The distribution of homogeneously grafted nanoparticles in polymer thin films and blends

Confinement-induced self-assembly of a diblock copolymer within a non-uniform cylindrical nanopore

The self-assembly of a diblock copolymer melt confined within a non-uniform cylindrical nanopore is studied using the self-consistent field theory. The non-uniformity manifests in the form of a converging-diverging cylindrical nanopore. The axial variation in pore diameter presents a range of curvatures within the same confinement pore as opposed to a single curvature in a uniform-diameter cylindrical pore. The introduction of multiple curvatures leads to the formation of novel microstructures not accessible in uniform cylindrical confinement. The well-known equilibrium structures like a single helix, double helices, and concentric lamella under cylindrical confinement transition into new morphologies such as hyperboloidal phases, microstructures containing rings with a bead, rings with spheres, and a squeezed helical phase as the pore diameter varies axially. The converging-diverging geometry of the confining pore renders the helical phases seen in the cylindrical pore less favorable. A phase diagram in the parametric space of the block fraction and the ratio of the smallest and largest pore radii has been constructed to depict the order-order transition of various microstructures. The ratio of radii, a measure of the non-uniformity of the pore, along with the pore length brings out some interesting morphologies. The mechanism of these structural transitions is understood as the interplay between the variation in pore curvature attributed to the non-uniformity, the spontaneous curvature of the block copolymer interface, and the enthalpic interaction between the segregated blocks.

Grafted Nanoparticle Surface Wetting during Phase Separation in Polymer Nanocomposite Films

Wetting of polymer-grafted nanoparticles (NPs) in a polymer nanocomposite (PNC) film is driven by a difference in surface energy between components as well as bulk thermodynamics, namely, the value of the interaction parameter, χ. The interplay between these contributions is investigated in a PNC containing 25 wt % polymethyl methacrylate (PMMA)-grafted silica NPs (PMMA-NPs) in poly(styrene-ran-acrylonitrile) (SAN) upon annealing above the lower critical solution temperature (LCST, 160 °C). Atomic force microscopy (AFM) studies show that the areal density of particles increases rapidly and then approaches 80% of that expected for random close-packed hard spheres. A slightly greater areal density is observed at 190 °C compared to 170 °C. The PMMA-NPs are also shown to prevent dewetting of PNC films under conditions where the analogous polymer blend is unstable. Transmission electron microscopy (TEM) imaging shows that PMMA-NPs symmetrically wet both interfaces and form columns that span the free surface and substrate interface. Using grazing-incidence Rutherford backscattering spectrometry (GI-RBS), the PMMA-NP surface excess (Z*) initially increases rapidly with time and then approaches a constant value at longer times. Consistent with the areal density, Z* is slightly greater at deeper quench depths, which is attributed to the more unfavorable interactions between the PMMA brush and SAN segments. The Z* values at early times are used to determine the PMMA-NP diffusion coefficients, which are significantly larger than theoretical predictions. These studies provide insights into the interplay between wetting and phase separation in PNCs and can be utilized in nanotechnology applications where surface-dependent properties, such as wettability, durability, and friction, are important.

Field-Theoretic Simulations for Block Copolymer Melts Using the Partial Saddle-Point Approximation

Field-theoretic simulations (FTS) provide an efficient technique for investigating fluctuation effects in block copolymer melts with numerous advantages over traditional particle-based simulations. For systems involving two components (i.e., A and B), the field-based Hamiltonian, Hf[W-,W+], depends on a composition field, W-(r), that controls the segregation of the unlike components and a pressure field, W+(r), that enforces incompressibility. This review introduces researchers to a promising variant of FTS, in which W-(r) fluctuates while W+(r) tracks its mean-field value. The method is described in detail for melts of AB diblock copolymer, covering its theoretical foundation through to its numerical implementation. We then illustrate its application for neat AB diblock copolymer melts, as well as ternary blends of AB diblock copolymer with its A- and B-type parent homopolymers. The review concludes by discussing the future outlook. To help researchers adopt the method, open-source code is provided that can be run on either central processing units (CPUs) or graphics processing units (GPUs).

