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<0.004 and the ionic depletion method. It was found that irrespective on the initial trength of/=5x10-3Mand 0 15 M are presented in Fig.7. As concentration of PSS in the suspension(varied between 1000 can be seen, the dependence of m] on pv for both ionic strength and 5000 ppm) the amount of PSS adsorbed on particles was can well be fitted by a linear regression. The slope of these lines almost constant and equal 2.5 x 10-3g per one gram of the zir- 1=0.15M. This is again much higher than the Einstein formula conia powder(this corresponds to 5 x 10-4gper square meter of the dry powder). By taking the affective cross-section of the PSs predicts for spherically shaped particles. It seems that a proper molecule as 91x 1l nm(1.06 x 10-16 m2)one can estimate that interpretation of these data can be sought in the highly non- the amount of adsorbed PSS corresponds to the dimensionles spherical shape of PSS molecules in solutions. Again, these data surface coverage of 0.45, which seems a quite reasonable value can be interpreted in terms of the Brenner model. However, in the case of PSS, the rotary Peclet number assumes much smaller Adsorption of PSS on zirconia decreased significantly the cient of PSS. By taking(G)=4 x 10s",L=91 nm(extended This is fully in accordance with the results of Fengqiu et all.s who determined zeta potential of zirconia powder in solutions of 1.30 Darvan C (an anionic polyelectrolyte with carboxylic groups) It was observed that for pH> 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 solu￾tion 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 per￾formed for PSS volume fraction range ΦV < 0.004 and the ionic strength of I = 5 × 10−3 M and 0.15 M are presented in Fig. 7. As can be seen, the dependence of [η] on ΦV for both ionic strength can well be fitted by a linear regression. The slope of these lines d[η]/dΦV was found equal to 50 for I = 5 × 10−3 M and 25 for I = 0.15 M. This is again much higher than the Einstein formula predicts for spherically shaped particles. It seems that a proper interpretation of these data can be sought in the highly non￾spherical shape of PSS molecules in solutions. Again, these data can be interpreted in terms of the Brenner model.19 However, in the case of PSS, the rotary Peclet number assumes much smaller values than for zirconia because of much higher diffusion coeffi- cient of PSS. By taking G = 4 × 103 s−1, L = 91 nm (extended Fig. 7. The dependence of the intrinsic viscosity of PSS [η] = ηs/η on its volume fraction ΦV, pH 6.5–10, () I = 5 × 10−3 M (curve 1) and () I = 0.15 M (curve 2). molecule length) and D = 1.8 × 10−7 cm2/s (for I = 5 × 10−3 M) 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 Brenner19 derived the approximate formula describing the intrinsic viscosity of prolate spheroid polymer solution: [η] = L¯ 2 15 3 ln 2L¯ − 0.5 + 1 ln 2L¯ − 1.5 + 8 5 (10) whereL¯ = 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 pertinent to the extended PSS molecule) [η] = 383, for L¯ = 50 (the molecule bend to the form of a semi-circle) [η] = 177 and for L¯ = 25 (the molecule bend to the form of a circle) [η] = 55. As can be seen, the latter intrinsic viscosity agrees well with the experimental value obtained for the ionic strength of 5 × 10−3. After measuring the viscosity of zirconia and PSS separately, the viscosity of mixtures was studied in order to estimate the improvement in the fluidity upon the addition of PSS. The flu￾idity can be increased by increasing the dispersion degree of the powder promoted by adsorption of PSS. The amount of poly￾electrolyte adsorbed on zirconia was determined by the solution depletion method. It was found that irrespective on the initial concentration of PSS in the suspension (varied between 1000 and 5000 ppm) the amount of PSS adsorbed on particles was almost constant and equal 2.5 × 10−3 g per one gram of the zir￾conia powder (this corresponds to 5 × 10−4 g per square meter of the dry powder). By taking the affective cross-section of the PSS molecule as 91 × 11 nm (1.06 × 10−16 m2) one can estimate that the amount of adsorbed PSS corresponds to the dimensionless surface coverage of 0.45, which seems a quite reasonable value in view of previous estimates.21 Adsorption of PSS on zirconia decreased significantly the zeta potential of particles for the entire range of pH (see Fig. 6). This is fully in accordance with the results of Fengqiu et all.5 who determined zeta potential of zirconia powder in solutions of Darvan C (an anionic polyelectrolyte with carboxylic groups). It was observed that for pH > 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 mecha￾nism 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 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 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-