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Langmuir 1997, 13, 3938-3943
Comparative Study on the Colloidal Stability Mechanisms of Sulfonate Latexes J. M. Peula,† A. Ferna´ndez-Barbero,‡ R. Hidalgo-A Ä lvarez,† and F. J. de las Nieves*,‡ Biocolloids and Fluid Physics Group, Department of Applied Physics, University of Granada, Granada 18071, Spain, and Group of Complex Fluid Physics, Department of Applied Physics, University of Almerı´a, Almerı´a 04120, Spain Received December 30, 1996. In Final Form: April 14, 1997X In this work the colloid stability mechanisms of two sulfonated latexes prepared by different methods are studied. One of the latexes (JM1) was prepared by surfactant-free emulsion copolymerization of styrene (St) and sodiun styrene sulfonate (NaSS), while the second latex (SN9) was prepared by a twostage “shot-growth” emulsion polymerization process using NaSS as ionic comonomer, which is included in a larger proportion in the second stage. The results are two latexes with nearly the same particle size but very different surface charge densities and, probably, one of them with a significant highly charged “hairy” surface. The anomalous electrokinetic behavior of the sulfonate polystyrene latexes was a consequence of their electric double-layer structure, and their high colloidal stability was not explained by the classical DLVO theory. This high colloidal stability could be a consequence of the hairy layer formed during the synthesis method (which includes the use of an ionic comonomer that can act as a polymerizable surfactant). By including several correction factors in the DLVO theory, such as the Stern layer thickness (ionic size) and the hydrodynamic interaction, a good correlation can be found between the theory and experimental results: the Hamaker constant value so obtained is equal to the theoretical one. If we try to explain the stability results by an electrosteric mechanism, it is possible to find a set of parameters which provide critical coagulation concentration (ccc) values which are in accordance with the experimental one; but, however, some controversies appear in relation to the values of some of the fitting parameters, because the Hamaker constant value is now lower than the theoretical one and the ions have to be dehydrated. Therefore, for the sulfonate latexes prepared by a “shot-growth” process, their high colloidal stability can be well explained by including some correction factors in the DLVO theory, and the use of a steric mechanism gives lower Hamaker constant values, which could mean that the hairy layer of these latexes does not seem to be large enough to produce a clear additional steric stabilization.
Introduction In the last decade, highly charged sulfonate latexes have received increasing interest as model polymer colloids, owing to the well defined and chemically stable functionality provided by the sulfonate group. Sulfonate polystyrene is an example of a latex with specific groups on the surface. This type of polymer colloid is prepared by a surfactant-free emulsion polymerization synthesis method where the pair styrene (St)/sodium styrene sulfonate (NaSS) is used. In this synthesis reaction the surfactant is replaced by a specific monomer that also introduces sulfonate groups on the particle surface. This functionality was selected to produce strong acid superficial end groups and to provide stability againts hydrolysis (Kolthoff reaction). Furthermore, using a shot-growth process makes it possible to prepare sulfonate latexes with independent control of the particle size and surface charge density through the variation of the NaSS amount in the second stage.1-3 The stability of suspensions, of proper importance in the study of systems as colloidal models, warrants detailed attention, since the development of different applications of these systems to biophysics, medicine, and modern technologies depends to a large extent on a better understanding of the colloidal interactions.4-7 Most * To whom correspondence should be addressed. † University of Granada. ‡ University of Almerı´a. X Abstract published in Advance ACS Abstracts, June 15, 1997. (1) Kim, J. H.; Chaney, M.; El-Aasser, M. S.; Vanderhoff, J. W. J. Polym. Sci., Polym. Chem. Ed. 1989, 27, 3187. (2) de las Nieves, F. J.; Daniels, E. S.; El-Aasser, M. S. Colloids Surf. 1991, 60, 107. (3) Tamai, H.; Niino, K.; Suzawa, T. J. Colloid Interface Sci. 1989, 131, 1.
