{"id":13345,"date":"2022-11-11T10:20:40","date_gmt":"2022-11-11T15:20:40","guid":{"rendered":"https:\/\/www.alpha-technologies.com\/?p=13345"},"modified":"2023-10-02T16:20:34","modified_gmt":"2023-10-02T20:20:34","slug":"part-1-ft-rheology-via-large-amplitude-oscillatory-shear-laos-a-five-part-series","status":"publish","type":"post","link":"https:\/\/www.alphatechnologies.cn\/en\/blog\/part-1-ft-rheology-via-large-amplitude-oscillatory-shear-laos-a-five-part-series\/","title":{"rendered":"Part 1: FT Rheology via Large Amplitude Oscillatory Shear (LAOS) &#8211; a five part series"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"13345\" class=\"elementor elementor-13345\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-top-section elementor-element elementor-element-681d5054 ot-traditional elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"681d5054\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-16bfe135 ot-flex-column-vertical\" data-id=\"16bfe135\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-inner-section elementor-element elementor-element-7f8ef5b elementor-section-full_width ot-traditional elementor-section-height-default elementor-section-height-default\" data-id=\"7f8ef5b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-2e8692f ot-flex-column-vertical\" data-id=\"2e8692f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-53794bd elementor-widget elementor-widget-image\" data-id=\"53794bd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/06\/DSCF0010-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail wp-image-12924\" alt=\"Male Engineer near Alpha Technology instrument\" srcset=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/06\/DSCF0010-150x150.jpg 150w, https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/06\/DSCF0010-720x720.jpg 720w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-50af64b ot-column-items-center ot-flex-column-vertical\" data-id=\"50af64b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7c0778e elementor-widget elementor-widget-heading\" data-id=\"7c0778e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<p class=\"elementor-heading-title elementor-size-default\">Michele Scacchi<\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a7affb3 elementor-widget elementor-widget-heading\" data-id=\"a7affb3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h6 class=\"elementor-heading-title elementor-size-default\">Alpha Technologies<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-bdccb5c elementor-widget elementor-widget-spacer\" data-id=\"bdccb5c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-inner-section elementor-element elementor-element-040e4c8 ot-traditional elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"040e4c8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-dc69c9a ot-flex-column-vertical\" data-id=\"dc69c9a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-87c7572 elementor-widget elementor-widget-heading\" data-id=\"87c7572\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Optimizing your Mixing Process Using LAOS<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-68cc53e elementor-widget elementor-widget-spacer\" data-id=\"68cc53e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0b832d8 elementor-widget elementor-widget-text-editor\" data-id=\"0b832d8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Filler dispersion can affect many compound properties including strength, rebound, heat build-up, fatigue and cracking. What\u2019s more, poor dispersion can cause poor processability, product failure and increased scrap costs. A traditional method of evaluating mixing efficiency utilizes the measurement of dynamic strain softening \u2013 also known as the <a href=\"https:\/\/www.alpha-technologies.com\/rubber-quality-control-using-the-payne-effect\/\">Payne effect<\/a>. Excellent, repeatable, reproducible Payne effect measurements can be made on Alpha\u2019s Premier\u2122 RPA.\u00a0<\/p><p>That said, the Payne effect can have issues when describing the non-linear behaviour of rubber compounds. \u00a0Fortunately, the application of Fourier Transformation to the shear stress signal is not only a powerful tool to quantify the level of long chain branching in polymers but also a very sensitive technique to optimize the mixing process of filled rubber compounds. This technique is called FT-Rheology.