1617
Ind. Eng. Chem. Res. 1991,30, 1617-1624 Harlacher, E. A.; Brown, W.G. A four parameter extension of the theorem of corresponding states. Znd. Eng. hocess Des. Dev. 1970,9, 479.
Majer, V.; Svoboda, V. Enthalpies of vaporization of Organic Compounds. Blackwell Scientific Publications: Boston, 1985. Peng, D.-Y.; Robinson, D. B. A new two constant equation of state.
Znd. Eng. Chem. Fundam. 1976,15,59. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids. McGraw-Hill Book Co.: London, 1987. Rogabki, M.; Carrier, B.; Solimando, R.; PBneloux, A. Correlation and Prediction of Physical Properties of Hydrocarbons with the Modified Peng-Robinson Equation of State. 2 Representation
of the Vapor Pressures and the Molar Volumes. Znd. Eng. Chem.
Res. 1990,29,659. Soave, G. Equilibrium constante from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 1972,27,1197. TRC Thermodynamical Tables, Hydrocarbons. The Texas A&M University System: College Station, TX, 1975-1986; Vol. IX (loose-leaf data sheets). Trouton, 1884. Cited by Barrow, G. M. Physical Chemistry; McGraw-Hill Book Co.: New York, 1961; pp 396-397.
Received for review July 23, 1990 Accepted February 12,1991
Model with Temperature-IndependentParameters for the Viscosities of Liquid Mixtures Hongqin Liu and Wenchuan Wang* Department of Chemical Engineering, Beijing Institute of Chemical Technology, 100029, Beijing, China
Chien-Hou Chang Department of Chemical Engineering, Tianjin University, 300027, Tianjin, China
On the basis of our previous reviaed free-volume theory, a new model with temperature-independent parameters is proposed for the calculation of viscosities for liquid mixtures. It is used to estimate and predict the viscosities for diverse binary and ternary mixtures, including aqueous and partially miscible systems. For 70 binaries (2033 data points), the grand absolute average deviation percent (AAD) is 1.60 from use of the parameters regressed from the data a t a constant temperature. Moreover, for 23 ternaries (560 data points) the AAD is 2.76. A rigorous comparison with the Teja and Rice method indicates that our method is a good improvement.
Introduction Much interest has been shown in establishing a predictive model for the liquid viscosity of mixtures. Over 50 empirical or semiempirical models have been put forward (Reid et d., 1987; Teja and Rice, 19811, and these models can be divided into three classes: (1)Predictive models: Only models for ideal solutions can be used to predict the viscosities of mixturea from the properties of pure substances. In contrast, for real solutions, moet of them need some information of the mixtures. Wei and Rowley (1985) proposed a local composition model, but vapor-liquid equilibrium (VLE) and heat of mixing data are needed. The group contribution method has been investigated by some researchers (Isdale et al., 1986; Wu, 1986; Reid et al., 1987). However, this method sometimes predicta the properties of mixtures with unexpected errors, especially for the strongly associated solutions, e.g., aqueous solutions. Furthermore, a considerable amount of binary experimental data is necessary for regressing the group interaction parameters (Wu, 1986). (2) Correlation models with temperature-dependent parameters, which have been developed by many workers: The models of McAllister (1960) and Dizechl and Marschall (1982a) and the local composition model (Tong and Li, 1981; Zhong, 1980) are representative of them. Almost all of these models are based on the absolute reaction rate theory of Eyring (Glasstone et al., 1941). Some of them (e.g., the model of Dizechl and Marschall, 1982a) can correlate liquid viscosities for various systems, include aqueous solutions. Since the model parameters change significantly with temperature, these models can be used only to correlate the experimental data at a constant temperature. (3) Models with temperature-independent parameters: A notable advantage over those in claes 2 is that the model
