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Microstructure and transport in midrange microemulsions
Physica A 157 (1989) 470-481 North-Holland. Amsterdam
MICROSTRUCTURE AND TRANSPORT IN MIDRANGE MICROEMULSIONS H.T.
DAVIS*,
J.F.
BODET**,
L.E.
SCRIVEN
and W.G.
Department of Chemical Engineering and Materials Science and Department University of Minnesota, Minneapolis, MN 55455, USA
MILLER of Chemistry,
Invited paper In microemulsions containing small amounts of oil in water (or water in oil), the fluid microstructure is usually that of swollen micelles (or swollen inverted micelles), i.e. the solution consists of small globules of oil (or water) coated with a surfactant layer and dispersed in a continuous water (or oil) rich medium. When the volume fractions of both oil and water are appreciable, microemulsions can be bicontinuous, i.e., they have both oil-continuous and water-continuous domains separated by surfactant-rich regions. The transition has been identified as a percolation process since it occurs when water and oil relative proportions reach a percolation threshold. Recently, however a transition between globular and bicontinuous microstructure has been found in microemulsions of nearly equal and fixed volumes of water and oil. In this paper we discuss these apparently different transitions and report the results of new viscosity studies in the equal oil to water volume microemulsions.
1. Introduction A surfactant
is an
drophilic) moiety forms association water phases another
a molecule
having
a water
soluble
(hy-
attached to a water insoluble (hydrophobic) moiety, which colloids such as micelles or liquid crystals when mixed with
or hydrocarbon. containing amphiphile
amphiphile,
Microemulsions are hydrodynamically stable isotropic water, and oil, and sometimes salt and/or surfactant, (often called a cosurfactant). Though isotropic on the scale
of the wavelength of light, microemulsions are heterogeneous on the scale of tens of nanometers. At this scale the solutions are heterogeneous media characterized by water-rich domains and oil-rich domains separated by sheetlike regions (often called surfactant films, layers, or membranes). In microemulsions containing small amounts of oil in water (or water in oil), the fluid microstructure is usually that of swollen micelles (or swollen inverted * Presently visiting: Ecole Superior de Physique et Chemie Industrielles, Laboratoire rodynamic et Mtcanique Physique, 10 Rue Vauquelin, 75231 Paris Cedex 0.5, France. ** Presently at: Centre de Recherche Paul Pascal, Domaine Universitaire, 33405 Talence France.
0378-4371/89/$03.50 0 Elsevier Science Publishers /\rfi..+r. U -11,. ,,a nl_._:__ n..l-l:-L:.-rX. . . x
B.V.
d’HydCedex.
H. T. Davis et al. I Microstructure
and transport in microemulsions
471
micelles), i.e. the solution consists of small globules of oil (or water) coated with a surfactant layer and dispersed in a continuous water (or oil) rich medium. When the volume fractions of both oil and water are appreciable, microemulsions can be bicontinuous , i. e . , they have both oil-continuous and water-continuous domains separated by surfactant-rich regions. The transition has been identified as a percolation process since it occurs when water and oil relative proportions reach a percolation threshold. Recently, however a transition between globular and bicontinuous microstructure has been found in microemulsions of nearly equal and fixed volumes of water and oil. In this paper we discuss these apparently different transitions and report the results of new viscosity studies in the equal oil to water volume microemulsions.
2. The transition when oil and water proportions vary The most important factor driving microemulsion research during the last several years is the possible use of microemulsions for enhancing oil recovery. Residual oil droplets are trapped in a waterflooded oil reservoir by the high interfacial tension between oil and water. By suitable choice of surfactant, cosurfactant (e.g., an alcohol) and salinity of aqueous brine, researchers in the petroleum industry [l] made microemulsions having ultralow tensions against coexisting oil and water phases. Such a microemulsion placed at an oil-water interface can lower tension and lead to recovery of residual oil droplets. Salt, usually NaCl, is most commonly introduced for fine tuning the phase and tension behavior of a microemulsion of an ionic surfactant. Fig. 1 illustrates typical results for a microemulsion system having the potential for enhancing oil recovery. In such a salinity scan, mixtures of equal values of oil and brine and a fixed percentage of surfactant and cosurfactant are typically prepared and allowed to equilibrate. At low salinity two phases form, the surfactant being primarily in the lower phase, hence the notation 24 indicating the presence of a lower phase microemulsion. At intermediate salinities there are three phases, denoted 34, and most of the surfactant is in the middle phase microemulsion. At high salinities two phases, denoted %J, form with most of the surfactant in the upper phase. The low salinity microemulsion is a water-continuous solution of oil-swollen micelles and the high salinity microemulsion is an oil-cintinuous solution of water-swollen inverted micelles. At intermediate salinities bicontinuous microemulsions can occur. The pattern of phase and interfacial behavior illustrated by fig. 1 is a generic one for oil-water-amphiphile mixtures [2]. The ultralow tensions are the result of selecting conditions so that the middle phase microemulsions are sandwiched in field variable space between not too widely separated critical endpoints, On
472
H. T. Davis et al.
I Microstructure
INTERFACIAL
TENSIONS
and transport
-)’ IN A SALINITY
CRITICAL END P?lNT 20
in microemulsions
:
SCAN
CRrrlCIL END
P?lNT 3e
:
G
1 o- 2 dYn Eii10-3
1 o- 4
10-5
0
1.5 Nat2
SALINITY
Fig. 1. Schematic of phase and interfacial tension oil-rich and/or water-rich phases in a salinity scan.
