661
Ind. Eng. Chem. Res. 1995,34, 661-673
Polygon Mapping with Two-Dimensional Solubility Parameters Irwin A. Wiehet Corporate Research Laboratories, Exxon Research and Engineering Co., Route 22 East, Annandale, New Jersey 08801-0998
I n the selection of liquids and liquid mixtures to dissolve a given material, the two-dimensional solubility parameter is shown to be both easier to use and much more accurate than the commonly used three-dimensional solubility parameter. The solubility parameter of each liquid is represented as a vector with complexing and field force components. The complexing solubility parameter component characterizes the ability of a liquid to form interactions that require a specific orientation between molecules while the field force solubility parameter component includes dipole interactions, which usually are only significant for associated liquids, like alcohols, and dispersion interactions. On the basis of five postulates, the solvent power of each liquid is represented by a point in two-dimensional solubility parameter space while the set of solvents for a given material are represented by the area of a polygon. The assignment of solubility parameter components for 50 liquids were made on the basis of their ability or inability to dissolve 35 polymers and 3 dyes in this study and 33 polymers from a previous study and resulted in a 99.5% accuracy of the placement of nonsolvents outside and of solvents inside the solubility areas. These solubility areas enabled the correct prediction of over 100 solvents formed from mixtures of liquids that individually are nonsolvents. Finally, as an example, the twodimensional solubility parameter was applied to the selection of solvents for forming colored, spherical polymer particles, encapsulated in clear polymer shells by spray drying.
Introduction In the application of solution thermodynamics to phase equilibria, most attention has been given to the dependency of the chemical potential on concentration, temperature, and pressure. Much less attention has been paid t o the selection of a liquid or liquid mixture for dissolving a material or for separating a mixture when the concentration dependency of the chemical potential of the material in the set of liquids or liquid mixtures is unknown. In the trial and error procedure of solvent selection one would like to minimize the number of trials. For instance, the success or failure of a set of liquids should enable one to predict the success or failure of the remaining liquids. While one might imagine trying all the potential pure liquids, it is impossible to try the full set of liquid mixtures. This is especially the case when one considers that mixtures of liquids can dissolve materials at the desired concentration even though each of the liquids individually cannot dissolve the material. Moreover, often in solution processes one needs the ability t o manipulate the “solvent power”, the measure of the goodness of a solvent. However, we are often lacking in our ability t o predict, even qualitathely, whether a given solvent for a material barely dissolves the material or whether it is such a good solvent that only large dilutions with a nonsolvent produces insolubility. Thus, in this paper the procedure developed and applied by the author over a number of years to meet these needs will be described and an example application will be discussed. The general technique of solvent selection has been reviewed by Kumar and Prausnitz (1975), and the design of solvents for liquid extraction based on the UNIFAC model (Fredenslund, Jones and Prausnitz, 1975) was discussed by Gani and Brignole (1983). The latter shows that chemical group contributions can be used to estimate parameters in a chemical potential Much of this work was done while the author was at Xerox, Webster, NY. +
0888-5885/95/2634-0661$09.00/0
model to extend the model to systems where no data exist. However, often insufficient data are available t o evaluate the chemical group contributions acurately enough for reliable predictions of solubility. The application of solvent selection science has developed most rapidly in the paint and coating industry because of the limited solubility of polymers and because of the many environmental, safety, economic, and performance demands on solvent systems. Most utilize a variation of the solubility parameter from the regular solution theory of Hildebrand (1933) and Scatchard (1931):
a2 = E v N
(1)
where 6 is the solubility parameter (positive root), (cay cm3)lI2;E v is the energy of vaporization t o an ideal gas, cal/g-mol; V is the molar volume, cm3/g-mol; and EvN is the cohesive energy density, cal/cm3. Although the regular solution theory was not intended to be applied to hydrogen bonding and highly polar liquids, the energy of vaporization measures all forms of interaction energy. Therefore, van Arkel (1946) first proposed partitioning the energy of vaporization into polar and dispersion contributions:
a2 = 6;
+ 6;
(3)
where d as a subscript or a superscript refers to dispersion and p as a subscript or a superscript refers to polar. This approach was applied by Blanks and Prausnitz (1964) t o predict the thermodynamic properties of polymer solutions when the polymer and/or solvent is polar but not hydrogen bonding. Hansen (1967a,b, 1969) added the hydrogen bonding contribution:
0 1995 American Chemical Society
662 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995
E,
E! E; v v +-+v v
-=-
E$
(4)
where h as a subscript or a superscript refers to hydrogen bonding. This three-dimensional solubility parameter has found wide application because Hansen did not confine it to the regular solution model for the chemical potential, as did Blanks and Prausnitz. Instead, Hansen mapped the solvents in three dimensions for each material using the three solubility parameter components as coordinates. This borrowed on the experience of Burrell (1955), Lieberman (19621, and Crowley et al. (19661, who made solubility maps with the solubility parameter as one coordinate and various measures of hydrogen bonding and/or polarity as other coordinates. Thus, the three-dimensional solubility parameter resulted in a graphical technique for predicting solubility in which the solvent power of each liquid is represented by a point in three-dimensional solubility parameter space, the solubility parameter vector. The solvent power of all mixtures of two liquids is on the line between the two points that represent the two liquids. The lever rule based upon volume fraction is used to determine the point on that line for a given ratio of liquids in the mixture. It is difficult with three-dimensional mapping t o determine graphically if a given point is inside or outside an arbitrary volume. Therefore, Hansen (1967a) approximated the solubility volumes by spheres after multiplying the dispersion solubility parameters by 2. While this approximation greatly eased the graphical problem, as will be shown later, the errors so introduced may have canceled out any advantage of three solubility parameter components over two components. While many investigators use either the overall solubility parameter or the three-dimensional solubility parameter (Hildebrand et al., 1970; Hanson and Beerbower, 1971; Barton, 1983), there have been few attempts to apply two-dimensional solubility parameters to systems with both polar and hydrogen bonding components. One exception is the two-dimensional solubility parameter of Bagley et al. (1971,1975). They extended the concept of Wiehe and Bagley (1967) that the internal pressure is a measure of the cohesive energy density of dispersion interactions to include all interactions except for hydrogen bonding:
(6)
a2 = 6; + 6,2
(7)
where (aE/aTr)T is the internal pressure in caVcm3,6, is a volume-dependent component of the solubility parameter due to dispersion and polar forces, and 6 h is a volume-independent component of the solubility parameter due to hydrogen bonding interactions. This has the additional advantage that the volume-dependent solubility parameter component can be measured directly for pure liquids and materials and the other component can be calculated from the overall solubility parameter and the measured component. However, as will be discussed later, this way of splitting the solubility parameter into two components does not provide the desired consistency with experimental solubility data, especially with highly associating liquids. In addition,
Bagley et al. restricted the solubility area to be a circle after multiplying 6, values by 2. Chen (1971,1972)used a similar circular area restriction but used a function of both the dispersion and the polar solubility parameter components as one dimension and the hydrogen bonding solubility parameter component as the second dimension.