parameters regressed from the data at one temperature can be adopted to predict the viscosities at other temperatures. A successful model, the generalized corresponding states principle (GCSP) method, is proposed by Teja and Rice (1981). This model (see Appendix) has one parameter and well correlates the viscosities for nonaqueous solutions over a certain temperature range. But it is not adequate for strongly associated systems, e.g., aqueous solutions, where a maximum occurs in mixture viscosities (Liu et al., 1989). Besides, this method needs the critical volume, which unfortunately is unavailable for some substances. As mentioned above, there are two problems in the calculation of mixture viscosities: a proper description of the temperature dependence, and the capability for aqueous solutions. It is worth noting that except the GCSP method, almost all of the previous models are based on the Eyring theory (Glasstone et al., 1941). In this theory the activation free energy is an important parameter; the temperature dependence, however, cannot be solved easily. Hilderand et al. (1977) denied the existence of an "activation energy" in liquids and suggested the use of the free-volume theory. But their model cannot be applied to strongly polar substances. Few efforta have been made to extend the free-volume theory to mixtures. Recently we proposed a revised free-volume model for liquids (Liu, 1988) and furthermore a correlation equation for the liquid viscosity of pure substances (Zhang and Liu, 1990). In this paper, on the basis of our previous works, we propose a new model for liquid mixtures whose parameters can be considered independent of temperature to a certain extent. The model is used to calculate the liquid viscoeitiea of binary and ternary mixtures for diverse systems, including aqueous solutions. All the binary parameters are regressed from the experimental data at a
0888-5885/91/2630-1617$02.50/0Q 1991 American Chemical Society
1618 Ind. Eng. Chem. Res., Vol. 30,No. 7, 1991
given temperature and then applied to the prediction of viscosities at other temperatures. Moreover, a predictive model that needs only the binary parameters is developed for ternary systems.
Derivation of the Model and Its Application to Binary Systems A revised free-volume model of liquids has been proposed recently (Liu, 1988), from which an equation to correlate liquid viscosity for a pure substance is obtained (Zhang and Liu, 1990): 4 = Bo(6 - 1) exp(C/ VRT) (1) where 4 is the fluidity (the reciprocal of viscosity p ) , 6 the reduced volume
6 = v/vo
(2)
where Vois a parameter describing molecular volume, and Bo and C are constants for the substance of interest. Over a wide temperature range, from the freezing point to the critical point, eq 1 satisfactorily represents viscosities for 83 substances, with 1044 data points, including those for polar, nonpolar, organic, and inorganic compounds with an overall average deviation 1.3%. The values of Voregressed from the viscosity data for the pure substances involved in this work are tabulated in Table 111. Most of them are from our previous work (Zhang and Liu, 1990). For a mixture eq 1can be written V , In 4, = B*,V, + V , In (6, - 1) + C,/RT (3) with B* = In Bo. Apparently, for a pure substance i, eq 1 becomes Vi In di = B*iVi + Vi In (Vi - 1) + C i / R T (4) Then, after rearrangement we get
c,
- CXiCi
where Bi is defined as
ei = xivi/v,
(6) Notice that in general C,di# 1. The following mixing rule for B*, is adopted in this work: B*, = CeiB*i i
For binary systems the mixing rule for C, is c, = C ~ X i X j C i =j X& + 2XlX2C12 + X22C2 i l
From eqs 5-8 our working equation is obtained:
where G12 = 2C12- C1 - C2, 6, = Vm/Vo,. The mixing rule for VOl is given by Vop CXixj Vo,
C
r l
The combining rule for Vouis
Val,= (1- kij)(Vo:/'
+V
oj
'1' )/8
where kij as well as G12in eq 9 are the binary interaction
parameters in our model. For a symmetric system whose constituent molecules are similar in sizes and polarities, Le., the interaction between molecules do not differ considerably, both the parameters k12and G12can be consequently taken as zero. Therefore, we obtain a predictive model for these binary systems, since there is no need of the parameters regressed from the experimental binary data:
v,-
In $, = Cei In 4i + In
1
- 1)Oi
1
(12)
I
