J. Phys. Chem. 1986, 90, 5441-5448
+
done with the system 0.03 m CTAB 0.04 and 0.08 m K(Br:Cl). The results for R(90) and Dappare plotted against the bromide molar fraction XB,in Figure 10, a and b. At 0.04 m both systems have small aggregates and the difference in all properties is small and monotonic from X,, = 0 to 1. At 0.08 m K(Br:Cl), R(90) and Dappare almost constant up to XB,= 0.6. At higher bromide content the growth is reflected in both properties. The parameter p 2 / r 2 *is related to the polydispersity of the system.” It has been mentioned that the polydispersity of spherical aggregates is smaller than for large cylinders.” From our results, we notice an increase in p 2 / r ? (Figure 1Oc) in the same range of concentration where the micellar growth is observed from R(90) and Dapp.For this system, X,, = 0.6 corresponds to an effective bromide concentration of 0.05 m. This value is the same as the growth limit observed when only KBr is added. (See Figure 7). This suggests that the micellar growth of CTAB aggregates is not dependent on the ionic strength but mostly on the bromide content of the mixed added salt K(Br:Cl). From this we suggest that if the bromide content of CTAB solutions is high enough to be over the growth limit, extra addition of chloride ions will have almost no effect on the size of the aggregates. If the system is initially under the growth limit, extra addition of chloride ions will result in an exchange of bromide for chloride counterions. We mentioned that the counterion binding of Br is higher for large aggregates. Taking 0.81 at 0.03 m and 0.9 at 0.3 m CTAB, we estimated that the binding constant increases by a factor of 2 when the aggregates become large. This is in agreement with the results of Porte and A ~ p e l lwho , ~ suggested that the binding constant of bromide ions is larger for rod-shaped than for spherical aggregates. Over the growth limit, the binding constant of Br increases and the effect of C1 is much smaller.
5441
This explains why Porte and Appel17observed almost no change of aggregate size for 0.006 M CTAB 0.2 M NaBr upon addition of 0.02 M NaC1. The bromide content of their system was well over the growth limit. Our hypothesis also explains why the CTAB aggregates do not grow for 0.03 m CTAB upon addition of KC1, since the bromide content is well below the growth limit.
+
Conclusions From neutron and light scattering measurements, we showed that a change in the interparticle interactions occurs prior to the micellar growth. We suggest that this change is related to an increase of the counterion binding. For CTAB without added salt, this increase in p would be about 0.08, in good agreement with heat capacity results8 This increase in counterion binding for CTAB > 0.03 m seems to occur at a constant free bromide concentration around 0.03 m. When KCI (up to 0.1 m ) is added to 0.03 m CTAB, the aggregates show no significant growth. When a mixture of KBr and KCl is added to CTAB solutions, the growth limit seems to be dependent only on the bromide concentration. The hypothesis we made in this paper holds for the systems and the range of concentrations we studied. We do not generalize our conclusions for every surfactant and added salt, but we feel it may give a new insight on the phenomena associated with micellar growth. Acknowledgment. F.Q. thanks the Conseil National de la Recherche en Science et en Genie and the Fonds Canadien de 1’Aide a la Recherche for financial support; L.J.M. thanks the National Science Foundation (Grant CHE-8308362). Registry No. CTAB, 57-09-0; KBr, 1910-42-5;KCI, 7447-40-7.
Correlation between Molecular Reorientation Dynamics of Ionic Probes in Pdlar Fluids and Dielectric Friction by Picosecond Modulation Spectroscopy Eva F. Gudgin Templeton and Geraldine A. Kenney-Wallace* Lash Miller Laboratories, University of Toronto, Toronto M5S 1A1, Canada (Received: December 2, 1985; In Final Form: March 20, 1986)
The dye molecules resorufin, thionine, and cresyl violet are studied in amides, alcohols, and water-alcohol binary systems in order to investigate the correlations between orientational relaxation times ( T , , ~ ) and properties of the single-solvent or binary systems. A sequence of normal and substituted alcohols, dimethyl sulfoxide, formamide, N-methylformamide, and dimethylformamide has been investigated. While good agreement with hydrodynamic-based theories is seen for the pure alcohol systems, the binary propanol-H20 systems show a surprising curvilinear dependence of T , , ~vs. 7 beyond the realms of any expectations in simple hydrodynamic responses, as has been shown previously. If a dielectric friction model is applied, then these curvilinear profiles are predicted at least qualitatively. The successful ingredients of such a model are discussed and its limitations assessed for its application to polar fluids, given the poor agreement with the relaxation times or trends in the dimethyl sulfoxide and amide solvents.
Introduction An understanding of the mechanisms responsible for rotational relaxation of molecules in liquid solution is required for a complete description of solution-phase reaction dynamics. Molecular interactions and solvent motion influence the shape of the potential energy surface, and reaction rates can be enhanced or impeded by molecular motions at the barrier crossing which might involve conformational or configurational changes as part of the reactive sequence. For small nonpolar molecules in noninteracting solutions, often reorientational motion can be adequately described with various modifications of the simple Debye-Stokes-Einstein (DSE) equation,’ which relates rotational reorientation time to 0022-3654/86/2090-544l$01.5d/0
the macroscopic solvent viscosity. These modifications include considerations such as changing boundary conditions from stick to slip,2 relative solvent-solute size,3 free space in the solvent structure causing deviations from continuum behavior,’” and ~~~
(1) (a) A good review of a number of hydrodynamic models is presented in: Dote, J. L. Kivelson, D.; Schwartz, R. N. J . Phys. Chem., 1981,85, 2169.
(b) Current theory, experiment and simulation approaches are discussed by a number of authors in: Barnes, A. J., Orville-Thomas, W., Yarwocd, J., Eds. Molecular Liquids: Dynamics and Interactions; (D. Reidel: Dordrecht, 1984). (2) Hu, C.-M.; Zwanzig, R. J . Chem. Phys. 1974, 60, 4354. (3) Gierer, A.; Wirtz, K. Z . Naturforsch. A , 1953, 8, 532.
0 1986 American Chemical Society
5442
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986
-0
a:o ' 0
Gudgin Templeton and Kenney-Wallace D I F F E RE NC E F R E 0 U ENC Y MODULATION S PECTR 0 SCOPY w, I w p ( p u m p =probe, visible) dye pulse train
w
my !
TS
! I
=bs
I
I I
Figure 1. Structures of the resorufin anion and the thionine and cresyl violet cations.
deviations of the solute from spherical shape.4 When such simple hydrodynamic models are applied to systems in which strong intermolecular interactions are possible, such as a charged solute in a polar solvent, it is to be expected that different behavior will be observed; however, much of the literature on such systems includes only application of hydrodynamic models, with deviations from predicted behavior explained in terms of changing boundary conditions. Hydrodynamic models actually have limited predictive power in microscopic terms; a description in terms of molecular parameters is required if we are to truly understand reorientational dynamics. While in some small-molecule experiments in simple liquids and in computer simulations there is elear evidence that a molecular dynamics approach is required to explain the early time behavior of reorientational and angular velocity correlation functions,Ib larger molecules moving in small molecule solvents over longer times exhibit relaxations that have both microscopic and hydrodynamic contribution^.^ We have previously observed that the transitory structural features experienced by a probe molecule in a pure liquid or binary system must depend on the magnitude of site-specific solutesolvent interactions in comparison to bulk solvent interactions. Relative length scales and time scales become important, because the correlation times characterizing the interactions can determine whether or not the probe environment appears as a bulk continuum, or a short range structure, or somewhere in between. A correlation was observed between the rotational reorientation time T~~~and dielectric relaxation time T~ in hydrogen-bonding solvents,5 where T~ is a relaxation time characteristic of the solvent Hbonding network and reflects the dynamics over an intermediate length scale. Some of the questions that remain to be answered in order to formulate a molecular model are as follows: What is the nature of the mechanism responsible for the correlation? Do specific solute-solvent interactions play a role? Will positively and negatively charged probes in general behave differently in similar solvents? Earlier work on the solvent torque model predicted that such differences would be seen.6 These questions have been pursued in this work by comparing the reorientational behavior of three probe molecules, resorufin, thionine, and cresyl violet (structures shown in Figure l ) , which possess rigid planar ring geometries and either a single positive or negative charge. The results are analyzed in terms of the dielectric friction mode1,7,* which can predict qualitatively, and in some cases serniquantitatively, the significant deviations observed from DSE behavior. The limitations of the theory in terms of its applicability to real systems are discussed. Experimental Section
The experimental apparatus used for these picosecond absorption recovery experiments was a synchronously mode-locked (4) Perrin, F. J . Phys. Radiat. 1934, 5 , 497. (5) Gudgin Templeton, E. F.; Quitevis, E. L.; Kenney-Wallace, G. A. J . Phys. Chem. 1985, 89, 3238. ( 6 ) Spears, K. G.; Cramer, L. E. Chem. Phys. 1978, 30, 1. (7) Madden, P.; Kivelson, D. J . Phys. Chem. 1982,86, 4244. (8) Hubbard, J. B.; Wolynes, P. G. J . Chem. Phys. 1978, 69, 998.
