Rigid bond

If the vibrations are small (e.g., low temperatures, rigid bonding framework), the higher order terms can be neglected. Thus the potential energy simplifies to... 

The hardness and strength of alloys can be explained in terms of bonding. The impurity atoms added may form localized and rigid bonds. These tend to prevent the slippage of atoms past each other, which results in a loss of malleability and an increase in hardness. 

Note that in case of VTES (I) there is a chemical interaction via the vinyl group between silane and the filler, which results in a sufficiently rigid bond between the matrix and filler. The agent (II) undergoes homopolymerization so that an elastic sublayer ( shell ) is formed around each filler particle, the tensile and impact strength of the composition increase as a result. 

Single bonds are flexible, and can bend and rotate easily. Double bonds are more rigid. A rigid bond does not allow the molecules to fit together easily, so they can t pack tightly into a solid. 

Atom dynamics Group contribution and rigid bonds/angels Specific adsorption Dipolar hard sphere SPC, ST2, TIPS Polarizable H Bonds... 

Liquid crystal behavior is a genuine supramolecular phenomenon based on the existence of extended weak interactions (dipole-dipole, dispersion forces, hydrogen bonding) between molecules. For the former two to be important enough, it is usually necessary for the molecules to have anisotropic shapes, able to pack efficiently so that these weak interactions can accumulate and co-operate, so as to keep the molecules associated in a preferred orientation, but free enough to move and slide, as they are not connected by rigid bonds. 

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

Rigid rotor The simple model of molecular rotation assuming that two atoms are connected by rigid bonds when rotating. 

ISO 1827 1991 Rubber, vulcanized or thermoplastic - Determination of modulus in shear or adhesion to rigid plates - Quadruple shear method ISO 1922 2001 Rigid cellular plastics - Determination of shear strength ISO 4587 2003 Adhesives - Determination of tensile lap-shear strength of rigid-to-rigid bonded assemblies... 

Complexity-related counts for rotatable (RTB) and rigid bonds (RGB), and the number of rings (RNG) [29] ... 

TABLE 2.3 Rigid-Bond Test for p-Nitropyridine-N-oxide at 30 K... 

The use of more sophisticated scattering models, in which bonding effects on the charge density are taken into account, discussed in chapter 3, leads to a significant improvement in the results of the rigid-bond test. An example, based on a low-temperature analysis of p-nitropyridine-N-oxide, is given in Table 2.3. 

The introduction of standard aspherical-atom scattering factors leads to a very significant improvement in Hirshfeld s rigid bond test. The results are a beautiful confirmation of Hirshfeld s (1992) statement that an accurate set of nuclear coordinates (and thermal parameters ) and a detailed map of the electron density can be obtained, via X-ray diffraction, only jointly and simultaneously, never separately or independently . 

The Na+ ions are surrounded by a pool of delocalized electrons, which acts as the glue that holds the metallic atoms together. This arrangement is referred to as the metallic bond. This mobile pool of electrons accounts for the characteristic properties of metals. For example, because the electrons are loosely attached, rigid bonds are not formed and atoms can easily be shaped because the electrons move freely throughout the structure. 

Rosenfield, R. E., Trueblood, K. N., and Dunitz, J. D. (1978). A test for rigid-body vibrations based on a generalization of Hirschfeld s rigid-bond postulate. Acta Cryst. A34, 828-9. 

It was only recently recognized (38) that such constraints, even when applied to a 1arge number of bonds simultaneously, need not appreciably increase the machine time required to do one integration step. Of course the mass-modified system does not have the same dynamics as the original system, and the rigid-bond system has neither the same dynamics nor the same statistical properties however, accurate dynamics is needed only in the bottlenecks— correct statistical properties are sufficient elsewhere. In view of the near-harmonicity of the bonded vibrations, it is probable that their effect on the statistical properties could be computed as a perturbation to the statistical properties of a rigid-bond system. 

We can understand some of the differences in standard molar entropies in terms of differences in structure. For example, let s compare the molar entropy of diamond, 2.4 J-K 1-mol, with the much higher value for lead, 64.8 JKr -mol-1. The low entropy of diamond is what we should expect for a solid that has rigid bonds at room temperature, its atoms are not able to jiggle around as much as the atoms of lead, which have less directional bonds, can. Fead also has much larger atoms... 

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