Ind. Eng. Chem. Prod. Res. Dev. 1983, 22, 146-149
146
into liquid was shown to occur in two distinct phases. In the first phase, for any time lower than 50 h, the plasticizer transfer was controlled by boundary layer phenomena, and the stirring of liquid was proven to be of importance. The second phase of plasticizer transfer was entirely controlled by internal diffusion in the PVC itself. The temperature and the percentage of plasticizer in PVC were important parameters, but the influence of the kind of the liquid was found to be decisive on the plasticizer transfer. Registry No. DOP, 117-81-7; PVC, 9002-86-2; n-heptane, 142-82-5; benzyl alcohol, 100-51-6; methanol, 67-56-1; ethanol, 64-17-5.
Literature Cited Crank, J. "The Mathematics of Diffusion", 2nd ed.; Clarendon Press: Oxford, 1976; pp 47-57. Figge. K. Food Cosmet. Toxicoi. 1972, 10, 815. Figge, K . J . Radionai. Chem. 1976, 32, 315.
Gilbert, S. G. J . Food Sci. 1976. 4 1 , 995. Haesen, G.; Schwarze. A. "Migratin Phenomena in Food Packaging"; Commission of the European Communttles: Petten Establ., 1978. Kampouris, E. M. Europ. folym. J. I975a, 1 1 , 705. Kampouris, E. M. Polymer. 1975b, 76, 840. Koros, W. J.; Hopfenberg. H. 6.Food Technoi. 1979, 54. Leimgruber, R. A. Kunstst. flast. 1974, 4 , 15. Messadi, D.; Vergnaud, J. M. J . Chim. fhys. 1980, 10, 935. Messadi, D.; Vergnaud, J. M. J. Appl. folym. Sci. 19818, 26, 667. Messadi, D.; Vergnaud, J. M. J . Appl. fo/ym. Sci. I 9 8 l b , 2 6 , 2315. Messadi, D.; Vergnaud, J. M. J . Appl. folym. Sci. 1962, in press. Troparevsky, A.: Troparevsky, M. L.; Mitta, A. E. A. Inis Atomidex. 1976, 7. Vergnaud, J. M.; Messadi, D.; Taverdet, J. L. 2nd International Flavor Conference, American Chemical Society, Athens, 1981a; July 20. Vergnaud, J. M.; Messadi, D.; Taverdet, J. L. 182nd National Meeting of the American Chemical Society, New York, NY, Aug 1981b. Vom Bruck, C. G.; Figge, K.; Piater, H.; Wolf, V. Dtsch. Lebensmiftel Rdsch. 1971, 6 7 , 444. Woggon, H.; Kohler, U. Kunststoffe 1967, 57, 583.
Received for review December 23, 1981 Accepted October 25, 1982
Thermodynamic Behavior of Single Polymer-Binary Solvent Systems. Qualitative Comparison with Solubility Parameter Approach S. Piccarolo' and G. Tltomanllo Istituto di Ingegneria Chimica, UniversltZ3 di falermo, falermo, Italy
Literature data on the thermodynamic behavior of single polymer-binary solvent systems are considered. A qualitative comparison with predictions obtained on the basis of solubillty parameters adopting the single liquid approximation is performed.
Introduction The thermodynamic behavior of polymers in the presence of mixed solvent systems has been the object of numerous investigations, both experimental and theoretical. In some cases the authors' attention was devoted to the study of precipitation temperature as a function of solvent composition and to the construction of isothermal phase diagrams (Shultz and Flory, 1953; Wolf and Molinari, 1973; Cowie and McEwen, 1974; Wolf and Blaum, 1975; Craubner, 1978). In other cases only the polymer solubility or its swelling was considered (Bristow and Watson, 1959; Beerbower and Diekey, 1969; Froehling et al., 1976; Rigbi, 1978; Piccarolo and Titomanlio, 1982). These phenomena are obviously related to the expression of free energy of mixing as a function of composition and temperature. Intrinsic viscosity is a measure of the volume occupied by a single macromolecule which in turn is again related to the free energy of mixing (Flory, 1953) and indeed it has been studied for several polymer-binary solvent systems (Palit et al., 1951; Shultz and Flory, 1955; Dondos and Patterson, 1967; Dondos et al., 1967; Dondos and Patterson, 1969; Dondos and Benoit, 1973). In addition, osmotic pressure, light scattering, and refractive index, which also are related to the volume occupied by a single macromolecule, have been considered (Palit et al., 1951; Cowie and McCrindle, 1972; Wolf and Willms, 1978; Gun Chu and Munk, 1978; Aminabhavi and Munk, 1979a,b; Horta and Fernandex-Pierola, 1981). In 0196-4321/83/1222-0146$01 SO/O
particular, the existence of maxima of intrinsic viscosity, osmotic pressure, and dissymmetry (light scattering) for the same solvent composition was verified with reference to the system polystyrene-acetone-methylcyclohexane (Palit et al., 1951). In many circumstances the properties mentioned above change monotonically with the solvent composition; in others maxima or minima have been observed. the data have been mostly analyzed on the basis of interaction parameters, xij, which are a scale for the contribution of each molecular contact to the free energy deviation from the entropic combinatorial term. For many of the systems studied, especially when the behavior was not monotonic with the solvent mixture composition, the data were only qualitatively described. The Hildebrand solubility parameter approach and its recent modifications (Hansen, 1967a,b) has been followed in a few cases (Beerbower and Dickey, 1969; Froehling et al., 1976; Rigbi, 1978; Piccarolo and Titomanlio, 1982);the interest in this approach is related to the fact that only single-component (instead of binary) parameters, easily available in the literature, are required. Obviously a loss of accuracy is expected with respect to models which use specific binary parameters. Literature data are briefly reconsidered in this work on the basis of the solubility parameter model with the aim of testing its ability to describe a t least the qualitative features of the experimental behavior shown by polymers 0 1983 American
Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 1, 1983
147
Table I. Influence of Solvent Composition on the Thermodynamic Behavior of Single Polymer-Binary Solvent Systems. Experimental Columns Report Monotony or Extrema of Free Energy of Mixing as Indicated by Literature Data. When a Minimum or a Maximum Is Present Also t h e Corresponding Solvent Volume Fraction Is Given with Reference to Solvent A. Solubility Parameter Predictions Are Obtained by Eq 2 and 3. Solvent Code and Solubility Parameter Components Are Specified in Table I1 solubility parameter predictions system no.
system
exptl monotony X,
1 2 3 4 5 6
PMMA/13 / 2 5 PMMA/4/6 PMMA/7 11 3 PMM A/ 3 17 PMMA/3 / 8 PMMA/ 2 16
min min min Yes Yes min
7 8 9 10 11 12 13 14 15 16 17
PMM A/ 8 11 2 PMMAI3 122 PMMA/3/26 PVC/23/17 PVC/24/20 PVC/5/20 PSI1 519 PSlSl21 PS/19/17 PSI218 PSI1217
Yes Yes Yes min min Yes min Yes Yes Yes max
18 19 20 21 22 23 24 25 26 27 28 29
PS/8/13 PS/3/7 PSI1 116 PS13/17 PS/1/8 PS/8/11 PSI1 4 /8 PSI1 118 PSI3122 PS/12/8 PSI3126 PSI7 11 3
min Yes min Yes min max min min Yes min Yes Yes
0.8 0.15 0.93 0.45
0.72 0.65
0.8
0.55 0.95 0.07 0.33 0.4 0.4 0.7
b = 0.4 -
b=O
monotony Yes min min yes Yes min Yes min Yes min min min min Yes Yes Yes Yes min Yes Yes Yes min min min min Yes min Yes Yes
X, 0.45
0.81 0.15 0.04
0.8 0.55 0.55 0.83
0.9
0.12 0.88 0.16 0.09 0.37
monotony min min min Yes yes min Yes min Yes min min min min Yes Yes Yes min min Yes min Yes min min min min Yes min Yes Yes
X,
0.81 0.4 0.83
exptl methoda a,b C
0.12
e e b d
0.12
e e C
0.8 0.65 0.55 0.76
a a a C
e
0.78
e e e
0.93
e e
0.12
C
0.03 0.86 0.01 0.08 0.62
b d d f d,e,g e e e e
ref Picorallo and Titomanilo (1982) Wolf and Blaum (1975) Dondos and Patterson (1969) Dondos and Patterson (1967) Craubner (1978) Horta and Fernandez-Pierola (1981) Dondos and Rempp (1967) Dondos and Rempp (1967) Dondos and Rempp (1967) Froehling et al. (1976) Froehling e t al. (1976) Froehling e t al. (1976) Shultz and Flory (1953) Shultz and Flory (1955) Shultz and Flory (1955) Dondos and Patterson (1969) Dondos and Rempp (1967); Dondos and Patterson (1969) Dondos and Patterson (1969) Dondos and Patterson (1967) Cowie and McEwen (1974) Craubner (1978) Cowie and McGrindle (1972) Wolf and Willms (1978) Gun Chu and Munk (1978) Palit e t al. (1951) Dondos and Rempp (1967) Dondos and Rempp (1967) Dondos and Rempp (1967) Dondos and Benoit (1973)
a Experimental method : a, swelling; b, solubility; c, precipitation temperature; d, light scattering; e, intrinsic viscosity; f , refractive index; g, osmometry.
