Lattice Disordering/Ordering and Demicellization/Micellization Transitions in Highly Asymmetric Polystyrene-block-Polyisoprene Copolymers

Liquid-Like States in Micelle-Forming Diblock Copolymer Melts

Large cell self-consistent field theory (SCFT) solutions for a neat, micelle-forming diblock copolymer melt, initialized using the structure of a Lennard-Jones fluid, reveal the existence of a vast number of liquid-like states, with free energies of order 10^-3 k_BT per chain higher than the body-centered cubic (bcc) state near the order-disorder transition (ODT). Computation of the structure factor for these liquids at temperatures below the ODT indicates that their intermicellar distance is slightly swollen compared to bcc. In addition to providing a mean-field picture of the disordered micellar state, the number of liquid-like states and their near-degeneracy with the equilibrium bcc morphology suggest that self-assembly of micelle-forming diblock copolymers navigates a rugged free energy landscape with many local minima. This picture provides a basis for the anomalously slow ordering kinetics of particle-forming diblock copolymer melts observed in experiments.

Ordered Microdomain Structures in Saccharide-Polystyrene-Saccharide Hybrid Conjugates

Hybrid conjugates consist of synthetic polymers and naturally occurring saccharides, and are capable of microphase separation at small molecular weights to form ordered domain structures. In this study, we synthesize ABA triblock-like conjugates with polystyrene as the synthetic mid-segment and either trisaccharide maltotriose (MT) or disaccharide maltose (Mal) as the end unit. Hybrid conjugates of varying compositions are prepared by a combination of atom transfer radical polymerization and a click reaction, and their morphologies are examined by small-angle X-ray scattering and transmission electron microscopy. The MT-containing conjugates are found to form well-ordered domain structures with a sub-10 nm periodicity, and morphology transition from cylinders to spheres to disordered spheres is observed with decreasing saccharide weight fraction. The Mal-containing conjugates also show microphase separation. However, the observed domain morphologies lack regular packing due to the close proximity of polymer glass transition temperature and order-disorder transition temperature. The saccharide-containing conjugates are also found to undergo an irreversible morphology change at high temperatures, attributed to saccharide dehydration-induced pentablock-like structure formation.

NMR Studies of Block Copolymer-Based Supramolecules in Solution

Hierarchical assemblies from block copolymer (BCP)-based supramolecules have shown immense potential as programmable materials owing to their versatility for incorporating functional molecules and provide access to arrays of hierarchical structures. However, there remains a knowledge gap on the formation of the supramolecule in solution. Here, we applied NMR techniques to investigate the solution-phase behavior of the most studied supramolecular systems, polystyrene-block-poly(4-vinylpyridine)(3-pentadecylphenol) (PS-b-P4VP(PDP)_r). The results show that the supramolecule likely adopts a coil-comb conformation, despite the small molecule's (PDP) rapid exchange between the bonded and free states. The exchange rate (>10⁴ s^-1) exceeds the NMR time scale at the frequency of interest. The supramolecules form under dilute conditions (∼2 vol %) and are attributed to the enthalpic gain of the hydrogen bonding between the PDP and 4VP. As the solute concentration increases (>10 vol %), the supramolecule forms micelle-like aggregates with PDP accumulated within the comb-block's pervaded volume based on analysis of the apparent molecular weight, viscosity, and chain dynamics. This work sheds light on the long-standing question regarding the evolution of the constituents in the BCP-based supramolecule in solution and provides valuable guidance toward their solution-based processing and morphological control.

Field theoretic approach for block polymer melts: SCFT and FTS

This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.

Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers

The phase behavior of poly(styrene)-b-poly(1,4-butadiene) diblock copolymers with a polymer block invariant degree of polymerization N[over ¯]_{b}≈800 shows no evidence of Frank-Kasper phases, in contrast to low molar mass diblock copolymers (N[over ¯]_{b}<100) with the same conformational asymmetry. A universal self-concentration crossover parameter N[over ¯]_{x}≈400 is identified, directly related to the crossover to entanglement dynamics in polymer melts. Mean-field behavior is recovered when N[over ¯]_{b}>N[over ¯]_{x}, while complex low symmetry phase formation is attributed to fluctuations and space-filling constraints, which dominate when N[over ¯]_{b}<N[over ¯]_{x}.

