Calorimeter AC

Figure 7.31 Construction principle of an AC calorimeter (according to Sullivan and Seidel, 1968).

The free-standing film is a very interesting physical system, in which the sample thickness can very easily be varied from two to a few hundred molecular layers. It can be used to test the theories of two-dimensional melting, the evolution of phase transitions as a function of the dimensionality of the system, and to investigate substrate-free, two-dimensional transitions and the effect of free surfaces [119]. In order to analyze the small heat capacity anomalies associated with phase transitions in very thin films, a new AC calorimeter technique has been set up [123]. Thus detailed calorimetric studies of free-standing liquid crystal films have been performed near the SmBhex-SmA transition of several compounds [ 124-126]. 

The obtained A 7 a() value and the energy equivalent of the calorimeter, e, are then used to calculate the energy change associated with the isothermal bomb process, AE/mp. Conversion of AE/ibp to the standard state, and subtraction from A f/jgp of the thermal corrections due to secondary reactions, finally yield Ac f/°(298.15 K). The energy equivalent of the calorimeter, e, is obtained by electrical calibration or, most commonly, by combustion of benzoic acid in oxygen [110,111,113]. The reduction of fluorine bomb calorimetric data to the standard state was discussed by Hubbard and co-workers [110,111]. 

Figure 2.36 Calorimetry results obtained in a bomb calorimeter. Reprinted with permission from J. E. Mark, Physical Chemistry of Polymers, ACS Audio Course C-89, American Chemical Society, Washington, DC, 1986. Copyright 1986, American Chemical Society.

M.R. Christy, R.V. Petrella, and JJ. Penkala, Controlled-Atmosphere Cone Calorimeter, Fire and Polymers II, ACS Symposium Series 599, Washington, DC, 1995. 

Regenass, W., Thermal and Kinetic Design Data from a Bench Scale Heat Flow Calorimeter, In Chemical Reaction Engineering—Houston, ACS Symposium Series (D. Luss and V. W. Weekman, eds.), p. 37 (1978). 

The polysiloxanes were characterized by Fourier transform-IR (FTIR) spectroscopy, H and Si NMR spectrometry, and by GPC. AC conductivities of the polymer electrolytes were measured under dry helium by using an automatic capacitance bridge (General Radio Corporation). Glass transition (Tg) and melt (TJ temperatures were recorded on a differential scanning calorimeter (Perkin Elmer DSC-4). More detailed experimental procedures are published elsewhere (9, 12). 

The adoped value for the Curie point, T = 631 K, is from the study of Connelly et al. (9), using an ac calorimetric method to measure relative heat capacity vlaues, and Vollmer et al. (6) using a high temperature adiabatic calorimeter. 

If we deal with a bomb calorimeter so that the volume is constant, rather than the pressure, the argument is unchanged. In all of the equations A/f s are simply replaced by AC/ s, and C s by C s. 

Huth H, Minakov AA, Serghei A, Kremer F, Schick C (2007) Differential ac-chip calorimeter for glass transition measurements in ultra thin polymeric films. Euro Phys J Special Topics 141 153-160... 

The molecular mobility in the polymers was determined by dielectric studies. Polymer films 300—500 pm thick cast between glass plates at room temperature were used. Dielectric measiu ements were made using the E8-4 ac bridge within a broad temperature range. The superimposed frequency of the external electric field was 1 kHz. The dependence of the coefficient of transmission of the cured polyester resin on the OP-10 content was determined using the FEC-56M photoelectric calorimeter. 

Here, we will focus on a specific high-resolution calorimetric technique, i.e. nonadiabatic scanning calorimetry. This technique implies a calorimeter apparatus capable of operating in the ac as well as in the relaxation mode. The combination of these modes makes it possible to distinguish between the continuous and discontinuous transitions. 

In order to determine precisely the latent-heat values, the calorimeter has to be operated in the relaxation mode. In the most recent version of this mode, the bath is accurately stabilized and then a linearly ramped power is applied to the sample [31], This mode of operation is sensitive not only to the continuous but also to the discontinuous part of the enthalpy change, i.e. the latent heat L. Hence, L can be quantitatively determined by subtracting the integrals of the resulting Cp and Cp ff anomalies of the ac and relaxation modes, respectively ... 

From the measured heating curve and known properties of the calorimeter, reactants, and products, it is possible to evaluate the standard molar enthalpy of combustion, AcH°, of the substance of interest at a particular temperature called the reference temperature, Tref. (Tref is often chosen to be 298.15 K, which is 25.00 °C.) With careful work, using temperature measurements with a resolution of 1 x 10 K or better and detailed corrections, the precision of Ac//° can be of the order of 0.01 percent. 

From the above considerations, it should be clear that running an adiabatic scanning calorimeter in the constant heating (or cooling) modes makes it possible to determine latent heats when present and distinguish between first-order and second-order phase transitions. On the basis of Cp = P/t, it is also possible to obtain information on the pretransi-tional heat capacity behavior, provided one is able to collect sufficiently detailed and ac-... 

Fire calorimetry (4,11,20,25) (see under Testing to Obtain Engineering Data) is used to obtain HRP as the slope of heat release rate versus external heat flux or as the ratio x c /hg = HOC/Lg, from individual measurements. Table 7 contains HOC and x (=HOC//ic ) for common polymers while HRP are listed in Table 8. The heat of combustion of the fuel gases, Ac , was measured separately in a p5Tolysis-combustion flow calorimeter (26) (see section on The Pyrolysis-Combustion Flow Calorimetry). 

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