5878
J. Phys. Chem. B 2007, 111, 5878-5884
Rotational Diffusion of Organic Solutes in Surfactant-Block Copolymer Micelles: Role of Electrostatic Interactions and Micellar Hydration K. S. Mali, G. B. Dutt,* and T. Mukherjee Radiation & Photochemistry DiVision, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India ReceiVed: December 11, 2006; In Final Form: March 26, 2007
Rotational diffusion of a cationic solute rhodamine 110 and a neutral solute 2,5-dimethyl-1,4-dioxo-3,6diphenylpyrrolo[3,4-c]pyrrole, DMDPP has been examined in the surfactant-block copolymer system of sodium dodecyl sulfate (SDS) and poly(ethylene oxide)20-poly(propylene oxide)70-poly(ethylene oxide)20 (P123). In this study, the mole ratio of SDS to P123 was varied from 0 to 5 in steps of one unit, to investigate the role of electrostatic interactions and micellar hydration on solute rotation. It has been noticed that there is a significant enhancement in the average reorientation time of rhodamine 110, when [SDS]/[P123] increased from 0 to 1. This has been rationalized on the basis of migration of rhodamine 110 from the interfacial region of P123 micelles to the palisade layer (corona region) due to the electrostatic interaction with negatively charged head groups of SDS, whose tails are embedded in the polypropylene oxide core. Further increase in the mole ratio of SDS to P123 has resulted in only a marginal decrease in the average reorientation time of rhodamine 110, which is probably due to the solute molecule experiencing a microenvironment similar to the interfacial region of SDS micelles. In contrast, a gradual decrease has been observed in the average reorientation time of DMDPP with [SDS]/[P123], which is due to the increase in hydration levels in the palisade layer (corona region) of the micelle. These explanations are consistent with the structure of the SDS-P123 micellar system that has been deduced from neutron scattering and viscosity measurements recently.
1. Introduction In recent times, numerous investigations1-14 have been undertaken to explore surfactant-block copolymer interactions since they have a profound influence on the self-assembly behavior of the copolymers. In a majority of the studies, PEOPPO-PEO triblock copolymers, where PEO and PPO represent repetitive units of ethylene oxide and propylene oxide, respectively, have been employed in conjunction with ionic surfactants such as cetyltrimethylammonium chloride (CTAC) and sodium dodecyl sulfate (SDS). One of the important findings from these studies is that an increase in the surfactant concentration gradually suppresses the formation of copolymer micelles. Recent investigations carried out by Jansson et al.12,13 with copolymers P123 (PEO20-PPO70-PEO20) and F127 (PEO97PPO69-PEO97) in presence of SDS and CTAC reveal that at low surfactant to copolymer mole ratio, a few ionic surfactant molecules associate with copolymer micelles and form a larger complex. In contrast, at high surfactant to copolymer mole ratio, the copolymer micelles are broken up and small surfactant micelles are formed with attachment of a few copolymer molecules. However, in the intermediate region, where the surfactant to copolymer mole ratio is in the range of 1-15, the scenario is somewhat conflicting. Jansson et al.12 report the existence of two types of copolymer-surfactant complexes, whereas Ganguly et al.14 show the presence of only one type of micellar aggregates. The latter have also characterized the SDS-P123 system using small-angle neutron scattering (SANS) and viscosity measurements.14 According to their findings, in the region of 1-5 mole ratio of SDS to P123, the copolymer forms mixed micelles with SDS, and the aggregation number * To whom correspondence should be addressed. E-mail: gbdutt@ barc.gov.in.
