Reptation in Artificial Tubes and the Corset Effect of Confined Polymer Dynamics
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Reptation in Artificial Tubes and the Corset Effect of Confined Polymer Dynamics Rainer Kimmicha, Nail Fatkullinb, Elmar Fischera, Carlos Matteaa, Uwe Beginnc a
Sektion Kernresonanzspektroskopie, Universität Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany b Kazan State University, Department of Physics, Kazan 420008, Tatarstan, Russia c RWTH-Aachen, DWI / ITMC / TexMC, Worringerweg 1, 52056 Aachen, Germany ABSTRACT A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined to nanoscopic strands which in turn are embedded in a quasi-solid and impenetrable methacrylate matrix. Both the molecular weight of the PEO and the mean diameter of the strands are variable to a certain degree. Chain dynamics of the PEO in the molten state was examined with the aid of field-gradient NMR diffusometry (time scale: 10-2 s … 100 s) and fieldcycling NMR relaxometry (time scale: 10-9 s … 10-4 s). The dominating mechanism for translational displacements probed in the nanoscopic strands by either technique is shown to be reptation. A corresponding evaluation formalism for NMR diffusometry is presented. It permits the estimation of the mean PEO strand diameter. Depending on the chemical composition of the matrix, the diameters range from 9 to 58 nm. The strands were visualized by electron microscopy. On the time scale of spin-lattice relaxation time measurements, the frequency dependence signature of reptation, that is T1 ∝ ν 3/ 4 , showed up in all samples. A “tube” diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. This “corset effect” is traced back to the lack of the local fluctuation capacity of the free volume in nanoscopic confinements. The confinement dimension is estimated at which the cross-over from “confined” to “bulk” chain dynamics is expected. INTRODUCTION In the frame of the tube/reptation model [1] polymer chain dynamics is treated under topological constraints represented by a tube the diameter of which is a free parameter. The nature of the “topological constraints” is usually considered to be due to so-called “chain entanglements”. In this model the “tube” is a fictitious object having no real counterpart. This is in contrast to the present study where we examine polymer chain dynamics in artificial “tubes” formed by nanoscopic pores in a solid, impenetrable matrix. Figure 1 shows typical electron micrographs of poly(ethylene oxide) (PEO) strands embedded in a quasi-solid methacrylate matrix [2],[3]. Variation of the chemical matrix composition allows one to vary the strand diameter in a range from 9 to 58 nm [4]. Note that the terms (polymer) “strand” and (matrix) “pore” will be used synonymously in the following. The objective of the present study is to elucidate chain dynamics in a polymer melt confined to such nanoscopic strands embedded in a quasi-solid, impenetrable matrix environment.
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Fig. 1: Typical freeze-fracture electron mic
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