The Glass Transition From The Point of View of DSC Measurements: Basic Principles
The glass transition is very sensitive to changes in molecular interaction.
Measurement of glass transition can be used to determine and characterize structural differences between samples or changes in a sample.
This article discusses the basic principles of the glass transition as well as its measurement and evaluation.
Introduction
The glass transition is a phenomenon that can in principle occur in all noncrystalline or semicrystalline materials. The requirement is a sufficiently large degree of molecular disorder at least in one direction.
To explain the processes that take place during a glass transition we assume for simplicity that we are dealing with a homogeneous liquid. In a liquid, in addition to the molecular vibrations and rotations (of atoms or groups of atoms) that also occur in solids, there are cooperative movements or rearrangements in which several molecules or segments of molecular chains participate.
The cooperative units can be regarded as temporary clusters that fluctuate with regard to both space and time. The size of these cooperative units is typically a few nanometers. This characteristic length decreases with increasing temperature. Another characteristic quantity is the time required for the cooperative rearrangements to take place.
It can be described by an internal relaxation time τ. The glass transition is very sensitive to changes in molecular interactions. Measurement of the glass transition can be used to determine and characterize structural differences between samples or changes in a sample.
The glass transition is therefore an important source of information that can be obtained from the thermal analysis of materials. This first article discusses a number of basic principles that aid the interpretation of results. Practical aspects of the glass transition will be dealt with in Part 2 in the next edition of UserCom.
The sample is cooled from A to C at a constant rate. Around B it passes through the region of the glass transition with the glass transition temperature Tg1. If the sample is then immediately heated up to the point A again, then the same glass transition temperature is measured. Any differences that arise between the glass transition temperature measured in this way on heating or cooling are due to effects of thermal conductivity within the sample. If the sample is held for some time at a temperature Ta, then it ages and the enthalpy becomes smaller. It attains the state designated by the point D.
On heating again, the enthalpy intersects the liquid line at the temperature Tg2 (point E). The glass temperature has changed through aging. The glass transition temperature Tg2 can also be attained by cooling from the melt at a lower cooling rate. On cooling, the cooperative units then have more time for their rearrangements to take place, which results in them freezing later. The slower the cooling rate, the lower the glass transition. As can be seen in Figure 2, hysteresis occurs between the cooling curve and the heating curve even under the same conditions.
This effect can be explained by assuming that the frozen movements do not thaw until a higher temperature is reached. Figure 3 shows the differences between the heating and cooling curves in the enthalpy versus temperature diagram. Curve 1 is a cooling curve. No overheating effects occur. The glass transition temperature Tg1 is the point of intersection of the extrapolated curves of the liquid and the glass. Curve 2 is the corresponding heating curve when the heating and cooling rates are the same. In this curve, relatively small overheating effects occur. The glass transition temperature is Tg1.
Curve 3 differs from curve 2 only in a more rapid heating rate. This leads to larger overheating effects but the glass transition temperature remains the same. If the heating rate is lower than the cooling rate, the glass transition temperature does not change, but the overheating effect is reduced. Curve 4 represents the measurement of a sample that was heated at the same rate as in curve 2, but which was stored for some time at a temperature Ta below the glass transition temperature. Two effects occur: the glass transition temperature is lower (Tg2) and the overheating peak is larger by an amount equal to the value of the enthalpy relaxation ÐH. The process of storage below the glass transition temperature is also known as physical aging.
Figure 4 shows the measurement curves of samples of polyethylene terephthalate (PET) that have been subjected to different periods of physical aging. The shift and the increase in size of the overheating peak can be clearly seen.
Visualization of The Glass Transition
The glass transition is a kinetic effect that occurs at the transition from a supercooled liquid to a glassy solid state. The processes that occur will be explained with the help of a model.
On cooling a sample that forms a glass, the characteristic relaxation time τ increases with decreasing temperature. This means that the cooperative rearrangements become slower. As can be seen in Figure 5, one can think of the continuous cooling process as being divided up into a series of small steps.
At high temperatures (point marked 1 in Figure 5), the relaxation time τ is so short that the sample can completely relax to equilibrium during such a step. The sample is then in equilibrium (liquid). At point 2, the relaxation time is already appreciably larger. Molecular rearrangements are, however, still rapid enough for the sample to just reach equilibrium during a step.
At point 3, the cooperative rearrangements have become so slow that there is not sufficient time for the sample to relax to equilibrium. The molecular rearrangements "freeze".
The heat capacity is thereby reduced by an amount corresponding to these rearrangements (cp step). Only the types of movement specific to solids remain. From this point of view, a glass behaves as a solid although its structure corresponds to that of a liquid.
Determination of the Glass Transition Temperature
Various quantities can be used to characterize the glass transition. Besides the glass transition temperature (Tg), the height of the cp step (Δcp) and the width of the glass transition (ΔT) are often determined. Other quantities that are used are the height of the overheating peak and its maximum temperature. In Figure 6, a number of characteristic quantities are shown.
Enthalpy Relaxation
Enthalpy relaxation in a glass depends on the mechanical and thermal conditions during manufacture and storage. It affects the overheating peak of heating curves. A method that is frequently used to determine the enthalpy relaxation is to first heat the sample up, then cool it down at the same rate and afterwards immediately heat it a second time. The subtraction of the second heating curve from the first yields the enthalpy relaxation.
The Glass Transition from the Point of View of DSC Measurements; Part 1: Basic Principles | Thermal Analysis Application No. UC 106 | Application published in METTLER TOLEDO Thermal Analysis UserCom 10