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Effect of surface charge density on the electrosurface properties of positively charged polystyrene beads
Colloids and Surfaces A: Physicochemical and Engineering Aspects 92 (1994) 121-126
COLLOIDS AND SURFACES
A
Effect of surface charge density on the electrosurface properties of positively charged polystyrene beads A. Fernkndez
Barbero,
R. Martinez
Garcia, M.A. Cabrerizo
Vilchez, R. Hidalgo-Alvarez
*
Biocolloid and Fluid Physics Group, Department of Applied Physics, University of Granada, 18071 Granada, Spain Received 2 December
1993; accepted
9 February
1994
Abstract An investigation of the effect of the surface charge density on the determination of [ potentials of positively charged polystyrene beads is described. The polystyrene beads were prepared by emulsion polymerization using a cationic initiator. The surface charge density depends on the solution pH since the superficial ionic groups (amidine) behave as weak base. The conversion of mobility values into [ potentials at two different surface charge densities was accomplished according to Dukhin, since this theoretical treatment takes anomalous surface conductance into account. Likewise, the computer program of R.W. O’Brien and L.R. White (J. Chem. Sot., Faraday Trans. 2, 77 (1978) 1607) was also used to calculate Keywords: Electrokinetic
[ potentials
from mobility
data.
processes; Polymer colloids
1. Introduction Polymer colloids play an important role in many industrial processes such as the manufacture of synthetic rubber, in surface coatings, in adhesives, as additives in paper, in textiles and in many other products. The rapid increase in the utilization of latices over the last two decades has been due to
a number of factors. Water-based systems avoid many of the environmental problems associated with organic-solvent-based systems; latices can be designed to overcome a wide range of application problems. The spherical shape of many polymer latex particles and their narrow size distribution makes them very suitable for fundamental studies requiring well-defined monodisperse systems. The interpretation of the electrokinetic potential in relation * Corresponding author. 0927-7757/94!$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZ 0927-7757(94)02829-H
to polymer colloids, however, has presented problems for many years. The expected continuous decrease in electrophoretic mobility with increasing electrolyte concentration is observed only at high concentrations. At lower concentrations, the mobility typically increases with concentration [l-18]. A number of possible explanations for the peculiar electrokinetic behavior of latices and for the discrepancy between theory and experiment have been proposed; however, this inconsistency is not yet very well understood. The objective of this work is to study the effect of the surface charge density on the electrokinetic behavior of polymer colloids in aqueous solutions of positively charged polystyrene beads.
2. Materials and methods A positively charged monodisperse latex was prepared by the emulsifier-free emulsion polymer-
122
A. Ferncindez Barber0 et al.lColloids Surfaces A: Physicochem. Eng. Aspects 92 (1994) 121-126
ization of styrene in the presence of azo-N’, N’-dimethyleneisobutyramidine hydrochloride (ADMBA) [ 193. The reaction temperature and the pH were maintained constant at 50°C and 3.0 respectively. The latex was cleaned by centrifugation and then by ion exchange over a mixed bed. The surface charge density (co) was obtained by conductometric and potentiometric titrations (a,, = +(20.0&0.4) uCcm-2 at pH 5, and go= + (8.5 + 0.2) uC cmm2 at pH 9.5). The average particle diameter, obtained by means of electron microscopy, was 265 f 5 nm. Electrophoretic mobilities were obtained with a Zeta-Sizer 11~.
