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\title{Modelling Two Different Disperse Polystyrene with Maxwell Fractional Model in SAOS Experiments}
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             \author[1]{Bruno Manuel Ribeiro  Alves}

             \affil[1]{  University of Minho}

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\date{\small \em Received: 6 December 2016 Accepted: 4 January 2017 Published: 15 January 2017}

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\begin{abstract}
        


The purpose of this work is to perform two adjustments of different disperse polystyrene using the technique of Alves (Alves, 2017) with the data present on Farias (Farias,  2009), data belonging to a group of eminent researchers. It is seen that the adjustments are of good quality for a polystyrene anionic polymerised and with an inferior quality for a free-radical polymerised polystyrene. It leads to a possible correlation with the polydispersity index and the quality of adjustment performed with Maxwell fractional model.It is concluded in this work that Maxwell fractional model is able to describe the behaviour when Mw/Mn is closer to 1 but the same is not completely valid for polydispersity index of 1.44.

\end{abstract}


\keywords{Maxwell fractional model; viscoelastic fluid; SAOS experiments; polystyrene; wolfram mathematica 10; non-linear regression; polydispersity index.}

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\let\tabcellsep& 	 	 		 
\section[{Modelling Two Different Disperse Polystyrene with Maxwell Fractional Model in SAOS Experiments}]{Modelling Two Different Disperse Polystyrene with Maxwell Fractional Model in SAOS Experiments}\par
Bruno Manuel Ribeiro Alves I. Introduction he purpose of this work is to perform two adjustments using the technique of Alves \hyperref[b1]{(Alves, 2017)} with the data present in Farias (Farias, 2009) that belongs to a group of eminent researchers.\par
On this work is checked a possible correlation of the polydispersity index with the chain branching thanks to the realisation of adjustments of SAOS dynamic polystyrene data (Farias, 2009) with a mathematical formulated viscoelastic fractional model, the Maxwell fractional model \hyperref[b7]{(Jaishankar \& McKinley, 2012)}.\par
Seeing the complexity level of Maxwell fractional model, is known that models on the literature can be more or less complex and divided in Newtonian (as Newton model) \hyperref[b11]{(Pinho, 2003)}, non-Newtonian inelastic (they are models that consider the variation of shear viscosity with shear rate) \hyperref[b11]{(Pinho, 2003)}and viscoelastic (Viscoelastic models combine viscous component and elastic component and they can have differential or integral mathematical formulations) \hyperref[b11]{(Pinho, 2003)}.\par
First viscoelastic linear models date from XIX century and are the linear viscoelastic model of Maxwell \hyperref[b8]{(Maxwell, 1867)} and the linear viscoelastic model of Kelvin-Voight \hyperref[b2]{(Bird, Armstrong, \& Hassanger, 1987)}. A possible representation of this genre of models is given by the combination of discrete elements as springs (Hooke Law), where tension (? ) is directly proportional to deformation ( ? )) to represent the elastic model, and dashpots (Newton law) \hyperref[b2]{(Bird et al., 1987)}.\par
With Fractional Viscoelastic models, an analogy with discrete elements can be done. On Figure  {\ref 1} is presented this new element, the "springpot", that allows the interpolation of the behaviour of traditional elements spring and dashpot through the order considered for the derivative. In this way is obtained a continuous variation between the behaviour of solids and liquids. Hooke law (spring -derivative of order 0 ( Abstract-The purpose of this work is to perform two adjustments of different disperse polystyrene using the technique of Alves \hyperref[b1]{(Alves, 2017)} with the data present on Farias  {\ref (Farias, 2009)}, data belonging to a group of eminent researchers. It is seen that the adjustments are of good quality for a polystyrene anionic polymerised and with an inferior quality for a free-radical polymerised polystyrene. It leads to a possible correlation with the polydispersity index and the quality of adjustment performed with Maxwell fractional model.\par
It is concluded in this work that Maxwell fractional model is able to describe the behaviour when Mw/Mn is closer to 1 but the same is not completely valid for polydispersity index of 1.44. 
