Computer-Aided Method for the Determination of Hansen Solubility

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Ind. Eng. Chem. Res. 1999, 38, 4470-4476

GENERAL RESEARCH Computer-Aided Method for the Determination of Hansen Solubility Parameters. Application to the Miscibility of Refrigerating Lubricant and New Refrigerant J.-C. Remigy,*,‡ E. Nakache,*,‡ and P. D. Brechot† Research Center of Mobil Oil Francaise, Notre Dame de Gravenchon, France, and ISMRA, CNRS UMR 6507, Caen, France

This article presents a method which allows one to find the Hansen solubility parameters by means of data processing. In the first part, we present the thermodynamical principle of Hansen parameters, and then we explain the model used to find parameters from experimental data. We validate the method by studying the solubility parameters of CFC-12 (dichlorodifluoromethane), HFC-134a (1,1,1,2-tetrafluoroethane), neopentylglycol esters, trimethylolpropane esters, dipentaerythritol esters, and pentaerythritol esters. Then, the variation of Hansen parameters are studied as well as the relation between the miscibility temperature (the temperature at which a blend passes from the miscible state to the immiscible state) and the interaction distance. We establish the critical interaction distance of HFC-134a which determines the solubility limit and we study its variation with temperature. I. Introduction Since the end of 1995, the manufacturing of CFC ceased compiling with the Montreal protocol1 and its amendments. The new refrigerants proposed to replace chlorofluorocarbons (CFCs) are hydrofluorocarbons (HFCs). The leading substitute for CFC-12 (CCl2F2) is HFC-134a (CF3-CH2F). This new refrigerant is not compatible with conventional refrigeration oil (i.e., mineral oil, poly-R-olefin (PAO), alkylbenzene (AB), etc.). The principal criterion of compatibility is the miscibility between the refrigerant and lubricant at low temperature (around -40 °C). This study focuses on the miscibility of HFC-134a with synthetic oils (polyol esters), and we try to correlate this phenomenon with Hansen solubility parameters. Coming from the thermodynamics of solutions, solubility parameters have been used conveniently to estimate the solubility or miscibility between two compounds.2 Methods, using these parameters, are used to formulate products in cosmetics, paints, or polymer blends. They can be used to formulate a final product which can be a solid or a liquid. In this article, we describe a new method used to determine Hansen solubility parameters with accuracy. We validate this new method by studying the Hansen solubility parameters of two refrigerants, CFC-12 (dichlorodifluoromethane) and HFC-134a (1,2,2,2-tetrafluoroethane), and of polyol esters. Then, we discuss the solubility parameters criteria used to predict liquid miscibility. * To whom correspondence should be addressed. E-mail: [email protected] or [email protected]. † Research Center of Mobil Oil Francaise. ‡ ISMRA.

A. Solubility Parameters. Thermodynamical principles indicate that the miscibility of two compounds is controlled by the Gibbs free energy of mixing ∆Gm which must be negative or null:

∆Gm ) ∆Hm - T∆Sm e 0

(1)

where ∆Hm and ∆Sm are respectively the enthalpy and entropy of mixing and T the absolute temperature. As ∆Sm is positive, ∆Hm must be negative or slightly positive to have ∆Gm e 0. So the miscibility of two liquids depends on the expression of ∆Hm. Scatchard3,4 and Hildebrand and Scott 5,6 have shown that, for a regular solution, ∆Hm depends on the solubility parameters from the equation

∆Hm ) (n1V1 + n2V2)(δ1 - δ2)2Φ1Φ2

(2)

where n1 and n2 are the number of moles of compound 1 and 2, Φ1 and Φ2 their volume fractions, V1 and V2 their molar volumes, and δ1 and δ2 their solubility parameters considered as constants (units MPa1/2 or (cal/cm3)1/2). From eqs 1 and 2, the miscibility occurs if δ1and δ2 are close. It is generally considered that the solubility is obtained when δ1 - δ2 is below 2 MPa1/2). The Hildebrand parameter is not a “thermodynamic” one for nonregular systems. Hansen7-9 has extended the theory developed by Hildebrand to polar and associated compounds by dividing the δ parameter in several partial parameters. For the interaction of hydrogen bonding, strictly a five-parameter approach is necessary, and then the Hansen three-parameter method is only semiempirical. The first parameter, δd, is related to

10.1021/ie990047x CCC: $18.00 © 1999 American Chemical Society Published on Web 10/09/1999

