12331
J. Phys. Chem. 1993,97, 12331-12338
A Luminescence Quenching Study of a Percolation Transition in a Propane/ Didodecyldimethylammonium Bromide/Water Microemulsion J. Zhang, J. L. Fulton, and R. D. Smith' Chemical Methods and Separations Group, Chemical Sciences Department, Pacific Northwest Laboratory,t Richland, Washington 99352 Received: August 18, 1993@
Luminescence quenching was used to explore the interdroplet exchange processes for a propane/didodecyldimethylammonium bromide/water microemulsion at a dispersed-phase volume fraction of 0.30. This system shows a percolation type of transition in electrical conductivity as the pressure of the liquid solution is reduced from 450 to 100 bar at 26.5 OC. Luminescence quenching results are consistent with a system of roughly spherical droplets, with size unaffected by the density of the continuous-phase solvent. However, the intermicellar exchange rate for the quencher is increased by a factor of 3 in the percolation regime. Only part of the increased exchange rate can be attributed to the decrease in the viscosity of the lower density propane, whereas the remainder is attributed to a clustering of the droplets resulting in more effective exchange. Lower propane density increases the strength of attractive interactions between the droplets, leading to extensive clustering and eventual electrical percolation. These results also confirm previous observations indicating that simply altering the strength of interdroplet interactions can induce electrical conductivity percolation. The observed behavior may be related to the early stages of a structural transition to a bicontinuous microemulsion that is believed to occur at higher volume fractions of the dispersed phase. These results also provide important new insights relevant to separation and reaction processes in near-critical microemulsion systems.
Introduction Micellesor microemulsionsreadily form in small alkane solvents (C2-C4) at higher densities where the microheterogeneous environment imparts unique properties to these supercritical or near-critical fluids.' Theabilitiesofthesemicrostructuredsystems to solubilize hydrophilic and amphiphilic molecules have led to a number of potentially important applications in separation science2v3and chemical rea~tions.~J In this paper we explore the structure of a microemulsion formed in near-critical propane. A near-critical fluid is herein defined as a liquid that is at a temperature above a reduced temperature (Tr = TIT,) of approximately 0.75 and below its critical temperature, T,. The physical and chemical properties of the solvent affect the stability of the microemulsion, and solvents that are slightly below their critical points are unique in this aspect. Due to the proximity to its critical point, a near-critical fluid is in a liquid state but still exhibits much greater compressibility than liquids at lower temperatures. The density, dielectric constant, and viscosity, as well as other physical properties of a near-critical fluid, can be varied to a significant extent by adjusting the pressure. The solvent properties of near-critical fluids are strongly related to the pressure-dependent molar density of the system. We have previously reported the possible existence of a bicontinuous microemulsion formed in propane using the surfactant didodecyldimethylammonium bromide (DDAB).6 Consistent with this type of structural transition, we observed a dramatic change in the electrical conductivity as the pressure of the system was adjusted. Our objective in this work is to apply the methodsof luminescence quenching in order to better describe the structural transition within this microemulsion. The use of near-critical propane allows one to *tunen the properties of the nonpolar solvent without altering the chemical composition of the solution and thus, we have one of the best-controlled systems for further exploring the basis of this structural transition. +
Operated by Battelle Memorial Institute. Abstract published in Advance ACS Abstracts, October 15, 1993.
0022-3654/93/2097-1233 1$04.00/0
Several recent studies have examined the pressure-dependent microemulsion structure in supercritical and near-critical fluids from both experimental7-I6and theoretical viewpoints.17J8 In normal liquids, details of microemulsion structure have come from studies of electrical conductivity or self-diffusion meas u r e m e n t ~ , ~small-angle ~-~~ neutron scattering (SANS), and freeze-fracture electron microscopy (FFEM).22-2sEvans et al.Z4 have reported extensively on the microstructure of DDAB microemulsions formed in various liquid alkanes. For these DDAB microemulsions, bicontinuous phases are frequently encountered at high volume fractions of the DDAB aqueous phase, whereas reverse droplet structures are seen when the volume fractions are lower. Studies of this type lead to a general conclusion that longer-range structures consisting of either bicontinuous networks or micellar clusters can exist. Luminescence quenching is another method that has been used to obtain quantitative structural and kinetic informationon microemulsion systems.2M3 The importance of luminescence quenching in microemulsions stems from its favorable time scale with respect to interphase transport processes and from the intrinsic sensitivity of emission decay processes to environmental influences. Thus, the characteristics of the intensity decay can be used to probe dynamic events in microemulsion environments. Following the basic kinetic model of luminescencequenching proposed by Infelta et al.44and T a ~ h i y for a ~ aqueous ~ micelles, the possibility of solute exchange in the water pools of reverse micelles was first pointed out by Menger et a1.46 and was later supported by the fluorescence measurements of Eicke and cow o r k e r ~ . ~A~transient ,~~ dimer model for the coalescing water droplets was proposed based upon the opening of a small water channel at the point of collision. The exchange of solutes is then described as a diffusion-controlled process through these channels during thecollision time ( lWo-lW' s). Toquantitativelyaccount for these exchange processes, Atik and Thomas3' extended the Infelta model to reverse micelle systems. Their experimental data showed that at low reactant concentrations the distribution among reverse micelles is well described by Poisson statistics.
