The contact angle and structure of water on the graphite-like substrate: A classical density functional approach

IF 3.5 3区 工程技术 Q2 ENGINEERING, CHEMICAL AIChE Journal Pub Date : 2024-12-07 DOI:10.1002/aic.18697
Jiarong Sang, Feng Wei, Junsu Jin
{"title":"The contact angle and structure of water on the graphite-like substrate: A classical density functional approach","authors":"Jiarong Sang, Feng Wei, Junsu Jin","doi":"10.1002/aic.18697","DOIUrl":null,"url":null,"abstract":"The influences of temperature and water−graphite interaction energy on the contact angle (<i>θ</i>) and structure of water on the graphite-like substrate have been investigated using the classical density functional theory. We find that the temperature-dependent behavior of cos<i>θ</i> is contingent upon the water−graphite interaction energy, manifesting in three distinct patterns: increasing, decreasing, or remaining nearly invariant with temperature within the examined range (273.16–640K). Furthermore, a novel simple equation has been derived to describe the temperature-dependent variation of cos<i>θ</i> at constant water−graphite interaction energy, that is, <span data-altimg=\"/cms/asset/2c57eb43-b526-412d-84e2-2636c4abe0e9/aic18697-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"4\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/aic18697-math-0001.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"21,22\" data-semantic-content=\"6\" data-semantic- data-semantic-role=\"equality\" data-semantic-speech=\"partial differential cosine theta slash partial differential upper T equals lamda divided by left parenthesis gamma Superscript l v Baseline right parenthesis squared\" data-semantic-type=\"relseq\"><mjx-mrow data-semantic-children=\"20,5\" data-semantic-content=\"4\" data-semantic- data-semantic-parent=\"23\" data-semantic-role=\"prefix operator\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-children=\"19\" data-semantic-content=\"0\" data-semantic- data-semantic-parent=\"21\" data-semantic-role=\"prefix operator\" data-semantic-type=\"prefixop\"><mjx-mi data-semantic- data-semantic-operator=\"prefixop,∂\" data-semantic-parent=\"20\" data-semantic-role=\"prefix operator\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mi><mjx-mrow data-semantic-children=\"1,17\" data-semantic-content=\"18,1\" data-semantic- data-semantic-parent=\"20\" data-semantic-role=\"prefix function\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"19\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"19\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"2\" data-semantic-content=\"3\" data-semantic- data-semantic-parent=\"19\" data-semantic-role=\"division\" data-semantic-type=\"postfixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"17\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"postfixop,/\" data-semantic-parent=\"17\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-mrow><mjx-mi data-semantic- data-semantic-operator=\"infixop,∂\" data-semantic-parent=\"21\" data-semantic-role=\"prefix operator\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mi><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"21\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"23\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"7,16\" data-semantic-content=\"8\" data-semantic- data-semantic-parent=\"23\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"22\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"22\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-msup data-semantic-children=\"14,15\" data-semantic- data-semantic-parent=\"22\" data-semantic-role=\"leftright\" data-semantic-type=\"superscript\"><mjx-mrow data-semantic-children=\"11\" data-semantic-content=\"12,13\" data-semantic- data-semantic-parent=\"16\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"14\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msup data-semantic-children=\"9,10\" data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"greekletter\" data-semantic-type=\"superscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em; margin-left: 0.051em;\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msup><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"14\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow><mjx-script style=\"vertical-align: 0.581em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"16\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00011541:media:aic18697:aic18697-math-0001\" display=\"inline\" location=\"graphic/aic18697-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"21,22\" data-semantic-content=\"6\" data-semantic-role=\"equality\" data-semantic-speech=\"partial differential cosine theta slash partial differential upper T equals lamda divided by left parenthesis gamma Superscript l v Baseline right parenthesis squared\" data-semantic-type=\"relseq\"><mrow data-semantic-=\"\" data-semantic-children=\"20,5\" data-semantic-content=\"4\" data-semantic-parent=\"23\" data-semantic-role=\"prefix operator\" data-semantic-type=\"infixop\"><mrow data-semantic-=\"\" data-semantic-children=\"19\" data-semantic-content=\"0\" data-semantic-parent=\"21\" data-semantic-role=\"prefix operator\" data-semantic-type=\"prefixop\"><mi data-semantic-=\"\" data-semantic-operator=\"prefixop,∂\" data-semantic-parent=\"20\" data-semantic-role=\"prefix operator\" data-semantic-type=\"operator\">∂</mi><mrow data-semantic-=\"\" data-semantic-children=\"1,17\" data-semantic-content=\"18,1\" data-semantic-parent=\"20\" data-semantic-role=\"prefix function\" data-semantic-type=\"appl\"><mi data-semantic-=\"\" data-semantic-font=\"normal\" data-semantic-operator=\"appl\" data-semantic-parent=\"19\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\">cos</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"appl\" data-semantic-parent=\"19\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\">⁡</mo><mrow data-semantic-=\"\" data-semantic-children=\"2\" data-semantic-content=\"3\" data-semantic-parent=\"19\" data-semantic-role=\"division\" data-semantic-type=\"postfixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"17\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">θ</mi><mo data-semantic-=\"\" data-semantic-operator=\"postfixop,/\" data-semantic-parent=\"17\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo></mrow></mrow></mrow><mi data-semantic-=\"\" data-semantic-operator=\"infixop,∂\" data-semantic-parent=\"21\" data-semantic-role=\"prefix operator\" data-semantic-type=\"operator\">∂</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"21\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">T</mi></mrow><mo data-semantic-=\"\" data-semantic-operator=\"relseq,=\" data-semantic-parent=\"23\" data-semantic-role=\"equality\" data-semantic-type=\"relation\">=</mo><mrow data-semantic-=\"\" data-semantic-children=\"7,16\" data-semantic-content=\"8\" data-semantic-parent=\"23\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"22\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">λ</mi><mo data-semantic-=\"\" data-semantic-operator=\"infixop,/\" data-semantic-parent=\"22\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo><msup data-semantic-=\"\" data-semantic-children=\"14,15\" data-semantic-parent=\"22\" data-semantic-role=\"leftright\" data-semantic-type=\"superscript\"><mrow data-semantic-=\"\" data-semantic-children=\"11\" data-semantic-content=\"12,13\" data-semantic-parent=\"16\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"14\" data-semantic-role=\"open\" data-semantic-type=\"fence\">(</mo><msup data-semantic-=\"\" data-semantic-children=\"9,10\" data-semantic-parent=\"14\" data-semantic-role=\"greekletter\" data-semantic-type=\"superscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"11\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">γ</mi><mi data-semantic-=\"\" data-semantic-font=\"normal\" data-semantic-parent=\"11\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\">lv</mi></msup><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"14\" data-semantic-role=\"close\" data-semantic-type=\"fence\">)</mo></mrow><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"16\" data-semantic-role=\"integer\" data-semantic-type=\"number\">2</mn></msup></mrow></mrow>$$ \\partial \\mathrm{cos}\\theta /\\partial T=\\lambda /{\\left({\\gamma}^{\\mathrm{lv}}\\right)}^2 $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, where <span data-altimg=\"/cms/asset/56cf5e89-ff3b-48db-a766-1b8cc21b7fe0/aic18697-math-0002.png\"></span><mjx-container ctxtmenu_counter=\"5\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/aic18697-math-0002.png\"><mjx-semantics><mjx-mrow><mjx-msup data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"gamma Superscript l v\" data-semantic-type=\"superscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em; margin-left: 0.051em;\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msup></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00011541:media:aic18697:aic18697-math-0002\" display=\"inline\" location=\"graphic/aic18697-math-0002.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msup data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"gamma Superscript l v\" data-semantic-type=\"superscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">γ</mi><mi data-semantic-=\"\" data-semantic-font=\"normal\" data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\">lv</mi></msup></mrow>$$ {\\gamma}^{\\mathrm{lv}} $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> is the water−vapor interfacial tension, and the value of <span data-altimg=\"/cms/asset/83d1e70b-ec82-4e16-9c91-dbcb26c26c12/aic18697-math-0003.png\"></span><mjx-container ctxtmenu_counter=\"6\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/aic18697-math-0003.png\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"lamda\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00011541:media:aic18697:aic18697-math-0003\" display=\"inline\" location=\"graphic/aic18697-math-0003.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"greekletter\" data-semantic-speech=\"lamda\" data-semantic-type=\"identifier\">λ</mi></mrow>$$ \\lambda $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> depends on the water−graphite interaction energy. According to different values of <span data-altimg=\"/cms/asset/41f03d64-2dbd-49f3-ab64-5f259f31fe77/aic18697-math-0004.png\"></span><mjx-container ctxtmenu_counter=\"7\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/aic18697-math-0004.png\"><mjx-semantics><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"lamda\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00011541:media:aic18697:aic18697-math-0004\" display=\"inline\" location=\"graphic/aic18697-math-0004.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"greekletter\" data-semantic-speech=\"lamda\" data-semantic-type=\"identifier\">λ</mi></mrow>$$ \\lambda $$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, this equation is able to successfully represent the three aforementioned patterns. At last, the density profile and hydrogen bonding structure of water near the substrate have been analyzed to offer microscopic insights.","PeriodicalId":120,"journal":{"name":"AIChE Journal","volume":"17 1","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2024-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIChE Journal","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/aic.18697","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
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Abstract

The influences of temperature and water−graphite interaction energy on the contact angle (θ) and structure of water on the graphite-like substrate have been investigated using the classical density functional theory. We find that the temperature-dependent behavior of cosθ is contingent upon the water−graphite interaction energy, manifesting in three distinct patterns: increasing, decreasing, or remaining nearly invariant with temperature within the examined range (273.16–640K). Furthermore, a novel simple equation has been derived to describe the temperature-dependent variation of cosθ at constant water−graphite interaction energy, that is, cosθ/T=λ/(γlv)2$$ \partial \mathrm{cos}\theta /\partial T=\lambda /{\left({\gamma}^{\mathrm{lv}}\right)}^2 $$, where γlv$$ {\gamma}^{\mathrm{lv}} $$ is the water−vapor interfacial tension, and the value of λ$$ \lambda $$ depends on the water−graphite interaction energy. According to different values of λ$$ \lambda $$, this equation is able to successfully represent the three aforementioned patterns. At last, the density profile and hydrogen bonding structure of water near the substrate have been analyzed to offer microscopic insights.
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石墨基板上水的接触角和结构:一个经典的密度泛函方法
用经典密度泛函理论研究了温度和水-石墨相互作用能对类石墨衬底上水的接触角(θ)和结构的影响。我们发现cost θ的温度依赖行为取决于水-石墨相互作用能,在检测范围(273.16-640K)内表现为三种不同的模式:随温度增加、减少或保持几乎不变。此外,我们还推导了一个新的简单方程来描述恒定水-石墨相互作用能时cost θ的温度变化,即∂cos (θ/∂T) =λ/(γlv)2 $$ \partial \mathrm{cos}\theta /\partial T=\lambda /{\left({\gamma}^{\mathrm{lv}}\right)}^2 $$,其中γlv $$ {\gamma}^{\mathrm{lv}} $$是水-蒸汽界面张力,λ $$ \lambda $$的值取决于水-石墨相互作用能。根据λ $$ \lambda $$的不同值,该方程能够成功地表示上述三种模式。最后,分析了衬底附近水的密度分布和氢键结构,以提供微观见解。
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来源期刊
AIChE Journal
AIChE Journal 工程技术-工程:化工
CiteScore
7.10
自引率
10.80%
发文量
411
审稿时长
3.6 months
期刊介绍: The AIChE Journal is the premier research monthly in chemical engineering and related fields. This peer-reviewed and broad-based journal reports on the most important and latest technological advances in core areas of chemical engineering as well as in other relevant engineering disciplines. To keep abreast with the progressive outlook of the profession, the Journal has been expanding the scope of its editorial contents to include such fast developing areas as biotechnology, electrochemical engineering, and environmental engineering. The AIChE Journal is indeed the global communications vehicle for the world-renowned researchers to exchange top-notch research findings with one another. Subscribing to the AIChE Journal is like having immediate access to nine topical journals in the field. Articles are categorized according to the following topical areas: Biomolecular Engineering, Bioengineering, Biochemicals, Biofuels, and Food Inorganic Materials: Synthesis and Processing Particle Technology and Fluidization Process Systems Engineering Reaction Engineering, Kinetics and Catalysis Separations: Materials, Devices and Processes Soft Materials: Synthesis, Processing and Products Thermodynamics and Molecular-Scale Phenomena Transport Phenomena and Fluid Mechanics.
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