Glassy polymers heat capacity

Its validity at normal temperatures was shown for more than 60 materials, ranging from pure metals to glassy polymers. Obviously, the polymers of the present study are good examples for Barker s rule. The product ot2E is linked to the difference of the two heat capacities c0 and cE, measured under constant stress and under constant strain, respectively [58], Also, a2E is linked to the difference of two Young s moduli Es, and ET measured adiabatically and isothermally [59]. 

Heat capacity and thermal expansion jumps are suitable parameters for comparison of glassy networks with linear polymers in terms of the hole model46,47). 

Differential scanning calorimetry (DSC) can be used to determine experimentally the glass transition temperature. The glass transition process is illustrated in Fig. 1.5b for a glassy polymer which does not crystallize and is being slowly heated from a temperature below Tg. Here, the drop which is marked Tg at its midpoint, represents the increase in energy which is supplied to the sample to maintain it at the same temperature as the reference material. This is necessary due to the relatively rapid increase in the heat capacity of the sample as its temperature is increases pass Tg. The addition of heat energy corresponds to the endothermal direction. 

Tg, glass transition temperature, is the temperature at which a polymer has an abrupt change in volume expansion coefiicient and heat capacity. As the temperature is raised through the Tg range, the polymer changes from a relatively hard, brittle, glassy material to a softer, more rubbery substance (3). 

The recommended heat capacity data are currently being analyzed in terms of chemical structure, structure of the polymers in the glassy, crystalline and molten states. The data are further being analyzed to study the effect of branching, molecular weight and tacticity on the heat capacity of polymers. Comprehensive tabulation of heat capacities of various structural units are being prepared and will be available in the near future. 

In the case of glassy systems, DSC can also be used to examine the discontinuity in the specihc heat capacity that is associated with the glass transihon. However, this transihon is generally broad and weak and, therefore, inferring Fg in this way can be difficult also, different authors choose to idenhfy Fg in different ways. As in the case of crystalUne polymers, polymer glasses are also never at equilibrium and, therefore, the form of the transihon that is... 

Cps Molar heat capacity of "solid" (glassy or crystalline) polymers at constant pressure. 

Figure 4.3. Correlation using topological and geometrical parameters, for the experimental heat capacities Cps of 95 "solid" (i.e., glassy or crystalline) polymers, at room temperature (298K). Cps(298K) is in J/(mole-K).

DSC defines the glass transition as a change in the heat capacity as the polymer matrix goes from the glassy state to the rubbery state. This is a second-order endothermic transition (requires heat to go through the transition), and so in DSC the transition appears as a step transition and not a peak such as might be seen with a melt transition. DSC is the classic and official way to determine even though in some cases there are polymeric materials that do not exhibit a sharp by DSC this has been the case of chitin and CS as well as cellulose [12, 39]. 

To look into this further, we show in Fig 4, in part (a), the behavior of the heat capacity of polypropylene, in units of J/K.(mol of -CH2-CH2(CH3)- repeat units) (35,36) in comparison with that of the molecular liquid 3-methyl pentane (37) (divided by 2 to have the same mass basis as the polymer repeat unit) (38). It is seen that the liquid heat capacity of the hexane isomer (x 0.S) falls not much above the natural extrapolation to lower temperatures of the heat capacity per repeat unit of the polymer. This implies that the main effect of polymerization, as far as the change in heat capacity at Tg is concerned, is to postpone the glass transition until a much higher vibrational heat capacity has been excited. This not only reduces the value of ACp but has a disproportionate effect on the ratio Cp,i/Cp,g at Tg. This happens despite a lower glassy heat capacity in the polymer than in the molecular liquid at the same temperature. The latter effect is a direct consequence of the lower Debye temperature (and lower vibrational anharmonicity) at a given temperature for in-chain interactions in the polymer than for intermolecular interactions in the same mass of molecules. 

LOW-TEMPERATURE EXCESS HEAT CAPACITY IN GLASSY POLYMERS. 

Figure 2.46 illustrates the completed analysis. A number of other polymers are described in the ATHAS Data Bank, described in the next section. Most data are available for polyethylene. The heat capacity of the crystalline polyethylene is characterized by a T dependence to 10 K. This is followed by a change to a linear temperature dependence up to about 200 K. This second temperature dependence of the heat capacity fits a one-dimensional Debye function. Then, one notices a slowing of the increase of the crystalline heat capacity with temperature at about 200 to 250 K, to show a renewed increase above 300 K, to reach values equal to and higher than the heat capacity of melted polyethylene (close to the melting temperature). The heat capacity of the glassy polyethylene shows large deviations from the heat capacity of the crystal below 50 K (see Fig. 2.45). At these temperatures the absolute value of the heat capacity is, however, so small that it does not show up in Fig. 2.46. After...

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