Abstract |
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[eng] One of the basic models describing the dynamics of a polymer chain is the Rouse model [1]. This model was introduced for a linear chain and described the dynamics of a polymer melt of linear chains in the unentangled regime. Here we extend the Rouse model to a star polymer with arbitrary number of arms. In particular we calculate the mean square displacement (MSD) of the branch point and the same quantity (MSD) for a general segment of an arm with Nα segments. We find that an arm segment behaves as a segment of a linear chain until it realises the existence of the branch point. Then a cross over to the branch-point dynamics occurs. Regarding the entangled regime we use the idea of localising the chain and defining a tube primitive by attaching to each segment (except the BP) of the Rouse star an additional spring which represents the constraints due to entanglements [2]. For this system, i.e. entangled stars of arbitrary number of arms, we calculate the general expression of the MSD of two different segments that belong to the same arm or different arms. The expressions are used in a dynamic version of the random phase approximation (RPA) which includes tube-tube correlations for the calculation of the normalized dynamic scattering function P(q,t) of the system. The predictions of the model are compared against neutron spin echo data, for early time scales, of a labelled three arm polyethylene star [3] revealing good agreement. In the calculation of P(q,t) we account for coherent and incoherent contribution to the spin echo signal. [1] P.E. Rouse, J. Chem. Phys., 21, 1272 (1953). [2] D.J. Read, K. Jagannathan, and A.E. Likhtman, Macromolecules, 41, 6843 (2008) [3] M. Zamponi, W. Hintzent, A. Wischnewski, M. Monkenbusch, L. Willnert, G. Kali, and D. Richter Macromolecules, 43, 518 (2010). |