The relaxation of concentrated polymer solutions

The focus of this paper is on the viscoelastic properties of concentrated polymer solutions and polymer melts. Dynamic mechanical measurements were performed on various polystyrene/ethylbenzene solutions with polymer concentrations ranging from 40% up to 100% and temperatures from Tg+30°C up to 70°C (230°C for polymer melts). The basis polymers are two commerical grade polystyrenes (BASF) with M _W = 247 kg/mol and 374 kg/mol, respectively. To avoid solvent loss due to evaporating during the measurements, a special sealing technique was used.A phenomenological model which describes quantitatively the relaxation spectrum of concentrated polymer solutions from the flow regime up to the glass transition regime is developed. The relaxation data of the respective polymer melt and the glass transition temperature of the solution are the only input parameters needed. The temperature dependence is described by a universal, concentration invariant WLF-equation. The relaxation spectra are divided into two parts accounting for the entanglement and the segmental relaxation modes, respectively. The relaxation strength related to the flow and entanglement regime scale with c ^2.3, whereas the segmental relaxation strength does not alter with concentration. All relaxation times change with concentration proportional to c ^3.5. Flow curves can be calculated from these relaxation spectra and thus, our results are useful for engineering applications.Roman Symbols a _T Time temperature superposition shift - factor - a _c Time concentration superposition - shift factor in the flow regime - a _c Time concentration superposition - shift factor in the glassy regime - b _T Modulus temperature superposition - shift factor - b _c Modulus concentration shift factor - in the flow regime - b _c Modulus concentration shift factor - in the glassy regime - B Virial coefficients - c Polymer mass fraction kg/kg - c ₁ WLF-parameter - c2 WLF-parameter K - g Relaxation strength of a relaxation Pa mode - G(t) Relaxation modulus Pa - G Storage modulus Pa - G Loss modulus Pa - GN Plateau modulus of linear flexible Pa polymers - (x) Delta function: (0) = 1, - (x<>0)=0 - h() Damping function - H() Relaxation spectrum Pa - J ₀ ^N Recoverable compliance Pa^–1 - m Mass kg - M _c Critical molecular weight kg/mol - M _e Entanglement molecular weight kg/mol - M _w Weight average molecular weight kg/mol - M Number of datapoints - n Scaling exponent - N Number of discrete relaxation modes - T Temperature °C - T _g Glass transition temperature °C - V Volume 1 Greek Symbols Scaling exponent - _f Thermal expansion coefficient K^–1 - Scaling exponent - Shear deformation - Shear rate s^t–1 - Relaxation time s - _c Characteristic relaxation time of thes Cross model - _e Entanglement relaxation time s - Viscosity Pa s - ₀ Zero shear viscosity Pa s - ₀ First normal stress coefficientPa s2 - Segmental friction coefficient - Frequency rad/s Indices f Flow and entanglement regime - g Glass transition regime - i Count parameter - p Polymer - ref Reference state - s Solvent Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland