Diffusion coefficient poly

The sedimentation and diffusion coefficients for three different preparations of poly(methyl methacrylate) were measuredf in /i-butyl chloride at 35.6 C (= 0) and in acetone at 20 C (> 0) and the following results were obtained ... 

Fig. 37. Diffusion coefficient as a function of molar volume for a variety of permeants in natural mbber and in poly(vinyl chloride) (PVC) (81—83).

The non-bonded interaction energy, the van-der-Waals and electrostatic part of the interaction Hamiltonian are best determined by parametrizing a molecular liquid that contains the same chemical groups as the polymers against the experimentally measured thermodynamical and dynamical data, e.g., enthalpy of vaporization, diffusion coefficient, or viscosity. The parameters can then be transferred to polymers, as was done in our case, for instance in polystyrene (from benzene) [19] or poly (vinyl alcohol) (from ethanol) [20,21]. 

Karigl [71] defined a format diffusion coefficient for bromine transport through a poly thy lene separator of a zinc-flow battery by considering the separator a diffusion layer. A value of Dsep(Br3 ) = 2.77 10 10 m2 s l was obtained. 

TABLE 2 Diffusion Coefficients (x 10 cm2/sec) of Various Drugs in Poly-e-caprolactone... 

Subsequent work by Johansson and Lofroth [183] compared this result with those obtained from Brownian dynamics simulation of hard-sphere diffusion in polymer networks of wormlike chains. They concluded that their theory gave excellent agreement for small particles. For larger particles, the theory predicted a faster diffusion than was observed. They have also compared the diffusion coefficients from Eq. (73) to the experimental values [182] for diffusion of poly(ethylene glycol) in k-carrageenan gels and solutions. It was found that their theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. Equation (73) is an example of the so-called stretched exponential function discussed further later. 

Polymer gels and ionomers. Another class of polymer electrolytes are those in which the ion transport is conditioned by the presence of a low-molecular-weight solvent in the polymer. The most simple case is the so-called gel polymer electrolyte, in which the intrinsically insulating polymer (agar, poly(vinylchloride), poly(vinylidene fluoride), etc.) is swollen with an aqueous or aprotic liquid electrolyte solution. The polymer host acts here only as a passive support of the liquid electrolyte solution, i.e. ions are transported essentially in a liquid medium. Swelling of the polymer by the solvent is described by the volume fraction of the pure polymer in the gel (Fp). The diffusion coefficient of ions in the gel (Dp) is related to that in the pure solvent (D0) according to the equation ... 

Figure 5 The mutual diffusion coefficient, D, of sodium chloride as a function of reciprocal matrix hydration, H, in various methacrylate gels. HPMA-GMA polyfhydroxypro-pyl methacrylate-co-glyceryl methacrylate) HEMA polyfhydroxyethyl methacrylate) MMA-GMA poly(methyl methacrylate-co-glyceryl methacrylate) HEMA-MMA poly-(hydroxyethyl methacrylate-co-methyl methacrylate) HPMA-MMA polyfhydroxypropyl methacrylate-co-methyl methacrylate) HPMA-GDMA polyfhydroxypropyl methacry-late-co-glyceryl dimethacrylate). (From Ref. 64.)...

Figure 15 The sorption of acetaminophen from a solution of limited volume by 10 X 4 poly (A-isopropylacry lam idc) gel, illustrating the use of Eqs. (34) and (35) to determine the diffusion coefficient of the solute. (Data from Ref. 174.)... 

Among all the polymers used in preparing ion-selective membranes, poly(vinylchloride) (PVC) is the most widely used matrix due to its simplicity of membrane preparation [32, 70], In order to ensure the mobility of the trapped ionophore, a large amount of plasticizer (approximately 66%) is used to modify the PVC membrane matrix (approximately 33%). Such a membrane is quite similar to the liquid phase, because diffusion coefficients for dissolved low molecular weight ionophores are high, on the order of 10 7-10 8cm2/s [59],... 

Radioactive 180 was diffused into a poly crystalline pellet of ZnO at 900°C for 48 h. The diffusion profile had a marked tail showing that extensive grain boundary diffusion had occurred. The variation of the concentration of the radioactive isotope with depth for the tail of the penetration profile is given in the following table. Calculate the grain boundary diffusion coefficient, Dgb, of 180 if the bulk diffusion coefficient at 900°C is 5.53 x 10-21 m2 s-1 and the grain boundary width is taken as 1 nm. 

Therefore we expect Df, identified as the fast diffusion coefficient measured in dynamic light-scattering experiments, in infinitely dilute polyelectrolyte solutions to be very high at low salt concentrations and to decrease to self-diffusion coefficient D KRg 1) as the salt concentration is increased. The above result for KRg 1 limit is analogous to the Nernst-Hartley equation reported in Ref. 33. The theory described here accounts for stmctural correlations inside poly electrolyte chains. 

Fig. 6.16 NSE relaxation curves obtained from a 16% volume fraction poly(fluorosilicone) gel in acetone using tbe bigb resolution NSE spectrometer INI5 at tbe ILL, Grenoble. Tbe existence of plateaus that represent tbe level of excess scattering from static inhomogenieties at low wave vector Q is clearly visible. Tbe decay rates times of tbe dynamic parts yield tbe collective diffusion coefficient of tbe gel. (Reprinted with permission from [291]. Copyright 2002 American Chemical Society)...

Figure 10. Proton conductivity diffusion coefficient (mobility) and self-diffusion coefficient of phosphorus for poly-(diallyldimethylammonium-dihydrogenphosphate)—phosphoric acid ((PAMA+H2P04 ) nH3P04), as a function of the phosphoric acid content. Note that the ratio DJDp remains almost constant (see text).

Figure 14. Solvent (water, methanol) diffusion coefficients of (a) Nafion 117 (EW =1100 g/equiv) and (b) sulfonated poly(arylene ether ketone)s, as a function of the solvent volume fraction. Self-diffusion data (AiaO. T eOi-i) are taken from refs 197, 224, 226, 255—263 and unpublished data from the laboratory of one of the authors) chemical diffusion coefficients (Z>h2o) are calculated from self-diffu-sion coefficients (see text), and permeation diffusion coefficients are determined from permeation coefficients. ...

Mechanistic Ideas. The ordinary-extraordinary transition has also been observed in solutions of dinucleosomal DNA fragments (350 bp) by Schmitz and Lu (12.). Fast and slow relaxation times have been observed as functions of polymer concentration in solutions of single-stranded poly(adenylic acid) (13 14), but these experiments were conducted at relatively high salt and are interpreted as a transition between dilute and semidilute regimes. The ordinary-extraordinary transition has also been observed in low-salt solutions of poly(L-lysine) (15). and poly(styrene sulfonate) (16,17). In poly(L-lysine), which is the best-studied case, the transition is detected only by QLS, which measures the mutual diffusion coefficient. The tracer diffusion coefficient (12), electrical conductivity (12.) / electrophoretic mobility (18.20.21) and intrinsic viscosity (22) do not show the same profound change. It appears that the transition is a manifestation of collective particle dynamics mediated by long-range forces but the mechanistic details of the phenomenon are quite obscure. 

---