We describe a highly optimized implementation of MPI domain decomposition in a GPU-enabled, general-purpose molecular dynamics code, HOOMD-blue (Anderson and Glotzer, 2013). Our approach is inspired ...by a traditional CPU-based code, LAMMPS (Plimpton, 1995), but is implemented within a code that was designed for execution on GPUs from the start (Anderson et al., 2008). The software supports short-ranged pair force and bond force fields and achieves optimal GPU performance using an autotuning algorithm. We are able to demonstrate equivalent or superior scaling on up to 3375 GPUs in Lennard-Jones and dissipative particle dynamics (DPD) simulations of up to 108 million particles. GPUDirect RDMA capabilities in recent GPU generations provide better performance in full double precision calculations. For a representative polymer physics application, HOOMD-blue 1.0 provides an effective GPU vs. CPU node speed-up of 12.5×.
We present a simulation study of how properties of symmetric diblock copolymers depend on the invariant degree of polymerization N̅, focusing on the vicinity of the order–disorder transition (ODT). ...Results from several coarse-grained simulation models are combined to cover a range of N̅ ≃ 200–8000 that includes most of the experimentally relevant range. Results are presented for the free energy per chain, the value of χe N at the ODT, the latent heat of transition, the layer spacing, the composition profile, and compression modulus in the ordered phase. Universality (i.e., model independence) is demonstrated by showing that equivalent results for all properties are obtained from corresponding thermodynamic states of different simulation models. Corresponding states of symmetric copolymers are states with equal values of the parameters χe N and N̅, where χe is an effective Flory–Huggins interaction parameter and N is a degree of polymerization. The underlying universality becomes apparent, however, only if data are analyzed using an adequate estimate of χe, which we obtain by fitting the structure factor in the disordered state to recent theoretical predictions. The results show that behavior near the ODT exhibits a different character at moderate and high values of N̅, with a crossover near N̅ ≃ 104. Within the range N̅ ≲ 104 studied here, the ordered and disordered phases near the ODT both contain strongly segregated domains of nearly pure A and B, in contrast to the assumption of weak segregation underlying the Fredrickson–Helfand (FH) theory. In this regime, the FH theory is inaccurate and substantially underestimates the value of χe N at the ODT. Results for the highest values of N̅ studied here agree reasonably well with FH predictions, suggesting that the theory may be accurate for N̅ ≳ 104. Self-consistent field theory (SCFT) grossly underestimates (χe N)ODT for modest N̅ because it cannot describe strong correlations in the disordered phase. SCFT is found, however, to yield accurate predictions for several properties of the ordered lamellar phase.
Simulations of simple bead-spring models of asymmetric diblock copolymers are used to study the dependence of order-disorder transitions and free energies upon the invariant degree of polymerization ...N̅ and the fraction f of beads in the minority block. Well-tempered metadynamics is used to determine values of (χN)ODT along the lamellar-disorder and hexagonal-disorder transitions over the range 0.1875 ≤ f ≤ 0.5 for two models with different values of N̅ = 480 and 1920, where χ is an effective Flory–Huggins interaction parameter, N is the degree of polymerization, and (χN)ODT is a value of χN at the order-disorder transition (ODT). More extensive studies are performed for systems with f = 1/4, which undergo a hexagonal-disorder transition. Equivalent results for both phase boundaries and free energies are obtained for one pair of systems with different numbers of beads per chain but matched values of f = 1/4 and N̅, in agreement with the corresponding state hypothesis. Comparison of results for (χN)ODT for systems with f = 1/4 and several values for N̅ show a systematic decrease in (χN)ODT with an increase N̅, consistent with the expected approach to the self-consistent field (SCFT) prediction as N̅ → ∞. Results for the free energy per chain in the disordered and hexagonal phases of systems with f = 1/4 show that SCFT gives rather accurate predictions for the free energy in the ordered hexagonal phase but that the random-mixing approximation underlying SCFT significantly overestimates the free energy of the disordered phase.
Self-consistent field theory (SCFT) is a powerful tool for the design and interpretation of experiments on block polymer materials. In this Perspective, we lower the barrier to entry to the use of ...SCFT by experimental groups by two means. First, we present a pedagogical introduction to an improved version of the open-source Polymer Self-Consistent Field (PSCF) software package and of the underlying theory. Second, we discuss methods for generating robust initial guesses for the fields that are computed in SCFT. To demonstrate our approach, we present two case studies in which a typical desktop computer has been used to simulate the structure of (i) body-centered cubic, face-centered cubic, A15, and Frank–Kasper σ sphere-forming phases of a diblock copolymer melt and (ii) two core–shell morphologies of ABAC tetrablock terpolymers. A companion Web site provides all of the relevant software and detailed instructions for reproducing all results contained herein.
