Similarly, block copolymers can be made of hydrophilic and hydrophobic blocks and form similar structures in water. Such an effect can be easily expanded into any selective solvent condition and thus, as long as the block copolymers are made of soluble and insoluble blocks, they can assemble into defined architectures.
The geometry and degree of order of these architectures depends on the concentration and the volume ratio between insoluble and soluble blocks – the insoluble soluble ratio (ISR). At very dilute concentrations, the soluble block compatibility with the host solvent is sufficient to maintain the copolymer as dissolved molecules (unimers). At a certain concentration called the critical aggregation concentration (CAC), block copolymers start to self-assemble so as to separate the insoluble blocks from the solvent. As the molecular mass and the ISR increase, the CAC decreases. At concentrations higher than CAC, block copolymers self-assemble into dispersed isotropic phases.
The structures are determined by the enforced curvature in the assembly arising from the relative sizes of soluble and insoluble domains, or from the ISR. The dimensionless packing parameter, ρ, originally developed for small amphiphiles in water, can be generalized and used to define the relative size of the nonsoluble region of a copolymer. The balance between solvent-phobic and solvent-philic interactions gives rise to an optimal surface area of the solvent-phobic block at the interface between the solvent-phobic and solvent-philic blocks (a0). This, together with the length and the volume of the nonsoluble domain, contributes to the packing parameter, defined as:
p = v / a0d
Where v is the volume and d is the length of the solvent-phobic block. The packing parameter is the ratio between the insoluble chain molecular volume and the volume actually occupied by the copolymer in the assembly. As a general rule, spherical micelles are formed when ρ ≤ ⅓, cylindrical micelles are formed at ⅓ < ρ ≤ ½ and membranes arise when ½ < ρ ≤ 1. As shown in fig 1, both cylindrical and spherical micelles consist of a no soluble core surrounded by a soluble corona. Membranes consist of two monolayer of block copolymers aligned so as to form a sandwich-like membrane: soluble block–insoluble block–soluble block. It is worth noticing that spherical micelles are self-contained assemblies and their diameter depends uniquely on the molecular characteristics of the block copolymer (i.e. chemistry and molecular mass). Conversely, for both cylindrical micelles and membranes, the molecular characteristics of the block copolymer only control the cylinder diameter and the membrane thickness, respectively.
Fig. 1. Different geometries formed by block copolymers in selective solvent conditions.
From a theoretical point of view, the most stable condition will be an infinitely long cylinder and infinitely large membranes. However, thermal fluctuations and the intrinsic fluid nature of these aggregates force finite dimensions. This means that in order to avoid contact between the solvent and the insoluble domains, a certain level of molecular frustration and consequently, curvature, is necessary. When molecular frustration is confined to a specific part of the assembly, cylindrical micelles are stabilized by end-caps into wormlike structures and membranes are stabilized by curved edges into disk-like micelles (sometime known as bicelles). When the molecular frustration is shared among all the molecules, the cylinders bend, forming toroidal micelles, while membranes close up, forming core-shell spherical structures known as vesicles. The two scenarios are energetically very different. Indeed, to form end-caps or curved edges, molecules assemble into structures with more interfacial curvature. Experimentally, it is most common to observe the formation of wormlike micelles and vesicles, respectively. It can be argued that in order to form end-caps on the cylinders only a smaller fraction of molecules are required compared with the formation of curved edges on membranes. Hence, energetically wormlike micelles and vesicles are more favorable than toroids and disk-like micelles. However, as the molecular mass of the copolymer increases, the energies change and local frustration becomes more unfavorable, as demonstrated by Bates and colleagues. In this way cylindrical micelles made of large molecular mass copolymers either grow very long or prefer to form more curved toroid-like structures. Similar structures have been observed by Förster studying the salt-controlled transition from spherical to cylindrical micelles in ionic block copolymers. Experiments conducted within Pochan's and Wooley's laboratories have also demonstrated that by introducing an extra interaction between block copolymers, both toroidal micelles, disk-like micelles, and even long helical cylindrical micelles can be stabilized.
Spheres, cylinders, vesicles, and occasionally toroidal and disk-like micelles are the result of equilibrating the different interactions between the two blocks and the solvent. This rule is independent of whether the different soluble and insoluble parts are arranged as a diblock (AB), triblock (
Although, the overall geometry is the same, multi-block copolymers have an extra level of control within the nanoparticles, introduced by the extra interaction between the blocks. ABC copolymers, where A and B are soluble, and C is insoluble, have been studied and developed for the foramtion of core-shell spherical micelles (fig 2b). Depending on the A/B ratio and the solvent condition (i.e. selective solvent plus good solvent), the two soluble blocks have been observed to form cylindrical and spherical domains on the corona of cylindrical micelles. ABC copolymers, where A and C are soluble, and B is insoluble, assemble into asymmetric ‘Janus’ (as in double-faced Roman god) particles. As shown in figures 2a, 2d, and 2g, depending on the ISR, Janus particles can be spherical, cylindrical, or vesicular. When A is soluble and B and C are both insoluble, the internal structure of the aggregate depends on the B/C ratio. Symmetrical copolymers (i.e. B and C with the same volume fraction) form insoluble core-shell spheres, cylinders (fig 2e), and disk-like micelles. When B and C have a different volume fraction, the insoluble domains will present an internal structure the geometry of which depends on the ratio between B and C. Spherical micelles with segregated cores that form spheres (raspberry-like micelles) and cylinders, segmented cylindrical micelles(fig 2f), and vesicles with hexagonally packed cylinders (fig 2i) have all been reported. That ABCA tetrablock copolymers, where A is soluble, and B and C are both insoluble, assemble into vesicles whose membrane has an internal morphology that changes from lamellar (fig 2h) to cylindrical on changing the volume fraction between B and C. All these morphologies seem to suggest that by modulating the different interactions between copolymer and solvent, we can engineer spherical, cylindrical, and membrane-enclosed nanoparticles. By adding a third chemical component, we can even engineer the same hierarchy of structures confined within the nanoscopic particles.