Molecular Dynamics of Janus Nanodimers Dispersed in Lamellar Phases of a Block Copolymer

We investigate structural and dynamical properties of Janus nanodimers (NDs) dispersed in lamellar phases of a diblock copolymer. By performing molecular dynamics simulations, we show that an accurate tuning of the interactions between NDs and copolymer blocks can lead to a close control of NDs' space distribution and orientation. In particular, NDs are preferentially found within the lamellae if enthalpy-driven forces offset their entropic counterpart. By contrast, when enthalpy-driven forces are not significant, the distribution of NDs, preferentially observed within the inter-lamellar spacing, is mostly driven by excluded-volume effects. Not only does the degree of affinity between host and guest species drive the NDs' distribution in the polymer matrix, but it also determines their space orientation. In turn, these key structural properties influence the long-time dynamics and the ability of NDs to diffuse through the polymer matrix.

Self-Assembly of Polymer Grafted Nanoparticles within Spherically Confined Diblock Copolymers

Geometric confinement plays an important role in the generation of interesting microstructures on account of structural frustration and confinement-induced entropy loss. In the present study, self-consistent field calculations have been performed to examine the self-assembly behavior of a mixture of diblock copolymers and polymer grafted nanoparticles within a spherical confinement. The analysis is aimed at obtaining the equilibrium distribution of nanoparticles with a high degree of order. The ordered mesophases of diblock copolymers provide useful templates to achieve ordering of nanoparticles in a selective domain. Self-assembly of nanoparticles within frustrated diblock copolymers is found to be very different from the bulk. A rich variety of equilibrium morphologies are observed depending on the degree of confinement and the extent of particle loading. In addition, the role of particle size and selectivity along with the length and the number of polymer chains grafted onto the surface of nanoparticles are analyzed to understand the self-assembly behavior. The specific interest is to obtain the chiral structures out of achiral block copolymers subjected to spherical confinement. The realization of various captivating microstructures, such as chiral ordering of nanoparticles, is highly essential to produce advanced nanomaterials with superior physical properties.

Diblock copolymer templated self-assembly of grafted nanoparticles under circular pore confinement

Geometrical confinement plays an important role in generating novel molecular organization arising out of structural frustration and confinement-induced entropy loss. In the present study, we perform self-consistent mean-field theoretical calculations to examine a mixture of a diblock copolymer and polymer grafted nanoparticles confined in a cylindrical nanopore. The two-dimensional analysis is aimed at constructing the equilibrium nanostructures decorated with particles in an ordered manner. The rich variety of ordered mesophases of the diblock copolymer under confinement provide a template to achieve the self-assembly of nanoparticles in a selective domain. The localization behavior of nanoparticles under confinement is found to be qualitatively different from that in a bulk system. In particular, for the concentric lamellar phase the particles tend to localize predominantly in the region of greater curvature within the curved lamella. The incorporation of grafted nanoparticles also results in a transition in ordered phases. Various equilibrium morphologies are observed depending upon the degree of confinement, particle loading, density of grafted segments and selectivity of the particle core to the polymeric species. The ordering of particles and the ensuing equilibrium nanostructures are analyzed. The comprehensive understanding of the self-assembly behavior of particles enables one to design novel nanomaterials with desirable material properties.

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.

Unveiling the Mechanism of the Location of the Grafted Nanoparticles in a Lamellar-Forming Block Copolymer

Through coarse-grained molecular dynamics simulation of polymer-grafted nanoparticles (NPs) in a lamellar-forming diblock copolymer (BCP), we systematically study the effects of the grafting density (N_g), the compatibility between the grafted chains and the A-block of BCPs (ε_gA), and the NP number (N) on the distance (D) of the NPs from the interface by proposing novel characterization parameters of the orientation and distribution of the grafted chains. The NP gradually migrates away from the interface and into the A-block region with the increase of ε_gA for all studied N_g, while slightly returning toward the interface at high ε_gA and great N_g, which is the first observation of nonmonotonic migration at the molecular level. We ascribe the reason of this to the behavior of the grafted chains that are near the interface. Furthermore, we classify the grafted chains into three types along the normal direction of the interface and the migration process is illustrated by the distribution and orientation of the different types of grafted chains, together with the radial distribution function between the NP and the A-block chains. We observe the formation of the NP layers parallel to the interface for N < 20, and a similar nonmonotonic migration of the layers is as well observed. The D is the largest for a small N because of the excluded volume effects between the NPs. Increasing N_g and N pushes the neighboring NP layers toward the interface due to the mutual repulsion. Generally, this study may shed some light on how to better understand and design high-performance polymer nanocomposites with a tunable location of NPs.

