412
Langmuir 1994,10,412-417
Colloidal Interactions in Water/2-Butoxyethanol Solvents Steven R. Kline and Eric W. Kaler* Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received June 1, 1993. I n Final Form: October 6, 1 9 9 9 The behavior of a colloidal silica dispersion in the mixed solvent of H2O or D2O and 2-butoxyethanol (C&) is studiedas a function of solvent composition and particlevolume fraction. Under certainconditions, the silica particles undergo a phase transition (gas/liquid)that is reversible on dilution or cooling. Small angle neutron scattering measurements are performed on one-phase samples, and the resulting scattering curves are modeled using appropriate forms of the pair interaction potential. In D20, the silica particles are highly charged and stabilized by Coulombic repulsion. As the C& content of the solvent is increased, Coulomb forces are diminished and the particles behave as hard spheres. At higher C& concentrations, attractive interparticle interactions become important and the particles behave like sticky hard spheres. The sticky hard sphere parameters obtainedfrom fits to the scattering data compare well to those required by theory to match the observed phase boundary.
to flocculation. Unmodified silica flocculates reversibly near the coexistence curve of a binary fluid mixture.1° Charged colloids are usually stable in water, and the Such particle aggregation is thought to result from merging factors governing their stability are well-known.' The of thick prewetting layers on the silica surfaces. Silica in addition of organic molecules to an aqueous colloidal water/dioxanell or water/alcohoF2 mixtures is either dispersion can modify the bulk properties of the solvent stabilized or destabilized by the adsorption of ionic and the surface properties of the colloids. Either change surfactant. Stability correlates with the zeta potential, can have a profound effect on the stability of the dispersion. which depends on the degree of surfactant adsorption and When the added organic molecules are surfactants, the the bulk solvent properties. effect is particularly strong.2 Colloidal stability is governed by the shape and sign of the interparticle potential. For small colloids, this poSystems of silica particles with an organic layer grafted to the surface have been studied in nonaqueous s0lvents3~~ tential can be probed accurately using small angle neutron scattering (SANS), and the measured spectra can be and display a temperature-dependent separation into two interpreted in terms of models of interparticle interactions. phases. The attractive interparticle interactions in these SANS thus provides an ideal way to monitor the changes systems arise from preferential mutual solvation of the in interparticle interactions that ultimately set the strucsurface layers and have been modeled in terms of an ture of the dispersion. adhesive hard sphere interaction potential. Silica made To investigate the relative roles of bulk and surface hydrophobic by adsorption of a cationic surfactant has properties in setting the stability of colloids in mixed been studied in solvents with a wide range of alcohol/ solvents, we have investigated a model dispersion of silica water ratios.5 The attractive interparticle interactions in in mixtures of water and the weak amphiphile 2-butoxthese systems are believed to be due to hydrophobic yethanol (C4E1). To be able to describe the silica particles interactions between the organophillic surfaces. A study in terms of equilibrium thermodynamic (rather than of Ludox TM in the presence of the nonionic surfactant kinetic) stability, the time scales for particle collision and CI2Essl7shows a temperature-dependent separation into doublet breakup must be much less than the time scale particle-rich and particle-poor phases. A bilayer of of the experiment. The characteristic collision time for adsorbs strongly to the silica surface, but at saturation particles of radius R and volume fraction 4 in a solvent only 75% of the surface is covered with surfactant, ~ breakup time, of viscosity p is tc ~ f i 3 / @ k T . 'Doublet presumably in patches. Attractions between the adsorbed tb ( f i 3 / k T )exp(V/kT), is governed by the depth of the surface patches apparently drive the phase separation. attractive well, V. For the silica particles in this study, Charge-stabilized colloids have been studied in mixed both of these characteristic times are estimated to be less solvent systems of ethanol/cyclohexane* and water/eththan 1ms; thus equilibrium behavior is expected in the ylene glycol? where supression of the surface charge leads time scale of our experiments ( 105 s). * To whom correspondence should be addressed. Theory e Abstract published in Advance ACS Abstracts, January 1,1994. (1) Verwey, E. J. W.; Overbeek, J. Th.G. Theory of the Stability of Sticky Hard Sphere Phase Behavior. Attractive Lyophobic Colloids; Elsevier: Amsterdam, 1948. interactions are modeled in terms of a sticky hard sphere (2) Hough, D. B.; Thompson, L. In Nonionic Surfactants, Physical (SHS)model. Baxter's solution14of the factorized OrnChemistry; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; Chapter 11. stein-Zernicke equation recently has been rederived as a (3) Duita, M. H. G.; May, R. P.;Vrij, A.; de Kruif, G. C.Langmuir 1991, perturbative solution16andhas been shown to be applicable 7, 62. Introduction
-
-
-
(4) Woutersen, A. T. J. M.; May, R. P.; de Kruif, C. G. J. Colloid.
