Letter Cite This: ACS Macro Lett. 2018, 7, 614−618
pubs.acs.org/macroletters
Detecting Branching in Wormlike Micelles via Dynamic Scattering Methods Michelle A. Calabrese† and Norman J. Wagner*,‡ †
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States Center for Neutron Science, Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, United States
‡
S Supporting Information *
ABSTRACT: Topological differences in a model series of wormlike micelles (WLMs) with varying degrees of branching are investigated via neutron spin echo (NSE) and dynamic light scattering (DLS). Branching was previously verified via microscopy, scattering methods, and rheology. NSE measurements reveal that on the shortest length scales, where WLMs are topologically similar, the dynamic behavior is independent of branching level. However, branching leads to deviations from wormlike chain behavior on length scales relevant to branching. These differences continue into the DLS regime, where two relaxation modes are observed. While measuring micellar branching is challenging, our measurements of segmental dynamics provide a direct dynamic measurement of WLM branching and demonstrate promise for future identification of topological changes in self-assembled materials.
M
easuring chain branching and its effects on polymer physics is a long-standing scientific challenge with significant technological importance. Branched surfactant wormlike micelles (WLMs) are a useful model system for studying polymeric branching, and in both systems, dynamic measurements have proven useful in topological differentiation due to differences in chain dynamics.1,2 In contrast to polymers, branches in WLMs are not chemically bound, which has important consequences for dynamic properties, such as rheology. Branching is induced by changes in temperature and concentration or salt addition, which makes branch formation favorable due to electrostatic screening.3−6 While small angle scattering can be used to characterize branching in dilute polymer solutions,7 the analysis of branching is not unambiguous in polymers and WLMs when electrostatic interactions are present or above the overlap concentration. In WLMs, sliding branch points provide additional stress relief mechanisms, and in contrast to linear micelles, an array of relaxation modes may be expected in highly branched micelles.3,5,8 Accordingly, pulsed gradient spin−echo nuclear magnetic resonance (PGSE-NMR) experiments have detected branching in reverse micelles,9 where deviations from Maxwellian behavior were observed at high frequencies. Besides simulation,6 PGSE-NMR and conductivity measurements are the only methods to link branching to WLM rheology due to the difficulty of measuring branching;8 however, these methods are limited to reverse micelles. Here, neutron spin echo (NSE) and dynamic light scattering (DLS) are used to identify signatures of branching in a wellcharacterized, semidilute WLM series where branching is tuned via salt addition (Figure 1a).5,10,11 The surfactant phase behavior has been mapped extensively10 and we have explored the © XXXX American Chemical Society
Figure 1. (a) WLM branching transition with salt addition. (b) SANS intensity and 2D patterns (inset) of the low (°, bottom pattern), high (+, middle), and branched network (□, top) WLMs.
Received: March 10, 2018 Accepted: May 9, 2018
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DOI: 10.1021/acsmacrolett.8b00188 ACS Macro Lett. 2018, 7, 614−618
Letter
ACS Macro Letters
at qc = 0.02 Å−1, which arises from strong repulsions between the cationic headgroups, leading to an intermicelle correlation distance of 300 Å. These interactions are screened with salt addition, leading to a gradual disappearance of the peak and increase in I(q) at low-q. NSE experiments were performed at the NCNR to probe segmental and network dynamics. The wavelengths, λ, and Fourier times, τ, ranged from 8 ≤ λ ≤ 17 Å and 0.2 ≤ τ ≤ 290 ns, respectively, covering 0.01 ≤ q ≤ 0.16 Å−1. The NISF, I(q,t)/ I(q,0), was determined for each q-value, accounting for D2O and appropriate resolution standards.17 Select NISFs and fits to eq 1 are shown in Figure 2 for the low branching and branched
