9492
J. Phys. Chem. 1992,96,9492-9491
KEK-PF, T~ukuba,1W& Vol. 6,p 45. (24)Takamuku, T.; Yamaguchi, T.; Wakita, H. J. Phys. Chem.1991.95, 10098. (25)Takamuku. T.; Ihara, M.; Yamaguchi, T.; Wakita, H. Z . Naturforsch. 1992, 47a, 485. (26)Talramuku, T.;Yoshikai, K.; Yamaguchi, T.; Wakita,H. Z. N o m forsch. 1992.47a. 841. (27)Lankhorsi D.; Schriever, J.; Leyte, J. C . Ber. Bunsen-Ges. Phys. Chem. 1982,86,215. (28)Van der Maarel, J. R. C.; Lankhorst, D.; De Bleijser, J.; Leyte, J. C. J. Phys. Chem. 1986.90. 1470. (29)Struii, R. P. W. J.; De Bleijser, J.; byte, J. C . J. Phys. Chem. 1987, 91, 1639. (30)Jonas, J.; DeFries, T.;Wilbur, D. J. J. Chem. Phys. 1976,65,582. (31) Lang, E. W.;Bradl, S.; Fink, W.; Radkowitsch, H.; Girlich, D. J. Phys.: Gmdens. Matter. 1990,2, 195.
(32)Lang, E. W.; Llldemann, H.-D. In NMR Basic Principles and Progress; Springer-Verlag: Berlin, 1990;Vol. 24,pp 13+187. (33) (a) Shimizu,A.; Taniguchi, Y. Bull. Chem. Soc. Jpn. 1990,63,1572. (b) Ibid. 1990,63,3255. (34)Harmon, J. F.;Sutter, E. J. J. Phys. Chem. 1978,82, 1938. (35) Lang, E. W.; Prielmeier, F. X. Be?. Bunsen-Ges. Phys. Chem. 1988, 92. 717. (36)Hasebe, T.;Tamamushi, R.; Tanaka, K. J. Chem. Soe., Faraday Tram. 1992, 88, 205. (37)Prielmeier, F.X.;Lang, E. W.; Speedy, R. J.; Ltidemann, H.-D. Ber. Bunsen-Ges. Phvs. Chem. 1988.92. 1 1 11. (38) Nakamura, Y.;Shimohwa,'S.; Futamata,K.; Shimoji, M. J. Chem. Phys. 1982, 77, 3258. (39)Stejskal, E. 0.;Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (40)Gmrd, C.;Braunetein, J.; Bacarella, A. L.; Benjamin, B. M.; Brown, L. L. J. Chem. Phys. 1977,67,1555.
Rheology of Ternary Microemuisions Chih-Ming cben and Gregory G.Wan* School of Chemistry, The University of Sydney, Sydney, NSW,2006, Australia (Received: January 22, 1992; In Final Form: June 16, 1992)
The flow of ternary microemulsions composed of didodecyldimethylammonium bromide, dodccane, and water under shear has been investigated in both Couette and capillary viscometers. At all compositions studied the liquids were found to be Newtonian up to very high shear rates (-3000 s-'), although some indirect evidence for elasticity was inferred from capillary viscometry. The dependence of viscosityon composition is discwed and interpreted in tenns of the structure of the microemulsion in both bicontinuous and water-in-oil domains.
Iatrodpction There have been a number of studies detailing the properties of three component microemulsions formed by double-chained The most quatanary ammonium surfactants with oil and common among these are systems comprising didodecyldim e t h y l a m " bromide (DDAB), water, and a c6+ alkane. DDAB is essentially insoluble in both alkanes and water, which makes it attractive as a model surfactant as an inventory of the total area of the alkane/water interface in the microemulsion may easily be kept. A partial isotropic phase diagram of the DDAB/dodecane/ water system, showing the singlephase microemulsion region, is given in Figure 1! Throughout most of the singlephase region, these microemulsions are bicontinuous, as inferred from conductivity,' diffusion coefficients? and small-angle ~cattering.~.' However at high water content they undergo a reverse percolation and a structural transformation into water droplets in oil. The boundary between discrete and continuous regions of the microemulsion is indicated by the dashed l i e in Figure 1. We are interested in the rheology of such liquids for a number of reasons. primarily we wish to study the relationship between structure and flow behavior. Three component DDAB microemulsions are ideal models for this study as their structure has been thoroughly examined using a number of techniques, as mentioned above. Importantly the structures formed depend on DDAB/oil/water composition, allowing a variety of equilibrium structures to be investigated within the framework of the same chemical system. It is known from previous work with solutions of cylindrical micelles**9that viscoelastic effects may arise, and the existence of transient bicontinuous networks has been postulated. Bicontinuous microemulsions might well be expected to display similar behavior. Previousstudies of the rheology of microemulsions are scarce. Those that do exist have concentrated on droplet structures, either oil-in-water'o or water-in41 dispersions,11with little attention to the shear rate dependence. Systematic study of the rheology of Author to whom correspondence should be a d d r d .
