conclusion that Walden''s rule is not applicable for a variety of dielectric liquids. Index Terms - Ion mobilities, silicone oil, transformers, Electrical property, ...
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W. F. Schmidt and K. Yoshino: Ion Mobilities in Non-Polar Dielectric Liquids: Silicone Oils
Ion Mobilities in Non-Polar Dielectric Liquids: Silicone Oils Werner F. Schmidt Formerly at Hahn-Meitner Institute Berlin, Germany and Katsumi Yoshino Shimane Institute for Industrial Technology Matsue, Japan
ABSTRACT Silicone oils have been applied as replacements for mineral oils in transformers and other electrical equipment. Investigations of their electrical and thermo-physical properties have been carried out. Few studies of the measurements of positive and negative ions in these liquids exist. The present paper summarizes the data published. The modes of charge transport in these liquids are discussed on the basis of the Stokes model, which leads to the Walden’s rule. Comparison with data of other dielectric liquids leads to the conclusion that Walden’s rule is not applicable for a variety of dielectric liquids. Index Terms - Ion mobilities, silicone oil, transformers, Electrical property, thermal property, physical property, Stokes model, Walden rule.
1 INTRODUCTION SILICONE oils are a class of synthetically produced nonpolar dielectric liquids, which find applications in various electrical installations. Japanese manufacturers use silicone oils as insulant and cooling agent in railway transformers [1]. Several studies of the electrical properties of silicone oils have been carried out [2,3], but data of the ion mobility in these liquids are scarce. Silicone oils – chemically labeled as polysiloxanes – are also of interest for basic physical and chemical investigations. One group of silicone oils are composed of alkane hydrocarbon groups attached to the - Si-O- backbone. In another class in addition aromatic groups are attached. In Figures 1a and 1b the structure formulae of poly-dimethysiloxane and polymethyl-phenylsiloxane are depicted.
The viscosity and the molecular weight of these oils increase with increasing chain length, or number of subunits n. The following table 1 gives some approximate data for Wacker silicone oils [4]. Table 1. Approximate data of chain length, viscosity and molecular weight for poly-dimethylsiloxanes.[4]
viscositycSt 0,65 50 100 1000 10000
n 0 40 70 200 500
MW[g/mol] 162 3000 5000 15000 37000
CH3 CH3
Si CH3
O
2 ION MOBILITY MEASUREMENTS
CH3 n
Figure 1a. Poly-dimethysiloxane; n number of subunits
Figure 1b. poly-methyl-phenylsiloxane; n number of subunits. Manuscript received on 28 October 2014, accepted 19 January 2015.
Since the oils are insulators with a large band gap thermal generation of charge carriers can be neglected. Ions have to be introduced by application of external agents. Ionization by high energy x-rays is one method to introduce excess charge carriers into the liquid sample. Energetic UV light can also be used to inject electrons from a photo cathode or to produce a layer of ionization behind a MgF2 window. Since the silicone oils exhibit a very low vapor pressure an electron beam impinging on the surface of a liquid layer can also induce ionization. Another method relying on tunnel diodes can be used for injection of positive and negative charges. Generally, the drift mobility of the charge carriers in an electric field is measured. In lack of theoretical treatments of the ion mobility in these liquids, the data are analyzed by means of Walden’s
DOI 10.1109/TDEI.2015.005036
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 22, No. 5; October 2015
rule [5], which states that the product of liquid viscosity and mobility is constant.
µr u K const
If ions change their transport mechanism the apparent mobility is given by
(1)
The rule was formulated in the beginning of the 20th century when Walden analyzed data of the conductivity of organic solvents. Schmidt and Holroyd [6] irradiated the silicone sample in a parallel plate conductivity cell with a short flash of high energy x-rays. The observed decay of the current in time is then due to the motion of positive and negative ions. The method has been described repeatedly (c.f. Schmidt [7]). The liquid was subjected to a nano-second pulse of x-rays. The observed current trace was due to the simultaneous drift of positive and negative ions. Defined negative ions could be produced by the addition of SF6, which captures the primarily generated electrons and produces negative SF6 ions. The mobility of the negative SF6 ions yielded a clear linear decay of the ionization current followed by the drift signal of the positive ions. Without an addition of a scavenger of positive ions the decay of the ionization current did not exhibit a clear linear decay but reached I=0, which seemed to indicate that ions of various mobilities were present. The values given in Figure 2 are the lowest mobilities consistent with the decay curves. Included are the data of Chemin [3], who generated positive ions by photo ionization.
