pubs.acs.org/Macromolecules Published on Web 08/18/2009 r 2009 American Chemical Society Macromolecules 2009, 42, 7091–7097 7091 DOI: 10.1021/ma901122s Polymer Diffusion Exhibits a Minimum with Increasing Single-Walled Carbon Nanotube Concentration Minfang Mu, † Nigel Clarke, ‡ Russell J. Composto, † and Karen I. Winey* ,† † Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6272, and ‡ Department of Chemistry, Durham University, Durham DH1 3LE, United Kingdom Received May 22, 2009; Revised Manuscript Received August 6, 2009 ABSTRACT: Nanoparticles present a new frontier for understanding polymer dynamics in complex, nanoscale environments. We report that the addition of single-walled carbon nanotubes (SWCNTs) produces a minimum in the diffusion coefficient with increasing nanoparticle concentration, φ. Initially, tracer diffusion coefficients (D) are suppressed with increasing φ and then increase beyond a critical concentration, φ crit < 1 vol %. Shorter tracer chains exhibit a greater slowing down than longer chains, whereas longer matrix chains decrease the value of φ crit . The experimental results are discussed in terms of locally anisotropic diffusion perpendicular and parallel to the nanotube filler and simulated using a trap model that defines a trap size and the extent of slowing perpendicular to the cylindrical trap. The simulated diffusion coefficients capture both the initial decrease in D attributed to isolated traps and the recovery of D above φ crit corresponding to trap percolation. Nanoparticles influence polymer diffusion in fascinating ways and will refine our understanding of polymer reptation and might also inform the study of biopolymer diffusion in living systems. 1. Introduction In 1855, Fick surmised that the flow of matter is analogous to the flow of heat and electricity and proposed that the flux of matter is proportional to its concentration gradient and later the chemical potential gradient. 1,2 Fick’s first law persists as the model for determining macroscopic diffusion coefficients. Sub- sequently, the atomic and molecular scale mechanisms of diffu- sion have been elucidated starting with Einstein’s 1906 work on liquids 3 and more recently with de Gennes’ 1971 reptation mechanism for polymer melts. 4 The reptation model describes the motion of a polymer along its contour as it passes the physical constraints imposed by the surrounding polymers and predicts the molecular weight dependence of the macroscopic diffusion coefficient. Polymer diffusion studies first focused on simple linear chains in matrices of equally simple polymers, 5,6 while subsequent studies explored more complex architectures includ- ing branched molecules, star molecules, and loops. 5,7-10 Here we investigate the diffusion of linear polymers in the presence of nanoparticles. Nanoparticles with desirable proper- ties are now widely available, and there has been an explosion of activities focused on combining nanoparticles with polymers to create polymer nanocomposites with unique and valuable prop- erties. 11-13 Nanoparticles also provide access to a new range of size differences between particles and polymers, wherein the radius of gyration (R g ) of the polymer is considerably larger than the nanoparticle. For example, C 60 fullerenes have diameters of 0.7 nm and a polystyrene (PS) of 75 000 g/mol molecular weight has 2R g = 15 nm. The addition of nanoparticles to polymers provides a new challenge to building a fundamental understanding of polymer dynamics in complex environments. In the example of C 60 and PS, one might predict that the addition of the nanoparticles to a polymer would act as a diluent and thereby smoothly increase both the free volume of the system and the diffusion coefficient as the fullerene concentration increases. In contrast, this study reports that the addition single-walled carbon nanotubes (SWCNTs) produces a minimum in the diffusion coefficient with increasing nanoparticle concentration. Thus, the addition of nanoparticles to polymers has unforeseen consequences on poly- mer diffusion, which in turn has direct impact on practical problems, such as the stability of nanoparticle dispersions. Since the 1980s, elastic recoil detection (ERD) has been used to study polymer diffusion 14 and thereby played a key role in testing leading polymer diffusion theories including reptation, constraint release, and mutual diffusion. 5,15,16 ERD is an ion beam techni- que that directly provides a concentration profile of diffusing species, typically a deuterated polymer, as a function of depth into a matrix. Polymer dynamics can also be explored using rheology, but this is limited to nanocomposites with low nano- particle concentrations to avoid solidlike behavior. 17 Gas permeability can indirectly probe polymer dynamics but is inappropriate when using SWCNTs because small molecules can be transported inside carbon nanotubes. 18,19 Using ERD, we follow tracer diffusion of deuterated polystyrene (dPS) in polystyrene (PS) nanocomposites to understand the influence of SWCNTs on polymer dynamics. This new understanding will enable better manipulation of polymer nanocomposite properties and melt processing, and could impact our understanding of macromolecular movement in living cells. 20,21 2. Experimental Methods 2.1. Materials. Single-walled carbon nanotubes were synthe- sized by a high-pressure carbon monoxide conversion (HiPco) method at Rice University. Raw SWCNTs were purified by thermal oxidization and a HCl treatment. 22 The residual metal is <5 wt %, as measured by TGA. Polystyrenes (PS) and deuter- ated polystyrenes (dPS) were purchased from Pressure Chemical and Polymer Source, respectively, and all used as received (Table 1). *Corresponding author: Tel 215.898.0593; Fax 215.573.2128; e-mail winey@seas.upenn.edu. Downloaded by UNIV OF PENN on September 16, 2009 | http://pubs.acs.org Publication Date (Web): August 18, 2009 | doi: 10.1021/ma901122s