Interface. Sci. 1992, 151, 410. (5) Shchukin, E. D.; Yaminsky, V.
V. Colloids Surf. 1988, 32, 19. (6)Cummins, P. G.; Staples, E.; Penfold, J. J.Phys. Chem. 1990,94,
3740. (7) Cummins, P. G.; Staples, E.; Penfold, J. J. Phys. Chem. 1991,95, 6902. (8) Vincent, B.; Kiraly, Z.; Emmett, S.; Beaver, A. Colloids Surf. 1990, 49, 121.
0743-7463/94/2410-0412$04.50/0
(9) Lyklema, J.; de Wit, J. N. Colloid Polym. Sci., 1978,266, 1110. (10) Gurfein, V.;Beysene, D.; Perrot, F. Phys. Rev. A 1989,40,2543. (11) Kandori, K.; Kon-no, K.; Kitahara, A.Bull. Chem. SOC. Jpn 1984, 57, 3419. (12) Eeumi, K.; Ikemoto, M.; Meguro, K. Colloids Surf. 1990,46,231. (13) Rueeel, W. B. TheDynamm of ColloidalSrcspeneions;University of Wiaconein Preas: Madison, WI,1987; Chapter 2. (14) Baxter, R. J. J. Chem. Phy8. 1968,49,2770.
0 1994 American Chemical Society
Colloidal Interactions in H2O/C$I Solvents
Langmuir, Vol. 10, No. 2, 1994 413 28, by q = (4r/X) sin 8. The function P(q) = ((F(q)I2), where F(q) is the single particle scattering amplitude and depends on the size and shape of the scatterer. S(q)is the structure factor and is a function of the interactions between the particles. To describe the colloid quantitatively, it is useful to fit a theoretical model to the experimental data. For the simple case of monodisperse spheres of radius R, the particle form factor P(q) can be easily calculated
la
3.41
,
,
0.00
,
,
,
,
0.10
0.05
.
0.20
Volume fraction 1.0
,
,
0.15
,
,
0.25
1 0.30
0
.
I
S(q) depends on the relative positions of the particles and is essentiallythe Fourier transform of the pair distribution functiong(r). For an isotropic dispersion of particles, this can be written as
+
S(q) = 1 4rnJOm[B(r)- l][(sin qr)/qr]r2dr
(4) By assuming a form for the pairwise interaction between particles, g(r) (and S(q)) can be calculated from the Ornstein-Zernicke equation
I..
0.0 0.00
,
. , . . 0.05
..,. 0.10
. .
., 0.15
.
..
. ,. 0.20
.
.
. , . . 0.25
.. I 0.30
Volume fraction Ludox TM
Figure 1. Phase diagrams of the SHS model and the experimental system. (a) Sticky hard sphere phase boundaries, using e = 0.02. The critical values are Ub = 3.75kT and & = 0.114. (b) Experimental system of Ludox in a mixed solvent of water and C&, showing correlation between SHS well depth and solvent composition.
to colloidal systems.16 The perturbation of the PercusYevick closure is a narrow square well, described by a depth UOand a width A, for a hard sphere of diameter d. The perturbation parameter is e = A/(d + A). The perturbative SHS solution displays the same behavior as Baxter’s results, but allows a more natural definition of the stickness parameter, T , in terms of the square well depth, as T = (1/12e) exp(Uo/kT). Particle concentration q is related to the true volume fraction 3,as q=- 3 (1) (1- 4 3 The phase diagram displays an asymmetrical gas-liquid coexistence curve, with the critical parameters T~ = (2 21/2)/6 and qc = (3/21/2)- 2. The phase diagram is plotted in Figure la, in terms of well depth versus volume fraction for t = 0.02. For this value of e, the critical values are U h -3.75kT and aC= 0.114. SANS Theory. Small angle scattering is a useful tool for probing colloidal systems and information can be obtained about particle size and shape and interparticle interactions.17J8 For small angles, the scattered intensity from a collection of colloidal particles is =“ ( q )
(2)
where n is the number density of particles. The magnitude of the scattering vector is related to the scattering angle (15) Menon, S. V. 96,9186.
