A Computer Controlled Microwave Spectrometer for Dielectric Relaxation Studies of Polar Molecules

Transcription

1 384 A Computer Controlled Microave Spectrometer for Dielectric Relaation Studies of Polar Molecules Jai N. Dahiya*, Santaneel Ghosh and J. A. Roberts+ Department of Physics and Engineering Physics, Southeast Missouri State University, Cape Girardeau, MO 63701, USA , , jndahiya@semo.edu +Department of Physics, University of North Teas, Denton, Teas 76203, USA roberts@unt.edu Abstract: A cylindrical microave resonant cavity in TE 011 mode is used to study the microave dielectric response of a molecule of nitrobenzene as a function of temperature and frequencies. The resonant cavity is used in a microave spectrometer operating in the -bands of frequencies. Slater s perturbation equations are used to relate the frequency shifts and Q-changes ith the real and imaginary parts of the comple dielectric constant. For temperature dependent studies dielectric relaation data depends on a number of variables that are controlled manually. The dielectric relaation near a phase change is a very quick process and it is very easy to introduce an error during the manual control of some of these variables. A computer interface technique seems to be very efficient in taking data. With this technique there seems to be a very nice correlation beteen frequency shifts and temperature data and maimum number of data points are taken for dielectric relaation near the phase change of nitrobenzene. Inde Terms: Microave resonant cavity, nitrobenzene, temperature and frequency, dielectric relaation I. INTRODUCTION Dielectric behavior of a material is a very important process and it reveals the electrical nature of that material. In a dc or lo frequency ac field the dipoles are able to follo the field very nicely and there is no lag beteen the dipoles and the field. As the frequency of the applied field increases some of the dipoles ill not be able to follo the field. This behavior becomes very distinct at microave frequencies. The permanent dipoles have a difficult time folloing frequencies of the order of GHz. This is the process of dielectric relaation at microave frequencies. A contribution from permanent dipoles to the polarization in an applied field does not necessarily mean that the molecules have complete freedom of rotation about one or more aes not coinciding ith the dipole ais. It is also possible that the dipole aes have a distinct number of positions of relatively minimal potential energy, separated by potential energy barriers. When the rotational energy allos a sufficiently frequent passage over these barriers, the contribution of the dipoles to the polarization in an applied field may be the same as in the case of free orientation. The relaation rate is defined as the rate at hich a system comes into equilibrium ith its surroundings hen various physical aspects of its surroundings such as temperature, electric and magnetic fields are changed. The rate at hich the portion of the dielectric polarization arising from the orientation of permanent molecular dipoles comes in to equilibrium ith an applied field is temperature dependent. Since the relaation rate is a measure of the time lag beteen the applied field and the system s response; it is called the relaation time. The nature of the dependence of the relaation rates on temperature is very significant in

2 385 understanding the physical nature of the process. In a process in hich the relaation rate depends on the temperature, it is certain that at some stage in the process a molecule or other unit involved is forced to ait until it has acquired a considerable amount of energy by thermal fluctuations, in ecess of the average thermal energy in the medium. Microave resonant cavity technique has been established as a standard technique to study the dielectric relaation behavior in different polar and non-polar materials. It is very interesting to study the dielectric response of a material as it goes through a phase change. The viscosity of the material changes during the phase change and this in turn translates in to a dramatic change in the dielectric behavior of the material. A cylindrical microave resonant cavity in the TE 011 mode is very sensitive in terms of the perturbation of the electric field along the ais of the cavity. A similar cavity has been used for the dielectric studies of a number of materials [1-5]. K. H. Hong and J. A. Roberts [6] used a cylindrical cavity resonating near 10 GHz in TM 010 mode to determine the dielectric properties of liquids and solids. It has proven to be a very interesting eperiment to find the dielectric response of a material near a phase transition region i.e., going from an ordered to a disordered phase. From a study of these nature important conclusions concerning molecular freedom may be dran. The microave resonant cavity used in this study is very successful in identifying a phase change in a polar molecule of nitrobenzene at 8.8 GHz. The frequency dependent studies of this molecule indicate a resonance behavior around 9.2 GHz. A cylindrical tunable resonant cavity in the TE 011 mode is used as a probe in a microave spectrometer to study the dielectric response of a sample of nitrobenzene. The dielectric relaation in this molecule is studied as a function of temperature and frequency. A very sensitive thermal bath is used to do the temperature dependent studies of liquid nitrobenzene beteen -20 C to 20 C at a microave frequency of 8.8 GHz. A Varian X-13 klystron is used to perform the frequency dependent studies of this molecule in the entire -band range of 8.0 GHz to 12.4 GHz at 22 C. II. THEORY, PROCEDURE, ANALYSIS Dielectric behavior of a material reveals very important information regarding the electrical nature of that material. It is measured in terms of the polarization capabilities of that particular material. The dielectric constant of a polar liquid arises from the orientation of molecular permanent electric dipoles and the electrical distortion of the molecules. Both of these effects can be epressed in terms of a quantity P, the polarization, or dipole moment per unit volume of a continuous material: P = ( N o / V ) µ Debye in his theory [8] eplained the relaation phenomenon and shoed that the polarization of a dielectric medium in an electric field might arise from the partial orientation of permanent molecular dipoles by the field as ell as from the distortion of electronic orbits in the molecules. The theory starts ith an assumption about the time variation of the polarization in response to a step function removal of field. The simplest assumption is of an eponential t /τ decay P( t) = P o e o (1) here µ o is the average dipole moment per molecule, N o is Avogardro s number, and V is the molar volume. The polarization process alays involves rapidly forming polarization that consists mainly of electronic polarization, and may also involve sloly forming polarization. here τ is the relaation time. The physical meaning of such decay is that the rate of change of polarization is proportional to the difference

