Langmuir 1994,10, 2929-2938
2929
Structure and Dynamics of Polymerizable Microemulsions A. P. Full and E.W. Kaler* Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received January 24, 1994. In Final Form: June 10, 1994@ The structureof polymerizable microemulsionscontaining styrene, dodecyltrimethylammonium bromide, and brine is investigated by small-angleneutron scattering (SANS) and quasielastic light scattering (QLS). SANS measurementssuggest that these microemulsions consist of a unimodal population of swollenmicelles that swell uniformly with the addition of styrene. The double exponential behavior of the autocorrelation function measured with QLS experimentsis attributed to collective and self-diffusionmodes. These modes appear in polydisperse systems at high volume fractions and are enhanced by repulsive interactions. The collective diffusion coefficient, which increases with added styrene and decreases with salt, depends on both hydrodynamic and thermodynamic interactions. The self-diffusioncoefficient decreases monotonically with added styrene. Adding salt does not affect the size of the swollen micelles but does screen micelle interactions sufficiently that the contribution to the autocorrelation function from self-diffusiondisappears. The experimental values characterizing hydrodynamic interactions agree well with a recently developed theory for small charged spheres.
Introduction Microemulsionsare thermodynamically stable solutions of oil and water stabilized by surfactant.l A signal feature of microemulsions is the presence of microstructure. They contain oil-rich and water-rich domains of 1to 100 nm in size that are separated by a n oriented, surfactant-rich layer. The configuration of the domains varies with composition, but common structures are oil droplets in water (olw), water droplets in oil (wlo), or one of bicontinuous, intertwined domains of oil and water.2 The relationship between microstructure and composition, temperature, or pressure within the one-phase microemulsion region remains a subject of academic interest and practical importance. An application that exploits the self-assembledstructure of solutions like microemulsions is the synthesis of polymeric materials. Although these synthesis schemes fail to reproduce the parent microstructure identically (e.g., latex particles produced by polymerization of o/w microemulsions are larger than the droplets in the original solution3),the reaction products have different characteristics than those produced by traditional polymerization method^.^ Reactions in o/w or w/o microemulsions usually produce polymers with high molecular weights (lo5to lo7) and particle radii of 10 to 1000 nm. Polymerizing styrene in bicontinuous microemulsions produces porous spongelike solid^.^ Fast reaction rates and large molecular weights can be achieved in these systems because initiation and propagation reactions are isolated in small loci. In order to understand and eventually control synthesis in microstructured fluids, the structure of the parent solution must be known. In particular, the course of freeradical polymerization in a n o/w microemulsion may depend on the droplet size in the unpolymerized solution, on the interactions between initiator radicals with the charged droplets, and on the transport of monomer to the growing polymer particle. A clearer picture of the micro-
* To whom correspondence should be addressed. Abstract published inAduance ACSAbstracts, August 1,1994. (1) Schulman, J. H.;Stoeckenius, W.; Prince, L. J.Phys. Chem. 1969, 63,1677. (2) Chevalier, Y.;Zemb, T. Rep. Prog. Phys. 1990, 53, 279. (3) Full, A. P.; Puig, J. E.; Gron, L. U.; Kaler, E. W.; Minter, J.R.; Mourey, T. H.; Texter, J. Macromolecules 1992,25, 5157. (4) Candau, F. In Polymerization in Organized Media; Paleous, C. M., Ed.; Gordon and Breach Philadelphia, PA, 1992; p 215. (5)Haque, E.; Qutubuddin, S. J.Polym. Sci., Polym. Lett. Ed. 1988, 26, 429. @
structure before reaction allows a better understanding of the effect of structure on polymerization kinetics and polymer characteristics. The reaction kinetics and latex characteristics resulting from the polymerization of microemulsions similar to those studied here have been published previ~usly.~~' A forthcoming paper will explain more thoroughly the role that microstructure plays in the kinetics of latex formation. To address issues concerning microstructure and interactions, we use quasielastic light scattering (QLS) and small-angle neutron scattering (SANS) to examine the structure of microemulsions containing styrene, dodecyltrimethylammonium bromide (DTAB), and a brine solution consisting of deuterium oxide (D20) and potassium bromide (KBr). The hydrogenated system was examined previously by QLS and electrical conductivity.6 The combination of QLS and SANS experiments provides selfconsistent information about microstructure and interactiorm8 SANS spectra yield time-average structural information while QLS autocorrelation functions give information about the dynamics of concentrated and strongly interacting systems. Difficulties arise from interpreting results from one experiment alone because microstructure and interactions vary with composition. Analysis of static scattering from microemulsions is usually done in terms of a model, and the quantitative results depend entirely on the assumed model.g Justification for using a model of swollen microemulsion droplets must come from other experiments. For the mixtures of interest here, for example, NMR'O and rheology'l measurements suggest that concentrated micellar solutions of DTAB contain spherical aggregates. Furthermore, the energetically preferred geometry of swollenmicelles made with surfactant similar in structure to DTAB is spheres.12 Finally the self-consistency of modeling results from dynamic and static scattering data ( 6 ) Perez-Luna, V. H.; Puig, J. E.; Castafio, V. M.; Rodriguez, B. E.; Murthy, A. K.; Kaler, E. W.Langmuir 1990, 6,1040. (7) Puig, J. E.; Full, A. P.; Kaler, E. W. ANTEC Conference Proceedings, 50th Meeting of the Society of Plastic Engineers, Detroit, MI, 1992; Vol. 11, p 2587. (8)Cebula, D. J.; Ottewill, R. H.; Ralston, J.; Pusey, P. N. J.Chem. Soc., Faraday Trans. 1 1981, 77, 2585. (9)Zemb, T.N.; Hyde, S. T.;Derian, P.-J.;Barnes, I. S.; Ninham, B. W. J.Phys. Chem. 1987,91, 3814. (10) Ceglie, A.;Das, K. P.; Lindman, B. Colloids Su$. 1987,28, 29. (11)Candau, S. J.; Hirsch, E.; Zana, R. J. Phys. (Paris) 1984, 45, 1263. (12) Nagarajan, R.;Ruckenstein, E. Langmuir 1991, 7, 2934.
