We present numerical calculations of lamellar phases of block copolymers at patterned surfaces. We model symmetric di-block copolymer films forming lamellar phases and the effect of geometrical and chemical surface patterning on the alignment and orientation of lamellar phases. The calculations are done within self-consistent field theory (SCFT), where the semi-implicit relaxation scheme is used to solve the diffusion equation. Two specific set-ups, motivated by recent experiments, are investigated. In the first, the film is placed on top of a surface imprinted with long chemical stripes. The stripes interact more favorably with one of the two blocks and induce a perpendicular orientation in a large range of system parameters. However, the system is found to be sensitive to its initial conditions, and sometimes gets trapped into a metastable mixed state composed of domains in parallel and perpendicular orientations. In a second set-up, we study the film structure and orientation when it is pressed against a hard grooved mold. The mold surface prefers one of the two components and this set-up is found to be superior for inducing a perfect perpendicular lamellar orientation for a wide range of system parameters.
We study block copolymers (BCP) on patterned substrates, where the top polymer film surface is not constrained but is a free interface that adapts its shape self-consistently. In particular, we investigate the combined effect of the free interface undulations with the wetting of the BCP film as induced by nano-patterned substrates. For a finite volume of BCP material, we find equilibrium droplets composed of coexisting perpendicular and parallel lamellar domains. The self-assembly of BCP on topographic patterned substrates was also investigated and it was found that the free interface induces …
We use a Ginzburg-Landau free energy functional to investigate diblock copolymer morphologies when the copolymer melt interacts with one surface or is confined between two chemically patterned surfaces. For temperatures above the order-disorder transition a complete linear response description of the copolymer melt is given, in terms of an arbitrary two-dimensional surface pattern. The appearance of order in the direction parallel to the surface is found as a result of the order in the perpendicular direction. Below the order-disorder point and in a thin-film geometry, our procedure enables th…
We investigate the morphology of diblock copolymers in the vicinity of flat, chemically patterned surfaces. Using a Ginzburg-Landau free energy, spatial variations of the order parameter are given in terms of a general two-dimensional surface pattern above the order-disorder transition. The propagation of several surface patterns into the bulk is investigated. The oscillation period and decay length of the surface $q$-modes are calculated in terms of system parameters. We observe lateral order parallel to the surface as a result of order perpendicular to the surface. Surfaces which has a finit…
We present NanoImprint lithography experiments and modeling of thin films of block copolymers (BCP). The NanoImprint lithography is used to align perpendicularly lamellar phases, over distances much larger than the natural lamellar periodicity. The modeling relies on self-consistent field calculations done in two- and three-dimensions. We get a good agreement with the NanoImprint lithography setups. We find that, at thermodynamical equilibrium, the ordered BCP lamellae are much better aligned than when the films are deposited on uniform planar surfaces.