3.0 (wt %)
behavior
of microemulsion
coexisting
with
the left in fig. 1, the lower phase microemulsion splits (with increasing salinity) at a critical point (called a critical endpoint in ternary phase diagrams) into the middle phase microemulsion and the lower phase in the 34 regions. On the right, the upper phase and the middle phase collapse at a critical point into the upper phase microemulsion. If the two critical end points were moved together (by varying some field variable such as temperature, pressure, activity of a cosurfactant, or the carbon number of the hydrocarbon) a tricritical point would result, with the consequence that yMo and yMw both vanish. Thus, the search for ultralow tension microemulsion systems for enhancing petroleum recovery amounts to the search for a region in field variable space lying near a tricritical point. Ideas initiated by Talmon and Prager [3], de Gennes and Taupin [4], and Widom [5] have given rise to a phenomenological free energy model which describes the above patterns of phase behavior of microemulsions. The basic assumptions are (1) that oil and water-rich domains are randomly interspersed in space (divided by Talmon and Prager into Voronoi polyhedra of average diameter c-l’3 and by others into cubes of size e), (2) the surfactant resides entirely in layers separating the oil and water-rich domains and (3) the free energy arises from the entropy of interspersion of the domains and from the
H. T. Davis et al. I Microstructure
and transport in microemulsions
473
energy of curvature of the surfactant layers. The most recent version of the model has been developed by Safran et al. [6]. The free energy density of their model is f = fs + fc, where the entropy contribution is f, =
wm3m 1%$J+ Cl- 4) loId - +)I
and the curvature
k is Boltzmann’s
contribution
is
constant and T is temperature. (b is the volume fraction associated with water-rich domains - to 4 is assigned all of the water and half of the surfactant, i.e., 6, = c&, + r&/2. H,, is the spontaneous mean curvature and K(S) is the film bending constant renormalized for long wavelength thermal fluctuations. For 5 6 5, the Helfrich formula [7] is used for K( 0, namely, K( 5) = K,,[l - log( t/a) /log( &la)]. K,, is the bare bending constant (K( 5) = K0 for 5 < a), a is a molecular length characteristic of the surfactant size and & is the surfactant film persistence length. When 5 > & the surfactant film becomes easier to bend owing to the existence of spontaneous crumpling. de Gennes and Taupin give for the persistence length the expression & = a exp[2nK,lkT]. The condition that the surfactant lie in the interdomainal films yields 5 = 644 1 - 4) /&. In the dimensionless form t$f/kT, the free energy becomes a universal function of 4, &&la and &H,,. Thus, in terms of the composition variables 4 and ~&,$~/a the predicted phase behavior depends only on the one adjustable parameter &ZY&,.Phase equilibria determined by variation of H, from negative to positive values yields a sequence of water-rich to oil-rich microemulsions, H, = 0 corresponding to the microemulsion of equal volumes of oil and water. The value of K, can be measured directly in swollen micellar solutions. In fact, in a paper presented to this conference, Bedeaux, Linden and van Dijk [8] use the Kerr effect to find K,,IkT = 0.76 (K. equals twice their quantity CL) for water swollen inverted micelles of aerosol OT in isooctane. While a theory based on a phenomenological free energy model is useful for rationalizing patterns of phase behavior, it is not a statistical mechanical theory in that it does not show how the patterns derive from molecular interactions and assumes rather than predicts fluid microstructure. Towards the development of molecular level theory, the recent efforts of Wheeler [9] and of Widom and coworkers [lo] on lattice models appear quite promising. The transition from swollen micelles to bicontinuous to swollen inverted micelles in the 2,3,? sequence has been beautifully shown in pulsed field gradient spin echo nuclear magnetic resonance (NMR) studies of the self-
414
diffusion results
H. T. Davis et al.
coefficients of one
diffuse
as a globular
oil and water
studies
swollen
At high salinity,
and transport
of the components
of these
water-continuous
I Microstructure
are
micellar
shown
and oil reverse
have the higher
of the microemulsion
diffusion
[ll,
121. The
in fig. 2. At low salinity,
region,
unit and water
water
in microemulsions
the oil and diffuses molecularly
roles and at intermediate coefficients
in the
surfactant molecules in continuous phase.
expected
salinities
both
for a bicontinuous
medium. The surfactant diffusivity is about 10 times lower than oil and water in the bicontinuous domain which is consistent with the fact that it is constrained to move along surfactant sheets. That the microemulsion is percolative in the sequence 2,3,2 is easily demonstrated by plotting the electrical conductivity versus the water volume fraction. At water fractions below the percolation threshold &,c for the oil-continuous to bicontinuous transition one would expect the electrical conductivity to be very small. The percolation threshold has been observed in numerous systems [13-171. Typical of the behavior observed in many systems [15] is that shown in fig. 3, in which well with the conductivity computed
the measured conductivity for a Voronoi tessellation
hedra are randomly decorated with conducting and Near a percolation threshold the electrical conductivity obey the scaling laws Km (&, below the 4 wc. Conductivity
agrees whose
nonconducting is expected
quite poly-
phases. [13, 181 to
- &-‘, &,, < &,c and Km (& - &.)‘, 4, > percolation threshold presumably arises from
Toluene
D/m2s-’ Water
A
/k--,-+
lO-g-
lO’O_
10-l’ L
I 3
ShITY
I I
I
I
5
6
7
( g/
100
crn3
I a
I 9
I 10
’
1
Fig. 2. Diffusivities of components of sodium dodecylsulfate (SDS), chloride brine. Vertical lines indicate 2-3 and 3-2 phase transitions.
butanol, toluene Ref. [ll].
and sodium
H. T. Davis et al. I Microstructure and transport in microemulsions
6
VOLUME
FRACTION
1.0
w z E
0.8
m
0.6
8 0 0
415
BRINE
Fig. 3. Conductivity and viscosity versus volume fraction for brine in microemulsion phase. From a salinity scan of Witco TRS lo-80 surfactant (an alkylaryl sodium sulfonate), tert-amyl alcohol, octane and NaCl brine. Ref. [15].