S0743-7463(96)02135-X CCC: $14.00
applications require colloidal particles to remain dispersed within a relatively large range of electrolyte concentrations. For these reasons a large number of papers has been written about the mechanisms which can induce aggregation or stabilization. The shot-growth polymerization process employed to prepare the highly sulfonate latexes lead to a highly charged “hairy” surface, with high concentrations of specifically adsorbed counterions.2,3 The experimental results obtained by several authors2,8,9 for the electrokinetic characterization of this particles confirm this hypothesis. Thus, the colloidal properties are under the influence of this “hairy” layer. According to Seebergh and Berg,10 the thickness of the hairy layer may be as great as 7 nm. Zimehl et al.11 have suggested that hairy particles are just one of the several types which may be formed during emulsion polymerization. The highly sulfonate latexes present an anomalously high critical coagulation concentration (ccc) that cannot be explained using the classical DLVO theory.9,12 In fact, in a previous paper13 we compare the colloid stability of two sulfonate latexes (4) Van den Hul, H. J.; Vanderhoff, J. W. J. Electroanal. Chem. 1972, 37, 161. (5) Fleer, G. H.; Scheutjens, J. M. H. M. J. Colloid Interface Sci. 1986, 111, 504. (6) Norde, W.; Lyklema, J. J. Colloid Interface Sci. 1978, 66, 257. (7) El-Aasser, M. S. In Future Directions in Polymer Colloids; ElAasser, M. S., Fitch, R. M., Eds.; NATO-ASI Series E: Applied Science; Kluwer Academic Publishers: Dordrecht, 1987. (8) Chow, R. S.; Takamura, K. J. Colloid Interface Sci. 1988, 125, 226. (9) Bastos, D.; de las Nieves, F. J. Colloid Polym. Sci. 1994, 272, 592. (10) Seeberg, J. E.; Berg, J. C. Colloids Surf. A 1995, 100, 139. (11) Zimehl, R.; Lagaly, G.; Ahrens, J. Colloid Polym. Sci. 1990, 268, 924. (12) Peula, J. M.; Hidalgo-AÄ lvarez, R.; de las Nieves, F. J. J. Biomater. Sci., Polym. Ed. 1995, 7, 241.
© 1997 American Chemical Society
Colloidal Stability Mechanisms of Sulfonate Latexes
synthesized with and without a second injection of NaSS, and the latex with a higher surface charge density (prepared with the second injection) presented a behavior completely contrary to DLVO theory. This situation appears because the DLVO theory generally fails to predict the stability of hairy layer particles3,9,13 when the dispersion medium is water. Therefore, the colloidal stability of this type of latexes could be a consequence of a combination of electrostatic and steric effects. The extent of these effects could change during the synthesis, so that the final degree of steric or electrosteric stabilization would depend on the composition of the starting emulsion but also on the way the particles were prepared. Furthermore, the purification process can strongly change the characteristics of the particle surface and, as a consequence, the electric double layer (e.d.l.) structure and, therefore, the stabilization mechanisms. Up till the middle eighties, steric stabilization has only been considered from a qualitative point of view. In 1986 Vincent et al.14 proposed a theoretical equation useful for quantifying the extent of the steric stabilization mechanism. It was found that the stability of polymer colloids with polyelectrolytes or ionic surfactants adsorbed on the particle surface is also due to electrostatic and steric effects. The combined effect of these two mechanisms is known as electrosteric stabilization.15,16 Copolymerization of St and NaSS comonomers leads to a final dispersion stabilized by the electrostatic effect and, maybe, by the existence of a hydrophilic oligomer on the particle surface.9,13 In this paper we are very interested in the study of the colloidal stability mechanism of sulfonate latexes and apply the theory of electrosteric stabilization in comparison with the results from DLVO theory, including the corrections due to the ionic size and the hydrodynamic effect. With this aim, two latexes with different interfacial properties were prepared by surfactant-free emulsion polymerization. NaSS, to a large extent located on the surface of the particle, acts as a polymerizable surfactant, and therefore the colloidal stability of the NaSS copolymer latex could include the electrosteric mechanism. Thus, the