3. Results and discussion
6r
5 I
2/
-3
For a proper understanding of the stability, rheology and many other properties of polymer colloids in liquid dispersions, a quantitative description of the distribution of charges and potentials around the particles is essential. The electrical aspects of the solid-liquid interfaces are particularly relevant because, under conditions that are common in practice, the range of electrical interactions can be substantial. Very often, the microelectrophoretic mobility is a powerful tool for studying the structure of the electric double layer of the polystyrene latex-aqueous solution interfaces. In Fig. 1 we show the electrophoretic mobility (PJ of the positively charged latex particles as a function of the 1: 1 electrolyte concentration (C) at two pH values. At acid pH, the pe-log C curve passes through a maximum, but the maximum disappears at pH 9.5. The conversion of mobility into the [ potential of the latex-aqueous solution interface encounters at least three obstacles: the polarization of the electric double layer in an external field, the possible existence of a boundary layer with reduced hydrodynamic mobility, and the significant roughness of the latex surface [20]. These difficulties can be partly resolved by using the theories developed for non-equilibrium electrosurface phenomena. Overbeek [ 213 and Booth [22] were the
I
Ii -2.5
-2
-1.5
-1
-0.5
0
log [KC11 Fig. 1. Electrophoretic tration at two different
mobility values vs. electrolyte concenpH values: 0, pH 5; q, pH 9.5.
first to incorporate polarization of the electric double layer into the theory. They considered that the transfer and charge redistribution processes involved only the mobile part of the electric double layer. Also, O’Brien and White [23], starting with the same set of equations as Wiersema et al. [24], have more recently published a theoretical approach to electrophoresis which takes into account any combination of ions in solution and the possibility of very high i potentials (up to 250 mV), far enough from the values expected under most experimental conditions. A simplified version and analytical form for this theory accurate to order ~/KU,valid for our purposes for electrokinetic radii ~a> 10, can be expressed as [25]
(1) where m is the dimensionless ion drag coefficient
A. Ferncindez Barber0 et al. JColloids Surfaces A: Physicochem. Eng. Aspects 92 (1994) 121-126
given as m=
~E,EN,~ kT
(2)
3vdl
All the above-cited theoretical approaches to convert mobility into the [ potential assume the absence of ionic conduction inside the shear plane. In an attempt to account for this phenomenon theoretically, Dukhin and Derjaguin [ 201 developed an equation incorporating both the dimensionless [ potential (e
where p is the ratio of the counterion diffusion coefficient near the wall to its bulk value. The calculation of 5 with allowance for electric double layer polarization within the framework of the Dukhin and Derjaguin theory requires a knowledge of the qd potential, which can be found on the basis of co [ZO]:
go
=
( sinh T‘h+ -,2,1 4,) tanh -4
(y)li’
g, = d--h g, =
p
($d/2) - cc& (t/2)1
[sinh ([d/2) - sinh (f/2)]
(4)
In cosh(z/4)
for pH 5 and 9.5 as a function of Ica are shown in Fig. 2. From the plots shown in Fig. 3 for is,,,, P&w and &, (where subscripts Sm, O-W and D denote
0
0 OO
0
q
Ka Fig. 2. tid Potential
values as a function
(q
This equation includes a correction for the curvature of the surface and assumes a diffuse structure of the double layer. It can be used to obtain $d because, as Baran et al. [5] have clearly shown, the assumption of a diffuse structure of the electric double layer in polystyrene beads is quite reasonable for 1: 1 electrolytes. The $d potential values
m)sinh’ (c/4)+ 2g,] + [2( 1+ 3m)sinh(%/2) - 3m[ + 2gJ4 KU+ 8 ( 1 - 3m)sinh’ (t/4) - 24m In cash (t/4) + 4g, where
123
of Ka at two different
pH values: 0, pH 5; 0, pH 9.5
124
A. Ferncindez Barber0 et al./Colloids Surfaces A: Physicochem. Eng. Aspects 92 (1994) 121-126
20
Fig. 3. Electrokinetic potential (Smoluchowski); A, [ potential
40
60
80
100
120
values vs. electrokinetic radius for the (O’Brien-White); 0, [ potential (Dukhin).