of these mixed micelles decreases with an increase in the mole ratio. However, the volume fraction of the micelles increases significantly in the presence of SDS because of an increase in the degree of hydration of the micelles in the corona region. It has been suggested that the increased hydration of the micelles is achieved by stretching of the PEO blocks in the corona region in the presence of SDS. In these mixed micelles, it has been assumed that the SDS molecules are dissolved in the core of P123 micelles and their head groups are in the corona region. This assumption has been made on the basis that the interaction between SDS and PPO units is significantly stronger than that between SDS and PEO units1 and also SANS contrast variation study.14 In essence, addition of SDS to P123 micelles in the mole ratio of 0 to 5, decreases the size, increases micellar hydration, and also facilitates the presence of charged headgroups of SDS in the corona region of the micelles. Of late, our efforts have been directed toward understanding dynamical processes such as rotational diffusion15-17 and photoisomerization18-20 in polymorphic environments of the block copolymer P123 by measuring the fluorescence anisotropy decays, lifetimes, and quantum yields of organic solutes solubilized in them. Other groups have also carried out somewhat similar studies in different block copolymer systems.21-25 According to the findings of our investigations, rotational diffusion of the solute molecules is sensitive to unimer-micelle transition as they experience different environments in both these phases of the block copolymer.15 In contrast, it has become evident that such measurements carried out with hydrophobic probes do not discern sol-gel transition, since the probes are solubilized in the corona region of the micelles in both the phases, which is not affected upon gelation.16 Rotational diffusion measurements carried out with an ionic solute, however, indicate that sol-gel transition has little or no effect
10.1021/jp068490q CCC: $37.00 © 2007 American Chemical Society Published on Web 05/10/2007
Surfactant-Block Copolymer Micelles
J. Phys. Chem. B, Vol. 111, No. 21, 2007 5879
Figure 2. Variation of steady-state anisotropy of rhodamine 110 (filled circles) and DMDPP (open circles) with mole ratio of SDS to P123. The lines passing through the data points are drawn as visual aid.
Figure 1. Molecular structures of the solutes used in the study.
on solute rotation even when it is located in the interfacial region of the micelles.17 This is because micelle-micelle entanglement, which is responsible for gelation, persists even in the micellar solution phase such that the friction on the rotating solute molecule is not decreased in a drastic manner. In case of reverse micelles, it has been observed that an enhancement in the water content facilitates solute rotation, which has been rationalized on the basis of migration of the solute from the hydrated polyethylene oxide region to polyethylene oxide-water interface within the core.17 So far, we have examined the influence of unimer-micelle transition, sol-gel transition, and also influence of water content on the rotational diffusion of neutral and ionic solutes by carrying out investigations in polymorphic environments of a block copolymer. Now, we wish to investigate the influence of electrostatic interactions and micellar hydration on solute rotation. For this purpose, we have chosen the abovementioned system of SDS-P123 and examined the rotational diffusion of a cationic solute rhodamine 110 and a neutral solute 2,5-dimethyl-1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole, DMDPP. Figure 1 gives the molecular structures of the solutes used in this study. From our earlier work,15-17 it has become evident that rhodamine 110 is solubilized in the interfacial region, whereas DMDPP is located in the palisade layer or the corona region. Thus, it would be interesting to find out the influence of added SDS on the rotational diffusion of both these solutes in P123 micelles.
were collected parallel I|(t), perpendicular I⊥(t), and at 54.7° I(t) orientations of the emission polarizer with respect to the polarization of the excitation radiation. The emission in all the three cases was monitored at 550 nm. A cut off filter OG 515 was also placed before the collection lens of the emission monochromator to eliminate the scattered light. For fluorescence lifetime (τf) measurements 10 000 peak counts were collected and in case of anisotropy measurements, 20 000 peak counts were collected for I|(t), and I⊥(t) was corrected for the polarization bias or the G-factor of the spectrometer. The decays were collected in 512 channels with a time increment of 20 or 40 ps/channel. Each measurement was repeated at least 2-3 times and the average values are reported. All the measurements were performed at 303 K and the sample