Flocculation of Microgel Particles with Sodium Chloride and Sodium

800 mM NaCl and over the temperature range 25-60 °C. The critical flocculation temperature (CFT) of the particles was determined as a function of NaC...
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Articles Flocculation of Microgel Particles with Sodium Chloride and Sodium Polystyrene Sulfonate as a Function of Temperature Mikael Rasmusson,† Alex Routh,‡ and Brian Vincent* School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom Received January 11, 2004 The flocculation behavior of poly(N-isopropylacrylamide) (PNIPAM) microgel particles, containing surface sulfate groups, has been studied as a function of sodium chloride [NaCl] concentration, between 0.1 and 800 mM NaCl and over the temperature range 25-60 °C. The critical flocculation temperature (CFT) of the particles was determined as a function of NaCl concentration. Three regions of NaCl concentration were established. First, at very low values of [NaCl] (∼100 mM), the electrostatic repulsion is screened out, and the CFT decreases linearly with [NaCl]. The reason for this decrease is the fact that aqueous solutions of NaCl become increasingly poorer solvent environments for PNIPAM with increasing [NaCl]. These trends are apparent also in the values determined for the hydrodynamic size of the stable PNIPAM particles as a function of [NaCl] and temperature. It is shown that the flocculation of the PNIPAM particles is consistent with a weak, reversible flocculation model. This is apparent, for example, from the fractal dimensions of the flocs (∼2.0), determined from the power law used to fit the time evolution of the hydrodynamic size of the flocs, and also from the estimated depth of the mimimum in the interparticle pair potential, based on the critical size of the primary particles where flocculation just begins to occur. The effect of adding sodium poly(styrene sulfonate) [PSS] to the PNIPAM dispersions, in the absence of NaCl, was also investigated. The minimum amount of PSS required to induce flocculation was found to decrease with increasing temperature.

Introduction Aqueous microgels are receiving growing attention due to their many potential applications, as well as their theoretical interest. Three recent review papers1-3 demonstrate the growing body of work within this field. The majority of the microgel systems that have been studied have been based on poly(N-isopropylacrylamide) (PNIPAM) or related copolymers, which exhibit both temperatureand salt-sensitive properties. In the high molecular weight limit, linear PNIPAM has a lower critical solution temperature (LCST) in water at about 32 °C.4,5 The transition temperature for swelling/ deswelling of PNIPAM microgel particles in water has, in general, been found to be slightly higher, up to 35 °C,1-3 depending on the degree of cross-linking. The average subchain length within the microgel becomes shorter the higher the degree of cross-linking.6 Another important difference is that the swelling/deswelling transition of †

Current address: AstraZeneca R&D, Mo¨lndal, S 43183, Sweden. Current address: Chemical and Process Engineering, University of Sheffield, Sheffield, S1 3JD, U.K.

microgel particles with increasing temperature is less sharp than for the linear polymer.6,7 The stability of PNIPAM microgels to aggregation has not been investigated to date as thoroughly as one might have expected. Pelton and Chibante8 studied the critical flocculation temperature (CFT) of PNIPAM microgel particles in the presence of CaCl2. Snowden and Vincent9 monitored the turbidity of PNIPAM microgel dispersions as a function of temperature. It was found that the CFT decreased with increasing concentration of NaCl. Zhu and Napper10,11 studied the aggregation kinetics of polystyrene core/PNIPAM shell latex particles. Aggregation was induced by adding different electrolytes, and some unexpected specific ion effects were observed. Duracher et al.12,13 investigated the stability of cationic polystyrene core/PNIPAM shell latex particles, below and above the LCST. They also determined the electrophoretic mobility of the particles below the LCST, which allowed them to calculate the effective Hamaker constant from the critical flocculation data. Duracher et al.14 have also

‡

(1) Saunders, B. R.; Vincent, B. Adv. Colloid Interface Sci. 1999, 80, 1. (2) Pelton, R. Adv. Colloid Interface Sci. 2000, 85, 1. (3) Saunders, B. R.; Vincent, B. Encyclopedia of Surface and Colloid Science; Hubbard, A. T., Ed.; Marcel Dekker: New York, 2002; p 4544. (4) Heskins, M.; Guillet, J. E. J. Macromol. Sci. (A2) 1968, 8, 1441. (5) Schild, H. G. Prog. Polym. Sci. 1992, 17, 163. (6) Wu, C.; Chou, S.; Au-Yeung, S. C. F.; Jiang, S. Angew. Makromol. Chem. 1996, 240, 123.