bicontinuous microemulsions has been hampered by a lack of knowledge about the equilibrium structure of the liquid, so that even thorough rheological examination must be analyzed by a more or less arbitrary parametrization.I2 Rheology is not the way to investigate structure. Rather it is the contrary, and a useful interpretation of rheological measurements requires some knowledge of the equilibrium structure so that the perturbative effect of shear may be ascertained. This is why the DDAB/dodecane/water system is ideal for such a purpose. Application of a shear field to a complex liquid such as a microemulsion holds the promise of a technique for determining the dynamics of reorganization of these systems. About this more is said in wnnection with the results. In our interpretation of the rheology of these model microemulsions we will need to make reference to what is known about their equilibrium structure and properties. Previous results and the models used for their interpretation are discussed in the following section, after which we return to the immediate issue of their flow behavior. S t " rad Re)crtkr of DDAB/Allrree/Water Micro. e " . The microemulsion phase, b,delineated by the phase boundary shown in Figure 1, is a singlaphase region within which surfactant, dodccBne, and water mix to form a clear, thermodynamically stable, isotropic liquid. Alkanes and water are immiscible, and an important feature of this system is that the surfactant DDAB has negligible solubility in either dodecane or water. This is atypical of microemulsions, in which the surfactant may be quite water soluble, and which often include cosurfactants with high oil and/or water solubilities. DDAB prefers insolubility in the case of dodecane and forms a lamellar liquid crystal or vesicular dispersion in water at concentrations above 1 X 10-4 M. In the microemulsion the surfactant can therefore safely be said to all reside at, and indeed stabilize, the internal interface which is formed between the immiscible liquids. Along the low water phase boundary the microemulsions are all electrically conducting, which indicates that water is a continuous phase in the liquid. As water is added to one of these microemulsions the conductivity decreases, eventually dropping by 3 orders of magnitude to become nonconducting.' Nuclear
~22-3654/92/2Q96-9492~Q3.QQ/Q 0 1992 American Chemical Society
Rheology of Ternary Microemulsions DDAB
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9493 ratio of the network which responds by favoring spheres over cylinders as structural elements. A smooth decrease in 2 for the network results in an abrupt percolation from bicontinuous to water in oil. The DOC cylinders model contains the important feature of preferred curvature of the interfacial surfactant monolayer. This is absent in previous descriptions, such as that of Talmon and PTager,ls and provides a physical basis for the length scales observed in these structured fluids. Within the framework of this model we refer to the interconnected water domains as the internal volume fraction, This and the area occupied by the surfactant film, 2, are given by6
Figure 1. Partial ternary-phase diagram for the system DDAB/dodecane/water showing microcmulsion-phase boundary. Water dilution paths along which the rheology of this system was inveStigatbd arc shown as solid lines. The percolation line (-) is also shown.
magnetic resonance yields water selfdiffusion coefficients which echo this observation, beginning at about half of their bulk value at the low water side of the phase diagram and decreasing slowly as water is added up to a certain point beyond which they drop suddenly by a factor of 10 or more. Dodecane self-diffusion coenicients are approximately coastant throughout the singlaphase region and are likewise about half of the value for neat dodecane. From this it is clear that the allrane is acting as a continuous phase at all compositions in the L2 region.s The qualitative model developed to account for this behavior was one of water conduits or tubules which were coated with an oriented monolayer of DDAB.’.” The microconduits were regarded as being flexible and having no preferred orientation, intersecting each other to form a random, three dihensional network with the alkane filling the remaining space. In this structure neither water nor dodecane can strictly be said to be the dispersed phase, and the other the continuous phase, so the liquid is referred to as bicontinuous. As water was added it was suggested that the structure transformed itself gradually into a mort conventional water-in4 (w/o) microemulsion, which would explain the conducting to nonconducting transition. The locus of points at which the system becomes nonconducting is referred to as the percolation line. This line is shown for dodccane in Figure 1.