temperature was maintained with the help of a thermocouple based temperature controller, which is regulated by a microprocessor (Eurotherm). The decays measured in this manner were convoluted with the instrument response function (IRF), which was measured by replacing the sample with a solution that scatters light. The full width at half-maximum of the IRF is about 50 ps. Lifetimes of rhodamine 110 and DMDPP were obtained from the measured fluorescence decays and the instrument response function, by iterative reconvolution method using Marquardt algorithm as described by Bevington.28 Likewise, the anisotropy decay parameters were obtained by simultaneous fit29,30 of parallel I|(t) and perpendicular I⊥(t) components. The criteria for a good fit were judged by statistical parameters such as the reduced χ2 being close to unity and the random distribution of the weighted residuals. Details concerning the analysis of the fluorescence and anisotropy decays have been mentioned in our earlier publication.31
2. Experimental Section The probes rhodamine 110 and DMDPP have been obtained from Exciton and Ciba Specialty Chemicals, Inc., respectively. The copolymer P123 and the surfactant SDS are from Aldrich and Gibco Life Technologies, respectively. All these chemicals are of the highest available purity and were used without further purification. Deionized water from Millipore A-10 was used in the preparation of the samples. These measurements were performed by keeping the concentration of P123 at 10 wt %, which corresponds to 17.2 mM and [SDS]/[P123] was varied from 0 to 5. Time-resolved fluorescence measurements were carried out using single-photon counting26 facility at the Tata Institute of Fundamental Research, Mumbai, and details of the system have been described elsewhere.27 In short, the frequency-doubled output of a picosecond Ti:sapphire laser (Tsunami, Spectra Physics) was used as the excitation source and the samples containing the probe rhodamine 110 and DMDPP were excited at 440 nm with a vertically polarized pulse. Fluorescence decays
3. Results The fluorescence decays of rhodamine 110 and DMDPP could be adequately described by single-exponential functions from 0 to 5 mole ratio of SDS to P123. The lifetime of rhodamine 110 in 10 wt % P123 is 4.07 ns and increases to 4.20 ns in the presence of equimolar ratio of SDS and P123. The variation in τf with further increase in the mole ratio of SDS to P123 is negligible. In contrast, the lifetime of DMDPP is more than a factor of 2 longer than that of rhodamine 110 in P123 and decreases marginally with an increase in [SDS]/[P123]. Figure 2 gives plots of steady-state anisotropy 〈r〉 versus [SDS]/[P123] for rhodamine 110 and DMDPP. It can be noticed from the figure that for rhodamine 110, the value of 〈r〉 increases from 0.052 to 0.086 as the mole ratio of SDS to P123 goes up from 0 to 1 and a further increase in [SDS]/[P123] does not result in a significant variation of 〈r〉. In contrast, the steadystate anisotropy of DMDPP decreases gradually with an increase in [SDS]/[P123]. Variation of the steady-state anisotropies as a
5880 J. Phys. Chem. B, Vol. 111, No. 21, 2007
Mali et al. TABLE 1: Fluorescence Lifetimes and Anisotropy Decay Parameters of Rhodamine 110 as a Function of [SDS]/[P123] at 303 Ka [SDS]/[P123]
τf/ns
β
τr1/ns
τr2/ns
〈τr〉b/ns
0:1 1:1 2:1 3:1 4:1 5:1
4.07 4.20 4.22 4.26 4.23 4.18
0.31 0.52 0.53 0.51 0.52 0.52
2.45 3.28 3.12 2.98 2.76 2.59
0.20 0.43 0.49 0.55 0.56 0.56
0.90 1.91 1.88 1.79 1.70 1.62
a The uncertainties on lifetimes and anisotropy decay parameters are 2% and 10%, respectively. b Calculated using eq 2.
TABLE 2: Fluorescence Lifetimes and Anisotropy Decay Parameters of DMDPP as a Function of [SDS]/[P123] at 303 Ka
Figure 3. Anisotropy decay curves of rhodamine 110 and DMDPP at 0 (open circles) and 5 (filled circles) mole ratios of SDS to P123. The smooth lines passing through the data points are the fitted ones. Notice that the anisotropy decay of rhodamine 110 is faster at lower [SDS]/ [P123]; in contrast, an opposite trend has been observed for DMDPP.
[SDS]/[P123]
τf/ns
β
τr1/ns
τr2/ns
〈τr〉b/ns
0:1 1:1 2:1 3:1 4:1 5:1
8.38 8.37 8.33 8.34 8.32 8.29
0.63 0.60 0.59 0.50 0.50 0.48
3.57 3.17 2.75 2.62 2.28 2.20
1.04 0.92 0.78 0.72 0.70 0.63
2.63 2.27 1.94 1.67 1.49 1.38
a The uncertainties on lifetimes and anisotropy decay parameters are 2% and 10%, respectively. b Calculated using eq 2.
Figure 4. Variation of average reorientation times of rhodamine 110 (filled circles) and DMDPP (open circles) with mole ratio of SDS to P123. The lines passing through the data points are drawn as visual aid. Different ordinate scales have been used for rhodamine 110 and DMDPP for the sake of clarity.
Figure 5. Plots of τr1 (filled circles) and τr2 (open circles) of rhodamine 110 vs mole ratio of SDS to P123. The lines passing through the data points are drawn as visual aid.
