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Effect of Polymeric Adlayers on Heteroaggregation Kinetics Anthony Y. Kim and John C. Berg* Department of Chemical Engineering, University of Washington, Seattle, Washington 98105 Received November 20, 2001. In Final Form: February 18, 2002 An interesting, hitherto unreported phenomenon involving interactions between polymer-coated, oppositely charged colloids is investigated experimentally and theoretically. Experimental stability for heteroaggregation of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) coated, oppositely charged polystyrene spheres is quantified as a function of monovalent salt concentration by dynamic light scattering and compared with a primitive extension of DLVO theory, where the average volume fraction of polymer in the adlayers is used as the adjustable parameter. The energy barrier to aggregation is predicted to increase with increasing electrolyte concentration, behavior exactly opposite that of an electrostatically stabilized colloid. Two regions of heterostability may be defined: (1) at low ionic strength, stability ratios are less than unity and independent of triblock molecular weight, and (2) at moderate to high ionic strength, stability ratios exceed unity and depend on the triblock molecular weight. A critical salt concentration delineating these two regions may be identified, below which aggregation is more rapid than diffusion alone would allow and above which the heterodispersion becomes increasingly stable, reaching full stability for high molecular weight triblock adlayers.
Introduction Poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymers (PEO/PPO/PEO) are an important class of materials for modifying the chemistry of surfaces1 and stability of colloids.2 These macromolecular surfactants adsorb to hydrophobic surfaces via their hydrophobic PPO blocks. The solvated PEO groups impart a repulsive, steric component to interactions between coated surfaces. Much information has been established on electrosterically stabilized colloids (i.e., electrostatically stabilized colloids with polymeric adlayers). Adsorption isotherms and adlayer thicknesses for several commercial PEO/PPO/PEO copolymers (PLURONIC series from BASF) on polystyrene spheres in water have been measured.3 Adlayers having a relatively low molecular weight triblock (MWPEO ) 650) caused the critical coagulation concentration for negatively charged polystyrene spheres to increase nearly an order in magnitude, while triblocks of somewhat higher molecular weight (MWPEO ) 1000) increased the stability 100-fold, eliminating rapid aggregation altogether for monovalent electrolyte concentrations as high as 2 M.4 For a mixture of triblocks (MWPEO ) 650 and MWPEO ) 10750), the larger molecular weight triblock preferentially adsorbed to the particle surface, and only a minor amount of the larger copolymer (1 wt % of the adlayer) was required for complete steric stabilization at high electrolyte concentration.5 The stability of electrosterically stabilized colloids has also exhibited a minimum as a function of electrolyte concentration, depending on the triblock molecular weight and electrolyte species.4,6 While much is known about the effect of polymeric adlayers on the stability of similarly charged particles, an examination of their effect on oppositely charged particles does not appear in the literature. (1) Amiji, M. M.; Park, K. J. Appl. Polym. Sci. 1994, 52, 539. (2) Napper, D. H.; Netschey, A. J. Colloid Interface Sci. 1971, 37, 528. (3) Baker, J. A.; Berg, J. C. Langmuir 1988, 4, 1055. (4) Einarson, M. B.; Berg, J. C. Langmuir 1992, 8, 2611. (5) Stenkamp, V. S.; Berg, J. C. Langmuir 1997, 13, 3827. (6) Stenkamp, V. S.; McGuiggan, P.; Berg, J. C. Langmuir 2001, 17, 637.
In this Letter, we report experimental stability measurements for mixtures of triblock-coated, oppositely charged particles as a function of background electrolyte concentration. The effect of triblock molecular weight on stability was also investigated. Experimental stabilities are interpreted in terms of a simple extension of DLVO theory7 with slight modifications, and reasonable agreement between theory and experiment is obtained. These results highlight the delicate balance between van der Waals, electrostatic, and steric interactions in determining stability. In this case, stability increases with electrolyte concentration, and a critical salt concentration can be identified beyond which full stability may be reached. This contrasts with the more familiar critical coagulation concentration for an electrostatically stabilized suspension, beyond which rapid aggregation occurs. Background The stability ratio, Wij, is the inverse collision efficiency for two colliding particles i and j to permanently stick together. It is defined as the ratio of the rapid aggregation rate constant to the measured rate constant for doublet formation
Wij )
krapid kij,meas
(1)
where krapid is the reference rate constant, which may be calculated from Smoluchowski’s equation for diffusionlimited aggregation or evaluated for an electrostatically stabilized colloid at high salt concentration (the approach used in this research). A stability ratio of unity implies diffusion-limited aggregation. A stability ratio less than unity indicates aggregation faster than that due to diffusion alone, as predicted8 and observed9 for oppositely (7) Einarson, M. B.; Berg, J. C. J. Colloid Interface Sci. 1993, 155, 165. (8) Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Trans. Faraday Soc. 1966, 62, 1638. (9) Ryde, N.; Matijevic, E. J. Chem. Soc., Faraday Trans. 1994, 90, 167.
