Network crosslink density

The Tg of linear polymers such as polyimides is heavily dependent on, and increases with, the molecular weight. The equivalent statement can also be said about crosslinked networks, where the glass transition temperature is dependent on the network crosslink density [111-117]. 

Fracture processes become very different in the glassy state as compared with the rubbery state. In the glassy state, the sensitivity of fracture to network topology is lost. The chemical structure of the network, crosslink density and the type of bond overloading do not play a key role and defects of glassy samples become very important. 

The extent of swelling is inversely proportional to network crosslink density and is highly dependent on the... 

Volume fraction of polymer in the swollen network = Crosslinked density... 

Fluorosilicones consist of PDMS backbones with some degree of fluoro-aliphatic side chains. The fluorinated group can be trifluoropropyl, nonafluorohexylmethyl, or fluorinated ether side group [78,28,79]. These polymers differ not only in substituent group, but also in the amount of fluoro-substitution relative to PDMS, the overall molecular weight and crosslink density, and the amount of branching. In most commercially available cases, these polymers are addition cure systems and the reactions are those discussed previously for silicone networks. 

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. 

Returning to the evaluation of the SAH network parameters, it should be noted that the crosslinking densities obtained from the modulus and swelling data agree satisfactorily with each other [22]. Analysis of the data from Refs. [18,90] confirms this conclusion. 

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. 

Additional parameters should be taken into account for polyester networks and hyperbranched polyesters, for example, crosslink density and degree of branching. 

Crosslinking resoles in the presence of sodium carbonate or potassium carbonate lead to preferential formation of ortho-ortho methylene linkages.63 Resole networks crosslinked under basic conditions showed that crosslink density depends on the degree of hydroxymethyl substitution, which is affected by the formaldehyde-to-phenol ratio, the reaction time, and the type and concentration of catalyst (uncatalyzed, with 2% NaOH, with 5% NaOH).64 As expected, NaOH accelerated the rates of both hydroxymethyl substitution and methylene ether formation. Significant rate increases were observed for ortho substitutions as die amount of NaOH increased. The para substitution, which does not occur in the absence of the catalyst, formed only in small amounts in the presence of NaOH. 

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... 

It is possible to calculate a number of different kinds of "effective" crosslink densities. Bauer et al have used a quantity they termed the "elastically effective crosslink density " (Cel) correlate cure with solvent resistance and other physical properties of coatings (7-10). The correlation was basically empirical. Formally, the is a calculation of the number of functional groups attached to the infinite network for which there are at least two other paths out to the network on the given polymer or crosslinker. Thus, chains with only one or two paths to the infinite network are excluded. The following expression can be written for... 

Generalization of Flory s Theory for Vinyl/Divinyl Copolvmerization Using the Crosslinkinq Density Distribution. Flory s theory of network formation (1,11) consists of the consideration of the most probable combination of the chains, namely, it assumes an equilibrium system. For kinetically controlled systems such as free radical polymerization, modifications to Flory s theory are necessary in order for it to apply to a real system. Using the crosslinking density distribution as a function of the birth conversion of the primary molecule, it is possible to generalize Flory s theory for free radical polymerization. 

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.

Table II shows Tg data obtained from DSC traces of the PHEMA-1 -PIB networks. The traces showed two Tgs indicating microphase separation into PHEMA and PIB domains. The presence of the PHEMA Tg at - 110°C indicates complete desilylation of all networks. The Tgs for the reference PIBs (see footnote a in Table II) are lower than the Tgs of the PIB incorporated into the network. This may be due to the flexible PIB chain-ends embedded in the glassy PHEMA matrix. The increase in the Tg of the PIB phase in the network with increasing % PIB is most likely due to an increase in crosslink density.

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