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Effect of field strength and temperature on viscoelastic properties of electrorheological suspensions of urea-modified silica particles
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Colloids and Surfaces A: Physicochem. Eng. Aspects 316 (2008) 89–94
Effect of field strength and temperature on viscoelastic properties of electrorheological suspensions of urea-modified silica particles Tom´asˇ Belza a , Vladim´ır Pavl´ınek a,∗ , Petr S´aha a , Otakar Quadrat b a
b
Tomas Bata University in Zl´ın, Faculty of Technology, TGM Sq. 275, 762 72 Zl´ın, Czech Republic Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Heyrovsky Sq. 2, 162 06 Prague 6, Czech Republic Received 19 January 2007; received in revised form 14 August 2007; accepted 23 August 2007 Available online 30 August 2007
Abstract Temperature dependence of dynamic properties of suspensions of silica nanoparticles modified with urea during transition from liquid to quasi-solid state in the absence or presence of electric field has been investigated. In the absence of electric field the loss modulus continuously decreased, whereas the complex viscosity and storage modulus decreased steeply as a result of increasing thermal motion of suspension particles and higher fluidity of the medium. To eliminate the temperature dependence of the field-off properties in the elastic structure of the particles polarized in the electric field, the relative moduli G /G0 and G /G0 have been proposed. Thus, while the relative loss modulus at a single low frequency (1.03 rad s−1 ) was virtually independent of temperature, the growth of relative storage modulus with temperature reflects higher rigidity of the suspension structure due to increasing particle polarization, in accordance with higher permittivity and lower relaxation time obtained from dielectric measurements. © 2007 Elsevier B.V. All rights reserved. Keywords: Electrorheology; Viscoelasticity; Silica; Nanoparticle; Urea
1. Introduction Electrorheological (ER) fluids first described by Winslow [1] more than 50 years ago has been the object of many studies. The origin of this phenomenon and the main results obtained so far are discussed in several review articles [2–8]. While a majority of studies deals with steady-state viscosity or shear stress behaviour, viscoelastic properties of ER fluids rank among little investigated problems. It is well demonstrated that in suspensions of electrically polarizable particles in a non-conducting medium, a fibrous chain structure of polarized particles is formed on electric field strength application and, consequently, an increase in viscosity of several orders of magnitude occurs. In this process a transition from liquid to quasi-solid state sets in accompanied by a yield stress appearance and a steep increase in elasticity of the system. At this transition point, which shows much similarity to physical gelation of polymers, the storage modulus, G , which is significantly lower at zero
∗
Corresponding author. Tel.: +420 576 031 205; fax: +420 576 031 444. E-mail address: [email protected] (V. Pavl´ınek).
0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.08.035
or low electric field strength than the loss modulus, G , begins to dominate, steeply increasing with the field strength. It has been assumed that at the beginning of the liquid-to-solid transition, when gelation starts, the same frequency dependences of dynamic moduli G and G are observed [9]. As expected, the experiments with monodisperse silica particle suspensions at increasing electric field strengths showed that the slope of loss tangent, tan δ = G /G , originally negative turns to positive values in the course of continuing gel solidification [10]. This suggests that the sol–gel transition starts before the chains of polarized particles appear in the suspension. In the suspensions of polydisperse irregular particles, the case of G = G did not occur in the whole frequency range and the frequency dependences of the moduli cross at different field strengths. In this case, the field strength for G = G at the adopted frequency as the criterion characterizing the sol–gel transition has been proposed. Using the assumption, the dynamic characteristics of silicone oil/polyaniline suspensions in electric field revealed that the field strength corresponding to the transition gel point decreases with the particle concentration and viscosity of suspension [9]. In our previous studies [11,12], the effect of coating of nanosilica particles with urea on the electrorheological
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behaviour of their suspensions has been investigated. Due to strong interparticle forces in silica, a much higher field-off suspension viscosity appeared than that of the urea-modified particles. In this work the influence of temperature on viscoelastic and dielectric properties of urea-modified silica particles in the electric field was examined. 2. Experimental 2.1. Materials Nanosilica particles (average particle size 10 nm, Aerosil A 200, Degussa, Germany) have been used. To modify silica with urea, 10 g of the nanoparticles was immersed in 500 ml of distilled water at 40–50 ◦ C. After 1 h stirring, 10 ml of 10 wt.% aqueous solution of urea (Aldrich, USA) was added and the suspension stirred for another 16 h. Then the suspension particles were filtered off, washed with ethanol and dried at 60 ◦ C in vacuum to constant weight. The amount of urea deposited on silica particles estimated with a thermogravimetric analyzer (Setaram SetSys Evolution, France) was about 1 wt.%. Suspensions containing 5 wt.% of silica and 5, 10, 15 or 20 wt.% of urea-coated silica particles in silicone oil (viscosity ηc = 200 mPa, density dc = 0.965 g cm−3 , Lukosiol M200, Chemical Works Kol´ın, Czech Republic) were used as electrorheological fluids.