+
0 1993 American Chemical Society
Zhang et al.
12332 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
Another interesting result is that ion transport only occurs on collision of the water pools with an efficiency of 51%. Similarly, Robinson et al.49 have deduced that the water droplet collision and solute exchange processes are relatively rapid, and thecollision rate was assumed to be diffusion controlled (- 1O1O M-I s-l). Further, a model was proposed involving the exchange of material between droplets occurring upon “sticky” collision^.^^ A related mechanism proposed by Jada et al.50 supports the presence of continuous water channels through transient merging of droplets. Very recently, the effect of the formation of micelle clusters on the exchange of quenchers was discussed by Almgren and Jbhannsson.42 (In this paper, we define a micelle cluster as a dynamic group of a small number of closely associated micelles. This micelle cluster is not necessarily the result of long-range critical phenomena.) All models generate a very similar conclusion; solubilizates can readily exchange during the transient micelle collisions. However, there are still uncertainties about whether the micelle size or structure effectively changes upon collision through a mechanism involving coalescenceso~slor whether ‘sticky encounters” (Le., micelle clustering) of generally intact micelles52953occur. A fundamental related issue is whether the somewhat chaotic nature of real micelle surfaces and the implications for micelle interactions can be effectively incorporated within the context of these simplistic models. In recent years, there has been an increasing interest in the electrical conductivity percolation phenomenon of microemulsions.20.21 It appears that this electrical transition corresponds to the percolation of the spherical droplet phase in the continuum. The description based on percolation implies the formation of clusters of water droplets that are sufficiently close to each other for an effective transfer of charge carriers between the droplets. Percolation is manifested by a rapid increase in both the dielectric constant and the electrical conductivity, and it can be induced by changing the temperature, surfactant chain length, or/and water content, etc.Sk56 However, pressure-induced percolation phenomena have not been ObSeNed previously. To explain the origin of electrical percolation, two approaches havebeen widelyaccepted. Thestatic percolation model attributes percolation to the appearance of the first stages of the transition to a bicontinuous structure. In the other words, the presence of the open water channels is responsible for electrical conduction. In the dynamic percolation model, the attractive interactions between droplets determine the formation of percolation clusters, but nomicelle coalescence takes place. Even below the percolation threshold, conductivity of a water-in-oil microemulsion is still much higher than that of the pure alkane solvent. In this regime, Eicke and co-workers56 used a charge fluctuation model to successfully describe charge transport. The spontaneous fluctuations in the number of ionic surfactant molecules and counterions on a single droplet result in a small percentage of the droplets carrying a positive or negative net charge. Therefore, the migration of these charged droplets in an external electric field causes a finite conductivity. This model was later improved somewhat by Halls7to better describe experimental data over a wide range of droplet sizes. Using the modified charge fluctuation model,s7Cametti et al.I9havewell explained their data below the percolation region. Above the percolation threshold, they applied a dynamic percolation model. In this model electrical conduction occurs either by charge hopping between nearest-neighbor micelles or by the electrophoretic motion of the guest micelle. However, from conductivity measurements alone, one cannot distinguish which model, static or dynamic, best describes the system. Very importantly, a correlation between electric percolation and the rate constant for solubilizate exchange between droplets (k,) was first discovered by Jada et al.50 Effects of surfactant chain length, counterions, headgroup size, oil nature, and additives in the water-in-oil microemulsion have been considered in the evaluation of transport processes, leading to a conclusion that above the percolation threshold the conductivity is mainly due to
the motion of counterions through transient water channels or conduits formed between droplets in a droplet cluster. In this paper, we explore the pressure-induced, electrical percolation phenomenon, in a propane/DDAB/water microemulsion to determine how the continuous-phase density affects the structure of the microemulsion. Luminescence quenching is used toelucidate theeffect ofpressureon theinterdroplet exchange process. We selected ruthenium tris(bipyridy1) ion?* Ru(bpy)P, as the luminescent probe and methylviologen as the excited-state quencher. The photophysical behavior of Ru(bp~)3~+ is well suited for the study of interdroplet exchange kinetics because it has a long-lived excited state and well-known excited-state photochemical rea~tions.5~46 This report addresses three important facets of these phenomena: (1) whether a bicontinuous or a droplet clustering mechanism best describes the percolation phenomena, (2) how the intermicellar exchange rate constant is correlated with the electrical percolation phenomenon, and (3) whether the exchange rate constant of the quencher molecules between droplets is pressure dependent.