Fig. 2. Assemblies formed in selective solvent conditions by multiblock copolymers: (a) Janus spheres, (b) core-shell spheres, (c) raspberry-like spheres, (d) Janus cylinders, (e) core-shell cylinders, (f) segmented cylinders, (g) asymmetric (Janus) membrane vesicles, (h) double-layer membrane vesicles, and (i) vesicles with hexagonally packed cylinders. Scale bar 50nm.
As the concentration increases, the block copolymer-solvent interaction becomes more intense, leading to an extra interaction between the isotropic phases. In order to minimize the free energy, long range order mesophases are formed. As the concentration increases, the local packing also changes, leading to a decrease of the local curvature. In other words, molecules that at low concentration form spherical aggregates will assemble into cylindrical and eventually membrane-like aggregates as the concentration increases. Hence as a general rule, going from low to high concentration, spherical micelles pack into cubic phases, (fig 3a) followed by hexagonally packed cylinders (fig 3b)eventually, at high concentrations, into lamellae. Cylindrical micelles pack directly into hexagonal phases while vesicles initially pack into hexagonally packed vesicles (fig 3e), then bicontinuous phases (fig 3f), and eventually lamellae. At high concentrations, membrane forming copolymers have also been observed to form either cubic or hexagonal inverse structures. Such a sequence of phases is strongly affected by the copolymer molecular weight. The size of the copolymer affects how the copolymers pack locally. Researches observed that the boundaries between spheres, cylinders and membranes shift to a smaller ISR as the copolymer molecular mass increases. At high concentrations this resolves into novel phases such as the disordered network seen in fig 3d .
Fig. 3. (a) Cubic micellar phase formed by poly(ethylene oxide)-poly(ethyl ethylene) in an epoxy network. (b) Hexagonally packed cylinders formed by poly(ethylene oxide)-poly(butadiene) in water. (c) Disordered lamellar phase formed by poly(styrene)-block-poly(butadiene)-block-poly-(methyl methacrylate) in an epoxy network. (d) Disordered network formed by poly(ethylene oxide)-poly(butadiene) in water. (e) Hexagonally packed vesicles formed by poly(ethylene oxide)-poly(butylene oxide) in water. (f) Im3m bicontinuous phase formed by poly(ethylene oxide)-poly(butylene oxide) in water.
The copolymer molecular mass also strongly affects the rigidity of the assembly. This is particularly important for membrane-enclosed structures as the membrane elasticity dictates the level of order at high concentrations. This affects both the boundaries of the phases and the final morphology of vesicular gels and bicontinuous phases. As for isotropic phases, the level of complexity can be increased by adding a third component to the block copolymer and therefore introducing a second level of hierarchy controlled by block-block interactions. A representative example is the structure in fig 3c where one level of hierarchy is dictated by the solvent-copolymer interaction (the lamellae) and a second level of hierarchy is dictated by interactions between the blocks (the cylinders).
The intrinsic ‘soft’ nature of copolymers makes them assemble into structures that can tolerate a high level of imperfections. Therefore, block copolymer mesophases exhibit Bragg peaks that cannot be indexed assuming homogeneous crystal structures. While this may limit the application of block copolymers for materials where a homogeneous crystal structure is a key requirement, the intrinsic soft nature makes block copolymers mesophases very sensitive to external fields. Modest external fields, such as electrical or shear stimulation, are sufficient to trigger macroscopic arrangements in specific directions. These properties are highly welcomed in modern material science as they allow the generation of highly ordered nano- and microstructured materials on demand. In addition to this, the intrinsic macromolecular nature of the copolymers leads to very slow and kinetically controlled phase transitions. The formation of a specific phase, whether dispersed or over a long-range, occurs at specific solvent-copolymer ratios and the transition from one to another is controlled both by the diffusion of the solvent and by the single chain within the copolymer. We have demonstrated that the diffusion coefficient of water within a membrane-forming copolymer drops by three orders of magnitude when the molecular mass of the copolymer is increased by just one order of magnitude.
Because of this slow kinetics, metastable or intermediate phases have longer lifetimes. Eisenberg and colleagues reported a zoo of morphologies in their original work on block copolymer assembly in water. In a later work they also reported the formation of mesosize aggregates with regular hollow internal structures made from a 2 wt% solution of poly(styrene)410-b-poly(acrylic acid)13, commonly known as PS(410)-b-PAA(13), where 410 and 13 denote the number of monomers in the polymer chain, in DMF/H2O mixture (fig 4 a and b). We have recently demonstrated that long-range ordered mesophases can be dispersed into nanometer-sized particles by fast dissolution of membrane-forming copolymers in water (fig 4c and d). Similarly, we have demonstrated that by playing with the copolymer-solvent interface, membrane-forming copolymers can self-assemble into long tubular structures with ordered internal structures (fig e and f).
Fig. 4. (a) and (b) Transmission electron micrographs (TEM) of mesosize aggregates with regular hollow internal structures made from a 2 wt% solution of PS(410)-b-PAA(13) in DMF/H2O mixture. (c) and (d) TEM of lamellarsomes produced by membrane-forming copolymers in water. (e) and (f) Confocal laser scanning micrographs of a myelin-like structures produced by a membrane-forming copolymer in water and stabilized by chloroform.
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