5989
J. Phys. Chem. 1991,95, 5989-5996
Polymers In Complex Fluids: Dynamic and Equlllbrlum Properties of Nanodroplet-ABA Block Copolymer Structures R. P.W.J. Struis and H.-F. Eicke* Institut fiir Physikalische Chemie der Universitdt Basel, Klingelbergstrasse 80, CH-4056, Basel, Switzerland (Received: November 15, 1990) Depending on the relative amount of hydrophilic A blocks (poly(oxyethy1ene))and hydrophobic B block (polyisoprene),ABA block copolymers dissolved in water-in-oil microemulsions (H20/AOT/isooctane) have been shown to form "core-shell" or "dimeric" complexes with the microemulsion nanodroplets. For both types of such complexes, the diffusional behavior as a function of the copolymer concentration is studied by using ('H)pulsed field gradient spin-echo (PFGSE) NMR technique. A self-consistent picture of the size and geometrical shape of these structures has been established, and it is demonstrated that up to fairly large copolymer concentrationsthese results are compatible with the earlier reported viscosity and conductivity patterns in these systems. Inferring from the NMR results further interlinking of the nanodroplets upon increasing amounts of copolymer was evidenced by probing of larger (most likely) side-branched structures, which can be considered as the onset of a three-dimensional transient network (gel) as indicated by viscosity and conductivity patterns at very high copolymer concentrations. TABLE I: Number-Average Molecular Weights M, (in g mor') and Conwitions of Tribloek Copolvmen
Introduction
Much of the recent interest in our laboratory has been focused on complex fluids, i.e., threecomponent (water/AOT/isooctane) microemulsions containing various amounts of triblock copolymers of the ABA type, where A is a hydrophilic (poly(oxyethy1ene) = POE) and B a hydrophobic (poiyisoprene = PI) moiety.'-3 The structure of the copolymer-free microemulsion can be described by well-defined nanometer-sized aqueous Due to the presence of both the A and B moieties in the copolymers and in view of their typical solvation preferences for either the polar nanodroplet water pool or the apolar dispersion medium (isooctane), the copolymers are insoluble in water and only very poorly soluble in isooctane; they dissolve, however, easily in a composite solvent, Le., the presently studied water-in-oil (W/O) microemulsions a t room temperature.' Several copolymers with different (relative) amounts of A and B blocks in H20/AOT/isooctane microemulsions, at constant total AOT and water concentration, have previously been studied with a variety of experimental The results obtained (at moderate copolymer concentrations) from electrical conductivity, viscosity, static light scattering, and transient electric birefringence experiments support the idea that the interaction between the copolymers and the nanodroplets could be arranged in two classes, Le., "coreshell" structures and "dimeric" complexes (see Figure 1).2 The former structure is characterized by two POE blocks confined within one nanodroplet, and for the dimeric complex, the POE blocks are dissolved in two different nanodroplets. In the latter case it was found that increasing the copolymer concentration induced further interlinking. At very high copolymer concentrations a transparent get with the structure of a "frozen" W/O microemulsion is obtained. The structures formed in the gelling system were found to be reversible in size with respect to dilution and heating.lJ To learn more about these systems, ('H) PFGSE N M R experiments have been performed with two types of copolymers in microemulsions that can be considered as typical representatives of the above-mentioned two copolymer-nanodroplet structures. The PFGSE NMR technique allows one to determine the timeaverage values of self-diffusion coefficients of all components, including new structural entities (if they posses sufficiently long lifetimes compared to the typical time scale of this technique). Earlier ('H) PFGSE NMR measurements with selectively deu-
copolymer Mn(POE) Mn(P1) POE/PI (w/w) Mn(C0P) monomeric units per copolymer: POE PI
COP-3 22000 39000 36/64 61000
307 905
500
574
terated (copolymer-free) microemulsions yielded clear evidence that water and AOT move equally fast in the system.' This observation is easily interpreted if formation of spherical (aqueous) nanophases is assumed, in which the water is almost completely confined. The use of deuterated isooctane permitted us primarily to focus attention on the diffusional behavior of the nanodroplets and those entities that were formed upon addition of copolymers. Since the self-diffusion coefficients of these entities are sensitive to confinement, size, and geometrical shape, PFGSE N M R measurements are expected to yield information about these quantities. Moreover, previously reported electrical conductivity and viscosity data were reconsidered in light of these measurements. The results from these different experimental sources support the underlying models remarkably well. We consider them a good confirmation of the proposed structural model of the copolymer-nanodroplet assembly.
Experimental Section Preparation of Samples. Copolymer-containing W/O microemulsions were prepared by mixing weighed amounts of the microemulsion with varying amounts of copolymers. In all samples the AOT and water concentrations were kept constant. The copolymer-free microemulsions were prepared as follows: Aerosol-OT (sodium bis(2-ethylhexyl) sulfosuccinate) or AOT from Fluka, Switzerland, was purified in an active carbon/MeOH slurry under stirring for about 24 h. The samples were filtrated and evaporated to dryness, and the residual water was removed (up to W, 1) under reduced pressure (3 X lo-' Torr). 98.8atom % deuterated 2,2,4trimethylpentane (d18-isooctane) was obtained from MSD Isotopes, Montreal, Canada (Lot No. 1381-L),and was used without further treatment. Deionized and twice distilled water was used. The triblock copolymers (COP-2 and COP-3) have been synthesized and characterized a t the Laboratoire de Chimie Macromoleculaire, ENSCM, Mulhouse, by Gu Xu. The polymer-
-
( I ) Xu, G. Ph.D. Thesis, University of Basel, Switzerland, 1990. (2) Eicke, H.-F.; Quellet, C.; Xu, G. Colloids SUI$ 1989, 36, 97. (3) Quellet, C.; Eicke, H.-F.; Xu, G.; Hauger. Y. Macromolecules 1990, 23. -3341. - (4) Eicke, H.-F.; Rehak. J. Helv. Chim. Acta 1916, 59, 2883. (5) Jahn, W.; Strey, R. J . Phys. Chem. 1988, 92. 2294. (6) Hilfiker, R.; Eicke. H.-F.; Steeb, C.; Hofmeier, U.J . Phys. Chrm. 1991, 95, 1478.
--.
0022-3654/91/2095-5989$02.50/0
COP-2 13500 61500 18/82 75000
(7) Geiger, s.;Eicke, H.-F. J . Colloid Inreflace Sci. 1986, 10, 181. (8
1991 American Chemical Society
5990 The Journal of Physical Chemistry, Vol. 95, No. 15, 19'9I
Copolymer conformations in solution
(a) extended coil conformation
(b) core -shell conformation
-
Nanodroplet copolymer complexes in microemulsions
(c) dimeric complex
I
( d ) "core-shell"complex
network
Figure 1. Possible conformations of the triblock copolymers, ABA ( A = hydrophilic block, B = hydrophobic block), and the proposed aqueous nanodroplet-copolymer complexes (from ref 2).
ization technique has been described in detail elsewhere.' The copolymer composition was determined by elementary analysis and NMR spectroscopy. Both methods yielded similar results. and comIn Table I, number average molecular weights (M,) positions of the triblock copolymers, as determined by gel permeation chromatography, are shown. The triblock copolymers were dissolved in the W/O microemulsion at room temperature and stirred for several days with a magnetic stirrer until the initially turbid solutions became clear. Prior to use,glassware and NMR tubes (7" i.d.) were heated in a NaHC03 solution, then heated in an EDTA solution, and stored for several days filled with distilled and deionized water. Relevant Parameters of the Samples Studied. The W/O microemulsions used in this study correspond to the optically transparent and low-viscious-phaseregion (L2phase) within the ternary phase diagram. They consist of well-defined nanodroplets with a moderate polydispersity at the water concentrations used in this investigation.* From the composition of the copolymer-free microemulsion the following properties can be derived to which we will refer throughout this study: cAOr = 0.1003 mol dm-3; mole ratio of water to AOT ( W,)= 62.0. The mean area of the W/O interface covered by one AOT molecule,AAOT), can be estimated ~ ~beAAOT) ), = 57.6 A2.9 from 59.6 - 46.8 e ~ p ( - 0 . 4 0 1 ( W ~ ) 'to The water core radius is calculated according to 3uwW,/[NJ(AOT)], where N A denotes Avogadro's number and ow the water molecular volume, Le., 18 cm3 mol-', thus, r(watercore) = 96.5 A. This latter figure yields a mean surface area of the water core of 1.17 X lo5 A2, which corresponds to 2032 AOT molecules/ nanodroplet. For the above-mentioned AOT concentration we finally obtain 2.97 X 1 Ot9 nanodroplets/dm3 of microemulsion. On the basis of chemical expertise, it has to be assumed that the sulfonate group of the AOT molecule is partially solvated by the 1 of the nanodroplet.'" Thus taking an effective length water of 9.5 one estimates from r(drop1et) = r(watercore) + effective AOT length, r(drop1et) = 106 A. The volume fraction occupied by nanodroplets is @ = 0.148. To allow for a direct comparison between the results obtained for the two different copolymer
!r
(8) Zulauf, M.; Eickc, H.-F. J. Phys. Chem. 1979, 83, 480. (9) Hilfiker, R.;Eicke, H.-F.; Hammerich, H. Helu. Chlm. Acfa 1987, 70,
1531.
(10) Day, R. A.;
Robinson, B. H.; Clarke, J. H. R.;Doherty, J. V. J .
Chem. Soc., Faraday Trans. I 1979, 75, 132.
Struis and Eicke compounds, the number ratio of copolymer molecules per nanodroplet, 93,has been used throughout this work. This ratio can be calculated by considering the weighed-in copolymer concentration and its number averaged molar mass, M,"P. Polydispersity, Le., Mw/Mn # 1, has been ignored. Experimental Setup and AM~YS~S. Self-diffusion coefficient measurements were performed in Karlsruhe, Germany, on a self-built 25-MHz pulse NMR spectrometer, using a commercially available pulse gradient unit (Bruker). A description of the pulsed field gradient method may be found in ref 1 1. The experiments were performed by varying the field gradient pulse duration, 6, typically between 0.1 and 1.4 ms, with a constant field gradient pulse interval, A, of 35 ms. The measurementswere made at 298.3 f 0.2 K. For accurate measurements special care was taken for an optimal calibration procedure.12 The field gradient was calibrated by using pure tetradecane for which the self-diffusion coefficient is known, Le., D(n-tetradecane) = 0.56 X 10-9 mz &.I3 For all the studied samples a variation of 6 resulted in a biexponential decaying echo amplitude (A). Hence, eq 1 was used to interpret the data, i.e. A = A,[x exp(-yG2D162(A- 6/3)) + (1 - x) exp(--vC2D262(A- 6/3))] (1) where A, is the echo amplitude in the absence of any gradient pulse, C is the field gradient strength, y is the proton gyromagnetic ratio, DI and D2 the two characteristic self-diffusion coefficients with peak amplitude fractions of x and (1 - x), respectively. D I , D2, A,, and x were determined by fitting the experimental data to eq 1 with the help of a Marquardt-Lmenberg a1g0rithm.I~ The estimated relative errors in Dl, Dzrand x are within &IO%, f1%, and f4%, respectively. The earlier reported viscosity and electrical conductivity exp e r i m e n t ~refer ~ , ~ to solutions with compositions similar to those prepared for the PFGSE NMR experiments, except that nondeuterated isooctane had been used, and W,was 60. The reader may convince himself that this small difference in W,is immaterial (as is the deuteration effect) for the interpretation. Kinematic and (via the density) dynamic viscosity data were obtained with an automatic Ubbelohde viscometer, Viscomatic MS (Fica, France), equipped with thermostatible capillaries. The estimated relative errors in 7 range within i 5 % . For moderate copolymer concentrations (as used in this investigation) no remarkable shear rate dependence of the viscosity was observed. The lack of a remarkable shear rate at moderate copolymer concentrations was confirmed qualitatively by measurements with different capillary diameters and by using a PAAR modified falling ball microviscometer allowing continuous variation of the shear rate. Electrical conductivity had been determined with the help of a Wayne-Kerr universal bridge, Model B221. A specifically designed conductance cell was used, consisting of two rectangular 30 X 5 mm2Pt electrodes at a fmed distance of 5 mm. The relative error in u is estimated to be within f l % .
Results and Discussion We divide this section into three main parts: the first part concerns the analysis and discussion of the PFGSE NMR results. The second and third parts present the results obtained from dynamic viscosity, and electric conductivity experiments. 1. ('H) PFGSE NMR. As already mentioned, a biexponential decaying echo amplitude was Observed for all microemulsions studied. The corresponding two characteristic self-diffusion coefficients, DI and Dz, and the normalized fractional peak amplitude contribution ( x ) to DI are shown in Table 11. In all cases one observes Dl >> D2. (1 1) Hrovat, M.1.; Wade, C. G. J. Magn. Reson. 1981,44,62; J. Magn. Reson. 1981, 45, 67. (12) Holz, M.;Weingirtner, H. J. Magn. Reson., in press. (13) Holz, M.;Weingirtner, H.;Sam, A. Baker Almanac; 1991,
Physical Tables. (14) Nash, J. C. Compact Numerical Methods; Adam Hilger: Bristol. 1979.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5991
Polymers in Complex Fluids TABLE II: Self-Diffusion Coefficients, D1 (in lo-' m2 d)and D 2 m2 d),rad N o d z e d Fnctioorl Peak Amplitude (in C~ntributi~n (x) to DI, Obtriaed by Fittins tbe PFGSE NMR Data to
Eq 10 R 0 0.123 0.152 0.203 0.393 0.539 0.554 0.733 0.824 1.118 1.370 1.457 1.589 1.906 2.191
COP-2 DI Dl 1.40 2.50 1.14 2.50 1.12 2.47 0.95 2.45 1.12 2.36 1.35 2.28 0.97 2.28 1.15 2.19 1.40 2.16 0.83 2.05 1.02 1.95 1.23 1.88 1.19 1.86 1.06 1.78 1.22 1.72
x
R
0.106 0.116 0.102 0.104 0.120 0.127 0.127 0.108 0.094 0.086 0.089 0.1 IO 0.116 0.134 0.120
0 0.122 0.165 0.189 0.356 0.478 0.866 1.218 1.067 2.665
DI 1.36 1.29 1.00 1.30 1.37 0.98 1.32 1.35 1.10 1.14
COP-3 Dl 2.47 2.41 2.38 2.35 2.11 1.95 1.66 1.43 1.20 0.916
-
n
L
r4
x
E
0.093 0.100 0.102 0.095 0.100 0.096 0.104 0.108 0.102 0.093
&
# W
n
0.5
The faster diffusion coefficient, DI, could unambiguously be identified with the diffusion of the deuterated isooctane, because spurious amounts (1.2%) of isooctane protons were still present. A constant diffusion coefficient of isooctane (i-C8), Le., D(i-C8) = (1.2 f 0.2) X IO4 m2 s-], with a constant amplitude fraction of x = 0.102 f 0.012, was obtained. This D(i-C8) value agrees reasonably well with observationsin similar microemulsions. One finds, e.g., D(i-C8) * 1.5 X lo4 m2 s-l in D20/0.18mol dm-3 AOT/i-C8 microemulsions at 298 K and W, = 5K7 The peak amplitude fraction agrees well with the amount of isooctane protons relative to the total amount present in the samples. In the copolymer-free microemulsion one estimates x = 0.092 for a degree of deuteration of 98.8 atom %. The diffusion coefficient, 4 , is at least 50 times smaller than D(i-C8). The remaining part of this section will entirely be concerned with the slower diffusion coefficient which will simply be denoted by D (without subscript). D can be attributed to the translational diffusion of both the AOT and water molecules of the spherical nanodroplets.' The quantitative relationship between D and the hydrodynamic radius r of the nanodroplets is given by the Stokes-Einstein relationship D = kBT/6rqr
(2)
where kB is Boltzmann's constant, T the absolute temperature, and 9 the viscosity. It should be particularly noted that in eq 2 the viscosity of the microemulsion, s(ME), and not of the pure dispersion medium, v(i-C8), has to be used.7 This choice is unambiguous, since for translational diffusion processes assuming a Gaussian diffusion with a relevant PFGSE NMR interval time of 35 ms and D(drop1et) 2.5 X IO-" m2 s-l, one estimates a root-mean-square nanodroplet displacement in the order of 13 340 A, which corresponds to about 80 mean free paths of the droplets. This calculation corresponds to Hayter's" one-component macrofluid: the colloidal particles are taken to be the only macroscopic objects in the suspension. The solvent is taken to have no structure as such and no painvise correlation either with each other or with the colloidal particles. According to eq 2 D(drop1et) = 2.54 X IO-" m2 s-I with T = 298 K, r(drop1et) = 106 A, and q(ME) = 0.81 CP in close agreement with the experimentally obtained values, i.e., D,,(R=O) = 2.50 X IO-" and 2.47 X lO-" m2 s-' (see Table 11). The remarkable coincidence between theory and experiment seems partially fortuitous because neither the possible effect of the deuteration of isooctane (.?(ME with i-C8D,8) > ?(ME with i-C8H18))nor the presence of molecularly dispersed AOT molecules in the oil medium, which should result in Dcxp > Dole? has been considered. One may conclude therefore that either one or both effects are within experimental inaccuracy or B. Faraday
DISCUSS. Chem. Soc. 1983, 76, 7.
.
1.0
#Estimated relative errors in D,, Dl, and x are within *IO%, *I%, and *4%, respectively.
(15) Hayter, J.
3.0
'
3
. .. 2
Figure 2. Translational self-diffusion coefficients, D,in copolymer containing microemulsions, as a function of 92 at 298 K. Experimental results: ( 0 )COP-2; ( 0 )COP-3. Theoretical results, Ow, as discussed in the text: (0)COP-2; (m) COP-3.