function of mole ratio of SDS to P123 can be used to gauge the mobilities of rhodamine 110 and DMDPP, since the changes in the respective lifetimes with [SDS]/[P123] are negligible. However, the magnitude of 〈r〉 also depends on the functional form of the time-resolved anisotropy decay curves. In view of this limitation, steady-state anisotropies have only been employed to obtain preliminary information pertinent to the rotational diffusion of the probes in this mixed micelle system. To get a better appreciation of the rotational diffusion of rhodamine 110 and DMDPP in SDS-P123 system, timeresolved anisotropy decays have been measured. The anisotropy decays of both the probes could be fit with two time constants and the functional form is given below:
r(t) ) r0[β exp(-t/τr1) + (1 - β) exp(-t/τr2)]
(1)
In the above equation, r0 is the limiting anisotropy of the solute, whose magnitude is dictated by the angle between the absorption and emission transition dipoles, τr1 and τr2 are the long and short components associated with the decay of anisotropy of the solute, respectively, and β is the percentage contribution of τr1. To compare the anisotropy decays of the probes measured at different values of [SDS]/[P123], the average reorientation time 〈τr〉 has been calculated using eq 2:
〈τr〉 ) βτr1 + (1 - β)τr2
(2)
Figure 3 displays anisotropy decays of rhodamine 110 and DMDPP measured at 0 and 5 mole ratios of SDS to P123. The interesting aspect that is to be noted from the figure is that anisotropy of rhodamine 110 decays significantly faster when [SDS]/[P123] ) 0 compared to the one at 5. On the other hand, an exactly opposite trend has been observed in case of DMDPP. The anisotropy decay parameters of rhodamine 110 and DMDPP as function of mole ratio of SDS to P123 are given in Tables 1 and 2, respectively, together with their lifetimes. Average reorientation times of rhodamine 110 and DMDPP are plotted as a function of [SDS]/[P123] in Figure 4. The variation of 〈τr〉 with [SDS]/[P123] more or less complements the steady-state anisotropy data. The sole disparity in the results obtained with the two methods is, an eighteen percent decrease in 〈τr〉 value of rhodamine 110 as the mole ratio of SDS to P123 increases from 1 to 5. In contrast, no variation has been observed in the value of 〈r〉 for rhodamine 110 in this region. To visualize how the individual components of the anisotropy decay are varying with [SDS]/[P123], τr1 and τr2 of rhodamine 110 and DMDPP have been plotted as a function of mole ratio of SDS to P123 in Figures 5 and 6, respectively. It is evident from Figure 5 that as [SDS]/[P123] increases from 1 to 5, τr1 decreases by 27%, whereas there is an enhancement in the value of τr2 by 30%. In case of DMDPP, however, both τr1 and τr2 decrease by more than 60% as the mole ratio of SDS to P123 increases from 0 to 5. 4. Discussion The results presented in the preceding section can be comprehended based on the structure of the micelles and also
Surfactant-Block Copolymer Micelles
J. Phys. Chem. B, Vol. 111, No. 21, 2007 5881 TABLE 3: Properties of SDS-P123 Micelles as a Function of Mole Ratio of SDS to P123
Figure 6. Plots of τr1 (filled circles) and τr2 (open circles) of DMDPP vs mole ratio of SDS to P123. The lines passing through the data points are drawn as visual aid.
the respective locations of the probes in SDS-P123 system. Organic solutes depending on their chemical properties such as charge and molecular structure occupy different regions of a micelle. Results from our earlier work15,16,31-33 indicate that the probe DMDPP is solubilized in palisade layer or the corona region of the block copolymer micelles and micelles formed with nonionic surfactants such as Triton X-100 and Brij-35 and a detailed discussion concerning this aspect has been presented in ref 15. In contrast, since rhodamine 110 is a charged solute, it is more likely to be solubilized in the interfacial region of P123 micelles. Concomitantly, the probe can also be distributed in the bulk water due to its ionic character. To find out whether rhodamine 110 is indeed distributed in aqueous phase, we have measured its reorientation time in water at 303 K and compared it with the ones (τr1 and τr2) measured in P123 micelles at the same temperature. The reorientation time of rhodamine 110 in water is 90 ps and τr1 and τr2 in P123 micelles are 2.45 and 0.20 ns, respectively. This exercise rules out the possibility that rhodamine 110 is distributed in the aqueous phase surrounding the micelles. However, it may be argued that the viscosity of 10 wt % aqueous P123 is 1.90 mPa s at 303 K,14 which is a factor of 2 higher than that of water and hence τr2 is longer than the measured reorientation time in water. The scenario at the microscopic level, on the other hand, is completely different. It must be noted that the critical micelle concentration (cmc) of a block copolymer is sensitive