Free volume thermal expansion coefficient

Several material properties exhibit a distinct change over the range of Tg. These properties can be classified into three major categories—thermodynamic quantities (i.e., enthalpy, heat capacity, volume, and thermal expansion coefficient), molecular dynamics quantities (i.e., rotational and translational mobility), and physicochemical properties (i.e., viscosity, viscoelastic proprieties, dielectric constant). Figure 34 schematically illustrates changes in selected material properties (free volume, thermal expansion coefficient, enthalpy, heat capacity, viscosity, and dielectric constant) as functions of temperature over the range of Tg. A number of analytical methods can be used to monitor these and other property changes and... 

LIG. 34 Schematic illustrations of changes in selected material properties (free volume, thermal expansion coefficient, enthalpy, heat capacity, viscosity, and dielectric constant) as functions of temperature over the range of Tg. 

The free volume theory originated some years later than the lubricity and the gel theories, when the evolution of different properties of polymers as a function of temperature, specific volume, thermal expansion coefficients, or viscosity was attempted to be explained.The relationships between these properties and some variables corresponding to polymer stracture, such as molecular weight or terminal groups content, the presence of another monomer and, of course, the presence of plasticizers, was also explained. For plasticized polymers the theory attempted to explain the diminution of the glass transition temperature with the plasticizer content. This theory is a contribution of different authors, but it was postulated by Fox and Floiy. The theory is still being used to explain some properties of plasticized polymers, i.e., viscoelastic properties. ... 

At low temperatures the thermal expansion of the Ln compounds exhibits anomalies due to the crystal field similar to the Schottky effect of the specific heat. The volume thermal-expansion coefficient /3 is a derivative of the free... 

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 ... 

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. 

Table 14.2 Values of WLF Cj0 and C2° Parameters, Fractional Free Volumes f0 and/ and Thermal Expansion Coefficient af for PAMAM, PPI and PBzE dendrimers ... 

Heating up amorphous solids, we observe an unsteady increase A0th of the thermal expansion coefficient in a characteristic temperature range. This effect is coupled with the formation of the free volume (Fig. 10) and a strong decrease of... 

According to Ferry12 the free-volume per cm of substance, i. e. the fractional free-volume /, is hard to define exactly and should be regarded as merely a useful semi quantitative concept. Specifically, the thermal expansion coefficients of liquids for the most part reflect the increase in fractional free-volume only a small part is connected with the anharmonic dependence of potential energy or interatomic and intermoleeular distances. 

It is generally assumed that fractional free-volume changes with temperature according to Eq. (16), where the thermal expansion coefficient is expressed by Eq. (19). 

Here oth is the fraction of thermal expansion connected with changes in hole concentration (free-volume expansion), ), is the energy of hole formation, r=M/p0 Vn Na, where NA is the Avogadro number,M molecular weight, p0 the density of a liquid without holes at absolute zero, and Vn the hole volume. For polymeric systems r is very small, and then ahTis the function of E IRTalone. The value Of, is identified with experimentally observed changes in the thermal expansion coefficients A a at Tg, i.e. 

The glass transition is characterized in part by an observed second-order transition distinguished by a discontinuity of the Gibbs free energy with respect to the aforementioned state variables, but by continuity of entropy, volume, and enthalpy. Hence, heat capacity, Cp, as well as the thermal expansion coefficient, a, as defined below, both exhibit a discontinuity at the glass transition temperature (McKenna, 1989). 

We propose to rationalize the observation by a phenomenon known as residual thermal stresses. Residual thermal stresses arise from the fact that carbon-fiber and epoxy have different thermal expansion coefficients and a quenching of the composite would conceivably produce residual stresses. Apparently, the quenching process may produce enough residual stresses to lower the toughness of the composite. In the absence of such residual stresses the free volume concept alone would predict a quenched glass to have larger amount of free volume and hence constitute a less brittle substance. 

As an amorphous polymer, lignin undergoes chain segment motion upon heating. This motion, a glass transition, is characteristic of all amorphous polymers, and is indicated by an endothermic shift in the DTA or DSC curves. This glass transition is accompanied by abrupt changes in free volume, heat capacity, and thermal expansion coefficient. 

Table IV. WLF Shift Constants, Fractional Free Volume, and Thermal Expansion Coefficient...

Based on the free volume theory, Vfj° and txj (thermal expansion coefficient) are assumed to be constant for different molecules. Vfj° has a value of 0.025 and clj has a value of 0.001 for small molecules such as solvent or monomer and 0.00048 for polymer long chains. The subscript j stands for species in the reaction mixture such as monomer, solvent, polymer, etc.. 

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