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Repeptization Determined by Turbidity and Photon Correlation Spectroscopy Measurements: Particle Size Effects
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
195, 289–298 (1997)
CS975178
Repeptization Determined by Turbidity and Photon Correlation Spectroscopy Measurements: Particle Size Effects ´ lvarez 1 J. A. Molina-BolıB var, F. Galisteo-Gonza´lez, and R. Hidalgo-A Biocolloid and Fluid Physics Group, Department of Applied Physics, Faculty of Sciences, University of Granada, 18071 Granada, Spain Received March 6, 1997; accepted September 12, 1997
The aggregation of four polystyrene latexes with similar surface charge and different diameter has been examined by small angle light scattering. The DLVO model including aggregation at the secondary minimum qualitatively agrees with the experimental dependence of colloidal stability on particle size. Repeptization experiments, where the flocs were redispersed by washing away the coagulating salt, were carried out using two different methods: dialysis–turbidity and dilution–photon correlation spectroscopy. It was found that for the larger latexes the aggregates fragment after dilution, while for the smaller latexes the aggregates do not fragment. These results correlate closely with the hypothesis that particles may be captured within the secondary minimum of the theoretical interaction energy curves. q 1997 Academic Press Key Words: colloidal stability; polymer colloids; flocculation; repeptization; secondary minimum; coagulation; primary minimum.
1. INTRODUCTION
Particles in dispersion are never thermodynamically stable and have an inherent tendency to aggregate. This is attributable to the attractive van der Waals forces. Only when this attractive force is counteracted by a repulsive force can some degree of stability be obtained. In the case of electrostatically stabilized colloids, the source of the repulsion is the electrical double layer. The stability of a colloidal dispersion is determined by the total interaction potential close to the surface. According to the DLVO theory (1, 2), this total interaction potential is the sum of the repulsive electrostatic interaction energy and the attractive London–van der Waals (dispersion) energy. Electrostatic repulsion decays approximately exponential with the separation distance H, whereas the van der Waals forces are proportional to H 01 . As a consequence, the interaction-energy distance curve is characterized by the presence of a shallow, secondary minimum at longer separation distances, an interaction barrier closer to the surface, and a deep, primary minimum at short separation (Fig. 1). From this, two different types of aggregation of particles might be anticipated: coagulation when aggregation occurs 1
To whom correspondence should be addressed.
in the deep primary minimum with the particle surfaces in intimate contact, and flocculation in the secondary minimum, when a liquid film is retained between the particles so the energy well is shallower. In Fig. 1, the energy difference, D Å Vmax 0 Vmin , is called the potential barrier and represents the energy opposing coagulation. If particles approach each other with sufficient kinetic energies to overcome D, coagulation will occur and the suspension will be destabilized. Flocculation takes place when particles remain at a distance corresponding to the secondary minimum because they fail to overcome the energy difference 0Vmin . It can be anticipated that it should not be possible to redisperse coagulated particles by elimination of the flocculating electrolyte (repeptization), since those particles have to overcome the potential barrier which, if high enough to prevent aggregation, is certainly high enough to prevent passage from the other side. However, as a consequence of the shallow secondary minimum, redispersion of a flocculated colloid readily occur by simply lowering the electrolyte concentration or through mechanical agitation (3–5). Flocculation can be distinguished from coagulation by the reversibility (in the colloidal, not in the thermodynamic, sense of the process) and by the equilibrium distances between the particles being of the order of a few times the thickness of the double layer. It is obvious both of practical and theoretical importance to know whether a flocculated system can be redispersed or not. The aim of this work is to examine the aggregation of four polystyrene latexes, ranging in diameter from 99 to 661 nm. To test the hypothesis that particles may be captured within the secondary minimum of the interaction energy curves, two experimental methods were used: dialysis–turbidity and dilution–photon correlation spectroscopy (PCS) to monitor the average aggregate size. 2. EXPERIMENTAL SECTION
2.1. Materials
All chemicals used were of analytical grade. Water was purified by reverse osmosis, followed by percolation through charcoal and a mixed bed of ion-exchange resins. pH was
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0021-9797/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
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The particle size distribution was determined by transmission electron microscopy (TEM) using an image analysis program (Bolero, AQ systems). All samples have a polysdispersity index (PDI) very near to unity, indicating high monodispersity. The weight concentration of the latex was determined gravimetrically. The particle concentration (particles per ml) was obtained assuming a density of 1.054 g ml 01 for polystyrene and using their TEM diameter. 2.2. Methods
2.2.1. Electrophoretic Mobility Electrophoretic mobility measurements were performed with a Zeta-Sizer IV (Malvern Instruments). The latexes were diluted in the desired medium. The reported mobilities are the average of six measurements at stationary level in a cylindrical cell. FIG. 1. Schematic illustration of potential energy of interaction, VT / kT, against surface to surface distance, H, for spherical electrostatically stabilized particles.
controlled using different buffers (acetate at pH 4–5, phosphate at pH 6–7, borate pH 8–10, constant ionic strength 2 mM). In this work, four anionic polystyrene latexes were used. Styrene monomer was purchased from Merck. It was distilled at reduced pressure (10 mmHg) at 407C. The purified monomer was stored at 057C until required. AS11 and MP2 latexes were synthetized by emulsifier-free emulsion polymerization in a discontinuous reaction using potassium persulfate (Fluka) as initiator according to the method of Goodwin et al. (6). The materials were poured into a three-necked glass flask and polymerized under a nitrogen atmosphere. To maintain continuous vigorous stirring, the T-shaped stirrer (1 1 15 cm) was fitted 1 cm from the bottom of the flask. S4CS9 latex was kindly provided by Joxe Sarobe (Chemical Engineering Group, University of the Basque Country) and prepared by means of a core–shell emulsion polymerization in a batch reactor. The core was prepared at 907C by batch emulsion homopolymerization of styrene using potassium persulfate as initiator and sodium dihexyl sulfosuccinate (Aerosol MA-80, Cyanamid) as surfactant. The shell was obtained by copolymerization of styrene and chloromethylstyrene (607C) using the seed obtained in the first step, which was not cleaned. Details are described elsewhere (7). PS3Ma latex was synthesized as AS11 and MP2 latexes but using MA-80 as surfactant in the synthesis and high temperature (907C). Some of the main characteristics of the latexes are summarized in Table 1. The latexes were cleaned by serum replacement. Surface charge was determined by conductometric automatic titration of the cleaned latex. All our latexes have similar surface charge density ( s0 ) (see Table 1).
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2.2.2. Measurement of Colloidal Stability The stability ratio (W ) is a criterion for the stability of the colloidal system: WÅ
kr ks
[1]
in which the rate constant kr describes rapid aggregation (all collisions result in aggregation) and ks is the rate constant for the slow aggregation regime (only a fraction of the collisions results in aggregation). Thus, the inverse of the stability ratio provides a measure of the effectiveness of collisions leading to aggregation. In this work, the stability ratio was obtained experimentally from the rate constant of coagulation of the colloidal particles measured by low angle light scattering. This technique was developed by Lips and Willis (8). The total scattering intensity for a dispersion of identical primary particles with a time-varying size distribution is given by (9): I(t, u ) Å 1 / 2knst Iu(0)
[2]
where Iu(0) is the initial intensity of light scattered at angle u, ns the number of primary particles, and k the rate constant. The scattered light intensity at low angles increases linearly with time, and the aggregation rate can be obtained from its slope if the number of primary particles is known. The scattered light intensity was followed at an angle of 107 during 100 s. The scattering cell shape is rectangular, with a 2 mm path length. Before use the cell was thoroughly cleaned with chromic acid, rinsed with distilled water and then dried using an infrared lamp. Equal quantities (1 ml) of salt and latex were mixed and introduced in the cell by an automatic mixing device. Dead time is quite short.