\section[{Keywords: Maxwell fractional model; viscoelastic fluid; SAOS experiments; polystyrene; wolfram mathematica 10; non-linear regression; polydispersity index.}]{Keywords: Maxwell fractional model; viscoelastic fluid; SAOS experiments; polystyrene; wolfram mathematica 10; non-linear regression; polydispersity index.} 
\section[{??}]{??}"spring-pot" ?? ( ) 2 2 2 1 1 2 2 2 1 2 1 2 ( ) ( ) 2 2 '( ) ( ) ( ) 2 2 Cos Cos G Cos ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? = ? ? ? + ? + ? ? ? ? ? ? ? (Equation 1) ( ) 2 2 2 1 1 2 2 2 1 2 1 2 ( ) ( ) 2 2 ''( ) ( ) ( ) 2 2 Sin Sin G Cos ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? = ? ? ? + ? + ? ? ? ? ? ? ? (Equation 2)\par
Fractional theory is not applied only in viscoelasticity. This theory is applied on migration of biological cells in complex spatial domains (Cusimano, Burrage, \& Burrage, 2013), on lithium-ion batteries involving fractional differentiation  {\ref (} On an engineering level these models can be applied on continuum mechanics (Drapaca \& Sivaloganathan, 2012), on the optimization of fractional order dynamic chemical processing systems (Flores-Tlacuahuac \& Biegler, 2014), on supercapacitors, batteries and fuel cells \hyperref[b4]{(Freeborn, Maundy, \& Elwakil, 2015)}. For more information it is necessary to consult two works, the "Evaluation of Reptation Model for predicting the linear viscoelastic properties of entangled linear polymers" \hyperref[b12]{(Ruymbeke et al., 2002)} and also the "Determination of the molecular weight distribution of the entangled linear polymers from linear viscoelasticity data" \hyperref[b12]{(Ruymbeke et al., 2002)}. 
\section[{II. Resources and Techniques}]{II. Resources and Techniques}\par
This data of G'(?) and G''(?) of SAOS experiments was placed on a computer program previous computed by Alveswhich is possible to be found on the article website (Alves, 2017), using the same principle.  ? , which means that in this case it obeys the thermodynamic restrictions. Therefore, for ? and ? the observation of the final result is 0< ? and ?<1, which gives valid thermodynamic results.\par
Figure \hyperref[fig_1]{2} shows an almost perfect adjustment for G'(?) and G''(?) in all the domain of ? with exception for ?>200 rad/s. For this value the result is not perfectly coincident, and means that the model is not valid for values of ?>200 rad/s. On Figure 3 is observed the same thing as Figure  {\ref 1} but here for values of ?>100 rad/s, which results on a bad coincidence result. Here, also for periods of ?<0.05 rad/s relative to G'(?) and G''(?) the fit is not good.\par
Below are presented the graphics of the adjustments done with the material functions G'(?) and G''(?) of Maxwell Fractional Model with the experimental data of Farias, the anionic polymerisation data of Polystyrene (Figure \hyperref[fig_1]{2}) and free-radical polymerisation data of Polystyrene (Figure 3). The anionic polymerized polystyrene as observed on section 5 has polydispersity index correspondent to 1.03 adjusting almost perfectly, which means that exist an high correlation between Maxwell fractional model and the polydispersity index of anionic polymerised polystyrene.\par
The free radical polymerization Polystyrene has a bigger polydispersity index equal to 1.44 and the quality of adjustment is not comparable to the anionic polymerisation of polystyrene, what means that for Mw = 1.44 Mn the correlation between Maxwell fractional model and polydispersity index of free radical based polymerisation cannot be done.\par
So, I think that with these proofs that the overall quality of Maxwell fractional model has a correlation with polydispersity index for anionic polymerisation polydispersity index however the same is not completely valid for free-radical based polymerisation of polystyrene. 
\section[{IV. Conclusion}]{IV. Conclusion}\par
With this work was possible to perform two fits for two different polystyrenes with an overall good quality obeying the thermodynamic restrictions imposed by Maxwell Fractional Model in SAOS dynamics. However is possible to find now a correlation with the polydispersity index of the polymer of Polystyrene with the Maxwell fractional model.\par
It is concluded in this work that Maxwell fractional model is able to describe the behaviour when Mw/Mn is closer to 1 but the same is not completely valid for polydispersity index of 1.44. 
