Stretching force, coulombic

Of these, the interfacial tension may be described by three terms, two of which have been described by Ruckenstein (5) who evaluated the noncoulombic and the coulombic part of the stretching force. The mechanical description (13) is... 

The next step is to assume particular functional forms for the various terms. These can be extremely elaborate, but most are usually based on a simple, chemically intuitive model of the interactions, e.g. stretching of bonds, changes in bond and torsion angles, Coulomb forces and van der Waals intermolecular interactions. Thus, for a molecular solid comprised of discrete molecules, we might well use... 

If the backbone as well as the side chains consist of flexible units, the molecular conformation arises out of the competition of the entropic elasticity of the confined side chains and the backbone [ 153 -155]. In this case, coiling of the side chains can occur only at the expense of the stretching of the backbone. In addition to the excluded volume effects, short range enthalpic interactions may become important. This is particularly the case for densely substituted monoden-dron jacketed polymers, where the molecular conformation can be controlled by the optimum assembly of the dendrons [22-26,156]. If the brush contains io-nizable groups, the conformation and flexibility may be additionally affected by Coulomb forces depending on the ionic strength of the solvent [79,80]. 

When the acidity or the basicity of the solute molecule is high enough to stretch the OH or OD bond to the point of rupture, then the molecule dissociates into ions in solution. Therefore the dissociation constants also serve as a measure of acidity or basicity of solute molecules, especially those which are subject to significant ionization. Since the coulombic forces causing repulsion of ions at membrane-solution interfaces extend to distances farther than those involved in the polar hydrogen bonding repulsions of nonionized solutes at such interfaces, one would expect that a dissociated molecule to be repelled and, in... 

Briefly returning to the Coulomb force theme of Section II, although not presented in Ref. 57, subsequent (unpublished) results have shown that Coulombic forces are dominant in the OH stretch relaxation. Figure 4 displays the results for the bend power spectrum for two different frequency ranges, including the contribution of Coulomb and non-Coulomb forces. From Fig. 4a, Coulomb forces clearly dominate over the full range of interest a similar behavior has also been found for the stretchings spectra (not shown).1 ... 

A classical force field is typically used in which the energy expression consists of harmonic terms for bond stretching and angle bending, a Fourier series for each torsional angle, and Coulomb and Lennard-Jones interactions between atoms separated by three or more bonds (Equations 1- 4). The latter non-bonded interactions are also evaluated between intermolecular atom pairs, and they are reduced by a factor of 2 for intramolecular 1,4-interactions. Inhibitors or substrates are represented in an all-atom format with OPLS-AA parameters" though sometimes with partial charges obtained from quantum mechanical wavefunctions. 

Many molecular modelling techraques that use force-field models require the derivatives of the energy (i e the force) to be calculated with respect to the coordinates. It is preferable that analytical expressions for these derivatives are available because they are more accurate and faster than numerical derivatives. A molecular mechanics energy is usually expressed in terms of a combination of internal coordinates of the system (bonds, angles, torsions, etc.) and interatomic distances (for the non-bonded interactions). The atomic positions in molecular mechanics are invariably expressed in terms of Cartesian coordinates (unlike quantum mechanics, where internal coordinates are often used). The calculation of derivatives with respect to the atomic coordinates usually requires the chain rule to be applied. For example, for an energy function that depends upon the separation between two atoms (such as the Lennard-Jones potential. Coulomb electrostatic interaction or bond-stretching term) we can write ... 

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