have effectively cancelled each other. We now discuss the change of D upon addition of copolymers (R> 0): Figure 2 shows that both block copolymers (COP-2 and COP-3) decrease D with increasing amounts (3).COP-2 changes D less prominent than COP-3. To analyze this different behavior, again the Stokes-Einstein relation will be used. For this relation it is important to emphasize the particular role of the viscosity 7 and of the hydrodynamic radius r: experimentally, the additions of COP-2 produces a moderate and of COP-3 a significant increment of the vis~osityl-~ (see also next section). With respect to 9 two extreme options could be considered: (1) the ratio q(R>O)/s(R=O) changes with R or (2) v(W>O) = q(R=O)= .rl(ME). Inserting option 1 in eq 2 results in apparent contradictionswith other experimental observations and physically unrealistic conclusions. To illustrate this point Figure 2 shows the calculated change of D (denoted by D ) according to option 1, while the value of r is kept unchanged-or both copolymers Dis smaller than Dap, although the discrepancy is less evident for COP-2 than for COP-3. Higher COP-3 concentrations make even very small as compared to DuP To account for these discrepancies, one could assume that for R > 0 faster diffusing, Le., smaller sized objects (smaller than nanodroplets) are probed in the PFGSE NMR experiments. It is difficult to imagine the origin of such objects; small sized copolymers (due to the polydispersity of the block copolymers) are insoluble in the oil. Also the possible role of the copolymers as cosurfactants and, hence, the decrease of the nanodroplet size could be excluded. The latter effect should be (roughly) similar for COP-2 and COP-3 due to comparable molecular weights of the POE chain in the copolymers. Finally, one could assume that collisions between complexes, and/or nanodroplets induce exchange of water and/or AOT molecules, diffusing over PFGSE NMR relevant distances. For copolymer-free microemulsions, it is known that collisions between nanodroplets occur. In fact this process is strongly related with the (moderate) polydispersity in the nanodroplet sizes.8s16 The experimental observation, however, that D(A0T) ss D(H20) D(drop1et)' contradicts the above-suggested fast transport mechanism. The addition of copolymer does not change this conclusion. We are particularly interested in the consequences that emerge from the equality q(W>O) = v(R=O),where v(R=O)is the viscosity in the copolymer-free microemulsion. This equality implies that the diffusion paths that make up the long-distance
-
(16) Eicke, H.-F.; Hilfiker,
R.;Holz, M.Helo. Chlm. Acta 198467,361.
5992 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
diffusion is controlled by the same interactions. This appears reasonable because the copolymers are preferentially dissolved in the nanodroplets. No significant change in the propoerties of the isooctane is therefore to be expected. Since addition of either copolymer decreases D with increasing R, it follows that also objects larger than nanodroplets have been probed by the PFGSE N M R experiments. Hence we conclude that copolymer-nanodroplet complexes are present as already proposed in the Introduction. For COP-2, the formation of "core-shell" complexes seems an adequate model. For moderate R values it is assumed that initially an 1 :1 copolymer-nanodroplet "core-shell" complex is formed. Because D decreases upon addition of COP-2, the effective hydrodynamic radii of these "core-shell" complexes must be somewhat larger than those of the copolymer-free nanodroplets. This is reasonable since the hydrophobic PI block prefers the apolar isooctane. At higher R values D approaches an asymptotic value. This can be explained by assuming each "core-shell" complex to host more than one copolymer. At the highest R value studied, D(R)/D(R=O) = 0.68; assuming that most of the nanodroplets have been transformed into spherically shaped "core-shell" complexes, one estimates the hydrodynamic "core-shell" radius to be approximately 1.5 times the nanodroplet radius. The interaction between COP-3 and nanodroplets cannot be adequately described by the formation of "core-shell" complexes; otherwise, conclusions are obtained that contradict experimental findings: From the observed diffusion coefficient at the highest R value one would derive an effective hydrodynamic "core-shell" radius that is, for example, about 2.8 times the nanodroplet radius. This radius is significantly larger than that estimated for COP-2. This result is inconsistent for two reasons: (i) COP-3 has a smaller PI chain than COP-2 and hence should form a more compact "core-shell" complex. (ii) The larger radius would result in an unrealistically large volume fraction of @ = 3.2. Thus we conclude that COP-3 and nanodroplets form (at moderate R values) "dimeric" complexes, i.e., complexes composed of two nanodroplets and one COP-3 molecule. At higher R values, particles larger than "dimeric" complexes may result. According to experimental information, we suggest the following equilibria to take place. 0 < R 50.5 2D + P PD2 (3a) 0.5 < R I1 PDI + P P2D2 (3b) 1 < R I 1.5
P2D2 + P
P3D2
(3c)
The particular choice of the R intervals was based on the average amount of copolymers per nanodroplet needed to form PD2, P2D2,etc. Equilibrium 3a is probably strongly shifted to the right, because COP-3 is solely soluble in the microemulsion. Equilibria 3b and 3c should merely be considered as a hypothetic model. It is to be expected that within the typical time range of 35 ms, as applied in the present PFGSE N M R experiments, for ?3 I0.5 essentially "dimeric" and, for larger 93 values, still relatively small complexes are probed. This follows from the experimentally observed destabilizing action of POE in W/O microemulsions' and from the fact that a gel is formed at very large COP-3 amounts. The gel continuously renews itself on a time scale (much) smaller than that applied in the PFGSE NMR experiments.' With respect to the destabilizing action of POE, it was found that triblock copolymers with very short PI chains and large POE/PI weight ratios coagulate the microemulsion. It is thought that this destabilizing effect of POE is compensated by the solubility of the PI block in the oil as far as "dimeric" complexes are concerned; this delicate thermodynamic balance is shifted to an even larger free energy of the system if the nanodroplet hosts more than one POE block. In fact, the change in this balance can be seen as the onset of the continuous renewal of the larger sized complexes and the gel formed at high R values.' The gel is formed if most of the nanodroplets are interconnected via the apolar PI blocks. According to the transient network theory,l'~'*the entanglement points of the network are the na(1 7) Green,
M.0.;Tobolsky, A. T.J . Chrm. Phys. 1946, 14, 80.
