Browsing by Subject "Fractional Calculus"

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    Uniaxial Extensional Behavior of A–B–A Thermoplastic Elastomers: Structure-Properties Relationship and Modeling
    (2015-05) Martinetti, Luca
    At service temperatures, A–B–A thermoplastic elastomers (TPEs) behave similarly to filled (and often entangled) B-rich rubbers since B block ends are anchored on rigid A domains. Therefore, their viscoelastic behavior is largely dictated by chain mobility of the B block rather than by microstructural order. Relating the small- and large-strain response of undiluted A–B–A triblocks to molecular parameters is a prerequisite for designing associated TPE-based systems that can meet the desired linear and nonlinear rheological criteria. This dissertation was aimed at connecting the chemical and topological structure of A–B–A TPEs with their viscoelastic properties, both in the linear and in the nonlinear regime. Since extensional deformations are relevant for the processing and often the end-use applications of thermoplastic elastomers, the behavior was investigated predominantly in uniaxial extension. The conceptual basis of the theories underlying each topical area was explained while the emphasis was kept on fundamental principles and the molecular viewpoint. The analysis herein is independent from the specific choice of the constituent blocks and thus applies to any microphase-segregated thermoplastic elastomer of the A–B–A type. The unperturbed size of polymer coils is one of the most fundamental properties in polymer physics, affecting both the thermodynamics of macromolecules and their viscoelastic properties. Literature results on poly(D,L-lactide) (PLA) unperturbed chain dimensions, plateau modulus, and critical molar mass for entanglement effect in viscosity were reviewed and discussed in the framework of the coil packing model. Self-consistency between experimental estimates of melt chain dimensions and viscoelastic properties was discussed, and the scaling behaviors predicted by the coil packing model were identified. Contrary to the widespread belief that amorphous polylactide must be intrinsically stiff, the coil packing model and accurate experimental measurements undoubtedly support the flexible nature of PLA. The apparent brittleness of PLA in mechanical testing was attributed to a potentially severe physical aging occurring at room temperature and to the limited extensibility of the PLA tube statistical segment. The linear viscoelastic response of A–B–A TPEs was first examined at temperatures where the A domains are glassy. Characteristic length scales and tube model parameters were determined, and the role of the glassy A domains on the entangled rubbery B network was assessed. Thermo-rheological complexity, observed near and below Tg,A, was attributed to augmented motional freedom of the B block ends at the corresponding A/B interfaces, in harmony with the theoretical treatment of thermo-rheological complexity for two-phase materials developed by Fesko and Tschoegl. When the magnitude of the steepness index was taken into account, the shift behavior was analogous to the response measured for pure B melts. Building upon the procedure proposed by Ferry and co-workers for entangled and unfilled polymer melts, a new method was developed to extract the matrix monomeric friction coefficient ζ0 from the linear response behavior of a filled system in the rubber-glass transition region, and to estimate the size of Gaussian submolecules. Stress relaxation beyond the path equilibration time was found qualitatively and quantitatively compatible with dynamically undiluted arm retraction dynamics of entangled dangling structures (originating either from a fraction of triblock chains having one end residing outside A domains or from diblock impurities). By employing tube models and rubber elasticity theories, suitably modified to account for microphase-segregation, the linear elastic behavior across the rubbery plateau and up to the entanglement time was modeled, and a simple analytical expression relating the Langley trapping factor with the fraction of entangled and unentangled dangling structures of the material was obtained. The critical-gel-like behavior typical of A–B–A TPEs at service temperatures approaching Tg,A was analyzed in terms of a power-law distribution of relaxation times derived from the wedge distribution, shown to be equivalent to Chambon–Winter's critical gel model and to the mechanical behavior of a fractional element. A relation between the observed power-law exponent and molecular structure was established. The measured low-frequency response, originating from the incipient glass transition of the A domains, was exploited and extrapolated to lower frequencies via a sequential application of the fractional Maxwell model and the fractional Zener model. With only a few, physically meaningful material parameters a realistic description of the A–B–A self-similar relaxation was obtained over a frequency range much broader than the experimental window and not accessible via time-temperature superposition. The relationship between large-strain response and network structure of A–B–A triblocks was investigated, by examining (1) the effect of linear relaxation mechanisms on the tensile behavior, (2) the sources of elastic and viscoelastic nonlinearities, and (3) the strain rate dependence of the ultimate properties. Because of the numerous typos that appear in the original papers as well as in a recent Macromolecules review, a detailed analysis of the Edwards–Vilgis slip-link model was performed and the main steps leading to the determination of the chemical and topological contributions to the reduced stress were outlined. After establishing an operational definition of initial modulus for critical-gel-like materials subjected to start-up extensional tests, it was possible to determine the relationship between the dimensionless stress in tensile tests at constant strain rate and the step-strain extensional damping function. Based on the molecular picture of the strain-induced structural changes gained from exposing time and strain effects, the governing mechanism of rupture was identified with ductile/fragile rupture of A domains. To the best of our knowledge, this is the first experimental evidence linking the strain rate dependence of ultimate properties of triblock TPEs to the strain-induced glass-rubber transition of the domains. In addition, experimental results on the ultimate properties of A–B–A/B–A blends were consistent with this mechanism of rupture. For the first time in the literature, the complex high-dimensional rheological signature of chewing gum was analyzed, especially in response to nonlinear and unsteady deformations in both shear and extension. A unique rheological fingerprint was obtained that is sufficient to provide a new robust definition of chewing gum that is independent of specific molecular composition.