6896
Langmuir 2007, 23, 6896-6902
Articles Wormlike Micelle Formation and Flow Alignment of a Pluronic Block Copolymer in Aqueous Solution V. Castelletto, P. Parras,† and I. W. Hamley* Department of Chemistry, UniVersity of Reading, Reading RG6 6AD, UK
P. Ba¨verba¨ck and J. Skov Pedersen Department of Chemistry and iNANO Interdisciplinary NanoScience Centre, UniVersity of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
P. Panine European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Ce´ dex ReceiVed February 9, 2007. In Final Form: April 13, 2007 The self-assembly into wormlike micelles of a poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) triblock copolymer Pluronic P84 in aqueous salt solution (2 M NaCl) has been studied by rheology, small-angle X-ray and neutron scattering (SAXS/SANS), and light scattering. Measurements of the flow curves by controlled stress rheometry indicated phase separation under flow. SAXS on solutions subjected to capillary flow showed alignment of micelles at intermediate shear rates, although loss of alignment was observed for high shear rates. For dilute solutions, SAXS and static light scattering data on unaligned samples could be superposed over three decades in scattering vector, providing unique information on the wormlike micelle structure over several length scales. SANS data provided information on even shorter length scales, in particular, concerning “blob” scattering from the micelle corona. The data could be modeled based on a system of semiflexible self-avoiding cylinders with a circular crosssection, as described by the wormlike chain model with excluded volume interactions. The micelle structure was compared at two temperatures close to the cloud point (47 °C). The micellar radius was found not to vary with temperature in this region, although the contour length increased with increasing temperature, whereas the Kuhn length decreased. These variations result in an increase of the low-concentration radius of gyration with increasing temperature. This was consistent with dynamic light scattering results, and, applying theoretical results from the literature, this is in agreement with an increase in endcap energy due to changes in hydration of the poly(ethylene oxide) blocks as the temperature is increased.
Introduction Wormlike micelles are formed by a one-dimensional selfassembly process of amphiphilic molecules. They can be considered “living” polymers due to the dynamical nature of the association and disassociation of the surfactant molecules. Wormlike micelles can break and reform on a time scale that depends on the type of amphiphile and the physicochemical conditions.1 This has been studied theoretically, and it is known that this gives rise to a broad distribution of micelle lengths.2 A characteristic time scale results from scission and reptation of the chains.1,2 In the semidilute regime, wormlike micelles can form entangled viscoelastic networks. A number of reports have discussed the effect of shear on wormlike micelles, particularly focusing on the rheological properties. The low-frequency rheology is well described by a Maxwell model with a single relaxation time. The influence of * Author for correspondence. E-mail address: I.W.Hamley@ reading.ac.uk. † Present address: Procter & Gamble Italy, via Ardeatina 100, 00041, Pomezia, Rome, Italy. (1) Rehage, H.; Hoffmann, H. Mol. Phys. 1991, 74, 933. (2) Cates, M. E.; Candau, S. J. Condens. Matter 1990, 2, 6869.
shear on the structure has been probed using small-angle light scattering3 (SLS) and small-angle neutron scattering (SANS). In addition to the alignment of micelles, more complex flow behavior has been observed, including shear-induced phase separation, which may result in shear banding, that is, the coexistence of regions with different shear rates. Shear banding has been inferred by the presence of a plateau in the flow curve (for examples, see refs 3 and 4), and via light scattering,3,5,6 birefringence measurements,4,5 and NMR velocimetry.7,8 Much of the previous work has been performed on wormlike micelles formed by cationic surfactants such as cetylpyridinium chloride in salt solution. It is also known that nonionic block copolymers can form wormlike micelles under appropriate conditions.9 For several Pluronic PEO-PPO-PEO [PEO ) poly(3) Waton, G.; Michels, B.; Steyer, A.; Schosseler, F. Macromolecules 2004, 37, 2313. (4) Lee, J. Y.; Fuller, G. G.; Hudson, N. E.; Yuan, X.-F. J. Rheol. 2005, 49, 537. (5) Wheeler, E. K.; Izu, P.; Fuller, G. G. Rheol. Acta 1996, 35, 139. (6) Kadoma, I. A.; van Egmond, J. W. Langmuir 1997, 13, 4551; Kadoma, I. A.; van Egmond, J. W. Phys. ReV. Lett. 1998, 80, 5679. (7) Britton, M. M.; Callaghan, P. T. Phys. ReV. Lett. 1997, 78, 4930. (8) Lo´pez-Gonza´lez, M. R.; Holmes, W. M.; Callaghan, P. T.; Photinos, P. J. Phys. ReV. Lett. 2004, 93, 268302.