in the presence of binary solvent mixtures,
Excess Free Energy and Solubility Parameters Both enthalpy and entropy contributions should be considered in evaluating the excess free energy with respect to the combinatorial entropy as derived by the FloryHuggins lattice model (Flory, 1970). The effect of the solvent mixture composition on the entropy contribution is neglected when the behavior of a polymer in a solvent mixture is considered by means of the solubility parameters (Beerbower and Dickey, 1969; Froehling et al., 1976; Rigbi, 1978; Piccarolo and Titomanlio, 1982). The problem is then reduced to the expression of the enthalpy of mixing, of which only the energy contribution is explicitly considered as a function of solvent mixture composition. Thus, monotonic behavior of the energy of mixing Emiximplies monotonic character of all the properties tightly related to the excess free energy and vice versa. The applicability of the original solubility parameter model was extended by treating these as vectors whose components account for different energy interaction modes (Hansen, 1967a,b, 1970). In particular, for each chemical species Hansen considered three components: 6d related to dispersion (London) forces, 6, related to dipole-dipole interactions, and bh related to all remaining interactions including hydrogen bonding and a-orbital bonding. The
energy of mixing in a binary system is then given by the equation
(1)
where 4 is the volume fraction of one component, V is the average molar volume calculated on the basis of mole fractions, and 6jeiare the solubility parameter components of the two chemical species. Obviously the quantity Q does not depend upon the system composition and thus is a scale factor for Emix; in the following it will be referred to as the "energy of mixing factor". Other authors modified the expression of Q with the aim of accounting for the polar induction energy between different species. Assuming it proportional to both the dipole and hydrogen contributions, one has (Beerbower and Dickey, 1969; Weimer and Prausnitz, 1965; Helpinstill and Vanwinkle, 1968)
Emix = dJ(1- dJ)V where b is the "polar induction parameter", which for the systems studied in the literature was found to be close to 0.4.
148
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 1, 1983
Table 11. Solvent Code and Solubility Parameter Components Adopted in the Evaluation of 6, bv Ea 2 and 3 solvent code
Sr,
6h
ref
acetone 2 acetonitrile 3 benzene 4 2-butanol 5 n-butyl acetate 6 1-chlorobutane I chloroform 8 cyclohexane 9 cyclohexanol 1 0 m-cresol 11 dimethylformamide 1 2 dioxane 1 3 ethanol 1 4 ethyl acetate 1 5 ethylcyclohexane 16 ethyl ether 11 methanol 18 methylcyclohexane 1 9 methyl ethyl ketone 20 nitromethane 21 tetrachloromethane 22 tetrahydrofuran 23 toluene 24 trichloroethylene 25 water 26 xylene PMMA [poly(methyl methacrylate ) ]
substance
1.58 1.5 8.95 7.7 7.7 8.0 8.65 8.18 8.5 8.8 8.52 9.3 1.13 7.44 1.96 7.05 1.42 7.8 7.71
5.1 8.8 0.5 2.8 1.8 2.7 1.5 0 2.0 2.5 6.7 0.9 4.3 2.6 0 1.4 6.0 0 4.4
3.4 3
a
1
a
1.1
a
3.1 1.0 2.8 0 6.6 6.3 5.5 3.6 9.5 4.5 0 2.5
a
10.9 0.5 2.5
a
7.7 8.65 8.22 8.82 8.78 9.54 7.8 8.68
9.2 0 2.8 0.1 1.5 8.12 0 2.8
2.5 0 3.9 1.0 2.6 8.62 0.5 3.8
a
PVC [ poly(viny1 chloride)] PS [polystyrene]
9.15
4.9
1.5
a
9.64
0.42
1.0
a
1
t d h
Figure 1. Geometrical rappresentation of eq 1 and 3: 1 represents the polymer, a and p the pure liquids; Q is the energy of mixing factor defined by eq 1; 6d, 6,, and Jh are solubility parameter components.