Nanocomposite materials made of block copolymer and nanoparticles display properties which can be different from the purely polymeric matrix. The resulting material is a crossover of the original properties of the block copolymer and the presence of the assembled nanoparticles. We propose a mesoscopic study via cell dynamic simulations to quantitatively assert the properties of such hybrid materials. The most relevant parameters are identified to be the fraction of nanoparticles in the system and its chemical affinity, while the nanoparticle size with respect to the block copolymer length scal…
In this article, we study the thermodynamic behavior of anisotropic shape (rod and disk) nanoparticle within the block copolymer matrix by using self-consistent field theory (SCFT) simulation. In particular, we introduce various defect structures of block copolymers to precisely control the location of anisotropic particles. Different from the previous studies using spherical nanoparticles within the block copolymer model defects, anisotropic particles are aligned with preferred orientation near the defect center due to the combined effects of stretching and interfacial energy of block copolym…
Block copolymer melts self-assemble in the bulk into a variety of nanostructures, making them perfect candidates to template the position of nanoparticles. The morphological changes of block copolymers are studied in the presence of a considerable filling fraction of colloids. Furthermore, colloids can be found to assemble into ordered hexagonally close-packed structures in a defined number of layers when softly confined within the phase-separated block copolymer. A high concentration of interface-compatible nanoparticles leads to complex block copolymer morphologies depending on the polymeric…
We investigate the effect of chemically patterned surfaces on the morphology of diblock copolymers below the order-disorder transition. Profiles for lamellar phases in contact with one surface, or confined between two surfaces are obtained in the weak segregation limit using a Ginzburg-Landau expansion of the free energy, and treating it with mean-field theory. The periodically patterned surface induces a tilt of the lamellae in order to match the surface periodicity. The lamellae relax from the constrained periodicity close to the surface to the bulk periodicity far from it. The phases we inv…
Surface-patterned ZnO thin films were fabricated by direct imprinting on ZnO sol and subsequent annealing process. The polymer-based ZnO sols were deposited on various substrates for the nanoimprint lithography and converted to surface-patterned ZnO gel films during the thermal curing nanoimprint process. Finally, crystalline ZnO films were obtained by subsequent annealing of the patterned ZnO gel films. The optical characterization indicates that the surface patterning of ZnO thin films can lead to an enhanced transmittance. Large-scale ZnO thin films with different patterns can be fabricated…
A hybrid block copolymer(BCP) nanocomposite computational model is proposed to study nanoparticles(NPs) with a generalised shape including squares, rectangles and rhombus. Simulations are used to study the role of anisotropy in the assembly of colloids within BCPs, ranging from NPs that are compatible with one phase, to neutral NPs. The ordering of square-like NPs into grid configurations within a minority BCP domain was investigated, as well as the alignment of nanorods in a lamellar-forming BCP, comparing the simulation results with experiments of mixtures of nanoplates and PS-\textit{b}-PMM…
A technique is presented which maps the parameters of a bead spring model, using the Flory Huggins theory, to a specific experimental system. By keeping only necessary details, for the description of these systems, the mapping procedure turns into an estimation of a few characteristic parameters. An asset of this technique is that it is simple to apply and captures the behavior of block copolymer phase separation. In our study this mapping technique is utilized in conjunction with a Monte Carlo (MC) algorithm to perform simulations on block copolymer systems. The microphase separation is inves…
A phenomenological mean-field theory is used to investigate the properties of solvent-diluted di-block copolymers (BCP), in which the two BCP components (A and B) form a variety of phases that are diluted by a solvent (S). Using this approach, we model mixtures of di-block copolymers and a solvent and obtained the corresponding critical behavior. In the low solvent limit, we find how the critical point depends on the solvent density. Due to the non-linear nature of the coupling between the A/B and BCP/solvent concentrations, the A/B modulation induces modulations in the polymer-solvent relativ…
Block copolymer are ideal matrices to control the localisation of colloids. Furthermore, anisotropic nanoparticles such as Janus nanoparticles possess an additional orientational degree of freedom that can play a crucial role in the formation of highly ordered materials made of block copolymers. This work presents a mesoscopic simulation method to assert the co-assembly of Janus nanoparticles in a block copolymer mixture, finding numerous instances of aggregation and formation of ordered configurations which can be related to dispersions of pure Janus colloids. Comparison with chemically homog…
Nanostructured thermosets may be obtained by self-assembly of amphiphilic block copolymers in a reactive solvent and fixation of the morphologies by the cross-linking reaction. Nanostructuration requires the presence of a bock that remains miscible in the polymer during polymerization. The selection of the miscible block depends on the particular system and in some cases (e.g., for epoxy-amine network based on diglycidyl ether of bisphenol A, and 4,4'- diaminodiphenylsulfone) it is very difficult to find such a block. In this manuscript it is shown that random copolymers of methyl methacrylate…
When polyelectrolyte-neutral block copolymers are mixed in aqueous solutions with oppositely charged species, stable complexes are found to form spontaneously. The mechanism is based on electrostatics, and on the compensation between the opposite charges. Electrostatic complexes exhibit a core-shell microstructure. In the core, the polyelectrolyte blocks and the oppositely charged species are tightly bound and form a dense coacervate microphase. The shell is made of the neutral chains and surrounds the core. In this paper, we report on the structural and magnetic properties of such complexes m…
We report on the structural properties of mixed aggregates made from rare-earth inorganic nanoparticles (radius 20 Angstroms) and polyelectrolyte-neutral block copolymers in aqueous solutions. Using scattering experiments and Monte Carlo simulations, we show that these mixed aggregates have a hierarchical core-shell microstructure. The core is made of densely packed nanoparticles and it is surrounded by a corona of neutral chains. This microstructure results from a process of controlled association and confers to the hybrid aggregates a remarkable colloidal stability.