3 386 beteen the instantaneous polarization and its final value. This relaation assumption is often used in the theory of the return to equilibrium of a perturbed system. some of the data using N = 1.6 is shon in Figure 1. A. Normalization of the fields in Slater s Equations A sample of material under study (nitrobenzene) is placed into a capillary tube that in turn is attached to a micrometer drive. The presence of the sample causes the perturbation of the fields inside the cavity and as a result of that there is a frequency shift f and Q-change of the resonant cavity. The frequency shifts and Q-changes are related to the real and imaginary parts of the comple dielectric constant through the perturbation equations [1]. Since the precise nature of the field in the cavity could not be ascertained, relative values of ε and ε are calculated for molecules in this investigation ith respect to ater as a standard. Constant parameters to be used in the Slater perturbation equations [1] are obtained for ater. The changes 1 in f and as a function of mass of the Q sample residing in the cavity can be epressed by a simple poer-la equation [7]. The data is fitted to equations of the form Figure 1. Frequency shift (MHz) as a function of mass (mg) and mass**(1.6) for ater at a resonant frequency of 10.1 GHz. Using equations (3) and (4) along ith Slater s perturbation equations (5) and (6) given belo v v f ε 1 Es Edv = v v f o 2 E EadV (5) one can rite 1 ε 1 = Q 2 v v Es Edv v v E E dv a (6) f = A + B( m) 1 = A + B Q ( m) N (3) (4) here A and C are the intercepts, B and D are the slopes, m is the fraction of sample mass advanced into the cavity and N is a constant hich depends upon the geometry of the electromagnetic fields inside the sample holder and the cavity. A computer analysis as made of the eperimental data in order to determine hat poer of N led to a best fit for the data. The best value of N appeared to be 1.6. A plot of N f ε 1 = B = fo F( E) ( m) 2 and 1 Q = D foε F( E) ( m) Where F(E) is given by F( E) = V r r Es E dv r r E E dv v a (7) (8) (9)

4 387 And is a functional form of ho the field interacts ith the sample, E a and E s are the fields as applied to the cavity and the sample inside the cavity, E is the total field of the system, f is the frequency shift, and Q is the quality factor of the resonant cavity respectively, and f o is the resonant frequency of the cavity. All the samples are placed into small capillary tubes of constant diameter of 2mm to eliminate any geometrical effects. No if F(E) is of the same form for all the samples, there arises a characteristic B and D for each sample of. If B and D are the corresponding values for ater one can epress relative values for dielectric material as follos: Figure 2(a). Block diagram of the microave spectrometer used in this investigation. B B ε 1 = ε 1 (10) and D D ε = ε (11) Equations (10) and (11) are used to calculate ε and ε for nitrobenzene using literature values of ε = 61.3 and ε = 29.7 for ater at 25 C at a frequency of 8.8 GHz. A similar procedure is used to calculate the real and imaginary parts of the comple dielectric constant for nitrobenzene as a function of temperature. The frequency shifts and Q-changes are dependent upon the location as ell as the dielectric nature of the perturbing sample. In this study the perturbing sample is placed along the symmetry ais of the resonant cavity used as a probe in a microave spectrometer. The details of such a spectrometer have been discussed elsehere [1] but for the continuity of this paper a block diagram of the spectrometer is shon in Figure 2(a) and 2(b). Figure 2(b). Block diagram of the computer control system used in this investigation. A klystron in the -band of frequencies ( GHz) is used to produce a microave signal at 8.8 GHz. The modulated absorption signal after being reflected from the resonant cavity and amplified by a tuned amplifier at 31 KHz appears on the oscilloscope in the form of a butterfly as shon in Figure 3. A series of markers are produced after miing a part of the microave signal ith a standard signal produced by a generator. A radio receiver is used to detect the difference in these to signals and in turn produces markers at a fied frequency interval. One of these markers is chosen to monitor the change in frequency as ell as the idth change of the signal as the sample to be studied is inserted into the resonant cavity. The resonant frequency shifts and the Q of the cavity also changes as a result of the sample inside the cavity.