cluster migration, cluster to cluster change hopping or dynamical cluster rearrangement. For several microemulsions of cyclohexane, water, sodium dodecylsulfate (SDS) and pentanol, Lagues and Sauterey [13] found t and s values in the range 1.4-1.8 and 1.1-1.4, respectively. If the percolation threshold is approached in temperature, the conductivity scaling laws are the same except that +c - &c is replaced by T- T,. Bhattacharya et al. [17] studied the temperature dependence of the conductivity of a decane, water and aerosol-OT (AOT) microemulsion near the percolation threshold and found t = 1.68 + 0.05 and s = 1.17 -+ 0.05, in agreement with Lagues and Sauterey. The static percolation values are s = 2~ - p = 1.2 [19] and t = 2.0 [20]. Near a percolation threshold the dielectric constant is expected [21] to obey the scaling law E(W) 0: mu-l with frequency w, where u = tl(s + t). Bhattacharya et al. found u = 0.63 + 0.04 and, in a study of isooctane, water, and AOT microemulsions, van Dijk et al. [22] found u = 0.62 + 0.02. Static percolation values of t and s yield u = 2/3.2 = 0.625 whereas measured values give u = 1.68/2.85 = 0.589, each in reasonable agreement with experiment, even though the experimental value for t is somewhat lower than the static value. The authors Lagues and Sauterey and Bhatacharya et al. argue that their microemulsions consist of flocculated clusters of swollen inverted micelles which become sample spanning at the percolation threshold. A lower frequency cutoff (
476
H. T. Davis et al.
I Microstructure
and transport
in microemulsions
percolation thresholds and a minimum occurs near the state of equal volumes of oil and water. The viscosities reported in fig. 3 were measured with a rolling ball viscometer. In a more accurate study [23] with a cone and plate viscometer, the viscosities were found to be somewhat shear rate dependent in the range 10 to lOOOs_‘, the stronger non-Newtonian behavior (which is shear thinning for microemulsions) occurring near the viscosity peaks. There is shear thinning in the equal volume oil/water microemulsion but not as much as in those near the percolation peaks. One can rationalize the viscosity trend in fig. 3 in terms of a rigid globule model [24]. Although the model seems reasonable in the swollen micelle domains, we believe a more physically realistic model must incorporate percolative clusters and bicontinuous microstructures. It is especially difficult to see the relevance of the model to the new viscosity results we present in the next section of this paper.
3. Transition
at equal oil and water volumes
The patterns of behavior described in the previous section are those that occur if one follows coexisting microemulsion through a field variable scan that generates the Z&3, !?! sequence of phases. This is only one possible path in parameter space. As an alternative we have recently studied [25] the properties of microemulsions along the one phase (14) corridor in the phase diagram shown in fig. 4 (which was determined by Kahlweit and Strey [26]). Fig. 4 is a temperature-surfactant composition phase diagram for a three component system whose water and oil (octane) mass proportions are fixed at 60 : 40. This corresponds to almost equal volumes of water and oil. The one-phase states we have studied are shown in Fig. 4 as filled circles and are identified by letters. Primed and unprimed pairs A, A’; B, B’, etc. refer to pairs having the same composition but different temperature. The diffusivities of the microemulsion constituents measured by pulsed field gradient spin echo NMR along the one phase corridor are presented in fig. 5 along with the diffusivities of water and octane in pure bulk phases at temperatures of the microemulsions. The unambiguous conclusion to be drawn from fig. 5 is that along the one phase corridor from lower to higher temperatures the microemulsion undergoes a transition from a water-continuous swollen micellar solution to a bicontinuous solution. The diffusivity of oil in solution A is three orders of magnitude smaller than that of A’, these two microemulsions being at the same composition but at 20.0 and 4O.l”C, respectively. Freeze-fracture replica transmission microscopy [2.5,27] also provides dramatic evidence of the transition from globular to bicontinuous microstructure in these mid-range microemulsions. Especially convincing are the
H. T. Davis et al. I Microstructure and transport in microemulsions
477
40
T
[“Cl 30
t 20
10
0
30
Fig. 4. Phase diagram of pentaethylene dodecyl glycol ether (C,,E,), water and octane (water/ octane = 60:40) ref. [26]. The microemulsions studied are indicated by the filled dots.
micrographs of Jahn and Strey [27] who find that oil and water regions have a different texture when the fracture surface replica is prepared as a mixed tantalum/tungsten film. One of their micrographs of bicontinuous microemulsion is given in fig. 6. It is plain from this micrograph that this bicontinuous microemulsion does not consist of flocculated globules. It is truly a bicontinuous chaotic interspersion of oil and water rich domains.
6 g 10-10 1
,o-ll
+
D, PURE H20
x D, PURE C,
n 1 o-12
l
10-13
A B C D E F G H I J
Mixture
D, C,2E5
I’ H’ G’ F’ E’ D’ C’ B’ A
#
Fig. 5. NMR self-diffusion coefficients in the microemulsions
indicated in fig. 4. Ref..[2j]
H. T. Davis et al. I Microstructure
478
Fig. 6. Freeze fracture electron micrograph 7wt% C,,E,. Bar = 1 I*. Ref. [27].
and transport in microemulsions
of the C,,E,.
water
and
octane
microcmulsion
at
It is interesting to observe in fig. 5 that there appear to be two transitions. The first occurs between B and D and is characterized by an abrupt increase of about a factor of 10 in the diffusivities of oil and surfactant, after this transition appear to be diffusing together. Between transition is from globular to bicontinuous microstructure. what is the nature the effective [25].
One
of the B to D transition.
diffusivity possibility,
coefficient which
The transition
determined
is consistent
with
which before and G and H or I the We are not sure is also observed
by quasielastic some
in
light scattering
freeze-fracture
replica
micrographs [28], is that states A and B correspond to slightly monodisperse spherical swollen micelles and that between B and D aggregation into clusters begins occurring. And then, between G and H or I, the clusters become sample spanning and thus result in bicontinuous microemulsion. With a cone and plate viscometer, we have explored the rheological behavior of microemulsion along the one phase corridor. In fig. 7, we present effective viscosities versus shear rate for selected microemulsions. All are shear thinning non-Newtonian fluids. The effective viscosities for a shear rate of 1 so ’ are compared in fig. 8 with the self-diffusion coefficient of the surfactant (the viscosity of fluid J was not measured in the cone and plate viscometer, instead
H. T. Davis et al. I Microstructure
c
v,
and transport in microemulsions
419
100
B
I
.l
. .
. ..
..I
.
.
.
. .
1
,l
..I
.