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TABLE 1 Main Characteristics of the Latexes Latex PS3Ma S4CS9 MP2 AS11
D (nm) (TEM)
PDI
{ { { {
1.007 1.0032 1.0046 1.002
99 201 361 661
64 6 14 18
s0 (mC cm02) 03.3 03.7 04.8 04.0
The latex dispersions used for these aggregation experiments have to be sufficiently dilute to minimize multiple scattering effects while still having an experimentally convenient coagulation time. The fresh suspensions of latex were sonicated for 2 min prior to experiments to break up any initial clusters.
{ { { {
0.4 0.2 0.9 0.2
A10 A20
A2 0 A20 A1 0 A10
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40 35 40 10
3. RESULTS AND DISCUSSION
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Electrophoretic mobilities of latexes at low ionic strength as a function of pH are shown in Fig. 2, and as function of electrolyte concentration (NaCl) in Fig. 3. The me values were almost constant when the pH was increased from 5 to 10 with a decrease at a lower (acid) pH. This decrease is more accentuated for the latex PS3Ma, which was synthesized at high temperature. As a consequence, some weak acid are present at the surface. Except for this, the electrokinetic behavior of the four latexes is practically the same. 3.2. Colloidal Stability Domains
Figure 4 shows the dependence of log W with log of the molar concentration of NaCl for the four latexes at pH 7.2. The particle concentrations used for these experiments were
[3]
The value of R should be equal to one with total repeptization and zero when repeptization does not occur. PCS measurements. Photon correlation spectroscopy (PCS) was used to measure the mean diffusion coefficient of the aggregates in the dispersion. The effective hydrodynamic particle diameters were obtained by the Stokes–Einstein equation. The PCS measurements were carried out using a Malvern 4700 system. The reference PCS measuring conditions were a temperature of 257C, a scattering angle of 907, and a wavelength of 488 nm (argon laser). Electrolyte solution (NaCl) added to particles suspension induces aggregation. At time zero, equal volumes of latex and salt solution (0.25 ml) were mixed in a test tube. The
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3.1. Electrokinetic Behavior
Dialysis. Repeptization coefficient (R) was obtained from turbidity measurements at 650 nm using a spectrophotometer. Aggregation was achieved by mixing colloid suspension and NaCl solution for a range of NaCl concentrations. Typically, 3 ml of dilute latex was added to 3 ml of NaCl solution. The tube was mixed by inversion, and aggregation was allowed to proceed for 2 h. The turbidity at 2 h is A1 . As a control, the turbidity of microspheres after water addition (A10 ) was also measured. A 5 ml of sample was then removed and placed in preboiled 14.3 mm diameter Visking dialysis tubing. This dispersion was dialyzed against 1000 ml of water for 6 h. Turbidity at 650 nm of the samples and the control dialysates were then measured: A2 and A20 , respectively. As some dilution occurs by dialysis, turbidity measurements had to be corrected with a dilution factor given by A10 /A20 . Repeptization coefficient (R) was taken as (10):
F S
03.02 { 0.2 02.74 { 0.21 01.76 { 0.26 01.57 { 0.08
ccc (mM NaCl)
change in diameter with time was measured using PCS for approximately 600 seconds. Then, 2 ml of deionized water was added to the test tube containing the sample, and the diameter was measured again.
2.2.3. Repeptization Studies
RÅ10
d log W/d log C
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FIG. 2. Electrophoretic movility of latex against pH: ( h ) PS3Ma, ( s ) S4CS9, ( n ) MP2, and ( L ) AS11.
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FIG. 3. Electrophoretic movility of latex against NaCl concentration: ( h ) PS3Ma, ( s ) S4CS9, ( n ) MP2, and ( L ) AS11.
dependence is also predicted by Marmur (13). In contrast, the strong increase of the slope with particle size, as predicted by Reerink and Overbeek (11) clearly does not account for the experimental results. According to Mamur’s model, at a given salt concentration, colloidal stability should display a maximum as a function of the particle radius. The lower ccc obtained for the AS11 latex could be explained this way. All this agreements supports the suggestion that the dependence of the colloidal stability on particle size is due to the combination of the two modes of aggregation: coagulation and flocculation. Possibly, the aggregation for small particles is at the primary minimum whereas for large particles it is at the secondary minimum. However, the experimentally observed size dependence of the slope of the log W –log C plots can be explained in different ways. Some models based on a nonhomogeneous distribution of charge densities among the particles can also explain this dependence (14, 15). Repeptization results should afford further information to distinguish these possible explanations. 3.3. Interaction Energy Curves
different for each latex, decreasing with increasing particle diameter. The critical coagulation concentration (ccc) values are summarized in Table 1. Log W decreases gradually with increasing NaCl concentration until a certain concentration is reached (ccc), at which the curve remains parallel to the log concentration axis. The latter part of the curve corresponds to the region of rapid aggregation, and the former part corresponds to the slow aggregation region. Adding salt to a dispersion initiates aggregation by suppressing the double layer repulsion between particles. According to the DLVO, above the ccc the double layer is entirely suppressed and the aggregation rate is independent of the salt concentration (rapid aggregation). Below the ccc, the thickness of the electrical double layer repulsion increases with decreasing salt concentration decreases. One of the most controversial results of the DLVO theory is the relationship between the slope of the stability curve, the Stern potential and the particle radius (11, 12). At constant Stern potential, the slope should increase in absolute value with increasing size. Marmur (13) developed a theoretical kinetic approach to primary and secondary minimum aggregations. Using the ideal gas kinetic theory to describe the kinetic energy distribution of the colloidal particles, Marmur assumed their aggregating at the primary minimum when the sum of their kinetic energies is greater than the potential energy barrier ( D ) and at the secondary minimum when the sum of their kinetic energies is less than the depth of the secondary minimum (Vmin ). As shown in Table 1, a dependence of the slope of log W –log C plots on the particle size is obtained. The slope decreases with increasing particle size. This relatively weak
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From a theoretical point of view it can be attempted to interpret the fragmentation of aggregates induced by decreasing the ionic strength of the suspending medium within of the DLVO model. According to DLVO the stability of an aqueous colloidal dispersion is determined by the balance of the van der Waals attractive and electrical double layer repulsive force: VT Å VA / VE
[3]
VE represents the repulsive interaction between the electrical double layers of the particles. According to the constant potential model for ka @ 1 and moderate potential, a reasonable expression to VE is (16, 17)
S D
VE Å 2Paee0
4kT g zi e
2
e 0 kH ,
[4]
where k is the Debye parameter and where
g Å tanh
S D ze cd 4kT
,
[5]
cd being the Stern potential, z the valency of the ion, a the particle radius, and H the distance between the particles. This equation is a good approximation for kH ú 1 and cd õ 50 mV. The London–van der Waals dispersion energy (VA ) is expressed as (18)
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FIG. 4. Dependence of the stability factor (W ) on the electrolyte concentration for (a) PS3Ma latex, ( h ) 4 1 10 10 part/ml and ( n ) 9.65 1 10 10 part/ml; (b) S4CS9 latex, 1.34 1 10 10 part/ml; (c) MP2 latex, ( h ) 3.07 1 10 9 part/ml; (d) AS11 latex, ( h ) 6.95 1 10 8 part/ml and ( , ) 5.31 1 10 9 part/ml.