to temperature. At 303 K, the cmc of P123 is 8.6 µM (0.005 wt %),34 which indicates that 9.995 wt % of the copolymer, is in the form of micelles. Hence, the increase in the viscosity of the aqueous copolymer solution is due to the presence of micelles but not as a consequence of free unimers in water. In other words, the viscosity of the aqueous phase surrounding the micelles should be identical to water. In fact, this hypothesis has been verified from the results of our earlier work,19 where we have measured the fluorescence lifetimes of an isomerization probe 3,3′-diethyloxadicarbocyanine iodide (DODCI) in 30% aqueous P123 as a function of temperature. According to our results, DODCI is distributed between micellar and aqueous phases. It has been noticed that 20-30% of DODCI is located in the aqueous phase surrounding the micelles, whose lifetimes are identical to the ones measured in water. Since DODCI is an isomerization probe, its lifetime is sensitive to local viscosity. Thus, these experiments, though carried out in a different context altogether, substantiate the fact that the viscosity of the aqueous phase surrounding the P123 micelles even in case of 30 wt % copolymer, is identical to water. The arguments presented here in conjunction with the above-mentioned experimental results, conclusively demonstrate that rhodamine 110 is not distributed in the aqueous phase. The discussion presented so far has established that rhodamine 110 and DMDPP are located in the interfacial region and palisade layer (corona region) of the micelles, respectively. The observed biexponential anisotropy decay is due to the probe
[SDS]/[P123]
Nagg
Rc/nm
Rhs/nm
τMa/µs
0:1 1:1 2:1 3:1 4:1 5:1
69 30 19
4.79 3.69 3.21 2.54b 2.14b 1.89
9.41 8.84 7.17 6.56b 5.90b 5.20
0.67 0.55 0.29 0.23 0.16 0.11
4
a
Calculated using eq 6. b Obtained from interpolation of the data in ref 14.
molecules undergoing two different kinds of motion in these micelles. Numerous rotational diffusion studies involving organic solutes in micelles31-33,35-39 and reverse micelles40-42 indicate that probe molecules solubilized at the interface or in the palisade layer (corona region) of these organized assemblies undergo a slow lateral diffusion on the curved surface and a fast wobbling motion in an imaginary cone and both these motions are coupled to the overall rotation of the micelle. This is known as the two-step model,43-46 and it can be used to obtain lateral and wobbling diffusion coefficients, order parameters and cone angles from the anisotropy decay parameters. This exercise will be performed in due course for the system under investigation. Small-angle neutron scattering studies carried out by Ganguly et al.14 indicate that 10 wt % aqueous P123 forms spherical micelles with a hard sphere radius Rhs of 9.4 nm, core radius Rc of 4.8 nm and an aggregation number Nagg of 69 at 303 K. Upon the addition of SDS, there is a gradual decrease in all these micellar parameters and they are summarized in Table 3. However, the important point that is to be noted from this data is that despite a decrease in hard sphere and core radii by 180% and 250%, respectively, with an increase in [SDS]/[P123] from 0 to 5, the radius or the thickness of the corona decreases by merely 40%. This is due to stretching of the PEO blocks in the corona region as a result of increased hydration and these aspects have been mentioned in the Introduction. Rhodamine 110, which is located at the interface in P123 micelles, migrates to the palisade layer (corona region) in SDS-P123 micellar system because of the electrostatic interactions with the anionic head groups of the SDS surfactant molecules whose tails are embedded in the core. As a consequence there is an increase in the average reorientation time of the probe by over a factor of 2. The decrease in the mobility is due to the probe molecule experiencing enhanced microviscosity in the palisade layer (corona region) compared to the interface as well as attractive interactions between the positively charged probe and the negatively charged surfactant head groups. However, as the mole ratio of SDS to P123 increases from 1 to 5 there is 18% decrease in the average reorientation time. This decrease could probably be due to the probe molecule experiencing a microenvironment akin to the interfacial region of aqueous SDS micelles. To test this hypothesis, we have carried out anisotropy measurements with rhodamine 110 in 17.2 and 86.0 mM aqueous SDS solutions. These two numbers correspond to the lowest and highest concentrations of SDS used in the preparation of SDSP123 system. The anisotropy decay parameters of rhodamine 110 at the two concentrations of SDS are identical and the values of β, τr1 and τr2 are 0.23, 2.74, and 0.50 ns, respectively. The values of the individual anisotropy decay components of rhodamine 110 in aqueous SDS micelles are similar to the ones obtained at higher mole ratios of [SDS]/[P123] (see Table 1). However, the value of β, which is the relative contribution of τr1, is lower by more than a factor of 2. In view of the disparity
5882 J. Phys. Chem. B, Vol. 111, No. 21, 2007 in the values of β, it is not possible to decisively infer that rhodamine 110 is experiencing identical microenvironment in the two micellar systems. As mentioned earlier, the probe DMDPP is located in the palisade layer or the corona region of P123 micelles and this region contains two types of water, mechanically trapped water in the crevices and also thermodynamically bound water to the PEO units. It has been well established from solvation dynamics studies47-49 that water present in this region of the micelles, especially bound water, has different properties compared to the bulk water. Thus, even a hydrophobic solute such as DMDPP is solubilized in this region. Micellar hydration or degree of hydration is defined as the number of grams of water per gram of the surfactant. In SDS-P123 system, this parameter gradually increases with an increase in the mole ratio of SDS to P123.14 This kind of increase in the micellar hydration decreases the microviscosity of the region, which leads to an observed increase in mobility of the probe DMDPP with [SDS]/[P123]. The average reorientation time as well as the individual anisotropy decay components, τr1 and τr2 reflect this trend (see Figures 4 and 6). As an alternative explanation, the observed result can be interpreted in the following manner. It can also be assumed that in the absence of SDS, DMDPP is solubilized in the core of P123 micelles and addition of SDS influences it to migrate from the core to corona region. In such a scenario, the decrease in the average reorientation time, in principle, should have been drastic as the differences in the microviscosities of the two regions (core and corona) of the micelle are significant. Instead, the decrease in the average reorientation time as well as the individual decay components is gradual with an increase in mole ratio of SDS to P123 from 0 to 5. This could probably be due to the gradual variation in the characteristics of P123 micelles upon the addition of SDS (see Table 3). As a consequence, the mobility of DMDPP, even if it migrates from core to the corona region, is not altered significantly. These kinds of alternative locations for DMDPP have been considered in light of the recent rotational diffusion and solvation dynamics studies by Grant et al.22 and Sen et al.,24 respectively, using hydrophobic coumarin probes. However, it must be noted that the evidence provided by us and by them regarding the locations of these probes in block copolymer micelles must be considered as circumstantial. Thus, according to our findings, DMDPP is located in the corona region in both P123 and SDS-P123 micelles and the gradual increase in the mobility of the probe with [SDS]/[P123] is a consequence of enhancement in the amount of water in this region. In this context, it is worth mentioning the results of Kumbhakar et al.25 who carried out rotational diffusion and solvation dynamics measurements to assess the relative hydration levels in the corona regions of P123 and F127 micelles using hydrophobic probes such as coumarin 153 and coumarin 151. On the basis of the mobilities of the probe molecules, they inferred that corona region of F127 micelles is more hydrated compared to P123 micelles. The results presented here in conjunction with those of Kumbhakar et al.25 indicate that hydrophobic solutes such as the ones used in these studies gauge the hydration levels in the corona regions of micelles formed with block copolymers and nonionic surfactants. At this juncture, it will be interesting to compare the rotational diffusion of rhodamine 110 with that of DMDPP in SDS-P123 micelles even though these two solutes are structurally and chemically different. However, the van der Waals volumes of the two solutes are almost identical (275 and 281 Å3, respectively, for rhodamine 110 and DMDPP).50,51 The reorientation
Mali et al. times of rhodamine 110 and DMDPP, which were calculated using Stokes-Einstein-Debye (SED) hydrodynamic theory52 with stick boundary condition are 135 ps (mPa s)-1 and 139 ps (mPa s)-1, respectively, at 298 K. This exercise indicates that despite of having dissimilar structure and chemical properties the reorientation times of these two solutes obtained with stick boundary condition are more or less identical. A similar trend has been noticed in case of the experimentally measured reorientation times of these solutes in water (around 100 ps for both rhodamine 110 and DMDPP at 298 K).15,17 These numbers are close to the ones calculated using the SED theory with stick boundary condition. Now turning our attention to their rotational diffusion in SDS-P123 micelles, the average reorientation time of DMDPP is nearly a factor of 