Ind. Eng. Chem. Res., Vol. 38, No. 11, 1999 4471

dispersion forces. The second one, δp, is related to polar forces, and the last one δh is related to specific interaction forces (hydrogen bond, acid/base, etc.). These three parameters are related to a total parameter δ (similar to the Hildebrand parameter) by the equation

δ2 ) δd2 + δp2 + δh2

(3)

In the Hansen theory, the enthalpy of mixing is given by the equation

∆Hm ) (n1V1 + n2V2)((δd1 - δd2)2 + (δp1 - δp2)2 + (δh1 - δh2)2)Φ1Φ2 (4) In this case, the miscibility will be obtained if each partial difference of partial parameters is low (i.e., (δd1 - δd2)2 + (δp1 - δp2)2 + (δh1 - δh2) ≈ 0). So the closer the three parameters, the more soluble or miscible the two compounds. Hansen suggests that each compound can be represented in a three-dimensional (3D) space, having the solubility parameters for axes. In this space, solvents of a compound are included in a solubility volume centered on the point having its coordinates equal to the three partial solubility parameters. Hansen8 has shown that, for resins, the solubility volume is a sphere but others authors10 use an ellipsoid to model this volume:

(x-δd)2 a2

+

(y-δp)2 b2

+

(z-δh)2 c2

e1

(5)

In this space and with the spherical model, the miscibility of two compounds A and B occurs when the center of B’s solubility volume is inside A’s solubility volume. The distance between the center, Rij, is given by the equation

Rij ) ((δdi -δdj)2 + (δpi - δpj)2 + (δhi - δhj)2)1/2

(6)

B. Solubility Parameter Determination. Solubility parameters can be determined by the use of the correlation between parameters and physical properties (refractive index, dipole moment, etc.) or by the use of the contribution groups method.11 But experimental determination is more accurate. The measurement of solubility parameters is based on the influence of solvent power on a physical property. This influence allows one to separate the true solvents and the nonsolvents. Then, the solubility volume is determined as the volume including the true solvents. From this series of experiments, the solubility volume is defined by the ellipsoid (or sphere) having the maximum of solvents and the minimum of nonsolvents in its volume. The center of the solubility volume gives the three solubility parameters. II. Materials and Methods A. Products. Dichlorodifluoromethane (CFC-12) and 1,1,1,2-tetrafluoroethane (HFC-134a) were supplied by Elf-Atochem. The oils were supplied by Mobil. We used polyolester oil synthesized from complete esterification of polyols and aliphatic acids (cf. Table 1). Two other synthetic oils, 31 cSt of viscosity at 40 °C, were supplied by

Table 1. Used Esters abbreviation PE-nC5 PE-nC7 PE-nC9 PE-nC18 PE-iC5 PE-iC8 PE-iC9 PE-iC18 NPG-nC7 TMP-nC7 DiPE-nC5 DiPE-nC7 DiPE-nC9 DiPE-iC9

alcohol

acid

pentaerythritol pentaerythritol pentaerythritol pentaerythritol pentaerythritol pentaerythritol pentaerythritol pentaerythritol neopentylglycol trimethyolpropan dipentaerythritol dipentaerythritol dipentaerythritol dipentaerythritol

n-pentanoic n-heptanoic n-nonanoic n-octadecanoic isopentanoica iso-octanoic 3,5,5-trimethylhexanoic iso-octadecanoic n-heptanoic n-heptanoic n-pentanoic n-heptanoic n-nonanoic 3,5,5-trimethylhexanoic

a Blend of 65% weight of isopentanoic and 35% n-pentanoic acids.

Mobil: poly-R-olefin base oil (PAO) and alkylbenzene base oil (AB). B. Measurement of Miscibility Temperature. The miscibility temperature is defined as the temperature beyond which a mixture composed of 10%w oil and 90%w refrigerant becomes miscible. In fact, because of experimental difficulties (refrigerant liquefaction), two different measurements were carried out. The first mixture temperature, T1, is taken from a mixture with an oil concentration, C1, above 10%w and the other temperature, T2, from a mixture with an oil concentration, C2, under 10%w. The miscibility temperature, TM, is calculated using eq 7 from these two values:

TM ) T 1 +

(10 - C1) (T - T1) (C2 - C1) 2

(7)

