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Sharma AK, Escobedo FA. Diffusionless rotator-crystal transitions in colloidal truncated cubes. J Chem Phys 2024; 161:034509. [PMID: 39017427 DOI: 10.1063/5.0216886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2024] [Accepted: 07/01/2024] [Indexed: 07/18/2024] Open
Abstract
Upon osmotic compression, rotationally symmetric faceted colloidal particles can form translationally ordered, orientationally disordered rotator mesophases. This study explores the mechanism of rotator-to-crystal phase transitions where orientational order is gained in a translationally ordered phase, using rotator-phase forming truncated cubes as a testbed. Monte Carlo simulations were conducted for two selected truncations (s), one for s = 0.527 where the rotator and crystal lattices are dissimilar and one for s = 0.572 where the two phases have identical lattices. These differences set the stage for a qualitative difference in their rotator-crystal transitions, highlighting the effect of lattice distortion on phase transition kinetics. Our simulations reveal that significant lattice deviatoric effects could hinder the rotator-to-crystal transition and favor arrangements of lower packing fraction instead. Indeed, upon compression, it is found that for s = 0.527, the rotator phase does not spontaneously transition into the stable, densely packed crystal due to the high lattice strains involved but instead transitions into a metastable solid phase to be colloquially referred to as "orientational salt" for short, which has a similar lattice as the rotator phase and exhibits two distinct particle orientations having substitutional order, alternating regularly throughout the system. This study paves the way for further analysis of diffusionless transformations in nanoparticle systems and how lattice-distortion could influence crystallization kinetics.
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Affiliation(s)
- Abhishek Kumar Sharma
- R.F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Fernando A Escobedo
- R.F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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2
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Escobedo FA. On the calculation of free energies over Hamiltonian and order parameters via perturbation and thermodynamic integration. J Chem Phys 2021; 155:114112. [PMID: 34551542 DOI: 10.1063/5.0061541] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, complementary formulas are presented to compute free-energy differences via perturbation (FEP) methods and thermodynamic integration (TI). These formulas are derived by selecting only the most statistically significant data from the information extractable from the simulated points involved. On the one hand, commonly used FEP techniques based on overlap sampling leverage the full information contained in the overlapping macrostate probability distributions. On the other hand, conventional TI methods only use information on the first moments of those distributions, as embodied by the first derivatives of the free energy. Since the accuracy of simulation data degrades considerably for high-order moments (for FEP) or free-energy derivatives (for TI), it is proposed to consider, consistently for both methods, data up to second-order moments/derivatives. This provides a compromise between the limiting strategies embodied by common FEP and TI and leads to simple, optimized expressions to evaluate free-energy differences. The proposed formulas are validated with an analytically solvable harmonic Hamiltonian (for assessing systematic errors), an atomistic system (for computing the potential of mean force with coordinate-dependent order parameters), and a binary-component coarse-grained model (for tracing a solid-liquid phase diagram in an ensemble sampled through alchemical transformations). It is shown that the proposed FEP and TI formulas are straightforward to implement, perform similarly well, and allow robust estimation of free-energy differences even when the spacing of successive points does not guarantee them to have proper overlapping in phase space.
