Heat capacity glass transition temperatures

While physicochemical and spectroscopic techniques elucidate valuable physical and structural information, thermal analysis techniques offer an additional approach to characterize NOM with respect to thermal stability, thermal transitions, and even interactions with solvents. Information such as thermal degradation temperature (or peak temperature), glass transition temperature, heat capacity, thermal expansion coefficient, and enthalpy can be readily obtained from thermal analysis these properties, when correlated with structural information, may serve to provide additional insights into NOM s environmental reactivity. 

Polymer chemists use DSC extensively to study percent crystallinity, crystallization rate, polymerization reaction kinetics, polymer degradation, and the effect of composition on the glass transition temperature, heat capacity determinations, and characterization of polymer blends. Materials scientists, physical chemists, and analytical chemists use DSC to study corrosion, oxidation, reduction, phase changes, catalysts, surface reactions, chemical adsorption and desorption (chemisorption), physical adsorption and desorption (physisorp-tion), fundamental physical properties such as enthalpy, boiling point, and equdibrium vapor pressure. DSC instruments permit the purge gas to be changed automatically, so sample interactions with reactive gas atmospheres can be studied. 

A sample of the polymer to be studied and an inert reference material are heated and cooled in an inert environment (nitrogen) according to a defined schedule of temperatures (scanning or isothermal). The heat-flow measurements allow the determination of the temperature profile of the polymer, including melting, crystallization and glass transition temperatures, heat (enthalpy) of fusion and crystallization. DSC can also evaluate thermal stability, heat capacity, specific heat, crosslinking and reaction kinetics. 

Figure 4.62 shows the first harmonic of the solution of Eq. (24), which represents the reversing heat capacity as normally computed (see Figure 4.29). The heavy line is the total Cp (curve B of Figure 4.29). Outside of the glass transition, this heat capacity is equal to the heat capacity measured with a standard DSC of the same cooling rate < >. In the glass transition region, it only approximates the apparent heat capacity of the standard DSC because of contributions of the type seen in Eq. (21). The reversing Cp decreases at a higher temperature than the total Cp because of its faster time scale of...

Besides the exothermal heat flow rate caused by the crystallization process, a decreasing heat capacity can be observed for most polymers during crystallization near the glass transition. Unfortunately, heat capacity cannot be measiued under isothermal conditions. But applying a small heating rate (temperature), perturbation during a quasi-isothermal measurement allows the determination of heat capacity as a function of time as discussed next. 

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 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. 

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.

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... 

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. 

At room temperature, atactic polystyrene is well below its glass transition temperature of approximately 100 °C. In this state, it is an amorphous glassy material that is brittle, stiff, and transparent. Due to its relatively low glass transition temperature, low heat capacity, and lack of crystallites we can readily raise its temperature until it softens. In its molten state, it is quite thermally stable so we can mold it into useful items by most of the standard conversion processes. It is particularly well suited to thermoforming due to its high melt viscosity. As it has no significant polarity, it is a good electrical insulator. 

Heat capacity measurements at the glass transition temperature, Tg, are based on the same differential concept. The weight fraction of amorphous phase is calculated as the ratio of changes of heat capacity of the semi-crystalline sample ACp(S) over the change in heat capacity of the melt (ACp(m)) at the glass transition. For a two-phase system, the degree of crystallinity is given as ... 

Figure 8.27 Heat capacity of some glass-forming liquids close to their glass transition temperatures ZnCl2 [45], GeSe2 [46], and a selected titanosilicate [47], aluminosilicate [48] and borosilicate [49] system.

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