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Electrorheological effects in suspensions of hydrophobically modified saponite
Colloids and Surfaces A: Physicochemical and Engineering Aspects 156 (1999) 257 – 269 www.elsevier.nl/locate/colsurfa
Electrorheological effects in suspensions of hydrophobically modified saponite T. Du¨rrschmidt, H. Hoffmann * Physical Chemistry I, Bayreuth Uni6ersity, PF-101251, D-95440 Bayreuth, Germany Received 24 July 1998; accepted 26 November 1998
Abstract The electrorheological (ER) properties of suspensions composed of hydrophobically modified particles of a synthetic clay mineral (saponite) in an oil (n-hexadecane) containing a stabilizing additive were investigated. A comparison was made between the ER response of suspensions with the same volume fraction but with different cationic surfactants adsorbed on the saponite surface and with different additives at various concentrations. The results of these investigations indicate that a direct relationship exists between the stability of the suspensions against sedimentation and the magnitude of the ER effect. In a second series of measurements, the type of surfactant on the saponite surface was kept constant and the volume fraction of the particles was changed. Rheological parameters (yield stress, shear viscosity and dynamic moduli) were measured in dependence of field strength, field frequency and particle concentration. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Saponite; Stability against sedimentation; Magnitude of the ER effect; Rheological parameters
1. Introduction A dramatic and reversible change of rheological properties of a fluid due to the application of a large external electric field was first reported by Winslow in 1949 [1]. This phenomenon is referred to as the electrorheological (ER) effect and has been reviewed in several publications [2 –9]. Electrorheological fluids (ERF) have attracted much attention, in industry because of their possible use in devices such as valves, dampers, clutches, brakes or robotic actuators [10,11]. However, * Corresponding author.
none of these applications has been commercialized yet, mainly because of a lack of effective fluids. The requirements that have to be met include a high ER performance (i.e. a large fieldinduced yield stress and a drastic increase in apparent viscosity), stability against sedimentation, chemical stability, low conductivity and fast response times. In addition, the fluids should be non-abrasive, non-corrosive and environmentally non-hazardous. A complete understanding of the underlying mechanisms would help developing high performance ER fluids which could be used in industrial applications. ERF are commonly composed of solid particles suspended in an insulating oil although some
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homogenous solutions of liquid crystals are known which also show an ER effect [12]. Most ER suspensions contain additives such as surfactants or activators. The former are added to improve colloidal stability of the dispersed particles but also to enhance ER activity [13 – 15] while the presence of the latter is essential for the suspension to display a significant ER effect. The most common ER activator is water although there are also some other polar substances such as alcohols, ethylene glycol, dimethyl amine or formamide which can activate ER suspensions [3]. The disadvantages of water activated ER suspensions, i.e. a restricted temperature range of operation and increased conductivity, have been overcome by the introduction of essentially water-free ERF [16]. When an ERF is exposed to an external electric field, the structure of the suspension is significantly altered. The particles align in field direction so that chains or columns of particles spanning the electrode gap are rapidly formed. This structurization is the origin of the ER effect causing gellification of the fluid and the appearance of a yield stress as well as the increase in apparent viscosity. Several models have been proposed to explain the ER effect: distortion and overlap of the electric double layers of the dispersed particles [17,18], formation of water bridges between the particles [19] and inter-electrode circulation of the particles [2]. The most popular mechanism, however, is the electrostatic polarization model which can explain many of the experimental results. According to this model, the magnitude of the ER effect depends on the dielectric mismatch between the dispersed and the continous phase in the suspension although it has turned out that in the presence of free charge carriers the conductivities of the particles and the continous phase also play a crucial role [8,20,21]. Due to the dielectric mismatch, the particles polarize in an electric field resulting in a force between neighbouring particles which leads to structure formation. The attractive force between two particles was predicted to be proportional to the square of the electric field strength and hence, the rheological parameters, i.e. the viscosity and the yield stress, should also increase with E 2 [4,6,20,22]. This prediction was
confirmed by many experimental investigations [1,13,17,23–26]. The present work is dedicated to the electrorheological properties of systems containing hydrophobically modified saponite. Saponite is a synthetic clay mineral similar to the natural montmorillonite. It can be made hydrophobic by the adsorption of cationic surfactants. The hydrophobically modified clay particles were suspended in an oil (n-hexadecane) which contained some additive for stability reasons. The first part of the article shows the dependence of rheological parameters (dynamic yield stress viscosity and moduli) on field strength, field frequency and particle concentration when the type of surfactant on the saponite surface and the type and concentration of additive are kept constant. In the second part a comparison is made between the ER response illustrated by the yield stress measured at various field strengths of systems with constant solid particle content but with different surfactants adsorbed on the saponite surface and with different additives at various concentrations.
2. Experimental procedure
2.1. Sample preparation Saponite which was supplied by Clariant is a layered silicate having a formula of [Mg3(Si3.67, Al0.33)O10(OH)2]Na0.33 · nH2O. The silicon atoms are partly replaced by aluminium and magnesium atoms which results in negative charges of a density of 1 e0 per 100 A, 2. The particles have an extension of 500 A, in diameter and 10 A, in thickness. Saponite forms stable suspensions in water and at a concentration of 2% by weight gellification takes place. In order to stabilize the hydrophilic saponite particles in an oil they have to be modified in such a way that they become more hydrophobic. This can be achieved by the adsorption of cationic surfactants which are bound on the particle surface by their positively charged head groups and with their alkyl chains extending away from the particle. It is important that the surfactant concentration is not too high because when a critical concentration is exceeded
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the surfactants will form bilayers on the particle surface and therefore the particles will become hydrophilic again [27]. The critical surfactant concentration can be determined by zeta potential measurements as the charge of the particles changes sign from an initially negative value to a positive one when bilayers are formed. The critical concentrations thus obtained are around 2 mM for all the cationic surfactants used in this study. The samples were prepared in the following manner: an aqueous solution of the surfactant was added to a suspension of saponite in water (0.5% by weight). The concentration of the surfactant was chosen in such a way that the critical value mentioned above was not exceeded in the mixture. After the addition of the surfactant solution, the hydrophobically modified saponite particles precipitated and settled down. The precipitate was washed several times with water in order to remove impurities. After freeze-drying, the particles were suspended in the continous oil phase using an IKA Ultra-Turrax T25 stirrer (Janke and Kunkel). The continous phase consisted of n-hexadecane (Merck) and an additive at different concentrations. The additives used here were some non-ionic surfactants and alcohols which had the function to stabilize the suspension against sedimentation.
in determining the apparent viscosity at a fixed shear rate than a stress controlled rheometer. Here, a cell of Couette geometry designed inhouse was used. The diameters of bob and cup were 45 and 46.6 mm, respectively, resulting in a gap size of 0.8 mm. The voltage was applied to the cup. Again, the connection with the bob was established by a thin metal wire which was in contact with the shaft of the bob. Both rheometers were connected with a thermostate in order to keep the temperature at 25°C throughout the measurements. DC voltage was supplied by a Heinzinger NCL 6000 power source whereas AC voltages were generated by a Wavetek 183 wave generator.
2.2. Rheological measurements
Fij(rij, uij)
The measurements were performed with two rheometers. A Bohlin CS 10 controlled stress rheometer was used to determine the dynamic yield stress and the dynamic moduli. The cell was of parallel plate geometry with a gap size of 1 mm. The upper plate had a diameter of 40 mm. It was connected to the rheometer by a shaft which was electrically isolated with the help of a teflon ring. The lower part of the cell was specially designed in order to allow to apply a voltage. Electric contact to the upper plate was established with the help of a thin metal wire with string contact. The second rheometer used in this study was a Contraves High Shear rheometer. Being a shear rate controlled instrument, it is more convenient
= − 12p o0 a 2b 2 E 2(a/rij)4
3. Theoretical considerations As mentioned in the introduction, the most widely used model to explain the ER effect is the electrostatic polarization model. In its simplest case, it is assumed that the ERF consists of monodisperse, hard and non-conducting spheres dispersed in a non-conducting Newtonian liquid. If it is further assumed that the distance between a pair of spheres, i and j, is very large compared with their diameter (the so-called point–dipole approximation), the force Fij imposed on them by a uniform electric field E is given by [4,9]:
× [(3 cos2 uij − 1)er + (sin 2uij)eu ]
(1)
where rij is the distance between the spheres i and j of radius a, uij is the angle between their line-ofcenters and the direction of the electric field and er and eu are unit vectors in r and u direction, respectively. o0 is the permittivity of free space and os is the permittivity of the continous phase. The dipole coefficient b is written b=
o p − os op + 2os
(2)
where op is the particle’s permittivity. It can be seen from Eq. (1) that the force Fij is attractive when the particles are aligned in field
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direction but it is repulsive when the field is perpendicular to their line-of-canters. If uij is between 0 and 90°, a torque results that forces the particles to align in field direction. Therefore, a direct consequence of the polarization of the particles in the electric field is the formation of chains or columns of particles spanning the electrode gap. Eq. (1) is only valid in the point – dipole limit, i.e. a/rij 0 and op/os :1. If the particles are assumed to be close to each other, multipole and multibody effects have to be considered. In this case, some dimensionless functions of a/rij and op/os must be introduced in Eq. (1) [4,8,9]. The general scaling of the electrostatic force on b 2 E 2, however, is not changed. Therefore, it has to be concluded from the polarization model that the strength of the structure formed in an ERF after the application of an external electric field is proportional to the square of the electric field strength. As the rheological parameters are directly related to the strength of the structure, they should also scale on E 2. The above said is only true when it is assumed that both the particles and the continous phase are non-conductive. In reality, all ERF show some conductivity due to the existence of free charge carriers in both phases. A simple description of an ERF consisting of conductive particles in a conductive fluid is given by the Maxwell– Wagner model [28,29]. In this case, the point– dipole approximation yields an equation for the pair-interaction force that is identical to Eq. (1) with the exception that b must be replaced by an effective dipole coefficient beff ( fel) which depends on the frequency of the electric field. In the limit of high or low frequencies, beff ( fel) is given by:
lim b 2eff ( fel) = f
op −os op +2os
lim b 2eff ( fel) = f 0
kp −ks kp +2ks
el
el
by their permittivities. The result is an interfacial polarization, i.e. the accumulation of free charge carriers at the solid/fluid interface. In a high frequency ac field, however, free charge carriers are not able to respond fast enough to the electric field. In this case, particle polarization is ruled solely by permittivities (Eq. (3)).
4. Results and discussion
4.1. Dependence of rheological parameters on field strength, field frequency and solid particle content 4.1.1. Yield stress The yield stress was determined in the usual manner by increasing the applied shear stress and measuring the corresponding shear rate. At a certain shear stress, a drastic increase in shear rate was observed. This value of shear stress was identified with the yield stress. Fig. 1 shows the dependence of yield stress on electric field strength for two samples containing different amounts of hydrophobically modified saponite in hexadecane with C12E9 at a concentration of 0.034 mol l − 1 as additive. These two samples, as well as others not shown in Fig. 1,
2
(3) 2
(4)
where kp and ks are the conductivities of the particles and the continous phase, respectively. It can be clearly seen from Eq. (4) that in a dc field, particle polarization is governed by the mismatch of particle’s and fluid’s conductivities, not
Fig. 1. Field strength dependence of the difference of yield stresses in the presence and in the absence of an electric field for two samples with different concentrations of hydrophobically modified saponite in n-hexadecane with 0.034 mol l − 1 of C12E9 as additive. Surfactant adsorbed on the saponite surface is (C16)2DMABr.
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exhibited a small or even rather high yield stress in the absence of an electric field. The value of this yield stress was determined by the solid particle content, i.e. increasing the concentration of hydrophobically modified saponite led to an ascending yield stress due to thickening and gellification of the samples. For comparing the effect of an electric field on the various samples it is desirable to get an information which is independent of the off-field value of the yield stress. Hence, the difference sy(E) −sy(E = 0) was chosen in Fig. 1. It can be seen from Fig. 1 that the yield stress is rising proportionally to E 2 for small field strengths whereas for higher values of E, a linear relationship between sy and E is found. The transition between the two regimes is around 1500 V mm − 1. This result is in contradiction with theoretical predictions which indicate that the yield stress should vary linearly with E 2 [4,6,20,22] (cf. Eq. (1)). This conclusion was confirmed by many experimental investigations [1,13,17,23 –26] although some researchers found a proportionality between sy and E rather than E 2 [30 – 32]. The behavior shown in Fig. 1 can be explained easily by dipole saturation [30]: in an electric field, the particles in an ERF are subject to a force which increases linearly with the product of induced dipole moment m and electric field strength E. As m is also proportional to E, this leads to a linear relationship between the electrostatic force (and hence sy) and E 2 (cf. Eq. (1)). However, when a certain critical field strength is exceeded, saturation of the induced dipole moment occurs resulting in a dependence of sy on E rather than E 2 as m will be independent of E. Fig. 2 demonstrates the behavior of a sample in an ac field. The highest yield stress is obtained in a dc electric field. Increasing the field frequency while the effective field strength is kept constant results in a decrease of yield stress until the offfield value is reached at high frequencies. The same features were observed by many other investigators [3,4,7,13,17,23,33]. The situation can be compared with the dipole relaxation, in an electromagnetic field: when the field frequency is too high, the dipoles are not longer able to follow the direction of the electric field. As a consequence, the dipoles are not aligned in field direction. The
261
Fig. 2. Dependence of yield stress on electric field frequency at a constant effective field strength of 700 V mm − 1. Sample consists of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at a concentration of 0.041g ml − 1; additive is C12E9 (c =0.034 mol l − 1). Horizontal lines indicate the values at zero frequency and in the off-field state, respectively.
result is a diminution of the dielectric constant to a value of 1 when the field frequency is large enough that the molecular dipoles are randomly distributed. The behavior of an electrorheological fluid in an ac field is analogous when the mismatch between particle’s and fluid’s conductivities is considerably larger than the mismatch between their dielectric constants. If this is true, the Maxwell–Wagner polarization model [28,29] which was briefly described in the previous section, predicts a decrease of the ER effect when the field frequency is raised. This is because the charge carriers that are responsible for the interfacial polarization cannot follow the electric field when the frequency is too high. The dependence of yield stress on particle concentration for different field strengths is given in Fig. 3. The following relationship is derived from Fig. 3: sy 8 c n(E)
(5)
with n(E) ranging from 1.8 for E= 0 to 1.3 for E=2400 V mm − 1. Exponents of 1.3 [26] and 1.5 [5] have been reported in the literature. The flattening of the curves with growing field strength can be explained by the fact that the relative ER effect is larger for dilute, low viscous suspensions
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than for higher concentrated ones which display higher yield stresses in the off-field state because of thickening and gellification of the samples. Hence, when the electric field strength is raised, the relative increase of rheological parameters is greater for dilute than for concentrated suspensions resulting in the observed flattening of the curves in Fig. 3.
4.1.2. Viscosity Some results of viscosity measurements of a sample consisting of hydrophobically modified saponite at a concentration of 0.030 g ml − 1 in n-hexadecane containing 0.034 mol l − 1 of C12E9 as an additive are plotted vs. the electric field strength in Fig. 4. To give a better insight into the effect of the electric field, the relative viscosity hrel, i.e. the viscosity measured at a certain shear rate and field strength divided by the viscosity measured at the same shear rate in the absence of an electric field, was chosen in Fig. 4. As can be seen from Fig. 4, the dependence of hrel on field strength is similar to the one observed for the yield stress (Fig. 1): in the beginning, hrel increases linearely with the square of the electric field strength whereas at higher values of E, around 1500 V mm − 1, a transition to a linear relationship between hrel and E takes place. It was already mentioned that this behavior can be attributed to dipole saturation.
Fig. 3. Dependence of yield stress on particle concentration for different field strengths. Samples consist of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane; additive is C12E9 (c= 0.034 mol l − 1).
Fig. 4. Plot of relative viscosity (hrel =h(g; , E)/hrel =h(g; , E = 0)) vs. field strength for two different shear rates. Sample consists of hydrophobically modified saponite (with surfactant (C16)2DMABr) at a concentration of 0.030 g ml − 1 in n-hexadecane containing 0.034 mol l − 1 of C12E9 as an additive.
In Fig. 5, the viscosity is plotted vs. shear rate for a samples containing 0.030 g ml − 1 of hydrophobically modified saponite in n-hexadecane with 0.034 mol l − 1 of C12E9 as an additive. The sample demonstrates shear-thinning behavior which can be described by a simple power-law dependence: h8 g; − m(E)
(6)
Fig. 5. Plot of viscosity vs. shear rate for different field strengths. Sample consists of hydrophobically modified saponite (with surfactant (C16)2DMABr) at a concentration of 0.030 g ml − 1 in n-hexadecane containing 0.034 mol l − 1 of C12E9 as an additive; the number m in the legend is the exponent in Eq. (6).
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The decrease of viscosity, and hence, of the magnitude of the ER effect, with growing shear rate at constant field strength can be explained by the fact that the structure built up in the electric field is gradually degraded when the shear rate is increased. After the yield stress is exceeded, different coexisting regions are formed in the ERF [22]: the chains or columns of particles are ruptured in the middle of the electrode gap or close to one of the electrodes. A shear zone is developed in which hydrodynamic forces dominate over electrostatic ones. Solid regions with densely packed particles remain at one or at both of the electrodes. An increase of shear rate is accompanied by a gradual degradation of the solid regions whereas the shear zone is broadened. Consequently, the magnitude of the ER effect must decrease when the shear rate is enhanced. At very high shear rates, the solid regions have almost vanished and only small aggregates have left in the shear zone. Hence, the ER effect is very small at large shear rates. The exponent m(E) in Eq. (6) depends on the applied field strength. m(E) grows when the field strength is enhanced (cf. the m values given in the legend of Fig. 5). That means that the viscosity decrease with increasing shear rate is steeper when the field strength is higher. This can be explained easily by the fact that at higher field strengths, stronger structures are formed under the action of the field. Increasing the shear rate causes the structures to degrade and therefore, the descent of the flow curves must be sharper at higher field strengths. Fig. 6 demonstrates the dependence of viscosity on ac field frequency when shear rate and effective field strength are kept constant. As in the case of yield stress (Fig. 2), the viscosity drops down from the dc value at low frequencies to the off-field value at very high frequencies. The origin of this behavior was already described in connection with Fig. 2.
4.1.3. Viscoelastic properties A typical example of a frequency-sweep measurement is shown in Fig. 7. The same behavior was observed for other concentrations and field strengths, too. Similar results were obtained by other workers [34,35]. It can be derived from Fig.
263
Fig. 6. Plot of shear viscosity (g; =50 s − 1) vs. field frequency at a constant effective field strength of 875 V mm − 1. Sample is composed of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at a concentration of 0.041 g ml − 1; additive is C12E9 (c =0.034 mol l − 1). Horizontal lines indicate the values at zero frequency and in the off-field state, respectively.
7 that the variation of the moduli with oscillation frequency is very weak whereas the complex viscosity declines linearly with frequency. The storage modulus turns out to be about one order of magnitude larger than the loss modulus indicating that the elastic properties dominate over the viscous ones. This has to be expected when it is taken into account that the samples undergo a transition from a viscous fluid to an elastic solid when exposed to an external electric field.
Fig. 7. Frequency-sweep measurement of a sample containing hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at a concentration of 0.085g ml − 1; additive is C12E9 (c =0.034 mol l − 1).
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Fig. 8. Plot of storage modulus (a) and loss modulus (b), measured at a frequency of 1 Hz, against electric field strength. Samples are composed of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at two different concentrations; additive is C12E9 (c= 0.034 mol l − 1).
To get a better insight into the dependence of the storage modulus on the field strength, the values of G% at a frequency of 1 Hz were taken and plotted against E (Fig. 8a); the corresponding curves of the loss modulus are shown in Fig. 8(b). It can be seen from Fig. 8(a and b) that the field strength dependence of the two moduli is qualitatively the same but the values of G% are about one order of magnitude larger than those of G%%. As in the case of the yield stress (Fig. 1) and the relative viscosity (Fig. 4), a linear relationship between the moduli and E 2 is observed for small field strengths whereas at higher values of E, G% and G%% increase proportionally with E. Fig. 9 shows the dependence of storage and loss modulus (taken at an oscillation frequency of 1 Hz) on ac electric field frequency for a sample containing 0.063 g ml − 1 of hydrophobically modified saponite in n-hexadecane with C12E9 (c= 0.034 mol l − 1) as an additive at a constant effective field strength of 700 V mm − 1. Again, the observed behavior equals the measurement results for the yield stress (Fig. 2) and the shear viscosity (Fig. 6): G% and G%% drop down from their dc values when the electric field frequency is raised and finally approach the values measured in the off-field state at very high frequencies. An explanation for this phenomenon was already given. The relationship between dynamic moduli and particle concentration is shown in Fig. 10(a and b). Like in the case of the yield stress (Fig. 3),
there is a power-law dependence between G% or G%% and particle concentration and the exponent depends on the applied field strength. For the storage modulus, the values of the exponent decrease from 2.7 for E= 0 to 1.4 for E= 2400 V mm − 1. The exponents of the loss modulus range from 2.3 for E= 0 to 0.8 for E=2400 V mm − 1.
4.2. The influence of surfactants To investigate the influence of adsorbed surfactants on the ER effect of saponite suspensions,
Fig. 9. Plot of storage and loss modulus ( f =1 Hz) vs. field frequency at a constant effective field strength of 700 V mm − 1. Sample is composed of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at a concentration of 0.063 g ml − 1; additive is C12E9 (c = 0.034 mol 1 − 1). Horizontal lines indicate the values of G% and G%% at zero frequency and in the off-field state, respectively.
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probably be connected with the different degree of sedimentation in the various samples. Sedimentation counteracts the structure-formation in an electric field and therefore, it is believed that the hydrophobically modified saponite particles that are less stable against sedimentation build up weaker structures in an electric field and consequently show a smaller ER effect. A measure of the extent of sedimentation is the ratio of the excess length to the volume of the whole sample after a certain period of time in which the sample stood at rest. This ratio, here designated as F, is plotted vs. the yield stress measured at 2000 V mm − 1 for various samples with different surfactants in Fig. 12. It shows that there is a direct relationship between the magnitude of the ER effect and the extent of sedimentation: under the same conditions, the largest values of the yield stress are achieved with the samples that are most stable against sedimentation.
4.3. The influence of additi6es
Fig. 10. Dependence of storage modulus (a) and loss modulus (b) ( f= 1 Hz) on particle concentration for different field strengths. Samples consist of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane; additive is C12E9 (c= 0.034 mol l − 1).
several different single and double chain cationic surfactants (cf. Table 1, footnote a) were used to modify saponite hydrophobically. The various saponite samples were suspended in n-hexadecane at a fixed concentration (6.1% per weight). Moreover, all suspensions contained 9.4% per weight of 1-decanol as a stabilizing additive. The ER effect of these samples can be compared by their yield stresses measured at different electric field strengths (Fig. 11). Fig. 11 demonstrates that there are some differences in the ER response that must be attributed to the presence of various surfactants. Especially the yield stresses obtained for the systems with double chain surfactants are, in general, larger than the ones with single chain surfactants. The origin of these differences can
Some additives, i.e. alcohols and non-ionic surfactants (cf. Table 1, footnote b) were used in order to increase the stability of the dispersed particles against sedimentation. As the cationic surfactants are expected to bind solely to the negatively charged sites on the saponite surface, there should remain some free sites. The idea behind the addition of alcohols or non-ionic surfactants was that these free sites on the saponite surface could be occupied by the additive molecules and therefore, the saponite would get more hydrophobic and hence more stable against sedimentation. To investigate the influence of the type of additive on the ER effect of saponite suspensions, samples were used that contained the same concentration of solid particles in n-hexadecane (6.1% per weight) and the same cationic surfactant on the saponite surface ((C16)2DMABr), but the type of additive was changed while its concentration was kept constant (0.06 M). The ER effect of these samples was measured in terms of the yield stress at different field strengths (Fig. 13). Fig. 13 shows a clear dependence of electrorheological properties on the type of additive. When
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Table 1 A summary of all the cationic surfactants and additives used in this study Surfactant
Formula
Supplier
Cationica Dodecyltrimethylammonium bromide (C12TMABr) puriss quality Tetradecyltrimethylammonium bromide (C14TMABr) puriss quality Hexadecyltrimethylammonium bromide (C14TMABr) puriss quality Dodecylpyridinium chloride (C12PyCl) puriss quality
C12H25N+(CH3)3Br− C14H29N+(CH3)3Br− C16H33N+(CH3)3Br−
Eastman Kodak Aldrich Merck Merck
Tetradecylpyridinium bromide (C14PyBr) puriss quality
Aldrich
Hexadecylpyridinium bromide (C16PyBr) puriss quality
Aldrich
Octadecylpyridinium chloride (C18PyCl) puriss quality
Henkel
Hexadecylhexyldimethylammonium bromide (C16C8DMABr) puriss quality Hexadecyloctyldimetylammonium bromide ((C16C8)DMABr) puriss quality Dodecylhexadecyldimetylammonium bromide ((C16C12)DMABr) puriss quality Dihexadecyldimethylammonium bromide ((C16)2DMABr) puriss quality Dioctadecyldimethylammonirum bromide (C18)2DMABr) puriss quality b Additive Decanol (C10OH) purum quality Octadecanol (C18OH) puriss quality Glycerol monooleate (GMO) Technical product containing 38–40% diglyceride, 16–18% triglyceride and 4–5% glycerol
Polyethyleneglycol ethers of alcohols (technical products): C12E9 C18E2.5 Pluriol P 2000, poly(propylene oxide), MW : 2000 a
(C16H33)(C6H13)N+(CH3)2Br−
Hoechst
(C16H33)(C8H17)N+(CH3)2Br− (C16H33)(C12H25)N+(CH3)2Br−
Hoechst
(C16H33)2N+(CH3)2Br−
c
(C18H37)2N+(CH3)2Br−
Hoechst
C10H21OH C18H37OH
Fluka Fluka Fluka
C12H25O(CH2CH2O)9H C18H37O(CH2CH2O)2H/ C18H37O(CH2CH2O)3H 1:1 H[CH(CH3)CH2O]m H, (m: 35)
Henkel
BASF
Cationic surfactants used for modifying saponite hydrophobically. Additives used to stabilize suspensions of hydrophobically modified saponite in n-hexadecane. c The substance was synthesised by the reaction of hexadecyldimethylamine and hexadecyl bromide in acetonitrile. b
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Fig. 11. Dependence of yield stress (sy) on electric field strength for samples containing 0.05 g ml − 1 of hydrophobically modified saponite and 0.47 mol l − 1 of 1-decanol in n-hexadecane. The surfactants adsorbed on the saponite particles are given in the legend.
the various curves in Fig. 13 are compared with each other it becomes evident that the critical field strength which determines the transition from E 2to E-dependence is not the same for different additives. In the case of the systems containing C12E9 the critical field strength is around 1500 V mm − 1 but its value seems to be considerably smaller for the suspensions with other additives. Therefore, the latter show a linear relationship between sy and E for nearly the whole range of field strengths up to very small values of E. Not only the type of additive influences the magnitude of the ER response but also its concen-
Fig. 12. Sedimentation parameter F(= Vexcess length/Vtotal) vs. yield stress at a field strength of 2000 V mm − 1 for samples containing 0.05 g ml − 1 of hydrophobically modified saponite and 0.47 mol l − 1 of 1-decanol in n-hexadecane. The surfactants adsorbed on the saponite particles are given in the legend. All samples stood 1 day at rest before F was measured.