Using eqs 9-12, we calculated the viscosities for 70 binaries. Among them 39 systems cover the temperature range as wide as 30-40 K, and 11 systems are aqueous solutions in particular, as shown in Table I. It should be pointed that the parameters k12and G12are regressed from the data at a constant temperature only, and then they are used to predict the viscosities at various temperatures. The results from the GCSP method are also listed for comparison. In this comparison, the same optimization mein eq A-7 (see thod is employed to derive the parameter Appendix A). According to the nature of molecular interactions, 70 binary systems are divided into five groups: (A) Symmetric systems, for which the predictive equation, eq 12, is adopted. The overall absolute average deviation percent (AAD) is 0.96 for 19 binaries (531 data points), which is less than that for the GCSP method (let #12= l.O), 3.93 for 17 systems. (B) Asymmetric nonpolar + nonpolar systems. The AAD for our model is 1.42 for five systems (90 data points). The GCSP method gives the deviation 2.11. (C) Nonpolar + polar systems. The AAD for this work is 1.57 for 21 systems (598 data points), less than that for the GCSP method, 2.4 for 18 systems. (D) Asymmetric polar + polar systems. Our model presents AAD 1.66 for 14 systems (405 data points). In contrast, the GCSP method shows a somewhat larger deviation, 2.85 for 11 systems. Notice that in the calculation for groups B-D eq 9 is used with only one parameter, C12. If k12is treatad as the second parameter, the calculation results can be further improved, e.g., for the system methanol + triethylamine (no. 50 in Table I), where a maximum viscosity exists due to association. Finally, (E) aqueous solutions, where eq 9 needs two parameters, k12 and GI2, and the AAD for 11systems (409 data points) is 2.47, while that for the GCSP method with one parameter is 7.32 for 9 systems. As seen in Table I, for 60 systems (1695 data points) the grand AAD is 3.90 for the GCSP method, while for 70 systems (2033 data points) 1.60 for our model eqs 9 and 12. Apparently our model is a good improvement over the former. The GCSP method has not been applied to the other 10 systems since the critical volume for the constituent pure substances needed in this method are unavailable in the literature (Reid et al., 1987; Beaton and Hewitt, 1989; Daubert and Danner, 1985).
Ternary Systems It is most important to establish a model that can predict viscosities for multicomponent systems only from the information of the constituent binary systems. As a mater of fact, we can easily extend our model to ternary systems using proper mixing rules for C, and V,. For example, if we simply adopt the mixing rule for C, similar to eq 8: C, = Xl2C, + ~ 2 ~ + C2 xS2C3 + 2~1~2C12 + 2 ~ 1 ~ 3 C 1+9 2X2XSc2S (13)
then from eqs 5, 7, and 12 we get
Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991 1619 cp
where C, = 2CU- Ci - Ci.Obviously, as a predictive model for ternaries, eq 14 contains only the binary parameters kjj and. Gij. Additonally, eq 14 can be derived through the threeinteracting-bodies model (McAllister, 1960; Dizechl and Marschall, 1982a). If the mixing rule for Vopis the same as eq 10 and C , is accordingly formulated as c, CzCxiXjXkCijk (15)
4.1
4.0
\' \\\
3.0
i l k
where c i j k are defined as Ciij = (Ci + 2Cij)/3 Cjii = Ciij, i, j = 1, 2 , 3
(16)
cizs = (ciz+ c13 + c23)/3 (17) then eq 14 is convincingly taken as our working equation for the viscosities of ternary systems. A comparison between the calculated and experimental viscosities for 23 ternaries (560 data points) is shown in Table 11. All the ki;s and G i i s needed in the prediction are simply taken from those in Table I. The systems listed are representatives of diverse mixtures, including four aqueous solutions. As seen in Table 11, the results are satisfactory with the grand AAD 2.76. It the constituent molecules are similar in sizes and polarities, the mixture viscosities can be predicted only from those of the pure substances (see nos. 1, 2, 18, and 19 in Table 11). The GCSP method has not been applied to ternary systems, since a judicious choice of reference substances is needed, which will cause some difficulties in the calculations (Kouris and Panayiotou, 1989).