Two-Dimensional Solubility Parameter If one is to use a graphical solubility parameter approach, two dimensions are much more convenient t o use than three dimensions. Thus, the objective is to devise a two-dimensional solubility parameter that has equal, or better, predictive ability as the three-dimensional solubility parameter. Relative Importance of Polar Interactions. By making order of magnitude calculations, several early investigators of solubility parameters (Hildebrand and Scott, 1950; Small, 1953; Burrell, 1955) came to the conclusion that for most liquids the contribution of dipole interactions could be neglected. Actually the interaction energy between two permanent dipoles depends on their relative orientation as well as their separation distance, r. If they are lined up in their most favorable orientation, the interaction energy, E , is given by
r' where u1 and u2 are the dipole moments of the two dipoles. However, because of thermal agitation, usually this orientation is greatly disrupted at normal temperatures. Including this effect, Keesom (1921, 1922) derived the expression for the average potential energy:
(9) One can compare this equation with that for the interaction energy due to dispersion forces as predicted by London (1930, 1937):
e=-
3a~-& @(I, + I J
(10)
where I is the ionization potential and a is the polarizability. In most cases one finds that the dispersion interaction energy is much greater than the polar interaction energy. The exceptions include associated liquids, such as ammonia, alcohols, and water, where rotation is strongly hindered and the polar interaction energy is closer t o eq 8 than eq 9 (Hildebrand and Scott, 1950). Further proof that dipole moment is not a significant parameter in solubility are provided by the disubstituted benzene isomers. Both the dichlorobenzenes and dinitrobenzenes show only slight differences in solubility among the three isomers even though differences in dipole moment are large (Hildebrand and Scott, 1950). What is significant, however, are the number and type of substituents. Electronegative atoms that cause dipole moment also provide molecules with one of the means to form electron donor-electron acceptor interactions. Thus, if an interaction requires a specific orientation of an atom of one molecule with a specific atom of another molecule, the energy of interaction can be large and we call it a complexing interaction. Examples are hydrogen bonds
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 663 Table 1. Materials Used for Solubility Tests material 65%/35%stvreneln-butyl methacrvlate coDolvmer propylene ;fide adduciof bisphenh A with &mark acid branched of polymer B polystyrene rosin modified phenol-formaldehyde rosin modified phenol-formaldehyde poly(l,2-propylene terephthalate) branched of polymer G poly(hexamethy1ene sebacate) block copolymer of HMS and 2-methy1-2-ethyl-1,l-propylidene sebacate block copolymer of HMS and 2-methy1-2-ethyl-1,l-propylidene sebacate polyamide polyester poly(hexy1enecyclohexanedicarboxylate) poly(hexy1eneterephthalate) poly(hexamethy1ene isophthalate) poly(2,2-dimethyl-l,3-propylene isophthalate) poly(hexy1eneisophthalate) segmented polyurethane, polyester based segmented polyurethane, polyester based poly(viny1idenefluoride) polyacetal copolymer poly(pheny1ene oxide) copolymer poly(pheny1ene oxide) poly(undecanamide)-Nylon 11 polycarbonate poly(N-vinylcarbazole) copolymer of poly(ethy1ene and terephthalate) and poly(ethy1ene isophthalate) polyester copolymer polyester polycarbonate polysulfone poly(ether sulfone) polystyrene-polybutadiene block copolymer 85%/15%methyl methacrylatelstyrene copolymer Oil Soluble Red dye Heliogen Blue dye 2,4,7-trinitro-9-fluorenone