Fig. 1. Dependence of the field-off storage G0 (䊉) and loss G0 () moduli and complex viscosity η∗0 (+) on angular frequency ω of 5 wt.% suspensions of silica (a) and urea-modified silica (b) particles in silicone oil.
3. Results
suspensions of urea-modified particles with medium fluidity (Fig. 1b). The study of the suspensions of urea-modified particles showed that particle loading crucially affects their field-off dynamic behaviour. The decrease in complex viscosity η∗0 with frequency in a 5 wt.% suspension at 25 ◦ C indicates a slight pseudoplastic character. The loss modulus, G0 , of the suspensions is higher than the storage modulus, G0 , and elasticity is low (Fig. 2a). At higher particles concentration, the values of the three characteristics are higher (Fig. 2b–d). The low-frequency storage modulus steeply increases and becomes dominant in the whole frequency range as a result of high elasticity of the system. This suggests that, in contrast to a loose particle arrangement at lower particle concentrations, a relatively strong, physically bonded, highly elastic network of bridged interacting particles arises at higher concentrations.
3.1. Field off behaviour
3.2. Electric field application
It is generally accepted that the field-off hydrodynamic properties of suspensions depend on the size and shape of suspended particles or their aggregates, in addition to viscosity of the medium, and on their interaction, which is controlled by compatibility of the components. Thus, a close relation of association of poly(ethylene oxide)/organoclay nanoparticles to viscoelastic properties have been observed [13]. We found that in suspension of silica particles, a quasi-solid structure with high pseudoplasticity and a yield stress arises due to strong interparticle interaction at a relative low particle loading (5 wt.%) and strong viscoelasticity with predominant storage modulus appears (Fig. 1a). In contrast, a loss component prevails in
A steep suspension viscosity increase accompanied by a yield stress appearance in the electric field depends on the rigidity of the chain structure formed by polarized particles. Understandably, the character of this structure may significantly influence both dynamic moduli of the material. As in the absence of electric field and at low field strengths (E = 0–45 V mm−1 ), the complex viscosity and the slope of the shear rate dependence of 5 wt.% silica suspension at 25 ◦ C were very small (Fig. 3). In contrast, a steep increase in pseudoplasticity appeared at higher field strengths (100 V mm−1 ). In the former case, the viscous modulus predominated over the elastic one in the whole frequency range, in the latter, the elastic modulus considerably
2.2. Rheological measurement Dynamic oscillatory experiments were performed on a rheometer Bohlin Gemini (Malvern Instruments, UK) with parallel plates 40 mm in diameter and a 0.5 mm gap. The plates were connected to a DC power supply, U = 0–1000 V (high-voltage source TREK 668B, TREK, USA). Measurements were carried out in the linear viscoelasticity region at 25–65 ◦ C. 2.3. Dielectric measurement The frequency dependences of relative permittivity, ε , and relative dielectric loss, ε , in the frequency range 10–105 Hz were measured with Hioki 3522 RLC HiTester (Hioki, Japan).
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Table 1 Silicone oil viscosity ηc and parameters of Eq. (1) for 5 wt.% suspension of silica particles modified with urea at T = 25, 45 and 65 ◦ C T (◦ C)
ηc (mPa s)
ε0
ε∞
ε
τc
1−α
β
25 45 65
200 170 145
3.97 4.14 4.26
2.67 2.62 2.65
1.30 1.51 1.61
0.00710 0.00270 0.00072
0.907 0.728 0.614
0.671 0.860 1.270
prevailed, which can be ascribed to the sol–gel transition due to the appearance of the quasi-solid particle chain arrangement at a critical field strength above 45 V mm−1 . 3.3. Effect of temperature
Fig. 2. Dependence of the field-off storage G0 and loss G0 moduli and complex viscosity η∗0 of suspensions of urea-modified silica particles on angular frequency ω at 25 ◦ C. Particle concentration [wt.%]: (a) 5, (b) 10, (c) 15, and (d) 20. For the meaning of points, see Fig. 1.
