Monte Carlo simulation of block copolymers

Preparation of Bioderived and Biodegradable Surfactants Based on an Intrinsically Disordered Protein Sequence

Surfactants, block copolymers, and other types of micellar systems are used in a wide variety of biomedical and industrial processes. However, most commonly used surfactants are synthetically derived and pose environmental and toxicological concerns throughout their product life cycle. Because of this, bioderived and biodegradable surfactants are promising alternatives. For biosurfactants to be implemented industrially, they need to be produced on a large scale and also have tailorable properties that match those afforded by the polymerization of synthetic surfactants. In this paper, a scalable and versatile production method for biosurfactants based on a hydrophilic intrinsically disordered protein (IDP) sequence with a genetically engineered hydrophobic domain is used to study variables that impact their physicochemical and self-assembling properties. These amphiphilic sequences were found to self-assemble into micelles over a broad range of temperatures, pH values, and ionic strengths. To investigate the role of the IDP hydrophilic domain on self-assembly, variants with increased overall charges and systematically decreased IDP domain lengths were produced and examined for their sizes, morphologies, and critical micelle concentrations (CMCs). The results of these studies indicate that decreasing the length of the IDP domain and consequently the molecular weight and hydrophilic fraction leads to smaller micelles. In addition, significantly increasing the amount of charged residues in the hydrophilic IDP domain results in micelles of similar sizes but with higher CMC values. This represents an initial step in developing a quantitative model for the future engineering of biosurfactants based on this IDP sequence.

Study of Segregation in Non-Dilute Solutions of Linear Diblock Copolymers and Symmetric Miktoarm (or Janus Star) Polymers Using Monte Carlo Simulations with the Bond Fluctuation Model

The bond fluctuation model was employed to characterize the approach to the mesophase separation transition of pure linear AB copolymers and symmetric miktoarms, also called Janus, star polymers, A_f/2B_f/2, where f = 6 or 12 is the total number of arms, in a common good solvent. We consider a concentration sufficiently high to mimic the melting behavior and also a lower concentration. The segregation between A and B units is represented by a repulsive interaction parameter, ε. Different total numbers of units are also considered. Results for different properties, such as the molecular size, the asphericity and orientational correlation of blocks, or arms, of different compositions are obtained as a function of the segregation parameter. We also calculate scattering structure factors. The initial effect of segregation on the scattering with opposite contrast factors between the A and B blocks can be explained with a common description based on the random phase approximation for both the linear copolymers and the f = 6 miktoarms, once the numerical form factors of the different molecules in their particular systems are considered. However, the results for f = 12 clearly deviate from this description probably due to some degree of ordering in the position of highly armed molecules.

Coarse grained simulation of the aggregation and structure control of polyethylene nanocrystals

Polyethylene (PE) telechelics with carboxylate functional groups at both ends have been shown to assemble into hexagonal nanocrystal platelets with a height defined by their chain length in basic CsOH-solution. In this coarse grained (CG) simulation study we show how properties of the functional groups alter the aggregation and crystallization behavior of those telechelics. Systematic variation of the parameters of the CG model showed that important factors which control nanoparticle stability and structure are the PE chain length and the hydrophilicity and the steric demand of the head groups. To characterize the aggregation process we analyzed the number and size of the obtained aggregates as well as intramolecular order and intermolecular alignment of the polymer chains. By comparison of CG and atomistic simulation data, it could be shown that atomistic simulations representing different chemical systems can be emulated with specific, different CG parameter sets. Thus, the results from the (generic) CG simulation models can be used to explain the effect of different head groups and different counterions on the aggregation of PE telechelics and the order of the obtained nanocrystals.

