Glass heat capacity

Note that in all cases, two sources of energy loss exist, a fast loss of vibrational energy, and a slow loss of configurational, or potential, energy. At the highest temperature the two cannot be distinguished. The lowest temperature, T, is included to show how the glass heat capacity relates to that of the supercooled liquid. 

When we look for a thermodynamic confirmation of the landscape height, however, we encounter a problem. Instead of finding that the jump in heat capacity at Tg is large in proportion to how fragile the polymer is, we find that it is much the same for all polymers (despite wide variation in fragility (27,28), and usually rather small compared with the polymer glass heat capacity at Tg. If this value is adopted for calculations using equation (3), all... 

Figure 4. (a) Heat capacity of polypropylene crystal, glass and liquid in J/K per mole of -CH2-CH2(CH3)-repeat units, from refs. 35 and 36 compared with the same properties of 3-methyl pentane (1/2 mole) from ref. 37. The comparison shows how the postponement of the glass transition to the higher tem rature, consequent on the extension of the carton chain, completely changes the relation between liquid and glass heat capacities, causing polymers to appear... 

Equations (54) and (55) can be criticised because they assume a unique value for ACp whereas this varies slightly as the liquid and glass heat capacities have different slopes. (For highest accuracy ACp should be determined for the mean of Tgf and T gr). Alternatively, enthalpy loss on annealing is often measured by using a result from a sample with low annealing (say... 

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

The glass-transition temperature, T, of dry polyester is approximately 70°C and is slightly reduced ia water. The glass-transitioa temperatures of copolyesters are affected by both the amouat and chemical nature of the comonomer (32,47). Other thermal properties, including heat capacity and thermal conductivity, depend on the state of the polymer and are summarized ia Table 2. 

Physical Dilution. The flame retardant can also act as a thermal sink, increasing the heat capacity of the polymer or reducing the fuel content to a level below the lower limit of flammabiHty. Inert fillers such as glass fibers and microspheres and minerals such as talc act by this mechanism. 

Its value at 25°C is 0.71 J/(g-°C) (0.17 cal/(g-°C)) (95,147). Discontinuities in the temperature dependence of the heat capacity have been attributed to stmctural changes, eg, crystaUi2ation and annealing effects, in the glass. The heat capacity varies weakly with OH content. Increasing the OH level from 0.0003 to 0.12 wt % reduces the heat capacity by approximately 0.5% at 300 K and by 1.6% at 700 K (148). The low temperature (<10 K) heat capacities of vitreous siUca tend to be higher than the values predicted by the Debye model (149). 

Phonon transport is the main conduction mechanism below 300°C. Compositional effects are significant because the mean free phonon path is limited by the random glass stmcture. Estimates of the mean free phonon path in vitreous siUca, made using elastic wave velocity, heat capacity, and thermal conductivity data, generate a value of 520 pm, which is on the order of the dimensions of the SiO tetrahedron (151). Radiative conduction mechanisms can be significant at higher temperatures. 

In plasma chemical vapor deposition (PCVD), the starting materials are typically SiCl, O2, 2 6 GeCl (see Plasma technology). Plasma chemical vapor deposition is similar to MCVD in that the reactants are carried into a hoUow siUca tube, but PCVD uses a moving microwave cavity rather than a torch. The plasma formed inside the microwave cavity results in the deposition of a compact glass layer along the inner wall of the tube. The temperatures involved in PCVD are lower than those in MCVD, and no oxide soots are formed. Also, the PCVD method is not affected by the heat capacities or thermal conductivities of the deposits. 

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

Experimental data for Van der Waals volumes Molar volumes Heat capacities Solubility parameter and glass transition temperature... 

Figure 25 ANN model (5-8-6) training and testing results for van der Waals volume, molar volume, heat capacity, solubility parameter, and glass transition temperature of 45 different polymers.

The most common type of glass transition is one that occurs for many liquids when they are cooled quickly below their freezing temperature. With rapid cooling, eventually a temperature region is reached where the translational and rotational motion associated with the liquid is lost, but the positional and orientational order associated with a crystal has not been achieved, so that the disorder remains frozen in. The loss of both translational and rotational motion leads to a large increase in viscosity and a large decrease in heat capacity. 

Figure 4.8 Heat capacity of glycerol as a function of temperature. The solid line indicates Cp,m for the liquid and glassy phase. The dashed line represents Cp m for the solid. The dotted line at the melting temperature of 291.05 K. indicates the change in heat capacity upon melting. A glass transition occurs in the supercooled liquid at approximately 185 K. The heat capacities of the solid and the glass approach one another as the temperature is lowered they are almost identical below 140 K.

Measurements of heat capacity jumps at the glass-transition temperatures, Tg, in the matrix material and the composites, carried out from heat-capacity experiments, were intimately related to the extent of the mesophase thickness. Further accurate measurements of the overall longitudinal elastic modulus of the composites and the... 

The experimental data show that the magnitude of the heat capacity (or similarly of the specific heat) under adiabatic conditions decreases regularly with the increase of filler content. This phenomenon was explained by the fact that the macromolecules, appertaining to the mesophase layers, are totally or partly excluded to participate in the cooperative process, taking place in the glass-transition zone, due to their interactions with the surfaces of the solid inclusions. 

Fig. 6. The variation of the heat capacity jumps at the respective glass transition temperatures versus inclusion-volume contents of iron-epoxy particulates of different diameters of inclusions. In the same figure is presented the variation of the coefficients X for the same composites and volume contents...

Moreover, the mesophase-volume fractions Oj for the same inclusion-contents were determined from the experimental values of heat-capacity jumps ACp at the respective glass transition temperatures T f by applying Lipatov s theory. Fig. 7 presents the variation of the differences Ars oi the radii of the mesophase and the inclusion (rf), versus the inclusion volume content, uf, for three different diameters of inclusions varying between df = 150 pm and df = 400 pm. 

Indeed, the multi-layered model, applied to fiber reinforced composites, presented a basic inconsistency, as it appeared in previous publications17). This was its incompatibility with the assumption that the boundary layer, constituting the mesophase between inclusions and matrix, should extent to a thickness well defined by thermodynamic measurements, yielding jumps in the heat capacity values at the glass-transition temperature region of the composites. By leaving this layer in the first models to extent freely and tend, in an asymptotic manner, to its limiting value of Em, it was allowed to the mesophase layer to extend several times further, than the peel anticipated from thermodynamic measurements, fact which does not happen in its new versions. 

The definition of the extent of mesophase and the evaluation of its radius r, is again based on the thermodynamic principle, introduced by Lipatov 11), and on measurements of the heat-capacity jumps AC and ACf, of the matrix material (AC ) and the fiber-composites (ACP) with different fiber-volume contents. These jumps appear at the glass-transition temperatures Tgc of the composites and they are intimately related, as it has been explained with particulates, to the volume fraction of the mesophase. 

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