Dilatometry

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, 

Dilatometry has been applied, for example, in the study of polymerisation or depolymerisation reactions that can lead, respectively, to a decrease or increase in volume [59]. Recently, Mayr and colleagues used this technique to study the kinetics of hetero Diels-Alder reactions, namely [2+ + 4] cycloadditions of iminium ions with 1,3-dienes [60]. 

Sample holders have most often tubular or rod shapes and are made of quartz (for temperatures up to 1100 °C), alumina (up to 1680 °C), graphite (up to 2800 °C) or tungsten (up to 3400 °C). The dilatometry measurements include initially both sample and holder dimensional changes, later on the results being corrected using reference materials [22]. 

The measurement of dimensional or volume changes can be used in appropriate instances to observe the progress of a solid state reaction. Line2ur expansion can be measured by dial gauges, micrometers, interferometer, telescopes, linear differential transformers and from X-ray patterns. Except for the X-ray techniques, the reaction can be studied in situ. Non-isotropic materials probably require measurements in several orientations. 

A dilatometer constructed by Sauer is shown in Fig. 45. The sensing element is a linear variable differential transformer, whose rectified output is recorded directly. A pivot arm connects the transformer (A) to the bearing arm (B) and a micrometer screw allows for calibration and adjustment of the transformer. By adjustment of the compensating screw, the pivot arm can be moved so that the contact point (B) is exactly one sample length from the fulcrum. Temperatures above and below ambient can be obtained by circulating gas round the specimen. 

Volume expansion is most easily measured by fluid displacement and is particularly suitable for organic materials which are not generally hard or highly oriented. In an apparatus devised by Loasby , the sample is enclosed in a bellows and the intervening space filled with oil. Expansion is recorded as a linear motion of the bellows. The sample size is made as large as possible so that it is just out of contact with the bellows at the point of maximum expansion. Smaller pieces can be used instead of a single specimen. This allows a more rapid approach to thermal equilibrium, but at the expense of sensitivity. 

Dannis used a different optical method. The movement of a mirror, partially 

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Mittemeijer E J, Gent A V and der Schaaf P J V 1986 Analysis of transformation kinetics by nonisothermal dilatometry Metall. Trans. A 17 1441... 

As-polymerized PVDC does not have a well-defined glass-transition temperature because of its high crystallinity. However, a sample can be melted at 210°C and quenched rapidly to an amorphous state at <—20°C. The amorphous polymer has a glass-transition temperature of — 17°C as shown by dilatometry (70). Glass-transition temperature values of —19 to — 11°C, depending on both method of measurement and sample preparation, have been determined. 

Ceramic bond formation and grain growth by diffusion are the two prominent reactions for bonding at the high temperature (1100 to 1370°C, or 2000 to 2500°F, for iron ore) employed. The minimum temperature required for sintering may be measured by modern dilatometry techniques, as well as by differential scanning calorimetry. See Compo et al. [Powder Tech., 51(1), 87 (1987) Paiticle Characterization, 1, 171 (1984)] for reviews. 

The procedures of measuring changes in some physical or mechanical property as a sample is heated, or alternatively as it is held at constant temperature, constitute the family of thermoanalytical methods of characterisation. A partial list of these procedures is differential thermal analysis, differential scanning calorimetry, dilatometry, thermogravimetry. A detailed overview of these and several related techniques is by Gallagher (1992). 

Temperature An examination has been made of the effect of temperature on the structural changes in polymer films produced from the three vehicles described earlier s. Three methods were used dilatometry, water absorption and ionic resistance. 

It was concluded that dilatometry was the most reliable method and water absorption is difficult to determine. Both methods use appreciable quantities of film, which contain both D and / areas. Resistance measurements, however, can be carried out on small areas of film and the relative properties of D and / areas studied. 

Using dilatometry in parallel with cyclic voltammetry (CV) measurements in lmolL 1 LiC104 EC-l,2-dimethoxy-ethane (DME), Besenhard et al. [87] found that over the voltage range of about 0.8-0.3 V (vs. Li/Li+), the HOPG crystal expands by up to 150 percent. Some of this expansion seems to be reversible, as up to 50 percent contraction due to partial deintercalation of solvated lithium cations was observed on the return step of the CV. It was concluded [87] that film formation occurs via chemical reduction of a solvated graphite intercalation compound (GIC) and that the permselective film (SEI) in fact penetrates into the bulk of the HOPG. It is important to repeat the tests conducted by Besenhard et al. [87] in other EC-based electrolytes in order to determine the severity of this phenomenon. 

Further mechanistic evidence was provided by Benkeser and Krysiak658, who determined the effects of added salts and water on the rates of cleavage of xylyltrimethylsilanes by p-toluenesulphonic acid in acetic acid at 25 °C, the progress of the reaction being followed by dilatometry the first-order rate coefficients are given in Table 227. Clearly the addition of water retards the reaction, as... 

The kinetics of cleavage of some of these compounds have been measured by dilatometry and in other acidic media, and the rate coefficients and relative rates are given in Table 233658, 673, 686, 687. It can be seen that there is relatively little variation in the spread of rate coefficients with change in the acid and this argues against nucleophilic participation of the acid in the rate-determining step... 

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... 

Kinetic data for the decomposition of diacetone alcohol, from Table 2-3. were obtained by dilatometry. The nonlinear least-squares fit of the data to Eq. (2-30) is shown on the left. Plots are also shown for two methods presented in Section 2.8 they are the Guggenheim method, center, and the Kezdy-Swinbourne approach, right. 

Shrinkage during sintering at high T can be determined experimentally by dilatometry, electrical conductivity, acoustic waves or thermal analysis . 

MSssbauer spectroscopy Electron spin resonance spectroscopy Colorimetry Thermoluminescence Thermal analysis differential thermal analysis, dilatometry... 

Pannetier and Souchay have reported the data below as an example of the application of dilatometry to kinetics studies. 

The experimental determination of density can be carried out by picnometry, density gradient column or by dilatometry. 

The copolymers consist of strictly alternating sequences of diene and olefin. C-NMR measurements Showed the microstructure of the butadiene units in BPR to be exclusively of the trans-1,4 configuration (Figure 8). The isoprene units in isoprene-ethylene copolymer (IER) contain 84 % trans-1,4, 15 % cis-1,4, and 1 % 3,4 structures (Figure 9). Spontaneous crystallization in unstretched BPR samples was detected by dilatometry and confirmed by X-ray diffraction and DSC measurements. The extrapolated equilibrium melting point is about -10 °C. 

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... 

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