Repulsive surface

As the pH is iacreased or decreased from the isoelectric point, the particles acquire a charge (surface potential) that can enhance repulsion. Surface charge on the particle can be approximated by measuring 2eta potential, which is the electrostatic potential at the Stem layer surrounding a particle. The Stem layer is the thickness of the rigid or nondiffiise layer of counterions at a distance (5) from the particle surface, which corresponds to the electrostatic potential at the surface divided by e (2.718...). 

Fig. 16. Schematic of the repulsive surface correlating to the triplet products illustrating...

Fig. 9.17 PE profiles for attractive and repulsive surfaces of an exothermic reaction.

Takatsuka and Gordon (21a) have developed a "full collision" formulation of photodissociation which describes a multichannel process on the repulsive surface for both direct and indirect events. The scattering wavefunctions that are used to generate the T-matrix and the FC overlaps are not zeroth-order uncoupled functions, but solutions of the coupled-channel problem. 

From this starting point, the authors develop equations leading to the evaluation of the real symmetric K matrix to specify the scattering process on the repulsive surface and propose its determination by a variational method. Furthermore, they show explicitly the conditions under which their rigorous equations reduce to the half-collision approximation. A noteworthy result of their approach which results because of the exact treatment of interchannel coupling is that only on-the-energy-shell contributions appear in the partial linewidth. Half-collision partial linewidths are found not to be exact unless off-the-shell contributions are accidentally zero or (equivalently) unless the interchannel coupling is zero. The extension of the approach to indirect photodissociation has also been presented. The method has been applied to direct dissociation of HCN, DCN, and TCN and to predissociation of HCN and DCN (21b). 

Fig. 1. Reaction coordinate diagram showing general locations of regions for repulsive (R), mixed (M) and attractive (A) energy release. For a mixed energy release surface the transition state will be near M, but for an attractive (repulsive) surface the transition state will be near R(A).

After pH adjustment, the water enters a precipitation/coprecipitation tank, where chemical reagents (such as iron or aluminum salts) are carefully added to form the precipitates. The resulting precipitates are often colloidal or are otherwise too fine grained to readily settle out of solution. They may also have repulsive surface charges that prevent them from agglomerating and settling. As shown in Figure 7.1,... 

Floe Agglomerates of suspended particles in a water treatment tank created by the addition of coagulants to neutralize repulsive surface charges on the particles (compare with coagulation and flocculation). 

Discussion of repulsive surfaces splits into two categories ... 

Repulsive surfaces are associated with the backward scattering of a rebound mechanism, in which A collides with BC in a head-on collision and AB rebounds backwards. 

These conclusions are confirmed by chemiluminescence and molecular beam experiments for some reactions with highly repulsive surfaces, but which, nonetheless, give both vibration and translation in the products. 

The two helical arms become uncoiled in unfolded state a, which is the result of turning off the attractive nonbonding B-B interactions (Cf. Fig. 3). However, the helical structure of the two arms is retained in this unfolded state. The corresponding R distributions are clearly influenced by immobilization, as well as by the type of surface (Cf. Fig. 4). In comparison to the freely diffusing polypeptide, the R distribution in unfolded state a on the attractive surface is seen to be more asymmetrical and shifted to longer values of R. The opposite trend is observed in the case of the repulsive surface, where the distribution becomes more symmetrical and shifts to lower values... 

Fig. 4 Distributions of end-to-end distance, R, under different conditions. Black, red and green correspond to the cases of free diffusion, repulsive surface-immobilization and attractive surface-immobilization, respectively. The results were converged to within an error bar of 5%.

In the case of the unfolded (either a or / ) freely diffusing polypeptide, C(t) is seen to decay on time scales of 10-100, which are significantly slower and correspond to a wider dynamical range in comparison to the folded state. This is consistent with the fact that the underlying interactions are of the excluded volume type, which are short-ranged so that the dynamics is mostly diffusive and relatively slow. Immobilization on a repulsive surface does not alter C(t), since the surface-polypeptide interactions are very similar to the intramolecular interactions in this case. However, C(t) is observed to decay... 

The decay of C(t) in the midpoint state (either a or ft) is characterized by an even wider dynamical range. The short time scales in the cases of freely diffusing and repulsive surface-immobilized polypeptides are attributed to dynamics within the folded and unfolded sub-populations mentioned above. An... 

The distributions of (R)tw obtained for a polypeptide immobilized on the repulsive surface are presented in Fig. 10. As expected, the results in the folded state are not affected by surface immobilization. The (R)tw distributions in unfolded states a and / are also seen to follow the same general trends as for the freely diffusing polypeptide. The behavior at the two midpoint states is however rather different from that observed in the case of the freely diffusing polypeptide. More specifically, the (R)tw distribution is not bi-modal for all values of Tw considered. Thus, the geometrical constraint represented by the repulsive surface is sufficient for introducing a significant bias toward the folded state at the midpoint. 

Fig. 10 The distributions of the time-window-averaged end-to-end distance for a repulsive-surface-immobilized polypeptide, as obtained for the indicated values of the averaging-time-window, Tw-...

Bowman, R.M., Dantus, M., and Zewail, A.H. (1990). Femtosecond transition-state spectroscopy of iodine From strongly bound to repulsive surface dynamics, Chem. Phys. Lett. 161, 297-302. 

For small values of e = 4 - d, a polymer chain in solution is nearly Brownian and a mean field method might reasonable results in this limit. Thus it is possible consider that the chains feel a potential V (x) which is the sum of the (attractive and repulsive) surface potential and of a self - consistent potential produced by the other chains. 

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