Struis and Eicke
TABLE III: Diffudos C0efRek.b of N w t C O P - 3 CO@X (298 K), As Derived from PFGSE NMR Data (Expdment) utd the F V o p d Geometrical Models Using Eqs 48- 5, utd 6 (Goom Model) %(COP-3) 0 0.122 0.165 0.189 0.356 0.478 0.866 1.218
complex droplet PDZ PDZ PD2 PD2 PD2 P2D2 P3D2
D(complex)/lO-ll m* s-1 Reom model
exut 2.47 1.86 1 .go 1.87 1.78 1.90 1.59 1.24
2.54" 1.92 1.92 1.92 1.92 1.92 1.72 1.56
"Calculated with eq 2. nodroplets that contain more than one POE block. From temperature-dependent viscosity it was concluded that the POEnanodroplet junctions are renewed in about 100 ms for R = 1, and 1 ms for R = 2.3 (where much larger clusters are to be expected) at 298 K, i.e., in the order of the lifetime of the unperturbed copolymer-free nanodroplets. One may expect therefore that in the PFGSE N M R experiment the diffusion of complexes smaller than the transient network are probed. If, on a PFGSE N M R time scale, a slow diffusing large transient network existed, then such entities should have been discovered as the echo amplitude would not have decayed to zero within the field gradient pulse duration employed in our experiment. This has not been observed with the two studied copolymers. It is interesting that preliminary dynamic light-scattering experiments (nanosecond time scale) in COP-3 containing microemulsions show the formation of large transient networks. Since the experimentally determined diffusion coefficients Dox is a weighed number-averaged quantity with respect to all dffusing species, it will be essentially controlled by the abovediscussed equilibria 3a-c. From the respective mass balances one expects the following relations to hold: 0 < W 5 0.5 De,,(%) = (RD(PD2) + (1 - 2R)D(droplet))/(l - 3) 0.5 < R I1
De,p(R) = 2(1 - R)D(PD2)
1
+ (254 - l)D(P2D2)
< 33 I1.5
(4b)
Dexp(R) = 2(R - l)D(P,D2) + (3 - 2R)D(P2D2) ( 4 ~ ) Equation 4a yields D(PD2) if D(exp) at a particular R and P (droplet) have been substituted. The adopted value of D(drop1et) is an average of the theoretically estimated and experimentally determined figure, Le., 2.50 X 10-" m2 s-I. The results are given in Table 111. One sees that constant D(PD2) values are obtained, which reveals equilibrium 3a to be strongly shifted to the right. Introducing the (averaged) D(PD2), and the other experimental data into eq 4b, D(P2D2)can be obtained, and so on. The results for D(P2D2)and D(P3D2)have also been included in Table 111. A more natural picture can be modeled by realizing that the complexes have a nonspherical symmetry. Transient electric birefringence measurements in similar copolymer containing W/O microemulsions show that the "dimeric" PD2 complexes can be visualized as a straight array of three nearly equally sized spheres? The diffusion of this complex might be thus interpreted in terms of the diffusion of a prolate ellipsoid, with semiaxes (a,b,b) as indicated in Figure 3. For prolate ellipsoids of revolution, the friction coefficient for translational diffusion can be described by a Stokes equation, i.e. D(el1ipsoid) = kT/f(ellipsoid) (5) According to Perrin19 and Herzog et al.20f(ellipsoid)is given by flellipsoid) = 6xq(ME)a(l - (b/a)2)'/2/ln l a [ ] + (1 - ( b / ~ ) ~ ) ' / ~(6) ]/b) (18) Lodge, A. Trans. Faraday Soe. 1956, 52, 120.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5993
Polymers in Complex Fluids
Figure 3. Possible conformation of the "dimeric" PD2 complex as discussed in the text.
Figure 5. Experimentally derived dynamic viscosity in copolymer containing microemulsions, as a function of ft at 298 K. (0)COP-2; ( 0 ) COP-3.
2 Figure 4. Translational self-diffusion coefficients, D, in COP-3 containing microemulsions, as a function of R at 298 K. Experimental results: (0). Theoretical results: (0)Ddl; (A) Oh.
For the "dimeric" complexes, a reasonable estimation of u and b is obtained by assuming a straight array of two spherical nanodroplets sandwiching a spherical copolymer, where r(drop1et) = 106 A and r(C0P-3) = R (COP-3) = 61 A. R denotes the radius of gyration calculated for the PI block?' krom simple geometric considerations one derives b = (r(drop1et) R,fOP-3)1/2 83.5 A and u = Zr(drop1et) + R,(COP-3) = 273 . This corresponds approximately to an ellipsiodal volume of (4/3)rab2 = 2V(droplet) + V(C0P-3). With the a and b values thus obtained, one finds from eqs 5 and 6 D(PD2) = 1.92 X lo-" m2 s-I. To estimate P2DZ,one could apply the same geometrical model, by assuming that the second copolymer is attached along the a axis. For this situation one calculates D(P2D2)= 1.72 X lo-" m2 s-l with b = 83.5 A and u = a(PD,) R4(COP-3) = 334 A. The predicted experimental diffusion coefficients, Ddd, are plotted as function of R in Figure 4. As seen from this figure, the agreement is good for R I0.5 in view of the simplified assumptions. Beyond 92 = 0.5, the coincidence is less satisfactory. This is to be expected because amount, size, and geometrical shapes of the larger complexes (including polydispersity effects)
-
+
+
(19) Perrin, F. J . Phys. Radium 1936, [7], 7 , 1. (20) Herzog, R. 0.;Illig, R.; Kudar, H.2. Phys. Chem. 1934, A167,329. (21) The radius of yration, R ,of the poliyisoprene block has been calculated with R, ((15,9 )/6)II2, w#erc (&*)I/ denota the mean end-to-end distance. Taking excluded-volume effects into account2*and assuming that the PI block, which consists of only 1,2 and 3,4 units,' has a freely rotating (2L,*)I/', with n the number of C C polymethylene chain, (L?)'l2 = bonds with a bond length. L.of 1.54 A. (22) de Gennes, P.-G; Skiing Conceprs in Polymer Physics; Cornell University Press: Ithaca, NY, 1988; p 40.
-
become increasingly uncertain. Moreover, possible branching of the larger complexes has to be considered, which is to be expected at very high R values. This phenomenon, however, does not seriously affect the results for R I1, because side branching should occur not before at least four elementary units are combined in a single complex. 2. Dynamic Viiosity. The experimentallydetermined viscosity in COP-2- and COP-3-containing W/O microemulsions (at 298 K) is plotted in Figure 5 as a function of R (the number ratio of copolymers per nanodroplet). One observes that upon addition of COP-2 a moderate and of COP-3 a significantly larger change of q occurs. It is now possible to derive from q the apparent volume fraction of solute @ as a function of R and to relate @ with nanodroplets and nanodroplet-copolymer complexes in the microemulsions. In particular, we will utilize the sensitivity of the viscosity toward deviations from spherical symmetry.23 To start with, some more general considerations have to be made. The specific viscosity, qrp, of an ideal solution of noninteracting dispersed spheres with volume fraction @ is, according to Einstein's relation, for low @ qap = 2 . H
(7)
It can easily be shown that within the concentration range employed in this study higher order terms of @ have to be taken into account. If we assume that the nanodroplets in the copolymer-free microemulsion (ME) are noninteracting "hard" spheres, one estimates 0 = 0.148 (as mentioned in the Experimental Section). Substituted in eq 7, one obtains qIp = 0.38. From the definition qIp = (q(ME)/q(neat i-C8)l - 1 and the experimentally derived data q(ME) = 0.81 CPand q(neati-C8H18)= 0.474 cP, one gets the significantly larger value 0.71. This disagreement makes it nectSSar to take higher order terms of @ into account, first given by SaitBYs and later improved by B e d e a ~ xhe ; ~ added ~ a function of the volume fraction, Le., S(@)that contains the effects due to correlations and hydrodynamic interactions between the spheres, i.e.
