Symmetric Diblock Copolymers Research Articles

Investigation of structural frustration in symmetric diblock copolymers confined in polar discs through cell dynamic simulation

Nanotechnology has opened new avenues for advanced research in various fields of soft materials. Materials scientists, chemists, physicists, and computational mathematicians have begun to take a keen interest in soft materials due to their potential applications in nanopatterning, membrane separation, drug delivery, nanolithography, advanced storage media, and nanorobotics. The unique properties of soft materials, particularly self-assembly, have made them useful in fields ranging from nanotechnology to biomedicine. The discovery of new morphologies in the diblock copolymer system in curved geometries is a challenging problem for mathematicians and theoretical scientists. Structural frustration under the effects of confinement in the system helps predict new structures. This mathematical study evaluates the effects of confinement and curvature on symmetric diblock copolymer melt using a cell dynamic simulation model. New patterns in lamella morphologies are predicted. The Laplacian involved in the cell dynamic simulation model is approximated by generating a 17-point stencil discretized to a polar grid by the finite difference method. Codes are programmed in FORTRAN to run the simulation, and IBM open DX is used to visualize the results. Comparison of computational results with existing studies validates this study and identifies defects and new patterns.

Competition of Composition Fluctuation Modes in Weakly Segregated Salt-doped Symmetric Diblock Copolymers

Competition of Composition Fluctuation Modes in Weakly Segregated Salt-doped Symmetric Diblock Copolymers

Molecular Simulations Revealing Effects of Non-concatenated Ring Topology on Phase Behavior of Symmetric Diblock Copolymers

Molecular Simulations Revealing Effects of Non-concatenated Ring Topology on Phase Behavior of Symmetric Diblock Copolymers

Photomodulated phase-separation kinetics in block copolymer melts: a DPD simulation study

ABSTRACT We study phase-separation kinetics of symmetric diblock copolymer (BCP) melt in 3 d subjected to sequential light on/off cycles. The incompatible blocks of each BCP chain are connected by a photosensitive bond, which undergoes breakage during photo-illumination (on-cycle) and recombination during the off-cycle. We set a shorter fixed time limit for each on-cycles and focus on analysing how the much longer duration of the light off-cycles affects the segregation kinetics. We explore two scenarios for each off-cycle time variation: one with equal and another with increasing durations. For both cases, we determine the rate constants for bond formation and degradation reactions and assess their influence on the dynamical scaling functions and the growth scale of evolving morphologies. The average domain size typically exhibits diffusive growth ( R ( t ) ∼ t 1 / 3 ) for a couple of cycles in the beginning. However, the domain growth nearly freezes during the rest of the cycles, resulting in bicontinuous and nearly frozen isotropic morphologies.

Two-state nanocomposite based on symmetric diblock copolymer and planar nanoparticles: mesoscopic simulation

A method for controlling the distribution and orientation of 2D fillers in the copolymer matrix is presented.

Phase behavior of symmetric diblock copolymers under 3D soft confinement.

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using self-consistent field theory. Soft confinement is realized in binary blends composed of AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in a homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particles to square SL. When the C homopolymers are strongly selective for the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, and homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement.

Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers

The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space.

Catalytic assembly of symmetric diblock copolymers in a thin film: a dissipative particle dynamics simulation study.

Obtaining a thin block copolymer film with a perfect structure by self-assembly is difficult because the system is, in general, trapped in a metastable state. We used dissipative particle dynamics (DPD) to investigate the self-assembly of AB symmetric diblock copolymers in a thin film. We discovered that addition of a small molecule (molecule C) as the third composition could help the system evade the metastable state. Therefore, imperfect structures could be corrected, and ordered structures formed. Analogous to the performance of a catalyst in catalytic chemistry, molecule C could promote assembly into an ordered structure, but was less involved within the polymer phase. Moreover, simulation results showed that the content of molecule C and its repulsive interactions with blocks A and B were quite important for promoting assembly into ordered structures effectively.

Dissipative particle dynamics study on the interfacial structure and tension for polymer blends of different copolymer chemical composition distributions

