Langmuir 1996, 12, 6211-6217
6211
Swelling Equilibrium of Small Polymer Colloids: Influence of Surface Structure and a Size-Dependent Depletion Correction Markus Antonietti,* Harald Kaspar, and Klaus Tauer Max Planck Institut fu¨ r Kolloid & Grenzfla¨ chenforschung, Kantstrasse 55, D-14513 Teltow-Seehof, Germany Received February 21, 1996. In Final Form: September 4, 1996X Small polymer latex particles in the size range 15 nm < R < 100 nm with different types of covalently bound surface stabilizing groups are made via emulsion polymerization using diverse functionalization techniques like incorporation of polar comonomers, surface-active initiators, or polymerizable surfactants. These colloidal dispersions in water are swollen with toluene in the absense of free surfactants until equilibrium swelling is reached. The equilibrium size of the swollen latices is determined by combining densitometry and dynamic light scattering. For all surface groups, we observe a pronounced dependence of the swelling ratio on particle size where absolute values of swelling are much lower than described by classical theories. A modified description is presented which considers size-relevant effects (such as the Kelvin pressure and depletion) by an additional osmotic pressure term which increases with the inverse of the particle size. Other classical effects of colloids such as a size dependence of the thermodynamic interaction parameter or the interface energy can be excluded by quantitative considerations. The presented modified swelling equation describes the experimental data well and is expected to have some broader relevance for swelling phenomena of all colloidal systems. Charge stabilization as compared to steric stabilization results in higher swelling ratios and significant lower values for the interface energy. This underlines the importance of coulombic repulsion between fixed charges on the same particle for the swelling process as well as the existence of a “surface anchoring” effect, both of which are not considered in current concepts of the swelling process, too.
I. Introduction The swelling of small colloidal particles dispersed in water with organic solvents or other low molecular weight components plays a major role not only for different techniques of colloid processing, e.g., emulsion polymerization and its mechanistic understanding, but also for diverse modern applications of colloidal systems, such as drug delivery or phase-transfer catalysis by colloidal systems. In emulsion polymerization, for instance, swelling means the uptake of hydrophobic monomer by the polymer particles during the polymerization as long as monomer is present. However, this does not lead to a disintegration of the particles even if the bulk polymer is completely soluble in the monomer. Furthermore, it was shown that there are no polymer molecules dissolved in the coexisting free monomer phase and also not in water.1 Swelling stops at a local thermodynamic equilibrium at a well-defined size of the swollen particles. Many other experiments underline the fact that the swelling process of colloidal objects with a solvent is in generalswithin the confinements of the dispersion stabilitysan equilibrium process leading to a thermodynamically stable state2-4 (It is stated that the thermodynamic equilibrium of the swelling of colloids only denotes the local equilibrium in each particle; this is not related to the point that colloidal stability is usually not a thermodynamic stability in a strict sense). However, it is a common observation that all currently accepted theories do not satisfactorily describe the experiX Abstract published in Advance ACS Abstracts, November 15, 1996.
(1) Gardon, J. L. J. Polym. Sci., Polym. Chem. Ed. 1968, 6, 2859. (2) Lo¨hr, G. In Polymer Colloids II; Fitch, R. M., Ed.; Plenum Press: New York 1980; pp 71-81. (3) Ugelstad, I.; Kaggerud, H.; Fitch, R. M. Polymer Colloids II; Plenum Press: New York, 1980; pp 83-93. (4) Vanzo, E.; Marchessault, R. H., Stannett, V. J. Colloid Sci. 1965, 20, 62.
S0743-7463(96)00159-X CCC: $12.00
ments on swelling. One central topic of the present work is therefore a quantitative description of the swelling of colloids by precise measurements of the swelling of some model polymer latex particles in dependence of the size and the adaptation of the existing theories to the experimental data. From another point of view, swelling of a model colloid with diverse stabilizing surface groups effects the extension of an existing surface and the creation of a new surface between the stabilizing groups. The creation of an interface is a well-known process in colloid science and occurs, for instance, in pure one-component systems during nucleation of liquid droplets out of supersaturated vapor.5 In the latter case the new surface has the same properties as the bulk material. This situation might be different for the surface area enlargement of a latex particle during swelling: the increase in the average distance between the surface molecules (charges, stabilizers, etc.) does not necessarily mean that the new surface produced has the same properties like the unstabilized bulk material, since additional energy contributions (such as electrostatic repulsion between surface charges) might play an important role. Vice versa, the ability to stabilize a slight excess of surface area is an important property of the respective type of surface stabilization and enables a quantitative understanding of surfactant efficiency as well as the mechanistic understanding of emulsion polymerization. An important parameter for these problems is the chemistry and the working principle of the stabilizing groups of the latices; their variation enables for instance comparison of the swelling of electrostatically stabilized latices (-SO4-- and SO3--functionalized particles) with sterically stabilized colloids (bearing dihydroxyethyl methacrylate - moieties or a special silicone surfmer at the surface). (5) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain; VCH: Weinheim, Germany, 1994; pp 57-59.
