Diffusion Coefficients of Small Molecules as Guests in Various Phases

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Langmuir 1999, 15, 5040-5047

Diffusion Coefficients of Small Molecules as Guests in Various Phases of Pluronic L64 Measured by One-Dimensional Electron Spin Resonance Imaging Yevgeniy N. Degtyarev and Shulamith Schlick* Department of Chemistry, University of Detroit Mercy, Detroit, Michigan 48219-0090 Received December 31, 1998. In Final Form: April 13, 1999 The diffusion coefficients of small nitroxide probes as guests in aqueous solutions of the triblock copolymer poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) EO13PO30EO13 (Pluronic L64) were measured at 300 K by one-dimensional electron spin resonance imaging (1D ESRI). The method is based on encoding the spatial distribution of the probes as a function of time in ESR spectra recorded in the presence of magnetic field gradients and simulation of these spectra in order to extract the diffusion coefficient, D. The rate of transport of each probe as a function of polymer content in the various phases (micellar, hexagonal, lamellar, and reverse micellar) of aqueous L64 depends on the probe location in the self-assembled system. The probe site was deduced from the analysis of the ESR spectra; the isotropic hyperfine splitting, aN, from the 14N nucleus of the >NO fragment in the probes was the polarity sensitive parameter. D values for the cationic probe 4-(N,N,N-trimethyl)ammonium-2,2,6,6-tetramethyl-piperidine1-oxyl iodide that is known to reside in the water domains follow the expression D ) D0 exp(-aw2), where D0 is the diffusion coefficient in the neat solvent and w2 is the weight fraction of the polymer. For the hydrophobic probe 5DSE, the methyl ester of doxylstearic acid where 5 indicates the carbon atom to which the doxyl group is attached, D is significantly lower and almost constant for w2 in the range 0.20-0.80. For the probe perdeuterio-2,2′,6,6′-tetramethyl-piperidone-N-oxide that is located at the interface between water and the EO domains, D decreases with increase in the polymer content, but the decrease is more prominent for w2 in the range 0.10-0.30; at w2 ) 0.90, D is similar to that of the polymer chains. The method of 1D ESRI enables the measurement of D values for guests present in small concentrations, typically e2 × 10-3 mol/L. This method and the results obtained in this study are relevant for assessing both the rate of transport of drugs in drug delivery systems and the partitioning of various guests in complex systems, for instance in biological membranes.

Introduction The triblock copolymers poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide), EOmPOnEOm (commercial name Symperonics, Pluronics, or Poloxamers), have been extensively studied in the past few years, because of their rich and complex structures in aqueous solutions and their numerous applications in drug-release systems, detergents, cosmetics, treatment of burns, and water purification. The maturity of the field is reflected in three important reviews,1 a book chapter,2 and a recent book.3 Detailed phase diagrams of several Pluronics have become available,4-8 and progress has been achieved in the general understanding of the process of self-assembly.1-9 The phase diagrams of the Pluronics10 are often compared to those of the nonionic surfactants of the oligo* To whom correspondence should be addressed. E-mail address: [email protected]. (1) (a) Alexandridis, P.; Hatton, T. A. Colloid Surf., A 1995, 96, 1. (b) Almgren, M.; Brown, W.; Hvidt, S. Colloid Polym. Sci. 1995, 273. (c) Alexandridis, P. Curr. Opin. Colloid Interface Sci. 1997, 2, 478. (2) Chu, B.; Zhou, Z. In Nonionic Surfactants; Marcel Dekker: New York, 1996; Chapter 3, p 67. (3) Amphophilic Block Copolymers: Self-Assembly and Applications, Alexandridis, P., Lineman, B., Eds.; Elsevier: Amsterdam, 1997. (4) Hang, K.; Khan, A. Macromolecules 1995, 28, 3807. (5) Alexandridis, P.; Olson, U.; Lindman, B. Macromolecules 1995, 28, 7700. (6) Alexandridis, P.; Olson, U.; Lindman, B. J. Phys. Chem. 1996, 100, 280. This study presents the phase diagram of a reverse Plutonic (EO block in the middle) in water-oil mixtures. (7) Alexandridis, P.; Zhou, D.; Khan, A. Langmuir 1996, 12, 2690. The phase diagram for L64 is more detailed compared to that published previously (ref 4). (8) Svensson, B.; Alexandridis, P.; Olson, U. J. Phys. Chem. B 1998, 102, 7541.

(ethylene oxide) type CmEOn (Cm is an aliphatic chain with m carbon atoms and n is the number of ethylene oxide units in the molecule).11,12 For both classes of compounds the micellization in water is determined by the hydrophobic part of the amphiphile and is modulated by the specific interactions of the solvent with the two blocks of different polarity. The strong temperature influence on the critical micelle concentration (cmc) is characteristic only for the EOmPOnEOm copolymers and has been explained by the increasing hydrophobicity of the EO and PO segments as the temperature increases, via the higher weights of the less polar chain conformations.13 We have initiated a study of the Pluronics using electron spin resonance (ESR) spectroscopy of nitroxide spin probes as a source of structural and dynamical data, ESR imaging for measurements of the translational diffusion coefficients, D, of the probes, and rheological measurements for an evaluation of the macroscopic properties.14-17 The (9) Wu, W.; Zhou, Z. K.; Chu, B. Macromolecules 1993, 26, 2117. Wu, W.; Chu, B. Macromolecules 1994, 27, 1766. Zhou, S.; Chu, B. J. Polym. Sci. Part B: Polym. Phys. 1998, 36, 889. (10) Plutonic and Tetronic Surfactants; Technical Brochure; BASF Corp.: Parsipanny, NJ, 1989. (11) (a) Medhage, B.; Almgren, M.; Alsins, J. J. Phys. Chem. 1993, 97, 7753. (b) Nilsson, P.-G.; Wennerstro¨m, H.; Lindman, B. J. Phys. Chem. 1983, 87, 1977. (12) Baglioni, P.; Bongiovanni, R.; Rivara-Minten, E.; Kevan, L. J. Phys. Chem. 1989, 93, 5574. (13) (a) Andersson, M.; Karlstro¨m, G. J. Chem. Phys. 1985, 89, 4957. (b) Linse, P. Macromolecules 1993, 26, 4437. (c) Hurter, P. N.; Scheutjens, J. M. H. M.; Hatton, T. A. Macromolecules 1993, 26, 5030. (14) Zhou, L.; Schlick, S. Polym. Prepr. (Am. Chem. Soc. Div. Polym. Chem.) 1996, 37, 829. (15) Malka, K.; Schlick, S. Macromolecules 1997, 30, 456. (16) Caragheorgheopol, A.; Pilar, J.; Schlick, S. Macromolecules 1997, 30, 2923.

10.1021/la9817718 CCC: $18.00 © 1999 American Chemical Society Published on Web 06/04/1999

