Dielectric ‘Loss Factor’ (e’’) Measurement Over RF Frequencies

Between 0.1 – 40.0 GHz for Common Organic Chemicals.

 

Abstract   Using an Agilent Network Analyzer with open ended dielectric measurement probe (85070e dielectric probe kit), the ‘loss factor’ (e’’) of common organic solvents has been measured between the range 0.1 to 40.0 GHz. Measurements were conducted in 250 mL pyrex reaction vessels filled with 125 mL of solvent, the end of the probe submersed to a depth of 5 mm. The magnitude of e’’ at the conventional microwave heating frequency 2.45 GHz is compared between solvents and to the existing data on the loss factor of water.   Keywords:Loss Factor, Dielectric Measurements, Microwave Heating, Organic Solvents.

 

 

LIST OF FIGURES

 

Figure		Page
1	Apparatus used to measure e’’ of the range of materials.	2
2	The trend of e’’ vs Frequency (MHz) on both linear and logarithmic scales.	3
3	Summarized values for e’’(max) wavelengths at different temperatures.	4
4	A table of organic solvents and reactants analysed with e’’ at 2.45 GHz.	4
5	A categorized table of RF absorbing materials..	5
6	Measured e’’ vs Frequency (MHz) for all of the chemicals used on a linear frequency scale.	7
7	Measured e’’ vs Frequency (MHz) for all of the chemicals used on a logarithmic frequency scale.	8
8	Measured e’’ vs Frequency (MHz) for solvents on a linear frequency scale.	9
9	Measured e’’ vs Frequency (MHz) for solvents on a logarithmic frequency scale.	10
10	Measured e’’ vs Frequency (MHz) for reactants on a linear frequency scale.	11
11	Measured e’’ vs Frequency (MHz) for reactants on a logarithmic frequency scale.	12

 

Introduction:

Microwave heating in commercial ovens operates at 2.45 GHz and is most commonly used to heat materials containing a large amount of water. It is also the most common frequency used for the microwave heating of organic chemicals. In this study we identify the molecular functional groups responsible for absorbing microwave energy at 2.45 GHz.

 

Microwave radiation will heat organic molecules by aligning molecular dipoles with the electric field, transferring power from the radiation into the movement of the organic molecule (heat). A molecular dipole occurs when two (or more) atoms are not distributing electron density evenly between them. The electronegative atoms (increasing from N, O, F and Br, Cl, F) have a tendency to withdraw a more dense could of electrons out of a bond (pair of shared electrons) and towards itself, hence ‘polarizing’ the bond. The polarization creates areas of negative (-) and positive (+) charge that has a static attraction to the electromagnetic field. Organic molecules don’t absorb electromagnetic radiation at discrete frequencies, instead a spectrum of intensities at different wavelengths occurs. Most references cover the all factors involved in microwave interactions between organic materials. Both permittivity (e’, ability of the material to be polarized and change the electromagnetic field) and loss factor (e’’, how efficiently the absorbed radiation is converted to heat) are measured and used to calculate the angle of the molecule as it moves to align with the magnetic field (‘loss tangent’, tan d). In this study we are only concerned with the capacity of a material to absorb radiation on a spectrum of frequencies and to use a measure of e’’ to compare with the reported values for water. In this study we look at how organic chemicals absorb electromagnetic radiation over the radiofrequency (RF) spectrum (0.1-40 GHz) using a measure of loss factor (e’’).

 

Description of the Procedure:

Dielectric measurements were taken using an Agilent Network Analyzer (E83613) with open-ended dielectric measurement probe (85070e dielectric probe kit).

The measurement apparatus was set up as follows;

 

 

Figure 1: Apparatus used to measure e’’ of the range of materials.

 

 

The tests were performed by filling the pyrex vessel (250 mL) with each organic material (125 mL) and the probe was submersed and held 5 mm below the surface of the liquid. The room temperature and solution temperature was ~22°C .The testing apparatus is shown in Figure 1. Values for e’’ were recorded over the range from 0.1 – 40 GHz, although no useful data could be collected on; Acetaldehyde (>36.20 GHz), Acetone (>37.15 GHz), Acetonitrile (>30.51 GHz) and Nitromethane (>30.51 GHz).

 

Analysis of the data:

Introduction: Water [REF]

The loss factor of materials can change depending on the frequency of the incident electromagnetic radiation. This is because the interaction of the RF radiation with the dipole of a molecule will reach an optimum value at a wavelength that rotates the molecule in a way that efficiently generates heat (vibration). The trend in loss factor (e’’) of water at frequencies from 0.1 - 30 GHz is shown in Figure 2 (reference data recorded at 20°C)^[1].

 

 

 

Figure 2: The trend of e’’ vs Frequency (MHz) on both linear and logarithmic scales.

 

The loss factors on the RF spectrum will also change with temperature. At higher temperatures the molecules are already vibrating fast and the frequency that best absorbs RF radiation (e’’ maximum) will change depending on the existing vibration within the molecule (temperature). The loss factor for water at 22°C (our experimental temperature) and 2.45 GHz is approximately 10 although it decreases with increasing temperature;

Temperature (loss factor at 2.45 GHz); 0°C (20), 20°C (11), 40°C (6), 60°C (3), 80°C (2) and 100°C (1.3).

 

The frequency of maximum RF absorbtion (e’’ max) increases with increasing temperature, although the magnitude of the e’’ decreases along the same trend. This means water as a polar solvent becomes ‘less polar’ with increasing temperature and more like an organic solvent. The RF frequency for maximum e’’ and reported loss factor is summarized below (Figure 3) at different temperatures^[1].

 

 

Figure 3: Summarized values for e’’(max) wavelengths at different temperatures^[1].

 

Experimental data: (Generated from the experimental setup)

Common organic solvents (AR grade) and a number of useful reactant chemicals (LR grade) were chosen for a study on dielectric loss factor (Figure 4) to examine the effect of functional groups on dielectric heating of both the solvent and reactant at 2.45 GHz. For each chemical, the measured loss factor (e’’) at 2.45 GHz  (~22°C) is tabulated in brackets.

 

 

Figure 4: A table of organic solvents and reactants analysed with e’’ at 2.45 GHz.

                                                           

Since solutions have been measured at ~22°C, the recorded data represents the initial heating capacity from room temperature. We compared the loss factor of materials at 2.45 GHz and considered materials with a loss factor of less than 1 to be mainly transparent, 1-5 is moderately absorbing and above 5 is highly absorbing (Figure 5).

 

 

Figure 5: A categorized table of RF absorbing materials.

 

Conclusions:

Microwave RF transparent chemicals

At 2.45 GHz, solvents containing the ‘Ether’ functional group (Diethylether and THF) were almost microwave transparent, as was the ‘Chlorinated Hydrocarbon’ DCM and ‘Ester’ (Ethyl Acetate) functional groups. The primary and secondary ‘Amine’ functional groups (n-Butylamine and Diethylamine respectively) were completely transparent. The ‘Aldehyde’ functional group (acetaldehyde) contains a ‘Carbonyl’ (C=O, bond) that was transparent in acetaldehyde. ‘Ketone’ functional group (Acetone) also has a carbonyl group, but showed some absorbance perhaps due to tautomeric forms of the ketone in the acetone molecule. Cyclohexanol, a secondary cyclic ‘Alcohol’, has an O-H bond similar to water, but in this case is attached to a larger structure and has low absorbance. .

 

Moderately RF absorbing chemicals

The tertiary aromatic amine (pyridine) is somewhat absorbing due to the dipole created by an electronegative nitrogen atom within the molecule. The ‘Carboxylic Acid’ functional group (acetic acid) shows only moderate absorbance at room temperature although this may be expected to change with temperature, since the molecule contains both ketone and O-H functionality, both of which contain electronegative oxygen atoms that create strong dipoles. The ‘Nitrile” functional group (acetonitrile) contains a polarized nitrogen-carbon triple bond and absorbs moderately. The ‘Nitro’ functional group (nitromethane) can be considered ‘ionic’ but shows only moderate absorbance. Isopropanol is a secondary alcohol (like cyclohexanol) and has an O-H group, but it is smaller and more able to rotate in the electromagnetic field. It has moderate absorbance that is significantly higher than the cyclic secondary alcohol cyclohexanol.

