Rubbery Diffusion

For amorphous polymers above the T, i.e. in the flexible and rubbery states there is more space available through which diffusing molecules may pass, and so these materials show comparatively high diffusion rates with diffusing fluids. 

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,... 

This relative importance of relaxation and diffusion has been quantified with the Deborah number, De [119,130-132], De is defined as the ratio of a characteristic relaxation time A. to a characteristic diffusion time 0 (0 = L2/D, where D is the diffusion coefficient over the characteristic length L) De = X/Q. Thus rubbers will have values of De less than 1 and glasses will have values of De greater than 1. If the value of De is either much greater or much less than 1, swelling kinetics can usually be correlated by Fick s law with the appropriate initial and boundary conditions. Such transport is variously referred to as diffusion-controlled, Fickian, or case I sorption. In the case of rubbery polymers well above Tg (De < c 1), substantial swelling may occur and... 

Pure PHEMA gel is sufficiently physically cross-linked by entanglements that it swells in water without dissolving, even without covalent cross-links. Its water sorption kinetics are Fickian over a broad temperature range. As the temperature increases, the diffusion coefficient of the sorption process rises from a value of 3.2 X 10 8 cm2/s at 4°C to 5.6 x 10 7 cm2/s at 88°C according to an Arrhenius rate law with an activation energy of 6.1 kcal/mol. At 5°C, the sample becomes completely rubbery at 60% of the equilibrium solvent uptake (q = 1.67). This transition drops steadily as Tg is approached ( 90°C), so that at 88°C the sample becomes entirely rubbery with less than 30% of the equilibrium uptake (q = 1.51) (data cited here are from Ref. 138). 

Represents the temperature of the conversion of an amorphous glassy or partially crystalline polymer into a rubbery viscous melt. Important for sensors, because polymers with high Tg require plasticizers for fast analyte diffusion and response time (see section 3.1). 

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

After phase separation, the creation of an isolated porous morphology is achieved by holding the sample at a temperature in the rubbery state, thus enabling for high diffusion rates well above the boiling point of the solvent. On the other hand the temperature must kept below the decomposition temperature of the network. Thus removal of the low molecular weight liquid is achieved by... 

When the encounter probability of reactive groups and the rate of reaction becomes controlled by the segmental mobility (viscosity of the medium), overall diffusion control sets In. The overall diffusion control is typical of polymer systems In which, as a result of the chemical reaction, the system passes from the liquid (rubbery) state Into the glassy state. 

It is clear, that MEK is a "good" solvent for both the elastomers and the epoxy resin. Note that at 10% rubber, the MEK absorption nearly doubles. This implies that a much higher concentration of MEK is present in the rubber phase than in the epoxy phase. This is possible because the MEK diffuses more rapidly into the rubbery CTBN phase owing to its greater segmental thermal motion. 

Other papers reported the phase separation behavior for the composition showing dual phase morphology [7,20,21,43-45], Delides et al. [43] proposed that the viscosity at the point of phase separation is sufficiently large enough to inhibit diffusion of the epoxy through the rubber (CTBN) and result in the generation of the occluded phase, which is the inclusion of epoxy domains within the rubbery phase. 

The reaction of curing the epoxy-amine system occurring in the diffusion-controlled mode has little or no effect on the topological structure of the polymer 74> and on its properties in the rubbery state. However, the diffusion control has an effect on the properties of glassy polymers 76 78). 

The above models describe a simplified situation of stationary fixed chain ends. On the other hand, the characteristic rearrangement times of the chain carrying functional groups are smaller than the duration of the chemical reaction. Actually, in the rubbery state the network sites are characterized by a low but finite molecular mobility, i.e. R in Eq. (20) and, hence, the effective bimolecular rate constant is a function of the relaxation time of the network sites. On the other hand, the movement of the free chain end is limited and depends on the crosslinking density 82 84). An approach to the solution of this problem has been outlined elsewhere by use of computer-assisted modelling 851 Analytical estimation of the diffusion factor contribution to the reaction rate constant of the functional groups indicates that K 1/x, where t is the characteristic diffusion time of the terminal functional groups 86. ... 

When a polymer is initially in the dry state, solvent must penetrate into the network by diffusion. When the polymer is rubbery, this diffusion process is rate limiting. If the polymer is in the form of a thin slab, then solvent uptake will initially be correlated with the square root of time [30,31]. When the polymer is in an initially glassy state, swelling kinetics become more complicated [30, 32-34]. While solvent diffusion into the polymer still initiates the swelling... 

---