Diffusion, polymer

NL Thomas, AH Windle. A deformation model for case II diffusion. Polymer 21 613-619, 1980. 

In addition, analogously to (20), for t < xz the mean square displacement of a diffusing polymer segment becomes... 

NMR is the most fundamental molecular specific probe of diffusion. Polymer motions and the spectroscopic signature of a given nucleus can be unambiguously related to a particular morphological domain. The size and time scale of the experiments are such that the fundamental hopping events of diffusing molecules can be sampled. 

Intraparticle diffusion limits rates in triphase catalysis whenever the reaction is fast enough to prevent attaiment of an equilibrium distribution of reactant throughout the gel catalyst. Numerous experimental parameters affect intraparticle diffusion. If mass transfer is not rate-limiting, particle size effects on observed rates can be attributed entirely to intraparticle diffusion. Polymer % cross-linking (% CL), % ring substitution (% RS), swelling solvent, and the size of reactant molecule all can affect both intrinsic reactivity and intraparticle diffusion. Typical particle size effects on the... 

In peroxyl-free-radical chemistry, H02702 " elimination reactions play a major role (Chap. 8.4). In polymer free-radical chemistry, these reactions are of special interest, because they lead to a conversion of slowly diffusing polymer-derived radicals into the readily diffusing HCV/CV radicals. The H02 /02 "-elimina-tion typically proceeds from an a-hydroxyalkylperoxyl radical [reaction (22)]. In poly(vinyl alcohol), for example, such an structural element is formed by H-abstraction and subsequent 02 addition [reactions (18) and (19)]. The same structural element may also be formed during the bimolecular decay of peroxyl radicals which carry an H-atom in [3-position [reactions (20) and (21)]. 

For slowly diffusing polymer molecules with Tk > Tth> the response of the concentration mode in Qhefi)to an excitation pulse starting at f = -Tp and ending at t = 0 is approximately given by... 

The simplest mechanisms leading to the dispersion (spreading) of a zone s molecules can be described by the classical random-walk model [9], as noted in Section 5.3. However this model does not fully account for the complexities of migration. It gives, instead, a simple approximation which inherits the most essential and important properties (foremost of all the randomness) of the real migration process. The random-walk model has been used in a similar first-approximation role in many fields (chemical kinetics, diffusion, polymer chain configuration, etc.) and is thus important in its own right. 

FIGURE 6.28 Schematic diagram of a drug diffusion/polymer erosion controlled system containing a dispersed drug. 

However, in many cases, dmg release takes place in parallel with polymer degradation. In such cases the mechanism of dmg release is complicated as dmg release occurs by dmg diffusion, polymer degradation and/or polymer dissolution. The permeability of the dmg through the polymer increases with time as the polymer matrix is gradually opened up by enzymatic/chemical cleavage. The references cited at the end of this chapter deal with the relevant mathematical treatments of this topic. 

It is well known from diffusion theory that different types of polymers have different diffusion behaviours. For example, the polyester type polymers like poly(ethylene terephthalate) (PET), poly(ethylene naphthalate) (PEN) and polycarbonate (PC) as well as rigid poly(vinyl chloride) (PVC), which have a high glass transition temperature, are low diffusive polymers. The migration of potential contaminants in these polymers will result in low migration values. In contrast, polyolefins like high density polyethylene (HDPE), polypropylene (PP) or low density polyethylene (LDPE), which... 

One crucial parameter for the evaluation of a super-clean recycling process producing a recyclate suitable for food contact is the contamination level of the input material. Due to the fact that diffusion is a reversible process, the higher diffusive polymer types should have higher input levels of post-consumer contaminants. The first step in the evaluation of PCR polymer should therefore be the determination of the input concentrations of post-consumer compounds in the polymer materials. Eor a review of concentration of post-consumer compounds in packaging materials intended for recycling see ref. 8. 

A theory for SINC must predict simultaneously the sorption, crystallization and cavitation behavior mentioned above. To accomplish this, one must combine adequate descriptions of non-Flckian diffusion, polymer/diluent crystallization, and local cavitation. 

Babak, V.G., Merkovich, E.A., Desbrieres, J., Rinaudo, M. Formation of an ordered nanostructure in surfactant polyelectrolyte complexes formed by interfacial diffusion. Polym. Bull. 2000, 45 (1), 77-81. 

In Figure 7-3, points 0, 1,..., j,... mark the positions of the center of nrass of a self-diffusing polymer chain at times 0, At,..., jAt, respectively, where At is a very short time interval. The vector from point 0 to point j is denoted by r, and the average of (r = rj ) over all chains in the solution by According to the theory of Brownian motion, rj )/jAt converges... 

D is the interdiffusion coefficient, A a and Ab are the segment mobilities of polymers A and B, respectively, Aa and Ab are the number of repeat units in each polymer, i a and are the molar fractions of each pol5uner and x is the Flory-Huggins interaction parameter. The slow-mode theory predicts that interdiffusion is dominated by the slow-diffusing polymer. Later, de Gennes [69] showed that the mobility was directly related to the diffusion coefficient of each polymer. The limitation of this theory is that it assumes that the fluxes of the two polymers are equal and opposite, which means that the interface remains symmetrical as interdiflfusion proceeds. 

A first limit rate expression is obtained when surface rate contributions are rate determining.The concentration profile is plotted in Fig. 18.22. Although the use of Henry s law (Equation [18.1]) as boundary conditions is usually limited to the case of molecular diffusion (polymer membranes), it can also be used to describe permeation across metallic membranes with surface rate-determining step (rds). In such cases, the dissociative physisorption step of H2 into H is assumed to be fast and at equilibrium. Steps (3) and (5) of the sorption mechanism are rds and the relationship between surface hydrogen ad-atoms and pressure is given by Equation [18.8] ... 

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