10
SHEAR RATE (set -’ ) Fig. 7. Effective
viscosity
versus
shear
rate of microemulsions
indicated
in fig. 4.
it was measured in a capillary viscometer and is hence not strictly comparable to the others). The trends in viscosity and diffusivity are roughly compatible but differ in significant detail. Whereas the diffusivities differ between A and B and between D and F, the corresponding viscosities differ by about a decade. Also in the sequence F’ to A’ the surfactant diffusivity remains about constant whereas viscosity increased by a decade. Since the concentration of swollen micelles is very high in the globular domain, one does not expect the Stokes-Einstein equation, R = kTl6nvD (connecting particle radius R to viscosity n and diffusivity) to be very accurate. Stokes radii computed for microemulsions A, B and D are 0.4, 3.5 and 2.0 A, respectively. From electron microscopy the globular sizes in these microemulsions are observed to be of the order of 200 A in diameter, and so these Stokes radii are meaningless. As
1000 +
DIFFUSION
MICROEMULSION Fig. 8. Comparison of trends in surfactant microemulsions indicated in fig. 4.
diffusivity
with effective
viscosity
(at 1 s-’ shear rate) of
480
H. T. Davis et al. I Microstructure
and transport in microemulsions
expected in a strongly microstructured fluid, the mechanisms of diffusive motion and shearing of microstructure are not related in any simple way. Clearly the transition discussed in this section cannot be viewed as a percolation threshold reached by increasing the oil/water or water/oil volume ratio to a percolation threshold from some subpercolation value. The ratio is in fact approximately unity and the transition is achieved by increasing temperature at fixed composition. What can be concluded from our observations is that increasing temperature drives the mean curvature of surfactant sheets from a negative value favoring swollen micelles towards the value of zero favoring bicontinuous microemulsion. In the context of the phenomenological free energy model discussed in the previous section, this could arise from a temperature dependent spontaneous curvature. This model, however, ignores interactions between the surfactant films which at the high concentrations involved here could be significant. In fact in surface force measurements, Claessen et al. [29] found that the solvation force between monolayers of C,,E,, separated by aqueous films a few nanometers thick, undergoes a transition from repulsive to attractive when the temperature reaches 30°C. This is close to the temperature at which the globular to bicontinuous microstructure transition occurs along the one-phase corridor in fig. 4. In a system of fixed composition, it seems reasonable that repulsive forces would favor globules to increase monolayer separation and attractive forces would favor bicontinuous structures to decrease the separation, and so the correspondence of temperature may be more than a coincidence. These equal oil and water volume microemulsions deserve a lot more attention in the future efforts to understand microemulsions.
Acknowledgements
This research was supported by a grant from the Department of Energy. One of us is grateful (HTD) for the hospitality extended by E. Guyon and J.P. Hulin during his stay at ESPCI.
References [l] R.N. Healy, R.L. Reed and D.C. Stenmark, Sot. Pet. Eng. J. 16 (1981) 747. [2] H.T. Davis, J.F. Bodet, L.E. &riven and W.G. Miller, in: Physics of Amphiphilic Meunier, D. Langevin and N. Boccara, eds. (Springer, Berlin, 1987), p. 310. [3] Y. Talmon and S. Prager, J. Chem. Phys. 69 (1978) 2984; 76 (1982) 1535. [4] P.G. de Gennes and C. Taupin, J. Phys. Chem. 86 (1982) 2294.
Layers,
J.
H. T. Davis et al. I Microstructure and transport in microemulsions
481
[5] B. Widom, J. Chem. Phys. 76 (1982) 1535. [6] S.A. Safran, D. Roux, S.T. Milner, M.E. Cates and D. Andelman, in: Physics of Amphiphilic Layers, J. Meunier, D. Langevin and N. Boccara, eds. (Springer, Berlin, 1987), p. 291; D. Andelman, M.E. Cates, D. Roux and A. Safran, J. Chem. Phys. 87 (1987) 7229. [7] W. Helfrich, J. Phys. (Paris) 48 (1987) 285. [8] D. Bedeaux, E. van der Linden and M.A. van Dijk, Physica A 157 (1989) 544, these Proceedings. [9] J.C. Wheeler, in: Physics of Amphiphilic Layers, J. Meunier, D. Langevin and N. Boccara, eds. (Springer, Berlin, 1987), p. 286. [lo] B. Widom et al., J. Chem. Phys. 84 (1986) 6943. [ll] P. Gutring and B. Lindman, Langmuir 1 (1985) 464. [12] M.T. Clarkson, D. Beaglehole and P.T. Callaghan, Phys. Rev. Lett. 54 (1985) 1722. [13] M. Laques, J. Phys. (Paris) Lett. 40 (1979) 331; M. LHques and C. Sauterey, J. Phys. Chem. 84 (1980) 3503. [14] B. Lagourette, J. Peyrelasse, C. Boned and M. Clausse, Nature 281 (1979) 60. [15] K.E. Bennett, J.C. Hatfield, H.T. Davis, C.W. Macosko and L.E. Striven, in: Microemulsions, I.D. Robb, ed: (Plenum, New York, 1982) p. 65. [16] E.W. Kaler, H.T. Davis and L.E. Striven, J. Chem. Phys. 79 (1983) 5685. [17] S. Bhattacharya, J.P. Stokes, M.W. Kim and J.S. Huang, Phys. Rev. Lett. 55 (1985) 1884. [18] M.J. Stephan, Phys. Rev. B 17 (1978) 4444. [19] D. Stauffer, Phys. Rep. 54 (1979) 3. [20] G.R. Jerauld, L.E. Striven and H.T. Davis, J. Phys. C 17 (1984) 3429. [21] J.M. Luck, Phys. Rev. A 18 (1985) 2061. [22] M.A. van Dijk, G. Casteleijn, J.G.H. Joosten and Y.K. Levine, J. Chem. Phys. 85 (1986) 626. [23] A.T. Papaioannou, L.E. Striven and H.T. Davis in Surfactants in Solution, K.L. Mittal and P. Bothorel, eds. (Plenum, New York, 1987). [24] K.E. Bennett, PhD Thesis, University of Minn., 1985; D. Quemada and D. Langevin, J. Met. Theor. & Appl., Suppl. (1985) 141. [25] J.F. Bodet, J.R. Bellare, H.T. Davis, L.E. Striven and W.G. Miller, J. Phys. Chem. 92 (1988) 1898. [26] M. Kahlweit and R. Strey, private communication, 1987. [27] W. Jahn and R. Strey, J. Phys. Chem. 92 (1988) 2294. [28] W. Jahn and R. Strey, private communication, 1988. [29] P. Clausson, H. Christenson and R. Kjellander, J. Chem. Sot., Faraday Trans. 1 82 (1986) 2735.
