Cassie’s Law Reformulated: Composite Surfaces from Superspreading to Superhydrophobic Article Swipe
Glen McHale
,
Rodrigo Ledesma‐Aguilar
,
Chiara Neto
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1021/acs.langmuir.3c01313
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1021/acs.langmuir.3c01313
In 1948, Cassie provided an equation describing the wetting of a smooth, heterogeneous surface. He proposed that the cosine of the contact angle, θc, for a droplet on a composite surface could be predicted from a weighted average using the fractional surface areas, fi, of the cosines of contact angles of a droplet on the individual component surfaces, i.e., cos θc = f1 cos θ1 + f2 cos θ2. This was a generalization of an earlier equation for porous materials, which has recently proven fundamental to underpinning the theoretical description of wetting of superhydrophobic and superoleophobic surfaces. However, there has been little attention paid to what happens when a liquid exhibits complete wetting on one of the surface components. Here, we show that Cassie's equation can be reformulated using spreading coefficients. This reformulated equation is capable of describing composite surfaces where the individual surface components have negative (droplet state/partial wetting) or positive (film-forming/complete wetting) spreading coefficients. The original Cassie equation is then a special case when the combination of interfacial tensions results in a droplet state on the composite surface for which a contact angle can be defined. In the case of a composite surface created from a partial wetting (droplet state) surface and a complete wetting (film-forming) surface, there is a threshold surface area fraction at which a liquid on the composite surface transitions from a droplet to a film state. The applicability of this equation is demonstrated from literature data including data on mixed self-assembled monolayers on copper, silver, and gold surfaces that was regarded as definitive in establishing the validity of the Cassie equation. Finally, we discuss the implications of these ideas for super-liquid repellent surfaces.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1021/acs.langmuir.3c01313
- OA Status
- hybrid
- Cited By
- 11
- References
- 33
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4385191206
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4385191206Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1021/acs.langmuir.3c01313Digital Object Identifier
- Title
-
Cassie’s Law Reformulated: Composite Surfaces from Superspreading to SuperhydrophobicWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-07-24Full publication date if available
- Authors
-
Glen McHale, Rodrigo Ledesma‐Aguilar, Chiara NetoList of authors in order
- Landing page
-
https://doi.org/10.1021/acs.langmuir.3c01313Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1021/acs.langmuir.3c01313Direct OA link when available
- Concepts
-
Wetting, Composite number, Contact angle, Composite material, Surface (topology), Materials science, Wetting transition, Monolayer, Nanotechnology, Geometry, MathematicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
11Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 6, 2024: 3, 2023: 2Per-year citation counts (last 5 years)
- References (count)
-
33Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4385191206 |
|---|---|
| doi | https://doi.org/10.1021/acs.langmuir.3c01313 |
| ids.doi | https://doi.org/10.1021/acs.langmuir.3c01313 |
| ids.pmid | https://pubmed.ncbi.nlm.nih.gov/37487028 |
| ids.openalex | https://openalex.org/W4385191206 |
| fwci | 1.59723909 |
| type | article |
| title | Cassie’s Law Reformulated: Composite Surfaces from Superspreading to Superhydrophobic |
| awards[0].id | https://openalex.org/G7972045444 |
| awards[0].funder_id | https://openalex.org/F4320334704 |
| awards[0].funder_award_id | FT180100214 |
| awards[0].funder_display_name | Australian Research Council |
| biblio.issue | 31 |
| biblio.volume | 39 |
| biblio.last_page | 11035 |
| biblio.first_page | 11028 |
| grants[0].funder | https://openalex.org/F4320334704 |
| grants[0].award_id | FT180100214 |
| grants[0].funder_display_name | Australian Research Council |
| topics[0].id | https://openalex.org/T10313 |
| topics[0].field.id | https://openalex.org/fields/25 |
| topics[0].field.display_name | Materials Science |
| topics[0].score | 0.9997000098228455 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2508 |
| topics[0].subfield.display_name | Surfaces, Coatings and Films |
| topics[0].display_name | Surface Modification and Superhydrophobicity |
| topics[1].id | https://openalex.org/T12141 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.9882000088691711 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2206 |
| topics[1].subfield.display_name | Computational Mechanics |
| topics[1].display_name | Fluid Dynamics and Thin Films |
| topics[2].id | https://openalex.org/T12776 |
| topics[2].field.id | https://openalex.org/fields/22 |
| topics[2].field.display_name | Engineering |
| topics[2].score | 0.980400025844574 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2208 |
| topics[2].subfield.display_name | Electrical and Electronic Engineering |
| topics[2].display_name | Electrohydrodynamics and Fluid Dynamics |
| funders[0].id | https://openalex.org/F4320334704 |
| funders[0].ror | https://ror.org/05mmh0f86 |
| funders[0].display_name | Australian Research Council |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C134514944 |
| concepts[0].level | 2 |
| concepts[0].score | 0.925061047077179 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q817136 |
| concepts[0].display_name | Wetting |
| concepts[1].id | https://openalex.org/C104779481 |
| concepts[1].level | 2 |
| concepts[1].score | 0.7379482388496399 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q50707 |
| concepts[1].display_name | Composite number |
| concepts[2].id | https://openalex.org/C6556556 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6816689968109131 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q899239 |
| concepts[2].display_name | Contact angle |
| concepts[3].id | https://openalex.org/C159985019 |
| concepts[3].level | 1 |
| concepts[3].score | 0.5363866686820984 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q181790 |
| concepts[3].display_name | Composite material |
| concepts[4].id | https://openalex.org/C2776799497 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5358656048774719 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q484298 |
| concepts[4].display_name | Surface (topology) |
| concepts[5].id | https://openalex.org/C192562407 |
| concepts[5].level | 0 |
| concepts[5].score | 0.523788571357727 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[5].display_name | Materials science |
| concepts[6].id | https://openalex.org/C157107126 |
| concepts[6].level | 3 |
| concepts[6].score | 0.504883348941803 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q7990179 |
| concepts[6].display_name | Wetting transition |
| concepts[7].id | https://openalex.org/C7070889 |
| concepts[7].level | 2 |
| concepts[7].score | 0.4264463782310486 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q902488 |
| concepts[7].display_name | Monolayer |
| concepts[8].id | https://openalex.org/C171250308 |
| concepts[8].level | 1 |
| concepts[8].score | 0.3326202929019928 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q11468 |
| concepts[8].display_name | Nanotechnology |
| concepts[9].id | https://openalex.org/C2524010 |
| concepts[9].level | 1 |
| concepts[9].score | 0.16139909625053406 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[9].display_name | Geometry |
| concepts[10].id | https://openalex.org/C33923547 |
| concepts[10].level | 0 |
| concepts[10].score | 0.10829082131385803 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[10].display_name | Mathematics |
| keywords[0].id | https://openalex.org/keywords/wetting |
| keywords[0].score | 0.925061047077179 |
| keywords[0].display_name | Wetting |
| keywords[1].id | https://openalex.org/keywords/composite-number |
| keywords[1].score | 0.7379482388496399 |
| keywords[1].display_name | Composite number |
| keywords[2].id | https://openalex.org/keywords/contact-angle |
| keywords[2].score | 0.6816689968109131 |
| keywords[2].display_name | Contact angle |
| keywords[3].id | https://openalex.org/keywords/composite-material |
| keywords[3].score | 0.5363866686820984 |
| keywords[3].display_name | Composite material |
| keywords[4].id | https://openalex.org/keywords/surface |
| keywords[4].score | 0.5358656048774719 |
| keywords[4].display_name | Surface (topology) |
| keywords[5].id | https://openalex.org/keywords/materials-science |
| keywords[5].score | 0.523788571357727 |
| keywords[5].display_name | Materials science |
| keywords[6].id | https://openalex.org/keywords/wetting-transition |
| keywords[6].score | 0.504883348941803 |
| keywords[6].display_name | Wetting transition |
| keywords[7].id | https://openalex.org/keywords/monolayer |
| keywords[7].score | 0.4264463782310486 |
| keywords[7].display_name | Monolayer |
| keywords[8].id | https://openalex.org/keywords/nanotechnology |
| keywords[8].score | 0.3326202929019928 |
| keywords[8].display_name | Nanotechnology |
| keywords[9].id | https://openalex.org/keywords/geometry |
| keywords[9].score | 0.16139909625053406 |
| keywords[9].display_name | Geometry |
| keywords[10].id | https://openalex.org/keywords/mathematics |
| keywords[10].score | 0.10829082131385803 |
| keywords[10].display_name | Mathematics |
| language | en |
| locations[0].id | doi:10.1021/acs.langmuir.3c01313 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S75741262 |
| locations[0].source.issn | 0743-7463, 1520-5827 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 0743-7463 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Langmuir |
| locations[0].source.host_organization | https://openalex.org/P4310320006 |
| locations[0].source.host_organization_name | American Chemical Society |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310320006 |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Langmuir |
| locations[0].landing_page_url | https://doi.org/10.1021/acs.langmuir.3c01313 |
| locations[1].id | pmid:37487028 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306525036 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | PubMed |
| locations[1].source.host_organization | https://openalex.org/I1299303238 |
| locations[1].source.host_organization_name | National Institutes of Health |
| locations[1].source.host_organization_lineage | https://openalex.org/I1299303238 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | publishedVersion |
| locations[1].raw_type | |
| locations[1].license_id | |
| locations[1].is_accepted | True |
| locations[1].is_published | True |
| locations[1].raw_source_name | Langmuir : the ACS journal of surfaces and colloids |
| locations[1].landing_page_url | https://pubmed.ncbi.nlm.nih.gov/37487028 |
| locations[2].id | pmh:oai:pubmedcentral.nih.gov:10413937 |
| locations[2].is_oa | True |
| locations[2].source.id | https://openalex.org/S2764455111 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | False |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | PubMed Central |
| locations[2].source.host_organization | https://openalex.org/I1299303238 |
| locations[2].source.host_organization_name | National Institutes of Health |
| locations[2].source.host_organization_lineage | https://openalex.org/I1299303238 |
| locations[2].license | cc-by |
| locations[2].pdf_url | https://pmc.ncbi.nlm.nih.gov/articles/PMC10413937/pdf/la3c01313.pdf |
| locations[2].version | submittedVersion |
| locations[2].raw_type | Text |
| locations[2].license_id | https://openalex.org/licenses/cc-by |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | Langmuir |
| locations[2].landing_page_url | https://www.ncbi.nlm.nih.gov/pmc/articles/10413937 |
| locations[3].id | pmh:oai:pure.ed.ac.uk:publications/5ed2a84c-dab1-4478-9164-ac17e999d1e4 |
| locations[3].is_oa | True |
| locations[3].source.id | https://openalex.org/S4306400320 |
| locations[3].source.issn | |
| locations[3].source.type | repository |
| locations[3].source.is_oa | False |
| locations[3].source.issn_l | |
| locations[3].source.is_core | False |
| locations[3].source.is_in_doaj | False |
| locations[3].source.display_name | Edinburgh Research Explorer (University of Edinburgh) |
| locations[3].source.host_organization | https://openalex.org/I98677209 |
| locations[3].source.host_organization_name | University of Edinburgh |
| locations[3].source.host_organization_lineage | https://openalex.org/I98677209 |
| locations[3].license | cc-by |
| locations[3].pdf_url | |
| locations[3].version | submittedVersion |
| locations[3].raw_type | |
| locations[3].license_id | https://openalex.org/licenses/cc-by |
| locations[3].is_accepted | False |
| locations[3].is_published | False |
| locations[3].raw_source_name | |
| locations[3].landing_page_url | https://www.research.ed.ac.uk/en/publications/5ed2a84c-dab1-4478-9164-ac17e999d1e4 |
| indexed_in | crossref, pubmed |
| authorships[0].author.id | https://openalex.org/A5085166028 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-8519-7986 |
| authorships[0].author.display_name | Glen McHale |
| authorships[0].countries | GB |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I98677209 |
| authorships[0].affiliations[0].raw_affiliation_string | Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, U.K. |
| authorships[0].institutions[0].id | https://openalex.org/I98677209 |
| authorships[0].institutions[0].ror | https://ror.org/01nrxwf90 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I98677209 |
| authorships[0].institutions[0].country_code | GB |
| authorships[0].institutions[0].display_name | University of Edinburgh |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Glen McHale |
| authorships[0].is_corresponding | True |
| authorships[0].raw_affiliation_strings | Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, U.K. |
| authorships[1].author.id | https://openalex.org/A5032693344 |
| authorships[1].author.orcid | https://orcid.org/0000-0001-8714-0556 |
| authorships[1].author.display_name | Rodrigo Ledesma‐Aguilar |
| authorships[1].countries | GB |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I98677209 |
| authorships[1].affiliations[0].raw_affiliation_string | Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, U.K. |
| authorships[1].institutions[0].id | https://openalex.org/I98677209 |
| authorships[1].institutions[0].ror | https://ror.org/01nrxwf90 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I98677209 |
| authorships[1].institutions[0].country_code | GB |
| authorships[1].institutions[0].display_name | University of Edinburgh |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Rodrigo Ledesma-Aguilar |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, U.K. |
| authorships[2].author.id | https://openalex.org/A5087796607 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-6058-0885 |
| authorships[2].author.display_name | Chiara Neto |
| authorships[2].countries | AU |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I129604602 |
| authorships[2].affiliations[0].raw_affiliation_string | School of Chemistry and the University of Sydney Nano Institute, The University of Sydney, Sydney, New South Wales 2006, Australia |
| authorships[2].institutions[0].id | https://openalex.org/I129604602 |
| authorships[2].institutions[0].ror | https://ror.org/0384j8v12 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I129604602 |
| authorships[2].institutions[0].country_code | AU |
| authorships[2].institutions[0].display_name | The University of Sydney |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Chiara Neto |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | School of Chemistry and the University of Sydney Nano Institute, The University of Sydney, Sydney, New South Wales 2006, Australia |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.1021/acs.langmuir.3c01313 |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Cassie’s Law Reformulated: Composite Surfaces from Superspreading to Superhydrophobic |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10313 |
| primary_topic.field.id | https://openalex.org/fields/25 |
| primary_topic.field.display_name | Materials Science |
| primary_topic.score | 0.9997000098228455 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2508 |
| primary_topic.subfield.display_name | Surfaces, Coatings and Films |
| primary_topic.display_name | Surface Modification and Superhydrophobicity |
| related_works | https://openalex.org/W4238463552, https://openalex.org/W4210991910, https://openalex.org/W2928547925, https://openalex.org/W3213134099, https://openalex.org/W205077278, https://openalex.org/W3110121864, https://openalex.org/W2007634794, https://openalex.org/W2321855875, https://openalex.org/W2890620599, https://openalex.org/W1996012980 |
| cited_by_count | 11 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 6 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 3 |
| counts_by_year[2].year | 2023 |
| counts_by_year[2].cited_by_count | 2 |
| locations_count | 4 |
| best_oa_location.id | doi:10.1021/acs.langmuir.3c01313 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S75741262 |
| best_oa_location.source.issn | 0743-7463, 1520-5827 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 0743-7463 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Langmuir |
| best_oa_location.source.host_organization | https://openalex.org/P4310320006 |
| best_oa_location.source.host_organization_name | American Chemical Society |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310320006 |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Langmuir |
| best_oa_location.landing_page_url | https://doi.org/10.1021/acs.langmuir.3c01313 |
| primary_location.id | doi:10.1021/acs.langmuir.3c01313 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S75741262 |
| primary_location.source.issn | 0743-7463, 1520-5827 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 0743-7463 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Langmuir |
| primary_location.source.host_organization | https://openalex.org/P4310320006 |
| primary_location.source.host_organization_name | American Chemical Society |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320006 |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Langmuir |
| primary_location.landing_page_url | https://doi.org/10.1021/acs.langmuir.3c01313 |
| publication_date | 2023-07-24 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W2485244922, https://openalex.org/W4248806376, https://openalex.org/W2152123134, https://openalex.org/W1975140804, https://openalex.org/W1969565648, https://openalex.org/W1983084194, https://openalex.org/W2118166595, https://openalex.org/W2073619391, https://openalex.org/W2034194925, https://openalex.org/W2894072689, https://openalex.org/W2164023377, https://openalex.org/W2032422642, https://openalex.org/W2044670534, https://openalex.org/W2067425900, https://openalex.org/W2103977241, https://openalex.org/W3024533427, https://openalex.org/W2335897577, https://openalex.org/W2913023590, https://openalex.org/W3200601918, https://openalex.org/W3133790996, https://openalex.org/W4292962084, https://openalex.org/W2020962620, https://openalex.org/W3037775544, https://openalex.org/W2008100855, https://openalex.org/W1971143490, https://openalex.org/W2165430885, https://openalex.org/W2087429510, https://openalex.org/W4249730227, https://openalex.org/W2023784114, https://openalex.org/W2022412941, https://openalex.org/W1153120094, https://openalex.org/W1992954434, https://openalex.org/W2062070676 |
| referenced_works_count | 33 |
| abstract_inverted_index.+ | 65 |
| abstract_inverted_index.= | 61 |
| abstract_inverted_index.a | 10, 25, 28, 35, 51, 71, 108, 162, 173, 182, 192, 197, 204, 211, 218, 226, 229 |
| abstract_inverted_index.He | 14 |
| abstract_inverted_index.In | 0, 188 |
| abstract_inverted_index.an | 4, 74 |
| abstract_inverted_index.as | 257 |
| abstract_inverted_index.at | 216 |
| abstract_inverted_index.be | 32, 126, 186 |
| abstract_inverted_index.in | 172, 259 |
| abstract_inverted_index.is | 134, 160, 210, 237 |
| abstract_inverted_index.of | 9, 19, 44, 47, 50, 73, 90, 92, 115, 136, 168, 191, 234, 263, 272 |
| abstract_inverted_index.on | 27, 53, 113, 176, 220, 244, 248 |
| abstract_inverted_index.or | 150 |
| abstract_inverted_index.to | 85, 104, 228 |
| abstract_inverted_index.we | 120, 268 |
| abstract_inverted_index.The | 156, 232 |
| abstract_inverted_index.and | 94, 203, 251 |
| abstract_inverted_index.can | 125, 185 |
| abstract_inverted_index.cos | 59, 63, 67 |
| abstract_inverted_index.for | 24, 77, 180, 275 |
| abstract_inverted_index.has | 81, 99 |
| abstract_inverted_index.one | 114 |
| abstract_inverted_index.the | 7, 17, 20, 39, 45, 54, 87, 116, 141, 166, 177, 189, 221, 261, 264, 270 |
| abstract_inverted_index.was | 70, 255 |
| abstract_inverted_index.This | 69, 131 |
| abstract_inverted_index.area | 214 |
| abstract_inverted_index.been | 100 |
| abstract_inverted_index.case | 164, 190 |
| abstract_inverted_index.data | 241, 243 |
| abstract_inverted_index.film | 230 |
| abstract_inverted_index.from | 34, 196, 225, 239 |
| abstract_inverted_index.gold | 252 |
| abstract_inverted_index.have | 145 |
| abstract_inverted_index.paid | 103 |
| abstract_inverted_index.show | 121 |
| abstract_inverted_index.that | 16, 122, 254 |
| abstract_inverted_index.then | 161 |
| abstract_inverted_index.this | 235 |
| abstract_inverted_index.what | 105 |
| abstract_inverted_index.when | 107, 165 |
| abstract_inverted_index.1948, | 1 |
| abstract_inverted_index.Here, | 119 |
| abstract_inverted_index.angle | 184 |
| abstract_inverted_index.could | 31 |
| abstract_inverted_index.i.e., | 58 |
| abstract_inverted_index.ideas | 274 |
| abstract_inverted_index.mixed | 245 |
| abstract_inverted_index.state | 175 |
| abstract_inverted_index.there | 98, 209 |
| abstract_inverted_index.these | 273 |
| abstract_inverted_index.using | 38, 128 |
| abstract_inverted_index.where | 140 |
| abstract_inverted_index.which | 80, 181, 217 |
| abstract_inverted_index.Cassie | 2, 158, 265 |
| abstract_inverted_index.angle, | 22 |
| abstract_inverted_index.angles | 49 |
| abstract_inverted_index.areas, | 42 |
| abstract_inverted_index.cosine | 18 |
| abstract_inverted_index.liquid | 109, 219 |
| abstract_inverted_index.little | 101 |
| abstract_inverted_index.porous | 78 |
| abstract_inverted_index.proven | 83 |
| abstract_inverted_index.state) | 201 |
| abstract_inverted_index.state. | 231 |
| abstract_inverted_index.average | 37 |
| abstract_inverted_index.capable | 135 |
| abstract_inverted_index.contact | 21, 48, 183 |
| abstract_inverted_index.copper, | 249 |
| abstract_inverted_index.cosines | 46 |
| abstract_inverted_index.created | 195 |
| abstract_inverted_index.discuss | 269 |
| abstract_inverted_index.droplet | 26, 52, 174, 227 |
| abstract_inverted_index.earlier | 75 |
| abstract_inverted_index.happens | 106 |
| abstract_inverted_index.partial | 198 |
| abstract_inverted_index.results | 171 |
| abstract_inverted_index.silver, | 250 |
| abstract_inverted_index.smooth, | 11 |
| abstract_inverted_index.special | 163 |
| abstract_inverted_index.surface | 30, 41, 117, 143, 179, 194, 202, 213, 223 |
| abstract_inverted_index.wetting | 8, 91, 112, 199, 206 |
| abstract_inverted_index.(droplet | 147, 200 |
| abstract_inverted_index.Cassie's | 123 |
| abstract_inverted_index.Finally, | 267 |
| abstract_inverted_index.However, | 97 |
| abstract_inverted_index.complete | 111, 205 |
| abstract_inverted_index.defined. | 187 |
| abstract_inverted_index.equation | 5, 76, 124, 133, 159, 236 |
| abstract_inverted_index.exhibits | 110 |
| abstract_inverted_index.fraction | 215 |
| abstract_inverted_index.negative | 146 |
| abstract_inverted_index.original | 157 |
| abstract_inverted_index.positive | 151 |
| abstract_inverted_index.proposed | 15 |
| abstract_inverted_index.provided | 3 |
| abstract_inverted_index.recently | 82 |
| abstract_inverted_index.regarded | 256 |
| abstract_inverted_index.surface, | 208 |
| abstract_inverted_index.surface. | 13 |
| abstract_inverted_index.surfaces | 139, 253 |
| abstract_inverted_index.tensions | 170 |
| abstract_inverted_index.validity | 262 |
| abstract_inverted_index.weighted | 36 |
| abstract_inverted_index.wetting) | 149, 153 |
| abstract_inverted_index.attention | 102 |
| abstract_inverted_index.component | 56 |
| abstract_inverted_index.composite | 29, 138, 178, 193, 222 |
| abstract_inverted_index.equation. | 266 |
| abstract_inverted_index.including | 242 |
| abstract_inverted_index.predicted | 33 |
| abstract_inverted_index.repellent | 277 |
| abstract_inverted_index.spreading | 129, 154 |
| abstract_inverted_index.surfaces, | 57 |
| abstract_inverted_index.surfaces. | 96, 278 |
| abstract_inverted_index.threshold | 212 |
| abstract_inverted_index.components | 144 |
| abstract_inverted_index.definitive | 258 |
| abstract_inverted_index.describing | 6, 137 |
| abstract_inverted_index.fractional | 40 |
| abstract_inverted_index.individual | 55, 142 |
| abstract_inverted_index.literature | 240 |
| abstract_inverted_index.materials, | 79 |
| abstract_inverted_index.monolayers | 247 |
| abstract_inverted_index.combination | 167 |
| abstract_inverted_index.components. | 118 |
| abstract_inverted_index.description | 89 |
| abstract_inverted_index.fundamental | 84 |
| abstract_inverted_index.interfacial | 169 |
| abstract_inverted_index.theoretical | 88 |
| abstract_inverted_index.transitions | 224 |
| abstract_inverted_index.demonstrated | 238 |
| abstract_inverted_index.establishing | 260 |
| abstract_inverted_index.implications | 271 |
| abstract_inverted_index.reformulated | 127, 132 |
| abstract_inverted_index.super-liquid | 276 |
| abstract_inverted_index.underpinning | 86 |
| abstract_inverted_index.applicability | 233 |
| abstract_inverted_index.coefficients. | 130, 155 |
| abstract_inverted_index.heterogeneous | 12 |
| abstract_inverted_index.state/partial | 148 |
| abstract_inverted_index.(film-forming) | 207 |
| abstract_inverted_index.generalization | 72 |
| abstract_inverted_index.self-assembled | 246 |
| abstract_inverted_index.θ<sub>1</sub> | 64 |
| abstract_inverted_index.θ<sub>c</sub> | 60 |
| abstract_inverted_index.superoleophobic | 95 |
| abstract_inverted_index.θ<sub>2</sub>. | 68 |
| abstract_inverted_index.θ<sub>c</sub>, | 23 |
| abstract_inverted_index.superhydrophobic | 93 |
| abstract_inverted_index.<i>f</i><sub>1</sub> | 62 |
| abstract_inverted_index.<i>f</i><sub>2</sub> | 66 |
| abstract_inverted_index.(film-forming/complete | 152 |
| abstract_inverted_index.<i>f</i><sub><i>i</i></sub>, | 43 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 94 |
| corresponding_author_ids | https://openalex.org/A5085166028 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 3 |
| corresponding_institution_ids | https://openalex.org/I98677209 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/16 |
| sustainable_development_goals[0].score | 0.6700000166893005 |
| sustainable_development_goals[0].display_name | Peace, Justice and strong institutions |
| citation_normalized_percentile.value | 0.79555328 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |