Solvents long-range interactions

Hydrodynamic interaction is a long-range interaction mediated by the solvent medium and constitutes a cornerstone in any theory of polymer fluids. Although the mathematical formulation needs somewhat elaborate methods, the idea of hydrodynamic interaction is easy to understand suppose that a force is somehow exerted on a Newtonian solvent at the origin. This force sets the surrounding solvent in motion away from the origin, a velocity field is created which decreases as ... 

In the continuum and semicontinuum models of es, long-range forces due to distant solvent molecules are usually represented by the optical and static dielectric constants. In a true continuum model, the continuity is extended to the origin or to the surface of the cavity. In some sense, the continuum and semicontinuum models both contain both short- and long-ranged interactions. The main difference is that in the semicontinuum model, the molecules in the first shell(s) are structured. 

It is however possible to find conditions, called unperturbed or theta conditions (because for each polymer-solvent pair they correspond to a well-defined temperature called d temperature) in which a tends to 1 and the mean-square distance reduces to Q. In 6 conditions well-separated chain segments experience neither attraction nor repulsion. In other words, there are no long-range interactions and the conformational statistics of the macromolecule may be derived from the energy of interaction between neighboring monomer units. For a high molecular weight chain in unperturbed conditions there is a simple relationship between the mean-square end-to-end distance < > and the mean-... 

The main aspect of these theories is the identification of the source of activation for the kinetics of the rate-determining process. The two sources of activation in the electrochemical literature are thermal and electrostatic. The first involves strong short-range forces and is associated with atomic bond stretches, while the second considers weak long-range interactions with the solvent regarded as a continuum dielectric undergoing microscopic fluctuations. 

In the sense of RG theory, bare interactions with

long-range interactions [289]. One source for r 4-dependent interactions is the attractive interaction of ions with rotating dipoles in solvent molecules. Hpye and Stell [304] argued that theories for the ion-solvent term can also be profitably employed for modeling ion-ion pair interactions. 

This metal dependence also carries over to the spin-paired species. In the low-dielectric-constant solvents, these can no longer be represented in terms of weak, long-range interactions possibly mediated by an intervening cation, but are now distinct, new molecular entities (Section III,B,5). 

The average extension of the chain in space can be modified by its interaction with the environment. This modification will occur in dilute solution, except in the special case where the chain is dissolved in a 0 solvent. The typical dilute solution is prepared using a good solvent, in which case the polymer-solvent interaction produces a positive excluded volume that causes expansion of a flexible chain. The introduction of the consequences of long-range interactions into the conformational description of a linear chain greatly complicates the theoretical description A5-181 The focus is on an expansion factor that can be defined as... 

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