Prediction of solute partition coefficients between polyolefins and alcohols using the regular solution theory and group contribution methods

1506 Znd. Eng. Chem. Res . 1991,30, 1506-1515

Calculations of Phase Diagrams and Thermochemistry; Chang, Y . A,, Smith, J. F., Eds.; TMS-AIME: Warrendale, PA, 1979.

Kaufman, S. M. Origins of Surface Tension Extrema in Metallic Solutions. Acta Metall. 1967, 15, 1089.

Kaufman, S. M.; Whalen, T. J. The Surface Tension of Liquid Gold, Liquid Tin, and Liquid Gold-Tin Binary Solutions. Acta Metall. 1965, 13, 797.

Kazakova, I. V.; Lyamkin, S. A.; Lepinshkikh, B. M. Density and Surface Tension of Pb-Bi Melts. Zh. Fir. Khim. 1984,58, 1534.

Kelly, A. The Strengthening of Metals by Dispersed Particles. Proc. R. SOC., A, 1964, 282,63.

Kelly, A.; Davies, G. J. The Principles of the Fibre Reinforcement of Metals. Met. Reu. 1965a, I O , 1.

Kelly, A.; Davies, G. J. Experimental Aspects of Fibre-Reinforced Metals. Met. Reu. 1965b, 10, 79.

Kingery, W. D. Metal-Ceramic Interactions. I.: Factors Affecting Fabrication and Properties of Cermet Bodies. J . Am. Ceram. SOC. 1953, 36, 362.

Korol’kov, A. M.; Igumnova, A. A. Izu. Akad. Nauk SSSR, Met. Topl. 1961, No. 6, 95.

Lancaster, J. F. Metallurgy of Welding, 3rd ed.; George Allen & Unwin: London, 1980.

Laty, P.; Joud, J. C.; Desre, P. Surface Tensions of Binary Liquid Alloys with Strong Chemical Interactions. Surf. Sci. 1976,60,109.

Lazarev, V. B. Experimental Study of the Surface Tension of Indi- um-Antimony Alloys. Zh. Fiz. Khim. 1964,38, 325.

Leonida, G. Handbook of Printed Circuit Design, Manufacture, Components and Assembly; Electrochemical Publishers: Scot- land, 1981.

MacKenzie, J. D. “Ceramic-to-Metal Bonding for Pressure Transducers”; Final Report to National Aerospace Administra- tion, NASA-Lewis Research Center, Contract No. NAG3-295, Report No. N84-22753, April 1984.

Manning, C. R., Jr.; Stoops, R. F. High-Temperature Cermets. 11.: Wetting and Fabrication. J . Am. Ceram. SOC. 1968, 51, 415.

Matuyama, Y. On the Surface Tension of Molten Metals and Alloys. Sci. Rep. Tohoku Imp. Uniu. 1927, 16, 555.

Mohn, W. R. Your MMC Product Will Stay Put. Res. Deu. 1987, July, 54.

Morgan, C. S.; Moorhead, A. J.; Lauf, R. J. Thermal-Shock Resistant Alumina-Metal Cermet Insulators. Am. Ceram. SOC. Bull. 1982, 61, 975.

Okajima, K., Sakao, H. Equations for Surface Tension Related with Thermodynamic Enthalpy and Activities of the Binary Molten Alloys. Trans. Jpn. Inst. Met. 1982,23, 121.

Pelzel, E. Die Oberflachenspannung flussiger Metalle and Legier- ungen 11. Berg- Huettenmaenn. Monatsh. 1949, 94, 10.

Pelzel, E.; Sauerwald, F. Dichtemeseungen bei hohen Temperaturen XII. 2 . Metallkde. 1941, 33, 229.

Predel, B. Association Equilibria in Liquid Alloys and Their Influ- ence on the Formation of Metallic G h . Calculation of Phase Diagrams and Thermochemistry; Chang, Y . A., Smith, J. F., Eds.; TMS-AIME: Warrendale, PA, 1979.

Predel, B.; Oehme, G. Kalorimetrische Untersuchung fliissiger In- dium-Antimon-Legierungen unter dem Aspekt eines Assozia- tions-gleichgewichts. 2. Metallkde 1976, 67, 826.

Prigogine, I.; Defay, R. Chemical Thermodynamics; Longmans, Green: London, 1954.

Scatchard, G. Equilibria in Non-Electrolyte Solutions in Relation to the Vapor Pressures and Densities of the Components. Chem. Rev. 1931, 8, 321.

Shimoji, M. Liquid Metals; Academic Press: New York, 1978. Sommer, F. Association Model for the Description of the Thermo-

dynamic Functions of Liquid Alloys. I: Basic Concepts. 2. Me- tallkde 1982a, 73, 72.

Sommer, F. Association Model for the Description of the Thermo- dynamic Functions of Liquid Alloys. 11: Numerical Treatment and Results. Z. Metallkde 198219, 73, 77.

Sommer, F. Homogenous Equilibria in Liquid Alloys and Glasses. Ber. Bunsen-Ges. Phys. Chem. 1983,87, 749.

Steeb, S.; Entress, H. Atomverteilung sowie spezifischer elekrischer Widerstand geschmolzener Magnesium-Zinn-Legierunger. 2 . Metallkde. 1966, 57, 803.

Steeb, S.; Hezel, R. Rontgenographische Strukuruntersuchungen an schmelzflussigen Silber-Magnesium-Legierungen. 2. Metallkde. 1966, 57, 374.

Stoicos, T. A Chemical-Physical Model for the Thermodynamics of Binary Metallic Solutions. M.S. Thesis, University of Illinois, 1980.

Taylor, J. W. The Surface Tensions of Liquid-Metal Solutions. Acta Metall. 1956, 4 , 460.

Thomas, A. G.; Huffadine, J. B.; Moore, N. C. Preparation Properties and Applications of Metal/Ceramic Mixtures. Met. Rev. 1963,8, 461.

Vinson, J. R.; Chou, T. Composite Materials and Their Uses in Structures; Wiley: New York, 1975.

Williams, J. C.; Nielsen, J. W. Wetting of Original and Metallized High-Alumina Surface by Molten Brazing Solders. J . Am. Ceram. SOC. 1959, 42, 229.

Wilson, J. R. The Structure of Liquid Metals and Alloys. Met. Rev. 1965, I O , 381.

Received for review October 30, 1990 Accepted November 9, 1990

Prediction of Solute Partition Coefficients between Polyolefins and Alcohols Using the Regular Solution Theory and Group Contribution Methods

Albert L. Baner and Otto 0. Piringer* Fraunhofer Insti tute for Food Technology and Packaging, Munich, Federal Republic of Germany

The regular solution theory using group contribution solubility parameter estimation methods was applied to the estimation of partition coefficients of solutes between polyolefii polymers and alcohol solvents. Quantitative prediction was improved by using only the Hansen dispersive type solubility parameters and adding an empirical correction term to account for polar type interactions between the solute and the solvent and polymer phases. The method fails to fully account for multiple functional groups and stearic hindrances. The correction term is a function of the solute’s functional groups, the solute molecular weight, and the solvent and polymer phases. The group contribution methods of Hoy and of Van Krevelen and Hoftyzer gave equivalent results.

Introduction The prediction of solute partition coefficients between

polymers and liquids is important in a number of applied fields such as protective clothing (Mansdorf et al., 1988), biomedical studies (Dunn et al., 1986), chromatography (Barton, 1983), chemical separations (Lee et al., 1989) and,

0888-5885191 1 2630-1506$02.50/0

of major interest for this study, packaging (Hotchkiss, 1988). Solubility coefficients are important in package design and food shelf-life prediction because they are used in modeling the migration of substances from the packaging into the food and from the food into the package (Vom Bruck et al., 1986; Reid et al., 1980; Chatwin and

0 1991 American Chemical Society

Ind. Eng. Chem. Res., Vol. 30, No. 7,1991 1507

and its sound theoretical basis, the accuracy of the regular solution theory should be tested on experimental data.

Polyolefin polymers (mostly low-density polyethylene, LDPE) are the most widely used polymers for food packaging due to their low cost and useful physical and mechanical properties. With their importance and simple chemical structure, the development of any partition model should start with the polyolefins. Foods have complex compositions and are difficult to work with; because of this is it often necessary to use food-simulating solvents. Al- cohols, particularly methanol and ethanol, are good simulants for the migration of substances between polyolefins and fatty type foods (Piringer, 1990, Schwartz, 1988). The alcohols do not swell the polyolefins, flavors and polymer additives are readily soluble in them, and they have clear analytical advantages over oil food simulants. The purpose of this paper is to test the effectiveness of the regular solution theory for estimating partition coefficients of solutes between polyolefin polymers and alcohol food simulants.

Katan, 1989). These migrations can affect the safety and quality of the packaged product as well as the mechanical properties of the package. Although a great amount of research studying the partitioning of aromas between foods and their polymeric packaging exists (Becker et al., 1983; Kwapong and Hotchkiss, 1987; Ikegami, 1987; DeLassus et al., 1988; Koszinowski and Piringer, 19891, very little work has been done on estimating these partition coefficients.

The estimation of partition coefficients of substances between foods and polymeric packaging is a complex problem. Foods can contain both solid and liquid phases containing a variety of macro- and microconstituents with varying polarities and chemical properties. The macro- constituent properties can range from very polar hydrogen-bonded systems, e.g., water and acids, to very nonpolar systems, e.g., oils and fats. The microconstituents of foods, such as flavor and aroma constituents, with concentration ranges of approximately 0.001-200 ppm (w/v) include all possible chemical compounds but mainly unsaturated and oxygenated compounds. Commonly used food packaging polymers can be semicrystalline (e.g., polyethylene), be oriented (e.g., polypropylene), have surface treatments (e.g., fluorination, sulfonization, metallization), contain various additives (e.g., plasticizers and antioxidants) and have a range of polarities (e.g., nonpolar, polyethylene, to polar, ethylenevinyl alcohol).

There are several methods in the literature that can be used for estimating partition coefficients between liquids. Reid et al. (1987) presents methods for estimating activity coefficients from which partition coefficients can be calculated. There are numerous examples of correlations developed for estimating partition coefficients (Bao et al., 1988; Kamlet et al., 1988; and Kasai et al., 1988). Com- puter modeling (Jorgensen et al., 1990) is rapidly devel- oping as a means of predicting partition coefficients directly from molecular structure. However, computer modeling is not yet ready for general application, and its use is dependent on the availability of mainframe com- puters and software. Of the methods presented in Reid et al. (1987) many are not applicable to this problem because they cannot be applied to polymer systems. Many also require experimental data that are not available for many aromas or they cannot be used with the wide variety of chemical substances found in aromas. Group contribution methods overcome the problem of estimating model parameters by assigning contributions to each of the functional groups making up the polymer, aroma, and solvent phases. The sum of these group contributions give an estimate of the parameter. Van Krevelen and Hoftyzer (1976) and Barton (1983) have reviewed the regular solution theory group contribution method applied to activity coefficient estimation in polymers. Goydan et al. (1989) have reviewed the use of three other group contribution methods that can be used for estimating solute activity coefficients in polymers. Recently Chen et al. (1990) have developed a group contribution equation-of-state method for estimating solute activity coefficients in mixtures containing polymers.

The regular solution theory is by far the simplest of the estimation methods to apply. However, the regular solution theory is not necessarily the most accurate and is applicable in theory only to regular solutions. In fact, Barton (1983) in his extensive review says that one should not expect that partition coefficients can be predicted in detail by solubility parameters, particularly for polar molecules. However, considering the large amount of literature devoted to the use of the solubility parameter

Regular Solution Theory Review The regular solution theory is by far one of the oldest

methods that can use group contribution methods which can be applied to polymers. The theory and its usefulness have been reviewed by Van Krevelen and Hoftyzer (1976), Barton (1983), and Rider (1985). The method has been achieved its widest acceptance in the paint and coatings industry, where it is used as a means of predicting the tendency of polymers to dissolve in solvents (Rider, 1985). Very few direct applications of the regular solution theory for the prediction of partition coefficients have been found in the literature (Barton, 1983). Most applications require modification of the regular solution theory using empirical terms, and there are many more examples of correlations using only solubility parameters (Barton, 1983).

The regular solution theory expression for predicting activity coefficients (y) in a binary mixture of solute 1 in solvent 2 is given by eq 1 (Hildebrand et al., 19701, where

(1)

Vl is the liquid molar volume of the pure liquid component at temperature T, R is the gas constant, and the volume fraction, iPz, is defined as

@ 2 = xzVz/(x1V1 + XZVZ) (2)

where x1 and x 2 are the molar fractions of components. The solubility parameter for component i ( S i ) is defined as

(3)

Where cii is the cohesive energy density of the pure liquid i and Vi is the molar internal energy, which is defined as the energy required isothermally to evaporate liquid i from a saturated liquid to the ideal gas phase (Reid et al., 1987). The internal energy at temperatures well below critical can be approximated by

(4)

where AHvi is the molar enthalpy of vaporization of pure liquid i at temperature T.

The solubility parameter defined in this manner is often referred to as the “Hildebrand” solubility parameter after its originator. Equation 1 is a result of the geometric mean assumption in eq 5, which implies that activity coefficients

y1 = ~ ~ P P / R T [ V ~ @ ~ ~ ( S ~ - 62)211

S i = C i i 1 / 2 = (V i / Vi)’/2

Vi == AH,,, - RT

c12 = (c11c22)1’2 (5 )

1508 Ind. Eng. Chem. Res., Vol. 30, No. 7,1991

can be predicted by using only pure component data and properties.

The importance of the geometric mean assumption is that it assumes that the interactions between different molecules in a mixture are similar to those the molecule experience between themselves in the pure substance. This assumption has been shown to be true for solutions of nonpolar molecules of similar sizes where only London or dispersive type interactions exist (Hildebrand et al., 1970). Further assumptions of the regular solution theory are as follows: (1) The volume change on mixing is quite small. (2) The excess entropy per mole of mixture is essentially zero (meaning only similar size molecules are present in the mixture).

The regular solution theory best models mixtures of nonpolar molecules. As such it gives good prediction for aliphatic hydrocarbon mixtures but only a broad qualitative indication of behavior for mixtures containing polar molecules (Prausnitz et al., 1986). Numerous modifications have been proposed to eq 1 to allow the theory to be extended to a wider class of mixtures (Barton, 1983). Hansen proposed for polar and hydrogen-bonding compounds on a semiempirical basis that solubility parameters can be broken down into a linear combination of nonpolar or dispersive type interactions (bd), polar interactions (6 ), and hydrogen bonding interactions (ah) (Barton, 1983f:

b2 = 6d2 + 6; + 6h2 (6)

Equation 1 using Hansen type parameters becomes 71 = exPll/RT[V1@2~((hj - 62d)2 4- (61, - 6 2 ~ ) ~ +

(61h - &d2)13 (7)

Barton (1983) has also reviewed several other systems for dividing solubility parameters into other linear combinations of dispersive, induction, and Lewis acids and bases to account for intermolecular interactions that the regular solution theory does not model.

