Nanoscale Motion of Soft Nanoparticles in Unentangled and Entangled Polymer Matrices

We have studied the motion of polyhedral oligomeric silsesquioxane (POSS) nanoparticles modified with poly(ethylene glycol) (PEG) arms immersed in PEG matrices of different molecular weight. Employing neutron spin echo spectroscopy in combination with pulsed field gradient (PFG) NMR we found the following. (i) For entangled matrices the center of mass mean square displacement (MSD) of the PEG-POSS particles is subdiffusive following a $t^{0.56}$ power law. (ii) The diffusion coefficient as well as the crossover to Fickian diffusion is independent of the matrix molecular weight and takes place as soon as the center of mass has moved a distance corresponding to the particle radius—this holds also for unentangled hosts. (iii) For the entangled matrices Rubinstein’s scaling theory is validated; however, the numbers indicate that beyond Rouse friction the entanglement constraints appear to strongly increase the effective friction even on the nanoparticle length scale imposing a caveat on the interpretation of microrheological experiments. (iv) The oligomer decorated PEG-POSS particles exhibit the dynamics of a Gaussian star with an internal viscosity that rises with an increase of the host molecular weight.

Figure 1

SANS intensity of the PEG-POSS nanoparticles in PEG melts (${\varphi }_{\mathrm{PEG}-\mathrm{POSS}}=0.01$). The line is a fit to a micellar form factor (see text). The inset shows the chemical structure of the POSS core.

Figure 2

Neutron spin-echo data from PEG-POSS nanoparticles in melts of $d$-PEG (a, 1.5; b, 20; c, 80 K). For 4 values of the scattering wave vector $Q=0.07$, 0.09, 0.14 and $0.19{\AA }^{-1}$. The dashed lines show the contribution of NP center of mass diffusion. The solid lines include also the internal dynamics of the PEG arms attached to the POSS particles (see text).

Figure 3

MSD of the POSS particle center of mass diffusion computed from the $Q=0.07{\AA }^{-1}$ NSE data by inversion of Eq. (1), open circles: 1.5 K, triangles and dots: 20 and 80 K $d$-PEG matrix. The dashed lines indicate the MSD extrapolated from NMR results. The dash-dotted line indicates the MSD value which separates the validity regimes of sublinear diffusion (red lines) from that of normal Fickian diffusion (black lines).

Figure 4

NSE data from PEG-POSS in 80 K $d$-PEG divided by the center of mass factor in $S(Q,t)$. The lines correspond to the dynamic contribution of the star shaped arms of the PEG-POSS. The $Q$ values are the same as in Fig. 2.