Crosslink concentration average

Validity of the stationary (steady) state hypothesis (SSH) for radicals (see QSSA of Section 3.2.1.1) (1) Determine the maximum rate of change (with time) of the total radical concentration (2) Divide (1) by the rate of initiation (3) If the ratio (plotted versus conversion or any other reaction indicator, e.g., crosslinker concentration or mole fraction) is much less than unity, the SSH is valid. Alternatively, one can check the ratio of propagation rate constant over the (number-average) termination rate constant, evaluated at different conversion levels. If the ratio is less than 0.001, the SSH is valid. More details can be found in references 128-131. 

Taking into account the obtained values of the W(j G) parameters, the recorded NMR spectra (Fig. 19) and the measured values of latent heat L, one can state that LCEs with lower crosslinker concentrations (xsc 0.075, Xmc 0.04) exhibit a prevalently subcritical behaviour, whereas the LCEs with higher crosslinker concentrations (xsc S 0.15, jcmc 0.12) exhibit a prevalently supercritical behaviour. In LCEs with intermediate concentrations the smeared criticaUty is most evident. Although being on average supercritical (judging from the value of (G)/Gc), the features of below-criticality such as a nonzero L and a pronounced broadening of the H-NMR spectral line at the phase transition are still present. 

Effect of crosslinker concentration on gel pore structure in a 6 %T crosslinked polyacrylamide hydrogel. Evolution of (a) crosslink strand molecular weight, and (b) average pore size (L/2) estimated from Equation 5 are plotted for crosshnker concentrations ranging from 1-8 %C. Polymerization conditions T=20 °C, UV intensity = 5 W/ml. 

BB] is the concentration of BB, and [B] = 2[BB], The number of crosslinks is simply the number of BB monomer molecules in which both B double bonds are reacted, that is, //[BB. The number of polymer chains is the total number of A and B double bonds reacted divided by the degree of polymerization, ([A] + [B])ppCw (the weight-average degree of polymerization is employed for reasons previously described in Sec. 2-10). The critical extent of reaction at the gel point pc occurs when the number of crosslinks per chain is and thus is given by... 

Taken from Ref.19 b taken from Ref.69 c taken from Ref. 8 d taken from Ref.67 taken from Ref, 731 r taken from Ref.,0) phr of sulfur h % of dicumyl peroxide number of crosslinking units per weight average PMA chain j average number of repeat units between crosslinks k concentration of chains between network joints, (mole/cm3)x 104 1 methyl group rotation m segmental motion motions within the crystalline part of the polymer... 

These sites can be used to initiate the polymerization of a small amount of di-vinylbenzene (DVB)8-10. The bifunctional monomer will polymerize to small tightly crosslinked nodules each of them is connected with the /chain ends which have participated in its initiation process. The average functionality /of the nodules is not directly accessible. However, it was shown in the case of star-shaped molecules that /increases with the overall concentration of the precursor, and, to a smaller extent, with the amount of DVB added per living end./is almost independent of the precursor chain length11. ... 

Figure 20 shows for a concentration series of microgels with a crosslink ratio of 1 20. From the long exposure measurements, the weight average hydro-dynamic radius R )c = 19.0 nm and a distribution width of... 

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