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 of a wide spectrum of mesophases. In particular, we find that the morphological phase diagram of this ternary system incorporates bicontinuous and lamellar phases at high copolymer concentrations, and finite-size aggregates, such as dispersed sheets or disk-like aggregates, spherical vesicles and rod-like vesicles, at low copolymer concentrations. The morphology of these mesophases can be controlled by tuning the THF/water relative content, which has a striking effect on the kinetics of self-assembly as well as on the resulting equilibrium structures. Our results disclose the fascinating potential of PEO-$\textit{b}$-PBMA copolymers for the templated synthesis of nanostructured materials and offer a guideline to fine-tune their properties by accurately selecting the THF/water ratio.
A versatile and transferable coarse-grained (CG) model was developed to investigate the self-assembly of two ubiquitous methacrylate-based copolymers: poly(ethylene oxide-b-methylmethacrylate) (PEO-b-PMMA) and poly(ethylene oxide-b-butylmethacrylate) (PEO-b-PBMA). We derive effective CG potentials that can reproduce their behaviour in aqueous and organic polymer solutions, pure copolymer systems, and at the air-water interface following a hybrid structural-thermodynamic approach, which incorporates macroscopic and atomistic-level information. The parameterization of the intramolecular CG poten…
We examine the condensed states of a simple semiflexible copolymer in which there are two monomer types that are immiscible with each other and with the solvent. Although this is similar to the well known problem of collapse for a semiflexible homopolymer we find that it gives rise to a much richer variety of condensed states. We predict the existence of these states using simple analytic arguments and also observe them directly using Brownian dynamics simulations.
We use a standard bead-spring model and molecular dynamics simulations to study the static properties of symmetric linear multiblock copolymer chains and their blocks under poor solvent conditions in a dilute solution from the regime close to theta conditions, where the chains adopt a coil-like formation, to the poorer solvent regime where the chains collapse obtaining a globular formation and phase separation between the blocks occurs. We choose interaction parameters as is done for a standard model, i.e., the Lennard-Jones fluid and we consider symmetric chains, i.e., the multiblock copolyme…
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…
Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent (S1) and a selective solvent (S2) for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending on the fraction of the selective solvent CS2, the concentration of the polymer CP, and the polymer-solvent interactions εij (i = A, B; j = S1, S2). Morphology diagrams are constructed as functions of CP, CS2, and/or εAS2. The copolymer morphological sequence from dissolved -> sphere -> rod-> ring/cage-> vesicle is obtained upon increasing CS2 a…
Molecular dynamics simulations are used to study the phase behavior of linear multiblock copolymers with two types of monomers, A and B, where the length of the polymer blocks $N_{A}$ and $N_{B}$ ($N_{A}=N_{B}=N$), the number of the blocks $n_{A}$ and $n_{B}$ ($n_{A}=n_{B}=n$), and the solvent quality varies. The fraction $f$ of A-type monomers is kept constant and equal to 0.5. Whereas at high enough temperatures these macromolecules form coil structures, where each block A or B forms rather individual clusters, at low enough temperatures A and B monomers from different blocks can join togeth…
We investigate the dynamics of the collapse of a single copolymer chain, when the solvent quality is suddenly quenched from good to poor. We employ Brownian dynamics simulations of a bead-spring chain model and incorporate fluctuating hydrodynamic interactions via the Rotne-Prager-Yamakawa tensor. Various copolymer architectures are studied within the framework of a two-letter HP model, where monomers of type H (hydrophobic) attract each other, while all interactions involving P (polar or hydrophilic) monomers are purely repulsive. The hydrodynamic interactions are found to assist the collapse…
We use molecular dynamics simulations to study the static properties of a single linear multiblock copolymer chain under poor solvent conditions varying the block length $N$, the number of blocks $n$, and the solvent quality by variation of the temperature $T$. We study the most symmetrical case, where the number of blocks of monomers of type A, $n_{A}$, equals that of monomers B, $n_{B}$ ($n_{A}=n_{B}=n/2$), the length of all blocks is the same irrespective of their type, and potential parameters are also chosen symmetrically, as for a standard Lennard-Jones fluid. Under poor solvent conditio…
This paper reports the experimental determination of the growth exponents and activation enthalpies for the ordering process of standing cylinder-forming all-organic polystyrene-block-poly (methyl methacrylate) (PS-b-PMMA) block copolymer (BCP) thin films as a function of the BCP degree of polymerization (N). The maximum growth exponent of 1/3 is observed for the smallest BCP at the border of the order disorder transition. Both the growth exponents and the activation enthalpies exponentially decrease with the BCP segregation strength (chi N) following the same path of the diffusivity.
