Relaxation of a single dendrimer

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 τ₁ ∼ f ^1-ν_c {(f - 1)f ^1-ν}^G-1P^2ν+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 _cP^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 τ₁/( 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.