(23) Tanford, C. Physical Chemistry of Macromolecules; John Wiley: New York, 1967.
5994 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
Struis and Eicke
TABLE IV: Volume Fraction of Solute, a(%),Derived from Dymmic V W t y in Copolymer-Combining Microemulsions (198 K ) by Using Eqs 8 and 9 COP-2 COP-3
R 0 0.27 1 0.325 0.541 0.649 0.8 I2 1.082 1.353 1.407 1.515 1.623 2.813
R 0.157 0.179 0.182 0.198 0.205 0.214 0.23 1 0.246 0.248 0.254 0.262 0.321
0 0.200 0.300 0.466 0.800 1.OOo 1.133
mi) 0.157 0.182 0.201 0.225 0.285 0.335 0.372
~(0) denotes the viscosity of the dispersion medium (neat i-Cs), and T ( @ ) denotes the viscosity of the copolymer-free ( R = 0) or the viscosity of the copolymer containing (92> 0) microemulsion. S(@)approaches zero if Q, = 0; for small values of @ eq 8 reduces to eq 7. If S = 0,one recovers an expression given originally by Sait6.2s Considering low shear values of the viscosity as in the present case, a virial expansion of S to third order in @ was derived from experimentally viscosity data obtained from systems closely resembling hard-sphere particle^.^' This expansion reads S(Q,)
3.08@- 3.15@’
9z Figure 6. Experimentally derived volume fraction of solute, a, in CQpolymer containing microemulsions, as a function of R. (0)COP-2 (drawn line represents eq IO); ( 0 )COP-3.
(9)
This virial expansion is to be preferred in the present case, because a direct expansion of T ( @ ) yields too inaccurate results.24 To avoid erroneous conclusions, we restrict Q, to a range comparable to that used in the derivation of eq 9. The volume fractions for COP-2- and COP-3-containing microemulsions as a function of Si are collected in Table IV and plotted in Figure 6. We start with the results from COP-2-containing microemulsions: the @ values are very well described by a quadratic exression, i.e. @(Si) = (0.1593 f 0,0010)
2
1
+ (0.0712 f 0.0016)W -
scheme used to explain the diffusion coefficients: we describe the nanodroplet-copolymercomplexes by prolate ellipsoids within the interval 0 < R I0.5, Le., for the equilibrium P + 2D PD2. According to the above discussions only nanodroplets and “dimers” will be considered. The volume fraction @(R)(Table IV) is expected to obey the following equation:
@(R)= @(droplet) + @(PD2)=
C(droplet)(( 1 - 2 3 ) V(drop1et) + RV(PD2) A(a,b)/2.5} (1 1)
where C(drop1et) denotes the number of nanodroplets in the copolymer-free microemulsion per unit volume, V(drop1et) the volume of a single spherical droplet, V(PD2) the volume of a single The limiting value of Q, obtained from eq 10 for R 0 coincides PD2complex, and (A(a,b)/2.5)a factor correcting for the deviation reasonably well with the volume fraction of the nanodroplets in of PD2 from spherical symmetry. A(a,b) is the asymmetry factor the copolymer-free microemulsion, Le., Q,(R=O)= 0.148 (see appearing in the more general expression of eq 7, Le., qlp = Experimental Section). The slightly higher limiting a ( R - 4 ) value A(a,b)@,as suggested by Simha.26 This asymmetry factor is 2.5 could indicate that a small amount of solvent is incorporated. for spheres and increases for asymmetric particles. To estimate Upon addition of COP-2, a systematic, although moderate, inthe volume of a PD2 complex, we take V(drop1et) = ( 4 / 3 ) ~ r crement in @ is observed, which tends to level off at higher R. ( d r ~ p l e t ) where ~, r(drop1et) = 106 A, and find V(PD2) = 2VThis trend agrees with the observation that the initial decrement (droplet) + V(C0P-3). V(C0P-3) has to be calculated from the of the diffusion coefficient decreases for higher R. In view of radius of gyration of the PI block, Le., Rg = 61 A. The axial ratio the proposed formation of ’core-shell” complexes in these systems, ( a / b )can be obtained from A(a,b) in the case of prolate ellipsoids one estimates that r(core shell) = r(dro~let)l@(B-)/Q,(R~)}l/~ by having resource to eq 12, valid for all ( a / b ) ratios? = 135 A for the largest R (=B& This result agrees reasonably with the estimate obtained from the diffusion coefficient; Le., at R = 2.19 one finds r(coreshel1) = 155 A. It is interesting that y(a2 + b2) 3ab2 the initial direct proportionality of @ and 92 can be interpreted quantitatively as the sum of the nanodroplet and the actual copolymer volume fractions at a particular R. Assuming that the volume occupied by each PI block equals a sphere determined by 3y(a2 + b2)J ’ 5 ~ 6 ~ [ 2 ( y a + b )6y(a2 ~ + b2) ?(a2 62)J the radius of gyration R,, one calculates from the linear term in (12) q 10 R,(COP-2) = 81 A; this value agrees well with the theoretical estimate R = 80 A.2’ here a, @, y, and, b are functions of a and 6, defined (in a Contrary to Cob-2 the increment of @ with R is much larger somewhat different notation) in Jeffery’s paper.27 Combining for COP-3 (see Figure 6). This cannot be understood from the the axial ratio ( 4 6 )with the ellipsoidal PD2volume of (4/3)rabz, “core-shell” model. Instead we interpret the data in line with the absolute values for a and 6 can be derived. In an analogous way (0.0050 f 0.0006)R2 (10)
-
]+L+ +
(24) Bedeeux, D. J. Colloid lntcrface Sci. 1987, 118. 80. (25) Sait6, N.J. Phys. Soc. Jpn. 19% 5, 4; 1952, 7, 447.
