Research Journal of Chemical Sciences ___ ______________________________ ______ ____ _ __ ISSN 22 31 - 606X Vol. 3 ( 2 ), 73 - 78 , February (201 3 ) Res. J. Chem. Sci. International Science Congress Association 73 Thermo acoustic study of acrylates with decane - 1 - ol Patil Sujata S. and Mirgane Sunil R.* PG Dept. of Chemistry, J.E.S. College, Jalna 431 203, MS, INDIA Available online at: www.isca.in Received 21 st December 201 2 , revis ed 18 th January 201 3 , accepted 25 th January 201 3 Abstract Thermodynamic data involving viscosity of binary liquid mixture methyl acrylate, ethyl acrylate and butyl acrylate with decane - 1 - ol at 298.15 and 308.15 K temperatures and at atmospheric pressu re have been measured. Values of viscosity further used to calculate deviation in viscosity of binary systems and were fitted to Redlich - Kister polynomial equation. Experimental viscosity data used to correlate with different semi - empirical equations such as Hind, Grunberg - Nissan, Tamura - Kurata, Choudhary - Katti, Heric  Brewer and McAllister three and four body model equations. Calculated deviations in viscosity were found to be negative for all binary liquid mixtures at both temperatures. Keywords Redlich - K ister e quation, Hind, Grunberg - Nissan, Tamura - Kurata, McAllister t hree and f our b ody m odel, b inary l iquid m ixtures. Introduction In the recent years, much importance has been given to the behavior of mixed solvents rather than a single solvent because of their wide range of applications in many chemical, industrial and biological processes. The physico - chemical data are often required in many industrial processes (flow, mass transfer or heat transfer calculation, polymerization, solvolysis, etc.) and a lso leads to the formulations of a large number of methods for correlating or predicting the physical properties. Therefore in view of practical importance of mixed solvents, a deeper knowledge of their solution structure and intermolecular interactions be tween component molecules at molecular level thus becomes essential. Recently researchers in this field have been focusing their interest more sharply on the molecular structure along with some representative macroscopic property that serves to characteriz e it. The composition and temperature dependence of volumetric, acoustic, transport and surface properties of associated liquid system provides substantial information of the molecular influence on the intensity of the intermolecular interactions among com ponent molecules and can be used as a powerful tool for studying intermolecular interactions in these systems. Thus, keeping both industrial and scientific interests in mind, here we report measured densities ( ρ) and ultrasonic velocity (u) of binary liquid mixtures of acrylic esters with decane - 1 - ol at 298.15 and 308.15 K temperatures. Material and Methods All chemicals decane - 1 - ol, methyl acrylate (MA), ethyl acrylate (EA) and butyl acrylate (BA) used of mas s fraction purities � 0.998 (E - Merck) were double distilled, middle fraction collected of all liquids was stored over 0.4 nm molecular sieves. Masses were recorded on a Mettlar balance, with an accuracy of 0.01 mg. Estimated uncertainty in mole fraction was 10 - 4 . The temperature was controlled using a constant temperature controlled water bath (Gemini Scientific Instruments, Chennai, India) having accuracy  0.02  C. The dynamic viscosities were measured 1 using an Ubbelhode suspended level viscometer , calibrated with conductivity water. An electronic digital stop watch with readability of  0.01 s was used for the flow time measurements. At least three repetitions of each data reproducible to  0.05 s were obtained and the results were averaged. Since all flow times were greater than 300 s and capillary radius (0.1 mm) was far less than its length (50 to 60) mm, the kinetic energy and end corrections, respectively, were found to be negligible. The accuracy in dynamic viscosities were of the order of  0.003 mPa.s. A comparison of measured values of viscosities of pure components with literature values in t able 1 shows a good agreement. Te viscosity deviations (∆η) were calculated using equation, ∆η  η 12  x 1 η 1  x 2 η 2 ( 1 ) were η 12 is the viscosity of the mixture and x 1 , x 2 and η 1 , η 2 are the mole fraction and the viscosity of pure components 1 and 2 respectively. Deviations in viscosity were fitted to Redlich - Kister 2 equation of the type, Y = x 1 x 2 ( 2) Where Y is ∆η and n is the degree of polynomial. Coefficient a i was obtained by fitting equation (2) to experimental results using a least - squares regression method. In each case, the optimum number of coefficients is ascertained from an examination of the variation in standard deviation ( s ). s was calculated using the relation, σ ( Y ) = (3) Research Journal of Chemical Sciences ___ _ _ _______________________________ ______________ _ ________ ISSN 22 31 - 606X Vol. 3 ( 2 ), 73 - 78 , February (201 3 ) Res. J. Chem. Sci. International Science Congress Association 74 Where N is the number of data points and n is the number of coefficients. The calculated values of the coefficients a i along wi th the standard deviations ( s ) are given in t able 3. Several semi - empirical relations have been proposed to evaluate the dynamic viscosity and to check the suitability of the equation for experimental data fits by taking into account the number of empiric al adjustable coefficients. The equations of Hind, Choudhary - Katti, Grunberg - Nissan and Tamura - Kurata have one adjustable parameter. The expression for Hind 3 equation is, η 12 = x 1 2 η 1 + x 2 2 η 2 + 2x 1 x 2 H 12 (4) where H 12 is the interaction parameter. The expression for Choudhary - Katti 4 equation is, ln ( η n V m ) = x 1 ln ( η 1 V 1 ) + x 2 ln ( η 2 V 2 ) + x 1 x 2 [Wvis/( RT )] (5) where Wvis is the interaction energy for activation of viscous flow. The expression for Grunberg - Nissan 5 equation is, ln η 12 = x 1 ln η 1 + x 2 ln η 2 + x 1 x 2 G 12 ( 6 ) where G 12 is a parameter proportional to the interchange energy. Tamura and Kurata 6 developed expression for viscosity of binary mixtures as, η = x 1 f 1 η 1 + x 2 f 2 η 2 + 2(x 1 x 2 f 1 f 2 ) 1/2 T 12 (7) where T 12 is the interaction parameter , f 1 and f 2 are the volume fractions. The calculated values of adjustable parameters H 12 , Wvis , G 12 and T 12 with standard deviations ( s ) calculated by equ ation (11) are given in t able 4. Heric  Brewer 7 proposed two parameter model of the form, ln η = x 1 ln η 1 + x 2 ln η 2 + x 1 ln M 1 + x 2 ln M 2 - ln( x 1 M 1 + x 2 M 2 ) + x 1 x 2 [ a 12 + a 21 ( x 1 - x 2 )] (8) where M 1 and M 2 are molecular weights of components of 1 and 2; a 12 and a 21 are interaction parameters which can be calculated from the least s quare method and other terms involved have their usual meaning. McAllister’s multibody interaction