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Langmuir 1995,11, 2352-2356
Measurement of Long Range Depletion Energies between a Colloidal Particle and a Flat Surface in Micellar Solutions D.L. Sober and J. Y . Walz* Department of Chemical Engineering, Tulane University, New Orleans, Louisiana 70118 Received February 27, 1995. I n Final Form: May 5, 1995@ The interaction energies between colloidal polystyrene latexes and a flat plat have been measured in the presence of cetyltrimethylammoniumbromide (CTAB)micellesusing total internal reflection microscopy (TIRM). Long range attractive depletion forces were observed down to micelle concentrations of 0.02% vol. Potential minima ranging from 1.5to 6 kT were measured at separation distances of 50-70 nm, with attractive interactions extending well above 100 nm separation. The relationship between the depth of the potential minima and the micelle volume fraction was found to agree well with the predicted contact potential for a hard-sphere-hard-wall interactionbetween a sphere and a flat plate. At CTAB concentrations greater than 2 mM (0.08% vol. micelles) the onset of an oscillatory energy profile was observed, thus indicating a structural contribution to the overall interaction energy.
Introduction The ability of nonadsorbing polymers to promote flocculation in colloidal dispersions has been documented since 1925 when Traubel reported on the creaming of natural rubbers by the addition of water-soluble polymers. Since that time, numerous other researchers have studied this phenomenon, often referred to as depletion flocculation or the depletion effecte2-11 Such investigations have important technological and physiological applications. Colloidal stability in mixed systems is an important concept in a variety of industrial and agricultural processes, such as the manufacture of paints, water-based inks, coatings, adhesives, milk, and many other food products. In addition, many biological systems, such as blood and tissue cells, can be described as mixtures of colloidal particles interacting with each other and with other noncolloidal components. The current generally accepted explanation for depletion flocculation was introduced during the 1950s by Asakura and 0osawa,l2J3who proposed that the attractive force between colloidal particles in a solution of macromolecules arises from osmotic pressure effects due to the exclusion of macromolecules from the region between the particles. As the distance between particles becomes less than the effective diameter of the macromolecules, the molecules are excluded from the region between the particles, since their inclusion would decrease the configurational entropy of the system. The region between the particles becomes essentially pure solvent, while the remainder of the solution remains a t the bulk solute concentration. The
* To whom correspondence may be addressed: telephone 504865-5620;fax 504-865-6744; e-mail
[email protected]. Abstract published in Advance ACS Abstracts, June 1, 1995. (1)Traube, I. Gummi Ztg. 1925,39, 434, 1647. (2) Li-in-on, F. K. R.; Vincent, B.; Waite, F. A. ACS Symp. Ser. 1975, No. 9, 165. (3)Cowell, C.;Li-in-on, F. K. R.; Vincent, B. J. Chem. SOC.,Faraday Trans. 1 1978,74,337. (4) Vincent, B.; Luckham, P. F.; Waite, F. A. J. Colloid Interface Sci. 1980,73,508. (5) de Hek, H.; Vrij, A. J. Colloid Interface Sci. 1979,70,592. (6) de Hek, H.; Vrij, A. J . Colloid Interface Sci. 1981,84,409. (7) Sperry, P. R.; Hopfenberg, H. B.; Thomas, N. L. J . Colloidlnterface Sci. 1981,82, 62. ( 8 ) Sperry, P. R. J. Colloid Interface Sci. 1982,87,375. (9) Liang, W.; Tadros, Th. F.; Luckham, P. F. Langmuir 1994,10, 441. (10)Luckham, P. F.; Klein, J. Macromolecules 1985,18,721. (11)Ma, C. Colloids Surf 1987,28,1. (12)Asakura, S.;Oosawa, F. J . Chem. Phys. 1954,22,1255. (13)Asakura, S.;Oosawa, F. J. Polym. Sci. 1958,33, 183. @
~~~
osmotic pressure between the particles, thus, becomes lower than that surrounding the particles, and a net attraction develops. Although relatively simple, this hardspherehard-wall interaction has been used successfully to predict the onset of phase separation in a variety of colloidal s y ~ t e m s . ~ - ~ J l J ~ The majority of the experimental work to date on depletion flocculation has concentrated on predicting forces between colloidal particles in the presence of neutral, nonadsorbing polymers, e.g., p o l y ~ t y r e n e , ~poly(eth~~J~ ylene o ~ i d e ) , ~ ,and ~JO hydroxy ethyl c e l l u l o ~ e .Little ~ , ~ work has been conducted on systems involving charged species in solution, such as polyelectrolyte molecules, smaller charged particles, or ionic micelles. Nevertheless, recent modeling studies performed by Walz and Sharma,15who extended the work ofAsakura and Oosawa to include long range electrostatic interactions, have indicated that both the magnitude and range of the depletion interaction are greatly increased in charged systems. Experimental evidence of such effects has recently been given by Richetti and Kekicheff, who measured interaction forces in a charged system of cetyltrimethylammonium bromide (CTAB) micelles and mica.16 One of the current shortcomings in the study of depletion forces is the lack of direct experimental measurements of the force. This is due primarily to the fact that t h e magnitude ofthe depletion interaction is below the typical sensitivity limits of the common force measurement techniques. Depletion forces in dilute solutions of macromolecules can be on the order of to N10J6while the resolution of typical force measurement techniques, such as the surface forces apparatus, is 10-8N.17Although Richetti and KekichefP were successfulin obtaining direct measurements of depletion forces between mica and CTAB micelles using the surface forces apparatus, relatively large concentrations of macromolecules were necessary (-1%to 7% vol) and interactions a t separation distances greater than 40 nm could not be detected. In the present paper we report the direct measurement of depletion forces between a colloidal particle and a flat plate in the presence of CTAB micelles using the optical technique total internal reflection microscopy (TIRM), (14) Gast, A. P.; Hall, C. K.; Russel, W. B. J. Colloid Interface Sci. 1983,96, 251. (15) Walz, J. Y.; Sharma, A. J. Colloid Interface Sci. 1994,168,485. (16) Richetti, P.;Kekicheff, P. Phys. Rev. Lett. 1992,68, 1951. (17)Israelachvili, J. N.Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1991; p 169.
0743-74631951241l-2352$09.00/0 0 1995 American Chemical Society
Langmuir, Vol. 11, No. 7, 1995 2353
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Micell-
To Data Acquisition Systcm
Fluid Well
I
Evan%& Wave Laser Beam (He-Ne)
Radiation ptessure Laser Beam (A r- ion)
/
Class Plate
..-.--________-. --a...
I...
Figure 1. Schematic of TIRM experimental setup for measurement of interaction energies between a colloidal sphere and a flat plate: inset a, expandedview of fluid well (not to scale);inset b, close-up of particldplate interaction (relative proportionsof particle and micelles similar to actual). which allows measurement of interaction forces down to N.18 The extreme sensitivity of this method has enabled us to observe depletion effects down to concentrations of 0.02%vol micelles and a t separation distances in excess of 100 nm.
Experimental Section Interaction energies between colloidal polystyrene latex spheres(7.5pm radius, Duke Scientific,Palo Alto,CAI and BK-7 optical glass were measured in solutions of CTAB (cetyltrimethylammoniumbromide, Cl&&+(CH&Br-, cmc = 0.9mM19) both aboveand below the cmc. TheCTAB, from SigmaChemicals, St. Louis,MO (99% purity),was used without further purification and water was deionized and filtered using a Barnstead NANOpurebioresearchgrade deionizationsystemequippedwith an ultrafilter. All experiments were carried out at 25 "C, above the Kram temperature of the surfactant (T~rafft = 19.6"CZo), and the CTAB solutions were prepared without pH adjustment (pH values for the tests ranged from -6 to 7). Prior to conducting force measurements, the glass slide and polystyrene particles were contacted with the CTAB solution overnight in order to equilibratethe surfaces with the surfactant. Potential energy measurements were conducted using total internal reflection microscopy(TIRM). Details of the technique have been given previously by Prieve and co-workers.18~21-23 A schematic of the apparatus is shown in Figure 1. The method employs a total internally reflected laser beam (He-Ne) to measure the interaction energies between a particle suspended in a CTAB solution and a glass plate. During measurement of the potential energy profiles, the particle is held in a fixed lateral position by radiation pressure (Ar-ion laser beam), also known (18) Walz,J. Y.; Prieve, D. C. Langmuir 1992,8,3073. (19) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1991; p 355. (20) Tsao, F-P.; Underwood, A. L. Anulytica Chimica Acta, 1982, 136, 129. (21) Prieve; D.C.; Luo, F.;Lanni, F.Famday Discuss. Chem. SOC. 1987,83,22. (22) Bike, S. G.; Prieve, D.C. Int. J. Multiphuse Flow 1990,16,727. (23) Prieve, D.C.; Frej N. A. Langmuir 1990,6,396.
as "optical tweezers". A discussion of the combined T I W radiation pressure technique has been givenby Walz and Meve. l8 In the current study,potential energymeasurementsbetween a glass plate and polystyrene particle were obtained first in a micellar solution of CTAB. The solution was then replaced with a 0.8 mM CTAB solution (just below the cmc) via an infusionwithdrawal pump while holding the particle in place using radiation pressure. Force measurements were then obtained in the submicellar solution, thus allowing direct comparison with the potential energy profiles obtained in the presence of macromolecular species.
Results and Discussion Plots of the interaction energies between a polystyrene latex sphere (R = 7.5pm) and glass plate a t various CTAB concentrations are shown in Figure 2 (note that the gravitational attraction has been subtracted from the overall interaction energies in these figures). Also shown are the potential energy profiles measured in submicellar solutions of CTAB (0.8mM). The micelle volume fractions (&) reported here were calculated assuming an aggregation number N of 9024*25 and a micelle radius a of 3 nm.25p26 The solid lines shown in the energy profiles represent an exponential fit to the potentials measured in the 0.8 mM CTAB solutions. At the separation distances encountered in the present study, the van der Waals interactions are negligible. Assuming the interactions in submicellarsolutions can be modeled using DLVO theory, the only significant energy contribution is, therefore, that of a long range electrostatic repulsion. For separation distances several times larger than the Debye length (cl, where K - ~= 10.75 nm a t 0.8 mM CTAB) the electrostatic (24) Lianos, P.; Zana, R. J. Colloid Interface Sci. 1981,84, 100. (25) Imae, T.; Kamiya, R.; Ikeda, S. J. Colloid Interface Sci. 1985, 108, 215. (26) Dorshow, R.; Briggs, J.; Bunton, C. A;Nicoli, D. F. J. Phys. Chem. 1982,86,2388.
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2354 Langmuir, Vol. 11, No. 7, 1995
4 3
0.8 mM CTAB
2 g 1
3 0 , d
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-1
1.2 mM CTAB 1.5 mM CTAB $,=4.5~10-~
$,=2.3x
-5
-5
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-,
~~~
0
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- I
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2.0 mM CTAB -5
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-6 0
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Qs
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I
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Figure2. Potentialenergy profiles measured between 7.5pmradius polystyrene sphere and BK-7 glass plate at variousconcentrations of CTAEL The measured gravitational attraction has been subtracted from the total interaction energy. Solid lines are exponential fit to the data at 0.8 mM CTAB. Measured Debye lengths from the 0.8 mM data are 8.16 (a), 10.49(b), 10.26(c), and 10.10(d)nm-l. potential between a flat plate and a spherical particle can be expressed using linear superposition and the Dejaguin approximation asz7
E J h ) = B exp(-Kh)
(1)
where B is a function ofthe sphere radius R and the surface potentials of the plate and the sphere. This expression is valid for R >> h >> K - ~and a symmetrical (z:z) electrolyte (Gouy-Chapman approximation). In the current work, the values for B were obtained by fitting eq 1 to the experimental results a t 0.8 mM CTAB so as to match the equilibrium separation distances. The values for K, on the other hand, were calculated from the ionic strength of the solutions. The results show that at CTAB concentrations below the cmc the potential energy profiles are in good agreement with those predicted by DLVO theory (eq 1). This is evident from comparisons between the Debye length calculated from the CTAB concentration ( K - I = 10.75 nm) and that obtained from a semilog plot of the experimental (27) Venvey, E. J. W.; Overbeek, J. Th.G. Theory ofthe Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948.
potential energy profiles. ln(E,,) = In B - ~h
(2)
An example of such a plot is shown in Figure 3 using the data from the 0.8 mM CTAB test shown in Figure 2d. The measured value of K - ~for this test was 10.10 nm. The measured Debye lengths for the other tests conducted a t 0.8 mM were 8.16, 10.49 and 10.26 nm, all comparing fairly well with the predicted value of 10.75 nm. At CTAB concentrations above the cmc, the potential energy profiles do not match those predicted by DLVO theory. Most notably, all the tests show a long range attractive minimum of 1.5 to 6 kToccurring a t separation distances ranging from 50 to 70 nm. This minimum is seen clearly to increase with increasing surfactant concentration (increasing &), while the separation distance decreases. In addition, the shape of the potential well changes with increasing micelle concentration. At higher micelle volume fractions, the attractive well becomes more narrow, acting over smaller separation distances. Similar results were observed by Richetti and Kekicheff,16 although a t smaller separation distances (10-40 nm) and
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Langmuir, Vol. 11, No. 7, 1995 2355 3
4
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3 2 -
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2.25 mM CTAB $,,=i0.2x104
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Figure 3. Semilog plot of measured potential energy versus separation distance. The data are from the 0.8 mM test shown in Figure 2d. Fitted value for K - ~= 10.10 nm.
much higher micelle concentrations (#,, = 0.009-0.073). It is interesting to note here that we observe attractive interactions well above 100 nm (see Figure la). Previous experimental and theoretical work on depletion interactions have suggested the development of a longer range repulsive potential energy barrier with increasing macromoleculec o n ~ e n t r a t i o n . ~ ~This J ~ *repulsive ~* barrier has been explained in terms of interactions among the macromolecules as they are forced into the confiningregion between p a r t i ~ 1 e s . lNo ~ ~such ~ ~ potential energy barriers were observed in the present study. This may be due to the low concentrations of macromolecules investigated. Such observations are not completely unexpected since Richetti and Kekicheff also reported on the absence of a potential barrier at low micelle concentrations (&, = 0.009, nearly a n order of magnitude higher than the highest concentration reported here). One interesting manifestation of the depletion interaction that has been observed by previous researcher^^^^^^^^^ is the formation of structural forces due to free energy changes upon packing of macromolecules in the confined space between approaching surfaces. These structural forces result in a n oscillatory interaction profile. Some evidence of this phenomenon was obtained in the current study. Figure 4 shows the results from a second test conducted a t 2.25 mM CTAB (& = 10.2 x The data show two distinct potential energy minima a t 35 and 60 nm separation. Similar observations were made for other tests conducted a t CTAB concentrations above 2 mM. While these results are not conclusive proof of a structural contribution to the interaction energy, the data certainly indicate the onset of a n oscillatory profile. Further studies a t higher micelle concentrations are needed to more accurately define this effect. As noted previously, the depth of the potential energy minimum was found to increase with increasing micelle concentration. A plot of the depth of this potential minimum versus micelle volume fraction is shown in Figure 5. The data can be reasonably well fitted by a straight line of slope 5450 and intercept of 0 kT (corresponding to no attractive interactions in the absence of micelles). As a quantitative comparison to this result, we consider the theoretical work performed by Asakura and Oosa(28)Feigin, R.; Napper, D. H. J.Colloid Interface Sei. 1980,75,525. (29) Parker, J. L.; Richetti, P.; Kekicheff, P. Phys. Reu. Lett. 1992, 68,1955. (30) Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 1989,133,
200
150
IO0
Separation Distance (nm)
Separation Distance (nm)
1.
