Our research is oriented to investigation of rheological and dynamic behaviors of polymer and related materials. Although we basically prefer theoretical approaches, we do experiments to support or apply theoretical investigations. Our research is balanced between purely academic one and practical applications to industries. We study deformation and flow of complex materials including polymer melts, polymer solutions, suspensions, and so on.



   Rheology can be used as a tool to identify molecular structure of polymers such as molecular weight distribution, structure of branch and mesoscopic ordered structure. For example, the length of long chain branch has not been analyzed by other conventional instruments such as infrared spectroscopy, nuclear magnetic resonance and light scattering. It is known that rheological measurement is most sensitive for nonlinear chain structure of branched polymers. Recent molecular theories can predict linear viscoelastic behavior of complex branched polymers with distributions of molecular weight and branching. However, it has not been developed how to identify the structure of branch polymers from viscoelastic measurement. Since difference in the structure of branched polymers results in small difference in linear viscoelasticity, it is expected that nonlinear viscoelasticity may be effective to analyze the structure of branched polymers.



   LAOS (Large Amplitude Oscillatory Shear) is one of the most convenient methods for nonlinear viscoelastic measurements. Conventional interpretation methods for the nonlinear data are the Fourier transform and strain sweep test. However, these methods suffer from weak physical basis. Recently, we developed a new theory which characterizes LAOS data on physical basis. The theory decomposes the shear stress of LAOS into elastic and viscous contributions.
Shear stress is no longer a sinusoidal function of time under large amplitude oscillatory shear flow. Thus, the well-developed theories of linear viscoelasticity cannot be applied to the interpretation of the nonlinear data. When the deviation from a sinusoidal function is small, dynamic moduli obtained from rheometer under strain sweep test mode may be a good approximation. However, they are not exact. We developed a new interpretation method, called stress decomposition, by using the symmetry of shear stress which must be an odd function of deformation. In stationary oscillatory flow, it is a reasonable assumption that shear stress is a function of strain and its time-derivatives. Since time-derivatives of strain of any order must be proportional to strain or strain rate in stationary oscillatory flow, it is clear that the shear stress is a function of strain and strain rate only. Then, we can decompose the shear stress into two parts: one is odd for strain and even for strain rate and the other is even for strain and odd for strain rate. It can be proved that the former is elastic and the latter is viscous. Since the elastic stress is in phase with strain and the viscous stress is in phase with strain rate, it is easy to identify the functional form of the shear stress as a function of strain and strain rate.


   Linear viscoelastic data can be measured in different types such as dynamic moduli, relaxation modulus and creep compliance. However, linear viscoelastic theory allows them to be converted to each other. The conversion relations can be done easily through the concept of relaxation spectrum. Unfortunately relaxation spectrum cannot be measured directly but it can be calculated from other measurable viscoelastic functions. Calculation of relaxation spectrum is known as ill-posed problem. We study development of new algorithms for both continuous and discrete spectra.


   Constitutive models or constitutive equations are models for material properties on deformation and flow. Hence it is used to be called rheological equation of state. Our philosophy for constitutive equation is that the constitutive equation must satisfy fundamental physical laws such as thermodynamics and conservation laws. We study the way to simplify micro mechanics of materials with preserving momentum balance and the second law of thermodynamics in order to develop a nonlinear viscoelastic constitutive equation. For example, Doi-Edwards model for nonlinear viscoelasticity does not consider the momentum conservation in the motion of polymer chain because it is based on Brownian dynamics of polymer chain which does not satisfy momentum conservation.