267
Fig. 13. Dependence of yield stress (sy) on electric field strength for samples containing 0.05 g ml − 1 of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane. Additives (c =0.06 M) are given in the legend
tration. This is illustrated by Fig. 14. Here, the solid particle content was constant again (6.1% per weight), as well as the type of cationic surfactant ((C16)2DMABr) and additive (C12E9), but the concentration of the latter was changed. Fig. 14 demonstrates a rise of the ER effect with increasing additive concentration. As in the case of the cationic surfactants discussed previously, the dependence of the ER response on the type and concentration of additive is probably due to different stabilization of the suspended particles against sedimentation. This is demonstrated by Fig. 15 where the sedimentation
Fig. 14. Dependence of yield stress (sy) on the concentration of C12E9 for samples containing 0.05 g ml − 1 of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at four different field strengths.
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Fig. 15. Sedimentation parameter F ( =Vexcess length/Vtotal) vs. yield stress at a field strength of 2000 V mm − 1 for samples containing 0.05g ml − 1 of hydrophobically modified saponite (adsorbed surfactant: (C16)2DMABr) and different additives in n-hexadecane. The type and concentration of additives are listed in the legend. All samples stood 1 day at rest before F was measured.
parameter of the investigated systems, F, is plotted vs. the yield stress measured at a fixed field strength. It shows that the systems that are most stable against sedimentation have the highest yield stresses. Besides, it should be mentioned that the least stable sample in Fig. 15 is the one that does not contain any additive.
5. Conclusions We have examined electrorheological fluids composed of hydrophobically modified saponite in an oil (n-hexadecane) containing a stabilizing additive. Saponite is a synthetic clay mineral. Its surface is negatively charged and therefore, cationic surfactants can be adsorbed on it in order to make the particles more hydrophobic. This is desirable to achieve a better stabilization of the particles in a non-polar oil. A series of investigations was performed with (C16)2DMABr as surfactant adsorbed on the clay particles and with C12E9 at a fixed concentration of 0.034 mol l − 1 as additive. The results of these measurements show that the relationship between different rheological
parameters (yield stress, shear viscosity, dynamic moduli) and field strength is always the same: at low field strengths, the rheological properties increase with E 2 whereas a transition from E 2- to E-dependence can be detected at higher applied voltages. This behavior can be attributed to saturation of induced dipole moments in the particles at the transition field strength. When an ac voltage is applied to the samples, all rheological parameters decrease with increasing field frequency and approach their off-field values at high frequencies. An explanation is given by the Maxwell–Wagner model in which it is assumed that the difference between the conductivities of the particles and the surrounding oil is much larger than their dielectric mismatch. In this case, the polarization of the particles is governed by the accumulation of free charge carriers at the solid/fluid interface. At higher frequencies, the charge carriers cannot respond fast enough to the electric field resulting in a diminution of the ER effect. A power-law relationship is found between rheological properties and particle concentration at a fixed field strength. The exponent decreases when the field strength is raised. This can be explained by the fact that the relative ER effect is larger for dilute, low viscous systems than for higher concentrated ones which show comparatively high values of viscosity or yield stress in the off-field state due to thickening or gellification effects. It has turned out that a direct relationship exists between the stability of the suspensions against settling and the magnitude of the electrorheological response. Different single and double chain cationic surfactants were adsorbed on the surface of the saponite particles. The best stabilization of the particles was achieved with the surfactant (C16)2DMABr. Suspensions of these particles have the highest values of the yield stress in an electric field in comparison with suspensions with the same solid particle concentration but with other cationic surfactants adsorbed on the saponite surface. Similar observations were made when the type and concentration of additive was varied. In general, suspensions that are better stabilized against sedimentation show higher yield stresses at a given field strength. This is probably
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due to the fact that setting counteracts the formation of chain-like or columnar structures in the electric field. Further investigations of similar systems containing hydrophobically modified clay particles and a stabilizing additive in an oil seem to be worthwhile in order to find suspensions that are both more stable against sedimentation and more effective with regard to their ER properties than the ones presented here.
Acknowledgements This project was supported by the Deutschen Forschungsgemeinschaft under the grant Nr. Ho 457/17-2 and the Fonds der Chemischen Industrie. Thomas Du¨rrschmidt is grateful for the financial support.
References [1] W.M. Winslow, J. Appl. Phys. 20 (1949) 1137. [2] Y.F. Deinega, G.V. Vinogradov, Rheol. Acta 23 (1984) 636. [3] H. Block, J.P. Kelly, J. Phys. D: Appl. Phys. 21 (1988) 1661. [4] A.P. Gast, C.F. Zukoski, Adv. Coll. Int. Sci. 30 (1989) 153. [5] T.C. Jordan, M.T. Shaw, IEEE Trans. Elect. Insul. 24 (1989) 849. [6] T.C. Halsey, Science 258 (1992) 761. [7] K.D. Weiss, J.D. Carlson, J.P. Coulter, J. Intell. Mat. Sys. Struc. 4 (1993) 13. [8] C.F. Zukoski, Ann. Rev. Mat. Sci. 23 (1993) 45. [9] M. Parthasarathy, D.J. Klingenberg, Mater. Sci. Eng. R17 (1996) 57.
.
269
[10] Z.P. Shulman, R.G. Gorodkin, E.V. Korobko, V.K. Gleb, J. Non-Newt. Fluid. Mech. 8 (1981) 29. [11] J.R. Wilson, in: Electrorheological (ER) Fluids 1993, U.S. Deparment of Energy, Office of Energy Research, Office of Program Analysis, U.S. Government Printing Office: Washington D.C., 1993, pp. 5.1. – 1. [12] I. Yang, A.D. Shine, J. Rheol. 36 (1992) 1079. [13] G.G. Petrzhik, O.A. Chertkova, A.A. Trapeznikov, Dokl. Akad. Nauk SSSR 253 (1980) 173. [14] A.A. Trapeznikov, G.G. Petrzhik, O.A. Chertkova, Kolloidn. Zh. 43 (1981) 1134. [15] O.A. Chertkova, G.G. Petrzhik, A.A. Trapeznikov, Kolloidn. Zh. 44 (1982) 83. [16] H. Block, J.P. Kelly, A. Qin, T. Watson, Langmuir 6 (1990) 6. [17] D.L. Klass, T.W. Martinek, J. Appl. Phys. 38 (1967) 67. [18] D.L. Klass, T.W. Martinek, J. Appl. Phys. 38 (1967) 75. [19] J.E. Stangroom, Phys. Tech. 14 (1983) 290. [20] L.C. Davis, Phys. Rev. A 60 (1992) 319. [21] L.C. Davis, J. Appl. Phys. 72 (1992) 1334. [22] D.J. Klingenberg, C.F. Zukoski, Langmuir 6 (1990) 15. [23] H. Uejima, Jpn. J. Appl. Phys. 11 (1972) 319. [24] Y.F. Deinega, G.V. Vinogradov, Kolloid. Zh. 24 (1962) 688. [25] L. Marshall, C.F. Zukoski, J.W. Goodwin, J. Chem. Soc. Faraday Trans. 85 (1989) 2785. [26] C.J. Gow, C.F. Zukoski, J. Colloid Interf. Sci. 136 (1990) 175. [27] Y. Yamaguchi, PhD Thesis, University of Bayreuth, 1997. [28] L.K.H. van Beek, Prog. Dielectr. 7 (1967) 69. [29] S.S. Dukhin, J. Surf. Coll. Sci. 3 (1970) 83. [30] Y. Shih, H. Conrad, Int. J. Mod. Phys. B 8 (1994) 2835. [31] Y. Otsubo, R. Edamara, J. Rheol. 38 (1994) 1721. [32] T. Sakai, K. Kobayashi, M. Sato, J. Colloid. Interf. Sci. 180 (1996) 315. [33] T.Y. Chen, P.F. Luckham, Colloid. Surf. 78 (1993) 167. [34] J.E. Martin, D. Adolf, C. Halsey, J. Colloid. Interf. Sci. 167 (1994) 437. [35] Y. Otsubo, K. Edamrura, J. Colloid. Interf: Sci. 172 (1995) 530.