<\/p><p>FT-Rheology via Large Amplitude Oscillatory Shear (LAOS) reveals more information about the filler-filler \/ filler-polymer interactions and provides a check at the end of the mixing process to determine if the full dispersion of the filler in the rubber matrix has been achieved.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-23fd069 elementor-widget elementor-widget-spacer\" data-id=\"23fd069\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ea72354 elementor-widget elementor-widget-heading\" data-id=\"ea72354\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Non-linear thinking is great. Non-linear torque not so much.<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-098fa05 elementor-widget elementor-widget-spacer\" data-id=\"098fa05\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cc07293 elementor-widget elementor-widget-text-editor\" data-id=\"cc07293\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In the non-linear region, the response of viscoelastic materials is no longer characterized by a sinus wave. The torque\/stress signal is distorted: the higher the imposed deformation the more pronounced the distortion of the torque response, see Figure 1.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0b8b6d6 elementor-widget elementor-widget-spacer\" data-id=\"0b8b6d6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21c9fde elementor-widget elementor-widget-image\" data-id=\"21c9fde\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"738\" height=\"713\" src=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F1.jpg\" class=\"attachment-medium_large size-medium_large wp-image-14955\" alt=\"\" srcset=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F1.jpg 738w, https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F1-300x290.jpg 300w, https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F1-720x696.jpg 720w\" sizes=\"(max-width: 738px) 100vw, 738px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 1: main differences between linear and non-linear VE regime <\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-4726b6a4 elementor-widget elementor-widget-text-editor\" data-id=\"4726b6a4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The only way to describe the real response of material tested in the nonlinear region (and quantify the distortion) is to apply FT-Rheology to account for all odd higher harmonics of the torque signal. In the comparison shown in the Figure 2, the torque was recorded without considering the contribution of higher harmonics (left) and then by considering all odd higher harmonics (right).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a3b9468 elementor-widget elementor-widget-spacer\" data-id=\"a3b9468\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-inner-section elementor-element elementor-element-3e28d10 ot-traditional elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3e28d10\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-730ee84 ot-flex-column-vertical\" data-id=\"730ee84\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c6fd68f elementor-widget elementor-widget-image\" data-id=\"c6fd68f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"301\" height=\"232\" src=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F2-B.jpg\" class=\"attachment-medium_large size-medium_large wp-image-14969\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Real response<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-d506e77 ot-flex-column-vertical\" data-id=\"d506e77\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-470e3e6 elementor-widget elementor-widget-image\" data-id=\"470e3e6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"721\" height=\"563\" src=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F2.jpg\" class=\"attachment-medium_large size-medium_large wp-image-14962\" alt=\"\" srcset=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F2.jpg 721w, https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F2-300x234.jpg 300w\" sizes=\"(max-width: 721px) 100vw, 721px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Not real response<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-ca280a1 elementor-widget elementor-widget-text-editor\" data-id=\"ca280a1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: center;\">Figure 2: distortion the torque signal at large deformation<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-43234aa elementor-widget elementor-widget-text-editor\" data-id=\"43234aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This approach was developed several years ago by A. Jeffrey Giacomin and John M. Dealy and is described in <em>Techniques in Rheological Measurement <\/em>(Chapman &amp; Hall, 1993)<em>. <\/em>According to this theory the shear stress signal can be described as a Fourier series, which is as the sum of all odd higher harmonics of G\u02b9 and G&#8221;, see Figure 3.