### 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 τ_{1} ∼ f ^{1-ν}_{c} {(f - 1)f ^{1-ν}}^{G-1}P^{2ν+1} for the longest relaxation time τ_{1} is derived, where ν ≈ 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 τ_{1}/( f ^{1-ν} _{c}P^{2ν+1}) is proportional to {( f - 1)f ^{1-x}}^{G-1}, where the exponent x corresponding to is estimated as x ≈ 0.66 for f = 3 and 0.63 for f = 4. It is found that τ_{1}/( f ^{1-ν} _{c} {(f - 1)f ^{1-x}}^{G-1}) ∝ P^{2y+1}, where the exponent y that corresponds to ν 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.

Original language | English |
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Article number | 064801 |

Journal | Journal of the Physical Society of Japan |

Volume | 82 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2013 Jun |

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### Keywords

- Branched polymer
- Brownian dynamics simulations
- Dendrimer
- Excluded volume effects
- Relaxation modes
- Relaxation times
- Single polymer

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*82*(6), [064801]. https://doi.org/10.7566/JPSJ.82.064801

**Relaxation of a single dendrimer.** / Iwaoka, Nobuyuki; Takano, Hiroshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 82, no. 6, 064801. https://doi.org/10.7566/JPSJ.82.064801

}

TY - JOUR

T1 - Relaxation of a single dendrimer

AU - Iwaoka, Nobuyuki

AU - Takano, Hiroshi

PY - 2013/6

Y1 - 2013/6

N2 - 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 fc, 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 τ1 ∼ f 1-νc {(f - 1)f 1-ν}G-1P2ν+1 for the longest relaxation time τ1 is derived, where ν ≈ 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 τ1/( f 1-ν cP2ν+1) is proportional to {( f - 1)f 1-x}G-1, where the exponent x corresponding to is estimated as x ≈ 0.66 for f = 3 and 0.63 for f = 4. It is found that τ1/( f 1-ν c {(f - 1)f 1-x}G-1) ∝ P2y+1, where the exponent y that corresponds to ν 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.

AB - 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 fc, 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 τ1 ∼ f 1-νc {(f - 1)f 1-ν}G-1P2ν+1 for the longest relaxation time τ1 is derived, where ν ≈ 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 τ1/( f 1-ν cP2ν+1) is proportional to {( f - 1)f 1-x}G-1, where the exponent x corresponding to is estimated as x ≈ 0.66 for f = 3 and 0.63 for f = 4. It is found that τ1/( f 1-ν c {(f - 1)f 1-x}G-1) ∝ P2y+1, where the exponent y that corresponds to ν 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.

KW - Branched polymer

KW - Brownian dynamics simulations

KW - Dendrimer

KW - Excluded volume effects

KW - Relaxation modes

KW - Relaxation times

KW - Single polymer

UR - http://www.scopus.com/inward/record.url?scp=84878918122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878918122&partnerID=8YFLogxK

U2 - 10.7566/JPSJ.82.064801

DO - 10.7566/JPSJ.82.064801

M3 - Article

AN - SCOPUS:84878918122

VL - 82

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 6

M1 - 064801

ER -