A dissipative particle dynamics simulation study on phase diagrams for the self-assembly of amphiphilic hyperbranched multiarm copolymers in various solvents

Self-assembly of amphiphilic hyperbranched multiarm copolymers (HMCs) has shown great potential for preparing all kinds of delicate supramolecular structures in all scales and dimensions in solution. However, theoretical studies on the influencing factors for the self-assembly of HMCs have been greatly lagging behind. The phase diagram of HMCs in selective solvents is very necessary but has not been disclosed up to now. Here, the self-assembly of HMCs with different hydrophilic fractions in various solvents was studied systematically by using dissipative particle dynamics (DPD) simulations. Three morphological phase diagrams are constructed and a rich variety of morphologies, ranging from spherical micelles, worm-like micelles, membranes, vesicles, vesosomes, small micellar aggregates (SMAs), and aggregates of spherical and worm-like micelles to helical micelles, are obtained. In addition, both the self-assembly mechanisms and the dynamic processes for the formation of these self-assemblies have been systematically investigated. The simulation results are consistent with available experimental observations. Besides, several novel structures, like aggregates of spherical and worm-like micelles, vesosomes and helical micelles, are firstly discovered for HMC self-assembly. We believe the current work will extend the knowledge on the self-assembly of HMCs, especially on the control of supramolecular structures and on fabricating novel self-assemblies.

Influence of Chain Stiffness, Grafting Density and Normal Load on the Tribological and Structural Behavior of Polymer Brushes: A Nonequilibrium-Molecular-Dynamics Study

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equilibrium behavior of the model brushes, we first study the shearing behavior of flexible chains at different grafting densities covering brush and mushroom regimes. Next, we focus on the effect of chain stiffness on the tribological behavior of polymer brushes. The tribological properties are interpreted by means of the simultaneously recorded density profiles. We find that the friction coefficient decreases with increasing persistence length, both in velocity and separation-dependency studies, over the stiffness range explored in this work.

Equilibrium Phase Behavior of a Continuous-Space Microphase Former

Periodic microphases universally emerge in systems for which short-range interparticle attraction is frustrated by long-range repulsion. The morphological richness of these phases makes them desirable material targets, but our relatively coarse understanding of even simple models hinders controlling their assembly. We report here the solution of the equilibrium phase behavior of a microscopic microphase former through specialized Monte Carlo simulations. The results for cluster crystal, cylindrical, double gyroid, and lamellar ordering qualitatively agree with a Landau-type free energy description and reveal the nontrivial interplay between cluster, gel, and microphase formation.

Surfactant or block copolymer micelles? Structural properties of a series of well-defined n-alkyl-PEO micelles in water studied by SANS

Here we present an extensive small-angle neutron scattering (SANS) structural characterization of micelles formed by poly(ethylene oxide)-mono-n-alkyl ethers (Cn-PEOx) in dilute aqueous solution. Chemically, Cn-PEOx can be considered as a hybrid between a low-molecular weight surfactant and an amphiphilic block copolymer. The present system, prepared through anionic polymerization techniques, is better defined than other commercially available polymers and allows a very precise and systematic testing of the theoretical predictions from thermodynamical models. The equilibrium micellar properties were elaborated by systematically varying the n-alkyl chain length (n) at constant PEO molecular weight or increasing the soluble block size (x), respectively. The structure was reminiscent of typical spherical star-like micelles i.e. a constant core density profile, ∼r(0), and a diffuse corona density profile, ∼r(-4/3). Through a careful quantitative analysis of the scattering data, it is found that the aggregation number, Nagg initially rapidly decreases with increasing PEO length until it becomes independent at higher PEO molecular weight as expected for star-like micelles. On the other hand, the dependency on the n-alkyl length is significantly stronger than that expected from the theories for star-like block copolymer micelles, Nagg ∼ n(2) similar to what is expected for surfactant micelles. Hence the observed aggregation behavior suggests that the Cn-PEOx micelles exhibit a behavior that can be considered as a hybrid between low-molecular weight surfactant micelles and diblock copolymer micelles.

