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Universality in electric light scattering properties of oxide aggregates in aqueous dispersions
Colloids and Surfaces A: Physicochemical and Engineering Aspects 104 ( 1995}259 264
ELSEVIER
COLLOIDS AND SURFACES
A
Universality in electric light scattering properties of oxide aggregates in aqueous dispersions I. Petkanchin*, K. Starchev, A. Dimitrova Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Solia. BMgaria Received 28 February 1995; accepted 19 April 1995
Abstract
The calculated saturated electric light scattering (ELSt effect (u.~) as a function of the product qRg (q = k sin O. Rg is the radius of gyration) is compared with experimentally measured values of c%. Aqueous suspensions from aggregates of SiO2 (Aerosil OX50), A1203 and TiO2 particles have been investigated. The aggregates in these systems are obtained by flame hydrolysis and could be described as mass fractal objects, having a characteristic fractal dimensionality (D}. D is determined by the use of the correlation between the time of centrifugation (t) and the final slope (&) of the ELS decay curve. The SiO2 and A1203 monodisperse fractions were obtained by centrifugation, while the TiO2 suspension was sonicated. The monodispersity of the fractions obtained was followed through the difference between the initial and tinal slopes of the ELS decay curves. As-received suspensions have characteristic mean hydrodynamic radii, determined from the relaxation time of the ELS decay curve. It was found that the experimental data for :~,: v e r s u s kRg for the different suspensions lie on a single curve; this is striking evidence of the universality of the regime of colloid aggregation.
k=2n/). 2 is the incident light wavelength, O is the angle of observation, and
Keywords: Aqueous dispersions; Electric light scattering; Oxide aggregates
1. Introduction
Oxides are widely used as model particles in studies of colloid chemistry. Besides, oxides are important for m a n y technological processes and are used as pigments, catalysts, etc. Oxides obtained by flame hydrolysis present aggregates built from nearly monodisperse spherical particles and can be successfully described by fractal geometry. The process of flame hydrolysis can be regarded as reaction-limited cluster aggregation (RLCA). Spherical oxide particles obtained by acid hydrolysis can be used for studying the kinetics of fast or slow coagulation (RLCA). The electric light scattering (ELS) m e t h o d was * Corresponding author. 0927-7757.'95/$09.50 ~:) 1995 Elsevier Science B.V. All rights reserved SSD1 0927-7757(95)03213-4
applied to elucidate the fractal dimensions of oxide aggregates and also to follow the kinetics of aggregation. Recently it has been found that different regimes of aggregation are independent of the chemical nature of the particles [ 1,2]. From this point of view it is interesting to follow the electrooptical behaviour of oxide aggregates with different chemical natures, and to c o m p a r e the electrooptical effect at full particle orientation with computer-simulated results, as well as to follow the dependence of the electric polarizability on fractal dimensions at different electrolyte concentrations.
2. Materials and methods
SiO 2, A1203, TiO 2 and ~-Fe203 oxides were studied. The oxides were obtained by flame hydrol-
260
~( Petkanchin et al./Colloids SurJaces A: Physicochem. Eng. Aspects 104 (1995) 259-264
ysis and in aqueous dispersions they present fractal aggregates built from spherical particles. The physical characteristics of each of the oxides are as follows: Aerosil OX50, particle diameter 40 nm, density 2.2 g cm 3 and surface density (50 _+ 15) m 2 g 1 [3]; aluminium oxide C, particle diameter 20nm, density 2 . 9 g c m -3 and surface density (100 + 15) m 2 g 1 I-4]; TiO2 P25, particle diameter 21 nm, density 3.8gcm -3 and surface density (50_+ 15)m 2 8 - 1 [4]. The ~-FezO3 primary particles were obtained by acid hydrolysis and the radius of nearly spherical particles is about 86 nm [5]. The kinetics of aggregation was studied in presence of MgSO4. The electro-optical effect is defined as [6]
~(t)
IE - I o = - Io
4re ~ i(O',~o)f(O',~o,t)dqb -
~
~ i(O',q0 d(/)
(1)
where IE and I o are the intensities of the scattered light in the presence of an applied electric field of strength E, and without a field, respectively, f(~',~0,t) is the orientational distribution function of the aggregates defined through the angles O' and q~; O' is the angle between the axis of the aggregate and the direction of the applied electric field; q~is the azimuthal angle, t is time; and i(O',q~) is the intensity of the light scattered by a single aggregate. ~o...d(b denotes integration on a sphere of radius unity. The steady state electro-optical effect depends on the electric moments responsible for the particle orientation, and on their optical behaviour. At a low degree of orientation U/kbT<<1 (u and kbT are the energy of orientation and the thermal energy, respectively) when the orientation is due only to an induced dipole moment (7 is the electric polarizability), 7st is given by [7] 7 ~st = 3 ~
E2ff22
(2)
where 02 is the optical function depending on the optical properties of the particles and their dimensions. The steady state electro-optical effect, ~st, increases linearly with E 2 independently of the optical properties (£22 terms). At high electric fields (U/kbT> >1), cqt is independent of the electric
polarizability and c~ reflects only the optical properties of the aggregates. So from Eq. (2) 7 can be calculated if ~c~2 is determined at the full particle orientation. The decay of the electro-optical effect at low field strengths is described by [6,8] ~(t) = ~st e x p ( - 6Drt),
(3)
where D r is the rotational diffusion coefficient. The latter is connected with an effective hydrodynamic radius Rh of the particle through [9]
3 kb T Dr - 4 6~r/R 3
(4)
For polydisperse systems at low degrees of orientation the decay of the electro-optical effect is polyexponential, and the initial slope (Si) of the decay curve gives an average rotational diffusion coefficient. The final slope (Sl) of the polyexponential decay refers to the largest aggregates: S l = - 6Dr,b
(5)
The ratio between SI and Si can be used as a criterion for the polydispersity [7] p = ~ / S l / S i.