10.1021/la015690e CCC: $22.00 © 2002 American Chemical Society Published on Web 03/27/2002
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Langmuir, Vol. 18, No. 9, 2002 3419
charged particles at low ionic strength, where aggregation is driven by electrostatic attraction superimposed on diffusion. Hogg, Healy, and Fuerstenau proposed an equation for the overall stability ratio for heteroaggregation, Wtot, accounting for homoaggregation (1-1 and 2-2) and selective heteroaggregation (1-2) events8
X12 X22 2X1X2 1 ) + + Wtot W11 W22 W12
(2)
where Xi is the fraction of total particles of type i, Wii is the homoaggregation stability ratio for particle i, and W12 is the stability ratio for selective heteroaggregation between particles 1 and 2. Equation 2 follows directly from eq 1 and the overall rate constant for doublet formation
ktot ) k11X12 + k22X22 + 2k12X1X2
(3)
where k11, k22, and k12 are the rate constants for 1-1, 2-2, and 1-2 doublets, respectively. Theoretical stability ratios may be calculated from knowledge of the total interparticle interaction potential. In the absence of a secondary minimum or in the case of a secondary minimum but infinite barrier to the primary minimum, the stability ratio may be calculated by integration of the total interparticle potential, Vij10
[ ]
Vij ∞ 1 dr Wij ) 2a 2a 2 exp kT r
∫
(4)
Equation 4, due to Fuchs, is a steady-state solution of a modified diffusion equation and, therefore, cannot account for accumulation of particles at a secondary minimum.11 When primary and secondary minimum aggregation occur simultaneously, the kinetic approach of Marmur,11 as modified by Wang,12 may be used to estimate the stability ratio. The equations of Wang are relatively simple to implement, requiring only the height of the energy barrier to the primary minimum, ∆Vmax, and the depth of the secondary minimum, Vmin (Figure 1). The aggregation kinetics, therefore, reflect the total interaction potential through Wij. Evaluation of the interaction potential has its foundations in the theory of Derjaguin and Landau and Verwey and Overbeek (DLVO theory), which assumes that the total potential energy of interaction for two particles can be represented by the sum of van der Waals and electrostatic potentials. To account for screening and retardation of van der Waals interactions, it is useful to divide the potential into zero- and nonzero-frequency terms. For spheres of equal size, the screened, zerofrequency component is
[
Aν)0(2κH)e-2κH 2a2 + VvdW,ν)0 ) 6 H2 + 4Ha 2a2 H2 + 4Ha + ln H2 + 4Ha + 4a2 H2 + 4Ha + 4a2
(
)]
(5)
where Aν)0 ) 2.7 × 10-21 J is the zero-frequency component of the nonretarded Hamaker constant for polystyrene (10) Shaw, D. J. Introduction to Colloid and Surface Chemistry, 3rd ed.; Butterworth: London, 1980. (11) Marmur, A. J. Colloid Interface Sci. 1979, 72, 41. (12) Wang, Q. J. Colloid Interface Sci. 1991, 145, 99.
media interacting across water calculated based on Lifshitz theory,13 a is the sphere radius, κ is the Debye screening parameter, and H is the surface-to-surface separation. The terms involving κ account for screening of the essentially electrostatic zero-frequency interaction.13,14 The retarded, nonzero frequency (dispersion) component is calculated using the empirical formula of Gregory,15 based on the Casimir-Polder theory
VvdW,ν>0 ) -
Aν>0a 5.32H λ ln 1 + 112H λ 5.32H
[
)]
(
(6)
where Aν>0 ) 1.08 × 10-20 J is the dispersion component of the nonretarded Hamaker constant for polystyrene across water calculated based on Lifshitz theory13 and λ is the characteristic wavelength, assumed to be 100 nm. The electrostatic energy is calculated for spheres of constant surface charge density using the expression of Wiese and Healy (WH),16 viz.