Experimental Section Materials and Sample Preparation. The surfactant, didodecyldimethylammonium bromide (99%, DDAB), and the luminescent probe, Ru(bpy)&lz (99.9%), were purchased from Eastman Kodak and Chemical Probes, Inc., respectively. The luminescence quenchers, potassium ferrocyanide (&[ Fe(CN)6], 99+%) and methylviologen dichloride hydrate (MV*+,98%), were purchased from Alfa Products, Inc., and Aldrich, respectively. Thepropanewasobtainedfromscott Specialty Gases (CPGrade). The probe and quencher were prepared in stock solutions of methanol for simple introduction into the cell and the subsequent solvent removal. Freshly degassed distilled-deionized water (Millipore Milli-Q) was used throughout. All reagents were used as received. A preweighed amount of DDAB (2.02 g) was loaded into the high-pressure optical cell ( N 13 mL) to give a final s/o ratio (surfactant-to-oil ratio in weight) equal to 0.41, and an overall volume fraction of the surfactant and water, qjd, of about 0.30. A small quantity of the probe and quencher stock solutions were then added into the cell. In all cases the probe concentration equaled 10 gM. The cell was evacuated for about 25 min to remove residual solvent and oxygen. Next, the system was filled with propane vapor, and while maintaining a slight overpressure of propane to exclude oxygen, freshly degassed distilled-deionized water (1.85 mL) was quickly injected using a microsyringe, yielding a water-to-surfactant molar ratio, w,equal to 24. The system was then filled with liquid propane and allowed to stir overnight for complete solubilization and equilibration. All experiments were performed in the one-phase region at 26.5 O C . A series of luminescence quenching or conductivity measurements were made by either increasing the pressure of the system by the addition of pure fluid or reducing the pressure by discharging small amounts of the microemulsion solutions. The former method increases the pressure at constant surfactant and water volume fractions, while the latter depressurization method holds constant the mole fractions of surfactant and water. Luminescence Quenching Apparatus. Figure 1 shows a sketch of the instrumental arrangement. A small fraction of the light from a pulsed Nd:YAG laser (6-10 ns, 535 nm) was used to excite the probe. A portion of the beam was reflected onto the photocathodeof the reference PMT (Hamamatsu, Model R-928) to trigger an oscilloscope (Lecroy 9450A. 300 MHz). The excitation beam was focused by a plano-convex lens (focal length = 50 mm) into the high-pressure optical cell. The luminescent emission was observed at 90° to the excitation. The emission signal was collected and collimated by the first lens, then it passed through multiple filters (Oriel, low fluorescence cutoff 550 nm, regular cutoff 590 nm, and a band-pass 600 nm), and finally was focused on the sample PMT (Hamamatsu, Model R-928) by the
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12333
Percolation Transition in Propane/DDAB/ Water
A general equation describingluminescence quenching for this type of system is given a~443~5
6-8nr
j 10%
I
NDF
Digital Oscilloscope
L3
* h
= Z(0) exp(-A,t + A,[exp(-A,t) - 11) (1) whereZ(t) and Z(0) are the luminescenceintensities at time t and 0, respectively, following excitation. A2, As, and A4 are the parameters fitted to the experimental decay curves. In the case of partitioning of quenchers within the microemulsion droplets, the expressions for A2, A3, and A4 are given by the following general relationships: Z(t)
I
I I
"5;:
I
SF h m p
Figure 1. Schematic of the luminescence quenching apparatus: QW, quartz wedge reflector; NDF,neutral density filter; BS,beam splitter; M, mirror; L, lens.
TABLE I: Lifetime Data Recovered from Our Instrument Commred to Literature Values (25.0 "C) solvents rMUuled (ns) CHiClz 504 EtOH 655
~~
H20
572
rlitcraturc (ns)
49060b 67066 580 & 1959
second lens. The output from the PMTs was digitized by the oscilloscope that was interfaced to a Macintosh IIci computer using LabView I1 software. The high-pressure luminescence cell (3 16 stainless steel) incorporated two sapphire windows at 90° to each other. These windows were sealed to the cell body with metal O-rings. A beam stop (stainless steel mesh) was placed inside the cell to eliminate internal reflections. The temperature of the cell was controlled using electric heaters regulated by a platinum resistance probe (Omega). A high-pressure pump (Varian 8500)was used to control fluid pressure with the aid of a digital pressure indicator (Model 300C, Setra Systems). The system was well stirred at each experimental pressure. Details of the high-pressure conductivity cell are described elsewhere.6 The measured luminescent lifetimes, TO, of R ~ ( b p y ) 3 ~in+ different solvents (25 "C) agreed well with the literature values given in Table I. A nonlinear fitting routine was used to recover luminescent decay times. For the studiesof probe in a pure solvent, the decay kinetics was well represented by a single-exponential curve, where the amplitude of the residuals was less than 1% of the I(0) intensity and the residuals showed little or no autocorrelation. For this system of a relatively high volume fraction of the dispersed phase in a continuous-phase solvent having a very low refractive index, there is a large amount of scattering of the excitation beam along with luminescenceemission. In addition, as the density (and refractive index) of the solvent is reduced, there is a corresponding increase in the scattering from thesolution. The strong scattering component could not be completely rejected, requiring that the first few channels (-40 ns) of the decay curve beexcluded in thedata analysis. Deconvolution of the instrument function was not required because the excitation pulse (6-10 ns) and instrument response times were much shorter than the luminescence lifetime (>SO0 ns). Variation of measurements from day to day was less than 2%. The Model of LuminescemeQuenching. The hydrophilic probe (Ru(bpy)p2+)and quenchers (Fe(CN)& and MV2+)are solubilized within the microemulsion droplets. The time-resolved luminescencequefiching techniquewas used to study the exchange of quencher molecules between droplets.