3 longer than that of rhodamine 110 in P123 micelles. Even though the reorientation times of the two solutes are almost identical in water, the significant differences in the average reorientation times as well as the individual anisotropy decay components are arising due to the solute molecules residing in two different regions of P123 micelles, namely the interface and corona region for rhodamine 110 and DMDPP, respectively. However, from 1-5 mole ratio of SDS to P123, the differences in the 〈τr〉 values of the two solutes is less than 20%. This is perhaps an indication that both rhodamine 110 and DMDPP are experiencing somewhat identical environment in the corona region of SDS-P123 micelles. To get a better appreciation of the anisotropy decay parameters in terms of the diffusional processes transpiring the SDSP123 system, the two-step model has been applied. The experimentally measured anisotropy decay parameters are related to the model parameters by the following equations:35
1 1 1 ) + τr1 τL τM
(3)
1 1 1 ) + τr2 τW τr1
(4)
β ) S2
(5)
Here, τL, τW, and τM are the time constants for lateral diffusion, wobbling motion, and the overall rotation of the micelle, respectively. β is the square of the order parameter S, which follows the inequality 0 e S2 e 1.35 The time constant for the overall rotation of the micelle τM has been calculated using the SED relation with stick boundary condition:52
τM )
4πRhs3η 3kT
(6)
In the above equation, Rhs is the hard sphere radius, η is the viscosity of water, k is the Boltzmann constant, and T is the absolute temperature. τM values calculated using eq 6 are given in Table 3. It is evident from the table that the time constants for the overall rotation of the micelles are considerably long, thus the contribution of τM to the anisotropy decays of the probes is negligible. In other words, τr1 essentially represents the time constant for lateral diffusion. From the order parameter, halfangle θ of the cone of the wobbling motion has been calculated with aid of the following relation.35
1 S ) cos θ (1 + cos θ) 2
(7)
The parameters τL, τW, S and θ have been calculated from these relationships and are given in Tables 4 and 5 for rhodamine
Surfactant-Block Copolymer Micelles
J. Phys. Chem. B, Vol. 111, No. 21, 2007 5883 Conclusions
TABLE 4: Order Parameters, Cone Angles, Lateral, and Wobbling Diffusion Coefficients for Rhodamine 110 in SDS-P123 System Obtained from Anisotropy Decay Parameters Using the Two-Step Model [SDS]/[P123]
S
θ0
DL × 1010/ m2 s-1
DW × 10-8/ s-1
0:1 1:1 2:1 3:1 4:1 5:1
0.56 0.72 0.73 0.71 0.72 0.72
47.9 36.9 36.1 37.6 36.9 36.9
60.2 6.9 5.5 3.6 2.8 2.3
7.4 2.1 1.7 1.5 1.4 1.3
TABLE 5: Order Parameters, Cone Angles, Lateral, and Wobbling Diffusion Coefficients for DMDPP in SDS-P123 System Obtained from Anisotropy Decay Parameters Using the Two-Step Model [SDS]/[P123]
S
θ0
DL × 1010/ m2 s-1
DW × 10-8/ s-1
0:1 1:1 2:1 3:1 4:1 5:1
0.79 0.77 0.77 0.71 0.71 0.69
31.5 33.1 33.1 37.6 37.6 39.0
10.7-41.3 7.2-41.1 6.2-31.2 4.1-27.4 3.3-25.4 2.7-20.5
0.5 0.7 0.8 1.1 1.1 1.3
110 and DMDPP, respectively. Lateral diffusion coefficient DL was calculated using the equation given below:36,44,45
DL )
R2 6τL
(8)
where R is the radius of the spherical surface on which lateral diffusion is taking place. In case of rhodamine 110 in P123 micelles, hard sphere radius was used to calculate DL as the probe is located at the interface. However, from 1-5 mole ratio of SDS to P123, core radius was employed for this purpose since rhodamine 110 is closer to the surface of the core. Even though DMDPP is in the corona region, the exact radius of the surface on which it is undergoing lateral diffusion is not known. Thus it is only possible to obtain the limits on lateral diffusion coefficients and the lower and upper limits on DL have been obtained by incorporating Rc and Rhs values, respectively, in eq 8. From the calculated values of θ, S, and τW, wobbling diffusion coefficients have been calculated with the help of eq 9:44,45
[
{(
)
cos2 θ(1 + cos θ)2 (1 + cos θ) 1 ln + 2 2 2(cos θ - 1) [(1 - S )τW] (1 - cos θ) (1 - cos θ) (6 + 8 cos θ - cos2 θ + 2 24
DW )
}
]
- 12 cos3 θ - 7 cos4 θ) (9) DL and DW values obtained in this manner are given in Tables 4 and 5 for rhodamine 110 and DMDPP, respectively. A quick glance at Table 4 reveals that there are no significant changes in the parameters as the mole ratio of SDS to P123 increases form 1 to 5. This is understandable considering the fact that micellar properties and the microenvironment experienced by the probe molecule are not altered considerably. However, DL and DW values of rhodamine 110 in case of P123 micelles (in the absence of SDS) are significantly high since the probe is located at the interface. In contrast, no drastic variations have been observed in the lateral diffusion and wobbling diffusion coefficients of DMDPP with an increase in the mole ratio of SDS to P123.