Electrorheological effects in suspensions of hydrophobically modified saponite T. Du¨rrschmidt, H. Hoffmann * Physical Chemistry I, Bayreuth Uni6ersity, PF-101251, D-95440 Bayreuth, Germany Received 24 July 1998; accepted 26 November 1998
Abstract The electrorheological (ER) properties of suspensions composed of hydrophobically modified particles of a synthetic clay mineral (saponite) in an oil (n-hexadecane) containing a stabilizing additive were investigated. A comparison was made between the ER response of suspensions with the same volume fraction but with different cationic surfactants adsorbed on the saponite surface and with different additives at various concentrations. The results of these investigations indicate that a direct relationship exists between the stability of the suspensions against sedimentation and the magnitude of the ER effect. In a second series of measurements, the type of surfactant on the saponite surface was kept constant and the volume fraction of the particles was changed. Rheological parameters (yield stress, shear viscosity and dynamic moduli) were measured in dependence of field strength, field frequency and particle concentration. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Saponite; Stability against sedimentation; Magnitude of the ER effect; Rheological parameters
1. Introduction A dramatic and reversible change of rheological properties of a fluid due to the application of a large external electric field was first reported by Winslow in 1949 [1]. This phenomenon is referred to as the electrorheological (ER) effect and has been reviewed in several publications [2 –9]. Electrorheological fluids (ERF) have attracted much attention, in industry because of their possible use in devices such as valves, dampers, clutches, brakes or robotic actuators [10,11]. However, * Corresponding author.
none of these applications has been commercialized yet, mainly because of a lack of effective fluids. The requirements that have to be met include a high ER performance (i.e. a large fieldinduced yield stress and a drastic increase in apparent viscosity), stability against sedimentation, chemical stability, low conductivity and fast response times. In addition, the fluids should be non-abrasive, non-corrosive and environmentally non-hazardous. A complete understanding of the underlying mechanisms would help developing high performance ER fluids which could be used in industrial applications. ERF are commonly composed of solid particles suspended in an insulating oil although some
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homogenous solutions of liquid crystals are known which also show an ER effect [12]. Most ER suspensions contain additives such as surfactants or activators. The former are added to improve colloidal stability of the dispersed particles but also to enhance ER activity [13 – 15] while the presence of the latter is essential for the suspension to display a significant ER effect. The most common ER activator is water although there are also some other polar substances such as alcohols, ethylene glycol, dimethyl amine or formamide which can activate ER suspensions [3]. The disadvantages of water activated ER suspensions, i.e. a restricted temperature range of operation and increased conductivity, have been overcome by the introduction of essentially water-free ERF [16]. When an ERF is exposed to an external electric field, the structure of the suspension is significantly altered. The particles align in field direction so that chains or columns of particles spanning the electrode gap are rapidly formed. This structurization is the origin of the ER effect causing gellification of the fluid and the appearance of a yield stress as well as the increase in apparent viscosity. Several models have been proposed to explain the ER effect: distortion and overlap of the electric double layers of the dispersed particles [17,18], formation of water bridges between the particles [19] and inter-electrode circulation of the particles [2]. The most popular mechanism, however, is the electrostatic polarization model which can explain many of the experimental results. According to this model, the magnitude of the ER effect depends on the dielectric mismatch between the dispersed and the continous phase in the suspension although it has turned out that in the presence of free charge carriers the conductivities of the particles and the continous phase also play a crucial role [8,20,21]. Due to the dielectric mismatch, the particles polarize in an electric field resulting in a force between neighbouring particles which leads to structure formation. The attractive force between two particles was predicted to be proportional to the square of the electric field strength and hence, the rheological parameters, i.e. the viscosity and the yield stress, should also increase with E 2 [4,6,20,22]. This prediction was
confirmed by many experimental investigations [1,13,17,23–26]. The present work is dedicated to the electrorheological properties of systems containing hydrophobically modified saponite. Saponite is a synthetic clay mineral similar to the natural montmorillonite. It can be made hydrophobic by the adsorption of cationic surfactants. The hydrophobically modified clay particles were suspended in an oil (n-hexadecane) which contained some additive for stability reasons. The first part of the article shows the dependence of rheological parameters (dynamic yield stress viscosity and moduli) on field strength, field frequency and particle concentration when the type of surfactant on the saponite surface and the type and concentration of additive are kept constant. In the second part a comparison is made between the ER response illustrated by the yield stress measured at various field strengths of systems with constant solid particle content but with different surfactants adsorbed on the saponite surface and with different additives at various concentrations.
2. Experimental procedure
2.1. Sample preparation Saponite which was supplied by Clariant is a layered silicate having a formula of [Mg3(Si3.67, Al0.33)O10(OH)2]Na0.33 · nH2O. The silicon atoms are partly replaced by aluminium and magnesium atoms which results in negative charges of a density of 1 e0 per 100 A, 2. The particles have an extension of 500 A, in diameter and 10 A, in thickness. Saponite forms stable suspensions in water and at a concentration of 2% by weight gellification takes place. In order to stabilize the hydrophilic saponite particles in an oil they have to be modified in such a way that they become more hydrophobic. This can be achieved by the adsorption of cationic surfactants which are bound on the particle surface by their positively charged head groups and with their alkyl chains extending away from the particle. It is important that the surfactant concentration is not too high because when a critical concentration is exceeded
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the surfactants will form bilayers on the particle surface and therefore the particles will become hydrophilic again [27]. The critical surfactant concentration can be determined by zeta potential measurements as the charge of the particles changes sign from an initially negative value to a positive one when bilayers are formed. The critical concentrations thus obtained are around 2 mM for all the cationic surfactants used in this study. The samples were prepared in the following manner: an aqueous solution of the surfactant was added to a suspension of saponite in water (0.5% by weight). The concentration of the surfactant was chosen in such a way that the critical value mentioned above was not exceeded in the mixture. After the addition of the surfactant solution, the hydrophobically modified saponite particles precipitated and settled down. The precipitate was washed several times with water in order to remove impurities. After freeze-drying, the particles were suspended in the continous oil phase using an IKA Ultra-Turrax T25 stirrer (Janke and Kunkel). The continous phase consisted of n-hexadecane (Merck) and an additive at different concentrations. The additives used here were some non-ionic surfactants and alcohols which had the function to stabilize the suspension against sedimentation.
in determining the apparent viscosity at a fixed shear rate than a stress controlled rheometer. Here, a cell of Couette geometry designed inhouse was used. The diameters of bob and cup were 45 and 46.6 mm, respectively, resulting in a gap size of 0.8 mm. The voltage was applied to the cup. Again, the connection with the bob was established by a thin metal wire which was in contact with the shaft of the bob. Both rheometers were connected with a thermostate in order to keep the temperature at 25°C throughout the measurements. DC voltage was supplied by a Heinzinger NCL 6000 power source whereas AC voltages were generated by a Wavetek 183 wave generator.
2.2. Rheological measurements
Fij(rij, uij)
The measurements were performed with two rheometers. A Bohlin CS 10 controlled stress rheometer was used to determine the dynamic yield stress and the dynamic moduli. The cell was of parallel plate geometry with a gap size of 1 mm. The upper plate had a diameter of 40 mm. It was connected to the rheometer by a shaft which was electrically isolated with the help of a teflon ring. The lower part of the cell was specially designed in order to allow to apply a voltage. Electric contact to the upper plate was established with the help of a thin metal wire with string contact. The second rheometer used in this study was a Contraves High Shear rheometer. Being a shear rate controlled instrument, it is more convenient
= − 12p o0 a 2b 2 E 2(a/rij)4
3. Theoretical considerations As mentioned in the introduction, the most widely used model to explain the ER effect is the electrostatic polarization model. In its simplest case, it is assumed that the ERF consists of monodisperse, hard and non-conducting spheres dispersed in a non-conducting Newtonian liquid. If it is further assumed that the distance between a pair of spheres, i and j, is very large compared with their diameter (the so-called point–dipole approximation), the force Fij imposed on them by a uniform electric field E is given by [4,9]:
× [(3 cos2 uij − 1)er + (sin 2uij)eu ]
(1)
where rij is the distance between the spheres i and j of radius a, uij is the angle between their line-ofcenters and the direction of the electric field and er and eu are unit vectors in r and u direction, respectively. o0 is the permittivity of free space and os is the permittivity of the continous phase. The dipole coefficient b is written b=
o p − os op + 2os
(2)
where op is the particle’s permittivity. It can be seen from Eq. (1) that the force Fij is attractive when the particles are aligned in field
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direction but it is repulsive when the field is perpendicular to their line-of-canters. If uij is between 0 and 90°, a torque results that forces the particles to align in field direction. Therefore, a direct consequence of the polarization of the particles in the electric field is the formation of chains or columns of particles spanning the electrode gap. Eq. (1) is only valid in the point – dipole limit, i.e. a/rij 0 and op/os :1. If the particles are assumed to be close to each other, multipole and multibody effects have to be considered. In this case, some dimensionless functions of a/rij and op/os must be introduced in Eq. (1) [4,8,9]. The general scaling of the electrostatic force on b 2 E 2, however, is not changed. Therefore, it has to be concluded from the polarization model that the strength of the structure formed in an ERF after the application of an external electric field is proportional to the square of the electric field strength. As the rheological parameters are directly related to the strength of the structure, they should also scale on E 2. The above said is only true when it is assumed that both the particles and the continous phase are non-conductive. In reality, all ERF show some conductivity due to the existence of free charge carriers in both phases. A simple description of an ERF consisting of conductive particles in a conductive fluid is given by the Maxwell– Wagner model [28,29]. In this case, the point– dipole approximation yields an equation for the pair-interaction force that is identical to Eq. (1) with the exception that b must be replaced by an effective dipole coefficient beff ( fel) which depends on the frequency of the electric field. In the limit of high or low frequencies, beff ( fel) is given by:
lim b 2eff ( fel) = f
op −os op +2os
lim b 2eff ( fel) = f 0
kp −ks kp +2ks
el
el
by their permittivities. The result is an interfacial polarization, i.e. the accumulation of free charge carriers at the solid/fluid interface. In a high frequency ac field, however, free charge carriers are not able to respond fast enough to the electric field. In this case, particle polarization is ruled solely by permittivities (Eq. (3)).
4. Results and discussion
4.1. Dependence of rheological parameters on field strength, field frequency and solid particle content 4.1.1. Yield stress The yield stress was determined in the usual manner by increasing the applied shear stress and measuring the corresponding shear rate. At a certain shear stress, a drastic increase in shear rate was observed. This value of shear stress was identified with the yield stress. Fig. 1 shows the dependence of yield stress on electric field strength for two samples containing different amounts of hydrophobically modified saponite in hexadecane with C12E9 at a concentration of 0.034 mol l − 1 as additive. These two samples, as well as others not shown in Fig. 1,
2
(3) 2
(4)
where kp and ks are the conductivities of the particles and the continous phase, respectively. It can be clearly seen from Eq. (4) that in a dc field, particle polarization is governed by the mismatch of particle’s and fluid’s conductivities, not
Fig. 1. Field strength dependence of the difference of yield stresses in the presence and in the absence of an electric field for two samples with different concentrations of hydrophobically modified saponite in n-hexadecane with 0.034 mol l − 1 of C12E9 as additive. Surfactant adsorbed on the saponite surface is (C16)2DMABr.
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exhibited a small or even rather high yield stress in the absence of an electric field. The value of this yield stress was determined by the solid particle content, i.e. increasing the concentration of hydrophobically modified saponite led to an ascending yield stress due to thickening and gellification of the samples. For comparing the effect of an electric field on the various samples it is desirable to get an information which is independent of the off-field value of the yield stress. Hence, the difference sy(E) −sy(E = 0) was chosen in Fig. 1. It can be seen from Fig. 1 that the yield stress is rising proportionally to E 2 for small field strengths whereas for higher values of E, a linear relationship between sy and E is found. The transition between the two regimes is around 1500 V mm − 1. This result is in contradiction with theoretical predictions which indicate that the yield stress should vary linearly with E 2 [4,6,20,22] (cf. Eq. (1)). This conclusion was confirmed by many experimental investigations [1,13,17,23 –26] although some researchers found a proportionality between sy and E rather than E 2 [30 – 32]. The behavior shown in Fig. 1 can be explained easily by dipole saturation [30]: in an electric field, the particles in an ERF are subject to a force which increases linearly with the product of induced dipole moment m and electric field strength E. As m is also proportional to E, this leads to a linear relationship between the electrostatic force (and hence sy) and E 2 (cf. Eq. (1)). However, when a certain critical field strength is exceeded, saturation of the induced dipole moment occurs resulting in a dependence of sy on E rather than E 2 as m will be independent of E. Fig. 2 demonstrates the behavior of a sample in an ac field. The highest yield stress is obtained in a dc electric field. Increasing the field frequency while the effective field strength is kept constant results in a decrease of yield stress until the offfield value is reached at high frequencies. The same features were observed by many other investigators [3,4,7,13,17,23,33]. The situation can be compared with the dipole relaxation, in an electromagnetic field: when the field frequency is too high, the dipoles are not longer able to follow the direction of the electric field. As a consequence, the dipoles are not aligned in field direction. The
261
Fig. 2. Dependence of yield stress on electric field frequency at a constant effective field strength of 700 V mm − 1. Sample consists of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at a concentration of 0.041g ml − 1; additive is C12E9 (c =0.034 mol l − 1). Horizontal lines indicate the values at zero frequency and in the off-field state, respectively.
result is a diminution of the dielectric constant to a value of 1 when the field frequency is large enough that the molecular dipoles are randomly distributed. The behavior of an electrorheological fluid in an ac field is analogous when the mismatch between particle’s and fluid’s conductivities is considerably larger than the mismatch between their dielectric constants. If this is true, the Maxwell–Wagner polarization model [28,29] which was briefly described in the previous section, predicts a decrease of the ER effect when the field frequency is raised. This is because the charge carriers that are responsible for the interfacial polarization cannot follow the electric field when the frequency is too high. The dependence of yield stress on particle concentration for different field strengths is given in Fig. 3. The following relationship is derived from Fig. 3: sy 8 c n(E)
(5)
with n(E) ranging from 1.8 for E= 0 to 1.3 for E=2400 V mm − 1. Exponents of 1.3 [26] and 1.5 [5] have been reported in the literature. The flattening of the curves with growing field strength can be explained by the fact that the relative ER effect is larger for dilute, low viscous suspensions
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than for higher concentrated ones which display higher yield stresses in the off-field state because of thickening and gellification of the samples. Hence, when the electric field strength is raised, the relative increase of rheological parameters is greater for dilute than for concentrated suspensions resulting in the observed flattening of the curves in Fig. 3.
4.1.2. Viscosity Some results of viscosity measurements of a sample consisting of hydrophobically modified saponite at a concentration of 0.030 g ml − 1 in n-hexadecane containing 0.034 mol l − 1 of C12E9 as an additive are plotted vs. the electric field strength in Fig. 4. To give a better insight into the effect of the electric field, the relative viscosity hrel, i.e. the viscosity measured at a certain shear rate and field strength divided by the viscosity measured at the same shear rate in the absence of an electric field, was chosen in Fig. 4. As can be seen from Fig. 4, the dependence of hrel on field strength is similar to the one observed for the yield stress (Fig. 1): in the beginning, hrel increases linearely with the square of the electric field strength whereas at higher values of E, around 1500 V mm − 1, a transition to a linear relationship between hrel and E takes place. It was already mentioned that this behavior can be attributed to dipole saturation.
Fig. 3. Dependence of yield stress on particle concentration for different field strengths. Samples consist of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane; additive is C12E9 (c= 0.034 mol l − 1).
Fig. 4. Plot of relative viscosity (hrel =h(g; , E)/hrel =h(g; , E = 0)) vs. field strength for two different shear rates. Sample consists of hydrophobically modified saponite (with surfactant (C16)2DMABr) at a concentration of 0.030 g ml − 1 in n-hexadecane containing 0.034 mol l − 1 of C12E9 as an additive.
In Fig. 5, the viscosity is plotted vs. shear rate for a samples containing 0.030 g ml − 1 of hydrophobically modified saponite in n-hexadecane with 0.034 mol l − 1 of C12E9 as an additive. The sample demonstrates shear-thinning behavior which can be described by a simple power-law dependence: h8 g; − m(E)
(6)
Fig. 5. Plot of viscosity vs. shear rate for different field strengths. Sample consists of hydrophobically modified saponite (with surfactant (C16)2DMABr) at a concentration of 0.030 g ml − 1 in n-hexadecane containing 0.034 mol l − 1 of C12E9 as an additive; the number m in the legend is the exponent in Eq. (6).
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The decrease of viscosity, and hence, of the magnitude of the ER effect, with growing shear rate at constant field strength can be explained by the fact that the structure built up in the electric field is gradually degraded when the shear rate is increased. After the yield stress is exceeded, different coexisting regions are formed in the ERF [22]: the chains or columns of particles are ruptured in the middle of the electrode gap or close to one of the electrodes. A shear zone is developed in which hydrodynamic forces dominate over electrostatic ones. Solid regions with densely packed particles remain at one or at both of the electrodes. An increase of shear rate is accompanied by a gradual degradation of the solid regions whereas the shear zone is broadened. Consequently, the magnitude of the ER effect must decrease when the shear rate is enhanced. At very high shear rates, the solid regions have almost vanished and only small aggregates have left in the shear zone. Hence, the ER effect is very small at large shear rates. The exponent m(E) in Eq. (6) depends on the applied field strength. m(E) grows when the field strength is enhanced (cf. the m values given in the legend of Fig. 5). That means that the viscosity decrease with increasing shear rate is steeper when the field strength is higher. This can be explained easily by the fact that at higher field strengths, stronger structures are formed under the action of the field. Increasing the shear rate causes the structures to degrade and therefore, the descent of the flow curves must be sharper at higher field strengths. Fig. 6 demonstrates the dependence of viscosity on ac field frequency when shear rate and effective field strength are kept constant. As in the case of yield stress (Fig. 2), the viscosity drops down from the dc value at low frequencies to the off-field value at very high frequencies. The origin of this behavior was already described in connection with Fig. 2.
