Dielectric-gravimetric measurements

The material presented in this chapter is organized as follows In Sect. 2 the basic experiments necessary for dielectric permittivity measurements is given, followed by an outline of the theory of dielectric polarization, which considers the uncertainties of measurements and gives several examples related to gas adsorption equilibria on microporous solids. In Sect. 3 combined dielectric-manometric and dielectric-gravimetric measurements of adsorption equilibria are considered briefly. In Sect. 4 the pros and cons of dielectric measurements are discussed. A hst of Symbols used is given in Sect. 5 followed by the references cited. 

DIELECTRIC-GRAVIMETRIC MEASUREMENTS OF PURE GAS ADSORPTION EQUILIBRIA... 

Figure 6.25. Experimental setup for combined dielectric-gravimetric measurements of pure gas adsorption equilibria. IFT University of Siegen, 1988.

Examples of combined dielectric-gravimetric measurements will be given in Sect. 3.2. 

Combined dielectric gravimetric measurements of adsorption equilibria Nitrogen (Na, 5.0), methane (CH4, 5.5) and carbon monoxide (CO, 3.7) on pellets AC-20 (Engelhard Process Chemicals, Nienburg) (Fig. 6.28). 

Combined dielectric gravimetric measurements of the uptake curve of hydrogen sulfide (HaS, 1.8) on molecular sieve MS13X (UOP, Erkrath) (Fig. 6.29). 

Measurements of gas solubilities in continuous materials like soft matter or highly viscous liquid polymers filled in the ring slit of the pendulum are normally very slow and may last for days and even weeks. Hence, it is often not easy to decide whether thermod)mamic equilibrium really has been attained. Accompanying gravimetric and / or dielectric impedance measurements can be very helpful to decide this question, cp. Chapts. 3, 6. 

Abstract The physical principles and basic experimental techniques of impedance spectroscopy, i. e. static or frequency dependent dielectric permittivity measurements of sorbent/sorbate systems are given. These measurements can be used to characterize the state of a sorbent material in industrial adsorption processes. Combined with either manometric or gravimetric measurements of adsorption equilibria leading to calibration curves, permittivity measurements also allow fairly simple and quick measurements of gas adsorption equilibria. Kinetic processes and catalytic reactions inside a sorbent/sorbate system also can be observed. Pros and cons of dielectric measurements are discussed. List of Symbols. References. 

Dielectric measurements of gas adsorption systems can be performed fairly quickly, typically within a few seconds [6.3]. Hence the kinetics of adsorption processes being slow on this time scale can be observed. Indeed these processes are sometimes invisible to purely manometric or even gravimetric measurements. As examples we mention internal diffusion, reorientation or catalytically induced chemical reaction processes of admolecules within a sorbent material. The mass of the adsorbed phase normally is constant during processes of this type, whereas the dipole moment of the admolecules and hence their polarization changes, cp. Sect. 3.2. 

Here s is a numerical shape factor being s = 1/3 for simple cubic crystals and freely rotating molecules [6.22, 6.24], For non-polar admolecules (p = 0) numerical values of a = aj gravimetric measurements (cp. examples given in Sect. 3.2). For polar admolecules the same is true at least at low frequencies (v < 1 MHz) of the electric field where often um tton and hence can be neglected compared to Oori- For both types of admolecules numerical data of (a) are between their values for the gas and the liquid phase of the adsorptive and normally depend on the amount adsorbed, i. e. degree of saturation. Hence they can give an indication of the nature of the site where the admolecule is adsorbed and also on the structure of the sorbate phase [6.3]. 

The impedance measurements of this system have been combined with oscillometric-gravimetric measurements leading to both the volume of the swelling polymer and the mass of CO2 sorbed at a given gas pressure, cp. Chap. 5. These combined measurements show that there are nearly linear relations between the dielectric permittivity and the gas pressure as well as the volume of the polymer in the sorption state and the gas pressure, cp. data and Figures given in Sect. 3.2. 

Combined dielectric gravimetric oscillometric measurements of sorption equilibria of methane (CH4, 5.5) in polycarbonate (Goodfellow, UK), cp. Chap. 5, Sect. 3.4, (Figs. 6.30, 6.31). 

Ad 4. Dielectric-gravimetric-oscillometric measurements of sorption equilibria of methane in (swelling) polycarbonate. 

Figure 6.31. Specific volume of polycarbonate (GoodfeUow, UK) swelling due to the sorption of methane (CH4, 5.5) at T = 308 K for pressures up to 4 MPa and static dielectric permittivity (8,) of the (methane loaded) polymer [52, 6.3]. The volume has been determined by combined osciUometiic-gravimetric measurements, cp. Chap. 5. Figures 6.30, 6.31 refer to the same set of combined oscillometric-gravimetric-dielectric experiments [6.3, 6.41].

The maximum pressure to which the gravimetric technique has been applied is about 15 MPa. The volumetric method is very seldom applied above 100 MPa [29]. Bose and co-workers [30] developed a precision dielectric method for the determination of gas-solid adsorption. This method is particularly suitable for adsorption measurements up to 200 MPa actually, adsorption data up to 650 MPa were reported [31]. The great advantage of the dielectric method is that it is self-sufficient up to the highest pressures and does not depend on the availability of compressibility factor values, as in volumetric or gravimetric measurements [29]. Other new, yet less widespread, adsorption measurement techniques include oscillometry [32,33], calorimetry [34,35], and electromagnetic measurements [36,37]. 

We are faced with special problems if the volume of the sample, e.g. of a polymer, is varied by swelling. Sorption on such materials may be investigated by means of a horizontally arranged rotary pendulum [7,8] in combination with gravimetric density determinations [9]. Sophisticated pendulum experiments may be replaced by impedance measurements for the determination of the (frequency-dependent) dielectric constant [10]. 

A simple nondestructive capacitance method is proposed (Adamyan et al, 2006) for the determination of basic PSi parameters such as layer thickness, porosity and dielectric permittivity. The method is based on two comparative measurements of the capacitance of the metal/PSi/single crystalline silicon/metal structure one measurement is taken when there are air-filled pores, while the other measurement involves pores filled by an organic compound with a high value of dielectric permittivity. Comparison of results obtained in Adamyan et al. (2006) by the ball lap and the gravimetric techniques before and after anodization, with the data of capacitance measurements carried out with the same samples prior to their destruction, shows sufficiently good agreement. 

Figure 1.24. Absolute masses (m ) measured by combined dielectric-calorimetric experiments and Gibbs surface excess masses (mj,g) measured manometiically and also gravimetrically of carbon dioxide CO2 (4.5) adsorbed on Wessalite (Degussa DAY) atT= 298 K, [1.54].

Figure 5.14. Training instrument for oscUlometric, volumetric, gravimetric, and dielectric measurements of gas adsorption equilibria in rigid and swelling sorbent materials. The pendulum (left) is covered by a plexiglass vessel allowing direct optical observations of its rotational oscillations.

Combining the dielectric measurements with either manometric, gravimetric or oscillometric measurements of gas adsorption equilibria states, one gets calibration curves allowing one the determination of Gibbs excess adsorbed masses by purely electric measurements which normally can be performed fairly quickly and on site in industrial situations. 

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