<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:x="urn:schemas-microsoft-com:office:excel" xmlns:p="urn:schemas-microsoft-com:office:powerpoint" xmlns:a="urn:schemas-microsoft-com:office:access" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:s="uuid:BDC6E3F0-6DA3-11d1-A2A3-00AA00C14882" xmlns:rs="urn:schemas-microsoft-com:rowset" xmlns:z="#RowsetSchema" xmlns:b="urn:schemas-microsoft-com:office:publisher" xmlns:ss="urn:schemas-microsoft-com:office:spreadsheet" xmlns:c="urn:schemas-microsoft-com:office:component:spreadsheet" xmlns:odc="urn:schemas-microsoft-com:office:odc" xmlns:oa="urn:schemas-microsoft-com:office:activation" xmlns:html="http://www.w3.org/TR/REC-html40" xmlns:q="http://schemas.xmlsoap.org/soap/envelope/" xmlns:rtc="http://microsoft.com/officenet/conferencing" xmlns:D="DAV:" xmlns:Repl="http://schemas.microsoft.com/repl/" xmlns:mt="http://schemas.microsoft.com/sharepoint/soap/meetings/" xmlns:x2="http://schemas.microsoft.com/office/excel/2003/xml" xmlns:ppda="http://www.passport.com/NameSpace.xsd" xmlns:ois="http://schemas.microsoft.com/sharepoint/soap/ois/" xmlns:dir="http://schemas.microsoft.com/sharepoint/soap/directory/" xmlns:ds="http://www.w3.org/2000/09/xmldsig#" xmlns:dsp="http://schemas.microsoft.com/sharepoint/dsp" xmlns:udc="http://schemas.microsoft.com/data/udc" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:sub="http://schemas.microsoft.com/sharepoint/soap/2002/1/alerts/" xmlns:ec="http://www.w3.org/2001/04/xmlenc#" xmlns:sp="http://schemas.microsoft.com/sharepoint/" xmlns:sps="http://schemas.microsoft.com/sharepoint/soap/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:udcs="http://schemas.microsoft.com/data/udc/soap" xmlns:udcxf="http://schemas.microsoft.com/data/udc/xmlfile" xmlns:udcp2p="http://schemas.microsoft.com/data/udc/parttopart" xmlns:wf="http://schemas.microsoft.com/sharepoint/soap/workflow/" xmlns:dsss="http://schemas.microsoft.com/office/2006/digsig-setup" xmlns:dssi="http://schemas.microsoft.com/office/2006/digsig" xmlns:mdssi="http://schemas.openxmlformats.org/package/2006/digital-signature" xmlns:mver="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns:mrels="http://schemas.openxmlformats.org/package/2006/relationships" xmlns:spwp="http://microsoft.com/sharepoint/webpartpages" xmlns:ex12t="http://schemas.microsoft.com/exchange/services/2006/types" xmlns:ex12m="http://schemas.microsoft.com/exchange/services/2006/messages" xmlns:pptsl="http://schemas.microsoft.com/sharepoint/soap/SlideLibrary/" xmlns:spsl="http://microsoft.com/webservices/SharePointPortalServer/PublishedLinksService" xmlns:Z="urn:schemas-microsoft-com:" xmlns:st="" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 12 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-serif";}
h1
{mso-style-link:"Heading 1 Char";
margin-top:12.0pt;
margin-right:0in;
margin-bottom:3.0pt;
margin-left:0in;
page-break-after:avoid;
font-size:16.0pt;
font-family:"Arial","sans-serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri","sans-serif";
color:windowtext;}
span.Heading1Char
{mso-style-name:"Heading 1 Char";
mso-style-link:"Heading 1";
font-family:"Arial","sans-serif";
font-weight:bold;}
.MsoChpDefault
{mso-style-type:export-only;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal align=center style='text-align:center'><a name="_Toc277715226"><b><span style='font-family:"Arial","sans-serif"'>CURVATURE DEPENDENT SURFACE ENERGY AND IMPLICATIONS FOR NANOSTRUCTURES<o:p></o:p></span></b></a></p><p class=MsoNormal align=center style='text-align:center'><span style='font-family:"Arial","sans-serif"'>by<o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center'><span style='font-family:"Arial","sans-serif"'>Prakash Chhapadia<o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-family:"Arial","sans-serif"'><o:p> </o:p></span></b></p><p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt;font-family:"Arial","sans-serif"'>Date: 23<sup>rd</sup> November, 2010 Time: 11:00 AM Location: W232 Engineering Bldg II<o:p></o:p></span></p><p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt;font-family:"Arial","sans-serif"'><o:p> </o:p></span></p><p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt;font-family:"Arial","sans-serif"'>Committee Members: Dr. Pradeep Sharma. Dr. Yashashree Kulkarni, Dr. Gemunu Gunaratne<o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center'><span style='font-family:"Arial","sans-serif"'><o:p> </o:p></span></p><h1 align=center style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:0in;margin-left:.3in;margin-bottom:.0001pt;text-align:center'><span style='font-size:12.0pt'>Abstract</span><span style='font-size:12.0pt'><o:p></o:p></span></h1><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial","sans-serif"'><o:p> </o:p></span></p><p class=MsoNormal style='text-align:justify;line-height:200%;text-autospace:none'><span style='font-size:12.0pt;line-height:200%;font-family:"Arial","sans-serif"'>At small length scales, several size-effects in both physical phenomena and properties can be rationalized by invoking the concept of surface energy. Conventional theoretical frameworks of surface energy, in both the mechanics and physics community, assume curvature independence. In this work we adopt a simplified and linearized version of a theory proposed by Steigmann-Ogden to capture curvature-dependence of surface energy. Connecting the theory to atomistic calculations and the solution to an illustrative paradigmatical problem of a bent cantilever beam, we catalog the influence of curvature dependence of surface energy on the effective elastic modulus of nanostructures. <o:p></o:p></span></p><p class=MsoNormal style='text-align:justify;text-indent:.3in;line-height:200%;text-autospace:none'><span style='font-size:12.0pt;line-height:200%;font-family:"Arial","sans-serif"'>The observation in atomistic calculations that the elastic modulus of bent nanostructures is dramatically different than under tension--sometimes softer, sometimes stiffer--has been a source of puzzlement in the scientific community. We show that the corrected surface mechanics framework provides a resolution to this issue. Finally, we propose an unambiguous definition of the thickness of a crystalline surface. </span><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>