VA Å 0
A 6
F
2a 2 2a 2 / H(4a / H) (2a / H) 2 / ln
H(4a / H) (2a / H) 2
G
,
[6]
where A is the Hamaker constant for particles interacting in the medium (water). Equations [4] and [6] can now be substituted into Eq. [3]. To solve this equation, we need the Hamaker constant and the Stern potential values for these systems. A Hamaker constant value accepted for polystyrene in the literature is 1 1 10 020 J (19, 20). As a first approximation, the use of the zeta potential ( z ) as cd for the computation of the repulsive interaction is
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frequently found in literature related to colloidal stability (21– 25). Zeta potential decreases with increasing electrolyte concentration, implying the need to measure this potential close to the critical coagulation concentration. However, mobility cannot be accurately measured under conditions where the colloid is aggregating, apart from the electrodes polarization problem which can arise with high electrolyte concentrations. Using the closest possible concentration (250 mM NaCl), zeta potentials have been estimated for each latex using the Smoluchowski equation, which is valid at high electrolyte concentration. Several authors (23, 24) also obtained this potential by extrapolating the mobility versus ionic strength curve to the specific ccc value. In Table 2 results are summarized for the four latexes using both methods.
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TABLE 2 Electric Potential Determined by Different Methods c (mV)
Latex PS3Ma S4CS9 MP2 AS11
By mobility 024 021 026 023
{ { { {
By extrapolation
By Eq. [7]
014 019 024 025
3 4 3 3
020 024 029 041
{ { { {
2 2 4 2
By fitting 028.6 027.5 029.5 021.6
On the other hand, considering the Gouy–Chapman theory for the electrical double layer, it is possible to calculate the diffuse potential value ( cd ) for any charged surface with a known surface charge density using the equation q
s Å 8ee0nkT sinh
S D ec 2kT
.
[7]
To obtain the value of cd at the ccc we need to know the charge density at this electrolyte concentration. Using s0 values, estimates of the electric potential have been calculated and presented in Table 2. Other possibilities to estimate the Stern potential ( cd ) can be found in the literature (16, 17, 26). They arise from the fitting of this value to match the experimental ccc with the salt concentration curve whose maximum potential equals 0. Results from these estimations are also shown in Table 2. From the four different methods here used to calculate the Stern potential, we have chosen the last one (fitting) as the most reliable. Apart from the inherent experimental problems of the other methods, the values obtained in this way seems to be closer to expectations: for similar surface charge densities, Stern potential values should be similar, too. Using these values of the Stern potential, estimates of the total potential energy of interaction as a function of the separation distance were computed for each latex (Figs. 5–8). In all Figures, it can be observed that the increase in electrolyte concentration provokes a decrease in the height of the potential maximum. The latter, which prevents aggregation, finally disappears when the electrolyte concentration is similar to the experimental ccc. The DLVO predictions for colloidal stability assume that particle retention occurs only when they cross the interaction energy barrier. The secondary minimum of the interaction energy profile (Figs. 5–8) only becomes prominent with increasing the particle size and ionic strength. So that larger particles can aggregate in the secondary minimum even though the energy barrier is sufficient to prevent aggregation in the primary minimum of the interaction energy curve. 3.4. Secondary Minimum Depth Correlation Studied with Repeptization Experiments The aggregation in secondary minimum (flocculation) should be reversible upon salt dilution since the secondary
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well can be reduced by decreasing the ionic strength (3, 5). From this, we checked this hypothesis by measuring turbidity before and after salt elimination by dialysis and by measuring average aggregates size before and after partial salt elimination by dilution. 3.4.1. PS3Ma latex. The repeptization coefficient (R) for PS3Ma latex was measured for NaCl concentration ranging from 150–800 mM. For all the electrolyte concentrations checked, the value of R was 0. This result indicates that dilution does not induce fragmentation of aggregates. This feature was corroborated with PCS measurements. The aggregation of latex as function of time was measured by PCS before and after the dilution of the sample. Experiments were carried out as a function of salt concentration. Figure 9 shows a typical experiment to determine repeptization of aggregation upon 1:5 salt dilution. Figure indicates that after dilution the average aggregate diameter does not increase with increasing time. The aggregation process is stopped because of the drastically reduced electrolyte and particle concentration. There is no repeptization after dilution, indicated by the unchanged average aggregate diameter. Table 3 presents the repeptization measurements for all latexes. Qualitatively, the features on the potential energy curve are reflected by the experimental observations. As observed in Fig. 5, only a primary minimum is predicted in the VT – H curves for all NaCl concentrations, suggesting that these particles only coagulate into the primary minimum. The PCS and dialysis data are in line with the predictions of the theory because dilution does not induce fragmentation. PS3Ma latex does not aggregate at 70 or 100 mM NaCl. The calculated energy barrier for these concentrations is 14.2kT and 12.1kT, respectively. Theory suggests that the
FIG. 5. Calculated total interaction potential (VT in kBT units) versus distance for PS3Ma latex: (1) 100, (2) 190, (3) 300, (4) 500, (5) 600, and (6) 700 mM, with Hamaker constant (A) 1 1 10 020 J and Stern potential ( cd ) 028.6 mV.
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FIG. 6. Calculated total interaction potential (VT in kBT units) versus distance for S4CS9 latex: (1) 100, (2) 250, (3) 370, (4) 409, (5) 556, and (6) 800 mM, with Hamaker constant (A) 1 1 10 020 J and Stern potential ( cd ) 027.5 mV.
FIG. 8. Calculated total interaction potential (VT in kBT units) versus distance for AS11 latex: (1) 40, (2) 90, (3) 120, (4) 150, (5) 250, (6) 300, and (7) 801 mM, with Hamaker constant ( A) 1 1 10 020 J and Stern potential ( cd ) 021.6 mV.
onset of repulsive conditions occurs when the interaction energy barrier exceeds approximately 10–15kT (27–30). 3.4.2. S4CS9 latex. Experiments to determine fragmentation of aggregates after dilution by dialysis are shown in Fig. 10 for S4CS9 and MP2 latexes. For the S4CS9 system, the repeptization coefficient (R) differs from zero up to 250 mM NaCl. Therefore, at least up to this concentration, there is fragmentation upon salt removal which can be associated with aggregation of the microspheres at the secondary mini-
mum. These results are in agreement with the PCS measurements (Table 3) which indicated that from 251 to 556 mM NaCl, a nonfragmentation of aggregates continues upon dilution of added salt. Repeptization was observed at 150 and 200 mM NaC1. The calculated secondary minimum (Vmin ) for 250 mM NaCl (from Figure 6) is –3.3kT, and its energy barrier ( D ) is 10.1kT. The value of Vmax decreases with increasing the electrolyte concentration, while Vmin increases. The energy barrier is lower than 10kT for electrolyte concentrations above
FIG. 7. Calculated total interaction potential (VT in kBT units) versus distance for MP2 latex: (1) 100, (2) 250, (3) 370, (4) 409, (5) 556, (6) 800, and (7) 1000 mM, with Hamaker constant ( A) 1 1 10 020 J and Stern potential ( cd ) 029.5 mV.
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FIG. 9. Aggregate average diameter (D) versus time for the system PS3Ma in 250 mM NaCl with dilution after 1000 s (open symbol) and without dilution (closed symbol).
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TABLE 3 Fragmentation of NaCl-Induced Aggregation for the Latexes Measured by PCSa [NaCl] (M) 70 100 115 130 150 200 251 300 351 409 556 752 1250
PS3Ma
S4CS9
— — No No No No No No No
— — — — Yes Yes No No No No No
No
MP2
AS11 Yes Yes Yes
Yes Yes Yes No No No
Yes Yes Yes Yes No No No
a ‘‘Yes,’’ repeptization occurs. ‘‘No’’, repeptization does not occur. ‘‘ —,’’ no aggregation observed.
