Hydrocarbon Chains: Hydrocarbon Chains: Stuck Unknots?Stuck Unknots?

By Michael White

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OverviewOverview

This talk will focus on the link between This talk will focus on the link between knots, stuck unknots and realizing knots, stuck unknots and realizing

these knots as long strings of these knots as long strings of hydrocarbons. hydrocarbons.

Can a hydrocarbon chain realize any Can a hydrocarbon chain realize any stuck unknots? stuck unknots?

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What is a Knot?What is a Knot?

www.aperfectworld.org/ metaphors.htm

http://www.ualberta.ca/CNS/RESEARCH/3DPrinter/ImageGallery/knot.dir.1024x1004.jpg

Images From:

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Deformations of KnotsDeformations of Knots

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Some DefinitionsSome Definitions

- Over Strand Over Strand

- Under StrandUnder Strand

- Crossing Number – denoted c(K)Crossing Number – denoted c(K)

Images from: www.knotplot.com

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The Trefoil, Unknot, and The Trefoil, Unknot, and Figure Eight KnotsFigure Eight Knots

Crossing Number: 3

Crossing Number: 0

Crossing Number: 4

Images From: www.knotplot.com

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Stick KnotsStick Knots

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

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Stick Knot EquationsStick Knot Equations

)()1)(87(*2/1 KSKc

)(2)()))2)((8255(*)2/1( KcKSKc

Equations from: Negami and Calvo

S(K) = stick number of a knotC(K) = crossing number of a knot

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Stuck UnknotsStuck 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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HydrocarbonsHydrocarbons

Images from: http://www.nyu.edu/pages/mathmol/library/hydrocarbons/

Nomenclature

Single bond – Alkane

Double bond – Alkene

Triple bond - Alkyne

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The Role of HydrocarbonsThe Role of Hydrocarbons

Image Created in: HyperChem Professional version 7.5

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Stuck Hydrocarbon ChainStuck Hydrocarbon Chain

Image Created in: HyperChem Professional version 7.5

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Why?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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ConclusionConclusion

I have shown that hydrocarbons can I have shown that hydrocarbons can make stuck unknots in certain make stuck unknots in certain

situations. This research has not situations. This research has not eliminated the possibility of stuck eliminated the possibility of stuck hydrocarbons with only alkenes or hydrocarbons with only alkenes or

alkanes, but it has proven that stuck alkanes, but it has proven that stuck unknots can be made by a combination unknots can be made by a combination

of single, double, and triple bonds. of single, double, and triple bonds.

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Thank YouThank You

Here are the people who helped me greatly in Here are the people who helped me greatly in bringing this project together:bringing this project together:

Dr. Jo Ellis-Monaghan – SMCDr. Jo Ellis-Monaghan – SMC

Dr. Kathleen Mondanaro – SMCDr. Kathleen Mondanaro – SMCDr. Heather Johnston – Vassar CollegeDr. Heather Johnston – Vassar College

Dr. Tim Comar – Benedictine UniversityDr. Tim Comar – Benedictine UniversityMary Cox – Grad Student at UVMMary Cox – Grad Student at UVM

Whitney Sherman – Undergrad Student at SMCWhitney Sherman – Undergrad Student at SMC

Thank you all for your support.Thank you all for your support.

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SourcesSourcesAlmost Regular KnotsAlmost Regular Knots, Timothy D. Comar and Jessica M. Tyrus, Benedictine University. , Timothy D. Comar and Jessica M. Tyrus, Benedictine University.

Stephanie H. Chanteau and James M. Tour, J. Org. Chem, Vol. 68, No. Stephanie H. Chanteau and James M. Tour, J. Org. Chem, Vol. 68, No. 23, 2003. pg. 8759.23, 2003. pg. 8759.

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

1039.1039.

The Knot BookThe Knot Book, Colin C. Adams. W. H. Freeman and Company, NY , Colin C. Adams. W. H. Freeman and Company, NY © 1994.© 1994.

www.aperfectworld.org/ www.aperfectworld.org/ metaphors.htmmetaphors.htmhttp://pass.maths.org.uk/issue15/features/knots/http://pass.maths.org.uk/issue15/features/knots/

http://www.ualberta.ca/CNS/RESEARCH/3DPrinter/ImageGallery/knot.dir.1024x1004.jpghttp://www.ualberta.ca/CNS/RESEARCH/3DPrinter/ImageGallery/knot.dir.1024x1004.jpghttp://http://www.nyu.edu/pages/mathmol/library/hydrocarbonswww.nyu.edu/pages/mathmol/library/hydrocarbons//

www.knotplot.comwww.knotplot.com

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Bridge NumberBridge Number

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1,2 ( ) /( ) ( )b K S K

Equation from: Almost Regular Knots, Timothy D. Comar and Jessica M. Tyrus, Benedictine University.

More Stick Knot EquationsMore Stick Knot Equations