Simulations of coarse-grained models are used to study relationships among chain motion, composition fluctuations, and stress relaxation in unentangled melts of symmetric diblock copolymers. ...Measurements of the dynamic structure factor S(q,t) are reported as a function of wavenumber q, time t, and χ N , where χ is the Flory–Huggins interaction parameter and N is degree of polymerization. The function S(q,t) is found to be a nearly exponential function of time, S(q,t) ∝ e–t/τ(q), for wavenumbers similar to or less than the wavenumber q* at which the static structure factor S(q) ≡ S(q,t=0) is maximum. The relationship between the decay time τ(q) and S(q) is used to define an effective wavenumber-dependent diffusivity D(q) for fluctuations of wavenumber q. The function D(q) is shown to change very little with changes in χ N and to be a monotonically decreasing function of the nondimensional wavenumber qR g, where R g is polymer radius of gyration. The linear shear stress relaxation modulus G(t) is inferred from measurements of the shear stress autocorrelation function. At low values of χ N , far from the order–disorder transition (ODT), the modulus G(t) agrees with predictions of the Rouse model. Near the ODT, G(t) develops an additional slowly decaying feature arising from slow decay of composition fluctuations with q ∼ q*. The behavior of G(t) near the ODT is predicted nearly quantitatively by a modified version of the model of Fredrickson and Larson (FL), in which the prediction of the FL theory for the slowly decaying component is added to the prediction of the Rouse theory for contributions arising from single-chain relaxation, using the independently measured behavior of S(q,t) as an input to the theory.
Simulations of several different coarse-grained models are used to characterize how the structure factor S(q) in melts of compositionally asymmetric diblock copolymers varies with changes in the ...volume fraction f of the minority block, the parameter χe N (where χe is an effective interaction parameter and N is degree of polymerization), and the invariant degree of polymerization N̅. We focus here on systems with 0.25 ≤ f < 0.5. Results obtained with several different models are consistent in the expected sense, demonstrating the validity of the corresponding states principle when applied to asymmetric copolymers. Analysis is simplified by a demonstration that the effective χ parameter for these simple models is almost independent of composition. Results are compared to renormalized one-loop theory predictions, which become rapidly less accurate with increasing asymmetry. In the absence of an adequate predictive theory, a quantitative empirical relationship is developed to describe the dependence of peak intensity on χe N, f, and N̅ over the range 0.25 < f < 0.5. The dependences of the peak intensity on χ N in asymmetric and symmetric copolymers are qualitatively similar and exhibit a crossover from a weakly fluctuating regime in which the random-phase approximation (RPA) is nearly valid to a regime of strong composition fluctuations, with a crossover centered on the RPA spinodal value of χ N . This crossover becomes noticeably sharper for more asymmetric systems, however, reflecting a more abrupt appearance of well-segregated disordered domains with increasing χ in asymmetric copolymer melts.
We use coarse-grained molecular dynamics to elucidate the influence of polydispersity on the adsorption of polydisperse bulk polyanionic chains onto a monodisperse polycationic brush. We consider ...primarily two different charge sequence scenarios, in which both polymer species are either block and alternating, for polyanions with a fixed dispersity Đ = 1.5. Polydispersity plays a negligible role when the brush cationic chains are in excess, since all polyanionic chains are adsorbed. In contrast, when the polyanions are in excess, polydispersity substantially decreases the fraction of chains adsorbed into the brush, irrespective of charge sequence, but increases the number of monomers adsorbed. These opposing trends are made possible by selective adsorption of long chains.
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Self-consistent field theory (SCFT) is a powerful approach for computing the phase behavior of block polymers. We describe a fast version of the open-source Polymer Self-Consistent Field (PSCF) ...code that takes advantage of the massive parallelization provided by a graphical processing unit (GPU). Benchmarking double-precision calculations indicate up to 30× reduction in time to converge SCFT calculations of various diblock copolymer phases when compared to the Fortran CPU version of PSCF using the same algorithms, with the speed-up increasing with increasing unit cell size for the diblock polymer problems examined here. Where double-precision accuracy is not needed, single-precision calculations can provide speed-up of up to 60× in convergence time. These improvements in speed within an open-source format open up new vistas for SCFT-driven block polymer materials discovery by the community at large.
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