Excluded-volume effect definition

In Flory s theory (/< ), a polymer-solvent system is characterized by a temperature 0 at which (i) excluded-volume effects are just balanced by polymer-solvent interactions, so that os=l, (ii) the second virial coefficient is zero, irrespective of the MW of the polymer, and (iii) the polymer, of infinite molecular weight, is just completely miscible with the solvent The fundamental definition of the temperature is a macroscopic one, namely that for T near 0 the excess chemical potential of the solvent in a solution of polymer volume fraction v2 is of the form (18) ... 

Let us begin with the estimation of the polymer volume fraction inside the coil formed by one long semiflexible macromolecule. It is well known that this estimation depends essentially on the strength of the excluded volume effect, i.e. on the value of the parameter z = vN /a, where v is the excluded volume of a monomer and a is the spatial distance between two neighbouring monomers. To be definite let us adopt for a moment the model shown in Fig. 1 b. Then, if we choose one segment as an elementary monomer, v 6. (see Eq. (2.4)) and a i.e. z p Consequently, the excluded volume effect is pronounced at N p and negligible at N [Pg.77]

What is the free energy of a polymer like, given the excluded volume interactions (See formula (7.19) for the definition of free energy.) Of course, it has the usual entropy term TS (which would be the only term in the case of an ideal gas or an ideal polymer). In addition, it includes the internal energy U of the segment interactions. This latter term is responsible for the swelling. In other words, it accounts for the excluded volume effect. All we need to know now is the contribution of the binary collisions to the internal energy U of the coil. 

The present chapter aims to describe some typical contributions from recent studies on stiff polymers in dilute solution. We will be mainly interested in (1) applicability of the wormlike chain model to actual polymers, (ii) validity of the hydrodynamic theories [2-4] recently developed for this model, and (iii) the onset of the excluded-volume effect on the dimensions of semi-flexible polymers. Yamakawa [5, 6] has generalized the wormlike chain model to one that he named the helical wormlike chain. In a series of papers he and his collaborators have made a great many efforts to formulate its static and dynamic properties in dilute solution. In fact, the theoretical information obtained is now comparable in both breadth and depth to that of the wotmlike chain (see Ref. [6] for an overview). Unfortunately, however, most of the derived expressions are too complex to be of use for quantitative anal) sis and interpretation of experimental data. Thus, we only have a few to be considered with reference to the practical aspects of the helical wormlike chain, and have to be content with mentioning the definition and some basic features of this novel model. 

Note, however, that these authors only consider a reaction to be diftusion controlled , if a system cannot reach an equilibrinm on the typical time scale of reaction and local depletion of reactants occurs. For termination reactions the typical time scale of reaction is severely decreased by intermolecular excluded volume effects, the mean time needed for reaction is larger than typical polymer relaxation times and consequently this reaction is not drSiision controlled. It is important to realize that this definition differs from the one used in this thesis. 

The formulation of the hydrodynamic constant theta and the definition of the Theta Point, where excluded volume effects are neutrahzed. These results were particularly important, because they allow a rational interpretation of physical measurements of dilute polymer solutions. 

Thus, there are two limitations of the pycnometric technique mentioned possible adsorption of guest molecules and a molecular sieving effect. It is noteworthy that some PSs, e.g., with a core-shell structure, can include some void volume that can be inaccessible to the guest molecules. In this case, the measured excluded volume will be the sum of the true volume of the solid phase and the volume of inaccessible pores. One should not absolutely equalize the true density and the density measured by a pycnometric technique (the pycnometric density) because of the three factors mentioned earlier. Conventionally, presenting the results of measurements one should define the conditions of a pycnometric experiment (at least the type of guest and temperature). For example, the definition p shows that the density was measured at 298 K using helium as a probe gas. Unfortunately, use of He as a pycnometric fluid is not a panacea since adsorption of He cannot be absolutely excluded by some PSs (e.g., carbons) even at 293 K (see van der Plas in Ref. [2]). Nevertheless, in most practically important cases the values of the true and pycnometric densities are very close [2,7],... 

As already stated in the Introduction, a problem that sometimes arises in pharmacophore approaches is the need to take into account possible adverse steric interactions between inactive compounds in a dataset and the target protein counterpart In these situations, the definition of ligand-forbidden zones by means of the addition of excluded volume spheres to a pharmacophore is nowadays considered a reasonable and effective improvement. 

Once this definition is adopted, the phenomenology and thermodynamics of this process encompass the interactions between the solute particle and its surroundings, as well as all the changes that take place internally in the solute and those accompanying the rearrangements of the solvent molecules and, if present, other solute particles due to the introduction of the solute particle. It is important to stress that not only the direct solute-solvent interactions be taken into account in the solvation process, but also the other changes mentioned. Excluded from consideration, by the insistence on the fixed positions in the two phases, are effects due to translational degrees of freedom of the solute, which are due to the different volumes at the disposal of the solute particle in these phases. 

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