where the partition coefficient, K,of quenchers within a micelle is given as
K = kJk-
(5) and k,, (M-I s-l) represents the second-order rate constant associated with collisions giving rise to migration of the reactants between miclles, k,, (s-l) is the pseudo-first-order intramicelle quenching rate constant, ko (= 1/70) is the luminescence decay rate constant in the absence of quencher, and [Q] and [MI are the quencher and micelle concentrations, respectively. k+ and kare the two rate constants describing quencher transfer between the free- and bound-water domains. When the ionic charges of the probe, quencher, and surfactant headgroups have the same sign electrostatic interactions strongly repel the probe and quencher toward the free-water core. Partitioning of quencher from the bound-water to the free-water region is essentially irreversible. Under this condition, eqs 2-4 can be reduced to A, = ko
+ kqmkcxkqm [QI + kcx[Ml
= (kqm+kqm k,,[M]
>'" [MI
(7)
Equations 6-8 are suitable for the systems where fast (comparable to TO) intermicellar exchange of the reactants takes place by collisions between micelle^.^^^*^' For the water/DDAB/ propane system, our preliminary SAXS results strongly favor a spherical droplet geometry for this microemulsion. Using R ~ ( b p y ) , ~as+a probe and MV2+as a quencher, equations 1 and 6-8 well describe the quenching process under the assumption of spherical droplets.
Results and Discussion Electrical Conductivity Measurement. Measurement of electrical conductivity is a simple and effective method for studying certain aspects of microemulsion structure. Variables which induce conductivity changes in microemulsions include volume fracti~n:~.~~ t e m p e r a t ~ r e ,and ~ ~ pressure? In systems that are predominately oil (cbOil > 0.70), a remarkable increase in conductivity is sometimes observed corresponding to what has been called a percolation threshold. However, the precise percolation mechanism is not always clear, and this behavior has been described both by static and dynamic percolation models. The static percolation model is consistent with micelle coalescence in a precursor to a bicontinuous phase, while percolation clusters
Zhang et al.
12334 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 0
3, 1=26.5
5 I '
'C
4'
5-
6-
0
100
200
300
400
500
Pressure (bar)
Figure 2. Conductivity of a DDAB microemulsion with (A)and without (0) 10 pM Ru(bpy)a2+ and 0.5 mM MV2+ at 26.5 OC.
from the dynamic percolation model are associated with "sticky encounters" due to attractive interactions. Earlier studies6 from this group showed that a large increase in the conductivity of a propane/DDAB/water microemulsion (s/o = 0.42) resulted as the pressure of the system was reduced and this was attributed to either a structural transition to a bicontinuousphase or micelle clustering due to attractive micelle interactions. We have reproducibly repeated conductivity measurements (Figure 2) in DDAB/HzO/propane systems in the absence and presence of probe, R ~ ( b p y ) 3 ~(10 + pM), and quencher, MV2+ (0.5 mM). As shown in Figure 2, the conductivity of a single-phase system is reduced by almost 3 orders of magnitude when the pressure is increased from 100 to 450 bar. The systems become two phase below 100 bar, so that reducing the pressure has the effect of bringing the system closer to a phase boundary. The system remains single phase up to at least 450 bar, the limit of our experimental apparatus. These changes were observed to occur at both constant volume fraction of surfactant and water (by increasing the pressure with addition of pure propane) and at constant overall mole fraction of surfactant and water (by dischargingsmall amounts of the propane solution). Over the pressure range from 100to 400 bar, the propane density increases by about 10%(from 0.51 to 0.56 g/mL), while that of the water increases only 1%. Such a large change in the conductivity with the system pressure was unexpected since the volume fractions of the water, surfactant, and propane remain essentially constant. Clearly, variation of the density of the oilcontinuous portion of the microemulsion is sufficient to induce a structural transition. From an electrical conductivity measurement alone,wecannot discern theexact nature of the pressure induced structural transition. To better understand the mechanism of exchange between the aqueous microemulsions in this near-critical propane, we apply the luminescence quenching method. Effects of Temperature and Pressure on the Probe Lifetime. The Ru(I1) complex is sensitive to its local solvent environment because of the existenceof the activated d-d states (Scheme I).58 The difference in decay time in different solvents is attributed to the interactions of either the MLCT state(s) or d-d state(s) with the solvent. Stabilization/destabilization of these two states by the solvent determines the energy barrier and deactivation rate constant from the MLCT to the d-d state(s). As a result, decay times can change dramatically from one solvent to another. The most acceptable mechanism describing its emissive process is given as a decay from the metal-to-ligand charge-transfer (MLCT)* excited state@) to the ground state (Scheme I). [(bPY)zRu"(bPY)l 2+ 5 [(bPY)zRu"'(bPY-)l 2+* ( 9 ) A good polarity-sensitive probe molecule must have a large
4 0
2000
1000
Time (ns)
Figure 3. Single-exponential fit of 10 mM R ~ ( b p y ) , ~in+DDAB/H20!w = 24)/propane, & = 0.30 (propanep = 0.53 1 g/mL) at 26.5 O C . The inset is a graph of the residuals.
-(d-a)*
hv,
hv, hv,
I l l
Metal Orbltals
Spectroscopic States
change in its permanent dipole moment upon going from the ground state to the excited state. This dipole change interacts strongly with the solvent dipoles and causes large effects on state energies and spectra. Ru(bpy)3*+is not a good solvent probeS8 in this respect because the promoted electron can distribute itself in a roughly spherical fashion, with no overall dipole change, yielding unpredictable changes in the absorption and emission. However, the Ru(bpy)32+lifetime can still be used to monitor whether or not changes in local environment have occurred. Because of the cationic natures of both the DDAB headgroups and R ~ ( b p y ) 3 ~probe, + the probe will be solubilized in the freewater region of the micelle core due to strong electrostaticrepulsion with the headgroups. Decay kinetics of Ru(bpy)3*+ in DDAB give an excellent single-exponentialfit (Figure 3), consistentwith the probe molecules residing in a single free-water environment. We have also examined the effect of pressure on the probe lifetime for both the water/DDAB/propane microemulsion and for propane-saturated water. The lifetime of Ru(bpy)s2+in the DDAB microemulsion,w = 24 (26.5 OC,T = 575 ns), is slightly higher than that in water (25.0 OC, T = 572 ns). As shown in Figure 4, lifetimes in both systemsshow no dependenceon system pressure,indicatingthat (1) a pressure-induced structural change does not affect the local environment inside the microemulsion droplet, (2) the water pool environment of the DDAB microemulsion is very similar to that of bulk water, and (3) the changes in the fluid density do not change the preferred solubilizationsite of probe molecules. Ru(I1) complex d-d state(s) can be thermally populated from the excited MLCT state@), and the formation of d-d state@) is a predominant pathway in photodeactivationand photochemistry (Scheme I). Thus, the probe is highly sensitive to temperature, resulting in large variationsin its dynamicproperties. To quantify
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12335
Percolation Transition in Propane/DDAB/ Water
TABLE Ik T h e d Deactivation Ener and Rete Constant for Formation of d-d State(s) in D D A B % ~ O / P ~ O ~ U ~ System as a Function of Density density (g/mL) AE (cm-l) k'(s-1) 0.509 0.527 0.531 0.534 0.543
3398 3463 3472 3456 3532 3464 3560
average in H20
0
100
200
300
400
6.01 X 6.05X 6.31 X 6.20X 6.73 X 6.26X
1OI2 lo** 10l2
1.00 x
1013
loL2 10l2
loL2
500
P m u m (bar)
Figure 4. Luminescence lifetimes of 10 pM R ~ ( b p y ) , ~in+DDAB/H20(w = 24)/propane, dd = 0.30 (0, 26.5 "C) and in propane-saturated 25.0 "C) as a function of pressure. water (0,
5ii -
-
1
o.oc+o
2.0c.3
1.0~-3
3.01-3
[Quencher] (M)
Figure 6. Stern-Volmer plots of Ru(bpy)s2+ in aqueous solution (25.0 "C) with either Fe(CN)& (0) or MV2+ ( 0 )as a quencher.
I
zoo4 20
30
SO
40
60
70
T(T I
Figure 5. Luminescence lifetimes of Ru(bpy)s2+ aqueous solution at different temperature was recovered from a linear fit. Increasing temperature decreases the decay time.
the rate constant and deactivation barrier between the thermally populated metal-centered d-d state(s) and MLCT state@), a relationship between temperature ( r ) and R ~ ( b p y ) 3 ~lifetime + ( ~ ( 7 )is) described as60 1 = k, + k,, + k'exp 7(
T)
of the propane microemulsion (w = 24) are compared to those in pure water (Table 11),wesee that the probe environment closely resembles that of the bulk water. The probe, by itself, provides only a limited amount of information on the issue of a possible structural transition inside the microemulsion. To further reveal how continuous-phase solvents affect interactions between solvent-surfactant and surfactant-surfactant, additionof a quencher to the systemallows us to probe the large-scale structural transition which occurs in this microemulsion as the fluid density is changed. Luminescence Quenching. For luminescencequenchers, such as Fe(CN)6+ and MV2+, an electron-transfer reaction is the predominate excited-state reaction. Dynamic quenching significantly changes the probe lifetime in a process described by the Stern-Volmer relationship
= 1 + kq7o[Ql = 1 + &[Q1 (12) where TO and T are the decay times in the absence and presence of quencher, respectively, kq is the bimolecular quenching rate constant, [Q] is the concentration of quencher, and K,,= k , ~ o is the Stern-Volmer quenching constant. Figure 6 gives plots of Ru(bpy)32+quenching by Fe(CN)6' and MVZ+in aqueous solutionsat 25 OC. Clearly,thequenchingefficiencyofFe(CN)& (k, = 3.9 X 1O1O M-l s-I) is about 2 orders of magnitude higher than that of MV2+ (k, = 2.4 X lo8 M-' s-I) due to favorable electrostatic interactions between the probe and quencher. We studied luminescencequenching behavior of these two quenchers in the DDAB microemulsion;MV2+was preferred over Fe(CN)& because MVz+remained in the free-water core region rather than being electrostatically attracted to the surfactant headgroup region.28b We found that the quencher, Fe(CN)&, partitioned strongly into the headgroup region, making interpretation of intermicellar exchange processes much more difficult. The quenching mechanism for MV2+ is described by the following electron-transfer reaction: TO/T
k' = kl& where k, and k,, are the radiative and nonradiative decay rate constants going from the emitting MLCT state(s) to the ground state (SO),respectively. A E is the energy gap between the d-d state(s) and the MLCT state(s), and k' is the Arrhenius preexponential factor for thermal activation of the d-d state(s) which is an overall rate constant for formation of d-d state(s). For R ~ ( b p y ) 3 ~the + decay from the d-d state(s) to the ground state is much more rapid than return to the MLCT state(s) (kz >> k - I ) . In this case, eq 11 reduces to k'= kl,and the formation of d-d state(s) is essentially irreversible. The plot of Ru(bpy)++ lifetime vs temperature is given in Figure 5 . We have used this model toexamine the temperature-dependent lifetime data of R ~ ( b p y ) 3 ~in+the DDAB/propane system under differing propane densities. The question arises as to whether or not propane densityor pressuremay affect the deactivationenergy and rate constant. The results, shown in Table 11, indicate that pressure has little effect on either parameter, suggesting that the kinetics describing by eq 10 are not affected by the density or pressure of the propane microemulsion. When hE and k'values
( R ~ ( b p y ) ~ ) ' ++ * MV2*
-
( R ~ ( b p y ) ~ ) ~++MV+ * (13)
Formation of [Ru(bpy)3I3+*gives rise to very low quantum
Zhang et al.
12336 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 I
0 ,
I
I
03,
I
h
c
E *
G-
.
v-
100
0
300
200
500
400
12
B
-6
0
400
800
1200
I600
Time (ns) Figure 7. Fit of experimental data by eq 1 for 10 fiM Ru(bpy)?+ in DDAB/HzO(w=24)/propane with 0.5 mM MVZ+at 350 bar and 26.5 O C . The inset is the residuals of this fit.
I V
,
,
,
100
,
200
,
,
300
,
I
400
500
1.01
0.9
yield, leading to not only shorter lifetime but also lower intensity. Thus, the quenching mechanisms described by eqs 1 and 6-8 adequately depict the MV2+ quenching of Ru(bpy)J2+ in the water/DDAB/propane microemulsion. Luminescence Quenching in the Microemulsion Phase. The inhomogeneous distribution of quenchers in the microemulsion leads to multiexponentialdecay processes. The quencher perturbs the probe luminescence decay through processes of inter- and intradroplet quenching as described by eqs 1 and 6-8. Nonexponential behavior was observed in all cases when the MVZ+ quencher concentration was above 0.1 mM for this propane microemulsion. Figure 7 shows the fit of eq 1 to the luminescence decay data in the presence of 0.5 mM MV2+at a pressure of 350 bar. In all cases the volume fraction of the dispersed droplet phase, &, was equal to 0.30, corresponding to a molar waterto-surfactant ratio of 24. The quenching process described by eq 1 provides an excellent fit to the experimental data over the full time scale (40 to 1600 ns). The residuals, shown in the inset of Figure 7, demonstrate the quality of the fit. At quencher concentrations above 0.5 mM, extensive quenching lowered the signal-to-noise ratio so as to reduce the quality of the fit. Figure 8 shows the recovered parameters (k,,, panel A; kqm, panel B; [MI, panel C) as a function of pressure for two different quencher concentrations, 0.1 and 0.5 mM. A large decrease was observed in the interdroplet exchange rate as the pressure of the system was increased. For example, k,, = 2.5 X lo9M-I s-l near the phase boundary at 100 bar and decreased by a factor of about 3 when the pressure was increased to 450 bar. The trend in the intermicellar exchange rate was similar to the behavior of the electrical conductivity, although the relative magnitudes of the two effects were different. kqm,also shown in Figure 8, is the pseudo-first-order, intramicellar quenching rate constant. This parameter not only reveals the efficiency of the quenchingprocess but also indicates changes in micelle size or polydi~persity.~~ Significant polydispersity can cause the experimentaldecay curve to show continuous curvature due t o low and high k,, corresponding to larger and smaller micelles, respectively. There is no evidence of variation of the micelle size as the pressure of the system is changed. Finally, the micelle concentration recovered from the fit of eq 1 illustrates that the micelle size is uniform over the entire pressure range studied (100450 bar). If we assume that the micelles are spherical, we can use the fluorescencedata to calculate that the water core radius, R,, is equal to 42 A from a simplegeometricargument based upon themicelle concentration and the amount of water added to the system. For comparison, we can also determine the water core radius from a small X-ray scattering measurement24hof the area occupied by a single surfactant headgroup (a0 = 68 A2)accordingto the simple formula R, = 3u, W/ao,where u, is the volume of single water molecule and W is the molar water-to-surfactant ratio. The value thus
,
.