 

Highly RF absorbing chemicals

The primary alcohol group (ethanol) absorb strongly, although Digol, which has two primary alcohols on the same carbon chain as ethanol, absorbs less strongly since it is symmetrical. The tertiary ‘Formyl Amide’ group (DMF) absorbs strongly since the carbonyl is polarized by both nitrogen and oxygen. Polarization occurs to a larger extent in the ‘Sulfoxide Ether’ group (DMSO) where sulphur is polarized by three oxygen atoms, as such the solvent DMSO is highly absorbing.

The reactant pentandione contains a ‘1,3-diketone’ system that exits as a tautomer to form the secondary ‘olefinic alcohol’. 1,3-Pentanedione shows higher absorbance that the ‘alkyl’ secondary alcohol (isopropanol) since the olefin contains more electrons that can be polarized. Ethanolamine contains both primary alcohol and primary amine functional groups on the same carbon chain as ethanol. The primary amine group (n-Butylamine) was proven to be RF transparent and the primary alcohol group (ethanol) strongly absorbing. The effect of having both on the same molecule was a decrease in absorption due to an increase in symmetry between electronegative atoms, decreasing the overall strength of the dipole.

The formamide molecule is a primary ‘formyl amide’ and has both carbonyl and amine groups, but is very small and has a large dipole. The loss factor for formamide at 0.1 MHz (~19) increases with frequency and reaches ~47 at 2.45 GHz (conventional microwave heating) to a maximum of ~51.5 at 4.27 GHz. It decreases towards ~15 as frequency is increased to 40 GHz.  The formamide absorbs five times as much microwave radiation at conventional heating frequencies (2.45 GHz) than water and is at close to optimal frequency for dielectric loss at 22°C. In contrast, the frequency maximum for dielectric loss in water at 22°C is  ~9.20 GHz with an e’’ value of 37, less than that of formamide at the conventional heating frequency.

 

Analysis of e’’ with Frequency

The RF highly absorbing chemicals formamide, DMSO and DMF reach their loss maximum at 6.63 and 19.4 GHz respectively and continue to absorb RF at an e’’ greater than 10 at frequencies toward 40 GHz. RF absorbing solvents commonly have a maximum dielectric loss at a specific frequency. The e’’ maximums measured were; isopropanol (7.8, 389 MHz), digol (10.4, 475 MHz), ethanol (11.0, 968.3 MHz), ethanolamine (8.9, 1.1 GHz), DMSO (21.8, 6.63 GHz), pentanedione (12.5, 8.6 MHz), DMF (22.0, 19.4 GHz). Loss factors for nitromethane, acetonitrile, begin to increase above 3.3 GHz whereas loss factors for pyridine and acetone begin to increase above 5.7 GHz. Acetaldehyde increases to a maxima at 8.1 GHz (e’’ = 3.0) and then steadily increases with frequency.

 

 

Graphed Data (All materials used):

                                                           

Figure 6. Measured e’’ vs Frequency (MHz) for all of the chemicals used on a linear frequency scale.

 

 

Figure 7. Measured e’’ vs Frequency (MHz) for all of the chemicals used on a logarithmic frequency scale.

 

 

Solvent/Reactant Breakdown:

 

Figure 8. Measured e’’ vs Frequency (MHz) for solvents on a linear frequency scale.

           

Figure 9. Measured e’’ vs Frequency (MHz) for solvents on a logarithmic frequency scale.

 

 

Figure 10. Measured e’’ vs Frequency (MHz) for reactants on a linear frequency scale.

 

 

Figure 11. Measured e’’ vs Frequency (MHz) for reactants on a logarithmic frequency scale.

 

 

 

Supporting data for all measurements are included in the PDF version.

 

References:

 

[1] Approximated valued are from; M.Chaplin. London South Bank University, http://www.lsbu.ac.uk/water/microwave.html.; J. B. Hasted, Liquid water: Dielectric properties, in Water A comprehensive treatise, Vol 1, Ed. F. Franks (Plenum Press, New York, 1972) pp. 255-309.