Ordered packing arrangements of spherical micelles of diblock copolymers in two and three dimensions

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.

Tuning conformational asymmetry in particle-forming diblock copolymer alloys

Self-consistent field theory is employed to compute the phase behavior of binary blends of conformationally asymmetric, micelle-forming diblock copolymers with miscible corona blocks and immiscible core blocks (a diblock copolymer "alloy"). The calculations focus on establishing conditions that promote the formation of Laves phases by tuning the relative softness of the cores of the two different Laves phase particles via independent control of their conformational asymmetries. Increasing the conformational asymmetry of the more spherical particles of the Laves structure has a stabilizing effect, consistent with the expectations of increased imprinting of the Wigner-Seitz cells on the core/corona interface as conformational asymmetry increases. The resulting phase diagram in the temperature-blend composition space features a more stable Laves phase field than that predicted for conformationally symmetric systems. The phase field closes at low temperatures in favor of macrophase separation between a hexagonally-packed cylinder (hex) phase and a body-centered cubic phase. Companion calculations, using an alloy whose components do not produce a hex phase in the neat melt state, suggest that the Laves phase field in such a blend will persist at strong segregation.

Free energy cost to assemble superlattices of polymer-grafted nanoparticles

Mesoparticles consisting of a hard core and a soft corona like polymer-grafted nanoparticles (PGNPs) can assemble into various superlattice structures, in which each mesoparticle assumes the shape of the corresponding Wigner-Seitz (or Voronoi) cell. Conventional wisdom often perceives the stability of these superlattices in a mean-field view of surface area minimization or corona entropy maximization, which lacks molecular interpretation. We develop a simulation method to calculate the free energy cost to deform spherical PGNPs into Wigner-Seitz polyhedra, which are then relaxed in a certain crystalline superlattice. With this method, we successfully quantify the free energy differences between model BCC, FCC and A15 systems of PGNPs and identify BCC as the most stable structure in most cases. Analysis of polymer configurations in the corona, whose boundary is blurred by chain interpenetration, shows that the radial distribution of grafted chains and the corresponding entropy are almost identical between BCC and FCC, suggesting that the higher stability of the BCC structure cannot be explained by the mean-field description of the corona shape.

Spherical Supramolecular Structures Constructed via Chemically Symmetric Perylene Bisimides: Beyond Columnar Assembly

Like other discotic molecules, self-assembled supramolecular structures of perylene bisimides (PBIs) are commonly limited to columnar or lamellar structures due to their distinct π-conjugated scaffolds and unique rectangular shape of perylene cores. The discovery of PBIs with supramolecular structures beyond layers and columns may expand the scope of PBI-based materials. A series of unconventional spherical packing phases in PBIs, including A15 phase, σ phase, dodecagonal quasicrystalline (DQC) phase, and body-centered cubic (BCC) phase, is reported. A strategy involving functionalization of perylene core with several polyhedral oligomeric silsesquioxane (POSS) cages achieved spherical assemblies of PBIs, instead of columnar assemblies, due to the significantly increased steric hindrance at the periphery. This strategy may also be employed for the discovery of unconventional spherical assemblies in other related discotic molecules by the introduction of similar bulky functional groups at their periphery. An unusual inverse phase transition sequence from a BCC phase to a σ phase was observed by increasing annealing temperature.

Apparatus for “on-the-fly” sample preparation of aerosol-grown block copolymer microdroplets

The morphology of phase separated amorphous A/B block copolymers depends not only on the relative volume fraction of the A and B components but also on external shape constraints imposed on the sample. Whereas it is well established that thin planar of microstructured copolymers differ considerably from the bulk materials, the influence of roughness and curvature, which are of practical importance in coating technology, are presently unknown. Because the simplest curved surface is a sphere, the effect of surface curvature on block copolymer microdomains can be conveniently studied by TEM observations of spherical microdroplets prepared with the apparatus described here.

Samples for microscopy are prepared by the “gunshot” technique: an atomized solution of the copolymer in a homogeneous solvent is allowed to fall onto carbon coated grids. During fall the solvent evaporates, leaving small spheres of the copolymer that continue falling. By means of a special set of tubes along the fall path, the spheres are annealed (by heating in a nitrogen atmosphere) and stained/fixed (by exposure to osmium tetroxide vapors).

