Force, electrostatic

Distribution of ions around a charged particle (dashed line separates Stem layer from the diffuse double layer). 

The factor k has the dimension of 1/length. Its inverse measures the thickness of the double layer, which is determined by the concentration of ions in the water phase (eq. 10.4.4). An electrostatic repulsion becomes noticeable when particles approach close enough for the double layers to overlap (kH 2). 

Very often, the basic elements of a soft phase will be charged, and the distribution of these charges can lead to assembly in solution. There is an attractive force between oppositely charged particles represented by the Coulomb force, 

The simple ideal gas equation assumes a gas in which there are no inter-molecular potentials and that the atoms of the gas occupy a negligible volume. In fact, a more accurate formula to describe the behavior of a real gas is given by the following equation, known as the van der Waals equation of state  

In the point-dipole approximation, one assumes that the dipole moment of a particle is not affected by the surrounding particles, and that the ratio Sp/S is near unity. The dipole 

Anderson (1992) and Davis (1992) have noted that because all ER fluids have some electrical conductivity, then for direct current (dc) or slow alternating current (ac) electric fields, charges will migrate to the particles, eventually completely screening out the dipoles within the particles. If the electrical conductivity of the medium,, differs from that of the particles, Up, then there will still be an effective particle polarizability but its magnitude 

The effective polarizability should still be given by Eq. (8-2) when an ac field is applied whose frequency co is fast compared to the inverse of the Maxwell-Wagner time fMW required for the mobile charges to screen the particle dipoles. When /mww 1 however, should be given instead by Eq. (8-2a). The Maxwell-Wagner time is given by (Parthasarathy and Klingenberg 1996)  

The important effect of even small levels of electrical conductivity was not appreciated until 

1992 hence in earlier work, the simple polarization model with p given by Eq. (8-2) was often applied even in the case of a dc electric field. 

Binding energy estimates from aminoacyl tRNA synthetases  

Estimated relative binding energies (not cat/ m) comparison of des-NHj valine with valine. A 

The specificity of trypsin for peptides which contain Lys or Arg next to the catalytic site can be clearly understood from the X-ray structure, which shows Glu 189 in the position to bind the side chain near the to be cleaved peptide bond [24]. In the absence of substrate, Glu 189 is likely heavily solvated by waters, with little tendency to ion pair. The binding of substrate displaces the water, and, without a cationic side chain nearby, there is a large loss in COO ... HjO interactions without compensating COO . .. H3N interactions. 

In Fig. 1 we show an electrostatic potential molecular surface view of the active site of trypsin and of trypsin inhibitor [25]. The complementarity of the electrostatic potentials (blue = positive red = negative) is apparent for the orientation shown here. 

In summary, there are many examples of specificity in non-covalent interactions of biological interest, but little evidence to suggest that the presence of such interactions (ion pairing, H bonding) provides a thermodynamic driving force for that association. 

These may develop between the growing polymer and a polarised molecule that approaches the polymer chain. They can directly influence the molecular aligmnent prior to reaction. 

---

Added to these interactions are the electrostatic forces related to the dielectric constants and which are important when it is necessary to separate ionic components. 

One fascinating feature of the physical chemistry of surfaces is the direct influence of intermolecular forces on interfacial phenomena. The calculation of surface tension in section III-2B, for example, is based on the Lennard-Jones potential function illustrated in Fig. III-6. The wide use of this model potential is based in physical analysis of intermolecular forces that we summarize in this chapter. In this chapter, we briefly discuss the fundamental electromagnetic forces. The electrostatic forces between charged species are covered in Chapter V. 

There are tliree important varieties of long-range forces electrostatic, induction and dispersion. Electrostatic forces are due to classical Coulombic interactions between the static charge distributions of the two molecules. They are strictly pairwise additive, highly anisotropic, and can be either repulsive or attractive. 

The interplay between favourable reactivity at a collinear geometry and electrostatic forces favouring a T-shaped geometry leads to a bent geometry at the transition state. 

Migration is the movement of ions due to a potential gradient. In an electrochemical cell the external electric field at the electrode/solution interface due to the drop in electrical potential between the two phases exerts an electrostatic force on the charged species present in the interfacial region, thus inducing movement of ions to or from the electrode. The magnitude is proportional to the concentration of the ion, the electric field and the ionic mobility. 

Smith, P.E and Van Gunsteren, W.F. Methc electrostatic forces in computer simulation ... 

