---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21764'
abstract:
- lang: eng
  text: "Colloidal fluids can exhibit complex phase behavior and determining phase
    diagrams via experiments or computer simulations can be laborious. We demonstrate
    that the dispersion relation ω(k), obtained from dynamical density functional
    theory for the uniform density system, is a highly versatile tool for predicting
    where in the phase diagram complex crystals form. The sign of ω(k) determines
    whether density modes with wave number k grow or decay over time. We demonstrate
    the predictive power by investigating the complex phase behavior of particles
    interacting via core-shoulder pair potentials. With complementary Monte Carlo
    simulations, we show that regions of the phase diagram where ωðkÞ has one or several
    unstable (growing) wave numbers are also where crystalline phases occur. Going
    further, by tuning these\r\nunstable wave numbers via the interaction-potential
    and state-point parameters, we design systems with quasicrystals in the phase
    diagram. We identify a system with a certain shoulder range exhibiting at least
    ten different phases. Our general approach accelerates considerably the mapping
    of complex phase diagrams, crucial for the design of new materials."
acknowledgement: "The authors thank Ms. Katrin Muck for her guidance related to the
  use of HPC. The MC\r\ncomputer simulation results presented here were enabled via
  a generous share of CPU time, offered by the Vienna Scientific Cluster (VSC) under
  Project No. 71263. A. J. A. gratefully acknowledges support from the EPSRC under
  Grant No. EP/P015689/1. This research was funded in part by the Austrian Science
  Fund (FWF) [Grant DOI: 10.55776/PIN8759524], gratefully acknowledged by G. K ."
article_number: '148203'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Michael
  full_name: Wassermair, Michael
  id: 23d132c4-4e98-11ef-b275-9e8d4cd8c917
  last_name: Wassermair
  orcid: 0009-0003-6339-4051
- first_name: Gerhard
  full_name: Kahl, Gerhard
  last_name: Kahl
- first_name: Roland
  full_name: Roth, Roland
  last_name: Roth
- first_name: Andrew J.
  full_name: Archer, Andrew J.
  last_name: Archer
citation:
  ama: Wassermair M, Kahl G, Roth R, Archer AJ. Navigating complex phase diagrams
    in soft matter systems. <i>Physical Review Letters</i>. 2026;136(14). doi:<a href="https://doi.org/10.1103/nbvt-fgjy">10.1103/nbvt-fgjy</a>
  apa: Wassermair, M., Kahl, G., Roth, R., &#38; Archer, A. J. (2026). Navigating
    complex phase diagrams in soft matter systems. <i>Physical Review Letters</i>.
    American Physical Society. <a href="https://doi.org/10.1103/nbvt-fgjy">https://doi.org/10.1103/nbvt-fgjy</a>
  chicago: Wassermair, Michael, Gerhard Kahl, Roland Roth, and Andrew J. Archer. “Navigating
    Complex Phase Diagrams in Soft Matter Systems.” <i>Physical Review Letters</i>.
    American Physical Society, 2026. <a href="https://doi.org/10.1103/nbvt-fgjy">https://doi.org/10.1103/nbvt-fgjy</a>.
  ieee: M. Wassermair, G. Kahl, R. Roth, and A. J. Archer, “Navigating complex phase
    diagrams in soft matter systems,” <i>Physical Review Letters</i>, vol. 136, no.
    14. American Physical Society, 2026.
  ista: Wassermair M, Kahl G, Roth R, Archer AJ. 2026. Navigating complex phase diagrams
    in soft matter systems. Physical Review Letters. 136(14), 148203.
  mla: Wassermair, Michael, et al. “Navigating Complex Phase Diagrams in Soft Matter
    Systems.” <i>Physical Review Letters</i>, vol. 136, no. 14, 148203, American Physical
    Society, 2026, doi:<a href="https://doi.org/10.1103/nbvt-fgjy">10.1103/nbvt-fgjy</a>.
  short: M. Wassermair, G. Kahl, R. Roth, A.J. Archer, Physical Review Letters 136
    (2026).
date_created: 2026-04-26T22:01:47Z
date_published: 2026-04-10T00:00:00Z
date_updated: 2026-04-28T07:03:48Z
day: '10'
ddc:
- '530'
department:
- _id: AnSa
- _id: GradSch
doi: 10.1103/nbvt-fgjy
external_id:
  arxiv:
  - '2603.18918'
file:
- access_level: open_access
  checksum: 8ffb139122a185fcddbe6a9c901a287c
  content_type: application/pdf
  creator: dernst
  date_created: 2026-04-28T06:58:40Z
  date_updated: 2026-04-28T06:58:40Z
  file_id: '21769'
  file_name: 2026_PhysicalReviewLetters_Wassermair.pdf
  file_size: 4336488
  relation: main_file
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file_date_updated: 2026-04-28T06:58:40Z
has_accepted_license: '1'
intvolume: '       136'
issue: '14'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Physical Review Letters
publication_identifier:
  eissn:
  - 1079-7114
  issn:
  - 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Navigating complex phase diagrams in soft matter systems
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 136
year: '2026'
...
