Generalization of a Double-Point Method to Determine the Intrinsic Viscosity in a Polymer-Solvent Mixture

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1 523 A publiation of CHEMICAL ENGINEERING TRANSACTIONS VOL. 32, 203 Chief Editors: Sauro Pierui, Jiří J. Klemeš Copyright 203, AIDIC Servizi S.r.l., ISBN ; ISSN The Italian Assoiation of Chemial Engineering Online at: Generalization of a Double-Point Method to Determine the Intrinsi Visosity in a Polymer-Solvent Mixture Eduardo Díez a, *, Ismael Díaz b, Javier Camaho a, Gabriel Ovejero a, María D. Romero a a Departamento de Ingeniería Químia, Faultad de C.C. Químias, Universidad Complutense, Avda. Complutense s/n, Madrid, Spain b Departamento de Ingeniería Químia Industrial y del Medio Ambiente, Universidad Politénia de Madrid, C/José Gutiérrez Abasal 2, Madrid, Spain ediezal@quim.um.es A double-point method proposed in literature for the determination of the Intrinsi Visosity of a polymersolvent solution and based on the Ram-Moham-Rao single point equation, have been extended to all single-point expressions available in literature. To assess the validity of the method, Intrinsi Visosity values of several rubber-solvent mixtures, alulated following the lassial proedure of looking for the ommon interept of Huggins and Kraemer plots, have been ompared with the ones alulated by means of the double-point methods. The deviations between the results obtained by both methodologies allows assuring that double-point equations are a reliable alternative of Huggins and Kraemer plots to determine Intrinsi Visosity values.. Introdution In the last deades, the importane of polymer-type materials is growing exponentially, as a onsequene of their almost infinite range of appliations. Beause most of them are obtained by means of dissolution proesses (Miller-Chou and Koenig, 2003), the rheology of the polymer-solvent systems is really important (Kragulja et al., 2009). Besides, the intrinsi visosity tehnique is one of the most employed methodologies with the aim of obtaining thermodynami parameters of suh mixtures (Mehrdad et al., 20), suh as Infinite Dilution oeffiients. The Intrinsi Visosity ([η]) is the visosity of and infinite diluted polymer solution. It is usually alulated from flow time measurements whih are extrapolated to infinite dilution by means of Huggins (942), Kraemer (938) or Shulz-Blashkle (94) expressions (Eqs, 2 and 3). ηsp = [ η] + K [ η] 2 H () ln( ) r = [ η] + K [ η] 2 K (2) ηsp [ ] [ ] = η +K SB ηη i (3) In these equations, is the onentration of polymer solution, K H is the Huggins onstant, K K is the Kramer onstant and K SB is the Shulz-Blashkle onstant. Relative visosity (η r ) is obtained as the relation between the flow time of the polymer solution through a apillary tube of known diameter and length and the flow time of the pure solvent through the same apillary tube. Speifi visosity (η sp ) is defined as relative visosity minus one, and represents the visosity inreasing due to the polymer. The intrinsi

2 524 visosity ([η]) is usually obtained from interept of the Kraemer, Huggins or Shulz-Blashkle relationships, using η r and η sp experimentally determined for different polymer solutions; theoretially, K K + K H = 0.5. However, single-point equations have been proposed with the aim of determining the intrinsi visosity by a single flow-time measurement. The most important expressions are the Solomon-Ciuta (963) one, Eq 4 the Deb-Chatterjee (968) one, Eq 5, the Ram-Mohan-Rao (986) one, Eq 6, the Kuwahara (963) one, Eq 7 and the Palit and Kar (967) one, Eq 8. 2 sp 2ln [ η] = η ( η ) 3 η = 3ln ηr + ηsp 3ηsp 2 2 η = sp ln r 2 η + η η = sp 3ln r 4 η + η [ ] 3 ( ) ( ) 2 [ ] ( ) [ ] ( ) [ η] = 4 4η 2η + η 4ln( η ) r sp sp sp r The former expressions are based on assuming K K + K H = 0.5 and have the advantage of being apable of extrapolating to infinite dilution by means of a single experimental measurement, while for applying Huggins or Kraemer plots, at least five measurements should be desirable. However, the main drawbak of employing these expressions is that the final Intrinsi Visosity result an be different depending on the polymer onentration in the solution employed to perform the single-point measurement. So, for all the reasons stated above, reently Curvale and Ceso (2009) proposed an intermediate strategy named as double-point equation, based on the Ram-Mohan-Rao expression, whih is represented in Equation 9. In this equation, and 2 are onentrations of the two polymer solutions (being 2 > ), η r, and η r,2 are the relative visosities, and η sp, and η sp,2 are the speifi visosities. [ ] ( ηr, ) η ln ( ηr,2 ) η ln (9) 2 sp, sp,2 η = So the final aim of this paper is to generalize the double-point method by extending it not only to Ram- Mohan-Rao expression but also to any single-point equation, and analysing its validity by omparing the obtained results with previously alulated ones by means of the lassial proedure of seeking the ommon interept of Huggins and Kraemer equations. 2. Theoretial bakground Assuming two polymer-solvent solutions of ompositions and 2 (being 2 > ), their Intrinsi Visosities determined by any of the single-point equations will be [η] and [η] 2, respetively. These values should be equal beause the Intrinsi Visosity is defined as an extrapolation of the visosity to infinite dilution onditions; however, due to all single point methods make this extrapolation from only one onentration point, the final Intrinsi Visosity value is not the same in both ases. So, a reasonable approximation ould be onsidering that the true Intrinsi Visosity value is in between the points (, [η] ) and ( 2, [η] 2 ). Assuming a linear relationship, the slope (m) of the straight line joining the points (, [η] ) and ( 2, [η] 2 ) will be (Eq 0): m = [ η] [ η] (4) (5) (6) (7) (8) (0)