0
0.6
C
1 1
0.54 0
'
,
'
'
100
200
8
300
'
'
400
I
500
Pressure (bar)
Figure 8. Recovered and calculated parameters from eqs 1 and 6-8 as a function of pressure for DDAB/HzO/propane in the presence of 0.1 mM (0)and 0.5 mM ( 0 )MVZ+,respectively: (A) k,,, the exchange rate constant; (B) k,,, the pseudo-first-order intramicellar quenching rate constant; (C) the micelle concentration (mM).
I 100
200
300
400
200
300
400
500
300
400
500
I
"6 . 100
500
0.61 0.5 100
200
Pressure (bar)
Figure 9. Effect of pressurization (0)and depressurization ( 0 )on the exchange process in a DDAB microemulsion ([MV2+] = 0.2 mM, 26.5 O C ) : (A) k,,, theexchange rate constant; (B) k,,, the pseudo-first-order intramicellar quenching rate constant; (C) the micelle concentration
derived is equal to 32 A. The two measurement methods are in reasonableagreement. The differencein these two measurements is attributed to the fact that the micelles may not be perfectly spherical but may be slightly elongated. As shown in Figure 9, we alsoexaminedtheeffects of pressurization and depressurization on the fitted parameters at a quencher concentration of 0.2 mM. Earlier conductivity measurements6 showed identical behavior
Percolation Transition in Propane/DDAB/Water
P w u m (bar)
Figure 10. Comparison of the exchange rate constant, k,, ( O ) , from the system with 10 pM Ru(bpy)a2+ in DDAB/H20(~=24)/propanesystem in the presence of 0.10 mM MV2+ with the viscosity-corrected exchange
rate constant, k,,(q/qo) (a). qo is the viscosity at the highest pressure (456 bar).
regardless of whether the pressure was increased or decreased. Since the water and surfactant phases are relatively incompressible between 100 and 450 bar, the volume fraction (and molarity) of the droplets is held nearly constant when pressurized with pure propane. Thus, the properties of the continuous-phase solvent can be changed independent of its chemical composition while leaving the volume of the droplet phase unchanged. In contrast, for the depressurization method, small quantities of the microemulsion solution are discharged from the cell, and the mole fractions of surfactant and water are held constant. Our dynamic quenching studies show no difference between fitted parameters derived from either method of changing the pressure of the solution. Intermicellar Exchange Processes. In the absence of interdroplet attractive interactions, the exchangeprocess can be simply described by two rate-limiting processes. The first is a diffusioncontrolled collision rate process, and the second is an interfacial diffusion process of the quencher through the interfacial region during the transient of the collisional dimer. Because exchange processes only occur when droplets collide, the micelle collision rate is a limiting factor. To quantify the micelle collision rate constant, the Smoluchowski and the Stokes-Einstein relationships can be used to estimate this diffusion-controlled rate constant (k~):~’,~’
k, = 8RTJ3000q Here R is the gas constant, T i s the absolute temperature, and is the solvent viscosity. Equation 14 is strictly valid for dilute, weakly interacting systems, but it can be used as a first approximation to account for the solvent viscosity change in the propane microemulsion. When the pressure of the system is changed,a corresponding change in the continuous-phaseviscosity occurs. Thus, changes in propaneviscosity can affect the diffusioncontrolled process (eq 14). For instance, from 100 to 400 bar at 27 OC, the viscosity of propane changes from 0.112 to 0.155cP, and hence, kD slowly decreases with increasing pressure. It is very interesting to note that the viscosity of a liquid alkane such as isooctane is about 4 times higher than that of propane, and hence, the collision rates in isooctane should be 4 times lower than that of propane. The ratio of kD/k,, is 220 at 100 bar and 550at 400 bar. Clearly, there is a higher barrier to intermicellar transport at higher pressure since 1 in 500 collisions result in exchange of quencher. At low pressures the collision rate will be larger than at higher pressure; this will lead to an increased exchange rate constant at low pressure. In order to remove this collision rate effect from the k,, vs pressure relationship, we examine the parameter keX(q/vo)which is plotted in Figure 10 along with k,, for a microemulsion containing 0.1 mM MV2+(TO r)
-
The Journal of Physical Chemistry, Vol. 97, NO. 47, 1993 12337 is the viscosity at the highest experimental pressure, herep = 456 bar). The “corrected” exchange rate, kex(r)/r)o), still increases with decreasing pressure, and therefore we conclude that a structural change in the microemulsion is occurring. Clearly, the more efficient exchange of solutes between micelles at lower pressure is an indication that the diffusion-controlled micelle collision rate (kD) is not the only factor affecting the rate of the solute exchange. Correlation between Exchange Rate Constants and Electrical Conductivity. At present, no single technique can thoroughly characterize structural transitions in this type of microemulsion. However, the combination of information from different techniques such as luminescencequenchingand electrical conductivity can be utilized to infer details