Polymers diffusion rate

Two mtyorlactors affect droplet size and density in the PIPS process types and relative concentration of materials used and cure temperature. The cure temperature influences the rate of polymerization, viscosity of the polymer, diffusion rate of the liquid crystal and solubility of the liquid crystal in the polymer. Each factor is affected differently by the cure temperature with the result that droplet size varies in a complex manner with cure temperature (Figure 5) and must therefore be empirically determined for each formulation. 

The model proposed by Tu and Ouano [43] for polymer dissolution assumes Fickian solvent penetration into the polymer. The polymer dissolution problem was modeled as a multi-phase Stefan problem [44], The key parameter in this model was the disassociation rate, R, which was defined as the rate at which the polymer transformed from a gel-like phase to a solution. It was proposed that the dissolution process was disassociation -controlled if the polymer diffusion rate in a liquid layer adjacent to the solvent-polymer interface was faster than the disassociation rate, or diffusion -controlled if the diffusion rate was slower than the disassociation rate. 

The sorption kinetics of the stabilizer molecules from the continuous phase to the organic-water interface changes with time. The time required for the sorption process to reach its steady-state is controlled by the transfer of the stabilizer molecules from the continuous phase to the droplet surface and their subsequent reconformation and rearrangement at the organic-water interface. As the stabilizer concentration increases, the time required for the system to reach equilibrium is reduced, indicating an increased polymer diffusion rate [21]. Nilsson et al. [22] argued that the stabilizer molecules diffuse very quickly to the liquid-liquid interface, but not in the more thermodynamically stable conformation and, thus, a rearrangement takes place until the system reaches its equilibrium. 

Crimp. The tow is usually relaxed at this point. Relaxation is essential because it gready reduces the tendency for fibrillation and increases the dimensional stabiUty of the fiber. Relaxation also increases fiber elongation and improves dye diffusion rates. This relaxation can be done in-line on Superba equipment or in batches in an autoclave. Generally saturated steam is used because the moisture reduces the process temperatures required. Fiber shrinkage during relaxation ranges from 10 to 40% depending on the temperature used, the polymer composition used for the fiber, and the amount of prior orientation and relaxation. The amount of relaxation is also tailored to the intended apphcation of the fiber product. 

Bulk Polymerization. This is the method of choice for the manufacture of poly(methyl methacrylate) sheets, rods, and tubes, and molding and extmsion compounds. In methyl methacrylate bulk polymerization, an auto acceleration is observed beginning at 20—50% conversion. At this point, there is also a corresponding increase in the molecular weight of the polymer formed. This acceleration, which continues up to high conversion, is known as the Trommsdorff effect, and is attributed to the increase in viscosity of the mixture to such an extent that the diffusion rate, and therefore the termination reaction of the growing radicals, is reduced. This reduced termination rate ultimately results in a polymerization rate that is limited only by the diffusion rate of the monomer. Detailed kinetic data on the bulk polymerization of methyl methacrylate can be found in Reference 42. 

Drying of the poly(vinyl alcohol) is critical to both the color and solubiHty of the final product. Excessive drying temperatures result in high product color and an increase in the crystallinity, which in turn reduces the solubiHty of the product. Drying is initially subjected to a flash regime, where the solvent not contained within the particles is flashed off. This first phase is foUowed by a period where the rate is controUed by the diffusion rate of solvent from the poly(vinyl alcohol) particles. Because the diffusion rate falls as the material dries, complete drying is not practical. The polymer is therefore generally sold at a specification of 95% soHds. 

Nutrients are released from POLYON-coated fertilizers by osmotic diffusion. The RLC process permits appHcation of ultrathin, hence lower cost, membrane coatings which distinguishes this technology from many other polymer-coated fertilizers. The coating thickness determines the diffusion rate and the duration of release. POLYON-coated urea at a 4% coating (44% N) will release at twice the rate and will have half the duration as an 8% coating... 

The lowest diffusion rates occur with crystalline polymers below the Tj, since there is very little space through which diffusing molecules may pass. 

For amorphous polymers above the T, i.e. in the flexible and rubbery states there is more space available through which diffusing molecules may pass, and so these materials show comparatively high diffusion rates with diffusing fluids. 

For crystalline polymers between and the diffusion rate is very dependent on the degree of crystallisation. 

When rfc = 0, the polymeric structure is considered to be open enough (i = 0) that any subsequent oxidation will not occur under conformational relaxation control, hence P = 1. Every polymeric chain at the poly-mer/solution interface acts as a nucleus a planar oxidation front is formed that advances from the solution interface toward the metal/polymer interface at the diffusion rate. 

Commonly of units cm s in magnitude D is the diffusion rate across the 1 cm-sided polymer cube considered earlier for Q (Section 23.4.2). Coefficient s is then calculable because Q is defined as the product Ds, and from Henry s law (Section 23.4.2) concentration c can then be obtained. 

The release of steroids such as progesterone from films of PCL and its copolymers with lactic acid has been shown to be rapid (Fig. 10) and to exhibit the expected (time)l/2 kinetics when corrected for the contribution of an aqueous boundary layer (68). The kinetics were consistent with phase separation of the steroid in the polymer and a Fickian diffusion process. The release rates, reflecting the permeability coefficient, depended on the method of film preparation and were greater with compression molded films than solution cast films. In vivo release rates from films implanted in rabbits was very rapid, being essentially identical to the rate of excretion of a bolus injection of progesterone, i. e., the rate of excretion rather than the rate of release from the polymer was rate determining. 

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

A quite different approach to rheo-NMR was taken by Xia and Callaghan [12], in an NMR microscopy measurement of the velocity profile of a high molecular weight polymer solution flowing through a capillary. In this study anomalous polymer diffusion was found at a radius within the pipe at which the local shear rate exceeded... 

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