(6)
Considering the investigated samples as fractal objects of mass M, the intensity of the scattered light is given by [ 10]
I(q) = G(MZ)F(q)Sm(qRg),
(7)
where q = k sin O, k = 2nil (L is the wavelength of the incident light and O is the angle of observation), the function G(M 2) describes the isotropic Rayleigh scattering, F(q) is the form factor, and Srn(qRg) is the static structure factor of clusters of mass M and radius of gyration Rg determined by the position of the particles in the cluster and the cluster orientation. Sm(qRg) reveals the structural anisotropy of the clusters. F(q)= 1 because the primary particles are much smaller than the wavelength and the Rayleigh scattering is isotropic. At high electric fields the aggregates are fully oriented, i.e. the aggregate axes are parallel to the field direction. In this case the electro-optic effect
t Petkanchin et aL/Colloids Surfaces A: Physicockem. Eng. A,wects 104 (1995) ++ ~ 9 +~6 4
is given by
polarization, ~ [11].
261
was calculated for different
Rg
2r~
4~ j" i+((p)d~0 o
~
-
1
j" i(@)dq~
(8)
"
3. E x p e r i m e n t a l results and discussion
q~
The decay of the electro-optical effect at high electric fields, when the aggregates are fully oriented, is given by [7] 3(1 . . . .
~=
--
5 2~"22
exp(-
6D~t).
(9)
Taking into account Eq. (7), F(q)= 1 and that Rayleigh scattering is isotropic, we can state that ~ is connected with the last term in [7]. The optical function (22 in Eq. (9) reflects the anisotropy of the structure factor Sm(qRg). The elaboration of an electro-optical theory for fractal objects needs the dependence of the scattered light intensity for different aggregate orientations. The possibility of obtaining an analytical form of this dependence is very slim because the aggregates are nonregular objects. Thus it is better to look for quantities that do not depend on the optics of the system, and to compare them with the results from computer simulations. For the orientation distribution functionf(O',~p,t) it is important that the angle 6)' is fixed in the same manner for all aggregates. The fractal aggregates do not have an axis of revolution like compact Euclidean rotational bodies. For convenience, the axis could be chosen to pass through the centers of mass and to be parallel to the maximal polarizability of aggregates. The following two models could be used [11]. In model I the axis passes through the centers of mass and is parallel to the axis between the two farthest end particles. This model corresponds to an orientation mechanism due to the movement of ions in the whole ionic atmosphere. In this case the orientation does not depend on the internal aggregate structure. In model II the axis passing through the centers of mass is so directed that the sum of the particles' projection radius vectors on the field direction is a maximum. This model corresponds to Mandel's model for the polarization of polyelectrolytes [12]. Using Eq. (8) and the two models for cluster
Fig. l(a) gives the calculated values of ~ for different qRg. The calculations were made on the basis of computer-simulated aggregates using the two models for aggregate orientation (model I, curve 1, and model I1, curve 2) [11].