Vel,WH )
[
π0a(ψ012 + ψ022)
2ψ01ψ02
2
(ψ012 + ψ022)
ln
(
]
)
1 + exp(-κH) - ln(1 - exp(-2κH)) (7) 1 - exp(-κH)
where ψ0i is the surface potential of sphere i at infinite separation, is the dielectric constant of water, and 0 is the permittivity of vacuum. DLVO theory can be extended to account for steric interactions by adding “non-DLVO” terms to the total interaction potential.7 Repulsive, steric interactions due to polymeric adlayer overlap arise from two factors: mixing of the polymer adlayers (an osmotic pressure effect) and elastic compression (an entropic effect). Two regions of interaction are defined in terms of the adlayer thickness, δ: interpenetrational domain (δ < H < 2δ) and interpenetrational-plus-compressional domain (0 < H < δ). As the opposing adlayers just begin to overlap (interpenetrational domain), the local polymer concentration between the surfaces increases, causing an osmotic pressure difference and net flow of solvent inward. On the basis of Flory-Krigbaum theory, an equation for the osmotic component of the steric energy has been derived17
VosmI )
4πakT H 1 (φp)2 - χ δ vs 2 2
(
)(
2
)
(8)
where k ) Boltzmann constant, T ) temperature, vs ) molecular volume of the solvent, φp ) volume fraction of polymer in the adlayer, and χ is the Flory-Huggins interaction parameter. As the surfaces approach to within one adlayer thickness (interpenetrational-plus-compres(13) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: San Diego, CA, 1992. (14) Mahanty, J.; Ninham, B. W. Dispersion Forces; Academic Press: New York, 1976. (15) Gregory, J. J. Colloid Interface Sci. 1981, 83, 138. (16) Wiese, G. R.; Healy, T. W. Trans. Faraday Soc. 1970, 66, 490. (17) Vincent, B.; Edwards, J.; Emmett, S.; Jones, A. Colloids Surf. 1986, 18, 261.
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Figure 1. Total potential energy curves for triblock-coated, oppositely charged polystyrene spheres at different monovalent electrolyte concentrations (a ) 150 nm, ψ01 ) -ψ02 ) 75 mV, δ ) 4.5 nm, φp ) 0.03). The barrier to primary minimum coagulation, ∆Vmax ) Vmax - Vmin, is indicated for 500 mM.
sional domain), elastic compression of the polymer chains contributes an additional term17
[ ( ( )) ( ) ( )]
H 2 36πakTδ2Fp(φp) H H δ I+C ln Vcomp ) MWp 3δ δ 2 H 3H δ + 12 ln 2 δ
(9)
where Fp and MWp are the density and molecular weight (mass per molecule) of the polymer in the adlayer. The osmotic contribution takes the form17
VosmI+C )
4πaδ2kT 1 H 1 H - - ln (φp)2 - χ vs 2 2δ 4 δ
(
)[
( )]
(10)
Total interparticle potential energy curves may be generated by combining eqs 5-10:
Vij ) VvdW,ν)0 + VvdW,ν>0 + Vel,WH + VosmI + VcompI+C + VosmI+C (11) Figure 1 shows potential energy curves for triblockcoated, oppositely charged polystyrene particles at different monovalent electrolyte concentrations calculated using eq 11. Typical values for the polymer adlayer thickness (δ ) 4.5 nm), volume fraction of polymer in the adlayer (φp ) 0.03), and χ-parameter were taken from Seebergh and Berg, with the increase in χ (decrease in solvency) with increasing salt concentration also taken into account.18 A PEO molecular weight of 950, corresponding to PLURONIC L35, surface potentials of +75 and -75 mV, and particle radii of 150 nm were used for the calculations. At 20 mM monovalent electrolyte, the potential energy becomes more negative as the separation distance is reduced; therefore the aggregation is spontaneous. At higher electrolyte concentrations, an energy barrier to aggregation into the primary minimum arises, and the magnitude of the barrier increases with salt concentration, behavior exactly opposite that of an electrostatically stabilized colloid. By 500 mM, the height of the energy barrier is about 15 kT. A secondary minimum is also observed, the depth of which is about 1.8 kT. While the electrostatic contribution to the total potential shows the largest change in absolute value as the salt concentration is increased, the dependence of the osmotic term on salt (through the χ-parameter) is important to the (18) Seebergh, J. E.; Berg, J. C. Langmuir 1994, 10, 454.
Figure 2. Measured stabilities for L35-coated, oppositely charged polystyrene spheres as a function of monovalent electrolyte concentration. Selective stability, W12, is calculated from Wtot and W22 using eq 2 with W11 set to infinity. Error bars on W12 represent minimum and maximum values based on one standard deviation in measured values of krapid, k22, and ktot.
location and value of the maximum in the total potential energy curve. Qualitatively, the stability of triblock-coated, oppositely charged particles should increase as the salt concentration is increased, since the interaction energies become less negative and the height of the barrier to primary coagulation increases. Experimental Section Particles were surfactant-free, sulfate- and amidine-functionalized, 120-nm diameter polystyrene spheres from Interfacial Dynamics Corporation, Portland, OR. According to the manufacturer, the negative latex (IDC 1-100, batch 10-294-19,1) had a parking area of 1033 Å2/SO4, and the positive latex (IDC 3-100, batch 792) had a parking area of 198 Å2/amidine. Triblock adlayers were formed by equilibrating N ) 1 × 109 cm-3 spheres with 500 µg/mL triblock for at least 40 h. Adlayer thicknesses were determined by hydrodynamic size measurements on bare and coated spheres in the absence of added electrolyte. Two commercial triblocks from BASF, Mount Olive, NJ, were investigated: (1) PLURONIC L35 with an average total MW ) 1900 and PEO MW ) 950, and (2) PLURONIC F108, average total MW ) 14000 and PEO MW ) 10750. Overall rate constants, ktot, for doublet formation were calculated from the initial slope of hydrodynamic diameter versus time, as measured by dynamic light scattering.19 Indifferent electrolyte concentration was varied from 0 to 200 mM KNO3. Since the L35-coated positive latex underwent some aggregation above 10 mM KNO3, rate constants for homoaggregation, k22, were also measured. Average rate constants were calculated from at least three replicate measurements (except k22 at 10 mM KNO3, which was based on a single measurement). Final particle number density was 5 × 108 cm-3, number ratio of positive-to-negative particles was 1, and triblock concentration was 250 µg/mL for all experiments, except for determination of krapid, the rate constant for aggregation of bare particles at 1 M KNO3. Measured rate constants were used to calculate overall stability ratios, Wtot, and stability ratios for selective heteroaggregation of oppositely charged particles, W12.
Results and Discussion Indeed, the stability to heteroaggregation of L35-coated, oppositely charged particles increases as KNO3 concentration is increased, as shown in Figure 2. Stability ratios were calculated from average rate constants using eqs 1, 2, and 3. The adlayer thicknesses were found to be 3.7 and 5.7 nm for the triblock-coated negative and positive spheres, respectively. The triblock-coated negative latex showed negligible aggregation over this salt concentration range, while the coated positive latex underwent homoaggregation above 10 mM monovalent salt (measurable W22). This indicates a dramatically different polymer (19) Virden, J. W.; Berg, J. C. J. Colloid Interface Sci. 1992, 149, 528.
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Figure 3. Comparison of selective stabilities, W12, for L35and F108-coated, oppositely charged polystyrene spheres as a function of monovalent electrolyte concentration. Error bars for F108 represent minimum and maximum values based on one standard deviation in measured values of krapid and k12.
configuration on the positive particles, possibly related to hydrogen bonding between amidine and PEO groups. The stability for selective heteroaggregation, W12, increases with KNO3 concentration, as anticipated, and essentially tracks the overall stability, Wtot. Below 1 mM KNO3, W12 is less than 1, indicating selective aggregation faster than that allowed by diffusion alone. At low ionic strength, strong attractive electrostatic interactions are superimposed on diffusion, enhancing the aggregation rate. As the ionic strength is increased, attractive electrostatic interactions are reduced, and steric, repulsive interactions due to overlapping adlayers become more important, causing the stability to increase. Below 10 mM KNO3, only selective heteroaggregation events occur, however there may be situations where selective heteroaggregation is desired at higher electrolyte concentrations. One way to improve homoaggregation stability is to increase the molecular weight of the triblock. The PEO chains of PLURONIC F108 are over 10 times as large as L35 in mass. F108 adlayer thicknesses were determined to be 13.9 and 12.7 nm, for the negative and positive spheres, respectively, or about 8 nm higher than for L35. F108 adlayers prevented any homoaggregation up to 200 mM KNO3, so that separate experiments were not necessary to evaluate the selective stability ratio from the overall stability. Figure 3 compares the effect of PLURONIC L35 and F108 adlayers on the selective stability. At low ionic strength, the stabilities are identical within experimental error. When attractive electrostatic interactions are strong, the molecular weight of the adlayer does not appear to affect heterostability. As salt is increased, the