and other electron donor-electron acceptor interactions. Compounds that have electronegative atoms that are spatially balanced, like 1,4-dioxane or p-dichlorobenzene, have no dipole moment and yet have the capacity to form electron donor-electron acceptor complexes. Otherwise, the polar interactions will be a small part of the overall interaction energy and can be grouped with the dispersion interaction that will also have an inverse sixth-power dependency on the separation distance (eqs 9 and 10). Since these interactions act over a field and are not destroyed by orientational changes, they are grouped as field force interactions. Solubility Parameter Components. The two solubility parameter components in this paper are identified as the field force solubilityparameter component, 6f,and the complexing solubility parameter component, 6,. Clearly, dispersion interaction energy is part of the field force solubility parameter component and hydrogen bonding interaction energy is part of the complexing solubility parameter component. The interaction energy that is caused by the dipole moment of the molecules but between randomized orientations of the molecules is part of the field force solubility parameter component. On the other hand, the interaction energy between an electron-rich atom of one molecule and an electrondeficient atom of another molecule and, thus, requires a specific orientation of the two molecules is part of the complexing solubility parameter component. Thus, there is no need t o have a separate solubility parameter component for interactions between polar molecules. Basic Postulates. Here, the two-dimensional solubility parameter formalism is expressed in terms of five
6,
df ~
~~
source
name
~
8.62 8.48 8.48 8.68 8.68 8.68 8.48 8.55 8.94
4.08 4.72 4.72 4.08 3.33 3.33 5.20 5.05 3.38
synthesis Atlas Atlas Dow synthesis synthesis synthesis synthesis synthesis
8.69
3.23
synthesis
Spar I1 branched Spar I1 PS-2
HMS
8.61 3.65 8.48 4.76 8.69 3.24 8.84 3.50 8.94 3.40 8.70 4.26 8.94 3.38 8.75 7.18 8.61 7.04 8.70 6.62 no solvent 9.28 1.50 9.28 1.50 no solvent 9.02 3.50 8.89 4.08 8.80 5.58
Emery Dow synthesis synthesis synthesis synthesis synthesis B.F. Goodrich B.F. Goodrich Pennwalt Celanese General Electric General Electric Aquitaine General Electric BASF Goodyear
Emerez 1540 Adipate 565
9.02 8.80 8.80 8.94 8.75 8.62 8.48 8.62 8.68 8.60
Du Pont Du Pont General Electric Union Carbide ICI, USA Shell synthesis -
Hytrel4055 49,000 Lexan 101 Udel P-3500 300 P Kraton 1101
3.50 5.58 4.60 5.22 7.76 3.12 5.28 5.08 4.08 6.08
Estane 58105 Estane 58092 Kynar 301 Celcon M 9004 N0ryl731-701
PPO Rilsan BM No. 42848 Lexan RL1676 PVK Flexclad
Eastman
postulates. The first four postulates are implied by analogy with the use of the three-dimensional solubility parameter while the fifth postulate is new. Let us postulate the following. 1. The ability of a liquid or a liquid mixture t o dissolve any other material is determined by two and only two variables:
6, L 0 and6,
2
0
Thus, the solvent power of a liquid or liquid mixture can be represented by a point in (6f, 6,) space. 2. The two variables 6f and 6, for each liquid are related to the solubility parameter, 6, by 2 d2 = Ev - = 6, V
+ 6,
2
This plus the addition rule below allows 6 t o be represented as a vector with components 6f and 6, (Leigh, 1968). 3. Mixtures of N liquids may be represented in (&, 6,) space using the mixing rules:
where superscript M refers to the mixture, subscript i refers to liquid i, and & is the volume fractions of liquid i. These mixing rules indicate that the solubility
664 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 Table 2. Solubility and Insolubility of Materials in Pure Liquidsa liquid no.b 1 2 3 4 5 6 7 8 9 A B C D E F G H I
J K L
M N 0 P Q R S T
U V W X Y Z AA AB AC
AD AE AF AG AH AI
AJ AK AL
material styreneln-butylmethacrylate copolymer propylene oxide adduct of BA with FA branched of polymer B polystyrene rosin modified phenol-formaldehyde rosin modified phenol-formaldehyde poly( 1,2-propylene terephthalate) branched of polymer G poly(hexamethy1ene sebacate) sebacate block copolymer sebacate block copolymer polyamide polyester poly(hexy1ene cyclohexadicarboxylate) poly(hexy1ene terephthalate) poly(hexamethy1ene isophthalate) poly(2,2-dimethyl-l,3propylene isophthalate) poly(hexy1ene isophthalate) segmented polyurethane 58105 segmented polyurethane 58092 poly(viny1idenefluoride) polyacetal copolymer poly(pheny1eneoxide) copolymer poly(pheny1eneoxide) poly(undecanamide)Nylon 11 polycarbonate poly(N-vinylcarbazole) terephthalate polyester copolymer polyester copolymer elastomer polyester polycarbonate polysulfone poly(ether sulfone) polystyrenehutadiene block copolymer polymethacrylate/styrene copolymer Oil Soluble Red dye Heliogen Blue dye 2,4,7-trinitro-9-fluorenone liquidb no. material