(7) Wu, C. Polymer 1998, 39, 4609. (8) Pelton, R. H.; Chibante, P. Colloids Surf., A 1986, 20, 247. (9) Snowden, M. J.; Vincent, B. J. Chem. Soc., Chem. Commun. 1992, 1103. (10) Zhu, P. W.; Napper, D. H. Phys. Rev. E 1994, 50, 1360. (11) Zhu, P. W.; Napper, D. H. Colloids Surf., A 1995, 98, 93. (12) Duracher, D.; Sauzedde, F.; Elaı¨ssar, A.; Pichot, C.; Nabzar, L. Colloid Polym. Sci. 1998, 276, 920. (13) Nabzar, L.; Duracher, D.; Elaı¨ssar, A.; Chauveteau, G.; Pichot, C. Langmuir 1998, 14, 5062.

10.1021/la049913n CCC: $27.50 © 2004 American Chemical Society Published on Web 03/19/2004

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investigated poly(N-isopropylmethacrylamide) (PNIPMAM) microgels. Linear PNIPMAM has an LCST of about 44 °C; it was found that the LCST decreased rather markedly with increasing degree of cross-linking of the microgel particles. They also reported that the LCST decreased with increasing ionic strength and that flocculation takes place when the temperature is raised above the LCST, provided the ionic strength is greater than about 10 mM. Two studies by Daly and Saunders15,16 essentially confirmed the findings referred to above. They investigated the effect of added NaCl on the CFT for aqueous PNIPAM microgel particle dispersions and found that the CFT coincided with the LCST values determined by Park and Hofmann.17 Daly and Saunders also reported some interesting, specific counter- and co-ion effects. Makino et al.18 have also studied the electrophoresis and flocculation of polystyrene core/PNIPAM shell latex particles, mainly at higher temperatures, in excess of the LCST. They fitted their electrophoretic mobility data using Ohshima and Kondo’s theory for a soft platelike particle.19 They found that steric interactions as well as electrostatic interactions play a role in helping stabilize microgel particles against flocculation. Recently, Routh and Vincent20 studied the flocculation of poly(NIPAM-co-acrylic acid) microgel particles, over a range of NaCl concentrations (up to 2 M) and temperatures (15-65 °C). They showed, using small-angle, static light scattering, that at a fixed, high NaCl concentration, where the net interparticle interaction is essentially (short-range) steric plus van der Waals, when the temperature was increased above the critical flocculation temperature for that NaCl concentration, the fractal dimension of the aggregates decreased from ∼2.0 to 1.75. The latter value is typical for irreversible aggregation into a relatively deep potential energy minimum (so-called “diffusion-limited” aggregation). The former value is more characteristic of weaker, reversible flocculation into a shallow potential energy minimum; the higher fractal dimension is associated with some rearrangement with time within the flocs. In this paper, the flocculation behavior of PNIPAM particles has been further investigated over a wide range of sodium chloride and sodium poly(styrene sulfonate) concentrations and temperatures, using turbidity and dynamic light scattering methods, with the aim of further understanding the mechanisms underlying the observed flocculation behavior. Materials and Methods Materials. The microgel dispersions were prepared as described in refs 1 and 21. Basically, a dispersion polymerization method was used, where the monomer, N-isopropylacrylamide (NIPAM), is soluble in the medium, but the polymer precipitates under the conditions of the reaction (70 °C) to form stable particles. N,N′-Methylenebisacrylamide (BA) was used as the cross-linking monomer (9% w/w on total monomer), and ammonium persulfate as the initiator. Sodium polystyrene sulfonate (molar mass, 100 000 g mol-1) was obtained from Acros, and sodium chloride from BDH. Methods. The hydrodynamic radius of the stable microgel particles and of the flocs as a function of time (up to 2 h) was (14) Duracher, D.; Elaı¨ssar, A.; Pichot, C. Colloid Polym. Sci. 1999, 277, 905. (15) Daly, E.; Saunders, B. Langmuir 2000, 16, 5546. (16) Daly, E.; Saunders, B. Phys. Chem. Chem. Phys. 2000, 2, 3187. (17) Park, T. G.; Hoffman, A. S. Macromolecules 1993, 26, 5045. (18) Makino, K.; Kado, H.; Ohshima, H. Colloids Surf., B 2001, 20, 347. (19) Ohshima, H.; Kondo, T. J. Colloid Interface Sci. 1989, 130, 281. (20) Routh, A. F.; Vincent, B. Langmuir 2002, 18, 5366. (21) Crowther, H. M.; Vincent, B. Colloid Polym. Sci. 1998, 276, 46.

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Figure 1. Hydrodynamic diameter of PNIPAM particles from dynamic light scattering measurements, as a function of (log) NaCl concentration, at six temperatures, as indicated. determined using a Brookhaven Instruments Zeta Plus instrument, fitted with a 635 nm He-Ne laser and with the detector set at 90°. Turbidity measurements were performed at a fixed wavelength of 600 nm using a Cary 4 spectrophotometer.

Results and Discussion Particle Size as a Function of Temperature and Ionic Strength. The diffusion coefficient of the PNIPAM microgel particles was determined using dynamic light scattering. In Figure 1, the corresponding values for the derived hydrodynamic diameter of the particles are plotted, as a function of NaCl concentration, at six different temperatures. All the measurements were made at a particle concentration of 0.003 wt % PNIPAM. Measurements made at lower particle concentrations gave slightly lower values for the diameter. This reflects the wellestablished fact that for hydrodynamic reasons, the diffusion coefficient for colloidal particles increases with decreasing particle concentration. However, the trends in the derived particle size with particle concentration were, in most cases, within the experimental error. It may be seen from Figure 1 that at very low NaCl concentrations (∼10-4 NaCl), the particle diameter decreases slightly with increasing [NaCl]; this probably reflects some electrolyte screening of the charge (SO4-) groups at the periphery of the microgel particles. This effect is smallest, as might be expected, for temperatures above 40 °C, when the particles are essentially deswollen. At intermediate NaCl concentrations, the size is more or less independent of [NaCl]. However, at higher [NaCl] (>10-2 to 1 M, depending on the temperature), the diameter decreases noticeably again. This reflects the fact that aqueous NaCl solutions become increasingly poorer solvents for PNIPAM in this [NaCl] range. The [NaCl] range over which the primary particle size could be measured, that is, where the dispersions remained stable to aggregation, decreased significantly with increasing temperature. At low temperatures, in the swollen state, the Hamaker constant of the particles is similar to that of the medium. Hence, the van der Waals interparticle attraction is greatly reduced. There is no driving force, therefore, for aggregation, even if the interparticle electrostatic repulsion is greatly reduced, as it is at high ionic strengths. At temperatures around 35 °C and greater, where the particles are deswollen, the van der Waals forces “switch in” again. Hence, there is a limit to the NaCl concentration that can be tolerated before aggregation sets in. This NaCl concentration becomes lower the higher

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Figure 2. Normalized turbidity of PNIPAM dispersions as a function of temperature, at seven NaCl concentrations, as indicated.

Rasmusson et al.

Figure 3. Critical flocculation temperature of PNIPAM dispersions as a function of NaCl concentration.

the temperature, that is, the greater the van der Waals interaction. This concept is discussed further in the next section, in the light of the turbidity measurements that were made. Whereas, in the current work, it may be concluded from Figure 1 that at temperatures well in excess of the LCST for PNIPAM (i.e., >40 °C) the particle size of the microgel particles is more or less independent of [NaCl] (below that required to induce aggregation), Garcı´a-Salinas et al.22 found that for microgel particles of PNIPAM co-polymerized with 2-acrylamido-2-methylpropanesulfonicacid, the diameter gradually decreased with increasing ionic strength, even well above the LCST. However, in their case the particles carried an internal, bulk charge as well as a surface charge. Ionic strength plays a significant role in electrostatic screening of this internal charge inside the particles and is the primary reason for the continued shrinkage that occurs with increasing electrolyte concentration that these authors observed, even at high temperatures. Turbidity as a Function of Temperature and Ionic Strength. The turbidity of the microgel dispersions was studied as a function of time, for a wide range of conditions. Figure 2 shows the turbidity (after 1 h) of the microgel dispersions at an initial particle concentration of 0.06 wt %, as a function of temperature, for eight different NaCl concentrations in the range 0.5-800 mM. In this case, all the curves have been normalized to the value of the initial turbidity at 20 °C, at this particle concentration, in the absence of NaCl. Note that the data for the two lowest NaCl concentrations studied (0.5 and 10 mM) coincide. The slow increase in turbidity with temperature, seen over most of the temperature range, simply reflects changes in refractive index, and therefore light scattering intensity, with temperature, in particular that for the aqueous media. The slightly stronger increase in the region of 35 °C has to do with the contraction of the particles around this temperature (the LCST). For the two lowest NaCl concentrations (0.5 and 10 mM), there is no change in the turbidity values with time. This is in accord with the dynamic light scattering results shown in Figure 1, where it is seen that the particles are indeed stable up to NaCl concentrations of 10 mM. However, at the higher NaCl concentrations, one may detect in Figure 2, at a given temperature, a distinct “discontinuity” in the turbidity/temperature plots. This is taken to be the CFT, for that NaCl (and particle) concentration. The CFT value was found to be invariant with time. The maximum, which appears in each curve at temperatures well above the corresponding CFT value, simply reflects the fact that by

then the flocs have grown to a sufficient extent that they are sedimenting out of the light path, with a consequent decrease in turbidity. Values of the CFT, at different NaCl concentrations, are listed in Table 1. These values could be determined to (0.5 °C. The CFT appears to be a thermodynamic boundary: 0.5 °C below the CFT, for a given NaCl concentration (and particle concentration), no flocculation was detected, even after long times. The CFT values are also plotted, as a function of NaCl concentration, in Figure 3, to illustrate the fact that three regions of ionic strength may be identified. First, at very low [NaCl], less than ∼25 mM, no flocculation could be induced, even at high temperatures (>40 °C). This is because, although the particles are collapsed at these higher temperatures, the interparticle electrostatic repulsion is sufficient to prevent flocculation. Second, between about 25 and 100 mM NaCl, the CFT decreases quite strongly with increasing ionic strength. This reflects the fact that within this range of ionic strengths, the interparticle electrostatic repulsion is weakened sufficiently for the van der Waals attraction to induce flocculation. The higher the electrolyte concentration, the lower the van der Waals attraction (i.e., net Hamaker constant) required, and hence the larger the critical particle size of the microgels, for the onset of flocculation to occur. That is, the CFT decreases with increasing ionic strength. Finally, above 100 mM NaCl, the CFT continues to decrease linearly with ionic strength, albeit less strongly. Extrapolation of this line back to zero [NaCl] corresponds to a temperature of 35.5 ( 0.5 °C, which is within the range of the LCST values for PNIPAM microgels in pure water reported in the literature,1-3 as discussed earlier. Several other investigations14,15,23 had in fact shown previously that the LCST of PNIPAM and the CFT of PNIPAM dispersions both decrease linearly as the ionic strength is increased, in this high NaCl concentration region. At these higher ionic strengths, the interparticle electrostatic repulsion is more or less screened out. The decrease in CFT with increasing ionic strength, in this

(22) Garcia-Salinas, M. J.; Romero-Cano, M. S.; de las Nieves, F. J. J. Colloid Interface Sci. 2001, 241, 280.

(23) Fujimoto, K.; Nakajima, Y.; Kashiwabara, M.; Kawaguchi, H. Polym. Int. 1993, 30, 237.

Table 1. CFT of the PNIPAM Dispersions as a Function of NaCl Concentration [NaCl] (mM)

CFT (°C)

[NaCl] (mM)

CFT (°C)

27 50 75

39.5 36.0 34.5

100 400 800

34.0 30.5 25.5

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range, reflects the decrease in solvency for PNIPAM with increasing [NaCl] at these higher concentrations, discussed earlier in connection with the observed decrease in particle diameters in this [NaCl] range and shown in Figure 1. Thus, since aqueous NaCl solution becomes a poorer solvent for PNIPAM with increasing NaCl concentration, one does not need to raise the temperature quite as much to deswell the particles to reach the critical size (and hence the net Hamaker constant) where flocculation can commence (at given particle concentration). Critical Conditions for Flocculation. In this section, we consider what actually determines the critical particle size (and hence the net Hamaker constant) for the onset of flocculation. From the data presented in Figure 1, it would seem that for the current PNIPAM particles, above about 10 mM NaCl (i.e., in the absence of any significant electrostatic repulsion), this critical size is around 250 nm. That is approximately the size of the primary particles determined for temperatures in the range 40-50 °C. However, it is known that even at these temperatures (well above the LCST for PNIPAM) the microgel particles still retain a significant amount of water within their bulk.3 The question of the actual (average) volume fraction of PNIPAM inside the microgel particles, at temperatures in the region of the LCST, is discussed in more detail below. It would seem though that even at high temperatures (>LCST) PNIPAM particles are still somewhat “softer” and “hairier”, when compared, say, to polystyrene latex particles. Because of the corresponding close range “steric” repulsion, it is not expected that the minimum in the pair potential, Vmin, that is, the net van der Waals attraction, for two PNIPAM particles of around 250 nm diameter, in “contact”, will be very large. Hence, the flocculation that occurs should be relatively weak and reversible. In that case, as discussed previously by one of us24 in the context of sterically stabilized particles, one ought to see a particle number concentration dependence of the CFT. One may interpret this in terms of the standard thermodynamic equation, linking the overall free energy change (∆G) for any physicochemical process (in this case flocculation) with the component energy (∆U) and entropy (∆S) parts,