0
0
- "3&
-3 -4 -5 -
Figure 4. Potential energy profile measured between 7.5 pm radius polystyrene sphere and a BK-7 glass plate in 0.8 and 2.25 mM CTAB.
.
t
0
2
4
6
8
IO
I2
Micelle Volume Fraction (@,,x104)
Figure 6. Depth of potential energy minimum versus micelle volume fraction. Data at each volume fraction represent averages of a number of experiments.
wa,12J3who modeled depletion interactions in the presence of neutral polymers using a volume exclusion approach and treating the macromolecules as hard spheres with a n effective diameter equal to the root mean square end-toend distance of the polymer. In such a system, the depletion attraction between a sphere of radius R and a flat plate separated by a gap width h can be calculated as
~ - 4aRh Ie J G~ - u 4a2R f
-k Rh2 -
for 0 Ih
Lo
for h
2a
(3)
2 2a
where e- is the bulk number density of macromolecules of radius a. A similar relationship has been derived previously for two identical hard spheres.15 In charged systems, the size of the particles and the macromolecules would be their "effective" size, equal to the physical size plus the electrostatic screening length. (For the particle, the effective size is essentially equal to the physical size since the particle radius is a few orders of magnitude larger than the screening length.) The effective contact point between the particle and the plate ( h = 0) then becomes the position of the secondary minimum.
2356 Langmuir, Vol. 11, No. 7, 1995
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Evaluating eq 3 at h = 0 and assuming the particle is much larger than the macromolecules (R>>a)gives
(4) Rewriting in terms of the volume fraction & gives
A similar relationship was developed by VrijS1 for two spheres interacting in dilute solutions of macromolecules. The two equations differ by a factor of l I 2 , reflecting the differences in geometry of the two systems. Plotting the contact energy (in kT) versus the volume fraction should thus produce a straight line of slope 3 R I a , or 7500 upon substitution of our values for the particle and the macromolecule radii (7.5 pm and 3 nm, respectively). This value compares relatively well with our measured slope of 5450. By use of the relationship given in eq 5, the micelle radius required to fit our data is 2.55 nm, which is in agreement with reported sizes ofa 2.53.5 nm.25326Similar comparisons were performed by Bibette et who found good agreement between the fitted potential energy depths of a n oil-in-water emulsion stabilized with sodium dodecyl sulfate (SDS)micelles and the predicted contact potentials for two interacting spheres. The agreement between our results and the hardsphere-hard-wall potential a t contact is somewhat surprising, since the effective size of the micelle is expected
-
(31)Vrij, A. Pure Appl. Chem. 1976,48, 471. (32)Bibette, J.;Roux, D.; Nallet, F. Phys. Rev. Lett. 1990,65,2470.
to be significantly larger than its physical size due to its high charge.26,33*34 Interactions in such charged systems have been shown recently by Walz and Sharma15to differ greatly from those predicted by a simple hard sphere approach, with both the magnitude and range of the interaction increased significantly by the electrostatic repulsion. Of course, applying a hard sphere model to these charged systems is a somewhat simplistic approach. Nevertheless, the results indicate that in micellar systems, the effect of long range interactions on the depletion force may be smaller than expected
Conclusions We have performed direct measurements of the interaction energy between colloidal polystyrene latexes and a flat plate in the presence of charged micelles of CTAB. The results show a n attractive minimum potential of 1.5 to 6 kT occurring a t separation distances of 50-70 nm. This potential minimum was seen to increase in magnitude with increasing micelle concentration. The relationship between the depth of the potential minimum was shown to agree well with the predicted values for the contact potential for a hard-sphere-hard-wall interaction between a sphere and a flat plate. Data obtained above 8 x volume fraction micelles ( 2 mM CTAB) show preliminary oscillatory behavior, indicating the onset of a structural contribution to the overall interaction profile. LA9501501 (33) Fernandez, M. S.;Fromherz, P. J.Phys. Chem. 1977,81,1755. (34)Dorshow, R.B.; Bunton, C. A.; Nicoli, D. F. J.Phys. Chem. 1983, 87,1409.