A styreneln-butyl methacrylate copolymer B propylene oxide adduct of BA with FA C branched of polymer B D polystyrene E rosin modified phenol- formaldehyde F rosin modified phenol-formaldehyde G poly(l,2-propyelene terephthalate) H branched of polymer G I poly(hexamethy1ene sebacate) J sebacate block copolymer K sebacate block copolymer L polyamide
1 0 11 12 13 14 15 16 Ac AcN AcPH B BA CS2 CC14 CB C CYH CYHONE DBM oDCB DMA DMF DMSO 1E 2 1 1 1E 1E 1 1 1 1E 1 1E 1E 1 1E 3 1 E 2
1
1
1
2
1
1E
1E
1
1E
2
1 E 2 2 2 2 3
1 1 1 E 2 2 1 1 1 1 E l E l 1 1 1 1 E l E l E l
1 1 1
2 1E 2
1 1 1
1E 1E 1E
1E 1E 1E
1 1 1E
1E 1E 1
2 3 2
2
1 1 1 E l E l E l
1
2
1
1E
1E
1E
1
2
1 E 2
1
1
3
1
1
1E
1
1
1E
2 3
1 2
3
1 1 E 2
2
1 E 1
2 3
2 3
1 E 1 1E1E
3 3
1 2
1E 1E
1E 1E
1 3
1E 3
2 2
3 3 3 3 2 3 1 E 2 2 -
1 E 1 3 2 1 E 1 2 2 3 2 2 2 1 1 1 E 2 1 E 1 2 2
1 1 2 1 1
E - 1 E 1 1 2 1 E E 1 1 E 1 1
3 2 2 3 3
1 1 2 1 1
1E 1E 2 1
1E 1E 2 1E 1E
2 2 2 1 2
3 2 3 1 2
2 2 3 1E 3
2
3
3 2
3 2
3 3
3 3
3 2
3 1 E 3 1 E l E 3
3 2
1E
3 1E
3 2
3 2
3 3
2
2
2
2
2
2
2
1 E l E 3
2
2
2
2
2
2
2 3
3 3
2 2
3
1E2 3
2 3
2 3
1E1E 3 3 3 3
2 2
1E 2
1E 3
2 1E
2 1E
3 1E
2
3
2
3
3
3
3
3
2
2
2
3
1E
2
1E
2 2 3
2 2 3
2 2 2
3 2 1
2 2 -
3 2 1E
3 2 2
3 3 2 2 2 3 1 1 E 3
2 2 2
-
2
3 2 1E
1E 2 -
1E 2 3
2 2 3
3 3
3 3
2 2
1E2 -
1E 3
3
2 2
1 E 3 3 2
2 2
-
2 3
-
2 3
3 3
2 3 2
2 3 2
2 1 1
2 1 2
2 3 2
2 1E 2
2 3 3
2 1 2
1 3 1 3 1 E 3
2 1 1
1E 1E 1
2 1E 2
2 1 1
2 1E 1E
2 2 2
2
2
2
2
2
2
2
2
1 E 2
2
2
2
2
2
2
2 2 2 2 2
2 2 3 3 3
1 2 2 2 1 2 1 E 3 1E 1
2 2 3 3 1E
2 2 2 3 1E
2 2 2 3 1
1 2 1 2 1
1E 1E 2 2 1E
2 2 1E 3 1E
1 2 1 1E 2
1E 2 1E 1E 2
2 2 2 1E 2
2 3
1
1
E
2
1E2 1E3
1 E 2
-
1E 1E 3 3 1 E 2
1 1 1E 1E 1 1 1 E l E 1 2 2 3
1 1 E 2
2
2 1 E 2 1 E 1E 1E 2 2 1 1 1
3
3 3 3 E
-
1
1
3
1
1E
1E
1
1E
2
1E 1 l E l 3 2
1 1 2
2 3 -
1 1 1
1 1 1
1E 1E 2
1 1 1
1 1E 1
1E 1E 1E
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 1,4D EA ETB EDC HEP HEX MCYH MC MEK NM STY THF T l l l T C E TCEY XYL 1
1
1
1
2
2
1
1
1
1
2
1
3
3
1
2
1 1 1
1 1E 1E
2 1 1
1 1 1
3 2 2
3 2 2
1 1 1
2 1 2
1
1E
1
1
3
3
1
2
1
1
1
1
3
3
1
3
1
1
1E 3
2 3
1 1
3 3
3 3
1 1
3 3
1
1 1 2
1 1 2
3 3
3 3
1 1
3 2
2
1E 3 1E 2 2 2
2
3
2
2
E
1 1
2
1
1
1
2
1
1
1
E
l
2
1 2
1 1
E 1 1
l
1
1
2
1
1
E
1
2
E 1 1
1 1 1
2 1 1
1
1
1
1
1
1
1E
E 1 2 1E 1 E 2
2 2
1 1
2 3
1
1 1
1 1
2
2
1E 1E 2
1
3
1
1 1 1
1
3
1
1
E
1
1
E
2
1
3
3
3 1
3 E 3
1
2 2
1 1
1
1 1 E
1
1 1 2
Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995 665 Table 2 (Continued) liquidb no. material
M N 0 P Q R S T
U V W
X Y
Z AA AI3
AC AD AE
AF AG AH AI AJ
AK AL
polyester poly(hexy1ene cyclohexanedicarboxylate) poly(hexy1eneterephthalate) poly(hexamethy1ene isophthalate)
DMPI HI Estane 58105 Estane 58092 poly(viny1idenefluoride) polyacetal copolymer poly(pheny1ene oxide) copolymer poly(pheny1ene oxide) poly(undecanamide)-Nylon 11 polycarbonate poly(N-vinylcarbozole) terephthalate polyester copolymer polyester copolymer elastomer polyester polycarbonate polysulfone poly(ether sulfone) polystyrenehutadiene block copolymer polymethacrylate/styrene copolymer Oil Soluble Red dye Heliogen Blue dye 2,4,7-trinitro-9-fluorenone
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 1,4D EA ETB EDC HEP HEX MCYH MC MEK NM STY THF T l l l T C E TCEY XYL 1 1
1 1 E 2 1
1 1
3 -
3 3
1 1 1 1
3 2
3 2
3 2
3 1
3 3
3 3
1E 2 2 2 2 2 2
2 2 3 3 2 2 2
2 2 2 2 3 2 2
1E 1 3 2 3 2 2
3 3 3 3 3 3 3
3 3 3 3 3 3 3
2 2 2 2 3 3 2 2 2 1 E 1 3 2 1 1E 2 2 1E
3 3 3 3 3
2 2 2 1E 2 2 1E 2 2 1 E 2 2 2 3 3 1E 2 1
1E 1E 1E 1 2 1
1
1
1
1 1 1
1 3 2
1 1
2
1
-
E
3 3
E
2 -
1 1
1 1
1 1
1 1
1
1E 1E
3 2
3 3
3 1E
3 3 1E 2
3 2
3 1E
3 2
2 3 3 3 2 2 3
2 1E 1E 1E 2 2 2 1E 3 2 2 2 1 2 1
2 2 3 3 3 2
2 2 3 3 3 2 2
2 1 3 3 3 2 1
2 2 3 3 3 2 2
2 2 2 2 2
2 3 2 3 2
1 3 2 2 2
2 2 2 2 2
3 3 3 2 3 3
2 2 3 2 2 2 2
3 3 3 3 3
2 3 1 1 1
3 3 3 3 3
3 2 2 3 2
3 3 2 3 2
1E 2 2 2 2 1 1 2 1E
3 3 3 3 3 2
3 3 3 3 3 2
1 1 1 1 2 2
3 3 3 3 3 1
2 2 2 2 2 1E
2 2 2 3 2 3
2 2 2 2 2 1
2 1E 1E 1E 2 1
2 2 2 2 3 1
2 2 2 2 3 1
2 2 2 2 3 1
2 2 2 2 3 1
1
3
3
1
3
1
1E
1
1
1
1
1
1E
1 1
2 3 3
2 3 3
1 1 1
2 3 3
1 1 1
1E 3 1E
1 1 1E
1 1 1
1 1 2
1 1 2
1 1 2
1 1 2
E
3
1 1E
1 3 2 2 2 2
E
1
3
E
a Solubility code: 1 = soluble; 1E = external solvent (on border of polygon); 2 = swells or partially soluble; 3 = no visible effect; - = not tested. Liquids are defined by both numbers and symbols in Table 3.