(26) Simha, R. J . Phys. Chem. 1940, 44, 25. (27) Jeffery, G. B. Proc. R. Soc. London 1923, AIO2, 163.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5995
Polymers in Complex Fluids TABLE V: !%minxes, P and b (A), Derived from Viscosity (q), and Diffusion Coefficients of Prolate EUipaoids, D(complex), Calculated with Eqs 5 and 6. Elupmid Represents the Proposed NadropletCOP-3 Complexes at 298 K
D(complex)/ lo-" m2 s-I %(COP-3) 0.200 0.300 0.466 0.800 1 .ooo
1.133
complex
o
PDZ PDZ PD2 P2D2 P2D2 P,D2
279 283 276 349 361 455
b 96.8 96.1 97.2 90.2 88.6 82.0
from n 1.77 1.77 1.78 1.62 1.60 1.44
aeom model" 1.92 1.92 1.92 1.72 1.72 1.56
"See also Table 111.
a and 6 parameters and (with eqs 5 and 6) diffusion coefficients of the anticipated complexes can be obtained (see Table V). Figure 4 shows D as predicted from the PFGSE NMR experiments plotted as a function of R. These predicted values (denoted as D+) are derived by inserting the diffusion coefficients of the complexes (derived via 7) into eqs 4a-c. It is seen that the results collected from viscosity data are in satisfactory agreement with the geometrical model and diffusion data of the proposed complexes. 3. Electrical Conductivity. The copolymer-free W/O microemulsion has the particular property of being electrically conductive.2s The surfactant AOT is a strong electrolyte of which a considerable portion is dissociated in contact with the water pool. Due to the accumulation of the surfactant molecules in the W/O interface, a semidiffuse electrical double layer is formed. Brownian motion of the nanodroplets and their frequent collisions result in pronounced charge fluctuations between the nanodroplets, i.e., cations and/or surfactant anions may be exchanged between the nanodroplets, leading to an electric conductivity, uo, due to the migration of charged nanodroplets in the electric field. This property can be utilized to probe changes in the conformational structure and mobility of copolymer-nanodroplet complexes upon addition of copolymers to the microemulsion. Conductivity experiments in these systems showed that addition of copolymer descreases uo and that the different conductive patterns reflect different structures of copolymer-nanodroplet complexes. As shown in Figure 7, "core-shell" complexes forming COP-2 has a very small effect, while "dimeric" complex forming COP-3 produces a large decrease of bo. In an earlier study,2 the initial decrement in the conductivity in COP3antaining microemulsions was interpreted only in terms of the decrement of "free" nanodroplets. In the present investigation, the contributions of the nanodroplets and of the proposed complexes will be taken into account. Thus for moderate COP-2 concentrations (3I l), it is assumed that mainly 1 :1 copolymer-nanodroplet "core-shell" complexes (PD) are formed. On the basis of the same physical reasoning as discussed earlier,28one may expect that the same charging mechanism is operative as for nanodroplets. Hence, one expects a specific conductivity u = 2auF[D] + 2a'u'F[PD] (13) where a,a', u, u', [D], and [PD] are the degrees of dissociation, the mean electrochemical mobilities, the equilibrium nanodroplet, and "core-shell" complex concentrations at given 3.F is the Faraday constant. In view of the equilibrium position, nanodroplet and "core-shell" complex concentrations are assumed to be direct proportional to the weighed-in amount of copolymer per nanodroplet, R,Le., due to the mass balance [D] = ( 1 - R)[Do] and [PD] = %[Do], where [Do] denotes the nanodroplet concentration in the copolymer-free microemulsion. If we approximately assume a' = a,we obtain u = 2auF[Do](l - R(l - u'/u)) = uo{l - R[1 - D(PD)/D(droplet)]) (14) (28) Eicke, H.-F.; Borkovec, M.;Das Gupta, B.J . Phys. Chrm. 1989, 93, 314.
2 i 7. Plots of the relative conductivity,u/u@ in copolymer containing microemulsions, as a function of 73 at 298 K. Experimental results: (0) COP-2; ( 0 )COP-3. Theoretical results as discussed in the text: ( 0 ) F
COP-2 (q15); (B) COP-3 (q17); (A, +) COP-3 (q18).
On the right-hand side of eq 14, the mean electrochemical mobilities are replaced by the selfdiffusion coefficients,and uodenotes the conductivity of the copolymer-free microemulsion. In view of eq 14, which corresponds to a "two-state" model, the results obtained from the PFGSE NMR experiments in COP-2-containing microemulsions can be introduced straight away, because the second factor of the right-hand side of eq 14 should be equal to the experimental ratio Dexp(R)/Dexp(R=O). Thus eq 14 becomes a/uo
= 4xp(R)/4xp(R=O)
(15)
This equality must hold for all R values. u/uo determined according to eq 15 is shown in Figure 7. In view of the simple assumptions a very satisfactory agreement is obtained for the directly and indirectly R dependence of u/uW As amply discussed, COP-3 forms with nanodroplets in the range 0 < R I 0.5, so-called "dimers". Such dimer formation also reduces the electric conductivity. A theoretical conductivity model predicts u/uo = 1 - R(2 - [a'u'/au]) = 1 - RI2 - [a'D(PD,)/aD(dropIet)]) (16) Assuming a'(PD2) = a(droplet) and introducing eq 4a, one may write ./go
= (1 - R ) 4 x , ( ~ ) / 4 x p ( ~ = o )
(17)
Comparable considerations for the equilibria given in eqs 3b and 3c lead to eq 18, which is expected to hold for all R values larger than 0.5. For theoretical comparison, however, it is noted that for the term D,,,(W) in eq 18, for equilibrium 3b (0.5 < R S l), eq 4b, and for equilibrium 3c (1 < R I1S ) , eq 4c has to be considered. u/.o
= ~exp(~)/24xp(R=O)
(18)
Also here it is assumed that the degree of dissociation of the proposed complexes is equal to that of the nanodroplets. In eq 17, the term (1 - R ) and in eq 18 the factor 2 have been introduced to compensate for the fact that Dwpis a normalized weighed number-averaged quantity, whereas u is not. In Figure 7, the u/uo values calculated with eqs 17 and 18 are presented. For equilibrium 3a, an acceptable agreement is obtained, which quantitatively confirms the formation and (reduced) mobility of the dimeric PD2 complexes. The agreement could be improved by realizing that the ratio (&/a)will most likely have a value between 1 and 2. The latter value follows from the fact that the PD2
5996
J . Phys. Chem. 1991, 95, 5996-6000
contains two nanodroplets. Closer inspection of the experimentally and theoretically derived data shows that agreement is obtained with a'/& = 1.4: Le., charge transfer due to collisions with PD2 dimers may be more inhibited by the geometric structure of the "dimer", and the fact that the dissociation of charges may lead to a dipolar PD2complex, which cannot contribute to the electrical conductivity. For R > 0.5, the calculated u/uo ratios become increasingly larger than the experimental values and seem to reach an asymptotic value for increasing 93. To emphasize this point, in Figure 7 also values have been plotted calculated by eq 18, and the experimentally determined diffusion coefficients obtained for 93 > 1.5. The above-considered two reasons would also explain the increasing discrepancy between theory and experiment at the higher 91 (>OS) values. It is thought that the experimentally observed drastic decrement in the electrical conductivity is due to the fact that the portion of nanodroplets and dimers become negligibly small due to the formation of larger, most likely, branched complexes with an inherent lower mobility.