10.1021/la700382y CCC: $37.00 © 2007 American Chemical Society Published on Web 05/25/2007
Wormlike Micelles of Pluronic Block Copolymers
Langmuir, Vol. 23, No. 13, 2007 6897
(ethylene oxide), PPO ) poly(propylene oxide)] copolymers, a transition from spherical to cylindrical micelles is observed upon raising the temperature.9 We consider here a change in micellar shape in dilute solution, and not the formation of a hexagonal packed cylindrical micelle structure at high concentration. The change in micellar shape is due to an increase in association number with increasing temperature, the transition occurring when the radius of the micelle core exceeds the stretched length of the hydrophobic block (or half-block for a triblock with a hydrophobic midblock). This has been most extensively studied for Pluronic P85.9 Other studies have been summarized by Booth and Attwood.10 Shear-induced phase separation of Pluronic P84 in the presence of salt has recently been studied by rheometry and SLS,3 and the present study builds on this work. The formation of micelles by a related PEO-PBO [PBO ) poly(butylene oxide)] diblock has also been reported.11 Wormlike micelles have also been noted for block copolymers in nonaqueous solvents.9 In the present paper, we present a comprehensive characterization of the self-assembly of Pluronic copolymer P84 in aqueous salt solution. Cloud point measurements were performed in the presence of various added compounds. The dimensions of wormlike micelles were probed using a combination of SLS and dynamic light scattering (DLS) with small-angle X-ray scattering (SAXS). The rheological properties of the solution were also probed via controlled stress rheometry. The flow curves were studied, and the frequency response was investigated. In a previous paper, we reported on the shear-flow behavior of 4 wt % P84 solutions in 2 M NaCl, using SAXS.12 However, that paper focused only on shear flow behavior and also considered another wormlike micellar system (cetylpyridinium chloride + sodium salicylate, CpCl/NaSal). Experimental Materials. Pluronic P84 (EO19-PO43-EO19, molecular weight: 4200 g mol-1), provided by BASF, was used without further purification. Solutions of P84 samples with and without added salt were prepared, although the main focus of the present work is on solutions in 2 M NaCl. Stock solutions were prepared using bidistilled deionized water, and kept in a refrigerator for further use. At this salt concentration, for a 4 wt % P84 sample, the critical micellar temperature and the cloud point are observed at 2 °C and 47 °C, respectively.13 Cloud Point Curves. Cloud point curves were measured upon the addition of NaCl, KCl, and urea. Samples were heated at approximately 1 °C/min, and the cloud point was identified visually. DLS and SLS. Experiments were performed using an ALV CGS-3 system with a 5003 multidigital correlator. The light source was a 20 mW He-Ne laser, linearly polarized, with λ ) 633 nm. Toluene was used to calibrate the Rayleigh ratio as per standard procedures for static light scattering.14 Scattering angles in the range 40° e θ e 150°, with ∆θ ) 10°, were used for all the experiments. DLS was performed for correlation time scales 2.5 × 10-4 e t/ms e 4.0 × 103. Samples were prepared in standard 0.5 cm diameter cylindrical glass cells. They were filtered through 0.2 µm Millex-GN nylon membrane filters from Millipore. DLS experiments measured the intensity correlation function: g(2)(q,t) ) /2
(1)
where q ) [4πn sin(θ/2)]/λ is the scattering vector (λ ) vacuum (9) Hamley, I. W. Block Copolymers in Solution; Wiley: Chichester, U.K., 2005. (10) Booth, C.; Attwood, D. Macromol. Rapid Commun. 2000, 21, 501. (11) Hamley, I. W.; Pedersen, J. S.; Booth, C.; Nace, V. M. Langmuir 2001, 17, 6386. (12) Castelletto, V.; Hamley, I. W. Polym. AdV. Technol. 2006, 17, 137. (13) Waton, G.; Michels, B.; Steyer, A.; Schosseler, F. Macromolecules 2004, 37, 2313.
wavelength of the radiation and n ) refractive index of the medium), and I(q,t) is the intensity scattered by the sample, after a correlation time t. The measured intensity correlation function is related to the field correlation function, g(1)(q,t), by the Siegert relationship:15 g(2)(q,t) ) 1 + [g(1)(q,t)]2
(2)
The program CONTIN16 can be used to determine the relaxation rate distribution of the system through the modeling of the field correlation function according to g(1)(t) )
∫
∞
0
G(Γ) exp(-Γt)dΓ
(3)
where G(Γ) is the relaxation rate distribution. CONTIN allows for the calculation of the inverse Laplace transform in eq 3 and provides a tool for calculating the diffusion coefficient of the system. The relaxation rate distributions for different scattering vectors can be used to construct a plot of Γ h versus q2 (where, for a unimodal distribution, Γ h is taken as the decay rate corresponding to the maximum in G(Γ)). The mutual diffusion coefficient is calculated as the slope D ) Γ h /q2, and it enables the apparent hydrodynamic radius RH to be calculated according to the Stokes-Einstein formula: RH )
kBT 6πη0D
(4)
where kB) 1.38 × 10-23 J K-1 is the Boltzmann constant, and ηo is the viscosity of water, taken to be ηo ) 6.92 × 10-4 and ηo ) 6.29 × 10-4 Pa s at 37 and 42 °C, respectively. The normalized SLS intensity was measured as ISLS ) R/Kc, where the term R in ISLS is the Rayleigh ratio, corrected by background subtraction and normalized by the scattering of the toluene, and c is the concentration of the sample. K ) 4π2no(dn/dc)2/NAλ4 is the optical constant, no is the solvent refractive index, (dn/dc) is the refractive index increment of the solute, and NA is Avogadro’s number. For P84, (dn/dc) ) 0.135 and 0.131 at 37 and 42 °C, respectively.17 Rheology. Rheological properties were measured using a controlled-stress TA Instruments AR-2000 rheometer. A cone-and-plate geometry was used for the experiments. The cone was 60 mm in diameter and had a 2° cone angle, and measurements were performed with a constant gap of 55 µm. Inertia corrections were applied, and thermal expansion compensation was also taken into account. Measurements were performed at 37 °C and 42.5 °C with an accuracy of (0.1 °C. For every measurement, a fresh sample was loaded into the instrument and allowed to equilibrate for 5-15 min before starting each run after monitoring the normal force. The compression mode of the head was chosen to be exponential to prevent distortion in the structure of the sample. Flow curves were always collected according to the same procedure in sequences of increasing and decreasing shear rate. Stress sweeps were done to identify the linear viscoelastic regime. Frequency sweeps in the range of 0.01-70 rad s-1 were performed with a constant shear stress σ ) 0.1 Pa. A solvent trap was used to prevent water evaporation during the experiments. Flow curve measurements were repeated at least five times (using fresh samples) to ensure reproducibility of results. SAXS. Experiments on samples under flow were carried out on beamline ID02 at the European Synchrotron Radiation Facility (ESRF, Grenoble, France), using a capillary flow shear cell. Details on the flow cell have been given elsewhere and will be omitted here.12 Basically, the sample flows at a constant shear rate through a capillary, such that the flow direction is perpendicular to the direction (14) Brown, W., Ed. Dynamic Light Scattering: The Method and Some Appilcations; Clarendon Press: Oxford, 1993. (15) Berne, B. J.; Pecora, R. Dynamic Light Scattering; Wiley-Interscience: New York, 1976. (16) Provencher, S. W. Makromol. Chem. 1979, 180, 201. (17) Brown, W.; Schille´n, K.; Almgren, M.; Hvidt, S.; Bahadur, P. J. Phys. Chem. 1991, 95, 1850.
6898 Langmuir, Vol. 23, No. 13, 2007 of the incident X-ray beam. A wavelength λ ) 1 Å together with a two-dimensional CCD camera were used at the ESRF. The SAXS data were corrected to allow for sample transmission, background scattering, and detector response. Static experiments on samples without flow were performed with the laboratory SAXS instrument in the Department of Chemistry, University of Aarhus.18 The instrument is a modified NanoSTAR (Bruker AXS) optimized for solution scattering, which uses a rotating anode (Cu KR) with cross-coupled Go¨bel mirrors. The samples are mounted in the integrated vacuum of the camera in quartz capillaries with an inner diameter of about 1.7 mm glued into special sealed holders that are inserted into a block, which is thermostated by circulating water from a water bath thermostat. The same capillaries are used for both sample and background measurements. The scattering data are recorded on a two-dimensional position-sensitive HiSTAR (Bruker AXS) detector and are corrected for variations in detector sensitivity and spatial distortions. The isotropic data are azimuthally averaged, and the scattering from a 2 M NaCl solution was subtracted as background to obtain the scattering intensity I(q), where q ) 4π sin(θ/2)/λ, θ is the scattering angle, and λ is the X-ray wavelength. The data covers the range of scattering vectors q from 0.0085 to 0.35 Å-1. Samples at low concentrations were measured at 37 and 42 °C in order to obtain the micelle form factor and information on the structure of the micelles. The samples with 2 M NaCl have a relatively low transmission (approx. 