Elastic nonlinearities are particularly relevant for soft materials because of their inherently small linear elasticity. Nonlinear elastic properties may even take over the leading role for the transformation at mechanical instabilities accompanying many phase transitions in soft matter. Because of inherent experimental difficulties, only little is known about third order (nonlinear) elastic constants within liquids, gels and polymers. Here we show that a key concept to access third order elasticity in soft materials is the determination of mode Grüneisen parameters. We report the first direct observation of third order elastic constants across mechanical instabilities accompanying the liquid-liquid demixing transition of semi-dilute aqueous poly(N-isopropylacrylamide) (PNIPAM) solutions. Immense elastic nonlinearities, leading to a strong strain-softening in the phase-separating PNIPAM solutions, are observed. Molecular mechanisms, which may be responsible for these immense elastic nonlinearities, are discussed. The importance of third order elastic constants in comparison to second order (linear) elastic constants in the demixing PNIPAM solutions evidences the need to focus more on the general role played by nonlinear elasticity at phase transitions within synthetic and biological liquids and gels.
A IntroductionFor so condensed matter, knowledge about its continuum mechanics plays a decisive role in understanding the molecular cohesion and organization.1-21 When so matter is subjected to a sufficiently small static strain, the mechanical response is controlled by linear elastic, but not viscoelastic, properties.21 If liquids, gels or polymers are excited by a dynamical mechanical probe, their viscoelastic properties become relevant. This relevance increases with the complexity of the molecular structure in terms of inter-and intramolecular degrees of freedom. At sufficiently high probe frequencies, oen lying in the upper MHz or GHz regime, the mechanical relaxation processes are dynamically clamped and the mechanical response of the system is purely elastic again. Hence, for so materials the mechanical response may be of linear elastic nature when probed either statically or at sufficiently high probe frequencies. In such case, it can be described by Hooke's law, using the second order elastic constants (SOECs) provided by the linear elastic stiffness tensor of 4 th order.Of course linear elasticity only describes one aspect of the complex mechanical behaviour of so matter. The regime of linear elastic response is oen soon abandoned for so materials as the stress or strain amplitude is increased in stress-strain or dynamic mechanical experiments (e.g. ref. 4-6, 8 and 11-14). In order to quantify this nonlinear elastic response of the material within the frame of continuum mechanics, Hooke's law must be extended. Usually the consideration of third order elastic constants (TOECs), but no higher order elastic constants, is sufficient to describe the nonlinear elastic response.
21,22Because of the usually...