Discussion and Conclusion As an important transport property, viscosity, especially for liquid mixtures, is investigated by many researchers. However, because of the complexity of this subject, it has been puzzling to make recommendations for practical calculations. In this paper, we have proposed an approach to estimate or predict viscosities for binary and ternary liquid mixtures. Our model has two advantages: parameters in equations are independent of temperature within a certain temperature range, and for multicomponent systems it is of predictive ability, i.e., only the information for the constituent binaries or pure substances is required. To prove the model, we extensively test it in terms of a large amount of experimental data. Moreover, the calculated results are compared with those from the GCSP method, which is well evaluated in the literature (Reid et al., 1987) for its reasonable capability and accuracy. From the calculated results for 70 binary and ternary systems, we find that our model gives better resulta than the GCSP method. In addition, our model does not need the critical properties of pure substances and can be easily applied to multicomponent systems. Many attempts to correlate the viscosities for aqueous solutions are unsuccessful, even by means of a model with some temperature-dependent parameters. Fortunately, our model gives satisfactory resulta, which are even better than thoee from some models with temperature-dependent parameters, e.g. McAllister model (1960) (Liu, 1988). In constrast, the GCSP method with one parameters fails in the prediction for some systems (see Figures 2 and 3). It is worth mentioning that there are two partially miscible systems in Table I (nos. 41 and 70). Sometimes, it is difficult to correlate the viscosities for two coexisting liquid phases with the same parameters simultaneously. However, as seen in Figures 1 and 3, our model still gives
2.0
1.0
0.4
a3
+
Figure 1. Viscosity for partially miscible system, n-hexane (1) benzyl alcohol (2). Experimentaldata: 0,at 303.15 K Q, 313.16 K, A, 323.15 K;0,333.15 K. (-) calculated from eq 9; (---) calculated from eq A-8.
r
tcp) AS
Figure 2. Viscosity for aqueou solution: 1-propanol (1) + water (2). Experimental data: 0,at 293.15 K,A, 313.15 K. (-) Calculated from eq 9; (- - -1 calculated from eq A-8.
satisfactory results for these systems. As is well-known, liquid viscosity is sensitive to temperature, which is the reason most of researchers focus on correlation at a given temperature. However, in this work we find that a model with temperature-independent parameters can correlate or predict mixture viscosities as accurately as those with temperature-dependent parame-
1620 Ind. Eng. Chem. Res., Vol. 30,No.7, 1991
8
3
9 *2
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0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
~ 0 0 0 0 0
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d 3
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Ind. Eng. Chem. Res., Vol. 30,No. 7,1991 1621
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1622 Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991 Table 11. Prediction Results of Eq 14 for Ternary Mixtures no. system no. of points 1 methanol + ethanol + 1-propanola 24 methanol + ethanol + 2-propanol' 2 12 3 methanol + ethanol + acetone 11 4 carbon tetrachloride + cyclohexane + 2-propanol 12 5 ethanol + acetone + cyclohexane 12 6 24 ethanol + benzene + n-heptane 7 ethanol + cyclohexane + 2-propanol 12 8 12 acetone + carbon tetrachloride + cyclohexane 9 12 acetone + ethanol + 2-propanol 10 12 acetone + n-hexane + ethanol 11 12 acetone + n-hexane + cyclohexane 12 12 dimethyl sulfoxide + chloroform + methanol 13 n-hexane + cyclohexane + ethanol 12 14 12 triethylamine + methanol + chloroform chlorobenzene + n-hexanol + benzyl alcohol 15 36 toluene + n-hexanol + benzyl alcohol 16 36 toluene + chlorobenzene + benzyl alcohol 17 36 52 18 ethylbenzene + toluene + bromobenzene' 19 p-xylene + m-xylene + o-xylene' 21 20 methanol + ethanol + water 112 methanol + acetone + water 21 28 22 24 methanol + 1-propanol + water 23 24 ethanol + 1-propanol + water grand average 560 Okij
temp, K 303.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.15-333.15 303.15-333.15 303.15-333.15 303.15-333.15 273.15-303.15 283.15-323.15 298.15 303.15 303.15
AAD
data 8ource Dizechl and Marschall (1982b) Wei and Rowley (1984b) Wei and Rowley (1984b) Wei and Rowley (1984b) Wei and Rowley (1984b) Kouria and Panoyiotou (1989) Wei and Rowley (1984b) Wei and Rowley (1984b) Wei and Rowley (1984b) Wei and Rowley (1984b) Wei and Rowley (1984b) Wei and Rowley (1984b) Wei and Rowley (1984b) Wei and Rowley (1984b) Singh and Sinha (1985) Singh and Sinha (1985) Singh and Sinha (1985) Singh et al. (1989) Serrano et al. (1990) Dizechl and Marschall (1982b) Noda et al. (1982) Dizechl and Marschall (1982b) Dizechl and Marschall(1982b)
1.81 0.60 0.58 2.21 3.92 1.67 1.68 1.93 2.71 2.11 0.82 2.58 1.63 5.67 4.23 3.83 2.23 3.83 0.55 2.82 5.19 3.11 1.38 2.76
= Gij = 0; i, j = 1, 2, 3.
Table 111. constants of Ea 1 Vo, cm3 no. compound mol-' 1 water 17.13 2 88.904 carbon tetrachloride 3 chloroform 75.253 4 68.283 l,2-dichloroethane 5 methanol 35.824 6 39.10 acetonitrile 7 ethanol 50.115 8 ethylene glycol 54.086 9 dimethyl sulfoxide 63.297 10 acetone 61.757 11 1-propanol 65.18 12 2-propanol 68.05 13 glycerol 72.414 14 1,4-dioxane 80.32 15 y -butyrolactone 72.131 16 pyridine 74.97 17 propyl acetate 103.764 18 benzene 83.864 94.554 19 chlorobenzene 20 bromobenzene 97.097 21 nitrobenzene 98.155 22 cyclohexane 99.109 23 n-hexane 111.742 24 n-hexanol 118.154 25 triethylamine 104.875 26 toluene 96.064 27 benzyl alcohol 93.37 28 anisole 100.279 29 n-heptane 127.449 30 methyl benzoate 115.633 31 ethylbenzene 111.354 32 o-xylene 112.972 33 m-xylene 113.273 34 p-xylene 113.297 35 n-tetradecane 247.058 36 n-hexadecane 280.608
C, J cm3 Bo, c P 1 44.8468 13.9197 4.1993 23.7428 39.4927 18.8497 53.7619 43.2062 60.9064 19.6655 123.233 292.864 10967.5 18.289 14.661 17.3478 18.964 15.5991 16.2752 13.04 10.1546 28.269 19.8678 115.637 20.052 20.4708 1556.1 29.044 21.2166 80.171 19.607 20.2033 20.0137 20.14 22.4196 20.3181
mol-* -18 371.5 -35 339.3 365 137 -219 660 -109 573 -109 733 -330 661 -430 391 -487 252 -33 245.9 -678 486 -836 064 -2 113700 -80 878.8 -88 186 -37 581.3 -49 447 108 751 2 109.9 -25 923 42 624.5 -245 635 -9 799.6 -1 065 260 -281 633 -55 450 -1 738 580 -260 570 -94 687 -764 640 -72 203 -37 479 -13 046 -35 229.7 -641 508 -800 374
ters, even for aqueous solutions. The temperature range for 39 systems involved in this work are 30-40 K. In these cases by using the parameters regressed from the data at a certain temperature, our calculated results are of satisfactory accuracy, even though the mixture viscosities change significantly with the temperature (e.g., see Figure 2). It should be pointed out that care must be taken to make temperature extrapolation for the binary systems
0
0.e1
a01
#.I
0.6
I O
2,
Figure 3. Viscosity for the partially miscible system triethylamine (1)+ water (2) at 292.15 K. 0 , experimental data. (-) Calculated from eq 9; (- - -1 calculated from eq A-8.
