Chapter 2: The potential of a novel frequency-response permittivity sensor in measuring soil and water properties

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Chapter 2: The potential of a novel frequency-response permittivity sensor in

measuring soil and water properties.

Naiqian Zhang , Biological and Agricultural Engineering Department, Kansas State University

[email protected]

ABSTRACT

Permittivity is an important property of dielectric materials such as soil and water. Permittivity

describes both conductive and dielectric (capacitive) behaviors of dielectric materials. Various

components in soil (salts, nutrients, organic matter, etc.) and pollutants in water (sediment, nutrients

introduced by fertilizers, pesticides, etc.) have different effects on the conductive and capacitive

behaviors of these dielectric materials. Thus, effectively measuring permittivity may lead to

accurate, quantitative detection of the components and pollutants. Since 2001, we have developed

a novel, frequency-response (FR) permittivity sensor that is capable of measuring both the

conductive and capacitive parameters of dielectric materials. The sensor has been successfully

tested in soils with different levels of water content, salinity, density, and different texture types. It

was also tested in waters with different concentrations of salts. Results of several experiments are

22 Introduction

Permittivity is the ability of a material to resist the formation of electric field in the material, or the

ability to transmit (or “permit”) the electric field. When an external electric field is applied to a

material, dipole molecules in the material tend to align up in the opposite directions. This process of

alignment, called polarization, hinders current flow. The actual amount of total current flowing in the

material is determined by both capacitive and conductive behaviors of the material. Thus,

permittivity can be directly related to electric susceptibility. For example, an increased permittivity of

the medium allows the same charge to be stored with a smaller electric field, leading to an

increased capacitance.

Responses of a material to an external alternating electric field typically depend on the frequency of

the electric field. At low frequencies, the polarity of the electric field changes slowly enough to allow

dipole molecules in the material to be aligned in the opposite directions. At high frequencies, the

dipole orientation cannot follow the change in the polarity of the electric field due to the binding

force between atoms. The applied energy is thus dissipated. This is called dielectric relaxation,

which can be thought of as an elastic response of the material to the applied electric field (Robinson

et al., 2003).

This relaxation process gives rise to a phase lag between the imposed field and the material’s

response to it. This phase lag is a function of the frequency of the imposed field. Because of this

phase lag, permittivity can be expressed in a complex form (Topp et al., 2000).

Another energy dissipation process arises from the electrical conductivity of the media. Conduction

can happen from two sources: surface conduction of electric charges on the solid surfaces in the

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of polarization, relaxation, and conductivity to permittivity are represented as follows (Topp et al.,

2000): o r

_ε

ε

ε

(2) ( ) ( ) ( )

ε

ω

δ

ωε

σ

ω

ε

ω

ε

ω

ε

o DC r

r

r = ′ −

     + ′′ − ′ = ) ( ) ( tan

ω

ε

ωε

σ

ω

ε

δ

where, ε is permittivity (F m-1), εo is permittivity of free space (8.85 x 10-12 F m-1), εr is relative

permittivity, ε’r is the real component of relative permittivity (energy storage due to polarization), ε”r

is the imaginary component of relative permittivity (energy loss due to dielectric relaxation), σDC is

DC electrical conductivity, tanδ _{is loss tangent,} ω _{is angular frequency (rad s}-1_{), and j is} −1.

In summary, permittivity of a dielectric material has three major contributing components: energy

storage due to polarization, energy loss due to relaxation, and energy loss due to conduction. Both

polarization and relaxation properties can be considered capacitive. Thus, permittivity describes

both the capacitive and conductive behaviors of dielectric materials. These behaviors can be used

to measure physical and chemical properties and compositions of dielectric materials in the solid

(including particulate or porous), liquid (including gelatinous), and gaseous phases.

As indicated in Equation (2), for each dielectric material, both the real and imaginary parts of

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permittivity is measured may provide specific information on individual properties of the measured

material.