This work presents a general and unified theory describing block copolymer self-assembly in the presence of free surfaces and nanoparticles in the context of Self-Consistent Filed Theory. Specifically, the derived theory applies to free and tethered polymer chains, nanoparticles of any shape, arbitrary non-uniform surface energies and grafting densities, and takes into account a possible formation of triple-junction points (e.g., polymer-air-substrate). One of the main ingredients of the proposed theory is a simple procedure for a consistent imposition of boundary conditions on surfaces with n…
During the past years we have investigated the complexation between nanocolloids and oppositely charged polymers. The nanocolloids examined were ionic surfactant micelles and inorganic oxide nanoparticles. For the polymers, we used homopolyelectrolytes and block copolymers with linear and comb architectures. In general, the attractive interactions between oppositely charged species are strong and as such, the simple mixing of solutions containing dispersed constituents yield to a precipitation, or to a phase separation. We have developed means to control the electrostatically-driven attraction…
The ordering of block copolymers into lamellar microstructures is an attractive route for creating nanopatterns on scales too small to be constructed by current photolithography techniques. This utilises a technique known as graphoepitaxy where topography is used to define the alignment of the pattern for precise placement of pattern features. One problem with this approach is the failure of lamellae to maintain continuity around corners, due to geometrical frustration. We report simulation results using the extended Cahn-Hilliard equation which suggest that this problem could be solved by usi…
The dissipative particle dynamics (DPD) simulation method has been shown to be a promising tool to study self-assembly of soft matter systems. In particular, it has been used to study block copolymer (BCP) self-assembly. However, previous parametrizations of this model are not able to capture most of the rich phase behaviors of block copolymers in thin films nor in directed self-assembly (chemoepitaxy or graphoepitaxy). Here we extend the applicability of the DPD method for BCPs to make it applicable to thin films and directed self-assembly. Our new reparametrization is able to reproduce the b…
Simulations and experiments of nanorods (NRs) show that co-assembly with block copolymer (BCP) melts leads to the formation of a superstructure of side-to-side NRs perpendicular to the lamellar axis. A mesoscopic model is validated against scanning electron microscopy (SEM) images of CdSe NRs mixed with polystyrene-block-poly(methyl methacrylate). It is then used to study the co-assembly of anisotropic nanoparticles (NPs) with a length in the same order of magnitude as the lamellar spacing. The phase diagram of BCP/NP is explored as well as the time evolution of the NR. NRs that are slightly l…
Co-assembly of inorganic nanoparticles (NPs) and nanostructured polymer matrix represents an intricate interplay of enthalpic or entropic forces. Particle size largely affects the phase behavior of the nanocomposite. Theoretical studies indicate that new morphologies would emerge when the particles become comparable to the soft matrix's size, but this has rarely been supported experimentally. By designing a multicomponent blend composed of NPs, block copolymer-based supramolecules, and small molecules, a 3-D ordered lattice beyond the native BCP's morphology was recently reported when the part…
Surface Block Identity Controls Transport of Symmetric Diblock Copolymer Through Nanopores
University of Pennsylvania（宾夕法尼亚大学）；Université de Lyon, CNRS, Université Claude Bernard Lyon 1, INSA Lyon, Université Jean Monnet（里昂大学、法国国家科学研究中心、里昂第一大学、里昂国立应用科学学院、让·莫内大学）；KU-KIST Graduate School of Converging Science and Technology, Korea University（高丽大学-韩国科学技术院融合科学与技术研究生院）
We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of confining flat surfaces. The surfaces are chemically patterned where different regions attract different parts of the copolymer chain. The surface pattern or template is decomposed into its Fourier modes, and the decay of these modes is analyzed. The persistence of the surface pattern into the disordered bulk is given for several types of patterns (e.g. uni…
Molecular dynamics simulations of dense and rarefied fluids comprising small chain molecules in chemically patterned nano-channels predict a novel switching from Poiseuille to plug flow along the channel. We also demonstrate behavior akin to the lotus effect for a nanodrop on a chemically patterned substrate. Our results show that one can control and exploit the behavior of fluids at the nanoscale using chemical patterning.
