Dynamical heterogeneity

Dynamical heterogeneity is a term used to describe the behavior of a polymer material undergoing phase transitions to the glassy state at varying rates.

Polymers

Polymer properties include viscoelasticity and may be synthetic or natural. When a polymeric liquid is cooled below its freezing temperature without crystallizing, it becomes a supercooled liquid. When the supercooled liquid is further cooled, it becomes a glass.^[1]

The temperature at which a polymer changes to glass by fast cooling is called the glass transition temperature T_g. At this temperature, viscosity reaches up to 10¹³ poise depending upon cooling-rate.

Phase transitions

It is possible for a phase transition from polymer to glassy state to take place. Polymer glass transitions have many determinants including relaxation time, viscosity and cage size. At low temperatures the dynamics become very slow (sluggish) and relaxation time increases from picoseconds to seconds, minutes, or more. At high temperatures, the correlation function has a ballistic regime for very short times (when particles do not interact) and a microscopic regime. In the microscopic regime, the correlation functions decay exponentially at high temperatures. At low temperatures the correlation functions have an intermediate regime in which particles have both slow and fast relaxations. The slow relaxation is an indication of cages in the glassy system. In glassy state density is not homogeneous i.e. particles are localized in different density distributions in space. It means that density fluctuations are present in the system. Particle dynamics become very slow because temperature is directly proportional to kinetic energy. The particles are trapped in local regions by each other due to cooperative motion and rattling inside that region. These regions in the glassy polymer are called cages. In the intermediate regime each particle has its own and different relaxation time.^[2]

The dynamics in all these cases are different, so at a small scale, there are a large number of cages in the system relative to the size of the whole system. This is known as dynamical heterogeneity in the glassy state of the system. A measurement of dynamical heterogeneity can be done by calculating time correlation functions like mean squared displacement, the intermediate scattering function, the dynamic structure factor, the Non-Gaussian parameter and four point correlation functions.^[3]

References

Further reading

• Berthier, Ludovic; Biroli, Giulio; Bouchaud, J.P.; Cipellettei, Luca; Saarloos, Wim van (2011). Dynamical Heterogeneities in Glasses, Colloids and Granular Media. New York: Oxford University Press. ISBN 978-0-19-969147-0.