Crosslink experimental determination

Crosslinking of many polymers occurs through a complex combination of consecutive and parallel reactions. For those cases in which the chemistry is well understood it is possible to define the general reaction scheme and thus derive the appropriate differential equations describing the cure kinetics. Analytical solutions have been found for some of these systems of differential equations permitting accurate experimental determination of the individual rate constants. 

Assuming a homogeneous distribution of crosslinks, the equality, given by Eq. (4), becomes independent of conversion. Thus on complete conversion (x = 1), Qx(x)reduces to Q°° (initial degree of dilution of the monomers) and Qv(x) can be replaced by the experimentally determined equilibrium swelling ratio Qv. Accordingly, the condition of phase separation becomes... 

On the basis of observations made on limited structural series, certain authors (e.g., Adamson, 1980) suggested that water absorption would occur by occupancy of the available free volume by water molecules. Despite its seductive intuitive character, this theory fails to explain why free-volume rich substances such as silicone rubbers, crosslinked polyethylene, or simply liquid aliphatic hydrocarbons are hydrophobic. Furthermore, experimentally determined apparent heat of dissolution values (Hs) and plasticization effects generally agree well with theoretical predic-... 

The average length (or molecular weight) of network chains in a crosslinked polymer can be experimentally determined from the equilibrium rubbery modulus. This relationship is a direct result of the statistical theory of rubber-like elasticity . In the last decade or so, modem theories of rubber-like elasticity 2127) further refined this relationship but have not altered its basic foundation. In essence, it is... 

Exposing the RIM elastomers to stress relaxation at low extension at three levels o temperature, the changes obtained in experimentally determined crosslink densities, minus the covalent calculated crosslink densities, Indicated how ast the crystalline micelles were decaying at the elevated temperatures. The data obtained were recorded in Tables VI and VII. 

Experimental determination of the contributions above those predicted by the reference phantom network model has been controversial. Experiments of Oppermann and Rennar (1987) on endlinked poly(dimethylsiloxane) networks, represented by the dotted points in Figure 4.4, indicate that contributions from trapped entanglements are significant for low degrees of end-linking but are not important when the network chains are shorter. Experimental results of Erman and Wagner (1980) on randomly crosslinked poly(ethyl acrylate) networks fall on the solid line and indicate that the observed high deformation limit moduli are within the predictions of the constrained-junction model. 

Concerning the divergence of Tio, the scaling law of eq.(10) has already mentioned as a critical behaviour near the gel point. Equation (10) was issued for p

gelation time, temperature k is the critical exponent determining the critical characteristics near the gel point. Experimental determination for k is not difficult provided that pc is known. If pc is unknown, eq.(20) is useful for the simultaneous determination of pc and k. 

The Hildebrand solubility parameter is readily obtained for liquids by inserting the appropriate experimentally determined quantities into eq. (4.70). Polymers degrade prior to vaporization and their solubility parameter values are determined indirectly by one of two essentially different techniques. In the first technique, the polymer is lightly crosslinked and then treated with a number of solvents with different solubility parameters. The best solvent, the one which swells the polymer the most, is then the one which has a solubility parameter which resembles the solubility parameter of the polymer (Fig. 4.14). The other technique involves the measurement of the intrinsic viscosity of solutions of the polymer in a number of solvents of different solubility parameters. 

Mark, J. E. (1982). Experimental determinations of crosslink densities. Rubber Chem. Technol. 55, 762. 

Of all the techniques, it is those of Group 1 that are likely to give the most realistic data, simply because they measure transport of charged species only. They are not the easiest experimental techniques to perform on polymeric systems and this probably explains why so few studies have been undertaken. The experimental difficulties associated with the Tubandt-Hittorf method are in maintaining nonadherent thin-film compartments. One way is to use crosslinked films [79], while an alternative has been to use a redesigned Hittorf cell [80]. Although very succesful experimentally, the latter has analytical problems. Likewise, emf measurements can be performed with relative ease [81, 82] it is the necessary determination of activity coefficients that is difficult. 

Progress in the theory and advances in practical applications of hydrogels are to a great extent determined by experimental study of their swelling and elasticity. However, investigating SAH is rather complicated because most of the available techniques are adapted mainly to highly crosslinked gels. 

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. 

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