Near gel-point

Superposition of reduced rate curve (eq. 5,6) for copolymerisatic of methyl methacrylate with ethylene glycol dimethacrylate or polyethylene glycol fumarate. Inset enlarged view of typical results near gel point - ordinate scale arbitrary. eq. 5,6 for disproportionation eq. C5, y = 3, for radical combination c model without diffusion control. Arrow observed gel point. 

The value of the exponent y/ = 4.5, determined by the authors, is in good agreement with the percolation model (4) and clearly differs from the mean field value (1). The authors give two values for the exponent vlfi 1.65 near gel point and 3.3 far from gel point. Tliese two exponents, although inaccurate, are closer to the percolation value (2) than to the classical value (O.S). 

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. 

With increasing distance from the gel point, the simplicity of the critical state will be lost gradually. However, there is a region near the gel point in which the spectrum still is very closely related to the spectrum at the gel point itself, H(A,pc). The most important difference is the finite longest relaxation time which cuts off the spectrum. Specific cut-off functions have been proposed by Martin et al. [13] for the spectrum and by Martin et al. [13], Friedrich et al. [14], and Adolf and Martin [15] for the relaxation function G(t,pc). Sufficiently close to the gel point, p — pc <4 1, the specific cut-off function of the spectrum is of minor importance. The problem becomes interesting further away from the gel point. More experimental data are needed for testing these relations. 

Steady shear flow properties are sensitive indicators of the approaching gel point for the liquid near LST, p < pc. The zero shear viscosity rj0 and equilibrium modulus Ge grow with power laws [16]... 

For the relaxation of the solid near the gel point, the critical gel may serve as a reference state. The long time asymptote of G(t) of the nearly critical gel, the equilibrium modulus Ge, intersects the G(t) = St n of the critical gel at a characteristic time (Fig. 6) which we will define as the longest relaxation time of the nearly critical gel [18]... 

De Gennes [41] predicted that percolation theory should hold for crosslink-ing of small molecule precursors. However, he argued that for vulcanizing polymers (high Mw), only a very narrow regime near the gel point exists for which percolation is valid, i.e. these polymers should exhibit more mean fieldlike behavior. 

This most simple model for the relaxation time spectrum of materials near the liquid-solid transition is good for relating critical exponents (see Eq. 1-9), but it cannot be considered quantitatively correct. A detailed study of the evolution of the relaxation time spectrum from liquid to solid state is in progress [70], Preliminary results on vulcanizing polybutadienes indicate that the relaxation spectrum near the gel point is more complex than the simple spectrum presented in Eq. 3-6. In particular, the relation exponent n is not independent of the extent of reaction but decreases with increasing p. 

Fig. 13. Shear stress t12 and first normal stress difference N1 during start-up of shear flow at constant rate, y0 = 0.5 s 1, for PDMS near the gel point [71]. The broken line with a slope of one is predicted by the gel equation for finite strain. The critical strain for network rupture is reached at the point at which the shear stress attains its maximum value...

The divergence of the longest relaxation time does not perturb the measurement. In comparison, steady state properties (the steady shear viscosity, for instance) would probe an integral over all relaxation modes and, hence, fail near the gel point. 

Dynamic mechanical data near the gel point allow easy determination of the parameters of the critical gel, Eq. 1-1. Tan 8, as shown in Fig. 26, gives the relaxation exponent n... 

Power law relaxation is no guarantee for a gel point. It should be noted that, besides materials near LST, there exist materials which show the very simple power law relaxation behavior over quite extended time windows. Such behavior has been termed self-similar or scale invariant since it is the same at any time scale of observation (within the given time window). Self-similar relaxation has been associated with self-similar structures on the molecular and super-molecular level and, for suspensions and emulsions, on particulate level. Such self-similar relaxation is only found over a finite range of relaxation times, i.e. between a lower and an upper cut-off, and 2U. The exponent may adopt negative or positive values, however, with different consequences and... 

Controlled sample preparation is difficult near the gel point where the rate of property change is largest. Physical gelation usually proceeds too rapidly so that the material near the gel point eludes the experiment or the application. However, chemical gelation is most suitable for controlling the evolving network structure. Several approaches have been explored in industrial applications and in research laboratories ... 

Off-balancing of stoichiometry by the right amount (depending on crosslinking system) allows preparation of materials near the gel point [66],... 

From a practical point of view, it is advantageous that critical gel properties depend on molecular parameters. It allows us to prepare materials near the gel point with a wide range of properties for applications such as adhesives, absorbents, vibration dampers, sealants, membranes, and others. By proper molecular design, it will be possible to tailor network structures, relaxation character, and the stiffness of gels to one s requirements. 

For low extents of crosslinking the curves lie between the limits of the curve near the gel point and that for linear chains. This behavior is understood when recalling that at low crosslinking the system mainly consists of linear chains. The highly crosslinked chain on the other hand approaches a molar mass independent master curve that, as expected, lies in the region of hard sphere behavior. 

As previously mentioned, a diffusion or mobility effect should be accounted for in the last stages of a curing process. The viscosity increases because of chain growth and cross-linking and several authors pointed out that, as a consequence, the movements of the reactants slow down or cease near the gel point [55] thus, the curing process is controlled by these motions rather than by chemical factors [7,8]. 

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