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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, oen 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 oen 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...

The phase separation of aqueous poly(N-isopropyl acrylamide) (PNIPAM) solutions is known to strongly affect their volume expansion behaviour and the elastic moduli, as the latter are strongly coupled to the macroscopic order parameter. On the molecular scale, considerable changes in H-bonding and hydrophobic interactions, as well as in the structure govern the demixing process. However, the relationship between the molecular and macroscopic order parameters is unclear for such complex phase-separating solutions. We contribute to the clarification of this problem by relating optical to volumetric properties across the demixing transition of dilute to concentrated aqueous PNIPAM solutions. Far from the demixing temperature, the temperature dependence of the refractive index is predominantly determined by thermal expansion. In the course of phase separation, the refractive index is dominated by the anomalous behaviour of the specific refractivity, which reflects the spatio-temporally averaged changes in molecular interactions and the structural reorganization of the demixing solutions. Moreover, the presence of relaxation processes is studied by the complex expansion coefficient using the novel technique of temperature modulated optical refractometry.

The demixing process of aqueous poly(N-isopropylacrylamide) (PNIPAM) solutions can occur either via a nucleation and growth process or via spinodal decomposition. The ensuing self-assembly, leading to heterogeneous morphologies within the PNIPAM solution, is codetermined by kinetic processes caused by molecular transport. By subjecting PNIPAM solutions to cyclic changes in temperature leading to repeated crossing of the demixing transition, we are able to assess the importance of kinetics as well as of overheating and supercooling of the phase transition within the metastable range delimited by the binodal and spinodal lines. First indications about the location of these stability limits for the low-and high-temperature phases, separated by about 1.6 K, could be gained by detailed kinetic studies of the refractive index. These investigations are made possible due to the novel technique of temperature-modulated optical refractometry.

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