J . Phys. Chem. 1987, 91, 6329-6331
6329
A Precision Dielectric Time Domain Spectroscopy Method in the Gigahertz Range B. Gestblom,* E. Noreland, Department of Physics, Uppsala University, S - 751 21 Uppsala, Sweden
and J. Sjoblom Institute for Surface Chemistry, S-114 86 Stockholm, Sweden (Received: June 29, 1987; In Final Form: October 2, 1987)
It is shown how the single transmission time domain spectroscopy (TDS)method can be used to accurately determine the dielectric spectra of low-permittivity liquids in the gigahertz range up to 16 GHz. The method is tested on dilute solutions of trioxyethylene dodecyl ether and 1-hexanol in n-heptane, and dispersions with a dielectric increment of a few hundredths are characterized.
Introduction The permittivity spectrum of a material is usually measured in the frequency domain by spot measurements over a wide frequency range. In recent years the development of time domain methods (TDS) has offered an alternative measurement technique. The dielectric properties of a sample are determined from a study of the influence of the sample on the shape of a step pulse propagating in a coaxial line. Various arrangements of the sample have been considered. In the single reflection method only the pulse reflected at the first interface between air and a long sample is used. Later development has given methods in which the totally reflected pulse shape from a short sample is studied. The sample can in this case be terminated in different ways-by a short circuit, by a matched circuit, or by an open circuit-each method having its advantages.’ Instead of studying the reflected pulse shapes, one can alternatively obtain the dielectric properties from the shape of the pulse transmitted through the sample. Also in this case a long sample can be used, the single transmission method, or the totally transmitted pulse through a short sample, the total transmission method.2 The TDS technique has been mostly used to study dielectrics of medium and high permittivity, typical examples being alcohols and aqueous solutions. However, precision total reflection methods have been presented where dispersions with a dielectric increment as low as 0.2 or less can be characterized in the range 1 GHz and below.3-s The total transmission method has been shown to be suitable for measurements up to N 10 GHz in systems of medium to high permitti~ity.~.’It is the aim of this letter to demonstrate how the single transmission method can also be adopted to give a permittivity spectrum with high precision in the gigahertz range for low-permittivity liquids. Theory The setup of the transmission TDS measurement is schematically illustrated in Figure 1. The step pulse from the pulse generator is divided by a power splitter into the two channels. The pulse registered in channel B is used for time referencing, with the pulse in channel A used for the actual measurements.8 The (1) For a review see: van Gemert, M. T. C. Philips Res. Rep. 1973, 28, 530. Cole, R.H.Annu. Rev. Phys. Chem. 197’1, 28, 283. (2) Gestblom, B.;Noreland, E. J. Phys. Chem. 1977, 81, 782. (3) Cole, R. H.; Mashimo, S.; Winsor, P. J. Phys. Chem. 1980,84, 786. (4) Nakamura, H.; Mashimo, S.; Wada, A. Jpn. J . Appl. Phys. 1982, 21, 1022.
(5) Chahine, R.;Bose, T. K. IEEE Trans. Instrum. Meas. 1983, 32,360. (6) Gestblom, B.; El-Samahy, A.; SjBblom, J. J . Solution Chem. 1985,14, 375. (7) Gabriel, C.; Grant, E. H.; Tata, R.; Brown, P. R.; Gestblom, B.; Noreland, E. Nuture (London) 1987, 328, 145.
0022-3654/87/2091-6329$01.50/0
incident pulse u(t) and the transmitted pulse r(t) are Fourier transformed into the frequency domain
F(w) = ~ : f ( t ) e - i ydtf and the transmission coefficient T(w) = R(w)/V(w)is evaluated. Transmission line theory gives the transmission coefficient as a function of w , Le., also as a function of the permittivity t * ( w ) = & ( w ) - it”(w). In a single transmission measurement the dielectric sample is sufficiently long to allow a study of only the first transmitted pulse through the sample. All subsequent parts of the totally transmitted pulse shape are then kept outside the studied time window. The transmission coefficient to be used when the pulse transmitted through the sample is compared to the pulse transmitted through the same length of air-filled line is given by
Here I is the sample length and c is the speed of light in free space. It is seen that the exponential term will create large phase shifts in the transmission coefficient. This property of the transmission coefficient also makes the method inherently suitable for precision TDS measurements at high frequencies. In a TDS measurement it is extremely important to have an accurate determination of a common time origin in the Fourier transformation of the two studied pulse shapes. A time origin error At will, as seen from eq 1, lead to a phase error A$ = wAt; Le., the phase error becomes progressively worse with increasing frequency. A timing uncertainty of 1 ps will thus at 10 GHz lead to a phase uncertainty of 3.6’. Such a phase error will for reflection TDS methods lead to large uncertainties in the calculated permittivity values. However, as seen from eq 2 the large phase shifts in T ( w ) , created by the long sample, makes the single transmission method less sensitive in this respect. For a lowpermittivity sample the phase of the transmission coefficient T ( w ) is essentially given by $ = wlv‘/7/c. A time reference uncertainty At will thus lead to a permittivity uncertainty of A& = 2cv’/’At/l. Again assuming At = 1 ps, for a sample length I = 0.3 m and a low permittivity e’ = 2, one obtains an uncertaintly as low as Ae’ N 0.003. In the time referencing method shown in Figure 1, the halfheight point of the time reference pulse is used as the time origin. This method has been found to give an uncertainty in an individual measurement of At < 0.5 ps. The remaining uncertainty is of random nature and not dependent on systematic errors in the time (8) Gestblom, B.; Jonsson, B. J . Phys. E 1980, 13, 1067.
0 1987 American Chemical Society
6330 The Journal of Physical Chemistry, Vol. 91, No. 25, 1987 CURRENT SUPPLY
Letters
DIODE 2 00
OSClLLOSCOPE
198
F q1 B
196
SAMPLER A
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Figure 1. Schematic diagram of the computer-controlleddual-channel
TDS system.
:
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referencing method. It can thus be reduced by repeated independent measurements and averaging, further reducing the remaining uncertainty in ef. The amplitude of the transmission coefficient I7l is essentially determined by the real part of the exponent, the attenuation Q (Y = w t f f / 2 c d / ; ; . coefficient for a2 low permittivity dielectric being An error in I'Zl will thus lead to an error in the loss factor of Aeff = 2cd/;;AlTJ/wllTl. For a low-permittivity liquid it can be estimated that at sample length 0.3 m a relative uncertainty in the amplitude of the transmission coefficient of 1% will lead to an uncertainty in cf' of order 0.001 in the gigahertz range. The random noise uncertainty in 1 i l can be brought down to this low level by repeated independent measurements and averaging. The presence of unwanted reflections in the coaxial line due to mismatches in connectors will introduce errors in the transmission (or reflection) coefficient to be used in evaluating the permittivity. The influence of these anomalies can be substantially reduced by measuring relative a sample with known dielectric parameters instead of relative an empty cell. If this reference sample has dielectric parameters close to those of the studied dielectric, the unwanted reflections will be nearly identical and according to the convolution theorem cancel out in the evaluation of the transmission coefficient. In a precision measurement one should thus compare the pulse transmitted through the reference dielectric, rrefto the pulse transmitted through the same cell filled with the sample under study, r ( t ) . The corresponding equation in €*(a)is (3)
where T(w) is given by eq 2 and Tref(w)is calculated from the same equation with the known dielectric spectrum E * ~ ~ ~ ( W ) .
Results The TDS method discussed above should be suitable in the study of the dielectric properties of dilute solutions of a polar compound in a nonpolar solvent. The appropriate reference liquid is the pure solvent for which the dielectric constant is accurately known. As tests of the method, two dilute solutions in n-heptane are investigated. The first sample was prepared by dissolving 0.8 mL of trioxyethylene dodecyl ether (CI2EO3,ultrapure) in 22 mL of nheptane. Measurements were done at 20 "C with a coaxial measuring cell of length 292.5 mm. In the measuring sequence the sample liquid and the reference liquid were alternatively injected into the measuring cell. This change of sample can be rapidly made without disassembling the coaxial line, which ensures the constancy of the measuring conditions. Each pulse shape is the average of 25 scans as discussed in ref 8. The transmitted pulse shapes were stored and the dielectric spectra worked out for the independent fillings of the cell with the sample liquid and
O
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=
2 00
E'
1 5
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Figure 2. Permittivity spectrum (with error bars) of a 3.5% solution of trioxyethylene dodecyl ether in n-heptane and its Cole-Cole plot. The full line gives the theoretical spectrum calculated with the Cole-Cole function, eq 4.
the n-heptane reference ( e , = 1.924). In a single transmission measurement the time window must be sufficiently long to allow the first transmitted pulse to reach its steady state but still short enough to keep the remaining part of the totally transmitted pulse shape outside the studied time window. At the same time the lengths of the coaxial line should be chosen so that the unavoidable reflections from the sampler and its connectors are kept outside the time window, thus not distorting the studied line shapes. In the present measurements a 5-11s time window was used. The requirement of a steady final level of the transmitted pulse makes the single transmission method less suited for the study of conducting samples. This is in contrast to the total transmission method, which is well-suited for conducting dielectrics and where the time domain pulse levels may in fact directly give the cond~ctivity.~ The stored pulse shapes were Fourier transformed and the e', e" values worked out at 25 frequencies in the range 400 MHz to 15.9 GHz. The mean value and its standard error obtained from 20 pairs of pulse shapes gave the final permittivity spectrum with its uncertainties. The result is presented in Figure 2 where a Cole-Cole diagram of the spectrum is also included. As seen from the diagram, a weak dispersion with a dielectric increment of a few hundreths can be accurately measured. The small standard errors show that good permittivity data can be obtained even up to 15.9 GHz with the present method. The spectrum is fitted by a Cole-Cole function (4)
with parameters e, = 2.014, e, = 1.947, 7 = 19.9 ps, and a = 0.201. The theoretical spectrum is included in the figure. The relaxation is due to the dipolar reorientations of the ethoxy units in the polar molecule. Due to conformational effects, a distribution ( a ) in relaxation times can be expected. As a second test case a 10% solution (by volume) of 1-hexanol in n-heptane was studied. In this case four independent mea(9)Gestblom, B.; Elmgren, H.Chem. Phys. Lett. 1982, 90, 412.
J. Phys. Chem. 1987, 91, 6331-6333
6331
surements of sample and reference were made. The result is presented in Figure 3. With the lower number of measurements the upper frequency is reduced to 11.7 GHz. The spectrum of pure 1-hexanol has been analyzed in terms of a three relaxation time Debye model functionlo €*(W)
=
e2 - e, 6s €1 - €2 ++ +1 + iwrl 1+iw2 1+i w e1
€,
(5)
~ ~
The main dispersion with relaxation time T~ is attributed to a cooperative relaxation involving the breaking of hydrogen bonds in the alcohol hydrogen-bonded network. The second dispersion has been explained by a reorientation of alcohol monomers characterized by a relaxation time 72. Finally, the relaxation 7 3 has been attributed to a rapid OH group reorientation. The model function eq 5 also fits the spectra of 1-hexanol in higher concentrations in a hydrocarbon like n-heptane." However, in their study of low-concentration l-hexanol solutions Glasser et a1.I2 used a two relaxation model function to fit their data, an introduction of the low-frequency relaxation process not being warranted by the experimental accuracy. With the increased number of frequencies from the TDS measurement this model function can be critically tested. The data in Figure 3 were fitted to the two relaxation time model function. In this fit the shortest relaxation time T~ was set to 3 ps as taken from the analysis of Glasser et a1.,12 this value being based on measurements a t frequencies above the TDS frequency window. With the low concentration studied it was also found appropriate to set e- to the n-heptane value of 1.924. The result of the fit is shown by the broken curve in Figure 3. Systematic deviations between experimental and theoretical data can be observed. (10) Garg, S. K.; Smyth, C. P. J . Phys. Chem. 1965, 69, 1294. (1 1) Noreland, E.; Gestblom, B.; Sjhblom, J., to be published. (12) Glasser, L.; Crossley, J.; Smyth, C. P. J. Chem. Phys. 1972, 57, 3977.
01
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'
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,
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Figure 3. Permittivity spectrum of a 10% solution of I-hexanol in nheptane. The broken line gives the best fit of a two relaxation time model function, while the full line gives the theoretical spectrum obtained by using a three relaxation time model function, eq 5.
The same fit with the three relaxation model eq 5 is shown by the full drawn curve. The parameters used are e, = 2.059, el = 2.043, e2 = 2.020, e, = 1.924, T~ = 164 ps, T~ = 40 ps, and r3 = 3 ps. The near-perfect agreement between experimental and theoretical data is seen in the root-mean-square deviation - c*theorl = 0.002. This indicates that the low-frequency dispersion still remains, albeit with a very low dielectric increment, also at the low concentration studied of 1-hexanol in n-heptane. Studies of 1-hexanolln-hexane solutions at higher concentrations give relaxation times r1which agree with the value of 164 ps obtained here for the 10% solution." The suggestion of Glasser et al.12 that the low-frequency process may remain to a small extent even in dilute alcohol solutions thus seems validated.
X-ray Photoelectron Spectroscopy Study of Molybdenum Clusters in Zeolite Y Y. S. Yong, R. F. Howe,* Chemistry Department, University of Auckland, Auckland, New Zealand
A. E. Hughes, H. Jaeger, and B. A. Sexton CSIRO Division of Materials Science and Technology, Clayton, Victoria, Australia 31 68 (Received: July 16, 1987)
An X-ray photoelectron spectroscopicstudy is described of Mo clusters in zeolite Y formed by the adsorption and decomposition of Mo(CO)~.The XPS data show that this method produces a uniform dispersion of Mo. The Mo clusters have a Mo 3d binding energy ca. 1.2 eV higher than that of bulk Mo, which is attributed to their small size (612 A).
The well-defined three-dimensional open pore structure of zeolite Y provides a unique environment to form small metal clusters and examine their catalytic properties. Zeolites containing the group VI11 (groups 8-10)15 metals in particular have been extensively studied.' The metal is usually ion exchanged into the zeolite as an ammine complex and then subjected to careful oxidation and reduction treatments to produce highly dispersed metal clusters. An alternative approach, suitable for metals which are not so readily reduced, is to adsorb a zerovalent carbonyl complex into the zeolite and remove the carbonyl ligands by mild heat treatment; this avoids the need for high-temperature reduction (1) Gallezot, P. Calal. Rev. Sci. Eng. 1979, 20, 121.
which can cause sintering and migration of metal out of the zeolite pores. * We have recently described the preparation of highly dispersed molybdenum clusters in zeolite Y by the adsorption and decomposition of M o ( C O ) ~in Provided that the zeolite contains no protons (which can oxidize Mo, generating H2), removal of the carbonyl ligands in the complete absence of O2should leave molybdenum in the zerovalent state. Similar chemistry has been proposed for Mo(CO), decomposition on extensively dehydrox(2) Howe, R. F. In Tailored Metal Catalysts; Iwasawa, Y . ,Ed.; Reidel: Amsterdam, 1986; p 141. (3) Yong, Y . S.; Howe, R. F. J . Chem. SOC.,Faraday Trans. 1 1986,82, 2887.
0022-3654/87/2091-633 1%01.50/0 0 1987 American Chemical Society
