Thermal Expansion and Density

Using concepts of thermoelasticity and the same general averaging approach used to predict electrical conductivities for composites consisting of grains in a continuous medium, Kerner (1965a,fe) derived a theoretical expression for the overall volume coefficient of expansion for a composite. 

For the case of a filled plastic this becomesf (Kerner, 1956b Nielson, 1967a) 

An equivalent expression was derived by Manabe et al. (1971) in a slightly different form  

Other equations have been proposed, though testing appears to have been limited. Turner (1946) suggested the following equation for isotropic fillers, where a is independent of size and shape  

Of course this equation can only be valid when the filler or dispersed phase can in fact undergo a phase inversion this cannot be the case for a rigid inorganic filler. Above Tg, equations (12.49) and (12.52) give almost the same values for these systems, and a linear additivity relationship holds. This presumably follows from the near equivalence of expansion coefficients so that the right-hand interaction term of equations (12.49) and (12.52) vanishes. 

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Crosslinked low-density polyethylene foams with a closedcell structure were investigated using differential scanning calorimetry, scanning electron microscopy, density, and thermal expansion measurements. At room temperature, the coefficient of thermal expansion decreased as the density increased. This was attributed to the influence of gas expansion within the cells. At a given material density, the expansion increased as the cell size became smaller. At higher temperatures, the relationship between thermal expansion and density was more complex, due to physical transitions in the matrix polymer. Materials with high density and thick cell walls were concluded to be the best for low expansion applications. 16 refs. 

For many applications of filled polymers, knowledge of properties such as permeability, thermal and electrical conductivities, coefficients of thermal expansion, and density is important. In comparison with the effects of fillers on mechanical behavior, much less attention has been given to such properties of polymeric composites. Fortunately, the laws of transport phenomena for electrical and thermal conductivity, magnetic permeability, and dielectric constants often are similar in form, so that with appropriate changes in nomenclature and allowance for intrinsic differences in detail, a general solution can often be used as a basis for characterizing several types of transport behavior. Useful treatments also exist for density and thermal expansion. 

COEFFICIENTS OF THERMAL EXPANSION AND DENSITIES OF FILLED POLYMERS. 

Practically, p Pi, and pi can be experimentally determined from the measurements of their cohesive energy density, thermal expansion, and density, extrapolated to 0°K. For blends comprised of m constituents, one resorts to the following procedure from the relation... 

To estimate the flow relaxation time scale, we simply set Fstress =0 in the preceding equation. This is valid because the picosecond laser pulses, as well as the time scales associated with all the physical processes such as thermal expansion and density change that initiate the flow process, are all much shorter than the flow response time. 

In aerospace appHcations, low density coupled with other desirable features, such as tailored thermal expansion and conductivity, high stiffness and strength, etc, ate the main drivers. Performance rather than cost is an important item. Inasmuch as continuous fiber-reinforced MMCs deUver superior performance to particle-reinforced composites, the former are ftequendy used in aerospace appHcations. In nonaerospace appHcations, cost and performance are important, ie, an optimum combination of these items is requited. It is thus understandable that particle-reinforced MMCs are increa singly finding appHcations in nonaerospace appHcations. 

Automated soldering operations can subject the mol ding to considerable heating, and adequate heat deflection characteristics ate an important property of the plastics that ate used. Flame retardants (qv) also ate often incorporated as additives. When service is to be in a humid environment, it is important that plastics having low moisture absorbance be used. Mol ding precision and dimensional stabiUty, which requites low linear coefficients of thermal expansion and high modulus values, ate key parameters in high density fine-pitch interconnect devices. 

The properties of glassy polymers such as density, thermal expansion, and small-strain deformation are mainly determined by the van der Waals interaction of adjacent molecular segments. On the other hand, crack growth depends on the length of the molecular strands in the network as is deduced from the fracture experiments. 

