Thermodielectric Properties of Bound Water Layers

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Thermodielectric Properties of Bound Water
Layers Guy Serbin Department of Plants, Soils
and Biometeorology Utah State University
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• Introduction
• Bound water layers exist everywhere on Earth-
  coating soils, metals, organic materials, etc.
• Such layers exist at lower energy states than
  that of free water, and are tightly bound to
  solid surfaces.
• Bound water content increases with the specific
  surface area of the material.

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• Bound water content is of interest in the
  following materials (and more (Hasted, 1973)
• Food, plant and animal tissues
• Wood and wood products (incl. paper)
• Rocks, minerals, soils, crystalline powders
• Natural and man-made fibers
• Desiccants
• Inks, paints, adhesives

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Theoretical considerations

• Complex dielectric permittivity
• The complex dielectric permittivity of a medium,
  er(f), describes the energy propagation
  characteristics of the electrical component of
  electromagnetic radiation within that medium.

• Dielectric losses are energy losses due to
  rotational polarization (relaxation), e"rel(f),
  and electrical conductivity (EC), sdc (von
  Hippel, 1954)

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The dielectric permittivities of most materials
may be described via the Cole-Cole (1941) model
where e8 is the dielectric constant at infinite
frequency, es the static dielectric constant
(where f 0 Hz) and b a factor accounting for
possible spread in relaxation frequencies. The
relaxation frequency and time trel are related
via
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• Relaxation losses are greatest at the relaxation
  frequency, frel.
• EC losses are greatest at lower frequencies, with
  the greatest loss occurring at f 0 Hz (DC).
• Where f ltlt frel, e(f) is proportional to the
  viscosity of the medium.
• frel is inversely related to viscosity.
• Viscosity is inversely proportional to
  temperature.
• As f increases toward frel, e(f) will begin to
  decrease, with the greatest decreases occurring
  in the vicinity of frel.

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• Soil elements affecting bulk soil dielectric
  permittivity
• Soil solids- dry minerals and organic matter in
  soils, with dielectric constants usually ranging
  between 3-8 and low losses.
• Air, with a dielectric constant of 1.00058-9
• Water content, composed of free water, or water
  which is not rotationally hindered by forces
  acting on it from mineral surfaces and bound
  water, which is bound to soil solid surfaces and
  exists at a lower energy state than free water.
  Bound water also relaxes at much lower
  frequencies than does free water.
• Soil salinity, which will affect dielectric
  losses and bind water molecules to dissolved ions.

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Free water dielectric behavior Dielectric
permittivity of water as predicted via the
Cole-Cole (1941) model and measured via network
analyzer at 5, 25 and 55C.
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Soil texture and dielectric properties- As the
specific surface area of a soil or medium
increases more water will be bound to solid
surfaces, thus clay soils will have lower
dielectric constants than sandy soils.
From Hallikainen et al. (1985)
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Bockris et al. (1966) thermodielectric models
Model A accounts for simple rotation of an
adsorbed water molecule within a dielectric
layer. Model B accounts for the energy necessary
to move a water molecule from one layer to
another.
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Bockris et al. (1966) Model A Model A allows for
calculation of the relaxation times of bound
water via temperature and the activation enthalpy
and entropy via (Bockris, et al., 1966 Hasted
1973)
where hP is Plancks constant, K is Boltzmanns
constant, T is the temperature in Kelvins, R is
the molar gas constant DSA,t and DHA,t are the
entropy and enthalpy of activation for dielectric
relaxation, respectively.
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Entropies and enthalpies of activation for
dielectric relaxation (Bockris et al., 1966)
Hydrogen bond energy DH19 kJ/mole (Hasted,
1973) Italicized values denote calculated values
using either an average value or from Model B.
CRC Handbook of Physics and Chemistry Effective
of H-bonds denotes an equivalent energy required
to break x H-bonds, not the actual number of
H-bonds each molecule experiences
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Bockris et al. (1966) Model B The Morse equation
for potential energy Up, as a function of the
dissociation energy, De, is given via
where the constant aB is given via
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the ground state vibration frequency fe is given
via
the effective or reduced mass of a diatomic
molecule meff is given via (Atkins, 2000)
where m1 and m2 are the masses of two atoms or
molecules and ae is the equilibrium distance
between two molecules.
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Bockris et al. (1966) model B potential energy
environment from a solid surface and outwards-
bound and free water
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The potential energy wells of the bound water
layers may then be used to calculate the heat of
wetting for a given material as a function of its
surface area. The total heat of wetting per mole
of water bound is given via
where DHL1 and DHL2 denote the local heats of
wetting for the first and second bound water
layers, respectively.
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Experimental evidence of bound water
thermodielectric significance Two different
soils, two different thermodielectric responses
(Serbin, 2001)
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Thermodielectric properties of starch (Jones and
Or, 2002)
Water content (wet basis)
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• Conclusions
• The thermodielectric behavior of bound water can
  have a significant effect in high surface area
  media on the dielectric properties at microwave
  frequencies.
• The variations in Brocko Loam 10 suggest that a
  discrete quantity of energy is required for bound
  water release. Thermodielectric bound water
  release and resorption appear to have hysteretic
  behavior.
• Bound water release effects appear to be visible
  mainly at lower water contents as at higher water
  contents these effects appear to be masked by the
  thermodielectric behavior of free water.
• Further research is needed to properly model the
  thermodielectric properties of porous media.