In order to resolve the structural details on a more appropriate scale, small-angle X-ray and neutron scattering studies were ~ndertaken.6.~ These confimed that the surfactant was exclusively presmt at the interface so that the internal alkane/water interface could be calculated from the surfactant concentration for any sample. Existing models for bicontinuous liquids were found to be inadequate for describing the structures of these microemulsions.1c16 The disordered open connected (DOC) cylinders model was developed as a convenient conceptual model for the microemulsion structure,6J6 largely in order to facilitate the interpretation of small-angle scattering spectra. In this model the liquid volume is divided into randomly distributed oil and water regions as follows. We regard the oil as the first continuous phase into which are dispersed n droplets of water coated with a monolayer of surfactant. The radius of these droplets is presumed to be determined by lateral interactions in the surfactant f h which cause it to adopt a preferred curvature. Each droplet is c o ~ e c t e d(on average) to 2 nearest neighbors by cylindrical segments satisfying the same curvature constraint. This model yields a unique n and 2 characterizing the liquid structure for a known water volume fraction and internal surface area (which is directly proportional to the surfactant content). The resultant structure is disordered and is both water and oil continuous. It is the only existing structural model which is consistent with the observation of structural transition from highly interconnected to isolated droplets with addition of water. This arises naturally from the model, as addition of water corresponds to decreasing the surface to volume
where Q is the solid angle made by a cylinder intersecting with a sphere and p = R/r, the ratio of the sphere radius to the cylinder radius. As the model contains a surface which is strictly two dimensional, the surfactant volume must be partitioned between oil and water volumes. In our use of this model we differ from most previous work in that we assign the entire surfactant volume as part of the dispersed phase. This is convenient in w/o systems as the surfactant tailsare attached to the water domains and move with them through the oil amtinuum, and we retain this convention for bicontinuous structurea. It is however mort commonto allocate the head group volume of 120 A3/molecule to the water domains and the tails (704 A3/molecule) to the oil domains.13 The constant DDAB:dodecane water dilution lines examined in this study thus correspond to (i) decreasing the surface area to internal volume ratio and (ii) increasing the internal volume fraction. Along such a dilution line the average 2 decreases from a maximum value of 13.4 to zero, the latter being a water-in-oil microemulsion. S d a r l y , dilution of a constant DDAB/water microemulsion with oil corresponds to constant ratio of surface After percolation, dilution to internal volume and decreasing ht. of the w/o microemulsion occurs trivially at constant 2,for Z = 0. Along an oil dilution line the number density of spheres or cylinder connections, n, decreases roughly linearly with .&t Using the DOC cylinders model to interpret small-angle scattering spectra, the above trends in connectivity and droplet density have been confiied, and the network structure has been successfully employed to simulate the experimental scattering The curvature constraints used in constructing the network also give a reasonable description of the phase boundaries of the L2 region, making it the most useful description of these microemulsions yet developed.
Experimental Section Microemulsions were prepared by mixing doubly distilledwater, dodecane (Laboratory grade, Fluka, 90-95%), and the surfactant didodecyldimethylammoniumbromide (DDAB, Kodak) at various compositions within the one-phase region (Figure 1). Two rheometers were used in this study. A Deer constant shear stress rheometer in both the concentric cylinder (Couette) and coneand-plate configurationswas used in the low shear rate range (0.3-200 5-l). In this apparatus the inner cylinder (or cone) on an air bearing is driven at a constant applied torque with the outer cylinder (or plate) fied, and the rotational rate determined o g tically. In the higher range of shear rates, from twenty to several thousand reciprocal seconds, a constant shear rate Couette apparatus was used. In this the outer cylinder is driven by an external motor at a particular rotational velocity which is measured directly by a revolution counter. The shear streas is determined from the deflection of a torsion wire from which the inner cylinder is suspended. Shear rates are calculated from the dimensions of the
9494
Chen and Warr
The Journal of Physical Chemistry, Vol. 96, No. 23, 19I92
31% A
-
1500
'
40% 46% 52%
3 2
102
1000 -
d
3
Q
2
10'
3 2
0
500
1000
1500
2000
1200
//I
///
HzO
102
101
Shear rate, I el
Shear rate, I d
I
loo
'
103
2
3
-
Figwe 3. Flow curves for DDAB/dodccane/water microemulsions, plotted as log 7 versus log 5/, for samples along the S:O &60 w/w water dilution line, showing linearity over several orders of magnitude of shear rate.
900
. c
600
300
n 0
1600
3200
4500
6400
Shepr rats, y / B-1 ( 7 ) versus shear rate (y), for DDAB/dodccane/water microemulsions with (a, top) S:O = 60:40 w/w and (b,bottom) S:O = 2080 at various water concentrations, determined using a Couette rheometer.
Figure 2. Flow curves, shear stress
two cylinders, and deflection angle calibrated against shear stress for Newtonian liquids of known shear viscosity. In addition, viscosities were determined using an Ubbelohde capillary viscometer. Flow times of order 60-150 min were o b served for various microemulsions under study. The radius of the capillary in this viscometer was 0.261 mm. The long flow times are partly responsible for some interesting effects described below. Glycerol-water mixtures of various compositions were used to calibrate the rheometers and viscometer because of their Newtonian behavior over a wide range of shear rates. The viscosities of aqueous glycerol solutions vary sensitively with temperature and concentration, so the purity of glycerol was determined before preparing the calibration solution. The viscosities of doubly distilled water and 10, 24, and 36 wt % ' glycerol solutions were measured in a capillary viscometer at 20 O C .