Thermal processing of diblock copolymer melts mimics metallurgy

Small-angle x-ray scattering experiments conducted with compositionally asymmetric low molar mass poly(isoprene)-b-poly(lactide) diblock copolymers reveal an extraordinary thermal history dependence. The development of distinct periodic crystalline or aperiodic quasicrystalline states depends on how specimens are cooled from the disordered state to temperatures below the order-disorder transition temperature. Whereas direct cooling leads to the formation of documented morphologies, rapidly quenched samples that are then heated from low temperature form the hexagonal C14 and cubic C15 Laves phases commonly found in metal alloys. Self-consistent mean-field theory calculations show that these, and other associated Frank-Kasper phases, have nearly degenerate free energies, suggesting that processing history drives the material into long-lived metastable states defined by self-assembled particles with discrete populations of volumes and polyhedral shapes.

Nucleation of the BCC phase from disorder in a diblock copolymer melt: Testing approximate theories through simulation

We examine nucleation of the stable body-centred-cubic (BCC) phase from the metastable uniform disordered phase in an asymmetric diblock copolymer melt. Our comprehensive, large-scale simulations of the time-dependent, mean-field Landau-Brazovskii model find that spherical droplets of the BCC phase nucleate directly from disorder. Near the order-disorder transition, the critical nucleus is large and has a classical profile, attaining the bulk BCC phase in an interior that is separated from disorder by a sharp interface. At greater undercooling, the amplitude of BCC order in the interior decreases and the nucleus interface broadens, leading to a diffuse critical nucleus. This diffuse nucleus becomes large as the simulation approaches the disordered phase spinodal. We show that our simulation follows the same nucleation pathway that Cahn and Hilliard found for an incompressible two-component fluid, across the entire metastable region. In contrast, a classical nucleation theory calculation based on the free energy of a planar interface between coexisting BCC and disordered phases agrees with simulation only in the limit of very small undercooling; we can expand this region of validity somewhat by accounting for the curvature of the droplet interface. A nucleation pathway involving a classical droplet persists, however, to deep undercooling in our simulation, but this pathway is energetically unfavourable. As a droplet grows in the simulation, its interface moves with a constant speed, and this speed is approximately proportional to the undercooling.

Hierarchically Mesostructured Polyisobutylene-Based Ionic Liquids

The formation and design of a hierarchically nanostructured poly(isobutylene)-based ionic liquid (PIB-ILs) is reported, displaying assembly into classical multiplets and an additional ordering of the aromatic counteranions. Three PIB-ILs (Mn = 3600 and 8600 g mol(-1) ), bearing imidazolium (1a), N-methylpyrrolidinium (1b), and triethylammonium cations (1c) together with the aromatic 2-(methylthio)benzoate anion are prepared via a combination of living carbocationic polymerization, "click" reactions and subsequent anion metathesis. The morphology of the novel PIB-ILs as well as its temperature-dependent behavior has been studied via small angle X-ray scattering, displaying two different transition temperatures: one originating from ordering of micelles within a cylinder, and the second from cylinder-cylinder arrangement. Furthermore, the incorporation of an aromatic, rigid, and bulky 2-(methylthio)benzoate anion into the PIB-ILs effects the formation of an internal assembly consisting of stacked cylindrical structures, composed from the mesoscale ordering of ionic "multiplets" characteristic for classical ionomers and from the typical distance of the cylinders themselves.

Micellization and adsorption behaviour of bile salt systems

Variation of enthalpy change with concentration of binary bile salt mixture.

Sphericity and symmetry breaking in the formation of Frank-Kasper phases from one component materials

Frank-Kasper phases are tetrahedrally packed structures occurring in numerous materials, from elements to intermetallics to self-assembled soft materials. They exhibit complex manifolds of Wigner-Seitz cells with many-faceted polyhedra, forming an important bridge between the simple close-packed periodic and quasiperiodic crystals. The recent discovery of the Frank-Kasper σ-phase in diblock and tetrablock polymers stimulated the experiments reported here on a poly(isoprene-b-lactide) diblock copolymer melt. Analysis of small-angle X-ray scattering and mechanical spectroscopy exposes an undiscovered competition between the tendency to form self-assembled particles with spherical symmetry, and the necessity to fill space at uniform density within the framework imposed by the lattice. We thus deduce surprising analogies between the symmetry breaking at the body-centered cubic phase to σ-phase transition in diblock copolymers, mediated by exchange of mass, and the symmetry breaking in certain metals and alloys (such as the elements Mn and U), mediated by exchange of charge. Similar connections are made between the role of sphericity in real space for polymer systems, and the role of sphericity in reciprocal space for metallic systems such as intermetallic compounds and alloys. These findings establish new links between disparate materials classes, provide opportunities to improve the understanding of complex crystallization by building on synergies between hard and soft matter, and, perhaps most significantly, challenge the view that the symmetry breaking required to form reduced symmetry structures (possibly even quasiperiodic crystals) requires particles with multiple predetermined shapes and/or sizes.

