Availableonlineatwww.sciencedirectcom ScienceDirect E噩≈RS ELSEVIER Joumal of the European Ceramic Society 27(2007)2209-2215 www.elsevier.comlocate/jeurceramsoc Characterization of rheological properties of colloidal zirconia B. Jachimska, Z Adamczyk Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, 30-239 Cracow, Niezapominajek 8, Poland Received 25 March 2006: received in revised form 12 July 2006: accepted 21 July 2006 Available online 22 September 2006 Dynamic viscosity of aqueous suspensions of nanosized zirconia(ZrO2)have been studied for the low volume fraction range. The specific surface area of dry powder was determined from the Bet method. The zeta potential of zirconia particles as a function of ph was measured by the microelectrophoretic method. The isoelectric point found in this way was 4.7. The particle density in aqueous suspensions was found by the dilution method. The dynamic viscosity of suspensions was measured by using a capillary viscometer that eliminated the sedimentation effects. Experimental data showed that for dilute zirconia suspension, the relative viscosity increased more rapidly with the volume fraction than that the Einstein formula predicts. This allowed one to calculate the specific hydrodynamic volume of particles in the suspensions and their apparent density. It was found that particles forming zirconia suspensions were composed of aggregates having porosity of 40-50%. The size of the primary particles orming these aggregates was 0.2 -m that agrees well with the BET specific surface data. The influence of an anionic polyelectrolyte polysodium 4-styrenesulfonate(PSS)on zirconia suspension viscosity also was studied. First the PSs viscosity alone was measured as a function of its volume fraction for various ionic strength of the solutions. The data were interpreted in terms of the flexible rod model of the polyelectrolyte. Then, the viscosity of Zro, in PSS solutions of fixed concentration was measured as a function of the concentration of zirconia. It was revealed that the viscosity of the mixtures was proportional to the product of the zirconia and polyelectrolyte viscosities taken separately. 2006 Elsevier ltd. all rights reserved. Keyword: ZrO2; Dispersants; Rheology; Suspensions 1. Introduction important studies focused on layer by layer deposition, which utilized electrostatic interactions between oppositely charged Understanding the rheological behavior of colloid suspen- species. There is a growing interest in the use of composite mate- sions is important in the analysis and control of the proper- rials in humidity sensors, batteries, microelectronic devices, ties of ceramic materials. High quality and reliability of these magnetic memories, and quantum dot devices. Novel compos- products can be achieved by using homogeneous suspensions ite materials containing inorganic nanoparticles embedded in a composed of well-dispersed particles. Besides stability of sus- polyelectrolyte matrix are currently under investigation for cat pensions and lack of aggregation processes, a high fluidity is vital alytic, optical and other applications for producing ceramics of complex geometrical shape with a Ceramic particles can be stabilized in aqueous solutions by defect-free microstructure after sintering. -3In many technolog- electrostatic and steric interaction. However, it is difficult to ical processes this is achieved by mixing ceramic powders with obtained homogenous, well-dispersed suspension of high solid organic dispersants to obtained better fluidity of the mixture. content. Surface chemical properties are influenced by many Organic-inorganic composites have attracted substantial atten- factors, such as the nature of the ceramic particles, size distribu- ion because of the potential of combining advanced properties tion, surface impurities, nature of solvent, pH value. 3. 5-7In such of organic and inorganic components. Formation of compos- a high solid loading system, the particles have a tendency toward te films based on polyelectrolyte and inorganic nanoparticles agglomeration. This may increass the viscosity of mixtures and has become the subject of extensiv imental work. Many decrease their moldability. The agglomerates can in principle b studied by using the electron microscopy techniques(for exam- ple scanning electron microscopy SEM). However, it is difficult Corresponding author. Tel. +48 12 6395104: fax: +48 12 425 1923 to identify individual agglomerates in the mixture because of kr.edu. pl(Z. Adamczyk) high packing density of the powder. Moreover, the examination 0955-2219/S-see front matter o 2006 Elsevier Ltd. All rights reserved. doi: 10. 1016/j-jeurceramsoc. 2006.07.013
Journal of the European Ceramic Society 27 (2007) 2209–2215 Characterization of rheological properties of colloidal zirconia B. Jachimska, Z. Adamczyk ∗ Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, 30-239 Cracow, Niezapominajek 8, Poland Received 25 March 2006; received in revised form 12 July 2006; accepted 21 July 2006 Available online 22 September 2006 Abstract Dynamic viscosity of aqueous suspensions of nanosized zirconia (ZrO2) have been studied for the low volume fraction range. The specific surface area of dry powder was determined from the BET method. The zeta potential of zirconia particles as a function of pH was measured by the microelectrophoretic method. The isoelectric point found in this way was 4.7. The particle density in aqueous suspensions was found by the dilution method. The dynamic viscosity of suspensions was measured by using a capillary viscometer that eliminated the sedimentation effects. Experimental data showed that for dilute zirconia suspension, the relative viscosity increased more rapidly with the volume fraction than that the Einstein formula predicts. This allowed one to calculate the specific hydrodynamic volume of particles in the suspensions and their apparent density. It was found that particles forming zirconia suspensions were composed of aggregates having porosity of 40–50%. The size of the primary particles forming these aggregates was 0.2m that agrees well with the BET specific surface data. The influence of an anionic polyelectrolyte:polysodium 4-styrenesulfonate (PSS) on zirconia suspension viscosity also was studied. First the PSS viscosity alone was measured as a function of its volume fraction for various ionic strength of the solutions. The data were interpreted in terms of the flexible rod model of the polyelectrolyte. Then, the viscosity of ZrO2 in PSS solutions of fixed concentration was measured as a function of the concentration of zirconia. It was revealed that the viscosity of the mixtures was proportional to the product of the zirconia and polyelectrolyte viscosities taken separately. © 2006 Elsevier Ltd. All rights reserved. Keyword: ZrO2; Dispersants; Rheology; Suspensions 1. Introduction Understanding the rheological behavior of colloid suspensions is important in the analysis and control of the properties of ceramic materials. High quality and reliability of these products can be achieved by using homogeneous suspensions composed of well-dispersed particles. Besides stability of suspensions and lack of aggregation processes, a high fluidity is vital for producing ceramics of complex geometrical shape with a defect-free microstructure after sintering.1–3 In many technological processes this is achieved by mixing ceramic powders with organic dispersants to obtained better fluidity of the