Block copolymer worm micelles in dilution: Mechanochemical metrics of robustness as a basis for novel linear assemblies

Authors

  • Kandaswamy Vijayan,

    Corresponding author
    1. Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
    2. Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104
    • Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
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  • Dennis E. Discher

    1. Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
    2. Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104
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Over the last decade, it has become increasingly clear that amphiphilic block copolymers composed of strongly segregating blocks will self-direct their assembly in water into the same basic aggregate structures found for small surfactants: spheres, cylinders, and vesicular membranes.1–3 For each of these morphologies, the idealized packing parameter p4 is readily determined by a comparison of the core volume per molecule to its interfacial area: p < 1/3 for spherical micelles, p = 1/3 − 1/2 for cylindrical worm micelles, and p = 1/2 − 1 for membrane-bound vesicles. This simple and widely used shape parameterization serves to show that worm micelles not only are an intermediate microphase but also occupy the narrowest sliver of the phase diagram: Δpsph = 0.333 versus Δpwm = 0.167 versus Δpves = 0.50. In other words, worm micelles not only require more carefully proportioned hydrophilic-to-hydrophobic block ratios to achieve stability but also are likely to be less stable than other morphologies. Indeed, although spherical micelles and vesicles of lipids and surfactants have been extensively characterized, there are relatively few studies and applications of lipid- or surfactant-based worm micelles, in part because stresses and thermal defects accumulate over the length of any embedded linear object and tend to disrupt it. Block copolymers lead to more robust assemblies and thus open up new opportunities.

What block copolymers provide, of course, is a broadened choice of both the composition and molecular weight versus small amphiphiles.2, 5 The simplest strong segregation theory balances the interfacial tension against the chain elasticity and predicts that core diameter d of worm micelles will scale with molecular weight N of the hydrophobic block. Within experimental error,6 the scaling is

equation image

where a is the monomer size. To understand the implications of such scaling for chemical stability as well as mechanical stability, particularly in stirring, extrusion, and sonication, old and new theories of surfactancy and soft-matter stability can be invoked. First, recent studies of polymer vesicles and polymersomes have taught us that interfacial tension γ, established at the semisolvated interface between the core and corona, is independent of N.7 For a series of diblock copolymers composed of poly(ethylene oxide) and polybutadiene (N ∼ 40–250), for example, γ is approximately 25 mN/m. For large N, metrics of stability are provided by the critical micelle concentration (cmc) and the critical mechanical stress (σc), and they are expected to be as follows:

  • Chemical stability metric (ϕ = constant):

    equation image
  • Residence time in an aggregate:

    equation image
  • Mechanical stability metric:

    equation image
  • Lifetime under stress σ:

    equation image

The first two expressions are modified for polymeric surfactants on the basis of derivations and observations for small molecule surfactants.4 The latter two expressions have been recently established from work on the defect-limited stability of lipid vesicles,8 but they seem generally applicable. Thus, for a series of typical diacyl phospholipids such as phosphatidylcholines, the cmc plotted against total number N of CH2 fits the aforementioned stretched exponential with γa2 = 0.7kT, which is very close to 0.85kT from the usual linear scaling with N.4 The typical molecular residence time in a phospholipid bilayer is to ∼ h, and this means that liposomes4, 8 and cells9 are dynamic, open systems that exchange surfactants with solution on timescales of days. Stresses will also activate disassembly, with stresses or tensions that exceed σc (∼1 mN/m) by 10-fold able to rupture liposome membranes and cells on a timescale of tc ∼ seconds or less.

Now consider a typical, strongly segregating block copolymer such as poly(ethylene oxide)–polybutadiene. With four CHn per monomer, γa2 ≈ 2.8kT (giving a very reasonable monomer size, a ∼ 0.6 nm), and with N ∼ 80, the predicted cmc is immeasurably small (<10−100 M). In addition, a residence time in an aggregate of to > 1021 years exceeds the estimated age of the universe by 1010-fold! However, for giant worm micelles of length L ∼ 25 μm exposed to stresses of Σ ∼ 100 kPa (1 atm), which might be imposed in processes such as extrusion10 and sonication,11 net tensions of σ = ΣL ∼ 25,000 mN/m are sufficient to rupture these noncovalent assemblies in seconds according to determinations of tc. Such estimates are consistent with our recent observations that processes such as sonication and extrusion can induce rupturing. The estimates also indicate in semiquantitative terms the robustness as well as finite stability of block copolymer worm micelles, and they serve to illustrate how block copolymer amphiphiles expand considerably the range of properties achievable with self-assembling molecules.