We present a systematic investigation of static and dynamic properties of block copolymer micelles with crosslinked cores, representing model polymer-grafted nanoparticles, over a wide concentration range from dilute regime to an arrested (crystalline) state, by means of light and neutron scattering, complemented by linear viscoelasticity. We have followed the evolution of their scattering intensity and diffusion dynamics throughout the non-ergodicity transition and the observed results have been contrasted against appropriately coarse-grained Langevin Dynamics simulations. These stable model …
We have studied structure formation in a confined block copolymer melt by means of dynamic density functional theory (DDFT). The confinement is two-dimensional, and the confined geometry is that of a cylindrical nanopore. Although the results of this study are general, our coarse-grained molecular model is inspired by an experimental lamellae-forming PS-PBD diblock copolymer system (Shin et al, Science, 306, 76 (2004)), in which an exotic toroidal structure was observed upon confinement in alumina nanopores. Our computational study shows that a zoo of exotic structures can be formed, although …
The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer composition but also on the size, shape, and surface properties of the colloids. The dynamics of this kind of systems using a hybrid mesoscopic approach has been studied in this work. A continuum description for the polymer is used, while colloids are individually resolved. The method allows for a variable preference of the colloids, which can have different sizes,…
We have investigated PLLA crystallization in lamellae-forming PS-b-PLLA confined to straight cylindrical nanopores under weak confinement (nanopore diameter D / equilibrium PS-b-PLLA period L0 larger than 4.8). Molten PS-b-PLLA predominantly forms concentric lamellae along the nanopores, but intertwined helices occur even for D/L0 = 7.3. Quenching PS-b-PLLA melts below TG(PS) results in PLLA cold crystallization strictly confined by the vitrified PS domains. Above TG(PS), PLLA crystallization is templated by the PS-b-PLLA melt domain structure in the nanopore centers, while adsorption on the n…
We present a systematic investigation of static and dynamic properties of block copolymer micelles with crosslinked cores, representing model polymer-grafted nanoparticles, over a wide concentration range from dilute regime to an arrested (crystalline) state, by means of light and neutron scattering, complemented by linear viscoelasticity. We have followed the evolution of their scattering intensity and diffusion dynamics throughout the non-ergodicity transition and the observed results have been contrasted against appropriately coarse-grained Langevin Dynamics simulations. These stable model …
Manipulating the self-assembly nanostructures with combined different control measures is emerging as a promising route for numerous applications to generate templates and scaffolds for nanostructured materials. Here, the two different control measures are a cylindrical confinement and an oscillatory shear flow. We study the phase behavior of diblock copolymer confined in nanopore under oscillatory shear by considering different $D/L_0$ ($D$ is the diameter of the cylindrical nanopore, $L_0$ is the domain spacing) and different shears via Cell Dynamics Simulation. Under different $D/L_0$, in t…
Poly(ethylene oxide)-$\textit{b}$-poly(butylmethacrylate) (PEO-$\textit{b}$-PBMA) copolymers have recently been identified as excellent building blocks for the synthesis of hierarchical nanoporous materials. Nevertheless, while experiments have unveiled their potential to form bicontinuous phases and vesicles, a general picture of their phase and aggregation behavior is still missing. By performing Molecular Dynamics simulations, we here apply our recent coarse-grained model of PEO-$\textit{b}$-PBMA to investigate its self-assembly in water and tetrahydrofuran (THF) and unveil the occurrence o…
We study the phase transitions of a fluid confined in a capillary slit made from two adjacent walls each of which are a periodic composite of stripes of two different materials. For wide slits the capillary condensation occurs at a pressure which is described accurately by a combination of the Kelvin equation and the Cassie law for an averaged contact angle. However, for narrow slits the condensation occurs in two steps involving an intermediate bridging phase, with the corresponding pressures described by two new Kelvin equations. These are characterised by different contact angles due to int…
Designing Multivalent Copolymers for Selective Targeting of Multicomponent Surfaces
Faculty of Chemistry and Chemical Engineering, University of Maribor（马里博尔大学化学与化工学院）；The Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska（沿海大学数学、自然科学与信息技术学院）；Institute for Environmental Protection and Sensors（环境保护与传感器研究所）；Department of Materials Science and Engineering, Johns Hopkins University（约翰斯·霍普金斯大学材料科学与工程系）
We studied solvent-driven ordering dynamics of block copolymer films supported by a densely cross-linked polymer network designed as organic hard mask (HM) for lithographic fabrications. The ordering of microphase separated domains at low degrees of swelling corresponding to intermediate/strong segregation regimes was found to proceed significantly faster in films on a HM layer as compared to similar block copolymer films on silicon wafers. The ten-fold enhancement of the chain mobility was evident in the dynamics of morphological phase transitions and of related process of terrace-formation o…
We have used the Scheutjens-Fleer self-consistent field (SF-SCF) method to predict the self-assembly of triblock copolymers with a solvophilic middle block and sufficiently long solvophobic outer blocks. We model copolymers consisting of polyethylene oxide (PEO) as solvophilic block and poly(lactic-co-glycolic) acid (PLGA) or poly({\ko}-caprolactone) (PCL) as solvophobic block. These copolymers form structurally quenched spherical micelles provided the solvophilic block is long enough. Predictions are calibrated on experimental data for micelles composed of PCL-PEO-PCL and PLGA-PEO-PLGA triblo…
Controlling the spatial distribution of liquid droplets on surfaces via surface energy patterning can be used to control material delivery to specified regions via selective liquid/solid wetting. While studies of the equilibrium shape of liquid droplets on heterogenous substrates exist, much less is known about the corresponding wetting kinetics. We make significant progress towards elucidating details of this topic by studying, via large-scale atomistic simulations, liquid nanodroplets spreading on chemically patterned surfaces. A model is presented for lines of polymer liquid (droplets) on s…
We extensively study the phase diagram of a diblock copolymer melt confined in a cylindrical nanopore using real-space self-consistent mean-field theory. We discover a rich variety of new two-dimensional equilibrium structures that have no analog in the unconfined system. These include non-hexagonally coordinated cylinder phases and structures intermediate between lamellae and cylinders. We map the stability regions and phase boundaries for all the structures we find. As the pore radius is decreased, the pore accommodates fewer cylindrical domains and structural transitions occur as cylinders …
Using the self-consistent field theory (SCFT) in spherical unit cells of various dimensionalities, D, a phase diagram of a diblock, A-b-B, is calculated in 5 dimensional space, d = 5. This is an extension of a previous work for d = 4. The phase diagram is parameterized by the chain composition, f, and incompatibility between A and B , quantified by the product \c{hi} N. We predict 5 stable nanophases: layers, cylinders, 3 D spherical cells, 4D spherical cells, and 5D spherical cells. In the strong segregation limit, that is for large \c{hi}N, the order-order transition compositions are determi…
We consider a nano-patterned planar wall consisting of a periodic array of stripes of width $L$, which are completely wet by liquid (contact angle $θ=0$), separated by regions of width $D$ which are completely dry (contact angle $θ=π)$. Using microscopic Density Functional Theory we show that in the presence of long-ranged dispersion forces, the wall-gas interface undergoes a first-order wetting transition, at bulk coexistence, as the separation $D$ is reduced to a value $D_w\propto\ln L$, induced by the bridging between neighboring liquid droplets. Associated with this is a line of pre-wettin…
When polyelectrolyte-neutral block copolymers are mixed in solutions to oppositely charged species (e.g. surfactant micelles, macromolecules, proteins etc), there is the formation of stable supermicellar aggregates combining both components. The resulting colloidal complexes exhibit a core-shell structure and the mechanism yielding to their formation is electrostatic self-assembly. In this contribution, we report on the structural properties of supermicellar aggregates made from yttrium-based inorganic nanoparticles (radius 2 nm) and polyelectrolyte-neutral block copolymers in aqueous solution…
Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering of extrinsic as well as intrinsic substrate geometry may provide such a controllable ordering mechanism for block copolymers films. We develop an effective two-dimensional model of thin films of striped-phase diblock copolymers on general curved substrates. The model is obtained as an expansion in the film thickness and thus takes the third dimension into a…
A series of amphiphilic LC block copolymers, in which the hydrophobic block is a smectic polymer poly(4-methoxyphenyl 4-(6-acryloyloxy-hexyloxy)-benzoate) (PA6ester1) and the hydrophilic block is polyethyleneglycol (PEG), were synthesized and characterized. The self-assembly of one of them in both the pure state and the dilute aqueous solution was investigated in detail. Nano-structures in the pure state were studied by SAXS and WAXS on samples aligned by a magnetic field. A hexagonal cylindrical micro-segregation phase was observed with a lattice distance of 11.2 nm. The PEG blocks are in the…
The effect of silica nanoparticles on transient microemulsion networks made of microemulsion droplets and telechelic copolymer molecules in water is studied, as a function of droplet size and concentration, amount of copolymer, and nanoparticle volume fraction. The phase diagram is found to be affected, and in particular the percolation threshold characterized by rheology is shifted upon addition of nanoparticles, suggesting participation of the particles in the network. This leads to a peculiar reinforcement behaviour of such microemulsion nanocomposites, the silica influencing both the modul…
Nanotube patterning may occur naturally upon the spontaneous self-assembly of biomolecules onto the surface of single-walled carbon nanotubes (SWNTs). It results in periodically alternating bands of surface properties, ranging from relatively hydrophilic to hydrophobic, along the axis of the nanotube. Single Chain Mean Field (SCMF) theory has been used to estimate the free energy of systems in which a surface patterned nanotube penetrates a phospholipid bilayer. In contrast to un-patterned nanotubes with uniform surface properties, certain patterned nanotubes have been identified that display …
We study both experimentally and theoretically the self-assembly of binary block copolymers in dilute solution, where self-assembly is triggered by changing the solvent from the common good solvent THF to the selective solvent water, and where the two species on their own in water form vesicles and spherical micelles respectively. We find that in water the inter-micellar exchange of these block copolymers is very slow so that the self-assembled structures are in local but not global equilibrium (i.e., they are non-ergodic). This opens up the possibility of controlling micelle morphology both t…
We report on DNA arrays produced by Dip Pen Nanolithography (DPN) on a novel Au-Ag micro patterned template stripped surface. DNA arrays have been investigated by atomic force microscopy (AFM) and scanning tunnelling microscopy (STM) showing that the patterned template stripped substrate enables easy retrieval of the DPN-functionalized zone with a standard optical microscope permitting a multi-instrument and multi-technique local detection and analysis. Moreover the smooth surface of the Au squares (abput 5-10 angstrom roughness) allows to be sensitive to the hybridization of the oligonucleoti…
In the present study, we have investigated, using Monte Carlo simulations (MC), the adsorption of polyelectrolytes on the charged nanopatterned surfaces. Different surface patterns were considered and we noticed that the amount of adsorption is directly dependent on the size of the domains. Also in the case of checkerboard configuration, it was observed that the polyelectrolytes are aligned along the diagonal of square domains.