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1a41984 elementor-widget elementor-widget-image\" data-id=\"1a41984\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"274\" height=\"218\" src=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F3-formulas.jpg\" class=\"attachment-large size-large wp-image-14976\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-84c3845 elementor-widget elementor-widget-spacer\" data-id=\"84c3845\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-366a51e elementor-widget elementor-widget-image\" data-id=\"366a51e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"645\" height=\"411\" src=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F4-formulas.jpg\" class=\"attachment-large size-large wp-image-14990\" alt=\"\" srcset=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F4-formulas.jpg 645w, https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F4-formulas-300x191.jpg 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 3: typical approach to describe the non-linear response by FT-Rheology<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-251c346 elementor-widget elementor-widget-text-editor\" data-id=\"251c346\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Typically, non-linear behavior of materials can be quantified by the ratio of the higher harmonics to the first, I<sub>n\/<\/sub><sub>1<\/sub> = I(n\u03c91)\/I(\u03c91)\u00a0 . The 3rd harmonic, In<sub>\/1<\/sub>= I(3\u03c9)\/I(\u03c9), has the highest relative intensity in comparison with the other odd harmonics (the following higher order terms typically decay rapidly), hence it is the most important in quantifying the non-linearity under LAOS. It was demonstrated that this ratio is the most sensitive to detect the filler\/polymer interactions of rubber compound.<\/p><p>The LAOS technique is more accurate than the traditional Payne effect approach to describe the non-linear behavior of uncured rubber compound specially to evaluate the micro-dispersion of filler.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-27e57c8 elementor-widget elementor-widget-spacer\" data-id=\"27e57c8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-05624de elementor-widget elementor-widget-heading\" data-id=\"05624de\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">How to evaluate filler dispersion by LAOS technique.<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2ebcaa8 elementor-widget elementor-widget-spacer\" data-id=\"2ebcaa8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-349fc05 elementor-widget elementor-widget-text-editor\" data-id=\"349fc05\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>One of the most interesting approaches used to study the complex set of events that occur along the mixing line with LAOS, was developed by Prof. Jean L. Leblanc.<\/p><p>Based on Leblanc\u2019s model the non-linear response of uncured rubber compounds, expressed in terms of third relative torque harmonic, I<sub>3\/1<\/sub>, vs. strain, can be described as the results of two combined effects:<\/p><ol><li>Effect due to the polymer component characterized by a sigma shape curve that becomes asymptotic to a straight line at high strain values<\/li><li>Effect due to the filler component that it is characterized by a curve passing through a maximum and then tends to zero at high strain values.