Experimental Gel Points

The two approaches to the problem of predicting the extent of reaction at the onset of gelation differ appreciably in their predictions of pc for the same system of reactants. The Carothers equation predicts the extent of reaction at which the number-average degree of polymerization becomes infinite. This must obviously yield a value of pc that is too large because polymer molecules larger than Xn are present and will reach the gel point earlier than those of size Xn. The statistical treatment theoretically overcomes this error, since it predicts the extent of reaction at which the polymer size distribution curve first extends into the region of infinite size. 

The gel point is usually determined experimentally as that point in the reaction at which the reacting mixture loses fluidity as indicated by the failure of bubbles to rise in it. Experimental observations of the gel point in a number of systems have confirmed the general utility of the Carothers and statistical approaches. Thus in the reactions of glycerol (a triol) with equivalent amounts of several diacids, the gel point was observed at an extent of reaction of 0.765 [Kienle and Petke, 1940, 1941], The predicted values of pc, are 0.709 and 0.833 from Eqs. 148 (statistical) and 2-139 (Carothers), respectively. Flory [1941] studied several systems composed of diethylene glycol (/ = 2), 1,2,3-propanetricarboxylic acid (/ = 3), and either succinic or adipic acid (/ = 2) with both stoichiometric and nonstoichiometric amounts of hydroxyl and carboxyl groups. Some of the experimentally observed pc values are shown in Table 2-9 along with the corresponding theoretical values calculated by both the Carothers and statistical equations. 

TABLE 2-9 Gel Point Determinations for Mixture of 1,2,3-Propanetricarboxylic Acid, Diethylene Glycol, and Either Adipic or Succinic Acid  

In many reaction systems the difference between the observed pc values and those calculated from Eq. 2-148 are at least partially ascribed to the failure of the assumption of equal reactivity of all functional groups of the same type. An example is the glycerol-phthalic acid system previously mentioned. The difference between the calculated and observed values of pc (0.709 vs. 0.765) would be decreased, but not eliminated, if the calculation were corrected for the known lower reactivity of the secondary hydroxyl group of glycerol. 

It is difficult to find crosslinking systems that are ideal in that all functional groups are of equal reactivity and intramolecular cyclization is negligible. The crosslinking of vinyl terminated poly(dimethylsiloxane) polymers with tri- and tetrafunctional silanes appears to be an exception. Thus the calculated and experimental pc values were 0.578 and 0.583, respectively, for the tetrafunctional silane and 0.708 and 0.703, respectively, for the trifunctional silane (with r — 0.999) [Valles and Macosko, 1979]. 

---

The experimental gel point, rge, is obtained from eqn. (23) when u2 tends to infinity, giving... 

ATRP was applied to the copolymerization of a monovinyl monomer and a divinyl cross-linker to study the experimental gelation behavior. The fundamental features of ATRP, including fast initiation and reversible deactivation reactions, resulted in a retarded gelation and the formation of a more homogeneous network in the ATRP process compared to gel formation in a conventional radical polymerization. The experimental gel point based on the monomer conversion in the ATRP reaction occurred later than the calculated value based on Flory-Stockmayer s mean-field theory, which was mainly ascribed to intramolecular cyclization reactions. The dependence of the experimental gel points on several parameters was systematically studied, including the ratio of cross-linker to initiator, the concentration of reagents, reactivity of vinyl groups, initiation efficiency of initiators, and polydispersity of primaiy chains. 

Atom transfer radical polymerization (ATRP) was selected as an exemplary CRP technique to systematically study the kinetics and gelation behavior during the concurrent copolymerization of monovinyl monomers and divinyl cross-linkers (Scheme 2). The effect of different parameters on the experimental gelation was studied, including the initial molar ratio of cross-linker to initiator, the concentrations of reagents, the reactivity of vinyl groups present in the cross-linker, the efficiency of initiation, and the polydispersity of primary chains. Experimental gel points based on the conversions of monomer and/or cross-linker at the moment of gelation, were determined and compared with each other in order to understand the influence of each parameter on the experimental gel points. 