Results and Discussioo Shear rate (9)versus shear stress ( T ) curves have been measured for DDAB/dodecane/water microemulsions of widely varying compositions. Microemulsions with dodecane:DDAB (0:s) ratios of 8020, 7030, 60:40, 5050, and 40:60 (w/w) were examined as a function of water content. The range of compositions studied along these dilution lines are shown in Figure 1. In addition, microemulsions with a fixed water:DDAB ratio of 76:24 were studied as a function of dilution with oil. This corresponds to dilution along the percolation line where the structure is essentially w/o droplets. The shear curves invariably showed Newtonian behavior over the shear range studied and in no samples could a yield stress be detected, some examples of flow curves are given in Figure 2 for two water dilution lines. The agreement between data collected from the two rheometers is very good in all systems examined. This is illustrated in Figure 3, where some examples of flow curves are plotted on logarithmic axes and can be seen to be linear over at least 3 orders of magnitude of +.
Recalling that throughout most of its region of stability the microemulsion is bicontinuous, its resolute Newtonian flow behavior is somewhat surprising. Previous experimental investigations have yielded the picture described in the Introduction of a three dimensional network of water tubules or conduits coated with an oriented monolayer of surfactantin an oil amtinuum. This structure is analogous to a swollen, cross-linked polymer or to a variety of polysaccharide gels, but it is to be stressed that the perceived microemulsions structure is a static or timeaverage one. The microemulsion is actually a fluctuating entity in dynamic equilibrium, and a much shorter time scale for rearrangement is anticipated in microemulsions than in either a swollen polymer or a gel. Previous work on microemulsion rheology has indicated that bicontinuous or "middle phase" microemulsions may be weakly shear thinning, particularly if their low-shear viscosities exceed about 10 cP.lzJS However, w/o and o/w microemulsions remain Newtonian up to high shear rates. It is well understood that the rheological behavior of a liquid depends upon how .).compares with the rate of various relaxation processes in the system. In the simple case of hard sphere suspensions, shear thinning is often idenflied by a characteristic shear rate, Tmor characteristicPeclet number, which describes the point at which the shear forces are comparable with Brownian forces. The common parameter used in this context is the Deborah number, which may be written as
DN
=w c (3) where X is a characteristic time scale for relaxation of the system and 1/qCis a characteristic time of the shear deformation. Complex liquids may have a number of relaxation giving rise to a distribution of relaxation times. A rheological measurement at a given .). examines the relaxation processes in a sample on a particular time scale, and non-Newtonian behavior can be interpreted as probing a relaxation which occurs in a particular time domain. This is germane to the present situation indirectly. The absence of a yield streas in any of the systems studied, together with the linearity of the flow curves, is evidence that there are no relaxation processes in these microemulsions slower than the smallest shear rate studied. It further indicates that there are no important relaxation processes Occurring for microemulsions throughout the entire range of shear rates examined. The maximum shear rate achieved was over 5000 s-', giving a characteristic time scale for the experiment of approximately 0.2 ms. This depended on the viscosity of the sample, and more typically the maximum shear range was 2000 s-l, Hence our results suggest that DDAB/dodecane/water " u l s i o n s have no time scale for relaxation longer than 0.5 ms. The structural fluctuations of the surfactant coated interface within the microemulsions are thus extremely rapid when compared with micellar systems, or with aqueous DDAB vesicle dispersions, in which
The Journal of Physical Chemistry, Vol. 96, No.23, 1992 9495
Rheology of Ternary Microemulsions
~~
s:o 3070 5050 3664 25:75 2080 1585
wt
96 HzO 61.1 52.3 43.2 34.6 29.2 25.0
4int
surface separation (exptl)/A
0.850 0.705 0.560 0.431 0.373 0.298
0 6 20 40 59 64
individual vesicles can be monitored for hours.19 Probably the most closely related systems which have been studied in any detail are semidilute solutions of flexible, cylindrical micelles.893 These are statically close to entangled linear polymers in structure, but unlike covalently bonded polymer chains they can reorganize by exchange of monomer and dissolution or breakup and re-formation of individual micelles. Hence they are often referred to as 'living polymers". The time scales associated with the relaxation of micellar solutions are 1 ms, which is typical for the 'fast" exchange of individual surfactant molecules, and from 100 ms to several seconds for the 'slow" dissolution/reformation process.z1 (These values are order of magnitude only and depend strongly on parameters such as alkyl chain length and ionic strength.) Living polymers, for example tetradecyl- and hexadecylpyridinium chloride micelles in the presence of sodium salicylate, begin to show non-Newtonian behavior at shear rates around 1-10 which is broadly consistent with the rates of micelle breakup. At lower shear rates than thii, such systems act as purely viscous liquids but cross over at higher shear rates to exhibit viscoelasticity and non-Newtonian behavior. A feature of the microemulsion under study is that the surfactant has negligible solubility in either the oil or the water which form the immiscible microdomains within the liquid. Rather, it is all located at the internal oil/water interface. The fast micellar relaxation process of molecular exchange thus has no parallel in these microcmulsions. We