COMPUTER SIMULATION OF LOCAL MOBILITY IN DENDRIMERS WITH ASYMMETRIC BRANCHING BY BROWNIAN DYNAMICS METHOD

The Brownian dynamics method has been used to study the effect of the branching asymmetry on the local orientational mobility of segments and bonds in dendrimers in good solvent. “Coarse-grained” models of flexible dendrimers with different branching symmetry but with the same average segment length were considered. The frequency dependences of the rate of the spin-lattice relaxation nuclear magnetic resonance (NMR) [1/T_1H(_H)] for segments or bonds located at different distances from terminal monomers were calculated. After the exclusion of the contribution of the overall dendrimer rotation the position of the maxima of the frequency dependences [1/T_1H(ω_H)] for different segments with the same length doesn’t depend on their location inside a dendrimer both for phantom models and for models with excluded volume interactions. This effect doesn’t depend also on the branching symmetry, but the position of the maximum [1/T_1H(ω_H))] is determined by the segment length. For bonds inside segments the positions of the maximum [1/T_1H(ω_H)] coincide for all models considered. Therefore, the obtained earlier conclusion about the weak influence of the excluded volume interactions on the local dynamics in the flexible symmetric dendrimers can be generalized for dendrimers with an asymmetric branching.

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PICTURES

 Fig. 1. Schematic representation of dendrimer models (a), (b) and corresponding branches (b), (g). Symmetrical (a) and asymmetrical (b) dendrimers of the 3rd generation are shown (G=3, where G is the generation number): black, grey and dark grey colors represent the central monomer, branch points and terminal (end) monomers, respectively. The first generation, representing dendrimer core, contains the segments two links in length; in subsequent generations two segments come out of each branch point: two links in length each (a), one link in length and three links in length (c). Schematic representation is given for branches of the symmetric (b) and asymmetric (g) dendrimers. bs  is the vector connecting links in the s-th layer. dmis the vector connecting the segment ends in the m-th layer. The numbering of layers and subgenerations begins with the end groups

 Fig. 2. The frequency dependences [1/T1H (ωH)]m   forsegments, belonging to different subgenerations mfor symmetrical (a) and asymmetrical (b) phantom model, symmetrical (c) and asymmetrical (g) model  with excluded volume (G=5). For symmetric dendrimers the data is shown for two links segments, for asymmetrical – for three links segments (for asymmetric case the frequency dependence of one link in length segments is shown in Fig. 5). For comparison calculation results are shown for segments of two (a), (b) and three links (b), (g) not included in the dendrimer 

  Fig. 3. Time dependence of the autocorrelation function P1 rot(t) for phantom model (a) and the model with the excluded volume (b)

 Fig. 4. The frequency dependences [1/T1H(ωH)]m  obtained after rotation separation as a whole  for segments belonging to different subgenerations m, for the symmetric (a) and asymmetric (b) phantom models (ph.m.) and models with excluded volume (ex. v.) (G=5)

 Fig. 5. The frequency dependences [1/T1H(ωH)]s for the links remoted differently from the end links in dendrimer for symmetric (a) and asymmetric (b) phantom model and symmetric (c) and asymmetric (d) model with excluded volume (G=5). Frequency dependence for separate segment model of two particles connected by a rigid link is also shown

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