40
60
80
cationic
160
180
polystyrene
latex
200
at
pH
5: 0,
[ potential
Smoluchowski equation. These differences are gradually smoothed out as the electric double layer becomes thinner, as would be expected. The larger values of in in comparison with cow are readily explained on the basis that in the first approach, the contribution to polarization from all ions of the diffuse layer is taken into account, whereas
Smoluchowski, O’Brien and White, and Dukhin respectively) as functions of the electrokinetic radius for the highly charged latex particles (pH 5), we see that the [ potential calculated with an allowance for electric double layer polarization, all the way up to real 100, is substantially greater than [ calculated according to the classical
20
140
100
120
140
160
180
200
Ka Fig. 4. Electrokinetic potential 0, Dukhin. O’Brien-White;
values vs. electrokinetic
radius
for the cationic
polystyrene
latex at pH 9.5: 0,
Smoluchowski;
A,
A. Fermindez Barber0 et al./Colloids
Surfaces A: Physicochem.
O’Brien and White [23] account for only the ions of the hydrodynamically mobile part of the electric double layer. This means that the anomalous surface conductance plays a marked role in the electrokinetic behavior of the polystyrene beads, and for this latex its contribution drops off substantially as the electric double layer is compressed, and it becomes negligibly small with k-a2 100; as a consequence, the difference between the values of &,, i ow and in disappears. The [ values obtained at pH 9.5 are very similar (see Fig. 4) independently of the theoretical approach used to convert mobilities into electrokinetic potential. This means that the polarization of the electric double layer is closely related to the surface charge density. An important result is that the factor p is equal to 0.5 at pH 5 (high cr,J and 0.7 at pH 9.5 (low a,), which is a test of the surface charge effect on the ionic diffusivity between the slipping plane and the polymer surface. Finally, it must be noted that the $d potential is always higher than the [ potential, which may be due to the formation of a liquid layer around the latex surface with low hydrodynamic mobility in which the ions retain a high mobility. It is also possible that the relationship $d > [ that we have found is a consequence of the surface roughness of the polymer beads.
4. Conclusions The conversion of mobility data for highly charged polystyrene beads into [ potentials should be carried out by means of a non-equilibrium theory that includes the inherent anomalous surface conductance of the polystyrene beads-electrolyte solution interface. This is partly satisfied by the Dukhin and Derjaguin theory, since it takes into account the anomalous surface conductance associated with the presence of a boundary layer.
List of symbols c k
n
electrolyte concentration Boltzmann constant ion concentration
Na T
Z
Eng. Aspects 92 (1994) 121-126
125
Avogadro constant absolute temperature valency of ions
Greek letters E CO
i rl 1
dielectric permittivity of the continuous phase dielectric permittivity of the vacuum electrokinetic potential viscosity of the continuous phase reciprocal of the double layer thickness limit equivalent conductance electrophoretic mobility surface change density diffuse layer potential
Acknowledgment
This research work was supported by CICYT (Spain), projects MAT 93-0530-CO2-01.
References
Cl1 J.R.
Golf and Ph. Luner, J. Colloid Interface Sci., 99 (1984) 468. 121 W.M. Brouwer and R.L.J. Zsom, Colloids Surfaces, 24 (1987) 195. F.J. de las Nieves, A.J. van der Linde c31 R. Hidalgo-Alvarez, and B.H. Bijsterbosch, Colloid Polym. Sci., 267 (1989) 853. F.J. de las Nieves, A.J. van der Linde c41 R. Hidalgo-Alvarez, and B.H. Bijsterbosch, Colloids Surfaces, 21 (1986) 259. N.M. Soboleva and O.S. c51 A.A. Baran, L.M. Dudkina, Chechnik, Kolloidn. Zh., 43 (1981) 211. Ccl B.R. Midmore and R.J. Hunter, J. Colloid Interface Sci., 122 (1988) 211. c71 J.J. Spitzer, CA. Midgley, H.S.G. Slooten and K.P. Lok, Colloids Surfaces, 39 (1989) 273. Colloids C81 T.J.J. van den Hoven and B.H. Bijsterbosch, Surfaces, 22 (1987) 187. J. Colloid c91 A.G. van der Put and B.H. Bijsterbosch, Interface Sci., 92 (1983) 499. Cl01 A.G. van der Put, Ph.D. Thesis, Agricultural University of Wageningen, 1980. 1111 R. Zimehl and G. Lagaly, Colloids Surfaces, 22 (1987) 225. Cl21 M. Elimelech and Ch.R. O’Melia, Colloids Surfaces, 44 (1990) 165. Kamel, M.S. El-Aasser, F.J. Micale and Cl31 A.A. J.W. Vanderhoff, J. Dispersion Sci. Technol., 2 (1981) 315. Cl41 L.P. Voegtli and CF. Zukoski IV, J. Colloid Interface Sci., 141 (1991) 92.
