Thermal expansion coefficients definition

By applying the definition of the thermal expansion coefficient, given by Equation 9-39, we obtain... 

The thermal expansion coefficients follow from the definitions for the specific thermal expansivity ... 

It has been demonstrated that molecular orientation can be achieved starting with a low molecular weight species which is oriented in an elongational flow and subsequently cured under UV-irradiation. The orientation of the monomer is frozen-in by the ultra-fast process of polymerization and crosslinking. Both extrusion and stretching can be carried out at relatively low temperatures and pressures. Polymer filaments produced in this way are definitely anisotropic as is evidenced by their birefringence and by a strong increase of the tensile modulus and a decrease of the thermal expansion coefficient in the axial direction. 

The characteristic velocity is determined by the ratio of the characteristic tangential (Marangoni) stress, 0(PAT/L), which drives this motion to the viscous forces ()(p,uc/d) that derive from this motion. The definition (6 212) also allows us to return to the condition for neglect of buoyancy forces compared with Marangoni forces as a potential source of fluid motion in the thin cavity. To do this, we introduce the thermal expansion coefficient, which we denote as a, so that the characteristic density difference Ap = O(paAT). Then the condition (Apge2t2/puc) 1 can be expressed in the form... 

An important feature of this approach is that only the standards that realize the unit of length require a documentary chain of evidence that links to the definition of the meter. In a typical dimensional measurement, there are many influence quantities that contribute to the uncertainty associated with the end result, such as workpiece temperature and thermal expansion coefficient. If it were required that all such influence quantities themselves be metrologically traceable, then since each of the quantities depends on other quantities and so on, such a requirement would lead to an infinite regress. 

Three separate definitions of the thermal expansion coefficient are currently employed. When presenting data, or comparing a measured value with tabulated values, it is necessary to state clearly which definition is being used. If a solid sample is heated from to T2 the length of the sample changes... 

Based on the Maxwell relations, the definitions of the isothermal compressibility (Kj or jSr), the isoentropic compressibility (Ks or jSr), and the thermal expansion coefficient (a) can be written with the In V removed as, respectively. 

For quasi-static measurements such as illustrated in Figure 8.2, the glass transition temperature, Tg, is often taken at the maximum rate of turndown of the modulus at the elbow, where E = lO Pa. Often the glass transition temperature is defined as the temperature where the thermal expansion coefficient (Section 8.3) undergoes a discontinuity. (Enthalpic and dynamic definitions are given in Section 8.2.9. Other, more precise definitions are given in Section 8.5.)... 

Using arguments similar to the proof of Eq. (C.7), and the definitions of the thermal expansion coefficient a, isothermal compressibility kj- and adiabatic compressibility ks, prove the relations given in Eqs. (C.8)-(C.10). 

In Section II. 1 the heat capacity is considered from the viewpoint of pheno-menolo cal thermod3mamics. In Section II.l.l the usual definitions are ven for the heat capacity Cy or Cp at constant volume V respectively constant pressure and constant quantity of matter. They are valid for thermodynamically simple systems. As far as liquids and solids are concerned (and polymers are alwaj in a condensed state) Cp is the quantity more available from the experiment and Cy that more available from the theory. In consequence, one is always constrained to convert both quantities. Such a conversion is rendered postible by Eq. (25a) if the thermal expansion coefficient a, the isothermal compressit ty x and the volume V (or the mass densitiy) of the system are known. In default of these data the formula (25b) of Nemst and lindemann is often used which, as approximation, follows from (25a). 

Figure 6.6 shows the temperature stability of the adsorbed nanolayers composed of three different homopolymers measured by in situ X-ray reflectivity. Hence, it is clear that both the flattened layers and interfacial sublayers exhibit nearly zero thermal expansion within the temperature range up to 200 °C [48, 52]. If we use the same definition of Fg as for bulk melts (i.e., a change in the thermal expansion coefficient when crossing the glass transition [88]), the XR data indicates that there is no glass transition of these adsorbed nanolayers up to 200 °C, while the bulk FgS of these polymers are about 100 °C. These findings may be consistent with... 

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