Switchable bistable ordering and real-time alignment dynamics in wormlike micelles

Abstract

Using a combination of rheology and magnetic resonance known as “rheo-NMR” we observe, in real time, the shear- and field-dependent dynamics of orientational order in a wormlike micelle (WLM). We construct a dynamical phase diagram, yielding a range where bistable shear-activated phase switching occurs in which WLMs are stably isotropic (> 12 h) before shearing, and yet realign with B₀ after shearing. Furthermore, we extract anisotropic viscoelastic coefficients for the first time in a WLM by precisely fitting nonlinear realignment data. This deepened understanding of complex surfactant fluid dynamics lights a path toward increased materials control in advanced lubricants and coatings, drug delivery, and tissue engineering.

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Cylindrical, or wormlike, micelles constitute an intermediate phase of soft matter, encompassing properties of liquid crystals, entangled polymers, and molecular amphiphiles, with applications as diverse as personal care products, oil exploration, and lubrication. Amphiphiles can associate into various supramolecular aggregates, including spheres, vesicles, lamellae, and cylinders, based on molecular functionality and the relative sizes of their hydrophobic and hydrophilic functionalities.^1,2 WLMs posess unique viscoelastic, patterning, and encapsulation properties and thus represent pivotal components used in fracturing fluids in oil fields,³ personal care product viscosity modifiers,³ electrospun tissue scaffolds,⁴ and drug delivery agents.⁵ WLMs can be made polymerizable,⁶ and can form effective polymerization templates in which the resulting polymer retains the high aspect ratio of the micellar template and exhibits narrow polydispersity.⁷ WLMs have also been shown to form viscoelastic gels⁸ which can be adopted as scaffolds for nanomaterial manufacture. After intense experimental and theoretical scrutiny, many fundamental behaviors of WLMs evade understanding, such as: How does ordering couple to viscoelastic behavior? What is the nature of WLM entanglement?

WLM systems exhibit properties similar to polymer solutions, such as nonlinear stress-strain behavior, as the wormlike “chains” entangle with one another in analogy to conventional polymer chains, and these cylinders can additionally align to form a nematic liquid crystalline phase.^1,9,10 Here, we study cetyltrimethylammonium bromide (CTAB) in the range 17–23 wt% in ²H₂O, where CTAB self-assembles into cylinders of ∼ 4 nm diameter.¹¹

We employ rheo-NMR^12,13 to provide detailed molecular-scale understanding of these materials under macroscopic shear forces. Rheo-NMR is non-destructive, in situ, allows for straightforward theoretical interpretation, and does not require optically transparent samples. Shear-induced behavior such as shear banding and the shear-dependence of the isotropic-to-nematic transition have been addressed using rheo-NMR,^14,15small-angle neutron scattering under shear (SANSUS),¹⁶ and theory.¹⁷ Here, we use ²H NMR spectroscopy to observe background solvent ²H₂O molecules, which report on local micellar order. Previous studies involving CTAB WLMs have used ²H NMR to show spontaneous (static) magnetic alignment in the nematic phase.¹⁸ The present study allows observations of a bistable shear-induced transition not previously observed in any WLM system. Futhermore, by time-resolving the complex director realignment dynamics (from shear to magnetic alignment), and employing a continuum Leslie-Ericksen theory formalism,^19,20 we extract the first measurements of Leslie-Ericksen anisotropic viscoelastic parameters for a WLM.

We monitor WLM phase alignment sensitively as a function of shear in situ, and construct a dynamical phase diagram of shear and magnetic alignment as a function of composition and temperature T. We find a broad range of composition and T over which the nematic WLMs spontaneously align with the spectrometer magnetic field (B₀), or they can shear align perpendicular to B₀ in our axial Couette cell. At higher T, CTAB solutions exhibit a region of isotropic behavior where they will not align with B₀ or applied shear. Furthermore, we observe a novel intermediate phase that maintains long-term isotropy in a magnetic field until aligned in a perpendicular shear field. When shear is ceased, the phase realigns and stabilizes along the much weaker magnetic field. This intermediate phase region persists in either isotropic (pre-shear) or magnetically-aligned nematic (post-shear) phase for > 12 h, with transition back to the isotropic pre-shear phase accomplished by a simple temperature cycle.