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1
1
P
P1 P2
P
P1P 2 P1 P2
or
1
(2a)
(2b)
The Holroyd data can be fitted to equations 2a and b. The conditions for negative ions are different (Figure 3).
Figure 3. Mobility of negative ions in poly dimethylsiloxane at T § 293K.
. Figure 2. Mobility of positive ions in poly-dimethylsiloxane oil at T § 293 K. One may speculate that the mechanism of migration of positive ions changes above 20cSt. At lower viscosities friction is the determining process (µ1), while at higher viscosities local arrangement of long molecules may influence the transport mechanism (µ2). In addition it is possible that the positive charge migrates along the molecular chain and then transferring to an adjacent molecule, or in other words, the whole charge-molecule complex remains more or less stationary, while the positive charge migrates along the chain.
While the data of Tsuchida [8] seem to follow Walden’s rule, the values of Holroyd and Chemin deviate considerably. Tsuchida’s negative ions were generated by the injection of electrons into the liquid from a tunnel diode. These electrons probably became attached to ever present impurities and migrated as ions. The most likely solute is oxygen, which would produce ions of smaller radius than that of the silicone oil molecules. On the other hand their data might also indicate that at viscosities above 100 cSt the same leveling off of the mobilities occurs as observed for positive ions of Schmidt and Holroyd (Figure 2). While the data of Tsuchida seem to follow Walden’s rule, die values of Holroyd and Chemin deviate considerably. Mobility measurements in poly-methylphenylsiloxane were presented by Watson [9]. A layer of liquid was irradiated by an electron beam, which served as an injection source of electrons. Another electron beam parallel to the surface measured the potential. From its variation in time the drift mobility was estimated. Three different liquids were investigated with n = 2, 7, 9 [see Figure 1b]. His data he attributed to the drift of negative ions. The viscosity was
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W. F. Schmidt and K. Yoshino: Ion Mobilities in Non-Polar Dielectric Liquids: Silicone Oils
changed by temperature. The evaluation according to Walden’s rule required a modification of equation (1) as,
µr u K N
const
(3)
The data are shown in Figure 4. The value of from 1.07 (n=9), to 1.37 (n=2).
N
varied
hydrocarbons [11, 12]. It is interesting to note that except in the work of Tsuchida et al [8] the mobility of the negative ions does not follow Walden’s rule strictly. The slope of the data is less than -1. In the simple model of Walden’s rule it is assumed that the bare ions surround themselves with a layer of tightly bound neutrals. This holds for instance for ions in water, where the size of the ionic core is comparable to the size of the neutrals. In silicone oils, the polysiloxane molecules are much bigger in size than the size of the scavenger molecules. The idea of a tightly bound solvation shell probably has to be replaced by a model where the migration of defined negative ions occurs with the participation of the movement of sections of the polymer molecule rather than with a movement of the whole ion/neutral complex.
3. DISCUSSION The scarce mobility data of ions in silicone oils do not allow the development of a clear model of the ionic transport. It is interesting to compare the silicone data with data of other non-polar dielectric liquids. Ion mobilities were reported for liquid alkanes and the applicability of Walden’s rule was found to hold for negative ions but the data of positive ions exhibited a Figure 4. Mobility of negative ions in poly-methyl-phenyl-siloxane; data from Watson [9].
Measurements of negative and positive ions in 50 cSt silicone oil have been published by Casanovas et a. [10]. Their results are summarized in Table 2. Table 2. Negative and positive ion mobilities in purified polymethyl siloxane oil containing N2, N2O or C7F14 (data of ref. [9])
These values fit into the general order of magnitude of mobilities of negative ions of Holroyd and Chemin depicted in Figure 3. Tsuchida et al. [10] studied the influence of various impurities on the mobility of negative ions in silicone oil of 10 cSt. Besides electron acceptor molecules they investigated also the influence of a group of alcohols CnH2n-OH on the ion mobility. Negative impurity ions generated by electron attachment to various acceptors exhibited a dependence on the molecular weight of the acceptor. The heavier acceptor gave lower mobilities. In the case of the alcohols there was an inverse dependence of the ion mobility on the molecular weight from n=1 to n=10. While electrons probably don’t attach to alcohols, the formation of some sort of solvation shell is possible, as has been found for negative ions in moist
dependence of the mobility µ+ on the viscosity as µ+ ~ K
-
3/2
[13]. A later attempt by Adamczweski and Calderwood [14] to rationalize this relationship did not yield any physical explanation. The kinematic viscosity of liquid hydrocarbons at 293K changes from 0.44 cSt for nhexane to 4.9 cSt for n-hexadecane. Silicone oils exhibit a much wider range of viscosities. While the low viscosity oils may be comparable to liquid hydrocarbons, the high viscosity siloxanes approach the properties of polymers. There are some examples, where Walden’s rule is obeyed approximately. Hilt et al [15] measured the mobility of defined positive and negative ions in liquid Xenon. The viscosity of the liquid xenon was varied by variation of the temperature. The ions observed drag a solvation shell with them, the size of which depends on the temperature. The Stokes’ law states that a balance exists between the externally applied force and the force exerted by friction on an object. It works well with iron balls falling in mineral oil. In a simple theory of ionic transport the ions are considered as spherical particles, which are under the influence of the electric force and the frictional force. For the mobility the Einstein- Stokes’ formula is obtained,
P
e 6SKR
(4)
We may speculate that Walden’s rule may also work better, if the ions are of bigger size. Measurements of the mobility of C60 and C70 ions in various liquid hydrocarbons gave good agreement with Walden’s rule [16]. Further development of the understanding of ion mobility in non-polar liquids requires theoretical
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 22, No. 5; October 2015
approaches for each liquid beyond Walden’s rule. Discussion of the data from liquid xenon shows that this is a challenging task [17]. In case of the silicones probably concepts, which have been developed for charge transport in polymers or liquid crystals have to be introduced [18].
REFERENCES [1]
S. Yasufuku, T. Umemura and Y. Ishioka, “Phenyl methyl silicone fluid and its application to high voltage stationary apparatus”, IEEE Trans. Electr. Insul., Vol. 12, pp. 402-410, 1977. [2] R.M. Hakim, R.G. Oliver and H. St-OngeA. Chemin, “The dielectric properties of silicone fluids”, IEEE Trans. Electr. Insul., Vol. 12, pp. 360-370, 1977. [3] A. Chemin, “Etude des mobilites ioniques dans les huiles silicones du type polydimethylsiloxane“, Doctorat de 3eme cycle, University Paul Sabatier, Toulouse, France, 1985. [4] A.G. Wacker, technical information, 2014. [5] P. Walden, “Über organische Lösungs- und Ionisierungsmittel III. Teil: Innere Reibung und deren Zusammenhang mit dem Leitvermögen” Z. Physik. Chem., Vol. 55, pp. 207-249, 1906 (in German). [6] W.F. Schmidt and R.A. Holroyd, “Ion mobilities and yields in xirradiated polydimethylsiloxane oils“, Int’l. J. Radiat. Appl. Insrtrum. Part C, Vol. 39, pp. 349-353, 1992. [7] W. F. Schmidt, Liquid State Electronics of Insulating Liquids, CRC Publishers, Baton Rouge, 1996. [8] N. Tsuchida and M. Ueda, “Ionic behaviours in silicone oil“, J. Phys. D: Appl. Phys., Vol. 13, pp. 1681-1687, 1980. [9] P.K. Watson, “A study of conduction processes in siloxane fluids, using an electron injection techniques for carrier generation“, IEEE Conf. Electr. Insul. Dielectr. Phenomena (CEIDP), pp. 53-56, 1966. [10] N. Tsuchida, H. Sawada and M. Ueda, ”The mobilities of various impurities ions in silicone oil“, J. IEE Japan, Vol. 99A, pp. 535-542, 1979 (in Japanese). [11] A.A. Balakin, B.Z. Kunnarzarov and B.S. Yakovlev, ”Hydrated ions in non-polar liquids, 1. oxygen ions in aqueous solutions of tetramethylsilane Khim. Fiz., Vol. 12, pp. 82-88, 1993 (in Russian). [12] A.A. Balakin, ”Formation of negative chlusterions with water molecules in nonpolar liquids“, IEEE Trans. Dielectr. Electr. Insul., Vol. 16, pp. 1632-1639, 2009. [13] I. Adamczewski Ionization, Conductivity and Breakdown in Dielectric Liquids, Taylor & Francis Ltd, London, 1969 [14] I. Adamczewski and J.H. Calderwood, "Viscosity and charge carrier mobility in the saturated hydrocarbons“, J. Phys. D: Appl. Phys., Vol. 8, pp. 1211-1218, 1975. [15] O. Hilt, W.F. Schmidt and A.G. Khrapak, “ Ionic mobilities in liquid xenon“, IEEE Trans. Dielectrics Electr. Insul.,Vol. 1, pp. 648-656, 1994. [16] G. Bakale, K. Lacmann and W.F. Schmidt, ”C60 and C70 Fullerene ions in nonpolar liquids: Mobility and radiationchemical changes“, J. Phys. Chem., Vol. 100, pp. 12477-12482, 1996. [17] W.F. Schmidt, O. Hilt, E. Illenberger and A.G. Khrapak, ”The mobility of positive and negative ions in liquid xenon“, Rad. Phys. and Chem., Vol. 74, pp. 152-159, 2005. [18] M.S. Mendolia and G.C. Farrington, ”Ionic mobility in macromolecular electrolytes: The failure of Walden’s rule“, Chem. Mater., Vol. 5, pp. 174-181, 1993. [19] K.Yoshino, N.Tanaka and Y. Inuishi, ”Anomalous Carrier Mobility in Smectic Liquid Crystal“, Jpn. J.Appl.Phys., Vol. 15, pp. 735736, 1976.