Equilibrium Field Theoretic Study of Nanoparticle Interactions in Diblock Copolymer Melts

Block copolymer matrices are often used to control nanoparticle (NP) dispersion behavior, but the effects of diblock domain interfaces on particle-particle interactions have not been well characterized. In this paper, polymer field theoretic simulations are used to quantify interactions between both bare and grafted spherical NPs in microphase-separated A-B diblock copolymers. It is shown that for bare NPs that have an athermal interaction with and a diameter similar to the B domain, the presence of an A-B interface leads to an effective interaction between the particles with multiple minima separated by a free energy barrier. It is further shown that these effects primarily result from chain stretching and compression near the A-B interface induced by particle-particle interactions as opposed to increases in A-B contact at the interfaces. Grafted chains largely prevent these effects and reduce particle-particle interaction strength. When confined by diblock domain interfaces, grafted chains have a reduced extension compared to what is expected for de-wetted brush chains, as commonly described in homopolymer results. Finally, these studies indicate a new route toward linking spherical NPs in a controlled fashion, allowing for tunable plasmonic properties in the case of metallic NPs.

Solvation Effects on the Permeation and Aging Performance of PIM-1-Based MMMs for Gas Separation

Membranes are particularly attractive for lowering the energy intensity of separations as they eliminate phase changes. While many tantalizing polymers are known, limitations in selectivity and stability slightly preclude further development. Mixed-matrix membranes may address these shortcomings. Key to their realization is the intimate mixing between the polymer and the additive to eliminate nonselective transport, improve selectivity, and resist physical aging. Polymers of intrinsic microporosity (PIMs) have inherently promising gas transport properties. Here, we show that porous additives can improve transport and resist aging in PIM-1. We develop a simple, low-cost, and scalable hyper-cross-linked polymer (poly-dichloroxylene, pDCX), which was hydroxylated to form an intimate mixture with the polar PIM-1. Solvent variation allowed control of physical aging rates and improved selectivity for smaller gases. This detailed study has allowed many interactions within mixed matrix membranes to be directly elucidated and presents a practical means to stabilize porous polymers for separation applications.

Radiopaque Fully Degradable Nanocomposites for Coronary Stents

Bioresorbable scaffolds (BRS) were introduced to overcome limitations of current metallic drug-eluting stents and poly-L-lactide (PLLA) has been used in the fabrication of BRS due to its biodegradability and biocompatibility. However, such polymers have weaker mechanical properties as compared to metals, limiting their use in BRS. We hypothesized that nanofillers can be used to enhance the mechanical properties considerably in PLLA. To this end, polymer-matrix composites consisting of PLLA reinforced with 5-20 wt% barium sulfate (BaSO4) nanofillers as a potential BRS material was evaluated. Stearic-acid (SA) modified BaSO4 nanofillers were used to examine the effect of functionalization. Rigid nanofillers improved the tensile modulus and strength of PLLA (60% and 110% respectively), while the use of SA-BaSO4 caused a significant increase (~110%) in the elongation at break. Enhancement in mechanical properties is attributed to functionalization which decreased the agglomeration of the nanofillers and improved dispersion. The nanocomposites were also radiopaque. Finite element analysis (FEA) showed that scaffold fabricated from the novel nanocomposite material has improved scaffolding ability, specifically that the strut thickness could be decreased compared to the conventional PLLA scaffold. In conclusion, BaSO4/PLLA-based nanocomposites could potentially be used as materials for BRS with improved mechanical and radiopaque properties.

