Glass transition free volume

Some thermodynamic aspects of the glass transition Free volume, entropy and enthalpy theories. J. Chem. Phys. To be published (1964). 

In this section we resume our examination of the equivalency of time and temperature in the determination of the mechanical properties of polymers. In the last chapter we had several occasions to mention this equivalency, but never developed it in detail. In examining this, we shall not only acquire some practical knowledge for the collection and representation of experimental data, but also shall gain additional insight into the free-volume aspect of the glass transition. 

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. 

As the temperature is decreased, free-volume is lost. If the molecular shape or cross-linking prevent crystallisation, then the liquid structure is retained, and free-volume is not all lost immediately (Fig. 22.8c). As with the melt, flow can still occur, though naturally it is more difficult, so the viscosity increases. As the polymer is cooled further, more free volume is lost. There comes a point at which the volume, though sufficient to contain the molecules, is too small to allow them to move and rearrange. All the free volume is gone, and the curve of specific volume flattens out (Fig. 22.8c). This is the glass transition temperature, T . Below this temperature the polymer is a glass. 

Other theories proposed dissipation of energy through crack interaction localised heating causing the material to be raised to above the glass transition temperature in the layers of resin between the rubber droplets and a proposal that extension causes dilation so that the free volume is increased and the glass transition temperature drops to below the temperature of the polyblend. 

Before providing such an explanation it should first be noted that progressive addition of a plasticiser causes a reduction in the glass transition temperature of the polymer-plasticiser blend which eventually will be rubbery at room temperature. This suggests that plasticiser molecules insert themselves between polymer molecules, reducing but not eliminating polymer-polymer contacts and generating additional free volume. With traditional hydrocarbon softeners as used in diene rubbers this is probably almost all that happens. However, in the... 

If we, however, consider that viscosity is inversely related to the fractional free volume, which increases from a small value at the glass transition temperature Tg linearly with temperature above this figure, then it is possible to derive an equation. 

In order for molecules or segments of molecules to move from place to place it is necessary that there should be some holes in the mass of material into which these molecules or segments may move—and simultaneously leave other spaces into which other molecules or segments may occupy. One interpretation of the glass transition temperature is that it is a temperature below which the free volume is really too small for much molecular movement. However, at and... 

Lipatov, Y. S. The Iso-Free-Volume State and Glass Transition in Amorphous Polymers New Development of the Theory. Vol. 26, pp. 63 —104. 

The glass transition temperature of a dilute system, according to the free volume changes, is determined by the diluent volume fraction Vd, and changes of the thermal expansion coefficient, a, at Tg by using ... 

The free volume model seems to be more adequate to describe the plasticization behaviour of the systems of lower amine content. According to Eq. (5), the higher is the change of the expansion coefficient the lower is the influence of the diluent volume fraction. The three TGDDM-DDS mixtures cured with 20, 30 and 50 PHR of hardener were characterized l2) by changes of the expansion coefficient at the glass transition, respectively, of 0.63, 1.08 and 2.94x 10 3 °C l. The more dense and stiffer resin crosslinked with 50 PHR of DDS should be, in principle, the less... 

Fluorinated poly(arylene edier)s are of special interest because of their low surface energy, remarkably low water absorption, and low dielectric constants. The bulk—CF3 group also serves to increase the free volume of the polymer, thereby improving various properties of polymers, including gas permeabilities and electrical insulating properties. The 6F group in the polymer backbone enhances polymer solubility (commonly referred to as the fluorine effect ) without forfeiture of die thermal stability. It also increases die glass transition temperature with concomitant decrease of crystallinity. 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

Glass transition temperature (Tg) Swelling will be reduced in an elastomer with a high Tg, that is, in an elastomer with relatively little free volume available to absorb liquid. 

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