main purpose of this work is to gain insight into the mechanisms of particle interactions and to obtain a better understanding of the effect of the interfacial properties on the stability of polymer colloids. Theoretical Background The stability factor W has been extensively used in the literature to characterize the stability of hydrophobic colloids. W is given as the ratio of the rate constants for rapid and slow coagulation kinetics, respectively. A typical experimental method developed to obtain W-values for a colloidal system is based on the study of the time evolution of the turbidity of a sample during an agglutination process. The experimental W-values can be used to calculate both the Hamaker constant (A), which characterizes the attraction between two particles, and the diffuse potential (ψd), which is related to the e.d.l. repulsion. This calculation can be carried out following different methods, which are briefly described below. Reerink and Overbeek,17 considering several approximations, showed a linear relationship between log W and log Ce, Ce being the electrolyte concentration in the bulk: (13) Peula, J. M.; Hidalgo-A Ä lvarez, R.; de las Nieves, F. J. Colloids Surf., A, in press. (14) Vincent, B.; Edwards, J.; Emment, S.; Jones, A. Colloids Surf. 1986, 18, 261. (15) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions; Academic Press: London, 1983. (16) Einarson, M. B.; Berg, J. C. J. Colloid Interface Sci. 1993, 155, 165. (17) Reerink, H.; Overbeek, J. Th. O. Discuss. Faraday Soc. 1954, 18, 74.
Langmuir, Vol. 13, No. 15, 1997 3939 log W ) -k′ log Ce + log k′′
(1)
where k′ and k′′ are constants. The slope of the stability curve, -d log W/d log Ce, is related to the radius of the particle, to the diffuse potential associated with the charged polymer surface, ψd, and to the electrolyte valence, z, by the expression
-d log W/d log Ce ) (2.15 × 109)aγ2/z2
(2)
where
γ ) tanh(zeψd /4kT) The Hamaker constant can be obtained experimentally from the slope of the stability curve and the critical coagulation concentration (ccc) of the latex. By use of a symmetrical electrolyte, the Hamaker constant can be obtained from the equation
A ) (1.315 × 10-21)(d log W/d log Ce)/az(ccc1/2)
(3)
Using the DLVO theory, the relation between the net interaction energy (V) and the stability factor was obtained by Fuchs18
exp
(kTV )
∫ (2a + H)
W ) 2a
∞
2
0
dH
(4)
where H is the distance between the boundary of two spheres and V is given by
V ) VR + VA ) 2π0a
( )
(
4kT 2 -κH A 2a2 γ e + ze 6 H(4a + H) 2
)
H(4a + H) 2a + ln 2 (2a + H) (2a + H)2
(5)
In the above expression 0 is the permittivity of the vacuum, is the dielectric constant of the electrolyte solution, e is the elementary charge, k is the Boltzmann constant, T is the absolute temperature, and κ is the Debye parameter, referred to as the reciprocal double-layer thickness. We have used the nonsimplified expression for the attractive potential.19 If the Stern layer thickness is considered, eq 5 must be modified, since, in the original DLVO theory, the reference planes for attractive and repulsive energy coincide. However, Vincent et al.20 refined this idea by shifting the reference plane for the repulsive energy outward over a distance corresponding to the thickness (∆) of the Stern layer. Taking into account this correction, the electrical double-layer repulsion between two equal spheres of radius a is given by
γ e (4kT ze )
VR ) 2π0(a + ∆)
2
-κ(H-2∆)
(6)
which should be introduced in eq 5. In addition to the colloidal forces between the particles, the hydrodynamic interaction effect can also diminish the coagulation rate. Spielman21 incorporated the viscous interaction between two spheres into the coagulation process. W can then be written as
∫
W ) 2a
( )
∞
0
D12∞ exp(V/kT) dH D12 (2a + H)2
(7)
where the Brownian diffusivity for the relative motion of two different particles (namely 1 and 2) is equal to D12 ) kT/f, with f the hydrodynamic resistance coefficient for the relative motion. The relative Brownian diffusion coefficient D12 depends on the (18) Fuchs, N. Z. Phys. 1934, 89, 736. (19) Overbeek, J. Th. O. Avd. Colloid Interface Sci. 1982, 16, 17. (20) Vincent, B.; Bijsterbosch, B. H.; Lyklema, J. J. Colloid Interface Sci. 1980, 37, 171. (21) Spielman, L. A. J. Colloid Interface Sci. 1970, 33, 562.