An empirical correction to the geometric mean assumption for c12 in eq 5 adds a binary interaction parameter to better reflect the intermolecular forces between molecules (Hildebrand et al., 1970). Not much success has been made in correlating this parameter for polar and hydrogen-bonding mixtures, so that evaluation of this parameter must be done experimentally (Reid et al., 1987).

For systems where there are large size difference effects between molecules, the Flory-Huggins equation has achieved success in predicting phase equilibrium (Reid et al., 1987). The Flory-Huggins theory was developed for polymer solutions where the polymer structure is sub- stantially altered due to dissolution of the polymer in a solvent and does not apply to systems such as this case where the polymer is not solved in a solvent. More com- plete discussions of this theory can be found in Flory (1953), Flory (1970), and Prausnitz et al. (1986).

Calculations Derivation of Partition Coefficient Equations. At

equilibrium the fugacity (f) of the solute (i) above the polymer (P) and the liquid (L) phases is given by

fiP = fiL (8) Where the fugacity is defined for the polymer and liquid phases respectively as

fiP = yipxipfi" (9)

fiL = YiLXiLfi0 (10)

where fi" is the fugacity of the pure liquid solute. Com-

bining eqs 9 and 10 with 8 gives

yiPriP = 7iLxiL (11)

For dilute concentrations of solute in the polymer and liquid phases the mole fraction can be approximated by the following equations:

X? ss cTVp/M,j (12)

X? ci'VL/M,,, (13)

where Mm,i is the molar mass (g/mol), VL is the molar volume of the liquid, and Vp is the molar volume of one polymer repeat unit by convention (Van Krevelen and Hoftyzer, 1976). Combining eqs 12 and 13 with eq 11 gives

c ~ / c ? = (YPVL) / (7iPVp) (14)

The equilibrium partition coefficient (Kp 3 can be defined as the ratio of the concentration (w/v) o# the solute in the polymer (c?) to the concentration (w/v) of the solute in the liquid (c?). Combining this definition with eq 1 gives the equation for calculating the partition coefficients:

KpIL = C ? / C ~ = VL/Vp exp(Vi/RT[@L2(bi - bLI2 - 9p2(Si - 6p)2]) (15)

Using Hansen type solubility parameters (eq 7), the equation for the partition coefficient becomes

KpIL = V ~ / v p exp(Vi/RT[@L2((8di - a d 2 -k ( b p i - ~ P L ) ~ + (6E - 8,)') - @p2((bdi - bdp)' -

( b p i - 6pp)' - (hi - 6 ~ ) ~ ) 1 1 (16)

Estimation of Solubility Parameters by Group Contribution Methods. The group contribution methods for estimating the values of solubility parameters a t 25 "C from Hoy (1985), Van Krevelen and Hoftyzer (19761, and Fedors (1974a,b) were used. The estimation methods of Hoy and of Van Krevelen and Hoftyzer can be used to estimate Hansen type solubility parameters, whereas the method of Fedors cannot. The polymer solubility parameter is calculated for the repeat unit of the polymer in all three methods. The polymer solubility coefficient can be calculated in theory only for amorphous polymers. There is no method for estimating the solubility parameters for semicrystalline polymers (Van Krevelen and Hoftyzer, 1976). For calculations using Hoy's method all alcohols were treated as individual molecules and the primary OH group contribution parameter was used. Table I gives examples of the solubility parameters used in these calculations. All three group contribution methods give approximately the same solubility parameter values.

When solubility parameters are calculated by using the group contribution methods, molar volumes are needed. Molar volumes at 25 "C can be calculated by dividing the molecular weight of the compound by ita density at 25 "C. For polymers, preliminary calculations showed the experimental density of the polymer bulk phase should be used rather than the amorphous density as called for by a strict interpretation of the regular solution theory. Where no experimental molar volume data or density data at 25 "C exist for a substance, the molar volumes can be estimated by using the molar volume group contribution method of Fedors (1974a,b), Although the accuracy of Fedors is sometimes rather poor, it does give a first approximation of a substance's molar volume (Van Krevelen and Hoftymr, 1976). In an effort to improve the prediction of Fedors' method the average molar contribution value of 16.45 cmg/mol for the CH2 group was used based on the

Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991 1509

Table 1. Solubility Parameters (J1la/cmala) at 25 "C"

Fedors HOY Van Krevelen and Hoftyzer compound V, cmg/mol d P h t d P h t t

polymer LDPE HDPE HPP COPP

solvent methanol ethanol acetone hexane

solutes n-alkanes

c12 C14 C16 C18 c20 c22

d-limonene diphenylmethane linalyl acetate camphor diphenyl oxide isoamyl acetate eugenol menthol phenylethyl alcohol cis-hexenol

polar

30.60 29.39 46.78 46.67

40.73 58.69 74.05

131.6

228.6 261.7 294.1 326.0 359.6 392.4

162.4 168.1 219.3 153.3 159.0 150.4 154.0 173.6 120.4 119.0

18.3 19.1 16.7 16.7

12.3 12.8 12.9 14.9

15.6 15.7 15.8 15.9 15.9 16.0

15.3 16.5 14.8 15.5 16.4 14.5 14.9 14.7 15.8 14.5

0 0 0 0

13.2 11.4 9.89 0

0 0 0 0 0 0

5.59

7.64 8.65

7.36

7.81

7.81

10.0

11.7

11.4

13.2

0 0 0 0

24.9 19.4 10.2 0

0 0 0 0 0 0

2.08 0.10 2.08 6.93 1.39 5.07

9.51

6.51

11.4

15.8

18.3 19.1 16.7 16.7

30.8 25.9 19.2 14.9

15.6 15.7 15.8 15.9 15.9 16.0

16.5 19.3 16.8 19.1 20.2 17.1 21.9 19.1 25.9 17.7

17.6 18.4 16.5 16.5

15.5 15.3 15.3 14.6

15.5 15.6 15.7 15.8 15.9 15.9

16.4 18.6 15.6 17.5 18.6 15.1 16.9 16.1 15.5 15.5

0 0 0 0

12.3 8.52

10.4 0

0 0 0 0 0 0

0 1.30 2.23 5.02 3.90 3.26 6.56 2.88 5.07 4.22

0 0 0 0

22.2 18.5 5.22 0

0 0 0 0 0 0

0 0 5.65 3.61 4.34 6.82 3.87

10.7 12.9 13.0

17.6 18.4 16.5 16.5

29.7 25.4 19.2 14.6

15.5 15.6 15.7 15.8 15.9 15.9

16.4 18.7 16.7 18.6 19.5 16.9 18.5 19.5 20.8 20.7

18.0 18.3 16.7 16.7

29.1 25.9 19.0 14.6

16.0 16.2 16.3 16.5 16.5 16.6

16.3 20.2 17.3 19.1 20.6 17.4 22.1 19.4 24.4 22.1

a Hoy (1985), Van Krevelen and Hoftyzer (1976), and Fedors (1974a,b) solubility parameter group contribution methods. d, Hansen dispersive solubility parameter. p , Hansen polar solubility parameter. h, Hansen hydrogen bonding solubility parameter. t , Hildebrand solubility parameter. V , molar volume at 25 "C. LDPE, low-density polyethylene, density = 0.918. HDPE, high-density polyethylene, density = 0.956. HPP, homopolymer polpropylene, density = 0.902. COPP, copolymer polypropylene, density = 0.900.

recommendation of Van Krevelen and Hoftyzer (1976). Experimentally measured molar volumes for polymers

can be found in Van Krevelen and Hoftyzer (1976). Densities and molar volumes for pure liquids can be found in Weast (19901, Windholz (19831, Synowietz (1983), and Arctander (1969). For substances that are normally solid a t 25 OC the method of Fedors was used to estimate their liquid molar volume.

