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Wormlike micelles (WLMs) are elongated, flexible aggregates formed by the self-organization of amphiphiles. Above a threshold concentration, their entanglement into a transient network imparts remarkable viscoelastic properties reminiscent of polymer solutions or gels (see Chapter 2). There is, however, a major difference arising from the fact that these structures are dynamic: aggregates continuously form and reform with surfactants constantly joining and leaving the ‘worms’. Critically, this gives WLMs the capacity to break and reform on a very short timescale, but also to change their morphology (from worms to spheres or to vesicles), based on small changes in composition, chemical structures of the amphiphiles, or external parameters such as temperature or pH, which, interestingly, can be exploited to impart responsiveness (see Chapter 6). As a result, WLMs have been exploited in numerous industrial and technological fields, in particular in the oil industry; some examples are given in the last part of this book (Chapters 12–14).

This short introductory chapter will provide the reader, and in particular those new to the field of wormlike micelles (WLMs), some basic luggage to equip them to embark onto the following chapters. The principles of WLM formation are presented, basic nomenclature is introduced, and fundamentals on the structural features of WLMs and their rheology are presented.

The incompatibility between the polar and apolar regions of amphiphilic molecules leads to their segregation in solvents that are selective: ‘good’ for one region, ‘poor’ for the other. In water, the polar (hydrophilic) region is referred to as the ‘head’, while the apolar (hydrophobic) section is the ‘tail’. Surfactants spontaneously self-assemble into a variety of structures, the morphology of which is dictated by the spontaneous curvature or packing parameter P of the amphiphile (Figure 1.1).1 

Figure 1.1

Schematic illustration of the relationship between the packing parameter P and the morphology of self-assembled surfactant aggregates. Reproduced from ref. 2 with permission from the Royal Society of Chemistry.

Figure 1.1

Schematic illustration of the relationship between the packing parameter P and the morphology of self-assembled surfactant aggregates. Reproduced from ref. 2 with permission from the Royal Society of Chemistry.

Close modal

The spontaneous curvature in solution merely reflects molecular asymmetry, i.e. the difference in effective packing area of the different molecular regions of the molecule (solvent-liking and solvent-hating). How molecules pack is thus dependent on the size of these antagonistic sections and their rigidity, but also the interactions present (such as hydrogen bonding or electrostatic forces), which can be tuned by parameters such as temperature, ionic strength, or pH (see Chapter 6). A high value of the spontaneous curvature reflects highly asymmetric molecules, and a tendency to assemble into spherical aggregates; on the other hand, low-curvature aggregates arise from relatively symmetric molecules and locally flat interfaces.

Israelachvili introduced the concept of the ‘critical packing parameter’ P,1  a geometrical quantity defined as v/lca0, where v is the volume of the lipophilic chain having maximum effective length lc, and a0 is the effective area per molecule at the surfactant/water interface. Cylindrical aggregates (thus WLMs) are expected for intermediate values of P (between 1/3 and 1/2), while spherical micelles (high spontaneous curvature) form at lower values of P (≤1/3) and bilayers (low curvature) are found for P>½ (above P=1, reverse micelles are formed, which are described in Chapter 3) (Figure 1.1).

The spontaneous curvature accounts for enthalpic contributions. Entropic effects come into play through: (i) bending of the cylindrical micelles (conformational entropy) and (ii) topological defects, such as end-caps (which increase the entropy by increasing the number of micelles) and branching points or junctions (which increase the configurational entropy). Both end-caps and branches have in common the formation of regions with different curvatures compared to the main cylindrical body, and incur different energetic penalties.3–5  The occurrence of intermicellar junctions has been invoked in several studies to explain a drop in the zero-shear viscosity, η0, as a function of surfactant, co-surfactant, or salt concentration, since the work of Cates6  and Lequeux,7  as the junctions are free to slide along the micellar body and thus provide an additional mechanism of relaxation. The presence of branches was later confirmed by cryo-TEM imaging (Chapter 7), which is about the only technique capable of identifying their presence. Recently however, pulsed field gradient (PFG) NMR measurements have been proposed as a new technique allowing a reliable determination of intermicellar junctions (more details on this technique, and its application specifically to reverse WLMs, can be found in Chapter 3).