stability increases in both cases, reflecting the increasing importance of steric repulsion as the attractive electrostatics are screened. The most striking difference is where the stability crosses over to values above 1, where aggregation becomes slow relative to diffusion-limited aggregation. The crossover for L35-coated spheres occurs near 100 mM KNO3, while for F108 it occurs at much lower salt, between 1 and 6 mM. The thicker adlayers of F108 result in steric interactions at larger separation distances, so that less electrostatic screening is required for steric interactions to dominate. The error bars begin to diverge for stability ratios above 1, since the change in average size is small relative to background, and stabilities of the F108-coated, oppositely charged particles at 10 and 20 mM KNO3 are much higher, as indicated by the arrows. Experimental stability ratios show the importance of electrolyte concentration and triblock molecular weight in determining
Langmuir, Vol. 18, No. 9, 2002 3421
Figure 4. Comparison of selective stabilities, W12, for L35and F108-coated, oppositely charged polystyrene spheres with theory. Error bars are shown for both L35 and F108. Table 1. Summary of Stability Ratio Modeling adlayer MWPEO δ (nm) φp (fit) CHC (mM) κ-1CHC (nm) κδCHC
PLURONIC L35 950 4.7 0.0316 85 1.0 4.7
PLURONIC F108 10,750 13.3 0.0167 5 4.3 3.1
heterostability. Theoretical modeling would be helpful to explain these data and predict the behavior of new systems. For each triblock, the effective volume fraction of polymer in the adlayer, φp, was found by fitting the bestdefined stability ratio above unity to the Wang model with the aid of eq 11. Surface potentials were taken to be equal to the zeta potentials of the bare spheres without added electrolyte (ψ01) -89 mV and ψ02 ) +120 mV), as calculated from electrophoretic mobility measurements and the method of O’Brien and White20 (MACMOBILITY program, University of Melbourne, Australia). Since polymeric adlayers can impact the zeta potential by changing the surface potential and location of the surface of slip, this is certainly a crude approximation. Although improvements to the model might be gained by using zeta potentials of the polymer-coated particles, this would add a degree of complexity without fully accounting for the electrostatic interactions during adlayer overlap. Average adlayer thicknesses of δ ) 4.7 and 13.3 nm for L35 and F108, respectively, and an average radius a ) 72 nm were used, based on hydrodynamic size measurements. For L35, φp is 3.2 vol %, and for F108, it is half that value, in qualitative agreement with expectations; random motions of higher molecular weight chains sweep out relatively more space per unit volume. Theoretical stability curves were then generated for each system over the entire salt concentration range. Figure 4 compares the experimental selective stabilities with theory, and Table 1 summarizes the findings. Agreement is good for both systems. The large difference between model and experiment for the F108-coated spheres at high electrolyte is related to the difficulty in measuring stability ratios above 1. In general, two regions of stability behavior may be defined. First, at low salt concentrations, stabilities are less than unity, reflecting enhancement of aggregation over diffusion by attractive interactions between the oppositely charged particles. Increasing the salt concentration causes only a modest increase in stability. In this region, attractive electrostatic interactions prevail, and the molecular weight of the (20) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1607.
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adlayer has little to no effect on the heterostability. The second region is marked by a steep increase in the stability with added electrolyte. (Stability is predicted to decrease above 400 mM KNO3 as the PEO groups become insoluble.) From the intersection of these two regions, a critical heteroaggregation concentration, or CHC, can be identified, below which extremely rapid heteroaggregation occurs and above which the suspension becomes stable. The CHC is 85 and 5 mM for L35 and F108, respectively (Table 1). Heterostability of polymer-coated, oppositely charged particles requires that the thickness of the double layer, κ-1, be reduced to about 25% of the adlayer thickness, or κδ ) 3-5. Conclusions Polymer-coated, oppositely charged colloids exhibit remarkable behavior, where stability of the mixed dispersion increases with added electrolyte, exactly opposite the
Letters
behavior of an electrostatically stabilized colloid. At low ionic strength, where attractive electrostatic and van der Waals interactions dominate over steric repulsions, heteroaggregation occurs faster than diffusion would normally allow. As the electrostatic interactions are screened, steric repulsions become increasingly important, and the stability increases. Beyond a critical salt concentration, a sharp increase in stability occurs. A primitive extension of DLVO theory captures the essence of the observed stabilities. Acknowledgment. The authors thank the Intel Foundation and the Center for Surfaces, Polymers, and Colloids at the University of Washington for financial support. LA015690E
