Excluded volume effect, steric

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... 

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. ... 

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. 

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. 

Surface-bound, neutral, hydrophilic polymers such as polyethers and polysaccharides dramatically reduce protein adsorption [26-28], The passivity of these surfaces has been attributed to steric repulsion, bound water, high polymer mobility, and excluded volume effects, all of which render adsorption unfavorable. Consequently, these polymer modified surfaces have proven useful as biomaterials. Specific applications include artificial implants, intraocular and contact lenses, and catheters. Additionally, the inherent nondenaturing properties of these compounds has led to their use as effective tethers for affinity ligands, surface-bound biochemical assays, and biosensors. 

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... 

Point-Uke monomers are assumed (no steric hindrance and excluded volume effects)... 

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). 

Dolan and Edwards (1974) first solved equation (11.58) for steric stabilization in the complete absence of excluded volume effects (i.e. sterically stabilized... 

On going from the isotropic to the anisotropic LC state, the orientation-dependent attractive interactions come into play [125,126] while the steric interactions (the excluded-volume effect) between the mesogenic rods are relaxed [127]. In the LC state, all molecules are required to take an asymmetric shape. Accordingly, chain segments adopt a unique conformer distribution called a nematic conformation [26,93-95,102,103,105]. The Y-Vsp relation determined in the aforementioned studies may be used to examine the mean-field potentials effective in nematic as well as isotropic hquids. After Frank [128] and HUdebrand and Scott [2,129], the intermolecular interaction potentials such as... 

In real polymers, the nature of the long range interaction is quite complicated the interaction will include steric effects, van der Waals attraction, and also may involve other specific interactions mediated by solvent molecules. However, as far as the property of large length scale is concerned, the detail of the interaction will not matter because the excluded volume effect is controlled by the interaction between distant parts of the chain. Thus the interaction between the polymer segments n and m can be expressed by a short range function... 

In a more general case one has a sum of different oscillators. The dispersion interactions are partially responsible for the well known attractive term a V between neutral molecules in the Van der Waals equation of state (p + ajV ) V — b)= RT. The corresponding energy is of the order of 0.1 kJ/M or 10 " eV/mol. By the way, the repulsive term (V — b) in the same equation that takes into account the excluded volume effect b is due to the steric interaction discussed next. 

Comparison of dimensions of the PVB chains with different hydroxyl contents requires measurement of the chain dimensions under 6 conditions where A2 vanishes and the chain assumes its unperturbed dimensions. The Matsuda and Inagaki calculation of freely rotating chain dimensions assumes that excluded volume effects are absent, and that there is no hindrance to rotation about C-C bonds. The ratio of the experimental unperturbed dimensions to the calculated freely rotating dimensions is the steric factor o, a characteristic parameter for a given polymer which is dependent on the hindrance to rotation. Although we have not directly measured the chain dimensions even in good solvents, estimation of the unperturbed dimensions can be made with several theories developed for use with intrinsic viscosities in good solvents, These include the theory of Berry 13... 

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