3940 Langmuir, Vol. 13, No. 15, 1997
Peula et al.
Table 1. Particle Size, Surface Charge Density, and Critical Coagulation Concentration (ccc) of Sulfonate Latexes latex
diameter (nm)
surface charge (µC/cm2)
ccc (pH ) 5) (mM)
ccc (pH ) 7) (mM)
JM1 SM9
195 ( 10 196 ( 10
-4.2 ( 0.6 -14.2 ( 1.2
360 ( 40 930 ( 30
366 ( 24 910 ( 40
Table 2. Diffuse Potential and Hamaker Constant Values (at Different Ionic Sizes) As Calculated by Using DLVO Theory sample pH JM1 SN9
viscosity, the particle dimensions, and the separation between particle centers. At large separations, D12 becomes equal to D12∞ ) D1 + D2, since there is no viscous interaction between them, D1 and D2 being the absolute diffusivity coefficients of each particle. The numerical evaluation of D12 has been performed using the formulas presented in the Appendix of Spielman’s article.21 To consider the viscous effect, the function D12/D12∞ must be included in the theoretical W expression. Vincent et al.14 made a quantitative study of the steric stabilization effect including two contributions: osmotic and coil compression. If there are polymeric chains covering the external surface of a particle, the average thickness of such coils being δ, then an osmotic effect will appear when the two particles are closer than a distance equal to 2δ. The osmotic pressure of the solvent in the overlap zone will be less than that in the regions external to it, leading to a driving force for the spontaneous flow of solvent into the overlap zone, which pushes the particles apart.22 In that case the osmotic potential of repulsion (Vosm) can be considered as
Vosm )
4πa 2 H φ (1/2 - χ) δ ν1 2
(
2
)
(8)
where ν1 is the molecular volume of the solvent, φ is the effective volume fraction of segments in the adlayer, and χ is the FloryHuggins solvency parameter. If, however, the two particles are closer than a distance equal to δ, at least some of the polymer molecules will be forced to undergo elastic compression. Thermodynamically, this compression corresponds to a net loss in configurational entropy. This effect gives rise to a new repulsion potential (Vvr) related to the restriction of the movement of the hydrophilic coils extended toward the solvent. This elastic-steric repulsion is given as
Vvr )
(
)( [ (
)]
2πa 2 H h 3 - H/δ ln φδ F2 MW δ δ 2
2
[
- 6 ln
]
3 - H/δ + 2 H 3 1+ (9) δ
(
))
where F2 and MW are the density and molecular weight of the adsorbed polymer. This modifies the osmotic potential, which is now given by
Vosm )
4πa 2 1 1 H H - χ δ2 φ - - ln ν1 2 2δ 4 δ
(
) [( )
( )]
(10)
For the electrosteric stabilization mechanism both effects (electrostatic repulsion and steric stabilization) must be combined. Conventionally, the total interaction energy is assumed to be the sum of all the attractive and repulsive potentials: V ) VR + VA + Vosm + Vvr. Nevertheless, this assumption of additivity (made in this work) has recently been questioned by Einarson and Berg,16 who claim that the electrostatic repulsion (VR) and the steric repulsions (Vosm and Vvr) are not totally independent.
Experimental Section Materials. Two sulfonate polystyrene latexes obtained by one shot-growth (JM1) and two shot-growths (SN9) were used in this work. More experimental details can be found in previous papers.2,13,23 The most important characteristics of both latexes, such as diameter and surface charge density, are summarized in Table 1. (22) Fischer, E. W. Z. Z. Polym. 1958, 160, 120. (23) Bastos, D.; de las Nieves, F. J. Colloid Polym. Sci. 1993, 271, 860.