∆Gfloc ) ∆Ufloc - T∆Sfloc

(1)

∆Ufloc (negative) increases with increasing Vmin, but ∆Sfloc (also negative) decreases with increasing particle concentration. For flocculation to occur, ∆Gfloc must be negative overall. The boundary condition is that ∆Gfloc equals zero. Thus, as the particle concentration increases (i.e., ∆Sfloc diminishes), then lower values of ∆Ufloc and hence Vmin are required for the onset of flocculation to be observed. This trend was borne out in the present experiments. When the particle concentration was increased, then the microgel dispersions at a given [NaCl] showed a reduced CFT value, that is, flocculated at a correspondingly larger critical particle size, and weaker net van der Waals interaction (reduced Vmin). For example, in the presence of 27 mM NaCl, the CFT decreased by approximately 1.5 °C on doubling the initial particle volume fraction from 6 × 10-4. Fractal Nature of Flocs. In Figure 4, the hydrodynamic floc size (as determined from dynamic light scattering experiments) is plotted as a function of time (on a log-log scale), in the presence of 800 mM NaCl, at different particle concentrations. Two sets of data are shown, one (24) Cowell, C.; Vincent, B. J. Colloid Interface Sci. 1982, 87, 518.

Figure 4. (Log) radius of PNIPAM flocs as a function of (log) time, from dynamic light scattering measurements, at two temperatures and different particle volume fractions, as indicated.

for flocculation at 25.5 °C and the second at 26.0 °C. At 25.5 °C, the dispersions are just on the edge of flocculation. Virtually no increase in size was detected for the first 10 min or so, but clearly the extent of flocculation increased with particle concentration, thereafter, as expected. The rate is very much faster at 26 °C, an increase of only 0.5 °C. This again demonstrates the sensitivity of such weak flocculation to the exact thermodynamic conditions. For aggregates showing fractal structures, with fractal dimension df, the radius (R) of the flocs increases with time (t) according to a power law,25

R ∼ tz

(2)

log R ) z log t + constant

(3)

that is,

where z ) 1/df, for particles undergoing diffusion-controlled aggregation (i.e., no energy barriers involved). It would seem from Figure 4 that for the PNIPAM dispersions, undergoing flocculation at 26 °C and 800 mM NaCl, the flocs are indeed fractal, and from the slopes of the log-log plots at the three different particle concentrations, a mean value of df ) 2.0 ( 0.1 is obtained. This is significantly greater than the value of 1.7-1.8, which is normally expected for particles undergoing diffusion-controlled, irreversible aggregation (i.e., of the Smoluchowski type) into a deep primary minimum of the interparticle pair potential. A value of 2.0 (i.e., closer packed flocs) is consistent with particles undergoing weak, reversible flocculation, as is believed to be occurring here. As discussed earlier, Routh and Vincent20 have recently shown, for similar PNIPAM-based microgel particles, also exhibiting a CFT at a given electrolyte concentration, that the value of df, as determined from small-angle static light scattering experiments, decreases from about 2.0 close to the CFT to around 1.75 at temperatures greatly in excess of the CFT (and well above the LCST). As the temperature is increased, so the particles become somewhat harder and the van der Waals attraction becomes correspondingly stronger; the value of Vmin gradually increases, and eventually aggregation reaches the (irreversible) diffusioncontrolled limit. The results of Routh and Vincent20 are consistent, therefore, with those reported in the present paper. (25) Asnaghi, D.; Carpineti, M.; Giglio, M.; Sozzi, M. Phys. Rev. Lett. 1992, 45, 1018.

