Relaxation Dynamics of Semiflexible Fractal Macromolecules

Relaxation dynamics of semiflexible treelike small-world polymer networks

We study the relaxation dynamics of the polymer networks that are constructed based on a degree distribution specific to small-world networks. The employed building algorithm generates polymers with a large variety of architectures, thus allowing for a detailed study of the structural transition from a pure linear chain to dendritic polymer networks. This is done by varying a single parameter p, which measures the randomness in the degree of the network's nodes. The dynamics is investigated in the framework of the generalized Gaussian structures model by monitoring the influence of the parameter p and of the stiffness parameter q on the behavior of the relaxation quantities: averaged monomer displacement, storage modulus, and loss modulus. The structure properties of the constructed polymers are described by the mean-square radius of gyration. In the absence of stiffness, in the intermediate frequencies domain of the dynamical quantities we encounter different behaviours, such as a dendritic behavior followed by a linear one for very small values of p or a single well-marked dendritic behavior for higher values of p. The stiffness parameter q influences drastically the relaxation dynamics of these polymer networks and in general no evident scaling regions were encountered. However, for some values of the parameter set (p,q), such as (0.8,0.4), an extremely short constant slope region, less than one order of magnitude, was found.

Marginally compact fractal trees with semiflexibility

We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness, the self-contact density gets drastically reduced.

Marginally compact hyperbranched polymer trees

Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution ρ_pair(r) or the shear-stress relaxation modulus G(t), are investigated theoretically and by means of computer simulations. We emphasize that albeit the self-contact density diverges logarithmically with the total mass N, this effect becomes rapidly irrelevant with increasing spacer length S. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time τ_p of mode p must scale as τ_p ∼ (N/p)^5/3 rather than the usual square power law for linear chains.