4 760 MHz
Figure 2. DFMS apparatus as described in text.
l
o
1 1 '
0 0
p
I
100
I 200
t
I
300
I 400
1
TIME / ps Figure 3. Natural logarithm of the anisotropy decay for CV' in I-PrOH. The residuals to the single-exponential fit are inset and are seen to be random. This decay yielded T~,,,= 461 ps.
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dye laser pumped by a continuous-wave mode-locked argon ion laser (Spectra Physics), from which we obtain pulses of 1 ps in duration at 82-MHz repetition rate and of 70-120-mW average power over the rhodamine 6G tuning range of 580-620 nm. The optical technique employed to measure the polarization anisotropy induced in these strongly absorbing dye solutions is based on difference frequency, multiple modulation spectroscopy (DFMS), which has been described in detail e l ~ e w h e r e and , ~ so only the salient features of the approach will be given here. The So S, visible absorption of the dyes is excited by an intense and polarized pump pulse such that the polarization selective depletion of the ground state creates an anisotropy in the ground-state orientational distribution of the molecules. The change in transmission (AT) of a weak probe pulse passing through the sample monitors the depletion and recovery of the absorption a t polarizations parallel, perpendicular, and at 54.7' to that of the incident pump pulse. The absorption recovery signal on the probe beam is approximately 0.1% of the total probe intensity and the sensitivity of the DFMS experiment is accomplished by modulating the pump (wl) and probe beams (a2)at 10.240 and 15.000 MHz, respectively, using acoustooptic modulators (AOM). Figure 2 illustrates the general experimental layout in which the pump and probe beams (wl = w 2 ) are created by splitting the output of the dye laser with a 955% pellicle beam splitter. The
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(9) Quitevis, E. L.; Gudgin Templeton, E. F.; Kenney-Wallace,G. A. Appl. Optics 1985, 24, 318. (IO) Weast, R. C., Ed. CRC Handbook of Chemistry and Physics, 56th ed.; CRC Press: Cleveland, OH, 1976. Dean, J. A,, Ed. Lunge's Handbook of Chemistry, 12th ed.; McGraw-Hill: New York, 1979. (11) Timmermans, J. The Physicochemical Constants of Binary Systems in Concentrated Solutions; Interscience: New York, 1960; Vol. 4. (12) Quitevis, E. L.; Gudgin Templeton, E. F.; Kenney-Wallace, G. A. Proceedings of the Society for Optical and Quantum Electronics Lasers '84; Corcoran, K. M., Sullivan, D. M., Stwalley, W. C., Eds.; STS Press: VA, 1985; p 153.
