Self-Diffusion of Polystyrene in a CO 2 -Swollen Polystyrene Matrix: A Real Time Study Using Neutron Reflectivity Ravi R. Gupta, † Kristopher A. Lavery, ‡ Timothy J. Francis, † John R. P. Webster, § Gregory S. Smith, ⊥,# Thomas P. Russell, ‡ and James J. Watkins* ,† Department of Chemical Engineering and Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003; ISIS, Rutherford Appleton Laboratory, Chilton, Didicot, Oxon, OX11 0QX, U.K.; and LANSCE, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Received July 29, 2002 ABSTRACT: The self-diffusivities of high molecular weight polystyrene chains in CO 2-swollen polystyrene matrices were measured in real time using neutron reflectivity. Bilayer films of hydrogenated and deuterated polystyrene (PS) were prepared on silicon substrates and exposed to compressed CO2. The broadening of the interface between the films as a function of time was determined from the reflectivity profiles, yielding the chain diffusivity. Diffusivity was studied as a function of polymer molecular weight, concentration of CO 2 in the polymer film, and temperature. Nearly an order of magnitude enhancement in the diffusivity of polystyrene chains (M ) 2 × 10 5 ), from 1.62 × 10 -16 to 9.35 × 10 -16 cm 2 /s, was found with a modest increase in the concentration of CO2 in the polystyrene (from 8.9 to 11.3 wt %) at 62 °C. This concentration dependence was modeled using the Vrentas-Duda free volume theory. 50-52 At a constant temperature and CO2 pressure the polystyrene diffusivity scaled as M -2.38 . The scaling of the self-diffusivity of PS in CO2-swollen PS with T - Tg, where Tg is the glass transition temperature depressed by the presence of the solvent, is discussed. Introduction Supercritical fluids (SCF’s) such as CO 2 are effective plasticizing agents for most polymers and upon sorption provide a “solventless” route for polymer modification and processing. 1-4 Although the thermodynamics of block copolymer (BCP) ordering in SCF’s has prompted extensive research recently, 5,6 there have been few attempts to understand the dynamics of polymer chains in the presence of CO 2 . Recently, RamachandraRao et al. showed that CO 2 enhances the ordering kinetics in high molecular weight BCP’s such as P(S-b-MMA), producing structures that are difficult or impossible to achieve by thermal annealing. 7 In the melt, ordering is impeded by slow kinetics due to the high degree of entanglement and the microphase separation of the copolymer. Chain mobility is also an important consid- eration in the reactive blending of two or more im- miscible polymers. In reactive blending, end-function- alized polymer chains diffuse through the respective bulk phases to the interface and react, forming a block copolymer that imparts long-term stability to the blend. The slow dynamics of chains in a high molecular weight polymer matrix causes the reaction to be diffusion- controlled. 8-10 CO 2 can be used to increase the mobility of the chains, thereby enhancing the kinetics. 11,12 Re- cently, Roberts et al. studied the reaction kinetics of the solid-state polymerization of poly(bisphenol A carbonate) swollen with CO 2 13 and ascribed the observed enhance- ment in polymerization rate to increased end-group mobility in the plasticized polymer. The diffusion of polymers, both in the melt 14-17 and in solution, 18-24 has been widely studied. In the high molecular weight regime (M > M e , where M e is the entanglement molecular weight) the reptation model, proposed by de Gennes 25 and later modified by Doi and Edwards, 26 captures the basic physics of polymer dy- namics. The theory predicts that the viscosity and diffusion coefficient of polymer chains scale with M 3 and M -2 , respectively, for times longer than the character- istic time for a polymer chain to diffuse a distance equivalent to its contour length (the reptation time). This model predicts five distinct time regimes for the mean-square displacement of the chain segment (g(t)). For times shorter than the reptation time g(t) ∼ t 0.25 . In this regime the entanglements start to influence the dynamics of chain segments relaxing via Rouse modes. At times longer than reptation time, the random walk result is recovered with g(t) ∼ t. Over the past two decades, numerous studies have been performed to test this model. 27-29 Using IR microdensitometry, Klein showed that for high molecular weights polyethylene diffusivity scaled as the inverse square of the molecular weight. 30 Richter et al., using spin echo spectroscopy and rheometry, showed the existence of an intermediate length scale in melts of poly(ethylene-propylene) that reduced the relaxation of the density fluctuation of the chains. 31 Also, the intermediate length scale was in excellent agreement with the entanglement distance predicted from reptation theory. Russell et al. used dynamic secondary-ion mass spectrometry (DSIMS) to demonstrate that polystyrene chains diffuse across the interface in a curvilinear motion, which supports the tenets of reptation. 32 Using Rutherford backscattering and forward recoil spectrometry, Green et al. studied † Department of Chemical Engineering, University of Massa- chusetts. ‡ Department of Polymer Science and Engineering, University of Massachusetts. § Rutherford Appleton Laboratory. ⊥ Los Alamos National Laboratory. # Presently at HFIR Center for Neutron Scattering, Oak Ridge National Laboratory, Oak Ridge, TN 37831. * To whom correspondence should be sent: e-mail watkins@ ecs.umass.edu. 346 Macromolecules 2003, 36, 346-352 10.1021/ma021215r CCC: $25.00 © 2003 American Chemical Society Published on Web 12/28/2002