Isothermal power compensation

Chapter 9, by Kiraly (Hungary), attempts to clarify the adsorption of surfactants at solid/solution interfaces by calorimetric methods. The author addresses questions related to the composition and structure of the adsorption layer, the mechanism of the adsorption, the kinetics, the thermodynamics driving forces, the nature of the solid surface and of the surfactant (ionic, nonionic, HLB, CMC), experimental conditions, etc. He describes the calorimetric methods used, to elucidate the description of thermodynamic properties of surfactants at the boundary of solid-liquid interfaces. Isotherm power-compensation calorimetry is an essential method for such measurements. Isoperibolic heat-flux calorimetry is described for the evaluation of adsorption kinetics, DSC is used for the evaluation of enthalpy measurements, and immersion microcalorimetry is recommended for the detection of enthalpic interaction between a bare surface and a solution. Batch sorption, titration sorption, and flow sorption microcalorimetry are also discussed. 

The two basic types of reaction calorimeters commonly used for safety assessments are isothermal (including both heat flow and power compensation calorimeters) and adiabatic. 

As mentioned above, titration methods have also been adapted to calorimeters whose working principle relies on the detection of a heat flow to or from the calorimetric vessel, as a result of the phenomenon under study [195-196,206], Heat flow calorimetry was discussed in chapter 9, where two general modes of operation were presented. In some instruments, the heat flow rate between the calorimetric vessel and a heat sink is measured by use of thermopiles. Others, such as the calorimeter in figure 11.1, are based on a power compensation mechanism that enables operation under isothermal conditions. 

Fig. 8.2 Main heat-flow rates that have to be considered in heat-flow, heat-balance and power-compensation reaction calorimeters running under strictly isothermal conditions [4]. The heat-flow rates inside a Peltier calorimeter are analogous (compare with Fig. 8.1). The direction of the heat-flow arrows corresponds to a positive heat-flow rate. For explanation of the different heat-flow rates, see the text.

The term differential scanning calorimetry has become a source of confusion in thermal analysis. This confusion is understandable because at the present time there are several entirely different types of instruments that use the same name. These instruments are based on different designs, which are illustrated schematically in Figure 5.36 (157). In DTA. the temperature difference between the sample and reference materials is detected, Ts — Tx [a, 6, and c). In power-compensated DSC (/), the sample and reference materials are maintained isothermally by use of individual heaters. The parameter recorded is the difference in power inputs to the heaters, d /SQ /dt or dH/dt. If the sample is surrounded by a thermopile such as in the Tian-Calvet calorimeter, heat flux can be measured directly (e). The thermopiles surrounding the sample and reference material are connected in opposition (Calvet calorimeter). A simpler system, also the heat-flux type, is to measure the heat flux between the sample and reference materials (d). Hence, dqjdi is measured by having all the hot junctions in contact with the sample and all the cold junctions in contact with the reference material. Thus, there are at least three possible DSC systems, (d), (c), and (/), and three derived from DTA (a), [b), and (c), the last one also being found in DSC. Mackenzie (157) has stated that the Boersma system of DTA (c) should perhaps also be called a DSC system. 

C) True Isothermal (i.e. both in space and in time) or extended isothermal (i.e. only isothermal in space) calorimeters Tq follows Ts these are proportional systems and include phase-change, power-compensation and heat-flowmeter calorimeters. 

Recrystallization time is very useful for the development of processing times for recrystallization upon cooling from the melting temperature. Recrystallization time is measured in an isothermic experiment in which the material is cooled to a predefined temperature and then held there iso-thermally until the recrystallization is complete. The time it takes to recrystallize is measured. A slight shift in mold temperature often saves time, thus increasing manufacturing throughput. The sensitivity and temperature control of a power-compensation DSC is ideal for this experiment (Fig. 9). 

Figure 9 The three curves displayed are the same sample quickly cooled to slightly different temperatures and then held isothermally until fully crystallized. This is an example of the type of resolution power compensation DSC is known for. This information may have been used to optimize a process.

Figure 9.7 The measured functions from Figure 9.6 shifted and tilted for zero heat flow rate in isothermal equilibrium (power-compensated DSC heating rate lOKmin ).

Garcia-Fuentes, L. Bar6n, C. Mayorga. O.L. (2008) Influence of dynamic power compensation in an isothermal titration microcalorimeter. Anal, Chem. 70, 4615-23. 

Figure 2.40 shows an isothermal crystallization curve of a high-density polyethylene sample recorded by a Perkin-Elmer DSC7 (see Fig. 2.41 for Avrami plots). In the study of isothermal crystallization, the power compensation DSC is the preferred instrument among the presently available commercial DSCs, because the temperature difference between the sample and the reference cells is negligible, as described in Section 2.3. 

DSC (Differential Scanning Calorimetry) has also been used in cement science investigations to some extent. It is based on a power compensated system. In this technique the reference and the sample imder investigation are maintained at a constant temperature throughout the heating schedule. The heat energy required to maintain the isothermal condition is recorded as a function of time or temperature. There are some similarities between DTA and DSC ineluding the appearance of thermal curves. DSC can be used to measure the heat capacities of materials. DSC measures directly the heat effects involved in a reaction. 

The calorimetric techniques for measuring heats of mixing two fluids can be classified into their mode of measurement and their principle of heat detection. The isothermal displacement calorimetry will refer to a static mode and flow calorimetry, to a dynamic mode . The principles of heat detection in the following examples will be power compensation or heat flux determination. 

The small furnaces of this system can be heated or cooled at very low rates to very high rates and are ideal for a range of different techniques, particularly fast scan DSC. Power-compensated DSC also permits true isothermal operation, since under constant temperature conditions both the sample and furnace are held isothermaUy. The temperature range of... 

The die land thickness differences can be compensated by using different land lengths such that the speed of the emerging melt is constant, resulting in a uniform product. If we assume a power-law viscosity model, a uniform pressure in the manifold and an isothermal die and melt, the average speed of the melt emerging from the die is... 

A summary of intraparticle transport criteria is given in Table 7.2. The most general of the criteria, 5(a) of Table 7.2, ensures the absence of any net effects (combined) of temperature and concentration gradients but does not guarantee that this may not be due to a compensation between heat- and mass-transport rates. (In fact, this is the case when y/f ). It may therefore be the most conservative general policy to see that the separate criteria for isothermality are met, for example, by the combination of 3 and 5(c), or of 3 and 4 in Table 7.2. The presentations of Table 7.2 deal with power-law kinetics only more complicated issues, such as what to do with complex kinetics or reactions involving volume change, have also been treated in the literature and are summarized by Mears [reference 5(b) in Table 7.2]. 

The isothermal method employs a similar Wheatstone s bridge circuit to the earlier method. However, the compensator is replaced by a fixed resistor, and the voltmeter is replaced by a feedback circuit (17) which governs the electrical power supplied to the catalytic element. In this way the heat liberated during reaction is sensed by the feedback circuit and the electrical power is reduced to maintain the element at a constant temperature. Thus, if P is the electrical power required to maintain the element at... 

For adiabatic-isothermal calorimeters, it is assumed, that (Tav -To) = 0 and the first term on the left-hand side of Eq. (3.82) is neglected. The thermal power P2(() is used to compensate Pi (7). 

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