Phase diagrams of block copolymer melts by dissipative particle dynamics simulations

Phase diagrams for monodisperse and polydisperse diblock copolymer melts and a random multiblock copolymer melt are constructed using dissipative particle dynamics simulations. A thorough visual analysis and calculation of the static structure factor in several hundreds of points at each of the diagrams prove the ability of mesoscopic molecular dynamics to predict the phase behavior of polymer systems as effectively as the self-consistent field-theory and Monte Carlo simulations do. It is demonstrated that the order-disorder transition (ODT) curve for monodisperse diblocks can be precisely located by a spike in the dependence of the mean square pressure fluctuation on χN, where χ is the Flory-Huggins parameter and N is the chain length. For two other copolymer types, the continuous ODTs are observed. Large polydispersity of both blocks obeying the Flory distribution in length does not shift the ODT curve but considerably narrows the domains of the cylindrical and lamellar phases partially replacing them with the wormlike micelle and perforated lamellar phases, respectively. Instead of the pure 3d-bicontinuous phase in monodisperse diblocks, which could be identified as the gyroid, a coexistence of the 3d phase and cylindrical micelles is detected in polydisperse diblocks. The lamellar domain spacing D in monodisperse diblocks follows the strong-segregation theory prediction, D∕N(1∕2) ~ (χN)(1∕6), whereas in polydisperse diblocks it is almost independent of χN at χN < 100. Completely random multiblock copolymers cannot form ordered microstructures other than lamellas at any composition.

Temperature-dependent phase behaviors in cylinder-forming block copolymers

We demonstrate that the temperature-dependent phase behaviors of parallel and perpendicular cylinder-forming block copolymers are governed by domain-domain segregation forces inherently present in block copolymer material itself. With increasing temperature, a parallel cylinder-forming block copolymer experienced a parallel cylinder straightening process before the order-disorder transition (ODT) and did not show long-range composition fluctuations near the ODT temperature due to the weak segregation forces between the block domains. A perpendicular cylinder-forming block copolymer with a strong segregation force between the block domains displayed cylinder orientation transition from perpendicular to parallel below the ODT temperature. On the other hand, a perpendicular cylinder-forming block copolymer material with an exceptionally strong segregation force between the block domains maintained its initial perpendicular cylinder orientation up to near the ODT temperature. In both cases of perpendicular cylinder-forming block copolymers, submicrometer-scale long-range composition fluctuations were observed well above the ODT temperature due to their intrinsically strong segregation forces between the block domains.

Transient Solidlike Behavior near the Cylinder/Disorder Transition in Block Copolymer Solutions

A nearly symmetric polystyrene-block-polyisoprene diblock copolymer dissolved at a concentration of 40% in styrene-selective solvents exhibited a cylinder-to-disorder transition upon heating. The solvents used were diethyl phthalate (DEP) and 75:25 and 50:50 mixtures of DEP with di-n-butyl phthalate (DBP). In DEP, the most styrene-selective of the three solvents, rheological measurements indicated a distinct plateau in the temperature-dependent elastic modulus across the 8 degrees C interval above the order-disorder transition temperature, T(ODT) = 116 degrees C. Previous small-angle neutron scattering measurements in this regime indicated the equilibrium phase to be a liquidlike solution of approximately spherical micelles. An isothermal frequency sweep in this regime indicated a very long relaxation time. Annealing eventually led to the recovery of liquidlike rheological response, over a time scale of hours. Qualitatively similar phenomena were also observed in 75:25 DEP/DBP and 50:50 DEP/DBP solutions, except the fact that the temperature window of the transient response is narrow and the time scale for the recovery diminishes significantly. Neither small-angle X-ray scattering nor static birefringence gave any clear signature of the transient structure. The structure that leads to the transient rheological response is attributed to micellar congestion due to the slow relaxation of anisotropic micelles into an equilibrium distribution of micelles. Possible origins of the remarkable solvent selectivity dependence are also discussed.