C. Niedermeier and P. Tavan. Fast version of the structure adapted multipole method — efficient calculation of electrostatic forces in protein dynamics. Mol. Sim., 17 57-66, 1996. 

In an atomic level simulation, the bond stretch vibrations are usually the fastest motions in the molecular dynamics of biomolecules, so the evolution of the stretch vibration is taken as the reference propagator with the smallest time step. The nonbonded interactions, including van der Waals and electrostatic forces, are the slowest varying interactions, and a much larger time-step may be used. The bending, torsion and hydrogen-bonding forces are treated as intermediate time-scale interactions. 

To separate the non-bonded forces into near, medium, and far zones, pair distance separations are used for the van der Waals forces, and box separations are used for the electrostatic forces in the Fast Multipole Method,[24] since the box separation is a more convenient breakup in the Fast Multipole Method (FMM). Using these subdivisions of the force, the propagator can be factorized according to the different intrinsic time scales of the various components of the force. This approach can be used for other complex systems involving long range forces. 

There are three different algorithms for the calculation of the electrostatic forces in systems with periodic boundary conditions (a) the (optimized) Ewald method, which scales like (b) the Particle Mesh... 

Fig. 1. CPU times (in hours) for 1 ps MD runs for various proteins using three different methods, direct velocity Verlet with a time-step 0.5 fs, r-RESPA with direct evaluation of electrostatic forces and an overall time-step of 4.0 fs, and r-RESPA/TFMM with an overall time-step 4.0 fs (combination of (2,2,2,2) in force breakup).The energy conservation parameter log AE for the three methods are comparable. The CPU time (hours) is for RISC6000 /MODEL 590 computer.

Smith P E and v an Gunsteren W F1993. Methods for the Evaluation of Long Range Electrostatic Forces. In van Gunsteren W F, P K Weiner and A J Wilkinson (Editors). Computer Simulation ofBiomolecular Systems. Leiden, ESCOM. 

In summary, there are indications that neither hydrophobic interactions, nor donor- acceptor interactions are predominantly driving the arene - arene interaction. Osnsequently, we contend that these interactions are mainly governed by London - dispersion and electrostatic forces. 

In this model, reaction is considered to occur preferentially at that position in the aromatic molecule to which the approach of the electrophile causes the smallest increase in zero energy. In molecules possessing polar or dipolar groups, long range electrostatic forces will initially be the most important. 

Hydrophilic and Hydrophobic Surfaces. Water is a small, highly polar molecular and it is therefore strongly adsorbed on a polar surface as a result of the large contribution from the electrostatic forces. Polar adsorbents such as most zeoHtes, siUca gel, or activated alumina therefore adsorb water more strongly than they adsorb organic species, and, as a result, such adsorbents are commonly called hydrophilic. In contrast, on a nonpolar surface where there is no electrostatic interaction water is held only very weakly and is easily displaced by organics. Such adsorbents, which are the only practical choice for adsorption of organics from aqueous solutions, are termed hydrophobic. 

Deep Bed Filters. Deep bed filtration is fundamentally different from cake filtration both in principle and appHcation. The filter medium (Fig. 4) is a deep bed with pore size much greater than the particles it is meant to remove. No cake should form on the face of the medium. Particles penetrate into the medium where they separate due to gravity settling, diffusion, and inertial forces attachment to the medium is due to molecular and electrostatic forces. Sand is the most common medium and multimedia filters also use garnet and anthracite. The filtration process is cycHc, ie, when the bed is full of sohds and the pressure drop across the bed is excessive, the flow is intermpted and solids are backwashed from the bed, sometimes aided by air scouring or wash jets. 

Electrophoresis (qv), ie, the migration of small particles suspended in a polar Hquid in an electric field toward an electrode, is the best known effect. If a sample of the suspension is placed in a suitably designed ceU, with a d-c potential appHed across the ceU, and the particles are observed through a microscope, they can all be seen to move in one direction, toward one of the two electrodes. AH of the particles, regardless of their size, appear to move at the same velocity, as both the electrostatic force and resistance to particle motion depend on particle surface this velocity can be easily measured. 

The combined effect of van der Waals and electrostatic forces acting together was considered by Derjaguin and Landau (5) and independently by Vervey and Overbeek (6), and is therefore called DLVO theory. It predicts that the total interaction energy per unit area, also known as the effective interface potential, is given by V(f) = ( ) + dl ( )- absence of externally imposed forces, the equiHbrium thickness of the Hquid film... 

---