Polymer clusters equilibrium size

The diffusion and permeabihty are closely interconnected with the solubility of a polymer. The permeation of the permeants through polymeric membrane film occurs in three stages (1) Sorption includes the initial adsorption, absorption, penetration, and dispersal of penetrant into the voids of the polymer membrane surface and cluster formation. The distribution of permeant in the membrane may depend on penetrant size, concentration, temperature, and swelling of the matrix as well as on time. The extent to which permeant molecules are sorbed and their mode of sorption in the polymer depends upon the enthalpy and entropy of permeant-polymer mixing, i.e., upon the activity of the permeant within the polymer at equilibrium. When both polymer-permeant and permeant-permeant interactions are weak relative to polymer-polymer interactions, i.e., dilute solution occurs, Henry s law is obeyed. The solubihty coefficient S is a constant independent of sorbed concentration at a given temperature. (2) Diffusion includes the transfer of the penetrant through the polymer membrane which depends on penetrant concentration that leads to a plasticization effect, penetrant size and shape, polymer Tg, time, and temperature. The diffusion coefficient is determined by Pick s first law of diffusion. (3) Desorption includes release of the penetrant from the opposite side of the membrane face. 

The use of dilute polymer solutions for molecular weight measurements requires the macromolecules to be in a true solution, i.e., dispersed on a molecular level. This state may not be realized in certain instances because stable, multimolecular aggregates may persist under the conditions of "solution" preparation. In such cases, a dynamic equilibrium between clustered and isolated polymer molecules is not expected to be approached and the concentration and size of aggregates are little affected by the overall solute concentration. A pronounced effect of the thermal history of the solution is often noted under such conditions. 

NMR data has shown that every bound surfactant molecule experiences the same environment, i.e. the surfactant molecules might be bound in micelle-like clusters, but with smaller size. Assuming that each polymer molecule consists of several effective segments of mass Ms (minimum molecular weight for interaction to occur), then each segment will bind a cluster of n surfactant anions, D , and the binding equilibrium may be represented by. 

Figure 4.3 shows several types of morphologies of the particles produced. The incompatibility of the seed polymer with the newly formed polymer results in phase separation and cluster formation. The size of the clusters increases by both polymerization and cluster aggregation. In addition, the clusters tend to reach an equilibrium morphology, which minimizes the interfacial energy of the system and depends on the polymer-polymer and polymer-water interfacial tensions [40-44]. 

The main factor that defines interconnection of local order and the fractal nature of the structure of solid polymers is the fact that both these features are a reflection of the key property of these polymers- their thermodynamical non-equilibrium nature. The scales of fractal behaviour and indicated above correspond very well to cluster structure border sizes - to statistical segment length - to distance... 

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