of the microstructure. Lang et al.s0+6749 were the first to discuss the correlation between the Occurrence of a percolation transition in microemulsions and the value of the exchange rate constant (kcx). A remarkable conclusion is that electrical conductivity percolation occurs whenever the rate constant k,, for interdroplet exchange of solubilizatesbecomes larger than (1-2) X lo9M-l s-I,irrespective of the nature of the surfactant (anionic, cationic), oil (alkane, aromatic), temperature, or volume fraction of the dispersed phase. Our results (for k,, and conductivity) are in good agreement with Lang et al.’s o b s e r v a t i ~ that n ~ when ~ ~ ~ k,, ~ ~is~above (1-2) X lo9 M-I s-I, electrical conductivity percolation occurs even though our collision rate constant is 4 times higher than for liquid alkane solvents of much higher viscosity. Based on this criterion, the threshold percolationpressure in our system should be around 350 bar. The sharp decrease in conductivity with increasing pressure indicates the disappearance of percolative conduction. The mechanism of conduction above the percolation threshold is thought to be one of the surfactant ions hopping from droplet to droplet within droplet clusters. This conclusion is consistent with our luminescencequenching results. The micelle concentration as measured by luminescence quenching is unchanged with increasing pressure, indicating that the micelle size is uniform over the entire pressure range (100-450 bar). This implies that no significant micelle coalescence or growth occurs when the pressure or density of the continuous phase solvent is varied and that the overall shape of the micelles in the clusters is little changed from the micelles that are individually dispersed. Such a mechanism is not consistent with formation of a bicontinuous microemulsion phase, where one would expect a large amount of merging of droplets into continuous water conduits. Still, this particular water/DDAB/oil microemulsion system is known to form bicontinuous structures at higher volume fractions of the dispersed phase in liquid alkanes.24 It may be that the micelle clustering is a precursor to a transition to a bicontinuous phase but that the bending energy of the interfacial film is too high under these conditions to allow curvature changes necessary for a transition to continuous water conduits. An earlier SANS study7’showed that there was a large increase in the attractive interactions between AOT/water microemulsion droplets dispersed in liquid propane. That study also showed that decreasing the pressure of the system greatly increased the magnitudeof the interdroplet attractiveinteractions. The present study is entirely consistent with the existence of such strong attractive interactions between the droplets. By increasing the strength of interactions (reducing the continuous propane phase density), the extent of micelle clustering increases until the onset of electrical percolation.
Conclusions We have demonstrated that simply changing the density of the near-critical fluid solvent at constant volume fraction of the dispersed phase is sufficient to induce electrical percolation in a water/DDAB/propane microemulsion. At low pressures, ex-
12338 The Journal of Physical Chemistry, Vol. 97, NO. 47, 1993
tensive micelleclusteringoccursdue to increases in the interdroplet attractive interactionsin the lower densitysolvent. Luminescence quenching results indicatethat theintegrity of the droplet structure is retained within the micelle cluster and that the rate of exchange between the droplets is strongly limited by slow transport of the aqueous-solublesolutes through the interfacial films. Thus, the present results support a dynamic percolation model. The interdropletexchangerate significantly increases at low pressures, in part becauseof the increased collision rates in the lower viscosity solvent. More importantly, there is an additional rate increase at low pressure that is attributed to greater exchange within a micellarcluster. Unlike liquid microemulsion systems previously studied, a percolation phenomenon in this near-critical fluid can be induced by changing the pressure of the system rather than the chemical composition or the temperature. Our results also support the earlier finding of Lang et al. that the electrical percolation cccurs when the rate of intermicellar exchange is greater than 1 X lo9 M-’ s-I regardless of the nature of the continuous-phase solvent. Significantly, this relationship is observed even though the collisional rate in propane is 4 times higher than that in liquid microemulsions.
Acknowledgment. We thank Gary R. Holtom of PNL for helpful suggestions in conductingthe lifetime measurements. This research was supported by the Director, Office of Energy Research, Office of Basic Energy Science, Chemical Science Division of the U.S. Department of Energy, under Contract DEAC06-76RLO 1830. References and Notes (1) Gale, R. W.; Fulton, J. L.; Smith, R. D. J . Am. Chem. SOC.1987, 109. 920. (2) Smith, R. D.; Fulton, J. L.; Jones, H. K.;Gale, R. W.; Wright, B. W. J. Chromatogr. Sci. 1989, 27, 309. (3) Khmelnitsky, Y. L.; Kabanov, A. V.; Klyachko, N. L.; Levashov, A.
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