Molecular glass transition

Vasanthavada, M., Z. V fong, Y. Joshi, and M. S. Kislalioglu. 2002. Comparison of the utility of thermally stimulated current and modulated differential scanning calorimeter to study sub-glass transition molecular motions of poly(vinylpyrrolidone). Paper presented at AAPS Annual Meeting, Toronto, October 8, 2002. 

Thus we may refer to a glass transition pressure. In a broader sense, the glass transition is multidimensional. We could also refer to the glass transition molecular weight (Section 8.7), the glass transition concentration (for diluted or plasticized species), and so forth. 

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 kinetic nature of the glass transition should be clear from the last chapter, where we first identified this transition by a change in the mechanical properties of a sample in very rapid deformations. In that chapter we concluded that molecular motion could simply not keep up with these high-frequency deformations. The complementarity between time and temperature enters the picture in this way. At lower temperatures the motion of molecules becomes more sluggish and equivalent effects on mechanical properties are produced by cooling as by frequency variations. We shall return to an examination of this time-temperature equivalency in Sec. 4.10. First, however, it will be profitable to consider the possibility of a thermodynamic description of the transition which occurs at Tg. 

Below T polymers are stiff, hard, britde, and glass-like above if the molecular weight is high enough, they are relatively soft, limp, stretchable, and can be somewhat elastic. At even higher temperatures they flow and are tacky. Methods used to determine glass-transition temperatures and the reported values for a large number of polymers may be found in References 7—9. Values for the T of common acrylate homopolymers are found in Table 1. 

Molecular Weight. The values of the mechanical properties of polymers increase as the molecular weight increases. However, beyond some critical molecular weight, often about 100,000 to 200,000 for amorphous polymers, the increase in property values is slight and levels off asymptotically. As an example, the glass-transition temperature of a polymer usually follows the relationship... 

Solution Polymers. Acryflc solution polymers are usually characterized by their composition, solids content, viscosity, molecular weight, glass-transition temperature, and solvent. The compositions of acryflc polymers are most readily determined by physicochemical methods such as spectroscopy, pyrolytic gas—liquid chromatography, and refractive index measurements (97,158). The solids content of acryflc polymers is determined by dilution followed by solvent evaporation to constant weight. Viscosities are most conveniently determined with a Brookfield viscometer, molecular weight by intrinsic viscosity (158), and glass-transition temperature by calorimetry. 

Polymer systems have been classified according to glass-transition temperature (T), melting poiat (T ), and polymer molecular weight (12) as elastomers, plastics, and fibers. Fillers play an important role as reinforcement for elastomers. They are used extensively ia all subclasses of plastics, ie, geaeral-purpose, specialty, and engineering plastics (qv). Fillets are not, however, a significant factor ia fibers (qv). 

In methacrylic ester polymers, the glass-transition temperature, is influenced primarily by the nature of the alcohol group as can be seen in Table 1. Below the the polymers are hard, brittle, and glass-like above the they are relatively soft, flexible, and mbbery. At even higher temperatures, depending on molecular weight, they flow and are tacky. Table 1 also contains typical values for the density, solubiHty parameter, and refractive index for various methacrylic homopolymers. 

T is the glass-transition temperature at infinite molecular weight and is the number average molecular weight. The value of k for poly(methyl methacrylate) is about 2 x 10 the value for acrylate polymers is approximately the same (9). A detailed discussion on the effect of molecular weight on the properties of a polymer may be found in Reference 17. 

The value of the glass-transition temperature, T, is dependent on the stereoregularity of the polymer, its molecular weight, and the measurement techniques used. Transition temperatures from —13 to 0°C ate reported for isotactic polypropylene, and —18 to 5°C for atactic (39,40). 

Strong-Acid Catalysts, Novolak Resins. PhenoHc novolaks are thermoplastic resins having a molecular weight of 500—5000 and a glass-transition temperature, T, of 45—70°C. The phenol—formaldehyde reactions are carried to their energetic completion, allowing isolation of the resin ... 

Substituted nonheat-reactive resins do not form a film and are not reactive by themselves, but are exceUent modifier resins for oleoresinous varnishes and alkyds. Thein high glass-transition temperature and molecular weight provide initial hardness and reduce tack oxygen-initiated cross-linking reactions take place with the unsaturated oils. 

The iatroduction of a plasticizer, which is a molecule of lower molecular weight than the resia, has the abiUty to impart a greater free volume per volume of material because there is an iucrease iu the proportion of end groups and the plasticizer has a glass-transition temperature, T, lower than that of the resia itself A detailed mathematical treatment (2) of this phenomenon can be carried out to explain the success of some plasticizers and the failure of others. Clearly, the use of a given plasticizer iu a certain appHcation is a compromise between the above ideas and physical properties such as volatiUty, compatibihty, high and low temperature performance, viscosity, etc. This choice is appHcation dependent, ie, there is no ideal plasticizer for every appHcation. 

Fig. 2. Glass-transition temperature—molecular weight relationship for poly(ethylene oxide) (-) represents classical T —mol wt relationship Q, data from...

Other Properties. The glass-transition temperature for PPO is 190 K and varies htde with molecular weight (182). The temperature dependence of the diffusion coefficient of PPO in the undiluted state has been measured (182). 

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