Discontinuous Transition in Semiflexible Polymers

It is known that the coil-globule transition in flexible polymers is well explained by the theory of the type discussed [22]. Note that the chain length and the solvent quality come into the theory in the following combined form x = BN1/2/l3, which is the only dimensionless parameter governing the transition. The presence of the master curve (see Fig. 3.5 below) implies that the phase behavior of the thermodynamic limit with N — oo is readily discussed from the measurement of shorter chains via finite-size scaling. 

What about semiflexible polymers It is, in principle, possible to include the effect of the chain stiffness through the parameter y in (3.1). As shown 

Carlo simulation is shown in Fig. 3.6(top), in which the gyration radius of the chain with L/a = 500 and l/a 20 is plotted as a function of the inverse temperature e/T. 

The mean radius of the torus is rather insensitive to the chain length. Consequently, as the chain length increases, the thickness of torus r increases more rapidly than the mean radius R. Beyond the critical length L (obtained as R L ) = r(L )), a hole is not formed, thus a fat disk would be formed. These predictions are in reasonable agreement with the results obtained from Monte Carlo simulations (Fig. 3.8). 

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