44858-AC7
X-ray Photon Correlation Spectroscopy Studies of Nanoscale Particle Motion Within Heterogeneous Complex Fluids
We are pursuing a research program that applies x-ray photon correlation spectroscopy (XPCS) to investigate the motion of nanoparticles suspended within glassy polymer melts and concentrated entangled polymer solutions. Due to its access to dynamics at short lengths and long times, XPCS is uniquely well suited to probe the motion of the particles on nanometer length scales. In last year's annual report, we described our study of nanoparticle motion in low-molecular-weight polystyrene (PS) melts in which we observe hyper-diffusive motion overtaking diffusion near the melt glass transition. We ascribe this hyper-diffusive motion to strain in response to heterogeneous stress relaxation [1]. In this report, we describe our main findings on the nanoparticle dynamics within entangled solutions. Here, we observe sub-diffusive motion that we associate with transient constraints of entanglements inhibiting particle mobility.
The experiments focus on nanometer-scale gold particles within highly entangled, concentrated PS solutions in xylene with polymer volume fractions ranging from c = 0.1 to 0.3 and polymer molecular weights between Mw = 3x105 g/mole and 3x106 g/mole. The Au particles have a radius of approximately 2 nm and are in a highly dilute concentration within the melt (Au volume fraction 0.0004). The particle surfaces are functionalized with a dense coverage of PS chains with molecular weight of approximately 13000 g/mole to stabilize the particles against aggregation. The resulting coronae give the particles a hydrodynamic radius of about 20 nm in xylene, as determined by dynamic light scattering. In the PS solutions, the dynamic structure factor, f(q,t), that we extract for the particle motion from the XPCS measurements is highly stretched. Specifically, f(q,t) ~ exp(-(t/t0)b), where q is the wave vector, t0 is the wave-vector-dependent correlation time, and the stretching exponent b falls in the range 0.3 < b < 0.5. (The wave-vectors covered by the measurements span 0.03 nm-1 < q < 0.2 nm-1.) The correlation times vary as a power law with the wave vector, t0 ~ q-p, with the exponent p in the range -6 < p < 4, so that the product b*p is approximately 2 as expected for particles undergoing uncorrelated thermal motion. These results imply that the mean-squared displacement MSD of the nanoparticles grows with time as MSD ~ tb. That is, the motion is strongly sub-diffusive. (b = 1 for diffusion.)
The obvious question that these results raise is: What are the dominant microscopic mechanisms that lead to this sub-diffusive motion? We note that one previous observation with dynamic light scattering of sub-diffusive colloidal dynamics in entangled and cross-linked polymer solutions has been reported [2]. In that paper, association of the particles with the polymer mesh was identified as being an important factor, and the particle motion was interpreted as Rouse-like dynamics. While such an interpretation is plausible also for our observations, particularly if one considers the possibility that the particles associate with surrounding polymer through entanglements of the PS chains on the nanoparticle surfaces, we can discount a Rouse mechanism for our system based on the molecular-weight dependence of the motion. Specifically, we find that t0 ~ Mw2, while Rouse dynamics should be independent of Mw. This strong dependence on molecular weight within such highly entangled solutions instead indicates that the dynamics of entanglements play an important role in dictating the sub-diffusive motion. We also find that the particle motion depends strongly on polymer concentration and that t0 has approximately the same temperature dependence as the viscosity of the solutions, indicating that the motion is coupled to the macroscopic mechanical properties. However, for these entangled concentrated solutions, the viscosity h varies with molecular weight as h ~ Mw3.4, an even stronger dependence than we observe for the sub-diffusive nanoparticle motion. Thus, the motion does not scale trivially with the macroscopic viscosity, despite the similarity in temperature dependences. Instead, the particle motion appears to be providing unique, local information about the micromechanical properties of the entangled polymer solutions particularly in regards to how the transient mesh created by the entanglements relaxes. Further analysis and modeling of these results is currently underway.
[1] H. Guo, G. Bourret, M. K. Corbierre, S. Rucareanu, R. B. Lennox, K. Laaziri, L. Piche, M. Sutton, J. L. Harden, and R. L. Leheny, submitted.
[2] J. Sprakel, J. van der Gucht, M. A. Cohen Stuart, and N. A. M. Besseling, Phys. Rev. Lettt. 99, 208301 (2007).
