Melt brushes of diblock copolymer

Structure and thermodynamics of grafted silica/polystyrene dilute nanocomposites investigated through self-consistent field theory

Polymer/matrix nanocomposites (PNCs) are materials with exceptional properties. They offer a plethora of promising applications in key industrial sectors. In most cases, it is preferable to disperse the nanoparticles (NPs) homogeneously across the matrix phase. However, under certain conditions NPs might lump together and lead to a composite material with undesirable properties. A common strategy to stabilize the NPs is to graft on their surface polymer chains of the same chemical constitution as the matrix chains. There are several unresolved issues concerning the optimal molar mass and areal density of grafted chains that would ensure best dispersion, given the nanoparticles and the polymer matrix. We propose a model for the prediction of key structural and thermodynamic properties of PNC and apply it to a single spherical silica (SiO2) nanoparticle or planar surface grafted with polystyrene chains embedded at low concentration in a matrix phase of the same chemical constitution. Our model is based on self-consistent field theory, formulated in terms of the Edwards diffusion equation. The properties of the PNC are explored across a broad parameter space, spanning the mushroom regime (low grafting densities, small NPs and chain lengths), the dense brush regime, and the crowding regime (large grafting densities, NP diameters, and chain lengths). We extract several key quantities regarding the distributions and the configurations of the polymer chains, such as the radial density profiles and their decomposition into contributions of adsorbed and free chains, the chains/area profiles, and the tendency of end segments to segregate at the interfaces. Based on our predictions concerning the brush thickness, we revisit the scaling behaviors proposed in the literature and we compare our findings with experiment, relevant simulations, and analytic models, such as Alexander's model for incompressible brushes.

Self-assembly in densely grafted macromolecules with amphiphilic monomer units: diagram of states

By means of computer modelling, the self-organization of dense planar brushes of macromolecules with amphiphilic monomer units was addressed and their state diagram was constructed. The diagram of states includes the following regions: disordered position of monomer units with respect to each other, strands composed of a few polymer chains and lamellae with different domain spacing. The transformation of lamellae structures with different domain spacing occurred within the intermediate region and could proceed through the formation of so-called parking garage structures. The parking garage structure joins the lamellae with large (on the top of the brushes) and small (close to the grafted surface) domain spacing, which appears like a system of inclined locally parallel layers connected with each other by bridges. The parking garage structures were observed for incompatible A and B groups in selective solvents, which result in aggregation of the side B groups and dense packing of amphiphilic macromolecules in the restricted volume of the planar brushes.

New strategy to create ultra-thin surface layer of grafted amphiphilic macromolecules

It was found first that macromolecules made of amphiphilic monomer units could form spontaneously an ultra-thin layer on the surface which the macromolecules are grafted to. The width of such layer is about double size of monomer unit consisting of hydrophilic A (repulsive) and hydrophobic (attractive) B beads. The hydrophilic A beads are connected in a polymer chain while hydrophobic B beads are attached to A beads of the backbone as side groups. Three characteristic regimes are distinguished. At low grafting density, the macromolecules form ultra-thin micelles of the shape changing with decrease of distance d between grafting points as following: circular micelles-prolonged micelles-inverse micelles-homogeneous bilayer. Those micelles have approximately constant height and specific top-down A-BB-A structure. At higher grafting density, the micelles start to appear above the single bilayer of amphiphilic macromolecules. The thickness of grafted layer in these cases is different in different regions of grafting surface. Only at rather high density of grafting, the height of macromolecular layer becomes uniform over the whole grafting surface. The study was performed by computer modeling experiments and confirmed in framework of analytical theory.

Swelling of chemical and physical planar brushes of gradient copolymers in a selective solvent

We propose a mean-field theory of chemical and physical planar brushes of linear gradient copolymers swollen in a selective solvent. The polymer chains are grafted to the substrate by the ends with the excess of insoluble monomer units, and the majority of the soluble units are located near the free ends of the chains. The grafting points are considered to be immobile (chemical brush) and mobile in-plane (physical brush). In the latter case the grafting density is determined from the equilibrium conditions (minimum of the free energy). A common peculiarity of the brushes of both types is that the polymer concentration gradually changes from a relatively high value near the substrate (collapsed region of the brush) to a small value near the free surface (swollen region of the brush). In the case of the chemical brush, a polymer depletion zone can appear in the middle of the brush if incompatibility between insoluble and soluble (A and B) units is high enough. Here the polymer density is even lower than near the free surface of the brush. The grafting density of the physical brush is inversely proportional to the chain length and increases with the decrease of the solvent quality for the insoluble (A) units. The latter can be accompanied by shrinkage of the brush thickness due to broad distribution of the insoluble units through the chain: a minor fraction of insoluble units near the free ends can aggregate with a major fraction of them near the substrate. As a result, the concentration of the soluble (B) units can have a maximum in the middle of the brush rather than near the free surface.

Chemical patterns from surface grafted resists for directed assembly of block copolymers

We demonstrate a direct e-beam patternable one-component block copolymer (BCP) resist to fabricate a chemical pattern for the directed assembly of a symmetric block copolymer. The resist consists of a low molecular weight poly(styrene-block-methyl methacrylate) with a hydroxyl group at the PMMA chain end (PS-b-PMMA-OH), which anchors the chains to the surface. This short-tethered PMMA block provided sufficient sensitivity to allow scission by e-beam. The length of the untethered PS block was fine-tuned to impart the required contrast between the patterned and the unpatterned region for 1:1 assembly of an overlying BCP blend. Two BCP resists with a PS fraction of 0.25 (16SM) and 0.34 (18SM), with a total molecular weight less than 20K, were synthesized, and the assembly of a ternary BCP blend was studied. 16SM- and 18SM-anchored substrates showed nonpreferential and PS preferential surfaces, respectively. Both 18SM and 16SM could be patterned by e-beam to fabricate a 1:1 chemical pattern with a line pitch of 70 nm for the assembly of a BCP ternary blend. 18SM gave fewer defects than 16SM due to an increased contrast in interfacial energies between adjacent stripes in the chemical surface pattern. Two additional PS-b-PMMA-OH polymers with a molecular weight of 39K (F(PS) = 0.76) and 69K (F(PS) = 0.83) were synthesized to study the effect of PS cross-linking upon exposure to e-beam. As the PS fraction increases, the line pattern becomes blurred and ultimately ineffective in guiding the BCP assembly. The blurring is attributed to cross-linking of adjacent PS chains.

Memory effects of diblock copolymer brushes and mixed brushes

Memory effects of microphase segregation in diblock copolymer brushes and binary mixed homopolymer brushes exposed to solvents of different quality and selectivity are studied using Single-Chain-in-Mean-Field (SCMF) simulations. We gauge these memory effects by a fluctuation memory measure, reflecting the correlation between the quenched fluctuations of grafting points and the microphase-separated morphology, and a domain memory measure, quantifying the correlation between surface morphologies during cyclic exposure to different solvents. The fluctuation and domain memory measures are closely correlated, and both of them have their root in the broken translational symmetry of the distribution of grafting points. They become stronger upon increasing the fluctuations of the grafting points. The effects of solvent quality and selectivity, grafting density, and composition of brushes on the memory measures are discussed.