Constant rate conversion degrees

In order to obtain the degree of cure and rate of curing, we must first measure the reaction. This is typically done using a differential scanning calorimeter (DSC) as explained in Chapter 2. Typically, several dynamic tests are performed, where the temperature is increased at a constant rate and heat release rate (Q) is measured until the conversion is finished. To obtain Qt we must calculate the area under the curve Q versus t. Figure 7.17 shows four dynamic tests for a liquid silicone rubber at heating rates of 10, 5, 2.5 and 1 K/min. The trapezoidal rule was used to integrate the four curves. As expected, the total heat Qt is the same (more or less) for all four tests. This is to be expected, since each curve was represented with approximately 400 data points. 

The analysis of the effects of the interaction contains the calculation of the confidence interval with respect to the increase in SO2 conversion when - for temperature Ti - the flow rate varies between Gi and G2 and when - for flow rate Gi -the temperature varies between Ti and T2. If dj is the mean value of the increase in the SO2 conversion degree for case i (i = l Ti = constant and the flow rate changes between and G2), then the confidence interval for this mean value will be ... 

Fig. 4A and 4B Experimental reactivity of various treated charcoals, as a fimction of the conversion degree. The dashed lines are model fits. Fig. 4C Experimentally derived correction factors to the specific reaction rate constant Ks (see text).

The effect of flow rate on degree of conversion has been determined by using a constant initial substrate concentration [S]0. Figure 4.13 shows the dependence of P on QIC as predicted by Eq. 4.24, and the experimental dependence of P on Q found for the immobilized ficin reactor. Good agreement is observed between the theoretical and the experimental results, and that complete conversion of substrate into product requires low flow rates and a high column capacity. The theoretical curves use constant [S]0 values that are a multiple of K m, in order to take changes in K m with flow rate into account. 

The curing kinetics of system EPS-l/DDM was studied by a method of reverse gas chromatography (RGC) [29]. The basic parameter received from processing of the experimental data, was the constant of reaction rate k determined for an interval of conversion degrees a = 0.1-0.7 of the kinetical curve degree of conversion-time (a-t). For the determination of k the standard procedure was used the dependences, a, on the reaction time t, as lg[a/(l-a)]=/ (t) which have appeared linear were made. Then the value k (see Equation (10.4)) was determined from a slope of these linear diagrams. Ketones (metyl ethyl ketone, 1,4-dioxane, cyclohexanone) were chosen as the standard substances for the determination of retention time with argon as the gas-carrier. 

Thus, the stated above results have shown that for curing reaction proceeding in fractal space the reaction rate constant reduction is typical. The formation of a large number of microgels with smaller molecular weight in comparison with reaction in Euclidean space at the same conversion degree is also typical for such reaction. The dimensional border between nanoreactor and nanoparticle for the considered curing reaction has been obtained. 

The data for high-temperature polycondensation of different disodium salts of the bisphenols with 4,4 -dichlorodiphenylsulfone (DCDPS) are used [47], The bisphenols denomination, their conventional signs and also the values of poly condensation rate constants k and En are adduced in Table 2. Besides, the kinetic curves conversion degree — reaction duration (Q -1) of polycondensation, adduced in the work [47], were used. 

In work [62] it has been shown, that temperature synthesis T increasing at high-temperature polycondensation of polyaiylates, obtained by interaction of diphenols of different chemical stracture with dianhydride of terephthalic acid, results to reaction rate constant growth (the value pj was used for polycondensation first stage up to conversion degree Q 0.30-0.50). The solvent nature, in solution of which synthesis was performed, influences perceptibly on value. So, the value - pj is higher at polycondensation in nitrobenzene enviromnent, than in diphenyloxide enviromnent. The systematic enhancement was found... 

Fig. 4 Dependence of the propagation and termination rate constants on the degree of conversion of an acrylate resin...

The kinetic parameters used in Eq. (4.46) were estimated on the basis of the experimental results for conversion degrees from constant heating rates [21]. By... 

Figure 4.20 Conversion degrees of decomposition from different thermal loading programs for powdery GFRP composites curves at constant heating rates from TGA and modeling and modeling curve based on ISO fire curve [30]. (With permission from SAGE.)...

Creep. In general, polymers exhibit a degree of visco-elastic behaviour and thus for full characterisation of such a material a knowledge of its rate dependent response is necessary. To determine the long-term behaviour of a material either stress relaxation or creep tests may be used. The former involves monitoring the time-dependent change in stress which results from the application of a constant strain to a specimen at constant temperature. Conversely,... 

Ito s model [68] bears resemblances to the model of Ref. [35], but is different by two aspects. Firstly, it assumes that the constant rate of the chain termination depends on the number of monomeric units (so-called polymerization degree) of tn and n radical chains taking part in the termination reaction and represents the sum of the independent contributions of m and n. Secondly, the dependence of the chain termination constant on the length of chains under two types of conditions is described the first condition is < n, controlled by segmental diffusion, and the second one is m > controlled by the reptation diffusion. In the reptation chemical mechanism of diffusion in the deep states of conversion the macroradicals move snake-like between the network joints. De Gennes connected a reptative moving of macroradicals with the dynamic properties of the medium with the use of scaling ratios [37-40] as applied in Refs. [41-46] for the description of constant chain termination in the late conversion state. 

For this reason we have studied the PS degradation in solutions with concentrations below 1.5%. Upon ozonolysis of dilutes PS solutions with concentrations below 0.5% we have observed a decrease of the average molecular weight (Fig. 37, 2). The rate of degradation is constant up to a conversion degree of 30%. 

To evaluate the apparent activation energy, the isoconversional methods are use as suitable analysis procedures. These methods are based on the assumption that at a constant extent of conversion degree (a), the decomposition rate da/dt is a function only of the temperature. In methods developed by Friedman and Flynn-Wall-Ozawa, linear functions are obtained from which slopes the apparent activation energy at constant conversion a is achieved. In the free kinetic method set by Kissinger is calculated from the slope of the linear function takes into consideration the relationship between the heating rate and peak temperature of the first-derivative thermogravimetric curve [97]. 

PU/PBMA ratio, mass % moM PBMA rate constant -10, S Onset of separation time, min Conversion degree at the separation onset, PU Conversion degree at the separation onset, PBMA... 

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