0 1994 American Chemical Society 0743-7463/94/2410-2929$04.50/0
2930 Langmuir, Vol. 10,No. 9,1994 presented here provide a posteriori justification of the droplet model. An additional consequence of the spherical droplet model is that a recently developed theory can be used to understand the observed hydrodynamic intera~ti0ns.l~ Subtle changes in droplet size and thermodynamic interactions as measured by SANS profoundly changethe QLS autocorrelationfunction. Hydrodynamicinteractions measured by QLS are consistent with theoretical predici tions for spheres with characteristics similar to swollen micelles. In particular, the self-diffisionof microemulsion droplets causes a slowly decaying mode observed in the QLS autocorrelation functions. This mode disappears from the QLS autocorrelation function when interactions are screened with added electrolyte.
Theory and Data Analysis Static Scattering. The coherent scattered intensity from a SANS experimentis proportional to the differential cross-section per unit sample per solid angle. For a monodisperse system of spherical particles, this intensity is given by14J5
Full and Kaler
ti
R:= shell radius
6 = fraction of dissociated counterions ,N = aggregation number z = valence = N,6
2rl
Solvent
Scattering Length Density (P )
I
S
I
0
Styrene BrDTA+
1
Core
I
R,
Rs
Figure 1. Micelle cross-section showing the distribution of molecules and the scattering-length-densityprofile assuming a spherical core-and-shell particle. The hydrophobic core contains surfactant tail groups and solubilized styrene, while the hydrates shell contains head group ions, condensed counterions, and their respective waters of hydration. 1
q is the scattering vector whose magnitude is ( 4 d i l ) sin(812)where 8 is the scattering angle, ilis the wavelength of the radiation, and n is the refractive index of the solvent. N p is the number of particles in the irradiated sample volume, V. The angular brackets represent an ensemble average over all irradiated particle positions and orientations. FN(q)is the amplitude factor of the Nth particle and depends on particle geometry. S(q)is the structure factor and depends only upon interparticle separation and thus upon the potential of interaction between particles. For polydisperse spheres, an approximate expression similar to eq 1is derived assuming that particle size is uncorrelated with position.16J7 The structure factor is approximated by S ( q ) = 1 #?(q)[S(q)- 11 and P(q) is given by
R =coreradius
D
D
where SM(q) replaces S(q)in eq 1. SM(q) more accurately describes the structure of polydisperse and polymodal systems and specificallyaccounts for cross terms neglected in the decoupling approximation. The S&) are related to the Fourier transforms of the total correlation functions.18 In this paper, the hypernetted chain (HNC) approximation22is the closure relation used to obtain correlation functions from the Ornstein-Zernike equations. For the special case of a bimodal system of monodisperse spheres, SM(q) is given by19
+
However, this decoupling approximation is not valid for concentrated dispersions where the average particle separation is small and interparticle correlations exist. Polydispersity can be accounted for more rigorously by using the partial structure factors &(a) determined from the matrix form of the Ornstein-Zernikeequation.18 Klein and co-workers16-21used this approach to define a measured structure factor for a polydisperse mixture of p different types of particles (13) Gem, U.; Klein, R. Physica A 1991,171,26. (14) Hayter, J. B. In Physics of Amphiphiles: Micelles, Vesicles,
Microemulsions; Degiorgio, V., Corti, M., Eds.; North-Holland: New York, 1985; p 59. (15) Chen, S.-H. Ann. Rev. Phys. Chem. 1986,37, 351. (16) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79, 2461. (17) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983,261, 1022. (18) Klein, R. In Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution; Chen, S.-H., Huang, J. S., Tartaglia, P., Eds.;Kluwer Academic: Boston, MA, 1992; p 39. (19) Krause, R.; D'Aguanno, B.; M6ndez-Alcaraz, J. M.; Nggele, G.; Klein, R.; Weber, R. J. Phys.: Condens. Matter 1991,3,4459. (20) D'Aguanno, B.; Klein, R. J. Chem. Soc., Faraday Trans. 1991, 87, 379. (21) D'Aguanno, B.; Klein, R.; Wagner, N. J. Mater. Res. SOC., Res. Proc. 1990, 177, 219.
For charged particles with radius Ri and valence Zi, structure factors are typically calculated using the repulsive Yukawa potentia120
Ug(rHBT=
-
- zgjLBe x p ( q ) exp( - ~ r ) r > oe (5) r
+
(1 KRi)(l
+KR~)
+
where ag = Ri Rj, LB = e2/(4neoek~T) is the Bjerrum length, and K = (4d$vA1)1/2 is the inverse Debye length. k B is the Boltzmann constant, T the temperature, e the charge of an electron, EO the permittivity of free space, E the solvent dielectric constant, NAAvogadro's number, and I the ionic strength of the solvent. This potential is approximately valid for K O ~less than 6.23 In this study, the micelles are modeled assuming a spherical core-and-shell geometry (Figure 1). The hydrocarbon core contains surfactant tail groups and solubilized styrene. The surrounding shell contains surfactant head group ions and bound counterions, as well as the (22)Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; Academic: London, 1986. (23) Verwey, E. J. W.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloids; Elsevier: New York, 1948.
Polymerizable Microemulsions
Langmuir, Vol. 10, No. 9, 1994 2931
water molecules that hydrate the ions. The number of water molecules hydrating the head group ions and counterions are one and four, re~pective1y.l~The continuous domain (solvent) contains the remaining water, dissocated counterions, added salt, and unaggregated surfactant, which is assumed to be an amount equivalent to the critical micelle concentration. All of these small ions contribute to the ionic strength, but the micelles do The shell radius, R,, and the fraction of aggregated surfactant molecules with dissociated counterions, 6, completely specify the micelle geometry. The known volume fraction of the dispersed phase, 4, determines the number density of micelles, e = NJV = 4/(4nR,3/3). Assuming that aggregated surfactant and styrene molecules are distributed equally among micelles (i.e., the micelles have identical compositions), the surfactant aggregation number, NWg,valence, z = 6Nagg,styrene aggregation number, NSw,and core radius, R,, are easily computed using mass balances and molecular volumes.25 For a spherical particle with a core-and-shell distribution of scattering length densities, the scattering amplitude is given by14J5
experimental values, and Npar is the number of parameters used to generate the model spectra. Confidence limits for the estimated model parameters are determined by a statistical analysis technique called boot~trapping.~ The ~ , ~bootstrap ~ method has the advantage of providing estimates of error without assuming parameter values are normally distributed.26 In this method, Monte Carlo simulations are used to create new spectra from the spectrum measured experimentally.28 This is accomplished by randomly selecting a measured error value (dT)without regard to its q value and then adding or subtracting dI to the original Ieq. The q value of the new Iexpis the same as the original lexp, so that the general shape of the simulated spectra is preserved. A new set of parameters is then determined by minimizing x2 for the newly simulated lev. Repeating this procedure many times produces a distribution of parameter values from which a confidenceinterval is determined. The 95% confidence intervals are reported without regard to the distribution of other parameters. Dynamic Light Scattering. The electric field correlation function isz9
where FaLS(q,t) is the measured dynamic structure factor.30 I
where e,, e,, and are the scattering length densities of the core, shell, and solvent, respectively. j 1 is the firstorder spherical Bessel function. Models of the scattered spectra were also calculated for a dispersion of polydisperse micelles. For this analysis, the shell radii are modeled by a Shultz distribution in order to calculate (IFN(q)I2)and B(q).14 In addition to the parameters R, and 6, this model introduces a n additional parameter, the standard deviation of the shell radius, that characterizes the width of the distribution. For a system of monodisperse spheres, the modeled intensity is calculated by specifylng R, and 6, as well as including two additional parameters, A, a scaling factor, and B , so that
(7) A accounts for the uncertainty in calibration of the absolute intensity and scattering length densities. This simple swollen micelle model does not allow water molecules to penetrate into the core and excludes styrene from the shell and solvent domains, which could cause the contrast to be overestimated. B accounts for the incoherent neutron scattering, a significant contribution whenever hydrogen atoms are present, as well as for some deviations from monodispersity or sphericity. A parameter optimization routine is employed to determine the best set ofparameters by minimizing x2
lev is the intensity measured experimentally, dZ is the error of the measured intensity, Nptsis the number of ~
~
~~
~
~
(24)Cantd, L.; Corti, M.; Degiorgio, V. Faraday Discuss. Chem. SOC. 1987,83,287. (25)Berr, S.S.;Coleman, J.; Jones, R. R. M.; Johnson, J. S. J . Phys. Chem. 1986,90,6492.
Y
Nv Nv
(10)
Vectors RNand RIM locate the centers of mass of particles
M and N , respectively. SQLs(q) (= FQLs(q,O))is the structure factor weighted by the particle scattering amplitudes and ;I"is the average over the distribution of scattering amplitudes squared. For dilute solutions of monodisperse spheres, where particle correlations disappear, eq 9 reduces
where Dois the free-particle diffusion coefficient. Small positive deviations from a single exponential decay in dilute suspensions usually indicate particle-size polydispersity, and in that case g(l)(t)is typically described by a second-order cumulant e ~ p a n s i o n . ~ ~ In more concentrated systems particle interactions become important. For narrow distributions W e i s ~ m a n ~ ~ proposed that particle correlations and dynamics are relatively insensitive to the particle-size distribution and that the major effect of polydispersity is to provide a distribution of scattering amplitudes. Pusey and cow o r k e r ~then ~ , ~showed ~ that a t sufficiently high volume fractions of hard spheres, two independent modes with well-separated decay times can appear, thus
(26)Efron, B.; Tibshirani, R. Statistical Sci. 1986,1 , 54. (27)LBger, C.; Politis, D. N.; Romano,J. P. Technometrics 1992,34, 378. (28)Press, W. H.;Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes: TheArt ofscientific Computing (FortranVersion) Cambridge University: New York, 1990;Chapter 14. (29)Stgpanek, P.In Dynamic Light Scattering: The Method and Some Applications; Brown, W., Ed.; Clarendon: New York, 1993;p 177. (30)Pusey, P. N.; Fijnaut, H. M.; Vrij, A. J. Chem. Phys. 1982,77, 4270. (31)Koppel, D. E. J . Chem. Phys. 1972,57,4814. (32)Weissman, M. J. Chem. Phys. 1980,72, 231.
Full and Kaler
2932 Langmuir, Vol. 10, No. 9, 1994
where x = 1 - (-a2 la-2 1. P(q,t),the full “ideal” dynamic structure factor, describes collective or “compressiondilation” motions, and F’&,t), the self-dynamic structure factor, describes single-particle or ”concentration-fluctuation” motions. The characteristic time scale studied in this paper is larger than the time required for a microemulsion droplet to diffuse a distance equal to its diameter, and the characteristic length scale probed by QLS ( 2 d q ) is much larger than the distance between micelles in the microemulsion (2n/qmax,where qmaxis the position of maximum intensity observed with SANS). In other words q is much smaller than qmaxand S(q) x S(0). At these characteristic length and time scales (the hydrodynamic regime), the dynamic structure factors are usually expressed as exponential functions of q2t with33
F1(q,t)= S(0)exp(-Dcq2t)
(13)
F‘, = exp(-D,q2t)
(14)
and
where D, and D, are the collective and self-diffusion coeffkients, respectively. Under these conditions
+
g(%) = a exp(-Dcq2t) (1- a)exp(-D,q2t)
(15)
where the amplitude a = (1 - x)S(0)lSQLsand SaLs= (1 - x)S(O) x . In concentrated dispersions, the short-time diffusion coefficients are affected by thermodynamic and hydrodynamic interaction^.^^ If the hydrodynamic interactions are described by a function H ( q ) ,then
+
(16) For a bimodal population of noninteracting, monodisperse spheres, g 9 t ) also decays as a sum of two exponential functions34
where D1 andDz are the free-particle diffusion coefficients and a’ is the contribution due to particles of type 1. The identical forms of eqs 15 and 17 illustrate the necessity of performing complementaryexperiments to validate an assumed model.
Experimental Section Reagent grade styrene from Scientific Polymer Products was distilled to remove oligomers. To inhibit further oligomer formation, 10 ppm hydroquinone (Aldrich, 99%) was added to freshly distilled monomer, which was then stored at 4 “C in an amber bottle. DTAB (TCI America, 98%) was recrystallized 3 times from 50/50 (v/v) acetone/ethanol to remove impurities. Potassium bromide (Aldrich, 99%) was dried at 100 “C under vacuum for 12 h before preparing brine solutions. Deuterium oxide (Cambridge Isotope Laboratory, 98%), acetone (Fisher, 99%), ethanol (Quantum), and hydroquinone were used as received. The single-phase o/w microemulsion region at 25 “C was determined visually by titrating aqueous solutions of DTAB with styrene. Phase boundaries were verified by preparing samples by weight below and above the concentrations where phase transitions occur. The inhibitor was not removed from styrene before samplepreparation, since small amounts of oligomersare (33) Pusey, P. N.; Tough, R. J. A. In Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy; Pecora, R., Ed.; Plenum: New York, 1985; p 85. (34)Schumacher, G . A.; van de Ven, T. G. M. Langmuir 1991, 7 , 2060.
DTAB
30
Brine
95
90
85
80
75
70
65
Styrene
Figure 2. Phase behavior at 25 “Cof DTAB,styrene, and KBr brine made with D2O. The lines represent the compositions defining the boundary between one-phase (la)and two-phase (2@)regions at the indicated salt concentration. Samples at high surfactant concentrations are viscous, so boundaries are not determined exactly (dashed lines). Open circles represent the concentrations examined by SANS in this work.
known to reduce the extent of the one-phase microemulsion region.36Microemulsionviscositieswere measured at 25 “C with Cannon-Fenske capillary viscometers, which were calibrated using 9.8 CPstandards (Brookfield). Small-angle scattering experiments were performedusing the W. C. Koehler 30-m SANS facility at Oak Ridge National Laboratory (ORNL) and NG-7 at the Cold Neutron Research Facility of the National Institute of Standards and Technology (NIST). At ORNL,the neutron wavelength was 4.75Awith AUA = 0.06, and scattered intensities were measured over a q-range from 0.003 to 0.19 A-1 using two different sample-to-detector distances. At NIST, the neutron wavelength was 7.0 A with MA = 0.097, and scattered intensities were measured over a q-range from 0.01 to 0.15 A-1. The samples were held in quartz cells of 1or 2 mm path lengths and maintained at 25.0 =k 0.1 “C. The scattering spectra were corrected for background, detector sensitivity, solvent and empty cell scattering, and sample transmission. The spectra were then radially averaged and placed on absolute scale using standards providedby the neutron facility. The error (dI)associated with each intensity data point reflects the counting statistics of the 2-D detector. Quasielastic light scattering experiments were made using equipment manufactured by Brookhaven Instrument Corporation (BI9000). Microemulsions thermostated at 25 “C were irradiated with 488-nm light produced from a Lexal2-W argonion laser. Scattered intensity fluctuations were correlated to delay times no smaller than 0.5 p s . Samples prepared for light scattering were filtered through 0.2-pm Millipore Acrodisc-13 filters directly into 5-mL acid-washed ampules. The ampules were flame-sealed to prevent evaporation and then centrifuged to remove entrapped air bubbles and sediment unfiltered dust. The refractive index and viscosityof the solventwere interpolated from values tabulated for different salt concentrations in water at 25 0C.36 The normalized intensity autocorrelation functions are fitted either using a second-order cumulant method if the function decayed as a single exponential or to eq 15 using the Levenberg-Marquardt method28 if the function decayed as a sum of two exponentials.
Results One-phase microemulsion regions for DTAB/D20brine/styrene exist at 25 “C (Figure 2). KI3r brine is assumed to be a single component for the purpose of representing four component mixtures on a ternary phase diagram. The phase behavior of this system was studied previously by us with HzO in the absence of KBr.6 The effect of isotopic substitution and the presence of salt (35) Gan, L. M.; Chew, C. H.; Friberg, S.E. J.Macromol. Sci. Chem.
1983,A19, 739.
(36) CRC Handbook of Chemistry and Physics, 67 ed.; Weast, R. C., Ed.; CRC Press, Inc.: Boca Raton, FL, 1986.
Polymerizable Microemulsions
Langmuir, Vol. 10,No.9,1994 2933
.840
E v
6-
.-5..
a
5
4-
VI
.d
p 30
e 2-
g
.-x
O"""""""""'~=
0.00
0.05
0.10
0.15
0.20
8
20
5
4(1A
Figure 3. SANS spectra of empty micelles showing the effect of increasing DTAB concentration. Symbols represent the measured intensity and lines represent the model intensity. Concentrations indicate the amount of DTAB in D2O.
'
0 a)
10
0 0.00
4
0.05
0.10
0.15
0.20
q (l/A,
Figure 5. SANS spectra of microemulsionsshowing the effect of increasing salt concentration. Symbols represent the measured intensity and lines represent the model intensity. Concentrations indicate the molarity of KBr in D2O for microemulsionscontaining4 w t % styrene in a solution of DTAB/ brine = 15/85 (w/w). The spectra for 0 M KBr are on absolute scale and has units of cm-l. The y-axes of the spectra for 0.05, 0.10,0.20, and 0.25 M KBr are shiffed upward by 5,10,15, and 20 cm-l, respectively. 0.05
0.10
0.15
0.20
q (1/A) b)
40
6.5 wt %
I
4 4 30 h
E Y
.-5
20
E
2 10
n
6.00
0.05
0.10
0.15
0.20
q WA, Figure 4. SANS spectra of microemulsionsshowing the effect of increasing styrene concentration. Symbols represent the measured intensity and lines represent the model intensity. Concentrations indicate the amount of styrene in a solution of (a)DTABm20 = 10/90(w/w) and (b) DTAB/DzO= 15/85 (w/w).