120 -N
/
1O0
,.<
\
/
\
/ ~ / ' / '
80
I
60
l,, //
40
\ / '/
i
\,
/~
\'.
i,'
0
,'~,
6'
20 ~
\
i i i i i
4
+1 6
3
4
]llll~mIJl~_mllltt
2 la)
kRg 70 60 5O ' iO Q •
"~ 40
• )
•
30 20 10 I
(b)
2
kR h
Fig. 1. Dependence of saturated electro-optical effect ~ on ) model I; curve 2 ! ' t model I. (b) Experimental values of z~ for SiO2 <''1. AI20+ (O) and TiO 2 I~,).
kRh. (a) Curve 1 (
262
I. Petkanchin et al./Colloids Surfaces A: Physieochem. Eng. Aspects 104 (1995) 2 5 9 ~ 6 4
The experimental values of c% for A1203, SiO2 and TiO2 were obtained with each oxide at an angle of observation of 90 ° by varying the wavelength 2 and particle hydrodynamic radius Rh. The fractions with different Rh values were obtained through centrifugation. The monodispersity was controlled through the p-criterion (Eq. 6), and for AI203 its value was between 0.6 and 0.75. c~ was measured at five different wavelengths (405, 450, 510, 546 and 620 nm) for each monodisperse fraction. The relaxation times of disorientation were determined using pulse accumulation. Five fractions of SiO2 were obtained at centrifugation times of 3-15 min, and those of A 1 2 0 3 at 10 50 min. The obtained experimental results (~o~/kRh) are shown in Fig. 1(b). The trends of the theoretical and experimental curves of ~oo/kRg (kRh) are similar, and cover the same range of kRg/kRh. A slight deviation in the positions of the maxima should be noticed. This discrepancy gives some idea of the adequacy of the theoretical description of aggregate dimensions with the radius of gyration, and how well it corresponds to the experimentally obtained hydrodynamic radius. The ratio (Rh/Rg) reflects the influence of rotational diffusion effects in the static light scattering. The relation here is Rh/Rg=0.7. Such a comparison can be found in Ref. [ 1], where it was shown that fl = Rh/Rg=0.93, obtained from static and dynamic light scattering experiments in the DLCA regime [1]. In our case the nonmonodispersity of the fractions influences the value of tiThe considerably higher and sharper maxima of the theoretically simulated curves 1 and 2 (c~/kRg) in Fig. 1(a) and the noncoincidence of the experimental values of e~ may be due to the fact that the investigated systems are not sufficiently monodisperse. Besides, the orientation mechanism of real fractal objects is not clear. The results of the polarization Model II seem to be closer to the experimental data. Some results on the aggregation of ~-Fe203 in the presence of MgSO4 are given in Fig. 2. The saturated electro-optical effect eo~ was measured at different times of aggregation. Simultaneously, the average hydrodynamic radius was calculated from the decay of the ELS effect. Curve 1 refers to
30
2O
C
10
0
I IIllllJll
0
Llllllll]lll
1
IlllllJ
2
3
kRg Fig. 2. Experimental values of c~ (~-Fe203 aggregates) on kR h for fast coagulation curve 1 02) (in the presence of 2 x 10 4 M I ~ MgSO4) and slow coagulation curve 2 ( V ) (10 4 M 1 MgSO 4) pH 5.17.
1 x 1 0 - 4 M 1-1 MgSO4, slow coagulation; and curve 2 refers to 2 x 1 0 - 4 M 1-] MgSO4, rapid coagulation. The same trends in the dependence of c~o~ on kRh as in Fig. 1(b) can be seen. At present these results should be regarded as preliminary. Some additional systematic experiments on the coagulation kinetics of ~-Fe203 particles in the presence of a bivalent electrolyte are needed. Fig. 3 shows (on a bilogarithmic scale) the dependence of the final slope of the electro-optical decay
-
0.1
/
i
w
II i
1
10
100
t, rain Fig. 3. Dependence of the final electro-optical decay slope S~ on the time of centrifugation for AI203.
L Petkanchin et al./Colloids SwJdces A." Physicochem. Eng. Aspects 104 (1995) 259 264
for A l 2 0 3 o n the time (t) of centrifugation. It is shown that from the electro-optical and centrifugation data the following correlation exists [13]
--
263
5 ¸ ~m
S I ~ t 3 . ( D - 11,
(10) •
where D is the fractal dimension. The essence of the method relies on the speed of centrifugation, which determines the hydrodynamic radius of the aggregates. This radius is also determined from the electro-optical decay. For A1203 we obtained the value of the fractal dimension D = 2 . 6 +_0.1. This allows us to conclude that the centrifugation causes some restructuring of the aggregates. The fractal dimension of SiO 2 is 2.5 +0.1 [7]. For TiO2, because of the instability of the suspension after centrifugation and the extremely high electric field needed to reach the full degree of orientation, another procedure was applied to obtain stable and monodisperse solutions; sonication for two different times: 60 and 90 s. For their fractal dimension a value of D < 2 was obtained by turbidity measnrements (results not shown) by determining the slope of the log ~ versus log L dependence, where r is turbidity of the solution and 2 is the wavelength of the light source [ 14]. The discrepancies between the D values of TiO 2, AI203 and SiO 2 could be due to the different methods of preparation of the monodisperse fractions. For SiO2 and A1203 the procedure of centrifugation was used to obtain different fractions, whereas the TiO 2 dispersions were only sonicated, and the aggregates obtained have a looser structure and D < 2. Obviously through centrifugation more compact aggregates are obtained, and D > 2. In Fig. 4 the dependence of the electric polarizability on Rh is given for A1203 in water, 1 x 10 s M NaCI and 5 x 10 5 M NaCI solutions. As is well known, an increase in the ionic strength causes a decrease in the electric polarizability of compact particles [6]. The studied fractal aggregates from A1203 do not show such a dependence and the electric polarizability scales linearly with Rh. These two facts probably reflect the difference of the polarization mechanisms of fractal aggregates compared with compact particles. For compact particles the dependence of 7 on Rh is power one with coefficients between 2 and 3. The features of the ramilied fractal structure, i.e. the presence of"dead'"
4
>- 3 ¸
.:
120
140
160
180 R h.
200
220
240
Dill
Fig. 4. D e p e n d e n c e of the electric p o l a r i z a b i l i t y of A I 2 0 ~ a g g r e g a t e s o n Rh: w i t h o u t electrolyte ( O ) . with 1 × 10 5 M N a C l ( 1 ) . a n d with 5 x 10 s M N a C I ( ' : I.
ends, possibly determine predominantly the polarization of the counterions situated in these "'local" ionic atmospheres and not in the "'outer" ionic atmosphere. Different types of curve fitting procedures were applied to the experimental results and the linear regression seems to be closer in comparison to the power one because the lowest value of the standard deviation of the residuals is 0.3 compared with 0.42 for the power one. This result coincides with those obtained for SiO, aggregates, where i' scales linearly with Rh [7]. We can conclude that the electric polarizability of fractal objects increases linearly with their hydrodynamic radii.
4. Conclusions
The experimental values of the saturated electrooptical effect c~ o n k R h for oxides with different chemical natures obtained by flame hydrolysis have the same form as those calculated theoretically, assuming two models for particle polarization. The difference in height of the maxima of the theoretical and experimental curves (:~./kRh) may be due to some non-monodispersity of the samples studied. The slight deviations in the positions of the maxima give some idea about the correspon-
264
I. Petkanchin et al./Colloids Surfaces A: Physicochem. Eng. Aspects 104 (1995) 259-264
dence of Rg to the experimentally measured Rh. The fractal dimension of AlzO 3 aggregates is D = 2.6 and their electric polarizability scales linearly with Rh. This result is in accordance with the results obtained for fractal SiO 2 aggregates.
Acknowledgement This work has been financially supported by the European Union, CIPA, Project CT-92 3013, "Physical properties and interparticle interaction of aqueous oxide colloids".
References 1-1] M.J. Lin, H.M. Lindsay, D.A. Weitz, R. Klein, R.C. Ball and P. Meakin, J. Phys.: Condens. Matter, 2 (1990) 3093.
I-2] M.J. Lin, H.M. Lindsay, D.A. Weitz, R.C. Ball, R. Klein and P. Meakin, Nature, 339 (1989) 360. [3] Degussa, Tech. Bull. Pig., No. 6 (1986). F4] Degussa, Tech. Bull. Pig., No. 64 (1988). I-5] K. Starchev, V. Peikov, S. Stoylov, I.B. Petkanchin, K.D. Streb and H. Sonntag, Colloid Surfaces A: Physiochem. Eng. Aspects, 76 (1993) 95; K.D. Streb, PhD Thesis, Berlin, 1985. [6] S.S. Stoylov, V.N. Shilov, S.S. Dukhin, S. Sokerov and I.B. Petkanchin, Electro-optics of Colloids, Naukova Dumka, Kiev, 1977 (in Russian); S. Stoylov, Colloid Electrooptics, Academic Press, London 1991. [7] K. Starchev, I. Petkanchin and S. Stoylov, Langmuir, 10 (1994) 1456. [-8] H. Benoit, Ann. Phys. (Paris), 6 (1951) 561. I-9] H.M. Lindsay, R. Klein, D.A. Weitz, M. Lin and P. Meakin, Phys. Rev. A, 38 (1988) 2614. El0] K. Starchev, PhD Thesis, Sofia, 1994. R. Klein, D.A. Weitz, M. Lin, H.M. Lindsay, R.C. Ball and P. Meakin, Prog. Colloid Polym. Sci., 81 (1990) 161. [11] K. Starchev, V. Pejkov and I. Gerroff, J. Phys. Chem., 99 (1995) 356. 1-12] M. Mandel, Molec. Phys., 4 (1961) 489. 1-13] K. Starchev and S. Stoylov, Phys. Rev. B, 47 (1993) 11725. [14] D. Horne, Faraday Disc. Chem. Soc., 83 (1987) 259.