It has been shown that, due to increasing thermal motion of particles and higher fluidity of the medium (Table 1) in the absence of electric field, increasing temperature caused a loss of the elastic quasi-solid structure of the suspensions and transition to the liquid state at which the loss modulus prevailed. While the complex viscosity of 10 wt.% suspension at 25 and 30 ◦ C indicated a significant pseudoplastic behaviour and nearly frequency-independent storage moduli exceeded the loss ones, a dramatic decrease in complex viscosity especially at low frequencies appeared at 35 ◦ C (Fig. 4a) and pseudoplasticity became very weak. At the same time, the storage modulus sank below the loss modulus and elasticity of the
Fig. 3. Dependence of complex viscosity η* (a) and storage G (full symbols) and loss G moduli (open symbols) (b) of suspensions of urea-modified silica particles on angular frequency ω in 5 wt.%, (c) suspension at 25 ◦ C. Field strength [V mm−1 ]: 0 (, ), 15 (䊉, ), 30 (, ), 45 (, ), 100 (, ♦), and 1000 (⊗, ×).
Fig. 4. Dependence of field-off complex viscosity η∗0 (a) and the storage G0 (full symbols) and loss G0 moduli (open symbols) (b) of suspensions of urea-modified silica particles on angular frequency ω in 10 wt.% suspension. Temperature [◦ C]: 25 (, ), 30 (, ), 35 (䊉, ) and 45 (, ).
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suspension was strongly reduced (Fig. 4b). The temperature increase to 45 ◦ C caused a shift in the three viscoelastic characteristics, η∗0 , G0 and G0 , to lower values in the whole frequency range. The dependences of field-off dynamic moduli in the temperature range 25–65 ◦ C at a single frequency (1.03 rad s−1 ) for various particle concentrations revealed that the temperature needed for loosening the physical particle network increases with particle loading, i.e. with the density of physical network structure. Thus, for 5 wt.% suspension, both moduli continuously decreased and the viscous component prevailed in the whole temperature range (Fig. 5a). At a higher particle content (10 wt.%), the intersection of the moduli-temperature dependences occurred at about 35 ◦ C; below this critical temperature the storage modulus predominated (Fig. 5b). For 15 wt.% suspension, the critical temperature increased up to 43 ◦ C (Fig. 5c) and at 20 wt.% the storage modulus exceeded the loss component in the whole range of the used temperatures (Fig. 5d). At the field strength 45 V mm−1 applied to the 5 wt.% suspension at 25 ◦ C, the loss modulus exceeded the storage one in the whole frequency range. At higher temperatures, however, the moduli dependences intersected (Fig. 6) and at lower frequencies the elastic behaviour predominated. The different viscoelastic character of suspensions at various temperatures characterized by the phase angle (tan δ), i.e. the ratio of the loss and storage moduli, is shown in Fig. 7. An increase in the critical frequency at tan δ = 1 with tempera-
Fig. 6. Dependence of storage G (full symbols) and loss G moduli (open symbols) of 5 wt.% suspension at field strength 45 V mm−1 on angular frequency ω. Temperature [◦ C]: (a) 25, (b) 45, and (c) 65.
ture corresponding to the frequency dependence of the transition of the quasi-solid to liquid character of the suspension, can be explained as a result of various relaxation times associated with the rate of particle polarization change. 3.4. Dielectric properties and viscoelastic behaviour It is well known that the frequency dependence of the complex permittivity ε* = ε − iε involving relative permittivity ε
Fig. 5. Dependence of field-off storage G0 (full symbols) and loss G0 moduli (open symbols) at a single angular frequency ω = 1.03 rad s−1 on temperature. Particle concentration [wt.%]: (a) 5, (b) 10, (c) 15, and (d) 20.
Fig. 7. Dependence of phase angle tan δ = G /G of 5 wt.% suspension at field strength 45 V mm−1 on angular frequency ω. Temperature [◦ C]: 25 (), 45 (䊉), and 65 ().
T. Belza et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 316 (2008) 89–94
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empirical equation [18] ε∗ =
Fig. 8. Dependence of permittivity ε (a) and dielectric loss factor ε (b) on angular frequency of 5 wt.% suspension. The solid lines were calculated according to Eq. (1). Temperature [◦ C]: 25 (), 45 (), and 65 (♦).
and dielectric loss ε is closely related to polarization of suspension particles [14,15]. As a criterion of the polarizability, the difference between the limit values of the relative permittivity at the frequencies below ε0 and above ε∞ the relaxation frequency fc , for which dielectric loss factor ε attains a maximum, has been proposed [16]. The frequency spectra of 5 wt.% suspension of silica particles under investigation show that the low-frequency permittivity rises with increasing temperature and the relaxation maxima shift to higher frequencies (Fig. 8). The Cole–Cole plot successfully used in evaluation of dielectric spectra of polyaniline-coated poly(methyl methacrylate) suspensions [17] showed increasing polarizability ε = ε0 − ε∞ (Fig. 9). Their dielectric characteristics calculated from the Havriliak–Negami
Fig. 9. Cole–Cole plot of the dielectric loss factor ε vs. permittivity ε . For the meaning of points, see Fig. 8.