shifts the phase boundaries in a n irregular manner. Forexample, when switching from H20 to D20, the maximum solubility of styrene increases from 14.1 to 16.4 w t % in a solution of DTAB/O M KBr = 20/80 (w/w), but decreasesfrom 17.5to 6.5wt% inasolutionofDTAB/0.25 M KBr = 20/80 (w/w). Discrepancies with previously published diagrams are attributed to oligomeric impurities in styrene. Samples from the one-phase region are
transparent and remain stable for days. Aged samples with compositions near the phase boundary eventually phase separate because the inhibitor becomes inactive and can no longer prevent oligomer formation. The viscosities of the microemulsions range from 2.5 to 45 CP and increase monotonically with styrene and KBr concentration. The viscosity of samples with high surfactant concentrations prevents the exact determination of the phase boundaries (dashed lines). The SANS spectra for micellar solutions of DTAB without styrene (Figure 3) display interaction peaks characteristic of dispersions of charged spheres. As the surfactant concentration increases, the position of maximum intensity (4") shifts to higher q concurrently with an increase of the maximum intensity. Both trends are consistent with a decrease of interparticle separation as the DTAB concentration increases. Modeling the spectra as monodisperse spheres with a core-and-shell scatteringlength-density profile (Figure 3 and Table 1)suggests that the micelle size remains constant and the number density of micelles increases with DTAB concentration. The modeling also suggests that the fraction of dissociated counterions, or equivalently the micelle valence, decreases with increasing micelle concentration. Adding styrene to solutions containing a constant ratio of surfactant to DzO causes the maximum intensity to increase and qmaxto shift to a smaller q (Figure 4). Data fitting shows (Figure 4 and Table 1)an increase in micelle radius, but there is no systematic trend in counterion dissociation. The valence of the micelles increases due to a n overwhelming increase of aggregation number. Increasing the salt concentration in the solvent dramatically changes the shape of the SANS spectra (Figure 5). Adding KBr screens the electrostatic repulsion between micelles and causes a decrease of the Debye
2934 Langmuir, Vol. 10, No. 9, 1994
Full and Kaler
Table 1. Parameters from Analyzing SANS Spectraa calculated parameters fitting parameters
composition
styrene(&%) DTABhrine(w/w) [KEirl(M) R.(& 0 0 2.2 4.1 0 2.0 6.5 4.0 4.0 4.0 4.0 4.0
0 0 0 0 0 0 0 0 0.05 0.15 0.20 0.25
5/95 10/90 10/90 10/90 15/85 15/85 15/85 15/85 15/85 15/85 15/85 15/85
23 23 28 32 23 28 35 33 34 33 33 33
6
A
B(cm-l)
x2
CP
0.29 0.26 0.19 0.21 0.20 0.12 0.16 0.16 0.11 0.06 0.04 0.03
1.02 0.98 0.91 1.12 0.94 0.95 1.02 1.00 0.97 1.00 1.03 0.99
0.27 0.62 1.08 1.06 0.40 0.61 1.28 1.70 2.05 2.05 1.97 1.76
1.4 5.5 5.4 6.6 3.3 21.3 12.3 6.4 9.6 5.5 3.4 2.4
0.06 0.13 0.15 0.17 0.17 0.22 0.26 0.24 0.24 0.24 0.25 0.25
e(x
1018cm-3) NaggN,ty 1.2 2.5 1.6 1.3 3.7 2.4 1.5 1.6 1.5 1.6 1.6 1.8
89 86 129 158 88 129 197 188 199 195 190 180
0 0 86 205 0 52 279 154 168 162 158 149
~ / K ( AK) R ~
2 25 22 2.5 33 17 16 31 30 21 11 8 6
15 12 13 13 11 13 12 12 10 7 6 6
1.6 2.0 2.2 2.5 2.2 2.1 2.9 2.8 3.5 4.8 5.3 5.7
a Modeling results assuming a core-and-shell scattering length density profile and monodisperse spherical micelles. R, is the shell radius. 6 is the fraction of dissociated counterions. A is the scale factor. B is the background intensity. x2 is defined by eq 8. @ is the volume fraction of micelles. e is the number density of micelles. Naggis the number of surfactant molecules per micelle. Nstyis the number of styrene molecules per micelle. 2 is the valence of the micelle. VK is the Debye screening length.
0
-1
-h h I
5.0 4.0
-2
00
s-
3.0
-3
2.0 -4
0
2
4
6
8
10
q*t (x10'0simZ)
Figure 6. Autocorrelationfunctionsof microemulsionsshowing the effect of increasing styrene concentration. Symbols represent the experimental data and the lines represent a double exponential model except for 0 wt % styrene. The solid line for 0 wt % styrene shows the result of a cumulant model fit. Numbers indicate the concentration (wt %) of styrene in a solution of DTAB/D20 = 15/85 (w/w). screening length (Table 1).The decreasing peak intensity suggests that particle interactions become weaker, and the increasing intensity in the limit of low q is consistent with a n increase of the osmotic compressibility of the colloidal suspension.14J8 Results of fitting the SANS data show that the size of the micelles does not change, so the
styrene (wt %) 0.0 1.0 1.5 2.0 3.0 4.0 5.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0
changes occuring in the spectra are solely due to the changing shape of the structure factor. Modeling the spectra suggests that counterion dissociation decreases with increasing KBr concentration. The 95% confidence limits for parameters are determined by bootstrapping of the SANS data for the microemulsion containing 4 wt % styrene in a solution of DTAEV DzO = 15/85 (w/w). The confidencelimits are narrow (dR, = +0.01 b, dd = h0.004, dA = hO.01, dB = h0.12 cm-'), because the error of the measured intensity (allx 100%) used to simulate data sets is small (less than 5%). The actual error of the SANS spectra, due to uncertainties of calibration standards, is a t most 10%. Changes in the dynamic behavior of microemulsions are monitored using QLS by first increasing the styrene concentration in a solution containing DTAEVD20 = 151 85 (w/w)(Figure 6). The autocorrelation function for the micellar solution (0 wt % styrene), shown on a plot of In g(l)(t)versus q2t, displays small deviations from a single exponential, suggesting that the micelles are somewhat polydisperse (Table 2). As styrene is added to the micellar solution, a second slower diffusing mode appears. Since the two modes are well-separated, analysis by the method of cumulants is no longer appropriate, and the autocorrelation functions are better modeled by a sum of two decaying exponentials (eq 15). The diffusion coefficients for the faster mode are of the same magnitude as the average diffusion coefficient for the micellar solution. The diffusion coefficients for the slower mode decrease by
Table 2. Parameters from Analyzing QLS Autocorrelation Functions composition cumulant? double exponentialb DTABhrine (wlw) [KBrl (M) c D,, ( x m2/s) ,u/D2cum c a D, ( x m2/s) D , ( x 15/85 15/85 15/85 15/85 15/85 15/85 15/85 15/85 15/85 15/85 15/85 15/85 15/85 15/85
0 0 0 0 0 0 0 0.00 0.01 0.05 0.10 0.15 0.20 0.25
0.40
0.60 0.57 0.68 0.68
2.44
0.908 0.640 0.538 0.449
m2/s)
0.194
0.148 0.044 0.083 0.108
0.42 0.45 0.47 0.51 0.49 0.57 0.53 0.45 0.66 0.59
0.77 0.67 0.67 0.70 0.64 0.62 0.60 0.73 0.82 0.87
1.92 1.96 2.20 2.50 2.29 2.30 2.25 2.10 1.59 0.961
0.347 0.255 0.207 0.161 0.0893 0.0776 0.0769 0.138 0.233 0.211
c is the instrument constant of the Seigart relation.29Dcumis the diffision coefficient determined from the methods of cumulants, and a is the amplitude ofthe collective mode. D, is the collective diffision coefficient and D, is the self-diffusion coefficient (see eq 15). a
p is the second-order cumulant.
Langmuir, Vol.10,No.9, 1994 2935
Polymerizable Microemulsions
A
t
"'
' "
I
0
D
o D
I
I
0.10M 2
0
4 $1
6
10
8
0.15
0.20
(x10'0s/m2)
0.30
0.25
Volume Fraction
I
I
t
DDa
-41 0
'
' 2
.
'
4
'
'
6
'
'
8
'
I A
A
J
IO
'6.00
q2t ( x ~ ~ ' ~ s / m ~ )
Figure 7. Autocorrelation functionsof microemulsionsshowing the effect of increasing salt concentration. Symbols represent the experimental data. (a)The lines show the results of a double exponential model fit. (b) The lines show the results of a cumulant model fit. Concentrations indicate the molarity of KBr brine in microemulsions containing 4 w t % styrene in a solution of DTAB/DzO-brine = 15/85 (w/w). almost a n order of magnitude as styrene is added. Concurrently, the contribution to the autocorrelation function by the slower mode appears to increase slightly (Table 2). This behavior of the autocorrelation function is consistent with a bimodal population of empty micelles coexisting with swollen microemulsion droplets, where the size of the droplets increases with styrene content. However, as shown below, modeling SANS spectra suggests that the double exponential behavior results from strong interactions between droplets in a unimodal population. As the brine concentration increases in microemulsions containing 4 wt % styrene in a solution of DTAB/brine = 15/85 (w/w),the two diffusion modes tend to merge (Figure 7a). For KBr concentrations of 0.10 M and higher, the two diffusion modes are no longer distinct, and the method of cumulants is used to extract a n average diffusion coefficient from the data (Figure 7b). At high KBr concentrations, the slope of the correlation function as plotted on a semilog plot decreases with added salt concentration. Figure 8 summarizes the composition dependence of the diffusion coefficients. The diffusion coefficients are scaled to the free-particle value (calculated using the radii determined by SANS) to account for the effect of changing size with composition. When necessary, radii from SANS were interpolated to match the compositions measured by QLS.
0.05
0.10
0.15
0.20
0.25
Wrl
Figure8. Diffision coefficientsfrom modeling autocorrelation functions showing the effect of increasing (a) styrene and (b) KBr concentration. Open triangles represent the diffusion coefficientsfrom a cumulant model fit. Solid squaresrepresent collectivediffision coefficientsand open squaresrepresent selfdiffusion coefficients from the double exponential model fit. Open circles connected by a line are the theoretical diffision coefficients taken from ref 13 for a 20 vol % suspension of 25 A radius particles with a valence of 20.
Discussion Model SANS spectra corresponding to several particle geometries were compared to the experimental spectra of the microemulsion containing 4 wt % styrene in a solution of DTAB/D20 = 15/85 (w/w). These geometries include monodisperse spheres with a uniform scattering-lengthdensity (sld)profile, polydisperse spheres with a uniform sld profile, monodisperse spheres with a core-and-shell sld profile, and polydisperse spheres with a core-and-shell sld profile. The shape of the experimental spectra, over the q-range measured, best resembled the spectra due to a system of monodisperse spheres with a core-and-shell sld profile. As mentioned above, models of polydisperse spheres require a n additional fitting parameter, which is usually the standard deviation of the radius. Using an additional fitting parameter does not improve the description of the experimental data.37 Spectra from monodisperse ellipsoids were not considered because a solution of polydisperse spheres yields a similar scattering pattern.14 However for a concentrated w/o microemulsion, a model of ellipsoidal droplets did produce a better fit of data a t low q than a model of polydisperse spheres.38 ~
~~~
(37) Cabane, B.; Duplessix, R.; Zemb, T. J.Phys. (Paris) lS85,46, 2161. (38) Caponetti,E.;Magid, L. J.;Hayter,J. B.;Johnson, J. S.Langmuir 1BS6,2,722.
2936 Langmuir, Vol. 10, No. 9, 1994
Full and Kaler
Table 3. Comparison of SANS Parameters for DTAB Micelles
DTAB concn ref
(MI (wtB) Nagg
0.10 0.05 0.10 0.20 0.40 0.60 this work 0.18 this work 0.36 this work 0.53 39 17 17 17 17 17
2.8 1.4 2.8 5.6 11.2 16.8 5.0 10.0 15.0
50 57 68 69 75 75 89 86 88
R(A) 21.9(1.2)" 19.7 21.2 21.2 21.9 21.9 23 23 23
6 0.31 0.33 0.24 0.29 0.24 0.24 0.29 0.26 0.20
A
X
1.98 0.7-1.3b 0.7-1.3 0.7-1.3 0.7-1.3 0.7-1.3 1.02 0.98 0.94
4.1 n.r.c n.r.
n.r. n.r. n.r. 1.2 2.3 1.8
a Minor axis for a prolate ellipsoid with an axial ratio of 1.2 Value reported to be within 30% of unity. Value not reported.
Hayter and Penfold17 also used a monodisperse coreand-shell geometry to model DTAB micelles, although they allowed a fraction of the methylene groups adjacent to the surfactant head group to be hydrated. used a prolate ellipsoid model to examine the effect of isotopic substitution on micelle structure of alkyltrimethylammonium bromides by varying the fraction of H20/D20 in the solvent. The results of those two independent SANS studies of DTAB micelles are compared with the current results in Table 3. The radii of the micelles do not depend on concentration and agree within the resolution of the experiments. The smallest measurable length scale is 15 in spectra measured for values of q below 0.2 kl. The aggregation numbers, which are proportional to the micelle volumes, are very sensitive to the value of the radii. The lower aggregation number of Berr's analysis could be a result of using an ellipsoidal geometry rather than a spherical one. Analysis assuming a spherical geometry results in aggregation numbers closer to 74, which is the value measured for a 2 wt % DTAB solution in HzO using time-resolved fluorescence quenching.40Discrepancies of results could also be accounted for by the use of different hydration numbers. As noted p r e v i ~ u s l y the , ~ ~micellar *~~ size depends mostly on the location of the peak in the SANS spectra and not the absolute magnitudes of the intensities. Adding styrene to DTAB micelles releases the constraint that the surfactant tails must meet a t the center of the micelle.12 In samples with constant surfactant/DzOratios, the volume of a microemulsion droplet grows with added styrene (Table 1). As micelles swell with styrene, the competing effects of increasing radius and decreasing micelle number density result in a constant intermicellar spacing. The effect of a broadened interaction peak and increased intensity a t low q in SANS spectra with increasing salt concentration (Figure 5) is also observed in other micellar ~ y ~ t e m ~ Those . ~ ~analyses , ~ ~ indicate , ~ ~ , that ~ ~aggregation numbers increase with added salt. For o/w microemulsions, we observe no systematic micelle growth with added salt and attribute the changes in the spectra entirely to the screening of intermicellar repulsion. These results indicate that increased counterion condensation occurs, but the presence of styrene molecules in the aggregate apparently reduces the tendency for micellar growth.