mixture. Organic–inorganic composites have attracted substantial attention because of the potential of combining advanced properties of organic and inorganic components. Formation of composite films based on polyelectrolyte and inorganic nanoparticles has become the subject of extensive experimental work.4 Many ∗ Corresponding author. Tel.: +48 12 639 5104; fax: +48 12 425 1923. E-mail address: ncadamcz@cyf-kr.edu.pl (Z. Adamczyk). important studies focused on layer by layer deposition, which utilized electrostatic interactions between oppositely charged species. There is a growing interest in the use of composite materials in humidity sensors, batteries, microelectronic devices, magnetic memories, and quantum dot devices. Novel composite materials containing inorganic nanopatrticles embedded in a polyelectrolyte matrix are currently under investigation for catalytic, optical and other applications. Ceramic particles can be stabilized in aqueous solutions by electrostatic and steric interaction. However, it is difficult to obtained homogenous, well-dispersed suspension of high solid content. Surface chemical properties are influenced by many factors, such as the nature of the ceramic particles, size distribution, surface impurities, nature of solvent, pH value.3,5–7 In such a high solid loading system, the particles have a tendency toward agglomeration. This may increass the viscosity of mixtures and decrease their moldability. The agglomerates can in principle be studied by using the electron microscopy techniques (for example scanning electron microscopy SEM). However, it is difficult to identify individual agglomerates in the mixture because of high packing density of the powder. Moreover, the examination 0955-2219/$ – see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2006.07.013
B. Jachimska, Z Adamczyk/Joumal of the European Ceramic Society 27 (2007)2209-2215 is carried out in a gaseous medium or in vacuum, so the sam- Table I ple needs to be dried that severely disturbs the real structure of Physicochemical data of zirconia aggregates in suspensions. Property Value Remarks Experimental evidence suggested that the degree of agglom- ration of particles in suspensions can be most directly assessed 0.64, 0.4 Malvern PCS, pH 10 standard deviation(um) by the dynamic viscosity measurement studied usually for the Specific surface area(m2/g)5 high volume concentration range of suspensions.8.9This lim- Zeta potential(mv) its the accuracy of such measurements because of the lack of an appropriate theoretical model of viscosity for high concentration Ph of the isoelectric point 47 Malvern Zetasizer titration rang Therefore, the goal of this paper is to prove experimen- 47, 5.79 Suspension dilution, producer lly that the structure of ceramic suspensions, in particular the Apparent density (g/ Viscosity measurements agglomeration degree can be accurately determined from low volume fraction viscosity measurements. We have chosen for our studies zirconia, which is extensively used in ceramic indus- Usus= 10cm, through capillary with internal diameter, R, was try, for producing biocompatible coatings and in the investment measure. The average flow rate was determined from the depen asting industry for producing forms of exceptional temperature dence(V)=vss/TR-t, where t is the time of passing the su resistance. As the model organic dispersant we have selected the pension through the capillary nionic polyelectrolyte: poly(sodium 4-styrenesulfonate)(PSS), The temperature of measurements was maintained at 293K, which is stable over a wide range of pH and ionic strengt using a thermostat. Various capillaries of internal diameter rang Additionally, its molecular structure, charge and conforma ing from 0.5 to 2 mm were used, depending on the viscosity in solutions are well characterized. II range. The device was calibrated using pure liquids of known viscosity, such as, water, butyl and amyl alcohols or ethylene 2. Experimental glycol. The accuracy of viscosity determination for the range 1-10mPas was estimated to be 0.5%o with the main source of 2.. Materials and methods error stemming from the suspension density measurements The zirconia suspensions of the volume fractions in the range The zirconia oxide used in this work was a commercial of 0.005-0.07, were prepared by dispersing zirconia powder in powder(nominal size fraction 99.5%)from distilled water or in of the appropriate PSS solutions concentra Ifa Easer a Johnson Matthey company. Anionic poly(sodium tion, at a pH adjusted by the standard solution of 0. I M NaoH 4-styrenesulfonate(PSS), Mw=70 000 g/mol)was purchased The amount of Pss required to form monolayer on the zirco from Aldrich. Solutions of PSS were prepared by dissolving nia particles surface was first dissolved in distilled water, then polyelectrolytes in deionized water and subsequent filtration the zirconia powder was added to the solution. The suspension using the 0.22 um filter. The ph was adjusted with standard was ultrasonicated for 30 min in order to break up aggregates analytical grade HCl or NaOH solutions. and to remove traces of gases. Every data point of the dynamic The specific surface area of the zirconia powder, determined viscosity was an average of five measurements means of N2 adsorption using B.E.T. multipoint method The amount of polyelectrolyte adsorbed onto zirconia was (Quantasorb Jr, Quantachrome, USA), was 5.0m2/g. The phase determined using the solution depletion method. After mixing and crystal structure of zirconia oxide was identified by X-ray the zirconia suspension with the polyelectrolyte solution, at the diffraction(XRD Philips ). The analysis shows that thethe zir- required concentration(depending on the volume fraction of conia powder has a monoclinic structure. The estimation of zirconia powder)under vigorous stirring, the mixture was cen- zirconia part or aggregate) diameter in aqueous solution trifuged at 10,000 rpm for 30 min. The time assured a complete was performed by dynamic light scattering(Malvern Zetasizer sedimentation of the particles. The supernatant was decanted Nano As). and the concentration of unadsorbed Pss was determined by The zeta potential of zirconia suspension was measured by UV spectroscopy at a wavelength of 225 nm. the microelectrophoretic method using Malvern Zetasizer Nano Zeta potential of Pss was determined by using the Malvern ZS apparatus. The ionic strength was adjusted using NaCl solu- Zetasizer Nano Zs. The effect of ph was studied for the range tion. Each zeta potential was averaged from 10 measurements. of 3-10 All measurement were performed at 293K. For sake of conve nience all the physicochemical data characterizing the zirconia 2. 2. Physicochemical characteristics of zirconia are collected in Table The dynamic viscosity of colloidal zirconia and PSs as a The size distribution of zirconia suspensions prepared function of the volume concentration was measured using a according to the above procedure at pH 10 and1=5 x 10-3M, is home made capillary viscometer in vertical orientation. Auto- shown in Fig. la. As can be observed, the size distribution of the matic detection of suspension level via electric conductivity suspension is rather broad and asymmetrical with the main pea proved very useful for non-transparent suspensions. In each at 0.5 um. This suggests that a significant fraction of aggregates experiments, the flow rate time t of the suspension volume was present in the zirconia suspension. The averaged particle