parameter components of any mixture of two liquids 1 and 2 lie on a line between points (&, 6,d and (6n,6,~). 4. The probability of a material, A, being dissolved by a given liquid or liquid mixture, B, increases as the absolute differences between their solubility parameter components
16,
- 6,Bl
are decreased. 5 . If each of two liquids individually dissolves a material up to a certain concentration, then any mixture of the two liquids also dissolves that material at least up to the given concentration. Postulate 1 allows one to conclude that the range of solvents for a given material at a given concentration can be represented by a mapping of points in (df, 6,) space. In practice this mapping is an area, unless all the solvent points fall on one line. Postulate 2 provides a relationship between 6f and 6, and recognizes them as components of the vector S. Thus, if one of the solubility parameter components is determined for a liquid and its cohesive energy density is known, its point in (df, 6,) space is fmed. Even if the individual solubility parameter components are not determined, postulate 2 restricts its location in (6f, 6,) space to a point on the positive quadrant of a circle of radius 161 with its center at the origin. Postulate 3 provides a rule for predicting the solvent power for a mixture of liquids. This is one of the most useful applications of solubility parameters because the number of combinations of solvents, even at discrete ratios of solvents, is far too many for one to attempt in a given application. Postulate 4 is derived from the basic premise of the regular solution theory that solubility is more likely in
a mixture as the solubility parameters of the components of the mixture are more closely matched. Here, this premise is extended t o two solubility parameter components. However, the equation for the chemical potential resulting from the regular solution theory is not adopted because it generally does not provide a good description of the experimental solubility data. Instead, the solubility or insolubility in a series of test liquids are used t o determine the area in (Sf,6,) space that defines solubility for each material. Then postulate 4 can be used to estimate the solubility parameter components of the material from the center of the solubility area. One should recognize that exact matching of the solubility parameter components only assures solubility if the material is a liquid. If the material is a crystalline solid with a high heat of fusion and the temperature is well below the melting point, the material may still be insoluble in a liquid of identical solubility parameter components. In addition, highly cross-linked polymers cannot be dissolved by any liquid but the liquid may dissolve into the polymer to form a swollen gel. The polymer becomes more swollen by a liquid by more closely matching the solubility parameter components of the liquid t o that of the polymer. Postulate 5 is based on what has been observed by the author and others as long as the liquids do not chemically react with each other or with the material to form a compound, salt, or complex that can be isolated as a stable species from the mixture. Thus, postulate 5 still applies with a chemical reaction but one needs to consider the stable species that forms as an additional component of the mixture and determine its solubility parameter components. For instance, Burell (1955) used the system cellulose acetate, aniline, and acetic acid as an example where mixtures of liquids that
666 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995
individually are solvents did not dissolve a material. However, it is well-known that acids readily convert amines, like aniline, into their salts. Thus, one should consider this case as a mixture of cellulose acetate, aniline, acetic acid, and the aniline-acetic acid salt, rather than modifying one of the solubility parameter components, as did Chen and Lai (1979). Nevertheless, postulate 5 has real practical significance by enabling sharp boundaries of the area of solubility to be defined in (df, 6,) space. For instance, it eliminates all concave mappings of such areas. In addition, by combining postulate 3 and postulate 5, the results are polygonshaped areas of solubility, formed with linear borders between the external points of the areas.