MICROSTRUCTURE AND TRANSPORT IN MIDRANGE MICROEMULSIONS H.T.
DAVIS*,
J.F.
BODET**,
L.E.
SCRIVEN
and W.G.
Department of Chemical Engineering and Materials Science and Department University of Minnesota, Minneapolis, MN 55455, USA
MILLER of Chemistry,
Invited paper In microemulsions containing small amounts of oil in water (or water in oil), the fluid microstructure is usually that of swollen micelles (or swollen inverted micelles), i.e. the solution consists of small globules of oil (or water) coated with a surfactant layer and dispersed in a continuous water (or oil) rich medium. When the volume fractions of both oil and water are appreciable, microemulsions can be bicontinuous, i.e., they have both oil-continuous and water-continuous domains separated by surfactant-rich regions. The transition has been identified as a percolation process since it occurs when water and oil relative proportions reach a percolation threshold. Recently, however a transition between globular and bicontinuous microstructure has been found in microemulsions of nearly equal and fixed volumes of water and oil. In this paper we discuss these apparently different transitions and report the results of new viscosity studies in the equal oil to water volume microemulsions.
1. Introduction A surfactant
is an
drophilic) moiety forms association water phases another
a molecule
having
a water
soluble
(hy-
attached to a water insoluble (hydrophobic) moiety, which colloids such as micelles or liquid crystals when mixed with
or hydrocarbon. containing amphiphile
amphiphile,
Microemulsions are hydrodynamically stable isotropic water, and oil, and sometimes salt and/or surfactant, (often called a cosurfactant). Though isotropic on the scale
of the wavelength of light, microemulsions are heterogeneous on the scale of tens of nanometers. At this scale the solutions are heterogeneous media characterized by water-rich domains and oil-rich domains separated by sheetlike regions (often called surfactant films, layers, or membranes). In microemulsions containing small amounts of oil in water (or water in oil), the fluid microstructure is usually that of swollen micelles (or swollen inverted * Presently visiting: Ecole Superior de Physique et Chemie Industrielles, Laboratoire rodynamic et Mtcanique Physique, 10 Rue Vauquelin, 75231 Paris Cedex 0.5, France. ** Presently at: Centre de Recherche Paul Pascal, Domaine Universitaire, 33405 Talence France.
0378-4371/89/$03.50 0 Elsevier Science Publishers /\rfi..+r. U -11,. ,,a nl_._:__ n..l-l:-L:.-rX. . . x
B.V.
d’HydCedex.
H. T. Davis et al. I Microstructure
and transport in microemulsions
471
micelles), i.e. the solution consists of small globules of oil (or water) coated with a surfactant layer and dispersed in a continuous water (or oil) rich medium. When the volume fractions of both oil and water are appreciable, microemulsions can be bicontinuous , i. e . , they have both oil-continuous and water-continuous domains separated by surfactant-rich regions. The transition has been identified as a percolation process since it occurs when water and oil relative proportions reach a percolation threshold. Recently, however a transition between globular and bicontinuous microstructure has been found in microemulsions of nearly equal and fixed volumes of water and oil. In this paper we discuss these apparently different transitions and report the results of new viscosity studies in the equal oil to water volume microemulsions.
2. The transition when oil and water proportions vary The most important factor driving microemulsion research during the last several years is the possible use of microemulsions for enhancing oil recovery. Residual oil droplets are trapped in a waterflooded oil reservoir by the high interfacial tension between oil and water. By suitable choice of surfactant, cosurfactant (e.g., an alcohol) and salinity of aqueous brine, researchers in the petroleum industry [l] made microemulsions having ultralow tensions against coexisting oil and water phases. Such a microemulsion placed at an oil-water interface can lower tension and lead to recovery of residual oil droplets. Salt, usually NaCl, is most commonly introduced for fine tuning the phase and tension behavior of a microemulsion of an ionic surfactant. Fig. 1 illustrates typical results for a microemulsion system having the potential for enhancing oil recovery. In such a salinity scan, mixtures of equal values of oil and brine and a fixed percentage of surfactant and cosurfactant are typically prepared and allowed to equilibrate. At low salinity two phases form, the surfactant being primarily in the lower phase, hence the notation 24 indicating the presence of a lower phase microemulsion. At intermediate salinities there are three phases, denoted 34, and most of the surfactant is in the middle phase microemulsion. At high salinities two phases, denoted %J, form with most of the surfactant in the upper phase. The low salinity microemulsion is a water-continuous solution of oil-swollen micelles and the high salinity microemulsion is an oil-cintinuous solution of water-swollen inverted micelles. At intermediate salinities bicontinuous microemulsions can occur. The pattern of phase and interfacial behavior illustrated by fig. 1 is a generic one for oil-water-amphiphile mixtures [2]. The ultralow tensions are the result of selecting conditions so that the middle phase microemulsions are sandwiched in field variable space between not too widely separated critical endpoints, On
472
H. T. Davis et al.
I Microstructure
INTERFACIAL
TENSIONS
and transport
-)’ IN A SALINITY
CRITICAL END P?lNT 20
in microemulsions
:
SCAN
CRrrlCIL END
P?lNT 3e
:
G
1 o- 2 dYn Eii10-3
1 o- 4
10-5
0
1.5 Nat2
SALINITY
Fig. 1. Schematic of phase and interfacial tension oil-rich and/or water-rich phases in a salinity scan.