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Zhu and Napper10,11 studied the aggregation of hard latex particles stabilized by grafted PNIPAM chains at 25 °C but at relatively high ionic strengths, that is, from 715 mM NaCl upward, where as we have seen (Figure 1), NaCl solutions become increasingly poorer solvents for PNIPAM. Clearly, it is the added NaCl which is causing the shrinkage of the PNIPAM sheaths around the particles and hence flocculation beyond some critical NaCl concentration, in this case. These authors also found a powerlaw dependence of the floc size with time, after some initial period, similar to that shown in Figure 4 here. At 25 °C, they found that the slope of the log-log plot decreased from 0.52 to 0.40, that is, df increased from 1.9 to 2.5, when the ionic strength increased from 715 to 800 mM,11 implying weak reversible flocculation. However one might have expected df to decrease, with increasing NaCl concentration, in the light of Routh and Vincent’s results.20 Nevertheless, these values are similar to the ones found in the present work, even though our system seems to be somewhat more stable since we did not observe any aggregation in 800 mM NaCl at 25 °C. In the Zhu and Napper system,10,11 however, the van der Waals forces will be that much stronger, because of the hard cores present in their particles. Composite Nature of PNIPAM Particles. As discussed above, PNIPAM microgel particles are composite particles, containing water, even at temperatures greater than the LCST. It seems that this trapped water cannot be removed by heating, even at temperatures well in excess of the LCST for PNIPAM. However, Crowther and Vincent26 showed that very similar PNIPAM microgel particles (i.e., also containing 9 mol % cross-linking monomer) could be collapsed further by adding a shortchain alcohol (methanol, ethanol, or 2-propanol) to the aqueous PNIPAM dispersions. In fact, on adding an alcohol, the microgel particles first reduced in size and then increased again, so that in the corresponding pure alcohol medium, at 25 °C, the particles were more or less the same size as in pure water. For example, at 25 °C, where the diameter of the particles in water was 630 nm, on adding 2-propanol to the aqueous dispersion, a minimum size of 350 nm was reached at ∼30 vol % 2-propanol; the size reached 630 nm again around 80 vol % 2-propanol and thereafter more or less leveled off. At 50 °C, the size initially in water was 380 nm, and this was reduced to a minimum value of 160 nm at ∼40 vol % 2-propanol. This deswelling effect of adding 2-propanol (or any short-chain alcohol) is essentially due to the fact that alcohol and water interact more strongly with each other than with PNIPAM.26 Dingenouts et al.27 used a combination of small-angle X-ray scattering and small-angle neutron scattering to calculate the volume fraction (φ) of polymer inside PNIPAM microgel particles at 25 and 43 °C. Furthermore, Wu et al.6 and Gila´nyi et al.28 both used a combination of static and dynamic light scattering to calculate φ for the particles, at different temperatures. These results have been collected together in Figure 5. φ may be calculated from the relationship

φ)

() dh ds

3

(4)

where dh is the diameter of the equivalent hard-sphere (26) Crowther, H. M.; Vincent, B. Colloid Polym. Sci. 1998, 256, 46. (27) Dingenouts, N.; Selenmeyer, S.; Deike, I.; Rosenfeldt, S.; Ballauff, M.; Lindner, P.; Narayanan, T. Phys. Chem. Chem. Phys. 2001, 3, 1169. (28) Gila´nyi, T.; Varga, I.; Me´sza´ros, R.; Filipcsei, G.; Zrı´nyi, M. Phys. Chem. Chem. Phys. 2000, 2, 1973.

Figure 5. Estimated volume fraction (φ) of polymer in PNIPAM particles as a function of temperature, from various literature sources, as indicated. The line through the 9 points is the best fit line to the literature data.

particles (no water inside) and ds is the diameter of the swollen microgel particles. Thus, using eq 4, φ may be calculated, as a function of temperature, at a given NaCl concentration (we chose 1 mM NaCl) from the data for the hydrodynamic diameter of the microgel particles presented in Figure 1, if the value for dh is known. We chose the value of dh which seems to give the best fit to the data in Figure 5, although the available data are somewhat scattered. The value of dh which seems to give the most reasonable fit is 95 nm. It is of interest to compare this result with the data of Crowther and Vincent,26 reported earlier in this section for the reduction in size, at 50 °C, induced by adding 2-propanol to the aqueous dispersion. In that case, the (maximum) reduction in size was a factor of 2.4. This compares well with the factor of 2.6 for the ratio of ds (250 nm, Figure 1) to dh (95 nm) suggested here. It would seem, therefore, that addition of the optimum amount of alcohol does remove a very large proportion of the water trapped inside the microgel particles at 50 °C. Evaluation of Vmin at the CFT. According to the theory set out in an earlier section, the value of Vmin at the CFT for a given NaCl concentration should be fixed for a given particle concentration. At [NaCl] concentrations >∼100 nm, the electrostatic interactions, as we have shown, are effectively eliminated. Vmin may then be calculated from the expression for the van der Waals attraction, VA, between two microgel particles,

