The gel point

We noted above that the presence of monomer with a functionality greater than 2 results in branched polymer chains. This in turn produces a three-dimensional network of polymer under certain circumstances. The solubility and mechanical behavior of such materials depend critically on whether the extent of polymerization is above or below the threshold for the formation of this network. The threshold is described as the gel point, since the reaction mixture sets up or gels at this point. We have previously introduced the term thermosetting to describe these cross-linked polymeric materials. Because their mechanical properties are largely unaffected by temperature variations-in contrast to thermoplastic materials which become more fluid on heating-step-growth polymers that exceed the gel point are widely used as engineering materials. 

The value of a to be used in these expressions is given by Eq. (5.45) for the specific mixture under consideration. At the point of gelation - l/(f- 1) according to Eq. (5.46). Equation (5.55) shows that n becomes infinite at this point while n remains finite. This merely means that there are still many molecules present at the gel point in addition to the network molecule of essentially infinite molecular weight. The ratio h /n indicates an immense expansion of the degree of heterogeneity as a ->. Expressions are also avail-... 

The reaction proceeds until aU. available monomer has reacted or until it is terminated by an acidic species. The gel point in these m situ polymerizations, as represented by the time of fixture, occurs within several seconds on strongly catalytic surfaces such as thermoset mbbers to several minutes on noncatalytic surfaces. 

Fig. 32. Maximum flux obtained with various protein solutions as a function of protein concentration according to equation 3. Feed flow rates, cm /min = A, 3000 B, 2000 C, 1000 and D, 500. The flux decreases exponentially as the protein concentration increases. The extrapolated protein concentration at no flux is the gel point for this type of solution (approx 28%). These results were obtained in a flow-through cell and demonstrate the...

Aging. When a gel is maintained in its pore Hquid, the stmcture and properties continue to change long after the gel point. This process is called aging. Four aging mechanisms can occur, singly or simultaneously polycondensation, syneresis, coarsening, and phase transformation (9,21). 

Solutions of methylceUuloses are pseudoplastic below the gel point and approach Newtonian flow behavior at low shear rates. Above the gel point, solutions are very thixotropic because of the formation of three-dimensional gel stmcture. Solutions are stable between pH 3 and 11 pH extremes wiU cause irreversible degradation. The high substitution levels of most methylceUuloses result in relatively good resistance to enzymatic degradation (16). 

The extent of the long-chain branching of a series of ethyl xanthogen disulfide modified polymers carried to increasing conversion is shown in Table 1. No branches are found until 56% conversion. The gel point is a Htfle over 82%. Polymer rheology deteriorates between 56 and 82% conversion. 

The addition of defoamers can restore some of this lost strength, but only to a certain point. The defoaming mechanism usually relies upon diffusion of gas bubbles together in the liquid adhesive to form larger bubbles, which, in turn, rise to the surface and break. Diffusion generally decreases with increasing viscosity and stops when the gel point is reached, i.e., when the viscosity approaches infinity, accordingly ... 

Table 1. Huggins parameters for a soluble MA-EDMA copolymer (before the gel point) and a linear PMA in acetic acid solutions at 299 K...

For MA-EDMA copolymers, the thermodynamic quality of the solvent characterized by Huggins parameter % for the soluble system up to the gel point changes in the same direction as PM A (Table 1) [21]. 

A recent series of papers [18, 24, 32-34] substantially clears up the three-dimensional polymerization mechanism in the AAm-MBAA system. Direct observation of the various types of acrylamide group consumption using NMR technique, analysis of conversion at the gel-point, and correlation of the elastic modulus with swelling indicate a considerable deviation of the system from the ideal model and a low efficiency of MBAA as a crosslinker. Most of these experimental data, however, refer to the range of heterogeneous hydrogels where swelling is not more than 80 ml ml-1 [24]. 

If monomers which have functionalities greater than 2 are used for step polymerisation the product that forms consists of an infinitely large three-dimensional network and the polymerisation is characterised by sudden gelation at some point before the reaction is complete. The gel point is observed readily as the time when the mixture suddenly loses fluidity as viscosity rises sharply... 

Gelation occurs at relatively low conversions of monomer to polymer hence the number-average molar mass at the gel point is low. By contrast, however, the weight-average molar mass becomes infinite at the gel point. 

Chambon, F. and Winter, H.H. Linear viscoelasticity at the gel point of crosslinking PDMS with imbalanced stoichiometry, J. Rheol, 31, 683, 1987. 

FIGURE 22.5 Schematic view of kinetically aggregated filler clusters in mbber below and above the gel point <1>. The left side characterizes the local stmcture of carbon black clusters, built by primary particles and primary aggregates. (Every black disk in the center figure [ and on the right-hand side

primary aggregate.) (From Kliippel, M. and Heinrich, G., Kautschuk, Gummi, Kunststojfe, 58, 217, 2005. With permission.)... 

If the denominator in equation 12 is less than or equal to zero, the mixture has gelled. In this case, the weight average molecular weight is infinite. In the absence of the self-condensation reaction - 0), the gel point is given by ... 

The process is repeated for the "crosslinker" component (lines 1180-1950). From the calculated expectation values, the program determines the ratio of A to B groups (line 1960) and the gel point in the absence of B group self-condensation (percent reaction of A groups at gel, line 1990). The various expectation values along with the gel point and the ratio of crosslinker to polymer functionality (1/R), are printed at the terminal (lines 2000-2220). 

BELOW THE GEL POINT, THE PROGRAM CALCULATES THE WEIGHT AVERAGE" MOLECULAR WEIGHT. ABOVE THE GEL POINT, THE PROGRAM CALCULATES"... 

Figures 2 and 5 show the increase of the mass average molar mass, R i, with conversion for the systems with branched and linear prepolymers, respectively. These results indicate that addition of the branching monomer in the first stage yields much higher values of R, and the gel point is reached at lower conversion than addition in the third stage. Translated into practical properties this means that the processing and application qualities (e.g. flow) of a paint based on formulation F40 will be inferior to those of one on the basis of for-...

As might be expected, these differences in the pre-gel properties are also reflected in the post-gel regime. The sol fraction varies more smoothly with conversion for the branched prepolymer compositions, cf. Figures 3 and 6. But because the gel point is at (so... 

Rn, and the gel point, Figure 16 concerns the sol fraction and Figure 17 the number of EANC s per monomer. The differences are most pronounced near the gel points and they vanish with completion of the reaction. 

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