The case of a polymer in presence of a liquid mixture is often analyzed by the so-called single-liquid approximation (Scott, 1949),considering the polymer and a “single liquid” having properties equivalent to those of the mixture. This approach is adopted also when dealing with interaction parameters. When the solubility parameters approach is followed, the parameters of the ”single liquid” are evaluated (Beerbower and Dickey, 1969) as where 6,* and 6F are the solubility parameters of the pure liquids and X is the volume fraction of one of them in the mixture of the two. The energy of mixing factor, Q, is then obtained by substitution into eq 1 or 2 of both the parameters 6,’of the polymer and those 6: of the single liquid. The curve of Q as a function of the volume fraction X may be either monotonic or have a minimum. This is graphically shown in Figure 1, where a geometric representation of eq 1and 3 is reported as X changes, the point representative of the single liquid moves on the segment joining points CY and /3 representative of the pure liquids. The distance of the single-liquid point from point 1 (representative of the polymer) is the geometrical equivalent of Q and, depending on the relative position of points CY, /3, and 1,may be either monotonic or have a minimum with X . Correspondingly, monotonic behavior or extrema are predicted for all the properties related to the excess free energy. Comparison and Discussion Many of the literature data concerning the thermodynamic behavior of a polymer in the presence of binary solvent systems are here reconsidered. Only cases sufficiently investigated to clearly detect monotonic character with solvent mixture composition or extrema (maxima or minima) are analyzed, however. This is because only the capability of predicting monotonic behavior (or vice versa) by means of the solubility parameters approach described above is investigated here. Data concerning the swelling of natural rubber by several binary liquid mixtures (Bristow and Watson, 1959) were already favorably analyzed (Beerbower and Dickey, 1969) by means of eq 2 and 3. The systems considered here are listed in Table I where the liquid mixture components are indicated by numbers according to which the solvents are reported in Table 11. Whether the properties reported
6d
a
b a a a
b a
b a a
a a
b a
a a a
a
c b a
a Koenhen and Smolders (1915). Hansen and Beerbower (1911). Hansen and Pierce (1974).
in the “experimental method” column of Table I show extrema of monotonic character with varying solvent mixture composition is indicated in the first of the two columns headed by “experimental”. Thus “yes” means that the property is monotonic; “min” and “max” mean that respectively a minimum or a maximum of the excess free energy is indicated by the data analyzed. The volume fraction X, (within the binary liquid mixture) corresponding to either the experimental minima or maxima is reported in the second “experimental” column with reference to the solvent identified by the first number. The corresponding characteristics of the energy of mixing factor Q as a function of the liquid mixture composition are reported in the other columns. The polar induction correction was both accounted for in eq 2 by using b = 0.4 and ignored by taking b = 0; this is because both alternatives have been followed in the literature (Beerbower and Dickey, 1969; Froehling et al., 1976; Rigbi, 1978; Piccarolo and Titomanlio, 1982). The solubility parameter components adopted for all species are given in Table 11;most of them were taken from the work of Koenhen and Smolders (1975) and in a few cases, when they were not available there, reference was made to Hansen and Beerbower (1971). The components of water, for which more recent values (Hansen and Pierce, 1974) were adopted, are the only exception to this. Before any other specific comment is made, it has to be pointed out that the data for systems no. 17 and 23 indicate a maximum in the free energy of mixing as a function of the liquid mixture composition. This would imply a maximum of the energy of mixing factor Q which,
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 1, 1983
on the contrary according to the analysis followed here, can only have a minimum. such an intrinsic limitation of the solubility parameters approach holds at least as long as eq 2 and 3 are adopted. As for the other cases, one may generally say that the monotonic character is mostly correctly predicted and that the experimental values of X, are often close to those evaluated on the basis of the curve of Q; furthermore, on the average only a very small improvement is obtained using b = 0.4 instead of b = 0, that is accounting of the polar induction energy contribution as sugggested in Beerbower and Dickey (1969), Weimer and Prausnitz (1965), and Helpinstill and Vanwinkle (1968). With reference to b = 0.4, a minimum in the curve of Q is predicted for the few casess left, i.e., systems 8 and 12 in Table I, instead of monotonic behavior. This together with the fact that a maximum of Q with X can never be obtained with eq 2 and 3 may be taken as a general trend that with solubility parameters, at least by using 2 and 3, the excess free energy of the three component system is somehow underestimated with respect to its value for the corresponding binary systems. Exceptions to this would be system 1,but only for b = 0, and to some extent system 24 for which, by taking b = 0.4, the value predicted for X, is so small as to indicate an essentially monotonic behavior. The reasons for the mentioned underestimate of excess free energy may be numerous; the expression of Q given in eq 2 may certainly be among these. Although this expression often resulted very successfully, some inaccuracy was sometimes observed also with binary systems (Hansen and Beerbower, 1971) and even binary correction constants were proposed (Funk and Prausnitz, 1970). Furthermore, the single-liquid approximation also gives rise to systematic errors in the results (Scott, 1949); this error is obviously related to the particular blending rule adopted in the evaluation of the single-liquid solubility parameters 8:: if the point representative of the singe-liquid moves in Figure 1 between the pure component points cy and /3 along a curve different from a segment, even a maximum of Q can be generated. Furthermore, the deviation of the behavior of system number 12 in Table I from the expectations on the basis of solubility parameter components was related (Froehling et al., 1976) to particularly strong donor/acceptor interactions between the solvents.
