664
J. Phys. Chem. 1984,88, 664-666
The Single Reflection Method In Dielectric Time Domain Spectroscopy B. Gestblom and E. Noreland* Institute of Physics, University of Uppsala, Uppsala, Sweden (Received: October 24, 1983)
It is shown that the dual-channel time domain spectroscopy (TDS) system can give a time referencing of sufficient accuracy to allow the direct use of the single reflection method for dielectric characterization of high-permittivity liquids. The method is tested on a 2 M glucose solution at 5 "C, and it is found that the method can give accurate permittivity data up to 14 GHz.
Introduction Dielectric time domain spectroscopy (TDS) makes it possible to determine the permittivity spectrum of a sample over a wide frequency range in a single measurement. Various ways of arranging the sample are possible, and advantages and disadvantages of the different methods have been assessed.' The development of computer-controlledTDS systems has led to large improvements in accuracy aqd shortening of measurement times.2" The first TDS measurements employed the single reflection method in which the first reflection of an incident pulse against a long sample.in a matched coaxial line is used. The reflection coefficient in the frequency domain in this case is given by
measurement pulse shape is used to determine the time origin to. The most common method is to extrapolate the reflected pulse back to the base level. The inherent error Ato in this method has been shown to be of order 1 ps, Le., too large to allow the straightforward use of the method on high-permittivity liquids.' A way to correct for this systematic error is to use some method with inherent higher accuracy at a number of frequencies to deduce to be applied to the measured reflection a correction factor PAL coefficient ~ ( w ) . ~ The dual-channel time domain spectrometer gives the possibility of obtaining a time reference which is independent of the measurement p u l ~ e . ~In, ~this case, the incident pulse is split between two channels, of which one is used to define a time origin, while the other constitutes the measurement line. The time reference uncertainty in an individual measurement pulse was in early experiments found to be COS ps. This remaining uncertainty in time origin is of random nature and not dependent on systematic errors. It can thus be reduced by repeated independent measurements and averaging, as with other errors of random noise type. The dual-channel TDS system should thus give a time referencing of sufficient accuracy to allow the use of the singlereflection method on aqueous systems up to frequencies 10 GHz, without the introduction of separate phase calibration methods at spot frequencies. It is well-known that a substantial reduction in remaining systematic errors due to unwanted reflections can be achieved by using as reference pulse the reflected pulse from a sample with known dielectric parameters, not widely different from those of the sample of interest.6~10~"For an aqueous system the obvious reference here is water, for which the dielectric parameters are well established as discussed in a recent critical assessment by Kaatze et al.12 With a reference sample to give a reference pulse r r ( t ) ,eq 1 is modified to
Here u ( t ) and r,(t) are the incident and the reflected pulses, while F(u(t)) symbolizes the Fourier transform of u ( t ) , and e* = d idr is the complex permittivity of the sample. The single reflection method has the advantage of giving a reflection coefficient of magnitude 0.3 C lpl C 1 over the whole frequency spectrum present in the incident pulse. It can thus be considered a true wide frequency method, even reaching > 10 GHz, if sufficient accuracy in p ( w ) can be achieved. The demands on the accuracy in p ( w ) are quite severe at high permittivities and high frequencies, and the method has been mostly used for liquids of medium permittivity. It is the purpose of this Letter to discuss a method to make single reflection measurements on high-permittivity liquids like aqueous systems.
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The Single Reflection Method The demands on the measurement accuracy in amplitude and phase of p(w) = A& are best visualized by drawing equireflection lines in the E', err plane (see Figure 1). The diagram shows how a phase error in p ( w ) becomes progressively severe with increasing permittivity. To achieve an uncertainty A d 5 1 for an aqueous system, the required uncertainty is Acp 5 0.1'. Similarly an uncertainty in A leads predominantly to errors in d, and a A d 5 1 requires AA 5 0.001. Reduction of errors in p ( w ) of random nature can be achieved by signal averaging. However, a crucial point in determining the phase cp is the establishment of a common time origin to in the evaluation of the Fourier transforms. An error Ato will introduce a systematic phase error Acp = wAto. The error quoted above, Acp 5 0.1', thus leads to a requirement Ato 5 0.03 ps if we want to reach 10 GHz in the permittivity spectrum. Time domain spectrometers described for reflection measurement are singlechannel systems in which some part of the recorded
A further advantage in using a reference liquid is that the same liquid cell is used in both reference and sample measurements, without the need to disassemble the transmission line between measurements. Instead the liquids are inserted and removed through holes drilled in the line. This eliminates the possibility of introducing small uncontrolable line impedance changes in reassembling the line. Although the influence of drift and jitter in the time base are to a large extent removed in the dual-channel system, a stabilization is valuable when the highest accuracy is desired. An exchange of the HP1105A tunnel diode power shpply for a NSLH0075 precision programmable regulator with improved stability
(1) For reviews see van Gemert, M. J. C. Philips Res. Rep. 1973, 28, 530. Cole, R. H. Annu. Rev. Phys. Chem. 1973, 28, 283. (2) Dawkins, A. W. J.; Sheppard, R.; Grant, E. H. J . Phys. E 1979, 12, 11091. (3) Dutuit, Y., ThEse, UniversitC de Bordeaux I. (4) Chahine, R.; Bose, T. K. J. Chem. Phys. 1980, 72, 808. (5) Gestblom, B.; Jonsson, 9. J. Phys. E 1980, 23, 1067. (6) Peyrelasse, J.; Boned, C.; Le Petit, J. P. J . Phys. E 1981, 24, 1002.
(7) Gestblom, 9. J . Phys. E 1981, 14, 895. (8) Suggett, A. J. Phys. 1975, 8, 327. (9) Cole, R. H.; Mashimo, S.; Winsor, P. J . Phys. Chem. 1980, 84, 786. (10) Campbell, C.; Crossley, J.; Glasser, L. A h . Mol. Relaxation Processes 1976, 9, 63. (1 1) Clarkson, T. S.; Glasser, L.; Tuxworth, R. W.; Williams, G.Adu. Mol. Relaxation Processes 1977, 10, 173. (12) Kaatze, U.; Uhlendorf, V. Z. Phys. Chem. (Frankfurt am Main) 1981, 126, 151.
0022-3654/84/2088-0664%01.50/0 0 1984 American Chemical Societv , , I
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The Journal of Physical Chemistry, Vol. 88, No. 4, 1984 665
Letters
Figure 1. Equireflection lines in the e', e" plane from the single-reflection coefficient p . Lines representing constant amplitude are broken while the solid lines show the constant p phase.
and a temperature stabilization of the sampler was in this respect found effective.
Experimental Section and Results The system was tested on a 2 M glucose solution at 5 'C. In the measuring sequence pure water and the glucose solution were alternately injected into the measuring cell of length 10 cm. For each liquid the reflected pulse shape was registered three times and the three recordings were stored on the disk memory. Each pulse shape is an average of 25 scans, and each scan is an average of 25 samplings at 1024 steps of the line base, as further discussed in ref 5. A time window of 5 ns was chosen which is sufficiently long for the transmitted pulse to reach its final steady level. A laboratory suction pump was used to remove the sample liquids and flush the cell with acetone between sample changes. In all 18 independent measurements of reference and sample pulse shapes were taken. Variation in time difference between time referencing and measurement pulses for the sample sequence during the measuring period of 3 h was found to be 0.4 ps. The stored pulses were Fourier transformed at 61 frequencies between 20 MHz and 20 GHz and the permittivity spectrum calculated and stored for the 36 independent neighboring pairs of pulse shapes. The mean and its standard deviation were calculated for e' and c" at each frequency to obtain the final spectrum with its estimated uncertainties. The resulting spectrum with error bars is shown in Figure 2. The diagram shows that accurate permittivities are obtained over the whole frequency range up to 14 GHz, where an uncertainty Ac', Ac'' 1 is observed. At lower frequencies smaller errors can be expected, with practically negligible error bars below 2 GHz. Judging from the data at 10 GHz, say, the quoted errors correspond to a phase uncertainty Acp = 0.1', Le., a time reference uncertainty Ato = 0.03 ps. The time reference method used, with averaging of independent spectra, thus seems to virtually eliminate the time referencing uncertainty. The obtained spectrum deviates considerably from that of pure water as calculated from a single relaxation time model function with tS = 8 5 . 8 , t- = 5.7, and 7 = 14.9 ps. The obtained spectrum cannot be fitted to such a model function. In previous studies of glucose solutions Suggett13 analyzed the data in terms of a model function with several relaxation times. The simplest such function is to assume two relaxation times e* =
+ 1 +- e , + 1 + -j W 2 t,
c,
tg
~
t,
~
WT,
~~
~~
(13) Suggett, A,; Clark, A. H.J . Solution Chern. 1976, 5, 1.
12)
Figure 2. Permittivity spectrum of 2 M glucose from single-reflection measurements. Open circles (with error bars) denote e' and filled circles denote e". The full lines give the two Debye process model. The broken lines show the reference spectrum of pure water. Inserted are Cole-Cole plots of the spectra where the ellipse sizes illustrate the experimental errors.
- c*exptl gave the theoretical spectrum A least-squares fit of included in Figure 2, with parameters t, = 76.1, t l = 54.9, e, = 5.7, 7 , = 21 ps, and r2 = 98 ps. The root mean square deviation of experimental and model spectra was 0.7. The introduction of a distribution parameter in r2 leads to a slightly improved fit; however, it was not significant enough to justify the introduction of an additional parameter.
J . Phys. Chem. 1984,88, 666-668
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Some disagreement between experimental and theoretical curves can be observed around 200 MHz. It is believed that this is due to an error obtained on truncating the pulses, which show a slightly rising slope even after 5 ns. This illustrates that, even after extensive signal averaging to eliminate noise errors, systematic errors may remain if steady initial and final levels have not been reached within the observational time window. The dielectric parameters correspond very well with those of S ~ g g e t t . 'The ~ interpretation would be to attribute T~ = 21 ps to relaxation in the bulk water, shifted from the free water value of 14.9 ps, while T~ is attributed to relaxation in the modified water of the hydrated glucose complex.
Conclusion It has been demonstrated that with a dual-channel TDS system the single-reflection method can be directly used to study high-
permittivity liquids, like aqueous systems. The method requires a reference liquid with known dielectric parameters which do not differ widely from those of the unknown sample. The measurements are self-contained in the sense that separate calibration measurements at spot frequencies to determine an accurate time origin are not needed. The proposed measuring sequence and averaging procedure showed a time referencing accuracy of 0.03 ps which made possible an extension of the frequency range to 14 GHz. For liquids of lower permittivity, the measurement accuracy and the frequency range can be expected to be even larger. For high-permittivity liquids showing nonnegligible dc conductivity the single-reflection method is unsuitable.' For such systems the total transmission or total reflection methods should be applied, where again the use of known reference liquid improves accuracy.
Thermal Decomposition of Hydrogen Cyanide behind Incident Shock Waves Attila Szekely,* Ronald K. Hanson, and Craig T. Bowman High Temperature Gasdynamics Laboratory, Department of Mechanical Engineering, Stanford University, Stanford, California 94305 (Received: October 26, 1983)
The thermal decomposition of hydrogen cyanide was studied over the temperature range 2700-3600 K by using a shock tube technique. HCN-Ar mixtures (12-200 ppmv HCN) were heated by incident shock waves and CN absorption at 388 nm (B2Z+, v = 0 X2Z+,v = 0 electronic transition) was used to follow the progress of the decomposition. The low-pressure rate coefficient for the reaction HCN + Ar H + CN + Ar (1) was closely fit by the Arrhenius expression k , = 10'6.0*0.15 exp[-(54650 & 111O)/v cm3/mol s. The present results are discussed and compared with previously published determinations.
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Introduction The low-pressure rate coefficient for the decomposition of hydrogen cyanide HCN
+ Ar
+
H
+ C N + Ar
(1)
has been studied by several over the combined temperature range 2200-5030 K. Roth and Just' used atomic resonance absorption spectroscopy (ARAS) to monitor the buildup of H atoms behind reflected shock waves in the temperature range 22OC-2700 K. Their data were best fit by the expression
k , = 5.7
X
loi6exp(-58910/T) cm3/mol s
Tabayashi et aI.* studied the decomposition of H C N behind incident shock waves over the temperature range 2600-3600 K, using C N broad-band absorption around 388 nm. Their reported rate expression
k l = 1.26 X 10l6 exp(-50170/T) cm3/mol s is a factor of 6 above the results of Roth and Just in the overlapping temperature range. More recently, we used C N emission to study reaction 1 over the temperature range 3570-5030 K behind incident shock waves.3 The reported rate coefficient
k l = 4.07
X
lOI4 exp(-44740/T) cm3/mol s
agrees reasonably well with extrapolations of the results of Roth and Just based on weak-exchange process theory4vsbut lies below (1) P. Roth and Th. Just, Ber. Bumenges. Phys. Chem., 80, 171 (1976).
(2) K. Tabayashi, T. Fueno, K. Takasa, D. Kajimoto, and K. Okada, Bull. Chem. SOC.Jpn., 50, 1854 (1977). (3) A. Szekely, R. K. Hanson, and C. T. Bowman, 'Shock Tubes and Waves", Proceedings of the 13th International Symposium on Shock Tubes and Waves, State University of New York Press, Albany, NY, 1982, p 617.
0022-3654/84/2088-0666$01.50/0
TABLE I: Kinetic Mechanism Employed in Modeling the HCN-AI System
reaction
+ A r + H + CN + Ar 2 H, + C N + H + HCN 3 CN + HCN+C,N, + H 4 C2N2+ Ar + 2 CN + Ar 1 HCN
5 H,
+ Ar+2
H
+ Ar
rate coefficient, cm3/mol s
ref
1.00 X 1 O I 6 exp(-54650/T)
this hork
7.5 x 1013 1.0 X l O I 3 6.47 X l o i 6 exp(-50040/T) 2.20 X 1014 exp(-48310/T)
6 7 8 9
the value reported by Tabayashi et al. by a factor of about 7 at 3600 K. In the present work, we have studied reaction 1 over the temperature range 2700-3600 K (nearly coincident with the temperature range covered by Tabayashi et al.) using CN broad-band absorption spectroscopy, and attempted to resolve the discrepancy between the results of ref 2 and the combined results of ref 1 and 3. Since this reaction is one of a few where rate data are available over such a wide temperature range (almost 3000 K), an accurate determination of kl should enable useful tests of unimolecular reaction rate theories.
Experimental Section The experiments were conducted behind incident shock waves in a 15.2-cm i.d. stainless-steel pressure-driven shock tube, which is described in more detail in ref 3. Mixtures of HCN in Ar (Airco Industrial Gases, 0.75% in Ar, with the following analyzed impurities:
