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Polymer conformation & chain dimension

Published on: Mar 4, 2016

Transcripts - Polymer conformation & chain dimension

• 1. PolymerConformation& ChainDimensionAman Pratap Singh Rajvi2010B2AB716P1
• 2. Model: Freely Jointed Model orRandom Flight Model Assumptions: No restrictions of – Valence Angle, Rotation &Vander-waals’ Volume Short range correlations betweenneighboring monomers are not excluded. Ideal chain models do not take interactionscaused by conformations in space intoaccount. Ideal chains allow the polymer to cross itself. Fully idealized hypothetical model.2
• 3. Model contd.3lhh=nll4h niilh 0h= end-to-enddistancen= number oflinks
• 4. Model contd.4niilh 0njjniiniinii llllhhh 00002...ninjjinn llllllllllh 0 03322112..........ninjijjinn llllllllllh 0 03322112cos.........ninjijjinn llllllllllh 0 03322112cos.........ninjijjill0 00cosbut So22322212... nllllh
• 5. Model contd. Mean square bond length: If all bonds are of same length, i.e., l Root Mean Square (RMS) end-to-end distance==5nlllll nav22322212 ...nhlav2222avnlh2222222...lnnlnlllllavnlnl2
• 6. Using Gaussian DistributionFunction n= no. of segments l= length of each link Gaussian DistributionFunction=6),,(22321zyxweb rbrdydxdz
• 7. Gaussian Distribution Functioncontd. Taking spherical coordinates7drrddrebdrw rb 22321sin),,(2223214)(22rebrw rbr=radius ofspherical shellb=3/2nl2
• 8. Gaussian Distribution Functioncontd. Which is same as what we got from FreelyJointed Chain Model820022)()(nldrrwdrrwrr RMS end-to-end Distance nl
• 9. Considering Real Chain Restriction due to valance bond angle9cos1cos122nlr
• 10. Real Chain contd. Restrictions because of Steric Hindranceas a result of presence of bulky group10cos1cos1cos1cos122nlr Dihedral angle
• 11. Real Chain contd. Correction due to excluded volume11lnCr N212)(Expansion factor which is ameasure of excluded volume220nlr0: Excluded volume1: No excluded volume22222.)( nlClnCr NN220nlrCNUnperturbed Mean squareend-to-end distanceMean square end-to-enddistance
• 12. Thank You12