First-and Second-Order Behaviors

It has been a persistent characteristic of shock-compression science that the first-order picture of the processes yields readily to solution whereas second-order descriptions fail to confirm material models. For example, the high-pressure, pressure-volume relations and equation-of-state data yield pressure values close to that expected at a given volume compression. Mechanical yielding behavior is observed to follow behaviors that can be modeled on concepts developed to describe solids under less severe loadings. Phase transformations are observed to occur at pressures reasonably close to those obtained in static compression. 

In spite of these representative first-order descriptions, experiments, theory, and material models do not typically agree to second order. Compressibility (derivatives of pressure with volume) shows complex behaviors that do not generally agree with data obtained from other loadings. Mechanical yielding and strength behavior at pressure show complexities that are not 

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As this examination shows, the order of a reaction with pathway 5.72 depends on the relative magnitudes of kKA and kK CA. Cases I and II, with first- and second-order behavior, respectively, are the extremes. In between, with the two terms in the denominator of eqn 5.74 of comparable magnitude, the order is between first and second and increases with conversion. It is even possible for the same reactant to have different reaction orders under different conditions, for instance, in different solvents. 

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