3% for a path length of 1.7 mm), and, as the concentrations and contrasts are very low, it is difficult to obtain good signal-to-noise ratios and reliable background subtractions. The SAXS contrasts can be estimated from the electron density of the salt solution and the apparent specific densities of the PPO and the PEO. The values are not available for exactly the same conditions used in the experiments; however, literature values under similar conditions can be used. At 25 °C, the density of a 2 M NaCl solution is 1.081 g/mL,19 and this gives an electron density of 0.356 e/Å3. At 40 °C, PEO in water has an electron density of 0.386 e/Å3, and that of PPO is 0.339 e/Å3.20 This gives electron density contrasts of 0.030 e/Å3 for PEO and -0.017 e/Å3 for PPO. These estimates are quite rough, as the solvation of both PEO and PPO might be influenced by the presence of the salt. The densities of PEO and PPO in water change significantly with temperature due to the gradual disordering of the tightly bound water. The ions might have a similar effect on the solvation and it is therefore relevant to consider the densities at 80 °C for PEO and PPO. For these, one gets 0.369 e/Å3 and 0.322 e/Å3, respectively, and the contrasts are thus 0.013 e/Å3 for PEO and -0.034 e/Å3 for PPO. The values can be compared to electron densities derived from the modeling of the SAXS data. SANS. SANS experiments were performed on the LOQ diffractometer at the ISIS spallation neutron source, Rutherford Appleton Laboratory, Didcot, UK. LOQ is a time-of-flight instrument that simultaneously uses a range of neutron wavelengths to cover a wide range of scattering vectors, q. In these experiments, 0.007 e q/Å-1 e 0.29. The solutions in D2O (to reduce background scattering and maximize the contrast with the hydrogenous copolymers) were filled in 1-mm standard quartz cuvettes (Hellma), and the gels were mounted in quartz cells. A water bath was used to control the temperature. The SANS data were corrected for the measured sample transmission and background scattering (using D2O as a reference) and placed on an absolute scale in reference to the scattering from a wellcharacterized partially deuterated blend of polystyrene. The data were collected using a two-dimensional area detector and reduced to a one-dimensional form by radial averaging to produce intensity curves I(q). Small-Angle Scattering Theory. The small-angle scattering of a dilute solution of particles can formally be written as (18) Pedersen, J. S. J. Appl. Cryst. 2004, 37, 369. (19) Zaccai, G.; Wachtel, E.; Eisenberg, H. J. Mol. Biol. 1986, 190, 97. (20) Sommer, C.; Pedersen, J. S.; Stein, P. C. J. Phys. Chem. B 2004, 108, 6242.
Castelletto et al. I(q) ) NP(q)S(q)
(5)
where N is the normalization factor, which includes the number density of particles, P(q) is the form factor of the particle, and S(q) is the interparticle interference factor, which tends to unity for weakly interacting systems. The form factor was modeled as that for semiflexible self-avoiding cylinders with a circular cross-section, as described by the wormlike chain model with excluded volume interactions developed by Pedersen and Schurtenberger.21 Details of this model are given in the original paper.21 Briefly, it depends on three parameters: the chain contour length L, the persistence length lp (or the Kuhn length b ) 2lp), and the radius of the cylinder cross-section R. The persistence length is defined as the length along the cylinder over which the flexible cylinder can be considered a rigid rod. The total form factor of the micelles can be taken as the product of a longitudinal PL(q,L,b) and a cross-section form factor PCS(q), so that P(q) ) PL(q,L,b) × PCS(q). Since the micelles are expected to have polydispersity of the length in terms of an exponential-like size distribution, the longitudinal form factor becomes
∫ D(L,L )P (q,L,b)dL ,b) ) ∫ D(L,L )dL ∞
av
2R
PL(q,Lav
L
(6)
∞
2R
av
with D(L,Lav) ) exp(-L/Lav)
(7)
where Lav is the number average length of the micelles. The micelles have a PPO core surrounded by a PEO corona, and these two components have, as estimated in the previous section, different contrast in SAXS (and also in SANS); therefore, the crosssection form factor was taken as that of a core-shell structure:
[
2J1(qRout) qRout
PCS(q) ) ∆Fshell(πRout2)
]
2J1(qRcore) qRcore
(∆Fshell - ∆Fcore)(πRcore2)
2
(8)
where J1 is the first-order Bessel function. The micelles have the core radius Rcore and outer radius Rout, and the respective excess scattering length densities of core and shell/corona are ∆Fcore and ∆Fshell. In practice, the ratio ∆Fshell/∆Fcore is used as a fit parameter. It furthermore turned out that Rout was most reliably determined from the SANS data, and it was thus fixed at this value in the SAXS fits. The structure factor was modeled using the random phase approximation,22,23 in which polydispersity effects were included empirically:24 S(q) )
1 1 + RPL(q,Lav,b)
(9)
The parameter R increases with the concentration of block copolymer. According to scaling theory (deGennes), R ∝ c5/4, whereas Monte Carlo simulations find that R ∝ c1.39.23,25 The SANS data at high q revealed scattering from the internal structure of the corona (blob scattering), which were described by the form factor of Gaussian chains added to the cross-section (eq 8): (21) Pedersen, J. S.; Schurtenberger, P. Macromolecules 1996, 29, 7602. (22) Edwards, S. F. Proc. R. Soc. London 1966, 88, 265. (23) Pedersen, J. S.; Schurtenberger, P. Europhys. Lett. 1999, 45, 666. (24) Jerke, G.; Pedersen, J. S.; Egenhaaf, S. U.; Schurtenberger, P. Phys. ReV. E 1997, 56, 5772. (25) Pedersen, J. S.; Schurtenberger, P. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 3081.