250 mM so the particles cannot be retained in the secondary minimum, because the energy barrier being not high enough to prevent aggregation in the primary minimum. However, for electrolyte concentrations lower than 250 mM, there exists a secondary minimum with a large energy barrier in the interaction energy profile and the particles only flocculate. 3.4.3. MP2 latex. Figure 10 shows the repeptization results obtained for this latex by dialysis. Fragmentation is evident up to 500 mM NaCl. These results are in line with the PCS experiments (Table 3). The fragmentation of aggregates becomes more prominent with increasing particle size. Repeptization coefficient never achieves the value 1, in accordance with the aging phenomenon usually described for aggregates (31–34) (partial dilution is induced during 5 h in the membrane dialysis). Figure 11 shows three experiments for measuring repeptization of aggregation by PCS. Repeptization causes (Fig. 11b) the average aggregate diameter to diminish after dilution. Average aggregate diameter does not change after dilution when there is no repeptization (Fig. 11a). As observed in Fig. 11b, repeptization is a very fast process. The dependence of repeptization on aggregation time is shown in Figure 11b. The results indicate that fresh flocs are easier to repeptize than aged aggregates (31–34). The fragmentation results obtained do correlate reasonably well with the secondary minimum profile. At 500 mM NaCl the values of Vmin and Vmax are 010.85kT and 01.1kT, respectively. Flocculation in the secondary minimum occurs at electrolyte concentrations lower than 500 mM because the energy barrier can prevent aggregation in the primary minimum, according to the 10–15kT energy barrier criteria that delineate the onset of repulsive conditions. Moreover, the similarity between the experimental points of the aggregation process quantified by the stability factor W (Fig. 4c)
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and the repeptization data shown in Fig. 10 for this latex, suggests that both processes are inverse of each other, i.e., particles falling or escaping from the secondary minimum. 3.4.4. AS11 latex. Repeptization studies by dialysis do not yield accurate results because there exist sedimentation and multiple scattering effects. Repeptization was observed by PCS from 70 to 300 mM NaCl (Table 3). Potential energy curves (Fig. 8) were obtained with a Stern potential of 021.6 mV (as stated in literature, to match the experimental ccc with the zero potential maximum). However, some experimental results cannot be explained by these potential energy curves. First, the Stern potential of AS11 latex is lower than the Stern potential of the other latexes, when the surface charge density is very similar for all of them. Second, repeptization occurs for 250 and 300 mM NaCl (Table 3), while there is not a secondary minimum for these electrolyte concentrations (Fig. 8). These are the problems which can be expected from the existence of a deep secondary minimum in large particles. In these systems, the classical interpretation of ccc as the situation where potential barrier disappears seems to fail. If the secondary minimum is deep enough ( ú10kT ), a rapid aggregation regime can be achieved in this well, turning out as a experimental ccc (14). With these assumptions, a new plot of interaction potential as a function of distance is presented in Fig. 12. Data has been fitted to get a secondary minimum of 010kT for a salt concentration of 150 mM NaCl (ccc). At least qualitatively, this new representation is more in line with experimental results. For example, it explains the fact that repeptization is taking place at 250 and 300 mM NaCl, since these curves now present a secondary minimum able to retain particles in a flocculated state ( 013.05kT and
FIG. 10. Repeptization coefficient (R) of NaCl-induced aggregation as a function of NaCl concentration: ( h ) S4CS9 latex and ( l ) MP2 latex.
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FIG. 11. Aggregate average diameter (D) versus time for the system MP2: (a) 556 mM, (b) 300 mM NaCl; ( l ) dilution at 1070 s and ( h ) dilution at 2830 s.
014.63kT, respectively). Moreover, the Stern potential de- dialysis and by photon correlation spectroscopy. The small duced in this case is 024 mV, higher than in the original particles only aggregate into the primary minimum (coagulacalculations ( 021.6 mV) and closer to the values obtained tion). The larger particles also aggregate into the secondary for the rest of latexes ( 028 mV). minimum at low concentrations (flocculation) but coagulate at higher concentrations (primary minimum). Qualitatively, the features on the potential energy curves deduced from 4. SUMMARY DLVO theory explain these experimental observations, alFragmentation of aggregates induced by decreasing the though not for the large latex (661 nm in diameter). For this ionic strength of the suspending medium for four latexes with latex, the classical concept of ccc seems to fail. A new apdifferent size but similar surface charge has been studied by proach is presented, assuming that ccc can be also achieved when the secondary minimum is deep enough to ensure maximum effectiveness of collisions leading to aggregation. When the interaction potential is calculated in this way, better agreement with experimental results is obtained. The experimental dependence of colloidal stability on the particle size at constant potential cannot be described by the Reerink and Overbeek DLVO approximation. More suitable models, still within the bounds of the DLVO theory, are those taking into account aggregation at the secondary minimum. Phenomena like aggregate aging also demonstrates that these experiments cannot be interpreted on the basis of the DLVO theory only. ACKNOWLEDGMENTS This work was supported by the ‘‘Comisio´n Interministerial de Ciencia y TecnologıB a CICYT’’, Project MAT 96-1035-03-CO2. The authors are very grateful to J. Sarobe, J. Forcada, M. Servando, M. Quesada, and A. Schmitt by providing the latex samples. FIG. 12. Calculated total interaction potential (VT in kBT units) versus distance for AS11 latex: (1) 120, (2) 150, (3) 250, (4) 300, (5) 450, and (6) 801 mM, with Hamaker constant ( A) 1 1 10 020 J and Stern potential ( cd ) 024 mV.
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REFERENCES 1. Derjaguin, B. V., and Landau, L., Acta Physicochim. USSR 14, 633 (1941).
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2. Verwey, E. J. W., and Overbeek, J. Th. G., ‘‘Theory of the Stability of Lyophobic Colloids,’’ Vols. 1 and 2, Elsevier, Amsterdam, 1952. 3. Jeffrey, G. C., and Ottewill, R. H., Colloid Polym. Sci. 266, 173 (1988). 4. Carmona-Ribeiro, A. M., J. Phys. Chem. 97, 11843 (1993). 5. Litton, G. M., and Olson, T. M., Colloids Surf. A 107, 273 (1996). 6. Goodwin, J., Hearn, J., Ho, C. C., and Ottewill, R. H., Colloid Polym. Sci. 252, 461 (1974). 7. Sarobe, J., and Forcada, J., Colloid Polym. Sci. 274, 8 (1996). 8. Lips, A., and Willis, E. J., J. Chem. Soc., Faraday Trans. 67, 2979 (1971). 9. Lips, A., and Willis, E. J., J. Chem. Soc., Faraday Trans. 69, 1226 (1973). 10. Tsuruta, L. R., and Carmona-Ribeiro, A. M., J. Phys. Chem. 100, 7130 (1996). 11. Reerink, H., and Overbeek, J. Th. G., Discuss. Faraday Soc. 18, 95 (1954). 12. Ottewill, R. H., and Shaw, J. N., Trans. Faraday Soc. 42, 154 (1966). 13. Marmur, A., J. Colloid Interface Sci. 72, 41 (1979). 14. Prieve, D. C., and Ruckenstein, E., J. Colloid Interface Sci. 73, 539 (1980). 15. Penners, N. H. G., and Koopal, L. K., Colloid Surf. 28, 67 (1987). 16. Overbeek, J. Th. G., Adv. Colloid Interface Sci. 16, 17 (1982). 17. Overbeek, J. Th. G., Pure Appl. Chem. 52, 1151 (1980). 18. Hiemenz, P., ‘‘Principles of Colloid and Surface Chemistry’’, p. 648. Dekker, New York, 1986.