Regulate the Stability of Gyroids of ABC-Type Multiblock Copolymers by Controlling the Packing Frustration

We propose to regulate the stability of gyroids of ABC-type multiblock copolymers by controlling the packing frustration of majority-component B-blocks. Accordingly, we investigate the self-assembly behaviors of the BABCB linear terpolymer with a variable length ratio τ of the middle B-block relative to the total B-blocks using self-consistent field theory. It is observed that the gyroid region exhibits a maximal width with respect to τ, which is attributed by the nonmonotonical change of the packing frustration of three B-blocks in the morphology of discrete domains, for example, cylinders. Then we further purposely design another ABC-type copolymer composed of an ABC linear triblock tethered by another B-block at the middle of the B-block. In contrast, the packing frustration of B-blocks of the second terpolymer drops down continuously as the middle B-block shortens, thus, expanding the stable regions of cylinders and spheres while contracting those of lamella and gyroid.

Control of the pore size of honeycomb polymer film from micrometers to nanometers via substrate-temperature regulation and its application to photovoltaic and heat-resistant polymer films

Honeycomb porous polystyrene (PS) films with an aspect ratio of pore depth to pore diameter at approximately 1.0 were fabricated using the breath figure (BF) method. Two modes of water droplet coalescence in the pore growth were observed in real-time by optical microscopy. Pore size significantly increases with the increase in humidity and the decrease in substrate temperature. The porous pattern could emerge even at room temperature under high humidity of 80%. Boiling point and solvent density significantly influence the pore distribution and pore depth. Chloroform and tetrahydrofuran achieve more uniform hexagonal patterns than benzene and dichloromethane. Subsequently, to obtain nanometer porous PS film, the fast-evaporation BF process was designed by regulating the gradient substrate temperature and evaporation time, and porous mesoscopic PS film was obtained. The minimum pore diameter and corresponding pore depth are about 120 nm and 27 nm, respectively. Finally, the fast-evaporation BF process was applied to the honeycomb film formation of photovoltaic polymer poly(3-hexylthiophene) (P3HT), and the heat-resistant polymers polysulfone (PSF) and polyimide (PI).

Interparticle Interactions in Dilute Solutions of Polyelectrolyte Complex Micelles

The application of dilute solutions of polyelectrolyte complex (PEC) micelles for delivering therapeutic nucleic acids into disease sites has gained momentum. This Letter reports a detailed characterization of PEC micelles in dilute solutions including their internal structures and the determination of the interparticle interactions. The polymer concentration ranges from 0.1 to 0.5 wt %, a regime where micelle-micelle interactions are infrequent. We employ synchrotron small-angle X-ray scattering (SAXS) to simultaneously probe the morphology, internal structure, and radius of gyration (R_g) of the self-assemblies formed by charged diblock polyelectrolytes and homopolyelectrolytes. The emerging appearance of the structure factor in SAXS profiles with the increasing polymer concentration demonstrates the presence of the repulsive intermicellar correlations, which is further confirmed by the differences between the "reciprocal R_g" estimated by Guinier approximation and the "real space R_g" determined by pair distribution functions. We find that the soft corona chains tethered on the surface of phase-separated complex domains are compressed when micelles come close to the point where a hard-sphere interaction takes over. These findings contribute to the fundamental understanding of the structure and space-filling constraints in the complexation-driven self-assemblies and advance the rational design of cationic polymer-based nonviral gene delivery vectors.

Surprising states of order for linear diblock copolymers

Thermal treatments unlock low-symmetry phases resembling those of metals and alloys

Order-disorder transition in thin films of horizontally-oriented cylinder-forming block copolymers: thermal fluctuations vs. preferential wetting

We present experimental and theoretical investigations of the order-disorder transition (ODT) in thin films of cylinder-forming diblock copolymers with asymmetric wetting conditions. Grazing incidence small-angle X-ray scattering (GISAXS) was implemented to determine the ODT temperatures (TODT) for poly(styrene-b-2-vinyl pyridine) (PS-P2VP) block copolymer thin films on a P2VP-preferential silicon substrate. Specifically, films consisting of multilayers of horizontally-oriented cylindrical structures (from 1- to 9-layers) were tested. We find that films with more than 2 cylindrical layers have a TODT comparable to the bulk case. However, TODT decreases as the film becomes thinner and the monolayer system has an ODT 30 °C below the bulk. Using self-consistent field theory (SCFT), we studied the ordering in corresponding thin films with asymmetric (top and bottom surface) wetting conditions. Surprisingly, SCFT is found to predict an opposite trend in TODT with film thickness than observed experimentally. Field-theoretic simulations with complex Langevin sampling were employed to resolve this discrepancy and demonstrate that thermal fluctuations in the PS-P2VP thin-film system dominate its ordering behavior in monolayer and bilayer films.

