Crosslink constant

These results are for a Flory-Huggins x = 0.32 and a crosslink constant pVyM = 0.0117, where p is the density of dry rubber, is the molar volume of the solvent, and is the molecular weight between crosslinks. The calculations are based on the assumption... 

Figure 3.4 Uj versus M" for polyisobutylene samples with three different degrees of crosslinking (T and a constant). [Reprinted with permission from P, J. Flory, Ind. Eng. Chem. 38 417 (1946). Copyright 1946, American Chemical Society.]...

Ion-exchange resins swell in water to an extent which depends on the amount of crosslinking in the polymer, so that columns should be prepared from the wet material by adding it as a suspension in water to a tube already partially filled with water. (This also avoids trapping air bubbles.) The exchange capacity of a resin is commonly expressed as mg equiv./mL of wet resin. This quantity is pH-dependent for weak-acid or weak-base resins but is constant at about 0.6-2 for most strong-acid or strong-base types. 

The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

Obviously, universal constant, cj) depends on the number of chains that are linked at a crosslink (junction functionality f) and probably on the chemical composition as well. 

Application of the Method of Mcanents. In order to apply the method of moments (6,7), the pseudo-kinetic rate constant for the crosslinking reaction should be defined as follows. 

By analogy to simple olefins, we propose that 0(3P) initially adds to the 1,4 or 1,2 double bonds in polybutadienes at ambient temperature. Since the rate constants for 0(3P) addition to cis-2-butene and 1-butene (as models for 1,4 and 1,2 double bonds, respectively) are in the ratio 4.2 1 at 298 K ( 6), preferential addition to the 1,4 double bonds is assumed to persist to very high vinyl contents (-8011). The biradical adducts then rearrange to epoxides and carbonyl compounds or give rise to chain rupture and/or crosslinking as a consequence of PIF, according to the scheme ... 

We use gel content analysis to determine the weight fraction of a crosslinked polymer that is bound into an insoluble network. We immerse a stainless steel mesh basket containing a known weight of the crosslinked polymer in a suitable solvent (which may be heated to facilitate dissolution). If necessary, we can slice or grind the sample to increase its surface area. After 24 hours or more, we remove the basket from the solvent and dry it to constant weight. We calculate the gel content from Eq. 5.6. 

Figure 2 shows a typical evolution of G(t, p) near the LST of a crosslinking polymer. The x axis shows the time of crosslinking reaction which corresponds to an extent of reaction, p. For each of the curves in Fig. 2, p is kept constant. The crosslinking reaction was stopped at discrete values of p, which increased from sample to sample. 

Fig. 22. Schematic evolution of dynamic moduli during crosslinking. The time period At corresponds to the time necessary for a rheological measurement in case of a reacting sample. If the reaction is stopped, At corresponds to the time in which the poison diffuses into the sample. The reaction is still carried on until the entire sample is poisoned. Then the moduli remain constant...

Crosslinking of many polymers occurs through a complex combination of consecutive and parallel reactions. For those cases in which the chemistry is well understood it is possible to define the general reaction scheme and thus derive the appropriate differential equations describing the cure kinetics. Analytical solutions have been found for some of these systems of differential equations permitting accurate experimental determination of the individual rate constants. 

In order to answer these questions, the kinetic and network structure models were used in conjunction with a nonlinear least squares optimization program (SIMPLEX) to determine cure response in "optimized ovens ". Ovens were optimized in two different ways. In the first the bake time was fixed and oven air temperatures were adjusted so that the crosslink densities were as close as possible to the optimum value. In the second, oven air temperatures were varied to minimize the bake time subject to the constraint that all parts of the car be acceptably cured. Air temperatures were optimized for each of the different paints as a function of different sets of minimum and maximum heating rate constants. 

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