Volume restriction interaction

A reduction of the configurational entropy of the chains in the interaction zone this entropy reduction results from the decrease in the volume available for the chains when these are either overlapped or compressed. This is referred to as volume restriction interaction, entropic or elastic interaction, and is described by a free energy of interaction, G j. 

The second contribution to the steric interaction arises from the loss of configurational entropy of the chains on significant overlap. This effect is referred to as entropic, volume restriction, or elastic interaction, Gei. The latter increases very sharply with a decrease in h when the latter is less than 8. A schematic representation of the variation of Gmix, Gei, G, and Gj =G X + Gei + Ga) is given in Fig. 10. The total energy-distance curve shows only one minimum, at h 25, the depth of which depends on 5, R, and A. At a given R and A, G decreases with an increase in 5. With small particles and thick adsorbed layers (5 > 5 nm), G, becomes very small (approaches thermodynamic stability. This shows the importance of steric stabilization in controlling the flocculation of emulsions and suspensions. 

Comparison with experimental data demonstrates that the bead-spring model allows one to describe correctly linear viscoelastic behaviour of dilute polymer solutions in wide range of frequencies (see Section 6.2.2), if the effects of excluded volume, hydrodynamic interaction, and internal viscosity are taken into account. The validity of the theory for non-linear region is restricted by the terms of the second power with respect to velocity gradient for non-steady-state flow and by the terms of the third order for steady-state flow due to approximations taken in Chapter 2, when relaxation modes of macromolecule were being determined. 

The negative of the slope of the lines are shown plotted against the measured intrinsic viscosity of the polymers in Figure 3. The previously described coacervatlon model (8) predicts that the slope of this line should be unity. A line with this slope accurately represents the data, as expected. These results indicate that polyacrylamide has no attractive interaction with the mlcroemulslon particles (or with its components) and the interaction is a repulsive, excluded volume one. This leads to the conclusion that polyacrylamide is similar to the other nonionic water soluble polymers, PEO, PVP and dextran in its behavior toward water external mlcroemulslons, possibly by a "volume restriction" mechanlsm(15). 

Entropic, volume restriction or elastic interaction, G p This results from the loss in configurational entropy of the chains on significant overlap. Entropy loss is unfavourable and, therefore, G j is always positive. A combination of G,. with G gives the total energy of interaction Gj (theory of steric stabilisation). 

Figure 14.13 Oil-in-water emulsions may be stabilized by (A) non-ionic surfactants, [B) poloxamer block copolymers or [C) polymeric materials. The hydrophilic chains produce repulsion by mixing interaction [osmotic) or volume restriction [entropic).

The second repulsive effect resulting from the presence of the adsorbed layers is the loss in configurational entropy of the chains when significant overlap occurs. This effect, which is always repulsive, is referred to as an entropic, volume-restriction or elastic interaction, Gei. 

Figure 5 Schematic representation of the entropic, volume restriction, or elastic interaction.

To summarize at this stage, the inteactions between the adsorbed polymer chains may be separated into (1) a mixing effect that produces either a repulsion or an attraction and (2) an elastic effect that is always repulsive (Table 4.4). The mixing effect is also described as an osmotic effect whereas the elastic effect is described as an entropic effect or a volume restriction effect. The free energy of the polymeric interaction can be written... 

Theoretical attempts to relate dimensions of polymers to chemical structure were pioneered by Flory (2). Statistical macromolecular size in solution can be modeled from first principles by considering the number and length of bonds along with valence bond angles and conformational restrictions. Excluded volume, segmental interactions, specific intramolecular interactions, and chain solvation contribute to dimensions. 

In order to cover the fidl range of multiscale dynamics, one needs a relatively large dimension of the sheet in our bond fluctuation top-down) approach as in studying the multiscale dynamics of polymer chains. As mentioned above, a composite consists of a number of components represented by particles, chains, and sheets. Multiscale characteristics of each component, for example, particles, chains, and sheets, are further modified when a large number of these constituents are placed in a simulation box, that is, by their concentrations (volume fractions). Interaction and physical constraints at higher concentrations introduce multiple relaxation times for composites to reach equilibrium or steady state. In order to carry out a systematic investigation and draw meaningful conclusions, we restrict ourselves to constituents... 

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