Volumetric expansion coefficients

Kea.tlte, Keatite has been prepared (65) by the crystallisation of amorphous precipitated silica ia a hydrothermal bomb from dilute alkah hydroxide or carbonate solutions at 380—585°C and 35—120 MPa (345—1180 atm). The stmcture (66) is tetragonal. There are 12 Si02 units ia the unit cell ttg = 745 pm and Cg = 8604 pm the space group is P42. Keatite has a negative volumetric expansion coefficient from 20—550°C. It is unchanged by beating at 1100°C, but is transformed completely to cristobahte ia three hours at 1620°C. 

R, = volume generation rate, ftVmin P = volumetric expansion coefficient, ftVlb-°F Q = heat input rate, Btu/min Cp = hquid heat capacity, Btu/lb-°F... 

Fig. 16. Variation of the expansion coefficient k as a function of the gas pressure in the volumetric line (67).

Au is the difference between the liquid and glassy volumetric expansion coefficients and the temperatures are in kelvin. "The WLF equation holds between I], or / f 10 K and abftut 100 K above 7A,. Above this temperature, for thermally stable polymers, Berry and Fox (28) have shown that a useful extension of the WLF equation is the addition of an Arrhenius term with a low activation energy. 

The expansion coefficient fi for water at 32°F should be used. This is estimated using liquid volumetric data from the steam tables over a short range of temperatures around 32°F. However, the steam tables do not provide liquid water specific volume data below 32°F. A value between 32°F and some appropriate higher temperature will suffice. From the steam tables ... 

The correlation results maybe used for calculation of thermal expansion coefficient of liquid and volumetric flow from thermal expansion. Examples are shown in Table 7-2. 

The analogy with thermal expansion coefficients is evident when one compares equations 1.98 and 1.99 with equations 1.90 and 1.91, respectively. For compressibility, as for thermal expansion, a mean coefficient that defines the volumetric variation (V2 — ft) for a finite pressure range (T2— I)) may be introduced. This coefficient, the mean volumetric isothermal compressibility, is given by... 

Octahedral distortion prevents calculation of the volumetric thermal expansion coefficient of the phase stemming from the linear polyhedral thermal expansion values. However, volumetric thermal expansions may be obtained by least-squares regression of the observed PVT relations. Table 5.10 lists, for instance, the coefficients of a thermal expansion relation of the type... 

TMA measures the mechanical responses of a polymer as a function of temperature. Typical measurements include (1) expansion properties, i.e., the expansion of a material leading to the calculation of the linear expansion coefficient (2) tension properties, i.e., the shrinkage and expansion of a material under tensile stress e.g., elastic modulus (3) dilatometric properties, i.e., the volumetric expansion within a confining medium e.g., specific volume ... 

Instead of measuring the force-temperature dependence at constant volume and length, one can measure this dependence at constant pressure and length but in this case it is necessary to introduce the corresponding corrections. The corrections include such thermomechanical coefficients as iso-baric volumetric expansion coefficient, the thermal pressure coefficient or the pressure coefficient of elastic force at constant length 22,23,42). 

Often for solids, linear thermal expansion coefficients, a, = (1 /L) x (.9L/dT)P, are tabulated. For an isotropic substance (the same in all directions), we can relate aL to the volumetric thermal expansion coefficient, defined in Eq. (8), by considering a cube with V = L ... 

Here x is the conversion of SiH4. combines the effect of the molar expansion in the deposition process as well as the change in the volumetric flow and the dispersion coefficient, D, with temperature. At low pressures and small Re in LPCVD reactors the dispersion occurs mainly by molecular diffusion, therefore, we have used (D/D0) = (T/T0)l 65. e is the expansion coefficient and the stoichiometry implies that e = (xi)q, the entrance mole fraction of SiH4. The expansion coefficient, e is introduced as originally described by Levenspiel (33) The two reaction terms refer to the deposition on the reactor wall and wafer carrier and that on the wafers, respectively. The remaining quantities in these equations and the following ones are defined at the end of the paper. The boundary conditions are equivalent to the well known Danckwerts1 boundary conditions for fixed bed reactor models. 

Fig. 5.24. The products of the temperature TL and volumetric expansion coefficient aw as functions of...

Volumetric thermal expansion coefficient of a "rubbery" polymer (T>Tg). 

Local anesthetics. Anesthetics interact with membranes and increase the gel to liquid-crystalline transition of fully hydrated bilayers. They induce a volume expansion which has the opposite effect of HHP and so they antagonize the effect of HHP on membranes fluidity and volume, making membranes more fluid and expanded. The application of HHP to membrane-anesthetic systems may even result in the expulsion to the aqueous environment. The local anesthetic tetracaine (TTC) can be viewed as a model system for a large group of amphiphilic molecules. From volumetric measiuements on a sample containing e.g. 3 mol% TTC, it has been found that the main tansition at ambient pressure shifts to a lower temperature. The expansion coefficient a drastically increases relative to that of the pure lipid system in the gel phase, and the incorporation of the anesthetic into the DMPC bilayer causes an about 15 % decrease of relative to that of the pure lipid system. The addition of 3 mol% TTC shifts the pressure-induced liquid-crystalline to gel phase transition towards somewhat higher pressures. Larger values for the compressibilities are found for both lipid phases by addition of 3 mol% TTC, and there is no apparent difference in the coefficient of compressibility between the gel and liquid-crystalline phases. Comparison of the IR spectra of DMPC and DMPC/TTC mixtures at pH 5.5 as a function of pressure shows an abrupt... 

The volumetric expansion coefficients, calculated from the equation ... 

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