Dose rate exponents

The reported values for the exponent of the dose-rate for the polymerization rate in gamma radiation-induced copolymerization of acrylamide with methyl chloride salt of A, A -dimethylaminoethyl methacrylate (DMAEM-MC) in aqueous solution was found to be 0.8 [16]. However, the dose-rate exponent of the polymerization rate at a lower dose-rate was found to be slightly higher than 0.5 for gamma radiation-induced polymerization of acrylamide in aqueous solution [45,62]. 

Equation (4) shows that the dose-rate exponent of the degree of polymerization agrees with the theory Eq. (2). However, the degree polymerization and the intrinsic viscosity decrease with increasing dose rate is probably due to increased termination reactions caused by the increasing radical population at high dose-rate [22]. 

Since the dose rate exponent of both the rate of polymerization and the average molecular chain length, as well as the over-all temperature coefficient, vary so markedly between the dry and the wet conditions, and the latter are accepted as being indicative of a free radical process, it becomes tempting to describe the dry process as being non-radical, and, by logical exclusion, ionic. Both the extreme sensitivity to water, ammonia, and amines and the data from the copolymerization with a-methylstyrene further support this thesis. 

Similar experiments were performed with 0.05-mm. thick films. The log-log plot of the conversion curves is shown in Figure 4. Here the autoacceleration index is / = 1.15. The break on the curves occurs at lower grafting ratios than for the 0.1-mm. films. The dose-rate exponent for the instantaneous rate at 10% weight increase is a = 0.45 as shown in Figure 3. 

From experiments conducted at the two dose rates investigated the dose-rate exponent is estimated to be a = 0.47. At the higher dose rate the reaction was diffusion controlled, heterogeneous films being obtained at elevated grafting ratios. 

The various data obtained for the kinetics of graft copolymerization onto PTFE films demonstrate that this reaction is complicated by the fact that the rate of diffusion of the monomer may become the controlling factor. It seems interesting at this point to compare and discuss together the results obtained with the different monomers. Table I summarizes the data obtained for autoacceleration indexes (/ ), dose-rate exponents (a), and over-all activation energies E, with styrene, acrylic acid, and vinylpyridine. Several conclusions can be derived from an examination of these data. 

Table I. Autoacceleration Indexes, / , Dose-Rate Exponents, a, and Over-all Activation Energies, , for the Direct Radiation Grafting of Various Monomers into PTFE Films...

This seems to be the case with styrene at 60 °C. where (3 is almost unity—i.e., where the reaction proceeds with a constant rate. The dose-rate exponent of this system indicates, however, more complicated kinetics. 

The dose-rate was varied by lining the irradiation chamber of the gamma cell irradiation by lead foil of uniform thickness [17]. The dose was kept constant at 0.15 and 0.35 KGy for copolymerization of AM-AANa and AM-DAEA-HCl system, respectively. The results are shown in Figs. 2 and 3, which show that the rate of polymerization, Rp increases while the degree of polymerization (DP ) and the intrinsic viscosity [17] decrease with the dose-rate. The exponents of the dose-rate for AM-AANa system [17,54] were determined to be ... 

However, the exponent of the dose-rate for AM-DAEA-HCl system was also determined to be [22] ... 

In experiments with normal recipes, Upr increases with / - (I = dose rate). The exponent is in accord (within experimental error) with the square root law, postulated for the dependence of the stationary radical concentration on light intensity with incomplete absorption of the quanta, and a termination reaction involving two radicals. 

R Dose rate or actual value of decay exponent N/A State dose rate in cGyph. See sample NBC4 for terms associated with this line. 

The polymerization rate is proportional to the dose rate to the power of unity. The monomer purity plays an important role in ionic polymerization, and the exponent of the dose rate is profoundly affected by it, being 0.5 for super-pure monomers. 

Due to the real bumup history of the irradiated THTR fuel elements (reduced bumup and longer cooling time prior to storage in the transport and storage casks max. bumup per fuel element container was approx. 8.8 % fima or 85,000 MW-d/t HM), the dose rate was reduced by about one decimal exponent to below 10 pSv/h. At a measured maximum surface dose rate of a loaded unshielded fuel element container of 10,000 mSv/h, this results in a weakening of the radioactive radiation by a factor of approx. 10. ... 

A comparison of these measuring results with the total-body dose rate limits from Annex X, Table XI, column 2 of the Radiation Protection Act shows that the measured values fall by several decimal exponents below the limits per person laid down in there. This statement is also valid for the partial-body doses that the employees received during inserting the screws into the still open screw holes. Here, monitoring was effected by means of finger badge dosimeters. 

Keeping the composition of copolymerization media constant the total comonomer concentration of which is varied. The absorbed dose was kept constant at 0.14 KGy for the AM-AANa and at 0.35 KGy for the AM-DAEA-HCl systems. The results are shown in Figs. 4 and 5, which show the rate of polymerization, Rp, the degree of polymerization, and the intrinsic viscosity increase with increasing monomer concentration. At comonomer concentration >2.1 M/L, DPn decreases with increasing comonomer concentration. From the logarithmic plots, exponents of the comonomer concentration for the AM-AANa system were determined to be [17,54]. 

Another measure of sensitivity can be obtained from the rate of dissolution of exposed versus unexposed film at various doses. The amount of energy needed to obtain some arbitrary ratio of rates or the exponent of the dissolution rate ratio versus dose at high doses may be used. In the present study, both a contrast curve and a solubility rate ratio versus dose data are reported for the copolymer of maleic anhydride with alphamethylstyrene. However, these tests are burdensome when many materials are to be screened... 

The exponent, n. is equal to 0.62 and is unchanged for all the radical concentrations examined. The rate constant, b, depends on the radiation dose and the thermal annealing after the irradiation. 

The exponent of tj, 0.62, is unchanged irrespective of the radiation dose and of the thermal annealing, and it is identical with the exponent determined for the alkyl radical in polyethylene. The rate constant, b, changes depending on the dose and the annealing treatment, as is shown in Fig. 13. 

Hence, in ionic radiation-induced polymerization the exponent of the rate of the absorbed dose can vary from 0.5 to 1.0 depending on the termination mechanism. Moreover, this order is an indication of the purity of the reaction system. A conclusion follows which is... 

The order of dependence, determined as 0.64 for styrene grafting into EEP [72], 0.58 for grafting of acrylic acid into FEP [82], and 0.53 for styrene-acrylic acid [83], is in agreement with the theoretical value of 0.5 for free radical polymerization. Momose et aL [70] reported that for the grafting of a,P,fl-trifluorostyrene (TFS) into ETFE, the grafting rate and final percent grafting increase with increasing preirradiation dose, with the dose exponent... 

The creep parameters of polycrystalline YAG were derived from creep tests performed on bulk ceramic samples prepared by conditions dose to those used for the fibers. The stress exponent was dose to unity and the apparent activation energy (Equation 10) was equal to 5M kJ/mol. It has been suggested that the operative mechanism is Nabarro-Herring creep, with a rate limited by the bulk diffusion of one of the Y or AT cations [105). 

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