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Effect of polyethyleneimine on the properties of concentrated suspensions of titanium dioxide microbeads
CHINA PARTICUOLOGY Vol. 2, No. 4, 182-184, 2004
EFFECT OF POLYETHYLENEIMINE ON THE PROPERTIES OF CONCENTRATED SUSPENSIONS OF TITANIUM DIOXIDE MICROBEADS Guanli Xu*, Lina Xu, Shunlong Pan and Guangzhi Song Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100101, China *Author to whom correspondence should be addressed. E-mail: [email protected]
Abstract The effect of polyethyleneimine (PEI) concentration on the properties of titanium dioxide (TiO2) suspensions is studied with or without the addition of an electrolyte (barium acetate). Measurements of the apparent viscosity and the stability of TiO2 suspensions showed that PEI is an effective dispersant for TiO2 particles in suspension in the absence of an electrolyte, not only reducing the viscosity of the suspension but also increasing its stability. In the presence of an electrolyte, however, small quantities of polyethyleneimine could neither disperse the TiO2 particles nor decrease the viscosity of the TiO2 suspensions; only PEI concentrations beyond saturation adsorption could perceptively improve the stability of TiO2 suspensions. Keywords
polyethyleneimine, titanium dioxide, viscosity, stability
1. Introduction Glass microspheres, especially microbeads with high refractive index, have been widely used in many applications, such as retroreflective sheeting for safety purposes, paint coatings for improved visual appearance, richness or depth of color, and aesthetic effect (Kuney & Clark, 1990). Several manufacturing techniques (Bica, 2000; Beck & O’Brien, 1968) have been developed for producing glass microspheres over the past decades. Recently, our team has applied for a patent on the synthesis of microbeads with high refractive index (Song et al., 1999), using titanium dioxide with a refractive index of 2.55 (589.3 nm, 25 oC). A three-step procedure was used in the preparation of the microbeads. First, a highly stabilized and dispersed titanium dioxide suspension was prepared by dispersing titanium dioxide powders in an electrolyte solution composed of zinc acetate, barium acetate, and other inorganic salts. Second, the homogeneous suspension was spray-dried to obtain a precursor of the objective powder. Then, the precursor was processed in a high-temperature flame for conversion into transparent glass microbeads. Finally, all the organic substances were burned completely out from the powder, to leave only the metal oxide. In this procedure, the preparation of the suspension with a high degree of homogeneity and stability was the key step. In the preparation of glass microbeads, much more electrolyte was added in the suspension than typical for a colloid, in order to avoid electrostatic repulsion between particles. In this paper, polyethyleneimine (PEI) was selected as a polymer dispersant, and its effect on the properties of TiO2 suspensions was studied with or without the addition of an electrolyte.
2. Experimental The titanium dioxide used was the rutile-type Tipaque R-930 supplied by Ishihara Industry Co., Tokyo. Its shape
as observed under an electron microscope was nearly spherical. Its mean volumetric diameter is 0.29 μm, and its 2 -1 BET specific surface area is 34.2 m .g . PEI solution (30% by weight, molecular weight 5.0×104) was obtained from Wuhan Qianglong New Chemical Materials Co., Ltd. At acidic pH, the PEI molecule is positively charged by the following reaction: +
CH2 CH2 NH
H 3O n
+
CH2 CH2 NH 2
n
+ H 2O .