Random isotropic structures and possible glass transitions in diblock copolymer melts

We study the microstructural glass transition in diblock-copolymer melts using a thermodynamic replica approach. Our approach performs an expansion in terms of the natural smallness parameter--the inverse of the scaled degree of polymerization N--which allows us to systematically study the approach to mean-field behavior as the degree of polymerization increases. We find that in the limit of infinite chain length, both the onset of glassiness and the vitrification transition (Kauzmann temperature) collapse to the mean-field spinodal, suggesting that the spinodal can be regarded as the mean-field signature for glass transitions in this class of microphase-separating system. We also study the order-disorder transition (ODT) within the same theoretical framework; in particular, we include the leading-order fluctuation corrections due to the cubic interaction in the coarse-grained Hamiltonian, which has been ignored in previous studies of the ODT in block copolymers. We find that the cubic term stabilizes both the ordered (body-centered-cubic) phase and the glassy state relative to the disordered phase. In melts of symmetric copolymers the glass transition always occurs after the order-disorder transition (below the ODT temperature), but for asymmetric copolymers, it is possible for the glass transition to precede the ordering transition.

Phase behavior and local dynamics of concentrated triblock copolymer micelles

We report a neutron-scattering study to characterize the ordering and local dynamics of spherical micelles formed by the triblock copolymer polyethylene oxide (PEO)--polypropylene oxide (PPO)--polyethylene oxide (Pluronic) in aqueous solution. The study focuses on two Pluronic species, F68 and F108, that have the same weight fraction of PEO but that differ in chain length by approximately a factor of 2. At sufficiently high concentration, both species undergo a sequence of phase changes with increasing temperature from dissolved chains to micelles with liquid-like order to a cubic crystal phase and finally back to a micelle liquid phase. A comparison of the phase diagrams constructed from small-angle neutron scattering indicates that crystallization is suppressed for shorter chain micelles due to fluctuation effects. The intermediate scattering function I(Q,t)I(Q,0) determined by neutron spin echo displays a line shape with two distinct relaxations. Comparisons between I(Q,t)I(Q,0) for fully hydrogenated F68 chains in D2O and for F68 with deuterated PEO blocks reveal that the slower relaxation corresponds to Rouse modes of the PPO segments in the concentrated micelle cores. The faster relaxation is identified with longitudinal diffusive modes in the PEO corona characteristic of a polymer brush.

Micellar aggregation in blends of linear and cyclic poly(styrene-b-isoprene) diblock copolymers

The morphology of micelles formed from blends of linear and cyclic poly(styrene-b-isoprene) (PS-b-PI) block copolymers has been investigated in solution using dynamic light scattering (DLS) and in thin solid deposits by atomic force microscopy (AFM) and transmission electron microscopy under cryogenic conditions (cryo-TEM). Micelles of the pure cyclic PS(290)-b-PI(110) copolymers are wormlike cylindrical objects built by unidirectional aggregation of 33 nm wide sunflower micelles, while the linear block copolymer having the same volume fraction and molar mass forms spherical micelles 40 nm in diameter. The DLS, AFM, and cryo-TEM results consistently show that the addition of the linear copolymer (even for amounts as low as 5% w/w) to the cyclic copolymer rather favors the formation of spherical micelles at the expense of the cylindrical aggregates. Those results clearly show that the linear block copolymer chains can be used to stabilize the thermodynamically unstable elementary sunflower micelle. The thermal stability of the micelles (from the pure copolymers and from the blends) has been examined in solid deposits with in situ AFM measurements. Coalescence starts at about 70 degrees C, and the surface roughness shows a two-step decrease toward a fully homogeneous and flat structure.

Static and dynamic structures of spherical nonionic surfactant micelles during the disorder-order transition

We have investigated the static and dynamic structures of nonionic surfactant micelles, a C(12)E(8)/water binary system, during the disorder-order transition using small angle x-ray scattering, static light scattering, and dynamic light scattering techniques. In the disordered phase, the micelles have spherical shape and intermicellar interactions are governed by the hard core and weak long ranged attractive potentials. With increase of the micellar concentration, the disordered micelles transform to the three characteristic ordered micellar phases, a hexagonally close packed lattice, a body centered cubic lattice, and an A15 lattice having area-minimizing structure. The stability of these phases is well explained by balance of a close packing rule and a minimal-area rule proposed by Ziherl and Kamien [Phys. Rev. Lett. 85, 3528 (2000)]. The role of hydrodynamic interactions in surfactant micellar solutions was compared with that in hard sphere colloidal particle suspensions.