Effect of Molar Ratios and Concentrations on Experimental Gel Points... 

Figure 2. Comparison of calculated and experimental gel points at different concentrations of [MA]o and molar ratios ofX = [EGDAJffEBrPJo experimental conditions [MA](/[EGDA](/[EBrP](/[CuBr](/[CuBr2](/ [PMDETA]o = 50/X/1/0.45/0.05/0.5, in DME at 60 °C. The experimental gel point was the moment when the reaction fluid lost its mobility at an upside down position for 10 seconds. (Adapted with permission from reference 24. Copyright 2008 American Chemical Society.)...

Figure 4. (A) Illustration of different structures ofpoly(MA-co-EGDA) and poly(MA-co-EGDMA) copolymers synthesized by ATRcP ofMA with different cross-linkers, and (B) comparison of their experimental gel points based on MA conversions experimental conditions [MAJffXJffR-BrJffCuBrJffCuBrJf [PMDETAJo = 50/X/1/0.45/0.05/0.5, [MAJo = 6.0Min DMFat 60 °C. (Adapted with permission from reference 25. Copyright 2008 American Chemical...

All of the systems discussed above employed an ATRP condition with high initiation efficiency ([PC]t [Initiator]o) and low polydispersity of primary chains (Mw/Mn < 1.1). ATRP allows further control of the relative initiation rate of initiators and the polydispersity of primary chains via rationally adjusting the structure of initiators, the solubility of catalysts, and the concentration of deactivators. Based on Eq. 3., it is expected that by fixing the initial molar ratio of cross-linker to initiator and their concentrations, a reduced initiation efficiency and/or a broadening distribntion of primary chains would decrease the onset of the experimental gel point based on monomer conversion and accelerate the gelation process. 

Figure 5. (A) Initiation efficiency of different ATRP initiators during the homopolymerization ofMMA, and (B) comparison of experimental gel points duringATRcP ofMMA andEGDMA by using different initiators with various ratios of X = [EGDMA]/[Initiator] experimental conditions [MMA](/[Initiator](/[CuBr](/[CuBr2](/[bpy]o = 50/1/0.4/0.1/1 for ATRP, and [MMA] (/[EGDMA](/[Initiator] o/[CuBr](/[CuBr2](/[bpy]o = 50/X/I/0.4/0.I/I for A TRcP, [MMA]o = 5.0 M in acetone at 50 °C linear polyMMA standards for...

The effect of polydispersity of primary chains on experimental gel points was also studied by using activators regenerated by electron transfer (ARGET) ° ATRP for the copolymerization of MA and EGDA. Decreasing the copper concentration from tens of ppm to a few ppm increased the polydispersity of primary chains from M /Mn = 1.1 to 2.0, which accelerated the experimental gel point during the copolymerization of monomer and crosslinker. 

Gao, H. Miasnikova, A. Matyjaszewski, K. Effect of cross-linker reactivity on experimental gel points during ATRP of monomer and cross-linker. Macromolecules 2008, 41 (21), 7843-7849. 

The experimental gel points, Vc, for the PDMS network-forming reactions were used to determine the corresponding values for Am, by solving Equation 7 ... 

Figure 5. a plot of b versus l/v for the PDMS-forming systems listed in Table 2. Individual data points were calculated via the A-R-S interpretation of the experimental gel points the plot for the chain-conformational analysis of a series of unperturbed, linear PDMS chains is also shown. 

This review summarizes the recent progress on the synthesis and application of covalently crosslinked hydrogels prepared using ATRP techniques. Section 2 briefly covers the fundamentals of the ATRP mechanism with particular emphasis on the recent progress to understand the structure/reactivity relationship and the development of new ATRP conditions that decrease the amount Cu catalyst. In Sect. 3, theoretical gel points and experimental gel points based on vinyl conversions are described. Emphasis focuses on understanding of the gelation process in... 

---