Diffusion Coefficients of Guest Molecules

ESR measurements are based on nitroxide spin probes varying in size, charge, hydrophilicity, and position of the nitroxide group relative to the probe headgroup. Most of our studies have focused on EO13PO30EO13 (Pluronic L64, Chart 1) and EO6PO34EO6 (Pluronic L62), whose phase diagrams in aqueous solutions have been deduced by 2H NMR, polarizing microscopy, and ocular inspection:4,7 in the vicinity of 300 K, the main phases detected in L64 with increasing polymer content are L1 (micellar), H (hexagonal), LR (lamellar), and L2 (reverse micellar). The size of the aggregates has been estimated by dynamic light scattering9 and small-angle X-ray scattering (SAXS).7 The cmc of L64 decreases with increasing temperature, and the critical micellization temperature (cmt) decreases with increasing polymer concentration.18 The nitroxide spin probe electron spin resonance (ESR) method offers a rich source of information on the dynamics, polarity, and self-assembly in surfactants. An important parameter is the isotropic nitrogen hyperfine splitting, aN, which is polarity sensitive. The location reported by the probe is reflected also in the line shapes (which reflect the dynamics) and in the correlation times τc deduced directly from the spectra or from simulations. By this approach it was possible to determine the local hydration and the hydration gradient in the nonpolar (PO) and polar (EO) domains, follow changes in the hydration of the EO blocks at various distances from the hydrophobic core in L62 and L64 aggregates on a scale of e20 Å, and explain the mechanism of phase transitions.14-17 The specific sites selected by the nitroxide probes in the self-assembled system are also reflected in the rate of transport of the probes: in the diffusion coefficients, D. The importance of diffusion data for solvent molecules in self-assembled surfactants in binary systems (water as solvent) or in ternary systems (water and an “oil”) has been demonstrated in recent studies.19,20 Pulsed-field gradient spin-echo nuclear magnetic resonance (PFGSE NMR) has emerged as the method of choice because of its ability to evaluate the diffusion coefficients of both solvents in a ternary mixture containing the surfactant. Together with the diffusion data, the concept of the effective selfdiffusion coefficient D/D0 (“obstruction factor”) for small molecules was formulated; D and D0 are the diffusion coefficients in the presence and in the absence of polymer aggregates, respectively.21,22 We will come back to this concept and will compare D/D0 ratios in simple and polymeric surfactants and in hydrophobic polymer aggregates. Imaging based on ESR (ESRI) provides information on the spatial distribution of paramagnetic diffusants23 and has been used for measuring diffusion coefficients.24 The determination of D for spin probes in liquid crystals and model membranes has been described in a series of papers by Freed and co-workers.25 The same group has demonstrated recently the application of 1D ESRI to an analysis (17) Caragheorgheopol, A.; Schlick, S. Macromolecules 1998, 31, 7736. (18) Alexandridis, P.; Holtzwarth, J. F.; Hatton, T. A. Macromolecule 1994, 27, 2414. (19) Lindman, B.; Shinoda, K.; Olson, U.; Anderson, D.; Karlstro¨m, G.; Wennerstro¨m, H. Colloids Surf. 1989, 38, 205. (20) Lindman, B.; Olson, U.; So¨derman, O. In Dynamics of Solutions and Fluid Mixtures by NMR; Delpuech, J. J., Ed.; Wiley: New York, 1995; Chapter 8, p 345. (21) Jo¨nsson, B.; Wennerstro¨m, H.; Nilsson, P. G.; Linse, P. Colloid Polym. Sci. 1986, 264, 77. (22) Anderson, D. M.; Wennerstro¨m, H. J. Phys. Chem. B 1990, 94, 8683. (23) Berliner, L. J.; Fujii, H. J. Magn. Reson. 1986, 69, 68. (24) Galtseva, E. V.; Yakimchenko, O. E.; Lebedev, Ya. S. Chem. Phys. Lett. 1983, 99, 301. Yakimchenko, O. E.; Degtyarev, E. N.; Parmon, V. N.; Lebedev, Ya. S. J. Phys. Chem. 1995, 99, 2038.

