Mesoscopic simulation of metastable microphases in the order–order transition from gyroid-to-lamellar states of PS–PI diblock copolymer

The formation of metastable microphases during the order–order transition (OOT) from gyroid-to-lamellar states of a poly(styrene)–poly(isoprene) (PS–PI) copolymer has been investigated on a mesoscopic level using dissipative particle dynamics simulations. The formation of the gyroid microphase was obtained via an order–disorder transition process (ODT). The microphase was then subjected to thermal heating cycles. A thermodynamic instability of poly(styrene) microdomains due to temperature effects induces anisotropic composition fluctuations in the gyroid structure and a microphase transformation from gyroid-to-lamellar takes place via an OOT. Two metastable microphases (hexagonal perforated layers and cylinders) were detected during the thermal process. Results are consistent with experimental and theoretical studies.     

Kinetic pathway to double-gyroid structure

We have investigated the structural development during order-order transitions to the double-gyroid (DG) phase of nonionic surfactant/water systems based on two-dimensional small-angle x-ray scattering patterns from highly oriented ordered mesophases. The lamellar (L) to DG transition proceeds through two intermediate structures, a fluctuating perforated layer structure having ABAB stacking and a hexagonal perforated lamellar structure with ABCABC stacking (HPLABC). For a hexagonally packed cylinder (H) to DG transition, we also observed the HPLABC structure as the intermediate phase, thus the HPLABC is an entrance structure for the DG phase. The hexagonal perforated lamellar (HPL) structure consists of hexagonally packed holes surrounded by the planar tripods, and the transition from HPL structure to the DG phase proceeds by rotation of the dihedral angle of connected tripods. A geometrical consideration shows that large deformations of HPL planes are necessary to form the DG structure from the HPLABC structure, whereas the transition from a HPL structure with ABAB stacking (HPLAB) to the DG structure is straightforward. In spite of the topological constraints, the HPLABC structure is observed in the kinetic pathway to the DG structure.     

Unexpected Intermediate State for the Cylinder‐to‐Gyroid Transition in a Block Copolymer Solution

The cylinder‐to‐gyroid transition in a concentrated solution of polystyrene‐block‐polyisoprene in dibutyl phthalate has been studied using rheology and small angle X‐ray scattering. Following an appropriate temperature quench, the oriented cylinder phase transforms to the gyroid structure epitaxially. Remarkably, an intermediate state appears for a deep quench, whereas for a shallow quench the transition proceeds directly; the intermediate state exhibits scattering signatures consistent with a hexagonally perforated layer structure.     

Real structure of KInS2 polytypes

KInS₂ crystallizes in a two dimensionally ordered structure, which is related to the TlGaSe₂-type structure. High-resolution transmission electron microscopy (HRTEM) and the analysis of diffuse scattering give evidence for defined shifts between ordered layers, which establish a lamellar nanostructure. The different arrangements of the lamellas, designated as A and B are fully compatible with the pseudosymmetry of KInS₂. Consequently no misfit of the real structure can be observed by HRTEM. Only in rare cases the arrangement of the layers is at least partially ordered within extended domains and the diffuse scattering narrows into Bragg reflections. Two different strategies for the simulation of the diffuse scattering are presented. Besides the approximation of the diffuse scattering by Bragg intensities which are calculated on the basis of an ordered supercell, the diffuse scattering can also be simulated in dependence of the probability of AB or BA neighbors.     

Influence of electric field on the phase transitions of the hexagonal cylinder phase of diblock copolymers.

We have used the cell dynamic simulations (CDS) method to study the evolution of asymmetric and symmetric diblock copolymers under electric fields. For symmetric diblock copolymers, long-range-ordered lamellar phases form readily under electric fields. For asymmetric diblock copolymers, sphere-to-cylinder phase transitions occur rapidly when strong electric fields are applied, but it takes longer for the system to form hexagonal cylinder structures. The results of these simulations suggest that the sphere phase is stable under weak electric fields, but a threshold electric intensity exists for the sphere-to-cylinder phase transition. In addition, we also studied the kinetic pathways of the transition of the lamellar phase to the hexagonal cylinder phase of the asymmetric diblock copolymers under electric fields. Hexagonal cylinder structures form when the lamellar phase is subjected to a sudden temperature jump. The scattering functions suggest that the hexagonal cylinder structures are very regular and possess very few flaws.     

Dissipative particle dynamics simulation of phase behavior of aerosol OT/water system

The phase behaviors of the binary mixture of an anionic surfactant aerosol OT (AOT) and water are investigated on a mesoscopic level using dissipative particle dynamics (DPD) computer simulations. With a simple surfactant model, various aggregation structures of AOT in water including the lamellar, viscous isotropic, and reverse hexagonal phases are obtained, which agree well with the experimental phase diagram. Special attention is given on the unusual lamellar regions. Water diffusivity shows much useful information to understand how the phase behaviors varied with concentration and temperature. It is proposed that the anomalous lamellar phenomena at intermediate AOT concentration (about 40%) are due to the formation of a defective structure, pseudoreversed hexagonal phase, which evidently decreases the water diffusivity. After increasing temperature above 328 K, the pseudoreversed hexagonal structure will be partly transformed to a normal lamellar phase structure and the system lamellar ordering is therefore enhanced.     

Self-assembly in block polyelectrolytes

The self-consistent field theory (SCFT) complemented with the Poisson-Boltzmann equation is employed to explore self-assembly of polyelectrolyte copolymers composed of charged blocks A and neutral blocks B. We have extended SCFT to dissociating triblock copolymers and demonstrated our approach on three characteristic examples: (1) diblock copolymer (AB) melt, (2) symmetric triblock copolymer (ABA) melt, (3) triblock copolymer (ABA) solution with added electrolyte. For copolymer melts, we varied the composition (that is, the total fraction of A-segments in the system) and the charge density on A blocks and calculated the phase diagram that contains ordered mesophases of lamellar, gyroid, hexagonal, and bcc symmetries, as well as the uniform disordered phase. The phase diagram of charged block copolymer melts in the charge density--system composition coordinates is similar to the classical phase diagram of neutral block copolymer melts, where the composition and the Flory mismatch interaction parameter χ(AB) are used as variables. We found that the transitions between the polyelectrolyte mesophases with the increase of charge density occur in the same sequence, from lamellar to gyroid to hexagonal to bcc to disordered morphologies, as the mesophase transitions for neutral diblocks with the decrease of χ(AB). In a certain range of compositions, the phase diagram for charged triblock copolymers exhibits unexpected features, allowing for transitions from hexagonal to gyroid to lamellar mesophases as the charge density increases. Triblock polyelectrolyte solutions were studied by varying the charge density and solvent concentration at a fixed copolymer composition. Transitions from lamellar to gyroid and gyroid to hexagonal morphologies were observed at lower polymer concentrations than the respective transitions in the similar neutral copolymer, indicating a substantial influence of the charge density on phase behavior.     

An X-ray scattering study of the lamellar/nematic/isotropic sequence of phases in decylammonium chloride/H2O/NH4Cl

An X-ray scattering study is presented of the lamellar/nematic/isotropic sequence in the lyotropic system DACI/H₂O/NH₄Cl. The whole reciprocal space of monocrystalline samples oriented in magnetic fields are reconstructed from their two dimensional sections on photographic films. Intense diffuse scatterings are observed in the lamellar phase, around and away from the Bragg spots. Their evolution close to the lamellar/nematic transition reveals the presence of intense structural fluctuations. They take place over temperature ranges which are significantly greater than those associated with the smectic/nematic transitions in thermotropic liquid crystals. A similar situation is observed in the isotropic phase in the vicinity of the nematic/isotropic transition.     

Pressure-induced hexagonal phase in a ternary microemulsion system composed of a nonionic surfactant, water, and oil

The pressure-induced phase transition in a microemulsion, consisting of pentaethylene glycol mono-n-dodecyl ether, water, and n-octane, was investigated by means of small-angle neutron scattering. A pressure-induced phase transition from a lamellar structure to a hexagonal structure was observed. The temperature-pressure phase boundary shows a positive slope with dTdP approximately 0.09 KMPa. The structure unit of the high-pressure hexagonal phase was an oil-in-water cylinder with the membrane thickness of 15.5 A, identical to the low-temperature hexagonal phase. Pressurizing was found to have the same effect by decreasing temperature. This behavior was satisfactorily explained with the pressure dependence of the spontaneous curvature of surfactant membranes. That is, the volume change of surfactant tails plays a dominant role in the structure change of the microemulsion with applying pressure.     