Conclusions The possibility of describing the thermodynamic behavior of polymers in the presence of binary solvent sys-
149
tems by means of solubility parameter components has been considered. The single liquid approximation, in the form usually adopted for such ternary systems, has been followed; a maximum of excess free energy as a function of the binary solvent mixture composition, sometimes indicated by the experiments, cannot be reproduced by this approach. The features shown by most of the data considered here were, however, at least qualitatively reproduced. Furthermore, the overall comparison indicates an underestimate of the ternary system excess free energy with respect to its values for the binary systems. Registry No. PMMA, 9011-14-7; PVC, 9002-86-2; PS, 900353-6.
Literature Cited Aminabhavi, T. M.; Munk, P. Macromolecules 1979a, 12, 1186. Amlnabhavi, T. M.; Munk, P. Mecromolecules 1979b, 12, 607. Beerbower, A.; Dickey, J. R. Am. SOC. Lubrlc. Eng. Trans. 1969, 12, 1. Bristow, G. M.; Watson, W. F. Trans. Inst. Rubber Ind. 1959, 3 5 , 73. Cowie, J. M. 0.; McEwen, I . J. J. Chem. Soc., Faraday Trans. I 1974, 7 0 , 171. Cowie, J. M. G.; McCrindle, J. T. Eur. folym. J. 1972, 8 , 1185. Craubner, H. Macromolecules 1978, 11, 1161. Dondos, A,; Benoit, H. Macromolecules 1973, 6, 242. Dondos, A.; Patterson, D. J. folym. Scl. A - 2 1967, 5 , 230. Dondos, A.; Patterson, D. J. folym. Sci. A - 2 1969, 7 , 209. Dondos, A.; Rempp, P.; Benoit, ti. Eur. folym. J. 1967, 3 , 657. Fiory, P. J. "Principles of Polymer Chemistry"; Cornell University Press: Ithaca, NY, 1953; Chapter 14 Fiory, P. J. Discuss. Faraday SOC. 1970, 49, 7. Froehling, P. E.; Koenhen, D. M.; Bantjes, A.; Smolders, C. A. Polymer 1976, 17, 835. Funk, E. W.; Prausnitz, J. M. Ind. Eng. Chem. 1970, 62(8),9. Gun Chu, S.; Munk, P. Macromolecules 1978, 1 1 , 879. Hansen, C. M. J. faint Techno/. I967a, 3 9 , 104. Hansen, C. M. J. faint Techno/. 1967b, 3 9 , 505. Hansen, C. M. J. Paint Techno/. 1970, 4 2 , 660. Hansen, C. M.; Beerbower, A. I n "Encyclopedia of Chemical Engineering", Kirk-Othmer Eds.; Wiley: New York, 1971; Suppl. Voi., p 887. Hansen, C. M.; Pierce, P. E. Ind. Eng. Chem. Process D e s . D e v . 1974, 13, 255. Helpinstill, J. G.; Vanwinkle, M. I n d . Eng. Chem. Process D e s . D e v . 1968, 7, 213. Horta, A.; Fernandez-Pierola. I.Macromolecules 1981, 14, 1519. Koehnen, D. M.; Smolders, C. A. J. Appl. folym. Sci. 1975, 19, 1163. Palit, S. R.; Colombo, G.; Mark, H. J. folym. Sci. 1951, 6, 295. Piccarolo, S.; Titomanlio, G. Makrolmol. Chem. 1982, 3 , 382. Rigbi, 2 . Polymer 1978, 19, 1229. Scott, R. L. J. Chem. fhys. 1949, 17, 268. Shukz, A. R.; Flory, P. J. J . Am. Chem. SOC. 1953, 7 5 , 5661. Shukz, A. R.; Flory, P. J. J. folym. Sci. 1955, 15, 231. Weimer, R. F.; Prausnitz, J. M. Hydrocarbon Process. 1965, 4 4 , 237. Wolf, B. A.; Blaum, G. J. folym. Sci., fhys. Ed. 1975, 13, 1115. Wolf, B. A.; Molinari, R. J. Makromol. Chem. 1973, 173, 241. Wolf, B. A,; Wiilms, M. M. Makromol. Chem. 1978, 179, 2285.
Received for review May 4, 1982 Accepted September 24, 1982