Because deuterium is a spin I = 1 nucleus with a large electric quadrupole moment, its unique properties can be exploited in NMR experiments. The electric quadrupole moment of the nucleus interacts with the electric field gradient of the molecular bond in which it resides to produce a splitting in the ²H spectrum.²¹ In our system, the deuterons on the ²H₂O probe molecules show a quadrupole splitting Δν_Q in the spectrum described by^21,22

Δν_Q = Q_pSP₂(cosϕ) = Q_pρS_matrixP₂(cosϕ) (1)

where Q_p is the principle quadrupole tensor component along the molecular bond axis (∼ 260 kHz), and S = 〈P₂(cosχ)〉 is the orientational order parameter of the ²H₂O probes. χ is the angle of an O–²H bond axis relative to the alignment axis (director) of the WLM matrix and 〈P₂(cosχ)〉 = 〈(3cos²χ − 1)/2〉 is the time and spatial average of the second Legendre polynomial. ϕ is the angle between the director of the WLM matrix and B₀. Because we are interested in the order parameter of the WLM matrix S_matrix, we express S = ρS_matrix as S_matrix = 〈P₂(cosα)〉 the ensemble average over the second Legendre polynomial where α is the angle between a particular micelle segment and the director of the WLM phase. ρ is a scaling factor determined by interactions between the probe molecule and the WLM matrix, and is generally insensitive to temperature^22,23 for a given probe-matrix system at a given composition.

Isotropic tumbling, as in a simple liquid, causes molecules to experience all angles χ rapidly compared with the NMR (Q_p) timescale, averaging the quadrupolar Hamiltonian (and thus the splitting) to zero.¹⁴ However, if a deuterated probe molecule (here, ²H₂O) is present in an aligned WLM system, the motional averaging of the deuterated probe tumbling within the constraints of the micelles will be incomplete, causing the molecule to “inherit” the order of its surroundings, and exhibit a doublet in the spectrum.^21–23 Thus, at a given temperature and composition with monodomain alignment, Δν_Q reports on the angle and degree of WLM matrix alignment under shear or magnetic fields. We observe only a single doublet in the spectrum during shear and B₀ alignment, indicating uniaxial monodomain alignment.

NMR spectra at equilibrium show that WLMs spontaneously align with B₀ over a wide range of temperatures. This alignment occurs due to the anisotropy of magnetic susceptibility (χ_a) of the cylindrical worms, and is attributed simply to the susceptibility difference between the WLMs and solvent coupled with the shape anisotropy of the cylinders. Field-induced orientational order is quite common in liquid crystalline materials²¹ and has been reported in nematic wormlike micelle systems.^9,18 Alignment with B₀ occurs with two timescales governed by distinct processes, with equilibrium typically reached in a few hours. The alignment dynamics follow Leslie-Ericksen continuum dynamic theory,^19,20 which is the basis for our mathematical treatment below. Further, we see an increase in quadrupolar splitting values with increasing concentration, which is likely due to the ²H₂O probe molecules being increasingly constrained as the WLM volume fraction rises (ρ rises).

In this WLM system, we investigate orientational order dependencies on concentration, shear rate (ranging from γ˙ = 0.01 to 130 s⁻¹), time after initiating shear, and T. Complete alignment under shear rate γ˙ = 1 s⁻¹ occurs significantly faster (∼ 10 s) than the spontaneous field alignment at the same T, signifying that even moderate shear forces are orders of magnitude greater than the alignment force of the B₀ field. We can define a “critical shear rate” (γ˙_c) at which shear and field alignment forces exactly cancel one another and provide a singlet in the spectrum. For example, with 20 wt% CTAB in ²H₂O at 28 °C, we find γ˙_c ∼ 0.06 s⁻¹.

Using data from both spontaneous field alignment and shear alignment experiments, we have constructed the dynamical phase diagram shown in Fig. 1. We observe two distinct regions, which we have labeled as “field alignement” (FA) and “shear alignment” (SA). In the FA region, the WLMs align parallel to B₀. In the SA region, the WLMs can be aligned perpendicular to B₀, notably over a range of T higher than where they spontaneously field align. The FA direction is signified by the 2 : 1 ratio of quadrupole splitting in the FAvs.SA states (−0.5Δν_Q^FA = Δν_Q^SA), following the P₂(cosϕ) dependence of eqn (1) (see Fig. 2). Note that eqn (1) has a zero at ϕ = 54.7° (the so-called “magic” angle), which causes the spectrum to again manifest as a singlet. This singlet appears solely because the micellar director rotates through 54.7°, not due to the system transitioning to the isotropic phase. Under static conditions, these two cases are indistinguishable, but we can separate them easily with our dynamical rheo-NMR measurements. Within the FA region, shear alignment can still be achieved; however, in the SA-only region, field alignment will not spontaneously occur without prior stimulus. Previous phase diagrams determined by NMR and birefringence^14,16,18 indicate regions of nematic, isotropic, and hexagonal behavior of the CTAB WLMs, but do not describe dynamic phase behavior induced by shear forces. The upper limit of the SA region is derived at shear alignment plateau values with γ˙ ≥ 10 s⁻¹.

Fig. 1 Dynamical phase diagram for CTAB in ²H₂O as a function of temperature and concentration. Two regions manifest in our rheo-NMR experiments: one where field alignment occurs spontaneously along with readily attainable shear alignment (labeled FA & SA), and a higher T region where micelles do not spontaneously field align, but do shear align (labeled SA).

Fig. 2 ²H NMR spectra showing WLM realignment after shear cessation. Data shown for 20 wt % CTAB at 31 °C, covering 3 h after cessation of shear (γ˙ = 31.42 s⁻¹). In accordance with eqn (1), the initial value of Δν_Q (first spectrum at t = 10 s) is approximately ½ that of the final value (after 3 h – field aligned), and there is a crossover (single peak) at t = 2.5 min when the director is along the magic angle ϕ = 54.7°.

In addition to the field and shear alignment properties discussed, we find that upon raising T a few degrees above the initial FA range (e.g., to 33 °C for 20 wt% CTAB), the WLMs will align as expected under shear, but also exhibit intriguing field alignment properties after shear (see Fig. 1). Specifically, upon cessation of shear, Fig. 2 shows WLM realignment with B₀, which occurs over the entire FA & SA phase region of Fig. 1, but surprisingly even at temperatures greater than the initial pre-shear field alignment range (in the SA-only region). The spectra in Fig. 2 also indicate that the transition between SA and FA occurs such that there is no breakup of domains that rotate at different rates. We do not observe broad signals or powder patterns (superpositions) in the NMR spectra on the averaging timescale of this NMR experiment (∼ 10 ms), and thus all domains rotate at the same rate during realingnment with minimal variation in angle between domains.

Fig. 3 shows a proposed WLM realignment scheme, wherein the highly entangled WLMs are broken apart by the shear forces into aligned domains along the shear direction. After shear cessation, small domains (likely encompassing shorter cylinders) can then rapidly realign with the magnetic field, and finally the small domains grow slowly into a monodomain with greater overall ordering, and likely encompassing longer worms. We note that the isotropic and field-aligned nematic phases have long-term stability (> 12 h) in the spectrometer magnetic field, and hence are bistable and switchable.