Wormlike Micelles of Pluronic Block Copolymers Pblob(q) )
2(exp(-x) - 1 + x) x2
Langmuir, Vol. 23, No. 13, 2007 6899 (10)
where x ) q2Rg2, in which Rg is the radius of gyration related to the blob scattering. The fitting parameters of the model in eqs 5-9 are Lav, b, Rcore, Rout, ∆Fshell/∆Fcore, R, an overall scale factor, and a flat background for the combined fits to the static light scattering and SAXS data, with Rout being fixed at the value determined from the fits to the SANS data. The average contour length Lav and the Kuhn length b were determined from the fits to the lowest concentration data with R fixed at zero, as the concentration is so low that interparticle interference effects are expected to be small. For the higher concentrations, Lav and b were fixed, and R was fitted. Lav is expected to depend on the concentration as Lav ∝ cβ, where β ) 0.5-0.6.2 However, as we do not have enough information on this growth and as the influence of the variation of the micellar average length is masked by concentration effects on the structure factor, it was fixed at the value determined for the lowest concentration. For the neutrons, the flat background was replaced by adding the blob scattering (eq 10) with a scale factor and Rg as fit parameters. Lav, b, and R were fixed at the values determined from the combined fits to the lowest concentration SLS and SAXS data, as the corresponding low-q range is not covered by the data.
Figure 1. Cloud point curves upon the addition of structure makers NaCl ([) and KCl (2) and the structure breaker urea (9).
Results Phase Diagrams. Cloud point curves were measured for aqueous solutions of P84 in NaCl, KCl, and urea for different solute concentrations and two fixed polymer concentrations (0.1 wt % and 1 wt %). Figure 1 shows data for 1 wt % solutions of P84. It is well-known that salts such as NaCl and KCl act as “structure makers”, increasing the self-hydration of water through hydrogen bonding and therefore reducing polymer solubility.26 On the other hand, urea is clearly a water “structure breaker” leading to enhanced solubility of the polymer. For many types of Pluronic copolymers, cylindrical or wormlike micelles are observed at high temperatures, just below the cloud point. For P84, adjustment of the cloud point curve by the addition of salt brings the region of wormlike micelle formation into an accessible temperature range.13 In the following, solutions of P84 were studied in 2 M NaCl, to enable comparison with previous rheology and small-angle scattering data.3 The cloud point was measured to be at T ) 47 °C (Figure 1). Rheology. The rheological properties of wormlike micellar solutions of P84 in 2 M NaCl have previously been investigated by Waton and co-workers,13 and we therefore do not dwell on this, apart from one or two novel features we have observed. Figure 2 shows a flow curve we obtained at T ) 42.5 °C for an experiment in which the shear rate was increased in logarithmic increments (allowing equilibration of torque at each step as described in the Experimental section). In addition to the pronounced stress plateau for intermediate shear rates, noted previously, we observe a peak with a maximum at γ˘ ) 0.02 s-1. The plateau and maximum stress were reproducible in repeat runs to (10%. The maximum in the stress upon increasing shear rate was absent upon decreasing the shear rate. These observations provide evidence for phase separation under shear, or so-called shear banding. Upon increasing stress (only), the stress increases to a maximum before decreasing to a plateau. The phenomenon has been accounted for theoretically in terms of metastable solutions to the flow equations,27 and has been observed experimentally for other wormlike micelle systems such as (26) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: Oxford, 1998.
Figure 2. Viscosity (n) and shear stress (0) versus shear rate for a 4 wt % solution of P84 in 2 M NaCl at T ) 42.5 °C. A maximum in the flow curve is indicated by an arrow. The maximum and plateau stresses are also indicated.
Figure 3. Frequency dependence of storage and loss shear moduli for a 4 wt % solution of P84 in 2 M NaCl at T ) 42.5 °C, compared to the predictions of the Maxwell model with allowance for solvent viscosity (eq 11).
aqueous solutions of the system CpCl/NaSal.27 The values of the Newtonian viscosities at high and low shear rates and the plateau shear stress in Figure 2 are very similar to those reported previously for this system.13 Figure 3 contains frequency sweep data and a fit to a modified Maxwell model that allows for viscous resistance from the solvent:28
G′(ω) ) G0ω2τ2/[1 + ω2τ2]
(11a)
G′′(ω) ) G0ωτ/[1 + ω2τ2] + ηω
(11b)
G0 in eq 11 is the shear modulus, ω is the frequency, τ is a relaxation time, and η is the solvent viscosity. It can be seen from Figure 3 that the Maxwell model does not fit the data; in particular, at high frequency, the broad minimum in G′′(ω) (27) Grand, C.; Arrault, J.; Cates, M. E. J. Phys. II 1997, 7, 1071. (28) Rehage, H.; Hoffmann, H. Mol. Phys. 1991, 74, 933.
6900 Langmuir, Vol. 23, No. 13, 2007
Castelletto et al.
Figure 5. SAXS and SLS data for 0.5 wt % (filled circles), 2 wt % (open circles), and 3 wt % (filled squares) P84 at 37 °C. The lines correspond to the theoretical fitting of the experimental data.