0.; Manohar, C.; Rao, K. S . J . Chem. Phys. 1991,
(16)Rao, K.5.;Goyal, P. S.;Daeannacharya,B. A.; Menon, S. V. G.; Kelkar,V. K.;Manohar, C.; Miehra, B. K. Physica B 1991,174,170. (17) Small Angle X-Ray Scattering; Glatter, O., Kratky, 0. Eds.; Academic Prese: New York, 1982. (18) Kaler, E. W. J. Appl. Crystallogr. 1988, 21, 729.
y(rI2) = WI2)- c(r12)= n J ~ ( r , , ) h ( r ~dF3 ~) (5) where r12 is the distance from particle 1to particle 2, c(r) is the direct correlation function, and h(r) = g(r) - 1. To solve the Ornstein-Zernicke equation for a given interparticle potential, a closure relation is needed to relate h(r) and c(r). The repulsive Coulombicpair potential describes charge ~ stabilized systems in terms of the Debye length 1 / and charge per particle z. U(r) = w r 2R (6) This potential was used along with the Rogers-Young closure relation,lS which mixes the Percus-Yevick (PY) and hypernetted chain (HNC) closures such that
with f(r) = 1 - exp(-cyr). The above relation reduces to the PY closure when the mixing parameter cy = 0 and to the HNC closure when CY = 03. The mixing parameter is chosen to achieve thermodynamicconsistency by matching the bulk modulus as predicted by the pressure and compressibility equations. The structure factor for the SHS potential is calculated from a factorized form of the Ornstein-Zernicke equation (5)and the P Y closure, c(r) = [l-exp(u(r)/kT)]g(r). The structure factor is then calculated as S(q1-l = 1- pc(q), where c(q) is the Fourier transform of c(r). Real colloidal systems are not in general monodisperse. Polydispersity has a significant effect on the scattered intensity and must be accounted for properly. Under the “decoupling” assumption that there is no correlation between position and particle size,polydispersityhas been accounted for in terms of an effective structure factor S’(q),2OJ1where S”
= 1+ P(q)[S(q)- 11
(8)
and where F ( q ) is the single particle scattering amplitude and the averages are taken over the size distribution. (19) Rogers, F. J.; Young, D. A. Phys. Reu. A 1984,30,999. (20) Hayter, J. B., Penfold, J. Colloid Polym. Sci. 1983, 261, 1022.
Kline and Kaler
414 Langmuir, VoZ. 10, No. 2, 1994 Table 1. Scattering Length Densities
compound H20 D2O
Pdd
cm/A9 4.0056 0.0634
compound CrEl Si02
Pdd
'qE1
cm/As) 0.00039 0.0349
The absolute scattered intensity depends on the contrast between the particles and the solvent. The coherent neutron scattering length is known for each nucleus22so a scattering length density can be calculated for a compound given its atomic composition,bulk density, and molecular weight. Scattering contrast ( A P ) ~is the differencein scatteringlength densitiesbetween the scatterer and the solvent. Table 1shows that the scattering length density of silica lies between that of C4E1 and D20. Thus at a particular C&/D20 composition,the scatteringlength densities of particles and solvent will match. At this contrast match point (-36 wt % C&) the contrast ( A P ) ~ is zero, and so is the scattered intensity. In many cases contrast matching can be a powerful tool for probing particle structure,23but here it is an experimentalnuisance.