structure and degree of branching using small angle neutron scattering (SANS), cryo-TEM, and rheo-optics.5,10−12 Our previous rheological measurements and calculations show differences in the stretching and breakage of these WLMs based on branching level,5,11 the former being consistent with trends in branched polymers.2 Here, we demonstrate that on the length scales relevant to branching, the diffusion coefficients, stretch exponents, and relaxation rates change systematically with the level of branching. As NSE has been used to distinguish free versus cross-linked chains in polymer networks,1 these methods may be extended to characterize topology in polymers and other soft materials. The fast segmental dynamics of WLMs have been detected via NSE,13,14 where the normalized intermediate scattering function (NISF), I(q,t)/I(q,0), is fit using the Zilman and Granek model15 (eq 1): I (q , t ) S(q , t ) = = exp( −(Γ(q)t )β ) I(q , 0) S(q , 0)
(1)
where β = 3/4 for a wormlike chain (WLC) and β = 2/3 for a flexible membrane when 1 ≪ qξ (ξ is a domain length). The relaxation rate, Γ(q), and segmental diffusion coefficient, DG, are related by
Γ(q) = DGq2/ β
(2)
These experiments verified the stretch exponent of β = 3/4 for WLMs, such that Γ(q) ∝ q8/3. The WLMs exhibited Maxwelllike behavior in the linear viscoelastic (LVE) regime,14 indicating that the solutions were composed of primarily linear WLMs within the fast-breaking limit.5,8 High branching levels lead to high-frequency deviations from Maxwellian behavior for both WLMs and polymers,2,8,16 suggesting that branching has a significant impact on dynamic relaxation. Three solutions of constant surfactant (1.5 wt %) and increasing sodium tosylate (NaTos) content are presented, referred to as low branching (0.01 wt % NaTos), high branching (0.25%), and branched network (0.50%). Previously reported length and time scales are confirmed via rheology (Figure S1) and SANS; for experimental protocols, see refs 5, 11, and 12. As salt screens electrostatic interactions and increases micelle flexibility, the relaxation time, τR, and persistence length, lp, decrease with branching,5,10,11 where τR = 6, 0.02, and 0.007 s and lp ≈ 1000, 200, and 150 Å for the low, high, and branched network solutions, respectively. The low branching solution exhibits Maxwell-like behavior with a single minimum in G″ at high frequencies; clear deviations are seen in the two more highly branched solutions, where most notably G′ does not exhibit a high frequency plateau. Additionally, the crossover modulus increases with branching due to the formation of interconnected structures. SANS was performed at the National Institute of Standards and Technology Center for Neutron Research (NCNR). Absolute scattering intensities are shown in Figure 1b, where the scattering vector, q, is related to real-space dimensions as q ≈ 2π/d. The intensities at short length scales (q > 0.03 Å−1, d < 200 Å) are nearly identical between samples. Using the flexible cylinder model, the micelle cross-sectional radius is rcs = 21.0 ± 0.1 Å for all solutions, in agreement with previous results.5,10,11 The congruence of the scattering curves at high q-values indicates that adding salt to induce branching does not fundamentally alter the cylindrical nature of the micelles. An interaction peak is observed for the low branching solution
Figure 2. NISFs and fits (eq 1) for the low branching (solid symbol/ line) and branched network (open symbol/dotted line) WLMs.
network solutions. The NISFs are nearly identical for all samples for the largest q-values, which correspond to motion of the micelle cross-section. As longer length-scale relaxations relevant to branching are probed, the NISFs begin diverging and significant differences are observed between branching levels. The relaxation rates and stretch exponents were calculated using eq 1 (Figure 3). At short length scales (q > 0.12 Å−1), the
Figure 3. WLM segmental relaxation rate. Γ(q) and β are statistically identical at high q (Γ ∝ q8/3), but diverge with decreasing q. Inset: Differences in the low-q NSE become prominent in the DLS fast mode, Γ1(q).