Calculation of Equilibrium Partition Coefficients of Solutes between Polymer and Liquid Phases. The regular solution theory is intended to be used only for predicting the behavior of liquids. The theory can be extended to amorphous polymers because amorphous polymers in the first approximation behave like liquids, However, it is not clear how best to apply the theory to semicrystalline polymers (Van Krevelen and Hoftyzer, 1976).

Comparisons between different group contribution methods for estimating solubility parameters from Fedors (1974a,b), Van Krevelen and Hoftyzer (19761, and Hoy (1985) were made. Consistent use of group contribution methods was made for estimating the solute, solvent, and polymer solubility parameters used for calculating the partition coefficient. The effectiveness of eqs 15 and 16 for predicting partition coefficients was compared. All calculations made here can be easily carried out on a hand-held calculator.

Although solubility parameters depend on temperature, the regular solution theory itself assumes that the excess entropy is zero. At constant composition the activity coefficient remains constant. This allows the activity coefficient to be calculated at any convenient temperature, which is customarily 25 "C. All calculations were carried out for 25 "C and the molar volumes are the molar volumes of the substances as liquids at 25 "C. By convention (Van

Krevelen and Hoftyzer, 1976) the molar volume for polymers is taken to be that of one repeat unit of the polymer.

Partition Coefficient Data. Experimental equilibrium partition coefficient values for solutes partition between polyolefins and alcohols were obtained from Becker et al. (1983), Koszinowski (1986a,b) and Koszinowski and Pir- inger (1989,1990). The partition coefficient measurements were carried out using a liquid measuring cell adapted from the method of Till et al. (1982). Briefly, a 35-cm3 glass vial with Teflon-coated septa cap was filled with the solute- solvent solution with an average concentration of 1 X M. Several disks of polymer film (4.45 cm2) were cut and mounted on a glass rod separated by glass beads and placed in the vial. The vials were kept in a temperature-controlled roller shaker. The concentration of the solute in the solvent was monitored over time by using gas chromatography until no change in solvent concentration with time was observed (Le., equilibrium was reached). The polymer disks were then removed from the vial and quickly washed with pure solvent phase (e.g., ethanol) to remove any absorbed solute on the surface of the polymer. The concentration of the solute sorbed in the film was measured by extracting the film twice with a large volume of hexane relative to the volume of film to ensure that all solute is extracted. The concentration of solute in hexane was measured by gas chromatography. Experiments were also made to ensure that equilibrium was reached in the polymer phase during the experiment where the concentration of solute was measured as a function of time in the polymer phase.

Interaction effects between the solvents and polymers were determined by calculating the solute diffusion coefficients in the polymer by using the relationship P, = DK, where the partition coefficient ( K ) is determined by using the experiments described in the preceding paragraph and

1510 Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991

the relative permeation coefficient (P,) is determined from the permeation pouch method described in Koszinowski (1986a). The pouch method uses a sealed pouch made from polymer film that is fded with solvent and solute and placed in a jar containing pure solvent. As the solute permeates through the film into the solvent in the jar, it is measured as function of time until it reaches steady-state permeation by using gas chromatography. Calculating diffusion coefficients using this method, Becker et al. (1983) observed that the solute diffusion coeficients in the polyolefins in contact with methanol and ethanol solvents have practically the same diffusion coefficients as with water as solvent. Water has essentially no interaction with polyolefins. Solutes in acetone showed a slight increase in the diffusion coefficient, and solutes in hexane, which swells the polymer, showed an increase of 1-2 orders of magnitude in the diffusion coefficient compared to water solvent.

Results and Discussion n -Alkanes. Hildebrand's regular solution theory (eq

15) and the Hansen multicomponent solubility parameters (eqs 6 and 16) were compared against experimentally measured partition coefficients for six n-alkanes ((212422) between LDPE and ethanol from Koszinowski (1986a). Equation 15 using the Hildebrand solubility parameters was tested by using the group contribution solubility parameter estimation methods of Hoy (1985), Van Krevelen and Hoftyzer (1976), and Fedors (1974a,b). All of these three solubility parameter estimation methods seriously overpredicted these partition coefficients. On average the calculated partition coefficient values were 1 X 104-1 X lo5 times that of the experimental value.

The failure of the regular solution theory to predict the partition of n-alkanes between ethanol and LDPE using Hildebrand solubility parameters appears to be mainly due to the difference between the alcohol and alkane solubility parameters (see Table I) being too large. I t is clear that for n-alkanes only dispersive attractive forces can exist between them and the LDPE and ethanol phases. Poly- ethylene is essentially a hydrocarbon, and it is observed that the difference between it and the n-alkane's solubility parameter is quite small relative to the difference between the n-alkane and the ethanol. This coupled with the grossly overpredicted partition coefficient suggests the error lies in the magnitude of the liquid solubility parameter term. Polar and hydrogen-bonding interactions are implicitly included in the ethanol Hildebrand solubility parameter even though these attractive force do not exist between the ethanol and the n-alkanes. The failure of the regular solution theory to model interactions between dissimilar molecules is a recognized limitation (Prausnitz et al., 1986). This failure can be largely traced to the geometric mean assumption (eq 5).

The Hansen solubility parameters offer a way of sepa- rating dispersive interaction forces from polar and hydrogen-bonding type interactions containing in the alcohol Hildebrand solubility parameters. With the dispersive Hansen solubility parameters (see eq 6) from Hoy and Van Krevelen and Hoftyzer, the partition coefficient can be predicted to within an order of magnitude as shown in Figure 1. However, the regular solution theory coupled with the dispersive solubility parameters does not predict the increase in the partition coefficient with increasing carbon number of the experimental data well. In Table I the calculated solubility parameters are relatively constant as the n-alkanes become larger, which cannot be true since the experimental partition coefficients show an increase with chain length. An empirical correction factor

1

c

n c I k l

-1 I 1 1 I I I I I I

160 180 200 220 240 260 280 300 320

molecular weight Figure 1. Linear regression curves of experimental and calculated partition coefficienta of n-alkanes partitioned between LDPE and ethanol as a function of n-alkane molecular weight at 25 O C : (0) Koszinowski (1986a); (A) Hoy (1985) solubility parameters; (m) Van Krevelen and Hoftyzer (1976) solubility parameters.

.- -2500 I-

Q) -3000 I , I I I 1 I I

160 180 200 220 240 260 280 300 320

molecular weight Figure 2. Linear regression curve of empirical correction (a) versua the molecular weight of n-alkanes partitioned between LDPE and ethanol. a back-calculated by using eq 17, Hoy (1985) solubility parameters, and experimental data from Koszinowski (1986a).

(a) with the units J/mol can be back-calculated by using the experimental partition coefficient and solubility parameters.