Entropy-Driven Crystallization Behavior in DNA-Mediated Nanoparticle Assembly

Herein, we report an example of entropy-driven crystallization behavior in DNA-nanoparticle superlattice assembly, marking a divergence from the well-established enthalpic driving force of maximizing nearest-neighbor hybridization connections. Such behavior is manifested in the observation of a non-close-packed, body-centered cubic (bcc) superlattice when using a system with self-complementary DNA linkers that would be predicted to form a close-packed, face-centered cubic (fcc) structure based solely on enthalpic considerations and previous design rules for DNA-linked particle assembly. Notably, this unexpected phase behavior is only observed when employing long DNA linkers with unpaired "flexor" bases positioned along the length of the DNA linker that increase the number of microstates available to the DNA ligands. A range of design conditions are tested showing sudden onsets of this behavior, and these experiments are coupled with coarse-grained molecular dynamics simulations to show that this entropy-driven crystallization behavior is due to the accessibility of additional microstates afforded by using long and flexible linkers.

The Role of Ligand Packing Frustration in Body-Centered Cubic (bcc) Superlattices of Colloidal Nanocrystals

This paper addresses the assembly of body centered-cubic (bcc) superlattices of organic ligand-coated nanocrystals. First, examples of bcc superlattices of dodecanethiol-capped Au nanocrystals and oleic acid-capped PbS and PbSe nanocrystals are presented and examined by transmission electron microscopy (TEM) and grazing incidence small-angle X-ray scattering (GISAXS). These superlattices tend to orient on their densest (110) superlattice planes and exhibit a significant amount of {112} twinning. The same nanocrystals deposit as monolayers with hexagonal packing, and these thin films can coexist with thicker bcc superlattice layers, even though there is no hexagonal plane in a bcc lattice. Both the preference of bcc in bulk films over the denser face-centered cubic (fcc) superlattice structure and the transition to hexagonal monolayers can be rationalized in terms of packing frustration of the ligands. A model is presented to calculate the difference in entropy associated with capping ligand packing frustration in bcc and fcc superlattices.

Cooling-induced formation of honeycomb patterns on pre-cast PMMA films at low temperatures

Surface patterns formed on pre-cast PMMA films. A typical AFM image shows the hexagon network.

Derivation of coarse-grained potentials via multistate iterative Boltzmann inversion

In this work, an extension is proposed to the standard iterative Boltzmann inversion (IBI) method used to derive coarse-grained potentials. It is shown that the inclusion of target data from multiple states yields a less state-dependent potential, and is thus better suited to simulate systems over a range of thermodynamic states than the standard IBI method. The inclusion of target data from multiple states forces the algorithm to sample regions of potential phase space that match the radial distribution function at multiple state points, thus producing a derived potential that is more representative of the underlying interactions. It is shown that the algorithm is able to converge to the true potential for a system where the underlying potential is known. It is also shown that potentials derived via the proposed method better predict the behavior of n-alkane chains than those derived via the standard IBI method. Additionally, through the examination of alkane monolayers, it is shown that the relative weight given to each state in the fitting procedure can impact bulk system properties, allowing the potentials to be further tuned in order to match the properties of reference atomistic and/or experimental systems.