2210 B. Jachimska, Z. Adamczyk / Journal of the European Ceramic Society 27 (2007) 2209–2215 is carried out in a gaseous medium or in vacuum, so the sample needs to be dried that severely disturbs the real structure of aggregates in suspensions. Experimental evidence suggested that the degree of agglomeration of particles in suspensions can be most directly assessed by the dynamic viscosity measurement studied usually for the high volume concentration range of suspensions.8,9 This limits the accuracy of such measurements because of the lack of an appropriate theoretical model of viscosity for high concentration range. Therefore, the goal of this paper is to prove experimentally that the structure of ceramic suspensions, in particular the agglomeration degree can be accurately determined from low volume fraction viscosity measurements. We have chosen for our studies zirconia, which is extensively used in ceramic industry, for producing biocompatible coatings and in the investment casting industry for producing forms of exceptional temperature resistance. As the model organic dispersant we have selected the anionic polyelectrolyte:poly(sodium 4-styrenesulfonate) (PSS), which is stable over a wide range of pH and ionic strength.10 Additionally, its molecular structure, charge and conformation in solutions are well characterized.11 2. Experimental 2.1. Materials and methods The zirconia oxide used in this work was a commercial powder (nominal size fraction 99.5%) from Alfa Aeaser a Johnson Matthey company. Anionic poly(sodium 4-styrenesulfonate (PSS), Mw = 70 000 g/mol) was purchased from Aldrich. Solutions of PSS were prepared by dissolving polyelectrolytes in deionized water and subsequent filtration using the 0.22 m filter. The pH was adjusted with standard analytical grade HCl or NaOH solutions. The specific surface area of the zirconia powder, determined by means of N2 adsorption using B.E.T. multipoint method (Quantasorb Jr., Quantachrome, USA), was 5.0 m2/g. The phase and crystal structure of zirconia oxide was identified by X-ray diffraction (XRD Philips). The analysis shows that the the zirconia powder has a monoclinic structure. The estimation of zirconia particle (or aggregate) diameter in aqueous solution was performed by dynamic light scattering (Malvern Zetasizer Nano AS). The zeta potential of zirconia suspension was measured by the microelectrophoretic method using Malvern Zetasizer Nano ZS apparatus. The ionic strength was adjusted using NaCl solution. Each zeta potential was averaged from 10 measurements. All measurement were performed at 293 K. For sake of convenience all the physicochemical data characterizing the zirconia are collected in Table 1. The dynamic viscosity of colloidal zirconia and PSS as a function of the volume concentration was measured using a home made capillary viscometer in vertical orientation. Automatic detection of suspension level via electric conductivity proved very useful for non-transparent suspensions. In each experiments, the flow rate time t of the suspension volume Table 1 Physicochemical data of zirconia Property Value Remarks Average particle size, standard deviation (m) 0.64, 0.4 Malvern PCS, pH 10, I = 10−3 M Specific surface area (m2/g) 5 BET Zeta potential (mV) −58 Electrophoresis, pH 10, I = 10−3 M pH suspension 10 pH of the isoelectric point 4.7 Malvern Zetasizer, titration method Specific density (g/cm3) 5.47, 5.79 Suspension dilution, producer Apparent density (g/cm3) 3.04 Viscosity measurements vsus = 10 cm3, through capillary with internal diameter, R, was measure. The average flow rate was determined from the dependence V = vsus/πR2t, where t is the time of passing the suspension through the capillary. The temperature of measurements was maintained at 293 K, using a thermostat. Various capillaries of internal diameter ranging from 0.5 to 2 mm were used, depending on the viscosity range. The device was calibrated using pure liquids of known viscosity, such as, water, butyl and amyl alcohols or ethylene glycol. The accuracy of viscosity determination for the range 1–10 mPa s was estimated to be 0.5% with the main source of error stemming from the suspension density measurements. The zirconia suspensions of the volume fractions in the range of 0.005–0.07, were prepared by dispersing zirconia powder in distilled water or in of the appropriate PSS solutions concentration, at a pH adjusted by the standard solution of 0.1 M NaOH. The amount of PSS required to form monolayer on the zirconia particles surface was first dissolved in distilled water, then the zirconia powder was added to the solution. The suspension was ultrasonicated for 30 min in order to break up aggregates and to remove traces of gases. Every data point of the dynamic viscosity was an average of five measurements. The amount of polyelectrolyte adsorbed onto zirconia was determined using the solution depletion method. After mixing the zirconia suspension with the polyelectrolyte solution, at the required concentration (depending on the volume fraction of zirconia powder) under vigorous stirring, the mixture was centrifuged at 10,000 rpm for 30 min. The time assured a complete sedimentation of the particles. The supernatant was decanted and the concentration of unadsorbed PSS was determined by UV spectroscopy at a wavelength of 225 nm. Zeta potential of PSS was determined by using the Malvern Zetasizer Nano ZS. The effect of pH was studied for the range of 3–10. 2.2. Physicochemical characteristics of zirconia The size distribution of zirconia suspensions prepared according to the above procedure at pH 10 and I = 5 × 10−3 M, is shown in Fig. 1a. As can be observed, the size distribution of the suspension is rather broad and asymmetrical with the main peak at 0.5m. This suggests that a significant fraction of aggregates was present in the zirconia suspension. The averaged particle
B. Jachimska, Z Adamczyk /Joumal of the European Ceramic Society 27(2007)2209-2215 10000 10000 (a) Size [nm (b) Size [nm] of the size 0.40 um. (b)Z O2 with PSS at pH 10. 1=5 x 10-M, averaged particle size 0.56um, standard deviation of the size 0. 25ul um standard deviation Fig.I. Particle size distribution of zirconia determined by the PCS method (a)Z O2 at pH 10. 1=5 x 10-3M, averaged particle size 0.6 diameter was 0.64 um with the standard deviation of 0.40 um. However, a prerequisite of a correct interpretation of viscos A similar but more narrow size distribution was obtained for zir- ity measurements is the knowledge of the volume fraction of conia suspension in PSS solution at pH 10 and 1=5 x 10-M the solid in the suspensions v. This quality can only be cal- as can be seen in Fig. lb. The averaged particle diameter was culated if the real density of particles in suspension is known 0.56 um with the standard deviation of 0. 25 um. The density was determined by the dilution method, i.e., from The size of primary particle of zirconia was determined by the dependence of the suspension density on the weight frac the scanning electron microscopy(SEM). From the SEM images tion of zirconia w= p/msus, where p is the particle mass (shown in Fig. 2)it was estimated that the size of primary parti cles was 0.2 um. It is interesting re this value with the BETdata, giving specific surface area S=5.0 m-/g as mentioned previously. By assuming a spherical shape of the particles and using the formula d=6/ppS(where Pp is the specific density of the solid zirconia, equal 5.79 g/cm, as specified by the pro- ducer)one obtains d=0. 