Permittivity measuring techniques have been developed mainly for detecting properties and

compositions of solid and liquid dielectric materials. Soil serves as an excellent example of

combinations of complex dielectric materials in all phases. Soil is a heterogeneous, particulate,

disperse, and porous medium composed of mineral matter, organic matter, water, and air. The

mineral matter consists of particles that vary in chemical composition as well as in size and shape.

Organic matter is derived from microorganisms such as fungi, bacteria, insects, earthworms, plant,

and animal residuals. Almost all the components in soil affect its permittivity. As a result, it is

possible to measure compositions of soils through permittivity measurement, although it is

challenging to separate the effects of individual components from measured permittivity.

Water also is a good example of dielectric materials. Various substances in water have different

influences on its conductive and capacitive characteristics. Many human health-related waterborne

pollutants have significant effects on permittivity. These include soil sediment, heavy metal, nutrient

residuals, herbicide residual, bacteria, and organic materials such as petroleum products. Solids

that dissolve in water, such as salts of various types (minerals) and heavy metals like lead, are the

dominating factors for electrical conduction carried out by anions and cations.

Most existing permittivity sensors were designed to measure either the conductive, or the capacitive

(dielectric) behavior, but not both. These sensors provide only one piece of information – apparent

EC or dielectric constant at a given frequency - and are unable to separate factors affecting these

parameters. Since 2001, we have been developing a novel, real-time FR permittivity sensor to

simultaneously measure multiple properties of dielectric materials (Zhang et al., 2004). In this

paper, results of preliminary tests using the sensor in soil and water are discussed.

25 Results and Discussion

t Results of Soil Tes

Design of the sensor probe for the soil test was a modified, four-electrode, Wenner-array structure (Figure 1).

Figure 1. Four-electrode, FR permittivity sensor probe for soil

The sensor was tested in 750 carefully prepared soil samples from three soil types, at combinations

of five salinity levels, five water contents, five densities, and two replications. The

frequency-response data were analyzed using the locally weighted PLS method. For measuring volumetric

water content at all combinations of soil types and densities, the model achieved coefficient of

determinations (R2 values) of 0.91 and root-mean-square (RMS) error of 0.013 m3 m-3. In measuring

salinity, the R2 value achieved by the models was 0.72, with an RMS error of 1.176 dS m-1 (Lee,

2005).

Preliminary Results of Water Tests

A modified sensor probe (Figure 2) was tested in water solutions of three salts, KNO3, KH2PO4,

and KCl. The experiment was conducted in two steps. During the first step, we tested the solutions

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individual cation and anions. For each salt, 11 solution samples were prepared in deionized water.

Frequency-response data were then taken three times using the sensor. Calibration models for

predicting the salt concentrations were established for individual salts. Results are shown in Table

1.

Figure 2. sensor probe used in water tests

Table 1. Prediction results for three salt solutions at high concentrations

(3,500 – 35,000 ppm)

Salt type R-square value RMS error (ppm)

KH2PO4 0.9985 390

KNO3 0.9848 1273

KCl 0.9927 857

In order to test the sensor’s ability to recognize specific ions in water solutions, FR data for all three

salts were combined to establish PLS models to quantitatively predict individual ions. The results

are shown in Table 2. The prediction results for potassium cation across three salt types are shown

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Table 2. Prediction results for ions and cation in three salt solutions at high concentrations

(3,500 – 35,000 ppm)

Anion/Cation R-square RMS error (ppm)

K+ 0.9801 640

Cl- 0.9532 1109

NO3- 0.9649 1238

PO4

-0.8323 3078

Figure 3. Prediction result for potassium cation concentration in three high-concentration

salt solutions

The second step of the experiment was to test salt solutions at low concentrations (0-4 ppm). The

salt tested was potassium nitrate. Samples of 11 concentrations were prepared using a dilution

procedure. Three independent sets of samples were prepared. One set was used for calibration;

the others for validation. The results are shown in Table 3. These results prove that the sensitivity of

the sensor is sufficient for measuring nutrient residual in water at the environmentally- and

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Table 3. Prediction results for K+ in three salt solutions at low concentrations

(0-4 ppm)

Data set R-square RMS error (ppm) Training data set 0.9988 0.0413

Validation data set 1 0.9217 0.7754

Validation data set 2 0.8710 1.408

Frequency signature

Conventional multivariate analysis tools, such as partial least square (PLS) method, have been

proven effective in spectroscopic data analysis. In order to reduce the number of frequencies used

in the model, “signature frequencies” for a specific agent, at which the frequency response of the

agent possesses distinguishable patterns from other agents, should be selected. One way to select

the signature frequencies is to locate the peaks (both positive and negative) in the loading factors

(principal components) derived from the PLS analysis for that specific agent.

