Avoiding waviness of relaxation spectra
Tóm tắt
Spectra are material functions, whose different integral transforms yield the measurable rheological quantities in the linear viscoelastic regime. Therefore, their knowledge is of high fundamental interest. However, the calculation of spectra from experimental data is an ill-posed problem. Thus, it is hampered by the problem that a too low density of relaxation modes does not lead to a good description of the input data, while a higher one usually causes a wavy spectrum which cannot be interpreted. To overcome this problem, an additional criterion assuming only gradual changes in the spectrum is introduced allowing for an increase in mode density without an enhanced waviness of the spectrum. This is novel in comparison to previously published spectra algorithms and commercial software packages.
Tài liệu tham khảo
Baumgärtel M, Winter HH (1989) Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheol Acta 28:511–519
Baumgärtel M, Winter HH (1992) Interrelation between continuous and discrete relaxation time spectra. J Non-Newton Fluid Mech 44:15–36
Dealy J, Larson RG (2006) Structure and rheology of molten polymers—from structure to flow behavior and back again. Hanser, Munich
Emri I, Tschoegl NW (1993) Generating line spectra from experimental responses. Part I: relaxation modulus and creep compliance. Rheol Acta 32(3):311–321
Friedrich C, Waizenegger W, Winter HH (2008) Relaxation patterns of long, linear, flexible, monodisperse polymers: BSW spectrum revisited. Rheol Acta 47(8):909–916
Kaschta J, Schwarzl FR (1994a) Calculation of discrete retardation spectra from creep data: 1. Method. Rheol Acta 33(6):517–529
Kaschta J, Schwarzl FR (1994b) Calculation of discrete retardation spectra from creep data: 2. Analysis of measured creep curves. Rheol Acta 33(6):530–541
Stadler FJ, Bailly C (2009) A new method for the calculation of continuous relaxation spectra from dynamic–mechanical data. Rheol Acta 48(1):33–49. doi:10.1007/s00397-00008-00303-00392
Stadler FJ, Münstedt H (2008) Terminal viscous and elastic rheological characterization of ethene-/α-olefin copolymers. J Rheol 52(3):697–712. doi:610.1122/1121.2892039
Stadler FJ, Gabriel C, Münstedt H (2007) Influence of short-chain branching of polyethylenes on the temperature dependence of rheological properties in shear. Macromol Chem Phys 208(22):2449–2454. doi:2410.1002/macp.200700267
Stadler FJ, Kaschta J, Münstedt H (2005) Dynamic–mechanical behavior of polyethylenes and ethene-/α-olefin-copolymers: part I: α′-relaxation. Polymer 46(23):10311–10320. doi:10310.11016/j.polymer.12005.10307.10099
Tschoegl NW, Emri I (1992) Generating line spectra from experimental responses. III. Interconversion between relaxation and retardation behavior. Int J Polym Mater 18(1–2):117–127
Tschoegl NW, Emri I (1993) Generating line spectra from experimental responses. Part II: storage and loss functions. Rheol Acta 32(3):322–327