The best-known and most studied WLM systems are cationic surfactants with long aliphatic chains, such as cetyltrimethylammonium bromide (CTAB) or cetylpyridinium bromide (CPBr), for which micellar growth takes place at relatively high concentration or in the presence of salt (a comprehensive list of systems, and the effect of the structure of counterions, are discussed in Chapter 11). Following these initial studies on cationic surfactants, numerous surfactants have been found to aggregate into WLMs, either in the presence of smaller headgroup-co-surfactants, other additives, salts, or with appropriate counterions.8,9  Chapter 4 offers a catalogue of more unorthodox amphiphiles which have also been reported to form WLMs and differ from the ‘classic’ hydrocarbon-based surfactants.

WLMs can be fully described by a number of structural parameters, which cover a broad range of length-scales. Figure 1.2 presents a schematic view of a WLM with the main dimensions of interest.

Figure 1.2

Schematic representation of a WLM showing characteristic length-scales: the overall radius of gyration Rg, contour length L, persistence length lp, and cross-section RCS. Reproduced from ref. 8 with permission from the Royal Society of Chemistry.

Figure 1.2

Schematic representation of a WLM showing characteristic length-scales: the overall radius of gyration Rg, contour length L, persistence length lp, and cross-section RCS. Reproduced from ref. 8 with permission from the Royal Society of Chemistry.

Close modal

The overall length of the micelles is referred to as the contour length L and varies from a few nanometres to micrometres. Cryo-TEM provides a direct visualization of the micelles and can be used to estimate the contour length; direct imaging techniques for WLMs are discussed in Chapter 7. Light scattering and small-angle neutron and X-ray scattering (SANS/SAXS) have also been used extensively to examine the structure of WLMs and are reviewed elsewhere.10,11  SAXS and SANS also offer a technique of choice to unravel the kinetics and formation pathways,12  which are discussed in Chapter 11.

A mean-field treatment of the growth process for either neutral or highly screened micelles gives a prediction of the average contour length in terms of volume fraction φ, temperature, and the end-cap energy Ec required to form two hemispherical end-caps as a result of rod scission:13 

Equation 1.1

For charged micelles in the absence of electrolyte, the scission energy has an additional component, Ee, due to the repulsion of charges along the backbone that favour shorter micelles. In this case the contour length L is given by:

Equation 1.2

Another important structural parameter in describing WLMs is the persistence length lp, the length over which micelles are considered rigid, which provides a measure of flexibility (it is related to the Kuhn length b by b=2lp). It is usually in the range 100 to ∼400 Å for uncharged surfactant WLMs,14  thus much larger than for polymers, due to the thickness of the cross-section (see Chapter 2 for a comparison of the rheology and structural differences between WLM and polymer solutions). For charged micelles, this value is highly dependent on the ionic strength.15–17 

Understanding how surfactant geometry impacts the structural characteristics of WLMs, and thus the rheology of their solutions, and how the self-assembly structures can be manipulated by appropriate parameters, offers a considerable challenge and is at the heart of many of the investigations reported in this book. In addition to imaging (Chapter 7) and scattering techniques, simulation techniques provide an avenue towards predictions of structure–properties relationships; recent developments in this area are reviewed in Chapter 10.

Above a critical concentration, the overlap concentration, C*, WLMs entangle into a transient network, which constantly breaks and re-form; for this reason WLMs are referred to as ‘living’ or ‘equilibrium’ polymers.18–20  The entanglement of WLMs imparts remarkable viscoelastic properties to their solution, which have been described by a model developed by Cates and coworkers.21  The dynamic behaviour of WLMs is central to the interest that they have generated, both at a fundamental level and in technological applications22–25  (see Chapters 12, 13, and 14). The fact that the peculiar rheological properties of WLMs originate from the spontaneous assembly of surfactants into these elongated structures, followed by their entanglement, implies that any change in the geometry of the building blocks—the surfactant—or their interactions, may drastically impact the architecture of the aggregates and thus the bulk properties. As a result, the rheological response is particularly sensitive to environmental triggers, which impact the assembly structures, and thus WLMs offer an ideal platform to create smart materials from small molecules, as discussed in Chapter 6. Since rheology underlies much of the interest in WLMs, the main concepts are briefly presented in this section, and are also a focus of Chapter 2. Pioneering work in the quantitative description of the rheological behaviour of WLMs is due to Rehage,26,27  Hoffmann,28  Shikata,29–32  Cates,6,19,21,33–36  Candau,37,38  and coworkers. Reviews on both linear and non-linear rheology can be found in ref. 8, 9, 39, 40.