---
_id: '18174'
abstract:
- lang: eng
  text: We investigate the phase ordering (pattern formation) of systems of two-dimensional
    core–shell particles using Monte Carlo (MC) computer simulations and classical
    density functional theory (DFT). The particles interact via a pair potential having
    a hard core and a repulsive square shoulder. Our simulations show that on cooling,
    the liquid state structure becomes increasingly characterized by long wavelength
    density modulations and on further cooling forms a variety of other phases, including
    clustered, striped, and other patterned phases. In DFT, the hard core part of
    the potential is treated using either fundamental measure theory or a simple local
    density approximation, whereas the soft shoulder is treated using the random phase
    approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC
    and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities
    and shortcomings. We find that having the liquid state static structure factor
    S(k) for wavenumber k is sufficient to identify the Fourier modes governing both
    the liquid and solid phases. This allows us to identify from easier-to-obtain
    liquid state data the wavenumbers relevant to the periodic phases and to predict
    roughly where in the phase diagram these patterned phases arise.
acknowledgement: The computational results presented here were enabled via a generous
  share of CPU time, offered by the Vienna Scientific Cluster (VSC) under Project
  No. 71263. The authors thank Ms. Katrin Muck for her guidance related to the use
  of HPC. A.J.A. gratefully acknowledges support from the EPSRC under Grant No. EP/P015689/1.
article_number: '124503 '
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Michael
  full_name: Wassermair, Michael
  id: 23d132c4-4e98-11ef-b275-9e8d4cd8c917
  last_name: Wassermair
- first_name: Gerhard
  full_name: Kahl, Gerhard
  last_name: Kahl
- first_name: Roland
  full_name: Roth, Roland
  last_name: Roth
- first_name: Andrew J.
  full_name: Archer, Andrew J.
  last_name: Archer
citation:
  ama: Wassermair M, Kahl G, Roth R, Archer AJ. Fingerprints of ordered self-assembled
    structures in the liquid phase of a hard-core, square-shoulder system. <i>The
    Journal of chemical physics</i>. 2024;161(12). doi:<a href="https://doi.org/10.1063/5.0226954">10.1063/5.0226954</a>
  apa: Wassermair, M., Kahl, G., Roth, R., &#38; Archer, A. J. (2024). Fingerprints
    of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder
    system. <i>The Journal of Chemical Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/5.0226954">https://doi.org/10.1063/5.0226954</a>
  chicago: Wassermair, Michael, Gerhard Kahl, Roland Roth, and Andrew J. Archer. “Fingerprints
    of Ordered Self-Assembled Structures in the Liquid Phase of a Hard-Core, Square-Shoulder
    System.” <i>The Journal of Chemical Physics</i>. AIP Publishing, 2024. <a href="https://doi.org/10.1063/5.0226954">https://doi.org/10.1063/5.0226954</a>.
  ieee: M. Wassermair, G. Kahl, R. Roth, and A. J. Archer, “Fingerprints of ordered
    self-assembled structures in the liquid phase of a hard-core, square-shoulder
    system,” <i>The Journal of chemical physics</i>, vol. 161, no. 12. AIP Publishing,
    2024.
  ista: Wassermair M, Kahl G, Roth R, Archer AJ. 2024. Fingerprints of ordered self-assembled
    structures in the liquid phase of a hard-core, square-shoulder system. The Journal
    of chemical physics. 161(12), 124503.
  mla: Wassermair, Michael, et al. “Fingerprints of Ordered Self-Assembled Structures
    in the Liquid Phase of a Hard-Core, Square-Shoulder System.” <i>The Journal of
    Chemical Physics</i>, vol. 161, no. 12, 124503, AIP Publishing, 2024, doi:<a href="https://doi.org/10.1063/5.0226954">10.1063/5.0226954</a>.
  short: M. Wassermair, G. Kahl, R. Roth, A.J. Archer, The Journal of Chemical Physics
    161 (2024).
corr_author: '1'
date_created: 2024-10-06T22:01:12Z
date_published: 2024-09-28T00:00:00Z
date_updated: 2025-09-08T09:55:52Z
day: '28'
ddc:
- '530'
department:
- _id: GradSch
doi: 10.1063/5.0226954
external_id:
  arxiv:
  - '2409.06447'
  isi:
  - '001325268300004'
  pmid:
  - '39344889'
file:
- access_level: open_access
  checksum: f3874e64ef94e94b2376f00a1fee24c3
  content_type: application/pdf
  creator: dernst
  date_created: 2024-10-07T11:25:00Z
  date_updated: 2024-10-07T11:25:00Z
  file_id: '18185'
  file_name: 2024_JourChemicalPhysics_Wassermair.pdf
  file_size: 15009000
  relation: main_file
  success: 1
file_date_updated: 2024-10-07T11:25:00Z
has_accepted_license: '1'
intvolume: '       161'
isi: 1
issue: '12'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
pmid: 1
publication: The Journal of chemical physics
publication_identifier:
  eissn:
  - 1089-7690
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fingerprints of ordered self-assembled structures in the liquid phase of a
  hard-core, square-shoulder system
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 161
year: '2024'
...