model 8 was widely used to correlate kinematic viscosity ( u) data. Two parameter McAllister equation based on Eyring’s teory of absolute reaction rates, tak en into account interactions of both like and unlike molecules by a two dimensional three body model. The three body model was defined by the relation, ln ν = x 1 3 ln ν 1 + x 2 3 ln ν 2 + 3 x 1 2 x 2 ln Z 12 + 3 x 1 x 2 2 ln Z 21 - ln[ x 1 +(x 2 M 2 /M 1 )] + 3 x 1 2 x 2 ln[(2/3) + ( M 2 / 3 M 1 )] + 3 x 1 x 2 2 ln[(1/3)+(2 M 2 /3 M 1 )] + x 2 3 ln( M 2 /M 1 ) (9) Similarly, the four body model was defined by the relation, ln ν = x 1 4 ln ν 1 + 4 x 1 3 x 2 ln Z 1112 + 6 x 1 2 x 2 2 ln Z 1122 + 4 x 1 x 2 3 ln Z 2221 + x 2 4 ln ν  ln[ x 1 + x 2 (M 2 /M 1 )] + 4 x 1 3 x 2 ln[(3+ M 2 /M 1 )/4] + 6 x 1 2 2x 2 2 ln[(1+ M 2 /M 1 )/2] + 4 x 1 x 2 3 ln[(1+3 M 2 /M 1 )/4] + x 2 4 ln (M 2 /M 1 ) (10) Where Z 12 , Z 21 , Z 1112 , Z 1122 and Z 2221 are model parameters and M i and ν i are the molecular mass and kinematic viscosity of pure component i . To perform a num erical comparison of the correlating capability of above equation (4 to 10) we have calculated the standard percentage deviation ( σ % ) using the relation, σ % = [1/( η expt  k)  ∑(100( η expt  η cal )/ η expt ) 2 ] 1/2 (11) where k represents t he number of numerical coefficients in the respective equations. The interaction parameters H 12 , Wvis , G 12, T 12 , a 12 , a 21, Z 12 , Z 21 , Z 1112 , Z 1122 and Z 2221 in the above Eq (4 to 10) have been considered as adjustable parameters, estimated by a non - lin ear regression analysis based on a least - squares method 9 . The parameters a 12, a 21, Z 12 , Z 21 , Z 1112 , Z 1122 and Z 2221 are presented with their standard percentage deviation ( σ % ) in t able 5. Table - 1 Viscosities (η) for Pure Components at T = (298.15 and 308.15) K Property T = 298.15 K T = 308.15 K Expt. Lit. Expt Lit. Decane - 1 - ol  (mPa.s) 11.793 11.790 12 8.116 8.124 12 Methyl Acrylate  (mPa.s) 0.449 0.449 13 0.390 0.391 13 Ethyl Acrylate  (mPa.s) 0.518 0.517 13 0.456 0.455 13 Butyl Acrylate  (mPa .s) 0.787 0.786 13 0.684 0.684 13 Research Journal of Chemical Sciences ___ _ _ _______________________________ ______________ _ ________ ISSN 22 31 - 606X Vol. 3 ( 2 ), 73 - 78 , February (201 3 ) Res. J. Chem. Sci. International Science Congress Association 75 Table - 2 Viscosities (η) and Viscosity Deviation (∆η) for Acrylates (1) + Decane - 1 - ol (2) at T = (298.15 and 308.15) K X 1 T = 298.15 K T = 308.15 K η ∆η η ∆η (mPa.s) (mPa.s) (mPa.s) (mPa.s) MA (1) + Decane - 1 - ol (2) 0 11.793 0 8.116 0 0.0552 9.846 - 1.317 6.864 - 0.823 0.0997 8.514 - 2.148 5.997 - 1.349 0.1555 7.095 - 2.935 5.063 - 1.852 0.1999 6.137 - 3.389 4.424 - 2.148 0.2554 5.118 - 3.778 3.738 - 2.405 0.3000 4.424 - 3.966 3.265 - 2.534 0.3555 3.689 - 4.071 2.758 - 2.611 0.3999 3.192 - 4.065 2.411 - 2.616 0.4538 2.676 - 3.970 2.047 - 2.563 0.4999 2.301 - 3.820 1.779 - 2.474 0.5554 1.919 - 3.573 1.503 - 2.322 0.5999 1.660 - 3.327 1.313 - 2.167 0.6550 1.386 - 2.977 1.111 - 1.945 0.6999 1.197 - 2.656 0.970 - 1.738 0.7555 0.998 - 2.2 24 0.819 - 1.460 0.7999 0.863 - 1.856 0.716 - 1.220 0.8555 0.720 - 1.369 0.605 - 0.902 0.8999 0.623 - 0.962 0.528 - 0.635 0.9555 0.519 - 0.434 0.446 - 0.287 1 0.449 0 0.390 0 EA (1) + Decane - 1 - ol (2) 0 11.793 0 8.116 0 0.0554 9.917 - 1.251 6.918 - 0.773 0.0 999 8.630 - 2.036 6.087 - 1.263 0.1553 7.257 - 2.785 5.189 - 1.737 0.1998 6.315 - 3.223 4.565 - 2.019 0.2556 