© 1996 American Chemical Society
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Figure 1. Schematic drawing of the changes during the swelling process. Monomer M is incorporated due to the gel pressure. This energy is counterbalanced by the production of surface between the stabilizing groups, which not necessarily has the same properties a a bare polymer surface.
γ the swelling depends on the particle size in a way that the higher the size, the higher the swelling, whereby φ1 ) 1 - φ2 as there are only polymer and swelling agent in a particle. However, this approach neglects our understanding of energy contributions which are highly relevant for liquid droplets in the nanometer range. It was stated by Derjaguin that the swelling of objects with restricted dimensions has to consider the disjoining pressure or the Kelvin pressure of the solvent.10 To generate small liquid droplets from supersaturated vapor, the surface energy of the nucleating droplet has to be counterbalanced by a thermodynamic supersaturation. This is usually expressed in the Kelvin equation:
RT ln (p/p0) ) 2γV1/r
(2)
II. Theoretical Approach Figure 1 illustrates the changes due to the swelling process of latex particles. In a first approach, swelling of a polymeric latex particle is comparable to that of a bulk polymer or gel. In the case of a linear polymer, the bulk material dissolves, and the swelling is just restricted by possible cross-links which can be described according to Stauff.6 In the case of colloidal particles the osmotic pressure is counterbalanced by the interfacial free energy between the latex particles and water; for cross-linked polymer colloids, the swelling is additionally restricted by the network that strains and stores elastic energy. Morton, Kaizermann, and Altier published in 1952 the first theoretical description of the swelling of latex particles.7 This approach is still accepted and used in the current literature.8,9 They considered the swollen particle in equilibrium with the free solvent and described the equilibrium condition for the partial molar free energy of h m1) the solvent (∆F h 1) with the osmotic contribution (∆F and the interfacial free energy contribution (∆F h t). In equilibrium, ∆F h 1 is zero, and the result is eq 1, known as the Morton-Kaizermann-Altier equation (MKA equation):
(
ln(1 - φ2) + 1 -
2V1γ 1 φ2 + χφ22 ) DP rRT
)
(1)
The left-hand side of eq 1, the osmotic contribution ∆F h m1, is the standard expression of the Flory-Huggins theory of polymer solutions where φ2 is the polymer volume fraction in the swollen particle, DP is the number-average degree of polymerization of the polymer molecules within the particles, and χ is the Flory-Huggins interaction parameter. The increase of the interfacial energy due to swelling is expressed as γ dA ) 8πr drγ with γ as the interfacial tension of the swollen particles to water and A as the swollen particle surface area. The volume increase of the particles can be expressed either as 4πr2 dr or dn1 × M1/F1 where dn1 is the number of solvent molecules imbibed by the particle, M1 is the molecular weight of the solvent, and F1 is the solvent density. Since M1/F1 is equal to the molar volume of the solvent and 8πr h t ) 2V1[γ/(rRT)], we obtain drγ ) 2V1(γ/r) follows for ∆F finally eq 1 for the swelling equilibrium. Equation 1 predicts that in the case of a high molecular weight polymer (1/DP ≈ 0) and for given values of χ and (6) Stauff, J. Kolloidchemie; Springer Verlag: Berlin, Germany, 1960; pp 685 ff. (7) Morton, M.; Kaizerman, S.; Altier, M. W. J. Colloid Sci. 1954, 9, 300. (8) Nilsson, H.; Silvergren, C.; To¨rnell, B. Eur. Polym. J. 1978, 14, 737. (9) Gilbert, R. G. Emulsion Polymerization: A Mechanistic Approach; Academic Press: New York, 1995; pp 57-59.