A
(39)Berr, S. S. J.Phys. Chem. 1987,91,4760. (40) Herrington, K. L.; Kaler, E. W.; Miller, D. D.; Zasadzinski, J. A. N.; Chiruvolu, S. J . Phys. Chem. 1993,97,13792. (41)Bendedouch, D.;Chen, S.-H.; Koehler, W. C . J . Phys. Chem. 1983,87,2621. (42) Chao, Y.-S.; Sheu, E. Y.; Chen, S.-H. J . Phys. Chem. 1985,89, 4862. (43)Berr, S. S.; Jones, R. R. M. Langmuir 1988,4,1247.
The degree of micelle ionization measured by SANS agrees well with the predictions from a recast version44 of the dressed micelle theory of Evans, Mitchell, and Ninham.45 However, as was also observed for systems of empty micelles,44the theory predicts a higher degree of dissociation than that observed experimentally when salt is added. This observation is complicated by the fact that the Yukawa potential only approximates the shape of the electrostatic potential for KRless than 3.23346This criterion is exceeded in this study for all the microemulsions with added *salt. Although the scattering spectra are adequately represented a t these extreme conditions, the valence measured by SANS should a t best be regarded as approximate.41 Other approximations often introduced in the analysis of SANS spectra include neglecting the correlation of the small ions by using a one-component macroion model (OCM) and using other approximate closure relations to solve the Omstein-Zernike equation. In the OCM, counterions and co-ions are not accounted for explicitly by the effective potential describing micelle-micelle interactionslsbut instead are treated as pointlike charges that contribute to the Debye screening length, K - ~ . In two-componentmodels (TCM),also referred to as primitive models (PM),McMillian-Mayer theory is used to describe the correlation between all ionic species on an equal basis.47 Comparisons of structures computed from the two models show that the micellar charges determined by fitting with the OCM are smaller than the actual charge.47 A TCM provides the opportunity to study the effects of finite ion size that are neglected by the OCM.48 Because of their lower screening ability, ions of finite size produce a stronger effective repulsion between macroions than pointlike charges.4s Thus a t low salt concentrations, the charges extracted from SANS data are overestimated by using the OCM. However, at high salt concentrations and with significantly larger ion sizes, the reverse can occur and the OCM underestimates the actual charge. So perhaps some of the trend of decreasing apparent charge with increasing salt concentration (Table 1)could be a n artifact of the approximations of the OCM. With respect to the approximate closure relations, the HNC theory used here generally gives considerable improvement over the mean spherical approximation, which is most often used for analyzing SANS data, but still underestimates the actual charge when compared to the results of numerical
simulation^.^^ To summarize the SANS results, the sizes of the microemulsion droplets can be extracted with confidence by modeling SANS data, but the apparent charges should be regarded as fitting parameters due to approximations made in modeling the interactions between the ionic species. With the advent of increasing computer power, SANS analysis using more accurate potentials and closure relations is becoming more routine, and more exact micellar charges will soon be attainable from scattering experiments. QLS experiments alone do not conclusively determine the type of particle populations in these microemulsions because the theoretical autocorrelation functions for a bimodal and a unimodal population are of the same mathematical form. The theoretical SANS spectrum for a bimodal population, however, is inconsistent with (44) Hayter, J. B. Langmuir 1992,8,2873. (45)Evans, D.F.; Mitchell, D. J.; Ninham, B. W. J . Phys. Chem. 1984.88. - - ,6344. ~ ~ (46) Hayter, J. B.; Penfold, J. Mol. Phys. 1981,42,109. (47) Linse, P. J. Chem. Phys. 1992,94,3817. (48) Nagele, G.; Klein, R.; Medina-Noyola, M. J . Chem. Phys. 1985, 83, 2560. >
Langmuir, Vol. 10,No. 9, 1994 2937
Polymerizable Microemulsions 70 I
Table 4. Hydrodynamic Factors composition
I
styrene DTABhrine [KBr] (e%) (wlw) (MI D,,dDoa DdDoa S(OIb H(0Y 0.0 15/85 0 2.9 0.064 0.1@ 1.0 15/85 0 2.5 0.075 0.19 0 2.6 0.072 0.18 1.5 15/85 2.0 15/85 0 3.1 0.068 0.21 3.0 15/85 0 3.7 0.061 0.22 4.0 15/85 0 3.6 0.054 0.19 5.0 15/85 0 3.8 0.047 0.18 4.0 15/85 0 3.6 0.054 0.19 0
E
0.00
0.05
0.10 q
0.15
0.20
(1/h
Figure 9. Comparison of the theoretical SANS spectra of unimodal (solid line) and bimodal (dashed line) populations with the experimentalspectrum for a microemulsion containing 4wt% styrene in a solutionof DTABD20 = 15/85(w/w)(circles). The solid line represents the best fit (lowest x2)spectrum for a unimodal population of monodisperse spheres. The dashed line represents the spectrum consistent with the QLS measurement assuming a bimodal distribution. This bimodal dispersion contains 1 mol % large particles (swollen micelles with Rs= 70 %i and z = 150) and 99 mol % small particles (emptymicelles with& = 23 %i andz = 17). The total dispersed volume fraction is 23 vol % for all spectra.