\section[{V. Acknowledgements}]{V. Acknowledgements}\par
The present work has got the software funding of Wolfram Software Mathematica 10.4.   \begin{figure}[htbp]
\noindent\textbf{120171}\includegraphics[]{image-2.png}
\caption{\label{fig_0}0D 1 D 2017 JFigure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 2 :}\end{figure}
  \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.7573813708260105\textwidth}P{0.04780316344463972\textwidth}P{0.007469244288224957\textwidth}P{0.03734622144112478\textwidth}}
\tabcellsep Mw (g/mol)\tabcellsep Mw/Mn\tabcellsep Test temperature °C\\
Anionic Polymerisation PS (PS a )\tabcellsep \multicolumn{2}{l}{355500 1.03}\tabcellsep 170\\
Free-radical\tabcellsep \tabcellsep \\
Polymerisation PS\tabcellsep \multicolumn{2}{l}{361100 1.44}\tabcellsep 170\\
(PS f )\tabcellsep \tabcellsep \\
\multicolumn{4}{l}{These two Polystyrenes were analysed}\\
\multicolumn{4}{l}{according to Farias on a rotational rheometer ARES}\\
\multicolumn{4}{l}{(Advanced Rheometric Expansion System) of controlled}\\
\multicolumn{4}{l}{deformation throughout dynamic experiments with}\\
\multicolumn{4}{l}{parallel plate geometry(Farias, 2009). The GPC (Gel}\\
\multicolumn{4}{l}{Permeation Chromatography) gives the medium molar}\\
\multicolumn{4}{l}{mass and the Polydispersity index with the help of a}\\
\multicolumn{4}{l}{liquid chromatographer Waters Alliance model GPC 1}\\
\multicolumn{4}{l}{V2000 equipped with refraction index(Farias, 2009).}\end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.05904580152671755\textwidth}P{0.5288167938931297\textwidth}P{0.06553435114503817\textwidth}P{0.055152671755725184\textwidth}P{0.0019465648854961831\textwidth}P{0.0025954198473282443\textwidth}P{0.035038167938931296\textwidth}P{0.0681297709923664\textwidth}P{0.013625954198473282\textwidth}P{0.0071374045801526715\textwidth}P{0.0077862595419847325\textwidth}P{0.005190839694656489\textwidth}}
\tabcellsep \tabcellsep \multicolumn{5}{l}{Modelling Two Different Disperse Polystyrene with Maxwell Fractional Model in SAOS Experiments}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 1 ?\tabcellsep ?\tabcellsep 2\tabcellsep ?\tabcellsep ?\tabcellsep R 2\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{3}{l}{Anionic Polymerisation PS (PS a )}\tabcellsep 1029000\tabcellsep 132900\tabcellsep 0.987\tabcellsep 0.120\tabcellsep 0.9987\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{4}{l}{Free-radical Polymerisation PS (PS f )}\tabcellsep 275800\tabcellsep 116400\tabcellsep 0.842\tabcellsep 0.126\tabcellsep 0.990\\
Year 2017\tabcellsep \multicolumn{6}{l}{The Maxwell Fractional model to be valid must be > 0 for 2 ? and 1 ? , and for ? and ? the observation}\tabcellsep Their characteristics are presented on Table 1.\tabcellsep Year 2017\\
30\tabcellsep \multicolumn{6}{l}{of the final result is 0 < ? and ? <1 (Jaishankar \& McKinley, 2012).}\tabcellsep 31\\
( ) Volume XVII Issue III Version I J\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep ( ) Volume XVII Issue III Version I J\\
Global Journal of Researches in Engineering\tabcellsep \multicolumn{6}{l}{(Ruymbeke, Keunings, Hagenaars, \& Bailly, 2002) and also "Determination of the molecular weight distribution of the entangled linear polymers from linear viscoelasticity data" (Ruymbeke et al., 2002). As seen on table 1, there are 2 different polystyrene synthesized On this work itis used data that Farias presented on her work (Farias, 2009), gently given by a group of eminent researchers and presented in work as "Evaluation of Reptation Model for predicting the linear viscoelastic properties of entangled linear polymers"}\tabcellsep Global Journal of Researches in Engineering\\
\tabcellsep by\tabcellsep anionic\tabcellsep polymerisation\tabcellsep and\tabcellsep free\tabcellsep radical\\
\tabcellsep \multicolumn{6}{l}{polymerisation tested at 170 °C (Farias, 2009) with}\\
\tabcellsep \multicolumn{3}{l}{different polydispersity index.}\tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{3}{l}{© 2017 Global Journals Inc. (US)}\tabcellsep \tabcellsep \end{longtable} \par
  {\small\itshape [Note: © 2017 Global Journals Inc. (US)]} 
\caption{\label{tab_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.7531645569620252\textwidth}P{0.09683544303797467\textwidth}}
\multicolumn{2}{l}{Accordingly to parameters values is observed}\\
that all values are >0 for\tabcellsep 2 ? and 1\end{longtable} \par
 