Self-assembly of ternary cubic, hexagonal, and lamellar mesophases using the lattice-Boltzmann kinetic method

We use a kinetic lattice-Boltzmann method to simulate the self-assembly of the cubic primitive (P), diamond (D), and gyroid (G) mesophases from an initial quench composed of oil, water, and amphiphilic particles. Here, we also report the self-assembly of the noncubic hexagonal phase and two lamellar phases, one with periodic convolutions. The periodic mesophase structures are emergent from the underlying conservation laws and quasi-molecular interactions of the lattice-Boltzmann model. We locate regions of the model's parameter space where the sequence of appearance of mesophases lamellar --> primitive --> hexagonal is in agreement with pressure jump experiments and the sequence cubic --> lamellar is in agreement with compositional variations reported in the literature. The ability of our lattice-Boltzmann model to simulate self-assembly of cubic and noncubic phases in a unified and consistent manner opens the way for further investigations into the transition pathways and kinetics of the phase transitions between these states as well as of the rheology of these phases.     

An X-ray scattering study of the lamellar/nematic/isotropic sequence of phases in decylammonium chloride/H2O/NH4Cl

Abstract

An X-ray scattering study is presented of the lamellar/nematic/isotropic sequence in the lyotropic system DACI/H₂O/NH₄Cl. The whole reciprocal space of monocrystalline samples oriented in magnetic fields are reconstructed from their two dimensional sections on photographic films. Intense diffuse scatterings are observed in the lamellar phase, around and away from the Bragg spots. Their evolution close to the lamellar/nematic transition reveals the presence of intense structural fluctuations. They take place over temperature ranges which are significantly greater than those associated with the smectic/nematic transitions in thermotropic liquid crystals. A similar situation is observed in the isotropic phase in the vicinity of the nematic/isotropic transition.     

Study of self-assembly of symmetric coil-rod-coil ABA-type triblock copolymers by self-consistent field lattice method

The self-assembly of symmetric coil-rod-coil ABA-type triblock copolymer melts is studied by applying self-consistent field lattice techniques in a three-dimensional space. The self-assembled ordered structures differ significantly with the variation of the volume fraction of the rod component, which include lamellar, wave lamellar, gyroid, perforated lamellar, cylindrical, and spherical-like phases. To understand the physical essence of these phases and the regimes of occurrence, we construct the phase diagram, which matches qualitatively with the existing experimental results. Compared with the coil-rod AB diblock copolymer, our results revealed that the interfacial grafting density of the separating rod and coil segments shows important influence on the self-assembly behaviors of symmetric coil-rod-coil ABA triblock copolymer melts. We found that the order-disorder transition point changes from f(rod)=0.5 for AB diblock copolymers to f(rod)=0.6 for ABA triblock copolymers. Our results also show that the spherical-like and cylindrical phases occupy most of the region in the phase diagram, and the lamellar phase is found stable only at the high volume fraction of the rod.     

Self-assembly of rod-coil molecules into molecular length-dependent organization

A series of rod-coil molecules (n-x, where n represents the number of repeating units in a PPO coil and x the number of phenyl groups in a rod segment) with variation in the molecular length, but an identical rod to coil volume ratio was synthesized, and their self-assembling behavior was investigated by using DSC and X-ray scatterings. The molecule with a short rod-coil molecule (16-4) shows a 3-D tetragonal structure based on a body-centered symmetry of the discrete bundles in addition to a lamellar structure. This 3-D lattice, on heating, collapses to generate a disordered micellar structure. Remarkably, the molecules based on longer molecular length (21-5 and 24-6) were observed to self-organize into, on heating, lamellar, tetagonally perforated lamellar, 2-D hexagonal columnar and finally disordered micellar structures. Further increase in the molecular length as in the case of 29-7 and 32-8 induces a 3-D hexagonally perforated lamellar structure as an intermediate structure between the lamellar and tetragonally perforated lamellar structures. Consequently, these systems demonstrate the ability to regulate the domain nanostructure, from 2-dimensionally continuous layers, long strips to discrete bundles via periodic perforated layers by small changes in the molecular length, at an identical rod-to-coil volume fraction.     