On the basis of the stability gains highlighted previously and furthered as needed, with crosslinked copolymers,12 we and others have begun to explore and exploit polymer-based cylindrical morphologies. Our own approach has relied most heavily on the fluorescent labeling of polymer assemblies and fluorescence microscopy as a means of visualizing the stability and tracking worm-micelle dynamics in real time.12 This allows facile measurements of micrometer-scale persistence lengths, which, for poly(acrylic acid)–polybutadiene, have proved to be strongly modulated by calcium as it intercalates into the negatively charged poly(acrylic acid) corona.13 On the basis of similar principles of ionic interaction, arrays of cadmium sulfide quantum dots within worm micelles have also been recently formed with poly(ethylene oxide)–polystyrene–poly(acrylic acid) triblock copolymers.14 Cadmium crosslinking of the poly(acrylic acid) core is protected by a polystyrene shell and a poly(ethylene oxide) corona; the addition of hydrogen sulfide then produces cadmium sulfide quantum dots that appear aligned as a loose necklace in electron microscopy images. Such soft-matter templated structures are an intriguing positive step toward nano-optoelectronic devices.

Seeing is believing, but the visualization of worm micelles by the various methods of fluorescence microscopy, electron microscopy, and atomic force microscopy is often usefully supplemented with less direct methods such as dynamic light scattering and neutron scattering, especially for monitoring morphological changes.15–17 Indeed, worm micelles are sometimes particularly sensitive to the solvent conditions and temperature. Reversible, thermal transitions have been demonstrated recently in heptane, with polystyrene–polyisoprene diblocks, which form worm micelles at 25 °C and spheres at 35 °C.18 Although such sharp transitions have yet to be described with diblocks in water as a more selective solvent, the ability to morph between microstructures over a narrow range of temperatures is an exciting prospect for applications. Worm micelles have also been shown to form in ionic liquids.19 Poly(ethylene oxide)–polybutadiene copolymers form morphologies in an ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate, similar to those that they form in water, independently of the temperature from 25 to 100 °C for either solution. The results present interesting opportunities for exploiting worm micelles as inclusions that modify the unique properties of ionic solvents.

An exciting new area is the development of nanostructured cylinders. One example is provided by miktoarm star polymers with three mutually immiscible polymer arms connected at a junction.20, 21 With poly(ethylene oxide) as the hydrophilic arm and immiscible hydrocarbon and fluorocarbon chains, the morphologies in aqueous solutions range from discrete, multidomain micelles to long, segmented-core, cylindrical micelles. Hollow nanotubes have also been reported, with both highly novel organometallic block copolymers22 and corona-crosslinkable triblocks.23 All these intricate morphologies raise questions of molecular organization that simulations have just begun to address.24 Manipulation and physicochemical control over the various cylinder morphologies are among the next challenges to be confronted.

Worm micelles in solution undergo macroscopic ordering under shear25 as expected. In dilution, they also permeate nanoporous gels that mimic soils and tissues.26 If charged with, for example, poly(acrylic acid)–polybutadiene, worm micelles can be transported by electrophoresis, and they can be stretched in resonance with an oscillating E-field.27 The electric mobility of the poly(acrylic acid)–polybutadiene worms in pure water is within a factor of about 10 of the mobilities reported for DNA and actin filaments; this is curious, given the much larger number of ionizable groups per copolymer. Understanding such charge effects may enable further advances in processes such as quantum dot growth within worm micelles.14 Lastly, because of the stability of worm micelles and their surprising ability to enter cells when targeted,28 block copolymer worm micelles are now finding applications in drug delivery. The hydrolytic degradation of poly(ethylene oxide)–poly(caprolactone)-based worm micelles has been demonstrated to be a viable option for the timed release of hydrophobic drugs.29 In summary, all these new block copolymers that yield stable and manipulable cylinder morphologies present a broad set of new scientific and technological opportunities, and they might be fruitfully compared to advances in other nanocylinders being widely developed, such as carbon nanotubes.