relaxation rate is independent of branching and scales as q8/3. The calculated segmental diffusion coefficient, DG, is identical between samples within the experimental uncertainty (Table 1) and is similar to results for other WLMs (DG ≈ 0.06 vs DG ≈ 0.05 nm8/3·ns−1 in ref 14). Paired t-tests were performed to 615
DOI: 10.1021/acsmacrolett.8b00188 ACS Macro Lett. 2018, 7, 614−618
Letter
ACS Macro Letters Table 1. Calculated Diffusion Coefficientsa NaTos
DG · 10−17, (m8/3/s)
D1 · 10−11, (m2/s)
D2 · 10−14, (m2/s)
(D2τR)1/2, Å
0.01 0.25 0.50
5.96 ± 0.10 5.81 ± 0.10 5.97 ± 0.08
10.1 ± 0.1 2.44 ± 0.02 1.72 ± 0.01
5.87 ± 0.18 58.4 ± 1.1 127.3 ± 2.0
5900 1000 950
In Figure 4, the low branching solution fit of β = 0.77 ± 0.05 agrees with the WLC model, which is reasonable based on its long persistence length and linear chain topology. For the branched network, β = 0.63 ± 0.05, which encompasses β = 2/3 predicted for a flexible membrane. The stretch exponent here reflects the high branch density and network interconnections, which lead to behavior similar to a membrane or sponge. While Figure 4 shows the NISFs for only one q-value, the differences in β are persistent across the full low-q region, as evidenced by the paired t-test result. At the lowest measured q-value, the length scale approaches ξM (≈900 Å) for the low branching solution;5,10 however, the β-value remains constant. Therefore, the observed differences in β result from differences in branching level, and not simply a difference in the probed length scale or domain size between samples. To support the NSE findings, larger-scale relaxations near the chain contour length were probed via DLS (ALV CGS-3, λ = 632.8 nm, 0.000571 ≤ q ≤ 0.00255 Å−112). The secondorder autocorrelation function, g2(t), was converted to the firstorder autocorrelation function, g1(t), via the Siegert relation.18 Two distinct relaxation modes were observed, which is common in semidilute solutions where chains are entangled or topologically constrained.19,20 Using a double stretched exponential,19−21 g1(t) is fit by
a DG occurs when Γ ∝ q8/3; D1 and D2 correspond to the fast and slow DLS modes, respectively. The reported uncertainty is the 95% confidence interval.
compare β values between samples at equal q values. In this region, β was independent of the branching level (p > 0.5) and was near the expected WLC value of β = 3/4. Thus, on the subsegmental length scale, the WLM dynamics are unaffected by branching, which is not surprising considering the structural similarities in this region (Figure 1b). The network-like properties of the WLMs become important as q decreases. Interestingly, in the intermediate-q range (0.02 < q < 0.08 Å−1), statistically significant differences in β are observed between samples (p < 0.05), which may correspond to differences in micellar flexibility. However, the relaxation rates in this region are statistically identical, suggesting that β is sensitive to small structural differences that may not affect the overall relaxation rate. Significant differences in the dynamics are observed starting at the correlation distance, qc. Here (q < 0.02 Å−1), statistically significant and reproducible differences are observed in both β and Γ(q) between the low branching and branched network solutions (p < 0.05). Only two samples were fully probed over this region; however, the data for the highly branched solution resembles the branched network data for this range (Figure S2). In the low branching sample where lp is long, a stretch exponent of β = 3/4 is expected whenever qξ ≫ 1. However, for the branched network, β = 3/4 is only expected on small length scales unaffected by the high branch density. At length scales near the mesh size, ξM, or distance between branch points, we hypothesized a transition to lower β values. Here, a β value near β = 2/3 seen in flexible membranes and sponges would be reasonable,15 as the WLMs may behave as a single, interconnected network. The results shown in Figure 4 support this reasoning, where the two low-q NISFs are plotted via the WLC scaling, q2t3/4. Significant differences are observed in β, and only the low branching solution scales with the model.
