Plasticizer diffusion coefficient

Figure 11.61 shows principles of diffusivity of plasticizers. Diffusion coefficient, k, comes from the following equation ... 

The retention volumes on poly(vinyl chloride) powders were correlated with their capacity for incorporating the plasticizer [153]. The diffusion of plasticizer in the polymer powder being controlled by the external smface, by the plasticizer diffusion coefficient and by a shape factor, some connection with gas chromatographic measurements is to be expected. The plasticizer adsorption was found to take place only at a temperature slightly above T,. 

Plastic Diffusion coefficient Solubility Temperature Source... 

The effect of copolymer composition on gas permeability is shown in Table 9. The inherent barrier in VDC copolymers can best be exploited by using films containing Htde or no plasticizers and as much VDC as possible. However, the permeabiUty of even completely amorphous copolymers, for example, 60% VDC—40% AN or 50% VDC—50% VC, is low compared to that of other polymers. The primary reason is that diffusion coefficients of molecules in VDC copolymers are very low. This factor, together with the low solubiUty of many gases in VDC copolymers and the high crystallinity, results in very low permeabiUty. PermeabiUty is affected by the kind and amounts of comonomer as well as crystallinity. A change from PVDC to 50 wt °/ VC or 40 wt % AN increases permeabiUty 10-fold, but has Httle effect on the solubiUty coefficient. 

Humidity does not affect the permeabihty, diffusion coefficient, or solubihty coefficient of flavor/aroma compounds in vinyhdene chloride copolymer films. Studies based on /n j -2-hexenal and D-limonene from 0 to 100% rh showed no difference in these transport properties (97,98). The permeabihties and diffusion coefficients of /n j -2-hexenal in two barrier polymers are compared in Table 12. Humidity does not affect the vinyhdene chloride copolymer. In contrast, transport in an EVOH film is strongly plasticized by humidity. 

In part the parabolic law may also apply to multilayer oxide systems where the cation diffusion coefficient is much higher in the lower oxide tlran in the higher oxide, which, growing as a thin layer, undergoes plastic deformation at high temperatures, thus retaining the overall oxide layer as impervious to enuy of tire gas. 

It should be recognized that all plastic materials over a time period allow a certain amount of water vapor, organic gas, or liquid to permeate the thickness of the material. It is only a matter of degree of permeation between various materials used as barriers against vapors and gases. It has been found that the permeability coefficient is a function of the solubility coefficient and diffusion coefficient. The process of permeation is explained as the solution of the vapor into the incoming surface of the barrier, followed by diffusion through the barrier thickness, and evaporation on the exit side. 

The kinetics of transport depends on the nature and concentration of the penetrant and on whether the plastic is in the glassy or rubbery state. The simplest situation is found when the penetrant is a gas and the polymer is above its glass transition. Under these conditions Fick s law, with a concentration independent diffusion coefficient, D, and Henry s law are obeyed. Differences in concentration, C, are related to the flux of matter passing through the unit area in unit time, Jx, and to the concentration gradient by,... 

Although many different processes can control the observed swelling kinetics, in most cases the rate at which the network expands in response to the penetration of the solvent is rate-controlling. This response can be dominated by either diffu-sional or relaxational processes. The random Brownian motion of solvent molecules and polymer chains down their chemical potential gradients causes diffusion of the solvent into the polymer and simultaneous migration of the polymer chains into the solvent. This is a mutual diffusion process, involving motion of both the polymer chains and solvent. Thus the observed mutual diffusion coefficient for this process is a property of both the polymer and the solvent. The relaxational processes are related to the response of the polymer to the stresses imposed upon it by the invading solvent molecules. This relaxation rate can be related to the viscoelastic properties of the dry polymer and the plasticization efficiency of the solvent [128,129],... 

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],... 

The material properties used in the simulations pertain to a new X70/X80 steel with an acicular ferrite microstructure and a uniaxial stress-strain curve described by er, =tr0(l + / )", where ep is the plastic strain, tr0 = 595 MPa is the yield stress, e0=ff0l E the yield strain, and n = 0.059 the work hardening coefficient. The Poisson s ratio is 0.3 and Young s modulus 201.88 OPa. The system s temperature is 0 = 300 K. We assume the hydrogen lattice diffusion coefficient at this temperature to be D = 1.271x10 m2/s. The partial molar volume of hydrogen in solid solution is... 

The moisture content E of a material to be dried of which the diffusion coefficient depends on the moisture content (e.g. with plastics) as a function of the drying time t is given in close approximation by the following equation ... 

In an attempt to justify the assumption of plasticization put forth in their interpretation of 3 in Eq (A-2), Raucher and Sefcik compare transport data and NMR data for the C02/pvC system This comparison has several questionable aspects To relate local molecular chain motions to the diffusion coefficient of a penetrant, one should use the so-called local effective coefficient, Deff O such as shown in Figure 5 rather than an average or "apparent" diffusion coefficient as was employed by these authors Deff(C) describes the effects of the local sorbed concentration on the ability of the average penetrant to respond to a concentration or chemical potential gradient in that region ... 

Carbon-13 rotating-frame relaxation rate measurements are used to elucidate the mechanism of gas transport in glassy polymers. The nmr relaxation measurements show that antiplasticization-plasticization of a glassy polymer by a low molecular weight additive effects the cooperative main-chain motions of the polymer. The correlation of the diffusion coefficients of gases with the main-chain motions in the polymer-additive blends shows that the diffusion of gases in polymers is controlled by the cooperative motions, thus providing experimental verification of the molecular theory of diffusion. Carbon-13 nmr relaxation... 

In conclusion, the average rotating-frame relaxation rate of the methylene- and methine-carbons correlate with the apparent diffusion coefficients for H2 and CO in PVC when the main-chain molecular motions of the polymer are altered by an additive. (Fig. 2). These results provide experimental evidence that main-chain cooperative motions control the diffusion of gases through polymers. In Section IIB we will show that perturbation of polymeric cooperative motions is not restricted to classical plasticizing additives. 

Water uptake in plasticized polyvinylchloride based ion selective membranes is found to be a two stage process. In the first stage water is dissolved in the polymer matrix and moves rapidly, with a diffusion coefficient of around 10 6 cm2/s. During the second stage a phase transformation occurs that is probably water droplet formation. Transport at this stage shows an apparent diffusion coefficient of 2 x 10 8 cm2/s at short times, but this value changes with time and membrane addititives in a complex fashion. The results show clear evidence of stress in the membranes due to water uptake, and that a water rich surface region develops whose thickness depends on the additives. Hydrophilic additives are found to increase the equilibrium water content, but decrease the rate at which uptake occurs. 

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