whose viscosity magnitudes of the two constituent components differ significantly. The glycerol + water system is an example, for which the viscosity of glycerol is about 300 CPagainst 0.66 CPfor water at 313.15 K. Besides, we fiid that for this system the G12)sare rather large as shown in Table I. ABa result, the parameter Gu should be treated as temperature dependent to ensure an AAD of less than 10.
Nomenclature A , B, D,E = constants in eqs A-9 and A-10
Ind. Eng. Chem. Res., Vol. 30,No. 7, 1991 1623
Bo, C = constants in eq 1 B* = In Bo Gij = interaction parameter in eq 8, J cm3 mol-2 k - = interaction parameter in eq 10 = molecular weight R = gas constant T = temperature, K T+ = T T J T , V = volume, cm3/mol yo = molecular volume in eq 2, cm3/mol V = reduced volume, V/Vo x1 = mole fraction
Hewitt, 1989; Daubert and Danner, 1985). Literature Cited
id
Greek Symbols I
V~/s(T,M)-'/2
ei = xivi/vm p $t
= viscosity, cP
= fluidity, c P 1
fi12 = interaction parameter in the GCSP method o = acentric factor
Subscripts
c = critical i, j , k = pure components i, j , k m = mixture Superscripts
rl, r2 = reference fluids 1, 2 Appendix: GCSP Method for the Viscosities of Liquid Mixtures The original equation proposed by Teja and Rice (1981) is In (pmcm) =
(A-6) (A-7) where qij is the interaction parameter regressed from experimental data. The two reference fluids (rl and r2) are the constituent pure substances 1and 2; from eq A-5, eq A-1 simplifies to (Reid et al., 1987) In (p,c,) = x1 In ( p ~ ) ( + ~ l x2 ) In ( p ~ ) ( ~ (A-8) ~ ) where In ( p # l ) and In are functions of the "characteristic temperature" T* (=TT,/T,) and expressed as lnp = A +B / P (A-9) or In p = A + B / P + D P + E P 2 (A-10) The constants A, B, D, and E in the equations are from the literature (Reid et al., 1987). If the data are unavailable, the experimental results for pure substances are uaed to regress A and B in eq A-9. The critical properties T, and V , for the pure substances involved in this work are from the literature (Reid et al., 1987; Beaton and
Aminabhavi, V. A,; Aminabhavi, T. M.; Balundgi, R.H. Evaluation of Excess Parameters from Densities and Viecoeitiea of Binary Mixtures of Ethanol with Anisole, NJV-Dimethylformamide, Carbon Tetrachloride, and Acetophenone from 298.15 to 313.15 K. Znd. Eng. Chem. Res. 1990,29,2106-2111. Beaton, C. F.; Hewitt, G. F. Physical Property Data for the Design Engineer; Hemisphere: New York, 1989; pp 50,52, 134. Chevalier, J. L. E.; Pertrino, P. J.; Gaston-Bonhomme, Y. H. viscosity and Density of Some Aliphatic, Cyclic, and Aromatic Hydrocarbons Binary Liquid Mixtures. J. Chem. Eng. Data 1990, 35,206-212. Daubert, T. E.; Danner, R.P. Data Compilation Tables of Properties of Pure Compounds; AIChE: New York, 1985; pp Ch202, C2h602. Dizechl, M.; Mmchall, E. Correlation for Viscosity Data of Liquid Mixtures. Znd. Eng. Chem. Prod. Des. Dev. 1982a, 21, 282-289. Dizechl, M.; Marschall, E. Viscosity of Some Binary and Ternary Liquid Mixtures. J. Chem. Eng. Data 1982b, 27,358-363. Garcia, B.; Ortega, J. C. Excess