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Viscosity of magnetic particle suspensions
Journal of Magnetism and Magnetic Materials 209 (2000) 228 } 230
Viscosity of magnetic particle suspensions Hyoung J. Choi!,*, Chul A. Kim!, Taeg M. Kwon", Myung S. Jhon" !Department of Polymer Science and Engineering, Inha University, Inchon 402-751, South Korea "Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Abstract A rheological approach was used to study the e!ects of microstructure on the viscosity of magnetic particle suspensions as functions of concentration and shear rate. Empirical formulas derived from mean-"eld theory and the Mooney equation were used to relate viscosity with particle concentration for both rod- and plate-like particles. The Casson equation was employed to investigate the shear rate dependence of the viscosity. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Magnetic particle suspension; Microstructure; Suspension viscosity
1. Introduction Magnetic particle suspensions have been extensively studied due to their many practical applications, especially in the magnetic tape industry. Magnetic recording media, in general, consist of a coating of "ne magnetic particles on a non-magnetic plastic substrate. The "nished product is greatly a!ected by the dispersion quality of the magnetic particle suspensions [1]. Therefore, the control of dispersion quality is a challenging problem in particulate media production as well as all other coating processes involving unstable particle suspensions. The overall suspension properties show non-Newtonian behavior, exhibiting either thixotropy or shear thinning, and also induced deviatoric normal stresses due to the ordering imparted by the external "eld. These properties can be measured via standard rheological methods. Understanding complex dynamic coupling, including interparticle and #uid/particle interactions, on a fundamental level is a challenging problem [2]. The measurement of the suspension's viscosity can be used to characterize the microstructural state of a dispersion. The shape and orientation e!ects of the magnetic particles or #ocs are then indirectly measured. Empirical
* Corresponding author. Tel.: #82-32-860-7486; fax: #8232-865-5178. E-mail address: [email protected] (H.J. Choi)
formulae from both mean-"eld (MF) theory and the Mooney equation are used to relate viscosity with particle concentration. Shape e!ects of magnetic particles, agglomeration phenomena at low concentration, and shear-induced breakage or agglomeration are investigated and provide complementary information to rheooptical and rheomagnetic techniques [2].
2. Experimental The magnetic particles used in our study (rod-like c-Fe O and CrO particles and plate-like Ba}ferrite 2 3 2 particles) are single domain particles used for commercial media production. The particles' size and shape were characterized using a transmission electron microscope (TEM). A vibrating sample magnetometer (VSM) was employed to characterize the particle magnetic properties for randomly oriented dry powders. The values of coercivity, saturation magnetization, density, diameter, and aspect ratio are reported in Ref. [3]. A cone-andplate viscometer was employed to measure shear viscosities of the magnetic particle suspensions over a wide range of shear rates and concentrations at 253C. A master solution of each magnetic suspension, with an approximate volume fraction of 0.05, was prepared by mixing the particle powder with ethylene glycol using a mini-Eiger motor mill. The volume concentration of the prepared master suspension was obtained using
0304-8853/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 6 9 5 - 2
H.J. Choi et al. / Journal of Magnetism and Magnetic Materials 209 (2000) 228}230
thermogravimetric analysis and rheomagnetic [4] concentration measurement devices. More dilute solutions were prepared by subsequent dilution of the concentrated master suspension.
3. Results and discussion A preliminary theoretical development to describe the experimental observation of rheological properties for magnetic particle suspensions is reported in Refs. [5,6]. Typical rheological characteristics of a particle suspension containing #ocs are shear thinning and concentration dependence on viscosity (g), is well represented by both the Mooney's equation [7]: g"g (1!/// )~*g+(= 0 = and MF theory [8]
(1)
ln(g/g )"[g]//(1!/// ) . (2) 0 = Here, g is the viscosity of the suspending #uid, / is the 0 = maximum packing concentration of magnetic particles, [g] is the intrinsic viscosity, and / is the particle volume concentration. The viscosity of the suspensions increases exponentially with particle concentration, irrespective of shear rate (c5). The nonlinear dependence of g on / implies that the interparticle interaction gives rise to a signi"cant e!ect on viscosity. It is noted that the interparticle interaction plays a subtle role in the microstructure of a suspension by exhibiting drastic di!erences between concentrated and dilute suspensions. The measured viscosity is "tted using Eqs. (1) and (2), and two parameters, [g] and / , are determined from "tting = the experiment data. The values of / depend on = the arrangement of the particles. Fig. 1 shows plots of viscosity versus particle volume concentration for rodlike CrO particle suspensions at various shear rates. The 2 measured viscosity "ts well with Eqs. (1) and (2).