Experimental Section Solubility tests were run using 32 liquids on 38 materials, 35 polymers and 3 dyes. The basic procedure was t o weigh a given amount of the material in a glass vial, add a given volume of the liquid or liquid mixture, screw on a cap with an aluminum insert, shake, and let stand at room temperature for 3-4 weeks. After checking and shaking each vial once a day and finding no change for a week, the solubility results were recorded. Crystalline polymers were given at least 6 weeks because of their slower rate of dissolution. Subsequent t o this work, it was found that the time could be greatly reduced in solubility tests by putting them on a shaker rack. Nevertheless, the concentrations used for this work was 0.1 g of polymer125 cm3 of liquid and 0.5 g of dye125 cm3 of liquid. The solubility results consisted in judging which of three groups to place each liquid-material combination: group 1(O),liquid completely dissolves the material; group 2 (W, liquid swells or partially dissolves the material; group 3 (XI, liquid does not appear to affect the material. This is much simpler than the six groups of Hansen (1967a) but is all that is required for most applications because one usually wants either a liquid that completely dissolves a material or a liquid that has no noticeable effect on .the material. In most cases the classification was obvious. However, in those cases where there was any doubt, a drop of the mixture was placed between a glass slide and a cover slip and observed at 600x under an optical microscope. Thus, particles that could not be resolved (less than 0.5 pm) were called soluble.
Evaluation of Components and Solubility Areas Solubility Parameter Components. Several methods were evaluated for estimating the field force solubility parameter component. The square root of the internal pressure as recommended by Bagley et al. (1971) offered the most promise. However, the twodimensional solubility parameter based on this estimate did not prove t o be a significantly better predictor of solubility than the three-dimensional solubility parameter of Hansen (1967a). One problem is the shortage of good internal pressure measurements of most liquids. In addition, the square root of the internal pressure seemed to produce values of 6f that were low for associated liquids. Several homomorph estimating approaches were also attempted, but it soon became clear that some empirical adjustments would always have to be made, as were done by Hanson (1967a) with an additional dimension to adjust.
In the end, Hansen’s dispersion solubility parameter components, dd, were used for initial estimates of &. Where possible, the overall solubility parameters of Hoy (1970) were used because of their high accuracy and consistency to calculate d,, using eq 11. Then the solubility data of Hansen (1967a) on 33 polymers and the present data on 38 materials were used to check for consistency in the two-dimensional solubility parameter diagrams for each material. The values of the solubility parameter components for each liquid were adjusted, when required, along their solubility parameter circles to best fit this large amount of data. After several trial and error cycles, the assignments grouped all the solvents for each material in an area that, except for a very few exceptions, excluded all nonsolvents. Fortunately, there are several features that confined the trial and error procedure. First, the location for each liquid is one point in (Sf,6,) space for all 71 materials. Second, the location of each liquid point is limited t o the positive quadrant of a circle, with a radius equal to the magnitude of the solubility parameter. Finally, the alkanes and carbon disulfide with no electronegative atoms or n electrons have zero complexing solubility parameter components. Thus, they are fixed on the 6f axis with no adjustments. These serve as reference points when evaluating df and 6, values for the other liquids while defining a solubility area for each material. The materials used for solubility tests in this study are listed in Table 1. The results of the solubility tests are in Table 2 for the 38 materials and 32 liquids. The assignments of the solubility parameter components that were consistent with these solubility data and that of Hansen (1967a,b) are the numbered liquids in Table 3. Hansen’s classification of 1; 2, 3, 4; and 5, 6 were taken to be equivalent to 1;2; and 3 respectively in the present study. Actually, four of the liquids, dibromomethane, dimethylacetamide, heptane, and methylcyclohexane, were not studied by Hansen. Of these, the two alkanes each have 6f equal to their overall solubility parameter, dd was provided by Hansen and Beerbower (1971) for dimethylacetamide, and the initial value of dibromomethane was estimated using a homomorph approach similar to Hansen (1967b). On the other hand, a number of liquids studied by Hansen were not included in this study. Of these, 18 assignments of twodimensional solubility parameter components were made, based upon Hansen’s data alone, and are listed in Table 3 as the unnumbered liquids. Of the 45 liquids in Table 3 with nonzero 6,, only 8 values of 6f (those indicated by footnote b ) remain at the initial guessed values (usually 6 d ) . The values of 6f of the six alcohols were all substantially higher than the equivalent values of Hansen’s d d . This is as expected because, as was discussed previously, the alcohols have significant contributions of dipole interactions owing to strongly hindered rotation caused by the association. Of course, the alcohols also have high values of 6, because of hydrogen bonding. Otherwise, for the other liquids about half of the remaining 6f were increased over the initially guessed dispersion solubility parameter component and about half were decreased. This also provides evidence that dipole interactions did not make large contributions to the df for unassociated liquids. The assignment of the solubility parameter components of the 50 liquids are shown graphically on a plot of complexing solubility parameter component versus field force solubility parameter component in Figure 1. These points remain fixed for all materials. Liquids with similar chemical functionalities are generally
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 667 Table 3. Solubility Parameter Components for Liquids no.
