Network structure crosslink density

For the amine system under non-isothermal cure at 0.2°C min goo of 245 °C causes devitrification to occur at a temperature more than 150°C above vitrification. The importance of this extended mobility-restricted cure on the final material s properties should be emphasised. For this tetrafunctional epoxy-diamine system, an increase in Tg of ca. 170°C, corresponding with a residual cure of ca. 44% and a reaction enthalpy of more than 230 J g is caused by diffusion-controlled reactions and drastically influences the flnal network structure (crosslink density). 

As in linear polymers, the relative influence of the molecular structure (scale of nanometers and monomers), and the macromolecular structure (crosslink density), on network properties, depends on temperature, as shown in Fig. 10.9. In the glassy state, the physical behavior is essentially controlled by cohesion and local molecular mobility, both properties being mainly under the dependence of the molecular scale structure. As expected, there are only second-order differences between linear and network polymers. Here, most of the results of polymer physics, established on linear polymers, can be used to predict the properties of thermosets. Open questions in this domain concern the local mobility (location and amplitude of the (3 transition). 

To determine the crosslinking density from the equilibrium elastic modulus, Eq. (3.5) or some of its modifications are used. For example, this analysis has been performed for the PA Am-based hydrogels, both neutral [18] and polyelectrolyte [19,22,42,120,121]. For gels obtained by free-radical copolymerization, the network densities determined experimentally have been correlated with values calculated from the initial concentration of crosslinker. Figure 1 shows that the experimental molecular weight between crosslinks considerably exceeds the expected value in a wide range of monomer and crosslinker concentrations. These results as well as other data [19, 22, 42] point to various imperfections of the PAAm network structure. 

The degradation of the matrix in a moist environment strongly dominates the material response properties under temperature, humidity, and stress fatigue tests. The intrinsic moisture sensitivity of the epoxy matrices arises directly from the resin chemical structure, such as the presence of hydrophilic polar and hydrogen grouping, as well as from microscopic defects of the network structure, such as heterogeneous crosslinking densities. 

Once P(F ° ) and P(Fg° ) have been calculated, it is possible to calculate a number of network structure parameters including the weight fraction of sol, wg, and the "effective" crosslink density. A given polymer or crosslinker will be part of the sol only if all of its groups are attached to finite chains. Thus, the weight of the sol is given by... 

Table II shows Tgs obtained from DSC traces. (Footnotes a and b in Table II show T s values of three reference polymers two PIBs, whose Mns are similar to the Mns of MA-PIB-MA used in the network synthesis, and a PDMAAm the difference in the Tg for the Mn=4,000 and 9,300 PIBs is due to the dependence of Tg on Mn(72)). The DSC traces of the networks exhibited two Tgs, one in the range of -63 to -52 °C (PIB domains) and another in the range of 90 to 115 °C (PDMAAm domains) indicating microphase separated structures. The Tgs associated with the PIB phase in the PDMAAm-1-PIB networks were higher than those of the reference homoPIBs which may be due to PIB chain-ends embedded in the glassy PDMAAm phase restricting segmental mobility. The Tg of the PIB phase in the PDMAAm-1-PIB increases by increasing the PIB content which may be due to an increase in crosslink density. In contrast, the Tg for the PDMAAm phase in the network decreases upon increasing the PIB content. Interaction of the (-CH2-CH-) moiety of the PDMAAm with the flexible PIB and thus the formation of a more flexible structure may explain this phenomenon.

In order to answer these questions, the kinetic and network structure models were used in conjunction with a nonlinear least squares optimization program (SIMPLEX) to determine cure response in "optimized ovens ". Ovens were optimized in two different ways. In the first the bake time was fixed and oven air temperatures were adjusted so that the crosslink densities were as close as possible to the optimum value. In the second, oven air temperatures were varied to minimize the bake time subject to the constraint that all parts of the car be acceptably cured. Air temperatures were optimized for each of the different paints as a function of different sets of minimum and maximum heating rate constants. 

Depending on the conditions of synthesis, copolymerization of divinyl/vinyl-monomers in the presence of an inert solvent leads to the formation of expanded (preswollen) or heterogeneous (porous) structures [54,99,100]. If the solvent remains in the network (gel) phase throughout the copolymerization, expanded networks are formed. If the solvent separates from the network phase the network becomes heterogeneous. According to Dusek et al., heterogeneities may appear in poor solvents due to the polymer-solvent incompatibility (x-induced syneresis), while in good solvents due to an increase in crosslink density (v-induced syneresis) [99]. 

If we accept the model proposed for these mixed monofunctional/ difunctional systems, we can draw some conclusions about the network structure in polymers based on I alone. For example, Fig. 7 shows how the Tg varied with the relative crosslink density in the mixed systems. The abcissa represents the probability that a monomer chosen at random is linked to the network at both ends. At moderate degrees of crosslinking, the expected relationship between Tg and crosslink density is linear, so the data were approximated by a straight line (10). From the extrapolation in Fig. 7, one concludes that a typical bis-phthalonitrile cured to a Tg of 280 0 has a relative crosslink density of 0.5, or about 70% reaction of nitrile groups. 

This is a theoretical study on the entanglement architecture and mechanical properties of an ideal two-component interpenetrating polymer network (IPN) composed of flexible chains (Fig. la). In this system molecular interaction between different polymer species is accomplished by the simultaneous or sequential polymerization of the polymeric precursors [1 ]. Chains which are thermodynamically incompatible are permanently interlocked in a composite network due to the presence of chemical crosslinks. The network structure is thus reinforced by chain entanglements trapped between permanent junctions [2,3]. It is evident that, entanglements between identical chains lie further apart in an IPN than in a one-component network (Fig. lb) and entanglements associating heterogeneous polymers are formed in between homopolymer junctions. In the present study the density of the various interchain associations in the composite network is evaluated as a function of the properties of the pure network components. This information is used to estimate the equilibrium rubber elasticity modulus of the IPN. 

Differences in Network Structure. Network formation depends on the kinetics of the various crosslinking reactions and on the number of functional groups on the polymer and crosslinker (32). Polymers and crosslinkers with low functionality are less efficient at building network structure than those with high functionality. Miller and Macosko (32) have derived a network structure theory which has been adapted to calculate "elastically effective" crosslink densities (4-6.8.9). This parameter has been found to correlate well with physical measures of cure < 6.8). There is a range of crosslink densities for which acceptable physical properties are obtained. The range of bake conditions which yield crosslink densities within this range define a cure window (8. 9). 

The variation of the domain sizes with crosslink density was recognized by Yeo et al. [28], investigating cross-poly(n-butyl acrylate)-inter-cross-polystyrene. Figure A shows the morphology of 50/50 compositions as a function of network I crosslinking level. The cellular structures are gradually transformed to finer, and more obviously cylindrical or worm-like shapes with increasing crosslink density. 

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],... 

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