Langmuir, Vol. 15, No. 15, 1999 5041 Chart 1. Pluronic L64 and Spin Probes

of D values for polydisperse polymer samples.26 In our lab 2D spatial-spectral ESRI based on nitroxide spin probes and paramagnetic MoV has been applied for the determination of the spatial distribution and diffusion coefficients of paramagnetic species in ion-containing polymers, polymer solutions, and cross-linked polymers swollen by solvents and in the various phases of L64.15,27-31 The 2D ESRI method gives the ESR spectrum as a function of the spatial coordinate and makes possible the determination of the rotational and translational diffusion in one experiment. The time required for data acquisition is, however, rather long, typically 20 min for a complete set of projections, and therefore only relatively slow diffusion processes can be measured by 2D ESRI. In this paper we present 1D ESRI measurements of the diffusion coefficients, D, at 300 K in the various phases of L64 for a hydrophilic probe, 4-(N,N,N-trimethyl)ammonium-2,2,6,6-tetramethyl-piperidine-1-oxyl iodide, (CAT1), that resides in the water-rich domains and for the hydrophobic probe 5DSE, the methyl ester of doxylstearic acid where 5 indicates the carbon atom to which the doxyl group is attached. Data for these two probes are compared with results obtained by 2D spatial-spectral ESRI for the spin probe perdeuterio-2,2′,6,6′-tetramethylpiperidone-N-oxide (PDTEMPONE or PDT).15 The probes are shown in Chart 1. The range of D values measured in this study was 1.0 × 10-5 to 1.0 × 10-7cm2 s-1. Experimental Section Materials. The copolymer L64 (molecular weight M ) 2900) was from BASF10 and was used without further purification. The spin probe CAT1 (M ) 340) was from Molecular Probes, Eugene, OR, 5DSE (M ) 414) was from Sigma, and PDT (M ) (25) Moscicki, J. K.; Shin, Y. K.; Freed, J. H. In EPR Imaging and in Vivo EPR; Eaton, G. R., Eaton, S. S., Ohno, K., Eds.; CRC Press: Boca Raton, FL, 1991; Chapter 19, p 189. Freed, J. H. Annu. Rev. Biophys. Biomol. Struct. 1994, 23, 1. (26) Xu, D.; Hall, E.; Ober, C. K.; Moscicki, J. K.; Freed, J. H. J. Phys. Chem. 1996, 100, 15856. (27) Schlick, S.; Pilar, J.; Kweon, S.-C.; Vacik, J.; Gao, Z.; Labsky, J. Macromolecules 1995, 28, 5780. (28) Kruczala, K.; Gao, Z.; Schlick, S. J. Phys. Chem. 1996, 100, 11427. (29) Gao, Z.; Schlick, S. J. Chem. Soc., Faraday Trans. 1996, 92, 4239. (30) Gao, Z.; Pilar, J.; Schlick, S. J. Phys. Chem. 1996, 100, 8430. (31) Schlick, S.; Eagle, P.; Kruczala, K.; Pilar, J. In Spatially Resolved Magnetic Resonance: Methods, Materials, Medicine, Biology, Rheology, Ecology, Hardware; Blu¨mler, P., Blu¨mich, B., Botto, R., Fukushima, E., Eds.; Wiley-VCH: Weinheim, 1998; Chapter 17, p 221.

5042 Langmuir, Vol. 15, No. 15, 1999 186) was synthesized according to a published procedure.32 All spin probes were used without further purification. Sample Preparation. Aqueous solutions of the polymer were prepared in small quantities (0.1 g) by direct weighing of the polymer and bidistilled water, stirring overnight, and keeping in a thermostat at 300 K for several days for complete mixing. The spin probes CAT1 and 5DSE were dissolved in methanol to a concentration of ≈2 × 10-2 mol/L and then divided into several vials. After evaporation of the solvent in air, a corresponding amount of L64 solution was added to yield a final spin probe concentration of ≈2 × 10-3 mol/L. The solution containing the spin probe was transferred with a syringe to the bottom of capillary tubes (1.5 mm o.d., ≈1 mm i.d.) to a height of h. The solution is given by eq 3, and the error function erf(x) by eq 4.

C(x,t) )

{

h-x h+x 1 C erf + erf 2 0 2xDt 2xDt

erf(x) ≡

2 xπ

∫0x exp(-ξ2) dξ

}

(3) (4)

The distribution function p(H*) (concentration profile of the probe in the presence of a given gradient Gx and at time t in the diffusion process) was calculated with D and h as parameters, convoluted according to eq 1 with the ESR line shape f0(H - H*), and compared with the experimental line shape; the best visual fit was used to (36) Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, U.K., 1993.