Experimental Section Materials. The silica dispersion Ludox TM (DuPont) was used assupplied. The dispersionis reportedto be discretespheres 22 nm in diameter and supplied as 50 w t % silica. The quoted bulk density value of 2.3 g/mL agreeswith the measured density of dilute Ludox solutions. The silica particles are stabilized by the dissociationof surfacehydroxyl groups,thus the surfacesare negative at high pH. The surface charge is screened by sodium salts at a concentrationof ca. 0.05 M. C4E1(LancasterSynthesis) was reported to be 99% pure, but proved to be less so by gas chromatography. The lower critical temperature of a 29 w t % solution was determined to be 46.8' C, while the accepted value for pure C4E1 is 48.7 OC.U C& from TCI America, on the other hand, clouded at 48.5 "Cand was thus consideredto be pure. The impuritiesin the Lancaster Synthesisproduct were not identified, but had only a minor effect on the particle phase behavior. The Lancaster Synthesis product was used for all measurements reported here. Water was distilled and deionized before pH adjustment with NaOH to match the pH 9 of the Ludox stock solution. PhaeeBehavior. Phasebehaviorpattermwererecordedafter preparingsamples (ona weight percent basis) and allowingthem to equilibrate in a water bath for 24 h at 25 'C. Most samples appearedto be equilibratedafterless than 30 min. Phasebehavior of samples near the two-phase boundary did not change after a week, an indicationthat the systemwas thermodynamically,and not kinetically, controlled during the time scale of the observations. All one-phase samples were transparent and blue, and as more C& was added, the color weakened due to the closer refractive index match of particles and solvent (ma= 1.46, ma1= 1.42, hbr = 1.33) Two-phase samples near the phase boundary appearedwhite and turbid upon mixing but ultimately split into two distinctly different phases. Both of these phases were transparent and blue, suggesting that an equilibrium structure had been reached. The lower, particle-richphase was often highly viscous. The two-phase samples far from the boundary contained a loose opaque gel upon mixing. In these samples,the white colorationpersisted, indicatingthe formation of irreversible aggregates and thus the presence of stronger attractive interactions that prevented the formation of an equilibrium structure. The transition from one to two phases was readilyreversibleby changing the samplecomposition, gently agitating and allowing the sample to reequilibrate for several (21) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79,2461. (22) Bacon, G. E. NeutronDiffraction;ClarendonPress: Oxford, 1975; p 39. (23) Williams, C. E In Neutron, X-Ray and Light Scattering: Introduction to an Investigation Tool for Colloidal and Polymeric Systems;Lindner, P., Zemb, Th., Eds.; North-Holland: New York, 1991; p 101.
(24) Kahlweit, M.; Strey, R. Agnew. Chem., Int. Ed. Engl. 1985,24,
654.
Ludox TM
Water
Figure 2. Ternary phase diagram for the system water/C&/
Ludox. Samples were equilibrated at 25 ' C for 24 h. SANS experiments were performed along paths marked A, B, and C. minutes. After several excursions across the boundary, most samplesbecame slightlymore turbid, suggestingsome formation of irreversible aggregates. SANS Measurements. SANSsampleswere prepared in the one-phaseregion by addition of C&l and D2O to a Ludox stock solution. The D20 was pD adjusted with NaOH to a pD of 9.0. Samplesprepared in D2O were at least as stable asthose prepared in HzO, but the phase diagram was not determined in D2O. Counterionconcentrationsused to calculateDebye lengths were determinedby measuringthe supernatantof centrifugedsamples with an ion-selective electrode. Sodium or pD measurements were made only in aqueous solvent. Small angle neutron scattering measurements were made on the 30-m SANS spectrometer at the National Institute for Standards and Technology at Gaithersburg, MD. Equilibrium samples were held in 1- or 2-mm quartz cells and measured at 25 "C with 7 A wavelength neutrons having a wavelength spread of AA/A = 0.097. The raw 2 - 0 intensity data were corrected by subtractingthe appropriatesolventbackground and then radially averagingto give one-dimensionaldata. The resulting intensity data were placed on an absolute scale using a polystyrene standard. Wavelength and collimation effects were simulated and found to be insignificantfor these instrumental conditions. Calculated model intensity was fit to the scattered intensity on absolute scale by a least-squares criteria, and the model intensity was multiplied by a scale factor to improve the fits to absolute scale. These scale factors were all within 10%of unity except for samples near the contrast match point. At that point small inaccuraciesin the scatteringlength densitieslead to larger errors in the calculated contrast. Particle size polydispersity was modeled using a Schultz distribution. In the q-range observed, the repulsive contact potential has to be greater than O.lkT or the SHS well depth more than 2kT in order for the calculated spectra to be significantly different from that calculated for a dispersion of the same-sized hard spheres. These tolerancesare significantlylower than the fitted repulsivecontact potential of -70kT and attractive well depth of -3kT.