ELSEVIER
COLLOIDS AND SURFACES
A
Universality in electric light scattering properties of oxide aggregates in aqueous dispersions I. Petkanchin*, K. Starchev, A. Dimitrova Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Solia. BMgaria Received 28 February 1995; accepted 19 April 1995
Abstract
The calculated saturated electric light scattering (ELSt effect (u.~) as a function of the product qRg (q = k sin O. Rg is the radius of gyration) is compared with experimentally measured values of c%. Aqueous suspensions from aggregates of SiO2 (Aerosil OX50), A1203 and TiO2 particles have been investigated. The aggregates in these systems are obtained by flame hydrolysis and could be described as mass fractal objects, having a characteristic fractal dimensionality (D}. D is determined by the use of the correlation between the time of centrifugation (t) and the final slope (&) of the ELS decay curve. The SiO2 and A1203 monodisperse fractions were obtained by centrifugation, while the TiO2 suspension was sonicated. The monodispersity of the fractions obtained was followed through the difference between the initial and tinal slopes of the ELS decay curves. As-received suspensions have characteristic mean hydrodynamic radii, determined from the relaxation time of the ELS decay curve. It was found that the experimental data for :~,: v e r s u s kRg for the different suspensions lie on a single curve; this is striking evidence of the universality of the regime of colloid aggregation.
k=2n/). 2 is the incident light wavelength, O is the angle of observation, and
Keywords: Aqueous dispersions; Electric light scattering; Oxide aggregates
1. Introduction
Oxides are widely used as model particles in studies of colloid chemistry. Besides, oxides are important for m a n y technological processes and are used as pigments, catalysts, etc. Oxides obtained by flame hydrolysis present aggregates built from nearly monodisperse spherical particles and can be successfully described by fractal geometry. The process of flame hydrolysis can be regarded as reaction-limited cluster aggregation (RLCA). Spherical oxide particles obtained by acid hydrolysis can be used for studying the kinetics of fast or slow coagulation (RLCA). The electric light scattering (ELS) m e t h o d was * Corresponding author. 0927-7757.'95/$09.50 ~:) 1995 Elsevier Science B.V. All rights reserved SSD1 0927-7757(95)03213-4
applied to elucidate the fractal dimensions of oxide aggregates and also to follow the kinetics of aggregation. Recently it has been found that different regimes of aggregation are independent of the chemical nature of the particles [ 1,2]. From this point of view it is interesting to follow the electrooptical behaviour of oxide aggregates with different chemical natures, and to c o m p a r e the electrooptical effect at full particle orientation with computer-simulated results, as well as to follow the dependence of the electric polarizability on fractal dimensions at different electrolyte concentrations.
2. Materials and methods
SiO 2, A1203, TiO 2 and ~-Fe203 oxides were studied. The oxides were obtained by flame hydrol-
260
~( Petkanchin et al./Colloids SurJaces A: Physicochem. Eng. Aspects 104 (1995) 259-264
ysis and in aqueous dispersions they present fractal aggregates built from spherical particles. The physical characteristics of each of the oxides are as follows: Aerosil OX50, particle diameter 40 nm, density 2.2 g cm 3 and surface density (50 _+ 15) m 2 g 1 [3]; aluminium oxide C, particle diameter 20nm, density 2 . 9 g c m -3 and surface density (100 + 15) m 2 g 1 I-4]; TiO2 P25, particle diameter 21 nm, density 3.8gcm -3 and surface density (50_+ 15)m 2 8 - 1 [4]. The ~-FezO3 primary particles were obtained by acid hydrolysis and the radius of nearly spherical particles is about 86 nm [5]. The kinetics of aggregation was studied in presence of MgSO4. The electro-optical effect is defined as [6]
~(t)
IE - I o = - Io
4re ~ i(O',~o)f(O',~o,t)dqb -
~
~ i(O',q0 d(/)
(1)
where IE and I o are the intensities of the scattered light in the presence of an applied electric field of strength E, and without a field, respectively, f(~',~0,t) is the orientational distribution function of the aggregates defined through the angles O' and q~; O' is the angle between the axis of the aggregate and the direction of the applied electric field; q~is the azimuthal angle, t is time; and i(O',q~) is the intensity of the light scattered by a single aggregate. ~o...d(b denotes integration on a sphere of radius unity. The steady state electro-optical effect depends on the electric moments responsible for the particle orientation, and on their optical behaviour. At a low degree of orientation U/kbT<<1 (u and kbT are the energy of orientation and the thermal energy, respectively) when the orientation is due only to an induced dipole moment (7 is the electric polarizability), 7st is given by [7] 7 ~st = 3 ~
E2ff22
(2)
where 02 is the optical function depending on the optical properties of the particles and their dimensions. The steady state electro-optical effect, ~st, increases linearly with E 2 independently of the optical properties (£22 terms). At high electric fields (U/kbT> >1), cqt is independent of the electric
polarizability and c~ reflects only the optical properties of the aggregates. So from Eq. (2) 7 can be calculated if ~c~2 is determined at the full particle orientation. The decay of the electro-optical effect at low field strengths is described by [6,8] ~(t) = ~st e x p ( - 6Drt),
(3)
where D r is the rotational diffusion coefficient. The latter is connected with an effective hydrodynamic radius Rh of the particle through [9]
3 kb T Dr - 4 6~r/R 3
(4)
For polydisperse systems at low degrees of orientation the decay of the electro-optical effect is polyexponential, and the initial slope (Si) of the decay curve gives an average rotational diffusion coefficient. The final slope (Sl) of the polyexponential decay refers to the largest aggregates: S l = - 6Dr,b
(5)
The ratio between SI and Si can be used as a criterion for the polydispersity [7] p = ~ / S l / S i.