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Degtyarev and Schlick

Figure 4. X-band ESR spectra of 5DSE at 300 K in aqueous L64 (polymer concentration of 80% (w/w)) in the absence of gradient (top) and for a gradient of 45.2 G/cm after 54 and 452 min of diffusion (middle and bottom).

extract the diffusion coefficient D. No correction for the sensitivity profile of the ESR cavity was needed, because only the initial stages of the diffusion process are used to deduce the diffusion coefficients. For a given probe in a given L64 concentration several samples, typically 1020, were measured for different gradients and diffusion times in order to evaluate the error limit of the method. The simulation of the line shapes in the presence of gradient for CAT1 is illustrated in Figure 5. For a diffusion time of 14 min, the range of the diffusion coefficient D was explored (Figure 5A) and found to be between 3 × 10-6 and 12 × 10-6 cm2 s-1, then D was determined in a finer grid (Figure 5B). For the results presented in Figure 5 (the solution containing 20% (w/w) L64), the D value chosen from the best fit was 6.3 × 10-6 cm2 s-1. The D values and the corresponding standard deviations are shown in Table 1. For the 5DSE spin probe it was important to deduce D values for longer diffusion times, as illustrated in Figure 6. The experimental image collected after 54 min of diffusion (Figure 6A) was simulated with D values of 3.7 × 10-8, 9.3 × 10-8, and 14.9 × 10-8 cm2 s-1. All three simulations reproduce the experimental spectrum: because of the slow diffusion, the changes in the concentration profiles after t ) 54 min are negligible, and it is necessary to allow longer diffusion times before attempting to select the D value. As seen in Figure 6B, after 452 min of diffusion significant differences between the simulations presented are detected, and the range of the diffusion coefficient can be established and measured in a narrower grid, as was done for CAT1. The diffusion coefficient deduced for the data given in Figure 6 (solution containing 80% (w/w) polymer) is 0.13 × 10-6 cm2 s-1. The diffusion coefficients of 5DSE in the L64 solutions are in the range 10 × 10-8 to 20 × 10-8 cm2 s-1, with typical standard deviations of 3 × 10-8 cm2 s-1 (Table 1). The progress of diffusion was measured during several hours. The variations of the diffusion coefficients for CAT1, 5DSE, and PDT are plotted as a function of the polymer concentration in Figure 7.

Figure 5. Simulation of the lower ESR spectrum shown in Figure 3 for CAT1 in aqueous L64 (polymer concentration of 20% (w/w)) by assuming the indicated values of the diffusion coefficient D: (A) to establish the range of the D values; (B) for D values in the vicinity of the best fit.

Discussion The D data presented in Figure 7 will now be discussed in view of the phase diagram for L64 presented in Figure 8.7 Effect of Probe Location on Transport Properties. The spin probes CAT1 and 5DSE offer a contrasting transport behavior in aqueous solutions of L64. Although the molecular masses M are similar, 340 for CAT1 (213 for the cation) and 414 for 5DSE, the corresponding D

Diffusion Coefficients of Guest Molecules

Langmuir, Vol. 15, No. 15, 1999 5045

Figure 7. Variation of the diffusion coefficient, D, at 300 K for CAT1, PDT, and 5DSE with L64 concentration.

Figure 8. Phase diagram for aqueous EO13PO30EO13 (Pluronic L64). L1 and L2 are isotropic micellar and reverse micellar phases, respectively, H is the hexagonal phase, and LR is the lamellar phase. Dotted lines indicate the uncertainty in the phase boundaries (from ref 7).

Figure 6. Simulation of the lower ESR spectrum shown in Figure 4 for 5DSE in aqueous L64 (polymer concentration of 80% (w/w)): (A) after a diffusion time of 54 min the simulations for three D values, 3.7 × 10-8, 9.3 × 10-8, and 14.9 × 10-8 cm2 s-1, are undistinguishable (see text); (B) for the indicated D values, after a diffusion time of 452 min.

values at each polymer content are very different. The ratio DCAT1/D5DSE is 35 in the micellar phase (polymer contents of 20 and 35% (w/w)), 11 in the hexagonal phase (polymer content 50% (w/w)), and 3.1 in the mixed L2 + LR phase (polymer content 80% (w/w)). Moreover, D5DSE values are similar to the diffusion coefficients of the polymer chains, DL64, measured by PFGSE NMR.37 For instance in the L64 solution containing 20% (w/w) polymer (L1 phase), D5DSE ) 0.18 × 10-6 cm2 s-1, and DL64 ≈ 0.25