3.0 (wt %)
behavior
of microemulsion
coexisting
with
the left in fig. 1, the lower phase microemulsion splits (with increasing salinity) at a critical point (called a critical endpoint in ternary phase diagrams) into the middle phase microemulsion and the lower phase in the 34 regions. On the right, the upper phase and the middle phase collapse at a critical point into the upper phase microemulsion. If the two critical end points were moved together (by varying some field variable such as temperature, pressure, activity of a cosurfactant, or the carbon number of the hydrocarbon) a tricritical point would result, with the consequence that yMo and yMw both vanish. Thus, the search for ultralow tension microemulsion systems for enhancing petroleum recovery amounts to the search for a region in field variable space lying near a tricritical point. Ideas initiated by Talmon and Prager [3], de Gennes and Taupin [4], and Widom [5] have given rise to a phenomenological free energy model which describes the above patterns of phase behavior of microemulsions. The basic assumptions are (1) that oil and water-rich domains are randomly interspersed in space (divided by Talmon and Prager into Voronoi polyhedra of average diameter c-l’3 and by others into cubes of size e), (2) the surfactant resides entirely in layers separating the oil and water-rich domains and (3) the free energy arises from the entropy of interspersion of the domains and from the
H. T. Davis et al. I Microstructure
and transport in microemulsions
473
energy of curvature of the surfactant layers. The most recent version of the model has been developed by Safran et al. [6]. The free energy density of their model is f = fs + fc, where the entropy contribution is f, =
wm3m 1%$J+ Cl- 4) loId - +)I
and the curvature
k is Boltzmann’s
contribution
is
constant and T is temperature. (b is the volume fraction associated with water-rich domains - to 4 is assigned all of the water and half of the surfactant, i.e., 6, = c&, + r&/2. H,, is the spontaneous mean curvature and K(S) is the film bending constant renormalized for long wavelength thermal fluctuations. For 5 6 5, the Helfrich formula [7] is used for K( 0, namely, K( 5) = K,,[l - log( t/a) /log( &la)]. K,, is the bare bending constant (K( 5) = K0 for 5 < a), a is a molecular length characteristic of the surfactant size and & is the surfactant film persistence length. When 5 > & the surfactant film becomes easier to bend owing to the existence of spontaneous crumpling. de Gennes and Taupin give for the persistence length the expression & = a exp[2nK,lkT]. The condition that the surfactant lie in the interdomainal films yields 5 = 644 1 - 4) /&. In the dimensionless form t$f/kT, the free energy becomes a universal function of 4, &&la and &H,,. Thus, in terms of the composition variables 4 and ~&,$~/a the predicted phase behavior depends only on the one adjustable parameter &ZY&,.Phase equilibria determined by variation of H, from negative to positive values yields a sequence of water-rich to oil-rich microemulsions, H, = 0 corresponding to the microemulsion of equal volumes of oil and water. The value of K, can be measured directly in swollen micellar solutions. In fact, in a paper presented to this conference, Bedeaux, Linden and van Dijk [8] use the Kerr effect to find K,,IkT = 0.76 (K. equals twice their quantity CL) for water swollen inverted micelles of aerosol OT in isooctane. While a theory based on a phenomenological free energy model is useful for rationalizing patterns of phase behavior, it is not a statistical mechanical theory in that it does not show how the patterns derive from molecular interactions and assumes rather than predicts fluid microstructure. Towards the development of molecular level theory, the recent efforts of Wheeler [9] and of Widom and coworkers [lo] on lattice models appear quite promising. The transition from swollen micelles to bicontinuous to swollen inverted micelles in the 2,3,? sequence has been beautifully shown in pulsed field gradient spin echo nuclear magnetic resonance (NMR) studies of the self-
414
diffusion results
H. T. Davis et al.
coefficients of one
diffuse
as a globular
oil and water
studies
swollen
At high salinity,
and transport
of the components
of these
water-continuous
I Microstructure
are
micellar
shown
and oil reverse
have the higher
of the microemulsion
diffusion
[ll,
121. The
in fig. 2. At low salinity,
region,
unit and water
water
in microemulsions
the oil and diffuses molecularly
roles and at intermediate coefficients
in the
surfactant molecules in continuous phase.
expected
salinities
both
for a bicontinuous
medium. The surfactant diffusivity is about 10 times lower than oil and water in the bicontinuous domain which is consistent with the fact that it is constrained to move along surfactant sheets. That the microemulsion is percolative in the sequence 2,3,2 is easily demonstrated by plotting the electrical conductivity versus the water volume fraction. At water fractions below the percolation threshold &,c for the oil-continuous to bicontinuous transition one would expect the electrical conductivity to be very small. The percolation threshold has been observed in numerous systems [13-171. Typical of the behavior observed in many systems [15] is that shown in fig. 3, in which well with the conductivity computed
the measured conductivity for a Voronoi tessellation
hedra are randomly decorated with conducting and Near a percolation threshold the electrical conductivity obey the scaling laws Km (&, below the 4 wc. Conductivity
agrees whose
nonconducting is expected
quite poly-
phases. [13, 181 to
- &-‘, &,, < &,c and Km (& - &.)‘, 4, > percolation threshold presumably arises from
Toluene
D/m2s-’ Water
A
/k--,-+
lO-g-
lO’O_
10-l’ L
I 3
ShITY
I I
I
I
5
6
7
( g/
100
crn3
I a
I 9
I 10
’
1
Fig. 2. Diffusivities of components of sodium dodecylsulfate (SDS), chloride brine. Vertical lines indicate 2-3 and 3-2 phase transitions.
butanol, toluene Ref. [ll].
and sodium
H. T. Davis et al. I Microstructure and transport in microemulsions
6
VOLUME
FRACTION
1.0
w z E
0.8
m
0.6
8 0 0
415
BRINE
Fig. 3. Conductivity and viscosity versus volume fraction for brine in microemulsion phase. From a salinity scan of Witco TRS lo-80 surfactant (an alkylaryl sodium sulfonate), tert-amyl alcohol, octane and NaCl brine. Ref. [15].
