Polymer dynamics and topology: Extension of stars and dendrimers in external fields

We study the influence of topology on the extension of branched polymers subjected to external forces. Such forces can be applied mechanically (by micromanipulation techniques such as laser tweezers) or electrically (in the case of charged polymers). We focus on the unfold dynamics of star and dendrimer type structures. Some of the dynamical quantities of interest are: (i) the structural average of the mean monomer displacement, (ii) the elastic and the loss moduli and (iii) the mean displacement of a specified monomer. In a Gaussian-type approach, (i) and (ii) depend only on the eigenvalues of the adjacency matrix whereas (iii) also requires the knowledge of the eigenvectors. Thus one can sometimes dispense with a full diagonalisation and use efficient recursion procedures. We highlight how the dynamic properties depend on topology: the number of branches and their length for stars and the number of generations for dendrimers. The intermediate time (crossover) behavior turns out to be most revealing of the underlying structure. We compare our results to those for fractal structures in external fields.