Figure 6. SAXS and SLS data for 0.5 (filled circles) and 1 wt % (open circles) P84 at 42 °C. The lines correspond to the theoretical fitting of the experimental data. Figure 4. Level curves of the SAXS patterns, recorded for 4 wt % P84 at 42 °C, using a flow rate of (a) 15, (b) 15, and (c) 136 s-1 (see text for further details on flow history sequence).
suggests a broad distribution of relaxation times. There is also evidence for a deviation from the expected scalings G′ ∼ ω2 and G′′ ∼ ω1 at low frequency. SAXS for Samples under Capillary Shear Flow. Simultaneous SAXS and flow experiments were carried out for the sample under continuous flow using flow rates in the range γ˘ ) (17-1020) s-1. The capillary flow cell mentioned above was used in these experiments. Isotropic and anisotropic SAXS patterns were observed during our experiments.12 Figure 4a-c shows three representative isointensity curves of the SAXS patterns obtained at 42 °C. Before shear, the pattern was isotropic. The shear starts at γ˘ ) 15 s-1, and Figure 4a was obtained after 4 s of shear (1 s measurement time). Figure 4b was recorded 7 s after starting shear, and shows some loss of an initial “lozenge shape”. The shear rate was then increased to γ˘ ) 27 s-1 for 6 s, and the SAXS pattern maintained its anisotropy, as it did for 5 s of shear at γ˘ ) 68 s-1. However, upon increasing shear rate to γ˘ ) 136 s-1, the anisotropy was lost (Figure 4c). A lozenge-shaped SANS pattern had already been identified in experiments where a polymer network was stretched and simultaneously studied by SANS.29 The lozenge pattern results from the superposition of isotropic and anisotropic (ellipsoidal) scattering patterns due to the coexistence of unoriented and oriented material.29 An ellipsoidal SANS pattern has been observed in several simultaneous shear flow/SANS experiments involving wormlike
Figure 7. SANS data for 1 wt % P84 at 42 °C. The solid line corresponds to the theoretical fitting of the experimental data.
or cylindrical micelles.30,31 The long axis of the ellipse is perpendicular to the cylinder axis. Theoretical modeling of such SANS patterns showed that the ellipsoidal shape results from a polydispersity in micellar width and that the length of the minor axis of the ellipse increases upon increasing the micellar polydispersity.30 The data in Figure 4a,b suggest that, apparently, the process of alignment of the wormlike micelles is not a one-step transition, but rather a progressive rearrangement of the micelles in the direction of the shear flow. Indeed, the process depicted in Figure 4a,b was observed in our experiments each time that the SAXS spectra changed from an isotropic to an anisotropic pattern at
Wormlike Micelles of Pluronic Block Copolymers
Langmuir, Vol. 23, No. 13, 2007 6901
Table 1. Parameters Extracted from the Modeling of the SAXS and the SANS Dataa SAXS SAXS SAXS SAXS SAXS SANS
T [°C]
C [wt %]
Lav [Å]
b [Å]
Rout [Å]
Rcore [Å]
∆Fshell/∆Fcore
R
RH [Å]
Rg [Å]
37 37 37 42 42 42
0.5 2 3 0.5 1 1
1660 ( 39 1660* 1660* 6900 ( 210 6900* 6900*
540 ( 50 540* 540* 390 ( 7 390* 390*
59* 59* 59* 59* 59* 59 ( 2
31.5 ( 0.6 30.8 ( 0.7 33.5 ( 0.9 32.7 ( 1.1 36.4 (1.2 34.7 ( 3.3
-0.070 ( 0.011 -0.112 ( 0.014 -0.123 ( 0.019 -0.101 ( 0.019 -0.208 ( 0.034 0.380 ( 0.064
0* 1.9 ( 0.10 5.3 ( 0.15 0* 1.1 ( 0.06 1.1*
477 572 448 818 818 818
660 1360
a
Results plotted in Figures 5-7. Hydrodynamic radius RH obtained from DLS is also listed for comparison. Parameters marked with an asterisk (*) were fixed during the fit.
