Entropic Tightening

• A. Yu Grosberg, et al, Phys. Rev. E 54, 6618 (96). [Flory theory]
• E. Orlandini, et al, J. Phys. A 31, 5953 (98). [simulations]
• V. Katrich, et al, Phys. Rev. E 61, 5545 (00). [phantom walks]

  Slip-links as surrogate (prime) knots:

• R.C. Ball, M. Doi, S.F. Edwards and M. Warner, Polymer 22, 1010 (1981).

    Entropy of a constrained slip-link (phantom chain in three dimensions):

  The most probable configurations are composed of a tight and an open loop!

  Self-avoiding Slip-links:

  A large body of work on polymer networks can be used to study slip-linked polymers.

• B. Duplantier, Phys. Rev. Lett. 57, 941 (1986).
• Y. Kafri, D. Mukamel, L. Peliti, Phys. Rev. Lett. 85, 4988 (2000).

  The number of configurations of a self-avoiding slip-link has the scaling form

  In the limit of a small (tight) loop, the above expression reduces to

• For d=3,     c 3 x 0.59 + 0.46 2.26
• For d=2,     c = 2 x 3/4 + 19/16 2.69

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