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The temperature dependence of characteristic length scales associated to the glass transition such as the cooperativity length scale introduced by Adam and Gibbs [cooperative rearranging region (CRR)] or the dynamic heterogeneity as estimated from the four point correlation function X4, is at the center of large interests. Broadband dielectric spectroscopy and temperature modulated differential scanning calorimetry allow to study the CRR size temperature dependence in the temperature range of ergodicity loss for glass-forming liquids, starting from the onset of cooperativity in the crossover region down to the glass transition temperature. Furthermore, the correlation between these two techniques allows to explore a large frequency range (from 1 mHz to 10 MHz). The goal of this work is to follow the cooperativity evolution along the Arrhenius plot for two different polymeric systems: poly(ethylene 1,4-cyclohexylenedimethylene terephthalate glycol) and poly(bisphenol A carbonate).
The effect of structural constriction on molecular mobility is investigated by broadband dielectric spectroscopy (BDS) within three types of molecular arrangements: monomers, oligomers and self-assembled monolayers (SAMs). While disordered monomers exhibit a variety of cooperative and local relaxation processes, the constrained nanodomains of oligomers and highly ordered structure of monolayers exhibit much hindered local molecular fluctuations. Particularly, in SAMs, motions of the silane headgroups are totally prevented whereas the polar endgroups forming the monolayer canopy show only one cooperative relaxation process. This latter molecular fluctuation is, for the first time, observed independently from other overlapping dielectric signals. Numerous electrostatic interactions among those dipolar endgroups are responsible for the strong cooperativity and heterogeneity of the canopy relaxation process. Our data analyses also revealed that the bulkiness of dipolar endgroups can disrupt the organization of the monolayer canopy thus increasing their ability to fluctuate as temperature is increased.
Understanding the evolution of the cooperative molecular mobility as a function of time and temperature remains an unsolved question in condensed matter physics. Many recent works concern the question of the molecular dynamic slowdown in a temperature domain ranging from the crossover temperature T c (beginning of cooperative relaxation) down to the calorimetric glass transition temperature T g. Recent studies have shown that the estimation of cooperativity length based on calorimetric investigations using Donth's approach can be extended to a wider temperature range from T g to T c. To describe the relaxation time evolution and the characteristic length evolution of cooperative motions, besides the Donth's fluctuation approach other models exist in the literature such as '4 points correlation function' model. Whatever the model used, calorimetric investigations are needed to estimate the heat capacity as a function of the temperature. In this work, we have focused our attention on the modulated temperature differential scanning calorimetry (MT-DSC) experiments and we have tested different MT-DSC protocols allowing the heat capacity determination. For this goal we decided to work on different amorphous glass formers in order to cover a large range of glass transition temperature. The influence of the protocol used on the cooperativity length calculation is discussed in detail. Lissajous figures were constructed to verify whether the steady state is reached.