Composite spring model in stretched polymer knots

The deformation of a knotted polymer under a stretching force is studied by modeling the deformed knot as a composite spring system. Our results predi ct that the elastic modulus of a knotted polymer is larger when compared to an equal-length linear chain. More complex knots are in general stiffer. T he increase in stiffness of knots relative to the linear chain is also deri ved. Monte Carlo simulations are also performed to investigate the strechin g of polymer knots. Chain lengths up to N = 82 and prime knots 0(1), 3(1), 4(1), 5(1), 6(1) and 8(1) are considered. Segregation of the crossings into a small tight region of the knot structure at strong forces is observed. T he increase in stiffness predicted by the composite spring model agree well with the simulation data. Our simulation data show that the scaling laws p roposed by de Gennes and Pincus for a single linear chain under traction fo rce still hold for the knotted type polymers.