21 um. As can be noticed this is similar to the primary particle size derived from the SEM observations 3. Result and discussion It is known that the stability and aggregation degree of oxides, in particular zirconia, depends to a critical extent on pH value that governs the number of hydroxyl groups increasing the neg- Ace.V Spot Magn Del WD H ative charge of particles. The increase in the surface char 150k2020000xSE111Z02 usually increases the absolute value of the zeta potential of par ticles(the electric potential in the slip plane)which results in an increased stability of suspensions. 2 The zeta potential is a quantity well accessible experimentally, e. g, by using the micro- electropheretic method as done in this work. The dependence of the zeta potential of ZrO2 suspensionon on the ph determined for a fixed ionic strength of 10-3M is shown in Fig 3.As can be noticed, for pH 4.7, the zeta potential of the suspension of pure zirconia was close to zero. This pH value is referred to as the isoelectric point. In this respect our data agree well with that reported by Ewais et al. and Crucean et al. 3,4 On the other hand,Fengqiuet al. reported pH 6 as the isoelectric point.Gen- ally, there is a rather large spread in the reported data, e.g Johnson et al. reported pH 7.5 as the isoelectric point of zirco- nia. This issue is discussed at length in the book of kosmulski. 14 These high values of zeta potential(in absolute terms)are expected to stabilize of the zirconia suspension. However, the dispersion of aggregates seems rather unlikely. This hypothe Fig 2. SEM image of zirconia powder deposited on mica surface: (a) ZrO2and sis was tested by using the dynamic viscosity measurements. (b)ZrO2 with PSS
B. Jachimska, Z. Adamczyk / Journal of the European Ceramic Society 27 (2007) 2209–2215 2211 Fig. 1. Particle size distribution of zirconia determined by the PCS method. (a) ZrO2 at pH 10, I = 5 × 10−3 M, averaged particle size 0.64m, standard deviation of the size 0.40m. (b) ZrO2 with PSS at pH 10, I = 5 × 10−3 M, averaged particle size 0.56m, standard deviation of the size 0.25m. diameter was 0.64m with the standard deviation of 0.40m. A similar but more narrow size distribution was obtained for zirconia suspension in PSS solution at pH 10 and I = 5 × 10−3 M as can be seen in Fig. 1b. The averaged particle diameter was 0.56m with the standard deviation of 0.25 m. The size of primary particle of zirconia was determined by the scanning electron microscopy (SEM). From the SEM images (shown in Fig. 2) it was estimated that the size of primary particles was 0.2m. It is interesting to compare this value with the BET data, giving specific surface area S = 5.0 m2/g as mentioned previously. By assuming a spherical shape of the particles and using the formula d = 6/ρpS (where ρp is the specific density of the solid zirconia, equal 5.79 g/cm3, as specified by the producer) one obtains d = 0.21m. As can be noticed this is similar to the primary particle size derived from the SEM observations. 3. Result and discussion It is known that the stability and aggregation degree of oxides, in particular zirconia, depends to a critical extent on pH value that governs the number of hydroxyl groups increasing the negative charge of particles. The increase in the surface charge usually increases the absolute value of the zeta potential of particles (the electric potential in the slip plane) which results in an increased stability of suspensions.12 The zeta potential is a quantity well accessible experimentally, e.g., by using the microelectropheretic method as done in this work. The dependence of the zeta potential of ZrO2 suspensionon on the pH determined for a fixed ionic strength of 10−3 M is shown in Fig. 3. As can be noticed, for pH 4.7, the zeta potential of the suspension of pure zirconia was close to zero. This pH value is referred to as the isoelectric point. In this respect our data agree well with that reported by Ewais et al.3 and Crucean et al.13,14 On the other hand, Fengqiu et al.5 reported pH 6 as the isoelectric point. Generally, there is a rather large spread in the reported data, e.g., Johnson et al.6 reported pH 7.5 as the isoelectric point of zirconia. This issue is discussed at length in the book of Kosmulski.14 These high values of zeta potential (in absolute terms) are expected to stabilize of the zirconia suspension. However, the dispersion of aggregates seems rather unlikely. This hypothesis was tested by using the dynamic viscosity measurements. However, a prerequisite of a correct interpretation of viscosity measurements is the knowledge of the volume fraction of the solid in the suspensions ΦV. This quality can only be calculated if the real density of particles in suspension is known. The density was determined by the dilution method, i.e., from the dependence of the suspension density on the weight fraction of zirconia w = mp/msus, where mp is the particle mass Fig. 2. SEM image of zirconia powder deposited on mica surface: (a) ZrO2 and (b) ZrO2 with PSS.
B. Jachimska, Z Adamczyk/Joumal of the European Ceramic Society 27 (2007)2209-2215 =1 Fig 3. Zetapotential of ZrO2 as a function of pH determined for 1=1x 10-3M. ig. 5. The dependence of the intrinsic viscosity [n]=ns /n of ZrO2 suspensions The broken line denotes the theoretical results calculated from Einstein formula and msus is the suspension mass. The weight fraction of zirco- n/n=1+2. 5 y and the solid line represent the linear regression fit nia was changed within the range 0-0.3 by taking appropriate assuming that the volume of the electrolyte remained the same 5.79 g/cm. The deviation is probably caused by the intrinsic upon mixing, the density of the zirconia/electrolyte mixture can porosity of zirconia particles. Some of the pores of primary par- be expressed by the formula ticles forming aggregates were probably closed, inaccessible for he solvent. By knowing the real density of particles, the volume pe (1) fraction can be calculated as v= wpss/Pp 1+u(pe/p-1) Typical experimental data presenting the dependence of the where pe is the solvent(electrolyte density)and P, is the density intrinsic viscosity (m =ns/n (where ns is the viscosity of the of zirconia oxide particles(dry). From Eq. (1)one can deduce that zirconia particle density in fraction of zirconia for the low concentration range(v <0.08 ion can be calculated from the depende are plotted in Fig. 5. It is interesting to note, that the weight frac tion of zirconia in these suspensions was much higher attaining 0.4 (for v=0.08). As can be seen, the dependence of [n] on (2) y of zirconia can well be fitted by a linear regression. How- where tg ais the slope of the pe/psus versus w dependence(which Einstein formula predicts. witten in the usual form results shown in Fig. 4 suggest that these dependencies can well be fitted by a linear regression line with the slope which gives b ns=1+ Cy Zirconia l oxide density 5.47 g/cm. This is slightly smaller than the value supplied by the producer for solid zirconia, equal were Cv is the dimensionless constant. In our case the slope was found equal 4.5, in stead of 2.5, which is 1. 8 times larger than predicted by the Einstein formula. The deviation from the Einstein formula occurring for the low volume fraction of suspensions rpreted in terms of the primary electroviscous effect stemming from shear induced deformations of ionic double layers surrounding suspended particles. This leads to increased dissipation of mechanical energy resulting in increased viscosity of suspensions over val- ues predicted by the Einstein model. This deviation is expressed in terms of the primary electroviscous function, expressed Cv=2.(1+p) 070050101202005 where p is the primary electroviscous function depending on the ionic strength and composition of the electrolyte 4. The dependence of Pe/psus on the weight fraction w of zrOz, determined In the case where the diffusion coefficients of ions forming the electrolyte do not differ too much, one can derive an analytical