(1)
At pH 6.0, about 60% of the PEI imino function group has completed the above protonizing reaction (Ringenbach et al., 2001; Hostetler & Swanson, 1974). The chemicals used in this study were all of analytical grade. Deionized water was used throughout this study. A certain amount TiO2 powders was ultrasonically dispersed into the polymer solutions with various concentrations of PEI. Then barium acetate was added to the suspension at 10 wt.% of the overall suspension. PEI concentration was expressed as mg/g TiO2. The ultrasonic irradiation apparatus was Model KQ250DE of Kunshan Ultrasonic Co. Ltd. The samples were conditioned on a meo chanical shaker for 24 h at 25 C before measurement. pH value of the dispersed suspension was measured and readjusted to 6.0 when necessary. Apparent viscosity was measured by Model NDJ-1 rotational viscometer of Shanghai Balance Co. Ltd. with four rotating speed, 6, 12, 30 and 60 rpm. The stability of titanium dioxide suspension was estimated approximately through sedimentation analysis in a glass cylinder with a height-to-diameter ratio of 8:1. The 20 wt.% TiO2 suspension was transferred to the glass cylinder for settling, to measure the top clear volume. The smaller the settling rate, the higher the dispersion stability of the suspension. Adsorption isotherm was measured by suspending 3.0 wt.% of TiO2 powder in polymer solutions of various con-
183
Xu, Xu, Pan & Song: Effect of Polyethyleneimine on the Properties of TiO2 Suspensions
o centrations at 25 C, and after 24 h, the TiO2 powder and the supernatant were separated in an ultracentrifuge (12000 rpm, 30 min). A UV-Vis spectrometer (JASCO Corp., UV-530) was used to measure the concentration of PEI in the supernatant liquor by reference to a calibration curve constructed at a wavelength of 210 nm. The adsorption isotherm was calculated from the difference in concentration of PEI before and after adsorption.
50
Apparent viscosity / mPa s
.
3. Results and Discussion
6 rpm 12 rpm 30 rpm 60 rpm
40 35 30 25 20 15 10 5 0
0
Adsorption of PEI on TiO2 powder
Amount of adsorption / mg/gTiO2
Fig. 1 shows the adsorption isotherm of PEI on the TiO2 powder, indicating a steep increase of adsorption at low PEI concentration, followed by a slow increase as adsorption approaches a maximum. At pH 6.0, the TiO2 powder surface is negatively charged (Xu et al., 2003), while the PEI molecule is positively charged due to protonization of the imino group. The electrostatic interaction between the negatively charged TiO2 powder and the cationic PEI molecules results in the initial steep increase of adsorption. Hydrogen bonding (N … H−O) occurs between the C−N bond in PEI and Ti−O bond at the powder surface, which is responsible for the slow increase in adsorption as it approaches the saturation value of about 30 mg/g TiO2. 35 30 25 20 15
40
80
120
160
200
240
280
PEI concentration / mg/g TiO2
Fig. 2
3.3
Variation of suspension viscosity with PEI concentration. The viscosities at zero concentration of PEI are 1225, 715.5, 340, 192.5 mPa·s with shearing rate of 6, 12, 30, 60 rpm respectively.
Effect of PEI concentration on viscosity of suspension with high eletrolyte
In order to study the effect of electrolyte on the apparent viscosity of the suspension, a certain amount of Ba(CH3COO)2 was added to the 20 wt.% suspensions with various concentrations of PEI. Previous test confirmed that PEI could be dissolved in this suspension without any flocculation. Fig. 3 shows the apparent viscosity of the suspension as a function of PEI concentration after the addition of an electrolyte, indicating that the electrolyte increases apparent viscosity apparently because the electrolyte can decrease the free water in suspension through the hydration of inorganic ions, thus leading to a thickening effect. Therefore PEI is not an effective dispersant for concentrated TiO2 suspensions in the presence of an eletrolyte.
10 300
5
6 rpm 12 rpm 30 rpm 60 rpm
. 270
Apparent viscosity / mPa s
3.1
45
0 -2
0
2
4
6
8
10 12 14 16 18 20 22 -1
PEI concentration / mg.mL
Fig. 1
Adsorption isotherm of PEI on TiO2 powder in aqueous media.
3.2
Effect of PEI concentration on viscosity of suspension
240 210 180 150 120 90 60 30 0
Fig. 2 shows the change of apparent viscosity for a 20 wt.% suspension with PEI concentrations at four different shear rates, indicating a minimum at about 25 mg/g TiO2. According to the viscosity curve we believe that some fragments of the polymer chain are anchored on the TiO2 powder surface, and surrounded by the so-called tails or loops of the solution, forming an adsorbed polymer layer on the powder surface (Li et al., 1994), which provides a steric barrier against the flocculation of TiO2 particles in concentrated suspensions. Therefore, in the absence of an electrolyte, PEI is itself an effective dispersant for concentrated TiO2 suspensions through steric stabilization.
0
50
100
150
200
250
300
PEI concentration / mg/g TiO2
Fig. 3
Variation of suspensions viscosity with PEI concentration in the presence of an eletrolyte.
In the absence of an electrolyte, at pH 6.0 the PEI molecule is ionized and shows positive charge. There exists electrostatic repulsive interactions between consecutive segments of PEI molecular chain, so the tails or loops on TiO2 powder surface are swollen and can provide enough thickness of polymer layer on powder surface to stabilize the suspension by steric stabilization mechanism. With the addition of an electrolyte, the charges on the
CHINA PARTICUOLOGY Vol. 2, No. 4, 2004 PEI molecular chain are screened from one another by the opposite ions in suspension changing the configuration of PEI molecule from flexible tails or loops to compact polymer coils (Bijsterbosch et al., 1999). In effect, the addition of electrolyte compresses the hydrodynamic volume of the polymer molecule (Dong et al., 2002a) and reduces the thickness of the polymer layer on powder surface, making the adsorbed PEI molecules incapable of improving the dispersion stability of the suspensions. So in the presence of an electrolyte, the PEI can not play the role of a dispersant to reduce the viscosity of a suspension, in a way markedly different from that without an electrolyte.
3.4
Stability of suspension with electrolyte concentration
0.55 0.50 0.45 . 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
Settling rate / mL min
-1
Fig.4 shows that the addition of an electrolyte increases the settling rate of TiO2 particles. The minimum of settling rate in Fig. 4 corresponds to the minimum of viscosity in Fig. 2., further confirming that PEI can improve the stability of the suspension. The slow decrease in settling rate beyond PEI concentration of 50 mg/g TiO2 is due to the increase of viscosity of the suspension. Though PEI concentration does not show obvious effect on the viscosity of the suspension in the presence of an electrolyte, the stability of the suspension obviously increases with the increase of PEI concentration. The slight increase of viscosity will obstruct the Brownian motion of TiO2 particles arising from random thermal forces, and reduce the collision among TiO2 particles. Moreover, the free compact polymer coils behave like a barrier to prevent mutual collision of TiO2 particles. So the addition of PEI can improve the stability of suspensions in the presence of an electrolyte. Generally, the presence of an electrolyte can deteriorate the stability of the suspension. Only with excess amount of PEI, the stability of suspension with an electrolyte approaches that of suspensions without electrolyte
No electrolyte
With electrolyte
0
30
60
90 120 150 180 210 240 270 300
PEI concentration / mg/g TiO2
Fig. 4
Variation of settling rate of TiO2 powder with PEI concentration, with and without electrolyte.
184
4. Conclusions At pH 6.0, PEI molecules are adsorbed on the TiO2 particle surface through electrostatic attraction and hydrogen bonding. The amount of saturation adsorption is about 30 mg/g TiO2 in the absence of any electrolyte. In this case the PEI is an effective dispersant to reduce the viscosity of a TiO2 suspension at its optimum concentration. Further addition of electrolyte counteracts the dispersive role of PEI, and there is no obvious minimum in the viscosity curve. But the excess nonadsorbed PEI molecules do not lead to steep increase of viscosity to improve the stability of the suspensions investigated. So, stable TiO2 suspension can be obtained by adding excessive amount of PEI in the presence of high concentration of electrolyte.
References Beck, W. R. & O’Brien, D. L. (1968). Glass bubbles prepared by reheating solid glass particles. U.S. Pat. 3365315. Bica, I. (2000). Formation of glass microspheres with rotating electrical arc. Mater. Sci. Eng., B, 77, 210-212. Bijsterbosch, H. D., Cohen Stuart, M. A. & Fleer, G. J. (1999). Effect of block and graft copolymers on the stability of colloidal silica. J. Colloid Interface Sci., 210(1), 37-42. Dong, Z. X., Wu, Z. L., Lin, M. Q. & Li, M. Y. (2002a). The study of the conformation and size of the linked polymer coils. Acta Polym. Sinica, 4, 493-497. (in Chinese) Dong, Z. X., Wu, Z. L., Lin, M. Q. & Li, M. Y. (2002b). The influence of salt concentration on the dimension of linked polymer coils in solution. Oilfield Chem., 19(1), 80-84. (in Chinese) Hostetler, R. E. & Swanson, J. W. (1974). Diffusion into and adsorption of polyethyleneimine on porous silica gel. J. Polym. Sci., 12(1), 12-29. Kuney, Jr. & Clark, G. (1990). Microsphere-based retroreflective articles with enhanced retroreflective brightness. U.S. Pat. 4957335. Li, J. T., Caldwell, K. D. & Rapoport, N. (1994). Surface properties of pluronic-coated polymeric colloids. Langmuir, 10(12) 44754482. Ringenbach, E., Chauveteau, G. & Pefferkorn, E. (2001). Adsorption of polyelectrolytes on soluble oxides induced by polyion complexation with dissolution species. J. Colloid Interface Sci., 61(1), 223-231. Song, G. Z., Hu, J. H. & Zhang, J. J. (1999). High-refractive index transparent ceramic micro-bead and its manufacture method and use. CN 1211558A. (in Chinese) Xu, G. L, Zhang, J. J., Li, G. Z. & Song, G. Z. (2003). Effect of complexation on the zeta potential of titanium dioxide dispersions. J. Disperison Sci. Technol., 24(4), 527-535. Manuscript received April 15, 2004 and accepted July 7, 2004.
EFFECT OF POLYETHYLENEIMINE ON THE PROPERTIES OF CONCENTRATED SUSPENSIONS OF TITANIUM DIOXIDE MICROBEADS Guanli Xu*, Lina Xu, Shunlong Pan and Guangzhi Song Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100101, China *Author to whom correspondence should be addressed. E-mail: [email protected]
Abstract The effect of polyethyleneimine (PEI) concentration on the properties of titanium dioxide (TiO2) suspensions is studied with or without the addition of an electrolyte (barium acetate). Measurements of the apparent viscosity and the stability of TiO2 suspensions showed that PEI is an effective dispersant for TiO2 particles in suspension in the absence of an electrolyte, not only reducing the viscosity of the suspension but also increasing its stability. In the presence of an electrolyte, however, small quantities of polyethyleneimine could neither disperse the TiO2 particles nor decrease the viscosity of the TiO2 suspensions; only PEI concentrations beyond saturation adsorption could perceptively improve the stability of TiO2 suspensions. Keywords
polyethyleneimine, titanium dioxide, viscosity, stability
1. Introduction Glass microspheres, especially microbeads with high refractive index, have been widely used in many applications, such as retroreflective sheeting for safety purposes, paint coatings for improved visual appearance, richness or depth of color, and aesthetic effect (Kuney & Clark, 1990). Several manufacturing techniques (Bica, 2000; Beck & O’Brien, 1968) have been developed for producing glass microspheres over the past decades. Recently, our team has applied for a patent on the synthesis of microbeads with high refractive index (Song et al., 1999), using titanium dioxide with a refractive index of 2.55 (589.3 nm, 25 oC). A three-step procedure was used in the preparation of the microbeads. First, a highly stabilized and dispersed titanium dioxide suspension was prepared by dispersing titanium dioxide powders in an electrolyte solution composed of zinc acetate, barium acetate, and other inorganic salts. Second, the homogeneous suspension was spray-dried to obtain a precursor of the objective powder. Then, the precursor was processed in a high-temperature flame for conversion into transparent glass microbeads. Finally, all the organic substances were burned completely out from the powder, to leave only the metal oxide. In this procedure, the preparation of the suspension with a high degree of homogeneity and stability was the key step. In the preparation of glass microbeads, much more electrolyte was added in the suspension than typical for a colloid, in order to avoid electrostatic repulsion between particles. In this paper, polyethyleneimine (PEI) was selected as a polymer dispersant, and its effect on the properties of TiO2 suspensions was studied with or without the addition of an electrolyte.
2. Experimental The titanium dioxide used was the rutile-type Tipaque R-930 supplied by Ishihara Industry Co., Tokyo. Its shape
as observed under an electron microscope was nearly spherical. Its mean volumetric diameter is 0.29 μm, and its 2 -1 BET specific surface area is 34.2 m .g . PEI solution (30% by weight, molecular weight 5.0×104) was obtained from Wuhan Qianglong New Chemical Materials Co., Ltd. At acidic pH, the PEI molecule is positively charged by the following reaction: +
CH2 CH2 NH
H 3O n
+
CH2 CH2 NH 2
n
+ H 2O .
(1)
At pH 6.0, about 60% of the PEI imino function group has completed the above protonizing reaction (Ringenbach et al., 2001; Hostetler & Swanson, 1974). The chemicals used in this study were all of analytical grade. Deionized water was used throughout this study. A certain amount TiO2 powders was ultrasonically dispersed into the polymer solutions with various concentrations of PEI. Then barium acetate was added to the suspension at 10 wt.% of the overall suspension. PEI concentration was expressed as mg/g TiO2. The ultrasonic irradiation apparatus was Model KQ250DE of Kunshan Ultrasonic Co. Ltd. The samples were conditioned on a meo chanical shaker for 24 h at 25 C before measurement. pH value of the dispersed suspension was measured and readjusted to 6.0 when necessary. Apparent viscosity was measured by Model NDJ-1 rotational viscometer of Shanghai Balance Co. Ltd. with four rotating speed, 6, 12, 30 and 60 rpm. The stability of titanium dioxide suspension was estimated approximately through sedimentation analysis in a glass cylinder with a height-to-diameter ratio of 8:1. The 20 wt.% TiO2 suspension was transferred to the glass cylinder for settling, to measure the top clear volume. The smaller the settling rate, the higher the dispersion stability of the suspension. Adsorption isotherm was measured by suspending 3.0 wt.% of TiO2 powder in polymer solutions of various con-
183
Xu, Xu, Pan & Song: Effect of Polyethyleneimine on the Properties of TiO2 Suspensions
o centrations at 25 C, and after 24 h, the TiO2 powder and the supernatant were separated in an ultracentrifuge (12000 rpm, 30 min). A UV-Vis spectrometer (JASCO Corp., UV-530) was used to measure the concentration of PEI in the supernatant liquor by reference to a calibration curve constructed at a wavelength of 210 nm. The adsorption isotherm was calculated from the difference in concentration of PEI before and after adsorption.
50
Apparent viscosity / mPa s
.
3. Results and Discussion
6 rpm 12 rpm 30 rpm 60 rpm
40 35 30 25 20 15 10 5 0
0
Adsorption of PEI on TiO2 powder
Amount of adsorption / mg/gTiO2
Fig. 1 shows the adsorption isotherm of PEI on the TiO2 powder, indicating a steep increase of adsorption at low PEI concentration, followed by a slow increase as adsorption approaches a maximum. At pH 6.0, the TiO2 powder surface is negatively charged (Xu et al., 2003), while the PEI molecule is positively charged due to protonization of the imino group. The electrostatic interaction between the negatively charged TiO2 powder and the cationic PEI molecules results in the initial steep increase of adsorption. Hydrogen bonding (N … H−O) occurs between the C−N bond in PEI and Ti−O bond at the powder surface, which is responsible for the slow increase in adsorption as it approaches the saturation value of about 30 mg/g TiO2. 35 30 25 20 15
40
80
120
160
200
240
280
PEI concentration / mg/g TiO2
Fig. 2
3.3
Variation of suspension viscosity with PEI concentration. The viscosities at zero concentration of PEI are 1225, 715.5, 340, 192.5 mPa·s with shearing rate of 6, 12, 30, 60 rpm respectively.
Effect of PEI concentration on viscosity of suspension with high eletrolyte
In order to study the effect of electrolyte on the apparent viscosity of the suspension, a certain amount of Ba(CH3COO)2 was added to the 20 wt.% suspensions with various concentrations of PEI. Previous test confirmed that PEI could be dissolved in this suspension without any flocculation. Fig. 3 shows the apparent viscosity of the suspension as a function of PEI concentration after the addition of an electrolyte, indicating that the electrolyte increases apparent viscosity apparently because the electrolyte can decrease the free water in suspension through the hydration of inorganic ions, thus leading to a thickening effect. Therefore PEI is not an effective dispersant for concentrated TiO2 suspensions in the presence of an eletrolyte.
10 300
5
6 rpm 12 rpm 30 rpm 60 rpm
. 270
Apparent viscosity / mPa s
3.1
45
0 -2
0
2
4
6
8
10 12 14 16 18 20 22 -1
PEI concentration / mg.mL
Fig. 1
Adsorption isotherm of PEI on TiO2 powder in aqueous media.
3.2
Effect of PEI concentration on viscosity of suspension
240 210 180 150 120 90 60 30 0
Fig. 2 shows the change of apparent viscosity for a 20 wt.% suspension with PEI concentrations at four different shear rates, indicating a minimum at about 25 mg/g TiO2. According to the viscosity curve we believe that some fragments of the polymer chain are anchored on the TiO2 powder surface, and surrounded by the so-called tails or loops of the solution, forming an adsorbed polymer layer on the powder surface (Li et al., 1994), which provides a steric barrier against the flocculation of TiO2 particles in concentrated suspensions. Therefore, in the absence of an electrolyte, PEI is itself an effective dispersant for concentrated TiO2 suspensions through steric stabilization.
0
50
100
150
200
250
300
PEI concentration / mg/g TiO2
Fig. 3
Variation of suspensions viscosity with PEI concentration in the presence of an eletrolyte.
In the absence of an electrolyte, at pH 6.0 the PEI molecule is ionized and shows positive charge. There exists electrostatic repulsive interactions between consecutive segments of PEI molecular chain, so the tails or loops on TiO2 powder surface are swollen and can provide enough thickness of polymer layer on powder surface to stabilize the suspension by steric stabilization mechanism. With the addition of an electrolyte, the charges on the
CHINA PARTICUOLOGY Vol. 2, No. 4, 2004 PEI molecular chain are screened from one another by the opposite ions in suspension changing the configuration of PEI molecule from flexible tails or loops to compact polymer coils (Bijsterbosch et al., 1999). In effect, the addition of electrolyte compresses the hydrodynamic volume of the polymer molecule (Dong et al., 2002a) and reduces the thickness of the polymer layer on powder surface, making the adsorbed PEI molecules incapable of improving the dispersion stability of the suspensions. So in the presence of an electrolyte, the PEI can not play the role of a dispersant to reduce the viscosity of a suspension, in a way markedly different from that without an electrolyte.
