Theories of Compatibility

Equilibrium is relatively easily achieved in dilute solutions and studies of such systems form the foundation of modern theories of compatibility. Application of such theories to practical problems involves the assumption that useful polymer mixtures require the selection of miscible ingredients and that compatibility can therefore ultimately be explained in terms of thermodynamic stability of the mixture. 

PRACTICAL APPROACHES IN USING THEORY OF COMPATIBILITY FOR PLASTICIZERS SELECTION... 

Practical approaches in using theory of compatibility for plasticizers selection... 

Senichev, V. Yii. Tereshatov, V. V., Theories of Compatibility in Handbook of Plasticizers, Wypych, G., Ed., ChemTec Publishing, Toronto 2004. 

The theory of Leibler holds for mainly compatible systems. Leibler developed a mean field formalism to study the interfacial properties of two polymers, A and B with an A-B copolymer. An expression for interfacial tension reduction was developed by Noolandi and Hong [ 18] based on thermodynamics to explain the emulsifying effect of the A-b-B in immiscible A-B blends (A-A-b-B-B). [18,19]. The expression for interfacial tension reduction Ar) in a binary lend upon the addition of divalent copolymer is given by ... 

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

The description of fuzzy, local density fragments is facilitated by the use of local coordinate systems, however, some compatibility conditions of such local coordinate systems must be fulfilled, reflecting the mutual relations of the fragments within the complete molecule. Manifold theory, topological manifolds, and in particular, differentiable manifolds [153-158], are the branches of mathematics dealing with the general properties of compatible local coordinate systems. 

Elastomers are solids, even if they are soft. Their atoms have distinct mean positions, which enables one to use the well-established theory of solids to make some statements about their properties in the linear portion of the stress-strain relation. For example, in the theory of solids the Debye or macroscopic theory is made compatible with lattice dynamics by equating the spectral density of states calculated from either theory in the long wavelength limit. The relation between the two macroscopic parameters, Young s modulus and Poisson s ratio, and the microscopic parameters, atomic mass and force constant, is established by this procedure. The only differences between this theory and the one which may be applied to elastomers is that (i) the elastomer does not have crystallographic symmetry, and (ii) dissipation terms must be included in the equations of motion. 

We wish to conclude with a simple kinetic model that is compatible with the above picture and is based on the theory of continu um Zip-reactions (46,47). Let us assume random initiation at sites distributed at random along a chain followed by zip in both directions with speed v. If we denote by p the linear density of such... 

Any theory of these reactions must explain their detailed features in terms of the minimum number of hypotheses, which must be compatible with the generally accepted principles of chemistry. 

The demonstration that neither of the ions-at-any-price views, the main rivals of the pseudo-cationic theory, is compatible with the facts does not, of course, prove the ester theory. As I pointed out in my introduction, it is not possible to prove any scientific theory. What has been demonstrated, however, is that the ester theory will account for most of the established facts it has the advantage of being based in conventional organic chemistry, and it provides interesting guide-lines for future research and innovation. 

He cites work including Paul Langevin s on the theory of the Kerr Phenomenon. He also calculates that the average calculated dipole length is on the order of tenths of an angstrom, compatible with the estimated distance of an angstrom between atoms, e g., in hydrogen chloride (602). 

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