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Werner F. Schmidt (SM’77) received a Master’s and Ph.D. degrees in physics from the Free University of Berlin, Germany. As a postdoctoral fellow and associate chemist, he spent three years at Brookhaven National Laboratory, New York, USA, working in areas of physical chemistry. In 1969, he entered the Hahn-Meitner-Institute, Berlin, where he initiated a research program on “excess charges in insulators.” As a Privatdozent at the Free University, he supervised the Ph.D. work of 15 graduate students in physics, chemistry and electrical engineering. In 1981 and 1988 he organized international conferences on dielectric liquids, held in Berlin. He published over 250 articles in refereed journals, authored several book chapters, and edited and published several books. During his tenure at the Hahn-Meitner-Institute he spent several sabbaticals at various research institutes: 2 weeks at the Institute for High Temperatures of the former Soviet Academy of Sciences, Moscow; 3 months at IREQ (Institut de Recherche d’Hydro-Quebec) Canada; 18 months at CERN, the European High Energy Physics Laboratory in Geneva, Switzerland, where he collaborated with Carlo Rubbia and Georges Charpak on the development of radiation detectors. Twice he received the prestigious JSPS Award (Japan Society for the Promotion of Science) for stays at Osaka University (1978) and Hokkaido University (1989). He was an Invited Professor at Iwate University, Morioka (1990/91), sponsored by the Japanese Ministry of Education. He organized as director a NATO Academic Study Institute on the properties of electrons in different phases of matter (Patras, Greece, 1993). At the ICDL 1999 he was the Hans Tropper Lecturer. He acted as a consultant for Exxon-Research, New Jersey, for the Istituto Nazionale di Física Nucleare, Rome, Italy and for CERN, Geneva. He was guest editor of IEEE Trans. Electr. Insul. Vol. 24, No 2, 1989. Recently, he served as Editor in Chief of the Journal “Advanced Science Focus” of American Scientific Publishers. Katsumi Yoshino was born in 1941 at Shimane, Japan. He received the B.E. degree from the Department of Electrical Engineering of Osaka University in 1964. After receiving the M.E., and the Ph.D. degrees from the same University, in 1969 he became a research associate at the Department of Electrical Engineering, Faculty of Engineering, Osaka University, and in 1972 he was lecturer at the same university. From 1974 to 1975 he was a visiting scientist at the HahnMeitner Institute for Nuclear Research. In 1978, he was promoted to an associate professor at the same university, and in 1988 he became a professor at the Department of Electronic Engineering, Faculty of Engineering, Osaka University and retired in 2005. Presently, he is Director General of Shimane Institute for Industrial Technology, Emeritus Professor of Osaka University, Guest Professor of Shimane University, Guest Professor of Nagasaki Institute of Applied Science and Guest Professor of Osaka University. His research fields are mainly electrical and electronic materials such as conducting polymers, insulating polymers, liquids, liquid crystals, ferroelectrics, carbons, nanomaterials, superconductors, photonic crystals and displays. He published more than 1400 papers and more than 150 patents. He has received many awards and honors such as IEEE Fellow, The Japan Society of Applied Physics Fellow, The Institute of Electrical Engineers of Japan Fellow, The Institute of Electronics, Information and Communication Engineers Fellow, The Japanese Liquid Crystal Society Award, The Society of Polymer Science, Japan Award, Osaka Scientific Award etc.. He contributed to the progress of science and technology in various societies as active members such as Vice President of The Institute of Electrical Engineers of Japan and President of The Japanese Liquid Crystal Society. He organized several International Conferences such as International Conference on Dielectric Liquids in 1999 at Nara and also contributed a lot as active members of International Conferences such as organizing committee member, advisory member and executive committee member etc..