5.305 - 3.607 3.888 - 2.270 0.2999 4.619 - 3.793 3.422 - 2.397 0.3554 3.883 - 3.903 2.916 - 2.477 0.4000 3.378 - 3.905 2.565 - 2.487 0.4555 2.840 - 3.818 2 .187 - 2.440 0.4999 2.472 - 3.684 1.924 - 2.362 0.5554 2.078 - 3.451 1.640 - 2.221 0.5999 1.808 - 3.221 1.442 - 2.079 0.6555 1.520 - 2.882 1.229 - 1.865 0.6999 1.323 - 2.578 1.082 - 1.672 0.7556 1.112 - 2.162 0.921 - 1.407 0.7999 0.968 - 1.805 0.811 - 1.177 0.855 5 0.814 - 1.334 0.691 - 0.872 0.8999 0.708 - 0.939 0.608 - 0.615 0.9555 0.595 - 0.425 0.518 - 0.279 1 0.518 0 0.456 0 BA (1) + Decane - 1 - ol (2) 0 11.793 0 8.116 0 0.0555 10.148 - 1.034 7.075 - 0.629 0.0998 9.000 - 1.694 6.340 - 1.034 0.1556 7.740 - 2.341 5.52 3 - 1.437 0.1998 6.865 - 2.729 4.950 - 1.681 0.2554 5.906 - 3.076 4.314 - 1.904 0.3000 5.235 - 3.257 3.864 - 2.023 0.3556 4.503 - 3.377 3.368 - 2.106 0.3998 3.995 - 3.398 3.018 - 2.127 0.4555 3.436 - 3.344 2.630 - 2.101 0.5000 3.046 - 3.244 2.356 - 2.044 0.5555 2 .621 - 3.058 2.053 - 1.934 0.5999 2.324 - 2.866 1.840 - 1.817 0.6555 1.999 - 2.580 1.603 - 1.641 0.6999 1.773 - 2.317 1.437 - 1.477 0.7554 1.525 - 1.954 1.252 - 1.250 0.7999 1.352 - 1.637 1.122 - 1.049 0.8545 1.167 - 1.222 0.980 - 0.786 0.8999 1.032 - 0.857 0.876 - 0.552 0.9550 0.889 - 0.393 0.764 - 0.255 1 0.787 0 0.684 0 Research Journal of Chemical Sciences ___ _ _ _______________________________ ______________ _ ________ ISSN 22 31 - 606X Vol. 3 ( 2 ), 73 - 78 , February (201 3 ) Res. J. Chem. Sci. International Science Congress Association 76 Table - 3 Adjustable parameters of Eq (2) and (3) for Viscosity Deviation (∆η) for binary liquid mixture of Acrylates (1) + Decane - 1 - ol (2) at T = (298.15 and 308.15) K Property T (K) a 0 a 1 a 2 a 3 a 4 σ MA (1) + Decane - 1 - ol (2) ∆ η (mPa.s) 298.15 - 15.2734 7.6920 - 3.1350 0.8481 0.0227 0.00281 308.15 - 9.8918 4.6871 - 1.7917 0.4135 0.0539 0.00203 EA (1) + Decane - 1 - ol (2) ∆ η (mPa.s) 298.15 - 14.7384 7.0946 - 2.6375 0.8462 - 0.2441 0.00095 308.15 - 9.4514 4.2371 - 1.4541 0.4356 - 0.1340 0.00083 BA (1) + Decane - 1 - ol (2) ∆ η (mPa.s) 298.15 - 12.9774 5.5119 - 1.8073 0.5129 - 0.1183 0.00043 308.15 - 8.1779 3.2097 - 0.9600 0.2375 - 0.0672 0.00033 Table - 4 Adjustable pa rameters of Eq (4), (5), (6), (7) and (11) for binary liquid mixture of Acrylates (1) + Decane - 1 - ol (2) at T = (298.15 and 308.15) K T (K) H 12 σ Wvis σ G 12 σ T 12 σ MA (1) + Decane - 1 - ol (2) 298.15 - 1.826 42.088 0.294 0.518 - 0.001 0.032 - 3.899 80.003 308 .15 - 0.868 31.002 0.288 0.506 - 0.001 0.040 - 2.254 60.118 EA (1) + Decane - 1 - ol (2) 298.15 - 1.484 34.942 0.170 0.229 0.000 0.024 - 3.027 58.839 308.15 - 0.589 25.056 0.163 0.207 - 0.001 0.036 - 1.616 43.010 BA (1) + Decane - 1 - ol (2) 298.15 - 0.382 19.667 0. 049 0.037 - 0.001 0.014 1.158 27.121 308.15 0.214 13.913 0.047 0.034 - 0.001 0.023 0.305 19.538 Table - 5 Adjustable parameters of Eq (8), (9), (10) and (11) for binary liquid mixture of Acrylates (1) + Decane - 1 - ol (2) at T = (298.15 and 308.15) K T (K) a 12 a 21 σ Z 12 Z 21 σ Z 1112 Z 1122 Z 2221 σ MA (1) + Decane - 1 - ol (2) 298.15 0.297 0.070 0.115 1.595 4.763 0.115 1.177 1.909 6.282 10.345 308.15 0.290 0.066 0.105 1.292 3.573 0.105 0.972 1.492 4.616 4.406 EA (1) + Decane - 1 - ol (2) 298.15 0.170 0.029 0.040 1.730 4.988 0.040 1.304 2.268 6.478 11.515 308.15 0.163 0.026 0.039 1.414 3.758 0.039 1.089 1.784 4.778 4.765 BA (1) + Decane - 1 - ol (2) 298.15 0.050 0.006 - 0.021 2.258 5.693 0.021 1.785 3.201 7.166 16.963 308.15 0.046 0.003 - 0.023 1.828 4.273 0.023 1. 