We have studied the phase behavior of the poly(n-butyl acrylate)-b-poly(acrylic acid) block copolymer in a mixture of two miscible solvents, water and tetrahydrofuran (THF). The techniques used to examine the different polymers, structures and phases formed in mixed solvents were static and dynamic light scattering, small-angle neutron scattering, nuclear magnetic resonance and fluorescence microscopy. By lowering the water/THF mixing ratio X, the sequence unimers, micron-sized droplets, polymeric micelles was observed. The transition between unimers and the micron-sized droplets occurred at X…
Using detailed atomistic simulations,we explore the conformational landscape of aggregates formed by biomimetic antimicrobial(AM) binary methacrylate copolymers,with hydrophobic and charged functional groups and the role of inclusion of polar functional groups on such aggregate morphologies.The effect of sequence of the constituent functional groups on aggregate conformation is also studied by considering random and block sequences along the polymer backbone.Our results suggest that block binary copolymers form large spherical aggregates with effective shielding of hydrophobic groups by charge…
Time-resolved small angle x-ray scattering (SAXS) was used to examine the kinetics of the transition from HEX cylinders to BCC spheres at various temperatures in poly(styrene-b- ethylene-co-butylene-b-styrene) (SEBS) in mineral oil, a selective solvent for the middle EB block. Temperature-ramp SAXS and rheology measurements show the HEX to BCC order-order transition (OOT) at ~127 oC and order-disorder transition (ODT) at ~180 oC. We also observed the metastability limit of HEX in BCC with a spinodal temperature, Ts ~ 150 oC. The OOT exhibits 3 stages and occurs via a nucleation and growth mech…
We propose a mean-field model to explore the equilibrium coupling between micelle aggregation and lattice choice in neutral copolymer and selective solvent mixtures. We find both thermotropic and lyotropic transitions from face-centered cubic to body-centered cubic ordered phases of spherical micelles, in agreement with experimental observations of these systems over a broad range of conditions. Stability of the non-closed packed phase can be attributed to two physical mechanisms: the large entropy of lattice phonons near crystal melting and the preference of the inter-micelle repulsions for t…
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…
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…
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…
We examined the kinetics of the transformation from the lamellar (LAM) to the hexagonally packed cylinder (HEX) phase for the triblock copolymer, polystyrene-b-poly (ethylene-co-butylene)-b-polystyrene (SEBS) in dibutyl phthalate (DBP), a selective solvent for polystyrene (PS), using time-resolved small angle x-ray scattering (SAXS). We observe the HEX phase with the EB block in the cores at a lower temperature than the LAM phase due to the solvent selectivity of DBP for the PS block. Analysis of the SAXS data for a deep temperature quench well below the LAM-HEX transition shows that the trans…
Solvent vapor annealing (SVA) is known to be a simple, low-cost and highly efficient technique to produce defect-free diblock copolymer (BCP) thin films. Not only can the solvent weaken the BCP segmental interactions, but it can vary the characteristic spacing of the BCP microstructures. We carry out systematic theoretical studies on the effect of adding solvent into lamellar BCP thin films on the defect removal close to the BCP order-disorder transition. We find that the increase of the lamellar spacing, as is induced by addition of solvent, facilitates more efficient removal of defects. The …
Molecular dynamics simulations are used to study the phase behavior of a single linear multiblock copolymer with blocks of A- and B-type monomers under poor solvent conditions, varying the block length $N$, number of blocks $n$, and the solvent quality (by variation of the temperature $T$). The fraction $f$ of A-type monomers is kept constant and equal to 0.5, and always the lengths of A and B blocks were equal ($N_{A}=N_{B}=N$), as well as the number of blocks ($n_{A}=n_{B}=n$). We identify the three following regimes where: (i) full microphase separation between blocks of different type occu…
The behaviour of rod-coil diblock copolymers close to a surface is discussed by using extended scaling methods. The copolymers are immersed in selective solvent such that the rods are likely to aggregate to gain energy. The rods are assumed to align only parallel to each other, such that they gain a maximum energy by forming liquid crystalline structures. If an aggregate of these copolymers adsorbs with the rods parallel to the surface the rods shift with respect to each other to allow for the chains to gain entropy. It is shown that this shift decays with increasing distance from the surface.…
We investigate the localization of a hydrophobic - polar (HP) - regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length $M$ on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copolymer chain perpendicular and parallel to the interface in terms of chain length N and block size M, as well as the selectivity parameter χ. The scaling relations differ for the case of weak and strong …
We carry out numerical simulations of vesicle formation based on the density functional theory for block copolymer solutions. It is shown by solving the time evolution equations for concentrations that a polymer vesicle is spontaneously formed from the homogeneous state. The vesicle formation mechanism obtained by our simulation agree with the results of other simulations based on the particle models as well as experiments. By changing parameters such as the volume fraction of polymers or the Flory-Huggins interaction parameter between the hydrophobic subchains and solvents, we can obtain the …
We study the conformational properties of complex polymer macromolecules, consisting in general of $n$ subsequently connected chains (blocks) of different lengths and distinct chemical structure. Depending on the solvent conditions, the inter- or intrachain interactions of some blocks may vanish, causing the rich conformational behavior. Our main attention is focused on the universal conformational properties of such molecules. Applying the direct polymer renormalization group approach, we derive the analytical expressions for the scaling exponent $γ(n)$, governing the number of possible confo…
Multiblock copolymer chains in implicit nonselective solvents are studied by Monte Carlo method which employs a parallel tempering algorithm. Chains consisting of 120 $A$ and 120 $B$ monomers, arranged in three distinct microarchitectures: $(10-10)_{12}$, $(6-6)_{20}$, and $(3-3)_{40}$, collapse to globular states upon cooling, as expected. By varying both the reduced temperature $T^*$ and compatibility between monomers $ω$, numerous intra-globular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and $n$-clusters with $n>3$ (lamellar and other), wh…
The phase behaviour of amphiphilic multiblock copolymers with a large number of blocks in semidilute solutions is studied by lattice Monte Carlo simulations. The influence on the resulting structures of the concentration, the solvent quality and the ratio of hydrophobic to hydrophilic monomers in the chains has been assessed explicitely. Several distinct regimes are put in evidence. For poorly substituted (mainly hydrophilic) copolymers formation of micelles is observed, either isolated or connected by the hydrophilic moieties, depending on concentration and chain length. For more highly subst…
Single-chain Monte Carlo simulations of amphiphilic diblock star copolymers were carried out in continuous space using implicit solvents. Two distinct architectures were studied: stars with the hydrophobic blocks attached to the core, and stars with the polar blocks attached to the core, with all arms being of equal length. The ratio of the lengths of the hydrophobic block to the length of the polar block was varied from 0 to 1. Stars with 3, 6, 9 or 12 arms, each of length 10, 15, 25, 50, 75 and 100 Kuhn segments were analysed. Four distinct types of conformations were observed for these syst…
A lattice model for a symmetrical copolymer "bottle brush" molecule, where two types (A,B) of flexible side chains are grafted with one chain end to a rigid backbone, is studied by a variant of the pruned-enriched Rosenbluth method (PERM), allowing for simultaneous growth of all side chains in the Monte Carlo sampling. Choosing repulsive binary interactions between unlike monomers and varying the solvent quality, it is found that phase separation into an $A$-rich part of the cylindrical molecule and a $B$-rich part can occur only locally. Long range order (in the direction of the backbone) doe…
We discuss in this paper the phase diagram of a diblock polyampholyte solution in the limit of high ionic strength as a function of concentration and charge asymmetry. This system is shown to be very similar to solutions of so-called charged-neutral diblock copolymers: at zero charge asymmetry the solution phase separates into a polyelectrolyte complex and almost pure solvent. Above a charge asymmetry threshold, the copolymers are soluble as finite size aggregates. Scaling laws of the aggregates radius as a function of pH of the solution are in qualitative agreement with experiments.