Here Q(t) denotes the heat input per unit volume accumulated up to time t, Cp is the specific heat per unit mass at constant pressure, Cv the specific heat per unit mass at constant volume, c is the sound velocity, oCp the coefficient of isobaric thermal expansion, and pg the equilibrium density. (4) The heat input Q(t) is the laser energy released by the absorbing molecule per unit volume. If the excitation is in the visible spectral range, the evolution of Q(t) follows the rhythm of the different chemically driven relaxation processes through which energy is... 

Pyroelectricity of several kinds of alternating LB films consisting of phenylpyrazine derivatives and stearic acid was measured by the static method at various temperatures. Effects of thermal expansion and molecular packing density of the film on pyroelectricity were also examined. The following conclusions were derived. 

Supercritical fluids represent a different type of alternative solvent to the others discussed in this book since they are not in the liquid state. A SCF is defined as a substance above its critical temperature (Tc) and pressure (Pc)1, but below the pressure required for condensation to a solid, see Figure 6.1 [1], The last requirement is often omitted since the pressure needed for condensation to occur is usually unpractically high. The critical point represents the highest temperature and pressure at which the substance can exist as a vapour and liquid in equilibrium. Hence, in a closed system, as the boiling point curve is ascended, increasing both temperature and pressure, the liquid becomes less dense due to thermal expansion and the gas becomes denser as the pressure rises. The densities of both phases thus converge until they become identical at the critical point. At this point, the two phases become indistinguishable and a SCF is obtained. 

The static and dynamic mechanical properties, creep recovery behaviour, thermal expansion and thermal conductivity of low-density foams made of blends of LDPE and EVA were studied as a function of the EVA content of the blends. These properties were compared with those of a foam made from a blend of EVA and ethylene-propylene rubber. A knowledge of the way in which the EVA content affects the behaviour of these blend foam materials is fundamental to obtaining a wide range of polyolefin foams, with similar density, suitable for different applications. 9 refs. 

The density of the hydroxyfunctional hyperbranched polyesters is 1.295 g cm" and pressure-volume-temperature (PVT) measurements show that the thermal expansion and compressibility are slightly lower compared to polar linear polymers, such as PVC, poly(e-caprolactone), and poly(epichlorohydrine). ... 

A piece of Invar (density = 8.00 g/ml) weighs 15.4726 g in air and 13.9213 g when suspended in liquid nitrogen at a temperature of - 196°C. What is the density of liquid nitrogen at that temperature (Invar has a very small coefficient of thermal expansion, and its change in density with temperature may be neglected in this problem.)... 

As indicated in Fig. 13, the fuel rod consists essentially of 0.325-iiich (0.82-centimeter) diameter, 0.390 inch long U02 pellets canned in a 0.382-inch (0.97-centimeter) outside diameter Zircaloy-4 tube. The high density fuel pellets are dished at both ends to allow fur axial differential thermal expansion and fuel volumetric grow ill with burnup. 

Arrhenius plots of conductivity for the four components of the elementary cell are shown in Fig. 34. They indicate that electrolyte and interconnection materials are responsible of the main part of ohmic losses. Furthermore, both must be gas tight. Therefore, it is necessary to use them as thin and dense layers with a minimum of microcracks. It has to be said that in the literature not much attention has been paid to electrode overpotentials in evaluating polarization losses. These parameters greatly depend on composition, porosity and current density. Their study must be developed in parallel with the physical properties such as electrical conductivity, thermal expansion coefficient, density, atomic diffusion, etc. 

Some properties are directly connected with mass and packing density (or its reciprocal specific volume), thermal expansibility and isothermal compressibility. Especially the mechanical properties, such as moduli, Poisson ratio, etc., depend on mass and packing. In this chapter we shall discuss the densimetric and volumetric properties of polymers, especially density and its variations as a function of temperature and pressure. Density is defined as a ratio ... 

The gas—liquid coexistence curve is known as the boiling curve. If one moves upwards along the boiling curve, increasing both temperature and pressure, the liquid then becomes less dense due to thermal expansion, and as the pressure rises the gas becomes denser. Eventually, the densities of the two phases converge and become identical, eliminating the distinction between gas and liquid. For example, the critical point of C02 occurs at a pressure of 73.8 bar and a temperature of 31.1 °C. 

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