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The glass transition temperature (Tg) is a narrow temperature range when the material changes from a glassy state with low free volume to a rubbery state with greater free volume (Zografi and Hancock, 1993).

If the liquid above Tm in Figure 1.2 is supercooled to produce an amorphous material, at temperatures below but close to the melting temperature Tm, the mean speed of molecular motions over atomic distances is very rapid (Hancock et al, 1995). Cooling of the supercooled liquid further reduces the molecular mobility of the material to a point when the material is unable to achieve equilibrium as it loses its thermal energy. This results in a change in the temperature dependence of the enthalpy and volume at a characteristic temperature, the glass transition temperature (Tg). On passing through the glass transition, a number of changes in the material’s physical properties are observed, including viscosity, density, and heat capacity. Slade and Levine (1991) describe the glass transition in amorphous systems as a material specific change from a glassy solid capable of supporting its own weight against flow to a rubbery viscous liquid that is capable of flow in real time. The Tg of an amorphous material determines its chemical and physical stability; the Tg usually becomes a critical parameter when the operating temperature is just below or above the Tg, as encountered during processing or storage of the amorphous material (Hancock and Zografi, 1994).

The glass transition event is usually considered to reflect the co-operative type translational molecular motions either by segments of a polymer molecule or smaller glass forming materials (Hancock et al, 1995). However, experimental studies of the glass transition temperature are complicated by the different types of molecular motions (such as rotational or translational), the effect of temperature on the type and extent of molecular motions, and the coupling or co-operativity of molecular motions (Hancock and Zografi, 1997). At the glass transition temperature, the average time taken for the predominant molecular motions to take place is 100 seconds, and the viscosity is 10^^ -

10^"^ Pa s (Hancock and Zografi, 1997 and Slade and Levine, 1988a).

The experimental measurement of the glass transition temperature occurs when the time scale of molecular motions coincides with the time scale of the experimental technique being used to measure the Tg (Hancock et al, 1995). If we consider a newly formed amorphous supercooled liquid just below the melting temperature (Tm), the mean speed of molecular motions in this region is typically a few seconds, compared to the time

scale of experimental methods (minutes to hours). However, cooling of the material further leads to the glass transition temperature where the time scale of molecular motions of the amorphous material and that of the experimental technique coincide (Hancock et al, 1995). Experimental determination of the Tg is usually carried out by detecting the change in heat capacity at the glass transition temperature which is observed as a shift in the baseline.

The gradient of the enthalpy or volume line in Figure 1.2 changes at the characteristic glass transition temperature (Tg). The change in gradient means that the temperature dependence of the enthalpy and volume has changed. Below the glass transition temperature, if further cooling takes place the molecular motions are reduced even further. The amorphous material below Tg is referred to as glassy due to its macroscopic properties. Below Tg the molecular mobility is reduced sufficiently such that it is unable to reach equilibrium in the time scale of the measurement. Molecular mobility in the glassy amorphous state occurs over a period above 100 seconds, and the viscosity is typically above 10^^ Pa s (Hancock and Zografi, 1997).

The temperature where the supercooled liquid line would then intersect the crystal line is called the Kauzmann temperature (Tk), as shown in Figure 1.2. It is thought to correspond to the lower limit of the experimental and theoretical glass transition temperature (Hancock and Zografi, 1997).

1.4.2 EFFECT OF MOLECULAR WEIGHT ON Tg

Increasing the molecular weight has the effect of increasing the glass transition temperature of the system. The effect of molecular weight on the glass transition temperature can be calculated using the Fox and Flory equation (1.5) (Fox and Flory,

1950).

Tg = Tg(oo)-K g (1.5)

M

Where M is the molecular weight. Kg is a constant, Tg (oo) is the limiting Tg at a high

The Tg increases j with increase in the molecular weight up to a plateau level where fiirther increases in the molecular weight show no further increase in the Tg (Levine and Slade, 1986). This linear relationship between the Tg and molecular weight is typical of polymers (Fox and Flory, 1950). The plateau level for the Tg corresponds to the molecular chain ‘entanglement coupling’ level at about 10^- 10^ Daltons. This is where for high molecular weight polymers there is formation of a random network. These ‘entanglements’ behave as if they are cross-links but do not appear to involve chemical bonding (Levine and Slade, 1986).

The glass transition temperature of dry sucrose is 57°C, whereas that of the maltodextrins, which have large molecular weights, is between 140°C and 190°C depending on the maltodextrin considered (Roos and Karel, 1991a). The effect of binary mixtures of maltodextrins and sucrose were investigated by Roos and Karel (1991a). They found that maltodextrins have a significant effect on the Tg of the binary mixture but only at levels above 50%. However, only small amounts of sucrose resulted in large decreases in the Tg of the binary mixture. This information could be useful in the selection of binary mixtures during formulation depending on processing and storage requirements (Roos and Karel, 1991a).