Physical Comparison of CTMD with Other Theoretical Contributions and Dynamic Models

After Chap.  7 ’s review of Ngai's coupling modelNgai's coupling model (CM) and Götze's mode coupling theoryGötze's mode coupling theory (MCT) (MCT), a comparison is presented between these approaches and the cooperative theory of materials dynamics (CTMD)Cooperative Theory of Materials Dynamics (CTMD). As to CM, it is shown that CTMD predicts that, at equilibrium and within linear viscoelasticity, the relationship of Ngai's CM is obeyed by the average response timeAverage response time and all individual cluster size-specific response timesCluster size-specific response times, with the CM parametersParameters being directly related to the reciprocals of CTMD's crossover frequencyCrossoverfrequency and average cooperativityCooperativity, the latter yielding the physical meaning of Ngai's quintessential parameterQuintessential parameter. A comparison of CTMD with MCT is itemized in eight contrasting features covering (1) the level of microscopic insightMicroscopic insight, (2) the meaning and knowledge of the relevant parameters, (3) the mathematical complexityMathematical complexity and computabilityComputability, (4) the prediction of a dynamic crossover temperatureCrossover temperature and the divergence problemDivergence problem, (5) the accessibility of non-equilibriumNon-equilibrium and (6) significantly low temperatureCrossovertemperature behaviorLow temperature behavior, (7) the potential to explain and quantify the cooperativity, dynamic heterogeneityDynamic heterogeneity and fragilityFragility of amorphous condensed matter, and (8) the extent to which the universalityUniversality and the extended exponentialExtended exponential KWW behavior may be explained. Various specific required theoretical characteristics and capabilities of fruitful theories are also discussed in a final section.