cluster migration, cluster to cluster change hopping or dynamical cluster rearrangement. For several microemulsions of cyclohexane, water, sodium dodecylsulfate (SDS) and pentanol, Lagues and Sauterey [13] found t and s values in the range 1.4-1.8 and 1.1-1.4, respectively. If the percolation threshold is approached in temperature, the conductivity scaling laws are the same except that +c - &c is replaced by T- T,. Bhattacharya et al. [17] studied the temperature dependence of the conductivity of a decane, water and aerosol-OT (AOT) microemulsion near the percolation threshold and found t = 1.68 + 0.05 and s = 1.17 -+ 0.05, in agreement with Lagues and Sauterey. The static percolation values are s = 2~ - p = 1.2 [19] and t = 2.0 [20]. Near a percolation threshold the dielectric constant is expected [21] to obey the scaling law E(W) 0: mu-l with frequency w, where u = tl(s + t). Bhattacharya et al. found u = 0.63 + 0.04 and, in a study of isooctane, water, and AOT microemulsions, van Dijk et al. [22] found u = 0.62 + 0.02. Static percolation values of t and s yield u = 2/3.2 = 0.625 whereas measured values give u = 1.68/2.85 = 0.589, each in reasonable agreement with experiment, even though the experimental value for t is somewhat lower than the static value. The authors Lagues and Sauterey and Bhatacharya et al. argue that their microemulsions consist of flocculated clusters of swollen inverted micelles which become sample spanning at the percolation threshold. A lower frequency cutoff (
476
H. T. Davis et al.
I Microstructure
and transport
in microemulsions
percolation thresholds and a minimum occurs near the state of equal volumes of oil and water. The viscosities reported in fig. 3 were measured with a rolling ball viscometer. In a more accurate study [23] with a cone and plate viscometer, the viscosities were found to be somewhat shear rate dependent in the range 10 to lOOOs_‘, the stronger non-Newtonian behavior (which is shear thinning for microemulsions) occurring near the viscosity peaks. There is shear thinning in the equal volume oil/water microemulsion but not as much as in those near the percolation peaks. One can rationalize the viscosity trend in fig. 3 in terms of a rigid globule model [24]. Although the model seems reasonable in the swollen micelle domains, we believe a more physically realistic model must incorporate percolative clusters and bicontinuous microstructures. It is especially difficult to see the relevance of the model to the new viscosity results we present in the next section of this paper.
3. Transition
at equal oil and water volumes
The patterns of behavior described in the previous section are those that occur if one follows coexisting microemulsion through a field variable scan that generates the Z&3, !?! sequence of phases. This is only one possible path in parameter space. As an alternative we have recently studied [25] the properties of microemulsions along the one phase (14) corridor in the phase diagram shown in fig. 4 (which was determined by Kahlweit and Strey [26]). Fig. 4 is a temperature-surfactant composition phase diagram for a three component system whose water and oil (octane) mass proportions are fixed at 60 : 40. This corresponds to almost equal volumes of water and oil. The one-phase states we have studied are shown in Fig. 4 as filled circles and are identified by letters. Primed and unprimed pairs A, A’; B, B’, etc. refer to pairs having the same composition but different temperature. The diffusivities of the microemulsion constituents measured by pulsed field gradient spin echo NMR along the one phase corridor are presented in fig. 5 along with the diffusivities of water and octane in pure bulk phases at temperatures of the microemulsions. The unambiguous conclusion to be drawn from fig. 5 is that along the one phase corridor from lower to higher temperatures the microemulsion undergoes a transition from a water-continuous swollen micellar solution to a bicontinuous solution. The diffusivity of oil in solution A is three orders of magnitude smaller than that of A’, these two microemulsions being at the same composition but at 20.0 and 4O.l”C, respectively. Freeze-fracture replica transmission microscopy [2.5,27] also provides dramatic evidence of the transition from globular to bicontinuous microstructure in these mid-range microemulsions. Especially convincing are the
H. T. Davis et al. I Microstructure and transport in microemulsions
477
40
T
[“Cl 30
t 20
10
0
30
Fig. 4. Phase diagram of pentaethylene dodecyl glycol ether (C,,E,), water and octane (water/ octane = 60:40) ref. [26]. The microemulsions studied are indicated by the filled dots.
micrographs of Jahn and Strey [27] who find that oil and water regions have a different texture when the fracture surface replica is prepared as a mixed tantalum/tungsten film. One of their micrographs of bicontinuous microemulsion is given in fig. 6. It is plain from this micrograph that this bicontinuous microemulsion does not consist of flocculated globules. It is truly a bicontinuous chaotic interspersion of oil and water rich domains.
6 g 10-10 1
,o-ll
+
D, PURE H20
x D, PURE C,
n 1 o-12
l
10-13
A B C D E F G H I J
Mixture
D, C,2E5
I’ H’ G’ F’ E’ D’ C’ B’ A
#
Fig. 5. NMR self-diffusion coefficients in the microemulsions
indicated in fig. 4. Ref..[2j]
H. T. Davis et al. I Microstructure
478
Fig. 6. Freeze fracture electron micrograph 7wt% C,,E,. Bar = 1 I*. Ref. [27].
and transport in microemulsions
of the C,,E,.
water
and
octane
microcmulsion
at
It is interesting to observe in fig. 5 that there appear to be two transitions. The first occurs between B and D and is characterized by an abrupt increase of about a factor of 10 in the diffusivities of oil and surfactant, after this transition appear to be diffusing together. Between transition is from globular to bicontinuous microstructure. what is the nature the effective [25].
One
of the B to D transition.
diffusivity possibility,
coefficient which
The transition
determined
is consistent
with
which before and G and H or I the We are not sure is also observed
by quasielastic some
in
light scattering
freeze-fracture
replica
micrographs [28], is that states A and B correspond to slightly monodisperse spherical swollen micelles and that between B and D aggregation into clusters begins occurring. And then, between G and H or I, the clusters become sample spanning and thus result in bicontinuous microemulsion. With a cone and plate viscometer, we have explored the rheological behavior of microemulsion along the one phase corridor. In fig. 7, we present effective viscosities versus shear rate for selected microemulsions. All are shear thinning non-Newtonian fluids. The effective viscosities for a shear rate of 1 so ’ are compared in fig. 8 with the self-diffusion coefficient of the surfactant (the viscosity of fluid J was not measured in the cone and plate viscometer, instead
H. T. Davis et al. I Microstructure
c
v,
and transport in microemulsions
419
100
B
I
.l
. .
. ..
..I
.
.
.
. .
1
,l
..I
.