The same is true for droplets of a liquid dispersed in another liquid which exchange via some dissolved molecules. Even in a stabilized state, the existence of a positive surface energy results in a “negative supersaturation” RT ln(c/c0) ) 2γV1/r, i.e., a concentration c inside the droplets being smaller than the equilibrium value c0 of the equivalent bulk material. This results in the Ostwald ripening, the disappearance of the small droplets and the growth of the bigger ones, and backs the thermodynamic instability of the pure liquid emulsions or implies for our problem the absence of pure toluene microdroplets in the swollen polymer dispersion. Swelling of a colloidal particle with a good solvent results in a thermodynamic equilibrium at some finite size again. Here, the negative Kelvin pressure is balanced by the stronger gel pressure of the swelling polymer particle. We obtain by addition of eqs 1 and 2:
(
ln(1 - φ2) + 1 -
2V1γ 1 c φ2 + χφ22 ) φ1 ln ) DP c0 rRT 2V1γ (2 - φ2) (3) rRT
)
The introduction of the φ1-term in front of the Kelvin term is simply due to the fact that eq 3 balances molar energies. The comparison with eq 1 shows that the consideration of a Kelvin pressure diminishes the swelling. Equation (3) also has a correct limit for the vanishing polymer volume fraction: the Kelvin equation is recovered, whereas the classical MKA approach produces a discontinuity and cannot handle the situation of small amounts of polymer in a liquid droplet. It is important to note that the introduction of only some polymer chain inside of a microdroplet induces a real thermodynamic equilibrium state and prevents Ostwald ripening. Besides the swelling of emulsion particles, this is important for many other modern heterophase polymerization techniques. El-Aasser et al. found that miniemulsion polymerization particles do not grow when a small amount of polymer is added to the droplet phase.11 In the present framework, this is described by the influence of the swelling pressure on the chemical potential. Antonietti et al. found that microemulsion polymerization exhibits an instable phase when the polymer chains formed at first add an osmotic swelling term to the energy balance of the microdroplets.12 Since (10) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. Surface Forces; Consultants Bureau: London, 1987. (11) Miller, C. M.; Blythe, P. J.; Sudol, E. D.; Silebi, C. A.; El Aasser, M. S. J. Polym. Sci., Part A: Polym. Chem. 1994, 32, 2365. (12) Antonietti, M.; Basten, R.; Lohmann, S. Macromol. Chem. Phys. 1995, 196, 441.
Swelling Equilibrium of Small Polymer Colloids
microemulsions exhibit very low interface energies, this is a special case of eq 3, too. For the swelling of polymer colloids, another energy contribution has to be considered. This is due to the fact that any polymer solution is repelled from any interface for purely entropic reasons: as pointed out by Casassa13,14 and later de Gennes,15 this “depletion” is caused by the effect that a polymer is losing conformations being close to an impenetrable boundary. Scheutjens and Fleer16 extended these treatments to semiconcentrated polymer solutions and showed that the decrease in polymer concentration near the interface is smaller than in dilute solutions. Vincent17 pointed out that the interface repulsion effect balances the osmotic pressure of the polymer solution; on this basis, he calculated an analytical expression for the shape of the depletion zone. Experimentally, the linear chain conformation inside of the latex particles was characterized by neutron scattering, and a remarkably big change of the form factor of large polymer chains as compared to the bulk state was observed.18 Recently, Ballauff et al. measured the thickness of the depletion zone in the latex particles with small-angle X-ray scattering;19 assuming a boxlike model, they determined a depletion shell thickness of 2.2 nm. Therefore, this depletion zone or the connected depletion pressure has to be considered in any description of the swelling of polymer latex particles. Without further assumptions, we can include it as a pressure ∆p in a way that
(
ln(1 - φ2) + 1 -
2V1γ 1 φ2 + χφ22 ) (2 - φ2) DP rRT ∆pV1 (4) RT
)
Up to now, the value of the depletion pressure ∆p cannot be analytically calculated from theory, which does not consider the special case of a polymer chain in a small spherical particle. Consequently, we use ∆p only as a fitting parameter. Since interface and volume are related for spheres via A/V ) 3r, in a first approximation we expect this pressure to increase with the inverse particle size. For very small particles, we are running in the single chain problem, and the concept of depletion cannot be applied. It is interesting to note that the depletion pressure can, in principle, exceed the thermodynamic swelling pressure at reasonable finite sizes; i.e., a situation can be expected in which very small polymer colloids do not swell at all. It must be also stated that depletion exhibits a significant molecular weight dependence and looses importance for very small polymer chains. For the sake of a better comparison, we decided to bypass this problem by adjusting the molecular weight in all experiments to values where the molecules are fully entangled and depletion does not depend on molecular weight. Some experiments were made with moderately cross-linked latex cores (with a bulk swelling ratio being much higher than the restricted swelling in the colloidal size range, i.e., colloidal swelling does not “see” cross-links), which also allow one to neglect molecular weight effects even at small particle sizes. (13) Casassa, E. F. J. Polym. Sci., Polym. Lett. Ed. 1967, 5, 773. (14) Casassa, E. F.; Tagami, Y. Macromolecules 1969, 2, 14. (15) de Gennes, P. G. Macromolecules 1981, 14, 1637. (16) Scheutjens, H. M.; Fleer, G. J. Adv. Colloid Interface Sci. 1982, 16, 361. (17) Vincent, B. Colloids Surf. 1990, 50, 241. (18) Linne, M. A.; Klein, A.; Sperling, L. H.; Wignall, G. D. J. Macromol. Sci., Phys. Ed. 1988, B27, 181. (19) Bolze, J.; Ballauff, M. Macromolecules 1995, 28, 7429.
