Transition Of Block Copolymers Research Articles

Simulations of shear-induced morphological transitions in block copolymers

In this review, we focus on simulation studies performed to provide a molecular-level understanding of shear-induced morphological transitions and domain alignment of block copolymers in the bulk and in thin films. Block copolymers are highly relevant for many scientific and industrial applications due to their ability to form uniform domains of controllable shape at nanometer length scales. In the bulk, morphologies depend on the constituent block interactions and their volume fractions, while for thin films the surface properties and film thickness also play important roles. Spontaneously formed samples do not usually have the long-range order required in many applications. Long-range order can be induced by external guidance, for example using electric fields, surface patterns, or shear forces. In particular, shearing of both bulk systems and thin films is an excellent method for achieving long-range order, and remarkable progress has been made in experimental techniques for controlling pattern formation and transferring them to materials of interest, e.g., metal nanowires. Many simulation studies of pattern formation in copolymer systems have been performed, but simulations using explicit representations of the chains and incorporating shear have only been attempted in recent years. Because of length- and time-scale limitations, most simulations of shear alignment are performed on coarse-grained models. We survey the methods used for obtaining parameters for coarse-grained models to represent specific block copolymer systems, and the simulation algorithms utilized to impose shear. The simulations are in general agreement with experiments on the relative ease of alignment of lamellar, cylinder-forming, and sphere-forming systems, and provide insights into alignment mechanisms. Both simulations and experiments display a strong dependence of alignment quality on film thickness and substrate–polymer interactions. The review closes with a summary of unresolved questions for future research.

Investigation of the reversibility of the unimer-to-aggregate transition in block copolymers by surface tension-measurements

Two DNA-block copolymers, poly(caprolactone)-DNA and poly(methyl metacrylate)-DNA, were synthesized by conjugation of a short single strand of DNA (12 or 22mer) to a single reactive group at one end of the synthetic polymer. These polymers self-assemble in water, without the need of any cosolvent, forming micelle-like aggregates that were imaged by TEM. The solution behavior of the bioconjugated polymers was investigated by surface tension measurements. In the direction of dilution, the surface tension was measured using a down-scaled Wilhelmy plate method. To proceed in the reverse direction (concentration), we measured the surface tension of a sessile drop during its evaporation. This latter method was firstly validated using ionic and non-ionic surfactants, including polymeric surfactants. It was then applied to investigate the unimer to micelles transition of the DNA-block copolymers. In all cases, a reversible transition was observed demonstrating the existence of a critical micellar concentration, close to 0.01mmolL−1 for all the conjugates. The CMC was only slightly influenced by the length of the hydrophilic DNA block.

Current-Induced Formation of Gradient Crystals in Block Copolymer Electrolytes

Conventional ordered phases such as crystals and liquid crystals have constant domain spacings. In this Letter, we report on the formation of coherently ordered morphologies wherein the domain spacing changes continuously along a specified direction. We have coined the term "gradient crystal" to refer to this structure, a signature of which is a small-angle X-ray scattering pattern that resembles a sundial. Gradient crystals composed of a gyroid morphology form spontaneously when ionic current is driven through a block copolymer electrolyte. We propose that this structure forms because it allows for a continuous change in domain spacing without requiring the introduction of defects. Previous studies have shown that applied electric fields ranging from 1000 to 40,000 V/mm can induce long-range structural order, alignment, and morphological transitions in block copolymers. Gradient crystals form under applied electric fields as low as 2.5 V/mm due to the presence of direct ionic currents that are absent in the aforementioned studies.

Self-consistent field simulations of self- and directed-assembly in a mixed polymer brush

While self-assembling block copolymer thin films have attracted attention as a promising high resolution lithographic tool, the self assembly of mixed polymer brushes for lithography is relatively unexplored. Here we study the directed self-assembly of a mixed polymer brush using self-consistent field theory (SCFT) simulations. Using the model equations and numerical methods introduced and verified in our previous study, the bulk phase behavior of a mixed melt brush is studied in depth through full three dimensional calculations. We assume that the mixed A/B polymer chains, which are of the same length, are exposed to a neutral top surface and are uniformly grafted at a high density. We identify phase-separated morphologies and calculate a phase diagram for the mixed brush under melt conditions as a function of the segregation force and composition. The observed lateral microphase separation is similar to that in block copolymer thin films, but the phase separation occurs at a smaller segregation force and the transition between cylindrical and spherical morphologies are quite different than the first-order phase transition in block copolymers. We demonstrate that lateral confinement can induce long-range, in-plane order in mixed brushes and suggest promising directed self-assembly methods for the application of self-assembled mixed polymer brushes in next-generation information storage and electronic devices.

Dynamics of shear-induced orientation transitions in block copolymers

This research investigates the dynamics of mechanical and structural transformations of styrene–butadiene–styrene block copolymer, known as RCM1, which has cylindrical mesophase morphology. The polymer was processed using a Multipass Rheometer (MPR) with simultaneous X-ray observation. The method allowed investigation of the dynamics with 1 second time resolution. Samples were processed at 160 °C and an apparent wall shear rate in the range ∼1.4 to 1125 s−1. Microstructural alignment was quantified using a second order X-ray orientation function. The polymer showed self-organization in the melt, aligning along the capillary walls. Shear flow disrupted the organization, which then rebuilt during the post-shearing pause, as the residual pressure relaxed across the capillary. The dynamics of structure ordering and disordering was a function of shear rate. The transition was faster for high shear rate cycles.

Coarse-grained molecular dynamics study of block copolymer/nanoparticle composites under elongational flow

Symmetric diblock copolymer/nanoparticle (NP) systems under planar elongational flow have been modeled and simulated using coarse-grained nonequilibrium molecular dynamics. The aim of our present study is to understand how the dispersion of NPs in a block copolymer system is influenced by elongational flow and how the presence of NPs changes the rheology and flow-induced morphology transition in block copolymers. We consider two different kinds of spherical NPs categorized with respect to their interaction potential with the polymeric blocks: (1) selective NPs that show a preference toward one of the blocks of a model diblock copolymer and (2) nonselective NPs that show equal attraction toward both blocks. For unrestricted simulation times during elongational flow, spatially and temporally periodic boundary conditions devised by Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] have been implemented. Our results show that the concentration peak of both selective NPs at the center of the preferred domain and nonselective NPs at the domain interface becomes broader with increasing elongation rate, suggesting that elongational flow can be used as another parameter to control nanocomposite self-assembly. In addition, our results reveal that the onset of flow-induced transition from lamellar to disordered morphology is greatly influenced by particle-particle and particle-polymer interactions.

Transition Behavior of Block Copolymer Thin Films on Preferential Surfaces

The phase transitions in block copolymers (BCPs), like the order-to-disorder transition, occur when the enthalpic term of free energy of mixing is equal to the entropic term. In thin films, interactions at the substrate/polymer and polymer/air interfaces influence this free energy balance, leading to a change in the transition behavior. Here, we report on the transition behavior of BCP thin films on a substrate modified by polymer chains that preferentially interact with one component of the BCP. The thickness dependence of the transition temperature shows that interfacial interactions enhance the orientation of the lamellar microdomain parallel to the film surface even in 40 L0 in thickness, where L0 is the equilibrium period of the BCP in the bulk. This phenomenon can be attributed to the fact that, in a thin film geometry with a preferential interaction of one component with the substrate, a high concentration of one component is pinned at the substrate leading to an amplification of a periodic variation in the composition and a shift of transition temperature.

Study of the conformational transition of polystyrene?poly(methyl methacrylate) block copolymers with temperature using measurements of the c** critical concentration

The conformational transition of block copolymers has been studied until now using measurements of the second virial coefficient and the radius of gyration (light scattering) or of the intrinsic viscosity. In this paper the conformational transition of polystyrene–poly(methyl methacrylate) diblock copolymers with temperature is studied using measurements of the critical concentration c** which is obtained in the dynamic state (viscometry) and in the static state (UV measurements).

A simple lattice model for phase transitions in block copolymers

Phase transitions in copolymers are considered in terms of configurational probabilities. It is shown that ordering transitions in block copolymers appear as a stepped increase in the probability of a dominating configuration and a simultaneous decrease of the probabilities for other configurations.

Pathway and Kinetics of Cylinder-to-Sphere Order−Order Transition in Block Copolymers

The pathway and kinetics for the cylinder-to-sphere order−order transition in a mixture of a matched diblock and triblock copolymer of styrene and ethylene−butene-1 is reported. The microstructure ...

Kinetics of phase transitions in block copolymers

A rich variety of equilibrium phases have been identified in block copolymer melts. In this paper we study the kinetics of phase transitions from one equilibrium state to another, from both experimental and theoretical points of view. The formation of ordered phases is often mediated by non-equilibrium intermediate states. In addition the phase transitions can proceed by either conventional nucleation, or by spinodal decomposition.

Evidence for a thermally reversible order–order transition between lamellar and perforated lamellar microphases in a triblock copolymer

The microstructure and microphase behavior of a poly(styrene- b-(ethylene- alt-propylene)- b-styrene) (PS-PEP-PS) triblock copolymer ( M n =50,000 g/mol and 50.8 wt% PS) were characterized by transmission electron microscopy (TEM) and dynamic rheology. The microstructure texture at room temperature and up to about 125°C consisted of alternating PS and PEP lamellae (LAM). Oscillatory shear experiments revealed thermally-reversible post- T g transitions at 125–130°C and 275°C that are attributed to an order–order transition (OOT) of the mesophase texture and an order–disorder transition (ODT), respectively. Evidence for a perforated lamellar (PL) microstructure of alternating PS and PEP lamellae with hexagonal-packed PS connectors perforating the PEP phase above the ODT and a thermally-reversible LAM ↔ PL OOT was obtained from TEM of quenched and slowly cooled samples. Unlike previous reports of reversible OOT transitions in block copolymers, the reversibility of the OOT for these block copolymers does not require shearing the sample.