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19. Ottewill, R. H., and Shaw, J. N., Disc. Faraday Soc. 42, 154 (1966). 20. Kotera, A., Furusawa, K., and Kudo, K., Kolloid Z. Z. Polym. 240, 837 (1970). 21. Schenkel, J., and Kitchener, J. A., Trans. Faraday. Soc. 56, 161 (1960). 22. Hunter, R. J., in ‘‘Foundations of Colloid Science,’’ Vol. 1, Chap. 7. Clarendon Press, Oxford, 1987. 23. Bastos, D., and de las Nieves, F. J., Colloid Polym. Sci. 272, 592 (1994). 24. Nakamura, M., Oshima, H., and Kondo, T., J. Colloid Interface Sci. 154, 393 (1992). 25. Stoll, S., and Pefferkorn, E., J. Colloid Interface Sci. 152, 247 (1992). 26. Carmona-Ribeiro, A. M., J. Phys. Chem. 93, 2630 (1989). 27. Adamczyk, Z., Dabros, Z., Czarnecki, T., and van de Ven, Th. G. M., Adv. Colloid Interface Sci. 19, 183 (1983). 28. Usui, S., in ‘‘Electrical Phenomena at Interfaces’’ (A. Kitahara and A. Watanabe, Eds.), Surfactant Science Series, Vol. 15, p. 15. Dekker, New York, 1984. 29. Vold, R. D., and Vold, M. J., ‘‘Colloid and Interface Chemistry’’, p. 269. Addison-Wesley, Reading, MA, 1983. 30. Chow, R. S., Colloids Surf. 61, 241 (1991). 31. Frens, G., and Overbeek, J. Th. G., J. Colloid Interface Sci. 38, 376 (1972). 32. Frens, G., and Overbeek, J. Th. G., J. Colloid Interface Sci. 36, 286 (1971). 33. Stoll, S., and Pefferkorn, E., J. Colloid Interface Sci. 152, 247 (1992). 34. Stoll, S., and Pefferkorn, E., J. Colloid Interface Sci. 152, 257 (1992).
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CS975178
Repeptization Determined by Turbidity and Photon Correlation Spectroscopy Measurements: Particle Size Effects ´ lvarez 1 J. A. Molina-BolıB var, F. Galisteo-Gonza´lez, and R. Hidalgo-A Biocolloid and Fluid Physics Group, Department of Applied Physics, Faculty of Sciences, University of Granada, 18071 Granada, Spain Received March 6, 1997; accepted September 12, 1997
The aggregation of four polystyrene latexes with similar surface charge and different diameter has been examined by small angle light scattering. The DLVO model including aggregation at the secondary minimum qualitatively agrees with the experimental dependence of colloidal stability on particle size. Repeptization experiments, where the flocs were redispersed by washing away the coagulating salt, were carried out using two different methods: dialysis–turbidity and dilution–photon correlation spectroscopy. It was found that for the larger latexes the aggregates fragment after dilution, while for the smaller latexes the aggregates do not fragment. These results correlate closely with the hypothesis that particles may be captured within the secondary minimum of the theoretical interaction energy curves. q 1997 Academic Press Key Words: colloidal stability; polymer colloids; flocculation; repeptization; secondary minimum; coagulation; primary minimum.
1. INTRODUCTION
Particles in dispersion are never thermodynamically stable and have an inherent tendency to aggregate. This is attributable to the attractive van der Waals forces. Only when this attractive force is counteracted by a repulsive force can some degree of stability be obtained. In the case of electrostatically stabilized colloids, the source of the repulsion is the electrical double layer. The stability of a colloidal dispersion is determined by the total interaction potential close to the surface. According to the DLVO theory (1, 2), this total interaction potential is the sum of the repulsive electrostatic interaction energy and the attractive London–van der Waals (dispersion) energy. Electrostatic repulsion decays approximately exponential with the separation distance H, whereas the van der Waals forces are proportional to H 01 . As a consequence, the interaction-energy distance curve is characterized by the presence of a shallow, secondary minimum at longer separation distances, an interaction barrier closer to the surface, and a deep, primary minimum at short separation (Fig. 1). From this, two different types of aggregation of particles might be anticipated: coagulation when aggregation occurs 1
To whom correspondence should be addressed.
in the deep primary minimum with the particle surfaces in intimate contact, and flocculation in the secondary minimum, when a liquid film is retained between the particles so the energy well is shallower. In Fig. 1, the energy difference, D Å Vmax 0 Vmin , is called the potential barrier and represents the energy opposing coagulation. If particles approach each other with sufficient kinetic energies to overcome D, coagulation will occur and the suspension will be destabilized. Flocculation takes place when particles remain at a distance corresponding to the secondary minimum because they fail to overcome the energy difference 0Vmin . It can be anticipated that it should not be possible to redisperse coagulated particles by elimination of the flocculating electrolyte (repeptization), since those particles have to overcome the potential barrier which, if high enough to prevent aggregation, is certainly high enough to prevent passage from the other side. However, as a consequence of the shallow secondary minimum, redispersion of a flocculated colloid readily occur by simply lowering the electrolyte concentration or through mechanical agitation (3–5). Flocculation can be distinguished from coagulation by the reversibility (in the colloidal, not in the thermodynamic, sense of the process) and by the equilibrium distances between the particles being of the order of a few times the thickness of the double layer. It is obvious both of practical and theoretical importance to know whether a flocculated system can be redispersed or not. The aim of this work is to examine the aggregation of four polystyrene latexes, ranging in diameter from 99 to 661 nm. To test the hypothesis that particles may be captured within the secondary minimum of the interaction energy curves, two experimental methods were used: dialysis–turbidity and dilution–photon correlation spectroscopy (PCS) to monitor the average aggregate size. 2. EXPERIMENTAL SECTION
2.1. Materials
All chemicals used were of analytical grade. Water was purified by reverse osmosis, followed by percolation through charcoal and a mixed bed of ion-exchange resins. pH was
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The particle size distribution was determined by transmission electron microscopy (TEM) using an image analysis program (Bolero, AQ systems). All samples have a polysdispersity index (PDI) very near to unity, indicating high monodispersity. The weight concentration of the latex was determined gravimetrically. The particle concentration (particles per ml) was obtained assuming a density of 1.054 g ml 01 for polystyrene and using their TEM diameter. 2.2. Methods
2.2.1. Electrophoretic Mobility Electrophoretic mobility measurements were performed with a Zeta-Sizer IV (Malvern Instruments). The latexes were diluted in the desired medium. The reported mobilities are the average of six measurements at stationary level in a cylindrical cell. FIG. 1. Schematic illustration of potential energy of interaction, VT / kT, against surface to surface distance, H, for spherical electrostatically stabilized particles.
controlled using different buffers (acetate at pH 4–5, phosphate at pH 6–7, borate pH 8–10, constant ionic strength 2 mM). In this work, four anionic polystyrene latexes were used. Styrene monomer was purchased from Merck. It was distilled at reduced pressure (10 mmHg) at 407C. The purified monomer was stored at 057C until required. AS11 and MP2 latexes were synthetized by emulsifier-free emulsion polymerization in a discontinuous reaction using potassium persulfate (Fluka) as initiator according to the method of Goodwin et al. (6). The materials were poured into a three-necked glass flask and polymerized under a nitrogen atmosphere. To maintain continuous vigorous stirring, the T-shaped stirrer (1 1 15 cm) was fitted 1 cm from the bottom of the flask. S4CS9 latex was kindly provided by Joxe Sarobe (Chemical Engineering Group, University of the Basque Country) and prepared by means of a core–shell emulsion polymerization in a batch reactor. The core was prepared at 907C by batch emulsion homopolymerization of styrene using potassium persulfate as initiator and sodium dihexyl sulfosuccinate (Aerosol MA-80, Cyanamid) as surfactant. The shell was obtained by copolymerization of styrene and chloromethylstyrene (607C) using the seed obtained in the first step, which was not cleaned. Details are described elsewhere (7). PS3Ma latex was synthesized as AS11 and MP2 latexes but using MA-80 as surfactant in the synthesis and high temperature (907C). Some of the main characteristics of the latexes are summarized in Table 1. The latexes were cleaned by serum replacement. Surface charge was determined by conductometric automatic titration of the cleaned latex. All our latexes have similar surface charge density ( s0 ) (see Table 1).
