Relation Between Tm and Tg

While Tm is a first order transition Tg is a second order transition and this precludes the possibility of a simple relation between them. There is, however, a crude relation between Tm and Tg. Boyer (1954) and Beamen (1952) inspected data for a large number of semicrystaUine polymers, some of which are shown in Table 2.2. They found that the ratio TgITm ranged from 0.5 to 0.75 when the temperatures are expressed in degrees Kelvin. The ratio is closer to 0.5 for symmetrical polymers such as polyethylene and polybutadiene, but closer to 0.75 for unsymmterical polymers, such as polystyrene and polyisoprene. The difference in these values may be related to the fact that in unsymmterical chains with repeat units of the type -(-CH2-CHX- an additional restriction to rotation is imposed by steric effects causing Tg to increase, and conversely, an increase in symmtery lowers Tg. 

The polymer being unsymmetrical, TgITm may be assumed to be about 0.75. 

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As was stated by Magill and Greet (1969) Eq. (15.32) does not hold in the vicinity of the melting point and even not for liquids of low molecular mass. So it is quite obvious that Eq. (15.32) cannot be used for semi-crystalline polymers in the temperature range between Tm and Tg. Sometimes values of E for this situation are mentioned in the literature, but these relate to formal application of Eq. (15.32) over a small temperature range. Such values of En increase with decreasing temperature. 

Selected factors affecting crystallinity regarding Tg and Tm are described in Chapter 2. Here we discuss the influence of crystallinity on the mechanical properties of polymers. For thermoplastics the relation between the degree of crystallinity and the physical nature is shown in Table 5.1. The general lack of difference in physical nature shown by largely crystalline polymers at... 

Accordingly, the ionic conductivity and viscosity of many ILs are a function of Tg. The Tg is thus not so important for electrodeposition from ILs, but is important for ion conduction of and in the ILs (see ionic conductivity). In the case of ILs, there are many examples that show both Tg and Tm. Detailed phase studies have been reported elsewhere [16]. The relation between Tg and Tm has already been discussed by Angell et al. [37] who observed that Tg is almost equal to two-thirds of Tm in Kelvin. 

At temperatures above Tg, or Tm for a semicrystalline polymer, the magnitude of the retention volume is a direct measure of the solubility of the probe in the polymer. At infinite dilution of the solute the relation between the bulk retention volume and the activity coefficient is (5,37,38)... 

A number of these Tm-value depending factors are also mentioned in the earlier mentioned list concerning the Tg-value (see 7.2.1) in fact there is a close agreement between the two lists. Hence, some relation between Tg and Tm can be expected and is indeed reported (the Tg/Tm ratio) in literature [24]. This Tg/Tm ratio appears to vary widely however, but indicative values might be ... 

A series of non-equilibrium Tm-values were measured on samples recrystallised from the melt under standard conditions (the so-called Tm2-values, see 1.1.4) and a number of nonequilibrium literature values were used to look for an improved correlation between Tm/Tg relations. We tried to improve the results of such a relation by distinguishing different groups of polymers instead of looking for one relation for all types of polymers. Three groups of polymers offering the best fitting correlations, were selected finally ... 

As a general rule those factors that tend to raise the Tg also tend to raise the crystalline melting point Tm. Therefore although there is no unique relation between Tg and Tm the correlation between the two is quite good. A useful rule-of-thumb (Brydson, 1972) is given by ... 

The unbranched polymer produced by P. polycephalum and related Physarum strains has a weight average molecular weight between 40,000 and 60,000 Daltons and a polydispersity of 1.5-3.0 depending on the culture conditions and the age of the samples [111]. The acid form of poly-/ -malate does not show either a Tg or a Tm in the solid state, by DSC analysis, below its thermal decomposition temperature of 185 °C. 

The relationship between Tg and microbial stability is the least studied of all the stability areas. Based mainly on mold germination data, Slade and Levine (1991) postulated that glass transition parameters, specifically Tm/Ts ratio, T g and W g (related to C defined previously in Figure 32), could be useful for predicting the microbial stability of concentrated and... 

Temperature intervals between the Tg and the Tm of polyphosphazenes are unusually small and generally fall outside the frequently cited empirical relation 0.5 < Tg/Tm (K) 0.67. This behavior could be related to complications in the first-order transition generally found with organo-substituted phosphazenes. Two first-order transitions within a temperature interval of... 

In the glassy state, the polymer backbone is considered to be almost completely immobile, causing the material to be brittle. Between Tg and Tm the system is not to be considered as a highly viscous liquid but as an elastic material the transition near Tg is called a glass-rubber transition. The crystallites act as cross-links between flexible stretches of the polymer chains, causing the material to have a rubbery consistency, with an appreciable elastic modulus. Above Tm a viscous liquid is formed. Figure 16.3b illustrates the rheological relations. 

The difference between the equilibrium Tm(o)-values and the non-equilibrium Tm-values was mentioned already. The lack of sufficient reliable Tm(o)-values hampers the determination of proper Tg/Tm(o) correlations. For the polymers of group A however a number of Tm(o)-values are available [25, 27]. These data are plotted in Figure 7.9 as a function of the corresponding Tg-values and result in the following relation ... 

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