In the dilute regime, WLMs usually behave as Newtonian fluids, with a viscosity η independent of the shear rate . However, shear-thickening (an increase of viscosity with shear rate) has also been observed in some systems,41,42  and attributed to the formation of shear-induced structures (SIS), reflecting phase separation between a surfactant-rich and a surfactant-poor phase. These transitions are ideally characterized by rheo-SANS, a method which combines microstructural SANS measurements with an applied deformation field to measure flow-induced structures in complex fluids, and is described in Chapter 8. Other types of complex flows are covered in Chapter 9 (which discusses the use of microfluidics to generate shear, elongated, and other types of flows in confined geometries) and Chapter 14 (which reports on WLM flows in process equipment and commercial devices).

At higher concentrations, the zero-shear viscosity η0 can reach values that are several orders of magnitude higher than that of the solvent (see for instance Chapter 2 and 6), depending on conditions such as temperature, salinity, or co-surfactant concentrations. The rheological behaviour usually becomes shear-thinning above a critical shear rate, c, which is attributed to the alignment of the wormlike chains in the shear flow. Viscoelasticity arises from the entanglements of WLMs, similar to what is observed in polymer solutions. In addition to the reptation found in entangled solutions of flexible polymers (a ‘reptile-like’ diffusion of the micelle along its own contour, determined by topological constraints and with a characteristic time τrep), WLMs display an additional stress-relaxation mechanism, which originates from the constant scission-recombination of the aggregates, characterized by τb. Two regimes can be distinguished:

  • If τbτrep, the dominant stress-relaxation mechanism is reptation and the micelles behave like polydisperse, unbreakable polymers, with a terminal relaxation time τR=τrep.

  • If τbτrep (the fast breaking limit), a micelle undergoes several scission and recombination processes within the reptation timescale. The behaviour is Maxwellian and the long-time behaviour of the stress relaxation can be described by a single exponential decay with a relaxation time τR given by:

The elastic, or storage, modulus (G′) and the viscous, or loss, modulus (G″) are described by the Maxwell equations:

Equation 1.3
Equation 1.4

where G0 is the elastic modulus extrapolated to t→0 (or infinite frequency) and τR is the relaxation time. This Maxwellian model has been found to apply to a vast number of WLM solutions, and for this reason a Maxwellian behaviour is often found in the literature to be synonymous with the presence of WLMs. However, a more ‘gel-like’ behaviour has also been reported in many WLM systems, with values of the storage and loss modulus fairly independent of frequency in the standard range of frequencies accessible to rheometers,43  usually accompanied by the absence of a low-shear-rate viscosity plateau (this is discussed in Chapter 2 and some examples are also given in Chapter 6).

Usually, WLMs exhibit a low-shear Newtonian plateau under steady state shear flow, which is followed by shear-thinning at a critical shear rate, c, the inverse of which gives an estimate of the longest micellar structural relaxation time τR.

In the dilute regime, the viscosity (η) increases linearly with increasing volume fraction of the surfactant (ϕ) following Einstein's viscosity equation:44 

Equation 1.5

In the semi-dilute regime, both steady zero-shear viscosity (η0) and dynamic rheological parameters (G0 and τR) instead follow a scaling law with theoretical scaling exponents 3.5, 2.25, and 1.25, respectively.15,45 

In addition to external parameters (such as temperature, pH, and light), the addition of nanoparticles has also been found recently to impact the structure of WLM networks, and therefore their rheology, a topic that is explored in Chapter 5.

Since the discovery over half a century ago that simple surfactants could thicken solutions, interest in WLMs has grown into a range of applications (some are described in Chapters 12–14) and new systems have emerged (Chapters 2–5), either based on reverse micelles (Chapter 3), involving biologically inspired building units (Chapter 4), combination with nanoparticles (Chapter 5), or showing responsiveness to external triggers (Chapter 6). In parallel to these developments, considerable progress has been made in understanding the properties and structure of WLMs. The combination of rheological and scattering techniques, rheo-SANS (Chapter 8), imaging techniques (Chapter 7), PGF-NMR (Chapter 3), and computer simulations (Chapter 10), offers great promise in terms of resolving structures over the whole range of relevant length-scales, while complex flow patterns can now be interrogated in microfluidic devices (Chapter 9). Characterization on the small and large scale, and better understanding of equilibrium properties and kinetic pathways (Chapter 11), may eventually lead to the ability to predict, and thus design, aggregate architecture and macroscale behaviour from chemical sequences.

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