2212 B. Jachimska, Z. Adamczyk / Journal of the European Ceramic Society 27 (2007) 2209–2215 Fig. 3. Zeta potential of ZrO2 as a function of pH determined for I = 1 × 10−3 M. and msus is the suspension mass. The weight fraction of zirconia was changed within the range 0–0.3 by taking appropriate mass of the zirconia powder and the solvent (electrolyte). By assuming that the volume of the electrolyte remained the same upon mixing, the density of the zirconia/electrolyte mixture can be expressed by the formula8: ρsus = ρe 1 1 + w(ρe/ρp − 1) (1) where ρe is the solvent (electrolyte density) and ρp is the density of zirconia oxide particles (dry). From Eq. (1) one can deduce that zirconia particle density in the suspension can be calculated from the dependence: ρp = ρe 1 + tg α (2) where tg α is the slope of the ρe/ρsus versuswdependence (which is negative in our case) that is expected to be a straight line. The results shown in Fig. 4 suggest that these dependencies can well be fitted by a linear regression line with the slope which gives for the zirconia oxide density 5.47 g/cm3. This is slightly smaller than the value supplied by the producer for solid zirconia, equal Fig. 4. The dependence of ρe/ρsus on the weight fraction w of ZrO2, determined for pH 10. Fig. 5. The dependence of the intrinsic viscosity [η] = ηs/η of ZrO2 suspensions on the volume fraction ΦV = wρsus/ρp determined for pH 10, I = 5 × 10−3 M. The broken line denotes the theoretical results calculated from Einstein formula ηs/η = 1 + 2.5ΦV and the solid line represent the linear regression fit. 5.79 g/cm3. The deviation is probably caused by the intrinsic porosity of zirconia particles. Some of the pores of primary particles forming aggregates were probably closed, inaccessible for the solvent. By knowing the real density of particles, the volume fraction can be calculated as ΦV = wρsus/ρp. Typical experimental data presenting the dependence of the intrinsic viscosity [η] = ηs/η (where ηs is the viscosity of the suspension and η is the viscosity of the electrolyte) on the volume fraction of zirconia for the low concentration range (ΦV < 0.08) are plotted in Fig. 5. It is interesting to note, that the weight fraction of zirconia in these suspensions was much higher attaining 0.4 (for ΦV = 0.08). As can be seen, the dependence of [η] on ΦV of zirconia can well be fitted by a linear regression. However, the slope of this line d[η]/dΦV was found larger than the Einstein formula predicts, written in the usual form: η¯ = ηs η = 1 + CVΦV (3) were CV is the dimensionless constant. In our case the slope was found equal 4.5, in stead of 2.5, which is 1.8 times larger than predicted by the Einstein formula. The deviation from the Einstein formula occurring for the low volume fraction of suspensions is interpreted in terms of the primary electroviscous effect stemming from shear induced deformations of ionic double layers surrounding suspended particles.15 This leads to increased dissipation of mechanical energy resulting in increased viscosity of suspensions over values predicted by the Einstein model. This deviation is expressed in terms of the primary electroviscous function, expressed as16–19: CV = 2.5(1 + p) (4) where p is the primary electroviscous function depending on the ionic strength and composition of the electrolyte. In the case where the diffusion coefficients of ions forming the electrolyte do not differ too much, one can derive an analytical
B. Jachimska, Z Adamczyk /Joumal of the European Ceramic Society 27(2007)2209-2215 expression for p, valid for spherical particles8 seems, therefore, that the non-spherical shape of zirconia parti- regates is not responsible for the deviation of the slope 22(1+ka2F(ka) (5) of ln] versus v dependence from the from Einsteins formula, which was, as previously estimated, about 180%0 where E is the dielectric constant of water(relative permittivity), The most likely explanation is that the zirconia aggregates s the zeta potential of the particle forming the suspension, D, form a loose structure, characterized by a high degree of poros the ith ion diffusion coefficient, F(xa) the function of the dimen- ity, as suggested by the SEM picture shown in Fig. 2. As a result, sionless ka parameter, K-=(e kT/8Ten 2 the double-layer the effective hydrodynamic volume of particles in the suspension thickness,k the Boltzmann constant, T the absolute tempera-(at fixed mass fraction )becomes larger than the net volume of ture, e the elementary charge, I the ionic strength of solution isolated primary particles, which results in a decreased appar and a=dn2 is the particle radius. ent density of particles. A similar model was effectively used For a ionic strength of l=3 x 10-M, Kaequals 56 for the zir- efore to explain the anomalous viscosity behavior of silica conia suspension(assuming 0.6 um as the averaged diameter of suspensions 8 It was postulated that upon contact with water, a the aggregate).As calculated in for this value of Ka, the value gel-like layer was formed on the surface of silica, having lower of the function(1+Ka) F(xa)is about 3 x 10-4. Then, by tak- apparent density than the core volume of particles ing S=-50mV and D=2 x 10-cm-/s one can estimate from Since the primary electroviscous effect remains negligible as Eq (5)thatp=7x 10-4. As can be seen, this nis value is more than previously estimated, the apparent density of the aggregates can three orders of magnitude smaller than experimentally found be calculated from the dependence& for zirconia, equal 0.8. The comparison proves quite unequivo- cally, that the primary electroviscous effect is not responsible for the deviation of zirconia suspension viscosity from the Einstein model By knowing the apparent density, one can calculated the aver- Therefore, the most probable reason of this deviation can age porosity of aggregates Ep from the formula be sought in the presence of aggregates in the suspension. For Pp=p aggregates of non-spherical shape, the increase in the intrinsic"PPp-Pe viscosity of suspensions occurs because of the increase in the fuid velocity gradients due to particle rotation. This effect was By substituting into described quantitatively by Brenner for spheroidal particles, iments, i.e., Pp=5.47 g/cm, p=3.03 g/cm, Pe=1.01 g/cm3 having both a prolate and an oblate shape. The parameter of one obtains Ep=0.55. Hence, the apparent volume fraction of primary significance governing suspension viscosity in this case solid in the aggregate equals 1-Ep=0.45. This seems a quite is the Peclet number( for rotary Brownian motion) defined as the reasonable estimate in view of the fact that the maximum packing ratio of the characteristic rotation velocity (G)d to the diffusion of spheres in three dimensions is 0.62.20 Our value is smaller velocity D/d because the aggregate structure is more loose than under the maximum packing