5 7 5 7
ccc (mM)
ΨD (mV)
360 ( 40 366 ( 30 930 ( 30 910 ( 40
13.1 ( 0.23 14.6 ( 0.3 15.1 ( 0.3 15.8 ( 0.3
1020A (J) 1020A (J) ∆ ) 0.096 nm ∆ ) 0.372 nm 0.27 ( 0.04 0.29 ( 0.04 0.23 ( 0.03 0.25 ( 0.04
0.59 ( 0.07 0.61 ( 0.07 0.72 ( 0.08 0.79 ( 0.09
Methods. The colloidal stability of both latexes was evaluated with a Spectronic 601 spectrophotometer (Milton Roy, U.S.A.), by measuring the optical absorbance as a function of time for different electrolyte concentrations. In a typical coagulation experiment, 2.4 mL of a buffered latex solution was put into the spectrophotometer cell and the optical absorbance was measured. Then, 0.6 mL of a sodium chloride solution at a given concentration was quickly added and mixed automatically. The final particle concentration in the cell was 1010 particles/mL The optical absorbance was measured immediately and recorded continuously via computer for a period of 30 s. The initial slope of such a curve is directly proportional to the initial coagulation rate. Therefore, the stability can be expressed in terms of the stability factor W, obtained as the ratio of the rate constants for rapid and slow coagulation. The experimental values of the critical coagulation concentration (ccc) were determined as the electrolyte concentration that makes the stability factor equal to unity.9,24 The ccc values of both latexes at pH 5 and 7 are shown in Table 1. Results and Discussion First, the classical theory described previously was used to interpret the experimental results of the ccc shown in Table 1. Although the colloidal stability of both latexes is high, the SN9 latex, which was synthesized by a “shotgrowth” process, shows a higher stability in comparison with the JM1 latex, obtained by only one stage. To calculate the Hamaker constant and the diffuse potential from the experimental data, it is necessary to know the ionic size, ∆, for the adsorbed ions of the Stern layer. So, it is possible to take into account the degree of hydration for the counterion, Na+, used in the stability experiments. An important dependence between the A values calculated from experimental data and the value ascribed to ∆ was found by Bijsterbosch.25 Different sets of values for this parameter were used by this author to calculate the Hamaker constant in terms of DLVO theory. Thus, when the counterions were completely dehydrated, so that only the ionic radius has to be counted, the most likely situation was obtained. However, a situation of total or partial ionic hydration has been found by other authors.26-28 When this result was taken into account, both options, hydration and dehydration, were used in our calculations. Therefore, the distance between the solid surface and the center of the counterion (Na+) is 0.096 nm in the dehydrated state and 0.372 nm when the hydration remains.29 The A and ΨD values obtained from DLVO theory considering the ionic size are showed in Table 2. Similar values of these parameters were found at pH 5 and 7 for (24) Rubio-Hernandez, F. J.; de las Nieves, F. J.; Hidalgo-A Ä lvarez, R.; Bijsterbosch, B. H. J. Dispersion Sci. Technol. 1994, 15, 1. (25) Bijsterbosch, B. H. Colloid Polym. Sci. 1978, 256, 343. (26) Papenhuijen, J.; Fleer, G. J.; Bijsterbosch, B. H. J. Colloid Interface Sci. 1985, 104, 553. (27) Duckworth, R. M.; Lips, J. J. Colloid Interface Sci. 1978, 64, 311. (28) Grygiel, W.; Starzak, M. J. Lumin. 1995, 63, 47. (29) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworth Ltd.: London, 1959.
Colloidal Stability Mechanisms of Sulfonate Latexes
Figure 1. Interaction potentials for the JM1 latex (pH 5) at different NaCl concentrations: ∆ ) 0.372 nm; ΨD ) 13.1 mV; A ) 0.59 × 10-20 J.