Fig. 1. Viscosity dependence on particle volume fraction and shear rate for suspensions of CrO particles dispersed in 2 ethylene glycol.
229
The analysis of [g] gives, in principle, information on the microstructure of the suspension [9] as a function of aspect ratio p, where p is usually de"ned in terms of its axis ratio for an ellipsoidal particle, p"a/b, with a (length of axis of revolution) and b (length of other axis of the particles). Therefore, for the prolate spheroids or rod-like particles such as c-Fe O and CrO , p is larger 2 3 3 than 1 and for oblate spheroids or disk-like shapes such as Ba}ferrite p is less than 1. Based on the theoretical predictions of [g] dependence on particle aspect ratio (p) [10], we thereby estimated the values such as for rod-like particles [g]+100, corresponding to p'35, and for plate-like Ba}ferrite particles [g]+80, corresponding to p(0.02. Some theoretical and experimental studies showed that rod-like magnetic particles are more stable in sideby-side #occulation [11] and plate-like particles are well known for face-on-face stacking #occulation [9]. However, according to the description of the #occulation mechanism, these aspect ratio values with p+35 for rod-like particles and p+0.02 for plate-like particles imply that in the case of rod-like particles, more than four primary particles are in end-to-end #occulation, while in the case of plate-like Ba}ferrite, more than "ve particles are in edge-to-edge #at #occulation. Thus direct microscopic observation of preferable con"guration for #occulation is required in future studies to resolve this issue. Additionally, considering the di!erence in dispersion medium and the intrinsic particle properties, as the viscosity of a suspending medium increases, #ocs become less mobile, therefore intrinsic viscosity decreases. For a description of time-independent viscosity, the most widely used model was proposed by Casson [12]: q1@2"q1@2#g1@2c51@2 . 0 =
(3)
Here, q is the yield stress, and g is the suspension 0 = viscosity at in"nite shear rate. Eq. (3) is used to estimate the shear rate dependence on the suspension viscosity, and the results are presented in Fig. 2 for Ba}ferrite
Fig. 2. q1@2 vs. c51@2 for Ba}ferrite particle suspensions with di!erent particle volume fraction (/).
230
H.J. Choi et al. / Journal of Magnetism and Magnetic Materials 209 (2000) 228}230
since the particles in suspension would exist as primary particles at in"nite shear rate. The larger value of [g] = for both CrO and c-Fe O is characteristic of rod-like 2 2 3 magnetic particles, whereas the smaller value of [g] for = Ba}ferrite is due to its plate-like shape. In conclusion, it was found that the concentration dependence on viscosity of magnetic particle suspensions is well represented by both Mooney's equation and MF theory, and the shear rate dependence on viscosity is well "tted by the Casson equation.
Acknowledgements
Fig. 3. [g] vs. c5~1@2 for various magnetic particle suspensions.
particle suspensions. For all types of particle suspensions, the Casson equation provides an excellent "t to the measured viscosity. The curve "tting clearly indicates that a "nite yield stress exists for the magnetic particle suspensions, and as the particle concentration decreases, the intercept related to yield stress approaches zero, i.e., the Newtonian #uid limit. In addition, the slope of the curve is related to the viscosity at "nite shear rate. Fig. 2 illustrates that dilute particle suspensions still show the existence of small, but "nite, yield stresses. This implies that the particles in suspension still exist as #ocs in the dilution regime. From the Casson equation plots, we obtained both the slope and intercept, and calculated q and g using these values for all particles. 0 = Furthermore, following Smith and Bruce [13], [g] = can be obtained as the asymptotic value of the intercept on the [g] vs. c5~1@2 curve, shown in Fig. 3. Values of [g] obtained by "tting Eq. (1) are plotted in Fig. 3. Due to limited data, it is di$cult to accurately obtain the asymptotic behavior. However, a linear dependence of the intrinsic viscosity on c5~1@2 can be observed in the region of c5~1@2"0.15}0.30 s~1@2. A rough estimate of the intercept gave values of [g] "26 for CrO and c-Fe O , = 2 2 3 and [g] "12 for Ba}ferrite. The values of [g] re#ect = = the characteristics of the di!erent shapes of particles,
This work was partially supported by the Korean Science and Engineering Foundation (Grant No. 9811109-049-2).