(6)
Considering the investigated samples as fractal objects of mass M, the intensity of the scattered light is given by [ 10]
I(q) = G(MZ)F(q)Sm(qRg),
(7)
where q = k sin O, k = 2nil (L is the wavelength of the incident light and O is the angle of observation), the function G(M 2) describes the isotropic Rayleigh scattering, F(q) is the form factor, and Srn(qRg) is the static structure factor of clusters of mass M and radius of gyration Rg determined by the position of the particles in the cluster and the cluster orientation. Sm(qRg) reveals the structural anisotropy of the clusters. F(q)= 1 because the primary particles are much smaller than the wavelength and the Rayleigh scattering is isotropic. At high electric fields the aggregates are fully oriented, i.e. the aggregate axes are parallel to the field direction. In this case the electro-optic effect
t Petkanchin et aL/Colloids Surfaces A: Physicockem. Eng. A,wects 104 (1995) ++ ~ 9 +~6 4
is given by
polarization, ~ [11].
261
was calculated for different
Rg
2r~
4~ j" i+((p)d~0 o
~
-
1
j" i(@)dq~
(8)
"
3. E x p e r i m e n t a l results and discussion
q~
The decay of the electro-optical effect at high electric fields, when the aggregates are fully oriented, is given by [7] 3(1 . . . .
~=
--
5 2~"22
exp(-
6D~t).
(9)
Taking into account Eq. (7), F(q)= 1 and that Rayleigh scattering is isotropic, we can state that ~ is connected with the last term in [7]. The optical function (22 in Eq. (9) reflects the anisotropy of the structure factor Sm(qRg). The elaboration of an electro-optical theory for fractal objects needs the dependence of the scattered light intensity for different aggregate orientations. The possibility of obtaining an analytical form of this dependence is very slim because the aggregates are nonregular objects. Thus it is better to look for quantities that do not depend on the optics of the system, and to compare them with the results from computer simulations. For the orientation distribution functionf(O',~p,t) it is important that the angle 6)' is fixed in the same manner for all aggregates. The fractal aggregates do not have an axis of revolution like compact Euclidean rotational bodies. For convenience, the axis could be chosen to pass through the centers of mass and to be parallel to the maximal polarizability of aggregates. The following two models could be used [11]. In model I the axis passes through the centers of mass and is parallel to the axis between the two farthest end particles. This model corresponds to an orientation mechanism due to the movement of ions in the whole ionic atmosphere. In this case the orientation does not depend on the internal aggregate structure. In model II the axis passing through the centers of mass is so directed that the sum of the particles' projection radius vectors on the field direction is a maximum. This model corresponds to Mandel's model for the polarization of polyelectrolytes [12]. Using Eq. (8) and the two models for cluster
Fig. l(a) gives the calculated values of ~ for different qRg. The calculations were made on the basis of computer-simulated aggregates using the two models for aggregate orientation (model I, curve 1, and model I1, curve 2) [11].
