Scission rate

The empirical frictional factor (T fric) is independent of shear rate but increases in poor solvent this permits to account for the dependence of the scission rate constant on solvent quality. The entanglement part (r enl), as given by Graessley s theory which considers the effect of entanglement and disentanglement processes, is a complex function of shear rate ... 

The normalization coefficient K is the global scission rate constant given by the contribution of all the individual rate constants for each fracture site ... 

In flow-induced degradation, K is strongly dependent on the chain length and on the fluid strain-rate (e). According to the rate theory of molecular fracture (Eqs. 70 and 73), the scission rate constant K can be described by the following equation [155]... 

From the Arrhenius form of Eq. (70) it is intuitively expected that the rate constant for chain scission kc should increase exponentially with the temperature as with any thermal activation process. It is practically impossible to change the experimental temperature without affecting at the same time the medium viscosity. The measured scission rate is necessarily the result of these two combined effects to single out the role of temperature, kc must be corrected for the variation in solvent viscosity according to some known relationship, established either empirically or theoretically. 

In a few studies, solvent viscosity was varied as a result of change in temperature [109, 165]. In transient flow, the direct effect of temperature on the scission rate was shown to be minimal (Sect. 5.7). Even so, it is desirable to look for a system where the solvent viscosity can be studied independently of the other kinetics parameters [166], Ideally, the solvents used should satisfy the following criteria ... 

Fig. 63. Scission rate constant for the ultrasonic degradation of dextran as a function of molecular weight (M), in different solvents (according to Ref. [179]) ( ) formamide (a) 10% MgSQ4 ( ) water...

W. F. Reed. C. B. Reed, and L, D. Byers. Random coil scission rates determined by time-dependent total intensiiy light scattering hyaluronaie depolymerization by hyaluromdase. Biopolymers30 1073 (1990). 

Here a(r) = random scission rate to end-chain scission rate. Now, for a distribution with initially large degree of polymerization under isothermal conditions, it may be confirmed by direct substitution into Equation 18.33 that the solutions of these equations for / > I arc... 

The fraction of monomer in the volatile species should be a strong function of the relative random scission rate and this is often taken as an indicator of the balance between end-chain and random scission in experimental observations.1 We should expect that when end-chain scission dominates, the fraction of monomer in the volatile species should be close to 1. As more random scissions occur, the fraction will reduce. When random scission dominates, the spectrum of volatile species should be approximately flat, implying that the fraction of monomers should approach I /(mv - 1) as a(r) —> °°. Figure 18.15 shows the monomer fractions (from numerical solutions of the... 

These results provide additional confirmation for the mechanism of pyrolysis of simple polyolefins. The absence of monomer in the volatile products, the maxima in the rate curves, and the sharp decrease in the intrinsic viscosity for linear polymethylene (29) and polypropylene (2, 6, 13, 30) all point to an essentially random scission, due to pronounced intermolecular chain transfer, Equation 2. However, deviations appear when a, the fraction of bonds broken, or, what amounts to the same, the number average DP is examined as a function of time. For small a, the former relation should be one of simple proportionality and hnearity in 1/P. Instead, for both polypropylene (6) and polymethylene [see Figure 5, in (29)] curvature appears, indicating a reduction of the scission rate after an initial period of rapid degradation. For polypropylene this has been interpreted as a breaking of weak and normal bonds. Between 250° and 280° C., one weak link per 2.4 X 10 is found (6). At 295° C., the existence of more than two types of bonds would have to be postulated. 

Overall, therefore, the available literature supports the generally held view that the durability of UF-bonded wood products is governed by the susceptibility of cured UF resin bonds to scission by both hydrolysis and swell/shrink stresses. Note, moreover, that in either case, the most likely product of scission will ultimately be formaldehyde and further that mechanical stress enhances the rates of many chemical reactions (37). In fact, simplistic calculations based on formaldehyde liberated from bond ruptures at least indicate the possibility that formaldehyde from swell/shrink stress rupture could contribute significantly to total emission. Assume, for example, that board failure occurs due to rupture of one chemical bond type which liberates one molecule of formaldehyde and consider two cases (a) a conservative one in which only 5 percent of those bonds rupture in 50 years, i.e., probable board durability greater that 50 years, and (b) a much less conservative case in which 30 percent of those bonds rupture in 20 years, i.e., probably failure in 20 years or less. Case (a) leads to a first order scission rate constant of 3.3 x 10 s and a hypothetical board emission rate (see Appendix 3a) that is below the maximum liberation rate permitted by the German E-1 standard (7). However, Case (b) leads to a first order scission rate constant of 5.7 x 10 s and a hypothetical board emission rate above that allowed by the HUD standard (8). (FormaIdehyde-wood interactions and diffusion effects would... 

Figure 10. Comparison of Chain Scission Rates in Stabilized and Unstabilized HDPE, Oxidation by Oxygen Uptake at 100°C and 1 Atmosphere...

Section 4.6.2 illustrates the experimental procedures that have recently been applied toward the study of high-pressure free-radical polymerization processes. Section 4.6.3 presents results of propagation, termination, chain-transfer (to monomer and to polymer), and P-scission rate coefficients for ethene homopolymerization. Recent results from experiments and modeling investigations into high-pressure copolymerizations (with ethene being one of the monomers) are reported in Section 4.6.4, together with information on homopolymerization rate coefficients of the comonomer species. 

The formation of considerable amounts of acetone and tert-butyl alcohol during the decomposition of 2,2-bi tert-butylperoxy utane in styrene indicate that the rates of scission and H-abstraction are competitive with addition to the styrene double bond. Niki and Kamiya [167,168] are in agreement that considerable H-abstraction betw n tert-butoxy radicals and PS takes place especially at high polymerization temperatures (125 °C). However, P-scission rate is in disagreement with Moad. As mentioned earlier, Moad found that the rate of vinyl addition by tcrt-butoxy radicals is 76 times faster than P-scission... 

In ultrasonic degradation, changing the temperature inevitably affects the vapor pressure of the solvent, and thus the dynamics of cavity collapse. Experimentally, the chain scission rate decreases with increasing temperature [137-139]. 

In ultrasonic irradiation, the scission rate decreases as polymer concentration increases [140-143], which is primarily ascribed to the suppression of the cavitation process caused by the high solution viscosity. 

After subjecting the two materials to ultrasonic irradiation, the formation of anthracene was confirmed by photoluminescence spectroscopy. The photoluminescence intensity increases with increasing sonication time (Fig. 30b), which confirms the arm-loss mechanism. Quantifying anthracene (using the photoluminescence intensity at 411 nm) yields two similar reaction constants (3.20 0.14) X 10 and (3.26 0.09) x 10 min for the star and linear polymers, respectively. Boydston also calculated the reaction constant based on refractive index signals (change of M. Again, he obtained two similar reaction constants (3.13 0.11) x 10 and (3.27 0.38) x 10 min for star and linear polymers, respectively. His result reveals the equivalence between star-shaped polymers and linear polymers in terms of chain scission rate if of star-... 

Church DC, Peterson GI, Boydston AJ (2014) Comparison of mechanochemical chain scission rates for linear versus three-arm star polymers in strong acoustic fields. ACS Macro Lett 3 648-651... 

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