Viscosity g,Excess Volume p,and Excess Free Energy of Activation AG*E at 283,293,303,313, and 323 K for Mixtures of Acetonitrile and Alkyl benzoates. J. Chem. Eng. Data 1988,33, 200-204. Glasstone, So;Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hik New York, 1941. Heric, E. L.; Brewer, J. G. Viscosity of Some Binary Liquid Nonelectrolyte Mixtures. J. Chem. Eng. Data 1967,12, 574-583. Hildebrand, J. H. Viscosity and Diffusivity; Wiley New York, 1977. Isdale, J. D.; MacGillivray, J. C.; Cartwright, G. "Prediction of Viecosity of Organic Liquid Mixtures by a Group Contribution Method"; Natl. Eng. Lab. Rep.: East Kilbride, Glaegow, Scotland, 1985. Joshi, S. S.; Aminabhavi, T. M. Densities and Shear Viscosities of Anisole with Nitrobenzene, Chlorobenzene, Carbon Tetrachloride, 1,2-Dichloroethane, and Cyclohexane from 25 to 40 OC. J. Chem. Eng. Data 1990,35, 247-253. Katti, P. K.; Prakash, 0. Viscosities of Binary Mixtures of Carbon Tetrachloride with Methanol and Isopropyl Alcohol. J. Chem. Eng. Data 1966,11,46-47. Kouris, S.; Panayiotou, C. Dynamic Viscosity of Mixtures of Benzene, Ethanol, and n-Heptane at 298.15 K. J. Chem. Eng. Data 1989,34, 200-203. Kumar, A.; Prakash, 0.;Prakash, S. Ultrasonic Velocities, Densities, and Viscosities of Triethylamine in Methanol, Ethanol, and 1Propanol. J. Chem. Eng. Data 1981,26,64-67. Landolt-Bijrnstein,Zahlenwerte und Funktionen aus Phys., Chem., Astron., Ceophys. und Tech., 11 Band, Eigenschuften der Materie in Zhren Aggregatzusthder, 5 Teil, Bandteil a, Transport PMinomene Z (Viskositiit und Diffusion);Springer-Verb. Berlin, 1969. The density data for liquid mixtures are from: LandoltBBmstein. Numerical Data and Functional Relationship in Science and Technology, New Series, Group ZV, Volume l a
Densities of Liquid Systems, Nonaqueous Systems and Ternary Aqueous Systems, 1974; Volume Ib, Densities of Binary Aqueous Systems and Heat Capacities of Liquid Systems; Springer-Ver-
lag: Berlin, 1977. Liu, H. Study of Liquid Viscosity and ita Measurement under Pressure. Ph.D. Dissertation, Tianjin University, China, 1988. Liu, H.; Wang, W.; Lu, H. Numerical Analysis of the Principle of Corresponding States. J. Beijing Zmt. Chem. Techn. (china) 1989,16, 21-29. McAUister, R. A. The Viscosity of Liquid Mixtures. AZChE J. 1960, 6,427-431. Noda, K.; Ohashl, M.; Ishlda, K. Viscosities and Densities at 298.15 K for Mixtures of Methanol, Acetone, and Water. J. Chem. Eng. Data 1982,27,326-328. Paez, 5.;Contreras, M. Densities and Viscoeitiee of Binary Mixtures of 1-Propanol and 2-Propanol with Acetonitrile. J. Chem. Eng. Chem. Eng. Data 1989,34,455-459. Ramkumar, D. H. S.; Kudchadker, A. P. Mixture Properties of the Water + y-Butyrolactone + Tetrahydrofuran System. J. Chem. Eng. Data 1989,34,459-465. Rathnam, M. V. Viscosities and Densities of Some Binary Liquid Mixtures of Esters at 303.15 K and 313.15 K. J. Chem. Eng. Data 1988, 33,509-511. Reid, R.C.; Prauenitz, J. M.; Poling, B.E. The Properties of Gweo and Liquids, 4th ed.; McGraw-Hill: New York, 1987.
