Conformations and Dynamics of Stars and Dendrimers: The Gaussian Self-Consistent Approach

Abstract

Some conformational and dynamical aspects of branched polymer are reviewed. We discuss the theoretical Gaussian Self-Consistent (GSC) approach proposed in our group and used to study the behaviour of regular star polymers and dendrimers in different solvent conditions. Within a single framework, we consider the unperturbed Θ state, as well as the goodsolvent state in comparison with other theoretical or simulation approaches, and with some experimental results. We also briefly report the further results obtained for amphiphilic copolymer stars in selective solvents so as to highlight the potentialities of the method, as well as its strengths and its shortcomings.

Dendrimers in Solution: Insight from Theory and Simulation

“…Ganazzoli, La Ferla, and Terragni generalized the approach of La Ferla to include excluded‐volume effects 42. 43 Here, the probability density of contact among pairs in the Gaussian approximation was introduced44 and the free energy arising from the excluded volume interactions was modeled on the basis of a second virial coefficient by making use of the aforementioned contact probability density. The free energy, including elastic and excluded‐volume contributions, was thereby minimized with respect to all expectation values 〈 l i l j 〉, where { l i } is the set of all bond vectors.…”

Conformations of dendrimers in dilute solution

“…A version of the Gaussian variational theory 15 , which relies on a somewhat problematic 16 virial representation of the excluded volume interactions 17,18 , has been used by Ganazzoli et al for describing the size, shape and intrinsic viscosity of dendrimers in a good solvent 19 . Based on this approach the dynamic properties such as the relaxation times spectrum, dynamic structure factor and the viscoelastic moduli, 20 , as well as the inter-chain theta-temperature 21 have been also investigated.…”

Starlike dendrimers in solutions: Structural properties and internal dynamics

“…8,9 The latter are summarized in more detail below. There are also a few computer simulations 16,17,[35][36][37] and theoretical studies 24,27,[38][39][40][41] addressing this topic.…”

“…However, due to the fact that the dendrimer topology is more complex compared to the architecture of the star polymers, the spectrum of eigenmodes contributing to the structural relaxation is also more complex and involves more extensive theoretical considerations. Theoretical studies on the internal dynamics of dendrimers include theories in the framework of the Rouse model 24 as well as in the Rouse-Zimm model under consideration of hydrodynamic interactions, both with [38][39][40] and without 27,39,41 excluded volume interaction, respectively. We followed the formalism of the Rouse-Zimm model of Cai and Chen 41 for the special case of starburst dendrimers with f = 3 and m =2 and generalized the theory to the case of starlike dendrimers with arbitrary architecture, i.e., arbitrary f, m, and n. In this way we obtain information about the spectrum and the physical nature of the eigenmodes contributing to the structural relaxation of the dendrimers.…”