Summarizing, the diffusion coefficients of complexes formed by the ABA triblock copolymers and microemulsion nanodroplets as probed by the IH PFGSE NMR technique are in line with the properties of the two copolymers. The diffusional features are nicely confirmed by viscosity and conductivity measurements of such polymeric solutions with complex fluids.
Acknowledgment. We are grateful to Professor H. G. Hertz, Institute for Physical and Electrochemistry, University of Karlsruhe, FRG, for his permission to use the spin-echo N M R equipment. R. Struis thanks, in particular, Dr. M. Holz for his hospitality, help, and support. He also thanks Dr. G. Xu for providing him with the copolymers and Dr. C. Quellet, Dr. G. Xu, and Y. Hauger for the viscosity and conductivity data. This work is part of the NFP19-project of the Swiss National Science Foundation and of KWF (Kommision zur FBrderung der Wissenschaftlichen Forschung), project number 1715.1. Registry No. (COP-2)(COP-3) (block copolymer), 122269-49-2.
Photoreduction of Alkylmethylviologens in Dioctadecyidimethyiammonium Chloride Veskles: Combined Effects of the Alkyimethylvioiogen Chain Length and the Additlon of Cholesterol To Control the Net Photoreduction Yield Masato Sakaguchit and Larry Kevan* Department of Chemistry, University of Houston, Houston, Texas 77204-5641 (Received: December 3, 1990; In Final Form: March 6, 1991)
Electron spin resonance spectroscopy has been used to detect the photoreduction yields of four alkylmethylviologens (AV2+) in rapidly frozen dicctadecyldimethylammoniumchloride (DODAC) vesicles containing concentrations of cholesterol from 0 to 33 mol W. The abundant radical is photoreduced alkylmethylviologencation radical (AV+) together with a lesser amount of an alkyl radical (DAC) from DODAC formed by photoconversion from AV+. The DAC intensity decreases with increasing cholesterol concentration even though electron spin echo modulation data shows that AV+ is in a less hydrated environment with increasing cholesterol concentration which should promote DAC formation. This is explained by high mole percentages of cholesterol increasing the distance between AV+ and the DODAC alkyl chains which decreases the DAC yield. The AV+ yield increases with alkyl chain length but decreases with increasing cholesterol. Analysis shows that the alkyl chain length effect is stronger than the cholesterol effect. This also holds for the total photoreduction yield. Although the alkyl chain length predominantly controls the photoreduction yield, it is shown that cholesterol addition can tune the magnitude of this effect over a narrow range.
Introduction
Organized molecular assemblies, such as unilamellar vesicles formed from phospholipids, enable molecular compartmentalization to be Vesicle-compartmentalized, photoionizable molecules have been used as model systems for artificial photosynthesis to achieve net photoinduced charge ~eparation.~ Modification of the vesicle interface and interior structure is one approach to control the net photoionization or photoreduction efficiency of a solubilized molecule. Recent work shows that such control factors include the phospholipid headgroup type: the alkyl chain length of the phosph~lipid,~ the interface charge of the and the incorporation of surface-active additives such as salts? alcohols? and cholesterol.'*12 A related approach to control the net photoefficiency is to add variable-length alkyl chains to a photoactive molecule.13 This is a control method for the location of the photoactive moiety relative to the vesicle interface. Electron spin echo modulation (ESEM), which measures weak electron-nuclear dipolar (hence distance) interactions, has been used successfully to monitor the degree of interface penetration of a photoactive molecule with variable-length alkyl chains." ESEM requires frozen solutions 'On leave from lchimura Gakuen Junior College, Inuyama, Japan.
so that the dipolar interaction is not averaged to zero. Thus, electron spin resonance (ESR) can be effectively used with ESEM measurements to monitor the net photoradical yields in rapidly frozen vesicle solutions.*J3J4 In the present study the combined effect of alkyl chain length (1) Fendler, J. H. Membrane Mimetic Chemistry; Wiley: New York, 1982. (2) Kalyonasundaram, K. Photochemistry In Microheterogeneous Sysrems; Academic: New York, 1987. (3) Sec for example: (a) Chamupathi, V . 0.; Tollin, G. fhotochem. fhotobiol. 1989,19,61. (b) Youn, H. C.; Baral, S.; Fendler, J. H. J . fhys. Chem. 1988,92.6320. (c) Patterson, B. C.; Thompson, D. H.; Hurst, J. K. J. Am. Chem. Soc. )1988,110,3656. (d) Kevan, L. In fhoroinduced Electron Transfer Part B Fox, M. A., Chanon, M., Eds.; Elsevier: Amsterdam, 1988; pp 329-384. (4) Hiff, T.; Kevan, L. J . fhys. Chem. 1988, 82, 2069. (5) Hiff, T.; Kevan, L. J . fhys. Chem. 1988, 92, 3982. (6) Li, A. S. W.; Kevan, L. J . Am. Chem. Soc. 1983, 105, 5752. (7) Lanot, M. P.; Kevan, L. J . Phys. Chem. 1989, 93, 998. (8) Sakaguchi, M.; Hu, M.; Kevan, L. J . fhys. Chem. 1990. 91, 870. (9) Hiff, T.; Kevan, L. J . fhys. Chem. 1989, 93, 3227. (10) Hiromitisu. 1.; Kevan, I. J . Am. Chem. Soc. 1987, 109, 4501. ( 1 I ) Hiff, T.; Kevan, L. J . fhys. Chem. 1989, 93, 1572. (12) Lanot. M. P.; Kevan, L. J . Phys. Chem. 1989, 93, 5280. (13) Colaneri, M. J.; Kevan, L.; Thompson, D. H. P.; Hurst, J. K. J . Phys. Chem. 1987, 91,4072. (14) Sakaguchi, M.: Kevan, L. J . Phys. Chem. 1989, 93,6039.
0022-365419 112095-5996$02.50/0 0 1991 American Chemical Society
