Steady state parameters, polymer crystal

An alternative to reorientation of the sample or the magnetic field is the application of shear during the NMR measurement [130-134]. For liquid-crystalline samples with high viscosity, such as liquid crystal polymers, the steady-state director orientation is governed by the competition between magnetic and hydrodynamic torques. Deuteron NMR can be used to measure the director orientation as a function of the applied shear rate and to determine two Leslie coefficients, and aj, of nematic polymers [131,134]. With this experiment, flow-aligning and tumbling nematics can be discriminated. Simultaneous measurement of the apparent shear viscosity as a function of the shear rate makes it possible to determine two more independent viscosity parameters [131, 134]. 

Equations (4.8)-(4.10) have been solved in simple steady state shear flow using Mathematica software (Leonov and Chen 2010). The stress components are expressed as function of shear rate y with the values of constitutive parameters 00, a,p, r, r2,Xe, and t o. Here Oq and t]o represent relaxation time and zero shear viscosity respectively. The other parameters XgandXv represent the tumbling for elasticity and viscosity. Rest of the characteristic parameters a,p,ri,r2 represent anisotropic properties of liquid crystal polymers. Among the eight parameters, only relaxation time and zero shear viscosity are determined from experimental data. The other six parameters can be obtained from cinve fitting data using the Mathematica software. 

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