low flow rates. In contrast, an isotropic pattern was observed at high flow rates (Figure 4c), suggesting perhaps a re-entrant “melting”, if the shear rate exceeds the micellar recombination rate, or a flow-induced instability. At present, we are unable to distinguish between these two possibilities. SLS, SAXS, and SANS for Samples at Rest. The SLS and SAXS was measured for 0.5, 2, and 3 wt % P84 at 37 °C and for 0.5 and 1 wt % P84 at 42 °C. Figures 5 and 6 show the experimental SAXS and SLS data obtained at 37 and 42 °C. Using the optical constant as given in the Experimental section, the scattering data were converted into molar mass units (Dalton), so that the q ) 0 value for the dilute samples without interparticle interference effects directly gives the molar mass of the micelles. All the curves show a smooth intensity decay with increasing scattering angle. The SLS and SAXS data q ranges do not overlap, but the theoretical modeling according to eqs 5-9, considering a wormlike chain model with excluded volume interactions (represented by lines in Figures 5 and 6), has been used as an extrapolation between both sets of data. The data for different concentrations coincide at high q, where the scattering originates from the cross-section structure of the micelles. The low-q part is influenced by concentration effects. At 37 °C (Figure 5), the average contour length Lav and the Kuhn length b were determined from the fits to the 0.5 wt % data with R fixed at zero. That means that structure factor effects are assumed to be absent at this low concentration. For the data for the 2 and 3 wt % solutions, Lav and b were fixed at the value for 0.5 wt %, and R was fitted. The model provides good fits for the 0.5% data, whereas the fits are poorer for the higher concentrations. Note that the 2% SAXS data had spurious contributions below q ) 0.04 Å-1, and the data below this q value have therefore been omitted. At 42 °C (Figure 6), the average contour length Lav and the Kuhn length b were determined from the fits to the 0.5 wt % data with R fixed at zero. For the 1 wt % data, Lav and b were fixed at the value for 0.5 wt %, and R was fitted. The fit is good for the 0.5% data, whereas the agreement is poorer for the 1% data. The SANS data was only measured for 1 wt % P84 at 42 °C, and the data are shown in Figure 7 together with the model curve. The low-q part of the model was generated using the parameters for the fits to the combined SLS and SAXS data for a 0.5 wt % solution at the same temperature. Including the blob scattering term (eq 10), the model is able to reproduce the data very well. (29) Read, D. J.; McLeish, T. C. B. Phys. ReV. Lett. 1997, 79, 87. (30) Penfold, J.; Staples, E.; Cummins, P. AdV. Colloid Interface Sci. 1991, 34, 451. (31) Croce, V.; Cosgrove, T.; Dreiss, C. A.; King, S. Langmuir 2005, 21, 6762. Schubert, B. A.; Wagner, N. J.; Kaler, E. W. Langmuir 2004, 20, 3564. Koehler, R. D.; Raghvan, S. R.; Kaler, E. W. J. Phys. Chem. B 2000, 104, 11035. Berret, J. F.; Gamez-Corrales, R.; Oberdisse, J.; Walker, L. M.; Lindner, P. Europhys. Lett. 1998, 41, 677. Cummins, P. G.; Staples, E.; Hayter, J. B.; Penfold, J. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2773.
Figure 8. Radial cross-section profile of the micelles. The solid line is for SAXS (electron densities) and the dashed line is for SANS (scattering length densities)
SAXS data obtained for the sample under flow (Figure 4) showed the formation of cylindrical micellar objects in the samples studied in this work. In good agreement with this result, Figures 5 and 6 show that the wormlike chain model with excluded volume interactions and a core-shell cross-section structure is in reasonable agreement with the scattering data, although some discrepancies at low q are present at higher concentrations. The parameters extracted from the fits are listed in Table 1. The number-average length is about 1700 Å at 37 °C and increases to about 7000 Å at 42 °C. Theory predicts a temperature dependence at a fixed concentration proportional to exp(Ea/kT), where Ea is the endcap energy.32 The hydration of the PEO changes strongly with temperature, and this leads to an increase in Ea, which more than compensates the increase in temperature, thus leading to an increase in contour length. The diameter (d ) 2Rout) is about 120 Å, so the micelles are long compared to their diameter with ratios of Lav/d ) 10-60. The Kuhn length is b ) 540-390 Å, so the micelles are relatively flexible, with the ratio b/d ) 3.3-4.5. For comparison, nonionic surfactant micelles have a diameter of 70 Å and a Kuhn length of 170 Å,33 giving the ratio b/d ) 2.4. The low-resolution cross-section electron density profile is shown in Figure 8. It shows, as expected, opposite signs of the electron densities in the core and in the shell, whereas the scattering contrasts in D2O of core and shell have the same sign. Since the SANS excess scattering length densities of dry PPO and PEO are similar,34 the SANS profile shows that there is a difference of a factor of 2.5 in the density of material in the core and in the shell. Using this for the SAXS profile, one can conclude that the dry excess electron densities of shell and core have a ratio of about -0.3. This is in very good agreement with the values estimated above in the SAXS experimental section for polymers without solvating water of 0.013 e/Å3 for PEO and -0.034 e/Å3 for PPO, corresponding to electron densities of 0.369 e/Å3 and 0.322 e/Å,3 respectively. The radius of gyration related to the blob scattering was determined to be (31 ( 10) Å, which is quite large compared to the expected unperturbed (32) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869. (33) Jerke, G.; Pedersen, J. S.; Egelhaaf, S. U.; Schurtenberger, P. Langmuir 1998, 14, 6013. (34) Mortensen, K.; Pedersen, J. S. Macromolecules 1993, 26, 805.