Phase separation in thin films of end‐grafted block copolymers

An atomic force microscopy investigation was carried out on various thick (30–120 nm) polymethyl methacrylate‐b‐polystyrene and poly(2‐(dimethyl amino)ethyl methacrylate)‐b‐polystyrene films prepared via a grafting‐from method. The structure of the films was examined with both topographic and phase imaging. Several different morphologies were observed including a perforated lamellar phase with irregular perforations. In addition, complementary small‐angle X‐ray scattering and reflectometry results measurements on a non‐grafted polymer are presented. Copyright © 2009 John Wiley & Sons, Ltd.     

Computer simulation of diffuse X-ray scattering by an aligned smectic C-like nematic phase

We report a new method for the quantitative analysis of diffuse X-ray scattering by some disordered smectic phases. Computer simulations of diffuse X-ray scattering are compared with actual diffraction patterns of a series of oriented liquid crystalline polymers TDI-C _m C _n . The simulation shows that both Bragg peaks (spots) and equidistant streaks (diffuse scatterings) are diffracted by one smectic C-like structure in which each of the molecular chains is displaced from its mean position by a random distance Δ _z , along the chain axis (z). This is a first type of disorder. By assuming a Gaussian distribution of the disordered displacements, the mean value of Δ _z has been determined from the position and intensity of the streaks and Bragg peaks for the polymers.     

Calculating the free energy of self-assembled structures by thermodynamic integration

We discuss a method for calculating free energy differences between disordered and ordered phases of self-assembling systems utilizing computer simulations. Applying an external, ordering field, we impose a predefined structure onto the fluid in the disordered phase. The structure in the presence of the external, ordering field closely mimics the structure of the ordered phase (in the absence of an ordering field). Self-consistent field theory or density functional theory provides an accurate estimate for choosing the strength of the ordering field. Subsequently, we gradually switch off the external, ordering field and, in turn, increase the control parameter that drives the self-assembly. The free energy difference along this reversible path connecting the disordered and the ordered state is obtained via thermodynamic integration or expanded ensemble simulation techniques. Utilizing Single-Chain-in-Mean-Field simulations of a symmetric diblock copolymer melt we illustrate the method and calculate the free energy difference between the disordered phase and the lamellar structure at an intermediate incompatibility chiN=20. Evidence for the first-order character of the order-disorder transition at fixed volume is presented. The transition is located at chi(ODT)N=13.65+/-0.10 for an invariant degree of polymerization of N=14 884. The magnitude of the shift of the transition from the mean field prediction qualitatively agrees with other simulations.     

Anisotropic fluctuations in ordered copolymer phases

The random phase approximation is reformulated to investigate the anisotropic fluctuations about an ordered polymer phase. This very general method is applied to the lamellar phase of block copolymers. The calculated anisotropic scattering intensity captures the main features observed experimentally including the secondary peaks due to fluctuations with hexagonal symmetry. We also determined the limits of metastability of the lamellar phase as well as the bending and elastic moduli of the lamellae.     

Self-organization process of ordered structures in linear and star poly(styrene)-poly(isoprene) block copolymers: Gaussian models and mesoscopic parameters of polymeric systems

Mesoscopic simulations of linear and 3-arm star poly(styrene)-poly(isoprene) block copolymers was performed using a representation of the polymeric molecular structures by means of Gaussian models. The systems were represented by a group of spherical beads connected by harmonic springs; each bead corresponds to a segment of the block chain. The quantitative estimation for the bead-bead interaction of each system was calculated using a Flory-Huggins modified thermodynamical model. The Gaussian models together with dissipative particle dynamics (DPD) were employed to explore the self-organization process of ordered structures in these polymeric systems. These mesoscopic simulations for linear and 3-arm star block copolymers predict microphase separation, order-disorder transition, and self-assembly of the ordered structures with specific morphologies such as body-centered-cubic (BCC), hexagonal packed cylinders (HPC), hexagonal perforated layers (HPL), alternating lamellar (LAM), and ordered bicontinuous double diamond (OBDD) phases. The agreement between our simulations and experimental results validate the Gaussian chain models and mesoscopic parameters used for these polymers and allow describing complex macromolecular structures of soft condensed matter with large molecular weight at the statistical segment level.