In this work, an attempt has been made to understand the role of electrostatic interactions and micellar hydration on solute rotation. For this purpose, fluorescence anisotropy decays of organic solutes, rhodamine 110 and DMDPP have been measured in the surfactant-block copolymer system of SDSP123 with varying amounts of SDS and the important conclusions are as follows. The average reorientation time of the cationic probe rhodamine 110 increases by more than a factor of 2 when the mole ratio of SDS to P123 goes up from 0 to 1. This is due to the change in the site of solubilization of the probe. Rhodamine 110, which is located at the interface in P123 micelles, migrates to the palisade layer (corona region) in SDSP123 system as a consequence of the electrostatic interactions with the anionic head groups of the SDS surfactant molecules that are present in this region. Only a marginal decrease in the average reorientation time has been noticed upon further increase in [SDS]/[P123], which is probably due to rhodamine 110 experiencing an environment somewhat similar to the headgroup region of SDS micelles. A completely opposite behavior has been observed in case of the neutral solute DMDPP in SDSP123 system. The average reorientation time gradually decreases as the mole ratio of SDS to P123 varies from 0 to 5. This is due to the increase in the amount of water present in the palisade layer (corona region) of the micelles, which decreases the microviscosity and hence facilitates the solute rotation. Based on the similarities in the average reorientation times of rhodamine 110 and DMDPP from 1-5 mole ratio of SDS to P123, it is reasonable to conclude that both the solutes are experiencing more or less the same microenvironment in the corona region of the micelles. Our conclusions are in tune with the structure of the SDS-P123 micelles that has been elucidated recently. Acknowledgment. We are grateful to Ms. M. H. Kombrabail of the Tata Institute of Fundamental Research for her help with time-resolved fluorescence experiments. We also acknowledge Dr. S. K. Sarkar for his encouragement throughout the course of this work. References and Notes (1) Almgren, M.; Stam, J. v.; Lindblad, C.; Li, P.; Stilbs, P.; Bahadur, P. J. Phys. Chem. 1991, 95, 5677. (2) Hecht, E.; Hoffmann, H. Langmuir 1994, 10, 86. (3) Hecht, E.; Mortensen, K.; Gradzielski, M.; Hoffmann, H. J. Phys. Chem. 1995, 99, 4866. (4) Kositza, M. J.; Rees, G. D.; Holzwarth, A.; Holzwarth, J. F. Langmuir 2000, 16, 9035. (5) Li, Y.; Xu, R.; Couderc, S.; Bloor, D. M.; Wyn-Jones, E.; Holzwarth, J. F. Langmuir 2001, 17, 183. (6) Dai, S.; Tam, K. C.; Li, L. Macromolecules 2001, 34, 7049. (7) Vangeyte, P.; Leyh, B.; Auvray, L.; Grandjean, J.; MisselynBauduin, A.-M.; Je´roˆme, R. Langmuir 2002, 18, 9019. (8) Thurn, T.; Couderc, S.; Sidhu, J.; Bloor, D. M.; Penfold, J.; Holzwarth, J. F.; Wyn-Jones, E. Langmuir 2002, 18, 9267. (9) De Lisi, R.; Milioto, S.; Munafo`, M.; Muratore, N. J. Phys. Chem. B 2003, 107, 819. (10) De Lisi, R.; Lazzara, G.; Milioto, S.; Muratore, N. J. Phys. Chem. B 2004, 108, 1189. (11) Senkov, S.; Roux, A. H.; Roux-Desgranges, G. Phys. Chem. Chem. Phys. 2004, 6, 822. (12) Jansson, J.; Schille´n, K.; Olofsson, G.; da Silva, R. C.; Loh, W. J. Phys. Chem. B 2004, 108, 82. (13) Jansson, J.; Schille´n, K.; Nilsson, M.; So¨derman, O.; Fritz, G.; Bergmann, A.; Glatter, O. J. Phys. Chem. B 2005, 109, 7073. (14) Ganguly, R.; Aswal, V. K.; Hassan, P. A.; Gopalakrishnan, I. K.; Kulshreshtha, S. K. J. Phys. Chem. B 2006, 110, 9843. (15) Dutt, G. B. J. Phys. Chem. B 2005, 109, 4923. (16) Mali, K. S.; Dutt, G. B.; Ganguly, R.; Mukherjee, T. J. Chem. Phys. 2005, 123, 144913.
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