Critical crosslink density

The critical network structural parameters that control the mechanical performance of epoxies are macroscopic heterogeneities in crosslink density and the network topography on the molecular level. 

The critical value of x2 for the three roots to appear is shown [11] to be 1/3 for a gel with infinitely long chains. In actual gels, the critical value must be appreciably larger than 1/3. Thus, a discontinuous transition rarely occurs in neutral gels, because it requires an unusually large concentration dependence of %. An NIPA gel with small crosslinking density is one such rare example. 

Figure 2 illustrates the temperature dependence of the swelling degree as a function of precursor polymer type. Methylcellulose (MC), hydroxypropyl-methylcellulose, type E (HPMC-E) and hydroxypropylmethylcellulose, type K (HPMC-K) gels have comparable effective crosslink densities of about 2 x 10 5 mol/cm3 (as determined from uniaxial compression testing), while the crosslink density of the hydroxypropylcellulose (HPC) gel is about half this [52]. The transition temperature for each gel is within several degrees of the precursor polymer lower critical solution temperature (LCST), except for the MC gel, which has a transition temperature 9 °C higher than the LCST. The sharpness of the transition was about 3%/°C, except for the HPC gel transition, which was much sharper - about 8%/°C. 

An average expectance of additional chains v, which is greater than unity allows for a non-zero probability of the randomly selected crosslinked chain belonging to an infinitely large system [79,83]. This gives the critical value of crosslinking density ac corresponding to the gel point. 

A more critical test of the gravimetric method for determination of crosslink density (1/7.) would be a comparison of results obtained on the basis of Eq. 16 for poly(Sty-co-DVB) samples made via free-radical polymerization in various... 

---