Relaxation of a Single Dendrimer

Abstract

Relaxation process of a single dendrimer with excluded volume effects is studied in the free-draining limit for various parameters characterizing the architecture of the dendrimer, which are the functionality of central segment f c , the functionality of branching segments f , the number of generations G and the number of bonds in each spacer between branching segments P. By assuming that the dendrimer relaxes hierarchically from the outermost generation to the central segment after relaxation of the spacers, a scaling law 1 $ f 1À c fð f À 1Þf 1À g GÀ1 P 2 þ1 for the longest relaxation time 1 is derived, where % 0:588 is the Flory exponent. Another scaling law for relaxation times of other antisymmetric relaxation modes is also derived. In order to verify the scaling laws, Brownian dynamics simulations of a single dendrimer are performed and relaxation times are estimated by the relaxation mode analysis method. The scaled relaxation time 1 =ð f 1À c P 2 þ1 Þ is proportional to fð f À 1Þf 1Àx g GÀ1 , where the exponent x corresponding to is estimated as x % 0:66 for f ¼ 3 and 0.63 for f ¼ 4. It is found that 1 =ð f 1À c fð f À 1Þf 1Àx g GÀ1 Þ / P 2yþ1 , where the exponent y that corresponds to is estimated as y % 0:58. The agreement with the predicted scaling law becomes better as G and f becomes larger, where the concentration of segments becomes larger. The other scaling law for other antisymmetric relaxation modes is also verified.

The Poisson–Boltzmann–Flory Approach to Charged Dendrimers: Effect of Generation and Spacer Length

“…The role of spacers and their local relaxation behavior were also considered in the study of the relaxation process of a single dendrimer based on the assumption that the molecule relaxes hierarchically from the outermost generation to the first one. As a result, scaling laws for various relaxation times were derived and supported by the results of Brownian dynamics simulations . Furthermore, according to some Monte Carlo simulations, swelling of charged dendrimers appears whose degree is affected by both the reduced temperature and spacer length.…”

“…As a result, scaling laws for various relaxation times were derived and supported by the results of Brownian dynamics simulations. 4 Furthermore, according to some Monte Carlo simulations, swelling of charged dendrimers appears whose degree is affected by both the reduced temperature and spacer length. In particular, for longer spacers the maximum swelling was found to shift to lower temperatures.…”

Dynamics of Shape-Persistent Giant Molecules: Zimm-like Melt, Elastic Plateau, and Cooperative Glass-like

“…In the θ solvent, h is 0.5 and the scaling exponent in the high frequency region correlates with the relaxation modes by 1/(2 – h ) ≈ 0.7. When considering viscoelastic hydrodynamic interaction, a recent approach can also give h > 0. , An alternative mechanism other than hydrodynamics interaction also exists. − In various models of dendrimers solutions, − relaxation modes decay slower than j 2 , h > 0, and scaling exponent larger than 0.5.…”

The Rouse Dynamic Properties of Dendritic Chains: A Graph Theoretical Method

“…Although there exist a number of experimental studies on the dynamic properties of these molecules, ,− little work has been carried out to analyze the dynamics in computer simulations. The simulations on dendrimers were mostly focused on their static properties − rather than dynamic properties ,,, because the relaxation behavior usually requires long simulation time.…”