A dissipative particle dynamics (DPD) simulation is used to study the interfacial structure and tension for the polymer blends of different copolymer chemical composition distributions. Four chain lengths of diblock copolymers NAB = 10, 20, 40, and 60 with different microstructures are utilized for simulation. As the copolymer microstructure varied from the nondispersed symmetric diblock copolymer to the bidisperse asymmetric diblock copolymer mixtures, the asymmetry of the copolymer varied from f = 0.5 to 0.9. Our simulations show that (i) increasing the copolymer chain length NAB will significantly enhance the interfacial tension, which indicates that the chain length of the diblock copolymer is the most important factor affecting the compatibilization efficiency. Only when the copolymer chain length NAB = 10 can the asymmetry significantly affect the compatibilization efficiency, and the length of the shorter block is the decisive factor in the compatibilization efficiency of asymmetric diblock copolymers; (ii) with an increase in the asymmetry of the diblock copolymer from f = 0.5 to 0.9, the effective chain length of the diblock copolymer with compatibilization decreases, which results in a reduced number of compatibilized beads of copolymers. Thus, the symmetric block copolymer AB is more effective in reducing the interfacial tension than the asymmetric diblock copolymer mixtures at the same concentration; and (iii) The symmetric diblock copolymers enrich faster at the interfaces when elevating the copolymer concentration, which results in a faster reduction in the interfacial tension than that of the asymmetric bidisperse diblock copolymer mixtures. Our research work expands the understanding of polymer blends containing bidisperse asymmetric diblock copolymer mixtures.

Combining Particle-Based Simulations and Machine Learning to Understand Defect Kinetics in Thin Films of Symmetric Diblock Copolymers

The self-assembly of soft matter provides a practical and scalable route toward the production of nanostructured materials, with minimal need for direct intervention at nanoscopic length scales. Symmetric diblock copolymers, which can self-assemble into a lamellar phase, are a prototype for this class of materials. In this work, we introduce a machine learning model that is trained by intermediate time-scale simulations of a soft, coarse-grained model. The aim of the model is to simulate defect kinetics in the lamellar morphology, as the material relaxes toward equilibrium. To do so, we exploit the physical characteristics of overdamped dynamics and formulate the problem of time evolution as a Markov chain. The trained artificial neural network (ANN) predicts a time-independent transition probability from one time step to the next. As a result, we arrive at a method that can be repeatedly applied to generate long-time trajectories. Predicting defect kinetics in this manner provides hitherto unavailable insights into the late-time dynamics of block copolymer relaxation. The neural network is purposely designed to be independent of input size, which enables training on small systems, and enabling predictions over large scales. As a demonstration of these capabilities, in this work, we leverage the ANN to obtain information about the statistics of defect motion and lifetimes over a long-range ordering process.

Compatibilization Efficiency of Additives in Homopolymer Blends: A Dissipative Particle Dynamics Study

We study the compatibilizing effect of copolymers of different architectures on the interface between two incompatible polymer phases by dissipative particle dynamics. Three base polymer systems are investigated, namely weakly incompatible (interspecies repulsion parameter of the dissipative particle dynamics interaction αAB: 25 < αAB < 30), intermediate-incompatible (30 ≤ αAB < 40), and strongly incompatible systems (αAB ≥ 40). We find that the compatibilization efficiency of all regular block copolymers in strongly incompatible systems can be predicted by a power-law function, which contains the Flory–Huggins interaction parameter, the areal concentration, and the mean block length of the compatibilizer. Regular multiblock copolymers have better compatibilization performance compared to the symmetric diblock copolymers at the same areal concentration. This is because smaller amounts of the multiblock copolymer are required to saturate a given interfacial area. For unsymmetric diblock copolymers in strongly incompatible systems, we find additionally that the length of the shortest block is a more important determinant for the compatibilization efficiency than the ratio of block lengths. Our work reveals the involved mechanisms of the compatibilization process, and it provides a promising route to predict the compatibilization efficiency of differently structured copolymer additives in the respective polymer blends.

Topological Effects Near Order–Disorder Transitions in Symmetric Diblock Copolymer Melts

Topological Effects Near Order–Disorder Transitions in Symmetric Diblock Copolymer Melts

3D bicontinuous diamond-like morphologies in thin films of soluted block copolymers.

As shown theoretically earlier via both weak segregation and self-consistent field theories, ordering of confined molten di- and tri-block copolymer morphologies in the presence of a proper 1D patterned substrate could induce the formation of 3D bicontinuous (in particular, diamond-like) morphologies (DLMs). The purpose of the present paper is to study, unlike the previous studies, how the stable DLMs are formed not in a melt but in a solution of symmetric diblock copolymers with a nonselective solvent that wets the thin film on the patterned substrate. It is shown, via a straightforward self-consistent field calculation of the total solution free energy for various competing phases, that the DLM could be formed in the solutions (with the solvent volume fraction of 0.5), which provides much faster thermodynamic equilibration of the solution as compared to the melt. The last circumstance can ease the production of stable DLMs in thin films of copolymers. The phase diagram describing the stable phases on the plane "the pattern period-the film thickness" is built.

