THE DETERMINATION OF COMPLEX SHEAR MODULUS OF DEIONIZED WATER USING KRAMER-KRONIG RELATION (KKR) METHOD
DOI:
https://doi.org/10.11113/jt.v74.4723Keywords:
Complex Shear Modulus (CSM), Kramer-Kronig Relation (KKR), Complex Response Function (CRF), Brownian Motion (BM)Abstract
Complex Shear Modulus (CSM) contains fruitful information about mechanical properties,especially in microrheologystudies. CSM calculation depends onComplex Response Function (CRF) of an object motion. The aim of this paper is to provide guidance on the determination of the CSM by using Kramer-Kronig Relation (KKR) method. The procedure takes advantage of Brownian Motion (BM) of a micron-sized polystyrene in water. The BM occurs when the particle were responseto the thermal force in fluids medium. We use Laplace Transform(LT) algorithm to analyze the BMand to find CRF and CSM.The result will be displayedas Radial Frequencies Function.
References
Rubinstein, M. and R.H. Colby. 2003. Polymer Physics. OUP Oxford.
Buchanan, M., et al. 2005. High-frequency Microrheology of Wormlike Micelles. Physical Review E. 72(1): 011504.
Toyabe, S. and M. Sano. 2008. Energy Dissipation of a Brownian Particle in a Viscoelastic Fluid. Physical Review E. 77(4): 041403.
Squires, T. M. and T. G. Mason. 2009. Fluid Mechanics of Microrheology. Annual Review of Fluid Mechanics. 42(1): 413.
Meirovitch, L. 2001. Fundamentals of Vibrations. International Edition ed. Singapore: McGraw-Hill Higher Education. 806.
Esteban, J. M. and M. E. Orazem. 1991. On the Application of the Kramers-Kronig Relations to Evaluate the Consistency of Electrochemical Impedance Data. Journal of the Electrochemical Society. 138(1): 67-76.
Nussenzveig, H. M. 1972. Causality and Dispersion Relations. United Kingdom: Academic Press. 95.
Grimm, M., S. Jeney, and T. Franosch. 2011. Brownian Motion in a Maxwell Fluid. Soft Matter. 7(5): 2076-2084.
Fischer, M. and K. Berg-Sorensen. 2007. Calibration of Trapping Force and Response Function of Optical Tweezers In Viscoelastic Media. Journal of Optics A: Pure and Applied Optics. 9(8): S239.
Popescu, G., A. Dogariu, and R. Rajagopalan. 2002. Spatially Resolved Microrheology Using Localized Coherence Volumes. Physical Review E. 65(4): 041504.
Gittes, F. and C.F. Schmidt. 1997. Signals and Noise in Micromechanical Measurements. Methods in Cell Biology. 55: 129-156.
De Grooth, B. G. 1999. A Simple Model for Brownian Motion Leading to the Langevin Equation. American Journal of Physics. 67(12): 1248-1252.
Yanagishima, T. 2011. Real-time Monitoring of Complex Moduli from Micro-Rheology. Journal of Physics: Condensed Matter. 23(19): 194118.
Michalet, X. 2010. Mean Square Displacement Analysis of Single-Particle Trajectories with Localization Error: Brownian Motion in an Isotropic Medium. Physical Review E. 82(4): 041914.
Schnurr, B. 1997. Determining microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks From Thermal Fluctuations. Macromolecules. 30(25): 7781-7792.
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