Diffusion repulsive interactions

Activated diffusion of the adsorbate is of interest in many cases. As the size of the diffusing molecule approaches that of the zeohte channels, the interaction energy becomes increasingly important. If the aperture is small relative to the molecular size, then the repulsive interaction is dominant and the diffusing species needs a specific activation energy to pass through the aperture. Similar shape-selective effects are shown in both catalysis and ion exchange, two important appHcations of these materials (21). 

For example, at MW = 4 X 10, c = 12 g/liter, and at MW = 5 X 10, c " = 62 g/liter. A polymer solution with concentration c > c is called a semidilute solution because mass concentration is low yet repulsive interactions between solutes are strong. Thermodynamics, viscoelasticity, and diffusion properties of semidilute polymer solutions have been studied extensively since the 1960s. 

At low Q the experiments measure the collective diffusion coefficient D. of concentration fluctuations. Due to the repulsive interaction the effective diffusion increases 1/S(Q). Well beyond the interaction peak at high Q, where S(Q)=1, the measured diffusion tends to become equal to the self-diffusion D. A hydrodynamics factor H(Q) describes the additional effects on D ff=DaH(Q)/S Q) due to hydrodynamics interactions (see e.g. [342]). Variations of D(Q)S(Q) with Q (Fig. 6.28) may be attributed to the modulation with H(Q) displaying a peak, where S(Q) also has its maximum. For the transport in a crowded solution inside a cell the self-diffusion coefficient is the relevant parameter. It is strongly... 

As pointed out before, the net effect of repulsive interaction is the overall increase of chemical diffusion at high coverages. It should be mentioned that this situation may occur in... 

To demonstrate this, in Section 9.2.2 we have studied a stochastic model for an extended ZGB-model including diffusion, desorption and energetic interactions as additional steps. We have used different values of the diffusion and the desorption rates and different values for the energetic parameters. In the case of repulsive interactions the system s behaviour is strongly influenced by. Eaa for large values of Yqo and by for small values of kco-The former parameter leads to a smooth phase transition at yi and the latter to a sharp transition at 2/1 The sharpness and the location of the phase transitions depend also on the diffusion and desorption rate of the A particles. The A-diffusion leads to an increase of the value of 2/2 due to the higher reactivity of the A particles. At lower values of Yco the system behaviour is nearly not influenced by the diffusion. The A-desorption increases the values of the critical points and smoothes the phase transition at 2/2- This effect becomes very important if Ca is large. 

The second strategy we mention in this rapid survey replaces the QM description of the solvent-solvent and solute-solvent with a semiclassical description. There is a large variety of semiclassical descriptions for the interactions involving solvent molecules, but we limit ourselves to recall the (1,6,12) site formulation, the most diffuse. The interaction is composed of three terms defined in the formula by the inverse power of the corresponding interaction term (1 stays for coulombic interaction, 6 for dispersion and 12 for repulsion). Interactions are allowed for sites belonging to different molecules and are all of two-body character (in other words all the three- and many-body interactions appearing in the cluster expansion of the Hss and HMS terms of the Hamiltonian (1.1)... 

Following the work of Amovilli and Mennucci [21] a model for repulsion interactions at diffuse interfaces has been developed. Since the repulsion energy depends on the solvent density it is then natural to replace the constant density p with a position-dependent density p(z). The first attempt made use of p(z) in the final expression for the repulsion energy [17]. Such a model has subsequently been improved by a derivation of a new repulsion expression [18]. 

In a very recent study the lattice calculations have been generalized to biased diffusion [44]. The difference between the tracer atom and the substrate atoms was taken into account by having different vacancy-tracer and vacancy-substrate exchange probabilities, while the rate of vacancy moves was kept constant. A repulsive interaction reduces, while a moderately attractive interaction increases the spreading of the tracer distribution. 

The potential in the diffuse layer decreases exponentially with the distance to zero (from the Stem plane). The potential changes are affected by the characteristics of the diffuse layer and particularly by the type and number of ions in the bulk solution. In many systems, the electrical double layer originates from the adsorption of potential-determining ions such as surface-active ions. The addition of an inert electrolyte decreases the thickness of the electrical double layer (i.e., compressing the double layer) and thus the potential decays to zero in a short distance. As the surface potential remains constant upon addition of an inert electrolyte, the zeta potential decreases. When two similarly charged particles approach each other, the two particles are repelled due to their electrostatic interactions. The increase in the electrolyte concentration in a bulk solution helps to lower this repulsive interaction. This principle is widely used to destabilize many colloidal systems. 

A quantitative treatment of the effects of electrolytes on colloid stability has been independently developed by Deryagen and Landau and by Verwey and Over-beek (DLVO), who considered the additive of the interaction forces, mainly electrostatic repulsive and van der Waals attractive forces as the particles approach each other. Repulsive forces between particles arise from the overlapping of the diffuse layer in the electrical double layer of two approaching particles. No simple analytical expression can be given for these repulsive interaction forces. Under certain assumptions, the surface potential is small and remains constant the thickness of the double layer is large and the overlap of the electrical double layer is small. The repulsive energy (VR) between two spherical particles of equal size can be calculated by ... 

The ability to correctly reproduce the viscosity dependence of the dephasing is a major accomplishment for the viscoelastic theory. Its significance can be judged by comparison to the viscosity predictions of other theories. As already pointed out (Section II.C 22), existing theories invoking repulsive interactions severely misrepresent the viscosity dependence at high viscosity. In Schweizer-Chandler theory, there is an implicit viscosity dependence that is not unreasonable on first impression. The frequency correlation time is determined by the diffusion constant D, which can be estimated from the viscosity and molecular diameter a by the Stokes-Einstein relation ... 

It appears that the data obtained in the above manner prove to be reliable for inferring the charge-potential relationship. Therefore, Fig 3.45 provides convincing evidence that in the case considered double layer repulsive interaction under the conditions of constant charge of the diffuse electric layer is operative. If so, the first integration of Eq. (3.90) predicts that... 

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