References [1] M.P. Sharrock, IEEE Trans. Magn. 25 (1989) 4374. [2] T.E. Karis, M.S. Jhon, Guest Editor, Colloids and Surfaces Vol. 80, No. (1), Special Issue, Ferro/Electro Fluids and Magnetic Particle Suspensions, 1993. [3] M.S. Jhon, T.M. Kwon, H.J. Choi, T.E. Karis, Ind. Eng. Chem. Res. 35 (1996) 3027. [4] T.M. Kwon, M.S. Jhon, H.J. Choi, T.E. Karis, Colloids Surf. 80 (1993) 39. [5] T.W. Kwon, H.J. Choi, M.S. Jhon, J. Magn. Soc. (Japan) 18 (S1) (1994) 253. [6] T.M. Kwon, M.S. Jhon, H.J. Choi, Mater. Chem. Phys. 49 (1997) 225. [7] R.J. Farris, Trans. Soc. Rheol. 12 (1968) 281. [8] M. Mooney, J. Colloid Sci. 6 (1951) 162. [9] L.G. Leal, E.J. Hinch, J. Fluid Mech. 46 (1971) 685. [10] T.M. Kwon, M.S. Jhon, H.J. Choi, J. Mol. Liquids 75 (1998) 115. [11] P.C. Scholten, J.A.P. Felius, C. Slob, IEEE Trans. Magn. 26 (1990) 72. [12] N. Casson, A #ow equation for pigment-oil suspensions of printing ink type, in: C.C. Mill (Ed.), Rheology of Disperse Systems, Pergamon Press, New York, 1959. [13] T.L. Smith, C.A. Bruce, J. Colloid Interface Sci. 72 (1979) 13.
Viscosity of magnetic particle suspensions Hyoung J. Choi!,*, Chul A. Kim!, Taeg M. Kwon", Myung S. Jhon" !Department of Polymer Science and Engineering, Inha University, Inchon 402-751, South Korea "Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Abstract A rheological approach was used to study the e!ects of microstructure on the viscosity of magnetic particle suspensions as functions of concentration and shear rate. Empirical formulas derived from mean-"eld theory and the Mooney equation were used to relate viscosity with particle concentration for both rod- and plate-like particles. The Casson equation was employed to investigate the shear rate dependence of the viscosity. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Magnetic particle suspension; Microstructure; Suspension viscosity
1. Introduction Magnetic particle suspensions have been extensively studied due to their many practical applications, especially in the magnetic tape industry. Magnetic recording media, in general, consist of a coating of "ne magnetic particles on a non-magnetic plastic substrate. The "nished product is greatly a!ected by the dispersion quality of the magnetic particle suspensions [1]. Therefore, the control of dispersion quality is a challenging problem in particulate media production as well as all other coating processes involving unstable particle suspensions. The overall suspension properties show non-Newtonian behavior, exhibiting either thixotropy or shear thinning, and also induced deviatoric normal stresses due to the ordering imparted by the external "eld. These properties can be measured via standard rheological methods. Understanding complex dynamic coupling, including interparticle and #uid/particle interactions, on a fundamental level is a challenging problem [2]. The measurement of the suspension's viscosity can be used to characterize the microstructural state of a dispersion. The shape and orientation e!ects of the magnetic particles or #ocs are then indirectly measured. Empirical
* Corresponding author. Tel.: #82-32-860-7486; fax: #8232-865-5178. E-mail address: [email protected] (H.J. Choi)
formulae from both mean-"eld (MF) theory and the Mooney equation are used to relate viscosity with particle concentration. Shape e!ects of magnetic particles, agglomeration phenomena at low concentration, and shear-induced breakage or agglomeration are investigated and provide complementary information to rheooptical and rheomagnetic techniques [2].