both latexes. This is a consequence of the strong acid character of the surface groups. Futhermore, the diffuse potential values were very similar for both latexes although the SN9 latex has a higher surface charge density. This can be a consequence of a special structure in the surface of the SN9 latex synthesized using a “shotgrowth” process. The Hamaker constant values must be compared with the theoretical value for polystyrene in water. A value of 1.37 × 10-20 J was obtained by Prieve and Russel30 using the Lifshitz theory for the nonretarded Hamaker constant. This value decreases if the retarded interaction of two polystyrene particles separated by water, with and without electrolyte, is considered. A relation of this effect and the separation distance between particles is studied by the same authors. At a separation of 2 nm the A value decreases until (0.9-1) ×10-20 J. This parameter has been studied by several authors using different procedures,9,25,31,32 and the obtained values range between 0.4 and 0.9 × 10-20 J. A complete review of the different methods used for the calculation of this constant was accomplished by Visser.33 According to this author, a comparison of the theoretically calculated Hamaker constants with those derived from experiments shows that in a large number of cases the values from colloidal studies deviate substantially from the theoretically calculated ones. This difference is a clear consequence of the use of incomplete theories. As can be seen in Table 2, the A values obtained in this work by including the ion size in eq 6 are different depending on the ionic size (∆) value used. The Hamaker constant values were more similar to the theoretical one when the ions were considered in a hydrated situation. Using eqs 5 and 6, and the values of A and ΨD shown in Table 2, it is possible to calculate the interaction potential energy between particles as a function of the separation distance. The curves obtained at different electrolyte concentrations for the JM1 and SN9 latexes (with the characteristic parameter values indicated in the figure legends) are shown in Figures 1 and 2, respectively. The energy barrier that prevents the aggregation of the particles disappears at an electrolyte concentration lower than the ccc for both samples. Thus, the colloidal stability found for the JM1 and SN9 latexes can not be explained (30) Prieve, D. C.; Russel, W. B. J. Colloid Interface Sci. 1987, 125, 1. (31) Rowell, R. L. In An Introduction to Polymer Colloids; Candau, F., Ottewill, R. H., Eds.; Kluwer Academic Publishers: Dordrecht, 1990. (32) Gregory, J. Adv. Colloid Interface Sci. 1969, 2, 296. (33) Visser, J. Adv. Colloid Interface Sci. 1972, 3, 331.
Langmuir, Vol. 13, No. 15, 1997 3941
Figure 2. Interaction potentials for the SN9 latex (pH 5) at different NaCl concentrations: ∆ ) 0.372 nm; ΨD ) 15.1 mV; A ) 0.72 × 10-20 J.
Figure 3. Numerical computation of the stability factor for the JM1 latex: *, experimental data; O, theoretical data with eq 4; 0, theoretical data with eq 7. Fitting parameters: ∆ ) 0.096 nm; for A and ΨD see Table 3. Table 3. Characteristic Parameters of the Colloid Stability as Obtained by Theoretical Adjustment of the Experimental Stability Factor Values under Different Conditions by Numerical Computation ΨD (mV) and 1020A (J) values DLVO and ionic size (eq 6)
ΨD (mV) and 1020A (J) values hydrodynamic interaction (eq 7)
∆ (nm)
0.096
0.372
0.096
0.372
JM1
ΨD ) 22.5 A ) 0.46 ΨD ) 24.3 A ) 0.40
ΨD ) 23.9 A ) 1.15 ΨD ) 25.0 A ) 1.00
ΨD ) 23.1 A ) 0.62 ΨD ) 24.9 A ) 0.58
ΨD ) 24.7 A ) 1.45 ΨD ) 25.3 A ) 1.34
SN9
using this theoretical treatment, and additional considerations should be taken into account. The stability factor W can be computed by numerical integration using eq 4. In this way, it is necessary to fit a theoretical curve to the experimental points of log W versus log [NaCl], using a pair of values of A and ΨD as fitting parameters.34 The diffuse potential is related to the slope of this curve while the Hamaker constant depends on the ccc value. Thus, both can be used as independent fitting parameters.17 Figure 3 shows the experimental values of the stability factor and the theoretical ones as computed by using eq 4 but including the ion size in the repulsive potential. The A and ΨD values are shown in Table 3 for two ionic sizes and both latexes. (34) Honing, E. P.; Roebersen, G. J.; Wiersema, J. J. Colloid Interface Sci. 1971, 36, 97.
