{"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}
引用次数: 0
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, , where is the water−vapor interfacial tension, and the value of depends on the water−graphite interaction energy. According to different values of , 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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