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2.2.2. Measurement of Colloidal Stability The stability ratio (W ) is a criterion for the stability of the colloidal system: WÅ
kr ks
[1]
in which the rate constant kr describes rapid aggregation (all collisions result in aggregation) and ks is the rate constant for the slow aggregation regime (only a fraction of the collisions results in aggregation). Thus, the inverse of the stability ratio provides a measure of the effectiveness of collisions leading to aggregation. In this work, the stability ratio was obtained experimentally from the rate constant of coagulation of the colloidal particles measured by low angle light scattering. This technique was developed by Lips and Willis (8). The total scattering intensity for a dispersion of identical primary particles with a time-varying size distribution is given by (9): I(t, u ) Å 1 / 2knst Iu(0)
[2]
where Iu(0) is the initial intensity of light scattered at angle u, ns the number of primary particles, and k the rate constant. The scattered light intensity at low angles increases linearly with time, and the aggregation rate can be obtained from its slope if the number of primary particles is known. The scattered light intensity was followed at an angle of 107 during 100 s. The scattering cell shape is rectangular, with a 2 mm path length. Before use the cell was thoroughly cleaned with chromic acid, rinsed with distilled water and then dried using an infrared lamp. Equal quantities (1 ml) of salt and latex were mixed and introduced in the cell by an automatic mixing device. Dead time is quite short.
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PARTICLE SIZE EFFECTS ON REPEPTIZATION
TABLE 1 Main Characteristics of the Latexes Latex PS3Ma S4CS9 MP2 AS11
D (nm) (TEM)
PDI
{ { { {
1.007 1.0032 1.0046 1.002
99 201 361 661
64 6 14 18
s0 (mC cm02) 03.3 03.7 04.8 04.0
The latex dispersions used for these aggregation experiments have to be sufficiently dilute to minimize multiple scattering effects while still having an experimentally convenient coagulation time. The fresh suspensions of latex were sonicated for 2 min prior to experiments to break up any initial clusters.
{ { { {
0.4 0.2 0.9 0.2
A10 A20
A2 0 A20 A1 0 A10
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40 35 40 10
3. RESULTS AND DISCUSSION
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Electrophoretic mobilities of latexes at low ionic strength as a function of pH are shown in Fig. 2, and as function of electrolyte concentration (NaCl) in Fig. 3. The me values were almost constant when the pH was increased from 5 to 10 with a decrease at a lower (acid) pH. This decrease is more accentuated for the latex PS3Ma, which was synthesized at high temperature. As a consequence, some weak acid are present at the surface. Except for this, the electrokinetic behavior of the four latexes is practically the same. 3.2. Colloidal Stability Domains
Figure 4 shows the dependence of log W with log of the molar concentration of NaCl for the four latexes at pH 7.2. The particle concentrations used for these experiments were
[3]
The value of R should be equal to one with total repeptization and zero when repeptization does not occur. PCS measurements. Photon correlation spectroscopy (PCS) was used to measure the mean diffusion coefficient of the aggregates in the dispersion. The effective hydrodynamic particle diameters were obtained by the Stokes–Einstein equation. The PCS measurements were carried out using a Malvern 4700 system. The reference PCS measuring conditions were a temperature of 257C, a scattering angle of 907, and a wavelength of 488 nm (argon laser). Electrolyte solution (NaCl) added to particles suspension induces aggregation. At time zero, equal volumes of latex and salt solution (0.25 ml) were mixed in a test tube. The
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3.1. Electrokinetic Behavior
Dialysis. Repeptization coefficient (R) was obtained from turbidity measurements at 650 nm using a spectrophotometer. Aggregation was achieved by mixing colloid suspension and NaCl solution for a range of NaCl concentrations. Typically, 3 ml of dilute latex was added to 3 ml of NaCl solution. The tube was mixed by inversion, and aggregation was allowed to proceed for 2 h. The turbidity at 2 h is A1 . As a control, the turbidity of microspheres after water addition (A10 ) was also measured. A 5 ml of sample was then removed and placed in preboiled 14.3 mm diameter Visking dialysis tubing. This dispersion was dialyzed against 1000 ml of water for 6 h. Turbidity at 650 nm of the samples and the control dialysates were then measured: A2 and A20 , respectively. As some dilution occurs by dialysis, turbidity measurements had to be corrected with a dilution factor given by A10 /A20 . Repeptization coefficient (R) was taken as (10):
F S
03.02 { 0.2 02.74 { 0.21 01.76 { 0.26 01.57 { 0.08
ccc (mM NaCl)
change in diameter with time was measured using PCS for approximately 600 seconds. Then, 2 ml of deionized water was added to the test tube containing the sample, and the diameter was measured again.
2.2.3. Repeptization Studies
RÅ10
d log W/d log C
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FIG. 2. Electrophoretic movility of latex against pH: ( h ) PS3Ma, ( s ) S4CS9, ( n ) MP2, and ( L ) AS11.
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FIG. 3. Electrophoretic movility of latex against NaCl concentration: ( h ) PS3Ma, ( s ) S4CS9, ( n ) MP2, and ( L ) AS11.
