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Journal of Electrostatics 67 (2009) 381–383

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Journal of Electrostatics

journal homepage: www.elsevier .com/locate/e lstat

Measurements of DC conductivity of suspensions in non aqueous media

Manuel Medrano, Carlos Soria-Hoyo, Alberto T. Perez*

Departamento de Electronica y Electromagnetismo, Facultad de Fısica, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain

a r t i c l e i n f o

Article history:Received 18 September 2008Received in revised form18 November 2008Accepted 11 January 2009Available online 27 January 2009

Keywords:Electrical conductivityColloidal suspensionDielectric liquidLow conducting liquid

* Corresponding author. Tel.: þ34 954556409; fax:E-mail addresses: mmedrano@us.es (M. Medrano),

alberto@us.es (A.T. Perez).

0304-3886/$ – see front matter � 2009 Elsevier B.V.doi:10.1016/j.elstat.2009.01.009

a b s t r a c t

The experimental determination of the electrical conductivity of very insulating liquids is as difficult asimportant in Electrohydrodynamics. Conductivity is a relevant property in many applications and basicphenomena. In colloidal suspensions the conductivity is directly related to the electrical and chemicalrelaxation times, the electrokinetic phenomena or the colloidal stability. Previous studies show theimportance of measuring the dependency of the conductivity on the solid fraction of the particles, s(4).In this paper we present a set of measurements of the conductivity of a suspension of silica nanoparticles(with a diameter of the order of 30 nm) synthesized by the Stober’s method. The measurements aremade with the help of a suitable device designed and built in our laboratory. The measurements havebeen done for up to 4% volume concentration, in a mixture of 70% of toluene and 30% of ethanol.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Colloidal suspensions in low conducting liquids have manyindustrial applications in painting, printing, xerography, and oilindustry. Their electrical properties are relevant in many processes.Not only those involving sophisticated electrical devices, e.g. liquidxerography, but also in common procedures as pumping or drain-ing. One of these relevant properties is the electrical conductivity.

The electrical conductivity determines, for example, the electricfield distribution in a non-homogeneous suspension subjected toan external electric field [1]. The conservation of charge imposesP$sE¼ 0 (s is the conductivity of the suspension and E the electricfield), and the way in which s depends on the particle concentra-tion determines the field distribution.

The electrical conductivity is also a key parameter in preventingfuel hazards. If the conductivity of the fuel is too low the ducts mayaccumulate charge when the liquid is pumped trough them. Thisaccumulation of charge may produce high voltages that, eventually,lead to electrical discharges, sparks and, finally, explosions. Toprevent these hazards fuels are usually doped with suitable addi-tives. It is then important to determine the influence of the addi-tives on the conductivity of the material.

The conductivity of dielectrics is related to their dielectricconstant. Polar liquids, with high dielectric constant, are goodconductors. Their polar molecules surround the ions in such a way

þ34 954239434.cshoyo@us.es (C. Soria-Hoyo),

All rights reserved.

that the electric field produced by the ion is screened. This mech-anism favors ion dissociation and the production of charge carriers.Apart from water, the conductivity of self-ionized liquids such asalcohols and acids is high.

On the contrary, low dielectric constant liquids do not self-ionize and exhibit a much lower conductivity. For these liquids thecharge carriers come from the ionization of impurities, in particularresidual water. When the samples are filtered and deionized theconductivity may decrease by several orders of magnitude. Shar-baugh (cited by Watson [2]) obtained for hexane conductivitya value as low as 10�17 U�1 m�1 after drying and purifying thesample. This is to be compared with 10�12 U–1 m�1, a typical valuefor grade hexane. Therefore, the conductivity of non-polar liquids issometimes a not well defined quantity. If the experimental condi-tions are not very carefully controlled it can vary erratically. Themain problem that we confront when trying to measure theinfluence of particles on the conductivity of a suspension in non-polar liquids is that we have to be able to measure small deviationsin an already ill defined quantity.

From the theoretical point of view the simplest model is that ofMaxwell–Wagner (see, for instance [3]). The influence of theparticles is taken into account just solving the potential problem ofa conducting sphere of conductivity sp immersed in a medium ofconductivity s0. The effective conductivity of the suspension isgiven by:

s ¼ s01þ 2Uf

1� Uf(1)

Fig. 2. Scanning electron microscope image of silica particles fabricated by directapplication on the Stober’s method with average diameter of 30 nm.

M. Medrano et al. / Journal of Electrostatics 67 (2009) 381–383382

where U is defined as:

U ¼ sp � s0

sp þ 2s0(2)

and f denotes the volume fraction of particles. For insulatingparticles and dilute suspensions this expression gives s¼ s0(1�34/2). However this formula is seldom of application because it doesnot take into account that the presence of the particles modifies theliquid environment.

Different authors have studied theoretically the dependence ofthe conductivity on the concentration of particles (see, for example,[4,5]). All these theories and models were elaborated for aqueoussuspensions and are based on the theory of the double layer ofDVLO, or modifications of it. Most authors agree that the DVLOtheory should be valid for non-aqueous media, even for veryinsulating liquids [6]. However, few experimental works existdevoted to measure the change in electrical conductivity of lowconducting liquids due to particle addition.

In this paper we present some measurements of the conduc-tivity of a suspension of silica particles in a mixture of toluene andethanol. The measurements have been done using a devicedesigned and built in our laboratory.

2. Description of the conductivity-meter

The main part of the conductivity meter is a pair of stainless-steel circular plane–parallel electrodes [7]. The gap between themis adjustable. The lower electrode has the shape of a vessel andcontains the sample. The upper electrode is surrounded by a guardring and is anchored to a very precise mechanical sliding system, toassure the parallelism between the electrodes at every gap width.The sliding system is driven by a stepper motor. The gap width ismeasured by means of a digital micrometer (Mitutoyo Absolute).Fig. 1 shows a vertical section of the device.

A voltage, produced by a programmable function generator(TTi TG1010A), is applied to the lower electrode. The electriccurrent intensity I is measured through the upper electrode. Theelectrode radius is 3 cm. The current intensity is measured bya highly precise electrometer (Keithley 6512). The whole system isgoverned by a desktop computer equipped with adequate inter-faces to communicate with the devices.

Fig. 1. Assembly section of the conductivity meter: sliding electrode (1), fixed elec-trode (2), guard ring (3), external frame (4), sliding system (5), Teflon block (6), Teflonring (7), driving motor (8), output BNC jack (9), input BNC jack (10), micrometer (11)and sliding system shafts (12).

Low conducting liquids often exhibit non-ohmic behavior.Among the mechanisms that may lead to non-ohmic behavior aresaturation, electric field enhanced dissociation, and injection. A briefdescription of these mechanisms may be found in [8]. Only when anohmic behavior is assured does the conductivity becomes a mean-ingful property. Therefore, we follow an automatized procedure inwhich, for a given gap, the electric current is measured for differentvoltages. For every value of the gap the linear behavior of the currentversus the voltage is checked. The resistance of the cell is computedand plotted versus the distance between the electrodes. From theslope of the last plot we obtain the conductivity.

3. Sample preparation

Silica particles have been synthesized using the method ofStober et al. [9]. This method provides a set of particles of welldefined size. The silica is obtained from the reaction of Tetra Ethyl

25

30

35

40

45

50

55

1 1.5 2 2.5 3 3.5 4

σ(μS

/m

)

Φ (%)

Fig. 3. Conductivity as a function of solid fraction for suspension of particles of averagediameter 30 nm in a toluene–ethanol mixture. Measurement uncertainties are of theorder of size of the symbols. The solid line is a linear fit to the data, without taking intoaccount the values for 4¼ 4%. The dotted line is the �3/2 slope from the Maxwell–Wagner equation.

M. Medrano et al. / Journal of Electrostatics 67 (2009) 381–383 383

Orthosilicate (TEOS) with water in alcoholic solution, usingammonia as a catalyst. These reactants are mixed in an Erlenmeyerflask and continuously stirred at laboratory temperature for severalhours. In order to stabilize the suspension a coating is added to theparticles. This coating is achieved by the addition of Phenyl-triethoxysilane (Fluka) at the final stage of the synthesis procedure,once the particles have reached their final sizes [10]. The amount ofammonia in the solution controls the size of particles. The less thequantity of ammonia used the smaller the size of the synthesizedparticles. Fig. 2 shows a photograph of the particles.

4. Results and discussion

Fig. 3 is a plot of the conductivity of a suspension of silicaparticles (diameter 30 nm) in a mixture of toluene and ethanol.Every point on the graph was obtained from several measurementsof the resistance of the cell for different spacing between theelectrodes, as we have explained above. The different pointscorrespond to different samples of the same flask. For the mostconcentrated sample the results present a bad reproducibility.

Initially conductivity tends to decrease with particle volumeconcentration. This decrease is faster than the expected 3/2 factorfor non-conducting particles (s¼ s0(1�34/2)). However, we havecomputed the volume fraction assuming that the particle size is theone measured with the Scanning Electron Microscope photographs.Aggregation may produce a greater effective size, and the slopewould differ from 3/2 in that case. An adsorption of ions in theinterface may be also at the origin of this deviation, but we thinkthat this adsorption will produce an increase of the conductivity,instead of a decrease.

The lack of reproducibility of the most concentrated samplesmay be due to the formation of gels. We have observed these gels at

this concentration, but they are not very stable and are easilydestroyed by simple agitation. The non-homogeneous formation ofthis gel could be at the origin of the dispersion in conductivity,though we do not have a definite proof of this statement.

Finally there remains the question of the influence of particlesize on the conductivity. Previous measurements [11] made forgreater particles showed that their presence clearly increases theconductivity of the suspension. Since the procedure of synthesis,the mixture and the technique of stabilization are the same thisdifference should be, in principle, attributed to a size effect. This isan open question that deserves further investigations.

Acknowledgments

This research has been supported by Spanish Ministerio deCiencia y Tecnologıa (contract FIS2006-03645) and Junta deAndalucıa (contract FQM-421).

References

[1] T. Perez, D. Saville, C. Soria, Europhys. Lett. 55 (2001) 425–431.[2] K. Watson, in: A. Castellanos (Ed.), Electrohydrodynamics, 1998, pp. 166.[3] F. Zukoski, D.A. Saville, J. Colloid Interface Sci. 115 (1986) 422–436.[4] A. Saville, J. Colloid Interface Sci. 91 (1983) 34–50.[5] A. Watillon, J. Stone-Masui, J. Electroanal. Chem. 37 (1972) 143–160.[6] V. Delgado, F. Gonzalez-Caballero, R.J. Hunter, L.K. Koopal, J. Lyklema, J. Colloid

Interface Sci. 309 (2007) 194–224.[7] M. Medrano, A.T. Perez, C. Soria-Hoyo, J. Phys. D Appl. Phys. 40 (2007)

1477–1482.[8] A. Castellanos, A.T. Perez, in: Tropea Cameron, Yarin Alexander L., Foss John F.

(Eds.), Electrohydrodynamic Systems, Springer Handbook of ExperimentalFluid Mechanics, 2007.

[9] W. Stober, A. Fink, E. Bohn, J. Colloid Interface Sci. 26 (1968) 62–69.[10] A.P. Philipse, A. Vrij, J. Colloid Interface Sci. 128 (1989) 121–137.[11] M. Medrano, C. Soria-Hoyo, A.T. Perez, IEEE Trans. DEIS 16 (2) (2009).