126
A. Ferncindez Barber0 et al.IColloids Surfaces A: Physicochem. Eng. Aspects 92 (1994) 121-126
[ 151 C.F. Zukoski IV and D.A. Saville, J. Colloid Interface Sci., 114 (1986) 32. [16] C.F. Zukoski IV and D.A. Saville, J. Colloid Interface Sci., 114 (1986) 5. [17] A. Chabalgoity, A. Martin, F. Galisteo and R. HidalgoAlvarez, Prog. Colloid Polym. Sci., 84 (1991) 416. [ 181 L.A. Rosen and D.A. Saville, J. Colloid Interface Sci., 140 (1990) 82. [19] J.W. Goodwin, R.H. Ottewill and R. Pelton, Colloid Polym. Sci., 257 (1979) 61.
[20] S.S. Dukhin and B.V. Derjaguin, Surf Colloid Sci Vol. 7, E. Matijevic (Ed.), Wiley, New York, 1974. [21] J.Th.G. Overbeek, Adv. Colloid Sci., 3 (1950) 97. [22] F. Booth, Proc. R. Sot. London, Ser. A, 203 (1950) 514. [23] R.W. O’Brien and L.R. White, J. Chem. Sot., Faraday Trans. 2, 77 (1978) 1607. [24] P.H. Wiersema, A.L. Loeb, J.Th.G. Overbeek, J. Colloid Interface Sci., 22 (1966) 78. [25] R.J. Hunter, Zeta Potential in Colloid Science, Academic Press, New York, 1981.
COLLOIDS AND SURFACES
A
Effect of surface charge density on the electrosurface properties of positively charged polystyrene beads A. Fernkndez
Barbero,
R. Martinez
Garcia, M.A. Cabrerizo
Vilchez, R. Hidalgo-Alvarez
*
Biocolloid and Fluid Physics Group, Department of Applied Physics, University of Granada, 18071 Granada, Spain Received 2 December
1993; accepted
9 February
1994
Abstract An investigation of the effect of the surface charge density on the determination of [ potentials of positively charged polystyrene beads is described. The polystyrene beads were prepared by emulsion polymerization using a cationic initiator. The surface charge density depends on the solution pH since the superficial ionic groups (amidine) behave as weak base. The conversion of mobility values into [ potentials at two different surface charge densities was accomplished according to Dukhin, since this theoretical treatment takes anomalous surface conductance into account. Likewise, the computer program of R.W. O’Brien and L.R. White (J. Chem. Sot., Faraday Trans. 2, 77 (1978) 1607) was also used to calculate Keywords: Electrokinetic
[ potentials
from mobility
data.
processes; Polymer colloids
1. Introduction Polymer colloids play an important role in many industrial processes such as the manufacture of synthetic rubber, in surface coatings, in adhesives, as additives in paper, in textiles and in many other products. The rapid increase in the utilization of latices over the last two decades has been due to
a number of factors. Water-based systems avoid many of the environmental problems associated with organic-solvent-based systems; latices can be designed to overcome a wide range of application problems. The spherical shape of many polymer latex particles and their narrow size distribution makes them very suitable for fundamental studies requiring well-defined monodisperse systems. The interpretation of the electrokinetic potential in relation * Corresponding author. 0927-7757/94!$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZ 0927-7757(94)02829-H
to polymer colloids, however, has presented problems for many years. The expected continuous decrease in electrophoretic mobility with increasing electrolyte concentration is observed only at high concentrations. At lower concentrations, the mobility typically increases with concentration [l-18]. A number of possible explanations for the peculiar electrokinetic behavior of latices and for the discrepancy between theory and experiment have been proposed; however, this inconsistency is not yet very well understood. The objective of this work is to study the effect of the surface charge density on the electrokinetic behavior of polymer colloids in aqueous solutions of positively charged polystyrene beads.
2. Materials and methods A positively charged monodisperse latex was prepared by the emulsifier-free emulsion polymer-
122
A. Ferncindez Barber0 et al.lColloids Surfaces A: Physicochem. Eng. Aspects 92 (1994) 121-126
ization of styrene in the presence of azo-N’, N’-dimethyleneisobutyramidine hydrochloride (ADMBA) [ 193. The reaction temperature and the pH were maintained constant at 50°C and 3.0 respectively. The latex was cleaned by centrifugation and then by ion exchange over a mixed bed. The surface charge density (co) was obtained by conductometric and potentiometric titrations (a,, = +(20.0&0.4) uCcm-2 at pH 5, and go= + (8.5 + 0.2) uC cmm2 at pH 9.5). The average particle diameter, obtained by means of electron microscopy, was 265 f 5 nm. Electrophoretic mobilities were obtained with a Zeta-Sizer 11~.
3. Results and discussion
6r
5 I
2/
-3
For a proper understanding of the stability, rheology and many other properties of polymer colloids in liquid dispersions, a quantitative description of the distribution of charges and potentials around the particles is essential. The electrical aspects of the solid-liquid interfaces are particularly relevant because, under conditions that are common in practice, the range of electrical interactions can be substantial. Very often, the microelectrophoretic mobility is a powerful tool for studying the structure of the electric double layer of the polystyrene latex-aqueous solution interfaces. In Fig. 1 we show the electrophoretic mobility (PJ of the positively charged latex particles as a function of the 1: 1 electrolyte concentration (C) at two pH values. At acid pH, the pe-log C curve passes through a maximum, but the maximum disappears at pH 9.5. The conversion of mobility into the [ potential of the latex-aqueous solution interface encounters at least three obstacles: the polarization of the electric double layer in an external field, the possible existence of a boundary layer with reduced hydrodynamic mobility, and the significant roughness of the latex surface [20]. These difficulties can be partly resolved by using the theories developed for non-equilibrium electrosurface phenomena. Overbeek [ 213 and Booth [22] were the
I
Ii -2.5
-2
-1.5
-1
-0.5
0
log [KC11 Fig. 1. Electrophoretic tration at two different
mobility values vs. electrolyte concenpH values: 0, pH 5; q, pH 9.5.
first to incorporate polarization of the electric double layer into the theory. They considered that the transfer and charge redistribution processes involved only the mobile part of the electric double layer. Also, O’Brien and White [23], starting with the same set of equations as Wiersema et al. [24], have more recently published a theoretical approach to electrophoresis which takes into account any combination of ions in solution and the possibility of very high i potentials (up to 250 mV), far enough from the values expected under most experimental conditions. A simplified version and analytical form for this theory accurate to order ~/KU,valid for our purposes for electrokinetic radii ~a> 10, can be expressed as [25]
(1) where m is the dimensionless ion drag coefficient
A. Ferncindez Barber0 et al. JColloids Surfaces A: Physicochem. Eng. Aspects 92 (1994) 121-126
given as m=
~E,EN,~ kT
(2)
3vdl
All the above-cited theoretical approaches to convert mobility into the [ potential assume the absence of ionic conduction inside the shear plane. In an attempt to account for this phenomenon theoretically, Dukhin and Derjaguin [ 201 developed an equation incorporating both the dimensionless [ potential (e
where p is the ratio of the counterion diffusion coefficient near the wall to its bulk value. The calculation of 5 with allowance for electric double layer polarization within the framework of the Dukhin and Derjaguin theory requires a knowledge of the qd potential, which can be found on the basis of co [ZO]:
go
=
( sinh T‘h+ -,2,1 4,) tanh -4
(y)li’
g, = d--h g, =
p
($d/2) - cc& (t/2)1
[sinh ([d/2) - sinh (f/2)]
(4)
In cosh(z/4)
for pH 5 and 9.5 as a function of Ica are shown in Fig. 2. From the plots shown in Fig. 3 for is,,,, P&w and &, (where subscripts Sm, O-W and D denote
0
0 OO
0
q
Ka Fig. 2. tid Potential
values as a function
(q
This equation includes a correction for the curvature of the surface and assumes a diffuse structure of the double layer. It can be used to obtain $d because, as Baran et al. [5] have clearly shown, the assumption of a diffuse structure of the electric double layer in polystyrene beads is quite reasonable for 1: 1 electrolytes. The $d potential values
m)sinh’ (c/4)+ 2g,] + [2( 1+ 3m)sinh(%/2) - 3m[ + 2gJ4 KU+ 8 ( 1 - 3m)sinh’ (t/4) - 24m In cash (t/4) + 4g, where
123
of Ka at two different
pH values: 0, pH 5; 0, pH 9.5
124
A. Ferncindez Barber0 et al./Colloids Surfaces A: Physicochem. Eng. Aspects 92 (1994) 121-126
20
Fig. 3. Electrokinetic potential (Smoluchowski); A, [ potential
40
60
80
100
120
values vs. electrokinetic radius for the (O’Brien-White); 0, [ potential (Dukhin).
40
60
80
cationic
160
180
polystyrene
latex
200
at
pH
5: 0,
[ potential
Smoluchowski equation. These differences are gradually smoothed out as the electric double layer becomes thinner, as would be expected. The larger values of in in comparison with cow are readily explained on the basis that in the first approach, the contribution to polarization from all ions of the diffuse layer is taken into account, whereas
Smoluchowski, O’Brien and White, and Dukhin respectively) as functions of the electrokinetic radius for the highly charged latex particles (pH 5), we see that the [ potential calculated with an allowance for electric double layer polarization, all the way up to real 100, is substantially greater than [ calculated according to the classical
20
140
100
120
140
160
180
200
Ka Fig. 4. Electrokinetic potential 0, Dukhin. O’Brien-White;
values vs. electrokinetic
radius
for the cationic
polystyrene
latex at pH 9.5: 0,
Smoluchowski;
A,
A. Fermindez Barber0 et al./Colloids
Surfaces A: Physicochem.
O’Brien and White [23] account for only the ions of the hydrodynamically mobile part of the electric double layer. This means that the anomalous surface conductance plays a marked role in the electrokinetic behavior of the polystyrene beads, and for this latex its contribution drops off substantially as the electric double layer is compressed, and it becomes negligibly small with k-a2 100; as a consequence, the difference between the values of &,, i ow and in disappears. The [ values obtained at pH 9.5 are very similar (see Fig. 4) independently of the theoretical approach used to convert mobilities into electrokinetic potential. This means that the polarization of the electric double layer is closely related to the surface charge density. An important result is that the factor p is equal to 0.5 at pH 5 (high cr,J and 0.7 at pH 9.5 (low a,), which is a test of the surface charge effect on the ionic diffusivity between the slipping plane and the polymer surface. Finally, it must be noted that the $d potential is always higher than the [ potential, which may be due to the formation of a liquid layer around the latex surface with low hydrodynamic mobility in which the ions retain a high mobility. It is also possible that the relationship $d > [ that we have found is a consequence of the surface roughness of the polymer beads.
4. Conclusions The conversion of mobility data for highly charged polystyrene beads into [ potentials should be carried out by means of a non-equilibrium theory that includes the inherent anomalous surface conductance of the polystyrene beads-electrolyte solution interface. This is partly satisfied by the Dukhin and Derjaguin theory, since it takes into account the anomalous surface conductance associated with the presence of a boundary layer.