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986 5443
Molecular Reorientation Dynamics of Ionic Probes TABLE I: Picosecond Rotational Reorientation Times of Resorufin at 298 K
solvent' H20 MeOH EtOH 1-PrOH 1-BuOH 2-PrOH 2-Me-I-PrOH DMF NMF HCONH2 Me2S0
dCPb
Tr0t/PSC
Trorf't
0.95 0.55 1.10 1.95 2.6 2.5 3.91 0.80 1.65 3.30 2.00
55 f 10d 78 f 14 2 1 6 f 45 361 f 47 434 f 69 472 f 70 655 f 63 54 f 14 210 f 2Sd 317 f 34 79 f 22d
58 f 10 140 f 30 200 f 40 190 f 20 170 f 10 190 f 30 170 f 10 68 f 20 130 f 10 96 f 5 40 f 5
solvent MeOH EtOH 1-PrOH 1-BuOH 1-PeOH 2-PrOH 2-Me-1-PrOH HCONH2
0.10 0.15 0.25 0.35 0.65 1.oo
= 0.00
0.95 2.00 2.45 2.70 2.70 2.30 1.95
55 f 10 77 f 20 140 f 20 156 f 20 252 f 20 280 f 20 361 f 47
58 f 39 f 57 f 58 f 93 120 f 190 f
*
0.25
0.35 0.65 1.oo
IO 10 8 7 8 10 20
T*,t/PS
0.55 1.10 1.95 2.6 2.5 3.9 3.4 3.30
81 f 7 225 f 17 385 f 28 573 f 60 478 f 63 915 f 100 710 f 60 398 f 52
rmtf't
150 f 200 f 200 f 220 f 190 f 230 f 210 f 120 f
10 20 IO 20 30 30 20 20
2.70 2.70 2.3 1.95
110 f 165 f 247 f 385 f
15 35 38 28
41 f 61 f 110 f 200 f
5 15 10 10
TABLE 111: Picosecond Rotational Reorientation Times of Cresyl Violet at 298 K
"In all tables, the following abbreviations are used: MeOH = methanol; EtOH = ethanol; PrOH = propanol; BuOH = butanol; PeOH = pentanol; Me = methyl; DMF = dimethylformamide;NMF = N-methylformamide; Me2S0 = dimethyl sulfoxide. bViscosities from ref 10 and 11. cValues from ref 5, unless otherwise noted. dThis work. Values for H 2 0 and MetSO differ slightly from those reported in ref 5 but are within the estimated error.
absorption recovery signal is monitored at the difference frequency of 4.760 MHz with a fast photomultiplier (PMT) and megahertz lock-in amplifier (LIA) as detector for the phase-sensitive signal. The reference signal for the LIA is derived from the AOM's, and full details of the electronics and triggering circuits for DFMS are given in ref 9. A M I N C 11-23 computer also controls the optical delay of the probe beam (w2) via a precision motor-driven translation stage (Ealing). A typical curve illustrating the time dependence of the polarization anisotropy R ( t ) is shown in Figure 3 together with the random residuals from an analysis of the data indicating a good fit for a single-exponential decay of R(t) (defined So) time in eq 1, where T~~~ is the ground-state recovery (S, and T , , ~ the rotational reorientation time5).
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N t ) = AT,[- ATL a exP(-t/Tgsr) exP(-t/rro,)
SfCP
Binary PrOH-H20 System x~.ROH =
Binary 1-PrOH-H20 Systems xI.prOH
TABLE 11: Picosecond Rotational Reorientation Times of Thionine at 298 K
solvent H2O MeOH EtOH I-PrOH 1-BuOH DMF NMF HCONH2 MezSO2
VICP 0.95 0.55
1.10 1.95 2.6 0.80 1.65 3.30 2.00
rm,/Qs
7,otJn
102 f 10 110 f 10" 210f20" 470 f 20 620 f 40" 150b 325 f 20' 630 f 80' 434 f 30
110 f 200 f 190f 240 f 240 f 190 200 f 190 f 220 f
10 20 20 10 10
110 f 90f 82 f 74 f 97 f 150 f 240 f
10 15 10 8 20 IO 10
10 30 10
Binary PrOH-H20 System xk.pro~=
0.00
0.10
0.15 0.25 0.35 0.65 1.oo
0.95 2.00 2.45 2.70 2.70 2.30 1.95
102 f 10 180 f 30 202 f 23 2 0 0 f 22 262 f 50 354 f 20 470 f 20
" X = 610 nm, ref 12 in comparison to X = 590 nm for these data. bReference 13e. CThiswork and ref 13e.
El
(1)
I-PeOH
Samples were prepared from dyes whose purity was checked via silica gel thin-layer chromatography, and resorufin (sodium salt, Aldrich), thionine (acetate salt, Aldrich), and cresyl violet (perchlorate salt, Exciton) all gave a single spot upon TLC analysis. The alcohols and amide solvents used were distilled in glass or spectroscopic grade, and deionized, distilled water was used throughout in the mixtures. Solutions were prepared to have an absorbance