In Figure 2 the empirical correction factor varies linearly with molecular weight. Equation 16 for these calculations then becomes KPIL =

where a = b + cMi, with Mi the solute molecular weight (relative molar mass), b the y intercept (J/mol), and c the slope (J/mol). The linear relationship of the empirical factor with molecular weight comes from the experimentally observed linear relationship between the log of the activity coefficient with carbon number for a homologous series of hydrocarbons which is directly proportional to molecular weight (Pierotti e t al., 1959; Herington, 1967). The a is a result of the solute behavior in the polymer and solvent phases. It can be thought of as a sum of the empirical corrections for the solute-solvent (UL) and the solute-polymer (ap) interactions:

a = UL + u p (18) It is clear from the preceding diecuseion that for n-alkanea

Ind. Eng. Chem. Res., Vol. 30, No. 7,1991 1511

- - ’Ooo I--

> 5000 -

g 1000 c * . v 0 - 0 A .....---A 2 -1000 r-

b -2000 +

- -3000 - ..-__...--.--A-

.- I - -4----J

; 6000 +

w 4000 - 7 3000 L

2000 - /* * I W

.- +

0 __.---- e ~&~/.---.- __.---- ___.--- __- - ....-- A

-4000 r .L -5000 r g -6000 .!---c---~-

@ -7000 I I I , I 1 I

160 180 200 220 240 260 280 300 320

molecular weight Figure 3. Linear regression curves of empirical correction (a) versus molecular weight of n-alkanes partitioned between LDPE and various solvents. a back-calculated by using eq 17, Hoy (1985) solubility parameters and experimental data from Koszinowaki (1986a): ( 6 ) methanol solvent; (0) ethanol solvent; (A) acetone solvent; (m) hexane solvent.

partitioned between ethanol and LDPE up must be small in comparison to the aL term. The n-alkane-polymer activity coefficient is likely to be significantly less than 1. Alessi et al. (1982a) measured infinite dilution activity coefficients for n-alkanes in n-alkane solvents that were less than 1. They also found that the larger the difference in molecular weight of the alkanes, the smaller the activity coefficient. The activity coefficients calculated here where n-alkanes are solved in LDPE (which is made up of very long hydrocarbon chains) are likely to be much less than 1. Another of the recognized deficiencies of the regular solution theory is ita inability to predict activity Coefficients less than 1. Calculated activity coefficients for n-alkanes in LDPE range from 1.9 for C12 to 2.4 for C22 by using the Hoy solubility parameters. Therefore, an empirical correction to the regular solution theory for n-alkanes in polymers (ap) must be negative and increase with molecular weight.

In comparison to the activity coefficients for n-alkanes in LDPE, the activity coefficients for n-alkanes in ethanol are greater than 1 and also increase with molecular weight. Data from Cori and Delogu (1986) shows that the activity coefficients of n-alkanes in ethanol increase with molecular weight. The regular solution correctly predicts this behavior with activity coefficients of 2.1 for C12 and 4.8 for C22 using Hoy’s dispersive solubility parameters. How- ever, the size of the regular solution theory activity coefficients are too small compared to the observations of Pierotti et al. (1959). As a result of these observations the empirical solute-solvent correction factor (aL) must be positive and increase with molecular weight.

Figure 3 shows the empirical correction for n-alkanes to be a function of the solvent phase while keeping the polymer phase (LDPE) constant. The y intercept decreases with the polarity of the solvent, and the slopes of the curves remain relatively constant as function of molecular weight. The decreasing empirical correction comes from the decreasing polarity of the solvent. The less polar the solvent (e.g., methanol > ethanol > acetone > hexane) the better the regular solution theory predicts the liquid activity Coefficient. However, this a t the same time worsens the underprediction effect from the solute- polymer activity coefficient. The qualitative prediction by the regular solution theory of the decrease in solute- solvent activity coefficient with the decrease in solvent polarity is illustrated for C20 with 7.0,4.0, 3.7, and 1.2 by

z- 7000 r--- E 6000 1 ‘1.

*

7- _ _ L _ _ _ _ _ _ _ _ . . . ..-A I

L 0 - .-

? 0, -1000 -1--

160 180 200 220 240 260 280 300

molecular weight Figure 4. Linear regression curves of empirical correction (a) versus molecular weight of n-alkanes partitioned between methanol solvent and various polyolefm. a back-calculated by using eq 17, Hoy (1985) solubility parameters, and experimental data from Koszinowaki (1986a): ( 6 ) LDPE (0) HDPE (A) homopolymer polypropylene (HPP); (B) copolymer polypropylene.

using Hoy’s solubility parameters for methanol, ethanol, acetone, and hexane solvents, respectively. The deviation of the slope for hexane from the other solutes shown in Figure 3 is explained by the hexane solvent swelling the LDPE. Interactions between the polymer and solvent phase violate the assumption made here of no interaction between the two phases.

The empirical correction factor in addition to varying with solute molecular weight and solvent also varies with the polymer phase. Figure 4 shows the variation of empirical correction terms for n-alkanes partitioned between methanol and polypropylene (PP) and high- and low- density polyethylene (HDPE and LDPE) polymers.

Polar Solutes. Equation 15 using the Hildebrand solubility parameters and eq 16 using the Hansen solubility parameters were applied to the prediction of partition coefficients for polar solutes partitioned between methanol and polymers with different polarities. As could be predicted from the previous discussions, both equations re- gardless of the group contributions used grossly overpredict and show no qualitative prediction of the partition coefficient. This failure is largely due to the regular solution theory not being applicable to polar substances. Prediction with eq 16 was better without difference terms where one of the solubility coefficients was 0. Better qualitative and quantitative predictions, to within 2 orders of magnitude, for these polar solutes are obtained by using only the dispersive Hansen solubility parameter for the solute, solvent, and polymer.

With the data of Koszinowski and Piringer (1990) empirical correction factors were back-calculated by using the experimental partition coefficient, the Hansen dispersive solubility parameters, and eq 17. As seen in Figure 5, which is similar to that for the n-alkanes, the n-aldehyde’s homologous series has a good linear correlation between the empirical correction and the number of saturated carbon atoms. The slope of the correlation is again positive and similar in magnitude to that of the n-alkanes. The y intercept is significantly smaller than that of the h e a . The positive slope means the functional group’s effect is diminished, and the molecule’s behavior becomes more like that of a hydrocarbon as the number of saturated carbon atoms increases.

The negative y intercept indicates the regular solution overpredicts the partition coefficient for the n-aldehydes. This is mainly due to the activity coefficient of the aldehyde in the LDPE being too small. Experimental ob-


4000

E 2000 k

-5000 1 0 j

- - E -6000 :

d - d

-7000

-8000 0

0 5 -9000 2 c

- -

-

- L 0 0 -lEo4 t A

- 0 -1.lE04 0 L

*- -1.2E04 .- P

A

0 1

t Q) -1.3E04I I I I 1 I

120 140 160 180 200 220

molecular we igh t Figure 5. Linear regression curve of empirical correction (a) versus molecular weight of n-aldehydes partitioned between methanol solvent and LDPE. a back-calculated by using eq 17, Hoy (1985) solubility parameters, and experimental data from Koazinowski and Piringer (1990): (0) n-aldehydes; (A) aldehydes with one double bond; (A) aldehyde with two double bonds; (0) phenyl aldehydes.

servations by Alessi et al. (1982b) show polar solutes in long-chain hydrocarbons can have large activity coefficients, and the more polar the solute the larger the activity coefficient. The activity Coefficients for CS and C12 aldehydes in LDPE from the regular solution theory are 2.4 and 3.0, respectively, using Hoy’s solubility parameters, whereas the activity coefficients for C8 and C12 aldehydes in methanol are 1.4 and 1.8, respectively. The experimental aldehyde-methanol activity coefficients from Pierotti et al. (1959) are 10.4 and 45.6 for CS and C12, respectively. Remembering that the partition coefficient is essentially a ratio of the solute-liquid activity coefficient to the solute-polymer activity coefficient leads to the conclusion that the aldehyde activity coefficients in the LDPE must be grossly underpredicted. The LDPE solubility coefficient and molar volume must not be very well estimated by using only the repeat unit of the polymer.

