Excluded volume steric interactions

These are repulsive interactions of short range (0.2-0.3 nm) arising from the highly unfavourable overlap of full electron clouds. They are sometimes called steric interactions because they restrict the relative spatial arrangement of pairs of segments on the same or different macromolecules. The excluded volume expression arises from the fact that the volume occupied by one biopolymer molecule in solution is not available to other biopolymer molecules. Thus the size and shape of the biopolymer molecule/particle (as determined by the macromolecular conformation/ flexibility or aggregate architecture) is of prime importance in relation to steric5 interactions. 

The excluded volume effect is associated with a reduction in the mixing entropy of the system. The resulting steric5 interactions contribute 

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Suppose we have a physical system with small rigid particles immersed in an atomic solvent. We assume that the densities of the solvent and the colloid material are roughly equal. Then the particles will not settle to the bottom of their container due to gravity. As theorists, we have to model the interactions present in the system. The obvious interaction is the excluded-volume effect caused by the finite volume of the particles. Experimental realizations are suspensions of sterically stabilized PMMA particles, (Fig. 4). Formally, the interaction potential can be written as... 

Both of the above approaches rely in most cases on classical ideas that picture the atoms and molecules in the system interacting via ordinary electrical and steric forces. These interactions between the species are expressed in terms of force fields, i.e., sets of mathematical equations that describe the attractions and repulsions between the atomic charges, the forces needed to stretch or compress the chemical bonds, repulsions between the atoms due to then-excluded volumes, etc. A variety of different force fields have been developed by different workers to represent the forces present in chemical systems, and although these differ in their details, they generally tend to include the same aspects of the molecular interactions. Some are directed more specifically at the forces important for, say, protein structure, while others focus more on features important in liquids. With time more and more sophisticated force fields are continually being introduced to include additional aspects of the interatomic interactions, e.g., polarizations of the atomic charge clouds and more subtle effects associated with quantum chemical effects. Naturally, inclusion of these additional features requires greater computational effort, so that a compromise between sophistication and practicality is required. 

If the branching density is sufficiently high to hinder segmental flexibility and impose strong excluded volume and even steric interactions, molecular dimensions become rigid. Measurements of solution and melt viscosity showed that the properties of dendritic molecules approached that of solid spheres as the... 

In Section 3.4a we examine a model for the second virial coefficient that is based on the concept of the excluded volume of the solute particles. A solute-solute interaction arising from the spatial extension of particles is the premise of this model. Therefore the potential exists for learning something about this extension (i.e., particle dimension) for systems for which the model is applicable. In Section 3.4b we consider a model that considers the second virial coefficient in terms of solute-solvent interaction. This approach offers a quantitative measure of such interactions through B. In both instances we only outline the pertinent statistical thermodynamics a somewhat fuller development of these ideas is given in Flory (1953). Finally, we should note that some of the ideas of this section are going to reappear in Chapter 13 in our discussions of polymer-induced forces in colloidal dispersions and of coagulation or steric stabilization (Sections 13.6 and 13.7). 

In the final section, we build on the thermodynamic theories of polymer solutions developed in Chapter 3, Section 3.4, to provide an illustration of how a thermodynamic picture of steric stabilization can be built when excluded-volume and elastic contributions determine the interaction between polymer layers. 

All excluded volume theories for branched chains suffer, however, from a principal deficiency since the assumption is tacitly made that all monomeric units in the molecule may have, in principle, the chance to interact with each other. This is, however, a too extensive assumption since for sterical reasons two remote segments can never form a contact. Hence, the excluded volume effect is highly overestimated for densely branched chains. In fact, highly branched polymers show the phenomenon of swelling but no detectable distortion of Gaussian chain behavior117,137,138,179. ... 

Fig. 25a and b. A protein resistant surface based on the steric repulsion argument commonly used in the colloid stability field U0). The interaction between a polyethylene oxide grafted surface and a protein solution is shown, a. suggests an excluded volume or steric repulsion mechanism b. the surface dynamics or polymer chain motion mechanism (from Ref., 33))... 

The competition between these opposite effects (increase and decrease of pendant double bond reactivity) depends on the concentration of multifunctional monomers, the length and flexibility of the primary chains, and the quality of thermodynamic interactions between monomers and macromolecules. As a rule, cyclization is more effective at the beginning of polymerization, whereas the steric excluded-volume effects are more effective at the later stages. 

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. 

The theories of polymer solutions upon which steric-stability theories are based are usually formulated in terms of a portmanteau interaction parameter (for example Flory s X Parameter and the excluded volume integral) which does not preclude electrostatic interactions, particularly under conditions where these are short range. It is thus appropriate to consider whether polyelect-roly te-stabilisation can be understood in the same broad terms as stabilisation by non-ionic polymers. It was this together with the fact that polyelectrolyte solutions containing simple salts show phase-separation behaviour reminiscent of that of non-ionic... 

In the case of 3,5 substitution, the excluded volume from the rotation of the disubstituted phenyl is large leading to an increased free volume. The local motions thus becomes easier in the glassy state. On the contrary, the 2,5 substitution, for which the net effect of the steric hindrance, the overall bulkiness of the substituents and absence of dipole-dipole interaction result in a higher segmental mobility, has not an important available free volume in the glassy structure. The... 

The purpose of this paper is to calculate the electrochemical potential and the double layer repulsion using a lattice model, applicable to hydrated ions of different sizes, that accounts for the correlation between the probabilities of occupancy of adjacent sites. As the other lattice models,4-7 this model accounts only for the steric, excluded volume effects due to ionic hydration. In feet, short-ranged electrostatic interactions between the ions and the dipoles of the water molecules, as well as the van der Waals interactions between the ions and the water molecules, are responsible for the formation of the hydrated ions. The long-ranged interactions between charges are taken into account through an electrostatic (mean field) potential. The correlation between ions is expected to be negligible for sufficiently low ionic concentrations. 

Excluded volume effects (2) in polymers are defined as those effects which come about through the steric interaction of monomer units which are remotely positioned along the chain contour. Each Individual interaction has only a small effect, but, because there can be many such interactions in a long polymer, excluded volume effects become very large. One consequence of excluded volume is to expand the polymer coil dimensions over that predicted from simple random walk models. The "unperturbed values of the... 

The model considered above does not impose any restriction on the relative positions of the bonds widely separated in the chain, or, in other words, does not prevent parts of the chain occupying the same space. In a real situation, however, this cannot happen as each part of an isolated polymer molecule excludes other more remotely connected parts from its volume. Because of these long-range steric interactions, the true RMS end-to-end distance, is greater than the... 

Excluded Volume Effects. These could be effective hard sphere potentials representing the finite size of the particles. Such potentials are important for the crystallization transition the left side of Figme 3.4 is an example. For ligated nanoparticles, the finite size is likely better represented by a soft sphere potential, the softness due to the steric interactions of the ligands (see below). 

Other extensions of the Dolan and Edwards approach Levine et al. (1978) have developed an elegant matrix procedure to evaluate both the segment density distribution functions and the steric interaction for tails, loops and bridges that are subject to excluded volume considerations. 

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