when, be definition, all particles must con- 6) tact with each other Having established the basic relationship for the pure zir- where(G)is the averaged shear rate in the capillary, D=kT/3nd conia suspension, we have studied the effect of the anionic the diffusion coefficient of the aggregate and d is the typical polyelectrolyte PSS on the viscosity of zirconia suspension. This diameter of the aggregate. polyelectrolyte, bearing sulfonic groups in chain was thoroughly In the case of the capillary viscometer the averaged shear rate characterized in our previous work. The extended length of the can be calculated as polyelectrolyte chain, having the molecular weight of 70,000 is 91 nm and the length to diameter ratio of the chain equal 3TR (7) 78. One can draw quantitative conclusions about the ionization degree of the Pss chain from the electrophoretic mobility mea By taking the typical experimental data: R=0.035 cm,Usus cm, t=50s, one obtains(G)=4 x 10s-l. Using this value surements as a function of the pH and ionic strength. The data compiled in Table 2 show that the zeta potential of PSs increased and taking d=0.66 um as the averaged size of the zirconia aggre- from -90-+5.0 mV for 1=1x 10-3M to-55+5.0mV for gate one can calculate from Eq. (7)that Pe=6.6x 10. Such a 1=0.15. that suggests a significant reduction in the number of large value of Pe indicates that the suspension viscosity was dominated by shear rather than diffusion. Thus, in the limit Table 2 of such large Peclet numbers, the intrinsic viscosity of parti- Zeta potential 5, of PSS (mv) at pH cle suspensions attains the limiting, high-shear values, tabulated by Brenner. For prolate spheroids having the length to width (M) Zeta potential (MV) aspect ratio of 3 the limiting value of [n]=2684, for aspect 1 x 10-3 ratio 4, [n]=2.801 and for aspect ratio 5, [n]=2.918. As can 5×10- be noticed, even for very elongated spheroids, i.e. for aspect 0.15 55±5.0 ratio 5. the correction to the einsteins formula is about 12%o. It
B. Jachimska, Z. Adamczyk / Journal of the European Ceramic Society 27 (2007) 2209–2215 2213 expression for p, valid for spherical particles18: p = 2εζ2(1 + κa) 2F(κa) 3πηDi (5) where ε is the dielectric constant of water (relative permittivity), ζ the zeta potential of the particle forming the suspension, Di the ith ion diffusion coefficient, F(κa) the function of the dimensionless κa parameter, κ−1 =(ε kT/8πe2I) 1/2 the double-layer thickness, k the Boltzmann constant, T the absolute temperature, e the elementary charge, I the ionic strength of solution and a = d/2 is the particle radius. For a ionic strength ofI = 3 × 10−3 M, κa equals 56 for the zirconia suspensioun (assuming 0.6 m as the averaged diameter of the aggregate). As calculated in18 for this value of κa, the value of the function (1+κa) 2F(κa) is about 3 × 10−4. Then, by taking ζ = −50 mV and D = 2 × 10−5 cm2/s one can estimate from Eq. (5) that p = 7 × 10−4. As can be seen, this value is more than three orders of magnitude smaller than experimentally found for zirconia, equal 0.8. The comparison proves quite unequivocally, that the primary electroviscous effect is not responsible for the deviation of zirconia suspension viscosity from the Einstein model. Therefore, the most probable reason of this deviation can be sought in the presence of aggregates in the suspension. For aggregates of non-spherical shape, the increase in the intrinsic viscosity of suspensions occurs because of the increase in the fluid velocity gradients due to particle rotation. This effect was described quantitatively by Brenner19 for spheroidal particles, having both a prolate and an oblate shape. The parameter of primary significance governing suspension viscosity in this case is the Peclet number (for rotary Brownian motion) defined as the ratio of the characteristic rotation velocity Gd to the diffusion velocity D/d: Pe = G d2 4D (6) where Gis the averaged shear rate in the capillary, D = kT/3πηd the diffusion coefficient of the aggregate and d is the typical diameter of the aggregate. In the case of the capillary viscometer the averaged shear rate can be calculated as G = 8vsus 3πR3t (7) By taking the typical experimental data: R = 0.035 cm, vsus = 10 cm3, t = 50 s, one obtains G = 4 × 103 s−1. Using this value and taking d = 0.66m as the averaged size of the zirconia aggregate one can calculate from Eq. (7) that Pe = 6.6 × 102. Such a large value of Pe indicates that the suspension viscosity was dominated by shear rather than diffusion. Thus, in the limit of such large Peclet numbers, the intrinsic viscosity of particle suspensions attains the limiting, high-shear values, tabulated by Brenner.19 For prolate spheroids having the length to width aspect ratio of 3 the limiting value of [η] = 2.684, for aspect ratio 4, [η] = 2.801 and for aspect ratio 5, [η] = 2.918. As can be noticed, even for very elongated spheroids, i.e., for aspect ratio 5, the correction to the Einstein’s formula is about 12%. It seems, therefore, that the non-spherical shape of zirconia particle aggregates is not responsible for the deviation of the slope of [η] versus ΦV dependence from the from Einstein’s formula, which was, as previously estimated, about 180%. The most likely explanation is that the zirconia aggregates form a loose structure, characterized by a high degree of porosity, as suggested by the SEM picture shown in Fig. 2. As a result, the effective hydrodynamic volume of particles in the suspension (at fixed mass fraction) becomes larger than the net volume of isolated primary particles, which results in a decreased apparent density of particles. A similar model was effectively used before to explain the anomalous viscosity behavior of silica suspensions.8 It was postulated that upon contact with water, a gel-like layer was formed on the surface of silica, having lower apparent density than the core volume of particles. Since the primary electroviscous effect remains negligible as previously estimated, the apparent density of the aggregates can be calculated from the dependence8: ρ∗ = 2.5ρp CV (8) By knowing the apparent density, one can calculated the average porosity of aggregates εp from the formula8: εp = ρp − ρ∗ ρp − ρe (9) By substituting into Eq. (9) the data obtained in our experiments, i.e., ρp = 5.47 g/cm3, ρ* = 3.03 g/cm3, ρe = 1.01 g/cm3 one obtains εp = 0.55. Hence, the apparent volume fraction of solid in the aggregate equals 1 − εp = 0.45. This seems a quite reasonable estimate in view of the fact that the maximum packing of spheres in three dimensions is 0.62.20 Our value is smaller because the aggregate structure is more loose than under the maximum packing when, be definition, all particles must contact with each other. Having established the basic relationship for the pure zirconia suspension, we have studied the effect of the anionic polyelectrolyte PSS on the viscosity of zirconia suspension. This polyelectrolyte, bearing sulfonic groups in chain was thoroughly characterized in our previous work.11 The extended length of the polyelectrolyte chain, having the molecular weight of 70,000 is 91 nm and the length to diameter ratio of the chain equals 78. One can draw quantitative conclusions about the ionization degree of the PSS chain from the electrophoretic mobility measurements as a function of the pH and ionic strength. The data compiled in Table 2 show that the zeta potential of PSS increased from −90 ± 5.0 mV for I = 1 × 10−3 M to −55 ± 5.0 mV for I = 0.15, that suggests a significant reduction in the number of Table 2 Zeta potential ζp of PSS (mV) at pH 10 I (M) Zeta potential (MV) 1 × 10−3 −90 ± 5.0 5 × 10−3 −83 ± 5.0 1 × 10−2 −74 ± 5.0 0.15 −55 ± 5.0