VA ) -

Aeffds 24h

(5)

where h is the separation for two particles in contact. The net or effective Hamaker constant (Aeff) may be calculated from the equation

Aeff ) (AM1/2 - AW1/2)2

(6)

where AM is the Hamaker constant of the (swollen) microgel particles, and AW is that for the continuous phase, water. An equation for calculating AM has been suggested by Vincent,29

AM ) [AP1/2φ + (1 - φ)AW1/2]2

(7)

where AP is the Hamaker constant of the actual polymer, PNIPAM. (29) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991; p 190.

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Figure 6. Minimum wt % of added PSS (molar mass, 100 000 g mol-1) required to induce flocculation of the PNIPAM particles, as a function of temperature, for three PNIPAM concentrations.

Combining eqs 6 and 7 leads to

Aeff ) (AP1/2 - AW1/2)2φ2

(8)

and including eq 4 for φ leads to

Aeff ) (AP1/2 - AW1/2)2

() dh ds

2/3

(9)

By choosing the values dh ) 95 nm, ds ) 250 nm (i.e., the critical particle radius for the onset of flocculation, for the volume fraction of particles used; see earlier), AP ) 6.2 × 10-20 J (the value for PNIPAM15), AW ) 3.7 × 10-20 J,29 and h ) 1 nm, we find that Aeff ) 0.16 × 10-20 J, and Vmin ∼ 8 kT. However, the value obtained for Vmin depends on the value chosen for h, which is somewhat arbitrary. Moreover, the assumption has been made that the microgel particles have a uniform bulk segment concentration. This is unlikely to be true; it is reasonable to expect the segment concentration to be lower at the periphery of the particles.30 This would have the effect of reducing Vmin significantly. However, we should emphasize that the actual value of Vmin calculated is not important; all we are attempting to demonstrate is that the “ballpark” value obtained is in the region where weak, reversible flocculation is likely to occur. Effect of Sodium Poly(styrene sulfonate). We have shown that at concentrations of NaCl < ∼25 mM no CFT value could be determined, because, under these low ionic strength conditions, the electrostatic repulsion is sufficiently strong to prevent any flocculation occurring, even though the van der Waals interaction becomes significant at high temperatures. An alternative way of inducing particle flocculation is through the depletion interaction which occurs in the presence of nonadsorbing polymers or polyelectrolytes. To this end, the addition of sodium polystyrene sulfonate [PSS] (molar mass, 100 000 g mol-1) to the PNIPAM dispersions was investigated, in the absence of any added NaCl. The results are shown in Figure 6, where the minimum concentration of PSS required to induce flocculation of the PNIPAM particles is plotted as a function of temperature, for three particle concentrations. There does not appear to be a significant effect of particle concentration over the small range studied. However, there is a strong decrease in the concentration of PSS required to achieve flocculation with (30) Crowther, H. M.; Saunders, B. R.; Mears, S. J.; Cosgrove, T.; Vincent, B.; King, S. M. Colloids Surf. 1999, 103, 9211.

increasing temperature. An equivalent statement would be that the CFT decreases with increasing PSS concentration. Snowden and Vincent9 have shown previously that PSS (molar mass, 50 000 g mol-1) did not induce depletion flocculation of PNIPAM particles at 25 °C (at least up to concentrations of PSS of 0.8 wt %, lower than the concentration range employed here; see Figure 6) but did so at 40 °C and that the minimum amount of PSS required decreased if NaCl was also added. At the highest concentration of PSS employed, around 3 wt %, the equivalent ionic strength is only 15 mM, so electrostatic interactions are still significant, and as we have seen, van der Waals forces alone are insufficient to induce flocculation, even at the highest temperatures. Over the relatively small temperature range shown in Figure 6 (23-33 °C), the particles do shrink (by about a factor of 2; see Figure 1), but this is still not sufficient for the van der Waals attraction to play a major effect. So the depletion interaction must be the dominant effect here. The question then arises as to why less PSS is required to induce flocculation at higher temperatures? One possibility has to do with the variation in “softness” of the PNIPAM particles with temperature. Jones and Vincent31 have discussed the depletion interaction for soft particles, in particular, particles carrying terminally grafted polymer chains. They demonstrated that the depletion interaction becomes weaker the softer the grafted layer, for a given core size. This is due to (partial) interpenetration of the free polymer chains into the periphery of the grafted layer. A similar situation could arise for swollen microgel particles. Any interpenetration of the free chains into the soft particle reduces the effective depletion layer thickness of the free chains. From the equations given in the Jones and Vincent paper, one can obtain the following approximate, analytical equation for the depth of the potential energy minimum, Vmin, between two soft particles, in contact, in the presence of nonadsorbing polymer:

Vmin ) 2πaP(∆ - p)2

(10)

where a is the particle radius, P is the osmotic pressure of the polymer solution (related to its concentration), ∆ is the depletion layer thickness (for dilute polymer solutions related to the molar mass of the polymer), and p is the depth of penetration of the free polymer chains into the soft particle. If one assumes, following the earlier discussion in this paper, that a given value of Vmin exists (for a given particle concentration) for the onset of flocculation, then for hard particles (i.e., where p ) 0), P ought to increase as the particle size decreases, in line with eq 10. Hence, as the PNIPAM particles reduce in size, on raising the temperature, a higher concentration of added PSS ought to be needed to induce flocculation, assuming they behave as hard, impenetrable spheres. However, it is observed here that a lower concentration is required. Two reasons may be given to account for this. First, the (albeit weak) van der Waals forces add to the depletion interaction, increasing the overall attraction between the PNIPAM particles. So, as the van der Waals forces become stronger with increasing temperature, a correspondingly weaker depletion interaction is then required to attain a given value of Vmin. Second, from eq 10, the (∆ - p)2 term is increasing, as the size is decreasing, with increasing temperature; that is, for a given value of ∆, p gets smaller as the particles get harder. We do not have any direct evidence that the free PSS chains do interpenetrate the periphery of the PNIPAM particles in their highly swollen (31) Jones, A.; Vincent, B. Colloids Surf. 1989, 42, 113.

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state at low temperatures, but it does not seem to be an unreasonable supposition. Jones and Vincent31,32 invoked such an explanation to account for their results regarding the depletion flocculation of sterically stabilized silica particles, carrying terminally grafted polymer chains, in the presence of added free chains. In particular, they were able in this way to account for the fact that the depletion interaction, at a given free polymer concentration, went through a minimum with increasing coverage of the grafted chains. Both effects described above probably play a role in accounting for the results shown in Figure 6. Conclusions From studies of the flocculation behavior of the PNIPAM microgel particles, as a function of the ionic strength and temperature, three regions of NaCl concentration have been established. First, at very low values, ∼100 mM, the electrostatic repulsion is screened out, and the CFT decreases linearly with temperature. The (32) Milling, A.; Vincent, B.; Emmett, S.; Jones, A. Colloids Surf. 1991, 57, 185.

Rasmusson et al.

reason for this decrease is the fact that aqueous solutions of NaCl become increasingly poorer solvent environments for PNIPAM with increasing [NaCl]. It is shown that the flocculation of the PNIPAM particles is consistent with a weak, reversible flocculation model. This is apparent, for example, from the fractal dimensions of the flocs (∼2.0), determined from the power law used to fit the time evolution of the hydrodynamic diameter of the flocs, and also from the estimated depth of the mimimum in the interparticle pair potential, based on the critical size of the primary particles where flocculation just begins to occur. However, this size is still considerably higher than that estimated for equivalent hard spheres of PNIPAM. Finally, the effect of adding a nonadsorbing polyelectrolyte, PSS, to the PNIPAM particles has been investigated. Two explanations are offered for the observed decrease in the amount of PSS required to induce flocculation with increasing temperature. First, as the interparticle van der Waals forces increase with increasing temperature, so the depletion interaction required becomes less strong. Second, some interpenetration of the free polyelectrolyte chains into the microgel particles occurs, but this decreases as the microgel particles become harder with increasing temperature; hence, the depletion interaction, for a given polymer concentration, is stronger the higher the temperature. Acknowledgment. M. Rasmusson gratefully acknowledges the Swedish Institute for financial support for his visit to Bristol University. A. Routh and B. Vincent acknowledge EPSRC for financial support (Grant Number GR/M58436). LA049913N