120 -N
/
1O0
,.<
\
/
\
/ ~ / ' / '
80
I
60
l,, //
40
\ / '/
i
\,
/~
\'.
i,'
0
,'~,
6'
20 ~
\
i i i i i
4
+1 6
3
4
]llll~mIJl~_mllltt
2 la)
kRg 70 60 5O ' iO Q •
"~ 40
• )
•
30 20 10 I
(b)
2
kR h
Fig. 1. Dependence of saturated electro-optical effect ~ on ) model I; curve 2 ! ' t model I. (b) Experimental values of z~ for SiO2 <''1. AI20+ (O) and TiO 2 I~,).
kRh. (a) Curve 1 (
262
I. Petkanchin et al./Colloids Surfaces A: Physieochem. Eng. Aspects 104 (1995) 2 5 9 ~ 6 4
The experimental values of c% for A1203, SiO2 and TiO2 were obtained with each oxide at an angle of observation of 90 ° by varying the wavelength 2 and particle hydrodynamic radius Rh. The fractions with different Rh values were obtained through centrifugation. The monodispersity was controlled through the p-criterion (Eq. 6), and for AI203 its value was between 0.6 and 0.75. c~ was measured at five different wavelengths (405, 450, 510, 546 and 620 nm) for each monodisperse fraction. The relaxation times of disorientation were determined using pulse accumulation. Five fractions of SiO2 were obtained at centrifugation times of 3-15 min, and those of A 1 2 0 3 at 10 50 min. The obtained experimental results (~o~/kRh) are shown in Fig. 1(b). The trends of the theoretical and experimental curves of ~oo/kRg (kRh) are similar, and cover the same range of kRg/kRh. A slight deviation in the positions of the maxima should be noticed. This discrepancy gives some idea of the adequacy of the theoretical description of aggregate dimensions with the radius of gyration, and how well it corresponds to the experimentally obtained hydrodynamic radius. The ratio (Rh/Rg) reflects the influence of rotational diffusion effects in the static light scattering. The relation here is Rh/Rg=0.7. Such a comparison can be found in Ref. [ 1], where it was shown that fl = Rh/Rg=0.93, obtained from static and dynamic light scattering experiments in the DLCA regime [1]. In our case the nonmonodispersity of the fractions influences the value of tiThe considerably higher and sharper maxima of the theoretically simulated curves 1 and 2 (c~/kRg) in Fig. 1(a) and the noncoincidence of the experimental values of e~ may be due to the fact that the investigated systems are not sufficiently monodisperse. Besides, the orientation mechanism of real fractal objects is not clear. The results of the polarization Model II seem to be closer to the experimental data. Some results on the aggregation of ~-Fe203 in the presence of MgSO4 are given in Fig. 2. The saturated electro-optical effect eo~ was measured at different times of aggregation. Simultaneously, the average hydrodynamic radius was calculated from the decay of the ELS effect. Curve 1 refers to
30
2O
C
10
0
I IIllllJll
0
Llllllll]lll
1
IlllllJ
2
3
kRg Fig. 2. Experimental values of c~ (~-Fe203 aggregates) on kR h for fast coagulation curve 1 02) (in the presence of 2 x 10 4 M I ~ MgSO4) and slow coagulation curve 2 ( V ) (10 4 M 1 MgSO 4) pH 5.17.
1 x 1 0 - 4 M 1-1 MgSO4, slow coagulation; and curve 2 refers to 2 x 1 0 - 4 M 1-] MgSO4, rapid coagulation. The same trends in the dependence of c~o~ on kRh as in Fig. 1(b) can be seen. At present these results should be regarded as preliminary. Some additional systematic experiments on the coagulation kinetics of ~-Fe203 particles in the presence of a bivalent electrolyte are needed. Fig. 3 shows (on a bilogarithmic scale) the dependence of the final slope of the electro-optical decay
-
0.1
/
i
w
II i
1
10
100
t, rain Fig. 3. Dependence of the final electro-optical decay slope S~ on the time of centrifugation for AI203.
L Petkanchin et al./Colloids SwJdces A." Physicochem. Eng. Aspects 104 (1995) 259 264
for A l 2 0 3 o n the time (t) of centrifugation. It is shown that from the electro-optical and centrifugation data the following correlation exists [13]
--
263
5 ¸ ~m
S I ~ t 3 . ( D - 11,
(10) •
where D is the fractal dimension. The essence of the method relies on the speed of centrifugation, which determines the hydrodynamic radius of the aggregates. This radius is also determined from the electro-optical decay. For A1203 we obtained the value of the fractal dimension D = 2 . 6 +_0.1. This allows us to conclude that the centrifugation causes some restructuring of the aggregates. The fractal dimension of SiO 2 is 2.5 +0.1 [7]. For TiO2, because of the instability of the suspension after centrifugation and the extremely high electric field needed to reach the full degree of orientation, another procedure was applied to obtain stable and monodisperse solutions; sonication for two different times: 60 and 90 s. For their fractal dimension a value of D < 2 was obtained by turbidity measnrements (results not shown) by determining the slope of the log ~ versus log L dependence, where r is turbidity of the solution and 2 is the wavelength of the light source [ 14]. The discrepancies between the D values of TiO 2, AI203 and SiO 2 could be due to the different methods of preparation of the monodisperse fractions. For SiO2 and A1203 the procedure of centrifugation was used to obtain different fractions, whereas the TiO 2 dispersions were only sonicated, and the aggregates obtained have a looser structure and D < 2. Obviously through centrifugation more compact aggregates are obtained, and D > 2. In Fig. 4 the dependence of the electric polarizability on Rh is given for A1203 in water, 1 x 10 s M NaCI and 5 x 10 5 M NaCI solutions. As is well known, an increase in the ionic strength causes a decrease in the electric polarizability of compact particles [6]. The studied fractal aggregates from A1203 do not show such a dependence and the electric polarizability scales linearly with Rh. These two facts probably reflect the difference of the polarization mechanisms of fractal aggregates compared with compact particles. For compact particles the dependence of 7 on Rh is power one with coefficients between 2 and 3. The features of the ramilied fractal structure, i.e. the presence of"dead'"
4
>- 3 ¸
.:
120
140
160
180 R h.
200
220
240
Dill
Fig. 4. D e p e n d e n c e of the electric p o l a r i z a b i l i t y of A I 2 0 ~ a g g r e g a t e s o n Rh: w i t h o u t electrolyte ( O ) . with 1 × 10 5 M N a C l ( 1 ) . a n d with 5 x 10 s M N a C I ( ' : I.
ends, possibly determine predominantly the polarization of the counterions situated in these "'local" ionic atmospheres and not in the "'outer" ionic atmosphere. Different types of curve fitting procedures were applied to the experimental results and the linear regression seems to be closer in comparison to the power one because the lowest value of the standard deviation of the residuals is 0.3 compared with 0.42 for the power one. This result coincides with those obtained for SiO, aggregates, where i' scales linearly with Rh [7]. We can conclude that the electric polarizability of fractal objects increases linearly with their hydrodynamic radii.
4. Conclusions
The experimental values of the saturated electrooptical effect c~ o n k R h for oxides with different chemical natures obtained by flame hydrolysis have the same form as those calculated theoretically, assuming two models for particle polarization. The difference in height of the maxima of the theoretical and experimental curves (:~./kRh) may be due to some non-monodispersity of the samples studied. The slight deviations in the positions of the maxima give some idea about the correspon-
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dence of Rg to the experimentally measured Rh. The fractal dimension of AlzO 3 aggregates is D = 2.6 and their electric polarizability scales linearly with Rh. This result is in accordance with the results obtained for fractal SiO 2 aggregates.
Acknowledgement This work has been financially supported by the European Union, CIPA, Project CT-92 3013, "Physical properties and interparticle interaction of aqueous oxide colloids".
References 1-1] M.J. Lin, H.M. Lindsay, D.A. Weitz, R. Klein, R.C. Ball and P. Meakin, J. Phys.: Condens. Matter, 2 (1990) 3093.
I-2] M.J. Lin, H.M. Lindsay, D.A. Weitz, R.C. Ball, R. Klein and P. Meakin, Nature, 339 (1989) 360. [3] Degussa, Tech. Bull. Pig., No. 6 (1986). F4] Degussa, Tech. Bull. Pig., No. 64 (1988). I-5] K. Starchev, V. Peikov, S. Stoylov, I.B. Petkanchin, K.D. Streb and H. Sonntag, Colloid Surfaces A: Physiochem. Eng. Aspects, 76 (1993) 95; K.D. Streb, PhD Thesis, Berlin, 1985. [6] S.S. Stoylov, V.N. Shilov, S.S. Dukhin, S. Sokerov and I.B. Petkanchin, Electro-optics of Colloids, Naukova Dumka, Kiev, 1977 (in Russian); S. Stoylov, Colloid Electrooptics, Academic Press, London 1991. [7] K. Starchev, I. Petkanchin and S. Stoylov, Langmuir, 10 (1994) 1456. [-8] H. Benoit, Ann. Phys. (Paris), 6 (1951) 561. I-9] H.M. Lindsay, R. Klein, D.A. Weitz, M. Lin and P. Meakin, Phys. Rev. A, 38 (1988) 2614. El0] K. Starchev, PhD Thesis, Sofia, 1994. R. Klein, D.A. Weitz, M. Lin, H.M. Lindsay, R.C. Ball and P. Meakin, Prog. Colloid Polym. Sci., 81 (1990) 161. [11] K. Starchev, V. Pejkov and I. Gerroff, J. Phys. Chem., 99 (1995) 356. 1-12] M. Mandel, Molec. Phys., 4 (1961) 489. 1-13] K. Starchev and S. Stoylov, Phys. Rev. B, 47 (1993) 11725. [14] D. Horne, Faraday Disc. Chem. Soc., 83 (1987) 259.