Results Phase Behavior. The phase diagram for the ternary system C4El/water/Ludox at 25 OC is shown in Figure 2. There is no liquid-liquid phase separation in the binary CaEl/water system, as its lower consolute point is 48.7 "C and the amount of salt present would not lower the critical point by more than 3 OC.25 There is a large region where the particles separate into "liquid" and "gas" phases. Replotting the phase diagram in terms of the weight fraction C4E1 in the solvent versus the volume fraction of (25) Firman, P.; Haase, D.; Jen, J.; Kahlweit, M.; Strey, R. Langmuir 1985,6,718.
,
Colloidal Interactions in H20ICJZl Solvents itn
.
i
.-100
c
0 . 0
100
Langmuir, Vol. 10, No. 2, 1994 415 150
1-
0.03
0.00
SANS of Ludox TM in D2O. Cwes are least-squares
Figure 4.
0.01
0.02
0
0.01
0.02
q (A-1)
Figure 3.
0.02
0.01
q
0.03
(A3
SANS of 2 w t % Ludox TM in D20/C& mixtures.
best fits to the data using a Coulombicinteraction potential and the Rogers-Young closure. The plots are (a) 4 = 0.0082,(b) 4 = 0.023,(c)4 = 0.029,and (d)4 = 0.0042. The increasein particle charge with volume fraction is a charge regulation effect.
Cwes are least-squaresbest fits to the data using SHSpotential. The plots are (a) 20% C&, (b)50% CIEI,(c) 70% C& and (d) 90% C&. The variation in absolute intensity is due to changes in contrast. The contrast match point is at 36% C&.
Table 2. Fitting Results Using RY Closure for Ludox TM in D,O 4 measured l/rc (A) 95 fit Z fit (e-) 0.010 91 0.0082 140 0.025 56 0.023 185 0.036 46 0.029 240 0.052 38 0.042 280
Table 3. Fitting Results Using SHS Model for Ludox TM in CIE~/DIOmixtures
particles (Figure lb) highlights the similarity with the SHS phase diagram (Figure la). Addition of C4E1modifies the interparticle potential and ultimately increases the attractive contribution to the potential to the level needed to drive phase separation. Compositions of the separated phases of Figure 2 have not been determined, but measurements of the densities and Ludox concentrations show partitioning of C4E1 between the two particle phases. C4El is carried along with the particles to make the particle-rich phase also rich in C4E1. The phase separation also depends on temperature, although that effect has not been fully studied. Adding octane to a mixture containing particles in a solvent of equal weights of C& and water forced a separation into oil-richand water-rich phases. The particles remained exclusively in the water-rich phase, and were stable, so the silica surface was not rendered permanently hydrophobic by C4E1. SANS Path A. SANS spectra of Ludox in DzO (path A on Figure 2) are shown in Figure 3. Model fits to the lowest Ludox volume fraction data suggested a particle radius of 142 A with a standard deviation of 26 A using a Schultz distribution, which is in agreement with the results of SANS from similar Ludox sols.26 These two particle parameters and the calculated Debye length were held constant during fitting, and only the particle charge, 2,and the volume fraction were changed to obtain the best least-squares fit. S(q) was calculated in the RY approximation and the resulting fitted parameters are shown in Table 2. The charge per particle increases with volume fraction and the fitted volume fractions are consistently 20% lower than volume fractions calculated from measured weight fractions. This adjustment of volume fraction was necessary to match the location of the interaction peak. Discrepancies with the model fits are most likely due to inaccuracies in the decoupling approximation a t low q values which become more visible at higher volume fractions. (26) Bunce, J.; Ramsay, J. D.F.;Penfold, J. J. Chem. SOC., Faraday Trans 1 1985,81,2846.
wt%
CrEl 20 50 70 90
6 fit 0.0097 0.0091 0.0087 0.0084
SHS
uo fit
prediction
(kT) 3.40 3.46 2.60 3.86