Fig. 3 Illustration of WLM realignment motif. a, isotropic solution of WLMs prior to shear, b, WLMs under strong shear flow (ϕ = 90°), c, backflow and realignment with spectrometer field (B₀) following cessation of shear, d, stable alignment with B₀ (ϕ = 0°). The arrow on the right indicates the direction of the magnetic field (perpendicular to shear direction), block arrows indicate WLM director alignment, and curved arrows indicate rotation direction in the B₀ field. As an example, the director is at ϕ ≈ 54.7° in part c, where the NMR splitting vanishes.

We fit our spectroscopic data based on the treatments of nematic liquid crystalline polymer (LCP) systems outlined by Martins et al.¹⁹ and Kothe et al.²⁰ The director dynamics follow that of backflow and realignment observed in similarly realigning LCPs. Because the value of χ_a has not yet been measured for the CTAB/²H₂O or any similar WLM system, our fit utilizes a fixed estimate of 1.0 × 10⁻⁷ cgs based on measurements of other lyotropic nematics.^24,25 Fit results using this estimate are excellent (see Fig. 4), and are quite sensitive to order of magnitude changes in χ_a.

Fig. 4 WLM realignment dynamics. Micellar director realigns with B₀ after (perpendicular) shear alignment (γ˙ = 31.42 s⁻¹). Δν_Q splittings are shown as squares and calculated dθ/dt values as diamonds. The solid line is the fit to dθ/dt, yielding viscoelastic parameters. The inset details the first 5 min of realignment. Composition is 20 wt % and T = 31 °C.

Our fitting program provides values for k₃₃/k₁₁,²⁶ γ₁, α₁, α₂, and η_c. Values for η_b, α₃, γ₂ are derived from the Parodi relations²⁷ and equations relating the Miesowicz viscosities²⁸ with the Leslie coefficients.^29,30Table 1 shows typical fit results for the CTAB/²H₂O system. It is important to note that we observe the expected sign in all cases, however our measured parameters are 1–2 orders of magnitude larger than those reported on LCPs by Martins.¹⁹ Because these are the first reported measurements of the viscoelastic parameters for a WLM system, here we make comparisons with other systems that behave as nematic liquid crystals. Sample preparation and rheo-NMR experimental details³¹ can be found in electronic supplementary information (ESI†).

We have investigated phase behavior and dynamics of shear and magnetic field alignment in CTAB/²H₂O WLMs as a function of composition, aligning field strength, and temperature. We observe a novel bistable shear-induced phase in which WLMs will not align along B₀ until after they have been shear aligned. This work, to our knowledge, is the first report of measurements of the anisotropic viscoelastic parameters for a WLM system. We are continuing to study this system by correlating solution rheology measurements to our rheo-NMR experiments. Additionally, we are using pulsed-field-gradient NMR techniques to investigate self-diffusion behavior of the WLMs in both the aligned and unaligned state, and have begun to experiment with inclusion of molecules which reside either in the core of the micelles or in between the micelles, for potential applications as variable NMR alignment media in biological structure determination. Deep understanding of these systems will promote further design of micellar materials, and allow tailoring of viscoelastic and long-range alignment behavior for applications in tissue engineering, oil extraction, and advanced coatings and lubricants.

Table 1 Fit results for 20 wt% CTAB in ²H₂O sample at 31 °C

Parameter	Value	Error
a Calculated from fit parameters.
k11qz^2 (dyn/cm^1)	600	± 1.8
k33/k11	1.51	± 0.007
γ1 (P)	44,800	± 2,100
α1 (P)	−60,000	± 7,400
α2 (P)	−28,000	± 1,700
ηc (P)	7,400	± 850
^a ηb (P)	3,900	± 1,800
^a α3 (P)	16,700	± 2,700
^a γ2 (P)	−11,300	± 3,200

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Acknowledgements

This material is based upon work supported in part by the U.S. Army Research Office under Grant W911NF-07-1-0452 Ionic Liquids in Electro-Active Devices (ILEAD) MURI. Acknowledgment is also made to Virginia Tech for startup funds.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c1sm06634j

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