolayer on a solid surface, when the molecules are attached to fixed locations on that surface and allowance is made for interaction between the adsorbed molecules. It has been shown in particular that, if there is an attractive field between two adsorbed molecules so that two adsorbed molecules in neighbouring locations are more tightly bound than when they are adsorbed separately at a distance, the adsorption isotherm shows critical phenomena. This feature of the isotherm may be used to give a generally successful interpretation of the well-known critical condensation phenomena discussed first in this manner by Langmuir and Frenkel. A recent example of experiments on this phenomenon is to be found in the work of Cockcroft on the deposition of cadmium on copper. The work of Peierls, who uses Bethe's method for approximating to the partition function for the adsorbed layer, shows in the most convincing way how interactions between neighbours in the single layer lead to critical phenomena for the degree of completion of the layer.

Statistical theory of adsorption with interaction between the adsorbed atoms

1936 ◽  
Vol 32 (3) ◽  
pp. 471-476 ◽  
Author(s):  
R. Peierls
Keyword(s):  
Statistical Theory ◽  
Adsorption Isotherm ◽  
Statistical Problem ◽  
Physical Problem ◽  
Adsorbed Atoms

In a recent paper, Fowler discusses the adsorption isotherm for a monatomic layer, assuming an interaction between neighbouring atoms in this layer. In this paper we do not intend to give a contribution to the physical problem, but merely to show how the statistical problem involved can be solved by a method due to Bethe.

scholarly journals Cloaking Using the Anisotropic Multilayer Sphere

Photonics ◽  
2020 ◽  
Vol 7 (3) ◽  
pp. 52 ◽  
Author(s):  
Sidra Batool ◽  
Mehwish Nisar ◽  
Fabrizio Frezza ◽  
Fabio Mangini
Keyword(s):  
Mathematical Model ◽  
Arbitrary Number ◽  
Static Approximation ◽  
Quasi Static Approximation ◽  
Number Of Layers ◽  
Multilayer Sphere ◽  
Tangential Directions

We studied a Spherically Radially Anisotropic (SRA) multilayer sphere with an arbitrary number of layers. Within each layer permittivity components are different from each other in radial and tangential directions. Under the quasi-static approximation, we developed a more generalized mathematical model that can be used to calculate polarizability of the SRA multilayer sphere with any arbitrary number of layers. Moreover, the functionality of the SRA multilayer sphere as a cloak has been investigated. It has been shown that by choosing a suitable contrast between components of the permittivity, the SRA multilayer sphere can achieve threshold required for invisibility cloaking.

A note on the two-dimensional electrostatic field produced by a line charge near a dielectric wedge

2019 ◽  
Vol 72 (3) ◽  
pp. 341-357
Author(s):  
A D Rawlins
Keyword(s):  
Electrostatic Field ◽  
General Problem ◽  
Line Source ◽  
Arbitrary Number ◽  
Mellin Transform ◽  
Two Dimensional ◽  
Dielectric Wedge ◽  
Line Charge

Summary We shall consider the problem of determining the correct electrostatic field produced when an infinite two-dimensional line source is influenced by an adjacent infinite dielectric wedge. This result corrects a number of previous attempts at this problem, which are shown to be in error. The method avoids using the Mellin transform which has lead to some of these earlier errors. The method is used to solve a more general problem of the electrostatic field produced by an arbitrary number of line sources located in an arbitrary number of contiguous dielectric wedges.

The lifetime of hydrogen adsorbed on a slightly oxidized nickel surface

1957 ◽  
Vol 240 (1222) ◽  
pp. 423-436 ◽  
Keyword(s):  
Oxide Film ◽  
Mass Spectrometer ◽  
Rate Constant ◽  
Molecular Beam ◽  
Copper Surface ◽  
Solid Surfaces ◽  
Nickel Surface ◽  
Order Process ◽  
Adsorbed Molecules ◽  
First Order

A method for investigating the lifetimes of adsorbed molecules on solid surfaces is described. A molecular beam of hydrogen was projected on to the surface of a spinning nickel disk, and the hydrogen evaporating from the surface at different times after deposition was collected and measured with a mass spectrometer. On a slightly oxidized nickel surface all the hydrogen was adsorbed. The subsequent evaporation was a first-order process with a rate constant of 4·5 x 10 11 exp ( -11·5 kcal/ RT ) S -1 . With a mixed molecular beam of hydrogen and deuterium no exchange was produced by the adsorption, which is considered to be molecular. Attempts to remove the oxide film from the nickel surface gave an un­stable surface on which no clear results were obtained. The lifetime of hydrogen on a copper surface was too short to measure.

A Statistical Derivation of Langmuir's Adsorption Isotherm

1935 ◽  
Vol 31 (2) ◽  
pp. 260-264 ◽  
Author(s):  
R. H. Fowler
Keyword(s):  
Adsorption Isotherm ◽  
Equilibrium State ◽  
Ab Initio ◽  
Statistical Methods ◽  
Adsorbed Layer ◽  
Gas Pressure ◽  
Saturation Effect ◽  
Adsorbed Molecules ◽  
Statistical Derivation ◽  
Image Position

The commonest form of Langmuir's adsorption isotherm iswhere θ is the fraction of the surface of the solid covered by adsorbed molecules, p the gas pressure in equilibrium with the adsorbed layer and A = A (T) a function of the temperature alone. This formula is usually derived by a kinetic argument which balances the rates of deposition and re-evaporation. It is perhaps not without interest to show that formula (1) and similar formulae can be obtained directly by the usual statistical methods which evaluate all the properties of the equilibrium state of any assembly. The ordinary derivation is apt to obscure the essentially thermodynamic character of (1) and to lead one to think that its form depends on the precise mechanisms of deposition and re-evaporation, whereas in fact it depends only on the whole set of states, adsorbed and free, accessible to the molecules in question. By suitable use of the usual technique for handling assemblies obeying the Fermi-Dirac statistics the saturation effect can be naturally incorporated in the theory ab initio.

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