In Figure 5 the empirical correction fador for aldehydes with different degrees of unsaturation and those containing phenyl groups are shown in comparison to the n-aldehyde homologous series. Relative to the homologous series for solutes with the same molecular weight the presence of one double bond (A) shifts the empirical correction by roughly -1600 J/mol, and the presence of two double bonds (A) shifts the empirical correction by about -3600 J/mol. The presence of a phenyl group (0) lowers the empirical correction by an average of -3500 J/mol with respect to the n-aldehydes. The scatter of the empirical correction for these aldehydes is due in part to structural effects, the group contribution parameters, and experimental error. From this example it can be seen that the empirical correction can be thought of as roughly the sum of contributions of individual functional groups.

Figure 6 shows linear regression empirical correction curves for solute partition coefficients between LDPE and methanol versus the solute molecular weight for solutes with different functional groups and well-defined structures using the Hoy solubility parameters. The group contribution method of Van Krevelen and Hoftyzer gives similar results. As the polarity of the solute functional group increases, the y intercept decreases significantly, but the slopes of all the curves remain relatively the same for all solutes. The more polar and greater ability to form hydrogen bonds the functional group has, the larger the molecular weight needed to offset the molecule’s increased polarity. The effect of increased polarity of the solute’s

d O b

0 - d 0 -2000 y

-4000 r * I’ I I

j - 1 2E04 ,-’. +

-: -1 4E04 , e -1 6E04 Q .- S @ - l . 8 E 0 4 L 1 ’ ’ ’ ’ I I ’ ‘ I

100 120 140 160 180 200 220 240 260 280 300

molecular weight

Figure 6. Linear regression curves of empirical correction (a) versus solute molecular weight of polar and nonpolar solutes partitioned between methanol solvent and LDPE. a back-calculated by using eq 17, Hoy (1985) solubility parameters, and experimental data from Koszinowski (1986b) and Koszinowski and Piringer (1990): (0) n- alkanes; (0) unsaturated hydrocarbons; (A) unsaturated aldehydes; (*) linear esters; (A) n-aldehydes; (+) phenyl esters; (e) primary alcohols; (0) phenyl alcohols; ( 0 ) phenols (ethanol solvent).

Table 11. Empirical Correction ( a ) for Solum Partitioned between LDPE and Methanol (cy Slope; ky y Intercept)?

a = b + cMi b = Ebi i

group contribution solubility parameter method

Hoy Van Krevelen and Hoftyzer solute functional c = 44 i 8.6 c = 54 12.8

group bi bi base value

functional group increments: alkene (>=<I -1300 -lo00 phenyl group -3800 -3500

etherb (R-O-R’) -4400 -5400 ester (R-COO-R’) -4700 -8Ooo ketone (R-CO-R’) -5100 -8Ooo aldehyde (R-CHO) 4900 -9600

n-alkane -7600 -7100

(Ph-R)

tertiary alcohole 4900 -11300 (CR’R”R’’’-OH)

secondary alcohol’ -8Ooo -11800 (CR’R’’-OH)

(R-OH) primary alcohol -9200 -12300

phenole -12900 -15000

acid’ (R-COOH) -13900 -15200 (R-Ph-OH)

Oa back-calculated by using eq 17 and experimental partition coefficienta from Koezinoweki and Piringer (1990). c = weighted average slope (J/mol) of regreasion lines in Figure 6. Mi = eolute molecular weight. No correlation found, estimated correction value. ‘Van Krevelen and Hoftyzer group parameters do not dis- tinguish between functional group position. * Eatimated by using average of tertiary and primary alcohol incrementa. ‘In ethanol solvent. Data from Koezinowski (1986b). ’Single data point.

functional groups increases the activity coefficient of the solute in the LDPE while decreasing the activity coefficient of the solute in the alcohol solvent. As discussed before, the regular solution theory’s underprediction of the solute-polymer activity coefficient increases with solute polarity.

The weighted average slope of the linear regression lines for the correction factor a versus solute molecular weight is approximately 44 J/mol for Hoy’s solubility parameters


Table 111. Prediction Accuracy of Solute Partition Coefficients between Methanol and LDPE' ~

K P / L

% % bred/ bred/

exp Hoy exp) V.K.H. exp) Good Predicted Solutes

diphenylmethane 0.27 0.16 59 0.32 120 isoamyl acetate 0.043 0.053 120 0.034 79 linalyl acetate 0.058 0.065 110 0.064 110 menthol 0.02 0.023 120 0.016 80 cis-3- hexenol 0.0024 0.0021 88 0.0024 100

d - 1 i m o n e n e 0.67 0.25 37 0.62 93 diphenyl oxide 0.23 0.024 10 0.036 16 camphor 0.062 0.14 230 0.11 180 eugenol 0.03 0.0007 2.3 0.0005 1.7 phenylethyl 0.0097 0.0037 38 0.0014 14

Poorly Predicted Solutes

alcohol

'pred, calculations using eq 17 and correlations from Table 11. KPI4 = polymer-liquid partition coefficient. exp, experimental partition coefficients from Becker et al. (1983). Hoy, group contribution method of Hoy (1985). V.K.H., group contribution method of Van Krevelen and Hoftyzer (1976).

and 54 J/mol for Van Krevelen and Hoftyzer's. Starting with the n-alkanes as a basis, additive increments for the correction factor's y intercept can be calculated for each functional group by using a best fit regression procedure. Table I1 gives the y intercept additive increments for the Hoy and the Van Krevelen and Hoftyzer group contribution methods. To calculate the correction factor for phenylethyl alcohol, as an example, the base group increment of the n-alkanes of -7600 is added to the increments of -3800 and -9200 for the phenyl and primary alcohol functional groups. This sum is then added to the product of the slope (44) and the solute molecular weight (122.2) to get the correction factor: a = -15 220.

The correlations for a in Table I1 are subject to the accuracy of the data base used to calculate them, the na- ture of the particular solutes used for calculating these values, and the limitations of the regular solution theory

and the group contribution methods. The values are specific for these two solubility parameter group contribution methods and the polymer-solvent combination of LDPE and methanol, which was used to make these correlations. The average molecular weight of the solutes used for calculating these correction factors ranged from 100 to 300. Extrapolations outside these molecular weights must be made with caution. It is stressed that the correlations for a given in Table I1 are only approximate and subject to further verification. These correlations do not fully take into account structural differences such as ring structures and hindrances and bonding effects such as conjugation. The correlations for ethers, secondary alcohols, and acids are estimated values due to the lack of data to make correlations with. The ethers' increments are estimated to be between the values of the phenyl and ester increments and the secondary alcohol to have an increment value between the tertiary and primary alcohol increment values. The acid correlation was made with only one ob- servation. No correlations could be made for nitrogen- containing compounds, but their increments are likely to fall in the range of the alcohol increments.

