Length scale of dynamic heterogeneity in polymer nanocomposites

Using Xray photon correlation spectroscopy measurements on gold nanoparticles embedded in polymethylmethacrylate we provide evidence for existence of an intrinsic length scale for dynamic heterogeneity in polymer nanocomposites similar to that in other soft materials.We also show how the dynamics varies in a complex way with various parameters. Polymer nanocomposites (PNC) are a novel class of multifunctional hybrid materials which are obtained by appropriate mixing of nanoparticles and polymers leading to a wide range of applications in terms of their unique electrical, optical, and thermo-mechanical properties [ 1 4 ]. They also belong to this new class of materials, under the umbrella of soft glassy materials, which exhibit rich and complex thermal, mechanical and rheological behavior [ 5 11 ]. Extensive experimental work has been performed over the decade or so on studying the modifications of thermal and mechanical properties imparted to the matrix polymer by addition of nanoparticles of various shapes and sizes [4,12-15]. Numerical simulations and theoretical calculations have started to emerge in the meanwhile to provide some insight and understanding into the static structure and phase behavior in various model nanoparticle polymer hybrid systems [16-20]. Homogeneous dispersion of nanoparticles in polymer matrices is a major obstacle [3] towards the ultimate goal of obtaining high performance materials. In this respect it has been observed by us [4] and a few other groups [21] that using a polymer capped nanoparticle in a matrix of chemically matched homopolymer matrix is a very effective way of ensuring homogeneous dispersion. However, the theory and simulations for the static structure and phase behavior for such systems are only just beginning to emerge [16-20] and a microscopic theory to treat the dynamics, of both polymer capped and uncapped nanoparticles in polymer matrices, including viscoelasticity, glass formation or diffusion of nanoparticles does not exist. Dynamics of soft glassy materials is extremely rich and complex [5,7,22-24 ]. Depending on various parameters like volume fraction, (φ) and temperature , (T) such systems exhibit complex slow dynamics characteristic , of glassy or jammed phase [5,7, 22-24 ]. Dynamic heterogeneity is a key feature of such systems and evidence of length scale dependent dynamic heterogeneity has been observed in simulations [ 10,25-26 ]and certain experiments [27, 28]. In this communication we provide evidence for existence of a length scale of dynamic heterogeneity for PNC. We also provide the first glimpse of the complexity and richness of phase behavior in dynamics of polymer nanocomposites as a function of φ, T and the wave vector, q , through detailed synchrotron multi-speckle x-ray photon correlation spectroscopy (XPCS) measurements. In XPCS one measures the intensity autocorrelation function [9,11,14,29], g2(q, t) = 1 + b| f (q, t)|. (1) Here, f (q, t) is the intermediate scattering function (ISF), b is the speckle contrast and t is the delay time. We have used ISF of general form, f (q, t) = exp − (t/τ), (2) 1 ar X iv :0 80 9. 52 55 v1 [ co nd -m at .s of t] 3 0 Se p 20 08