<\/li><\/ol><p>Furthermore, Leblanc observed that all compounds during the mixing process show a local maximum located typically in the range between 400-600% of strain. The stronger is the filler-filler interaction the more pronounced is this local maximum, see Figure 4<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-68dbc31 elementor-widget elementor-widget-spacer\" data-id=\"68dbc31\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5a43bd8 elementor-widget elementor-widget-image\" data-id=\"5a43bd8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"376\" height=\"274\" src=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F4.jpg\" class=\"attachment-large size-large wp-image-14983\" alt=\"\" srcset=\"https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F4.jpg 376w, https:\/\/www.alphatechnologies.cn\/wp-content\/uploads\/2022\/12\/BP1-LAOS-F4-300x219.jpg 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Figure 4: Leblanc's model to describe the behavior of filled rubber compounds<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3c4cfee elementor-widget elementor-widget-text-editor\" data-id=\"3c4cfee\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>As the mixing process proceeds, less filler-filler interactions can be observed, which means that the filler network is significantly destroyed, and the local maximum is less and less pronounced. At the end of mixing if the full dispersion of the filler has been achieved the local maximum is almost vanished.<\/p><p>Therefore, the non-linear response of rubber compounds is dominated in the low range of strain by filler component, while in the high range of strain it is dominated by the polymer component.<\/p><p>That\u2019s the theory and maths behind FT-Rheology via LAOS. Now let\u2019s put it into practice. In Part 2 of this post, I will provide real examples of LAOS experiments to track the progress of filler dispersion along the mixing line.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-92948ca elementor-widget elementor-widget-spacer\" data-id=\"92948ca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-39802b0 elementor-widget elementor-widget-heading\" data-id=\"39802b0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">References<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-64bdd42 elementor-widget elementor-widget-spacer\" data-id=\"64bdd42\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-501d9bf elementor-widget elementor-widget-text-editor\" data-id=\"501d9bf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li><span data-ccp-props=\"{}\">L<\/span><span data-contrast=\"auto\">eblanc, J.L.; Rubber Chemistry and Technology, 78, 54-75 (2005)\u00a0<\/span><span data-ccp-props=\"{}\">\u00a0<\/span><\/li><li><span data-contrast=\"auto\">Leblanc J.L., Chapelle C. de la; Rubber Chemistry and Technology, 76, 287 (2003)\u00a0<\/span><span data-ccp-props=\"{}\">\u00a0<\/span><\/li><li><span data-contrast=\"auto\">Leblanc J.L.; Rubber Chemistry and Technology, 86, 261\u2013285 (2013)<\/span><span data-ccp-props=\"{}\">\u00a0<\/span><\/li><li><span data-contrast=\"auto\">Leblanc J.L.; Journal of Applied Polymer Science 109, 1271 (2008)\u00a0<\/span><span data-ccp-props=\"{}\">\u00a0<\/span><\/li><li><span data-contrast=\"auto\">Nijman, G., Leblanc, J.L.; Journal of Applied Polymer Science 112, 942 (2009)\u00a0<\/span><span data-ccp-props=\"{}\">\u00a0<\/span><\/li><li><span data-contrast=\"auto\">Leblanc, J.L., Nijman, G.; Journal of Applied Polymer Science 112, 1128 (2009)<\/span><span data-ccp-props=\"{}\">\u00a0<\/span><\/li><li><span data-contrast=\"auto\">Nijman, G.; GAK 68, 400 (2015)<\/span><span data-ccp-props=\"{}\">\u00a0<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b877bd7 elementor-widget elementor-widget-spacer\" data-id=\"b877bd7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f527871 elementor-grid-eael-col-4 elementor-grid-tablet-eael-col-2 elementor-grid-mobile-eael-col-1 elementor-widget elementor-widget-eael-post-grid\" data-id=\"f527871\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;eael_post_grid_columns&quot;:&quot;eael-col-4&quot;,&quot;eael_post_grid_columns_tablet&quot;:&quot;eael-col-2&quot;,&quot;eael_post_grid_columns_mobile&quot;:&quot;eael-col-1&quot;}\" data-widget_type=\"eael-post-grid.