Langmuir, Vol. 12, No. 26, 1996 6213
Figure 2. Free energy of swelling ∆Fs per latex particle in dependence of the size of the swollen latex, r. Curve 1 is the classical MKA energy. Curves 2-4 include an additional pressure term of ∆p ) 0.7 × 105 Pa, ∆p ) 1.0 × 105 Pa, and ∆p ) 2.0 × 105 Pa, respectively. For simplicity, the pressure is not assumed to be r-dependent.
Figure 2 presents for a better illustration some calculated energy curves in dependence of the size of the swelling colloid particle according to eq 4. For the particular case, a polystyrene latex with a radius ro ) 20 nm, swollen with toluene (χ ≈ 0.45), was modeled. The monomer as well as the polymer volume fraction has been expressed with the relation φ2 ) 1 - φ1 ) (r/r0)3, and the whole energy curve was numerically calculated for all possible radii of the swollen latices. It is clearly seen that the MKA formalism does not generate a minimum at some finite latex size, and infinite swelling is predicted. Introduction of a weak additional pressure term in the order of 105 Pa, however, the results in occurrence of a real minimum which shifts to smaller swelling ratios when the pressure is increased. If this pressure is related to depletion, it can be adjusted in a wide range by variation of the molecular weight. Interestingly, this backs the Ugelstadt approach for the production of very large, monodisperse latex spheres by the ultrahigh swelling of primary dispersions consisting of very small polymer chains without further theoretical or mechanistic assumptions.20,21 III. Experimental Section III.1. Emulsion Polymerization of Diverse Latices. Styrene, epoxypropyl methacrylate, 1,3-diisopropenylbenzene (DIPB), and 1,4-butylglycol dimethacrylate (BGDMA, Aldrich) were distilled under reduced nitrogen pressure and stored at 4 °C. Borax, KPS (Riedel), AIBN (Aldrich), and SDS (Serva) were used without further purification. Sodium sulfopropylmyristylmaleate (NaSPMM) was prepared separately in our lab according to ref 22. Polymerizable siloxanoyl-modified gluconamide surfactants were prepared as described in ref 23. Latices with Sulfonate Functionalities. The preparation of the sulfonate surface functionalyzed latices 2/3/1 was carried out via a batch polymerization in a thermostated glass reactor as follows: 200 mL of water (conductivity < 0.2 mS/cm), 20 g of purified styrene, 1.2 g of sodium (20) Ugelstadt, J.; Mork, P. C.; Berge, A.; Ellingsen, T.; Khan, A. In Emulsion Polymerization; Piirma, I., Ed.; Academic Press: London, 1982; p 383. (21) Ugelstadt, J. Makromol. Chem. 1978, 179, 815. (22) Tauer, K.; Goebel, K. H.; Kosmella, S.; Sta¨hler, K.; Neelsen, J. Makromol. Chem. Macromol. Symp. 1990, 31, 107. (23) Wagner, H.; Richter, L.; Wessig, R.; Schmaucks, G.; Weiland, D.; Weissmu¨ller, J.; Reiners, J. Appl. Organometallic Chem. in press.
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Table 1. Colloid-Analytical Data of the Investigated Fractionsa charge density (µC/cm2)
applied RCF
D/nm
σ
φ1
sulfonate groups
8.6 (average of raw latex)
hydroxy groups, sulfate groups
1.9 1.9
2.570 10.280 23.120 41.100 64.230 72.170 256.910 2.570 10.280 10.280
84.6 75.5 72.7 61.4 48.4 41.3 31.2 71.6 71.2 60.2 198.8 146.3 110.5 128 91.5 92.6 68.7 48.5
0.10a 0.09a 0.08a 0.06a,c 0.10a 0.12a 0.15a 0.15a 0.14a 0.16a 0.04b,c 0.06b,c 0.05b,c
0.608 0.571 0.554 0.496 0.456 0.388 0.340 0.290 0.232 0.266 0.598 0.525 0.521 0.539 0.461 0.448 0.357 0.231
sample 2/3/1#1 2/3/1#2 2/3/1#3 2/3/1#4 2/3/1#5 2/3/1#6 2/3/1#7 1/2/2#1 1/2/2#2 1/3/1#2 1/4/2 1/5/1 1/6/1 T6/1#3 T6/1#4 T6/1#5 T6/1#6 T6/1#7
surface str.
siliconate-glucono groups
1,3 no charge
10.280 23.120 41.100 64.230 92.490
a Standard deviations of particle diameters are determined by DLS. b Standard deviations determined by TEM. c Formation of colloidal crystals observed. The table also includes the volume fraction of solvent, φ1, after equilibrium swelling, as determined with densitometry.