× 10-6 cm2 s-1; in the polymer solution containing 35% (w/w) L64, D5DSE ) 0.10 × 10-6 cm2 s-1 and DL64 ≈ 0.05 × 10-6 cm2 s-1. The similar ranges of D5DSE and DL64, together with the very low aN values for the 5DSE, clearly indicate that the probe is located in the polymer aggregates and diffuses slowly, together with the polymer chains. The DCAT1 values show a marked decrease with increasing polymer content and are in the range 17.3 × 10-6 cm2 s-1 (in neat water) to 0.4 × 10-6 cm2 s-1 (solution containing 80% (w/w) polymer). In neat water DCAT1 is close to the self-diffusion of water molecules, 25 × 10-6 cm2 s-1 at 300 K.38 The molecular weight of the probe cation is 213, more than 10 times that of water; yet D is much larger than that expected for either an M-1/3 or an M-1/2 dependence predicted by some models.39 It seems (37) Zhang, K.; Lindman, B.; Coppola, L. Langmuir 1995, 11, 538. The data include D values in the isotropic phases only (L1 and L2). The D values we quoted were read from a plot of log D vs L64 content (Figure 5 in above paper) and are therefore approximate values. (38) Yasunaga, H.; Ando, I. Polym. Gels Networks 1993, 1, 83.

5046 Langmuir, Vol. 15, No. 15, 1999

that the diffusion of the probe is accelerated by that of the solvent (water);40 this effect is possible because the probe is located in the water regions, as deduced from the ESR spectra.17 The dependence of DCAT1 on polymer content follows the expression D ) D0 exp(-aw2), where D0 is the diffusion coefficient of the probe in neat water and w2 is the weight fraction of the polymer. The straight line in Figure 7 shows the excellent agreement between this expression and the experimental results for CAT1. This behavior is consistent with the expression suggested by Phillies for diffusion of probes:41 D ) D0 exp(-Rcν), where c is the polymer concentration and R and ν are constants. Moreover, we have used a similar expression, D ) D0 exp(R(1 - φ2)), where φ2 is the volume fraction of the polymer and D0 and R are fitting parameters, for simulating the dependence of the diffusion coefficient of pure solvents and solvent mixtures in cross-linked polyisoprene swollen by the solvents.40 Data for CAT1 therefore suggest a behavior typical of a solvent. From these considerations it is clear that the major factor that controls the transport rate of the guests is their location. Obstruction Factor. Because CAT1 is located in the solvent domains, it is logical to assume that the selfassembled polymer aggregates decrease the rate of diffusion of the probe, compared to the value in the neat solvent. In this context it is interesting to apply the concept of “obstruction” introduced by Jo¨nsson et al.21,22 The obstruction effects are expressed as the “obstruction factor” or “effective diffusion coefficient”, Deff ) D/D0. The dependence of D/D0 has been calculated as a function of φ2, the volume fraction of the obstructing particles, for particles of different geometries: spheres, long prolates, and oblates with different axial ratios. For noninteracting particles, the limiting value of D/D0 is 2/3 in large oblates.21 For the diffusion of D2O in isotropic solutions of the nonionic surfactants C12(EO)4 and C12(EO)3, the concept of obstruction was considered as a way to distinguish between the various shapes of the aggregates: 42 D eff values close to unity were taken as an indication of spherical aggregates and Deff in the range 0.6-0.7 as evidence for the presence of large oblate particles. For the diffusion of water in the presence of poly(methyl methacrylate) (PMMA) latex spheres, the Deff values as a function of the obstructing volume fraction, φ2, in the range 0-0.5 is lower than, but close to, the calculated values.21 The obstruction factors D/D0 for CAT1 and PDT are plotted in Figure 9 as a function of L64 content. (This type of data is not available for 5DSE, because the probe is not soluble in neat water.) For both probes D/D0 decreases significantly even at low polymer concentrations and is 0.4 in the isotropic micellar phase (L1, 20% (w/w) polymer). In the hexagonal and lamellar phases the D/D0 factors are different for the two probes, and much lower, in the range 0.1-0.01; the lowest value, 0.01, was measured for PDT in the isotropic reverse micellar phase, L2. A reasonable explanation for these very low D/D0 values is the interaction between the probe and the solvent and/or polymer. The presence of water inside the aggregates, (39) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (40) Schlick, S.; Gao, Z.; Matsukawa, S.; Ando, I.; Fead, E.; Rossi, G. Macromolecules 1998, 31, 8124. An interesting result of this study was that the diffusion coefficient of cyclohexane at 300 K increases from 1.43 × 10-5 cm2 s-1 (neat solvent) to 2.03 × 10-5 cm2 s-1 in a 1/1 (v/v) mixture containing benzene, but that of benzene, 2.32 × 10-5 cm2 s-1, remains unchanged. (41) Phillies, G. D. J. J. Phys. Chem. 1989, 93, 5029. (42) Nilsson, P.-G.; Lindman, B. J. Phys. Chem. 1984, 88, 4764.

