Dielectric capacitance measurements

Figure 22-5. Electrical bridge (AC) for dielectric capacitance measurement.

The measurement of surface forces calls for a rigid apparatus that exhibits a high force sensitivity as well as distance measurement and control on a subnanometre scale [38]. Most SFAs make use of an optical interference teclmique to measure distances and hence forces between surfaces. Alternative distance measurements have been developed in recent years—predominantly capacitive techniques, which allow for faster and simpler acquisition of an averaged distance [H, 39, 40] or even allow for simultaneous dielectric loss measurements at a confined interface. 

Capacitance measurements are quite simple. A typical drawback is the need of coaxial cables that introduce a thermal load which is not negligible in low-power refrigerators. On the other hand, capacitance bridges null the cable capacitance. Multiplexing is more difficult than for resistance thermometers. In principle, capacitors have low loss due to Joule heating. This is not always true losses can be important, especially at very low temperatures. Dielectric constant thermometers have a high sensitivity capacitance differences of the order of 10-19F can be measured. 

Capacitive Measuring is based on detecting changes in the dielectric constant as a result of changing gas concentration. These sensors are mostly used for measuring humidity, but can also detect C02. One major drawback of these systems is... 

The macroscopic dielectric constant of PS is very sensitive to the frequency range investigated. For very high frequencies the dielectric constant can be obtained by optical measurements. In this regime the effective medium approximation has been found to be an adequate description [Th3]. For lower frequencies the dielectric constant e is commonly obtained by capacitance measurements of metal/PS/ Si structures. AC conductivity measurements of such structures indicate a hop-... 

D had a large experimental uncertainty, but is nevertheless close to the later result of 4.16 0.4 D (Kulakowska et al. 1974), obtained from capacitance measurements of a solution in dioxane. The diffraction method has the advantage that it gives not only the magnitude but also the direction of the dipole moment. Gas-phase microwave measurements are also capable of providing all three components of the dipole moment, but only the magnitude is obtained from dielectric solution measurements. 

When applying an alternating electric field to a polymer placed between two electrodes, the response is generally attenuated and the output current is out of phase compared with the input voltage. This response stems from the polymer s capacitive component and its conductive or loss component, as represented by a complex dielectric permittivity measured frequencies f, and temperatures T ... 

An ECT system is composed of three basic components (1) a capacitance sensor, (2) a data acquisition system, and (3) a computer system for reconstruction and viewing. Figure 1 is a sketch of the ECT system with all three components (Warsito and Fan, 2003). The capacitance sensor is made of nr capacitance electrodes distributed around the wall of the process vessel. The ne capacitance electrodes provide up to ne(ne—1)/2 combinations of independent capacitance measurements between the electrode pairs. The capacitance measurements are related to the local dielectric constant (permittivity) filling the process vessel between electrode pairs (Figure 2) (Warsito and Fan, 2001b). The relation between the electric potential and the permittivity distributions follows Poisson equation shown in Equation (1). 

From the above equation, the measured capacitance between the source and the detector electrodes of the electrode pair i is determined from the given dielectric constant (permittivity) distribution of the medium under investigation. The processes of finding the capacitance for a given permittivity distribution is referred to as the forward problem. On the other hand, the process of finding the permittivity distribution from a set of capacitance measurements is referred to as the inverse problem. 

Equipment is available that is based on the capacitance measurement of a dielectric medium. Any change in the dielectric constant due to skin surface hydration verification alters the capacitance of... 

Dielectric spectroscopy or culture capacitance measurement is used as an on-line, non-invasive method for biomass estimation (see the chapter by Sonnleitner in this issue - the section on electrical properties) and responds mainly to living cells [43,44]. Observed difficulties in using the signal as a pure biomass concentration sensor, i.e. deviations from the simple correlation with cell density, were attributed to dependencies on the physiological state [43], and could be used to discriminate different populations in yeast cultures [45]. Connections with morphological features could be found for budding yeast... 

The limitations of capacitance measurements in undoped a-Si H have resulted in a greater emphasis on measurement techniques which use the shift of with a trapped space charge (Eq. (4.18)). An example is the field effect experiment, which is of special interest because it was the first technique used to obtain N E) in a-Si H (Madan, LeComber and Spear 1976). The experimental configuration is shown in Fig. 4.19. A voltage across the dielectric layer induces a space charge Q = C Vj in the a-Si H film, where is the capacitance of the dielectric. The Fermi energy in the a-Si H near the interface... 

The use of capacitance measurement is based upon the principle that the concentration changes as particles settle through a suspension and will alter the effective dielectric constant between the sensing electrodes. A complete capacitance transducer consists of capacitance sensing electrodes together with capacitance sensing electronics, which is essentially a capacitance to voltage converter. 

Experimentally, the polarity of molecules is measured indirectly by measuring the dielectric constant, which is the ratio of the capacitance of a cell filled with the substance to be measured to the capacitance of the same cell with a vacuum between the electrodes. Orientation of polar molecules in the electric field partially cancels the effect of the field and results in a larger dielectric constant. Measurements at different temperatures allow calculation of the dipole moment for the molecule, defined as... 

The use of a small electrolyte covered resist area around the microelectrode is essential when capacitance measurements are performed, as the resist capacitance is parallel to the electrode capacitance. With a specific resistance of a = 1012 LI cm and a dielectric constant of e = 1.5 for the resist, and assuming a typical electrode capacitance of 10pFcm 2 with a 50 tm electrode, an error of 5% is obtained, if the electrolyte covered surface is 10 3cm2 (/=1000Hz) [88]. Thus, for capacitance measurements, the use of nanoliter droplets is essential. 

Dielectric constant measurements were performed with an automatic Hewlett Packard (HP-4270A) capacitance bridge on 2.5 micron low molecular weight SPI-100 films on Al-wafers. A second Al-electrode was sputtered on to the polyimide and patterned with Shipley 1470 photoresist to provide a pattern of dots varying in diameter from. 050 to. 200 inches (1.3-5.1 mm) (see Figure 3). 

The reliability of dynamic film thickness determinations by capacitance measurements is an open question, principally because there are no absolute standards by which to judge. In their investigation of elastohydrodynamic lubrication, Archard and Kirk [6] determined film thicknesses over the range 20 to 1000 nm the uncertainty of their determinations ranged from 20 nm for films of the order of 20-50 nm thick to 250 nm for films 750-1000 nm thick. Crook s comparisons of film thicknesses determined by his two capacitance methods indicated an uncertainty of 200 nm [8]. Orcutt reported that the voltages required for his capacitance measurements exceeded the dielectric strength of the oil film for thicknesses less than 150 nm [10]. 

Two approaches are proposed to resolve this difficulty. The first is based on generation of a high-purity acoustic field in a spherical, unharmonic resonator, and the second is based on comparison of a set of transducers with limited but overlapping dynamic ranges. In the second approach, simultaneous measurement of a broadband signal produces an accurate characterization over the entire range. Candidates for sensor fabrication include solid dielectric capacitive sensors, piezoelectric transducers, and high-temperature lithium niobate or quartz transducers. 

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