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on P84 concentration is shown in Figure 9b, for T ) 37 and T ) 42 °C. The values for the hydrodynamic radius are also listed in Table 1, to be compared with the parameters extracted from the modeling to the SAXS and SANS data shown. It should be pointed out that RH for cylinders is an effective value for “equivalent spheres”, hence we do not expect RH to equal the cylinder radius. Indeed, if P84 micelles are modeled as rigid rods, it is possible to use the approximation37
RH ∼
L 2 ln(L/d)
(12)
where L is the length of the rod, and d is its diameter. Equation 12 can be used to evaluate the flexibility of P84 micelles. Assuming L ) Lav and d ) 2Rout from Table 1, it is possible to calculate RH ) 314 Å and 848 Å at 37 °C and 42 °C, respectively. The agreement with the measured values (Table 1) is reasonable considering the crude nature of the approximation (being very good at high temperatures). Figure 9. Variation of (a) decay rate Γ with q2 (3 wt % P84 at 37 °C) and (b) hydrodynamic radius RH with polymer concentration. Open circles: 42 °C; closed circles: 37 °C.
radius of gyration of the PEO chains of only about 12 Å, which suggests a possible stretching of the chains. The unperturbed radius of gyration is calculated using the Kuhn length of PEO of 10 Å35 and a contour length of 19 EO units of the PEO chains. The structure of P84 (EO19-PO43-EO19) can be compared to the structure of spherical micelles of P85 (EO25-PO40-EO25) in D2O36 with similar molecular mass of the blocks. In spite of the slightly higher molecular mass of the central PPO block of the present micelles, the core radius is smaller (32 Å compared to about 38 Å for P85). The profile used for the modeling of the P85 micelles is quite different, and therefore a comparison of outer radii is difficult; however, with an outer radius of the corona of the P85 of about 80 Å, the results are not in contradiction. Note that the mass density in the core relative to that in the shell for the P85 micelles is larger than about 5, which is much larger than the factor of 2.5 determined in the present case. DLS. Experiments were carried out for 0.5, 1, 2, and 3 wt % solutions of P84 in 2 M NaCl at 37 °C and for 0.5 and 1 wt % P84 at 42 °C. As mentioned above, CONTIN was used to calculate the relaxation rate distribution G(Γ) as a function of the angle. All the resulting G(Γ) functions were characterized by only one peak. The position of the peak maximum in G(Γ) was taken as the average relaxation rate, Γ h , of the system. The average relaxation rate Γ h plotted as a function of q2 is shown in Figure 9a for a 0.5 wt % P84 sample, at 37 °C. This shows that the data could be fitted with a straight line with an intercept of zero, indicating a diffusive process time. The apparent hydrodynamic radius RH was then calculated using eq 4. The dependence of RH (35) Fetters, L. J.; Lohse, D. J.; Richter, D.; Witten, T. A.; Zirkel, A. Macromolecules 1984, 27, 4639. (36) Pedersen, J. S.; Gerstenberg, M. C. Colloids Surf., A: Physicochem. Eng. Aspects 2003, 213, 175. (37) Riseman, J.; Kirkwood, J. G. J. Chem. Phys. 1950, 18, 512.
Conclusions In the present paper, we describe a comprehensive study of the self-assembly of Pluronic copolymer P84 in aqueous salt solution. Rheological studies of the wormlike micellar solutions of P84 in 2 M NaCl have revealed a new feature, in particular, the maximum in the flow curve in Figure 2. This gives evidence for phase separation under shear flow, for shear rates around γ˘ ) 0.02 s-1. The frequency dependence of the dynamic loss modulus is more accurately modeled by including solvent viscosity as an extra term in the Maxwell model equation (eq 11b). Simultaneous SAXS and shear flow experiments at 37 and 42 °C showed that the wormlike micelles can be aligned along the shear direction for low shear rates, but that the sample becomes isotropic again at high shear rates, presumably due to shearinduced breakage of the micelles. SAXS, SANS, and SLS curves were measured for dilute solutions of P84 at 37 and 42 °C. The combination of SAXS and SLS data in a single scattering curve provides structural information across a range of length scales and allows the micelle length and the Kuhn length to be obtained, as well as information about intermolecular interactions. The combination of SAXS and SANS enabled micellar radii (core and shell) to be obtained, as well as scattering density profiles. SANS provided the radius of gyration for the PEO chains in the corona. The form factor could be described by the wormlike chain model with excluded volume interactions.21 Although the micellar radius remained stable against temperature changes, the average length of the micelles increased with increasing T. This was consistent with DLS results, and can be explained as being caused by an increase in endcap energy upon increasing T.2 Acknowledgment. This work was supported by EPSRC grant GR/S73037 to I.W.H. We are grateful to Dr. S. M. King for assistance with the SANS experiments at ISIS. We thank T. Fini and J. Guiet (summer placement students at Reading) for the cloud point measurements. LA700382Y