Effects of Polymer Block Length Asymmetry and Temperature on the Nanoscale Morphology of Thermoresponsive Double Hydrophilic Block Copolymers in Aqueous Solutions

By complementing small-angle neutron scattering (SANS) with Fourier transform infrared (FTIR) spectroscopy measurements, the influence of temperature as an external stimulus and block length asymmetry is studied on nanoscale assemblies of thermoresponsive double hydrophilic block copolymers in aqueous solutions. Morphologies and molecular hydration characteristics of two poly(N-isopropylacrylamide)-block-poly(oligo ethylene glycol methyl ether acrylate) (PNIPAM-b-POEGA) diblock copolymers, which differ in the length of the PNIPAM block, are compared. SANS provides insights into the nanostructure of the assemblies and FTIR probes vibrations of selected functional groups at the molecular level. Upon temperature increase, the solutions undergo transformations from hierarchical assemblies to more well-defined spherical morphologies. Variations in the block lengths lead to distinct morphological transformations. The variable morphological transformations originate from differences in the strength and/or amount of hydrogen bonding and hydrophobic interactions, as well as the chain density in the clusters formed and hydration. We identify transformations from hierarchical structures to fractal core–shell morphologies in the asymmetric block copolymer with the long PNIPAM block, while spherical and core–shell spherical morphologies are formed for the symmetric diblock copolymer with the short PNIPAM block. In these assemblies of PNIPAM-b-POEGA with the short PNIPAM block, the methyl side group hydration sensitively depends on the temperature increase at temperatures even beyond the nominal volume phase transition temperature. For both blocks, the evolution of the amide I band reflects that solvent–polymer interactions are still favorable even at the highest temperatures. Morphological variations after cooling to ambient temperature are reflected in both SANS and FTIR, pointing to remnant hydrogen bond interactions.

Symmetric Diblock Copolymers in Cylindrical Confinement: A Way to Chiral Morphologies?

We investigate the confinement-induced formation and stability of helix morphologies in lamella-forming AB diblock copolymers via large-scale, particle-based, single-chain-in-mean-field simulations. Such helix structures are rarely observed in bulk or thin films. Structure formation is induced by quenching incompatibility, χN, from a disordered morphology. If the surfaces of the cylindrical confinement do not prefer one component over the other, we observe that stacked lamellae, with their normals along the cylinder axis, are the preferred morphology. Kinetically, this morphology initially forms close to the cylinder surface, whereas the spontaneous, spinodal microphase separation in the cylinder's interior gives rise to a microemulsion-like morphology, riddled with defects and no directional order. Subsequently, the ordered morphology on the cylinder surface progresses inward, pervading the entire volume. In case that the cylindrical pore is only partially filled, the additional confinement along the cylinder axis generally gives rise to incommensurability between the equilibrium spacing of stacked lamellae and the cylinder height. To accommodate this mismatch, the lamella normals will tilt away from the cylinder axis and generate helices of lamellae on the surface of the cylinder. Again, this order progresses from the cylinder surface inward, generating a chiral morphology. Because the spacing between the internal AB interfaces decreases upon approaching the helix center, the concomitant stress results in a decrease in the number of lamellae and the formation of unique dislocation defects. This type of chiral defect morphology is reproducibly formed by the kinetics of structure formation in partly filled cylindrical pores with nonpreferential surfaces and may find applications in photonic applications.

Simulation of diblock copolymer surfactants. III. Equilibrium interfacial adsorption.

Monte Carlo simulations are used to study adsorption of highly asymmetric diblock copolymers to a polymer-polymer interface, and the results compared to self-consistent field theory (SCFT) predictions. The simulation model used here is a bead-spring model that has been used previously to study equilibrium and kinetic properties of spherical micelles [J. A. Mysona et al., Phys. Rev. E 100, 012602 (2019)2470-004510.1103/PhysRevE.100.012602; Phys. Rev. E 100, 012603 (2019)10.1103/PhysRevE.100.012603; Phys. Rev. Lett. 123, 038003 (2019)10.1103/PhysRevLett.123.038003]. Interfacial copolymer concentration Γ and interfacial tension γ are measured as functions of bulk copolymer concentration at concentrations up to the critical micelle concentration over a range of values of the Flory-Huggins χ parameter. The dependence of interfacial pressure Π = γ_{0}-γ on Γ (where γ_{0} is the interfacial tension in the absence of copolymer) is found to be almost independent of χ and to be accurately predicted by SCFT. The bare interfacial tension γ_{0} and total interfacial tension γ(Γ) can also be accurately predicted by SCFT using an estimate of χ obtained from independent analysis of properties of symmetric diblock copolymer melts. SCFT predictions obtained with this estimate of χ do not, however, adequately describe the thermodynamics of the coexisting bulk copolymer solution, as a result of contraction of the strongly interacting core block of dissolved copolymers. Accurate predictions of the relationship between bulk and interfacial properties can thus only be obtained for this system by combining SCFT predictions of the interfacial equation of state with a fit to the measured equation of state for the bulk solution.

Regulation Mechanism of Bubbling Deformation and Fracture Toughness of the Membrane by Asymmetric Phospholipids: A Model System Study.

