Method for estimating the cooperativity length in polymers

Interplay between structure and relaxation in polyurea networks: the point of view from a novel method of cooperativity analysis of dielectric response

The influence of structural constraints on the relaxation dynamics of three polyurea networks with a varying degree of crosslinking, has been studied by means of a thorough analysis of broadband dielectric spectroscopy measurements. Two different relaxation processes are observed, namely, a fast process involving the soft poly(propylene oxide) chains, and a slower and much broader process associated with the immediate surroundings of the hard crosslinkers. Microphase separation in soft and hard domains characterizes the systems in the presence of hydrogen bonding. In this case, different confinement conditions are explored by varying the soft chain length; overall, so called "adsorption" effects dominate. With respect to both cooperativity and the rearrangement energy threshold in fast relaxation, it is found that the enhancement of configurational constraints is similar to cooling, but only on qualitative grounds. An upper bound of the hard domains' interface thickness, in which the slow relaxation is believed to take place, is estimated from the analysis of the fast relaxation in the system characterized by the highest degree of confinement, taking into account the results of the structural analysis. Dropping the hydrogen bonding mechanism, phase separation does not occur anymore and the configurational constraints at the ends of the soft chains are reduced, leaving just those imposed by the rigid crosslinkers. This leads to a significant increase in cooperativity on approaching the glass transition, and to a complex behavior that is thoroughly discussed in comparison with those observed in the micro-segregated systems.

Cooperativity in plastic crystals

A statistical mechanical model previously adopted for the analysis of the α-relaxation in structural glass formers is rederived within a general theoretical framework originally developed for systems approaching the ideal glassy state. The interplay between nonexponentiality and cooperativity is reconsidered in the light of energy landscape concepts. The method is used to estimate the cooperativity in orientationally disordered crystals, either from the analysis of literature data on linear dielectric response or from the enthalpy relaxation function obtained by temperature-modulated calorimetry. Knowledge of the specific heat step due to the freezing of the configurational or conformational modes at the glass transition is needed in order to properly account for the extent to which the relaxing system deviates from equilibrium during the rearrangement processes. A number of plastic crystals have been analyzed, and relatively higher cooperativities are found in the presence of hydrogen bonding interaction.

Correlated and cooperative motions in segmental relaxation: Influence of constitutive unit weight and intermolecular interactions

This work clarifies the notion of correlated and cooperative motions appearing during the α-relaxation process through the role of the molecular weight of the constitutive units and of the interchain dipolar interactions. By studying amorphous copolymers of poly(ethylene-co-vinyl acetate) with different vinyl acetate contents, we show that the correlated motions are not sensitive to the interchain dipolar interactions, in contrast to the cooperative motions, which increase with a strengthening of the intermolecular interactions for this sample family. Concerning the influence of the molecular weight m_{0}, the notion of "correlated motions" seems to be equivalent to the notion of "cooperative motions" only for low m_{0} systems.

Cooperativity at the glass transition: A perspective from facilitation on the analysis of relaxation in modulated calorimetry

The glass transition region in nonconfined polymeric and low-molecular-weight supercooled liquids is probed by temperature-modulated calorimetry at a frequency of 3.3 mHz. From the distribution of relaxation times derived by analyzing the complex heat capacity, the number N_{α} of cooperatively rearranging units is estimated. This is done by resorting to a method in which cooperative motion is viewed as a result of a spontaneous regression of energy fluctuations. After a first, local, structural transition occurs, the energy threshold for the rearrangement of adjacent molecular units decreases progressively. This facilitation process is associated to a corresponding evolution of the density of states in a canonical representation and may be considered as a continuous spanning through different dynamic states toward a condition in which configurational constraints disappear. A good agreement is found with the N_{α} values obtained from the same calorimetric data within the framework of Donth's fluctuation theory. It is shown that, at variance from previous treatments, N_{α} can be estimated from just the relaxation function, without resorting to the knowledge of the configurational entropy. Examples point to a modest dependence of the N_{α} estimates on the experimental method used to derive the relaxation function.