2. Experimental The magnetic particles used in our study (rod-like c-Fe O and CrO particles and plate-like Ba}ferrite 2 3 2 particles) are single domain particles used for commercial media production. The particles' size and shape were characterized using a transmission electron microscope (TEM). A vibrating sample magnetometer (VSM) was employed to characterize the particle magnetic properties for randomly oriented dry powders. The values of coercivity, saturation magnetization, density, diameter, and aspect ratio are reported in Ref. [3]. A cone-andplate viscometer was employed to measure shear viscosities of the magnetic particle suspensions over a wide range of shear rates and concentrations at 253C. A master solution of each magnetic suspension, with an approximate volume fraction of 0.05, was prepared by mixing the particle powder with ethylene glycol using a mini-Eiger motor mill. The volume concentration of the prepared master suspension was obtained using
0304-8853/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 6 9 5 - 2
H.J. Choi et al. / Journal of Magnetism and Magnetic Materials 209 (2000) 228}230
thermogravimetric analysis and rheomagnetic [4] concentration measurement devices. More dilute solutions were prepared by subsequent dilution of the concentrated master suspension.
3. Results and discussion A preliminary theoretical development to describe the experimental observation of rheological properties for magnetic particle suspensions is reported in Refs. [5,6]. Typical rheological characteristics of a particle suspension containing #ocs are shear thinning and concentration dependence on viscosity (g), is well represented by both the Mooney's equation [7]: g"g (1!/// )~*g+(= 0 = and MF theory [8]
(1)
ln(g/g )"[g]//(1!/// ) . (2) 0 = Here, g is the viscosity of the suspending #uid, / is the 0 = maximum packing concentration of magnetic particles, [g] is the intrinsic viscosity, and / is the particle volume concentration. The viscosity of the suspensions increases exponentially with particle concentration, irrespective of shear rate (c5). The nonlinear dependence of g on / implies that the interparticle interaction gives rise to a signi"cant e!ect on viscosity. It is noted that the interparticle interaction plays a subtle role in the microstructure of a suspension by exhibiting drastic di!erences between concentrated and dilute suspensions. The measured viscosity is "tted using Eqs. (1) and (2), and two parameters, [g] and / , are determined from "tting = the experiment data. The values of / depend on = the arrangement of the particles. Fig. 1 shows plots of viscosity versus particle volume concentration for rodlike CrO particle suspensions at various shear rates. The 2 measured viscosity "ts well with Eqs. (1) and (2).
Fig. 1. Viscosity dependence on particle volume fraction and shear rate for suspensions of CrO particles dispersed in 2 ethylene glycol.
229
The analysis of [g] gives, in principle, information on the microstructure of the suspension [9] as a function of aspect ratio p, where p is usually de"ned in terms of its axis ratio for an ellipsoidal particle, p"a/b, with a (length of axis of revolution) and b (length of other axis of the particles). Therefore, for the prolate spheroids or rod-like particles such as c-Fe O and CrO , p is larger 2 3 3 than 1 and for oblate spheroids or disk-like shapes such as Ba}ferrite p is less than 1. Based on the theoretical predictions of [g] dependence on particle aspect ratio (p) [10], we thereby estimated the values such as for rod-like particles [g]+100, corresponding to p'35, and for plate-like Ba}ferrite particles [g]+80, corresponding to p(0.02. Some theoretical and experimental studies showed that rod-like magnetic particles are more stable in sideby-side #occulation [11] and plate-like particles are well known for face-on-face stacking #occulation [9]. However, according to the description of the #occulation mechanism, these aspect ratio values with p+35 for rod-like particles and p+0.02 for plate-like particles imply that in the case of rod-like particles, more than four primary particles are in end-to-end #occulation, while in the case of plate-like Ba}ferrite, more than "ve particles are in edge-to-edge #at #occulation. Thus direct microscopic observation of preferable con"guration for #occulation is required in future studies to resolve this issue. Additionally, considering the di!erence in dispersion medium and the intrinsic particle properties, as the viscosity of a suspending medium increases, #ocs become less mobile, therefore intrinsic viscosity decreases. For a description of time-independent viscosity, the most widely used model was proposed by Casson [12]: q1@2"q1@2#g1@2c51@2 . 0 =
(3)
Here, q is the yield stress, and g is the suspension 0 = viscosity at in"nite shear rate. Eq. (3) is used to estimate the shear rate dependence on the suspension viscosity, and the results are presented in Fig. 2 for Ba}ferrite
Fig. 2. q1@2 vs. c51@2 for Ba}ferrite particle suspensions with di!erent particle volume fraction (/).