From the first three principal components (PC) derived from the PLS analysis on potassium cation

(K+) using 33 solution samples of KCl, KNO3, and KH2PO4 (11 samples for each), 30 signature

frequencies were selected from 606 frequencies originally used in the FR data. PLS models

established using the 30 signature frequencies were tested in samples of individual and combined

salt solutions to predict the concentrations of potassium cation (K+). As shown in Table 4, the 30

signature frequencies did a very good job in detecting the cation concentration with high R2 values and

low RMS errors, especially for the KCl and KH2PO4 solutions. This result indicates that, once

correctly identified, the signature frequencies can be used to detect specific ions in water samples

with unknown pollutants. The reduced number of frequencies would not only speed up the

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Table 4. Prediction results for K+ in different salt solutions using a PLS model established

based on 30 “signature frequencies”

Solutions tested Number of samples tested

R2 RMS error (ppm)

KCl 11 0.9909 503

KNO3 11 0.8084 4401

KH2PO4 11 0.9999 25

KCl, KNO3, and KH2PO4 33 0.9071 1383

When the 30 signature frequencies obtained using high-concentration solutions were used to

predict low-concentration (0-4 ppm) KNO3 solutions, the R 2

value for the training data set was

basically unchanged. For validation, the R2 value slightly decreased for data set 2 but increased for

data set 3 (Table 5). The difference between these two was greatly reduced. This demonstrates the

effectiveness of the frequency signature in describing the FR patterns of specific types of ions and

in avoiding model overfitting.

Table 5. Effectiveness of frequency signature in reducing the number of frequencies while achieving

better prediction for low concentration (0-4ppm) KNO3.

Data set Data set 1 (Training) Data set 2 (Validation) Data set 3 (Validation) Frequencies used 606 (original) 30 (Signature) 606 (original) 30 (Signature) 606 (original) 30 (signature) R2 values 0.9991 0.9992 0.9560 0.9153 0.8207 0.9140

Conclusions

1. Results of soil and water tests indicated that the FR permittivity sensor has a great potential for

simultaneously measuring multiple properties of dielectric materials.

2. The sensor simultaneously measured soil volumetric water content and salinity in soil samples

with different textures and densities. Water content was measured with a higher accuracy than

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3. The sensor successfully measured potassium cation among three different salt solutions.

4. Frequency signatures selected through multivariate analysis greatly reduced the number of

frequencies required for the measurement while maintaining the measurement accuracy.

Acknowledgement

The author acknowledges the financial support provided for this research by the Kansas Water

Resources Institute.

References

Lee, K.H. 2005. A dielectric permittivity sensor for simultaneous measurement of multiple soil

properties. Unpublished PhD diss. Manhattan, Kansas: Kansas State University, Department of

Biological and Agricultural Engineering.

Robinson, D.A., S. B. Jones, J. M. Wraith, D. Or, and S. P. Friedman. 2003. A review of advances

in dielectric and electrical conductivity measurement in soils using time domain

reflectometry. Vadose Zone Journal 2:444-475.

Topp, G.C., S. Zegelin, and I. White. 2000. Impact of the real and imaginary components of relative

permittivity on Time Domain Reflectometry measurements in soils. Soil Sci. Soc. Am. J.

64:1244-1252.

Zhang, N., G. Fan, K. H. Lee, G. J. Kluitenberg, and T. M. Loughin. 2004. Simultaneous

Measurement of Soil Water Content and Salinity Using a Frequency-Response Method. Soil