Table I11 compares calculated with experimental partition coefficients for 10 solutes partitioned between LDPE and ethanol and methanol solvents that were not used in the empirical correction data base. The solutes with good predicted partition coefficients are in general linear molecules and have well-defined structures with no functional group stearic hinderances (e.g., cis-3-hexenol and isoamyl acetate). The linear molecules better preserve the assumptions of the additivity of correction increments here and in the group contribution methods. The poorly predicted solutes are more complex structures often with multiple functional groups. Solutes with poor predictions have ring-containing molecular structures such as d-limonene and camphor (bicyclic) and have two functional groups (eugenol, with phenolic OH and an ether group) or have a stearic hindrance of the functional group (diphenyl oxide, with two phenyl groups hindering the ether group). Predictions are further complicated for menthol and camphor because these substances are crystals a t 25

Table IV. Method Prediction for Solute Partition Coefficients between Alcohols and Polyolefins4 K P I L

LDPE HDPE HPP COPP exp pred exp pred exp pred exp pred

Between Polyolefins and Methanol diphenylmethane 0.27 0.16 0.27 0.13 0.33 0.13 0.34 0.13 isoamyl acetate 0.043 0.053 0.043 0.038 0.11 0.063 0.12 0.063

menthol 0.02 0.023 0.014 0.015 0.018 0.029 0.019 0.028 cis-3-hexenol 0.0024 0.0021 0.003 0.0016 0.0037 0.0025 0.005 0.0034 d-limonene 0.67 0.25 0.74 0.19 1.0 0.26 1.1 0.26

camphor 0.062 0.14 0.07 0.11 0.12 0.14 0.13 0.14 eugenol 0.03 0.0007 0.02 0.0005 0.015 0.0007 0.016 0.0007 phenylethyl alcohol 0.0097 0.0037 0.007 0.0030 0.0074 0.0032 0.009 0.0032

Between Polyolefiie and Ethanol diphenylmethane 0.25 0.17 0.24 0.14 0.20 0.31 isoamyl acetate 0.046 0.053 0.046 0.048 0.10 0.079 linalyl acetate 0.065 0.074 0.067 0.046 0.066 0.11 menthol 0.0087 0.027 0.019 0.019 0.018 0.035 cis-3-hexenol 0.0024 0.0029 0.014 0.0021 0.0062 0.0034 d-limonene 0.42 0.30 0.36 0.22 0.45 0.31

camphor 0.064 0.16 0.057 0.13 0.042 0.16 eugenol 0.013 0.008 0.024 0.0006 0.020 0.0007 phenylethyl alcohol 0.0024 0.0029 0.012 0.0036 0.0087 0.0038

linalyl acetate 0.058 0.065 0.059 0.040 0.055 0.092 0.06 0.091

diphenyl oxide 0.23 0.024 0.23 0.020 0.27 0.02 0.29 0.020

diphenyl oxide 0.14 0.027 0.16 0.022 0.22 0.022

Oprod, predictionr wing Hoy'e group contribution solubility parameters, eq 17, and correction factor from Table 11. Kp L, polymer-liquid partition coefficient. exp, experimental partition coefficients from Becker et al. (1983) and Koezinoweki and Piringer (1989).


"C, which requires that their liquid molar volumes be estimated by using a molar volume group contribution method. The predictive abilities of the group contribution methods of Hoy and Van Krevelen-Hoftyzer are approximately the same.

As a first approximation, the empirical corrections in Table I1 can be used for solutes partitioned between other polyolefins and methanol or ethanol solvents. This can be done because the differences between partition coefficients for solutes in different polyolefins do not vary greatly from one to another and are within the uncertainty of this method. Table IV shows the partition coefficient results for 10 solutes partitioned between methanol and ethanol solvents and various polyolefins. For example, the experimental partition coefficients for diphenylmethane in methanol are 0.27,0.27,0.33, and 0.34 for a low-density polyethylene (LDPE), a high-density polyethylene (HDPE), a polypropylene homopolymer (HPP), and a polypropylene copolymer (COPP), respectively (Becker et al., 1984). Predicted partition coefficients using the Hoy group contribution method gave results of 0.16,0.13,0.13, and 0.13, which corresponds to 59.3%, 48.1%,39.4%, and 38.2% of the experimental value for LDPE, HDPE, HPP, and COPP, respectively. Although the predictions become worse the further the system is from the LDPE-methanol system, eq 17 with the correction increments in Table I1 still gives predictions within an order of magnitude for most substances. The worst predicted substances in Table IV are 3.8 times too large for camphor partitioned in HPP-ethanol and 40 times too small for eugenol partitioned in COPP-ethanol. Even though these are seemingly large errors, it should be pointed out that these partition coefficient predictions are being made for a partition coefficient range spanning 3 orders of magnitude: from approximately 0.001 to 1.0.

This empirical correction method using the regular solution theory and group contribution methods could be extended to include solutes partitioning between other polymer-solvent combinations. An ultimate goal of any partition coefficient prediction method for predicting the partitioning of solutes between package and food is to extend the method to aqueous solvents. The regular solution theory is in principle limited to solutions of organic molecules, but it should be possible to extend this method to aqueous solvents by using this empirical correction. In light of the large amount of data required to generate accurate correlations and the need to account for all possible structural shapes and stearic hindrances, the method will be practically restricted to using general es- timates of the empirical correction factors made by using limited amounts of data. As it stands the method is at best a first approximation method. Further investigations using prediction methods better suited to predictions for polar molecules and different molecule shapes such as UNIFAC (Goydan et al., 1989) and modified equations of state (Chen et al., 1990) are recommended.

Conclusions As could be expected, the application of the regular

solution theory to nonregular solutions in its originally proposed form and with the modifications proposed by Hansen gave large errors for partition coefficient predictions for solutes partitioned between polyolefins and alcohols.

To improve the partition coefficient predictions to these nonregular solutions an empirical correction term can be applied. This empirical term is a function of the solute functional groups, the solute's molecular weight, and the polymer and solvent phases.

The solubility parameter group contribution methods of Hoy (1985) and Van Krevelen and Hoftyzer (1976) give comparable partition coefficient prediction results and accuracies. In favor of using a simpler calculation method, the group contribution method of Van Krevelen and Hoftyzer is preferred.

The partition coefficient estimation method described here represents a first approximation method. The method does not fully account for structural effects present in solute, polymer, and solvent phases. The method can in principle be applied to all other polymer-solvent systems, but its further development is limited by the availability of good data bases for the correction factors. Other predictive methods more applicable to nonregular solutions should be investigated to obtain more accurate partition coefficient predictions.

Acknowledgment We thank the Deutsche Bundesministerium fur

Ern&ung, Landwirtschaft und Forsten for their support. Additionally, A.L.B. thanks the Center for Food and Pharmaceutical Packaging Research at Michigan State University for their support.

Registry No. PE, 9002-88-4; PP, 9003-07-0; MeOH, 67-56-1; PhMePh, 101-81-5; EtOH, 64-17-5; Ph(CHJ,OH, 60-12-8; isoamyl acetate, 123-92-2; linalyl acetate, 115-95-7; menthol, 89-78-1; cis-3-hexenol, 928-96-1; d-limonene, 5989-27-5; diphenyl oxide, 101-84-8; camphor, 76-22-2; eugenol, 97-53-0.

Literature Cited Alessi, P.; Kikic, I.; Alessandrini, A.; Fermeglia, M. Activity Coeffi-

cients at Infinite Dilution by Gas-Liquid Chromatography. 1. Hydrocarbons and n-Chloroparaffins in Organic Solvents. J . Chem. Eng. Data. 1982a, 27,445-448.

Alessi, P.; Kikic, I.; Nonino, C.; Visalgerghi, M. 0. M. Activity Coefficients at Infinite Dilution by Gas-Liquid Chromatography. 2. Polar Compounds in Organic Solvents. J. Chem. Eng. Data.

Arctander, S. Perfume and Flavor Chemicals; Steffen Arctander: Elizabeth, NJ, 1969; Vol. I, 11.

Bao, Y. T.; Samuel, K. P.; Pitt, C. G. The Prediction of Drug Solu- bilities in Polymers. J . Polym. Sci., Part C: Polym. Let t . 1988, 26,41-46.

Barton, A. F. M. CRC Handbook of Solubility Parameters and Other Cohesion Parameters; CRC Press: Boca Raton, FL, 1983.

Becker, K.; Koszinowski, J.; Piringer, 0. Permeation von Reich-und Aromastoffen durch Polyolefine. Dtsch. Lebensm.-Rundsch. 1983, 79(8), 257-266.