230
H.J. Choi et al. / Journal of Magnetism and Magnetic Materials 209 (2000) 228}230
since the particles in suspension would exist as primary particles at in"nite shear rate. The larger value of [g] = for both CrO and c-Fe O is characteristic of rod-like 2 2 3 magnetic particles, whereas the smaller value of [g] for = Ba}ferrite is due to its plate-like shape. In conclusion, it was found that the concentration dependence on viscosity of magnetic particle suspensions is well represented by both Mooney's equation and MF theory, and the shear rate dependence on viscosity is well "tted by the Casson equation.
Acknowledgements
Fig. 3. [g] vs. c5~1@2 for various magnetic particle suspensions.
particle suspensions. For all types of particle suspensions, the Casson equation provides an excellent "t to the measured viscosity. The curve "tting clearly indicates that a "nite yield stress exists for the magnetic particle suspensions, and as the particle concentration decreases, the intercept related to yield stress approaches zero, i.e., the Newtonian #uid limit. In addition, the slope of the curve is related to the viscosity at "nite shear rate. Fig. 2 illustrates that dilute particle suspensions still show the existence of small, but "nite, yield stresses. This implies that the particles in suspension still exist as #ocs in the dilution regime. From the Casson equation plots, we obtained both the slope and intercept, and calculated q and g using these values for all particles. 0 = Furthermore, following Smith and Bruce [13], [g] = can be obtained as the asymptotic value of the intercept on the [g] vs. c5~1@2 curve, shown in Fig. 3. Values of [g] obtained by "tting Eq. (1) are plotted in Fig. 3. Due to limited data, it is di$cult to accurately obtain the asymptotic behavior. However, a linear dependence of the intrinsic viscosity on c5~1@2 can be observed in the region of c5~1@2"0.15}0.30 s~1@2. A rough estimate of the intercept gave values of [g] "26 for CrO and c-Fe O , = 2 2 3 and [g] "12 for Ba}ferrite. The values of [g] re#ect = = the characteristics of the di!erent shapes of particles,
This work was partially supported by the Korean Science and Engineering Foundation (Grant No. 9811109-049-2).
References [1] M.P. Sharrock, IEEE Trans. Magn. 25 (1989) 4374. [2] T.E. Karis, M.S. Jhon, Guest Editor, Colloids and Surfaces Vol. 80, No. (1), Special Issue, Ferro/Electro Fluids and Magnetic Particle Suspensions, 1993. [3] M.S. Jhon, T.M. Kwon, H.J. Choi, T.E. Karis, Ind. Eng. Chem. Res. 35 (1996) 3027. [4] T.M. Kwon, M.S. Jhon, H.J. Choi, T.E. Karis, Colloids Surf. 80 (1993) 39. [5] T.W. Kwon, H.J. Choi, M.S. Jhon, J. Magn. Soc. (Japan) 18 (S1) (1994) 253. [6] T.M. Kwon, M.S. Jhon, H.J. Choi, Mater. Chem. Phys. 49 (1997) 225. [7] R.J. Farris, Trans. Soc. Rheol. 12 (1968) 281. [8] M. Mooney, J. Colloid Sci. 6 (1951) 162. [9] L.G. Leal, E.J. Hinch, J. Fluid Mech. 46 (1971) 685. [10] T.M. Kwon, M.S. Jhon, H.J. Choi, J. Mol. Liquids 75 (1998) 115. [11] P.C. Scholten, J.A.P. Felius, C. Slob, IEEE Trans. Magn. 26 (1990) 72. [12] N. Casson, A #ow equation for pigment-oil suspensions of printing ink type, in: C.C. Mill (Ed.), Rheology of Disperse Systems, Pergamon Press, New York, 1959. [13] T.L. Smith, C.A. Bruce, J. Colloid Interface Sci. 72 (1979) 13.