3 525 If we now onsider a generi point i (whose onentration is i ) belonging to the previous straight line, its Intrinsi Visosity ([η] i ) will be able to be alulated with Eq (), taking into aount that the slope of the line is desribed by means of Eq 0. [ ] ( ) [ ] [ η] [ η] η = + η = + η ( ) [ ] m i i i 2 If we now onsider the ase when i tends to 0 (beause the Intrinsi Visosity is the visosity of an infinite polymer solution), the Eq is transformed into Eq 2. () [ η ] = [ η] [ η] 0 2 (2) In this last expression, the terms [η] and [η] 2 an be replaed by any of the Eqs 4 to 8. The final result is that the Intrinsi Visosity of whatever polymer-solvent mixture an be determined with Eq 2, by simply two flow-time measurements at two different ompositions, and 2, and alulating the relative and speifi visosities (whih appear in [η] and [η] 2 terms) by any Eq from 4 to Results and disussion To assess the reliability of the generalized double-point proposed here, we have ompared the results that we have previously determined for different poly (styrene-butadiene) rubber-ylohexane mixtures at 30 ºC, following the lassial proedure of finding the ommon interept of Huggins and Kraemer plots, with the obtained values with the Eq 2 ombined with all the Eqs 4 to 8. The studied polymers employed as examples were, on one hand a poly (styrene-b-butene/ethylene-bstyrene) triblok opolymer (SEBS) (Ovejero et al., 2007) and, on the other hand, three poly (styrene butadiene styrene) triblok opolymers (SBSs) with different struture and styrene ontent, named C4, C500 and C50 respetively (Ovejero et al., 200). The main harateristis of these materials are summarized in Table. The Table also shows the Intrinsi Visosity values ([η]) of eah ylohexanepolymer mixtures, obtained from the ommon interept of Huggins and Kraemer plots (values named as [η] real ). Table. Main harateristis of the employed polymers POLYMER Mw (kg/kmol) ρ (kg/m 3 ) [η] real at 30 ºC SEBS C C C On the other hand, Tables 2 to 5 show the Intrinsi Visosity values determined for eah ylohexanepolymer-binary mixture at different ompositions with any single-point (subsript ) or double point (subsript 2) method (values named as [η] al ). As it an be observed, the double-point methods perform, in many ases, better estimations than the single-point methods, espeially when working with the most diluted ompositions; this is espeially notieable in the ase of the mixtures with C4 and C500 rubbers. To further reinfore what previously said, Figures and 2 show the deviations of the [η] al values with respet to the [η] real values. The deviations have been alulated aording to Eq 3. [ η] [ η] real [ η] al Deviation = abs 00 real (3)

4 526 Table 2. [η] Values obtained by single and double point methods when omparing with Table values, for ylohexane SEBS mixtures PROCEDURE [η] al at 30 ºC (Solomon-Ciuta) (Deb-Chatterjee) (Ram-Mohan-Rao) (Kuwahara) (Palit and Kar) (Solomon-Ciuta) (Deb-Chatterjee) (Ram-Mohan-Rao) (Kuwahara) (Palit and Kar) Table 3. [η] Values obtained by single and double point method when omparing with Table values, for ylohexane C4 mixtures PROCEDURE [η] al at 30 ºC (Solomon-Ciuta) (Deb-Chatterjee) (Ram-Mohan-Rao) (Kuwahara) (Palit and Kar) (Solomon-Ciuta) (Deb-Chatterjee) (Ram-Mohan-Rao) (Kuwahara) (Palit and Kar) Table 4. [η] Values obtained by single and double point method when omparing with Table values, for ylohexane C500 mixtures PROCEDURE [η] al at 30 ºC (Solomon-Ciuta) (Deb-Chatterjee) (Ram-Mohan-Rao) (Kuwahara) (Palit and Kar) (Solomon-Ciuta) (Deb-Chatterjee) (Ram-Mohan-Rao) (Kuwahara) (Palit and Kar)

5 527 Table 5. [η] Values obtained by single and double point method when omparing with Table values, for ylohexane C50 mixtures PROCEDURE [η] al at 30 ºC (Solomon-Ciuta) (Deb-Chatterjee) (Ram-Mohan-Rao) (Kuwahara) (Palit and Kar) (Solomon-Ciuta) (Deb-Chatterjee) (Ram-Mohan-Rao) (Kuwahara) (Palit and Kar) a) b) Figure. Deviations of the [η] al values with respet to the [η] real values, for a) ylohexane SEBS mixture and b) ylohexane C4 mixture a) b) Figure 2. Deviations of the [η] al values with respet to the [η] real values, for a) ylohexane C500 mixture and b) ylohexane C50 mixture Another important point is that both single-point and double-point methods approximate better to the real Intrinsi Visosity value (being the real value the one obtained by getting the ommon slope of Huggins and Kraemer plots) whenever the ompositions are as low as possible. This seems to be logial, taking into aount that Intrinsi Visosity is defined as the visosity of an infinite diluted polymer-solvent solution. As a final remark simply omment that double-point methods have demonstrated to be a reliable alternative to obtain aurate values on Intrinsi Visosity. With them, it is possible to ahieve a reasonable time saving beause one two experimental points are needed, while to draw a proper straight line are neessary at least five points.

6 Conlusion A generalized double-point method to determine the Intrinsi Visosity of a polymer-solvent mixture is proposed here. The assessment of this method was done by omparing the Intrinsi Visosity values obtained by this method, with the ones obtained following the traditional proedure (ommon interept of Huggins and Kraemer plots). In all ases a good agreement between both methodologies was reahed, espeially when applying the low omposition values to the double-point method. Referenes Curvale R.A., Ceso J.C., 2009, Intrinsi visosity determination by single point and double point equations. Appl. Rheol. 9, Deb P.C., Chatterjee S.R., 968, Unperturbed dimension of polymer moleules from visosity measurements, Die Makromolekulare Chemie 20, Huggins M.L., 942, The visosity of dilute solutions of long-hain moleules. 4. Dependene on onentration, J. Am. Chem. So. 64, Kraemer E.O., 938, Moleular weights of elluloses and ellulose derivatives, Ind. Eng. Chem. Res. 30, Kragula K., Solji I., Vidovi E., Juki A., 2009, Misibility and interations of rheology improvers based on funtional polymetharylate in toluene solutions, Chemial Engineering Transations, 7, , DOI: /CET729. Kuwahara N., 963, On the polymer-solvent interation in polymer solutions. J. Polym. Si. A, Mehrdad A., Saghatforoush L.A., Marzi G., 20 Effet of temperature on the intrinsi visosity of poly(ethylene glyol) in water/dimethyl sulfoxide solutions, J. Mole. Liquids 6, Miller-Chou B.A., Koenig J.L., 2003, A review of polymer dissolution, Prog. Polym. Si. 28, 223:270. Ovejero G., Perez P., Romero M.D., Guzman I., Díez E., 2007, Determination of solubility parameters of polymers by using intrinsi visosity method, Proeedings of European Congress of Chemial Engineering (ECCE-7) 2, Copenhagen. Ovejero G., Romero M.D., Díez E., Díaz I., 200 Thermodynami interations of three SBS (styrene butadiene styrene) triblok opolymers with different solvents, by means of intrinsi visosity measurements, Eur. Polym. J. 46, Palit S.R., Kar I., 967, Polynomial expansion of log relative visosity and its appliation to polymer solutions, J. Polym. Si. 5, Ram-Mohan-Rao M.V., Yassen M., 986, Determination of intrinsi visosity measurement, J. Appl. Polym. Si. 3, Shulz G.V., Blashke F., 94, An equation for alulating the visosity number for very small ompositions, J. Prakt. Chem. 58, Solomon O.F., Ciuta I.Z., 962, Determination de la visosité intrisèque de solutions de polymères par una simple détermination de la visosité, J. Appl. Polym. Si. 6,