The used glass tubes were dried in an oven at 110 °C to eliminate water; then 0.9 g of oil is introduced in each tube. The tubes are cooled with dry ice. Then the refrigerant is liquefied at low temperature. When the estimated volume of the refrigerant is introduced, the tube is sealed by fusion and then is weighed to determine the true concentration. Starting from the ambient temperature, the homogenized tubes are cooled in an alcohol bath with dry ice at a speed around 1 °C/min. The miscibility temperature is taken when two phases appear. If the mixture is immiscible at ambient temperature, then the tube is warmed in a water bath and the miscibility temperature is taken when the miscibility appears. C. Experimental Data for Hansen Parameter Determination. A set of 104 solvents (or mixed solvents) was used to determine the miscibility profile of the tested products. The solubility parameters of the mixed solvents were calculated with eq 8,

δxm )

∑i Φiδxi

with x ) d, p, h

(8)

where Φi is the volume fraction and δxi are the Hansen parameters of pure solvents. CFC-12 and HFC-134a, which are gaseous at ambient temperature, were liquefied at low temperature in a glass tube containing the solvent. Then, this tube is sealed by fusion. Also, the measurements are taken under a pressure slightly higher than the atmospheric pressure, but the influence of pressure on the solubility parameters is low so the final results are acceptable.12

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Ind. Eng. Chem. Res., Vol. 38, No. 11, 1999

Figure 1. Schematic representation of the calculated distance in the δd-δp plane. Table 2. Equations Used calculation of CS (or CN)

CS2 ) (xs - δd)2 + (ys - δp)2 + (zs - δh)2

calculation of coordinate of M1 and M2

The equation leads to a quadratic equation giving x1 and x2. Rx2 + βx + γ ) 0 with

R)

β)

γ)

1 g2 i2 + 2+ 2 2 a b c 2g(h-δp) b2 δd2 2

+

+

2i(j-δh) c2

(h-δp)2

a

b

2

+

-

2δd

(j-δh)2 c2

a2 -1

with

g)

i)

(ys-δp) (ys-δd) (zs-δh) (xs-δd)

h)

j)

ys(xs-δd)-xs(ys-δp) , (xs-δd)

zs(xs-δd)-xs(zs-δh) (xs-δd)

y and z are given by the following equations: y ) xg + h and z ) xi + j calculation of CM1 and CM2

CM1 ) (x1 - δd)2 + (y1 - δp)2 + (z1 - δh)2 CM2 ) (x2 - δd)2 + (y2 - δp)2 + (z2 - δh)2 with δd, δp, and δh: Hansen parameters of studied substance xs, ys, and zs: Hansen parameters of solvents x, y, z: coordinate of point M (M1 and M2)

For each solvent, 5 cm3 of the substance is mixed with 5 cm3 of the solvent in a glass tube. The mixture is vigorously stirred for 30 s. The tube is placed in a thermostatic bath at the temperature T ( 0.5 °C (T ) 20, 0, -20, -40 °C) without agitation for a minimum of 15 min (a longer period can be used in doubtful cases). The miscibility behavior of the tested substance was visually appreciated as miscible when one phase is visible or immiscible when two phases are visible. D. Determination of Hansen Solubility Parameters from Experimental Data. This new method allows one to position, in the Hansen space, the solubility volume in relation to the solvents and nonsolvents with good accuracy. The solubility volume was assumed to be an ellipsoid which is defined by eq 5. The value of the six ellipsoid parameters is calculated by an optimization of the position and the shape of the ellipsoid in relation to the experimental data. A maximum of true solvents and a minimum of nonsolvents are located inside the solubility volume while a maximum of nonsolvents and a minimum of true solvents are outside this volume.

Figure 1 shows, schematically, the calculated distances: CS, distance between the volume center and the point representing a miscible solvent; CN, distance between the volume center and the point representing an immiscible solvent; CM1 and CM2, distance between the volume center and the intersection point between an ellipsoid and the CS line; CM′1 and CM′2, distance between the volume center and the intersection point between an ellipsoid and the CN line. Table 2 gives the equations used. The algorithm used allows one to change the shape and the position of the solubility volume so as to maximize the classification success fraction. The classification success fraction is defined as the total number of miscible solvents at the right place (i.e., in the volume) and the number of immiscible solvents out of the volume, divided by the total number of solvents used. The optimal classification success fraction must be obtained if the rate of miscible solvents in the volume approximately equals the rate of immiscible solvents out of the volume. Practically, this optimization is obtained by changing the value of the ellipsoid parameters (a, b, c, δd, δp, δh). δd, δp, and δh

Ind. Eng. Chem. Res., Vol. 38, No. 11, 1999 4473 Table 3. Validation of the New Method: Published and Experimental Hansen Parameters values (MPa1/2) at 20 °C

δ

δd

classification δh success fraction

δp

CFC-12

published10 experimental

12.5 12.3 2.1 0.0 12.3 12.1 2.2 0.0

96%

HFC-134a


13.9 15.3

7.2 7.4 9.4 8.4 8.9 9.2

95%

PE-nC9


15.5 14.9 2.9 3.3 15.4 14.9 2.6 3.3

95%

PE-iC9

published10

15.1 14.3 3.3 3.7 15.0 14.2 3.6 3.4

95%

experimental

Table 4. Experimental Hansen Parameters and Volume Coefficients of Refrigerants at 20, 0, -20, and -40 °C (in MPa1/2) temperature (°C) refrigerant

δ

δd

δp

a

δh

b

c

20d

CFC-12 12.3 12.1 HFC-134a 15.3 8.4

2.2 8.9

0.0 7.4 21.8 26.1 9.2 10.1 25.2 18.2

0

CFC-12 13.9 13.0 HFC-134a 16.9 9.7

4.8 9.8

0.0 7.4 15.4 25.5 9.7 10.0 18.0 16.0

-20

CFC-12 15.5 14.0 6.6 0.0 HFC-134a 17.7 9.9 10.6 10.1

6.7 14.0 25.4 9.5 18.0 16.1

-40

CFC-12 17.3 15.3 8.1 0.0 HFC-134a 18.5 10.2 11.3 10.6

5.9 10.0 25.7 9.5 17.4 15.4

Table 5. Experimental Hansen Parameters and Volume Coefficients of Oils at 20 °C (in MPa1/2) oils

δ

δd

δp

δh

a

b

c

poly-R-olefin (PAO) alkylbenzene (AB) PE-nC5 PE-nC7 PE-nC9 PE-iC8 PE-iC9 DiPE-nC5 DiPE-nC7 DiPE-iC9 TMP-nC7 NPG-nC7

17.3 18.4 15.6 15.3 15.4 15.4 15.0 15.7 15.8 15.7 15.4 16.6

17.3 18.0 14.1 14.3 14.9 14.3 14.2 14.3 14.8 14.7 13.7 13.3

0.0 3.6 4.8 3.6 2.6 4.1 3.6 4.7 3.9 3.9 4.8 6.8

0.0 0.8 4.6 4.0 3.3 4.0 3.4 4.7 4.0 4.1 5.3 7.3

5.1 7.0 5.9 5.9 6.9 5.0 5.9 5.6 5.0 5.9 6.0 5.9

10.3 7.9 15.5 14.0 10.2 14.5 14.7 16.4 14.0 12.0 13.6 15.0

15.6 17.6 7.0 17.5 16.4 14.8 17.8 16.2 13.9 14.1 15.8 15.0

allow one to change the volume’s position in the space and a, b, and c allow one to change the shape. Finally, the limit of the experimental volume is not the same as that of the optimized ellipsoid; then a “skin’s thickness” e must be introduced. When the value of δ is known (from the vaporization enthalpy, for example), the values of δd, δp, and δh must match the relation δ2 ≈ δd2 + δp2 + δh2. This was checked during the study of CFC-12 parameters: δ obtained from vaporization enthalpy equals 12.5 MPa1/2.13 The value, calculated from experimental values of δd, δp, and δh equals 12.3 MPa1/2. Thus, good agreement between theses two results is a first proof of the validity of this method. There is also a good agreement between the experimental values and the previous published values10 (cf. Table 3). The accuracy of experimental values depends on several factors. The first one is the number of experiments which delimit the solubility volume and it is also interesting to have the same number of solvents and nonsolvents. Another factor is related to the skin’s thickness: a high value of e corresponds to low accuracy; this high value may be due to the volume’s shape which is not corresponding to an ellipsoid. It is the case for HFC-134a. This can explain the significant difference between the experimental and published values of δ.

Table 6. Experimental Hansen Parameters and Volume Coefficient of Oils at 0 °C (in MPa1/2) oils

δ

δd

δp

δh

a

b

c


17.7 18.9 16.9 16.3 16.1 16.8 17.4 17.4 16.9 16.7 17.2 18.0

17.7 18.5 14.3 14.7 15.2 15.0 14.5 14.9 15.1 15.1 14.7 14.1

0.0 3.7 6.0 4.0 2.9 5.3 5.4 5.8 4.9 4.9 6.3 7.8

0.0 0.9 6.5 5.8 4.4 5.4 5.3 5.3 5.8 5.0 6.4 7.8

5.0 6.4 5.9 5.7 6.6 5.0 5.6 5.0 5.0 5.0 5.4 5.9

9.5 7.8 15.5 14.0 10.0 14.5 13.9 14.5 14.0 13.9 13.6 14.3

14.0 17.0 17.0 16.0 13.4 14.8 15.6 14.5 13.9 13.3 15.0 13.5

Table 7. Experimental Hansen Parameters and Volume Coefficient of Oils at -20 °C (in MPa1/2) oils

δ

δd

δp

δh

a

b

c


18.4 19.5 17.7 18.2 16.9 18.7 18.2 18.2 18.4 18.5 17.7 19.3

18.4 19.1 14.7 15.3 15.7 16.2 14.9 15.5 16.4 16.8 15.1 14.9

0.0 3.7 6.8 6.6 3.4 6.6 6.7 6.3 5.0 5.5 6.8 8.6

0.0 0.9 7.0 7.3 5.3 6.9 7.3 7.1 6.6 5.4 6.5 8.8

4.7 5.0 5.9 5.4 6.4 4.5 5.4 4.8 4.9 4.2 5.3 5.6

8.2 7.8 15.5 11.0 8.5 9.8 12.3 13.4 9.6 10.2 13.5 13.2

12.0 16.5 17.0 11.3 11.2 10.1 13.1 13.2 8.7 10.0 14.6 13.3

Table 8. Experimental Hansen Parameters and Volume Coefficient of Oils at -40 °C (in MPa1/2) oils

δ

δd

δp

δh

a

b

c


19.1 19.7 19.4 21.6 17.6 20.9 19.7 19.7 20.9 19.7 18.3 20.6

19.1 19.4 15.4 17.5 16.0 17.2 15.7 16.2 18.5 17.6 15.5 15.7

0.0 3.8 8.4 8.1 4.0 8.0 7.4 7.7 5.7 5.9 7.0 9.1

0.0 0.8 8.4 9.7 6.3 8.6 8.5 8.2 7.8 6.6 6.8 9.8

4.4 4.4 5.9 5.0 6.0 4.4 5.3 4.4 3.9 4.0 5.0 5.6

9.8 7.9 15.0 9.4 7.0 5.5 10.0 9.1 4.3 9.2 8.4 13.2

9.3 15.1 16.5 5.8 7.5 7.8 11.0 9.3 7.1 9.3 14.0 13.5

This method is particularly interesting when the studied parameters are extremely high (δd, δp, δh) or low (δd) because we are able to define all the ellipsoids by just delimiting experimentally one part of the volume, i.e., without having to find too many solvents on “both sides” of this volume. For example, in the HFC134a case, the parameter δd is very low so there is no easy usable solvent with a δd below 10 MPa1/2. Then, the volume was defined with solvents having a δd above 14.3 MPa1/2. This method was also used to obtain the solubility parameters of several oils and refrigerants at different temperatures (20, 0, -20, -40 °C). The results are shown in Tables 4-8. We notice that the Hansen parameters decrease when the temperature increases as predicted by the relations between the parameters and the temperature.14,15 With these measurements, we studied the variations of the solubility parameters as the variations of the distances of interaction with temperature. This distance is defined as the length which separates the centers of the solubility volume of two different substances.

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Table 9. Distances CN and CS, Refrigerants/Oils at 20 °C in MPa1/2 refrigerants CFC-12 oils PAO AB PE-nC9 PE-iC9 PE-nC5

HFC-134a

temperature of miscibility

distance CS or CN

d1-d2

+60 °C -32 °C 60

Hansen radius of interaction which depends on the sphere radius. B. Determination of the Critical Distance of Interaction of HFC-134a. The critical distance is defined as the existing distance when the miscibility occurs between two substances. So, at the miscibility temperature, the interaction distance equals this critical distance. For a refrigerant, for instance, knowing the interaction distance of several substances with one compound, at the miscibility temperature, we can reach the variation of the critical distance with temperature. Starting from the interaction distances measured at 20, 0, -20, and -40 °C of several oils (see Table 10), we can calculate the critical distance of interaction of HFC-134a by interpolation. For example, the critical distance of HFC-134a is obtained at the temperature of miscibility of HFC-134a and PE-iC8 (i.e., -6 °C) by interpolating the distance of interaction between HFC134a and PE-iC8 at 0 and -20 °C. We cannot calculate this distance if the miscibility temperature is not known with accuracy as in the case of PE-nC5, DiPE-nC5, PEnC9, AB, and PAO. Figure 3 shows the experimental variation of the critical distance of interaction of HFC134a with temperature. From this curve, at 20 °C, HFC-134a has a critical distance of interaction equal to ≈9.7 MPa1/2. At -40 °C, this distance is reduced to 7 MPa1/2; it can be noticed that the critical distance of interaction decreases when the temperature increases. And consequently, the interaction between the molecules must be more and more similar to get miscibility at low temperature. Figure 4 displays the distance of interaction of each oil with HFC-134a. On this figure, the critical distance of interaction of HFC-134a is represented by a dotted line. In the studied temperature range, we can see that immiscible oils (PAO, AB, and PE-nC9) have a distance of interaction superior to the critical distance. Inversely, miscible oils, like PE-nC5 or DiPE-nC5, have a distance of interaction inferior to the critical distance. Polyolesters having an intermediate miscibility temperature (PE-

