Electrostatic and van der Waals

The PEF is a sum of many individual contributions, Tt can be divided into bonded (bonds, angles, and torsions) and non-bonded (electrostatic and van der Waals) contributions V, responsible for intramolecular and, in tlic case of more than one molecule, also intermoleculai interactions. Figure 7-8 shows schematically these types of interactions between atoms, which arc included in almost all force field implementations. 

Fhe van der Waals and electrostatic interactions between atoms separated by three bonds (i.c. the 1,4 atoms) are often treated differently from other non-bonded interactions. The interaction between such atoms contributes to the rotational barrier about the central bond, in conjunction with the torsional potential. These 1,4 non-bonded interactions are often scaled down by an empirical factor for example, a factor of 2.0 is suggested for both the electrostatic and van der Waals terms in the 1984 AMBER force field (a scale factor of 1/1.2 is used for the electrostatic terms in the 1995 AMBER force field). There are several reasons why one would wish to scale the 1,4 interactions. The error associated wilh the use of an repulsion term (which is too steep compared with the more correct exponential term) would be most significant for 1,4 atoms. In addition, when two 1,4... 

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres. 

This means that the relative importance of the electrostatic and van der Waals forces will vary with the size of the particle, with electrostatic forces more important for larger particles and van der Waals forces dominant for smaller particles. 

All this being said, perhaps the most definitive study of the relative roles of electrostatic and van der Waals forces was performed by Gady et al. [86,101,102]. In their studies, they attached a spherical polystyrene particle, having a radius between 3 and 6 p.m, to the cantilever of an atomic force microscope. They then conducted three distinct measurements that allowed them to distinguish between electrostatic and van der Waals forces that attracted the particle to various conducting, smooth substrates. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Although this model seems to reflect well some experimental observations of contact and separation [6,7] the assumptions made in its formulation are in fact unphysical. They assume that the solids do not interact outside the contact region, whereas in reality electrostatic and van der Waals forces are nonzero at separations of several nanometers. The assumptions made by JKR lead to infinite values of stress around the perimeter of the connecting neck between sphere and plane. 

Roth, CM Lenhoff, AM, Electrostatic and van der Waals Contributions to Protein Adsorption Comparison of Theory and Experiment, Langmuir 11, 3500, 1995. 

Components of the tear attach to contact lenses by electrostatic and van der Waals forces and build up to form deposits. Deposits on the surface and in the lens matrix may result in reduced visual acuity, irritation, and in some instances serious ocular complications. The composition of deposits vary because of the complexity of an individual s ocular physiology-pathology. Lysozyme is a major component of soft lens deposits, especially found on high-water-content ionic lenses [312]. Calcium [313] and lipids [314] are infrequent components of deposits, occurring as inorganic salts, organic salts, or as an element of mixed deposits, or as a combination thereof [315,316]. 

From (2.70), it follows that the free energy cannot be divided simply into two terms, associated with the interactions of type a and type b. There are also coupling terms, which would vanish only if fluctuations in AUa and AUb were uncorrelated. One might expect that such a decoupling could be accomplished by carrying out the transformations that involve interactions of type a and type 6 separately. In Sect. 2,8.4, we have already discussed such a case for electrostatic and van der Waals interactions in the context of single-topology alchemical transformations. Even then, however, correlations between these two types of interactions are not... 

With this pathway, the separation between the electrostatic and van der Waals contributions in the LIE equation (12.61) is only approximate. Indeed, the vertical,... 

The free energy calculations were calculated with electrostatic and van der Waals contributions evaluated separately for both the complex and the isolated ligand. The total free energy change of -10.3 kcal/mol agreed with experimental measurements of -11.5 kcal/mol6 for netropsin... 

CNT can markedly reinforce polystyrene rod and epoxy thin film by forming CNT/polystyrene (PS) and CNT/epoxy composites (Wong et al., 2003). Molecular mechanics simulations and elasticity calculations clearly showed that, in the absence of chemical bonding between CNT and the matrix, the non-covalent bond interactions including electrostatic and van der Waals forces result in CNT-polymer interfacial shear stress (at OK) of about 138 and 186MPa, respectively, for CNT/ epoxy and CNT/PS, which are about an order of magnitude higher than microfiber-reinforced composites, the reason should attribute to intimate contact between the two solid phases at the molecular scale. Local non-uniformity of CNTs and mismatch of the coefficients of thermal expansions between CNT and polymer matrix may also promote the stress transfer between CNTs and polymer matrix. 

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