Rate of Bond Scission

A rate of bond scission can be defined in terms of time as d[R]/dt or in terms of strain as d[R]/de. The relation between the two rate expressions is defined by the identity 

A change of temperature will affect the rate of radical production in three ways. Firstly the number N of highly extended chains will decrease if thermally activated slip becomes possible. Secondly the activation energy U(T) decreases with increasing temperature. Thirdly the sample modulus E and the crystalUne modulus are affected by temperature. 

If in a region of sufficiently low temperatures chain slip can be excluded i.e. if 

Employing the same values as used in the evaluation of Eq. (7.3) one arrives at A(L/Lo) = 1.7 Ae at 20 C and at A(L/Lq) = 1.6 Ae at -60 °C. This means for example that a given distribution of segments with relative lengths L/Lq between 1.1 and 1.3 break at room temperature within the strain interval from 12 to 13.5%. At a temperature of —60 °C sample strains of between 13.5 and 15.1% are required. 

The low temperature transition was assigned to the transition of amorphous PE to the glassy state, the other to slippage of chains within crystal lamellae [19]. 

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Much fewer experiments are available in solution where the few reported data are generally more concerned about the effect of molecular structure than about bond dissociation energy. In simple shear, it is generally agreed that chain flexibility dominantly influences the rate of bond scission, with the most rigid polymers being the easiest to fracture [157]. The results are interpreted in terms of the presence of good and poor sequences in the chain conformation. 

Although some depolymerases act processively in cleaving their polymeric substrates, others act by what can be described as multiple attack which results in nonselective scission or random scission. The analysis of cleavage products during the course of enzyme-catalyzed depolymerization can provide important clues about the nature of the reaction. With random scission, the rate of bond scission must be proportional to the total number of unbroken bonds present in the solution. Thomas measured the rate of base addition in a pH-Stat (a device with an automated feedback servomotor that expels ti-trant from a syringe to maintain pH) to follow the kinetics of DNA bond scission by DNase. The number of bonds cleaved was linear with time, and this was indicative of random scission. In other cases, one may apply the template challenge method to assess the processivity of nucleic acid polymerases. See Processivity... 

Tanford presented a cogent kinetic treatment of random scission of a polymer, and the complete analysis is beyond the scope of this Handbook. The basic idea is that a molecule M, can yield a molecule (where x and y indicate the degree of polymerization, and where y > x) in two different ways. The x-mer formation rate from y-mers is twice the rate of bond scission at the concentration of the y-mer thus,... 

Another common method for determination of alpha-samylase involves measurement of the diminution of the iodine-stainability of whole starch or amylopectin )8-limit dextrin. These methods are useful, as very small quantities of alpha-amylase may be estimated in this way. They are comparative, and cannot be used to determine rates of bond scission, unless they are carefully calibrated by a method that measures reducing end-groups. Such a calibration has been made for the action of hog-pancreas alpha-amylase on waxy-maize starch, although the validity of the reducing-power determinations, made with iodine and thiosulfate, has been confirmed for maltose only thus, it is not yet known whether the calibration is actually valid for the experimental system in which larger oligomers, for example, the triose and tetraose, are also formed. 

A third technique for determination of alpha-amylase is the viscometric method. This is the most sensitive method for studying the initial attack on amylose, but it is too time-consuming to be used as a routine method for enzymic assay. If the relation between viscosity and molecular weight is known for the substrate, an estimate of the rate of bond scission may be made. (This estimation would be valid only if completely random attack were occurring.)... 

Estimations of and inhibition studies are, however, more valid, because determinations of absolute rates of bond scission are not necessary. The Michaelis constants for several alpha-amylases have been determined, and are shown in Table XI it may be seen that wide variations occur. For hog-pancreas alpha-amylase, it has been claimed that the value of depends on the degree of hydrolysis of the substrate this is probably true for all alpha-amylases when high degrees of hydrolysis are reached. 

Reactions of compounds containing more than one R group proceed stepwise, allowing intermediate products to be obtained if a deficiency of HX is used [e.g., Eq. (i)]. Rates of bond scission vary also, usually the ease of cleavage is M—aryl>M—alkyl. Cleavage of nonmetal element-C bonds with protonic acids can occur ... 

Figure 6. Arrhenius plot for the rate of bond scission in air (%) and...

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