2214 B. Jachimska, Z Adamczyk/ Joumal of the European Ceramic Sociery 27(2007)2209-2215 molecule length)and D=1.8x 10-7cm2/s(for 1=5 x 10-3M) one can calculate from Eq (7)that Pe=0. 46. For higher ionic strength this should be definitely smaller because of the smaller length of the molecule. Since this value is smaller than unity, the suspension viscosity is dominated by the rotary diffusion of PSS molecules rather than by the shear as was the case for the zirconia suspension. In this limit, of diffusion dominated vis- cosity Brenner derived the approximate formula describing the intrinsic viscosity of prolate spheroid polymer solution nj 10 15ln2-0.5 where L= L/d is the ratio of the length to width of the spheroid It can be calculated from Eq (10)that for L=78(the value Fig. 6. Zeta potential as a function of ph determined for I=l x 10M.(a) pertinent to the extended PSS molecule)[n]=383, for L=50 (the molecule bend to the form of a semi-circle)[n]=177 and for L= 25(the molecule bend to the form of a circle)[n]=55 ionic groups at the PSS molecule surface. On the other hand, As can be seen, the latter intrinsic viscosity agrees well with the the dependence of the zeta potential of Pss on ph of the solu- experimental value obtained for the ionic strength of 5 x 10 in Fig. 6. As can be seen, for the pH range studied, i.e.,5-1 After measuring the viscosity of zirconia and PSS separately, the viscosity of mixtures was studied in order to estimate the the zeta potential of PSS remains fairly constant that suggests improvement in the fluidity upon the addition of PSS. The flu- a pH-independent ionization degree of surface groups of this idity can be increased by increasing the dispersion degree of the molecule The result of viscosity measurements of PSs solutions per- electrolyte adsorbed on zirconia was determined by the solution formed for PSS volume fraction range v 3 zeta potential of zirconia became negative upon adsorption of Darvin C attaining a minimum value of -60 m V forpH8. It is not obvious what is the physical mecha- nism of adsorption of anionic polyelectrolytes(PSs and Darvin 1.1 C)on negatively charged zirconia surface, which is the case for pH>5 as can be deduced from the data shown in Fig 3.It seems that a possible explanation of this fact is the heteroge neous nature of zirconia particles dispersed in solution. Hence, adsorption of Pss may occur on surface areas bearing locally a positive charge in the nanoscale, although the net charge of -000100000001000200030.0040.005 zirconia surface, in the microscale, remains negative. Certainly, a unequivocal confirmation of this hypothesis requires further systematic studies, which are outside the scope of this work, Fig. 7. The dependence of the intrinsic viscosity of PSS [n]= ns/n on its volume however. fractionφv,pH6.5-10,(△)l=5×10-3M( curve)and(◆)l=0.5M( curve It is interesting to mention that, in contrast to the results reported by Fengqiu et al.in our case, adsorption of PSs on zir-
2214 B. Jachimska, Z. Adamczyk / Journal of the European Ceramic Society 27 (2007) 2209–2215 Fig. 6. Zeta potential as a function of pH determined for I = 1 × 10−3 M. () ZrO2 with PSS (curve 1); () PSS (curve 2). ionic groups at the PSS molecule surface. On the other hand, the dependence of the zeta potential of PSS on pH of the solution measured for a fixed ionic strength I = 1 × 10−3 M is shown in Fig. 6. As can be seen, for the pH range studied, i.e., 5–10 the zeta potential of PSS remains fairly constant that suggests a pH- independent ionization degree of surface groups of this molecule. The result of viscosity measurements of PSS solutions performed for PSS volume fraction range ΦV 3 zeta potential of zirconia became negative upon adsorption of Darvin C attaining a minimum value of−60 mV for pH 8. It is not obvious what is the physical mechanism of adsorption of anionic polyelectrolytes (PSS and Darvin C) on negatively charged zirconia surface, which is the case for pH > 5 as can be deduced from the data shown in Fig. 3. It seems that a possible explanation of this fact is the heterogeneous nature of zirconia particles dispersed in solution. Hence, adsorption of PSS may occur on surface areas bearing locally a positive charge in the nanoscale, although the net charge of zirconia surface, in the microscale, remains negative. Certainly, a unequivocal confirmation of this hypothesis requires further systematic studies, which are outside the scope of this work, however. It is interesting to mention that, in contrast to the results reported by Fengqiu et al.5 in our case, adsorption of PSS on zir-
B. Jachimska, Z Adamczyk /Joumal of the European Ceramic Society 27(2007)2209-2215 Analogous measurements of the viscosity of the anionic polyelectrolyte-PSS used to enhance the stability of zirconia suspensions showed that the slope of the intrinsic viscosity vs. volume fraction attained values as high as 50 for 1=5 X 10-M. This effect was interpreted in terms of the flexible rod model According to this model, for higher electrolyte concentration, the PSS molecule assumes the shape of a semi circle or sinusoidal curve rather than a random coil structure as often suggested. It was further confirmed experimentally that adsorption of PSS on zirconia decreased significantly the negative zeta poten- tial but did not influence too significantly the dispersion degree of zirconia particles. Also the viscosity of the zirconia suspen- sion in PSS solutions was found equal to the product of the viscosity of zirconia dispersed in PSS free solution of the same composition and the viscosity of Pss al Fig 8. The dependence of the intrinsic viscosity Inl=ns/n ZrO2 vS the volume raction v= wpssPp pH 10, 1=5x 10-3M. ()ZrO2, the line denotes the Acknowledgements near regression [nI=1+4.5dv21o, (curve 2):(O)ZrO2+PSS mixture, the solid line denoted the product of intrinsic viscosities [n]=[ o, +Inlpss (1+4.5V2o,)+(1+50vgs)( curve 1) This work was supported by MNiS W Grant 4T08B 03425 help of Ms K. Kusak in perfo ormins penitents conia did not increase too significantly the dispersion degree of kindly acknowledged. aggregates. This is evident from the particle size measurements showing that the average size of zirconia particles dispersed in References PSS(at pH 7.4)was 0.56 um, which does not differ much from the value observed in PSS free solutions. The limited influence of 1. Liu, D M, Ceram. Int, 2000, 26, 279 2. Baklouti, S. M., Romdhane, R. B, Boufi, Pagnoux, S C. Chartier, Tand PSS on the dispersion degree of zirconia also was confirmed by Baumard. J F. J. Eur. Ceram. Sci., 2003, 23, 905. the viscosity measurements whose results are shown in Fig 8. As 3. Ewais, E, Zaman, A. A and Sigmund, W, J. Eur Ceram. Sci., 2002, 22, can be seen, the dependence of the intrinsic viscosity of zirconia 2805 dispersed in PSS solution(variable polymer concentration from 4 Decher, G,Multilayer Thin Films.Wiley-VCH, 2002. 350 ppm to 2000 ppm, pH 10, 1=5 x 10-3 M)on the volume 5. Fengqiu, T, Xiaoxian, H, Yufeng, Z. and Jingkun, G, Ceram. Int, 2000, fraction solid can well be fitted by a line with the slope being the 6. Johnson, S. B. Franks, G. V, Scales, P. J, Boder, D. V and Healy, T.W. product of the viscosity of zirconia dispersed in PSS free solution IntJ. Miner: Process. 2000. 