Kinetics and anisotropic fluctuations in weakly ordered block copolymers

In weakly ordered block copolymer nanostructures, fluctuations in the order parameter are important. Because of the periodic order of the structures, these fluctuations are anisotropic. The anisotropic fluctuations are crucial for determining the stability limit of an ordered structure, the pathways of order-order and order-disorder transitions, as well as for. consistently interpreting small angle neutron or X-ray scattering data. Some recent advances include the understanding of the nature of the anisotropic fluctuations and the kinetics of order-order and order-disorder transitions in block copolymers.

Microhardness under strain. 2. Microhardness behavior during stress-induced polymorphic transition in block copolymers of poly(butylene terephthalate)

In addition to homopoly(butylene terephthalate) (homo-PBT), the microhardness technique was applied to its multiblock copolymers for examination of the stress-induced polymorphic transition. Drawn and annealed at 170°C for 6 h with fixed ends in a vacuum, bristles of poly(ether ester) (PEE) having PBT as hard segments and poly(ethylene oxide) (PEO) with molecular weight 1000 as soft segments (PBT/PEO = 57/43 wt%) were characterized with respect to their microhardness H at various stages of tensile deformation. A sharp H decrease (by 20%) in a narrow deformation interval (2—4%) due to the stress-induced α-β polymorphic transition is observed followed by an increase and decrease of H. The transition is registered at much higher relative tensile deformations (between 25% and 30%) compared with the case of homo-PBT. This is explained by the presence of a very soft amorphous phase of PEO, which deforms first. The same phase, distinguished by low viscosity in which the PBT crystallites are “floating,” is the reason for the very low H values measured (between 25 and 35 MPa, depending on the amount of α-and β-modifications). The stress-induced polymorphic transition in copolymers of PBT with PEO is demonstrated for the first time, also supporting the recently proposed concept of the microhardness depression effect.

Effect of shear on order–disorder and order–order transitions in block copolymers

We have studied theoretically the role of an external constant shear on the extent of suppression of composition fluctuations and stabilization of different ordered morphologies in block copolymer systems. The dependence of steady state structure factor on constant shear is calculated self-consistently in the weak segregation limit. The effect of shear rate on order–order and order–disorder transitions involving lamellar and cylindrical morphologies is computed. Previous theoretical work calculated effects to the lowest order in shear rate. This paper performs a numerical calculation that is not limited to small shear rates. This more general approach is required in order to explain experimental results. Our results are in good agreement with known experimental data and make new quantitative predictions. The controversy involving an apparent discrepancy between experimental data and previous predictions from perturbation analysis is resolved.

Simulation of Lamellar Phase Transitions in Block Copolymers. [Erratum to document cited in CA121:58371

Simulation of Lamellar Phase Transitions in Block Copolymers. [Erratum to document cited in CA121:58371

Simulation of Lamellar Phase Transitions in Block Copolymers and Surfactants

Abstract Simulations of the lamellar phase transitions of symmetric amphiphilic chains are carried out on a cubic lattice, with the amphiphilic chain length N varied from 6 to 48 lattice sites, corresponding to lengths ranging from surfactants to short block copolymers. We find that the effective interaction energy parameter χN (which incorporates the effect of added solvant) at which the transition from the lamellar ordered state to the disordered state occurs is roughly equal to 18-21. While this result is consistent with an extrapolation of the Fredrickson-Helfand weak-segragation theory to N values in the range of the simulations, the amplitude of the sinusoidal compositional wave in the ordered state near the transition is large for all N studied, in disagreement with the weak segregation theories. Thus, for values of N up to 48, the transition occurs in a “moderate,” rather than weak-segregation regime. Near the disordering transition, fluctuating “bridge” or “hole” defects in the lamellae spontaneo...

Simulation of Lamellar Phase Transitions in Block Copolymers

Monte Carlo simulations of the lamellar phase transitions for symmetric amphiphilic chains are carried out on a cubic lattice, with the amphiphilic chain length N as large as 192 lattice sites, corresponding to lengths typical of those in experimental systems. We find that there is a qualitative change in the orderdisorder transition when N exceeds about 50. For N≤ 50, the compositional order parameter S at the transition is large; S ≃ 0.8 on the ordered side of the transition. For N≥ 50, the jump is more modest, around 0.50 or less

Fluctuation effects in the density functional theory of order-disorder transitions in block copolymers

Fluctuation effects in the density functional theory of order-disorder transitions in block copolymers

Polydispersity effects on the microphase-separation transition in block copolymers [Erratum to document cited in CA113(2):7140f

Polydispersity effects on the microphase-separation transition in block copolymers [Erratum to document cited in CA113(2):7140f