Table 2. Applied Compositions and Conditions in the Preparation of Hydroxy-Functionalized Latices sample
SDS (g)
shell monomer component (g)
shell monomer component added after
1/2/2 1/3/1 1/4/2 1/5/1 1/6/1
0.92 2.00 0.20 0.40 0.30
2.00 2.50 0.53 1.09 0.97
60 min 40 min 20 h 5.5 h 6.0 h
sulfopropylmyristylmaleate, and 0.2 g of AIBN were stirred vigorously under a nitrogen atmosphere at room temperature until the system reached equilibrium (1 h). The temperature was raised to 60 °C for 2 days. After complete polymerization took place, some coagulated bulk polymer was removed by simple filtering (the occurrence of which is due to polymerization inside the monomer droplets initiated by the lypophilic initiator), and the latex was carefully purified for 4 weeks in a Berghof ultrafiltration cell with a 25 nm diameter porous membrane. The final surface tension of the dispersion amounts to 71.4 mN/m. The latex particle diameter (measured by TEM, see below) was DN) 41.6 nm with a broad particle size distribution of DW/DN ) 1.5. Titration of the dispersion in a Mu¨tek particle charge detector with a benzethonium chloride solution indicated an average charge density of 8.55 µC/cm2. The available colloid-analytical data of these latices are summarized in Table 1. Latices with Hydroxy Functionalities. The hydroxy surface functionalized latices (slightly cross-linked) were prepared in a thermostated glass reactor at 60 °C, using 20 g of styrene/cross-linker mixture (molar ratio S/DIPB ) 150), 0.13 g of KPS, and 0.17 g of borax in 215 mL of water in each experiment. The variations in the amount of added SDS and epoxypropyl methacrylate/cross-linker (EPMA/EGDMA ) 150, molar ratio) as shell monomer component are listed in Table 2. The shell monomer component was added slowly in the end of growth period, indicated by the disappearence of monomer droplets. The added amount of the shell monomers was calculated to create a shell layer thickness of approximately 2 nm. Polymerization was completed after 2 days in all cases. The latices were purified as above and characterized by DLS, TEM, and titration (see also Table 1). Although these latices can be regarded to be mainly stabilized by the dihydroxypropyl methacrylate units, a minor amount of anionic charges is fixed at the latices due to the initiation process. The charge density of these units is also given in Table 1.
Latices with Gluconosiloxane Functionality. The gluconosiloxane latexes were prepared in a semibatch polymerization with a polymerizable siloxanoyl-modified gluconamide (M2D-C8-glucono methacrylate) as emulsifier24 and a PEGA200 initiator.25,26 A thermostated glass reactor was charged with 100 g of water as the dispersing agent, 4.5 g of the M2D-C8-glucono methacrylate emulsifier, and 5 g of styrene as the monomer and was heated up under gentle stirring to 343.15 K polymerization temperature while the reaction mixture was slightly purged with nitrogen. After the temperature was reached the mixture was stirred for a further 15 min before the reaction was started by feeding 2.06 g of PEGA200 initiator dissolved in 5 g of styrene. The reaction started immediately after feeding the initiator. After 30 min feeding of 40 g of styrene to the reactor with a rate of 0.525 g/min was started. After 9 h total polymerization time, the reaction was completed, and a stable latex with 34% solid content was obtained. The latex had a particle size distribution in between 30 and 140 nm particle diameter. The latex particles are only sterically stabilized as no charges were brought with the polymerization recipe into the system. The latex was purified as described previously and fractionated by ultracentrifugation. The colloid-analytical data of the diverse latex fractions are summarized in table 1, too. III.2. Particle Size Characterization. Dynamic light scattering for the characterization of the parental polystyrene microgels was carried out using a Nicomp C370 particle sizer with the ability of multiangle detection. Only correlations with excellent contrast and correlation strengths above 0.6 were taken. Using the software of the particle sizer, the correlation functions are fitted with a Gaussian distribution of relaxation times, thus resulting in a mean hydrodynamic radius rH and the width of its Gaussian distribution, σ. The agreement of the particle characterization data with those obtained with our standard setup described below is good. In some special cases, the samples were also characterized with our standard set-up for combined static and dynamic light scattering consisting of an ALV ISP86 goniometer and an ALV5000 multi-τ correlator; the measurements are performed using the 532.8 nm line of a cw frequency-doubled, diode-pumped Nd-YAG laser (ADLAS 425c) with 300 mW output power. Light scat(24) Tauer, K.; Wagner, H. To be published. (25) Tauer, K. Polym. Adv. Technol. 1995, 6, 435. (26) Tauer, K.; Kosmella, S. Polym. Int. 1993, 30, 253.