4.1.3. Viscoelastic properties A typical example of a frequency-sweep measurement is shown in Fig. 7. The same behavior was observed for other concentrations and field strengths, too. Similar results were obtained by other workers [34,35]. It can be derived from Fig.
263
Fig. 6. Plot of shear viscosity (g; =50 s − 1) vs. field frequency at a constant effective field strength of 875 V mm − 1. Sample is composed of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at a concentration of 0.041 g ml − 1; additive is C12E9 (c =0.034 mol l − 1). Horizontal lines indicate the values at zero frequency and in the off-field state, respectively.
7 that the variation of the moduli with oscillation frequency is very weak whereas the complex viscosity declines linearly with frequency. The storage modulus turns out to be about one order of magnitude larger than the loss modulus indicating that the elastic properties dominate over the viscous ones. This has to be expected when it is taken into account that the samples undergo a transition from a viscous fluid to an elastic solid when exposed to an external electric field.
Fig. 7. Frequency-sweep measurement of a sample containing hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at a concentration of 0.085g ml − 1; additive is C12E9 (c =0.034 mol l − 1).
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Fig. 8. Plot of storage modulus (a) and loss modulus (b), measured at a frequency of 1 Hz, against electric field strength. Samples are composed of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at two different concentrations; additive is C12E9 (c= 0.034 mol l − 1).
To get a better insight into the dependence of the storage modulus on the field strength, the values of G% at a frequency of 1 Hz were taken and plotted against E (Fig. 8a); the corresponding curves of the loss modulus are shown in Fig. 8(b). It can be seen from Fig. 8(a and b) that the field strength dependence of the two moduli is qualitatively the same but the values of G% are about one order of magnitude larger than those of G%%. As in the case of the yield stress (Fig. 1) and the relative viscosity (Fig. 4), a linear relationship between the moduli and E 2 is observed for small field strengths whereas at higher values of E, G% and G%% increase proportionally with E. Fig. 9 shows the dependence of storage and loss modulus (taken at an oscillation frequency of 1 Hz) on ac electric field frequency for a sample containing 0.063 g ml − 1 of hydrophobically modified saponite in n-hexadecane with C12E9 (c= 0.034 mol l − 1) as an additive at a constant effective field strength of 700 V mm − 1. Again, the observed behavior equals the measurement results for the yield stress (Fig. 2) and the shear viscosity (Fig. 6): G% and G%% drop down from their dc values when the electric field frequency is raised and finally approach the values measured in the off-field state at very high frequencies. An explanation for this phenomenon was already given. The relationship between dynamic moduli and particle concentration is shown in Fig. 10(a and b). Like in the case of the yield stress (Fig. 3),
there is a power-law dependence between G% or G%% and particle concentration and the exponent depends on the applied field strength. For the storage modulus, the values of the exponent decrease from 2.7 for E= 0 to 1.4 for E= 2400 V mm − 1. The exponents of the loss modulus range from 2.3 for E= 0 to 0.8 for E=2400 V mm − 1.
4.2. The influence of surfactants To investigate the influence of adsorbed surfactants on the ER effect of saponite suspensions,
Fig. 9. Plot of storage and loss modulus ( f =1 Hz) vs. field frequency at a constant effective field strength of 700 V mm − 1. Sample is composed of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at a concentration of 0.063 g ml − 1; additive is C12E9 (c = 0.034 mol 1 − 1). Horizontal lines indicate the values of G% and G%% at zero frequency and in the off-field state, respectively.
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probably be connected with the different degree of sedimentation in the various samples. Sedimentation counteracts the structure-formation in an electric field and therefore, it is believed that the hydrophobically modified saponite particles that are less stable against sedimentation build up weaker structures in an electric field and consequently show a smaller ER effect. A measure of the extent of sedimentation is the ratio of the excess length to the volume of the whole sample after a certain period of time in which the sample stood at rest. This ratio, here designated as F, is plotted vs. the yield stress measured at 2000 V mm − 1 for various samples with different surfactants in Fig. 12. It shows that there is a direct relationship between the magnitude of the ER effect and the extent of sedimentation: under the same conditions, the largest values of the yield stress are achieved with the samples that are most stable against sedimentation.
4.3. The influence of additi6es
Fig. 10. Dependence of storage modulus (a) and loss modulus (b) ( f= 1 Hz) on particle concentration for different field strengths. Samples consist of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane; additive is C12E9 (c= 0.034 mol l − 1).
several different single and double chain cationic surfactants (cf. Table 1, footnote a) were used to modify saponite hydrophobically. The various saponite samples were suspended in n-hexadecane at a fixed concentration (6.1% per weight). Moreover, all suspensions contained 9.4% per weight of 1-decanol as a stabilizing additive. The ER effect of these samples can be compared by their yield stresses measured at different electric field strengths (Fig. 11). Fig. 11 demonstrates that there are some differences in the ER response that must be attributed to the presence of various surfactants. Especially the yield stresses obtained for the systems with double chain surfactants are, in general, larger than the ones with single chain surfactants. The origin of these differences can
Some additives, i.e. alcohols and non-ionic surfactants (cf. Table 1, footnote b) were used in order to increase the stability of the dispersed particles against sedimentation. As the cationic surfactants are expected to bind solely to the negatively charged sites on the saponite surface, there should remain some free sites. The idea behind the addition of alcohols or non-ionic surfactants was that these free sites on the saponite surface could be occupied by the additive molecules and therefore, the saponite would get more hydrophobic and hence more stable against sedimentation. To investigate the influence of the type of additive on the ER effect of saponite suspensions, samples were used that contained the same concentration of solid particles in n-hexadecane (6.1% per weight) and the same cationic surfactant on the saponite surface ((C16)2DMABr), but the type of additive was changed while its concentration was kept constant (0.06 M). The ER effect of these samples was measured in terms of the yield stress at different field strengths (Fig. 13). Fig. 13 shows a clear dependence of electrorheological properties on the type of additive. When
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Table 1 A summary of all the cationic surfactants and additives used in this study Surfactant
Formula
Supplier
Cationica Dodecyltrimethylammonium bromide (C12TMABr) puriss quality Tetradecyltrimethylammonium bromide (C14TMABr) puriss quality Hexadecyltrimethylammonium bromide (C14TMABr) puriss quality Dodecylpyridinium chloride (C12PyCl) puriss quality
C12H25N+(CH3)3Br− C14H29N+(CH3)3Br− C16H33N+(CH3)3Br−
Eastman Kodak Aldrich Merck Merck
Tetradecylpyridinium bromide (C14PyBr) puriss quality
Aldrich
Hexadecylpyridinium bromide (C16PyBr) puriss quality
Aldrich
Octadecylpyridinium chloride (C18PyCl) puriss quality
Henkel
Hexadecylhexyldimethylammonium bromide (C16C8DMABr) puriss quality Hexadecyloctyldimetylammonium bromide ((C16C8)DMABr) puriss quality Dodecylhexadecyldimetylammonium bromide ((C16C12)DMABr) puriss quality Dihexadecyldimethylammonium bromide ((C16)2DMABr) puriss quality Dioctadecyldimethylammonirum bromide (C18)2DMABr) puriss quality b Additive Decanol (C10OH) purum quality Octadecanol (C18OH) puriss quality Glycerol monooleate (GMO) Technical product containing 38–40% diglyceride, 16–18% triglyceride and 4–5% glycerol
Polyethyleneglycol ethers of alcohols (technical products): C12E9 C18E2.5 Pluriol P 2000, poly(propylene oxide), MW : 2000 a
(C16H33)(C6H13)N+(CH3)2Br−
Hoechst
(C16H33)(C8H17)N+(CH3)2Br− (C16H33)(C12H25)N+(CH3)2Br−
Hoechst
(C16H33)2N+(CH3)2Br−
c
(C18H37)2N+(CH3)2Br−
Hoechst
C10H21OH C18H37OH
Fluka Fluka Fluka
C12H25O(CH2CH2O)9H C18H37O(CH2CH2O)2H/ C18H37O(CH2CH2O)3H 1:1 H[CH(CH3)CH2O]m H, (m: 35)
Henkel
BASF
Cationic surfactants used for modifying saponite hydrophobically. Additives used to stabilize suspensions of hydrophobically modified saponite in n-hexadecane. c The substance was synthesised by the reaction of hexadecyldimethylamine and hexadecyl bromide in acetonitrile. b
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Fig. 11. Dependence of yield stress (sy) on electric field strength for samples containing 0.05 g ml − 1 of hydrophobically modified saponite and 0.47 mol l − 1 of 1-decanol in n-hexadecane. The surfactants adsorbed on the saponite particles are given in the legend.
the various curves in Fig. 13 are compared with each other it becomes evident that the critical field strength which determines the transition from E 2to E-dependence is not the same for different additives. In the case of the systems containing C12E9 the critical field strength is around 1500 V mm − 1 but its value seems to be considerably smaller for the suspensions with other additives. Therefore, the latter show a linear relationship between sy and E for nearly the whole range of field strengths up to very small values of E. Not only the type of additive influences the magnitude of the ER response but also its concen-
Fig. 12. Sedimentation parameter F(= Vexcess length/Vtotal) vs. yield stress at a field strength of 2000 V mm − 1 for samples containing 0.05 g ml − 1 of hydrophobically modified saponite and 0.47 mol l − 1 of 1-decanol in n-hexadecane. The surfactants adsorbed on the saponite particles are given in the legend. All samples stood 1 day at rest before F was measured.
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Fig. 13. Dependence of yield stress (sy) on electric field strength for samples containing 0.05 g ml − 1 of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane. Additives (c =0.06 M) are given in the legend
tration. This is illustrated by Fig. 14. Here, the solid particle content was constant again (6.1% per weight), as well as the type of cationic surfactant ((C16)2DMABr) and additive (C12E9), but the concentration of the latter was changed. Fig. 14 demonstrates a rise of the ER effect with increasing additive concentration. As in the case of the cationic surfactants discussed previously, the dependence of the ER response on the type and concentration of additive is probably due to different stabilization of the suspended particles against sedimentation. This is demonstrated by Fig. 15 where the sedimentation
Fig. 14. Dependence of yield stress (sy) on the concentration of C12E9 for samples containing 0.05 g ml − 1 of hydrophobically modified saponite (with surfactant (C16)2DMABr) in n-hexadecane at four different field strengths.
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Fig. 15. Sedimentation parameter F ( =Vexcess length/Vtotal) vs. yield stress at a field strength of 2000 V mm − 1 for samples containing 0.05g ml − 1 of hydrophobically modified saponite (adsorbed surfactant: (C16)2DMABr) and different additives in n-hexadecane. The type and concentration of additives are listed in the legend. All samples stood 1 day at rest before F was measured.
parameter of the investigated systems, F, is plotted vs. the yield stress measured at a fixed field strength. It shows that the systems that are most stable against sedimentation have the highest yield stresses. Besides, it should be mentioned that the least stable sample in Fig. 15 is the one that does not contain any additive.
5. Conclusions We have examined electrorheological fluids composed of hydrophobically modified saponite in an oil (n-hexadecane) containing a stabilizing additive. Saponite is a synthetic clay mineral. Its surface is negatively charged and therefore, cationic surfactants can be adsorbed on it in order to make the particles more hydrophobic. This is desirable to achieve a better stabilization of the particles in a non-polar oil. A series of investigations was performed with (C16)2DMABr as surfactant adsorbed on the clay particles and with C12E9 at a fixed concentration of 0.034 mol l − 1 as additive. The results of these measurements show that the relationship between different rheological
parameters (yield stress, shear viscosity, dynamic moduli) and field strength is always the same: at low field strengths, the rheological properties increase with E 2 whereas a transition from E 2- to E-dependence can be detected at higher applied voltages. This behavior can be attributed to saturation of induced dipole moments in the particles at the transition field strength. When an ac voltage is applied to the samples, all rheological parameters decrease with increasing field frequency and approach their off-field values at high frequencies. An explanation is given by the Maxwell–Wagner model in which it is assumed that the difference between the conductivities of the particles and the surrounding oil is much larger than their dielectric mismatch. In this case, the polarization of the particles is governed by the accumulation of free charge carriers at the solid/fluid interface. At higher frequencies, the charge carriers cannot respond fast enough to the electric field resulting in a diminution of the ER effect. A power-law relationship is found between rheological properties and particle concentration at a fixed field strength. The exponent decreases when the field strength is raised. This can be explained by the fact that the relative ER effect is larger for dilute, low viscous systems than for higher concentrated ones which show comparatively high values of viscosity or yield stress in the off-field state due to thickening or gellification effects. It has turned out that a direct relationship exists between the stability of the suspensions against settling and the magnitude of the electrorheological response. Different single and double chain cationic surfactants were adsorbed on the surface of the saponite particles. The best stabilization of the particles was achieved with the surfactant (C16)2DMABr. Suspensions of these particles have the highest values of the yield stress in an electric field in comparison with suspensions with the same solid particle concentration but with other cationic surfactants adsorbed on the saponite surface. Similar observations were made when the type and concentration of additive was varied. In general, suspensions that are better stabilized against sedimentation show higher yield stresses at a given field strength. This is probably
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due to the fact that setting counteracts the formation of chain-like or columnar structures in the electric field. Further investigations of similar systems containing hydrophobically modified clay particles and a stabilizing additive in an oil seem to be worthwhile in order to find suspensions that are both more stable against sedimentation and more effective with regard to their ER properties than the ones presented here.
Acknowledgements This project was supported by the Deutschen Forschungsgemeinschaft under the grant Nr. Ho 457/17-2 and the Fonds der Chemischen Industrie. Thomas Du¨rrschmidt is grateful for the financial support.
References [1] W.M. Winslow, J. Appl. Phys. 20 (1949) 1137. [2] Y.F. Deinega, G.V. Vinogradov, Rheol. Acta 23 (1984) 636. [3] H. Block, J.P. Kelly, J. Phys. D: Appl. Phys. 21 (1988) 1661. [4] A.P. Gast, C.F. Zukoski, Adv. Coll. Int. Sci. 30 (1989) 153. [5] T.C. Jordan, M.T. Shaw, IEEE Trans. Elect. Insul. 24 (1989) 849. [6] T.C. Halsey, Science 258 (1992) 761. [7] K.D. Weiss, J.D. Carlson, J.P. Coulter, J. Intell. Mat. Sys. Struc. 4 (1993) 13. [8] C.F. Zukoski, Ann. Rev. Mat. Sci. 23 (1993) 45. [9] M. Parthasarathy, D.J. Klingenberg, Mater. Sci. Eng. R17 (1996) 57.
.
269
[10] Z.P. Shulman, R.G. Gorodkin, E.V. Korobko, V.K. Gleb, J. Non-Newt. Fluid. Mech. 8 (1981) 29. [11] J.R. Wilson, in: Electrorheological (ER) Fluids 1993, U.S. Deparment of Energy, Office of Energy Research, Office of Program Analysis, U.S. Government Printing Office: Washington D.C., 1993, pp. 5.1. – 1. [12] I. Yang, A.D. Shine, J. Rheol. 36 (1992) 1079. [13] G.G. Petrzhik, O.A. Chertkova, A.A. Trapeznikov, Dokl. Akad. Nauk SSSR 253 (1980) 173. [14] A.A. Trapeznikov, G.G. Petrzhik, O.A. Chertkova, Kolloidn. Zh. 43 (1981) 1134. [15] O.A. Chertkova, G.G. Petrzhik, A.A. Trapeznikov, Kolloidn. Zh. 44 (1982) 83. [16] H. Block, J.P. Kelly, A. Qin, T. Watson, Langmuir 6 (1990) 6. [17] D.L. Klass, T.W. Martinek, J. Appl. Phys. 38 (1967) 67. [18] D.L. Klass, T.W. Martinek, J. Appl. Phys. 38 (1967) 75. [19] J.E. Stangroom, Phys. Tech. 14 (1983) 290. [20] L.C. Davis, Phys. Rev. A 60 (1992) 319. [21] L.C. Davis, J. Appl. Phys. 72 (1992) 1334. [22] D.J. Klingenberg, C.F. Zukoski, Langmuir 6 (1990) 15. [23] H. Uejima, Jpn. J. Appl. Phys. 11 (1972) 319. [24] Y.F. Deinega, G.V. Vinogradov, Kolloid. Zh. 24 (1962) 688. [25] L. Marshall, C.F. Zukoski, J.W. Goodwin, J. Chem. Soc. Faraday Trans. 85 (1989) 2785. [26] C.J. Gow, C.F. Zukoski, J. Colloid Interf. Sci. 136 (1990) 175. [27] Y. Yamaguchi, PhD Thesis, University of Bayreuth, 1997. [28] L.K.H. van Beek, Prog. Dielectr. 7 (1967) 69. [29] S.S. Dukhin, J. Surf. Coll. Sci. 3 (1970) 83. [30] Y. Shih, H. Conrad, Int. J. Mod. Phys. B 8 (1994) 2835. [31] Y. Otsubo, R. Edamara, J. Rheol. 38 (1994) 1721. [32] T. Sakai, K. Kobayashi, M. Sato, J. Colloid. Interf. Sci. 180 (1996) 315. [33] T.Y. Chen, P.F. Luckham, Colloid. Surf. 78 (1993) 167. [34] J.E. Martin, D. Adolf, C. Halsey, J. Colloid. Interf. Sci. 167 (1994) 437. [35] Y. Otsubo, K. Edamrura, J. Colloid. Interf: Sci. 172 (1995) 530.