J. Serb. Chem. Soc. 82 (4) S208 S220 (2017) Supplementary material

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1 J. Serb. Chem. Soc. 82 (4) S8 S2 (7) Supplemetary material SUPPLEMENARY MAERIAL O Experimetal measuremets ad modellig of solvet activity ad surface tesio of biary mixtures of poly(viyl pyrrolidoe) i water ad ethaol MAJID AGHIZADEH* ad SABER SHEIKHVAND AMIRI Chemical Egieerig Departmet, Babol Noshirvai Uiversity of echology, P. O. Box 484, Babol , Ira J. Serb. Chem. Soc. 82 (4) (7) ABLE S-I. Measured desities of PVP solutios ad parameters of Eq. () at various temperatures; the desities are give as mea ± stadard deviatio / a b c ARE ρ exp / g cm -3 w = w = w = K + water ± 0.9 ± ± 0.9 ± 0.9 ± ± ± ± ± ± 0.95 ± ± 0.9 ± 0.9 ± ± ± ± ± ± 0.9 ± ± ± ± ± K + water ± ± 0.98 ± ± ± ± 0.9 ± ± ± * Correspodig author. m_taghizadehfr@yahoo.com S8 w = 5 RMSE R².22 ± ± ± ± ± ± ± ± ± ± ±

2 SUPPLEMENARY MAERIAL S9 ABLE S-I. Cotiued / a b c ARE ρ exp / g cm -3 w = w = w = K + water ± ± ± 0.93 ± 0.95 ± ± ± ± ± ± ± ± 0.9 ± 0.9 ± ± K + ethaol 0.7 ± ± ± 0.75 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.7 ± 0.76 ± ± K + ethaol ± ± ± ± 0.77 ± ± ± ± ± ± ± ± ± ± 0.89 ± 0.7 ± ± ± ± 0.7 ± ± ± 0.7 ± 0.88 ± w = 5 RMSE R².9 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

3 S20 AGHIZADEH ad AMIRI ABLE S-II. Measured viscosities of PVP solutios ad parameters of Eq. (2) at various temperatures; the viscosities are give as mea ± stadard deviatio / a b c d ARE w = K + water ± ± ± ± ± ± ± ± K + water ± ± ± ± ± ± ± ± K + ethaol ± ± ± ± η exp / mpa s w = w = 37.6 ± ±.5.6 ± ± ± ± ± ± ± ± ± ±. 2.7 ± ± 8.6 ± ± 37.0 ± ± ± ± ± ± ± ± ± ± 2.7. ± ±.9.2 ± ± ± ± ± ± ± ± ± ± ± ± 3.3 w = ± ± ± ± ± ± ± ± ± ± ± ± ± ±.4 38 ± ± ±. 85 ± ± ± 9.8 R 2

4 SUPPLEMENARY MAERIAL S2 ABLE S-II. Cotiued / a b c d ARE η exp / mpa s w = w = w = K + ethaol ± ±.0 ± ± ± ± ± ± 0.6 ± ± ± ±.5 K + ethaol ± ± ± ± ±.5 ± ± ±.5 ± ± ±.3 ± ± ± 0.9 ± ± ± 0.5 ± ± ± 0.7 ± ± ± 0.5 ±.9 w = ± ±.4 ± ± ± ± ± ± ± ± ± ± 5.5 R 2 hermodyamic model for solvet activity A thermodyamic model based o the Eyrig absolute rate theory was proposed to calculate the activity of solvets i biary PVP polymer solutios. Geerally, measurig the viscosity ad desity of polymer solutios are much easier tha measurig the solvet activity. For this reaso, i this model, the viscosity ad desity of the polymer solutio were used to calculate the solvet activity. Accordig to the Eyrig viscosity model, the viscosity of a liquid solutio is calculated by the followig equatio: 2,3 g E l( ηυ) = xil( ηiυi) + (S-) R i where η, υ, η i ad υ i are the viscosity, molar volume of the solutio, viscosity of pure compoet i ad molar volume of pure compoet i, respectively. X i is the molar fractio of compoet i i the mixture, is the absolute temperature, R is

5 S22 AGHIZADEH ad AMIRI the gas costat ad g* E is the excess Gibbs eergy of viscous flow required to move the fluid particles from a stable state to a activated state. here is a equivalece relatioship betwee the excess Gibbs eergy (g*) ad the equilibrium excess Gibbs free eergy of mixig (g): g E = l( ηυ) xil( ηυ i i) (S-2) R i he first ad secod terms o the right-had side of Eq. (2) are related to the real viscosity of the solutio ad the ideal viscosity of the solutio, respectively. I this paper, dimesioless terms were used istead of the real ad ideal viscosity as follows: ge ( ) xi( i i) R = ηυ ( R R) ηυ η υ η i Rυ (S-3) R where η R ad υ R are the viscosity ad molar volume of a referece compoet, respectively. I this work, compoet 2 was selected as the referece compoet. hus: 2 ge ( ηυ) xi( ηυ i i) = ( 2 2) (S-4) R η υ η i 2υ = 2 E g R ηυ x η υ x2η2υ2 = ηυ 2 2 ηυ 2 2 ηυ 2 2 (S-5) Hece, the viscosity ad desity values of compoets ad 2 are required to calculate the excess Gibbs free eergy by Eq. (S-5). he desity ad viscosity of the solutios that were used to verify the model were measured experimetally ad fitted by quadratic equatios. O the other had, activity coefficiet of the solvet (γ ) ca be expressed as a fuctio i terms of the excess Gibbs eergy: E g R l γ= g + ( x) x E g ( x ) g lγ = + R R x E E (S-6) (S-7) With respect to the relatioship betwee a (activity of the solvet) ad γ (activity coefficiet of the solvet) (a = x γ ), by determiig the term g E / x ad substitutig the term g E / x ito Eq. (S-7), oe obtais the followig relatio:

6 SUPPLEMENARY MAERIAL S23 ( x ) ηυ x η υ x2η 2υ2 ge l a = + + l x ηυ 2 2 ηυ 2 2 ηυ 2 2 R x 2 3 mx + m2x2 ( a bw cw dw ) ge a bw cw2 + + xη υ x2η2υ2 = R ηυ 2 2 ηυ 2 2 ηυ 2 2 m2( x) w2 = mx + m2( x) 2 ' 3 mx + m2x2 ( a + bw + cw + d w ) 2 a+ bw+ cw l a = ηυ 2 2 x ηυ x2η2υ2 ( x ) ge + + l x ηυ 2 2 ηυ 2 2 R x (S-8) (S-9) (S-0) his model ca predict the solvet activity i biary mixtures by usig experimetal desity ad viscosity values. hermodyamic model for surface tesio A thermodyamic model based o the Butler Equatio 4 for the predictio of the surface tesio of biary polymer solutios is preseted. For calculatig the surface tesio of a polymer solutio, it is assumed that oe phase is cofigured at the surface. he chemical potetial of compoet i the bulk of a oelectrolyte biary solutio is expressed as follows: μ 0 b = μb + Rl ab (S-) where μ 0 b ad a b are the stadard chemical potetial ad the activity of compoet i the bulk phase, ad R ad are the gas costat ad temperature, respectively. he chemical potetial of compoet at the surface phase ca be calculated usig the followig equatio: μ 0 s = μs + Rl as σa (S-2) where μ 0 s is the stadard chemical potetial at the surface, ad σ ad a s are the surface tesio of the solutio ad the activity of compoet at the surface phase, respectively, while A is the molar surface area (cm 2 mol ) of compoet i solutio. he followig equatio is used for the pure compoets:

7 S24 AGHIZADEH ad AMIRI μ0 0 s μb = σ A (S-3) where A ad σ are the molar surface area ad surface tesio of compoet, respectively. At equilibrium, the chemical potetial of compoet i the bulk ad surface phases are equivalet: μ s = μ (S-4) By combiig the above equatios, the followig equatio is obtaied: σ b s A σa Rl a ab = + (S-5) he activity of compoet i both the bulk ad surface phases is achieved usig the activity coefficiets: σ γs = + (S-6) γ s A σa Rl x xb where x b, x s, γ b ad γ s ad are the mole fractio of compoet i the bulk, the mole fractio of compoet at the surface, the activity coefficiet of compoet i the bulk ad the activity coefficiet of compoet at the surface, respectively. Equatio (S-6), which is kow as the Butler Equatio, could be writte as the followig: 4 R l x s s σ = σ + (S-7) A xb γb he molar surface area is determied by the UNIFAC method as follows: Ai = υkqk (S-8) where Q k ad υ k are the UNIFAC parameter ad the umber of group k, respectively. Here, is a ormalizatio factor. 9 o calculate the activity of each compoet at the surface ad i the bulk of a biary liquid mixture, the Flory Huggis Equatio 5 is used: l a 2 = l ϕ+ ( ) ϕ2 + χϕ2 (S-9) υ2 υ2 l a 2 2 = l ϕ2 + ( ) ϕ+ χ2ϕ (S-) υ where a ad a 2 are the solvet activity ad polymer activity, φ ad φ 2 are the volume fractio of the solvet ad polymer, υ ad υ 2 are the partial molar volume of the solvet ad polymer, respectively, ad χ ad χ 2 are the iteractio parameters betwee the polymer ad the solvet. υ γ b

8 SUPPLEMENARY MAERIAL S25 A polymer molecule cosists of r elemets. heoretically, the volume of a polymer elemet is equal to the volume of a solvet molecule. 6 hus, the volume of oe mole of polymer is r times larger tha the volume of oe mole of solvet: υ2 r υ = (S-2) he iteractio parameter is obtaied from the followig equatio: ( δ 2 δ2) υ χ = (S-22) R Equatio (S-7) ca be writte for compoet ad 2 accordig to the followig assumptios: A= A2 = A γs = γb = (S-23) ( b 2s 2 ) R l x R l x σ σ + + = A x 0 2b A xs If the first ad secod terms of Eq. (S-23) are equal to C 2, the followig equatio is obtaied: A x2s = xsexp( C2 ) (S-24) R herefore, the mole fractio of the compoets at the surface, the activity coefficiet at the surface, ad fially, the surface tesio of the solutio are obtaied usig Eq. (S-5). ABLE S-III. Activity of water for various solutios of K ad K i water ad ethaol at differet temperatures ad mass fractios; experimetal activities are give as the mea ± stadard deviatio; OAARE: overall average absolute relative error w a a Exp a Model RMSE RE AARE w a a Exp a Model RMSE RE AARE K water ( = ) K water ( = ) ±

9 S26 AGHIZADEH ad AMIRI ABLE S-III. Cotiued w a Model RMSE RE K water ( = ) ± K ethaol ( = ) ± K ethaol ( = ) OAARE = 5 a Exp a AARE w a Model RMSE RE AARE K water ( = ) K ethaol ( = ) ± K ethaol ( = ) a Exp a ABLE S-IV. Surface tesios of various solutios of K ad K i water ad ethaol at differet temperatures ad mass fractios; experimetal surface tesios are give as the mea ± stadard deviatio; OAARE: overall average absolute relative error σ exp mn m ± 60.9 ± ± σ model mn m - RE K water RMSE AARE w = σ exp σ model mn m - mn m ± 57.6 ± 57. ± RE K water RMSE AARE

10 SUPPLEMENARY MAERIAL S27 ABLE S-IV. Cotiued σ exp mn m ± ± ± 56.0 ± ±.0 ± 24.3 ± 23.5 ± 23. ± 22.7 ± 22.6 ± 22.5 ± 22.3 ± 58.0 ± 57.3 ± 56.5 ±. ± 53.9 ± 53.0 ± 52.0 ± σ model mn m - RE RMSE AARE w = K water K ethaol K water w = 7.38 σ exp σ model mn m - mn m ±.6 ± 54.5 ± 53.2 ± 5.8 ± 24.8 ± 24. ± 23.4 ± 22.7 ± 22.2 ± 2.5 ± 2.2 ± 2 ± 57.0 ± 56.3 ±.8 ±.2 ± 54.2 ± 53. ± 5.8 ± RE RMSE AARE K water K ethaol K water

11 S28 AGHIZADEH ad AMIRI ABLE S-IV. Cotiued σ exp mn m -.7 ± 23.5 ± 23.2 ± 22.9 ± 22.2 ± 22.0 ± 2.8 ± 2.7 ± 2.6 ± 56.8 ± 56.3 ±.2 ± 54.0 ± 53.0 ± 52.3 ±.8 ±.0 ± 22.9 ± 22.6 ± σ model mn m - RE K water K ethaol K water K ethaol RMSE AARE w = w = 6.76 σ exp σ model mn m - mn m - 5 ± 23. ± 22.5 ± 22.0 ± 2.4 ± 2.2 ±.5 ± 2 ± 9.2 ± 54.5 ± 54.0 ± 53.5 ± 53. ± 52.2 ± 5.3 ±. ± ± RE K water.6 0. K ethaol K water RMSE AARE

12 SUPPLEMENARY MAERIAL S29 ABLE S-IV. Cotiued OAARE = 5.69 σ exp mn m ± 2.7 ± 2.5 ± 2.2 ±.9 ±.8 ± σ model mn m - RE w = K ethaol RMSE.0423 AARE 3.86 Statistical aalysis. Relative error Xexp Xcal RE = 00 X exp 2. Average relative error ARE = ( RE) i = 3. Average absolute relative error AARE = RE i = 4. Root mea squared error RMSE = ( 2 Xexp Xcal) i i = 5. Stadard deviatio SD = ( ) 2 Xi X i = where X i is the amout of each data, X is the average of the data poits, ad is the umber of data poits.

13 S2 AGHIZADEH ad AMIRI 6. Coefficiet of determiatio R2 = [ 2 2 Xexp Xcal] i [ Xexp X] i i= i= with: X = [ Xexp ] i i = REFERENCES. M. aghizadeh, A. Eliassi, M. Rahbari-Sisakht, J. Appl. Polym. Sci. 96 (05) J.. Schrodt, R. M. Akel, J. Chem. Eg. Data 34 (989) 8 3. W. Cao, A. Fredeslud, P. Rasmusse, Id. Eg. Chem. Res. 3 (992) J. A. V. Butler, Proc. R. Soc., A (932) E. Egeme, N. Nirmalakhada, C. revizo, Eviro. Sci. echol. 34 (00) W. C. Forsma, Polymers i Solutio: heoretical Cosideratios ad Newer Methods of Characterizatio, Spriger, Pleum Press, New York, 986.