Generalized Gaussian Structures: Models for Polymer Systems with ComplexTopologies

Gurtovenko, Andrey A.; Blumen, A.

doi:10.1007/b135561

Cited by 126 publications

(220 citation statements)

References 227 publications

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“…For example, the intrinsic viscosity of a dendrimer with the hydrodynamic interaction shows a maximum as the generation increases, 7,35,36) while for linear and star polymers it increases monotonically with the molecular weight. 2,4,37) Since the intrinsic viscosity is associated with the relaxation modes, 2,6) it is interesting how the picture of the relaxation process discussed in the present study relates to such unique features in the presence of the hydrodynamic interaction. …”

Section: Summary and Discussionmentioning

confidence: 85%

“…[1][2][3][4][5][6] As new polymeric materials with complex architectures are synthesized, it becomes more important to reveal the relation between the architecture of polymers and their dynamic behavior. In particular, much recent interest has been focused on branched polymers.…”

Section: Introductionmentioning

confidence: 99%

“…2,6,[13][14][15][16][17][18][19][20][21][22][23] The relaxation modes fX p g satisfy hX p ðtÞX q ð0Þi / p;q expðÀ p tÞ, where hX p ðtÞX q ð0Þi denotes the equilibrium correlation of X p at time t and X q at time 0. The quantity p is called the relaxation rate of X p and the reciprocal of p gives the corresponding relaxation time, i.e., characteristic time of the pth mode.…”

Section: Introductionmentioning

confidence: 99%

“…[13][14][15][16][17] In the case of simple Gaussian chains, which consist of beads connected by linear springs without excluded volume effects and hydrodynamic interaction, the relaxation modes are identical to the normal coordinates of the linear Langevin equation for the beads and can be calculated exactly in a straightforward way, even if the topology becomes complex. 6) The relaxation modes and related properties of the Gaussian chains have been studied in detail for branched polymers such as stars or dendrimers. 6,[18][19][20][21] Moreover effects of hydrodynamic interaction on such Gaussian chains were studied in terms of preaveraging approximation.…”

Section: Introductionmentioning

confidence: 99%

“…6) The relaxation modes and related properties of the Gaussian chains have been studied in detail for branched polymers such as stars or dendrimers. 6,[18][19][20][21] Moreover effects of hydrodynamic interaction on such Gaussian chains were studied in terms of preaveraging approximation. 22,23) However the excluded Fig.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Relaxation of a Single Dendrimer

Iwaoka

Takano

2013

J. Phys. Soc. Jpn.

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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.

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Section: Summary and Discussionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Relaxation of a Single Dendrimer

Iwaoka

Takano

2013

J. Phys. Soc. Jpn.

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References

2016

Magnetic Resonance Elastography

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Models for the Dynamics of Hyperbranched Macromolecules

Blumen¹,

Jurjiu²,

Koslowski

et al. 2006

Macromolecular Symposia

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Summary:We focus on the motion of hyperbranched macromolecules in solution, paying particular attention to the relation between underlying topological structure and dynamics; we consider especially the mechanical moduli. Under the prominent representatives of hyperbranched polymers are both regular structures (such as the dendrimers) as well as disordered structures (such as irregular Cayley-trees). Evidently, batch-prepared hyperbranched macromolecules are closer to the latter. In order to theoretically determine their mechanical moduli we employ the method of generalized Gaussian structures (GGS), which allows us to study the situation including or excluding the hydrodynamic interactions (HI). Disordered hyperbranched structures display a complex dynamics; here we recall several analytical and numerical schemes for determining it and compare our theoretical results to the experimental data.

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Generalized Gaussian Structures: Models for Polymer Systems with ComplexTopologies

Cited by 126 publications

References 227 publications

Relaxation of a Single Dendrimer

Relaxation of a Single Dendrimer

References

Models for the Dynamics of Hyperbranched Macromolecules

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