Viscoelastic ECAH: Scattering analysis of spherical particles in suspension with viscoelasticity

Particle elastic modulus analysis of waterborne polyurethane nanoparticles by ultrasound scattering method

“…In previous studies, we have performed various particle analyzes and found very good agreement between experiment and ECAH theory. 8,21,32,33,44,45) For α, the solid line is relatively satisfactory for experimental results. On the other hand, for the phase velocity, it deviates beyond the error in our experimental accuracy.…”

“…In previous studies of validation, homogeneous spherical particles in the glassy state were often used, and in such cases, the ECAH-LB model successfully reproduced the experimental results when the bulk polymer sheet was measured separately and the results were substituted as the particle properties. 8,45) The difference between the particle properties and those of the bulk polymer sheet in this case is clearly beyond experimental error, suggesting that the particle properties are different from those of the bulk polymer. In the future, such analysis will be useful for monitoring the film formation process, etc.…”

“…Although not shown here, micron-sized particles were prepared by emulsifying WPU in water and examined for the appearance of specific resonance scattering (quadrupole) peaks in the megahertz frequency region, 8,45) no such peaks originating from solids were observed. Hence, this droplet can be regarded as a liquid with c S2 = 0 in the ultrasonic frequency range.…”

Relation between quadrupole ultrasonic resonance and shear viscoelasticity of polymer droplets with different glass transition temperatures

“…[1][2][3] In the case of a film sample, the bulk elastic modulus, shear modulus, Young's modulus, and Poisson's ratio of the film can be evaluated. 4) When a suspension containing microparticles is measured as a sample, the size of the particles 5) and the elasticity and viscosity of the particles [6][7][8] can be quantified. When evaluating these properties, we focus on particle resonance scattering.…”

“…Recently we have studied ECAH analysis considering viscoelasticity, which simultaneously takes into account both shear modulus and shear viscosity, regardless of whether the particles are liquid or solid, and showed that polydimethylsiloxane elastomer and impact-resistant polycarbonate exhibit viscoelasticity in a single independent particle unit. 6) Since the time derivative of strain is dγ/dt = iωγ, elasticity and viscosity can be understood in a unified manner in terms of Hookian elasticity, where the coefficient of γ is generalized as the complex elastic modulus where =i 1 and ω is the angular frequency. 16) As can be realized from the timetemperature superposition rule, deforming a material over a long period of time and observing it at a low frequency are equivalent to observing the deformable material at a high temperature.…”