3.4
Stability of suspension with electrolyte concentration
0.55 0.50 0.45 . 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
Settling rate / mL min
-1
Fig.4 shows that the addition of an electrolyte increases the settling rate of TiO2 particles. The minimum of settling rate in Fig. 4 corresponds to the minimum of viscosity in Fig. 2., further confirming that PEI can improve the stability of the suspension. The slow decrease in settling rate beyond PEI concentration of 50 mg/g TiO2 is due to the increase of viscosity of the suspension. Though PEI concentration does not show obvious effect on the viscosity of the suspension in the presence of an electrolyte, the stability of the suspension obviously increases with the increase of PEI concentration. The slight increase of viscosity will obstruct the Brownian motion of TiO2 particles arising from random thermal forces, and reduce the collision among TiO2 particles. Moreover, the free compact polymer coils behave like a barrier to prevent mutual collision of TiO2 particles. So the addition of PEI can improve the stability of suspensions in the presence of an electrolyte. Generally, the presence of an electrolyte can deteriorate the stability of the suspension. Only with excess amount of PEI, the stability of suspension with an electrolyte approaches that of suspensions without electrolyte
No electrolyte
With electrolyte
0
30
60
90 120 150 180 210 240 270 300
PEI concentration / mg/g TiO2
Fig. 4
Variation of settling rate of TiO2 powder with PEI concentration, with and without electrolyte.
184
4. Conclusions At pH 6.0, PEI molecules are adsorbed on the TiO2 particle surface through electrostatic attraction and hydrogen bonding. The amount of saturation adsorption is about 30 mg/g TiO2 in the absence of any electrolyte. In this case the PEI is an effective dispersant to reduce the viscosity of a TiO2 suspension at its optimum concentration. Further addition of electrolyte counteracts the dispersive role of PEI, and there is no obvious minimum in the viscosity curve. But the excess nonadsorbed PEI molecules do not lead to steep increase of viscosity to improve the stability of the suspensions investigated. So, stable TiO2 suspension can be obtained by adding excessive amount of PEI in the presence of high concentration of electrolyte.
References Beck, W. R. & O’Brien, D. L. (1968). Glass bubbles prepared by reheating solid glass particles. U.S. Pat. 3365315. Bica, I. (2000). Formation of glass microspheres with rotating electrical arc. Mater. Sci. Eng., B, 77, 210-212. Bijsterbosch, H. D., Cohen Stuart, M. A. & Fleer, G. J. (1999). Effect of block and graft copolymers on the stability of colloidal silica. J. Colloid Interface Sci., 210(1), 37-42. Dong, Z. X., Wu, Z. L., Lin, M. Q. & Li, M. Y. (2002a). The study of the conformation and size of the linked polymer coils. Acta Polym. Sinica, 4, 493-497. (in Chinese) Dong, Z. X., Wu, Z. L., Lin, M. Q. & Li, M. Y. (2002b). The influence of salt concentration on the dimension of linked polymer coils in solution. Oilfield Chem., 19(1), 80-84. (in Chinese) Hostetler, R. E. & Swanson, J. W. (1974). Diffusion into and adsorption of polyethyleneimine on porous silica gel. J. Polym. Sci., 12(1), 12-29. Kuney, Jr. & Clark, G. (1990). Microsphere-based retroreflective articles with enhanced retroreflective brightness. U.S. Pat. 4957335. Li, J. T., Caldwell, K. D. & Rapoport, N. (1994). Surface properties of pluronic-coated polymeric colloids. Langmuir, 10(12) 44754482. Ringenbach, E., Chauveteau, G. & Pefferkorn, E. (2001). Adsorption of polyelectrolytes on soluble oxides induced by polyion complexation with dissolution species. J. Colloid Interface Sci., 61(1), 223-231. Song, G. Z., Hu, J. H. & Zhang, J. J. (1999). High-refractive index transparent ceramic micro-bead and its manufacture method and use. CN 1211558A. (in Chinese) Xu, G. L, Zhang, J. J., Li, G. Z. & Song, G. Z. (2003). Effect of complexation on the zeta potential of titanium dioxide dispersions. J. Disperison Sci. Technol., 24(4), 527-535. Manuscript received April 15, 2004 and accepted July 7, 2004.