suppose instead that the reorganization taka place via a breaking or pinching-off of water cylinders, which reconnect to another nearby water domain. Thii is in some ways analogous to the breakup of cylindrical micelles into smaller segments, which has been proposed by Rehage and Hoffmannz2 and othersm to explain viscoelasticity of such solutions. A variation on this mechanism has also been proposed in connection with the viscosity of the or sponge phase.23 The structure of this phase is analogous to the bicontinuous microemulsion, but with the oriented surfactant monolayer replaced by a bilayer separating two interpenetrating water labyrinths. The structure is proposed to relax by a shrinking of the (bilayer-coated) tubules followed by a fusion of the membrane, in many ways similar to pinching-off a water tubule in the present system, but probably rate limited by an activation energy for the membrane fusion. These systems are reported to be Newtonian in the range of shear rates from 0.1 to around 100 s-'. Small-angle X-ray and neutron scattering spectra of these microemulsions interpreted according to the DOC cylinders model yield average interdroplet surface separations on the scale of Zr surfactant chain length (approximately 30 A). Some relevant values for a range of compositions of DDAB/dodecane/water systems are listed in Table I.' From this it is apparent that the length scale of the fluctuations required to reorganize the structure is at most tens of angstroms, and the fast rate of rearrangement with respect to shear is understandable. The low microemulsion/oil interfacial tensions observed for these systems" suggest that cylinder breakage or pinching has little or no energy barrier to overcome, so that diffusion of a 50-A object through the solvent should give a reasonable estimate of the characteristic time for reorganization. With treatment of the microemulsion in this way, diffusion over a distance of 50 A to re-form a connection occurs in a time of order 0.1 ms. This time scale is at the limit of our range, and
4
40t \ 1
t
01 20
A\
I
I 40 Wt'k
60
1
wrm
F'igure 4. Viscosities (Q) of microemulsions versus weight percent of water along the dodscane:DDAB = 8020 (w/w) water dilution line determined using Couette (W) and capillary ( 0 )viscometers. The percolation threshold determined by conductivity is shown by an arrow.
we therefore wauld not expect to be able to probe relaxation effects. Dilute Mlcroemulsiom: A Hint of Elasticity. Viscosities extracted from shear curves along the O S = 8020 water dilution line are shown in Figure 4. This curye is in qualitative agreement with the data of Evans et al.' for octane and decane microemulsions, determined using a capillary viscometer at around the same dodecane:DDAB ratio. The essential features are that the bimtinuous, low water m t e n t microemulsion has a high viscosity which decreases as water is added and the structure transforms into a w/o dispersion. The viscosities determined at the onset of the single-phase region (low water) are all consistent and have the following trend octane, 22.5 C Pdecane, 21.5 cP; dodecane, 20.0 CP. Capillary viscometry on the same microemulsions also shows the same qualitative behavior, although the viscosities obtained are noticeably different in the bicontinuous composition r6gime (Figure 4). The Couette and capillary viscosities do however coincide for the w/o systems, as expected for an essentially noninteracting dispersion of spheres. The difference between viscosities determined by Couette and capillary Viscometry suggest viscoelastic behavior for bicontinuous DDAB microemulsions. However, if we assume that the system is Newtonian, then the average shear rate in the capillary Viscometer is about 95 s-l, and the maximum (wall) shear rate only 175 s-1.25 The shear rate at all points within the capillary is therefore much less than the maximum examined in the Couette cell, so shear viscoelasticity is ruled out as an explanation for the anomalous viscosities. The other assumption implicit in the determination of viscosities from capillary flow is that the pressure difference between the ends of the capillaries is not substantially altered by effects of the This problem entry flow of the liquid into the capillary, hN. is largely solved for inelastic liquids such as noninteracting spherical dispersions, either Newtonian or shear thinning, and hN for such fluids is small in standard capillary viscometers. For non-Newtonian liquids, however, elastic effects may become important in the acceleration and elongation which occurs at such contractions, invalidating the purely viscous interpretation of flow through a capillary.26 It has been suggestedz7that such effects intrude in the flow behavior of polymer gels at much lower elongational than shear rates. We suspect that this is the cause of the apparent disagreement between viscosities derived from the two measurements and are investigating further. In any case this result cautions against accepting quantitatively the viscosities derived for such microemulsions by capillary viscometry.' In the remainder of this paper we focus on Newtonian (low shear) viscosity of DDAB + dodecane + water microemulsions. Due to the differing extents to which theoretical models can contribute to the interpretation, w/o and bicontinuous regions of the microemulsion are considered separately. The Wator-hdwI (w/o) Region. At water:DDAB ratios greater than 76:24, shown by the dashed line of Figure 1, the structure of the microemulsion is a simple dispersion of surfactant-coated
94%
The Journal of Physical Chemistry, Vol. 96, No. 23, I992
120
. L5
3
1I
I
!
random close packing 4, of 0.63. At t$ > 0.6, however, the dispersions were obrved to shear thin. All such dispersions were shear thinning at a shear rate of 10 s-' and above t$ = 0.65 were non-Newtonian down to 0.01 s-l, remarkably different behavior
.
