Volume dilatometry

Volume dilatometry measures changes in the specific volume, the reciprocal of density. The degree of crystallinity is calculated using the assumptions that ... 

The simplest volume recovery experiment performed is the down-jump. In this experiment, a material initially above Tg and at equilibrium is subjected to a temperature down-jump to an aging temperature Ta below Tg. The isothermal evolution of volume at T, as indicated by the downward arrow in Figure 1, is monitored with time via length or volume dilatometry. Figure 2 shows tjq)i-cal data replotted from Kovacs data (9) for a series of aging temperatures for poly(vinyl acetate). These curves, called intrinsic isotherms, are plotted as the relative departure from equilibrium 5 versus the logarithm of time, with S defined as... 

Thermomechanical analysis (TMA) measures the deformation of a material contacted hy a mechanical prohe, as a function of a controlled temperature program, or time at constant temperature. TMA experiments are generally conducted imder static loading with a variety of probe configurations in expansion, compression, penetration, tension, or flexime. In addition, various attachments are available to allow the instrument to operate in special modes, such as stress relaxation, creep, tensile loading of films and fibers, flexural loading, parallel-plate rheometry, and volume dilatometry. The type of probe used determines the mode of operation of the instrument, the manner in which stress is apphed to the sample, and the amount of that stress. 

Most of the thermal expansion coefficients were determined by volume dilatometry. Measurement of the buoyancy in a liquid whose density is accuratdy known as a function of temperature is also an accurate method. Some values were determined from refractive index data at different temperatures, assuming the molar refraction to be a constant. Values reported as v dv/dT were converted to dv/dT where necessary by the use of available density data. Linear coefficients of expansion were simply multiplied by three to obtain v Mv/dT, then converted to dv/dT using reported densities. 

A compression mode B tension mode volume dilatometry mode... 

With semicrystalline polymers having moderate to high crystallinity, Tg may be poorly resolved. Other static methods used to measure Tg are the following refractive index gas difiusion/solubility thermal conductivity chain mobility [nuclear magnetic resonance (NMR)] specific volume (dilatometry). Experimentally observed Tg is a function of several variables including molecular weight, plasticizer content, test rate/fi equency, sample size, copolymers/blends, cross-linking, crystallinity, and tacticity. 

Symbolize as y, the proportionality constant between species i and its contribution to the property (i.e., the partial molar volumes in dilatometry, molar absorptivities in spectrophotometry, etc.). Then at any time the instrument reading is... 

For the first case, as the sample is heated, there will be a change in the volume of the sample that can be followed by a technique known as dilatometry. For changes in entropy, use can be made of the fact that AG = 0, and from Eq. (8.51) we find that... 

Dilatometry utilizes the volume change that occurs on polymerization. It is an accurate method for some chain polymerizations because there is often a high-volume shrinkage when monomer is converted to polymer. For example, the density of poly(methyl methacrylate) is 20.6% lower than that of its monomer. Polymerization is carried out in a calibrated reaction vessel and the volume recorded as a function of reaction time. Dilatometry is not useful for the usual step polymerization where there is a small molecule by-product that results in no significant volume change on polymerization. 

During the induction periods caused by adding antioxidants, a small contraction in volume occurred because of the formation of dimers of chloroprene (14). This reaction occurs during the oxidation but was most easily studied by dilatometry in the absence of oxygen. A few values of the initial rate of dimerization of chloroprene, inhibited against polymerization with 2,2,6,6-tetramethylpiperidine-l-oxyl, are given in Table III. Their dependence on temperature is given by... 

A dilatometer consists essentially of a glass tube (the body ), containing the reaction mixture, to which a straight capillary tube is attached (usually, but not always, vertical). The movement of the meniscus of the reaction mixture in the capillary amplifies changes in the volume of the reaction mixture and is measured, as a function of time, with a cathetometer or by some automatic device. Dilatometry has been used for a very long time because it is simple, cheap, convenient and can be made very accurate. 

Dilatometry is a convenient method for measuring polymerization rate. The method is based on a decreasing volume of the examined system along with conversion of monomer to polymer. For simple polymerization, usually carried out in solution in capillary dilatometer, the decrease in volume, Av, is calculated from measurements of the decrease in the level of reacting mixture ho - h = Ah in capillary with radius, r. Using equation ... 

The methods recommended here all require a considerable investment in equipment. The best method available in the absence of suitable magnetic resonance equipment is dilatometry (Hannewijk et al., 1964). Dilatometry takes advantage of the fact that solid fat is more dense than the corresponding liquid oil therefore, the change in volume of a fixed amount of oil with temperature can be used as a precise indication of solids content. Dilatometry remains a recommended method of the AOCS (Method Cd 10-57 Firestone, 1998), but has, to a large extent, been supplanted by the NMR-based... 

Price and Wendorff31 > and Jabarin and Stein 32) analyzed the solidification of cholesteryl myristate. Under equilibrium conditions it changes at 357.2 K from the isotropic to the cholesteric mesophase and at 352.9 K to the smectic mesophase (see Sect. 5.1.1). At 346.8 K the smectic liquid crystal crystallized to the fully ordered crystal. Dilatometry resulted in Avrami exponents of 2, 2, and 4 for the respective transitions. The cholesteric liquid crystal has a second transition right after the relatively quick formation of a turbid homeotropic state from the isotropic melt. It aggregates without volume change to a spherulitic texture. This process was studied by microscopy32) between 343 and 355.2 K and revealed another nucleation controlled process with an Avrami exponent of 3. 

In dilatometry, specific volumes V or densities of materials are measured by use of a pycnometer, dilatometer, or density-gradient column. The data obtained are then interpreted through the equation... 

It is prudent at this point to note that dilatometry does not fulfil the initial requirement of a reaction at constant volume (see Sections 3.2.1 and 3.5.2.1), so the definition of reaction rate needs to be revised to take account of the possibility that the volume may change as the reaction proceeds. Thus, for a first-order reaction, for example,... 

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