ε∞ + (ε0 − ε∞ )
β
(1 + (i2πfτc )1−α )
(1)
are presented in Table 1. Here τ c = 1/2fc is the relaxation time, α the scattering degree of relaxation times and β is related to the asymmetry of the relaxation time spectrum. Large values of α mean a great scattering of relaxation times. When α differs much from zero and β much from unity, the relaxation spectrum becomes more asymmetrical. A comparison of the temperature dependences of the dynamic moduli at a low single frequency (1.03 rad s−1 ) at various field strengths showed a steep decrease in the field-off storage modulus G0 with temperature (Fig. 10a). This suggests that the dynamic moduli of suspensions in the electric field, in particular the elastic component, may be significantly affected by the field-off properties of these materials and does not reflect the real influence of temperature on particle polarizability. It can be assumed that in the relative moduli G /G0 and G /G0 , the field-off dynamic properties would be eliminated. Thus, in contrast to a flat dependence of relative loss moduli, G /G0 , an increase in relative storage moduli, G /G0 , in dependence on temperature appeared (Fig. 10b), which indicates increasing elasticity due to stronger particle polarization in agreement with increasing differences between relative permittivities ε = ε0 − ε∞ and lower relaxation time.
Fig. 10. Dependence of storage G (full symbols) and loss G moduli (open symbols) (a) and their relative values G /G0 and G /G0 (b) of 5 wt.% suspension at the single frequency of 1.03 rad s−1 on temperature. Field strength [V mm−1 ]: 0 (, ), 30 (, ), 45 (, ), and 100 (, ♦).
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4. Conclusion Apart from particle loading, compatibility of particles with the liquid medium crucially affects the field-off dynamic properties of electrorheological suspensions. It is understandable that the character of the primary structure of particle arrangement in the absence of electric field controls an increase in both dynamic moduli with electric field strength and the transition from liquid to quasi-solid state. Also temperature is a significant factor influencing this behaviour. It is clear that the temperature dependence of the complex permittivity of the suspension in the electric field reflects the effect of temperature on the polarization of suspended particles and may be a tool for explanation of changes in dynamic moduli. Acknowledgement The authors wish to thank the Ministry of Education, Youth and Sports of the Czech Republic (MSM 7088352101) for financial support. References [1] W.M. Winslow, Induced fibrillation of suspensions, J. Appl. Phys. 20 (1949) 1137–1140. [2] H.J. Block, P. Kelly, Electrorheology, J. Phys. D Appl. Phys. 21 (1988) 1661–1677. [3] T.C. Jordan, M.T. Shaw, Electrorheology, IEEE Trans. Electric Insul. 24 (1989) 849–861. [4] K.M. Blackwood, H. Block, Semi-conducting polymers in electrorheology: a modern approach to smart fluids, Trends Polym. Sci. 14 (1993) 98–104. [5] M. Parthasarathy, D.J. Klingenberg, Electrorheology: mechanisms and models, Mater. Sci. Eng. R 17 (1996) 57–103.