I4
so -
3
0.0
0.2
0.4
0.6
Chen and Warr
0.8
Volume fraction of surfactant + wator, wt
Figure 5. Viscosities (9) of microemulsions versus internal volume fraction along the water:DDAB = 76:24 (w/w) oil dilution line, determined using a Couette viscometer. Also shown is the best fit of cq 3 to the data with &, = 0.68 (- - -) and 0.74 (-).
water droplets in an oil continuum. Because the behavior of such systems is amenable to quantitative treatment, we will deal with this region before addressing the more complicated, bicontinuous domain. As these microemulsions have an easily identifiable dispersed and continuous phases, it is convenient to represent the viscosity as a function of the dispersed-phase volume fraction. This is regarded as the sum of the water and surfactant volume fractions, obtained from known compoeitions (weight percent) and densities. Visawity as a function of internal volume fraction t$htalong the water:DDAB = 76:24 oil dilution line is plotted in Figure 4. The range of compositions used spans the entire single-phase region of the microemulsion. We have neglected the effect of oil penetration into the surfactant layer surrounding the water droplets as this should be small for the present system6and in any case adds an adjustable parameter which is not needed to describe the results. The microemulsion droplets carry no net charge and should interact only by excluded volume effects. Viscosities, q, for such hard sphere systems have been described by Dougherty and KriegerZ*and should obey the equation (4)
where qo is the solvent viscosity, 4, is the volume fraction of the dispersed phase, and t$, is the maximum packing density which the dispersed phase can achieve. [q] is the intrinsicviscosity which for hard spheres takes the Einstein value of 2.5,29and this value has been used together with the solvent visoosity qo = 1.89 CPfor dodecane throughout the droplet region. The Dougherty and Krieger equation describes the e x m e n t a l viscosities very well for values of 4, between 0.68 and 0.74, as shown in Figure 5. t$, = 0.68 gives somewhat better agreement with the data for the more dilute microemulsions (4 < 0.5), but in the more concentrated region r$m = 0.74 yields the better fit, and is adequate over the entire range of compositions. Both of these values are greater than the maximum density of 0.63 which is usually obtained for randomly packed uniform hard spheres.m This may reflect ordering of the droplets, size polydispersity, or some other nonideality not considered in the hard sphere model. As 4, = 0.74 corresponds to closest packing, a face-centered cubic array, this highly ordered structure might be expected to give rise to a diffraction pattern. In the only existing studies of which we are aware,6*' there is only the faintest indication of such ordering from small-angle scattering. The scattering pattern is indeed consistent with dense random packing, suggesting that crystal-like order is not responsible for the observed 4,. Further to this, recent results for model hard sphere dispersions3* have demonstrated that there are two distinct volume fraction regions for rheological purposes. Below 4 = 0.6 the dispersions were Newtonian and their low viscosities were consistent with
from the w/o microemulsions of this study. The transition between Newtonian and elastic behavior has been identified with ordering of the hard spheres due to hydrodynamic interaction^.^^*^^ An ordered lattice forms which minimizes collisions between particles, thus lowering the viscosity. The ordering of dispersions interpretation is consistent with the results, of which the most pertinent here is a Dougherty-Krieger analysis of the limiting high shear viscosities of such suspensions. This analysis yielded 4, = 0.71 for viscosities extrapolated to infinite shear rates?' suggestive of the close packing of an ordered dispersion. Limiting low shear viscosities were consistent with the random close packing value of 0.63 for 4,. Thus formation of an ordered dispersion would be expected to coincide with shear thinning, which is totally absent from the present systems. It is more likely that the high value of 9, arises directly from the calculation of &. In assuming that all of the surfactant foras part of the d i s p e d phase, we treat the water dropids as if they were coated by a compact layer of surfactant. This is almost certainly untrue; the surfactant tails will be largely extended into the oil, giving rise to the notion of oil penetration into the tails. It is by this mechanism that the oil affects the spontaneous curvature of the surfactant interface. 