The effects of the length of each hydrophobic end block N_{st} and polymer concentration \barϕ_{P} on the transition broadness in amphiphilic ABA symmetric triblock copolymer solutions are studied using the self-consistent field lattice model. When the system is cooled, micelles are observed, i.e.,the homogenous solution (unimer)-micelle transition occurs. When N_{st} is increased, at fixed \barϕ_{P}, micelles occur at higher temperature, and the temperature-dependent range of micellar aggregation and half-width of specific heat peak for unimer-micelle transition increase monotonously. Compare…
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…
Monte Carlo simulation on the crystallization of double crystalline diblock copolymer unravels an intrinsic relationship between block asymmetry and crystallization behaviour. We model crystalline A-B diblock copolymer, wherein the melting temperature of A-block is higher than that of the B-block. We explore the composition dependent crystallization behaviour by varying the relative block length with weak and strong segregation strength between the blocks. In weak segregation limit, we observe that with increasing the composition of B-block, its crystallization temperature increases accompanyi…
Encapsulation of dsDNA fragments (contour length 54 nm) by the cationic diblock copolymer poly(butadiene-b-N-methyl 4-vinyl pyridinium) [PBd-b-P4VPQ] has been studied with phase contrast, polarized light, and fluorescence microscopy, as well as scanning electron microscopy. Encapsulation was achieved with a single emulsion technique. For this purpose, an aqueous DNA solution is emulsified in an organic solvent (toluene) and stabilized by the amphiphilic diblock copolymer. The PBd block forms an interfacial brush, whereas the cationic P4VPQ block complexes with DNA. A subsequent change of the q…
We explore the shape and internal structure of diblock copolymer (di-BCP) nanoparticles (NPs) by using the Ginzburg-Landau free-energy expansion. The self-assembly of di-BCP lamellae confined in emulsion droplets can form either ellipsoidal or onion-like NPs. The corresponding inner structure is a lamellar phase that is either perpendicular to the long axis of the ellipsoids (L$_\perp$) or forms a multi-layer concentric shell (C$_\parallel$), respectively. We focus on the effects of the interaction parameter between the A/B monomers $τ$, and the polymer/solvent $χ$, as well as the NP size on t…
Single Chain Expulsion from Diblock Copolymer Micelles with Dense Corona
South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology（华南软物质科学与技术高等研究院，新兴软物质学院，华南理工大学）；Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology（广东省功能性与智能型杂化材料与技术重点实验室，华南理工大学）；State Key Laboratory of Pulp and Paper Engineering, South China University of Technology（华南理工大学制浆造纸工程国家重点实验室）
We study conformations assumed by single diblock star copolymers in a poor solvent by means of the Gaussian variational theory and Monte Carlo simulation in continuous space. Cases of stars with internal and external hydrophobic blocks are analysed. While in the former case the collapsed state has an obvious micellar shape, the latter case exhibits two nontrivial conformational structures. Apart from the equilibrium state of a globular hydrophobic core with hydrophilic daisy loops, one also finds here a metastable state of outstretched hydrophilic blocks with hydrophobic subglobules at their e…
The first three-dimensional simulation of shear-induced phase transitions in a polymeric system has been performed. The method is based on dynamic density-functional theory. The pathways between a bicontinuous phase with developing gyroid mesostructure and a lamellar/cylinder phase coexistence are investigated for a mixture of flexible triblock ABA-copolymer and solvent under simple steady shear.
In recent experiments, small, thick-walled vesicles with a narrow size distribution were formed from copolymers where the degree of polymerisation of the hydrophobic block, N_B, was significantly greater than that of the hydrophilic block, N_A. Using a mean-field theory, we reproduce several aspects of the behaviour of these vesicles. Firstly, we find a minimum in the free energy of the system of vesicles as a function of their radius, corresponding to a preferred size for the vesicles, when N_B is several times larger than N_A. Furthermore, the vesicle radius diverges as N_B is increased towa…
We propose a simple scaling theory describing the variation of the mean first passage time (MFPT) $τ(N,M)$ of a regular block copolymer of chain length $N$ and block size $M$ which is dragged through a selective liquid-liquid interface by an external field $B$. The theory predicts a non-Arrhenian $τ$ vs. $B$ relationship which depends strongly on the size of the blocks, $M$, and rather weakly on the total polymer length, $N$. The overall behavior is strongly influenced by the degree of selectivity between the two solvents $χ$. The variation of $τ(N,M)$ with $N$ and $M$ in the regimes of weak a…
PEP-PEO block copolymer micelles offer the possibility to investigate phase behaviour and interactions of star polymers (ultra-soft colloids). A star-like architecture is achieved by an extremely asymmetric block ratio (1:20). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by SANS can be quantitatively described in terms of an effective potential developed for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid/solid transition. Whereas for intermediate f a b…
We study the effect of the molecular architecture of amphiphilic star polymers on the shape of aggregates they form in water. Both solute and solvent are considered at a coarse-grained level by means of dissipative particle dynamics simulations. Four different molecular architectures are considered: the miktoarm star, two different diblock stars and a group of linear diblock copolymers, all of the same composition and molecular weight. Aggregation is started from a closely packed bunch of $N_{\text a}$ molecules immersed into water. In most cases, a single aggregate is observed as a result of …
We develop a lattice-based Monte Carlo simulation method for charged mixtures capable of treating dielectric heterogeneities. Using this method, we study oil-water mixtures containing an antagonistic salt, with hydrophilic cations and hydrophobic anions. Our simulations reveal several phases with a spatially modulated solvent composition, in which the ions partition between water-rich and water-poor regions according to their affinity. In addition to the recently observed lamellar phase, we find tubular, droplet, and even gyroid phases reminiscent of those found in block copolymers and surfact…
The interactions between nanoparticles and solvents play a critical role in the formation of complex, metastable nanostructures. However, direct observation of such interactions with high spatial and temporal resolution is challenging with conventional liquid-cell transmission electron microscopy (TEM) experiments. Here, a windowless system consisting of polymer nanoreactors deposited via scanning probe block copolymer lithography (SPBCL) on an amorphous carbon film is used to investigate the coarsening of ultrafine (1-3 nm) Au-Pt bimetallic nanoparticles as a function of solvent evaporation. …
Motivated by the deficiencies of the previous MARTINI models of poly(ethylene oxide) (PEO), we present a new model featuring a high degree of transferability. The model is parametrized on (a) a set of 8 free energies of transfer of dimethoxyethane (PEO dimer) from water to solvents of varying polarity; (b) the radius of gyration in water at high dilution; and (c) matching angle and dihedral distributions from atomistic simulations. We demonstrate that our model behaves well in five different areas of application: (1) it produces accurate densities and phase behavior or small PEO oligomers and …
