Arrhenius regression analysis nonlinear

Section 5.1 shows how nonlinear regression analysis is used to model the temperature dependence of reaction rate constants. The functional form of the reaction rate was assumed e.g., St = kab for an irreversible, second-order reaction. The rate constant k was measured at several temperatures and was fit to an Arrhenius form, k = ko exp —Tact/T). This section expands the use of nonlinear regression to fit the compositional and temperature dependence of reaction rates. The general reaction is... 

In 1991 Moffat, Jensen and Carr employed RRKM theory in the form of a nonlinear regression analysis of experimental data to estimate the high-pressure Arrhenius parameters for elimination of H2 from SM4 as logA = 15.79 0.5 s 1, E = 59.99 2.0 kcalmor1 and A//j(SiH2) = 65.5 1.0 kcalmorl62. 

Kinetic analysis Statistical data analysis was performed using the Statistica program version 6.0 (30). The usual kinetic models reported in literature to describe kinetic of compoimd formation are zero order [c= cO + kt], first order [c=cO exp (kt)] or second order [1/c = 1/cO + kt] reaction models. The Arrhenius equation k = kref exp (- Eai/R ( 1/T - 1 / Tref))] is usually applied to evaluate the effect of temperature on the reaction rate constant (31). For both levels of oxygen concentration a one step nonlinear regression method was performed and a regression analysis of the residuals was also carried out (32). 

The chemistry for a stoichiometrically balanced reaction suggests that m = 1 and n = 2 in Eq. (2.86). For real systems, values are often close to these values but not identical. In the epoxy-amine reaction the alcohol, which may be present initially in small concentrations but is also a product of the reaction, catalyzes further reaction, resulting in autocatalysis. Since there are four unknowns ki, k2, m, and n) nonlinear regression analysis must be employed, although ki can be evaluated independently as the extrapolated reaction rate at a = 0. Autocatalytic kinetics are usually evaluated by the derivative form of the autocatalytic rate equation [Eq. (2.86)] with data coUected by isothermal method 1 measurements. Activation energy E and preexponential factor A are measured from the Arrhenius equation... 

The reaction orders obtained from nonlinear analysis are usually nonintegers. It is customary to round the values to nearest integers, half-integers, tenths of integers, etc. as may be appropriate. The regression is then repeated with order(s) specified to obtain a revised value of the rate constant, or revised values of the Arrhenius parameters. 

The Arrhenius form of the parameters are used, i.e., ki=Aie, Ki=Aje, and the exponent % were estimated using the nonlinear regression software package SAS (Statistical Analysis Software). The Proc Model (with Marquardt-Levenberg method) and Fit Procedures in SAS were used for this purpose. The results are shown in Table 1 and Table 2. 

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