Swelling Equilibrium of Small Polymer Colloids
Langmuir, Vol. 12, No. 26, 1996 6215
Figure 3. Particle size distribution of the raw sulfonated latex, as obtained by sizing of 1845 particles with electron microscopy. The raw product is treated with an analytical ultracentrifuge under the given RCF fields (.), and seven narrow fractions with the given particle size distribution are obtained (straight lines, determined with dynamic light scattering).
tering experiments for the characterization of the polyelectrolyte structure in highly diluted solutions are carried out in water at 20.0 °C with the mixed-bead ion-exchange resin inside the cuvette. All solutions are filtered through 0.45 µm Millipore filters. III.3. Latex Fractionation by Preparative Ultracentrifugation. Latex fractionation was carried out in a Beckman L-70 preparative ultracentrifuge (with a 70 Ti rotor, rrot ) 91.9 mm) on all described latices except for the 1/4/2, 1/5/1, and 1/6/1 latices from the hydroxyfunctionalized series which were obtained already with narrow distribution from the core-shell emulsion polymerization. Broad particle size distributions are divided up into a series of monosized latex fractions by increasing the applied relative centrifugation force (RCF), which is given by RCF ) rω2/g. The fractions are taken by repeated decanting of the supernatant colloidal dispersions from the viscous sediment. The diverse fractions were characterized by DLS. Figure 3 shows a typical result of the fractionation on the very broad distributed latex 2/3/1 by comparing the TEM histogram of the raw latex with the particle size distributions from DLS for all latex fractions. The spontaneous formation of colloidal latex crystals was observed for some fractions of latices with high surface charge (see Table 1). The results of colloidal analysis of all investigated latex fractions were already given in Table 1. III.4. Determination of Degree of Swelling by Density Measurements. The latices were swollen with toluene for 24 h in a thermostated water bath at 25 °C under stirring. Measurements of the swelling kinetics indicate that equilibrium is reached after 18 h even under unfavorable conditions. After complete saturation the upper toluene phase was removed, and densities of the swollen dispersions as well as the unswollen latices were measured. The measurements were carried out in a Paar DMA 602 densiometer at constant temperature. Densities were calculated from vibration periods according to:
Figure 4. Apparent volume fraction of polymer, φ2app, is plotted versus the apparent valume fraction of solvent, φ1app, as taken from densitometric measurements at different concentrations. The slope of the curve amounts to the real volume fraction of solvent inside the swollen latex, φ1.
The monomer volume fraction φ1 of the swollen latex particle can be calculated according to:
φ2 )
VTol,app. mTol,app/FTol ) (6) VTol,app + VPol,app mTol,app/FTol + mPol,app/FPol
with
mTol,app ) 1/FD,sw - 1/FH2O + mPoly(1/FD,sw - 1/FPoly) 1/FTol - 1/FD,sw
- mTol,H2O
and
mPol,app )
1/FDisp + 1/FH2O 1/FPoly + 1/FDisp
(5)
where mPol,app and mTol,app are the apparent masses of polymer and toluene inside the dispersion, respectively, mTol,H2O is the apparent amount of toluene inside the water phase (determined to be 1.263 × 10-4 g/L in a seperate measurement), FDisp is the density of the unswollen dispersion, FD,sw is the density of the swollen dispersion, and FPoly is the polymer density in the latex particle (determined to be FPoly) 1.0599 g/cm3 in a separate set of measurements). Since such a vibration densitometer is, to our knowledge, not regularly applied to heterophase systems, the reliability of the presented method of determination of the swelling degree is proven by an additional measurement. Several weight concentrations of latex 2/9/1 (DDLS ) 25.3 nm, σ ) 0.20) were swollen with toluene and treated in the described way. Figure 4 illustrates the good reproducibility of the swelling data as well as the absence of a concentration dependence of the determined φ1 of the polymer colloid concentration. Each data value amounts to a particular φ1, and the standard deviation of the φ1 values of σ ) 0.03 is a measure for the accuracy of the presented method.
where F1 is the density and T1 the related vibration period of the pure solvent sample, whereas the index 2 indicates the colloidal dispersion. A is a calibration constant that is determined with pure liquids of known densities (in the present case water, nonane, and cyclohexane). Water was used for recalibration after each measurement.
The swelling ratios of all latices as determined by density measurements calculated according to eqs 5 and 6 are summarized in Table 1. Already from the numerical values it is seen that the anionically stabilized particles swell much better than
1 F1 - F2 ) (T12 - T22) A
IV. Results and Discussion
6216 Langmuir, Vol. 12, No. 26, 1996
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Figure 5. MKA plot of the swelling behavior of different latex particles where the Flory-Huggins term is plotted versus the inverse particle size: ([) sulfonated latices; (9) hydroxylated latices; (2) latices with gluconosiloxane functionalities. All curves are forced to cross the Y-axis at the same intercept (arrow).