\caption{\label{tab_3}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_4}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_5}}\end{figure}
 			\footnote{© 2017 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Normand et al. ()]{b10}\label{b10} 	 		\textit{Choosing Initial Parameter Values For Nonlinear Regression},  		 			M D Normand 		,  		 			M Eisenberg 		,  		 			M Peleg 		.  		2012. Wolfram Demonstrations Project.  	 
\bibitem[Friedrich et al. ()]{b5}\label{b5} 	 		‘Constitutive behavior modeling and fractional’.  		 			C Friedrich 		,  		 			H Schiessel 		,  		 			A Blumen 		.  		 S0169-3107(99)80038-0.  		 \url{https://doi.org/http://dx.doi.org/10.1016/}  	 	 		\textit{Advances in the Flow and Rheology of Non-Newtonian Fluids},  				1999. 8 p. .  	 
\bibitem[Pinho and De ()]{b11}\label{b11} 	 		\textit{Cálculo De Escoamentos De Fluidos Não Newtonianos Em Regime Laminar},  		 			F M C T Pinho 		,  		 			De 		.  		2003.  	 
\bibitem[Bird et al. ()]{b2}\label{b2} 	 		‘Dynamics of polymeric liquids, Fluid mechanics’.  		 			B R Bird 		,  		 			R C Armstrong 		,  		 			O Hassanger 		.  	 	 		\textit{Journal of Polymer Science Part C}  		1987.  	 
\bibitem[Ruymbeke et al. ()]{b12}\label{b12} 	 		‘Evaluation of Reptation Models for Predicting the Linear Viscoelastic Properties of Entangled Linear Polymers’.  		 			E Ruymbeke 		,  		 			Van 		,  		 			R Keunings 		,  		 			A Hagenaars 		,  		 			C Bailly 		.  	 	 		\textit{Macromolecules}  		2002. p. .  	 
\bibitem[Henry et al. ()]{b6}\label{b6} 	 		‘Fractional cable models for spiny neuronal dendrites’.  		 			B I Henry 		,  		 			T A M Langlands 		,  		 			S L Wearne 		.  		 \xref{http://dx.doi.org/10.1103/PhysRevLett.100.128103}{10.1103/PhysRevLett.100.128103}.  		 \url{https://doi.org/10.1103/PhysRevLett.100.128103}  	 	 		\textit{Physical Review Letters}  		2008. 100  (12)  p. .  	 
\bibitem[Freeborn et al. ()]{b4}\label{b4} 	 		‘Fractional-order models of supercapacitors, batteries and fuel cells: A survey’.  		 			T J Freeborn 		,  		 			B Maundy 		,  		 			A S Elwakil 		.  		 \xref{http://dx.doi.org/10.1007/s40243-015-0052-y}{10.1007/s40243-015-0052-y}.  		 \url{https://doi.org/10.1007/s40243-015-0052-y}  	 	 		\textit{Materials for Renewable and Sustainable Energy}  		2015. 4  (3)  p. .  	 
\bibitem[Sabatier et al. ()]{b13}\label{b13} 	 		‘Lithium-ion batteries modeling involving fractional differentiation’.  		 			J Sabatier 		,  		 			M Merveillaut 		,  		 			J M Francisco 		,  		 			F Guillemard 		,  		 			D Porcelatto 		.  		 \xref{http://dx.doi.org/10.1016/j.jpowsour.2014.02.071}{10.1016/j.jpowsour.2014.02.071}.  		 \url{https://doi.org/10.1016/j.jpowsour.2014.02.071}  	 	 		\textit{Journal of Power Sources}  		2014. 262 p. .  	 
\bibitem[Alves ()]{b1}\label{b1} 	 		‘Modeling Insite ® Technology Ethylene ?-olefin resins with Standard FOV fluid in 1D’.  		 			B M R Alves 		.  		 \xref{http://dx.doi.org/10.1016/j.jksues.2017.01.001}{10.1016/j.jksues.2017.01.001}.  		 \url{https://doi.org/10.1016/j.jksues.2017.01.001}  	 	 		\textit{Journal of King Saud University -Engineering Sciences}  		2017.  	 
\bibitem[Michailas et al. ()]{b9}\label{b9} 	 		‘On fractional models for human motion tracking’.  		 			R Michailas 		,  		 			T Martin 		,  		 			K Lasse 		,  		 			Manoli Yiannos 		.  		 \xref{http://dx.doi.org/10.1177/1077546313479637}{10.1177/1077546313479637}.  		 \url{https://doi.org/10.1177/1077546313479637}  	 	 		\textit{Journal of Vibration and Control}  		2014. 20  (7)  p. .  	 
\bibitem[Ahmed et al. ()]{b0}\label{b0} 	 		\textit{On fractional order cancer model},  		 			E Ahmed 		,  		 			A H Hashis 		,  		 			F A Rihan 		.  		2012. 3 p. .  	 
\bibitem[Flores-Tlacuahuac and Biegler ()]{b3}\label{b3} 	 		‘Optimization of fractional order dynamic chemical processing systems’.  		 			A Flores-Tlacuahuac 		,  		 			L T Biegler 		.  		 \xref{http://dx.doi.org/10.1021/ie401317r}{10.1021/ie401317r}.  		 \url{https://doi.org/10.1021/ie401317r}  	 	 		\textit{Industrial and Engineering Chemistry Research}  		2014. 53  (13)  p. .  	 
\bibitem[Jaishankar and Mckinley ()]{b7}\label{b7} 	 		‘Power-law rheology in the bulk and at the interface: quasiproperties and fractional constitutive equations’.  		 			Jaishankar 		,  		 			G H Mckinley 		.  		 \xref{http://dx.doi.org/10.1098/rspa.2012.0284}{10.1098/rspa.2012.0284}.  		 \url{https://doi.org/10.1098/rspa.2012.0284}  	 	 		\textit{Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}  		2012. 1989. p. .  	 
\bibitem[Maxwell (1867)]{b8}\label{b8} 	 		‘XV. On the Dynamical Theory of Gases’.  		 			J C Maxwell 		.  		 \xref{http://dx.doi.org/10.1098/rstl.1867.0004}{10.1098/rstl.1867.0004}.  		 \url{https://doi.org/10.1098/rstl.1867.0004}  	 	 		\textit{Philosophical Transictions of the Royal Society of London}  		1867. January. 157 p. .  	 
\end{bibitemlist}
 			 		 	 
\end{document}