[6] T. Hao, Electrorheological fluids, Adv. Mater. 13 (2001) 1847–1857. [7] T. Hao, Electrorheological suspensions, Adv. Colloid Interf. Sci. 97 (2002) 1–35. [8] O. Quadrat, J. Stejskal, Polyaniline in electrorheology, J. Ind. Eng. Chem. 12 (2006) 352–361. [9] P. Hiamtup, A. Sirivat, A.M. Jamieson, Electrorheological properties of polyaniline suspensions: field-induced liquid to solid transition and residual gel structure, J. Colloid Interf. Sci. 295 (2006) 270–278. [10] B.D. Chin, H.H. Winter, Field-induced gelation, yield stress, and fragility of an electro-rheological suspension, Rheol. Acta 41 (2002) 265– 275. [11] T. Belza, V. Pavl´ınek, P. S´aha, O. Quadrat, Electrorheological properties of suspensions of silica nanoparticles modified by urea and N,N-dimethylformamide, Colloid Surf. A-Physicochem. Eng. Aspects 297 (2007) 142–146. [12] T. Belza, V. Pavl´ınek, I. Kuritka, P. S´aha, O. Quadrat, Electrorheological and dielectric properties of urea/SiO2 nanocomposite suspensions modified by N,N-dimethylformamide, electrorheological properties of urea/SiO2 nanocomposite suspensions modified by DMF, in: 10th International Conference on Electrorheological Fluids and Magnetorheological Suspensions, Lake Tahoe, USA, 2006. [13] Y.H. Hyun, S.T. Lim, H.J. Choi, M.S. Jhon, Rheology of poly(ethylene oxide)/organoclay nanocomposites, Macromolecules 34 (2001) 8084– 8093. [14] H. Block, J.P. Kelly, A. Qin, T. Watson, Materials and mechanisms in electrorheology, Langmuir 6 (1990) 6–14. [15] H.J. Choi, M.S. Cho, K. To, Electrorheological and dielectric characteristics of semiconductive polyaniline-silicone oil suspensions, Phys. A 254 (1998) 272–279. [16] F. Ikazaki, A. Kawai, K. Uchida, T. Kawakami, K. Edamura, K. Samuraj, H. Anzai, Y. Asako, Mechanisms of electrorheology: the effect of the dielectric property, J. Phys. D Appl. Phys. 31 (1998) 336–347. [17] M.S. Cho, Y.H. Cho, H.J. Choi, M.S. Jhon, Synthesis and electrorheological characteristics of polyaniline-coated poly(methyl methacrylate) microsphere: size effect, Langmuir 19 (2003) 5875–5881. [18] S. Havriliak Jr., S.J. Havriliak, Dielectric and mechanical relaxation in materials, Hanser, Munich, 1997.
Colloids and Surfaces A: Physicochem. Eng. Aspects 316 (2008) 89–94
Effect of field strength and temperature on viscoelastic properties of electrorheological suspensions of urea-modified silica particles Tom´asˇ Belza a , Vladim´ır Pavl´ınek a,∗ , Petr S´aha a , Otakar Quadrat b a
b
Tomas Bata University in Zl´ın, Faculty of Technology, TGM Sq. 275, 762 72 Zl´ın, Czech Republic Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Heyrovsky Sq. 2, 162 06 Prague 6, Czech Republic Received 19 January 2007; received in revised form 14 August 2007; accepted 23 August 2007 Available online 30 August 2007
Abstract Temperature dependence of dynamic properties of suspensions of silica nanoparticles modified with urea during transition from liquid to quasi-solid state in the absence or presence of electric field has been investigated. In the absence of electric field the loss modulus continuously decreased, whereas the complex viscosity and storage modulus decreased steeply as a result of increasing thermal motion of suspension particles and higher fluidity of the medium. To eliminate the temperature dependence of the field-off properties in the elastic structure of the particles polarized in the electric field, the relative moduli G /G0 and G /G0 have been proposed. Thus, while the relative loss modulus at a single low frequency (1.03 rad s−1 ) was virtually independent of temperature, the growth of relative storage modulus with temperature reflects higher rigidity of the suspension structure due to increasing particle polarization, in accordance with higher permittivity and lower relaxation time obtained from dielectric measurements. © 2007 Elsevier B.V. All rights reserved. Keywords: Electrorheology; Viscoelasticity; Silica; Nanoparticle; Urea
1. Introduction Electrorheological (ER) fluids first described by Winslow [1] more than 50 years ago has been the object of many studies. The origin of this phenomenon and the main results obtained so far are discussed in several review articles [2–8]. While a majority of studies deals with steady-state viscosity or shear stress behaviour, viscoelastic properties of ER fluids rank among little investigated problems. It is well demonstrated that in suspensions of electrically polarizable particles in a non-conducting medium, a fibrous chain structure of polarized particles is formed on electric field strength application and, consequently, an increase in viscosity of several orders of magnitude occurs. In this process a transition from liquid to quasi-solid state sets in accompanied by a yield stress appearance and a steep increase in elasticity of the system. At this transition point, which shows much similarity to physical gelation of polymers, the storage modulus, G , which is significantly lower at zero
∗
Corresponding author. Tel.: +420 576 031 205; fax: +420 576 031 444. E-mail address: [email protected] (V. Pavl´ınek).
0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.08.035
or low electric field strength than the loss modulus, G , begins to dominate, steeply increasing with the field strength. It has been assumed that at the beginning of the liquid-to-solid transition, when gelation starts, the same frequency dependences of dynamic moduli G and G are observed [9]. As expected, the experiments with monodisperse silica particle suspensions at increasing electric field strengths showed that the slope of loss tangent, tan δ = G /G , originally negative turns to positive values in the course of continuing gel solidification [10]. This suggests that the sol–gel transition starts before the chains of polarized particles appear in the suspension. In the suspensions of polydisperse irregular particles, the case of G = G did not occur in the whole frequency range and the frequency dependences of the moduli cross at different field strengths. In this case, the field strength for G = G at the adopted frequency as the criterion characterizing the sol–gel transition has been proposed. Using the assumption, the dynamic characteristics of silicone oil/polyaniline suspensions in electric field revealed that the field strength corresponding to the transition gel point decreases with the particle concentration and viscosity of suspension [9]. In our previous studies [11,12], the effect of coating of nanosilica particles with urea on the electrorheological
90
T. Belza et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 316 (2008) 89–94
behaviour of their suspensions has been investigated. Due to strong interparticle forces in silica, a much higher field-off suspension viscosity appeared than that of the urea-modified particles. In this work the influence of temperature on viscoelastic and dielectric properties of urea-modified silica particles in the electric field was examined. 2. Experimental 2.1. Materials Nanosilica particles (average particle size 10 nm, Aerosil A 200, Degussa, Germany) have been used. To modify silica with urea, 10 g of the nanoparticles was immersed in 500 ml of distilled water at 40–50 ◦ C. After 1 h stirring, 10 ml of 10 wt.% aqueous solution of urea (Aldrich, USA) was added and the suspension stirred for another 16 h. Then the suspension particles were filtered off, washed with ethanol and dried at 60 ◦ C in vacuum to constant weight. The amount of urea deposited on silica particles estimated with a thermogravimetric analyzer (Setaram SetSys Evolution, France) was about 1 wt.%. Suspensions containing 5 wt.% of silica and 5, 10, 15 or 20 wt.% of urea-coated silica particles in silicone oil (viscosity ηc = 200 mPa, density dc = 0.965 g cm−3 , Lukosiol M200, Chemical Works Kol´ın, Czech Republic) were used as electrorheological fluids.
Fig. 1. Dependence of the field-off storage G0 (䊉) and loss G0 () moduli and complex viscosity η∗0 (+) on angular frequency ω of 5 wt.% suspensions of silica (a) and urea-modified silica (b) particles in silicone oil.
3. Results
suspensions of urea-modified particles with medium fluidity (Fig. 1b). The study of the suspensions of urea-modified particles showed that particle loading crucially affects their field-off dynamic behaviour. The decrease in complex viscosity η∗0 with frequency in a 5 wt.% suspension at 25 ◦ C indicates a slight pseudoplastic character. The loss modulus, G0 , of the suspensions is higher than the storage modulus, G0 , and elasticity is low (Fig. 2a). At higher particles concentration, the values of the three characteristics are higher (Fig. 2b–d). The low-frequency storage modulus steeply increases and becomes dominant in the whole frequency range as a result of high elasticity of the system. This suggests that, in contrast to a loose particle arrangement at lower particle concentrations, a relatively strong, physically bonded, highly elastic network of bridged interacting particles arises at higher concentrations.
3.1. Field off behaviour
3.2. Electric field application
It is generally accepted that the field-off hydrodynamic properties of suspensions depend on the size and shape of suspended particles or their aggregates, in addition to viscosity of the medium, and on their interaction, which is controlled by compatibility of the components. Thus, a close relation of association of poly(ethylene oxide)/organoclay nanoparticles to viscoelastic properties have been observed [13]. We found that in suspension of silica particles, a quasi-solid structure with high pseudoplasticity and a yield stress arises due to strong interparticle interaction at a relative low particle loading (5 wt.%) and strong viscoelasticity with predominant storage modulus appears (Fig. 1a). In contrast, a loss component prevails in
A steep suspension viscosity increase accompanied by a yield stress appearance in the electric field depends on the rigidity of the chain structure formed by polarized particles. Understandably, the character of this structure may significantly influence both dynamic moduli of the material. As in the absence of electric field and at low field strengths (E = 0–45 V mm−1 ), the complex viscosity and the slope of the shear rate dependence of 5 wt.% silica suspension at 25 ◦ C were very small (Fig. 3). In contrast, a steep increase in pseudoplasticity appeared at higher field strengths (100 V mm−1 ). In the former case, the viscous modulus predominated over the elastic one in the whole frequency range, in the latter, the elastic modulus considerably
2.2. Rheological measurement Dynamic oscillatory experiments were performed on a rheometer Bohlin Gemini (Malvern Instruments, UK) with parallel plates 40 mm in diameter and a 0.5 mm gap. The plates were connected to a DC power supply, U = 0–1000 V (high-voltage source TREK 668B, TREK, USA). Measurements were carried out in the linear viscoelasticity region at 25–65 ◦ C. 2.3. Dielectric measurement The frequency dependences of relative permittivity, ε , and relative dielectric loss, ε , in the frequency range 10–105 Hz were measured with Hioki 3522 RLC HiTester (Hioki, Japan).