g1(t ) = A1 exp(− (Γ1(q)t )β1 + (1 − A1)exp(− (Γ2(q)t )β2 )
(3)
where, for entangled polymers, β1 = 1 (fast mode) and β2 < 1 (slow mode). The fast mode is attributed to cooperative, translational diffusion of the short chain segments or blobs between entanglement points.20,22 While its origins are debated, the slow mode is generally attributed to diffusion resulting from hindered motions of interacting or entangled chains, which may reflect long-range correlated fluctuations.19−23 Figure 3 (inset) confirms the diffusive q2-scaling for both modes. The differences in Γ(q) from NSE continue into this regime and appear to correspond to the fast mode, Γ1(q), as expected.14 Here, Γ1(q) is largest in the low branching solution and smallest in the branched network solution. For the slow mode, these trends are reversed: Γ2(q) is smallest in the low branching solution and largest for the branched network. The slow mode is the most stretched in the low branching solution, such that β2,low < β2,high < β2,network (Figures S3−S5). Calculated apparent diffusion coefficients for both modes, D1 and D2, are shown in Table 1. For both modes, Γ(q) versus q2 gives a near-zero y-intercept, indicating translational diffusion. Table 1 also gives a length scale associated with the slow mode. This scale is smallest, and nearly identical (≈ξM), for the two branched solutions. Based on their similar DLS and NSE behavior and similar crossover modulus (Figure S1), which strongly correlates with interconnected structures,5 these two solutions likely have similar levels of branching. The large-scale dynamics of the low branching solution are dominated by electrostatic interactions. It is well-documented that increasing solution ionic strength in polymers and polyelectrolytes decreases D1 and increases D2.24−26 One explanation is coupled dynamics between the WLMs and counterion cloud.26 Thus, we expect D1 to be fastest for the low branching solution and decrease for the branched solutions where electrostatic interactions are screened. Dipole−dipole interactions from the counterion cloud may cause temporary aggregates to form in low salt WLMs, thereby decreasing D2.26 However, these interactions cannot quantitatively account for the entire
Figure 4. NISFs and eq 1 fits for the low branching (solid points, line) and branched network (open, dashed) solutions, plotted via the WLC scaling q2t3/4. Only the low branching solution consisting of linear entangled micelles scales with the model. 616
DOI: 10.1021/acsmacrolett.8b00188 ACS Macro Lett. 2018, 7, 614−618
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ACS Macro Letters
and the Institut Laue-Langevin for providing the scattering facilities used in this work. Access to the Neutron Spin Echo Spectrometer was provided by the Center for High Resolution Neutron Scattering, a partnership between NIST and the NSF under Agreement No. DMR-1508249. This manuscript was prepared under cooperative agreement 70NANB12H239 and 70NANB15H260 from NIST. The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the view of NIST or the U.S. Department of Commerce. The authors thank Antonio Faraone and Michi Nagao for assistance with NSE experiments.
slow mode, suggesting that entanglement and cross-linking effects also strongly contribute.26 Accordingly, the slow mode likely stems from internal motion of the entangled or branched network,20,22 governed by intermicelle interactions and entanglement phenomena that impact the relaxation time. Thus, it is not surprising that the branched network relaxes fastest, as τR,low ≈ 103τR,network; τR for these samples scales with the zero-shear viscosity, η0.5 As decreases in η0 with salt addition cannot be explained by electrostatic screening alone,27 the measured τR results from a combination of screening and branching effects. As interactions are screened with salt addition, branching effects become more prominent. Sliding branch points can relieve entanglements, thereby decreasing hindrance to motion and, consequently, the prominence of the slow mode,20 unlike in star polymers where branching promotes additional modes.28 This mode thus reflects differences in τR resulting from both branching and electrostatic screening, though quantifying the relative contributions is difficult because branching is inherently linked to the ionic environment. Here, we have demonstrated that the dynamic behavior of WLMs on the segmental length scale is indicative of the underlying morphology. As in branched polymers, significant branching in WLMs leads to deviations from Maxwellian rheological behavior, which is clearly reflected in the network and segmental dynamics. The stretch exponent β, an indicator of topology, exhibits precisely the behavior hypothesized for micellar branching, namely a transition from chain-like to sheetor sponge-like dynamics. At short length scales, β and Γ(q) are independent of branching, and SANS shows that the same wormlike structure is always observed. At the segmental length scale, significant differences in β and Γ(q) are observed. While some of the differences in Γ(q) can be attributed to electrostatic effects, changes in β give firm evidence of morphological differences. The low branching solution always acts like a wormlike chain, whereas the branched network solution behaves like a membrane or sponge when longer length scales are probed. While direct detection of WLM branching is challenging, NSE now provides a robust method complementary to PGSE-NMR for doing so. These findings establish techniques for identifying micellar and polymeric branching, and morphology differences in self-assembled systems.
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(1) Ewen, B.; Richter, D. Neutron Spin Echo Spectroscopy Viscoelasticity Rheology; Springer, 1997; pp 1−129. (2) Snijkers, F.; Vlassopoulos, D.; Lee, H.; Yang, J.; Chang, T.; Driva, P.; Hadjichristidis, N. Start-up and relaxation of well-characterized comb polymers in simple shear. J. Rheol. 2013, 57, 1079−1100. (3) Oelschlaeger, C.; Schopferer, M.; Scheffold, F.; Willenbacher, N. Linear-to-branched micelles transition: a rheometry and diffusing wave spectroscopy (DWS) study. Langmuir 2009, 25, 716−723. (4) Sachsenheimer, D.; Oelschlaeger, C.; Müller, S.; Küstner, J.; Bindgen, S.; Willenbacher, N. Elongational deformation of wormlike micellar solutions. J. Rheol. 2014, 58, 2017−2042. (5) Calabrese, M. A.; Rogers, S. A.; Murphy, R. P.; Wagner, N. J. The rheology and microstructure of branched micelles under shear. J. Rheol. 2015, 59, 1299−1328. (6) Dhakal, S.; Sureshkumar, R. Topology, length scales, and energetics of surfactant micelles. J. Chem. Phys. 2015, 143, 024905. (7) Kratky, O. Possibilities of x-ray small angle analysis in the investigation of dissolved and solid high polymer substances. Pure Appl. Chem. 1966, 12, 483−524. (8) Rogers, S. A.; Calabrese, M. A.; Wagner, N. J. Rheology of Branched Wormlike Micelles. Curr. Opin. Colloid Interface Sci. 2014, 19, 530−535. (9) Angelico, R.; Amin, S.; Monduzzi, M.; Murgia, S.; Olsson, U.; Palazzo, G. Impact of branching on the viscoelasticity of wormlike reverse micelles. Soft Matter 2012, 8, 10941−10949. (10) Schubert, B. A.; Kaler, E. W.; Wagner, N. J. The Microstructure and Rheology of Mixed Cationic/Anionic Wormlike Micelles. Langmuir 2003, 19, 4079−4089. (11) Calabrese, M. A.; Rogers, S. A.; Porcar, L.; Wagner, N. J. Understanding steady and dynamic shear banding in a model wormlike micellar solution. J. Rheol. 2016, 60, 1001−1017. (12) Calabrese, M. A. PhD Thesis; University of Delaware, 2017. (13) Seto, H.; Kato, T.; Monkenbusch, M.; Takeda, T.; Kawabata, Y.; Nagao, M.; Okuhara, D.; Imai, M.; Komura, S. Collective motions of a network of wormlike micelles. J. Phys. Chem. Solids 1999, 60, 1371− 1373. (14) Nettesheim, F.; Wagner, N. J. Fast dynamics of wormlike micellar solutions. Langmuir 2007, 23, 5267−5269. (15) Zilman, A.; Granek, R. Undulations and dynamic structure factor of membranes. Phys. Rev. Lett. 1996, 77, 4788. (16) Khatory, A.; Lequeux, F.; Kern, F.; Candau, S. Linear and nonlinear viscoelasticity of semidilute solutions of wormlike micelles at high salt content. Langmuir 1993, 9, 1456−1464. (17) Azuah, R. T.; Kneller, L. R.; Qiu, Y.; Tregenna-Piggott, P. L.; Brown, C. M.; Copley, J. R.; Dimeo, R. M. DAVE: a comprehensive software suite for the reduction, visualization, and analysis of low energy neutron spectroscopic data. J. Res. Natl. Inst. Stand. Technol. 2009, 114, 341. (18) Siegert, A. J. F. MIT Rad. Lab.; 1943, Rep. No. 465. (19) Moitzi, C.; Freiberger, N.; Glatter, O. Viscoelastic Wormlike Micellar Solutions Made from Nonionic Surfactants: Structural Investigations by SANS and DLS. J. Phys. Chem. B 2005, 109, 16161−16168. (20) Li, J.; Ngai, T.; Wu, C. The slow relaxation mode: from solutions to gel networks. Polym. J. 2010, 42, 609−625.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.8b00188. Figures S1−S5, including rheology measurements, additional NSE results, and DLS spectra (PDF).
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Michelle A. Calabrese: 0000-0003-4577-6999 Norman J. Wagner: 0000-0001-9565-619X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, 617
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DOI: 10.1021/acsmacrolett.8b00188 ACS Macro Lett. 2018, 7, 614−618
