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Self-assembly is particularly important for soft condensed matter. It may lead to manifold equilibrium or non-equilibrium structures and macroscopic properties of soft materials. The self-organization may be induced by changes in environmental conditions such as temperature, pH and irradiation by light. Among the different polymer families, the stimuli-responsive polymers are particularly sensitive to external stimuli. A structural instability, which is usually related to a demixing phase transition, commonly occurs for stimuli-responsive polymer systems. For such aqueous polymer solutions and hydrogels, a demixing transition of the Lower Critical Solution Temperature (LCST) type often happens, this means that the segregation occurs upon heating. Its macroscopic order parameter is attributed to the difference in mass concentration within the segregated state. Since the variation in mass density is a closely related quantity, the transition is also called a volume phase transition. In case of hydrogels, the order parameter also is the macroscopic deformation. In consequence the related susceptibility is the isothermal compressibility and the demixing transition is denoted as being ferroelastic. In this thesis, basic aspects of the static, kinetic and dynamical nature of the LCSTtype demixing transition are analyzed. Aqueous solutions of the thermo-responsive model homopolymer poly(N-isopropylacrylamide) (PNIPAM) are studied. Part of the phase diagram is probed by varying the polymer concentration in solution and the temperature. In part unconventional experimental techniques were used to access the macroscopic order parameter susceptibilities, like the dynamical volume expansion coefficient, and linear and nonlinear elastic properties at GHz frequencies. The major experimental technique is Temperature Modulated Optical Refractometry (TMOR), which has recently been developed in collaboration with the company Anton Paar (Seelze, Germany) and patented in 2012 by the University of Luxembourg. First studies by Brillouin spectroscopy were carried out on the segregation of aqueous PNIPAM solutions. The linear and in particular nonlinear elastic moduli are much more affected than the thermal expansion coefficient by this phase transition. Furthermore, it could be shown that the specific refractivity is astonishingly sensitive, probably to the changes in molecular interactions, during segregation. This allows for a novel perspective on the microscopic order parameters of the transition. The key investigations of this thesis focus on kinetics and thermo-mechanical relaxation processes related to the segregation, studying optical and mechanical quantities by TMOR. Sinusoidal temperature perturbations were therefore applied around the demixing temperature of different PNIPAM solutions. First direct indications for the location of the binodal and spinodal lines could be