Branching parameter

In an analogous fashion, the weight average long chain branching parameters per molecule (B ) and per 1000 repeat units (Xy) can be calculated. First Bu(V) can be determined from the Zimm-Stockmayer equation (20),... 

The whole polymer Mfj, Mj, B, and X values obtained using the MWBD method and e = 0.75 for these three LDPE resins are shown in Table IV. The molecular weights and branching parameters are in agreement with expectations b ed on the levels of conve sioji. With increasing conversion M remains constant whereas Bj, and X increase. 

Since the branching parameter a is greater than unity (usually it is 2), it is conceivable that under certain circumstances the denominator of the overall rate expression could become zero. In principle this would lead to an infinite reaction rate (i.e., an explosion). In reality it becomes very large rather than infinite, since the steady-state approximation will break down when the radical concentration becomes quite large. Nonetheless, we will consider the condition that Mol - 1) is equal to (fst T fgt) to be a valid criterion for an explosion limit. 

Polychloroprene latex adhesives, 1 533-534 Polychloroprene latexes, 19 854-861 applications for, 19 857, 859-861 compounding, 19 857-859 global product line of, 19 855 stabilization of, 19 855-857 Polychloroprene polymers branching parameters of, 19 839 commercial, 19 851-852 crystallization of, 19 843-844 cure site for, 19 837... 

Branching Parameter g from. SEC/LALLS. The effect of polymer branching upon the dilute solution configuration of polymers is conveniently expressed as the ratio of intrinsic viscosities of branched and linear polymers of the same chemical composition and molecular weight (35), i.e.. 

Like the rules discussed above, the Stockmayer-Fixman rule assumes that g is a function of g0 independent of the type of branching present. This rule gave estimates of the branching parameters for branched poly(vinyl acetate) and cross-linked polystyrene in good agreement with those derived from kinetic studies and molecular weights respectively. 

The three papers just referred to share a further assumption, namely that a steady state is set up in the continuous reactor, so that all time derivatives in the kinetic equations may be equated to zero. Graessley (91) considered the unsteady state during the start-up of a continuous stirred reactor and found that Mw may in certain cases increase without bound instead of reaching a steady state this will occur if a branching parameter exceeds a critical value. His reaction scheme is restricted to mono-radicals, and the effect of loss of radicals from the reactor is not taken into account. If a steady state is set up, the MWD obtained is Beasley s, when termination by combination and branching by copolymerization of terminal double bonds are absent. Since there is reason (92) to doubt the validity of Beasley s conclusions, as discussed above, the same doubt must apply to this work of Graessley s. 

Fig. 4.3.3b. Voltage/current dependence for the middle and high current branches. Parameters as in Fig. 4.3.3a.

Fig. 17 Radiation of dilute PVME solutions. Top Effect of y-irradiation on Mw and viscosity [77] in comparison with the Kuhn-Mark-Houwink relationship (

FIGURE 12-51 Plot of the branching parameter, X, versus conversion for polychloroprene. 

The intrinsic viscosity [ry] of both linear and branched macromolecules and the branching parameter values of the star-branched copolymers were also calculated by the GPC software and are reported in Table IV. The ratio [vlhAvlim, between the intrinsic viscosity of the... 

Table IV. Intrinsic Viscosity and Branching Parameter (g ) by GPG-Viscometry...

Figure 11. Variations of the branching parameter as a function of the number of branches in the star-branched copolymer PMl.

A complicated problem is the modeling of branched polymerization. Theoretical aspects of this problem, including the choice of the most suitable mathematical methods and the determination of branching parameters, can be found in the studies of Bamford and Tompa97), Zaidel and Katz98), Zeman and Amundson99, and Graisley et al.100. ... 

A recent paper presented a Schulz-Flory polymerization mechanism for the synthesis (22). This scheme is a simplified form of SCG obtained by setting the branching parameter f equal to zero. 

In this paper we report experimental results on the kinetics of the polyaddition reaction in the melt and in solution (diglyme) using two different catalysts, namely tetrabutyl ammonium hydroxide (TBAH) and benzyl triethyl ammonium chloride (BTAC) at different temperatures. By simultaneous measurements of a, and in two cases we have also evaluated the critical branching parameters. 

FIGURE 1.7 Plots of viscomelric branching parameter, g, versus branch functionahty, p, for star chains on a simple cubic lattice (unfilled circles), together with experimental data for star polymers in theta solvents , polystyrene in cyclohexane , polyisoprene in dioxane. Solid and dashed lines represent calculated values via Eqs. (1.70) and (1.71), respectively. (Adapted... 

Previous observations regarding of characteristics of lignin molecules in solution were included the intrinsic viscosity, branching parameter and the degree of polydispersity. 

The measurements of the branching parameter of various lignin fractions, led to conclusion that the chains of the lignin molecules in solution are densely packed or crosslinked [110, 111]. Rezanowich and co-workers [112] observed by electron microscopy that the lignosulphonates (LS) form spherical particles of a wide range of sizes. Recently, the results obtained using AFM (atomic force microscopy) had confirmed the fact that LS molecules in aqueous solutions form a crosslinked network structure, the shape of LS molecules changing with its concentration in aqueous solution [96]. 

The characteristic branching parameter (grafting density), n/m = specifies the onset of counterion localization inside the molecular brush. Note that in the osmotic regime, the spacers get fully extended, /t m. It is therefore not surprising, that the counterion localization in a cylindrical molecular brush coincides (in scaling terms) with the Manning condensation threshold [25] for a charged cylinder, qh = 1. 

FIGURE 3 The dependence of parameter 8 on branching parameter g forPHE. 

In principle, the branching parameters gvw andgV can be measured simultaneously by on-line viscometer and LALLS, respectively. The weight fraction of the branched portion in a mixture can be calculated. 

---