Gel point condition

Indefinite continuation of the structure is possible if, on average, one bond issues from a unit on generation g > 0 to the next generation. Since the distribution for the number of such bonds is given by F(z) and F (l) is the corresponding average, the gel point condition is given by... 

Fig. 3.14 Gel point condition as seen from the existence of a path that continues to infinity.

Thus, the gel point condition (3.77) is also derived from the branching coefficient method. 

Considering CREAM, a sudden decrease in G modulus was observed 15 min and 32min after the gel point time, respectively. The rapid increase in the G modulus followed by a sudden decrease was always observed for this sample. This experiment has been carried out three times giving reproducible results. As this phenomenon could result from a sliding of the cone caused by syneresis, experiments were performed using a ridge cone and reduced stress conditions. The shape of the G curve obtained in these conditions was similar to the results reported in Fig. 10. It was concluded that this... 

Despite the importance of initiators, synthesis conditions, and diluents on the properties of a gel, composition is, of course, the most important variable. When growing polymeric chains are first initiated, they tend to grow independently. As the reaction proceeds, different chains become connected through cross-links. At a critical conversion threshold, called the gel point or the sol-gel transition, enough growing chains become interconnected to form a macroscopic network. In other words, the solution gels. The reaction is typically far... 

Rubbery materials beyond the gel point have been studied extensively. A long time ago, Thirion and Chasset [9] recognized that the relaxation pattern of a stress r under static conditions can be approximated by the superposition of a power law region and a constant limiting stress rq at infinite time ... 

Under the same reaction conditions macrogelation occurs later in the polymerization of 1,3-DVB. Moreover, the [r ] of the microgels from 1,3-DVB is much smaller than that from 1,4-DVB. The exponent a of Mark-Houwink equation for the 1,3-DVB polymers in toluene was found to be only 0.25 [250] and 0.29 [251 ] compared with 0.48 for 1,4-DVB polymers obtained under similar reaction conditions [230]. The delay of the gel point and the small hydro-dynamic volumes of 1,3-DVB microgels, compared with 1,4-DVB microgels also illustrate that the extent of cyclization is much higher in 1,3-DVB polymerization. 

One can see that for a polymer obtained from BA2 at aB = 0.95, ( Af)2 =191 while (Af)n = 19. If this polymer is crosslinked with a bifunctional crosslinking agent C2 under stoichiometric conditions, the gel point conversion is about 0.07. However, the gel point conversion is expected to be somewhat higher not only because of the lower polydispersity of the hyperbranched polymer, but also because some cyclization can occur or multiple crosslinks can be formed during crosslinking. 

The term S represents the strength of the network. The power law exponent m was found to depend on the stochiometric ratio r of crosslinker to sites. When they were in balance, i.e. r = 1, then m - 1/2. From Equations (5.140) and (5.141) this is the only condition where G (co) = G (cd) over all frequencies where the power law equation applies. If the stochiometry was varied the gel point was frequency dependent. This was also found to be the case for poly(urethane) networks. A microstructural origin has been suggested by both Cates and Muthumkumar38 in terms of a fractal cluster with dimension D (Section 6.3.5). The complex viscosity was found to depend as ... 

Crosslinking is distinguished by the occurrence of gelation at some point in the polymerization. At this point, termed the gel point, one first observes the visible formation of a gel or insoluble polymer fraction. (The gel point is alternately taken as the point at which the system loses fluidity as measured by the failure of an air bubble to rise in it.) The gel is insoluble in all solvents at elevated temperatures under conditions where polymer degradation does not occur. The gel corresponds to the formation of an infinite network in which polymer molecules have been crosslinked to each other to form a macroscopic molecules. The gel is, in... 

To derive the condition for the gel point in random crosslinking of existing chains of arbitrary molecular weight distribution, let us consider a primary chain selected at random having P monomer units. If one unit of the selected chain happens to be crosslinked, the probability that this unit is a part of the selected chain is equal to the weight fraction wP of the P-mer. The expected number of additional crosslinked units in the P-mer is then q(P — 1). The mean expected number of additional crosslinked units in a chain is... 

The method that we have sought to exploit provides a very sensitive indication of the balance between processes leading to production of new polymer molecules and those producing crosslinks. Since this indicator operates under conditions where no gel has appeared, it makes it much more reliable than any technique that depends on the actual detection of gel. In all the instances studied, the gel point lay 6-8% above the crossover points. Thus, we would appear to be in a position to study more precisely and objectively the effects of varying the experimental parameters. 

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