List of symbols c k
n
electrolyte concentration Boltzmann constant ion concentration
Na T
Z
Eng. Aspects 92 (1994) 121-126
125
Avogadro constant absolute temperature valency of ions
Greek letters E CO
i rl 1
dielectric permittivity of the continuous phase dielectric permittivity of the vacuum electrokinetic potential viscosity of the continuous phase reciprocal of the double layer thickness limit equivalent conductance electrophoretic mobility surface change density diffuse layer potential
Acknowledgment
This research work was supported by CICYT (Spain), projects MAT 93-0530-CO2-01.
References
Cl1 J.R.
Golf and Ph. Luner, J. Colloid Interface Sci., 99 (1984) 468. 121 W.M. Brouwer and R.L.J. Zsom, Colloids Surfaces, 24 (1987) 195. F.J. de las Nieves, A.J. van der Linde c31 R. Hidalgo-Alvarez, and B.H. Bijsterbosch, Colloid Polym. Sci., 267 (1989) 853. F.J. de las Nieves, A.J. van der Linde c41 R. Hidalgo-Alvarez, and B.H. Bijsterbosch, Colloids Surfaces, 21 (1986) 259. N.M. Soboleva and O.S. c51 A.A. Baran, L.M. Dudkina, Chechnik, Kolloidn. Zh., 43 (1981) 211. Ccl B.R. Midmore and R.J. Hunter, J. Colloid Interface Sci., 122 (1988) 211. c71 J.J. Spitzer, CA. Midgley, H.S.G. Slooten and K.P. Lok, Colloids Surfaces, 39 (1989) 273. Colloids C81 T.J.J. van den Hoven and B.H. Bijsterbosch, Surfaces, 22 (1987) 187. J. Colloid c91 A.G. van der Put and B.H. Bijsterbosch, Interface Sci., 92 (1983) 499. Cl01 A.G. van der Put, Ph.D. Thesis, Agricultural University of Wageningen, 1980. 1111 R. Zimehl and G. Lagaly, Colloids Surfaces, 22 (1987) 225. Cl21 M. Elimelech and Ch.R. O’Melia, Colloids Surfaces, 44 (1990) 165. Kamel, M.S. El-Aasser, F.J. Micale and Cl31 A.A. J.W. Vanderhoff, J. Dispersion Sci. Technol., 2 (1981) 315. Cl41 L.P. Voegtli and CF. Zukoski IV, J. Colloid Interface Sci., 141 (1991) 92.
126
A. Ferncindez Barber0 et al.IColloids Surfaces A: Physicochem. Eng. Aspects 92 (1994) 121-126
[ 151 C.F. Zukoski IV and D.A. Saville, J. Colloid Interface Sci., 114 (1986) 32. [16] C.F. Zukoski IV and D.A. Saville, J. Colloid Interface Sci., 114 (1986) 5. [17] A. Chabalgoity, A. Martin, F. Galisteo and R. HidalgoAlvarez, Prog. Colloid Polym. Sci., 84 (1991) 416. [ 181 L.A. Rosen and D.A. Saville, J. Colloid Interface Sci., 140 (1990) 82. [19] J.W. Goodwin, R.H. Ottewill and R. Pelton, Colloid Polym. Sci., 257 (1979) 61.
[20] S.S. Dukhin and B.V. Derjaguin, Surf Colloid Sci Vol. 7, E. Matijevic (Ed.), Wiley, New York, 1974. [21] J.Th.G. Overbeek, Adv. Colloid Sci., 3 (1950) 97. [22] F. Booth, Proc. R. Sot. London, Ser. A, 203 (1950) 514. [23] R.W. O’Brien and L.R. White, J. Chem. Sot., Faraday Trans. 2, 77 (1978) 1607. [24] P.H. Wiersema, A.L. Loeb, J.Th.G. Overbeek, J. Colloid Interface Sci., 22 (1966) 78. [25] R.J. Hunter, Zeta Potential in Colloid Science, Academic Press, New York, 1981.