### Date:

**Speaker: **Prof. Romano Lapasin (UniTS)

**Room:** SISSA - Santorio A - room 137

**Abstract: **

Complex systems (typically polymeric and disperse systems) possess molecular or structural length scales much larger than atomic and then they differ from simple liquid and solids whose mechanical behaviour is quite simpler and can be described by linear constitutive equations (the Newton law or the Hooke equation) and hence characterized by a single property (viscosity or elastic modulus), whose value does not depend on flow intensity or deformation amplitude, respectively. Complex systems display mechanical responses that are in a certain sense intermediate between those of liquids and solids because they contain both viscous and elastic components, albeit definitely more complex than in simple systems. Their behaviour is viscoelastic and nonlinear, depending on both type and magnitude of the field conditions (i.e. local stresses, strains or strain rates) as well as on their duration and variation over time. Consequently, diverse material functions must be used in the place of simple properties to fully characterize the viscoelastic responses even under simple (shear or extensional) kinematic conditions. Moreover, for every viscoelastic system the relative balance between viscous and elastic components depends on the timescale at which the system is probed. It is properly weighed through the Deborah number (De), a dimensionless quantity defined as the ratio between the relaxation time of the material, and a time constant, which characterizes the kinematic conditions. At high De the system behaves like an elastic solid, while its response is liquid-like at low De. Far from asymptotic conditions, it displays more or less complex viscoelastic responses, depending on the whole kinematic history previously experienced. Consequently, the viscoelastic behavior can be conveniently characterized only resorting to simple experimental procedures with simple kinematic conditions and histories. The various procedures usually adopted to analyze the rheological responses under shear conditions (at controlled stress, strain or shear rate) are illustrated together with the relevant material functions. Accordingly, the different shear- and time-dependent behaviours exhibited by various polymeric and disperse systems can be distinguished and rationally described. Particular attention is paid to oscillatory tests that permit to characterize the linear viscoelastic behaviour of a material, by defining its mechanical spectrum and the extension of the linear viscoelastic regime as well. So doing, different categories of polymer systems (melts, solutions, gels) can be suitably recognized and rational criteria can be established to individuate the sol/gel transition manifested by several disperse and polymeric systems. The final part of the seminar is dedicated to rheological models, written in differential or integral form, which can be used to describe linear viscoelastic behaviours of different complexity.

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