Glass transition temperature relation

Sun Y, Xi H, Ediger MD, Richert R, Yu L (2009) Diffusion-Controlled and Diffusionless Crystal Growth near the Glass Transition Temperature Relation between Liquid Dynamics and Growth Kinetics of Seven ROY Polymorphs. J Chem Phys, pp 131 Sun Y, Tao J et al (2010) Solubilities of crystalline drugs in polymers an improved analytical method and comparison of solubilities of indomethacin and nifedipine in PVP, PVP/VA, and PVAc. J Pharm Sci 99(9) 4023-4031... 

Many polymers expand with increasing temperature. This can be predicted with simple analytic equations relating the volume at a given temperature V T) to the van der Waals volume F and the glass transition temperature, such as... 

In addition to thermodynamic appUcations, 62 values have also been related to the glass transition temperature of a polymer, and the difference 62-61 to the viscosity of polymer solutions. The best values of 6 have been analyzed into group contributions, the sum of which can be used to estimate 62 for polymers which have not been characterized experimentally. 

The glass-transition temperature in amorphous polymers is also sensitive to copolymerization. Generally, T of a random copolymer falls between the glass-transition temperatures of the respective homopolymers. For example, T for solution-polymerized polybutadiene is —that for solution-polymerized polystyrene is -HlOO°C. A commercial solution random copolymer of butadiene and styrene (Firestone s Stereon) shows an intermediate T of —(48). The glass-transition temperature of the random copolymer can sometimes be related simply as follows ... 

T and are the glass-transition temperatures in K of the homopolymers and are the weight fractions of the comonomers (49). Because the glass-transition temperature is directly related to many other material properties, changes in T by copolymerization cause changes in other properties too. Polymer properties that depend on the glass-transition temperature include physical state, rate of thermal expansion, thermal properties, torsional modulus, refractive index, dissipation factor, brittle impact resistance, flow and heat distortion properties, and minimum film-forming temperature of polymer latex... 

Thermal Properties. Thermal properties include heat-deflection temperature (HDT), specific heat, continuous use temperature, thermal conductivity, coefficient of thermal expansion, and flammability ratings. Heat-deflection temperature is a measure of the minimum temperature that results in a specified deformation of a plastic beam under loads of 1.82 or 0.46 N/mm (264 or 67 psi, respectively). Eor an unreinforced plastic, this is typically ca 20°C below the glass-transition temperature, T, at which the molecular mobility is altered. Sometimes confused with HDT is the UL Thermal Index, which Underwriters Laboratories estabflshed as a safe continuous operation temperature for apparatus made of plastics (37). Typically, UL temperature indexes are significantly lower than HDTs. Specific heat and thermal conductivity relate to insulating properties. The coefficient of thermal expansion is an important component of mold shrinkage and must be considered when designing composite stmctures. 

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. 

Tackifying resins enhance the adhesion of non-polar elastomers by improving wettability, increasing polarity and altering the viscoelastic properties. Dahlquist [31 ] established the first evidence of the modification of the viscoelastic properties of an elastomer by adding resins, and demonstrated that the performance of pressure-sensitive adhesives was related to the creep compliance. Later, Aubrey and Sherriff [32] demonstrated that a relationship between peel strength and viscoelasticity in natural rubber-low molecular resins blends existed. Class and Chu [33] used the dynamic mechanical measurements to demonstrate that compatible resins with an elastomer produced a decrease in the elastic modulus at room temperature and an increase in the tan <5 peak (which indicated the glass transition temperature of the resin-elastomer blend). Resins which are incompatible with an elastomer caused an increase in the elastic modulus at room temperature and showed two distinct maxima in the tan <5 curve. 

The simple relation (6.1) is quite useful. It allows an estimate of the gain or loss in yield strength if the glass transition temperature is changed, as for instance by the progress of the curing reaction, by radiation damage, or by absorption of water and of solvents. The ATe is determined fairly easily by thermoanalytical measurements. 

Apparently local motions indicating differences in packing are closely related to the mechanical properties of glassy polymers. One of the puzzling features of the P-relaxation in PC as in other glassy polymers 3 6 76 77) is that it often is suppressed if the glass transition temperature is lowered by adding a plasticizer. The material then becomes brittle, which severely limits the applications of such polymers. Such low... 

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 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. 

FIGURE 13.2 Calculated relation between the solubility parameter and glass transition temperature (Jg) for a variety of ethylene-propylene copolymers (EPMs) grafted with polar monomers the window for rubbers with an oil resistance similar to or better than hydrogenated acrylonitrile-butadiene copolymer (NBR) (20 wt% acrylonitrile) is also shown. 

The all-important difference between the friction properties of elastomers and hard solids is its strong dependence on temperature and speed, demonstrating that these materials are not only elastic, but also have a strong viscous component. Both these aspects are important to achieve a high friction capability. The most obvious effect is that temperature and speed are related through the so-called WLF transformation. For simple systems with a well-defined glass transition temperature the transform is obeyed very accurately. Even for complex polymer blends the transform dominates the behavior deviations are quite small. 

Temperature dependence (related to the temperature dependence of the conformational structure and the morphology of polymers) of the radiation effect on various fluoropolymers e.g., poly (tetrafluoroethylene-co-hexafluoropropylene), poly(tetrafluoroethylene-co-perfluoroalkylvinylether), and poly(tetrafluoroethylene-co-ethylene) copolymers has been reported by Tabata [419]. Hill et al. [420] have investigated the effect of environment and temperature on the radiolysis of FEP. While the irradiation is carried out at temperatures above the glass transition temperature of FEP, cross-linking reactions predominate over chain scission or degradation. Forsythe et al. [421]... 

Firstly, some of the important characteristics of the performance properties of copolymers can be expressed through the fractions of these sequences. So, for example, dealing with copolymers they normally make extensive use of semiempiri-cal relationships relating the glass transition temperature, T , with the fractions of dyads in macromolecules [7]. The simplest of such relationships reads ... 

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