Diffusion crosslink density

Kofinas et al. (1996) have prepared PEO hydrogels by a similar technique. In this work, they studied the diffusional behavior of two macromolecules, cytochrome C and hemoglobin, in these gels. They noted an interesting, yet previously unreported dependence between the crosslink density and protein diffusion coefficient and the initial molecular weight of the linear PEGs. 

By varying the length of the esterdlol, the crosslink density was varied. Differences In chemical composition resulted In variations In polarity. Differences In permeability were largely due to differences In solubility hence diffusion through the polymeric film was not noticeably affected by crosslink density or polarity. 

High crosslink densities may severely depress polymer reactivity as a result of large decreases in swelling and diffusion rate within the polymer. Diffusion control in a polymer reaction can be detected by the inverse dependence of rate on polymer particle size (radius for spherical particle, thickness for film or sheet) [Imre et al., 1976 Sherrington, 1988]. 

Thus the factor (Mc — M )/(Mn — M ) may be thought of as the sieving term mentioned in the theory of Yasuda et al. [150], In the Peppas-Reinhart theory, the sieving mechanism takes an understandable form which is a function of the structure of the network. It must be noted that the presence of semicrystalline regions in the polymer membrane leads to deviations from the predicted dependencies in this theory. These researchers found that as the crosslinking density in the polymer membrane increased, the solute diffusion coefficient decreased, further illustrating the importance of structural parameters of the polymer network in predicting the solute diffusion coefficient [156],... 

The diffusion and the permeability are inversely related to the density, degree of crystallinity, orientation, filler concentration, and crosslink density of a polymeric film. As a general rule, the presence of plasticisers or residual solvents increases the rate of diffusion in polymers. Films cast from poor solvents have high permeability. The rate of diffusion or permeability is independent of the molecular weight of the polymer, providing the polymer has a moderately high molecular weight. 

The diffusion coefficient D is always related inversely to the crosslink density of vulcanized elastomers. When Z)is extrapolated to zero concentration of the diffusate, it is related to the weight of the principal section of the elastomer, i.e., the weight of the segments between crosslinks. 

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. ... 

In copolycondensation for example, the more reactive monomer is expected to become exhausted more rapidly than the less reactive one. If the functionalities of the polyfunctional crosslinker are more reactive, short chains are formed in the beginning of the reaction and long chains in the end. If we assume equilibrium conditions throughout the reaction, the unreacted functionalities of the crosslinker on different growing trees, with short links in the beginning, are expected to react more likely with each other and as a result a part of the final network may be more crosslinked than the other part. This may eventually lead to phase separation. If the reaction is diffusion-controlled (177), cores with higher crosslinking density may be formed. 

The collective diffusion coefficient D, on the other hand, is very sensitive to the crosslink density, and TDFRS is well suited for its measurement since, because of the small scattering angles, there is no need to extrapolate for q—> 0. 

Figure 5.14 shows the toluene distribution of the solvent-diffused sample (5 min cured). The image contrast is based on the difference in swelling capability throughout the sample. More toluene is imbibed into the PBD-rich matrix and less solvent is imbibed into the ZDA-rich domains. Therefore, the ZDA-rich domain is shown as low intensity (blue) and PBD-rich region is shown as high intensity (red, yellow or green). The difference in toluene distribution results from the differences in solubility and crosslink density. 

The mean-square displacement of the chain segments of BR swollen with deuterated benzene was observed to be independent of diffusion time, indicating restricted diffusion around an attractive centre. The mean-squared displacement decreased with increasing crosslinking density and was approximately equal to the mean-squared collective fluctuations calculated for these polymers. 

It can be shown that the specific diffusion control is not operative for the conventional mechanisms of curing of epoxy resins. The situation becomes somewhat complicated when high crosslinking densities are reached. 

High crosslink density at the irradiated surface (depth of penetration controlled by monomer diffusion)... 

Tang et al. (2004) presented a cure model that captures transient, thermal and chemical effects that are ignored in typical threshold-based models. This new model incorporates as inputs photoinitiation rates, reaction rates, diffusion and temperature distributions, and is able to determine the spatial and temporal distributions of monomer and polymer concentrations, molar masses, crosslink densities and degree of cure. 

---