Repulsive potential barrier

The presence of the large repulsive potential barrier between the secondary minimum and contact prevents flocculation. One can thus see why increasing ionic strength of a solution promotes flocculation. The net potential per unit area between two planar surfaces is given approximately by the combination of Eqs. V-31 and VI-22 ... 

R.J. Smith, M. hotya, J.N. Coleman, The importance of repulsive potential barriers for the dispersion of graphene using surfactants, New Journal of Physics, 12 (2010) 125008. 

A soft repulsive potential barrier, the wall, surrounds the sample and keeps the molecules inside a circular region of radius / = 13.2a. Its form is analogous to that of Eq. (6.3), corrected and truncated so that potential and force due to the wall are purely repulsive. 

When suitable expressions are available for the attractive and repulsive potential energies, e.g. Equation 10.4, then the total potential energy (DLVO theory) can be calculated and plotted as function of the interparticle distance. High values, above IS-lSksT (IcbT=4.12x 10 J at 25 °C), of the repulsive potential barrier indicate stable (actually metastable) colloidal systems. One example is shown in Figure 11.1. 

The relative value of the two potentials reveals the destabdization action of salts added to the emulsion. Addition of an electrolyte to the continuous phase causes a reduction of the electric double-layer repulsion potential, whereas the van der Waals potential remains essentially unchanged. Hence, the reduced electric double-layer potential causes a corresponding reduction of the maximum in the total potential, and at a certain concentration of electrolyte the maximum barrier height is reduced to a level at which the stabdity is lost. 

The height of the potential barrier decreases with the decrease of the transfer distance. Therefore, the contribution of the transitions between excited vibrational states increases and so does the transition probability. However, short-range repulsion between the reactants increases with a decrease of R, and the reaction occurs at an optimum distance R which is determined by the competition of these two factors. In principle, we may imagine the situation when the optimum distance R corresponds to the absence of a potential barrier for the proton. However, we should keep in mind that the transitions between certain excited states may become entirely adiabatic at short distances.40,41 In this case, the further increase of the transition probability with the decrease of R becomes quite weak, and it cannot compensate for the increased repulsion between the reactants, so that even for the adiabatic transition, the optimum distance R may correspond to sub-barrier proton transfer. 

This fact allows the effective relaxation of steric repulsion. The potential barrier for the motion around the C—C single bonds is smaller than that corresponding to the motion around the central C=C bond. Using the potential functions computed for these motions, and assuming a Boltzmann distribution, average torsional angles of 7.7 and 7.1, at 300 K, are obtained for rotations around Cl—C3 and C1=C2, respectively. This torsional motion seems to be due to the nonplanar structure observed experimentally. 

Usually, MD methods are applied to polymer systems in order to obtain short-time properties corresponding to problems where the influence of solvent molecules has to be explicitly included. Then the models are usually atomic representations of both chain and solvent molecules. Realistic potentials for non-bonded interactions between non-bonded atoms should be incorporated. Appropriate methods can be employed to maintain constraints corresponding to fixed bond lengths, bond angles and restricted torsional barriers in the molecules [117]. For atomic models, the simulation time steps are typically of the order of femtoseconds (10 s). However, some simulations have been performed with idealized polymer representations [118], such as Bead and Spring or Bead and Rod models whose units interact through parametric attractive-repulsive potentials. 

Attack on the problem of development of a theory of the potential barriers was begun by Eyring,84 who made approximate quantum-mechanical calculations of the interactions of the hydrogen atoms of the two methyl groups. Various suggestions and calculations about the importance of van der Waals repulsion between attached groups,... 

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