Relaxation processes, glass transition

Determination of the glass-transition temperature, T, for HDPE is not straightforward due to its high crystallinity (16—18). The glass point is usually associated with one of the relaxation processes in HDPE, the y-relaxation, which occurs at a temperature between —100 and —140° C. The brittle point of HDPE is also close to its y-transition. 

Molecular Motion in amorphous atactic polystyrene (PS) is more complicated and a number of relaxation processes, a through 5 have been detected by various techniques as reviewed recently by Sillescu74). Of course, motions above and below the glass transition temperature Tg have to be treated separately, as well as chain and side group mobility, respectively. Motion well above Tg as well as phenyl motion in the glassy state, involving rapid 180° jumps around their axes to the backbone has been discussed in detail in Ref.17). Here we will concentrate on chain mobility in the vicinity of the glass transition. 

When a penetrant diffuses into a polymer, the perturbation will cause the polymer molecules to rearrange to a new conformational state. The rate at which this conformational adaptation occurs depends on the mobility of the polymer chains. At temperatures well above the glass transition, this occurs quite rapidly and the diffusive process resembles that in the liquid state. At temperatures near or below the glass transition, the conformational change does not take place instantaneously. Instead, there is a finite rate of polymer relaxation induced by the... 

A particular characteristic feature of dynamic processes in the vicinity of the glass transition is the ubiquity of the Kohlrausch-Williams-Watts (KWW) stretched exponential relaxation 1,7-9... 

This reasoning also means that we were not really describing a thermodynamic measurement of the glass transition in a polymer melt but instead a macroscopic determination of the temperature dependence of volume-related internal relaxation processes, i.e., a dynamic measurement in the disguise of a thermodynamic measurement. 

The answer to our question at the beginning of this summary therefore has to be as follows. When you want to locate the glass transition of a polymer melt, find the temperature at which a change in dynamics occurs. You will be able to observe a developing time-scale separation between short-time, vibrational dynamics and structural relaxation in the vicinity of this temperature. Below this crossover temperature, one will find that the temperature dependence of relaxation times assumes an Arrhenius law. Whether MCT is the final answer to describe this process in complex liquids like polymers may be a point of debate, but this crossover temperature is the temperature at which the glass transition occurs. 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

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