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Affiliation(s)
- Fernando A Escobedo
- Robert Frederick Smith School of Chemistry and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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3
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Quintela Matos I, Escobedo F. Congruent phase behavior of a binary compound crystal of colloidal spheres and dimpled cubes. J Chem Phys 2020; 153:214503. [DOI: 10.1063/5.0030174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Isabela Quintela Matos
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Fernando Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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4
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Mahynski NA, Hatch HW, Witman M, Sheen DA, Errington JR, Shen VK. Flat-histogram extrapolation as a useful tool in the age of big data. MOLECULAR SIMULATION 2020. [DOI: 10.1080/08927022.2020.1747617] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Nathan A. Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Harold W. Hatch
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | | | - David A. Sheen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Jeffrey R. Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA
| | - Vincent K. Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
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5
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Affiliation(s)
- Aleks Reinhardt
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, United Kingdom
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6
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Desgranges C, Delhommelle J. A new approach for the prediction of partition functions using machine learning techniques. J Chem Phys 2018; 149:044118. [DOI: 10.1063/1.5037098] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Caroline Desgranges
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
| | - Jerome Delhommelle
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
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Schieber NP, Dybeck EC, Shirts MR. Using reweighting and free energy surface interpolation to predict solid-solid phase diagrams. J Chem Phys 2018; 148:144104. [PMID: 29655343 DOI: 10.1063/1.5013273] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Many physical properties of small organic molecules are dependent on the current crystal packing, or polymorph, of the material, including bioavailability of pharmaceuticals, optical properties of dyes, and charge transport properties of semiconductors. Predicting the most stable crystalline form at a given temperature and pressure requires determining the crystalline form with the lowest relative Gibbs free energy. Effective computational prediction of the most stable polymorph could save significant time and effort in the design of novel molecular crystalline solids or predict their behavior under new conditions. In this study, we introduce a new approach using multistate reweighting to address the problem of determining solid-solid phase diagrams and apply this approach to the phase diagram of solid benzene. For this approach, we perform sampling at a selection of temperature and pressure states in the region of interest. We use multistate reweighting methods to determine the reduced free energy differences between T and P states within a given polymorph and validate this phase diagram using several measures. The relative stability of the polymorphs at the sampled states can be successively interpolated from these points to create the phase diagram by combining these reduced free energy differences with a reference Gibbs free energy difference between polymorphs. The method also allows for straightforward estimation of uncertainties in the phase boundary. We also find that when properly implemented, multistate reweighting for phase diagram determination scales better with the size of the system than previously estimated.
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Affiliation(s)
- Natalie P Schieber
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Eric C Dybeck
- Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Michael R Shirts
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA
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Mahynski NA, Errington JR, Shen VK. Multivariable extrapolation of grand canonical free energy landscapes. J Chem Phys 2018; 147:234111. [PMID: 29272947 DOI: 10.1063/1.5006906] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat-histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single flat-histogram simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also show how to combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to accurately compute properties at arbitrary temperatures and chemical potentials. This method may significantly increase the computational efficiency of biased grand canonical Monte Carlo simulations, especially for multicomponent mixtures. Although approximate, this approach is amenable to high-throughput and data-intensive investigations where it is preferable to have a large quantity of reasonably accurate simulation data, rather than a smaller amount with a higher accuracy.
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Affiliation(s)
- Nathan A Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
| | - Jeffrey R Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
| | - Vincent K Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
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Mahynski NA, Jiao S, Hatch HW, Blanco MA, Shen VK. Predicting structural properties of fluids by thermodynamic extrapolation. J Chem Phys 2018; 148:194105. [PMID: 30307179 PMCID: PMC6183068 DOI: 10.1063/1.5026493] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We describe a methodology for extrapolating the structural properties of multicomponent fluids from one thermodynamic state to another. These properties generally include features of a system that may be computed from an individual configuration such as radial distribution functions, cluster size distributions, or a polymer's radius of gyration. This approach is based on the principle of using fluctuations in a system's extensive thermodynamic variables, such as energy, to construct an appropriate Taylor series expansion for these structural properties in terms of intensive conjugate variables, such as temperature. Thus, one may extrapolate these properties from one state to another when the series is truncated to some finite order. We demonstrate this extrapolation for simple and coarse-grained fluids in both the canonical and grand canonical ensembles, in terms of both temperatures and the chemical potentials of different components. The results show that this method is able to reasonably approximate structural properties of such fluids over a broad range of conditions. Consequently, this methodology may be employed to increase the computational efficiency of molecular simulations used to measure the structural properties of certain fluid systems, especially those used in high-throughput or data-driven investigations.
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Affiliation(s)
- Nathan A. Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
| | - Sally Jiao
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Harold W. Hatch
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
| | - Marco A. Blanco
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
- Institute for Bioscience and Biotechnology Research, University of Maryland, Rockville, Maryland 20850, USA
| | - Vincent K. Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA
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Sharma AK, Thapar V, Escobedo FA. Solid-phase nucleation free-energy barriers in truncated cubes: interplay of localized orientational order and facet alignment. SOFT MATTER 2018; 14:1996-2005. [PMID: 29388998 DOI: 10.1039/c7sm02377d] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The nucleation of ordered phases from the bulk isotropic phase of octahedron-like particles has been studied via Monte Carlo simulations and umbrella sampling. In particular, selected shapes that form ordered (plastic) phases with various symmetries (cubic and tetragonal) are chosen to unveil trends in the free-energy barrier heights (ΔG*'s) associated with disorder to order transitions. The shapes studied in this work have truncation parameter (s) values of 0.58, 0.75, 0.8 and 1. The case of octahedra (s = 1.0) is studied to provide a counter-example where the isotropic phase nucleates directly into a (Minkowski) crystal phase rather than a rotator phase. The simulated ΔG*'s for these systems are compared with those previously reported for hard spheres and truncated cubes with s = 0.5 (cuboctahedra, CO) and s = 2/3 (truncated octahedra, TO). The comparison shows that, for comparable degrees of supersaturation, all rotator phases nucleate with smaller ΔG*'s than that of the hard sphere crystal, whereas the octahedral crystal nucleates with a larger ΔG*. Our analysis of near-critical translationally ordered nuclei of octahedra shows a strong bias towards an orientational alignment which is incompatible with the tendency to form facet-to-facet contacts in the disordered phase, thus creating an additional entropic penalty for crystallization. For rotator phases of octahedra-like particles, we observe that the strength of the localized orientational order correlates inversely with ΔG*. We also observe that for s > 0.66 shapes and similar to octahedra, configurations with high facet alignment do not favor high orientational order, and thus ΔG*'s increase with truncation.
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Affiliation(s)
- Abhishek K Sharma
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA.
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11
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Escobedo FA. Optimizing the formation of colloidal compounds with components of different shapes. J Chem Phys 2017; 147:214501. [DOI: 10.1063/1.5006047] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Fernando A. Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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12
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Escobedo FA. Optimizing the formation of solid solutions with components of different shapes. J Chem Phys 2017; 146:134508. [DOI: 10.1063/1.4979091] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Fernando A. Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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13
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Escobedo FA. Effect of inter-species selective interactions on the thermodynamics and nucleation free-energy barriers of a tessellating polyhedral compound. J Chem Phys 2016; 145:211903. [DOI: 10.1063/1.4953862] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Affiliation(s)
- Fernando A. Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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14
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Escobedo FA. Engineering entropy in soft matter: the bad, the ugly and the good. SOFT MATTER 2014; 10:8388-8400. [PMID: 25164392 DOI: 10.1039/c4sm01646g] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The role of entropic interactions, often subtle and sometimes crucial, on the structure and properties of soft matter has a well-recognized place in the classic and modern scientific literature. However, the lessons learned from many of those studies do not always form part of the standard arsenal of strategies that are taught or used for de novo studies relevant to the engineering of new materials. Fortunately, a growing number of examples exist where entropic effects have been designed a priori to achieve a desired or new outcome. This tutorial review describes some recent such examples, selected to illustrate the potential benefits of a more pro-active approach to harnessing the often overlooked power of entropy.
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Affiliation(s)
- Fernando A Escobedo
- School of Chemical & Biomolecular Engineering, Cornell University, Ithaca, NY 14953, USA.
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15
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Khadilkar MR, Escobedo FA. Heuristic rule for binary superlattice coassembly: mixed plastic mesophases of hard polyhedral nanoparticles. PHYSICAL REVIEW LETTERS 2014; 113:165504. [PMID: 25361268 DOI: 10.1103/physrevlett.113.165504] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2014] [Indexed: 06/04/2023]
Abstract
Sought-after ordered structures of mixtures of hard anisotropic nanoparticles can often be thermodynamically unfavorable due to the components' geometric incompatibility to densely pack into regular lattices. A simple compatibilization rule is identified wherein the particle sizes are chosen such that the order-disorder transition pressures of the pure components match (and the entropies of the ordered phases are similar). Using this rule with representative polyhedra from the truncated-cube family that form pure-component plastic crystals, Monte Carlo simulations show the formation of plastic-solid solutions for all compositions and for a wide range of volume fractions.
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Affiliation(s)
- Mihir R Khadilkar
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Fernando A Escobedo
- Department of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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Thapar V, Escobedo FA. Extensions of the interfacial pinning method and application to hard core systems. J Chem Phys 2014; 141:124117. [DOI: 10.1063/1.4896054] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Vikram Thapar
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Fernando A. Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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