Many polymers

  The force on a single polymer, attached to a needle, is around 0.1 pico-Newton at 0.1 micron separation.

 This force, however, can be increased by attaching many polymers to the tip.

 In the limit of small opening angle (a needle), we can utilize the large literature on star polymers:

"Statistics of many arm star polymers," K. Ohno, Phys. Rev A 40, 1524 (1989)

"Scaling theory of star polymers and general polymer networks in bulk
      and semi-infinite good solvents," K. Ohno & K. Binder, J. Phys. France 49, 1329 (1988)

 At the lowest order in ε-expansion, the force is simply multiplied by the number of polymers;

corrections are expected at higher orders, with the force increasing faster than linearly (as f 3/2 ?)