Small Angle Neutron Scattering Observation of Chain Retraction after a Large Step Deformation

Abstract

Article:Blanchard, A., Graham, R.S., Heinrich, M. et The process of retraction in entangled linear chains after a fast nonlinear stretch was detected from time-resolved but quenched small angle neutron scattering (SANS) experiments on long, well-entangled polyisoprene chains. The statically obtained SANS data cover the relevant time regime for retraction, and they provide a direct, microscopic verification of this nonlinear process as predicted by the tube model. Clear, quantitative agreement is found with recent theories of contour length fluctuations and convective constraint release, using parameters obtained mainly from linear rheology. The theory captures the full range of scattering vectors once the crossover to fluctuations on length scales below the tube diameter is accounted for. Both fundamental and applied understanding of polymer dynamics through the use of molecular based theories has seen rapid progress in the past 20 years [1]. This progress stems from the realization that surrounding chains severely limit global motion of a test chain in directions perpendicular to its contour but do not prohibit motion along it, confining each chain to a tubelike region defined by its own contour [2]. This physical picture is beautifully cast into a physical theory by the reptation model of de Gennes [3]. The current challenge is to augment this concept of onedimensional diffusion of a chain along a tube into a quantitative molecular approach describing both the linear and nonlinear rheological properties as well as the underlying molecular motions [4 -6].One important question in this context relates to the chain relaxation in elongational flow. A large step extensional elongation is expected to affinely deform the chain contour. This will cause the chain radius of gyration parallel to the flow to increase and conversely the one in the perpendicular direction to decrease. After cessation of the strain, one expects the first relaxation process to be a retraction of the chain within the still affinely deformed tube. The longest time scale of this process should be the equilibration time R (Rouse time) of the chain along the tube. This mechanism is related by a fluctuationdissipation theorem to the chain contour length fluctuations, entropically driven extension and retraction of the chain contour which recently was corroborated directly on a molecular level [7].Chain retraction in the elongated tube should reduce the radius of gyration in all directions. Therefore R perp g is expected to attain a minimum, manifested as an increase in perpendicular scattered intensity, at some time after the deformation determined by the Rouse time, before diffusive mechanisms return it to equilibrium. This nonmonotonic behavior, with the minimum at a time consistent with the time scale of Rouse chain retraction, was not observed in previous experiments on polystyrene [8,9] and poly(ethylethylene) melts [10]. The requirement of a measurable Rouse time demanded prohibitively large overall chain dimensions so observations were pos...

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