4, therefore depends on where the droplet drains, i.e. on what fraction of the surfactant layer is assigned to the solvent. This in turn determines to what extent the alkyl tails from nearby droplets can interpenetrate. We have chaaen no penetration as one extreme. The other, calculated assuming that only the water and head group volumes comprise the dispersed phase as in the Introduction, gives as a lower bound 9, = 0.58. That this is a poor fit is evidenced by the [ q ] of approximately 3.7 accompanying this value, which is well away from reasonable values for spheres. Accurate determination of the position of the "shear planel for the surfactant tails within these limits is probably not possible from this work, and indeed would serve little purpose. Inverting the problem, an assumed 4, = 0.63 gives at least a plausible value of 3096 of the chain in addition to the head groups as a nondraiig coating on the water droplet. This interpretation goes some way to vindicating the idea of oil and chain penetration and obviates the need to invoke polydispersity to explain the observed visoosities. As the inclusion of 100% of the surfactant overestimates the dispersephase volume fraction at all annpitions, this explanation is also consistent with the absence of shear thinning behavior to be expected for hard sphere dispersions at volume fractions above about 0.6. The top axis of Figure 5 rescales the volume fractions to an estimated 4, = 0.63 and shows that most samples in the w/o region are too dilute to shear thin. Vircw Elow io the B h t i " u s Region. Figure 6 shows the viscosities derived from T versus curves for more concentrated microemulsions (higher DDAB:dodecane ratio) along water dilution lines. These are strikingly different from the more dilute case in that the viscosity of the liquid increases as water is added up to and beyond the percolation line. In the dilute microemulsions of F w e 4, the viscosity decreases as water is added, finally leveling off beyond the percolation line, where the system consists of a dilute diepgaion of spheres. Further addition of water changes the volume fraction but little, so the viscosity is approximately constant here. This behavior is broadly consistent with the gradual decrease in connectivity accompanying the structural transformation from a network into a discrete dispersion as described by the DOC model. In dilute microemulsions the dependence of viscosity on composition is governed by the connectivity of the liquid. In the more concentrated systems a progrmsion is in evidence. The viscosity initially incrqws with water addition, but in at least the S:O = 3070 and 40:60 cases a downturn in viscosity occurs at the percolation point (arrow4 in Figure 6) before it rises again as further water is added. At these higher volume fractions,
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9497
Rheology of Ternary Microemulsions
higher shear rate measurements which accurately probe relaxation times. The Newtonian viscusitics in the w/o region are consistent with a dispersion of hard sphere water droplets coated with a partially draining surfactant layer, although no details of the layer could be discerned. The role of the bicontinuous structure in determining the rheological properties is really only in evidence for dilute microemulsions, with 0 : s ratios greater than 7030. More concentrated microemulsions have behavior dominated by excluded volume effects which mask the subtleties of water connectivity. In capillary flow behavior some anomalous viscosities were determined for dilute microemulsions, and these were ascribed to elongational rather than shear flow effects. We are investigating this in more detail.
I
Acknowledgment. We would like to thank Professor David Boger for helpful discussions. We would also like to acknowledge one of the reviewers who pointed out some “exotic” references of which we were unaware. 10
30
vl%wsiex
50
70
Figwe 6. Viscosities ( q ) of microemulsions versus weight percent of (u), 5050 water along DDABdodecane = 2080 (e),3070 (0), (A), and 60:40(V)(w/w) water dilution lines, determined using Couette viscometers. The arrows denote the percolation thresholds for each of the dilution lines. Solid lines are a guide for the eye.
References pad Notes (1) Chen, S.J.; Evans, D. F.; Ninham, B. W. J. Phys. Chem. 1984,88, 1631. (2) Ninham, B. W.; Chen, S. J.; Evans, D. F. J. Phys. Chem. 1984,88, 5855. (3) Warr, G. G.; Sen, R.; Evans, D. F.; Trend, J. E. J. Phys. Chem. 1988, 92, 774. (4) Fontell, K.; Ceglie, A.; Lindman, B.; Ninham, B. W. Acta Chem. S c a d . 1986, A40, 247. (5) Blum, F. D.; Pickup, S.;Ninham, B. W.; Chen, S.J.; Evans, D. F. J. Phys. Chem. 1985.89. 71 1. -(6) Zemb, T. N:; Barnes, I. S.;Hyde, S. T.; W n , P.-J.;Ninham, B. W. J. Phys. Chem. 1987,91, 3814. (7) Bames, I. S.; Hyde, S.T.; N h m , B. W.; Derian, P.-J.;Drifford, M.; Warr, G. G.; Zemb, T. N. Prog. Colloid Polym. Scf. 1988, 76,90. (8) Angel, M.;Hoffmann, H.; E b l , M.;Reizlein, K.;Thum,H.; Wunderlich, I. Prog. Colloid Polym. Sci. 1984, 69, 12. (9) Candau, S. J.; Hirsch, E.; Zana, R.; Delsanti, M. hngmuir 1989,5,
