Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
B. Chacko, C. Chalmers, and A. J. Archer, “Two-dimensional colloidal fluids exhibiting pattern formation,” J. Chem. Phys. 143, 244904 (2015).
Y. Zhuang and P. Charbonneau, “Equilibrium phase behavior of the square-well linear microphase-forming model,” J. Phys. Chem. B 120, 61786188 (2016).
B. A. Lindquist, R. B. Jadrich, and T. M. Truskett, “Assembly of nothing: Equilibrium fluids with designed structured porosity,” Soft Matter 12, 26632667 (2016).
G. Zhang, F. H. Stillinger, and S. Torquato, “Probing the limitations of isotropic pair potentials to produce ground-state structural extremes via inverse statistical mechanics,” Phys. Rev. E 88, 042309 (2013).
A. Jain, J. R. Errington, and T. M. Truskett, “Dimensionality and design of isotropic interactions that stabilize honeycomb, square, simple cubic, and diamond lattices,” Phys. Rev. X 4, 031049 (2014).
E. Marcotte, F. H. Stillinger, and S. Torquato, “Optimized monotonic convex pair potentials stabilize low-coordinated crystals,” Soft Matter 7, 23322335 (2011).
W. D. Piñeros, M. Baldea, and T. M. Truskett, “Breadth versus depth: Interactions that stabilize particle assemblies to changes in density or temperature,” J. Chem. Phys. 144, 084502 (2016).
T. Dotera, T. Oshiro, and P. Ziherl, “Mosaic two-lengthscale quasicrystals,” Nature 506, 208211 (2014).
K. Barkan, H. Diamant, and R. Lifshitz, “Stability of quasicrystals composed of soft isotropic particles,” Phys. Rev. B 83, 172201 (2011).
S. Torquato, “Inverse optimization techniques for targeted self-assembly,” Soft Matter 5, 11571173 (2009).
A. Jain, J. A. Bollinger, and T. M. Truskett, “Inverse methods for material design,” AIChE J. 60, 27322740 (2014).
A. Jain, J. R. Errington, and T. M. Truskett, “Inverse design of simple pairwise interactions with low-coordinated 3D lattice ground states,” Soft Matter 9, 38663870 (2013).
E. Marcotte, F. H. Stillinger, and S. Torquato, “Communication: Designed diamond ground state via optimized isotropic monotonic pair potentials,” J. Chem. Phys. 138, 061101 (2013).
W. Humphrey, A. Dalke, and K. Schulten, “VMD—Visual molecular dynamics,” J. Mol. Graphics 14, 3338 (1996).
M. Z. Miskin, G. Khaira, J. J. de Pablo, and H. M. Jaeger, “Turning statistical physics models into materials design engines,” Proc. Natl. Acad. Sci. U. S. A. 113, 3439 (2016).
R. L. Marson, T. D. Nguyen, and S. C. Glotzer, “Rational design of nanomaterials from assembly and reconfigurability of polymer-tethered nanoparticles,” MRS Commun. 5, 397406 (2015).
A. F. Hannon, Y. Ding, W. Bai, C. A. Ross, and A. Alexander-Katz, “Optimizing topographical templates for directed self-assembly of block copolymers via inverse design simulations,” Nano Lett. 14, 318325 (2014).
A. W. Long and A. L. Ferguson, “Nonlinear machine learning of patchy colloid self-assembly pathways and mechanisms,” J. Phys. Chem. B 118, 42284244 (2014).
D. Barber, Bayesian Reasoning and Machine Learning (Cambridge University Press, 2012).
M. S. Shell, “The relative entropy is fundamental to multiscale and inverse thermodynamic problems,” J. Chem. Phys. 129, 144108 (2008).
W. G. Noid, “Perspective: Coarse-grained models for biomolecular systems,” J. Chem. Phys. 139, 090901 (2013).
A. Chaimovich and M. S. Shell, “Coarse-graining errors and numerical optimization using a relative entropy framework,” J. Chem. Phys. 134, 094112 (2011).
M. C. Rechtsman, F. H. Stillinger, and S. Torquato, “Optimized interactions for targeted self-assembly: Application to a honeycomb lattice,” Phys. Rev. Lett. 95, 228301 (2005).
α ≈ 0.02 worked well for the cases studied here.
The magnitude of the spring constant is chosen such that the radial distribution function has sharp crystalline features, but the peaks are still integrable. Generally this corresponded to a range of 1600-2800 kBT/σ2, but we do not anticipate that the exact value is critical as long as the g(r) is consistent with a stable crystal and not a fluid.
D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. E. Mark, and H. J. C. Berendsen, “Gromacs: Fast, flexible, and free,” J. Comput. Chem. 26, 17011718 (2005).
S. Plimpton, “Fast parallel algorithms for short-range molecular dynamics,” J. Comput. Phys. 117, 119 (1995).
A Nosé-Hoover thermostat with a time constant of τ = 100dt is employed, where dt is the time step.
J. Mewis and N. J. Wagner, Colloidal Suspension Rheology (Cambridge University Press, 2013).
C. N. Likos, K. A. Vaynberg, H. Löwen, and N. J. Wagner, “Colloidal stabilization by adsorbed gelatin,” Langmuir 16, 41004108 (2000).

Data & Media loading...


Article metrics loading...



Inverse methods of statistical mechanics have facilitated the discovery of pair potentials that stabilize a wide variety of targeted lattices at zero temperature. However, such methods are complicated by the need to compare, within the optimization framework, the energy of the desired lattice to all possibly relevant competing structures, which are not generally known in advance. Furthermore, ground-state stability does not guarantee that the target will readily assemble from the fluid upon cooling from higher temperature. Here, we introduce a molecular dynamics simulation-based, optimization design strategy that iteratively and systematically refines the pair interaction according to the fluid and crystalline structural ensembles encountered during the assembly process. We successfully apply this probabilistic, machine-learning approach to the design of repulsive, isotropic pair potentials that assemble into honeycomb, kagome, square, rectangular, truncated square, and truncated hexagonal lattices.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd