Resonating valence bonds andd-wave superconductivity

1988 ◽  
Vol 37 (7) ◽  
pp. 3664-3666 ◽  
Author(s):  
G. Kotliar
Keyword(s):  
Valence Bonds

Temperature Dependence of the Mechanical and Stress-Optical Behavior of Elastomers

1960 ◽  
Vol 33 (3) ◽  
pp. 763-789
Author(s):  
J. Kruse ◽  
T. Timm
Keyword(s):  
Elastic Modulus ◽  
Natural Rubber ◽  
Optical Constant ◽  
General Rule ◽  
Absolute Temperature ◽  
Double Refraction ◽  
Temperature Function ◽  
Entropy Elasticity ◽  
Optical Behavior ◽  
Valence Bonds

Abstract The temperature functions of the elastic modulus K2 and of the stress-optical constant K1 or its reciprocal 1/K1 were investigated for several elastomers. In the case of a hypothetical rubber which we have called “ideal” rubber—in analogy to gases—theory requires a direct proportionality between K2 or 1/K1 and the absolute temperature. The temperature functions of K2 and 1/K1 which we found by experiments with “real” elastomers show characteristic negative and positive deviations Δa2 and Δa1 from “ideal” values. When we put these values of Δa2 and Δa1 into a coordinate system, we find a certain orderly arrangement of the different elastomers, which allows us to picture a relationship between molecular structure and the values of Δa2 and Δa1. This brings up the possibility of explaining the experiments with the help of already known molecular-physical concepts. Although other explanations are conceivable the attempt is made to develop the simplest and most obvious ideas. It is conjectured that negative values of Δa2 and Δa1 come about from a loosening of secondary valence bonds—in certain ways, like crystal bonds— between neighboring molecules. Negative Δa1 values were found only in the crystallizable elastomers. It is further conjectured that positive values of Δa2 and Δa1 may result from the liberation by heat, of blocked, bulky molecular segments. These molecular segments can then contribute to the entropy elasticity only at higher temperatures. Positive Δa2 and Δa1 values are found chiefly in strongly crosslinked elastomers. Brief attention is given to the physical processes which are responsible for the elongation—double refraction and the entropy-elasticity. From this, it seems that the stress-optical constant and its temperature function are connected with properties of the molecular chains and on their orientability and crystallizability. The elastic modulus and its temperature function are strongly affected by the structure of the network and the molecular cohesive forces. Worthwhile hints about crystallization tendency, polarity and degree of symmetry of the different systems are given by the Δa1 and Δa2 values in the above mentioned coordinate systems. Natural rubber was tested in different recipes. The results of milling, of sulfur and accelerator additions, of time and temperature of vulcanization, on the values of K2, 1/K1, Δa2 and Δa1 were all investigated. The values of 1/K1 are at their highest level for dried latex films (unvulcanized). Milling and vulcanization, particularly the use of rather long periods and high temperatures, lower the value of 1/K1. A drop in the value of 1/K1, which regularly appears with a reduction of the negative Δa1 value, is explained as a loosening of secondary valence molecular couplings. According to this, natural rubber in the latex state is most strongly associated. According to this explanation, stretching in the unvulcanized condition is sufficient to loosen the secondary valence molecular bonds. Milling and vulcanization also act to loosen the linkages. Secondary valence bonds which are loosened by warming, as a general rule, are reestablished by prolonged cooling. It is to be supposed that the secondary valence molecular bonds under consideration are limited to small regions, somewhat comparable to the ordering in liquids. With an increasing degree of vulcanization, the Δa2 values go through a maximum which perhaps coincides with the condition of optimum vulcanization. This is explained as a maximum of the entropy-elasticity. In the case of slightly milled natural rubber which is appropriately vulcanized, the value of Δa2 can become practically zero. The change of the elastic modulus with temperature then is “ideal.” Nevertheless, no “ideal” rubber exists here, for Δa1 is less than zero.

scholarly journals Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4

2018 ◽  
Vol 8 (3) ◽  
Author(s):  
Itamar Kimchi ◽  
Adam Nahum ◽  
T. Senthil
Keyword(s):  
Quantum Magnets ◽  
Valence Bonds

Chains of Metallic Clusters With Ligands

2021 ◽  
pp. 96-119
Keyword(s):  
Geometric Approach ◽  
Higher Dimension ◽  
Metallic Clusters ◽  
The Core ◽  
Metal Atoms ◽  
Dimension Space ◽  
Metal Chain ◽  
Valence Bonds

This chapter geometrically investigated the structure of clusters, the core of which represent the metal chains (linear or curved) of both identical and different elements. It was shown that the dimension of the structures of these clusters is more than three. To create a model of these chains in a higher dimension space, a new geometric approach has been developed that allows us to construct convex, closed polytopes of these chains. It consists of removing part of the octahedron edges necessary for constructing the octahedron and adding the same number of new edges necessary to build a closed polytope chain while maintaining the number of metal atoms and ligands and their valence bonds. As a result, it was found that metal chain polytopes consist of polytopes of higher dimension, adjacent to each other along flat sections.

scholarly journals Valence bonds in planar and quasi-planar boron disks

2019 ◽  
Vol 21 (2) ◽  
pp. 729-735 ◽  
Author(s):  
Issofa Patouossa ◽  
Athanasios G. Arvanitidis ◽  
Jules Tshishimbi Muya ◽  
Minh Tho Nguyen ◽  
Arnout Ceulemans
Keyword(s):  
Boron Clusters ◽  
Electron Counting ◽  
Counting Rules ◽  
Valence Bonds

Valence bonds within the perimeter of disk-like boron clusters with a concentric topology follow simple 4n and 8n electron counting rules.

scholarly journals Resonating valence bonds and mean-fieldd-wave superconductivity in graphite

2007 ◽  
Vol 75 (13) ◽  
Author(s):  
Annica M. Black-Schaffer ◽  
Sebastian Doniach
Keyword(s):  
Valence Bonds

scholarly journals On the Possibility of Mixed Rydberg-Valence Bonds

1999 ◽  
Vol 103 (18) ◽  
pp. 3575-3580 ◽  
Author(s):  
Alexander I. Boldyrev ◽  
Jack Simons
Keyword(s):  
Valence Bonds

scholarly journals On the Edge Metric Dimension of Certain Polyphenyl Chains

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Muhammad Ahsan ◽  
Zohaib Zahid ◽  
Dalal Alrowaili ◽  
Aiyared Iampan ◽  
Imran Siddique ◽  
...  
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Metric Dimension ◽  
Chain Graph ◽  
Minimum Number ◽  
Valence Bonds

The most productive application of graph theory in chemistry is the representation of molecules by the graphs, where vertices and edges of graphs are the atoms and valence bonds between a pair of atoms, respectively. For a vertex w and an edge f = c 1 c 2 of a connected graph G , the minimum number from distances of w with c 1 and c 2 is called the distance between w and f . If for every two distinct edges f 1 , f 2 ∈ E G , there always exists w 1 ∈ W E ⊆ V G such that d f 1 , w 1 ≠ d f 2 , w 1 , then W E is named as an edge metric generator. The minimum number of vertices in W E is known as the edge metric dimension of G . In this paper, we calculate the edge metric dimension of ortho-polyphenyl chain graph O n , meta-polyphenyl chain graph M n , and the linear [n]-tetracene graph T n and also find the edge metric dimension of para-polyphenyl chain graph L n . It has been proved that the edge metric dimension of O n , M n , and T n is bounded, while L n is unbounded.

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