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Received for review July 26, 1990 Reuised manuscript receiued February 11, 1991 Accepted February 22,1991
Polystyrene Thermodegradation. 2. Kinetics of Formation of Volatile Productst Paolo Cadti,**'Pier Luigi Beltrame,t Massimo Armada,' Antonella Gervasini,*and Guido Audisiol Dipartimento di Chimica Fisica ed Elettrochimica, Universitd di Milano, via Golgi 19, 1-20133 Milano, Italy, Eniricerche, via Maritano 26, 1-20097 S. Donato M i l s e , Italy, and Zstituto di Chimica delle Macromolecole del CNR, via Bassini 15/A, 1-20133 Milano, Italy
Volatile products obtained from the thermal degradation of polystyrene (PS),carried out in tubes sealed under vacuum, were identified by GC-MSand quantitatively determined. The reaction temperature was in the range 360-420"C. The thermal degradation of PS followed first-order kinetics in the initial part of the reaction. A lumped procedure was employed for the overall kinetic interpretation. and the kinetic parameters of the reaction were evaluated bv an optimization procedure. TGe lumped kinetics has been rationalized accordingly to a free-radical mechanism.
Introduction In recent years many studies have been devoted to the degradation of polymers. One of the principal purposes of these studies is connected with the recovering of waste polymers. The aim is to reduce pollution as well as to reutilize the potential energy content of these wastes. Synthetic polymers can be degraded to both chemicals (among them the original monomer) and fuels (Sinnet al., 1976;Kaminsky et al., 1979;Poller, 1980). Polystyrene (PS) constitutes an important part of industrial and domestic solid wastes, due to ita wide production and utilization. The thermal or catalytic degradation of PS can be performed under different conditions (under vacuum, in inert atmosphere, in air, in stream, in a closed system, etc.) leading to Werent product distributions (Madorsky, 1964; Menzel, 1974; Sinn et al., 1976;Lucchesi et al., 1980,Ogawa et al., 1981;Costa et al., 1982;Ide et al., 1984;Schrader et al., 1984;Peev et al., 1987;Nanbu et al., 1987). A good
comprehension of the reaction mechanism for any possible condition could allow one to direct the process to desired products. In previous studies on degradation of PS (Audisioet al., 1987,1990) as well as of polypropylene (Audisio et al., 1984) and of polyethylene (Beltrame et al., 19891, the distribution patterns of products evidenced that the mechanism involving radicals in the pure thermal degradation was changed by the presence of some catalysts (silica-aluminas and zeolites) in a different mechanism involving also ions. To elucidate the differences between the thermal and the catalytic reactions, we undertook a comparative investigation starting from the study of the kinetics of formation of radicals in the thermal degradation of PS by means of a direct determination of radicals through ESR spectroscopy (Carniti et al., 1989). The PS degradation was carried out in sealed tubes in the temperature range 350-420 OC. The reaction kinetically followed by ESR analysis was found to be the initiation step of the thermal degradation, which is a well-known free-radical chain process including initiation, p r o p a g a t i o n , transfer, and termination steps (Guyot, 1986). In the present work we analyzed the products of the thermal degradation of PS. The study was carried out by
'Part 1: Carniti e t el., 1989.
* Universita di Milano.
8 Eniricerche.
Istituto di Chimica delle Macromolecole del CNR. 008S-58S5/91/2630-1624$02.50/0
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1991 American Chemical Society
