Crowded, Confined, and Frustrated: Dynamics of Molecules Tethered to Nanoparticles

Above a critical chemistry-dependent molecular weight, all polymer molecules entangle and, as a result, exhibit slow dynamics, enhanced viscosity, and elasticity. Herein we report on the dynamics of low molecular weight polymers tethered to nanoparticles and find that even conventionally unentangled chains manifest dynamical features similar to entangled, long-chain molecules. Our findings are shown to imply that crowding and confinement of polymers on particles produce topological constraints analogous to those in entangled systems.

Figure 1

Broadband dielectric loss ${\epsilon }^{\prime \prime }$ spectra as follows: (a) Untethered polyisoprene with molecular weight ($M_w$) of $5000\mathrm{g}/\mathrm{mol}$. The loss maximum at low frequency corresponds to the normal mode relaxation of the polymer chains. It is also evident that the position of the maximum shifts to higher frequency with increasing temperature, implying thermal speeding up of the polymer chain relaxation. (b) Nanoparticle tethered polyisoprene with molecular weight of $5000\mathrm{g}/\mathrm{mol}$. The volume fraction of silica nanoparticles in this sample is 10%.

Figure 2

Normal mode relaxation time as a function of temperature for untethered (open symbols) and tethered polyisoprene ($M_w=5000\mathrm{g}/\mathrm{mol}$), at different nanoparticle volume fractions. Nanoparticle volume fraction is varied by changing the polymer grafting density.

Figure 3

Comparison of the relaxation time of nanoparticle tethered and untethered PI for different polymer molecular weight. Solid lines are fits with the Vogel-Fulcher-Tamman equation discussed in the Supplemental Material.

Figure 4

Schematic representation of the following: (a) Particle-tethered polymer chain confined in a tube owing to crowding by neighboring chains; (b) Arm retraction mechanism for the relaxation of the tethered polymer chain.