Figure 6. Calculated depletion pressures ∆p in dependence of the particle size according to eq 4. A systematic increase of the pressure values toward smaller particle sizes is observed. Note that the sulfonated latices show a significant smaller depletion pressure as compared to the other particles. For an explanation of the symbols, see Figure 5.
their counterparts being sterically stabilized with the siloxanoyl-modified gluconamide surfmer or the poly(dihydroxypropyl methacrylate) shell which mutually behave quite similarly. A presentation of the data according to the MKA equation where the Flory-Huggins term is plotted versus the inverse particle size is shown in Figure 5, thus resulting in a fit of the interface energy γ, only. For this plot, we took for the system polystyrene/ toluene the known literature values of χ (in dilute solution χ ) 0.432,27 and for concentrated solutions χ(φ2) ) 0.431 - 0.311 φ2 - 0.036 φ22: 28 Although linearization is not bad, the resulting γ values are much too large and out of any physically acceptable range. We obtain γapp ) 83 mN/m for the sulfonate latices and γapp ) 230-270 mN/m for the sterically stabilized particles. For polystyrene and water, a value of γ ≈ 32.7 mN/m is reported,29 with toluene having a very similar value, so that a composition shift is expected to be neglectible. In addition, all curves cross the Y-axis (infinitely large particles) at a positive energy, which is physically meaningless. We have to conclude that the MKA formalism, although widely accepted, is not appropriate to describe the swelling of polymer latex particles. This theory clearly overestimates the swelling, and the experimentally determined swelling ratios are well below the predicted ones. Also, considering a Kelvin effect only does not result in a satisfactory description of the data; the description improves, but the resulting fitted interface energies are still far too large. It is known that interface energy and the cohesion energy of a colloid depend on particle size. Gibbs and Tolman derived for a liquid droplet in equilibrium with its own vapor phase an expression to describe this dependence.30,31 The size of the droplet where this effect becomes visible, the Tolman length, is, however, very small and on the order of 1 nm, at maximum. When the interface energy decreases, the hydrophilic character of the polymer in direct proximity to the water phase is increased. This might induce a less swellable interface zone. Following
Gibbs arguments, it is calculated that this zone is only some low multiple of the Tolman length. Even in very unfortunate cases, this effect dies out within 5 nm, whereas the experimental deviations come up to the 100 nm size scale, and, consequently, there is no chance to describe the observed size dependence with these phenomena. On the other hand, the characteristic length scales of the found swelling restrictions are typical for polymers, and the predicted depletion pressure described above is in the correct size range. (For concentrated solutions, the characteristic length of the depletion effect is on the order of the entanglement length, i.e., ca. 16 nm for a 50% polystyrene solution in toluene.) As a consequence, we apply eq 4 and calculate from each data point with the literature value of χ the extra pressure to correct for the difference between experimental results and theoretical values. Since the pressure term and surface tension work into the same direction, a simultaneous determination of both γ and ∆p is impossible. To avoid negative pressures, a relative low interface energy of the sulfonate-stabilized particles had to be assumed. A value of γ ≈ 12 mN/m was taken for optimal stabilization of the fit, but any similarly low value results in similar going results. For the sterically stabilized latex particles, the validity of the literature value of γ ) 32.7 mN/m was accepted. The resulting depletion pressures are shown in dependence of the inverse particle size (Figure 6): It is observed that the calculated extra pressure values depend significantly on the particle size: the smaller the size, the higher is the required extra pressure to explain the experimental data. The absolute pressure values are rather high and on the order of typical osmotic gel pressures, i.e., up to 100 bar. This size dependence as well as the magnitude go well with the proposed depletion mechanism. The straight line describes a pressure scaling of ∆P ∝ R-5/4, but due to an adding up of errors related to the assumptions, this scaling is inflicted with high errors. Independent of the rather low γ-value which was necessary to be assumed, the pressure curve of the sulfonate-stabilized particles is significantly below the curve of the sterically stabilized latices. GPC measurements reveal that the molecular weight of the sulfonated polymers is well above the entanglement molecular weight (Mw ) 410 000 g/mol), which rules out the molecular weight to be the source of these deviations. A possible explanation
(27) Brandrup, J.; Immergut, E. H. Polymer Handbook, 3rd ed.; Wiley: New York, 1989. (28) Noda, I.; Higo, Y.; Ueno, N.; Fujimoto, T. Macromolecules 1984, 17, 1055. (29) Vijayendran, B. R. J. Appl. Polym. Sci. 1979, 23, 733. (30) Gibbs, J. W. Collected Works; Longman & Green: London, 1928; p 299. (31) Tolman, R. C. J. Chem. Phys. 1948, 16, 758; 1949, 17, 118, 333.
