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Hydrocarbon Chains: Stuck Unknots? By Michael White

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2 Overview This talk will focus on the link between knots, stuck unknots and realizing these knots as long strings of hydrocarbons. Can a hydrocarbon chain realize any stuck unknots?

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3 What is a Knot? www.aperfectworld.org/ metaphors.htm http://www.ualberta.ca/CNS/RESEARC H/3DPrinter/ImageGallery/knot.dir.1024 x1004.jpg Images From:

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4 Deformations of Knots

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5 Some Definitions - Over Strand - Under Strand - Crossing Number – denoted c(K) Images from: www.knotplot.com

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6 The Trefoil, Unknot, and Figure Eight Knots Crossing Number: 3 Crossing Number: 0 Crossing Number: 4 Images From: www.knotplot.com

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7 Stick Knots Image From: http://pass.maths.org.uk/issue15/features/knots/

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8 Stick Knot Equations Equations from: Negami and Calvo S(K) = stick number of a knot C(K) = crossing number of a knot

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9 Stuck Unknots Images from: Non Trivial Embeddings of Polygonal Intervals and Unknots in 3- Space, Heather Johnston and Jason Cantarella, J.Knot Theory Ramifications 7 (1998), no. 8, 1027-1039.

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10 Hydrocarbons Images from: http://www.nyu.edu/pages/ mathmol/library/hydrocarbo ns/ Nomenclature Single bond – Alkane Double bond – Alkene Triple bond - Alkyne

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11 The Role of Hydrocarbons Image Created in: HyperChem Professional version 7.5

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12 Stuck Hydrocarbon Chain Image Created in: HyperChem Professional version 7.5

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13 Why? Stephanie H. Chanteau and James M. Tour, Stephanie H. Chanteau and James M. Tour, J. Org. Chem, Vol. 68, No. 23, 2003. pg. 8759.

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14 Conclusion I have shown that hydrocarbons can make stuck unknots in certain situations. This research has not eliminated the possibility of stuck hydrocarbons with only alkenes or alkanes, but it has proven that stuck unknots can be made by a combination of single, double, and triple bonds.

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15 Thank You Here are the people who helped me greatly in bringing this project together: Dr. Jo Ellis-Monaghan – SMC Dr. Jo Ellis-Monaghan – SMC Dr. Kathleen Mondanaro – SMC Dr. Heather Johnston – Vassar College Dr. Tim Comar – Benedictine University Mary Cox – Grad Student at UVM Whitney Sherman – Undergrad Student at SMC Thank you all for your support.

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16 Sources Almost Regular Knots, Timothy D. Comar and Jessica M. Tyrus, Benedictine University. Stephanie H. Chanteau and James M. Tour, J. Org. Chem, Vol. 68, No. 23, 2003. pg. 8759. Non Trivial Embeddings of Polygonal Intervals and Unknots in 3-Space, Heather Johnston and Jason Cantarella, J.Knot Theory Ramifications 7 (1998), no. 8, 1027- 1039. The Knot Book, Colin C. Adams. W. H. Freeman and Company, NY © 1994. www.aperfectworld.org/ metaphors.htm www.aperfectworld.org/ metaphors.htm http://pass.maths.org.uk/issue15/features/knots/ http://www.ualberta.ca/CNS/RESEARCH/3DPrinter/ImageGallery/knot.dir.1024x1004.jpg http://www.nyu.edu/pages/mathmol/library/hydrocarbons/ www.knotplot.com

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17 Bridge Number

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18 Equation from: Almost Regular Knots, Timothy D. Comar and Jessica M. Tyrus, Benedictine University. More Stick Knot Equations

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