Regression analysis of nonlinear Arrhenius plots: an empirical model and a computer program.

Area of Science:

• Physical Chemistry
• Biophysics
• Chemical Kinetics

Background:

• Reaction rates in physical, chemical, and biological systems are temperature-dependent.
• Experimental data often show transitions, appearing as two distinct linear segments on Arrhenius plots.

Purpose of the Study:

• To present an empirical hyperbolic model for analyzing systems with temperature-induced transitions.
• To describe a nonlinear regression program for fitting this model to experimental data.
• To accurately determine transition temperatures, ordinate values, and activation energies.

Main Methods:

• Development of a general hyperbolic empirical model.
• Implementation of a nonlinear regression program for data fitting.
• Application to experimental data exhibiting sharp or broad transitions.

Main Results:

• The hyperbolic model effectively fits data with temperature-dependent transitions.
• The nonlinear regression program accurately estimates transition parameters.
• Best estimates and standard errors for transition temperature, ordinate value, and two activation energies are obtained.

Conclusions:

• The proposed hyperbolic model and regression program provide a robust method for analyzing complex temperature-dependent processes.
• This approach enhances the understanding of physical, chemical, and biological systems exhibiting distinct transition points.
• Accurate determination of activation energies is crucial for mechanistic insights.