Ind. Eng. Chem. Res., Vol. 38, No. 11, 1999 4475

Figure 3. Variation of the critical distance critique of the interaction of HFC-134a with temperature.

Figure 4. Variation of interaction’s distances of oils with HFC-134a and variation of the critical distance of the interaction of HFC-134a.

iC8 and PE-iC9) have an interaction distance with HFC134a inferior at high temperature, and superior at low temperature, to the critical distance. For PE-iC8, this method gives the miscibility temperature with HFC134a: the intersection of the two curves is around -16 °C while the experimental miscibility temperature is -13 °C. Concerning PE-iC9, the chart shows two intersection points, at -40 and +20 °C, although the experimental miscibility temperature is -32 °C. In this case, we can deduce that to establish miscibility temperature, a higher number of experiments is necessary. IV. Conclusion This new method gives access to the experimental value of solubility parameters with good accuracy. We found the Hansen solubility parameters of 12 substances at 4 different temperatures. We show that the classical criterion are not sufficient to predict miscibility. The distance between the centers of solubility volumes

is clearly a better criterion to predict miscibility (and, of course, solubility). We show that there is a critical distance of interaction which determines miscibility. This distance depends on the studied substances and on the temperature. From these results, it would be interesting to apply this method to other refrigerants or eventually to other mixing substances. Acknowledgment The authors acknowledge A.D.E.M.E. (Paris, France), the French environmental agency, for their financial support. Literature Cited (1) Unep, United Nations Environmental Program. Handbook for the Montreal Protocol on Substances that Deplete the Ozone Layer, 3rd ed.; Ozone Secretariat, Aug 1993. (2) Special Issue on Self-stratifying Coatings. Prog. Org. Coatings 1996, 23, 3.

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(3) Scatchard, G. Equilibria in Nonelectrolyte Solutions in Relation to the Vapor Pressures and Densities of the Components. Chem. Rev. 1931, 8, 321. (4) Scatchard, G. Equilibrium in Nonelectrolyte Mixtures. Chem. Rev. 1949, 44, 7. (5) Hildebrand, J. H.; Scott, R. L. The Solubility Of NonElectrolytes, 3rd ed.; Reinhold Publ. Corp.: New York, 1950. (6) Hildebrand, J. H.; Scott, R. L. Regular Solutions; Prentice Hall: Englewood Cliffs, NJ, 1962. (7) Hansen, C. M. J. Paint Technol. 1967, 38 (503), 104. (8) Hansen, C. M. J. Paint Technol. 1967, 39 (504), 505. (9) Hansen, C. M. Ind. Eng. Chem. Prod. Res. Dev. 1969, 8 (1), 2. (10) Inoue, K.; Iwamoto, A. Mutual Solubility Of HFC-134a and Synthetic Ester Base Stocks. Sekiyu Gakkaishi 1992, 35 (1), 7683.

(11) Van Krevelen, D. W. Properties of Polymers: Their Correlation with Chemical Structure, Their Estimation and Prediction from Additive Group Contributions; Elsevier: Amsterdam, 1990. (12) Otmer, K. Encyclopedia of Chemical Technology, 2nd ed.; Standen, A., Ed.; Wiley: New York, 1971; Suppl. Vol., pp 889910. (13) Barton, A. F. M. Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd ed.; CRC Press Inc.: Boca Raton, FL, 1991. (14) Burrell, H. Solubility Parameters. Interchem. Rev. 1955, 14, 3-16 and 31-46. (15) Zelers, E. T. J. Appl. Polym. Sci. 1993, 50, 513.

Received for review January 19, 1999 Revised manuscript received July 20, 1999 Accepted August 4, 1999 IE990047X

Computer-Aided Method for the Determination of Hansen Solubility

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