472 2.504 5.266 7.032 Results and Discussion A graphical representations of the viscosity deviations ( D  ) for the binary mixtures of acrylic esters with decane - 1 - ol at 298.15 and 308.15 K are shown in f ig ure 1 and f ig ure 2, respectively. It is known th at the strength of the intermolecular electric donor - acceptor interaction is not the only factor that influences the viscosity deviation in liquid mixtures. The molecular size and shape of the components and average degree of association of the mixture are equally important factors. In the present investigation the negative values of D  may be attributed to the same effect. Weak specific interaction may be present or dispersion forces may be operating in the systems. The observed large negative values of D  in general indicate a high dilution of 1 - alkanol viscosities in the presence of the ester species. The decrease in viscosity values can be ascribed to the breaking up of decane - 1 - ol associates by unlike acrylic ester molecules. This type of interaction se ems to be dominant when the share of ester in the mixture is small. In the ester - rich mixtures dispersion interactions are expected to be replaced by ester - ester like interactions indicated by the closeness of the viscosity values. Table 3 shows that the standard deviations are very close to each other at 298.15 and 308.15 K. The Redlich - Kister equation was originally developed to correlate te excess Gibb’s energy function and to calculate the values of the activity coefficients. It turned out to be such a powerful and versatile correlating tool that its use has been extended to other properties, particularly Research Journal of Chemical Sciences ___ _ _ _______________________________ ______________ _ ________ ISSN 22 31 - 606X Vol. 3 ( 2 ), 73 - 78 , February (201 3 ) Res. J. Chem. Sci. International Science Congress Association 77 excess molar volumes and excess enthalpies of mixing. It suffers from the important drawback that the values of the adjustabl e parameters change as the number in the series is increased, so that no physical interpretation can be attached to them 10 . Redlich - Kister regressor is very powerful and frequently used to correlate vapor - liquid equilibrium data and excess properties 11 . Experimental viscosity data used to correlate with different semi - empirical equations. Their parameters with standard errors are summarized in t able 4. All these equations are having single parameter. From the equations such as Hind (H 12 ), Choudhary - Katti (Wvis), Grunberg - Nissan (G 12 ), Tamura and Kurata (T 12 ); the least standard error is observed for Grunberg - Nissan equation parameter. Therefore the order of correlating ability of these equations will be G 12 � Wvis � H 12 � T 12 . The interaction parameter der ived from the Tamura - Kurata equation shows highest values of the standard errors in all the binary liquid mixtures in all the sections. Parameters evaluated from the equations proposed by Heric  Brewer, McAllister three and four body models are summarized with their standard percentage deviations in Table 5. The values of standard errors of Heric  Brewer and McAllister three body model are exactly equal and higher as compared to standard error of McAllister four body model for the binary liquid mixtures of methyl acrylate and ethyl acrylate with decane - 1 - ol at both temperatures. Therefore