156
4 The Dielectric Properties and Dynamic Structure of Water and Ice
The amount of power, P, (in W/m
3 ) that is absorbed by the medium is determined
by the level of absorption of electromagnetic waves by the medium (i.e., heating)
and is given by
P = ε
(ω)ε 0 ωE
2
= σ (ω)E
2
,
(4.15)
where ω = 2πν is the angular frequency, σ (ω) is the dynamic conductivity, 0 is
the permittivity of vacuum, and E is the potential gradient (strength of the electric
field in V/m), induced by the electromagnetic wave. Equation 4.15 means that the
conductivity is a measure of dielectric losses. The higher the conductivity, the more
effective the absorption of electromagnetic waves.
The typical operating frequency of the domestic microwave oven is 2.45 GHz.
Microwaves are especially good for heating water, because it has a high level of
absorption (the high dynamic conductivity, σ (ω)) in the corresponding frequency
range. Although there is a special defrosting regime in domestic microwave ovens,
ice is quite transparent for microwaves, thus, does not interact with electromagnetic
waves of the corresponding frequency as effectively as water. However, the ice surface
is always covered with a quasi-liquid layer, which effectively absorbs microwaves,
and then transfers the heat to the rest of the ice. Thus the defrosting regime is less
powerful than the normal heating regime to avoid the evaporation of the quasi-liquid
layer prior to heat transfer to the ice volume. Figure 4.10a shows the dielectric
spectra of water at room temperature and at 100
◦ C. The operating frequency of the
domestic microwave oven is shown by the arrow. It lies on the left-hand side of the
Debye relaxation band (see blue bell-shaped contour) and does not correspond to
the maximum adsorption of electromagnetic waves. However, the electromagnetic
wave sources of the higher frequencies are much more expensive, and the usage of
this frequency is not economically viable.
A common misconception is that the microwaves rotate the molecular dipoles of
water, allowing them to move faster and in this way increasing the temperature of the
medium. In fact, the characteristic frequencies of the molecular orientations (both
free and hindered) are much higher than those used in microwave ovens, and lie in
the terahertz frequency range (see Sect. 2.6), thus, cannot be directly responsible for
microwave heating. We showed above that the dielectric relaxation (and therefore
the microwave absorption) is caused by the dynamics of short-lived ionic species
of H 3 O
+ and OH
− , most of which live about 3 ps, although some of them exist
significantly longer, contributing to the static conductivity. The ambipolar diffusion
of interacting ionic species was shown to be responsible for the dielectric response of
water below 0.1 THz (see Sect. 4.5.1), including the operating range of microwave
ovens. Thus, according to the ionic model, the short-lived ionic species are dragged
by the field, heating the environment as shown in Fig. 4.10b. As the ionic species
are surrounded by neutral molecules, they are also dragged, but the main drivers of
heating are ions.
Taking E = 100 V/m (the maximal electric field strength in the domestic
microwave oven), n ± ≈ 1 mol/l, κ = 0.07 N/m, and using (4.9), (4.12), and (4.13),
we get from (4.15) that P ≈ 10 W/cm
3 . Thus, to heat a cup of water (250 ml) from
4 The Dielectric Properties and Dynamic Structure of Water and Ice
The amount of power, P, (in W/m
3 ) that is absorbed by the medium is determined
by the level of absorption of electromagnetic waves by the medium (i.e., heating)
and is given by
P = ε
(ω)ε 0 ωE
2
= σ (ω)E
2
,
(4.15)
where ω = 2πν is the angular frequency, σ (ω) is the dynamic conductivity, 0 is
the permittivity of vacuum, and E is the potential gradient (strength of the electric
field in V/m), induced by the electromagnetic wave. Equation 4.15 means that the
conductivity is a measure of dielectric losses. The higher the conductivity, the more
effective the absorption of electromagnetic waves.
The typical operating frequency of the domestic microwave oven is 2.45 GHz.
Microwaves are especially good for heating water, because it has a high level of
absorption (the high dynamic conductivity, σ (ω)) in the corresponding frequency
range. Although there is a special defrosting regime in domestic microwave ovens,
ice is quite transparent for microwaves, thus, does not interact with electromagnetic
waves of the corresponding frequency as effectively as water. However, the ice surface
is always covered with a quasi-liquid layer, which effectively absorbs microwaves,
and then transfers the heat to the rest of the ice. Thus the defrosting regime is less
powerful than the normal heating regime to avoid the evaporation of the quasi-liquid
layer prior to heat transfer to the ice volume. Figure 4.10a shows the dielectric
spectra of water at room temperature and at 100
◦ C. The operating frequency of the
domestic microwave oven is shown by the arrow. It lies on the left-hand side of the
Debye relaxation band (see blue bell-shaped contour) and does not correspond to
the maximum adsorption of electromagnetic waves. However, the electromagnetic
wave sources of the higher frequencies are much more expensive, and the usage of
this frequency is not economically viable.
A common misconception is that the microwaves rotate the molecular dipoles of
water, allowing them to move faster and in this way increasing the temperature of the
medium. In fact, the characteristic frequencies of the molecular orientations (both
free and hindered) are much higher than those used in microwave ovens, and lie in
the terahertz frequency range (see Sect. 2.6), thus, cannot be directly responsible for
microwave heating. We showed above that the dielectric relaxation (and therefore
the microwave absorption) is caused by the dynamics of short-lived ionic species
of H 3 O
+ and OH
− , most of which live about 3 ps, although some of them exist
significantly longer, contributing to the static conductivity. The ambipolar diffusion
of interacting ionic species was shown to be responsible for the dielectric response of
water below 0.1 THz (see Sect. 4.5.1), including the operating range of microwave
ovens. Thus, according to the ionic model, the short-lived ionic species are dragged
by the field, heating the environment as shown in Fig. 4.10b. As the ionic species
are surrounded by neutral molecules, they are also dragged, but the main drivers of
heating are ions.
Taking E = 100 V/m (the maximal electric field strength in the domestic
microwave oven), n ± ≈ 1 mol/l, κ = 0.07 N/m, and using (4.9), (4.12), and (4.13),
we get from (4.15) that P ≈ 10 W/cm
3 . Thus, to heat a cup of water (250 ml) from