Ordering mechanisms in triblock copolymers

Theoretical simulations of nanostructures self-assembled from copolymer systems

This article provides an overview of recent simulation investigations of the nanostructures and structure–property relationships in copolymer systems.

Proposal for manipulating functional interface properties of composite organic semiconductors with addition of designed macromolecules

The arrangement of the electronic levels in an interface between organic semiconductors is crucial for the operation of devices such as solar cells and light emitting diodes. With the addition of designed macromolecules, we show that it is possible to control the relative position of the highest occupied molecular orbital and lowest unoccupied molecular orbital levels, and consequently improve the performance. The designed macromolecules consist of two end segments, each compatible with one of the interface components, and a central segment which adds functionality to the interface. The tails control the position and the orientation of the functional units. When the central functional unit is an electric dipole, an electrostatic field is created due to the orientation of the dipoles, which shifts the electronic levels in a controlled way. We develop a theoretical framework, based on self-consistent field theory, to study the concentration and the orientation of the central functional units. We find that the levels can shift by as much as several tenths of an eV.

Ordering and reverse ordering mechanisms of triblock copolymers in the presence of solvent

Self-consistent field theory is used to study the self-assembly of a triblock copolymer melt. Two different external factors (temperature and solvent) are shown to affect the self-assembly. Either one or two-step self-assembly can be found as a function of temperature in the case of a neat triblock melt, or as a function of increasing solvent content (for non-selective solvents) in the case of a triblock-solvent mixture. For selective solvents, it is shown that increasing the solvent content leads to more complicated self-assembly mechanisms, including a reversed transition where order is found to increase instead of decreasing as expected, and re-entrant behavior where order is found to increase at first, and then decrease to a previous state of disorder.

Effect of Architecture on the Tensile Properties of Triblock Copolymers in a Lamellar Phase

We have used self-consistent field theory to calculate the tensile moduli of triblock copolymers in lamellar microstructures prepared from linear and star architectures. The extensional moduli K(33) are the main contributors to the tensile moduli, and the contribution of K(U)33 (the internal energy contribution to K(33)) is the main component of the value of K(33). We find that the tensile moduli of ABC three-miktoarm star terpolymers are smaller than those of ABC linear triblock copolymers having identical components, presumably for two main reasons. First, for the ABC three-miktoarm star terpolymers, the contributions of K(U)33 are larger than those of the linear triblock copolymers; we attribute this phenomenon to the star terpolymers having smaller lamellar domain sizes at equilibrium relative to those of the linear triblock copolymers. Second, conformational entropies play an important role in affecting the tensile moduli, mainly because of the different degrees of freedom of the various chains. In contrast, the shear moduli contribute negligibly to the tensile moduli.

Phase Behavior in Thin Films of Confined Colloid−Polymer Mixtures

Using self-consistent-field and density-functional theories, we first investigate colloidal self-assembly of colloid-polymer films confined between two soft surfaces grafted by polymers. With increasing colloidal concentrations, the film undergoes a series of transitions from disordered liquid --> sparse square --> hexagonal (or mixed square-hexagonal) --> dense square --> cylindrical structures in a plane, which results from the competition between the entropic elasticity of polymer brushes and the steric packing effect of colloidal particles. A phase diagram displays the stable regions of different in-layer ordering structures as the colloidal concentration is varied and layering transitions as the polymer-grafted density is decreased. Our results show a new control mechanism to stabilize the ordering of structures within the films.

Density-functional theory for fluid mixtures of charged chain particles and spherical counterions in contact with charged hard wall: Adsorption, double layer capacitance, and the point of zero charge

We consider a density-functional theory to describe nonuniform fluids composed of chain molecules, containing a charged segment each, and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is applied to study the structure of adsorbed layers, the excess adsorption isotherms, the capacitance of the double layer, and the potential of the zero charge. We show that all electric properties are strongly dependent on the length of the chain molecules. Moreover, these properties are also dependent on the position of the charged segment in the chain.

Reentrant ordering transition of asymmetric copolymer solution film confined between polymer-grafted surfaces

We study the equilibrium morphology of an asymmetric A-B diblock copolymer solution film confined between homopolymer-grafted substrates by using self-consistent-field calculations. We find that on decreasing the copolymer concentration, a reentrant structural transformation between hexagonal --> lamellar --> hexagonal phases occurs as a result of the competition between the wetting effect of the brush surface and the bulk phase behavior of the asymmetric copolymer driven by the A-B interfacial tension.

Effect of polydispersity on the tensile modulus of diblock copolymers in a lamellar phase

We have calculated the tensile moduli of nanomaterials having lamellar microstructures prepared through the self-assembly of a polydisperse diblock copolymer. We observed that the extensional moduli K33 provided the major contribution to the tensile modulus and that the value of K33 depended mainly on the contribution of K33(U) (the internal energy contribution to K33). We found that a larger polydispersity index (PDI) weakens the material for our polydisperse model; we attribute this phenomenon to the larger lamellar domain size at equilibrium when the polydispersity of the block increases and to the competition between short and long chains. We found that longer chains in this system strengthen the material, but shorter chains weaken it as a result of the influence of the PDI. The shear modulus contributed negligibly to the extensional moduli.

Interactions between Colloidal Particles Induced by Polymer Brushes Grafted onto the Substrate

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by the use of a self-consistent-field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate the existence of a repulsive energy barrier of several kBT, which can be interpreted by separating the interaction energy into three parts: colloid-polymer interfacial energy, entropic contribution due to "depletion zone" overlap of colloidal particles, and entropic elastic energy of grafted chains by the compression of particles. The existence of a repulsive barrier which is of entirely entropic origin can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach for controlling the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density.

Density-functional theory and Monte Carlo simulation for the surface structure and correlation functions of freely jointed Lennard-Jones polymeric fluids

We present a nonlocal density-functional theory of polymeric fluids consisting of freely jointed Lennard-Jones chains with explicit consideration of the segment size, van der Waals attraction, and structural correlations due to chain connectivity. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the short-ranged repulsion and the first-order thermodynamic perturbation theory for chain connectivity. The contribution of the long-ranged attraction to the Helmholtz energy functional is taken into account using a quadratic density expansion with the direct correlation function obtained from the first-order mean-spherical approximation. The numerical performance of the density-functional theory is compared well with the simulation results from this work as well as those from the literature for the segment-level density profiles and correlation functions of Lennard-Jones chains in slit pores, near isolated nanoparticles, or in bulk.

Ordering mechanism of asymmetric diblock copolymers confined between polymer-grafted surfaces

Using self-consistent-field calculation, we study the equilibrium morphology of asymmetric block copolymer melts between two brush-covered surfaces. We discuss systematically the morphologies formed as a function of the grafting density of brushes and show a series of reentrant structural transformations between the lamellar and hexagonal phases. Such a selection of ordered microdomains has been attributed to the interplay among entropy effects of stretched brushes, the preferential interaction of the blocks with the grafted substrate, and the bulk microphase-separated behavior of asymmetric copolymers. Interestingly for the affinitive brush-copolymer interfaces, the bulk hexagonal phase may still be remained due to entropy elasticity of brushes, and the frustration can be relieved by deforming the shape of "soft" polymer-brush surface, in contrast to the hard-wall cases. The result demonstrates a simple way to realize molecular self-assembly for confined copolymer films with well-controlled thickness and interfacial environment.