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"eael-post-grid-f527871\" class=\"eael-post-grid-container\">\n            <div class=\"eael-post-grid eael-post-appender eael-post-appender-f527871 eael-post-grid-style-one\" data-layout-mode=\"masonry\"><article class=\"eael-grid-post  eael-post-grid-column eael-pg-post-14877 category-blog tags-laos-large-amplitude-oscillatory-shear-rpa-rubber-process-analyzer\" data-id=\"14877\">\n        <div class=\"eael-grid-post-holder\">\n            <div class=\"eael-grid-post-holder-inner\"><div class=\"eael-entry-wrapper\"><header class=\"eael-entry-header\"><h2 class=\"eael-entry-title\"><a class=\"eael-grid-post-link\" href=\"https:\/\/www.alphatechnologies.cn\/en\/blog\/part-3-using-laos-to-quantify-long-chain-branching-and-to-predict-processability\/\" title=\"Part 3: Using LAOS to Quantify Long Chain Branching and to Predict Processability\">Part 3: Using LAOS to Quantify Long Chain Branching and to Predict Processability<\/a><\/h2><\/header><div class=\"eael-entry-content\">\n                        <div class=\"eael-grid-post-excerpt\"><p>Michele Scacchi Alpha Technologies ICYMI \u2013 Recap for people who...<\/p><a href=\"https:\/\/www.alphatechnologies.cn\/en\/blog\/part-3-using-laos-to-quantify-long-chain-branching-and-to-predict-processability\/\" class=\"eael-post-elements-readmore-btn\">Read More<\/a><\/div>\n                    <\/div><div class=\"eael-entry-footer\"><div class=\"eael-author-avatar\"><a href=\"https:\/\/www.alphatechnologies.cn\/en\/author\/amiesedlock\/\"><img alt='Amie Sedlock' src='https:\/\/secure.gravatar.com\/avatar\/fb9f11b8e87f9e5cf4376bec7b97805f31f284050697ff9e90f192c000186ebf?s=96&#038;d=mm&#038;r=g' srcset='https:\/\/secure.gravatar.com\/avatar\/fb9f11b8e87f9e5cf4376bec7b97805f31f284050697ff9e90f192c000186ebf?s=192&#038;d=mm&#038;r=g 2x' class='avatar avatar-96 photo' height='96' width='96' \/><\/a><\/div><div class=\"eael-entry-meta\"><span class=\"eael-posted-by\"><a href=\"https:\/\/www.alphatechnologies.cn\/en\/author\/amiesedlock\/\" title=\"Posts by Amie Sedlock\" rel=\"author\">Amie Sedlock<\/a><\/span><span class=\"eael-posted-on\"><time datetime=\"2022\u5e7412\u670812\u65e5\">2022\u5e7412\u670812\u65e5<\/time><\/span><\/div><\/div><\/div><\/div>\n        <\/div>\n    <\/article><article class=\"eael-grid-post  eael-post-grid-column eael-pg-post-14863 category-blog tags-laos-large-amplitude-oscillatory-shear-rpa-rubber-process-analyzer\" data-id=\"14863\">\n        <div class=\"eael-grid-post-holder\">\n            <div class=\"eael-grid-post-holder-inner\"><div class=\"eael-entry-wrapper\"><header class=\"eael-entry-header\"><h2 class=\"eael-entry-title\"><a class=\"eael-grid-post-link\" href=\"https:\/\/www.alphatechnologies.cn\/en\/blog\/part-4-case-studies-determination-of-long-chain-branching-in-polymer-and-prediction-of-processability\/\" title=\"Part 4: Case Studies: Determination of Long Chain Branching in Polymer and Prediction of Processability\">Part 4: Case Studies: Determination of Long Chain Branching in Polymer and Prediction of Processability<\/a><\/h2><\/header><div class=\"eael-entry-content\">\n                        <div class=\"eael-grid-post-excerpt\"><p>Michele Scacchi Alpha Technologies ICYMI &#8211; Recap for people who...<\/p><a href=\"https:\/\/www.alphatechnologies.cn\/en\/blog\/part-4-case-studies-determination-of-long-chain-branching-in-polymer-and-prediction-of-processability\/\" class=\"eael-post-elements-readmore-btn\">Read More<\/a><\/div>\n                    <\/div><div class=\"eael-entry-footer\"><div class=\"eael-author-avatar\"><a href=\"https:\/\/www.alphatechnologies.cn\/en\/author\/amiesedlock\/\"><img alt='Amie Sedlock' src='https:\/\/secure.gravatar.com\/avatar\/fb9f11b8e87f9e5cf4376bec7b97805f31f284050697ff9e90f192c000186ebf?s=96&#038;d=mm&#038;r=g' srcset='https:\/\/secure.gravatar.com\/avatar\/fb9f11b8e87f9e5cf4376bec7b97805f31f284050697ff9e90f192c000186ebf?s=192&#038;d=mm&#038;r=g 2x' class='avatar avatar-96 photo' height='96' width='96' \/><\/a><\/div><div class=\"eael-entry-meta\"><span class=\"eael-posted-by\"><a href=\"https:\/\/www.alphatechnologies.cn\/en\/author\/amiesedlock\/\" title=\"Posts by Amie Sedlock\" rel=\"author\">Amie Sedlock<\/a><\/span><span class=\"eael-posted-on\"><time datetime=\"2022\u5e7412\u670809\u65e5\">2022\u5e7412\u670809\u65e5<\/time><\/span><\/div><\/div><\/div><\/div>\n        <\/div>\n    <\/article><article class=\"eael-grid-post  eael-post-grid-column eael-pg-post-13345 category-blog tags-laos-large-amplitude-oscillatory-shear-rpa-rubber-process-analyzer\" data-id=\"13345\">\n        <div class=\"eael-grid-post-holder\">\n            <div class=\"eael-grid-post-holder-inner\"><div class=\"eael-entry-wrapper\"><header class=\"eael-entry-header\"><h2 class=\"eael-entry-title\"><a class=\"eael-grid-post-link\" href=\"https:\/\/www.alphatechnologies.cn\/en\/blog\/part-1-ft-rheology-via-large-amplitude-oscillatory-shear-laos-a-five-part-series\/\" title=\"Part 1: FT Rheology via Large Amplitude Oscillatory Shear (LAOS) &#8211; a five part series\">Part 1: FT Rheology via Large Amplitude Oscillatory Shear (LAOS) &#8211; a five part series<\/a><\/h2><\/header><div class=\"eael-entry-content\">\n                        <div class=\"eael-grid-post-excerpt\"><p>Michele Scacchi Alpha Technologies Optimizing your Mixing Process Using LAOS...<\/p><a href=\"https:\/\/www.alphatechnologies.cn\/en\/blog\/part-1-ft-rheology-via-large-amplitude-oscillatory-shear-laos-a-five-part-series\/\" class=\"eael-post-elements-readmore-btn\">Read More<\/a><\/div>\n                    <\/div><div class=\"eael-entry-footer\"><div class=\"eael-author-avatar\"><a href=\"https:\/\/www.alphatechnologies.cn\/en\/author\/amiesedlock\/\"><img alt='Amie Sedlock' src='https:\/\/secure.gravatar.com\/avatar\/fb9f11b8e87f9e5cf4376bec7b97805f31f284050697ff9e90f192c000186ebf?s=96&#038;d=mm&#038;r=g' srcset='https:\/\/secure.gravatar.com\/avatar\/fb9f11b8e87f9e5cf4376bec7b97805f31f284050697ff9e90f192c000186ebf?s=192&#038;d=mm&#038;r=g 2x' class='avatar avatar-96 photo' height='96' width='96' \/><\/a><\/div><div class=\"eael-entry-meta\"><span class=\"eael-posted-by\"><a href=\"https:\/\/www.alphatechnologies.cn\/en\/author\/amiesedlock\/\" title=\"Posts by Amie Sedlock\" rel=\"author\">Amie Sedlock<\/a><\/span><span class=\"eael-posted-on\"><time datetime=\"2022\u5e7411\u670811\u65e5\">2022\u5e7411\u670811\u65e5<\/time><\/span><\/div><\/div><\/div><\/div>\n        <\/div>\n    <\/article><article class=\"eael-grid-post  eael-post-grid-column eael-pg-post-14282 category-blog tags-laos-large-amplitude-oscillatory-shear-rpa-rubber-process-analyzer\" data-id=\"14282\">\n        <div class=\"eael-grid-post-holder\">\n            <div class=\"eael-grid-post-holder-inner\"><div class=\"eael-entry-wrapper\"><header class=\"eael-entry-header\"><h2 class=\"eael-entry-title\"><a class=\"eael-grid-post-link\" href=\"https:\/\/www.alphatechnologies.cn\/en\/blog\/finding-balance-measure-cure-and-blowing-reactions-using-an-rpa\/\" title=\"Finding Balance: Measure Cure &#038; Blowing Reactions Using an RPA\u00a0\">Finding Balance: Measure Cure &#038; Blowing Reactions Using an RPA\u00a0<\/a><\/h2><\/header><div class=\"eael-entry-content\">\n                        <div class=\"eael-grid-post-excerpt\"><p>Whether you are extruding or injection molding, the production of...<\/p><a href=\"https:\/\/www.alphatechnologies.cn\/en\/blog\/finding-balance-measure-cure-and-blowing-reactions-using-an-rpa\/\" class=\"eael-post-elements-readmore-btn\">Read More<\/a><\/div>\n                    <\/div><div class=\"eael-entry-footer\"><div class=\"eael-author-avatar\"><a href=\"https:\/\/www.alphatechnologies.cn\/en\/author\/amiesedlock\/\"><img alt='Amie Sedlock' src='https:\/\/secure.gravatar.com\/avatar\/fb9f11b8e87f9e5cf4376bec7b97805f31f284050697ff9e90f192c000186ebf?s=96&#038;d=mm&#038;r=g' srcset='https:\/\/secure.gravatar.com\/avatar\/fb9f11b8e87f9e5cf4376bec7b97805f31f284050697ff9e90f192c000186ebf?s=192&#038;d=mm&#038;r=g 2x' class='avatar avatar-96 photo' height='96' width='96' \/><\/a><\/div><div class=\"eael-entry-meta\"><span class=\"eael-posted-by\"><a href=\"https:\/\/www.alphatechnologies.cn\/en\/author\/amiesedlock\/\" title=\"Posts by Amie Sedlock\" rel=\"author\">Amie Sedlock<\/a><\/span><span class=\"eael-posted-on\"><time datetime=\"2022\u5e7410\u670825\u65e5\">2022\u5e7410\u670825\u65e5<\/time><\/span><\/div><\/div><\/div><\/div>\n        <\/div>\n    <\/article><\/div>\n            <div class=\"clearfix\"><\/div>\n        <\/div>            <div class=\"eael-load-more-button-wrap eael-force-hide\">\n                <button 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class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Related Links<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-inner-section elementor-element elementor-element-ec5f2d4 ot-traditional elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ec5f2d4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-da3b6bc ot-flex-column-vertical\" data-id=\"da3b6bc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div 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