CHEM 4214 Lecture Notes - Lecture 15: Persistence Length, Bond Length, Unit Vector
Document Summary
Recap long flexible chains are walks root mean square end to end length n = # backbone bonds. N = # chemical repeat units l = bond length (if hypothetically stretched out) = statistical segment length if no entanglement, cinfty = 1 but usually greater than 1, usually 6. Semiflexible wormlike chain discrete model fixed bond length small angle theta between random dihedral. Krafty parod (freely rotating) diffusing along unit sphere Take l --> 0, , but fixed continuum limit. 0 < s < l e. g. dna u = unit vector correlations undergoes diffusion on unit sphere lp = persistence length. Ex: poly(p-phylene) can"t be in any conformation other than straight line unless bond angles change lp = 130 angstroms. Dna (double helix) lp = 600 angstroms end-end. Limits: rod-like l << lp in opposite limit, coil-like l>>lp coil rod. Chem4212 polymers page 4 smooth transition between rod-like and coil-like behavior hydrocarbons have short persistence length.
