Accounting for the ultraviolet divergence in field-theoretic simulations of block copolymer melts.

This study examines the ultraviolet (UV) divergence in field-theoretic simulations (FTSs) of block copolymer melts, which causes an unphysical dependence on the grid resolution, Δ, used to represent the fields. Our FTSs use the discrete Gaussian-chain model and a partial saddle-point approximation to enforce incompressibility. Previous work has demonstrated that the UV divergence can be accounted for by defining an effective interaction parameter, χ=z∞χb+c2χb 2+c3χb 3+⋯, in terms of the bare interaction parameter, χb, used in the FTSs, where the coefficients of the expansion are determined by a Morse calibration. However, the need to use different grid resolutions for different ordered phases generally restricts the calibration to the linear approximation, χ ≈ z∞χb, and prevents the calculation of order-order transitions. Here, we resolve these two issues by showing how the nonlinear calibration can be translated between different grids and how the UV divergence can be removed from free energy calculations. By doing so, we confirm previous observations from particle-based simulations. In particular, we show that the free energy closely matches self-consistent field theory (SCFT) predictions, even in the region where fluctuations disorder the periodic morphologies, and similarly, the periods of the ordered phases match SCFT predictions, provided the SCFT is evaluated with the nonlinear χ.

Fluctuation correction for the order-disorder transition of diblock copolymer melts.

The order-disorder transition (ODT) of diblock copolymer melts is evaluated for an invariant polymerization index of N¯=104, using field-theoretic simulations (FTS) supplemented by a partial saddle-point approximation for incompressibility. For computational efficiency, the FTS are performed using the discrete Gaussian-chain model, and results are then mapped onto the continuous model using a linear approximation for the Flory-Huggins χ parameter. Particular attention is paid to the complex phase window. Results are found to be consistent with the well-established understanding that the gyroid phase extends down to the ODT. Furthermore, our simulations are the first to predict that the Fddd phase survives fluctuation effects, consistent with experiments.

Calibration of a lattice model for high-molecular-weight block copolymer melts.

The Morse calibration is applied to a lattice model designed for efficient simulations of two-component polymer melts of high molecular weight. The model allows multiple occupancy per site, which results in high invariant polymerization indices, and interactions are limited to monomers within the same site, which enhances the computational speed. The calibration maps the interaction parameter of the lattice model, α, onto the Flory-Huggins χ parameter of the standard Gaussian-chain model, by matching the disordered-state structure function, S(k), of symmetric diblock copolymers to renormalized one-loop predictions. The quantitative accuracy of the calibration is tested by comparing the order-disorder transition of symmetric diblock copolymer melts to the universal prediction obtained from previous simulations. The model is then used to confirm the universality of fluctuation corrections to the critical point of symmetric binary homopolymer blends.

Calibration of the Flory-Huggins interaction parameter in field-theoretic simulations.

Field-theoretic simulations (FTS) offer a versatile method of dealing with complicated block copolymer systems, but unfortunately they struggle to cope with the level of fluctuations typical of experiments. Although the main obstacle, an ultraviolet divergence, can be removed by renormalizing the Flory-Huggins χ parameter, this only works for unrealistically large invariant polymerization indexes, N¯. Here, we circumvent the problem by applying the Morse calibration, where a nonlinear relationship between the bare χb used in FTS and the effective χ corresponding to the standard Gaussian-chain model is obtained by matching the disordered-state structure function, S(k), of symmetric diblock copolymers to renormalized one-loop predictions. This calibration brings the order-disorder transition obtained from FTS into agreement with the universal results of particle-based simulations for values of N¯ characteristic of the experiment. In the limit of weak interactions, the calibration reduces to a linear approximation, χ ≈ z∞χb, consistent with the previous renormalization of χ for large N¯.

Monte Carlo phase diagram for diblock copolymer melts.

The phase diagram for diblock copolymer melts is evaluated from lattice-based Monte Carlo simulations using parallel tempering, improving upon earlier simulations that used sequential temperature scans. This new approach locates the order-disorder transition (ODT) far more accurately by the occurrence of a sharp spike in the heat capacity. The present study also performs a more thorough investigation of finite-size effects, which reveals that the gyroid (G) morphology spontaneously forms in place of the perforated-lamellar (PL) phase identified in the earlier study. Nevertheless, there still remains a small region where the PL phase appears to be stable. Interestingly, the lamellar (L) phase next to this region exhibits a small population of transient perforations, which may explain previous scattering experiments suggesting a modulated-lamellar (ML) phase.

The development of genomics-derived pharmaceuticals.

Messenger RNAs for the large majority of human genes are now available. Most of those contained in the Human Genome Sciences database are capable of producing functional proteins. We have sequenced the clones of approximately 8000 that are believed to be involved in cell signaling, and have produced small amounts of the corresponding proteins. These are being screened for biological activity; four have been entered into clinical trials, with one demonstrating clinical activity thus far.