Short-range attraction interaction potential

The rheology of many of the systems displayed gel-like viscoelastic features, especially for the long-range attractive interaction potentials, which manifested a non-zero plateau in the shear stress relaxation function, C/t), the so-called equilibrium modulus, which has been considered to be a useful indicator of the presence of a gel. The infinite frequency shear rigidity modulus, was extremely sensitive to the form of the potential. Despite being the most short-... 

Here, we propose a more realistic model of protein-electrolyte mixture. In the present case all the ionic species (macroions, co-ions and counterions) are modelled as charged hard spheres interacting by Coulomb potential as for the primitive model (Sec. 2), but the macroions are allowed to form dimers as a result of the short-range attractive interaction. Numerical evaluation of this multicomponent version of the dimerizing-macroion model has been carried out using PROZA formalism, supplemented by the MSA closure conditions (Sec. 3). 

Two specific interaction schemes are considered a) the particles interact by predominantly hard-sphere repulsive forces b) a short range attractive interaction between particles exists, such that a weak tendency for self association results. Likely candidates for the attractive potential between PSM primary aggregates are hydrophobic and/or hydrogen-bonding interactions of the carbohydrate side chains S. 

The first term on the right-hand side of Eq. 12.9 or 12.14 describes the short-range, repulsive interaction between molecules as they get very close to one another. The second term accounts for the longer-range, attractive potential (i.e the dispersion interaction between the molecules). The final term is the longest-range interaction, between the dipole moments JTj and JTj of the two molecules. In the case where one or both of the dipole moments are zero, the Stockmayer potential reduces to the Lennard-Jones potential discussed in Sec 12.2.1. 

We will briefly discuss the molecular dynamics results obtained for two systems—protein-like and random-block copolymer melts— described by a Yukawa-type potential with (i) attractive A-A interactions (saa < 0, bb = sab = 0) and with (ii) short-range repulsive interactions between unlike units (sab > 0, aa = bb = 0). The mixtures contain a large number of different components, i.e., different chemical sequences. Each system is in a randomly mixing state at the athermal condition (eap = 0). As the attractive (repulsive) interactions increase, i.e., the temperature decreases, the systems relax to new equilibrium morphologies. 

Calculations carried out by Johnson and Morrison [Jj for alumina particles of 0.25 pm radius covered by 22.5 A shells show that the potential energy of interaction is reduced from about —175 kT to about —25 kT. The major effect of the shell is to eliminate the short-range attraction by separating the particles. Differences due to the Hamakcr constant of the shell arc also significant, the difference between the shallowest and deepest well being 20 kT. 

Physisorption or physical adsorption is the mechanism by which hydrogen is stored in the molecular form, that is, without dissociating, on the surface of a solid material. Responsible for the molecular adsorption of H2 are weak dispersive forces, called van der Waals forces, between the gas molecules and the atoms on the surface of the solid. These intermolecular forces derive from the interaction between temporary dipoles which are formed due to the fluctuations in the charge distribution in molecules and atoms. The combination of attractive van der Waals forces and short range repulsive interactions between a gas molecule and an atom on the surface of the adsorbent results in a potential energy curve which can be well described by the Lennard-Jones Eq. (2.1). 

One of the simplest and therefore computationally less expensive potential functions for ion-water consists of the sum of long-range Coulorabic electrostatic interactions plus short-range dispersion interactions usually represented by the Lennard-Jones potential. This last term is a combination of 6 and 12 powers of the inverse separation between a pair of sites. Two parameters characterize the interaction an energetic parameter e, given by the minimum of the potential energy well, and a size parameter a, that corresponds to the value of the pair separation where the potential energy vanishes. The 6-th power provides the contribution of the attractive forces, while repulsive forces decay with the 12-th power of the inverse separation between atoms or sites. 

At the end of the precipitation reaction, the solid particles must be colloidally stable if a uniform particle-size distribution is to be observed. A question important to final uniformity is the particle size when this stability is achieved. The particles will always feel the long-range van der Waals attractive interactions. Interactions of an electrostatic or solvation origin can give rise to a repulsive barrier that can provide kinetic stabilization. At the end of the reaction, particles precipitated from TEOS and titanium alkoxides have final particle number densities, N , of 1016—1018 m-3. These particles are suspended in a solvent with an ionic strength of approximately 10-4 M and have surface potentials of 10-35 mV. Our studies indicate that the particles also feel a short-range repulsive interaction that we have modeled as a solvation interaction with decay... 

The only interaction in this model is a link-link repulsion it is short-range and of the order of a lattice edge. Actually, this approximation is a rather imperfect representation of reality. The true interaction contains simultaneously, a short-range repulsive interaction, or hard core, and an attractive part whose range is a little longer and which results from van der Waals forces. Experimentally, the fact that the mixing of the polymer with the solvent is endothermic is a manifestation of these attractive forces. The shape of the true potential is indicated in Fig. 4.5. 

Figurel2.8isacontourplotofy(r)inunitsofy, forP > Oandcox = coc/10,with r s (p, z) = r (sin cos i ) (the angle cp is neglected due to the cylindrical symmetry of the problem). Darker regions correspond to a stronger repulsive potential, while the white region at p 0 is the short-range, attractive part of the interaction. The repulsion...

To study gelation phenomena in globular proteins, colloid dispersions, etc., Baxter s adhesive hard sphere (AHS) system [38] is often used as a model system. Particles in the AHS system interact with each other through strongly attractive short-range square well potentials. 

Lennard-Jones potential a mathematical model for the energy potential of two electrically neutral, interacting atoms or molecules the Lennard-lones potential accounts for short-ranging repulsive interaction (Born repulsion) and longer-ranging attractive interaction (dispersion forces, van-der-Waals attraction), which are described by a power-law approach with the exponents 12 and 6, respectively. 

The potential model describes the variation of energy of the system as a function of the atomic coordinate. This energy is derived from the long-range electrostatic forces and short-range attractive and repulsive forces, or the coulombic contribution, whereas the short-range interactions are described using simple parameterized functions. A potential model that accurately describes the lattice properties is essential if quantitative resnlts are to be obtained. This is particularly important for surfaces for which it is necessary to describe the interaction at distances possibly far removed from those found in the bulk lattice (Allan et al. 1993). 

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