ArticleProceedings of the National Academy of Sciences of the United States of America2014
Understanding shape entropy through local dense packing.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 52 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
52 citing papers in PubMed.
- Reaction Medium as an Architect of Nanocrystal Superlattices.Journal of the American Chemical Society · 2026Article
- Review
- Amorphous-amorphous transitions in granular packings.Nature communications · 2025Article
- Prospects of Nanoscience with Nanocrystals: 2025 Edition.ACS nano · 2025Review
- Plasmonic Polymorphs by Combining Shape Anisotropy and Soft Interactions in Bipyramid Thin Films.Small (Weinheim an der Bergstrasse, Germany) · 2025Article
- Dual production of biconvex polymer particles via surfactant-laden microfluidic ternary droplets.Scientific reports · 2025Article
- Article
- Enhance Ethanol Sensing Performance of Fe-Doped Tetragonal SnOSensors (Basel, Switzerland) · 2024Article
- Direct observation of phase transitions in truncated tetrahedral microparticles under quasi-2D confinement.Nature communications · 2024Article
- Quantum fluctuations drive nonmonotonic correlations in a qubit lattice.Nature communications · 2024Article
- Entropy-Mediated Nanoparticle Cellular Uptake.Small science · 2024Article
- Competition between deformation and free volume quantified by 3D image analysis of red blood cell.Biophysical journal · 2023Article
- Coarse-grained modelling to predict the packing of porous organic cages.Chemical science · 2022Article
- Entropy as a Geometrical Source of Information in Biological Organizations.Entropy (Basel, Switzerland) · 2022Article
- Assembly of planar chiral superlattices from achiral building blocks.Nature communications · 2022Article
- Shape and interaction decoupling for colloidal preassembly.Science advances · 2022Article
- Coloration in Supraparticles Assembled from Polyhedral Metal-Organic Framework Particles.Angewandte Chemie (International ed. in English) · 2022Article
- A theory of entropic bonding.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- How Does Immunomodulatory Nanoceria Work? ROS and Immunometabolism.Frontiers in immunology · 2022Article
- Flower-Like Colloidal Particles through Precipitation Polymerization of Redox-Responsive Liquid Crystals.Angewandte Chemie (International ed. in English) · 2021Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
5 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. Here, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems and compute them for several hard particle systems. We show they are on the order of a few times the thermal energy ([Formula: see text]) at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. We show that this mechanism occurs in a wide class of systems and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes, incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.