3942 Langmuir, Vol. 13, No. 15, 1997
Figure 4. Interaction potentials for the SN9 latex at different NaCl concentrations. ∆ ) 0.096 nm; ΨD ) 24.30 mV; A ) 0.40 × 10-20 J.
Peula et al.
Figure 5. Interaction energy between two particles with electrosteric stabilization.
We can evaluate the influence of the viscous interactions on the modified stability factor defined in eq 7 by using the equations presented in the Spielman article.21 Fernandez-Barbero et al.35 have found an important decrease in the modified diffusion coefficient when the particle separation is smaller than the particle radius. In the absence of repulsion, ignoring viscous interactions could lead to greatly erroneous values of the Hamaker constant obtained from stability experiments. A reasonable agreement between theoretical and experimental Hamaker constant values was found by these authors using the hydrodynamic correction. The Hamaker constant and diffuse potential values obtained by numerical computation of the stability factor with and without viscous interaction are shown in Table 3. The fit between experimental and theoretical data for the JM1 latex when ∆ ) 0.096 nm is also shown in Figure 3. As can be seen in Table 3, the diffuse potential values are again very similar for both latexes although they have very different surface charge densities. However, the most important notice is the possibility to obtain Hamaker constant values very close to the theoretical one when we include the hydrodynamic effect. Even if we do not consider the hydrodynamic interaction and include an ionic size of 0.372 nm, the A values were good, which indicates a more significant influence of the ionic size in comparison with the hydrodynamic effect, at least for these sulfonate latexes. Therefore, including in the DLVO theory the corrections due to the size of the hydrated ions and the hydrodynamics effects, we can explain the colloidal stability of the sulfonated latexes. The problem of the colloid stability of latexes considered as “hairy” latexes, can be addressed by the study of the interaction potential energy between particles as a function of the separation distance and including some electrosteric effects.36 In that way Ortega-Vinuesa et al.36 explained the colloidal stability of a hydrophilic (PSHEMA) latex. We have tried to use this type of treatment to check if the colloid stability of the SN9 latex could be due to an additional steric stabilization, as a consequence of the presence of a hairy layer on the surface of these particles. Figure 4 shows the interaction potential energies for the SN9 latex at different electrolyte concentrations using the A, ΨD, and ∆ values from Table 3. There are important
differences in the energetic aspect, because the energy barrier disappears at a NaCl concentration much lower than the experimental ccc. In Figure 4 we use the A and ΨD values which correspond to a ∆ value of 0.096 nm, but if we use the A and ΨD values calculated when ∆ ) 0.372 nm, the theoretical ccc is even lower. For latex SN9 the electrostatic repulsive contribution cannot justify a ccc of 900 mM, the experimental value. These latex particles could have an additional mechanism of stabilization to reach so high a ccc value. This mechanism could be a consequence of the “shot-growth” polymerization method used for the synthesis, which produces a layer of oligomers or polyelectrolytes chemically bound on the particle surface. In this case the stability is a combination of two mechanisms, electrostatic and steric contributions, i.e., an electrosteric stabilization. For this type of stabilization, the total interaction energy is obtained by the combination of an attractive and three repulsives terms: electrostatic, osmotic, and elastic. Figure 5 shows all the energy contributions as a function of the separation distance between the particles, and the total interaction potential energy which controls the aggregation process. We have used this electrosteric stabilization mechanism to explain the stability behavior of the SN9 latex. First, a numerical computation of the stability factor has been done using eq 4, where the total interaction potential includes the steric contributions. If eqs 8-10 are used, it is necessary to know the value for the solvency parameter, χ, the thickness of the oligomeric layer, δ, and the volume fraction occupied for these segments, φ. The Flory-Huggins solvency parameter is tabulated for a lot of polymers in different solvents;37 according to Papenhuijen et al.,26 for the sulfonated polystyrene in water, if χ > 0.5, the dispersion medium is a bad solvent for the polymeric molecules and an attraction will occur between the steric layers. Only when χ < 0.5, is the dispersion medium a good solvent and the steric repulsion operative.38 Depending on the source of our oligomers (latex synthesis method), χ has to be around 0.45, slightly below the critical value (0.5). The thickness and the volume fraction were used as fitting parameters. The best fit between the theoretical and the experimental stability factors was obtained with δ ) 0.9 nm and φ ) 0.1. This situation corresponds with oligomers of NaSS of four units and a molecular weight of 730 g/mol. These values would be in agreement with
(35) Fernandez-Barbero, A.; Martin, A.; Callejas, J.; Hidalgo-A Ä lvarez, R. J. Colloid Interface Sci. 1994, 162, 257. (36) Ortega-Vinuesa, J. L.; Martı´n-Rodrı´guez, A.; Hidalgo-Alvarez, R. J. Colloid Interface Sci. 1996, 184, 259.
