Theory and Fundamental Principles

Dielectrics and dielectric properties of materials are defined, and the fundamental relationships of dielectric properties with electromagnetic energy are discussed. The dielectric constant and the dielectric loss factor are components of the complex relative permittivity, which is also explained. The dielectric constant is associated with the ability of a material to store energy in the electric field in the material, and the loss factor is associated with the ability of the material to absorb or dissipate energy, that is, to convert electric energy into heat energy. The variation in the dielectric properties of materials-with respect to the frequency of the fields to which they are subjected, the temperature of the materials, and the density of the materials-is discussed. Because water is an important component of agricultural materials, the dielectric behavior of water is included in the discussion.

Keywords

Density; dielectric constant; dielectric loss factor; dielectric properties; electromagnetic energy; frequency; permittivity; temperature

The dielectric properties of materials are those electrical characteristics that determine the interaction of materials with electric fields. In radio-frequency (RF) and microwave heating of foods, agricultural products, and other dielectric materials, it is the interaction of the materials with the electric field component of the electromagnetic waves that produces the desired heating effects (Nelson and Trabelsi, 2014). Strictly speaking, radio frequencies range from about 10 kHz to about 100 GHz. These are the frequencies practicable for radio transmission; they span that portion of the electromagnetic spectrum between the audio frequencies and the infrared region (IEEE, 1990). Thus, the RF range includes those frequencies used for microwave heating. However, because RF dielectric heating applications were developed first in the frequency range of about 3-40 MHz, and microwave heating applications came later, there is a tendency-particularly in the food industry-to refer to the lower frequency applications as RF dielectric heating, and to refer to dielectric heating at microwave frequencies, about 1 GHz and higher, as microwave heating. Frequencies for RF communication are further designated as high frequency (HF, 3-30 MHz), very-high frequency (VHF, 30-300 MHz), ultra-high frequency (UHF, 300-3000 MHz), super-high frequency (SHF, 3-30 GHz), and extremely-high frequency (EHF, 30-300 GHz).

1.1 Dielectric Properties of Materials

Dielectrics are a class of materials that are poor conductors of electricity, in contrast to materials such as metals that are generally good electrical conductors. Many materials, including foods, living organisms, and most agricultural products, conduct electric currents to some degree, but they are still classified as dielectrics. The electrical nature of these materials can be described by their dielectric properties, which influence the distribution of electromagnetic fields and currents in the region occupied by the materials, and which determine the behavior of the materials in electric fields. Thus, the dielectric properties determine how rapidly a material will warm up in RF or microwave dielectric heating applications. Their influence on electric fields also provides a means for sensing certain other properties of materials, which may be correlated with the dielectric properties, by nondestructive electrical measurements. Therefore, dielectric properties of agricultural products may be important for quality-sensing applications in the agricultural industry as well as in dielectric heating applications.

A few simplified definitions of dielectric properties are useful in discussing their applications. A fundamental characteristic of all forms of electromagnetic energy is their propagation through free space at the velocity of light, . The velocity of propagation of electromagnetic energy in a material depends on the electromagnetic characteristics of that material and is given as:

=1µe (1.1)

where is the magnetic permeability of the material and is the electric permittivity. For free space, this becomes:

=1µoeo (1.2)

where o and o are the permeability and permittivity of free space. Most food and agricultural products are nonmagnetic, so their magnetic permeability has the same value as o. These materials, however, have different permittivities when compared to free space. The absolute permittivity a can be represented as a complex quantity,

a=e´a-jea? (1.3)

where =-1. The complex permittivity relative to free space is then given as:

r=eaeo=e´r-jer? (1.4)

where o is the permittivity of free space (×10-12farad/m); the real part ´r is called the dielectric constant, and the imaginary part r? is called the dielectric loss factor. These latter two quantities are the dielectric properties of practical interest, and the subscript will be dropped for simplification in the remainder of this book. The dielectric constant ´ is associated with the ability of a material to store energy in the electric field in the material, and the loss factor ? is associated with the ability of the material to absorb or dissipate energy, that is, to convert electric energy into heat energy. The dielectric loss factor, for example, is an index of the tendency of the material to warm up in a microwave oven. The dielectric constant is also important because of its influence on the distribution of electric fields. For example, the electric capacitance of two parallel conducting plates separated by free space or air will be multiplied by the value of the dielectric constant of a material if the space between the plates is filled with that material.

It should also be noted that =e´-je?=|e|e-jd where is the loss angle of the dielectric. Often, the loss tangent,tand=e?/e´, or dissipation factor, is also used as a descriptive dielectric parameter, and sometimes the power factor, d/1+tan2d, is used. The ac conductivity of the dielectric in S/m is =?eoe?, where =2pf is the angular frequency, with frequency in hertz (Hz). In this book, ? is interpreted to include the energy losses in the dielectric due to all operating dielectric relaxation mechanisms and ionic conduction.

1.2 Variation of Dielectric Properties

The dielectric properties of most materials vary with several influencing factors (Nelson, 1981, 1991; Nelson and Datta, 2001). In hygroscopic materials such as agricultural products, the amount of water in the material is generally a dominant factor. The dielectric properties also depend on the frequency of the applied alternating electric field, on the temperature of the material, and on the density, composition, and structure of the material. In granular or particulate materials, the bulk density of the air-particle mixture is another factor that influences the dielectric properties. Of course, the dielectric properties of materials are dependent on their chemical composition and especially on the presence of mobile ions and the permanent dipole moments associated with water and any other molecules making up the material of interest.

1.2.1 Frequency Dependence

With the exception of some extremely low-loss materials, that is, materials that absorb essentially no energy from RF and microwave fields, the dielectric properties of most materials vary considerably with the frequency of the applied electric fields. This frequency dependence has been discussed previously (Nelson and Datta, 2001; Nelson, 1973, 1991). An important phenomenon contributing to the frequency dependence of the dielectric properties is the polarization, arising from the orientation with the imposed electric field, of molecules which have permanent dipole moments. The mathematical formulation developed by Debye to describe this process for pure polar materials (Debye, 1929) can be expressed as:

=e8+es-e81+j?t (1.5)

where 8 represents the dielectric constant at frequencies so high that molecular orientation does not have time to contribute to the polarization, s represents the static dielectric constant, that is, the value at zero frequency (dc value), and is the relaxation time, the period associated with the time for the dipoles to revert to random orientation when the electric field is removed. Separation of Eq. (1.5) into...