Self-assembly of diblock copolymers confined in cylindrical nanopores

Self-assembly of AB diblock copolymers confined in cylindrical nanopores is studied using a simulated annealing technique. The pore diameter and surface preference are systematically varied to examine their effects on the self-assembled morphologies and the chain conformations. For bulk lamella-forming and cylinder-forming diblock copolymers, novel structures such as helices and concentric (perforated) lamellae spontaneously form when the copolymers are confined in cylindrical pores. The observed equilibrium morphologies are compared with that obtained from experiments, theory, and other simulations. A simple model is proposed for symmetric diblock copolymers, which gives a reasonable description of the layer thickness for the concentric lamellae. It is found that chains near the pore surfaces are compressed relative to the bulk chains, which can be attributed to the existence of the surfaces. The dependence of the chain conformation on the degree of confinement and strength of the surface preference are reasonably explained. The energetics is discussed qualitatively and used to account for the appearance of the complex phase behavior observed for certain intermediate conditions.

Self-assembled morphologies of diblock copolymers confined in nanochannels: Effects of confinement geometry

The self-assembly of diblock copolymers confined in channels of various shaped cross sections is studied using a simulated annealing technique with the "single-site bond fluctuation" model. In the bulk, the asymmetric diblock copolymers used in this study form hexagonally packed cylinders with period L0. The cross sections of the confining channels are of different shapes including regular triangles, rectangles, squares, regular hexagons, regular octagons, and ellipses. For a given geometry, the channel size (characterized by one or two lengths) is varied from very small to several times of L0. It is found that the geometry and size of the confining channels have a large effect on the structure and symmetry of the self-assembled morphologies. Multiple packed cylinders with the symmetry of the confining channels are the major morphologies for low-symmetry cross sections such as triangle, rectangle, and square. More complex structures such as helices or stacked toroids spontaneously form when the confining channels are shaped such as a regular hexagon, a regular octagon, or an ellipse. The domain spacing of the self-assembled structures can be altered by the shape and size of the confining channels. Our results are consistent with available experiments. These results indicate that the self-assembled structures of block copolymers can be manipulated by the shape of the confining channels.

Morphology of multi-component polymer systems: single chain in mean field simulation studies

Recent work exploring phase separation and self-assembly in multicomponent polymer fluids using a particle-based self-consistent field simulation method is reviewed. The computational method is placed in the context of classical molecular dynamics and Monte Carlo simulations as well as field-theoretic approaches. Its potential is illustrated by applications ranging from spinodal decomposition in symmetric polymer blends and the ordering of diblock copolymers in the bulk to more complex phenomena such as solvent evaporation from thin polymer films and the fabrication of three-dimensional bicontinuous diblock copolymer morphologies reconstruction on patterned substrates.

Simulated annealing study of asymmetric diblock copolymer thin films

We report a simulated annealing study of the morphology of asymmetric diblock copolymer thin films confined between two homogeneous and identical surfaces. We have focused on copolymers that form a gyroidal morphology in the bulk. The morphological dependence of the confined films on the film thickness and the surface-polymer interaction has been systematically investigated. From the simulations it is found that much richer morphologies can form for the gyroid-forming asymmetric diblock copolymer thin films, in contrast to the lamella-forming symmetric and cylinder-forming asymmetric diblock copolymer films. Multiple morphological transitions induced by changing the film thickness and polymer-surface interactions are observed.

Effect of surface field on the morphology of a symmetric diblock copolymer under cylindrical confinement

We have used lattice Monte Carlo simulations to investigate the molecular assembly of symmetric diblock copolymer melts within cylindrical nanochannels. We studied the effect that the surface field has on the copolymer morphology in three cylinders having different diameters. Upon varying the strength of the surface field, we observed a variety of morphologies, including stacked-disk, single-helix, catenoid-cylinder, gyroidal, stacked-circle, and concentric cylindrical barrel structures. The results of these simulations should be helpful when designing polymeric nanomaterials confined in cylindrical nanochannels.

