Bond, chemical length

This is one factor determining the spatial extention of matter. In much the same way, the Pauli principle gives chemical bonds their length. The valence electrons of one atom are not allowed (at least not readily) to penetrate the occupied shells of the neighboring atom, and thus atoms cannot be pressed too close. This is the second way in which the Pauli principle acts to give matter its... 

The spherical angles 0 and 4> give the orientation of the B-C chemical bond of length q , leading to the following Cartesian coordinates ... 

Fig. 1.3. A portion of the node-link-blob superlattice model for p > Pc-The distance between two nodes of the lattice (say A and B) is while the chemical length of the tortuous bond of the superlattice is Lc.

As discussed in Section 1.2.1, for such systems near the percolation threshold Pc the nearest-neighbour occupied bonds (or sites) form a statistically defined super-lattice , made of tortuous link-bonds (of chemical length Lc) crossing at nodes separated by an average distance the percolation correlation length (see Fig. 1.3 of Chapter 1). The external stress... 

Second, every vdW systems contains at least one vdW bond, the length of which is much greater than that of any chemical bond and which equals about 0.2-0.5 nm. 

The qualitative relationships between the three bond properties, length, dissociation energy and force constant are often useful in predicting or interpreting physical and chemical properties. Since we know how each of them depends on the bond order, we can infer the dependence of any one of them on another. Specifically, we have the following ... 

The simplest models of covalently bonded chemical substances are the so-called ball-and-stick models, in which the atoms are represented by balls and the sticks represent the bonds. In constructing such models it is usual to make use of so-called standard bond lengths and standard bond angles . In addition, certain orientations of groups of atoms around bonds are also assumed, i.e. preferred torsional angles . These standards correspond approximately to properties of the real molecules and control the possible shapes that the molecules can take. What are the reasons for these values and what are they for various types of molecule ... 

The first topological index to be published was the Wiener index, W, which is half the sum of the bond-by-bond path lengths between each pair of atoms. The Wiener index has some interesting mathematical properties and can correlate well with chemical properties such as melting point and viscosity. It can be calculated from each off-diagonal element of the path length matrix, Djj, of a structure ... 

The low conductivity of the sulfonated aromatic PEMs at low RH has been attributed to the fact that sulfonated aromatic polymers have fewer connected water domains as well as more phase mixing of the hydrophobic and hydrophilic domains [33], Block copolymers, consisting of covalently bonded chemically dissimilar sequences, exhibit highly periodic microphase-separated structures [34], The characteristic lengths of the structures are determined by the molecular size and are in the 10-100 nm range. Therefore, many research studies have focused on the development of sulfonated multiblock copoly(ether sulfone)s for improving the nanophase-separated structures and proton conductivity under a low RH. 

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