5 388 cavity temperature is varied. This behavior is shon in Figures 5 and 6 for a sample of nitrobenzene. The to parameters f and (1/Q) are related to the real and imaginary parts of the permittivity of the perturbing sample and measurements on these to parameters enable the values for ε ' and ε " to be obtained via Equations 3 and 4 respectively. Figure 3. Dual trace oscilloscope display for frequency markers and cavity derivative profile for a typical scan. The marker spacing for this scan is 8.00 MHz ith center frequency at 8.8 GHz. The block diagram of the thermal bath used in this investigation for temperature dependent studies is shon in Figure 4. Figure 5. Frequency shift of the resonant cavity as a function of temperature for a sample of nitrobenzene at a resonant frequency of 8.8 GHz. Figure 4. Block diagram of the thermal bath used in this investigation The thermal bath used in this eperiment is very sensitive in terms of maintaining the temperature of the material hen it is going through the phase change. A computer interface system is used to control the amount of air going through the thermal bath and in turn cooling the microave resonant cavity to the desired temperature. With this technique temperature can be varied by 0.1 C intervals. The resultant change in the frequency shift and the quality factor Q are monitored as the Figure 6. Change in the Q-factor of the resonant cavity as a function of temperature for a sample of nitrobenzene at a resonant frequency of 8.8 GHz. The frequency dependent behavior of nitrobenzene is shon in Figures 7 and 8. The real and imaginary parts of the dielectric constant sho a resonance behavior around 9.2 GHz. Using Debye s theory of polar molecules [8] the relaation times for this molecule at different temperatures are of the order of sec. Thus, it seems that the dielectric relaation

6 389 mechanism in polar molecules is a chemical rate process and that the solid to liquid phase change in the molecule is related to the changes in the free energy of activation for dipole orientation in the sample. Figure 7. Change in Q-factor of the resonant cavityas a function of klystron frequency for a sample of nitrobenzene at 22 C [3] J. N. Dahiya, R. D. Ward, and E. C. Zimmerman, Temperature Dependence of the Microave Dielectric Response of Liquid Crystals, Proc. 5th Int. Symp. on Recent Advances in Microave Tech., Kiev, Ukraine, pp , 1995 [4] J. N. Dahiya, Microave Dielectric Response of Ferroelectric Materials, J. Mater. Educ., Vol. 14, No. 5 and 6, pp , [5] Hiroshi Kobayashi and Seiya Ogaa, Dielectric Constant and Conductivity Measurement of Poder Samples by the Cavity Perturbation Method, Japanese J. of Appl. Phys., Vol. 10, No. 3, pp , [6] K. H. Hong and J. A. Roberts, Microave Properties of Liquids and Solids Using a Resonant Cavity as a Probe, J. Appl. Pys., Vol. 45, No. 6, pp , [7] Haniotis, Z. and Gunthard, H. H., Agne, Z., Math. Phys., 20, 1969, p. 771 [8] P. Debye, Polar Molecules, Chemical Catalog, Ne York, Chap. V, Figure 8. Frequency shifts of the resonant cavity as a function of klystron frequency for a sample of nitrobenzene at 22 C. REFERENCES [1] J. N. Dahiya, S. K. Jani, and J. A. Roberts, Phase Transition Studies in Polar and Nonpolar Liquids at Microave Frequencies, J. Chem. Phys., Vol. 74, No. 6, pp , March [2] J. N. Dahiya, Dielectric Properties of Garmanium and Silicon as Determined in the Microave Field, J. Mater. Educ., Vol. 13, pp , 1991.