Polymers are among the most important materials in the modern society being found almost in every activity of our daily life. Understanding their chemical and physical properties lead to improvements of their usage. The correlation functions are one of most important quantities to understand a physical system. The characteristic way it behaves describe how the system fluctuates, and much of the progress achieved to understand complex systems has been due to their study. Of particular interest in polymer science are the space correlations which describe its mechanical behavior. In this work I study the stiffness of a polymer immersed in a magnetic medium and trapped in an optical tweezers. Using Monte Carlo simulations the correlation function along the chain and the force in the tweezers are obtained as a function of temperature and density of magnetic particles. The results show that the correlation decay has two regimes: an initial very fast decay of order the monomer-monomer spacing and a power law in the long distance regime. The power law exponent has a minimum at a temperature $T_{min}$ for any non zero density of magnetic particles indicating that the system is more correlated in this region. Using a formula for the persistence length derived from the WLC theory one observed that it has a maximum at the same temperature. These results suggest that the correlations in the system may be a combination of exponential and power law.
An analytical coarse-graining method which preserves the free energy, structural correlations, and thermodynamic state of polymer melts from the atomistic to the mesoscale