Hexagonal-to-cubic phase transformation in composite thin films induced by FePt nanoparticles located at PS/PEO interfaces

The organization process of asymmetric poly(styrene-block-ethylene oxide) (PS-b-PEO) copolymer thin films blended with FePt nanoparticles is studied. In a first step, it is shown that FePt nanoparticles stabilized by oleic acid ligands are distributed within the PS matrix phase, whereas the same particles partially covered with short dopamine-terminated-methoxy poly(ethylene oxide) (mPEO-Dopa) are located at PS/PEO interfaces. The swelling of PS domains, induced by FePt_oleic acid nanoparticles during the solvent annealing process, results in formation of a disordered microstructure in comparison to the well-organized hexagonally close-packed (HCP) cylinder phase formed in the neat PS-b-PEO copolymer. The evolution of the microstructure of PS-b-PEO/FePt_mPEO-Dopa composite has been investigated for different solvent annealing treatments. Under high-humidity conditions during the vapor annealing process, the addition of FePt nanoparticles results in formation of spheres in the film split into terraces. The upper and lower terraces are occupied by spheres organized in an unusual square and HCP phases, respectively. Under low-humidity conditions, undulated PEO cylinders oriented parallel to substrate are formed in the presence of FePt nanoparticles. In this case, we observe that most of the nanoparticles accumulate within the core of topological defects, which induces a low nanoparticle concentration at the PS/PEO interfaces and so stabilizes an intermediate undulated cylinder phase.

Investigation of Diblock Copolymer thin film Morphology for Nanolithography

The microphase separated morphology of diblock copolymers can be used to generate well-ordered nanometer scale patterns over a large area. To achieve this goal, it is important to understand and control the behavior of diblock copolymer thin films on substrates, which can differ from the bulk behavior. We have investigated the morphologies and ordering in thin polystyrene-polybutadiene (PS-PB) diblock copolymer films on bare silicon and silicon nitride substrates, and also on polymethylmethacrylate (PMMA) coated substrates. The PS-PB copolymers are synthesized to form, in bulk, PB cylinders or spheres in a PS matrix. In thin films (10–60 nm thick), prepared by spin-coating, we observe that the morphology and ordering of the microdomains are affected by strong wetting constraints and a reduced chain mobility on the substrate. The thinnest self-assembled layer of the copolymer films shows no in-plane microphase separation on both types of substrates. The PS blocks wet the PMMA substrates whereas the PB blocks wet the bare substrates as well as the air interface. Hence, different film thicknesses are necessary on the two types of substrates to obtain a uniform film of the first self-assembled cylindrical or spherical microdomain layer. The first layer of the cylindrical copolymer can vary from cylindrical to spherical morphology with a few nanometer decrease in film thickness. In the case of spherical PS-PB diblock copolymer films, we observe that the ordering of the microdomains is improved in the films on the PMMA substrates, compared to those on the bare substrates. We also demonstrate a successful transfer of the microdomain patterns to silicon nitride substrates by a reactive ion etching technique.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite chi N . With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical ( S (cp) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd ( O(70) morphology, showing that conformational asymmetry has a significant effect on its stability.

Substrate wetting and topographically induced ordering of amorphous PI-b-PFS block-copolymer domains

The substrate wetting of an amorphous, low-glass-transition-temperature spherical poly(isoprene-block-ferrocenylsilane) (PI-b-PFS) block copolymer and the alignment of the microdomains in grooves of various geometry are studied. Compositional analysis by time-of-flight secondary ion mass spectrometry depth profiling (TOF-SIMS) indicates the presence of both PI and PFS directly at the film-substrate interface on silicon and silica substrates. The TOF-SIMS depth-profiling study indicates a transition in the packing of the domains between the two-dimensional (2D) monolayer and 3D, thicker layers. In a monolayer of domains, a hexagonal packing is adopted. In films of two or three layers, the hexagonal packing reorganizes towards a body-centered cubic (bcc) packing by the extension of the copolymer chains in the direction normal to the substrate, as indicated by an increase in spacing between PFS layers and an increase in domain size. For thicker layers, a bcc morphology with the (110) plane parallel to the substrate is found to extend from the free surface downwards. Films of one monolayer of domains of the copolymer exhibit long-range lateral ordering on the micrometer scale on flat substrates without high-temperature annealing. On topographically patterned silicon substrates the position of the domains of the minority PFS phase directly near the side walls is fixed by the neutral wetting condition. Successful positioning of the block-copolymer spheres in linear and hexagonal grooves is achieved in grooves up to 1.3 microm wide, whereby the hexagonal grooves demonstrate complete 2D alignment. In circular pits, this graphoepitaxial effect is absent.

