Diffusion molecular weight

Figure 10. Graph of Number of Compounds against Error % Obtained from the Linear Regression of the Graph of the Corrected Peak Dispersion (Z) against the Reciprocal of the Diffusivity Molecular Weight to the Power of 0.833...

Polymerization in the melt is widely used commercially for the production of polyesters, polyamides, polycarbonates and other products. The reactions are controlled by the chemical kinetics, rather than by diffusion. Molecular weights and molecular weight distributions follow closely the statistical calculations indicated in the preceding section, at least for the three types of polymers mentioned above. There has been much speculation as to the effect of increasing viscosity on the rates of the reactions, without completely satisfactory explanations or experimental demonstrations yet available. Flory [7] showed that the rate of reaction between certain dicarboxylic acids and glycols was independent of viscosity for those materials, in the range studied. The viscosity range had a maximum of 0.3 poise, however, far below the hundreds of thousands of poises encountered in some polycondensations. 

Porosity, pore size >1 ml/g, 2-50 nm Resistance to diffusion, molecular weight sieving, flow properties, enzyme retention... 

In dilute solutions, tire dependence of tire diffusion coefficient on tire molecular weight is different from tliat found in melts, eitlier entangled or not. This difference is due to tire presence of hydrodynamic interactions among tire solvent molecules. Such interactions arise from tire necessity to transfer solvent molecules from tire front to tire back of a moving particle. The motion of tire solvent gives rise to a flow field which couples all molecules over a... 

Small molecules can penetrate and penneate tlirough polymers. Because of this property, polymers have found widespread use in separation teclmology, protection coating, and controlled delivery [53]. The key issue in these applications is the selective penneability of the polymer, which is detennined by the diffusivity and the solubility of a given set of low-molecular-weight compounds. The diffusion of a small penetrant occurs as a series of jumps... 

Figure C2.1.18. Schematic representation of tire time dependence of tire concentration profile of a low-molecular-weight compound sorbed into a polymer for case I and case II diffusion. In botli diagrams, tire concentration profiles are calculated using a constant time increment starting from zero. The solvent concentration at tire surface of tire polymer, x = 0, is constant.

It ls not surprising chat such a relation should hold at the Limit of Knudsen diffusion, since Che Knudsen diffusion coefficients are themselves inversely proportional to the square roots of molecular weights, but the pore diameters in Graham s stucco plugs were certainly many times larger chan the gaseous mean free path lengths at the experimental conditions. 

The proof that these expressions are equivalent to Eq. (1.35) under suitable conditions is found in statistics textbooks. We shall have occasion to use the Poisson approximation to the binomial in discussing crystallization of polymers in Chap. 4, and the distribution of molecular weights of certain polymers in Chap. 6. The normal distribution is the familiar bell-shaped distribution that is known in academic circles as the curve. We shall use it in discussing diffusion in Chap. 9. 

Assuming that Eq. (2.67) applies to small molecules in the limit as n 1, calculate To, using D = 3 X 10" m sec" for a typical low molecular weight molecule. Use this value of Tq to estimate t for a polymer with n = 10. Based on Eq. (2.63), evaluate diffusion coefficient for bulk... 

Note that the diffusion coefficient for a polymer through an environment of low molecular weight molecules is typically on the order of magnitude of 10"" m" sec". If the first subscript indicates the diffusing species, and the second the surrounding molecules, and P stands for polymer and S for small molecules, we see that the order of diffusion coefficients is Ds g > Dp g > Dp P sequence which makes sense in terms of relative frictional resistance. 

The reaction step in mechanism (5.F) is entirely comparable to the same reaction in low molecular weight systems. Such reactions involve considerably larger activation energies than physical processes like diffusion and, hence, do proceed slowly. 

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

This chapter contains one of the more diverse assortments of topics of any chapter in the volume. In it we discuss the viscosity of polymer solutions, especially the intrinsic viscosity the diffusion and sedimentation behavior of polymers, including the equilibrium between the two and the analysis of polymers by gel permeation chromatography (GPC). At first glance these seem to be rather unrelated topics, but features they all share are a dependence on the spatial extension of the molecules in solution and applicability to molecular weight determination. 

In a solution of molecules of uniform molecular weight, all particles settle with the same value of v. If diffusion is ignored, a sharp boundary forms between the top portion of the cell, which has been swept free of solute, and the bottom, which still contains solute. Figure 9.13a shows schematically how the concentration profile varies with time under these conditions. It is apparent that the Schlieren optical system described in the last section is ideally suited for measuring the displacement of this boundary with time. Since the velocity of the boundary and that of the particles are the same, the sedimentation coefficient is readily measured. 

Protein molecules extracted from Escherichia coli ribosomes were examined by viscosity, sedimentation, and diffusion experiments for characterization with respect to molecular weight, hydration, and ellipticity. These dataf are examined in this and the following problem. Use Fig. 9.4a to estimate the axial ratio of the molecules, assuming a solvation of 0.26 g water (g protein)"V At 20°C, [r ] = 27.7 cm g" and P2 = 1.36 for aqueous solutions of this polymer. 

Many challenging industrial and military applications utilize polychlorotriduoroethylene [9002-83-9] (PCTFE) where, ia addition to thermal and chemical resistance, other unique properties are requited ia a thermoplastic polymer. Such has been the destiny of the polymer siace PCTFE was initially synthesized and disclosed ia 1937 (1). The synthesis and characterization of this high molecular weight thermoplastic were researched and utilized duting the Manhattan Project (2). The unique comhination of chemical iaertness, radiation resistance, low vapor permeabiUty, electrical iasulation properties, and thermal stabiUty of this polymer filled an urgent need for a thermoplastic material for use ia the gaseous UF diffusion process for the separation of uranium isotopes (see Diffusion separation methods). 

The rationale for the development of such fibers is demonstrated by their appHcation in the medical field, notably hemoperfusion, where cartridges loaded with activated charcoal-filled hoUow fiber contact blood. Low molecular weight body wastes diffuse through the fiber walls and are absorbed in the fiber core. In such processes, the blood does not contact the active sorbent direcdy, but faces the nontoxic, blood compatible membrane (see Controlled RELEASE TECHNOLOGY, pharmaceutical). Other uses include waste industrial appHcations as general as chromates and phosphates and as specific as radioactive/nuclear materials. 

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. 

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