the order of correlating ability of these equations in the form of their parameters is, ( a 12, a 21 )  (Z 12 , Z 21 ) � (Z 1112 , Z 1122 , Z 2221 ). For butyl acrylate + decane - 1 - ol the correlating ability of the Heric - Brewer equation is good as compared to the McAllister three body models. Hence, in this system the order of the correlating ability of var ious models can be given as, ( a 12, a 21 ) � (Z 12 , Z 21 ) � (Z 1112 , Z 1122 , Z 2221 ). Figure - 1 Variation of deviation in viscosity for Acrylates (1) + Decane - 1 - ol (2) at 298 .15 K Figure - 2 Variation of deviation in viscosity for Acrylates (1) + Decane - 1 - ol (2) at 308 .15 K Research Journal of Chemical Sciences ___ _ _ _______________________________ ______________ _ ________ ISSN 22 31 - 606X Vol. 3 ( 2 ), 73 - 78 , February (201 3 ) Res. J. Chem. Sci. International Science Congress Association 78 Conclusion The main effect in viscosity deviation of binary liquid mixtures is breaking of self interactions in compounds during mixing process, in this, H - bonding and dipole - dipole interactions. The presence of new OH - O interactions in mixtur e increases viscosity, but according to experimental result, effect is not as important as breaking of self interactions. Negative viscosity deviations means system has an easier flow than pure liquids. Acknowledgement Author (SSP) acknowledge the Departm ent of Science and Technology, New Delhi, Government of India, for financial support by awarding Junior Research Fellowship. Authors are thankful to Prof. B. R. Arbad, Dr. B. A. M. University, Aurangabad for their valuable suggestions. References 1. Patil S. S. and Mirgane S.R., Thermodynamic properties of binary liquid mixtures of industrially important acrylates with octane - 1 - ol with at different temperatures, Int. J. of Che., Pharma. and Envi. Res., 2 , 72 - 82 ( 2011 ) 2. Redlich O. and Kister A. T., Algebraic Rep resentation of Thermodynamic Properties and The Classification of Solutions, Ind. Eng. Chem. ( 1948 ) 3. Hind R.K., Lauglin E.M. and Ubbelhode A.R., Structure and viscosity of liquids Camphor + Pyrene mixtures, Trans Faraday Soc. , 56 , 328 ( 1960 ) 4. Katti P.K. and Choudhary M.J., Viscosity of binary mixtures of Benzyl Acetate with Dioxane, Aniline and m - Cresol, J. Chem. Eng. Data , 9 , 442 ( 1964 ) 5. Grunberg L. and Nissan H., Nature (London) , 164 , 779 ( 1949 ) 6. Tamura M. and Kurata M., Bull Chem. Soc Japan, 25 , 32 ( 1952 ) 7. Heric E.L. and Brewer J.G., Viscosity of some binary liquid nonelectrolyte mixtures, J. Chem. Eng. Data , 12 , 574 (1967) 8. McAllister R.A., AICHEJ , 6 , 427 (1960) 9. Pal A. and Bhardwaj R. K., Ind. J. of Chem. , 41 ,706 (2002) 10. Peralta R.D., Infante R., Cortez G. an d Wisniak J., Volumetric properties of the binary systems of dimethyl sulphoxide with methacrylic acid, vinyl acetate, butyl methacrylate and allyl methacrylate at 298.15 K, J. Sol. Chem., 34 (5) , 515 (2005) 11. Peralta R.D., Infante R., Cortez G., Rodriguez O. and Wisniak J., Volumetric properties of toluene with ethyl acrylate, butyl acrylate, methyl methcrylate and styrene at 25  C, J. Sol. Chem ., 31 (3) , 175 (2002) 12. Sastry N.V. and Valand M.K., Viscosities and Densities for Heptane + 1 - Pentanol, +1 - Hexanol , +1 - Heptanol +1 - Octanol, +1 - Decanol, and +1 - Dodecanol at 298.15 K and 308.15 K, J. Chem. Eng. Data, 41 , 1426 (1996) 13. Sastry N.V. and Valand M. K., Int. J of Thermophysics , 18 ( 1997 )