Experimental study of the thermodynamic and transport properties of binary mixtures of poly(ethylene glycol) diacrylate and alcohols at different temperatures J. Serb. Chem. Soc. 80 (7) 933–946 (2015) UDC 547.421–036.7+547.42+ JSCS–4770 544.032.4:532.13+532.14 Original scientific paper 933 Experimental study of the thermodynamic and transport properties of binary mixtures of poly(ethylene glycol) diacrylate and alcohols at different temperatures JELENA M. VUKSANOVIĆ#, IVONA R. RADOVIĆ#*, SLOBODAN P. ŠERBANOVIĆ# and MIRJANA LJ. KIJEVČANIN# Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11120 Belgrade, Serbia (Received 9 October 2014, revised 16 January, accepted 19 January 2015) Abstract: Experimental density ρ, refractive index nD and viscosity η data of three binary systems of poly(ethylene glycol) diacrylate (PEGDA) + ethanol, + 1-propanol and + 1-butanol were measured at eight temperatures from 288.15 to 323.15 K, with temperature step of 5 K, and at atmospheric pressure. The experimental data were correlated as a function of the PEGDA mole fraction and temperature. The densities and refractive indices of the investigated mix- tures could be fitted well with exponential function vs. composition, including the temperature dependence of the parameters, while in the case of the visco- sities, a polynomial function fits well the composition of the mixtures. In the case of the temperature correlation, all three properties (ρ, ln η and nD) exhi- bited linear trends. The viscosity modeling was performed using four models: the UNIFAC–VISCO, ASOG–VISCO, McAllister and the Teja–Rice models. For application of the UNIFAC–VISCO model, interaction parameters of fol- lowing groups were determined: CH2=CH/CH3, CH2=CH/CH2, CH2=CH/OH, CH2=CH/CH2O and CH2=CH/COO. In addition, in the same way, the binary interaction parameters used in the ASOG–VISCO model of the following groups were determined: CH2=CH/CH2, CH2=CH/OH, CH2=CH/CH2O and CH2=CH/COO. Keywords: density; viscosity; refractive index; new UNIFAC–VISCO para- meters; new ASOG–VISCO parameters. INTRODUCTION For a complete understanding of the thermodynamic and transport properties of pure organic compounds and multicomponent liquid mixtures, knowledge of their thermodynamic and transport properties over wide composition and tem- * Corresponding author. E-mail: ivonag@tmf.bg.ac.rs # Serbian Chemical Society member. doi: 10.2298/JSC141009005V _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ 934 VUKSANOVIĆ et al. perature ranges is necessary. Studies of thermodynamic properties contribute to the understanding of the behavior of various organic compounds and their functional groups, and are of great importance for the understanding of the mole- cular interactions in multicomponent mixtures. This work is a continuation of ongoing research related to determination of thermophysical and transport pro- perties of mixtures containing polymers.1–5 In this work, a biodegradable and biocompatible polymer, i.e., poly(ethylene glycol) diacrylate (PEGDA), was investigated in binary mixtures with small chain alcohols, i.e., ethanol, 1-pro- panol, and 1-butanol. Poly(ethylene) glycol diacrylate (PEGDA) is a low volatility and medium viscosity clear liquid with good flexibility and elongation, good water disper- siblity, low skin irritancy and good reactivity. It is soluble in water and is used as a functional co-monomer for flexible plastics and as a cross linking agent between the molecular chains of polymers.6 Furthermore, PEGDA is a synthetic, hydrophilic starting material for the production of hydrogels in the presence of a photo-initiator and UV light. This polymer is widely known as a biocompatible and non-immunogenic material suitable for various chemical manipulations, with application in tissue engineering and regenerative medicine.7 One of the impor- tant usages of PEGDA in biological and biomedical applications could be for controlled release of drugs by producing well defined micro- or nano-channels inside the polymer, which would make the release of drugs through the pathways more readily predictable and controlled. A procedure for producing PEGDA par- ticles with specific, internal channels for drug release is described in detail in the literature.8 The investigated short-chain alcohols are completely miscible with water and used as solvents in various fields of industry. In this particular case, their application in pharmaceutical industry is of great importance because mixtures of PEGDA and alcohols could be potentially applied in the pharmaceutical industry for the controlled release of drugs. In addition, they find application for the rem- oval of CO2 from the air or in biochemical applications.6 Alcohols are polar compounds with the following dipole moments: 5.67×10– 30 C·m for ethanol, 5.67×10–30 C·m for 1-propanol and 6.00×10–30 C·m for 1-butanol.9 PEGDA, as a hydrophilic polymer, contains polar or charged func- tional groups (carbonyl groups adjacent to an ether linkage) which make them soluble in polar compounds, such as alcohols. From the chemical structures of PEGDA and alcohols, it is evident that alcohols contain a hydrogen responsible for hydrogen bonding between the molecules of the same alcohol or with an oxygen from the polymer, while in the PEGDA molecule, ester COO groups are present. It could be conclude that these molecules might form intermolecular hydrogen bonds, i.e., hydrogen from the hydroxyl group in alcohols with the oxy- gen from the COO group in a polymer. There are also van der Waals dispersion _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ VOLUMETRIC PROPERTIES AND VISCOSITIES OF POLY(ETHYLENE GLYCOL)DIACRYLATE + ALCOHOLS 935 forces and dipole–dipole interactions between alcohols and polymer, and mole- cules of the same compound. The hydrogen bonding and dipole–dipole inter- actions will be much the same for all the alcohols, but the dispersion forces will increase as the alcohol becomes larger. The intention of this work was to investigate how the thermodynamic and transport properties of PEGDA and alcohol mixtures change with respect to the alcohol chain length and with temperature, bearing in mind the possible inter- actions between the above-mentioned components. Thus, in this work, the den- sities ρ, refractive indices nD and viscosities η of three binary systems of poly- (ethylene glycol) diacrylate (PEGDA) + ethanol or + 1-propanol or + 1-butanol were measured at eight temperatures (288.15, 293.15, 298.15, 303.15, 308.15, 313.15, 318.15 and 323.15 K) and at atmospheric pressure. Additionally, the vis- cosity data were modeled using the UNIFAC–VISCO, ASOG–VISCO, McAllis- ter and Teja–Rice models. Generally, if a viscosity calculation is based on already determined parameters given in the literature, the UNIFAC–VISCO and ASOG–VISCO models are actually predictive. However, since in the case of the systems investigated in the present study, some of the parameters were not known, the intention was to determine accurately their values and the UNIFAC– –VISCO and ASOG–VISCO models were considered as correlative. EXPERIMENTAL Chemicals Poly(ethylene glycol) diacrylate (PEGDA), with molecular formula C2n+6H4n+6On+3 and with number average molecular weight 700 g mol-1, was purchased from Aldrich (CAS No.: 26570-48-9, Cat. No.: 455008, Lot No.: MKBH4151V). Alcohols of reagent grade: ethanol (≥ 99.9 mass %), 1-propanol (≥ 99.5 mass %), and 1-butanol (≥ 99.5 mass %) were purchased from Merck. The chemicals were kept in dark bottles under an inert atmosphere and ultrasoni- cally degassed before sample preparation. Apparatus and procedures The density ρ measurements were performed using an Anton Paar DMA 5000 digital vibrating U-tube densimeter (with automatic viscosity correction). The temperature in the cell was regulated to ±0.001 K with a built in solid-state thermostat. Calibration of the apparatus was performed daily using ambient air and Millipore quality water. A Mettler AG 204 bal- ance, with a precision 1×10-7 kg, was used for precise measurement of mass composition for all binary mixtures, using the cell and the procedure described previously.10 The uncertainty of the mole fraction calculation was less than ±1×10-4. The experimental uncertainty in den- sity was about ±1×10-2 kg m-3. The refractive index nD measurements were performed using an automatic Anton Paar RXA 156 refractometer, which works with the wavelength of 589 nm. Throughout this pro- cedure, the temperature of the sample was kept constant with a built-in thermostat within an accuracy of ±0.03 K. The estimated experimental uncertainties in the refractive index were about ±1×10-4. The viscosity, η, measurements were performed using a digital Stabinger viscometer (model SVM 3000/G2). The instrument contains two measuring cells; one of which is used _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ 936 VUKSANOVIĆ et al. for measuring the density of the sample, while the other one measures the dynamic viscosity. The kinematic viscosity was calculated from the measured density and dynamic viscosity. During this procedure, the temperature in the cells was regulated to ±0.01 K with a built in solid-state thermostat. The relative uncertainty in the dynamic viscosity measurements was estimated to be 0.35 %. The densities, dynamic viscosities and refractive indices of the pure substances at several temperatures and at atmospheric pressure are compared with literature values7,11-19 in Table I. The agreement with the literature for the density measurements in most cases was within 0.55 kg m-3, while the viscosity measurements were within 0.02 mPa s. The experimental refractive indices of pure components agree with literature values within 8×10-4 for alcohols and within 0.002 for PEGDA. TABLE I. Densities, ρ, viscosities, η, and refractive indices, nD, of the pure components at temperature T and at atmospheric pressure; the standard uncertainties σ for each variables are σ(T) = 0.01 K; σ(p) = 5 %; σ(x1) = ±1×10 -4, and the combined uncertainties σc are σc(ρ) = = ±1×10-2 kg m-3; σc(nD) = ±1×10 -4; σc(η) = 0.35 %, at the 0.95 level of confidence (k ≈2) Substance T / K ρ / 103 kg m-3 η / mPa s nD This work Lit. This work Lit. This work Lit. PEGDA 293.15 1.47012 1.470 7 303.15 1.46618 1.465 7 313.15 1.46228 1.460 7 Ethanol 293.15 0.789547 0.790011 1.1885 1.209711 298.15 0.785257 0.785711 1.0838 1.099011 1.35999 1.3592212 303.15 0.780942 0.780911 0.98999 0.997111 313.15 0.772202 0.773311 0.82807 0.828011 323.15 0.763276 0.763613 0.69427 0.708113 1-Propanol 288.15 0.807931 0.8074914 293.15 0.803946 0.8037514 298.15 0.799932 0.7997514 1.9222 1.94315 1.38334 1.3837 16 303.15 1.7158 1.72515 1-Butanol 293.15 0.810205 0.809714 2.9321 2.94116 1.39929 1.3992916 298.15 0.806384 0.806014 2.5656 2.57116 1.39725 1.3974116 303.15 0.802538 0.8019118 2.2518 2.27116 1.39519 1.395919 308.15 0.798659 0.7980718 RESULTS AND DISCUSSION The experimental data of density, viscosity, and refractive index for three binary systems (PEGDA + ethanol, PEGDA + 1-propanol, and PEGDA + 1-but- anol) at eight temperatures (288.15 to 323.15 K), over the entire composition range and at atmospheric pressure are reported in Table S-I of the Supplementary material to this paper. Fitting of the experimental values of density and refractive index was per- formed as a function of PEGDA mole fraction with temperature dependant para- meters. The quality of the fitting was estimated by the deviation between experi- _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ VOLUMETRIC PROPERTIES AND VISCOSITIES OF POLY(ETHYLENE GLYCOL)DIACRYLATE + ALCOHOLS 937 mental value and those calculated by different equations. The best results were obtained using the following equation: ( ) ( ) 10 11 D 00 01 1 20 21 , exp A A T n A A T x A A T ρ  + = + +  + +   (1) where A00, A01, A10, A11, A20 and A21 are the fitting parameters, x1 is PEGDA mole fraction and T is temperature. The viscosity values, unlike density and refractive index values, varied greatly with change in temperature and hence, a single equation that combined the temperature and composition dependencies did not give good results and so fitting the viscosity values as a function of PEGDA mole fraction or temperature was performed separately using the following equations: 320 1 1 2 31 1B B x B x B xη = + + + (2) 10ln C C T η = + (3) where B0, B1, B2, B3, C0 and C1 are the fitting parameters, x1 is the PEGDA mole fraction and T is the temperature. For the three binary mixtures at different temperatures and compositions, the parameters of Eq. (1) are presented in Table S-II and the parameters of Eqs. (2) and (3) in Table S-III (Supplementary material). The corresponding root-mean- -square deviations (rmsd) σ, defined by Eq. (4) are presented in Tables S-II and S-III of the Supplementary material: ( ) 1/2 2 exp cal σ    −   =          n i Y Y n (4) Yexp and Ycal are experimental and calculated values of ρ, η or nD, respectively, and n is the number of experimental data points. Comparison of the densities, viscosities and refractive indices of binary sys- tems of PEGDA and alcohols at 288.15 and 323.15 K and at atmospheric pres- sure are given in Fig. 1a–c, respectively. It is obvious from Fig. 1 that the expe- rimental values of the density, viscosity, and refractive index data of pure PEGDA are significantly higher than those of the analyzed alcohols. In addition, it is evident that the densities and refractive index data of the mixtures increased exponentially with increasing PEGDA mole fraction, while the increase in the viscosities vs. PEGDA composition followed a polynomial trend. It can be obs- erved that the density and refractive index increased considerably in the range of _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ 938 VUKSANOVIĆ et al. lower PEGDA concentrations (from 0 to 0.3 mole fraction), while approaching higher PEGDA mole fractions, the curves trended to constant values. This means that the influence of PEGDA on the overall densities and refractive indices of the PEGDA + alcohol mixtures was far greater in comparison to the influence of the alcohols. In the case of viscosity, there was a constant increase in the values with increasing PEGDA mole fraction. In addition, it is noticeable that the densities, viscosities and refractive indices of pure compounds and their mixtures decreased as the temperature increased. This temperature influence was the most pro- nounced for the viscosity data. Namely, the viscosity of pure PEGDA at 288.15 K was almost six times higher than at 323.15 K. Fig. 1. Comparison of experimental data for: a) density, b) viscosity and c) refractive index vs. mole fraction for the three systems at 288.15 and 323.15 K and at atmospheric pressure, where the symbols refer to: PEGDA (1) + ethanol at (■) 288.15 and (□) 323.15 K; PEGDA (1) + 1-propanol (2) at (▲) 288.15 and (Δ) 323.15 K; PEGDA (1) + 1-butanol (2) at (●) 288.15 and (○) 323.15 K; the lines present the results calculated by Eq. (1) for the ρ and nD data and by Eq. (2) for the η data. Experimental values of the density and refractive index against temperature at atmospheric pressure are presented in Figs. 2 and 3, respectively, while ln η vs. 1/T changes at atmospheric pressure are depicted in Fig. 4. One can conclude that density and refractive index data exhibit linear depen- dences on temperature, with a decreasing tendency of the property with inc- reasing temperature. Figs. 2 and 3 also prove that the changes of densities and _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ VOLUMETRIC PROPERTIES AND VISCOSITIES OF POLY(ETHYLENE GLYCOL)DIACRYLATE + ALCOHOLS 939 refractive indices are greater in the range of smaller PEGDA mole fractions (from 0 to 0.3). Function of ln η vs. 1/T exhibited a linear trend as well, confirming that with increasing temperature the PEGDA + alcohols mixtures become less viscous (Fig. 4). Fig. 2. Experimental data of density, ρ, vs. temperature, T (288.15 to 323.15 K), at atmospheric pressure, for the systems: a) PEGDA (1) + ethanol (2); b) PEGDA (1) + 1-propanol (2); c) PEGDA (1) + 1-butanol (2). The symbols refer to mole fractions of PEGDA: (◊) 0; (♦) 0.05; (○) 0.1; (●) 0.2; (Δ) 0.3; (▲) 0.4; (□) 0.5; (■) 0.6; (∇) 0.7; (▼) 0.8; (+) 0.9; (◄) 1. In addition, modeling of viscosity experimental data was performed using predictive and correlative types of models. In this work UNIFAC–VISCO20,21 and ASOG–VISCO22 models were used for the determination of the dynamic viscosity of the three binary mixtures. UNIFAC–VISCO and ASOG–VISCO are group contribution models aimed at activity coefficient determination. In both methods, the activity coefficients in the mixtures are related to interactions between structural groups. Consequently, the parameters characterizing interac- tions between pairs of structural groups, called group interaction parameters, are necessary (αnm for UNIFAC–VISCO and mkl and nkl for ASOG–VISCO). If the parameters are given in the literature, it is not necessary to determine them again. In this work, new group interaction parameters were determined from the experi- _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ 940 VUKSANOVIĆ et al. mentally measured viscosities using the Marquardt23 optimization technique for the minimization of the objective function: 2 exp cal exp1 1 min n i i OF n η η η =  − = →      (5) where ηexp and ηcal denote the experimental and calculated values of the dynamic viscosity η and n is the number of experimental data points. Fig. 3. Experimental data of the refractive index, nD, vs. temperature, T (288.15 to 323.15 K), at atmospheric pressure, for the systems: a) PEGDA (1) + ethanol (2); b) PEGDA (1) + 1-propanol (2); c) PEGDA (1) + 1-butanol (2). The symbols refer to mole fractions of PEGDA: (◊) 0; (♦) 0.05; (○) 0.1; (●) 0.2; (Δ) 0.3; (▲) 0.4; (□) 0.5; (■) 0.6; (∇) 0.7; (▼) 0.8; (+) 0.9; (◄) 1. The new UNIFAC–VISCO interaction parameters, αnm, between the follow- ing groups: CH2=CH/CH3, CH2=CH/CH2, CH2=CH/OH, CH2=CH/CH2O and CH2=CH/COO are summarized in Table II. The remaining interaction para- meters were taken from the original model20,21 and previous papers.5,24 In the similar way, new ASOG–VISCO group interaction parameters, mkl and nkl, of following groups CH2=CH/CH2, CH2=CH/OH, CH2=CH/CH2O, _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ VOLUMETRIC PROPERTIES AND VISCOSITIES OF POLY(ETHYLENE GLYCOL)DIACRYLATE + ALCOHOLS 941 CH2=CH/COO were determined using the original interaction parameters22 and parameters from previous papers.3,24 The results are summarized in Table III. Fig. 4. Experimental data of viscosity, ln η, vs. 1/T (288.15 to 323.15 K), at atmospheric pressure, for the systems: a) PEGDA (1) + ethanol (2); b) PEGDA (1) + 1-propanol (2); c) PEGDA (1) + 1-butanol (2). The symbols refer to mole fractions of PEGDA: (◊) 0; (♦) 0.05; (○) 0.1; (●) 0.2; (Δ) 0.3; (▲) 0.4; (□) 0.5; (■) 0.6; (∇) 0.7; (▼) 0.8; (+) 0.9; (◄) 1. TABLE II. The UNIFAC–VISCO interaction parameter, αnm n/m CH3 CH2 CH2=CH OH CH2O COO CH3 0 –709.5 a –570.861d 594.4a –50.17b –172.4a CH2 66.53 a 0 1161.742d 498.6a –319.930b 1172a CH2=CH –872.856 d 1489.036d 0 –869.851d –2243.897d –57.440d OH 1209a –634.5a –549.041d 0 –619.360b 68.35a CH2O 456.91 b –340.250b 248.157d 25.340b 0 –56.95c COO –44.25a 541.6a –445.344d 186.8a –137.945c 0 aOriginal UNIFAC–VISCO parameters;20,21 bUNIFAC–VISCO parameters from the literature;5 cUNIFAC– –VISCO parameters from the literature;24 dnew UNIFAC–VISCO parameters Moreover, the experimental viscosity data were correlated with the one- parameter Teja and Rice,25,26 and McAllister27 two-parameter three-body and _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ 942 VUKSANOVIĆ et al. three-parameter four-body models. These models are described in detail in a previous papers.28,29 TABLE III. The ASOG–VISCO interaction parameters k/l CH2 CH2=CH OH CH2O COO mkl CH2 0 0.2428 d –0.3570a –10.9924b 0.3682a CH2=CH 1.7603 d 0 1.6245d –6.3287d –2.5891d OH 14.1460a –0.3330d 0 –2.2661b –40.2000a CH2O –33.9591 b –173.2012d 1.5287b 0 –2.9720c COO 0.0952a 197.1496d 19.1310a –4.7468c 0 nkl CH2 0 356.102 d 469.650a –1.928b 112.590a CH2=CH 187.229 d 0 413.379d 299.095d 298.614d OH –6137.000a 476.584d 0 –14.965b 11583.000a CH2O –8.176 b 298.966d –127.018b 0 –835.188c COO –383.600a 300.577d –5747.000a –433.643c 0 aOriginal ASOG–VISCO parameters;22 bASOG–VISCO parameters from the literature;3 cASOG–VISCO parameters from the lierature;24 dnew ASOG–VISCO parameters The ability of these models to predict successfully the dynamic viscosities of the investigated binary mixtures and to correlate the experimental viscosity data is presented with percentage deviations, PDmax, between the experimental and calculated viscosities, using the following equation: exp calmax exp max1 100 ( ) n i i PD n η η η = − =  (6) where (ηexp)max is the maximum of the experimental η values. The results obtained by the UNIFAC–VISCO, ASOG–VISCO, Teja–Rice and McAllister models for the mixtures of PEGDA + ethanol or 1-propanol or 1-butanol over the investigated temperature range are given in Table IV. A gra- phical presentation of the experimental viscosity deviation from the values obtained by the selected models is given in Fig. 5. TABLE IV. Results of the viscosity prediction and correlation for the investigated binary systems at the temperatures (288.15 to 323.15) K and at atmospheric pressure T / K Predictive approach Correlative approach UNIFAC–VISCO ASOG–VISCO Teja–Rice McAllister-3 McAllister-4 PDmax / % PDmax / % PDmax / % PDmax / % PDmax / % PEGDA (1) + ethanol (2) 288.15 7.62 2.16 11.03 4.46 1.59 293.15 5.79 2.65 10.48 4.66 1.67 298.15 4.08 2.40 10.10 4.88 1.84 303.15 2.82 1.76 9.70 4.97 1.84 _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ VOLUMETRIC PROPERTIES AND VISCOSITIES OF POLY(ETHYLENE GLYCOL)DIACRYLATE + ALCOHOLS 943 TABLE IV. Continued T / K Predictive approach Correlative approach UNIFAC–VISCO ASOG–VISCO Teja–Rice McAllister-3 McAllister-4 PDmax / % PDmax / % PDmax / % PDmax / % PDmax / % PEGDA (1) + ethanol (2) 308.15 2.20 1.08 9.38 5.15 1.92 313.15 2.19 0.66 9.04 5.32 2.05 318.15 2.95 1.17 8.88 5.49 2.20 323.15 3.74 1.57 8.51 5.50 2.15 PEGDA (1) + 1-propanol (2) 288.15 4.66 1.54 5.96 3.01 1.11 293.15 3.14 0.77 5.68 3.13 1.15 298.15 1.76 0.50 5.52 3.30 1.15 303.15 0.87 0.84 5.29 3.40 1.20 308.15 1.39 1.34 5.07 3.49 1.27 313.15 2.78 1.95 4.90 3.59 1.31 318.15 4.17 2.61 4.72 3.66 1.36 323.15 5.32 3.07 4.65 3.73 1.42 PEGDA (1) + 1-butanol (2) 288.15 4.56 1.56 3.89 2.13 0.65 293.15 3.46 0.78 3.79 2.22 0.68 298.15 2.47 0.66 3.63 2.32 0.78 303.15 1.69 0.51 3.57 2.45 0.72 308.15 1.04 0.47 3.49 2.54 0.78 313.15 0.72 0.44 3.41 2.64 0.82 318.15 1.25 0.44 3.35 2.74 0.86 323.15 1.98 0.45 3.35 2.78 0.92 UNIFAC–VISCO model gave very good results for the prediction of the viscosity of the three investigated binary systems. In almost all cases, the max- imum percentage deviation PDmax did not exceed 5 %. The largest deviations were obtained at the lowest temperature (systems with ethanol and 1-butanol), or at the highest investigated temperature in the case of the system containing 1-propanol. Inspection of Figs. 5a and 5b confirms this conclusion. The ASOG– –VISCO model gave even better results, with maximum percentage deviations PDmax of 2.65 % in almost all cases. The best results were obtained for the PEGDA + 1-butanol binary mixture, with PDmax of less than 0.78 %, except at 288.15 K, when the deviation was 1.56 %. However, this model fits the experi- mental data satisfactorily (Fig. 5c). From the results obtained from correlative models, it could be concluded that the best results for all three systems were obtained with the McAllister-4 model. This conclusion is supported by the gra- phical representation given for the systems PEGDA + ethanol, or + 1-butanol (Fig. 5a and c) where the model correlates the experimental points very well. The Teja–Rice model gave the worst correlations of the experimental data, with the _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ 944 VUKSANOVIĆ et al. highest PDmax values, up to 11.03 % for the PEGDA + ethanol binary mixtures. This conclusion is obvious from Figs. 5b and 5c, especially at lower tempe- ratures. The best results for all three types of correlative models were obtained for the PEGDA + 1-butanol binary system, for which the lowest PDmax devi- ations were obtained for theMcAllister-4 model (less than 1 %). Fig. 5. Modeling of the viscosity data for the systems: a) PEGDA (1) + ethanol (2), b) PEGDA (1) + 1-propanol (2) and c) PEGDA (1) + 1-butanol (2). The symbols refer to experimental points (●) at 288.15 and (▲) at 323.15 K, while the lines present the results calculated by models given in Table IV: (—) ASOG–VISCO, (---) Teja–Rice and (…) McAllister-4 models. CONCLUSIONS In this work, the experimental data of the density ρ, viscosity η, and refract- ive index nD are reported for PEGDA + ethanol, PEGDA + 1-propanol and PEGDA + 1-butanol binary mixtures at temperatures in the range 288.15 to 323.15 K, with a temperature step of 5 K, over the whole composition range, and at atmospheric pressure. All measured physical properties increased with inc- reasing PEGDA mole fraction and with decreasing temperature. The measured physical properties were correlated as a function of temperature and of PEGDA mole fraction. The densities and refractive indices of the mixtures showed _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ VOLUMETRIC PROPERTIES AND VISCOSITIES OF POLY(ETHYLENE GLYCOL)DIACRYLATE + ALCOHOLS 945 exponential dependence vs. composition, including the temperature dependence of the parameters, while the viscosities exhibited polynomial dependence over the mixture composition. In the case of the temperature correlation, all three pro- perties (ρ, ln η and nD) exhibited linear trends. The influence of temperature on the viscosity of the mixtures was larger than its influence on the density and refractive index. Moreover, the influence of the PEGDA mole fraction on the overall densities and refractive indices of the PEGDA + alcohol mixtures was far greater in comparison to the influence of the alcohol type. In addition, viscosity modeling was performed using two types of models: the predictive UNIFAC– –VISCO and ASOG–VISCO, and the correlative McAllister and Teja–Rice models. The predictive ASOG–VISCO gave better results between the predictive models, while of the correlative models, the best results were obtained using the McAllister-4 equation, for all three investigated binary systems. Furthermore, new UNIFAC–VISCO and ASOG–VISCO binary interaction parameters were determined from the experimental viscosity data. SUPPLEMENTARY MATERIAL Experimental data of densities ρ, viscosities η and refractive nD indices and fitting parameters and root-mean-square deviations for Eqs. (1)–(3) of PEGDA + alcohol binary mixtures are available electronically from http://www.shd.org.rs/JSCS/ or from the corres- ponding author on request. Acknowledgement. The authors gratefully acknowledge the financial support received from the Research Fund of the Ministry of Education, Science and Technical Development of the Republic of Serbia and the Faculty of Technology and Metallurgy, University of Belgrade (Project No. 172063). И З В О Д EКСПЕРИМЕНТАЛНО ИСПИТИВАЊЕ ТЕРМОДИНАМИЧКИХ И ТРАНСПОРТНИХ СВОЈСТАВА БИНАРНИХ СМЕША ПОЛИ(ЕТИЛЕНГЛИКОЛ)-ДИАКРИЛАТА И АЛКОХОЛА НА РАЗЛИЧИТИМ ТЕМПЕРАТУРАМА ЈЕЛЕНА М. ВУКСАНОВИЋ, ИВОНА Р. РАДОВИЋ, СЛОБОДАН П. ШЕРБАНОВИЋ и МИРЈАНА Љ. КИЈЕВЧАНИН Технолошко–металуршки факултет, Универзитет у Београду, Карнегијева 4, 11120 Београд Експериментални подаци за густину, ρ, индекс рефракције, nD, и вискозност, η, три бинарна система поли(етиленгликол)-диакрилата (PEGDA) + етанол, + 1-пропанол и + 1-бутанол су мерени на осам температура (288,15 to 323,15 K), са кораком 5 K, и на атмосферском притиску. Експериментални подаци су корелисани у функцији молског удела PEGDA и температуре. Густине и индекси рефракције испитиваних смеша су фитовани експоненцијалном функцијом у зависности од састава, док се у случају вис- козности полиномска функција показала као најбоља кроз цео опсег молских удела. У случају температурне зависности, све три величине (ρ, ln η и nD) показују линеаран тренд. Вискозност је моделована помоћу четири модела: UNIFAC–VISCO, ASOG–VISCO, Mc-Allister и Teja–Rice. Помоћу UNIFAC–VISCO модела одређени су интеракциони параметри следећих група: CH2=CH/CH3, CH2=CH/CH2, CH2=CH/OH, CH2=CH/CH2O и CH2=CH/COO. Такође, на исти начин помоћу ASOG–VISCO модела су одређени и бинар- _________________________________________________________________________________________________________________________ (CC) 2015 SCS. All rights reserved. Available on line at www.shd.org.rs/JSCS/ 946 VUKSANOVIĆ et al. ни интеракциони параметри следећих група: CH2=CH/CH2, CH2=CH/OH, CH2=CH/CH2O and CH2=CH/COO. 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