Statics and dynamics of the freely jointed polymer chain with Lennard-Jones interaction

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Abstract
Using a dynamic Monte Carlo method we investigated the thermodynamics of static and time‐dependent properties of the freely jointed polymer chain with Lennard‐Jones type intramolecular forces. The Θ temperture is calculated to kBΘ/−=3.70±0.01 (− is the Lennard‐Jones energy parameter). We give estimates for the equilibrium values of end‐to‐end distances, radii of gyration, and densities for chains consisting of up to N=63 segments and for various temperatures. The detailed structure of the extended coil state (T≳Θ) and the dense globular state (T<Θ) are demonstrated by their average internal distances and their structure functions. The results seem to confirm the predicted scaling laws. Especially we found that for T=Θ the mean size of the coil is ∼N1/2 but the detailed structure is different from a random walk shape. Although the specific heat exhibits a maximum below the Θ temperature, the finite size effects are too serious to confirm the predicted logarithmic divergency. The dynamics of our Monte Carlo method simulate the Rouse model. The density correlation function and the associated relaxation time are calculated. The results are consistent with dynamic scaling predictions. The segment correlation function exhibits the initial ∼t1/2 behavior and the diffusional behavior ∼ t at large times.