Dynamical heterogeneity describes the behavior of glass-forming materials when undergoing a phase transition from the liquid state to the glassy state. In dynamical heterogeneity, the dynamics of cooling to a glassy state show variation within the material.

Polymers

Polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

properties include

viscoelasticity In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly wi ...

and may be synthetic or

natural Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are p ...

. When a polymeric liquid is cooled below its freezing temperature without crystallizing, it becomes a

supercooled Supercooling, also known as undercooling, is the process of lowering the temperature of a liquid or a gas below its melting point without it becoming a solid. It achieves this in the absence of a seed crystal or nucleus around which a crystal ...

liquid. When the supercooled liquid is further cooled, it becomes a

glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...

. The

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

at which a polymer becomes a glass by fast cooling is called the

glass transition The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rubb ...

T_g. At this temperature,

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

reaches up to 10¹³ poise depending upon cooling-rate.

Phase transitions

It is possible for a

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

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 Ballistics may refer to: Science * Ballistics, the science that deals with the motion, behavior, and effects of projectiles ** Forensic ballistics, the science of analyzing firearm usage in crimes ** Internal ballistics, the study of the proce ...

regime for very short times (when particles do not interact) and a

microscopic The microscopic scale () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens (optics), lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded a ...

regime. In the microscopic regime, the

correlation functions The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors. The cross-correlation matrix is used in various digital signal processing algorithms. D ...

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 In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

causing the particles trapped in local regions by each other. Particles are doing rattling motion inside these cages and cooperate with each other. These regions in the glassy polymer are called cages. In the intermediate regime each particle has its own and different relaxation time. 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 Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...

of dynamical heterogeneity can be done by calculating

like Non-Gaussian parameter, four point

(Dynamic Susceptibility) and three

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...

Polymers

Phase transitions

References

Further reading