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some of the difficulties on the way to a more quantitative description of the charge repulsion effect. More definite answers therefore have to await experiments on a broader base of sample sets including larger particles, different molecular weights, and different locations of the charges within the chain. V. Conclusion and Outlook
Figure 7. Illustration of the surface anchoring effect. Each polymer chain contains on the average seven charges which are pitched to the surface and reduce the loss of conformations and the related depletion. Coulombic interaction between charges supports the swelling and decreases the apparent interface energy.
can be derived from a paper by Gilbert et al.,32 who published on the scattering behavior of swollen latex spheres. In this work, differences in the scattering profiles were related to a so-called “surface anchoring effect”, i.e., a fixing of the polymer chain at the interface due to incorporated charges or surface-active groups. It is straightforward to assume that the GilbertOttewill mechanism is also responsible for the rather small depletion pressures observed in our swelling experiments, since such chains are attracted by the particle interface and counterbalance that way a large part of the entropy loss. From the absolute surface charge density and the size of the latices, for instance, latex 2/3/1#7, and the molecular weight of the polymer at least 826 charges, i.e., each chain has to incorporate on the average 7 ionic groups (surfmers) at minimum. The working principle of this pinning mechanism is graphically illustrated in Figure 7. Within the same picture, the rather low interface energy of the sulfonated latex particles is explained by charge/ charge interactions. For the whole series of particles, we can calculate from the structural data and the absolute charge density an averaged area per charge of 1.85 nm2/ sulfonate group. In other words, the charges are in rather close proximity of each other, and strong coulombic repulsion between the charges might be expected. This repulsion assists swelling and explains a decrease of the force to create a unit area of new surface, i.e., the surface tension. For additional information, we also performed capillary electrokinetic measurements where the electrophoretic mobilities of some selected latices before and after the swelling were measured in dependence of the ionic strength of a series of salt solutions.33 The fit of these data according to Overbeek-Wiersama (which is possible only in an intermediate range of the ionic strength) results in the ζ-potential of the systems.34 For the latex 2/3/1#3, we find for instance ζ ) 92.4 mV and ζ ) 102.7 mV for the unswollen and the swollen states, respectively; i.e., the ζ-potential is even increasing with swelling (where absolute charge density should decrease). This underlines (32) Mills, M. F.; Gilbert, R. G.; Napper, D. H.; Rennie, A. R.; Ottewill, R. H. Macromolecules 1993, 26, 3553. (33) Kaspar, H. Ph.D. Thesis Potsdam, 1996. (34) Wiersama, P. H.; Loeb, A. L.; Overbeek, J. T. G. J. Colloid Interface Sci. 1966, 22, 78.
The swelling of pure monodisperse latex fractions with different surface functionalities was examined with densitometry and dynamic light scattering. It turned out that the data contradict the classical description of Morton, Kaizermann, and Altier. Moreover, a systematic trend of the smaller particles to swell less was observed. A new approach considering the effects of a Kelvin and a depletion pressure was presented, thus allowing the description of the experimental data. Within the framework of this model, extra pressures of up to 100 bar have been calculated; i.e., these effects play a major and significant role for the swelling of polymer colloids. Latex particles carrying a larger number of charges on their surface show a much better swelling than their weakly charged or sterically stabilized counterparts. Two reasons for this behavior were given: besides a “surface anchoring” effect, first proposed by Gilbert et al., which pitches the polymer chains to the surface via their ionic charges and neutralizes a part of the depletion pressure, a strong coulombic ion-ion repulsion of surface charges was supposed. Based on the presented data, some relevant problems become evident which have to be examined in a forthcoming work. For instance, it is interesting to examine the dependence of the swelling on the molecular weight of the polymer chains constituting the latex particles, which enables one to check some characteristics of the proposed depletion mechanism. The surface anchoring effect can be analyzed in terms of a varying composition and positioning of charges of the polymer chains. In addition, some data of the swelling of larger particles must be elaborated, since effects of an altered surface tension as compared to depletion effects become most important in the size range of some 100 nm. On the other hand, there are a number of restrictions to produce latex particles of any size with any composition, since swelling and latex synthesis mutually influence each other; e.g., a latex with high swelling ratio has some tendency to grow large already during synthesis, and surface-active chains with low depletion pressures will assist formation of a larger number of smaller particles. These problems of the reaction engineering offer vice versa some important possibilities: a better control of the swelling effects in emulsion polymerization will definitely allow a better control of latex properties, i.e. particle size, particle stability, reaction kinetics as well as inner architecture. Acknowledgment. Financial support by the Max Planck Society is gratefully acknowledged. We want to thank H. Co¨lfen for the fractionation of the colloidal dispersions with ultracentrifugation. LA960159I