(37) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: New York, 1953. (38) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, 1986; Vol. 1.
Colloidal Stability Mechanisms of Sulfonate Latexes
Figure 6. Numerical computation of the stability factor for the SN9 latex with an electrosteric mechanism of stabilization: 0, experimental data; O, theoretical data by eq 4 including the contributions from eqs 9 and 10. Fitting parameters: ∆ ) 0.096 nm; A ) 0.78 × 10-20 J; ΨD ) 24.75 mV; δ ) 0.9 nm; φ ) 0.1.
Figure 7. Interaction potentials for the SN9 latex at different NaCl concentrations. ∆ ) 0.096 nm; ΨD ) 24.75 mV; A ) 0.78 × 10-20 J; δ ) 0.9 nm; φ ) 0.1.
the origin of these oligomers. Figure 6 shows the good agreement between the theoretical and experimental log W/log [NaCl] curves. The value obtained for the Hamaker constant value (0.78 × 10-20 J) is near the theoretical one, although it is lower than that obtained in Table 3 by including the ionic size. Figure 7 shows the total interaction potential energy as calculated with these parameter values, for different electrolyte concentrations. The energy barrier disappears at a concentration of 900 mM, which is similar to the experimental ccc of this latex. Using, therefore, a theoretical model that takes into
Langmuir, Vol. 13, No. 15, 1997 3943
account an electrosteric mechanism of stabilization, it is possible to explain the high colloidal stability of this sulfonate latex from an energetic point of view. But in this case the Hamaker constant value is 0.78 × 10-20 J, while in Table 3 the A value was 1.34 × 10-20 J for the same latex when the hydrodynamic interaction and the ionic size were taken into account as correction factors of the DLVO theory. These results with hairy latexes and the influence of the hydration layer due to the ionic size could be in agreement with those recently found by Wu and van de Ven.39 These authors have indicated that the hairy latexes do not present steric stabilization due to the hairy layer. Instead, a layer of immobilized water in the hairy layer effectively lowers the Van der Waals interactions, thus increasing the relative importance of electrostatic repulsion. In short, we have tried to explain the high colloidal stability of sulfonated polystyrene latexes as a consequence of the special structure of the e.d.l. formed during the synthesis method. By including several correction factors in the DLVO theory, such as the ionic size and the hydrodynamic effect, the correlation between theory and experiment seems to be very good and we can obtain a Hamaker constant value which is equal to the theoretical one. If we try to explain the stability results by an electrosteric mechanism, it is possible to find a set of parameters which provide ccc values which are in accordance with the experimental one; but, however, some controversies appear in relation with the values of some of the fitting parameters, because the Hamaker constant value is lower than the theoretical one and the ions have to be dehydrated. Therefore, for the sulfonated latexes prepared by a “shot-growth” process, their high colloidal stability can be well explained by including some correction factors in the DLVO theory. If we try to use an electrosteric mechanism, the Hamaker constant has to take a value lower than the theoretical one, which could mean that the hairy layer of these latexes (if it exists) does not seem to be large enough to produce a clear additional steric stabilization. Acknowledgment. The financial support from Comisio´n Interministerial de Ciencia y Tecnologı´a (CICYT), under project MAT96-1035-C03-03, is gratefully acknowledged. The authors wish to express their gratitude to Dra. Delfina Bastos for kindly supplying the SN9 latex. LA962135H (39) Wu, X.; Van de Ven, T. G. M. Langmuir 1996, 12, 3859.