Block copolymers in tomorrow's plastics

In this era of portability and rapid technological advances, polymers are more than ever under pressure to be cheap and offer tailored property profiles. Often, the key lies in designing blends and alloys carefully structured at the appropriate scale (preferably less than a micrometre) from existing polymers. Block copolymers - two or more different polymer chains linked together - have long been thought to offer the solution. Local segregation of the different polymer blocks yields molecular-scale aggregates of nanometre size. Recent progress in synthetic chemistry has unveiled unprecedented opportunities to prepare tailored block copolymers at reasonable cost. Over twenty years of intense academic research and the advent of powerful statistical theories and computational methods should help predict the equilibrium and even non-equilibrium behaviour of copolymers and their blends with other polymers. The gap between block copolymer self-assembly and affordable nanostructured plastics endowed with still-unexplored combinations of properties is getting narrower.

Formation of spindlelike aggregates and flowerlike arrays of polystyrene-b-poly(acrylic acid) micelles

In this letter we describe a simple physical method for the ordered aggregation of scattered single spherical polystyrene-b-poly(acrylic acid) (PS-b-PAA) micelles. First, narrow dispersed spindlelike aggregates, about 60 nm in diameter and 1.5 microm in length, are obtained from the aggregation of single spherical PS-b-PAA micelles at 0 degrees C on a glass slide. Then, the yielding spindlelike units can further aggregate into long-ranged, close-packed, flowerlike arrays after a given amount of freeze-thaw cycles. The formation of the interesting arrays is ascribed to the templated aggregation of micelles on the water polycrystal at the freezing point.

Simulation study of intra- and intermicellar ordering in triblock-copolymer systems

We report a numerical study of the structure and phase behavior of a model for a triblock-copolymer solution. The aim of this study is to investigate the nature of the dense micellar phase that can form in such systems. The simulations were performed on a lattice model for PEO (poly(ethylene-oxide))-PPO (poly(propylene-oxide))-PEO polymers. At high volume fractions, the structure factor of the amphiphile-solvent system can be mapped onto that of a monodisperse hard-sphere fluid. Yet, a low-density hard-sphere model cannot account for the properties of the dilute micellar solution. Moreover, direct inspection of the snapshots of the suspension show that these model triblock-copolymer micelles are neither hard, nor spherical, nor monodisperse.

Monte Carlo investigations of dense copolymer systems. III. Properties of triblock copolymers in good and theta solvent

The present article gives an analysis of XYX triblock copolymers in a good solvent and in a theta solvent, the segments of type X and type Y being repulsive for each other. The results are compared to homopolymers as well as to copolymers in a selective solvent that is a good one for the outer blocks and a theta solvent for the inner one and vice versa, the strength of repulsion between blocks being the same as in the present types of copolymers. A lattice model is used for the investigations and the concentration ranges from a volume fraction phi = 0 up to phi = 0.8. In the limit phi --> 0 the triblocks in good solvent are slightly more expanded than homopolymers and in theta solvent mean square dimensions of triblocks are considerably increased compared to homopolymers due to the repulsion between blocks. With increasing concentration the dimensions decrease but then they increase again and for large concentrations they become similar for all types of copolymers studied, as the effect of the solvent levels off making the repulsive interaction between blocks the dominant interaction. This leads to an orientation effect and as a consequence to microphase separation which is demonstrated by the concentration dependence of various quantities as well as by visualization of snapshots.

Tricontinuous cubic structures in ABC/A/C copolymer and homopolymer blends

Using the Monte Carlo lattice-simulation technique, we present numerical evidence of the formation of gyroid and nongyroid tricontinuous cubic phases in high polymeric systems of ABC/A/C triblock copolymer and homopolymer blends. By increasing the volume fraction of homopolymer, a remarkable phase sequence G (gyroid) --> D (diamond) --> P (primitive) is observed, which is common to certain surfactant systems. Our results indicate that the ABC triblock copolymer system with blending homopolymers may be a zoo of cubic phases, suitable for comparative studies of these phases.