Field-Theoretic Simulations of the Distribution of Nanorods in Diblock Copolymer Thin Films

Using block copolymer microphases to guide the self-assembly of nanorods in thin films can give rise to polymeric materials with unique optical, thermal, and mechanical properties beyond those found in neat block copolymers. Often the design and manufacture of these materials require exquisite control of the nanorod distribution, which is experimentally challenging due to the large parameter space spanned by this class of materials. Simulation approaches, on the other hand, can access the thermodynamics that contribute to the nanorod distribution and hence offer valuable guidance toward the design and manufacture of the materials. In this work, we employ complex Langevin field-theoretic simulations to examine the thermodynamic forces that govern the assembly of nanorods in thin films of block copolymers with a particular focus on vertically oriented cylindrical and lamellar domains. Our simulations show that the nanorod geometry, the substrate selectivity for the distinct blocks of the copolymer, and the film thickness all play important roles in engineering both the nanorod orientation and spatial distribution in diblock copolymer thin films. In addition, we employ thermodynamic integration to examine how the nanorods alter the stability of vertical and horizontal domains in thin films, where we find that the tendency of the nanorods to stabilize a vertical orientation depends on both the film thickness and the nanorod concentration.

Surface Segregation and Bulk Aggregation in an Athermal Thin Film of Polymer-Nanoparticle Blends: Strategies of Controlling Phase Behavior

The phase behavior of an athermal film of a polymer-nanoparticle blend (PNB) driven by depletion attraction is investigated by dissipative particle dynamics for nanospheres and nanocubes. Surface segregation is observed at low nanoparticle concentrations, while bulk aggregation is seen at high concentrations. Surface excess and the aggregation number can be controlled by tuning the nanoparticle concentration. As surface-roughened or polymer-grafted nanoparticles are used, uniform PNBs are acquired due to the lack of depletion. Thus, addition of surface-roughened nanoparticles into PNBs of smooth nanoparticles can be employed to tune the phase characteristics. It is found that bulk aggregation is suppressed for both polymer-nanosphere and polymer-nanocube blends. However, surface segregation is impeded for polymer-nanosphere blend but enhanced for polymer-nanocube blend owing to the distinct influence of the nanoparticle shape on depletion.

Solvent vapor annealing in block copolymer nanocomposite films: a dynamic mean field approach

Polymer nanocomposites are an important class of materials due to the nanoparticles' ability to impart functionality not commonly found in a polymer matrix, such as electrical conductivity or tunable optical properties. While the equilibrium properties of polymer nanocomposites can be treated using numerous theoretical and simulation approaches, in experiments the effects of processing and kinetic traps are significant and thus critical for understanding the structure and the functionality of polymer nanocomposites. However, simulation methods that can efficiently predict kinetically trapped and metastable structures of polymer nanocomposites are currently not common. This is particularly important in inhomogeneous polymers such as block copolymers, where techniques such as solvent vapor annealing are commonly employed to improve the long-range order. In this work, we introduce a dynamic mean field theory that is capable of predicting the result of processing the structure of polymer nanocomposites, and we demonstrate that our method accurately predicts the equilibrium properties of a model system more efficiently than a particle-based model. We subsequently use our method to predict the structure of block copolymer thin films with grafted nanoparticles after solvent annealing, where we find that the final distribution of the grafted nanoparticles can be controlled by varying the solvent evaporation rate. The extent to which the solvent evaporation rate can affect the final nanoparticle distribution in the film depends on the grafting density and the length of the grafted chains. Furthermore, the effects of the solvent evaporation rate can be anticipated from the equilibrium nanoparticle distribution in the swollen and dry states.

Microphase separation of short wormlike diblock copolymers with a finite interaction range

We investigate several structural properties of low-molecular weight AB diblock copolymer melts, focusing on a number of features that substantially deviate from those of high-molecular weight copolymer melts. The study is based on the wormlike chain formalism aided by random phase approximation and self-consistent field theory. We examine the effects that stemmed from both the finite molecular weight and the finite interaction range between unlike AB monomers. The latter yields profound effects on systems consisting of short wormlike block copolymers. The noticeable shift of the order-disorder transition point is discussed. Attention is also paid to the strong-segregation regime, where low molecular weight polymers are subject to finite stretchability.

Dispersion and alignment of nanorods in cylindrical block copolymer thin films

Although significant progress has been made in controlling the dispersion of spherical nanoparticles in block copolymer thin films, our ability to disperse and control the assembly of anisotropic nanoparticles into well-defined structures is lacking in comparison. Here we use a combination of experiments and field theoretic simulations to examine the assembly of gold nanorods (AuNRs) in a block copolymer. Experimentally, poly(2-vinylpyridine)-grafted AuNRs (P2VP-AuNRs) are incorporated into poly(styrene)-b-poly(2-vinylpyridine) (PS-b-P2VP) thin films with a vertical cylinder morphology. At sufficiently low concentrations, the AuNRs disperse in the block copolymer thin film. For these dispersed AuNR systems, atomic force microscopy combined with sequential ultraviolet ozone etching indicates that the P2VP-AuNRs segregate to the base of the P2VP cylinders. Furthermore, top-down transmission electron microscopy imaging shows that the P2VP-AuNRs mainly lie parallel to the substrate. Our field theoretic simulations indicate that the NRs are strongly attracted to the cylinder base where they can relieve the local stretching of the minority block of the copolymer. These simulations also indicate conditions that will drive AuNRs to adopt a vertical orientation, namely by increasing nanorod length and/or reducing the wetting of the short block towards the substrate.

The dynamics of unentangled polymers during capillary rise infiltration into a nanoparticle packing

Although highly packed polymer nanocomposites (PNCs) are important for a wide array of applications, preparing them remains difficult because of the poor dispersion of NPs at high loading fractions. One method to successfully prepare PNCs with high loadings is through capillary rise infiltration, as previously shown by Huang et al., although the mechanism of polymer infiltration remains largely unknown. We use molecular dynamics simulations to directly simulate the process of capillary rise infiltration, and we show that the polymers follow Lucas-Washburn dynamics. We observe a wetting front that precedes bulk infiltration, and chains belonging to this front are highly adsorbed to NPs. We also investigate the viscosity of the model polymers both globally and locally in supported and free-standing films, and we find reduced viscosity near the surface of the films and increased viscosity near the supporting substrate, similar to the results of local relaxation times. The reduction in the viscosity at the free surface for short, oligomeric polymers is smaller than for higher molecular weight polymers, and the ratio of the surface viscosities is most consistent with the predictions of the Lucas-Washburn equation. Our results introduce the mechanism by which polymers infiltrate a highly packed NP film, which may shed light on better ways to prepare these materials for energy storage applications and protective coatings.

Polymer-mediated nanorod self-assembly predicted by dissipative particle dynamics simulations

Self-assembly of nanoparticles in polymer matrices is an interesting and growing subject in the field of nanoscience and technology. We report herein on modelling studies of the self-assembly and phase behavior of nanorods in a homopolymer matrix, with the specific goal of evaluating the role of deterministic entropic and enthalpic factors that control the aggregation/dispersion in such systems. Grafting polymer brushes from the nanorods is one approach to control/impact their self-assembly capabilities within a polymer matrix. From an energetic point of view, miscible interactions between the brush and the matrix are required for achieving a better dispersibility; however, grafting density and brush length are the two important parameters in dictating the morphology. Unlike in previous computational studies, the present Dissipative Particle Dynamics (DPD) simulation framework is able to both predict dispersion or aggregation of nanorods and determine the self-assembled structure, allowing for the determination of a phase diagram, which takes all of these factors into account. Three types of morphologies are predicted: dispersion, aggregation and partial aggregation. Moreover, favorable enthalpic interactions between the brush and the matrix are found to be essential for expanding the window for achieving a well-dispersed morphology. A three-dimensional phase diagram is mapped on which all the afore-mentioned parameters are taken into account. Additionally, in the case of immiscibility between brushes and the matrix, simulations predict the formation of some new and tunable structures.

The Effect of Thermophoresis on Unsteady Oldroyd-B Nanofluid Flow over Stretching Surface

There are currently only a few theoretical studies on convective heat transfer in polymer nanocomposites. In this paper, the unsteady incompressible flow of a polymer nanocomposite represented by an Oldroyd-B nanofluid along a stretching sheet is investigated. Recent studies have assumed that the nanoparticle fraction can be actively controlled on the boundary, similar to the temperature. However, in practice, such control presents significant challenges and in this study the nanoparticle flux at the boundary surface is assumed to be zero. We have used a relatively novel numerical scheme; the spectral relaxation method to solve the momentum, heat and mass transport equations. The accuracy of the solutions has been determined by benchmarking the results against the quasilinearisation method. We have conducted a parametric study to determine the influence of the fluid parameters on the heat and mass transfer coefficients.

Predicting the structure and interfacial activity of diblock brush, mixed brush, and Janus-grafted nanoparticles

We develop a field theoretic simulation model to study the interfacial properties of grafted nanoparticles as a function of the grafting architecture.