Interfacial energy difference

During homogenization of a solution of polymer (Z3), solvent (Z,l, and water, droplets of different sizes are formed. Because of the interfacial energy difference, a transport of Z from the smaller to the larger droplets will take place. If droplets smaller than the critical size are formed, Aese droplets, especially, will rapidly lose Z to the surrounding larger droplets. The viscosity within these small droplets will increase and a further degradation may be mechanically hindered. In the presence of Zj, two effects that win facilitate subdivision of the emulsion may be encountered. 

The free energy 0 of formation of a rectangular nucleus of critical size at an undercooling AT is proportional to a "specific interfacial energy difference Ay (38. ... 

Figure 1. Plot (according to Equation 5b) of the specific interfacial energy difference Ay against the relative undercooling at which a heterogeneity nucleates the polymer. A, B Heterogeneous nucleations C Homogeneous nucleation.

Figure 3.45. Plots of the relative specific interfacial energy difference Ay/y versus the relative undercooling AT/T at which a heterogeneity nucleates the polymer (1) and (2) two different heterogeneous nucleations (3) homogeneous nucleation [Frensch and Jungnickel, 1989].

Ay,- Specific interfacial energy difference between a nucleating species of type i and the polymer... 

The kinetics of spinodal decomposition is complicated by the fact that the new phases which are formed must have different molar volumes from one another, and so tire interfacial energy plays a role in the rate of decomposition. Anotlrer important consideration is that the transformation must involve the appearance of concenuation gradients in the alloy, and drerefore the analysis above is incorrect if it is assumed that phase separation occurs to yield equilibrium phases of constant composition. An example of a binary alloy which shows this feature is the gold-nickel system, which begins to decompose below 810°C. 

As mentioned earlier, the contact-mechanics-based experimental studies of interfacial adhesion primarily include (1) direct measurements of surface and interfacial energies of polymers and self-assembled monolayers (2) quantitative studies on the role of interfacial coupling agents in the adhesion of elastomers (3) adhesion of microparticles on surfaces and (4) adhesion of viscoelastic polymer particles. In these studies, a variety of experimental tools have been employed by different researchers. Each one of these tools offers certain advantages over the others. These experimental studies are reviewed in Section 4. 

The interfacial energy of the repulsive wall, for instance, should be completely independent of the adsorption energy e at the adsorbing wall one expects 7 to be a function of the bulk density only (and of temperature, of course, but we consider only k T = here). Since different choices of e in our geometry with finite thickness do lead to different pb, we get different results for for the various choices of e, albeit all data should be part... 

In a fundamental sense, the miscibility, adhesion, interfacial energies, and morphology developed are all thermodynamically interrelated in a complex way to the interaction forces between the polymers. Miscibility of a polymer blend containing two polymers depends on the mutual solubility of the polymeric components. The blend is termed compatible when the solubility parameter of the two components are close to each other and show a single-phase transition temperature. However, most polymer pairs tend to be immiscible due to differences in their viscoelastic properties, surface-tensions, and intermolecular interactions. According to the terminology, the polymer pairs are incompatible and show separate glass transitions. For many purposes, miscibility in polymer blends is neither required nor de-... 

In terms of the two-phase system which comprises dispersions of solids in liquids, the minimum energy requirement is met if the total interfacial energy of the system has been minimized. If this requirement has been met, chemically, the fine state of subdivision is the most stable state, and the dispersion will thus avoid changing physically with time, except for the tendency to settle manifest by all dispersions whose phases have different densities. A suspension can be stable and yet undergo sedimentation, if a true equilibrium exists at the solid-liquid interface. If sedimentation were to be cited as evidence of instability, no dispersion would fit the requirements except by accident—e.g., if densities of the phases were identical, or if the dispersed particles were sufficiently small to be buoyed up by Brownian movement. 

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