58. 267. of pss alone. henc 7. Picon, C. and Maccauro, G. Biomaterials, 1999, 20. 1 our results seem to confirm the effective medium hypothesis. 8. Adamczyk, Z, Jachimska, B and Kolasiniska, M, J. Colloid Interface Sci according to which the relative viscosity of a suspension having 9. Okada, K and Nagase, Y,. Chem. Eng. Jpn., 2000, 33, 168 the solid concentration v, v2(where v, is the volume 10. Atkins, A Physical Chemistry. Oxford University Press, Oxford, 1994, p fraction of zirconia and v, is the volume fraction of Pss) equals to the product of relative viscosities n(v)i(v,). 11. Adamczyk, Z, Zembala, M, Warszynski, P and Jachimska, B, Langmuir, 2004,20,10517 4. Concluding remarks 12. Hunter, R, Foundations of Colloid Science. Oxford, 2001 13. Crucean, E. Rand. B and Brit, T.J., Ceram. Soc., 1979. 78, 96. 14. Kosmulski, M, Che. Properties Mater: Surf: Surf. Sci. Ser, 2001, 102 It has been demonstrated experimentally that the relative vis- 15. Masiliyah, J H, Neale, G, Malysa, K and van de Ven, T.G.M, Chem. cosity of dilute zirconia suspensions increased more rapid Emg.Sci,1987,42,245 with the volume fraction that the Einstein formula predicted. 16. Honig, E P Punt, W.F. J and Offermans, P H.G.,J. Colloid Interface Sc This discrepancy could not be explained in terms of the pri- 17. Adamczyk, Z, Siwek, B. and Zembala, M, Bull. Pol. Acad. Chem., 2000, mary electroviscous effect because of small thickness of the electric double-layer. As a plausible explanation the presence of 18 Laven, J and Stein, H N, J. Colloid Interface Sci., 2001, 238.8 aggregates in the zirconia suspension was given, which were 19. Brenner, H, Int J Multiphase Flow, 1974,1, 195 composed of primary particles of the size ca. 200 nm. The 20. Greenwood, R, Luckham, P F and Gregory, T.J. Colloid Interface Sc hypothesis of the presence of aggregates was also confirmed 21. Stoll. s and chodanowski p Macromolecules, 2002. 35.9556 by the SEM. The viscosity measurements allowed one to deter- 22. Pal, R, Rheology of emulsions containing polymeric liquids In Encyclop mine the averaged solid content in these aggregates, which was dia of Emulsion Technology, Vol. 4, ed P. Becher. Marcel Dekker, Newyork, found close to 0.45 Basel, Hong Kong, 1996
B. Jachimska, Z. Adamczyk / Journal of the European Ceramic Society 27 (2007) 2209–2215 2215 Fig. 8. The dependence of the intrinsic viscosity [η] = ηs/η ZrO2 vs. the volume fraction ΦV = wρsus/ρp, pH 10, I = 5 × 10−3 M. () ZrO2, the line denotes the linear regression [η] = 1 + 4.5 ΦVZrO2 (curve 2); () ZrO2 + PSS mixture, the solid line denoted the product of intrinsic viscosities [η] = [η]ZrO2 + [η]PSS = (1 + 4.5 ΦVZrO2 ) + (1 + 50 ΦVPSS ) (curve 1). conia did not increase too significantly the dispersion degree of aggregates. This is evident from the particle size measurements showing that the average size of zirconia particles dispersed in PSS (at pH 7.4) was 0.56 m, which does not differ much from the value observed in PSS free solutions. The limited influence of PSS on the dispersion degree of zirconia also was confirmed by the viscosity measurements whose results are shown in Fig. 8. As can be seen, the dependence of the intrinsic viscosity of zirconia dispersed in PSS solution (variable polymer concentration from 350 ppm to 2000 ppm, pH 10, I = 5 × 10−3 M) on the volume fraction solid can well be fitted by a line with the slope being the product of the viscosity of zirconia dispersed in PSS free solution of the same composition and the viscosity of PSS alone. Hence, our results seem to confirm the effective medium hypothesis22 according to which the relative viscosity of a suspension having the solid concentration ΦV1 + ΦV2 (where ΦV1 is the volume fraction of zirconia and ΦV2 is the volume fraction of PSS) equals to the product of relative viscosities ¯η(ΦV1 )¯η(ΦV2 ). 4. Concluding remarks It has been demonstrated experimentally that the relative viscosity of dilute zirconia suspensions increased more rapidly with the volume fraction that the Einstein formula predicted. This discrepancy could not be explained in terms of the primary electroviscous effect because of small thickness of the electric double-layer. As a plausible explanation the presence of aggregates in the zirconia suspension was given, which were composed of primary particles of the size ca. 200 nm. The hypothesis of the presence of aggregates was also confirmed by the SEM. The viscosity measurements allowed one to determine the averaged solid content in these aggregates, which was found close to 0.45. Analogous measurements of the viscosity of the anionic polyelectrolyte-PSS used to enhance the stability of zirconia suspensions showed that the slope of the intrinsic viscosity vs. volume fraction attained values as high as 50 for I = 5 × 10−3 M. This effect was interpreted in terms of the flexible rod model. According to this model, for higher electrolyte concentration, the PSS molecule assumes the shape of a semi circle or sinusoidal curve rather than a random coil structure as often suggested. It was further confirmed experimentally that adsorption of PSS on zirconia decreased significantly the negative zeta potential but did not influence too significantly the dispersion degree of zirconia particles. Also the viscosity of the zirconia suspension in PSS solutions was found equal to the product of the viscosity of zirconia dispersed in PSS free solution of the same composition and the viscosity of PSS alone. Acknowledgements This work was supported by MNiSW Grant 4T08B 03425. The help of Ms. K. Kusak in performing the experiments is kindly acknowledged. References 1. Liu, D. M., Ceram. Int., 2000, 26, 279. 2. Baklouti, S. M., Romdhane, R. B., Boufi, Pagnoux, S. C., Chartier, T. and Baumard, J. F., J. Eur. Ceram. Sci., 2003, 23, 905. 3. Ewais, E., Zaman, A. A. and Sigmund, W., J. Eur. Ceram. Sci., 2002, 22, 2805. 4. Decher, G., Multilayer Thin Films. Wiley-VCH, 2002. 5. Fengqiu, T., Xiaoxian, H., Yufeng, Z. and Jingkun, G., Ceram. Int., 2000, 26, 93. 6. Johnson, S. B., Franks, G. V., Scales, P. J., Boder, D. V. and Healy, T. W., Int. J. Miner. Process., 2000, 58, 267. 7. Piconi, C. and Maccauro, G., Biomaterials, 1999, 20, 1. 8. Adamczyk, Z., Jachimska, B. and Kolasinska, M., ´ J. Colloid Interface Sci., 2004, 273, 668. 9. Okada, K. and Nagase, Y., J. Chem. Eng. Jpn., 2000, 33, 168. 10. Atkins, A., Physical Chemistry. Oxford University Press, Oxford, 1994, p. C18. 11. Adamczyk, Z., Zembala, M., Warszynski, P. and Jachimska, B., ´ Langmuir, 2004, 20, 10517. 12. Hunter, R., Foundations of Colloid Science. Oxford, 2001. 13. Crucean, E., Rand, B. and Brit, T. J., Ceram. Soc., 1979, 78, 96. 14. Kosmulski, M., Chem. Properties Mater. Surf.: Surf. Sci. Ser., 2001, 102. 15. Masiliyah, J. H., Neale, G., Malysa, K. and van de Ven, T. G. M., Chem. Eng. Sci., 1987, 42, 245. 16. Honig, E. P., Punt, W. F. J. and Offermans, P. H. G., J. Colloid Interface Sci., 1990, 134, 169. 17. Adamczyk, Z., Siwek, B. and Zembala, M., Bull. Pol. Acad. Chem., 2000, 48, 231. 18. Laven, J. and Stein, H. N., J. Colloid Interface Sci., 2001, 238, 8. 19. Brenner, H., Int. J. Multiphase Flow, 1974, 1, 195. 20. Greenwood, R., Luckham, P. F. and Gregory, T., J. Colloid Interface Sci., 1997, 191, 11. 21. Stoll, S. and Chodanowski, P., Macromolecules, 2002, 35, 9556. 22. Pal, R., Rheology of emulsions containing polymeric liquids. In Encyclopedia of Emulsion Technology, Vol. 4, ed. P. Becher. Marcel Dekker, Newyork, Basel, Hong Kong, 1996.