dependence is also predicted by Marmur (13). In contrast, the strong increase of the slope with particle size, as predicted by Reerink and Overbeek (11) clearly does not account for the experimental results. According to Mamur’s model, at a given salt concentration, colloidal stability should display a maximum as a function of the particle radius. The lower ccc obtained for the AS11 latex could be explained this way. All this agreements supports the suggestion that the dependence of the colloidal stability on particle size is due to the combination of the two modes of aggregation: coagulation and flocculation. Possibly, the aggregation for small particles is at the primary minimum whereas for large particles it is at the secondary minimum. However, the experimentally observed size dependence of the slope of the log W –log C plots can be explained in different ways. Some models based on a nonhomogeneous distribution of charge densities among the particles can also explain this dependence (14, 15). Repeptization results should afford further information to distinguish these possible explanations. 3.3. Interaction Energy Curves
different for each latex, decreasing with increasing particle diameter. The critical coagulation concentration (ccc) values are summarized in Table 1. Log W decreases gradually with increasing NaCl concentration until a certain concentration is reached (ccc), at which the curve remains parallel to the log concentration axis. The latter part of the curve corresponds to the region of rapid aggregation, and the former part corresponds to the slow aggregation region. Adding salt to a dispersion initiates aggregation by suppressing the double layer repulsion between particles. According to the DLVO, above the ccc the double layer is entirely suppressed and the aggregation rate is independent of the salt concentration (rapid aggregation). Below the ccc, the thickness of the electrical double layer repulsion increases with decreasing salt concentration decreases. One of the most controversial results of the DLVO theory is the relationship between the slope of the stability curve, the Stern potential and the particle radius (11, 12). At constant Stern potential, the slope should increase in absolute value with increasing size. Marmur (13) developed a theoretical kinetic approach to primary and secondary minimum aggregations. Using the ideal gas kinetic theory to describe the kinetic energy distribution of the colloidal particles, Marmur assumed their aggregating at the primary minimum when the sum of their kinetic energies is greater than the potential energy barrier ( D ) and at the secondary minimum when the sum of their kinetic energies is less than the depth of the secondary minimum (Vmin ). As shown in Table 1, a dependence of the slope of log W –log C plots on the particle size is obtained. The slope decreases with increasing particle size. This relatively weak
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From a theoretical point of view it can be attempted to interpret the fragmentation of aggregates induced by decreasing the ionic strength of the suspending medium within of the DLVO model. According to DLVO the stability of an aqueous colloidal dispersion is determined by the balance of the van der Waals attractive and electrical double layer repulsive force: VT Å VA / VE
[3]
VE represents the repulsive interaction between the electrical double layers of the particles. According to the constant potential model for ka @ 1 and moderate potential, a reasonable expression to VE is (16, 17)
S D
VE Å 2Paee0
4kT g zi e
2
e 0 kH ,
[4]
where k is the Debye parameter and where
g Å tanh
S D ze cd 4kT
,
[5]
cd being the Stern potential, z the valency of the ion, a the particle radius, and H the distance between the particles. This equation is a good approximation for kH ú 1 and cd õ 50 mV. The London–van der Waals dispersion energy (VA ) is expressed as (18)
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FIG. 4. Dependence of the stability factor (W ) on the electrolyte concentration for (a) PS3Ma latex, ( h ) 4 1 10 10 part/ml and ( n ) 9.65 1 10 10 part/ml; (b) S4CS9 latex, 1.34 1 10 10 part/ml; (c) MP2 latex, ( h ) 3.07 1 10 9 part/ml; (d) AS11 latex, ( h ) 6.95 1 10 8 part/ml and ( , ) 5.31 1 10 9 part/ml.
VA Å 0
A 6
F
2a 2 2a 2 / H(4a / H) (2a / H) 2 / ln
H(4a / H) (2a / H) 2
G
,
[6]
where A is the Hamaker constant for particles interacting in the medium (water). Equations [4] and [6] can now be substituted into Eq. [3]. To solve this equation, we need the Hamaker constant and the Stern potential values for these systems. A Hamaker constant value accepted for polystyrene in the literature is 1 1 10 020 J (19, 20). As a first approximation, the use of the zeta potential ( z ) as cd for the computation of the repulsive interaction is
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frequently found in literature related to colloidal stability (21– 25). Zeta potential decreases with increasing electrolyte concentration, implying the need to measure this potential close to the critical coagulation concentration. However, mobility cannot be accurately measured under conditions where the colloid is aggregating, apart from the electrodes polarization problem which can arise with high electrolyte concentrations. Using the closest possible concentration (250 mM NaCl), zeta potentials have been estimated for each latex using the Smoluchowski equation, which is valid at high electrolyte concentration. Several authors (23, 24) also obtained this potential by extrapolating the mobility versus ionic strength curve to the specific ccc value. In Table 2 results are summarized for the four latexes using both methods.
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TABLE 2 Electric Potential Determined by Different Methods c (mV)
Latex PS3Ma S4CS9 MP2 AS11
By mobility 024 021 026 023
{ { { {
By extrapolation
By Eq. [7]
014 019 024 025
3 4 3 3
020 024 029 041
{ { { {
2 2 4 2
By fitting 028.6 027.5 029.5 021.6
On the other hand, considering the Gouy–Chapman theory for the electrical double layer, it is possible to calculate the diffuse potential value ( cd ) for any charged surface with a known surface charge density using the equation q
s Å 8ee0nkT sinh
S D ec 2kT
.
[7]
To obtain the value of cd at the ccc we need to know the charge density at this electrolyte concentration. Using s0 values, estimates of the electric potential have been calculated and presented in Table 2. Other possibilities to estimate the Stern potential ( cd ) can be found in the literature (16, 17, 26). They arise from the fitting of this value to match the experimental ccc with the salt concentration curve whose maximum potential equals 0. Results from these estimations are also shown in Table 2. From the four different methods here used to calculate the Stern potential, we have chosen the last one (fitting) as the most reliable. Apart from the inherent experimental problems of the other methods, the values obtained in this way seems to be closer to expectations: for similar surface charge densities, Stern potential values should be similar, too. Using these values of the Stern potential, estimates of the total potential energy of interaction as a function of the separation distance were computed for each latex (Figs. 5–8). In all Figures, it can be observed that the increase in electrolyte concentration provokes a decrease in the height of the potential maximum. The latter, which prevents aggregation, finally disappears when the electrolyte concentration is similar to the experimental ccc. The DLVO predictions for colloidal stability assume that particle retention occurs only when they cross the interaction energy barrier. The secondary minimum of the interaction energy profile (Figs. 5–8) only becomes prominent with increasing the particle size and ionic strength. So that larger particles can aggregate in the secondary minimum even though the energy barrier is sufficient to prevent aggregation in the primary minimum of the interaction energy curve. 3.4. Secondary Minimum Depth Correlation Studied with Repeptization Experiments The aggregation in secondary minimum (flocculation) should be reversible upon salt dilution since the secondary
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well can be reduced by decreasing the ionic strength (3, 5). From this, we checked this hypothesis by measuring turbidity before and after salt elimination by dialysis and by measuring average aggregates size before and after partial salt elimination by dilution. 3.4.1. PS3Ma latex. The repeptization coefficient (R) for PS3Ma latex was measured for NaCl concentration ranging from 150–800 mM. For all the electrolyte concentrations checked, the value of R was 0. This result indicates that dilution does not induce fragmentation of aggregates. This feature was corroborated with PCS measurements. The aggregation of latex as function of time was measured by PCS before and after the dilution of the sample. Experiments were carried out as a function of salt concentration. Figure 9 shows a typical experiment to determine repeptization of aggregation upon 1:5 salt dilution. Figure indicates that after dilution the average aggregate diameter does not increase with increasing time. The aggregation process is stopped because of the drastically reduced electrolyte and particle concentration. There is no repeptization after dilution, indicated by the unchanged average aggregate diameter. Table 3 presents the repeptization measurements for all latexes. Qualitatively, the features on the potential energy curve are reflected by the experimental observations. As observed in Fig. 5, only a primary minimum is predicted in the VT – H curves for all NaCl concentrations, suggesting that these particles only coagulate into the primary minimum. The PCS and dialysis data are in line with the predictions of the theory because dilution does not induce fragmentation. PS3Ma latex does not aggregate at 70 or 100 mM NaCl. The calculated energy barrier for these concentrations is 14.2kT and 12.1kT, respectively. Theory suggests that the
FIG. 5. Calculated total interaction potential (VT in kBT units) versus distance for PS3Ma latex: (1) 100, (2) 190, (3) 300, (4) 500, (5) 600, and (6) 700 mM, with Hamaker constant (A) 1 1 10 020 J and Stern potential ( cd ) 028.6 mV.
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FIG. 6. Calculated total interaction potential (VT in kBT units) versus distance for S4CS9 latex: (1) 100, (2) 250, (3) 370, (4) 409, (5) 556, and (6) 800 mM, with Hamaker constant (A) 1 1 10 020 J and Stern potential ( cd ) 027.5 mV.