Symmetry breaking of in-plane order in confined copolymer mesophases

Packing of spherical-domain block copolymer mesophases confined to a thin film is investigated as a function of the number of layers n. We find an abrupt transition from hexagonal to orthorhombic in-plane ordering of domains when n is increased from 4 to 5. As n increases further (up to 23 in this study), the symmetry of the orthorhombic phase asymptotically approaches that of the body-centered cubic (110) plane. These results are interpreted in terms of the energetics of competing packings in the bulk and at the film interfaces. Detailed structural and thermodynamic properties are obtained with self-consistent field theory.

Porous thin films based on photo-cross-linked star-shaped poly(D,L-lactide)s

Self-assembly processes and subsequent photo-cross-linking were used to generate cross-linked, ordered microporous structures on the surfaces of well defined four-arm star-shaped poly(D,L-lactide) (PDLLA) thin films. The four-arm star-shaped PDLLAs were synthesized using an ethoxylated pentaerythritol initiator. Solutions of the PDLLAs were cast in a humid environment, and upon solvent evaporation, ordered honeycomb structures (or breath figures) were obtained. Correlations between molar mass, polymer solution viscosity, and pore dimensions were established. The average pore dimension decreased with increasing polymer solution concentration, and a linear relationship was observed between relative humidity and average pore dimensions. Highly ordered microporous structures were also developed on four-arm star-shaped methacrylate-modified PDLLA (PDLLA-UM) thin films. Subsequent photo-cross-linking resulted in more stable PDLLA porous films. The photo-cross-linked films were insoluble, and the honeycomb structures were retained despite solvent exposure. Free-standing, structured PDLLA-UM thin films were obtained upon drying for 24 h. Ordered microporous films based on biocompatible and biodegradable polymers, such as PDLLA, offer potential applications in biosensing and biomedical applications.

Three-dimensional self-assembly of spherical block copolymer domains into V-shaped grooves

The self-assembly of a spherical-morphology block copolymer into V-shaped grooves has been investigated. Although spherical morphology block copolymers typically form a bcc sphere array in bulk, the V groove promotes the formation of a well-ordered fcc close-packed sphere array with the (111) planes of the array parallel to the groove walls. The sphere size in the block copolymer adjusts depending on the commensurability between the periodicity of the block copolymer and the film thickness within the V groove. The top surface of the close-packed array, parallel to the substrate, shows a square symmetry, unlike the hexagonal symmetry seen in monolayers of spherical domains, which may provide a useful geometry for block copolymer lithography.

SEBS aggregate patterning at a surface studied by atomic force microscopy

The morphologies of films spin coated from dilute block copolymer solution onto a mica substrate were studied by atomic force microscopy (AFM). Variables of interest were the polymer concentration, solvent, heating temperature, aging, and ultrasonic effect. It is shown that the solution concentration is the predominant factor in determining the shape of the aggregates displayed from spheres and rods to irregular patches with increasing concentration. The solubility parameter of the solvent plays an important role in modifying the distribution and the size of clusters at the surface. The structures of the aggregates at the surface are metastable, which could evolve with temperature from rodlike aggregates into regular stripes when annealed at a temperature higher than the order-disorder transition temperature of SEBS, whereas those in solution could evolve with aging and ultrasonic treatment into a more stable network structure.

Polymer surfaces with reversibly switchable ordered morphology

Honeycomb macroporous films fabricated by the "breath figures" method were composed of poly2-vinylpyridine (P2VP) distributed in the holes of polystyrene (PS). The porous films exhibited reversible behavior responding to water and different solvent vapors. When the porous film was treated with water, the honeycomb pattern would change to the hexagonal islandlike pattern. Once heated to remove the water, the honeycomb pattern emerged again. When the porous film was exposed to different solvent vapors, the same reversible process appeared. Carbon disulfide (CS(2)), toluene (TOL), and tetrahydrofuran (THF) solvent vapors induced the honeycomb pattern into the ordered islandlike pattern, and ethanol, chloroform, methyl ethyl ketone (MEK), and dimethylformamide (DMF) solvent vapors made the islandlike pattern come back to the honeycomb pattern. The hygroscopic property of P2VP and the polymer-solvent interaction are the driving force for the reversibly switchable morphology. The appropriate control of the hole depth is very crucial in determining the reversible changes.