excluded volume interactions are responsible for the change in viscosity with addition of water in both the bicontinuous and w/o regions. The behavior of the more concentrated systems leads us to conclude that the hydrodynamics of these microemulsions are governed by two competing effects: internal volume fraction and network structure. At higher surfactant concentrations the volume fraction of the “dispersed” (water plus some attached surfactant) phase is sufficient that excluded volume interactions 1225. have an increasing effect, and the structure of the network is (10) Sino, D. B.; Bock,J.; Myer, P.; Ruascl, W. B. Colloids Surf.1987, relegated to a relatively minor role in determining flow behavior. 26, 1987. The viscosity curves retain only echoes of the structural contri(11) Berg, R. F.; Moldover, M. R.; Huang, J. S . J. Chem. Phys. 1987,87, bution to flow through the minimum or inflection point at the 3687. percolation threshold of each dilution line. The magnitude of these (12) Quemada, D.; Langevin, D. J. MZc. ThZor. Appl. 1985 (NumCro Sp&ial), 201. “adiminishes as the surfactant content increases, reflecting (13) Chen, V.; Warr, G. G.; Evans, D. F.; Prendergast, F. J. Phys. Chem. the preponderance of excluded volume over structure in the flow 1988, 92, 768. behavior. (14) De Gennes,P. G.; Taupin, C. J. Phys. Chem. 1982,86, 2294. Not surprisingly, Dougherty-Krieger and related m o d e l ~ ~ * , ~ ~ (15) Talmon, Y.; Prager, S . J. Chem. Phys. 1978,69,2984. (16) Hyde, S. T.;Ninham, B. W.; Zemb, T. N. J . Phys. Chem. 1989,93, are unsuccessful in reproducing the details of the concentration1464. dependent viscosities along water dilution paths where the mi(17) Bames, I. S.; Zemb, T. N. J. Appl. Crystalfogr. 1989, 21, 373. croemulsion structure is changing markedly. The dependence of (18) Bennett, K. E.; Davis, H. T.; Maoosko, C. W.; Scriven, L. E. Paper viscosity on composition is not itself sufficiently structured that No. SPE-10061,prarented at the SPE 56th Annual Technical Confercna and Exhibition, San Antonio, Oct 5-7, 1981. detailed information on the connectivity can be extracted. Note (19) Miller, D. D. Ph.D. Thesis, University of Minnesota,1988. however that beyond the percolation line all the w/o system (20) Cates, M.E. J. Phys. Fr. 1988,49, 1593. Cates, M.E. Macromolviscosities fall onto a master curve when plotted against volume ecules 1987, 20, 2289. fraction. (21) Aniansson, E. A. G.; Wall, S. N.; Almgrcn, M.;Hoffman, H.;
Conclusions DDAB/dodccane/water microemulsions were found to be Newtonian up to shear rates of a few thousand reciprocal m n d s over the entire composition range investigated. This means that, despite the vanishingly small solubility of DDAB in alkanes and water, that reorganizational processes in these systems have a characteristic time scale no longer than 0.5 ms. This is fast not only in comparison with DDAB vesicle dispersions, but also compared with w o d i e living polymer micelles which begin to show non-Newtonian character around 10 s-’. Because of the small distances involved in reorganizations of concentrated microcmulsions, such rapid relaxations may be rationalized assuming a diffusion-limited reorganization. It is possible that calculations involving bending energies would do better, but these should await
Kielman, I.; Ulbricht, W.; a n a , R.; Lang, J.; Tondre, C. J. Phys. Chem. 1976,80, 905. (22) Rehage, H.; Hoffmann, H. J . Phys. Chem. 1988,92,4712. (23) Snabre, P.; Porte, G. Europhys. Lett. 1990, 13, 641. (24) Allen, M.;Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J. Phys. Chem. 1987,91, 2320. (25) Oxtoby, D. W. J . Chem. Phys. 1975, 62, 1463. (26) Boger, D. W. Annu. Rev. Fluid Mech. 1987, 19, 157. (27) Yamamoto, M.J. Phys. Soc. Jpn. 1957, 12, 1148. (28) Krieger, I. M.; Dougherty, T. J. Trans. Soc. Rheol. 1959, 3, 137. (29) Einstein, A. Theory of the Brownian Mwement; Dover: New York, 1956. (30) van der Werff, J. C.; de Kruif, C. G. J. Rheol. 1989, 33, 421. (31) Jones, D. A. R.; Leary, B.; Boger, D. V. J. Colloid Interface Sci. 1991, 147, 479, (32) Hoffman, R. L. J . Colloid Interface Sci. 1974, 46, 491. (33) Ackerson, B. J. 3. Phys.: Condew. Matter 1990, 2, SA389. (34) Quemada. D. E. In Advances in Rheology: Vol. 2, Fluids; Mena, B., et al., Eds.;Universidad Nacional Aut6nama de Mexico: Mexico City, 1984.