FIG. 8. Calculated total interaction potential (VT in kBT units) versus distance for AS11 latex: (1) 40, (2) 90, (3) 120, (4) 150, (5) 250, (6) 300, and (7) 801 mM, with Hamaker constant ( A) 1 1 10 020 J and Stern potential ( cd ) 021.6 mV.
onset of repulsive conditions occurs when the interaction energy barrier exceeds approximately 10–15kT (27–30). 3.4.2. S4CS9 latex. Experiments to determine fragmentation of aggregates after dilution by dialysis are shown in Fig. 10 for S4CS9 and MP2 latexes. For the S4CS9 system, the repeptization coefficient (R) differs from zero up to 250 mM NaCl. Therefore, at least up to this concentration, there is fragmentation upon salt removal which can be associated with aggregation of the microspheres at the secondary mini-
mum. These results are in agreement with the PCS measurements (Table 3) which indicated that from 251 to 556 mM NaCl, a nonfragmentation of aggregates continues upon dilution of added salt. Repeptization was observed at 150 and 200 mM NaC1. The calculated secondary minimum (Vmin ) for 250 mM NaCl (from Figure 6) is –3.3kT, and its energy barrier ( D ) is 10.1kT. The value of Vmax decreases with increasing the electrolyte concentration, while Vmin increases. The energy barrier is lower than 10kT for electrolyte concentrations above
FIG. 7. Calculated total interaction potential (VT in kBT units) versus distance for MP2 latex: (1) 100, (2) 250, (3) 370, (4) 409, (5) 556, (6) 800, and (7) 1000 mM, with Hamaker constant ( A) 1 1 10 020 J and Stern potential ( cd ) 029.5 mV.
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FIG. 9. Aggregate average diameter (D) versus time for the system PS3Ma in 250 mM NaCl with dilution after 1000 s (open symbol) and without dilution (closed symbol).
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TABLE 3 Fragmentation of NaCl-Induced Aggregation for the Latexes Measured by PCSa [NaCl] (M) 70 100 115 130 150 200 251 300 351 409 556 752 1250
PS3Ma
S4CS9
— — No No No No No No No
— — — — Yes Yes No No No No No
No
MP2
AS11 Yes Yes Yes
Yes Yes Yes No No No
Yes Yes Yes Yes No No No
a ‘‘Yes,’’ repeptization occurs. ‘‘No’’, repeptization does not occur. ‘‘ —,’’ no aggregation observed.
250 mM so the particles cannot be retained in the secondary minimum, because the energy barrier being not high enough to prevent aggregation in the primary minimum. However, for electrolyte concentrations lower than 250 mM, there exists a secondary minimum with a large energy barrier in the interaction energy profile and the particles only flocculate. 3.4.3. MP2 latex. Figure 10 shows the repeptization results obtained for this latex by dialysis. Fragmentation is evident up to 500 mM NaCl. These results are in line with the PCS experiments (Table 3). The fragmentation of aggregates becomes more prominent with increasing particle size. Repeptization coefficient never achieves the value 1, in accordance with the aging phenomenon usually described for aggregates (31–34) (partial dilution is induced during 5 h in the membrane dialysis). Figure 11 shows three experiments for measuring repeptization of aggregation by PCS. Repeptization causes (Fig. 11b) the average aggregate diameter to diminish after dilution. Average aggregate diameter does not change after dilution when there is no repeptization (Fig. 11a). As observed in Fig. 11b, repeptization is a very fast process. The dependence of repeptization on aggregation time is shown in Figure 11b. The results indicate that fresh flocs are easier to repeptize than aged aggregates (31–34). The fragmentation results obtained do correlate reasonably well with the secondary minimum profile. At 500 mM NaCl the values of Vmin and Vmax are 010.85kT and 01.1kT, respectively. Flocculation in the secondary minimum occurs at electrolyte concentrations lower than 500 mM because the energy barrier can prevent aggregation in the primary minimum, according to the 10–15kT energy barrier criteria that delineate the onset of repulsive conditions. Moreover, the similarity between the experimental points of the aggregation process quantified by the stability factor W (Fig. 4c)
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and the repeptization data shown in Fig. 10 for this latex, suggests that both processes are inverse of each other, i.e., particles falling or escaping from the secondary minimum. 3.4.4. AS11 latex. Repeptization studies by dialysis do not yield accurate results because there exist sedimentation and multiple scattering effects. Repeptization was observed by PCS from 70 to 300 mM NaCl (Table 3). Potential energy curves (Fig. 8) were obtained with a Stern potential of 021.6 mV (as stated in literature, to match the experimental ccc with the zero potential maximum). However, some experimental results cannot be explained by these potential energy curves. First, the Stern potential of AS11 latex is lower than the Stern potential of the other latexes, when the surface charge density is very similar for all of them. Second, repeptization occurs for 250 and 300 mM NaCl (Table 3), while there is not a secondary minimum for these electrolyte concentrations (Fig. 8). These are the problems which can be expected from the existence of a deep secondary minimum in large particles. In these systems, the classical interpretation of ccc as the situation where potential barrier disappears seems to fail. If the secondary minimum is deep enough ( ú10kT ), a rapid aggregation regime can be achieved in this well, turning out as a experimental ccc (14). With these assumptions, a new plot of interaction potential as a function of distance is presented in Fig. 12. Data has been fitted to get a secondary minimum of 010kT for a salt concentration of 150 mM NaCl (ccc). At least qualitatively, this new representation is more in line with experimental results. For example, it explains the fact that repeptization is taking place at 250 and 300 mM NaCl, since these curves now present a secondary minimum able to retain particles in a flocculated state ( 013.05kT and
FIG. 10. Repeptization coefficient (R) of NaCl-induced aggregation as a function of NaCl concentration: ( h ) S4CS9 latex and ( l ) MP2 latex.
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PARTICLE SIZE EFFECTS ON REPEPTIZATION
FIG. 11. Aggregate average diameter (D) versus time for the system MP2: (a) 556 mM, (b) 300 mM NaCl; ( l ) dilution at 1070 s and ( h ) dilution at 2830 s.
014.63kT, respectively). Moreover, the Stern potential de- dialysis and by photon correlation spectroscopy. The small duced in this case is 024 mV, higher than in the original particles only aggregate into the primary minimum (coagulacalculations ( 021.6 mV) and closer to the values obtained tion). The larger particles also aggregate into the secondary for the rest of latexes ( 028 mV). minimum at low concentrations (flocculation) but coagulate at higher concentrations (primary minimum). Qualitatively, the features on the potential energy curves deduced from 4. SUMMARY DLVO theory explain these experimental observations, alFragmentation of aggregates induced by decreasing the though not for the large latex (661 nm in diameter). For this ionic strength of the suspending medium for four latexes with latex, the classical concept of ccc seems to fail. A new apdifferent size but similar surface charge has been studied by proach is presented, assuming that ccc can be also achieved when the secondary minimum is deep enough to ensure maximum effectiveness of collisions leading to aggregation. When the interaction potential is calculated in this way, better agreement with experimental results is obtained. The experimental dependence of colloidal stability on the particle size at constant potential cannot be described by the Reerink and Overbeek DLVO approximation. More suitable models, still within the bounds of the DLVO theory, are those taking into account aggregation at the secondary minimum. Phenomena like aggregate aging also demonstrates that these experiments cannot be interpreted on the basis of the DLVO theory only. ACKNOWLEDGMENTS This work was supported by the ‘‘Comisio´n Interministerial de Ciencia y TecnologıB a CICYT’’, Project MAT 96-1035-03-CO2. The authors are very grateful to J. Sarobe, J. Forcada, M. Servando, M. Quesada, and A. Schmitt by providing the latex samples. FIG. 12. Calculated total interaction potential (VT in kBT units) versus distance for AS11 latex: (1) 120, (2) 150, (3) 250, (4) 300, (5) 450, and (6) 801 mM, with Hamaker constant ( A) 1 1 10 020 J and Stern potential ( cd ) 024 mV.
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