Hidden Hyperuniformity in Soft Polymeric Materials

We investigate the nature of long-range density fluctuations in melts of model “soft” polymers, specifically stars and bottlebrushes, over a wide temperature range by molecular dynamics simulation. The cores of the stars and the backbones of bottlebrush polymers are found to have a hyperuniform distribution; i.e., they exhibit anomalously small density fluctuations over a wide temperature range above the glass transition temperature. The hyperuniformity of these substituent polymer subregions is hidden since the fluid as a whole does not exhibit this property. These findings offer a strategy for the practical design of hyperuniform polymeric materials.

Figure 1

Total static structure factor $S(q)$ (continuous line) and partial structure factors of star and bottlebrush polymer melts. The relation between the $S(0)=\rho k_{B}T{\kappa }_T$ for $S(q)$ and a schematic of the packing for bottlebrush and star polymers are also presented.

Figure 2

Partial static structure factor of bottlebrush polymer melts, corresponding to backbone correlations $S_b(q)$ (symbols), and of star polymers, corresponding to core particle correlations $S_{\mathrm{c}}(q)$ (continuous lines). Results for different temperatures are also presented. The dashed lines correspond to fits based on a power-law relation: $S_b(q)=S_0(1+c{q}^2)$, where $c$ and $S_0$ are fitting parameters. The dot-dashed line corresponds to $S_b(q)=1.1q^2$. Inset: Radial distribution function of the intra- and interbackbone chains at $T=0.8$, represented by the blue dashed line and continuous red line, respectively.

Figure 3

Hyperuniformity parameter of bottlebrush polymer melts as a function of temperature $T$. Results for total and backbone correlations are presented. The highlighted regions represent the regions at which glassy dynamics and the hyperuniform states emerge. The dot-dashed lines corresponds to the $h$ parameter found for polymer grafted nanoparticles; for details see Ref. [26]. The upper double dot-dashed line shows $h$ for a reference linear polymer melt [21] and the data are described by a power law relation, $h=c{T}^{\delta }$ and $(c,\delta )=(0.03,2.69)$. Correspondingly, we find $(c,\delta )=(0.00174,2.12)$ and $(c,\delta )=(0.00033,1.87)$ for the bottlebrush backbones and star cores, respectively.