Natural rubber diffusion coefficients

Figure 2.20 Permeant diffusion coefficient as a function of permeant molecular weight in water, natural rubber, silicone rubber and polystyrene. Diffusion coefficients of solutes in polymers usually lie between the value in natural rubber, an extremely permeable polymer, and the value in polystyrene, an extremely impermeable material [28]...

Figure 8.3 Diffusion coefficient as a function of molar volume for a variety of permeants in natural rubber and in polyfvinyl chloride), a glassy polymer. This type of plot was first drawn by Gruen [8], and has been used by many others since...

Table 4.3 shows the permselectivity characteristics of pure, semicrystalline PEO films [76]. The selectivity characteristics for 02/N2 are rather similar to those for silicone rubber and natural rubber shown in Table 4.2. However, the values of permselectivity for C02 relative to the various light gases shown are all much higher than Table 4.2 shows for the rubbery polymers listed there and even for polysulfone except for C02/CH4. Comparison of the data in Tables 4.2 and 4.3 makes it clear that this high permselectivity of PEO stems from its high solubility selectivity for C02 versus other gases this is augmented by modest values of diffusivity selectivity. Data in Table 4.4 for the C02/N2 pair illustrate that this effect can be translated into various block-copolymer structures when the PEO content is high enough to ensure it is the continuous phase. In fact, nearly all these materials have higher permselectivity and solubility selectivity for C02/N2 than does pure PEO (see Table 4.3) however, the diffusion selectivity for these copolymers is much closer to, or even less than, unity than seen for pure PEO. Furthermore, the copolymers all have much higher absolute permeability coefficients than does PEO.

Figure 1. Correlation of diffusion coefficients (D ) of small gaseous molecules in amorphous polyethylene (natural rubber) with their reduced molecular diameters (d-0.5 (Reproduced with permission from Ref. 3. Copyright 1961 John Wiley Sons.)...

FIG. 18.12 Relation between diffusion coefficient D and liquid viscosity p for various liquids in natural rubber at 25 °C (after Southern and Thomas, 1967). 

Bueche et al. (1952) derived that the coefficient for self-diffusion of poly(n-butyl acrylate) is inversely proportional to the bulk viscosity of this polymer. Also in the natural rubber (polyisoprene) diffusion system a clear connection appears to exist between diffusion coefficient and bulk viscosity. In general the following expression may be used as a good approximation ... 

Solvents produce different effects than do corrosive chemicals. Both silica and carbon black filled natural rubbers were more resistant to solvents than unfilled rubber. Also, the cure time was important, indicating that the bound rubber plays a role in the reduction of a solvent sorption. The diffusion coefficient of solvents into rubbers decreases with longer cure times and higher fillers loadings. Polychloroprene rubber swollen with solvent has a lower compression set when it is filled with carbon black. 

Figure 1. Diffusion coefficients for a variety of penetrants in natural rubber at 25 °C and rigid poly(vinyl chloride) at 30 °C. The van der Waals volumes are taken from The Handbook of Chemistry and Physics, 35th ed., 1953-54, page 21-24 to 21-26, CRC, Cleveland, Ohio.

Graham, who was one of the first to consider the permeabilities of natural rubber films to a wide range of gases, found responses such as that seen in Fig. 2a. The description he formulated in 1866 of the so-called "solution-diffusion" mechanism still prevails today (30). He postulated that a penetrant leaves the external phase in contact with the membrane by dissolving in the upstream face of the film and then undergoes molecular diffusion to the downstream face where it evaporates into the external phase again. Mathematically, one can state the solution-diffusion model in terms of permeability, solubility and diffusivity coefficients, as shown in Eq(2). 

Studies of the diffusion of benzene in natural rubber represent some of the earliest detailed examinations of the interaction of an organic solvent with a polymer. Hayes and Park carried out measurements at low concentrations by the vapor sorption method (1), and at higher concentrations by determining the concentration distribution using an interferometric method (2). Complementary measurements by vapor transmission to determine the diffusion coefficient from time-lag data were carried out at low concentrations by Barrer and Fergusson (3). The main results of these studies have been summarized in Fujita s review (4) of organic vapor diffusion in polymers above the glass transition temperature. However, the problems with these measurements were not referenced. 

It is possible that the lower than required values of D2 reflect a problem with incorrect values of Q, which if too large would result in smaller values of D2. In an interferometric study of the diffusion of toluene in an uncrosslinked natural rubber sample, Mozisek (15) reported results for the mutual diffusion coefficient which were similar to the results of Hayes and Park. In the absence of thermodynamic data from Mozisek s work, correction factors calculated for the present work were applied to his data. The results are shown in Figure 7, which reproduces Mozisek s data along with the values for D2. The extrapolated value at 1, would exceed the self diffusion coefficient for toluene by about two orders of magnitude, similar to the discrepancy seen with Hayes and Park s data. This indicates that the fault with the results in the present case is not due to overly high values of the correction factors. Moreover, the method of calculating D from D12 has been confirmed experimentally by Duda and Vrentas (16) in a comparison of vapor sorption results for toluene diffusion in molten polystyrene with the values of D1 obtained directly using radio-labeled toluene. 

Figure 7. Comparison of Dj versus volume fraction of solvent in natural rubber, calculated from results of Von Mozisek using thermodynamic correction factors from present study, with self-diffusion coefficient for pure toluene. D, obtained using Q from Rory—Huggins (Chi=0.36).

Figure 2. Concentration dependence of the diffusion coefficient of water in natural rubber using samples (%) initially dry and (O) initially containing water. Line calculated using Equation 9 with s a = 6.3 X 10" and Ci = 0.1%.

Cw = 10" gm cm" the value of D is found to be 10 cm sec which compares favourably with the experimental value of 5 X 10 1 cm sec from measurements on a thin natural rubber sample (vulcanizate A, 0.3 mm thick) immersed in distilled water. The factor of 5 is not regarded as significant in view of the uncertainties in the values of the constants used. It is noteworthy that the apparent diffusion coefficient is four orders of magnitude lower than the estimated true diffusion coefficient in pure rubber. 

Theories have been advanced which account for the equilibrium amount of water absorbed and for the diffusion of water in natural rubber. The equilibrium swelling theory is an Improved version of that of Briggs et al. (2) in that a more reallsltic calculation of the rubber pressure is used. The diffusion theory accounts for the experimental observations both in predicting the correct order of magnitude of the diffusion coefficient of water in rubber and also its concentration dependence. 

FIGURE 20.4-2 Ratio of dilfusiviiies in a 30% crystalline and a 0% crystalline polyethylene as a function of the van der Waals volume of the penetrant. The diffusion coefficients foramotphous polyethylene were taken to be equivalent to those of unvulcanized natural rubber. ... 

It is paradoxical that the abilities of ethylene oxide to penetrate materials that make it an effective sterilant are the same abilities that create residues. Polymeric materials are very permeable to ethylene oxide. Permeability is affected by the solubility of the gas in the polymer and the diffusivity of the polymer to ethylene oxide. Ethylene oxide is less soluble in polyethylene and polyesters (around lO.CMX) ppm) than in say cellulosics or PVC (around 30.0(K) to 40,000 ppm according to the level of plasticizers present in the formulation) soft plastics and natural rubbers have higher diffusion coefficients for ethylene oxide than harder polymers such as acrylics and styrenes [14]. Polymers with high diffusion coefficients will reach saturation solubility quicker than those with lower diffusion coefficients. A polymer that takes up residues only slowly will release them only slowly. Since devices may often be manufactured with several different types of polymeric material, it is difficuli to predict or quantify overall residue levels and practical rates of dissipation. A component such as the rubber plunger lip may as a result of its high diffusivity and thickness amount fur most of the residues in a hypodermic syringe, although it is in itself only a minor component. 

The barrier properties of starch nanocrystals/natural rubber nanocomposites were also investigated [39]. For these systems, the water vapour transmission rate, the diffusion coefficient of oxygen, the permeability coefficient of oxygen and its solubility, were measured. It was observed that the permeabiUty to water vapour, as well as to oxygen, decreased when starch nanocrystals wctc added These effects were ascribed to the platelet-like morphology of the nanocrystals. 

Fig. 3. Diffusion coefficients of nitrogen in diene rubbers and in butyl rubber as a function of T - Tg (Data from Ref 104). H Chloroprene rubber (neoprene) styrene butadiene rubber B natural rubber B nitrile butadiene rubber B butyl rubber.

Fig. 3. Diffusion coefficients for a variety of penetrants in natural rubber at 25°C. n-Cs,n-C4, and n-Cs designate straight chain alkanes.

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