Chatwin, P. C.; Katan, L. L. The Role Of Mathematics In Diffusion. Packag. Technol. Sci. 1989,2, 75-84.

Chen, F.; Fredenslund, A.; Rasmussen, P. Group-Contribution Flory Equation of State for Vapor-Liquid Equilibria in Mixtures with Polymers. Ind. Eng. Chem. Res. 1990,29,875-882.

Cori, L.; Delogu, P. Infinite Dilution Activity Coefficients of Etha- nol-n-Alkanes Mixtures. Fluid Phase Equilib. 1986,27,103-118.

DeLassus, P. T.; Tou, J. C.; Babinec, M. A.; Rulf, D. C.; Karp, B. K.; Howell, B. A. Transport of Apple Aromas in Polymer Films. In: Food and Packaginz Interactions; Hotchkiss, J., Ed.; Washington,

1982b, 27,448-450.

DC, 1988; Chapter-2. Dunn. W. J.. Block, J. H., Pearlman, R. S., Eds. Partition Coeffi-

cient: Determination and Estimation; Pergamon Press: New York, 1986.

Fedors, R. F. A Method for Estimating Both The Solubility Param- eters and Molar Volumes of Liquids. Polym. Eng. Sci. 1974a,

Fedors, R. F. A Method for Estimating Both the Solubility Param- eters and Molar Volumes of Liquids Supplement. Polym. Eng. Sci. 1974b, 14(6), 472.

Flory, P. J. Principles of Polymer Chemistry; Cornel1 University Press: Ithaca, NY, 1953.

Flory, P. J. Thermodynamics of Polymer Solutions. Discuss. Fara- day SOC. 1970,49, 7-29.

Goydan, R.; Reid, R. C.; Tseng, H.-S. Estimation of the Solubilities of Organic Compounds in Polymers by Group Contribution Methods. Ind. Eng. Chem. Res. 1989,28,445-454.

14(2), 147-154.


Protective Clothing: Second Symposium; ASTM STP 989; ASTM: Philadelphia, PA, 1988.

Pierotti, G. J.; Deal, C. H.; Derr, E. L. Activity coefficients and Molecular Structure. Znd. Eng. Chem. 1959,51(1), 95-102.

Piringer, 0. Ethanol und Ethanol/Wasser-Gemische als PrDflebensmittel fiu die Migration aus Kunstatoffen. Dtsch. Le- bensm.-Rundsch. 1990,86(2), 35-39.

Prausnitz, J. R.; Lichtenthaler, R. N.; Azevedo, E. G. Mokcular Thermodynamics of Fluid-Phase Equilibrium, 2nd ed.; Pren- tice-Hall: Englewood Clifs, NJ, 1986.

Reid, R. C.; Sidman, K. R.; Schwope, A. D.; Till, D. E. Loss of Ad- juvants From Polymer Films to Foods or Food Stimulants. Effect of the External Phase. Znd. Eng. Chem. Prod. Res. Dev. 1980,19, 580-587.

Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Cases and Liquids; McGraw-Hill: New York, 1987.

Rider, P. E. Theories of Solvency and Solution. In Applied Polymer Science, 2nd ed.; Tess, R. E., Poehlein, G. W. Eds.; American Chemical Society: Washington, DC, 1985.

Schwartz, P. S. Food Packaging Regulation in the United States. Food Addit. Contam. 1988,5, Suppl. 1, 537-541.

Synowietz, C., Ed. D’Ans Lax Taschenbuch fur Chemiker und Physiker, 4th ed.; Springer-Verlag: Berlin, 1983; Vol. 2.

Till, D. E.; Ehnholt, 0. J.; Reid, R. C.; Schwartz, P. S.; Schwope, A. P.; Sidman, K. R.; Whelen, R. H. Migration of Styrene Monomer from Crystal Polystyrene to Foods and Food Simulating Liquids. Znd. Eng. Chem. Fundam. 1982,21,161-168.

Van Krevelen, D. W.; Hoftyzer, P. J. Properties of Polymers: Their Estimation and Correlation with Chemical Structure; Elsevier: Amsterdam, 1976.

Vom Bruck, C. G.; Bieber, W.-D.; Figge, K. Interactions Between Food and Packaging Materials and its Consequences on Migra- tion. In Food Packaging and Preservation; Mathlouthi, M., Ed.; Elsevier Applied Science: Amsterdam, 1986.

Weast, R. C., Ed. CRC Handbook of Chemistry and Physics; CRC Press, Boca Raton, FL, 1979.

Windholz, M., Ed. The Merck Index; Merck and Co.: Rahway, NJ, 1983.

Received for review August 2, 1990 Revised manuscript received January 2, 1991

Accepted January 22, 1991

Herington, E. F. G. The Thermodynamics of Gas-Liquid Chroma- tography. In Vapor Phase Chromatography; Desty, D. H., Harbourn, C. L. A. Eds.; Butterworths Scientific Publishers: London, 1957.

Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions: The Solubility of Cases, Liquids and Solids; Van Nostrand Reinhold: New York, 1970.

Hotchkiss, J. H., Ed. Food and Packaging Interactions; American Chemical Society: Washington, DC, 1988.

Hoy, K. L. The Hoy Tables of Solubility Parameters; Union Carbide Corp.: South Charleston, WV, 1985.

Ikegami, T.; Shimoda, M.; Koyama, M.; Osajima, Y. Sorption of Volatile Compounds by Plastic Polymers for Food Packaging. Nippon Shokuhin Kogyo Cakkaishi. 1987,34(5), 267-273.

Jorgensen, W. L.; Briggs, J. M.; Contreras, M. L. Relative Partition Coefficients for Organic Solutes from Fluid Simulations. J. Phys. Chem. 1990,94, 1683-1686.

Kasai, K.; Umeyama, H.; Tomonaga, A. The Study of Partition Coefficients. The Prediction of Log P Value Based on Molecular Structure. Bull. Chem. SOC. Jpn. 1988,61, 2701-2706.

Kamlet, M. J.; Doherty, R. M.; Abraham, M. H.; Marcus, Y.; Taft, R. W. Linear Solvation Relationships. 46. An Improved Equation for Correlation of Octanol/Water Partition Coefficients of Organic Nonelectrolytes (Including Strong Hydrogen Bond Donors So- lutes). J . Phys. Chem. 1988,92, 5244-5255.

Koszinowski, J. Diffusion and Solubility of n-Alkanes in Polyolefins. J . Appl. Polym. Sci. 1986a, 31, 1805-1826.

Koszinowski, J. Diffusion and Solubility of Hydroxy Compounds in Polyolefins. J. Appl. Polym. Sci. 1986b, 31, 2711-2720.

Koszinowski, J.; Piringer, 0. The Influence of Partition Processes Between Packaging and Foodstuffs or Cosmetics on the Quality of Packed Products. Verpackungs-Rundsch, 1989,40(5), 39-44.

Koszinowski, J.; Piringer, 0. Diffusion und relative Loslichkeit von Riechstoffen in Polyolefinen. Verpackungs-Rundsch. 1990,41(3),

Kwapong, 0. Y.; Hotchkiss, J. H. Comparative Sorption of Aroma Compounds by Polyethylene And Ionomer Food-Contact Plastics. J. Food Sci. 1987,52(3), 761-785.

Lee, Y. M.; Bourgeois, D.; Belfort, G. Sorption, Diffusion, and Per- vaporation of Organics In Polymer Membranes. J . Membr. Sci. 1989,41, 161-181.

Mansdorf, S. Z., Sager, R., Nielson, A. P., Eds. Performance of

15-17.

Documents

Prediction of solute partition coefficients between polyolefins and alcohols using the regular solution theory and group contribution methods