10
SHEAR RATE (set -’ ) Fig. 7. Effective
viscosity
versus
shear
rate of microemulsions
indicated
in fig. 4.
it was measured in a capillary viscometer and is hence not strictly comparable to the others). The trends in viscosity and diffusivity are roughly compatible but differ in significant detail. Whereas the diffusivities differ between A and B and between D and F, the corresponding viscosities differ by about a decade. Also in the sequence F’ to A’ the surfactant diffusivity remains about constant whereas viscosity increased by a decade. Since the concentration of swollen micelles is very high in the globular domain, one does not expect the Stokes-Einstein equation, R = kTl6nvD (connecting particle radius R to viscosity n and diffusivity) to be very accurate. Stokes radii computed for microemulsions A, B and D are 0.4, 3.5 and 2.0 A, respectively. From electron microscopy the globular sizes in these microemulsions are observed to be of the order of 200 A in diameter, and so these Stokes radii are meaningless. As
1000 +
DIFFUSION
MICROEMULSION Fig. 8. Comparison of trends in surfactant microemulsions indicated in fig. 4.
diffusivity
with effective
viscosity
(at 1 s-’ shear rate) of
480
H. T. Davis et al. I Microstructure
and transport in microemulsions
expected in a strongly microstructured fluid, the mechanisms of diffusive motion and shearing of microstructure are not related in any simple way. Clearly the transition discussed in this section cannot be viewed as a percolation threshold reached by increasing the oil/water or water/oil volume ratio to a percolation threshold from some subpercolation value. The ratio is in fact approximately unity and the transition is achieved by increasing temperature at fixed composition. What can be concluded from our observations is that increasing temperature drives the mean curvature of surfactant sheets from a negative value favoring swollen micelles towards the value of zero favoring bicontinuous microemulsion. In the context of the phenomenological free energy model discussed in the previous section, this could arise from a temperature dependent spontaneous curvature. This model, however, ignores interactions between the surfactant films which at the high concentrations involved here could be significant. In fact in surface force measurements, Claessen et al. [29] found that the solvation force between monolayers of C,,E,, separated by aqueous films a few nanometers thick, undergoes a transition from repulsive to attractive when the temperature reaches 30°C. This is close to the temperature at which the globular to bicontinuous microstructure transition occurs along the one-phase corridor in fig. 4. In a system of fixed composition, it seems reasonable that repulsive forces would favor globules to increase monolayer separation and attractive forces would favor bicontinuous structures to decrease the separation, and so the correspondence of temperature may be more than a coincidence. These equal oil and water volume microemulsions deserve a lot more attention in the future efforts to understand microemulsions.
Acknowledgements
This research was supported by a grant from the Department of Energy. One of us is grateful (HTD) for the hospitality extended by E. Guyon and J.P. Hulin during his stay at ESPCI.
References [l] R.N. Healy, R.L. Reed and D.C. Stenmark, Sot. Pet. Eng. J. 16 (1981) 747. [2] H.T. Davis, J.F. Bodet, L.E. &riven and W.G. Miller, in: Physics of Amphiphilic Meunier, D. Langevin and N. Boccara, eds. (Springer, Berlin, 1987), p. 310. [3] Y. Talmon and S. Prager, J. Chem. Phys. 69 (1978) 2984; 76 (1982) 1535. [4] P.G. de Gennes and C. Taupin, J. Phys. Chem. 86 (1982) 2294.
Layers,
J.
H. T. Davis et al. I Microstructure and transport in microemulsions
481
[5] B. Widom, J. Chem. Phys. 76 (1982) 1535. [6] S.A. Safran, D. Roux, S.T. Milner, M.E. Cates and D. Andelman, in: Physics of Amphiphilic Layers, J. Meunier, D. Langevin and N. Boccara, eds. (Springer, Berlin, 1987), p. 291; D. Andelman, M.E. Cates, D. Roux and A. Safran, J. Chem. Phys. 87 (1987) 7229. [7] W. Helfrich, J. Phys. (Paris) 48 (1987) 285. [8] D. Bedeaux, E. van der Linden and M.A. van Dijk, Physica A 157 (1989) 544, these Proceedings. [9] J.C. Wheeler, in: Physics of Amphiphilic Layers, J. Meunier, D. Langevin and N. Boccara, eds. (Springer, Berlin, 1987), p. 286. [lo] B. Widom et al., J. Chem. Phys. 84 (1986) 6943. [ll] P. Gutring and B. Lindman, Langmuir 1 (1985) 464. [12] M.T. Clarkson, D. Beaglehole and P.T. Callaghan, Phys. Rev. Lett. 54 (1985) 1722. [13] M. Laques, J. Phys. (Paris) Lett. 40 (1979) 331; M. LHques and C. Sauterey, J. Phys. Chem. 84 (1980) 3503. [14] B. Lagourette, J. Peyrelasse, C. Boned and M. Clausse, Nature 281 (1979) 60. [15] K.E. Bennett, J.C. Hatfield, H.T. Davis, C.W. Macosko and L.E. Striven, in: Microemulsions, I.D. Robb, ed: (Plenum, New York, 1982) p. 65. [16] E.W. Kaler, H.T. Davis and L.E. Striven, J. Chem. Phys. 79 (1983) 5685. [17] S. Bhattacharya, J.P. Stokes, M.W. Kim and J.S. Huang, Phys. Rev. Lett. 55 (1985) 1884. [18] M.J. Stephan, Phys. Rev. B 17 (1978) 4444. [19] D. Stauffer, Phys. Rep. 54 (1979) 3. [20] G.R. Jerauld, L.E. Striven and H.T. Davis, J. Phys. C 17 (1984) 3429. [21] J.M. Luck, Phys. Rev. A 18 (1985) 2061. [22] M.A. van Dijk, G. Casteleijn, J.G.H. Joosten and Y.K. Levine, J. Chem. Phys. 85 (1986) 626. [23] A.T. Papaioannou, L.E. Striven and H.T. Davis in Surfactants in Solution, K.L. Mittal and P. Bothorel, eds. (Plenum, New York, 1987). [24] K.E. Bennett, PhD Thesis, University of Minn., 1985; D. Quemada and D. Langevin, J. Met. Theor. & Appl., Suppl. (1985) 141. [25] J.F. Bodet, J.R. Bellare, H.T. Davis, L.E. Striven and W.G. Miller, J. Phys. Chem. 92 (1988) 1898. [26] M. Kahlweit and R. Strey, private communication, 1987. [27] W. Jahn and R. Strey, J. Phys. Chem. 92 (1988) 2294. [28] W. Jahn and R. Strey, private communication, 1988. [29] P. Clausson, H. Christenson and R. Kjellander, J. Chem. Sot., Faraday Trans. 1 82 (1986) 2735.