Degtyarev and Schlick

Figure 9. Variation of the obstruction factor D/D0 at 300 K for CAT1 and PDT as a function of the L64 concentration. D0 is the diffusion coefficient of each probe in neat water.

and the location of the probes in water that interacts with the aggregates (“bound water”) can lead to lower rates of transport. These results emphasize the complexity of the systems consisting of EO and PO blocks and the different behavior compared to the systems that contain strictly hydrophobic obstructing particles such as PMMA or to self-assembled systems such as surfactants of the type CmEOn, where the hydrophobic and hydrophilic parts of the molecule are more clearly defined than those in the Pluronics. Can the Stokes-Einstein (SE) Formula be Applied to L64 Phases? This formula, D ) kBT/(6πηRH), where kB is the Boltzmann constant, T the absolute temperature, η the solvent viscosity, and RH the hydrodynamic radius of the diffusant, has been often applied19,20 and is correct in the limit of infinite dilution. Corrections for a finite volume fraction of the aggregates have also been introduced.20 We have measured the viscosities of aqueous solutions of L64 at 300 K.43 In the entire range of concentrations, 0-100% L64, η has two maxima: a strong maximum, η ≈ 1430 P, for a polymer content of 50% (w/w) (hexagonal phase) and a second maximum, η ≈ 247 P, for a polymer content of 80% (w/w) (L1 + LR). The viscosity of neat L64 is 7.6 P. According to the SE formula, minima for the diffusion coefficients are expected at the highest viscosities; experimentally, however, the D values for PDT and CAT1 decrease gradually with increase in L64 content. A gradual increase of the rotational correlation time, τc (τc ) 4τηRH3/(3kBT)), for PDT was also measured.15 It is clear that the macroscopic viscosity is not a major driving force for either D or τc and that the SE cannot be applied; the local viscosity deduced from spectroscopic studies seems a more appropriate parameter, at least at low polymer concentrations.44 The numerous models proposed for the diffusion of small molecules in polymeric systems attest to the complexity of the problem.45 The results presented in this study suggest that the transport properties of guests in complex fluids are intimately related to the local sites selected by the guests and to the interactions on the molecular level in the system. (43) Malka, K.; Schlick, S. Unpublished results.

Diffusion Coefficients of Guest Molecules

These considerations are important when designing drugrelease systems and also when considering the specific domain of a biological system where the drugs are selectively located. A case in point appeared in a recent study by surface tension of the partitioning of local anesthetics in model membranes (cationic surfactants):46 The results have indicated that the partitioning (in the water and micellar phases) depends on the hydrophobicity of the drug, and a good correlation was established between the partitioning into the hydrophobic environment and the anesthetic potency of the drugs. Summary and Conclusions The diffusion coefficients of small nitroxide molecules as guests in aqueous solutions of the triblock poly(ethylene (44) In the case of PDT, the hydrodynamic radius RH can be calculated from the value of τc in neat water (τc ) 2.6 × 10-11 s/rad); we obtain RH ) 3.1 Å, a very reasonable value for PDT. The D values can then be deduced from RH and τc, using D ) 2RH2/(9τc). For L64 concentrations up to 40% (w/w) the D values so calculated are in the same range (within a factor of