Dynamic regulation of the deformation modulus and fracture toughness of a membrane is critical to organelles and cells for matching their conflicting needs of resilient and fractured behaviors. These properties implement the protection of the function in the normal condition and the fission function in the endocytosis condition of a membrane. Naturally, a membrane contains phospholipids that have different hydrophilic and hydrophobic group length. The diffusion and aggregation of the phospholipids with asymmetry of the hydrophilic-hydrophobic ratio on the membrane play a key role in regulating the mechanical behaviors passively to the external force. In present work, the effects of the asymmetry of phospholipids on the bubbling deformation and fracture toughness of the membrane to external stretching are investigated in a model system. A disk-shaped micelle formed from the blend of symmetric and asymmetric diblock copolymers in a selective solvent is considered as the membrane sheet. Its mechanically responsive behaviors are investigated by self-consistent field theory. By analyzing the evolution of different components during the stretching process, the mechanism of formation of the bubbling structure is revealed. Moreover, the fracture toughness depending on the asymmetry of the phospholipids is determined quantitatively.

Molecular theory of the tilting transition and computer simulations of the tilted lamellar phase of rod-coil diblock copolymers.

Symmetric rod-coil diblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter. It has been found that the tilted lamellar phase appears to be the most stable one at strong segregation. The rod-coil copolymer tilt angle and orientational order parameters have been determined as functions of the segregation strength. The density functional theory of rod-coil diblock copolymers has been generalized to the case of the tilted lamellar phase and used to study the stability of the orthogonal lamellar phase with respect to tilt. The orthogonal phase indeed appears to be unstable in the broad region of the parameter space in the case of relatively strong segregation. It has also been shown that the transition into the tilted lamellar phase is determined by a strong coupling between two independent tilt order parameters.

Segregation of Maghemite Nanoparticles within Symmetric Diblock Copolymer and Triblock Terpolymer Patterns under Solvent Vapor Annealing.

Block copolymers (BCPs), through their self-assembly, provide an excellent guiding platform for precise controlled localization of maghemite nanoparticles (MNPs). Diblock copolymers (di/BCP) represent the most applied matrix to host filler components due to their morphological simplicity. A series of nanocomposites based on diblock copolymer or triblock terpolymer matrices and magnetic nanoparticles were prepared to study and compare the influence of an additional block into the BCP matrix. MNPs were grafted with low molecular weight polystyrene (PS) chains in order to be segregated in a specific phase of the matrix to induce selective localization. After the mixing of the BCPs with 10% w/v PS-g-MNPs, nanocomposite thin films were formed by spin coating. Solvent vapor annealing (SVA) enabled the PS-g-MNPs selective placement within the PS domains of the BCPs, as revealed by atomic force microscopy (AFM). The recorded images have proven that high amounts of functionalized MNPs can be controllably localized within the same block (PS), despite the architecture of the BCPs (AB vs. ABC). The adopted lamellar structure of the “neat” BCP thin films was maintained for MNPs loading approximately up to 10% w/v, while, for higher content, the BCP adopted lamellar morphology is partially disrupted, or even disappears for both AB and ABC architectures.

Dynamics and Viscoelasticity of Disordered Melts of Symmetric Diblock Copolymers

Simulations of coarse-grained models are used to study relationships among chain motion, composition fluctuations, and stress relaxation in unentangled melts of symmetric diblock copolymers. Measurements of the dynamic structure factor S(q,t) are reported as a function of wavenumber q, time t, and χN, where χ is the Flory–Huggins interaction parameter and N is degree of polymerization. The function S(q,t) is found to be a nearly exponential function of time, S(q,t) ∝ e–t/τ(q), for wavenumbers similar to or less than the wavenumber q* at which the static structure factor S(q) ≡ S(q,t=0) is maximum. The relationship between the decay time τ(q) and S(q) is used to define an effective wavenumber-dependent diffusivity D(q) for fluctuations of wavenumber q. The function D(q) is shown to change very little with changes in χN and to be a monotonically decreasing function of the nondimensional wavenumber qRg, where Rg is polymer radius of gyration. The linear shear stress relaxation modulus G(t) is inferred from measurements of the shear stress autocorrelation function. At low values of χN, far from the order–disorder transition (ODT), the modulus G(t) agrees with predictions of the Rouse model. Near the ODT, G(t) develops an additional slowly decaying feature arising from slow decay of composition fluctuations with q ∼ q*. The behavior of G(t) near the ODT is predicted nearly quantitatively by a modified version of the model of Fredrickson and Larson (FL), in which the prediction of the FL theory for the slowly decaying component is added to the prediction of the Rouse theory for contributions arising from single-chain relaxation, using the independently measured behavior of S(q,t) as an input to the theory.