Density networks

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different defonnation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the fonnation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]- The reason for these conspicuously different defonnation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

Aldehydes (glutaric, succinic [53-56]) are used to crosslink PVA, the network density being controlled by the ratio of aldehyde to OH-groups. The swelling degree of these hydrogels does not exceed 35-40 ml g-1, and there are almost quantitative correlations of the network density with the crosslinker concentration... 

The effect of the network density on the polyelectrolyte hydrogel elasticity can be understood taking into account the fact that the elastic modulus is closely connected with the swelling pressure (see, for example, Refs. [20, 115]) ... 

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 salt attack is also an important factor determining the SAH efficiency in the soil medium. In terms of Eq. (4.3), it is manifested by a sharp decrease of the coefficients y and B. The hydrogel structure prediction for specific application conditions requires to take into account universal (ionic strength) and specific (collapse) suppression phenomena and, therefore, a rather delicate balancing in search for a compromise between swelling gains due to the network density (n ) and the ionicity ((3). 

Void-free phenolic-epoxy networks prepared from an excess of phenolic novolac resins and various diepoxides have been investigated by Tyberg et al. (Fig. 7.37).93 -95 The novolacs and diepoxides were cured at approximately 200°C in the presence of triphenylphosphine and other phosphine derivatives. Network densities were controlled by stoichiometric offsets between phenol and... 

This process is highly suitable for rubbers with poor solubility. In this process, the rubber sheet is soaked in TEOS or quite often in TEOS-solvent mixture and the in situ sUica generation is conducted by either acid or base catalysis. The sol-gel reaction is normally carried out at room temperature. Kohjiya et al. [29-31] have reported various nonpolar mbber-silica hybrid nanocomposites based on this technique. The network density of the rubber influences the swelling behavior and hence controls the silica formation. It is very likely that there has been a graded silica concentration from surface to the bulk due to limited swelling of the rubber. This process has been predominantly used to prepare ionomer-inorganic hybrids by Siuzdak et al. [48-50]. 

The application of swelling measurements allows us also to estimate the influence of polyfunctional H-siloxanes 5 (R = H) on the network density. Highest values are achieved in stoichiometric mixtures. With excess of the H-siloxane the network density increases rapidly. 

Our results show that the network density (vg - 1/Q Q = swelling degree) of the crosslinked polymers is a function of the light intensity, the exposure time, the acrylate content, the molecular weight of the uncrosslinked silicone, and also of the length of the spacer group between the acrylate or methacrylate unit and the silicone backbone. Oxygen influences only the polymerization kinetics, but it does not influence the network density. 

The application of a modified swelling test [3] allows us to estimate the network density as a function of exposure time and of the thiol content. Highest values are achieved in stoichiometric mixtures. 

Calculated network densities and corresponding crosslink functionalities... 

As pointed out in the first part of this work, tetrafunctionally crosslinked PDMS also shows some dependence of the energy part of the modulus on network density and on the measuring method, but the effects observed there, are much smaller than the great variation of /a with branching density in case of networks... 

As pointed out in the experimental section, there are two ways to calculate the network density of networks with comb-like... 

The glass transition is mainly governed by chain interactions and chain mobility. Cross-linking will hardly influence the interactions, but the mobility is hindered by the cross-links. Tg will, therefore, increase with increasing network density. 

By introducing the reduced polymer network density, p, and the re-defined reduced temperature, t, the isobar is written in a simple form... 

This function increases monotonically with network density < ) and has a large Maxwell s loop for the large ionization parameter f. The swelling curves of N-isopropylacrylamide gels at low ionization were essentially well described by this equation [10]. 

These features are qualitatively discussed as follows. When the gel is illuminated, the chromophore absorbs the light energy and the local temperature of the polymer network rises. The increment of the temperature should be proportional to the intensity of the incident light and also to the concentration of the chromophore, and therefore, to the polymer network density <)>. It may thus be assumed that... 

If T0 is fixed in Eq. (5), the polymer network density can be calculated as a function of incident light intensity I0. The rescaling of the swelling curves from polymer network density to gel diameter d which was measured in the present study is straightforward and is given by the following equation,... 

These results clearly indicate that the multi-frequency dynamic analysis method allows us to estimate the contribution of different relaxation mechanisms during curing of elastomers, and the changes in chemical and physical networks densities can be studied separately. 

This empirical relationship remains valid for light inorganic materials such as calcium carbonate, silica, aluminium, etc., and allows the density to be predicted with a maximum error of 10% in the range of most usual organic network densities (1100 < p < 1400 kg m 1). In this range, density can be approximated by a linear relationship ... 

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