Bond strength, defined

The thermal vibrations of atoms in molecules lead to absorption bands in the infrared (IR) region (Bellamy, 1964 Colthup et al., 1964 Hesse et al., 1984). IR bands are most intense if a dipole is induced by the vibration (OH, NH, CH, C=0, C=N). The mass of the interacting atoms Ml and M2 and the bond strengths defined by a force constant f determine the wave number n or energy of an infrared absorption band v = K(f/M ) , where the reduced mass is M = MjM2/Mj+M2 and K is a constant conversion factor. The frequency n for the CH-stretch vibration is around 2900 cm for C=0 close to 1700 cm. Hydrogen bonds lead to a broadening and low-frequency shift of OH and NH vibrations (3400 cm —> 3200 cm ). 

This mechanism implies that the Co-C bond in the coenzyme is not particularly strong because it requires the Co-C bond to be spontaneously homolyzing at ambient temperatures at a rate fast enough to account for the rapid turnover seen for the B -dependent enzymes ( 10 s ). Halpern estimated Co-C bond strengths—defined by Eq. 16.8—in Bi2 models by two methods. The first involves measuring the equilibrium constant for Eq. 16.6. From the Aif and values, and given the known heats of formation of PhCH=CH2 and PhCH—CH3, the A// and AS for Eq. 16.8 can be deduced. 

Only a small amount of work has been done up to now concerning the prediction of bond strengths and other properties based on the results of the analysis of the resin. Ferg et al. [59] worked out correlation equations evaluating the chemical structures in various UF-resins with different F/U molar ratios and different types of preparation on the one hand and the achievable internal bond as well as the subsequent formaldehyde emission on the other hand. These equations are valid only for well defined series of resins. The basic aim of such experiments is the prediction of the properties of the wood-based panels based on the composition and the properties of the resins used. For this purpose various structural components are determined by means of - C NMR and their ratios related to board results. Various papers in the chemical literature describe examples of such correlations, in particular for UF, MF, MUF and PF resins [59-62]. For example one type of equation correlating the dry internal bond (IB) strength (tensile strength perpendicular to the plane of the panel) of a particleboard bonded with PF adhesive resins is as follows [17]... 

The density matrix can also be used to generate information about bond strengths. A quantitative measure is given by the Bond Order (BO). It was originally defined" from bond distances as... 

Defining ethane, ethylene and acetylene to have bond orders of 1, 2 and 3, the constant a-is found to have a value of approximately 0.3 A. For bond orders less than 1 (i.e. breaking and fonning single bonds) it appears that 0.6 A is a more appropriate proportionality constant. A Mulliken style measure of the bond strength between atoms A and B can be defined from the density matrix as (note that this involves the elements of the product of the D and S matrices). 

In a stable ionic structure the valence (ionic charge) of each anion with changed sign is exactly or nearly equal to the sum of the electrostatic bond strengths to it from adjacent cations. The electrostatic bond strength is defined as the ratio of the charge on a cation to its coordination number. 

The order of a bond may be defined as the number of electron pairs that constitute the bond. Thus the bond orders of single, double, and triple bonds are respectively 1, 2, and 3. As the number of electron pairs forming the bond increases, the attraction of the bonding electrons for the two atomic cores increases, so the bond strength increases and the bond length decreases. 

The T-bond strength Erot(T) can be defined as the energy barrier of the cis-trans isomerization. Significant data for the double bonds >C=C< and >Si=Si< are summarized in Table 1. 

The most striking vertical trend concerns the metal-hydride bond strengths, as summarized in Table 4.55. We define the first M—H bond strength (A mh(1)) for each species as the energy needed to break the first M—H bond ... 

It has become clear in the past decade that strong hydrogen bonding has associated with it several characteristic properties. In particular, as hydrogen-bond strength changes, maxima or minima are observed in nmr chemical shifts, the isotope effect on the chemical shift A[5( H) — 8( H)] defined on p. 271, ir Vah/vad band ratios, and in the isotope-fractionation factor, p. 

This method derives from the observation that the degree of enrichment in a set of cogenetic silicate minerals (expressed as oxygen isotope index I- 0) can be related to bond strengths in minerals (Taylor, 1968). The oxygen isotope index for phase A is defined by... 

The relationships between rate of cleavage, bond strength and radical-anion redox potential can be combined in one concept. In this, cleavage rate is dependent on a reaction driving force, defined as the difference between the redox potential of the substrate radical-anion and the redox potential of the product anion in equ-librium with the coiresponding radical (E° for bromine ion, bromine radical as an example). 

Effective cluster interactions. The second important parameter in all cluster models is a series of interaction coefficients that define the bond strengths. An... 

Analyses of metal coordination and the bond strengths started with the publication by Pauling (1929) of an article entitled The Principles Determining the Structure of Complex Ionic Crystals. In this article Pauling defined the bond strength as listed above. Later, it became clear from measurements of bond lengths by X-ray crystallographic analyses that... 

The most probable valence for the external bonds of an anion is called the anion bonding strength, 5a, and is defined by eqn (4.1) ... 

In Section 4.5 it was shown that the bonding strengths of soft cations are less well defined than those of hard cations since they are able to form stable compounds with anions having a wider range of anion bonding strengths. Consequently they also display a wider range of coordination numbers. Thus the soft Zn + cation is found in four and six coordination in contrast to the similar, but hard, cation which is usually found only in 6-coordination. Most hard... 

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