experimental results (Figure 9). The presence of 'even a small number of large spheres in a dispersion consisting mostly of small spheres causes the intensity at low q to increase dramatically. We therefore conclude that these microemulsionscontain a unimodal population of particles and use eq 15 to analyze QLS data. These observations correct an analysis reported earlier by one of US.^ Even though the SANS spectra were interpreted as a monodisperse population of spheres, the particles must be somewhat polydisperse, at least with respect to scattering power, to account for the double exponential form of the experimentally observed autocorrelation h c t i o n s . Equation 15 is strictly valid only when the scattering power polydispersity is decoupled from size; however, its form is useful for interpreting experimental results. The dynamic behavior for a system of charged polydisperse spheres with coupled polydispersity of scattering power and size has yet to be developed. Double exponential behavior has been observed for other types of concentrated microemulsions.8~49-53 The short time diffusion coefficient, D, or D,,, for colloidal dispersions can exhibit a maximum as the volume fraction of particles increases because of the interplay of hydrodynamic and thermodynamic interactions (eq 16).13954955 Recently Genz and Klein13 have investigated theoretically the many-body hydrodynamic interactions for monodispersecharged spheres using a renormalization approach first reported by BeenakkeP for hard spheres. (49)Bellocq,A.M.; Fourche, G.; Chabrat, P.;Letamendia, L.;Rouch, J.; Vaucamps, C. Opt. Acta 1980,27,1629. (50) Cazabat,A. M.: Chatenay, D.; Langevin, D.; Meunier, J.; Leger, L. In Surfactants in Solution: Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984;Vol. 3, p 1729. (51)Clarke, J. H.R.; Nicholson, J. D.; Regan, K. N. J. Chem. Soc., Faraday Trans. 1 1985,81,1173. (52)Marion, G.;Graciaa, A.; Lachaise, J. J . Phys. Chem. 1988,92, 1553. (53)Bodet, J.-F.;Bellare, J. R.; Davis, H. T.; Scriven, L. E.; Miller, W. G. J . Phys. Chem., 1988,92,1898. (54)Walrand, S.;Belloni, L.; Drifford, M. J. Phys. (Paris)1986,47, 1565. (55) Chatenay, D.; Urbach, W.; Messager, R.; Langevin, D. J . Chem. Phys. 1987,86,2343. 156)Beenakker, C. W. J.; Mazur, P. Phys. Lett. A 1983,98,22.
4.0 4.0 4.0 4.0 4.0 4.0
15/85 15/85 15/85 15/85 15/85 15/85
0.01 0.05 0.10 0.15 0.20 0.25
1.5
1.1 0.89 0.74
3.5 2.6 1.6
0.050 0.094 0.15 0.21 0.27 0.34
0.17 0.25 0.23d 0.22d 0.24d 0.25d
a Dowere calculatedfromR, of SANS. Values were interpolated to q = 0.00242 A-1 from SANS analysis. Calculated using eq 16. Calculated from D-lD,.
Hydrodynamic interactions can be quantified experimentally by extrapolating the structure factors from SANS to the q value measured by QLS and using eq 16. The results are in Table 4. Experimentally determined hydrodynamic factors (0.18-0.23) correspond closely to the theoretical value of 0.2 calculated for a 20 vol % suspension of 25 radius particles with a valence of 20.13 These parameters are similar to the droplet characteristics determined by SANS for these microemulsions. The collective diffusion coefficient is also predicted to decrease with increasing salt concentration as is observed (Figure 8b). An approximate expression suggests that D, depends on the volume fraction of parti~1es.l~ Furthermore, D$Do is believed to scale with macroscopic solution properties such as the viscosity.57 Experimentally, the self-diffusion coefficient of concentrated DTAB micelles has been measured directly by the fluorescence recoveryafier Eringe patern photobleaching (FRAPP) technique,55 and D$Do decreases monotonically as the micellar volume fraction of DTAB increases. The ratio also decreases for the microemulsions studied here when the volume fraction is increased by adding styrene (Figure 8a). For DTAB solutions of fmed volume firaction, Chatenay et al.55claim that the self-diffusion coefficients are insensitive to interactions, since the behavior of D$Do did not change significantly upon the addition of salt. However for the larger microemulsion droplets studied here, the selfdiffusion coefficient increases by 3 times with increasing salt concentration (Figure 8b).
A
Conclusions Static and dynamic scattering experiments can provide structural information about polymerizable microemulsions. The results of SANS analysis show the dependence of droplet size and composition on the overall microemulsion composition. In particular, the droplet size increases from 23 to 35 as styrene concentration increases from 0 to 6 wt % in solutions with a DTAB/D20-brine = 15/85 (w/w) and is independent of brine concentration. The apparent micelle ionization decreases from 16 to 3%with increasing salt content, but precise determination of ionization requires more accurate thermodynamic models. The two diffusion modes of a polydisperse unimodal dispersion cause the double exponential behavior observed in the QLS autocorrelation function. The inherent poly-
A
(57) Kops-Werkhoven, M. M.; Fijnaut, H. M. J . Chem. Phys. 1982, 77,2242.
2938 Langmuir, Vol. 10, No. 9, 1994 dispersity of microemulsions droplets allows the simultaneous measurement of the collective and self-diffusion coefficients. Extracting structural information from dynamic experiments requires careful consideration of both hydrodynamic and thermodynamic interactions. By use of SANS t o independently measure the static structure factor, hydrodynamic effects are quantified using QLS measurements. Hydrodynamic factors correspond closely to those predicted by Genz and Klein.I3 The ability to control microemulsion droplet size by adjusting the overall composition provides a systematic method for studying hydrodynamic and thermodynamic effects on collective and self-diffusion.
Acknowledgment. We are grateful t o Bruno D’Aguanno for providingthe computer program to compute static structure factors and to Professors N. J . Wagner
Full and Kaler and J. E. Puig for useful discussions. The Statistical Laboratory a t the University of Delaware assisted us in devising a bootstrapping method for estimating parameter confidence limits. SANS experiments performed a t the Oak Ridge Naltional Laboratory were supported in part by the Division of Materials Science, U.S. Department of Energy, under Contract No. DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc. We acknowledge the support of the National Institute of Standards and Technology,U.S.Department of Commerce, in providing the facilities used for experiments performed there. Some of this material is based upon activities supported by the National ScienceFoundation under Agreement No. DMR9122444. The assistance of George Wignall, Charlie Glinka, and John Barker during the experiments is gratefully acknowledged.