T. Belza et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 316 (2008) 89–94
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Table 1 Silicone oil viscosity ηc and parameters of Eq. (1) for 5 wt.% suspension of silica particles modified with urea at T = 25, 45 and 65 ◦ C T (◦ C)
ηc (mPa s)
ε0
ε∞
ε
τc
1−α
β
25 45 65
200 170 145
3.97 4.14 4.26
2.67 2.62 2.65
1.30 1.51 1.61
0.00710 0.00270 0.00072
0.907 0.728 0.614
0.671 0.860 1.270
prevailed, which can be ascribed to the sol–gel transition due to the appearance of the quasi-solid particle chain arrangement at a critical field strength above 45 V mm−1 . 3.3. Effect of temperature
Fig. 2. Dependence of the field-off storage G0 and loss G0 moduli and complex viscosity η∗0 of suspensions of urea-modified silica particles on angular frequency ω at 25 ◦ C. Particle concentration [wt.%]: (a) 5, (b) 10, (c) 15, and (d) 20. For the meaning of points, see Fig. 1.
It has been shown that, due to increasing thermal motion of particles and higher fluidity of the medium (Table 1) in the absence of electric field, increasing temperature caused a loss of the elastic quasi-solid structure of the suspensions and transition to the liquid state at which the loss modulus prevailed. While the complex viscosity of 10 wt.% suspension at 25 and 30 ◦ C indicated a significant pseudoplastic behaviour and nearly frequency-independent storage moduli exceeded the loss ones, a dramatic decrease in complex viscosity especially at low frequencies appeared at 35 ◦ C (Fig. 4a) and pseudoplasticity became very weak. At the same time, the storage modulus sank below the loss modulus and elasticity of the
Fig. 3. Dependence of complex viscosity η* (a) and storage G (full symbols) and loss G moduli (open symbols) (b) of suspensions of urea-modified silica particles on angular frequency ω in 5 wt.%, (c) suspension at 25 ◦ C. Field strength [V mm−1 ]: 0 (, ), 15 (䊉, ), 30 (, ), 45 (, ), 100 (, ♦), and 1000 (⊗, ×).
Fig. 4. Dependence of field-off complex viscosity η∗0 (a) and the storage G0 (full symbols) and loss G0 moduli (open symbols) (b) of suspensions of urea-modified silica particles on angular frequency ω in 10 wt.% suspension. Temperature [◦ C]: 25 (, ), 30 (, ), 35 (䊉, ) and 45 (, ).
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suspension was strongly reduced (Fig. 4b). The temperature increase to 45 ◦ C caused a shift in the three viscoelastic characteristics, η∗0 , G0 and G0 , to lower values in the whole frequency range. The dependences of field-off dynamic moduli in the temperature range 25–65 ◦ C at a single frequency (1.03 rad s−1 ) for various particle concentrations revealed that the temperature needed for loosening the physical particle network increases with particle loading, i.e. with the density of physical network structure. Thus, for 5 wt.% suspension, both moduli continuously decreased and the viscous component prevailed in the whole temperature range (Fig. 5a). At a higher particle content (10 wt.%), the intersection of the moduli-temperature dependences occurred at about 35 ◦ C; below this critical temperature the storage modulus predominated (Fig. 5b). For 15 wt.% suspension, the critical temperature increased up to 43 ◦ C (Fig. 5c) and at 20 wt.% the storage modulus exceeded the loss component in the whole range of the used temperatures (Fig. 5d). At the field strength 45 V mm−1 applied to the 5 wt.% suspension at 25 ◦ C, the loss modulus exceeded the storage one in the whole frequency range. At higher temperatures, however, the moduli dependences intersected (Fig. 6) and at lower frequencies the elastic behaviour predominated. The different viscoelastic character of suspensions at various temperatures characterized by the phase angle (tan δ), i.e. the ratio of the loss and storage moduli, is shown in Fig. 7. An increase in the critical frequency at tan δ = 1 with tempera-
Fig. 6. Dependence of storage G (full symbols) and loss G moduli (open symbols) of 5 wt.% suspension at field strength 45 V mm−1 on angular frequency ω. Temperature [◦ C]: (a) 25, (b) 45, and (c) 65.
ture corresponding to the frequency dependence of the transition of the quasi-solid to liquid character of the suspension, can be explained as a result of various relaxation times associated with the rate of particle polarization change. 3.4. Dielectric properties and viscoelastic behaviour It is well known that the frequency dependence of the complex permittivity ε* = ε − iε involving relative permittivity ε
Fig. 5. Dependence of field-off storage G0 (full symbols) and loss G0 moduli (open symbols) at a single angular frequency ω = 1.03 rad s−1 on temperature. Particle concentration [wt.%]: (a) 5, (b) 10, (c) 15, and (d) 20.
