Self-diffusion molecular weight

Several theories have appeared in the Hterature regarding the mechanism of protection by -PDA antiozonants. The scavenger theory states that the antiozonant diffuses to the surface and preferentially reacts with ozone, with the result that the mbber is not attacked until the antiozonant is exhausted (25,28,29). The protective film theory is similar, except that the ozone—antiozonant reaction products form a film on the surface that prevents attack (28). The relinking theory states that the antiozonant prevents scission of the ozonized mbber or recombines severed double bonds (14). A fourth theory states that the antiozonant reacts with the ozonized mbber or carbonyl oxide (3) in Pig. 1) to give a low molecular weight, inert self-healing film on the surface (3). 

In the special case that A and B are similar in molecular weight, polarity, and so on, the self-diffusion coefficients of pure A and B will be approximately equal to the mutual diffusivity, D g. Second, when A and B are the less mobile and more mobile components, respectively, their self-diffusion coefficients can be used as rough lower and upper bounds of the mutual diffusion coefficient. That is, < D g < Dg g. Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal AIChE]. 30, 641 (1984), Ertl and Dullien, AIChE J. 19, 1215 (1973), and Vadovic and Colver, AIChE J. 18, 1264 (1972)]. 

Even though the rate of radical-radical reaction is determined by diffusion, this docs not mean there is no selectivity in the termination step. As with small radicals (Section 2.5), self-reaction may occur by combination or disproportionation. In some cases, there are multiple pathways for combination and disproportionation. Combination involves the coupling of two radicals (Scheme 5.1). The resulting polymer chain has a molecular weight equal to the sum of the molecular weights of the reactant species. If all chains are formed from initiator-derived radicals, then the combination product will have two initiator-derived ends. Disproportionation involves the transfer of a P-hydrogen from one propagating radical to the other. This results in the formation of two polymer molecules. Both chains have one initiator-derived end. One chain has an unsaturated end, the other has a saturated end (Scheme 5.1). 

Rymden, R. Stilbs, P. (1985b). Concentration and molecular weight dependence of counterion self-diffusion in aqueous poly(acrylic acid) solutions. Journal of Physical Chemistry, 89, 3502-5. 

Figures 8 and 9 show the dependence of the self-diffusion constant and the viscosity of polyethylene melts on molecular weight [47,48]. For small molecular weights the diffusion constant is inversely proportional to the chain length - the number of frictional monomers grows linearly with the molecular weight. This behavior changes into a 1/M2 law with increasing M. The diffusion...

The molecular weight (M) dependence of the steady (stationary) primary nucleation rate (I) of polymers has been an important unresolved problem. The purpose of this section is to present a power law of molecular weight of I of PE, I oc M-H, where H is a constant which depends on materials and phases [20,33,34]. It will be shown that the self-diffusion process of chain molecules controls the Mn dependence of I, while the critical nucleation process does not. It will be concluded that a topological process, such as chain sliding diffusion and entanglement, assumes the most important role in nucleation mechanisms of polymers, as was predicted in the chain sliding diffusion theory of Hikosaka [14,15]. 

The prediction for the diffusion constant at Eq. (4) is in very good agreement with measurements of the self-diffusion constants of polymer melts [14] while results on the viscosity have consistently given a stronger dependence of the characteristic times and viscosities on molecular weight of approximately The investigation of these discrepancies in the context of linear polymers has de-... 

Fig. 3.28 Melt self-diffusion data for hydrogenated (or deuterated) polybutadiene samples adjusted to 175 °C as a function of molecular weight [82] [83], S [84],H[85],S [86], [87]. (Reprinted with permission from [82]. Copyright 1999 The American Physical Society)...

Fig. 2. Self-diffusion of component A in a binary solution of polydimethylsiloxanes (10% A, 90% B) as function of the molecular weight of B. Each curve represents a separate value of the molecular weight of A, labelled, (after Ref. M), with permission).

Fig. 3. Self-diffusion of polydimethylsiloxanes in various solvents as function of concentration. Polymer molecular weights varied from 4,6 x 103 (PDS2, top) to 8 x10s (PDS5, bottom), (after Ref. with permission).

Fig. 4. Self-diffusion in cis-polyisoprene melts as function of molecular weight, at five temperatures. Curves are single fit of Eq. (8) with Eq. (9) to all data. (Ref.41>, with permission).

Fig. 7. Self-diffusion of linear (open symbols) and three-armed star (filled symbols) polystyrenes (squares) and polybutadienes (circles) in CC14 extrapolated to infinite dilution, as function of polymer molecular weight (Ref. 53>, with permission).

Fig. 2.48 Self-diffusion of nearly symmetric diblock copolymers measured using forced Rayleigh scattering (Dalvi et al. 1993). (a) Diffusivities, D, for the lower molecular weight PS-PVP sample, which is disordered at these temperatures, have been scaled down by a factor of 0.48, assumming Rouse dynamics (b) D for the lower molecular weight symmetric PEP-PEE diblock copolymer have been scaled down by a factor of 0.40, assuming reptation dynamics. The solid line indicates a fit of the standard Williams-Landel-Ferry (WLF) temperature dependence to the data for the lower molecular weight sample. Values of M are in g mol1.

Theory for the self- and tracer-diffusion of a diblock copolymer in a weakly ordered lamellar phase was developed by Fredrickson and Milner (1990). They modelled the interactions between the matrix chains and a labelled tracer molecule as a static, sinusoidal, chemical potential field and considered the Brownian dynamics of the tracer for small-amplitude fields. For a macroscopically-oriented lamellar phase, they were able to account for the anisotropy of the tracer diffusion observed experimentally. The diffusion parallel and perpendicular to the lamellae was found to be sensitive to the mechanism assumed for the Brownian dynamics of the tracer. If the tracer has sufficiently low molecular weight to be unentangled with the matrix, then its motion can be described by a Rouse model, with an added term representing the periodic potential (Fredrickson and Bates 1996) (see Fig. 2.50). In this case, motion parallel to the lamellae does not change the potential on the chains, and Dy is unaffected by... 

The experimental temperature dependence is much more closely reproduced by the empirical correlations of Dawson et al. (43) and of Mathur and Thodos (44). The exact experimental values are not reproduced by any of the methods. However, considering the difference in molecular weight between toluene and tolu-ene-d0,the approximations involved,and the error in the experimental values (which gets higher as the density decreases), the correlation of Mathur and Thodos gives a very good estimation of the self diffusion coefficient in supercritical toluene. 

Diffusion is a physical process that involves the random motion of molecules as they collide with other molecules (Brownian motion) and, on a macroscopic scale, move from one part of a system to another. The average distance that molecules move per unit time is described by a physical constant called the diffusion coefficient, D (in units of mm2/s). In pure water, molecules diffuse at a rate of approximately 3xl0"3 mm2 s 1 at 37°C. The factors influencing diffusion in a solution (or self-diffusion in a pure liquid) are molecular weight, intermolecular... 

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