Fig. 7. Dependence of phase angle tan δ = G /G of 5 wt.% suspension at field strength 45 V mm−1 on angular frequency ω. Temperature [◦ C]: 25 (), 45 (䊉), and 65 ().
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empirical equation [18] ε∗ =
Fig. 8. Dependence of permittivity ε (a) and dielectric loss factor ε (b) on angular frequency of 5 wt.% suspension. The solid lines were calculated according to Eq. (1). Temperature [◦ C]: 25 (), 45 (), and 65 (♦).
and dielectric loss ε is closely related to polarization of suspension particles [14,15]. As a criterion of the polarizability, the difference between the limit values of the relative permittivity at the frequencies below ε0 and above ε∞ the relaxation frequency fc , for which dielectric loss factor ε attains a maximum, has been proposed [16]. The frequency spectra of 5 wt.% suspension of silica particles under investigation show that the low-frequency permittivity rises with increasing temperature and the relaxation maxima shift to higher frequencies (Fig. 8). The Cole–Cole plot successfully used in evaluation of dielectric spectra of polyaniline-coated poly(methyl methacrylate) suspensions [17] showed increasing polarizability ε = ε0 − ε∞ (Fig. 9). Their dielectric characteristics calculated from the Havriliak–Negami
Fig. 9. Cole–Cole plot of the dielectric loss factor ε vs. permittivity ε . For the meaning of points, see Fig. 8.
ε∞ + (ε0 − ε∞ )
β
(1 + (i2πfτc )1−α )
(1)
are presented in Table 1. Here τ c = 1/2fc is the relaxation time, α the scattering degree of relaxation times and β is related to the asymmetry of the relaxation time spectrum. Large values of α mean a great scattering of relaxation times. When α differs much from zero and β much from unity, the relaxation spectrum becomes more asymmetrical. A comparison of the temperature dependences of the dynamic moduli at a low single frequency (1.03 rad s−1 ) at various field strengths showed a steep decrease in the field-off storage modulus G0 with temperature (Fig. 10a). This suggests that the dynamic moduli of suspensions in the electric field, in particular the elastic component, may be significantly affected by the field-off properties of these materials and does not reflect the real influence of temperature on particle polarizability. It can be assumed that in the relative moduli G /G0 and G /G0 , the field-off dynamic properties would be eliminated. Thus, in contrast to a flat dependence of relative loss moduli, G /G0 , an increase in relative storage moduli, G /G0 , in dependence on temperature appeared (Fig. 10b), which indicates increasing elasticity due to stronger particle polarization in agreement with increasing differences between relative permittivities ε = ε0 − ε∞ and lower relaxation time.
Fig. 10. Dependence of storage G (full symbols) and loss G moduli (open symbols) (a) and their relative values G /G0 and G /G0 (b) of 5 wt.% suspension at the single frequency of 1.03 rad s−1 on temperature. Field strength [V mm−1 ]: 0 (, ), 30 (, ), 45 (, ), and 100 (, ♦).
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4. Conclusion Apart from particle loading, compatibility of particles with the liquid medium crucially affects the field-off dynamic properties of electrorheological suspensions. It is understandable that the character of the primary structure of particle arrangement in the absence of electric field controls an increase in both dynamic moduli with electric field strength and the transition from liquid to quasi-solid state. Also temperature is a significant factor influencing this behaviour. It is clear that the temperature dependence of the complex permittivity of the suspension in the electric field reflects the effect of temperature on the polarization of suspended particles and may be a tool for explanation of changes in dynamic moduli. Acknowledgement The authors wish to thank the Ministry of Education, Youth and Sports of the Czech Republic (MSM 7088352101) for financial support. References [1] W.M. Winslow, Induced fibrillation of suspensions, J. Appl. Phys. 20 (1949) 1137–1140. [2] H.J. Block, P. Kelly, Electrorheology, J. Phys. D Appl. Phys. 21 (1988) 1661–1677. [3] T.C. Jordan, M.T. Shaw, Electrorheology, IEEE Trans. Electric Insul. 24 (1989) 849–861. [4] K.M. Blackwood, H. Block, Semi-conducting polymers in electrorheology: a modern approach to smart fluids, Trends Polym. Sci. 14 (1993) 98–104. [5] M. Parthasarathy, D.J. Klingenberg, Electrorheology: mechanisms and models, Mater. Sci. Eng. R 17 (1996) 57–103.
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