liquid name
1 acetone 2 acetonitrile 3 acetophenone aniline 4 benzene 1-bromonaphthalene n-butanol 5 n-butyl acetate 6 carbon disulfide 7 carbon tetrachloride 8 chlorobenzene 9 chloroform 10 cyclohexane cyclohexanol 11 cyclohexanone 12 dibromomethane 13 o-dichlorobenzene diethylamine diethyl ether 14 Nfl-dimethylacetamide 15 Nfl-dimethylfonnamide 16 dimethyl sulfoxide 17 1,4-dioxane dipropylamine ethanol 18 ethyl acetate 19 ethylbenzene 20 ethylene dichloride furan 21 n-heptane 22 n-hexane isophorone methanol 23 methylcyclohexane 24 methylene chloride 25 methyl ethyl ketone nitrobenzene nitroethane 26 nitromethane 2-nitropropane n-pentanol n-propanol propylene carbonate pyridine 27 styrene 28 tetrahydrofuran tetralin 29 toluene 30 1,1,l-trichloroethane 31 trichloroethylene 32 p-xylene
liquid symbol Ac AcN AcPH
6"
9.62 12.11 10.58 An 11.04 B 9.16 BN 10.25 ButA 11.60 BA 8.69 cs2 9.92 CC14 8.55 CB 9.67 C 9.16 CYH 8.19 CYHOL 10.95 CYHONE 10.42 DBM 10.40 oDCB 10.04 DEA 8.04 DEE 7.62 DMA 10.80 DMF 11.79 DMSO 12.93 1,4D 10.13 DPA 7.97 EtA 12.78 EA 8.91 ETB 8.84 EDC 9.86 FUR 9.09 HEP 7.50 HEX 7.27 ISOP 9.36 MtA 14.50 7.80 MCYH MC 9.88 MEK 9.45 NITROB 10.62 NE 11.09 NM 12.90 2-NP 10.02 PentA 11.12 PrA 12.18 PC 13.30 PY 10.62 STY 9.35 THF 9.52 Tet 9.50 T 8.93 11lTCE 8.57 TCEY 9.16 m 8.83
6f
6,
7.31 6.25 7.50b 9.51 8.55b 6.23 8.00 7.61 8.95b 1.95 9.70 3.31 9.42 6.78 7.43 4.50 9.92 0.00 8.55 0.25 9.39 2.30 8.6@ 3.01 8.19 0.00 9.48 5.48 8.50 6.03 9.25 4.74 9.66 2.74 7.40 3.14 7.05b 2.88 8.50 6.66 8.52b 8.15 9.00b 9.28 8.00 6.21 7.16 3.50 9.25 8.82 7.44b 4.90 8.73 1.40 9.39 3.00 8.82 2.20 7.50 0.00 7.27 0.00 7.78 5.20 9.04 11.35 7.80 0.00 9.03 4.00 7.72 5.45 9.47 4.80 7.50 8.17 7.95 10.16 7.36 6.80 9.51 5.76 9.34 7.82 8.20 10.47 9.36 5.00 9.13 2.00 8.22 4.80 9.35 1.72 8.83 1.30 8.25 2.33 8.88 2.25 8.82 0.40
Reference for 6 is Hoy (1970) except for liquids 12,15, and 23 from Lieberman (1962) and 16, 28, and 31 from Hansen (1967a). Originally estimated value. a
grouped together at locations approximately expected for measuring complex and field force interactions. For instance, aromatic and halogenated compounds are low in 6, and high in 6r; ketones and esters have moderate 6, and low df, except aromatic and naphthenic ketones, which have moderate 6r; and secondary amines and linear ethers have low 6, and 6f. The alkanols are located on a line a t high Q,and high 6f. If water is on this line, it should be expected t o be located at 6f = 8.12 and 6, = 22.08, based on 6 = 23.53 at 25 "C (Hoy, 1970). Polygon Solubility Areas. The solubility area for each material is defined as the minimum area in (df, 6,) space that includes all solvents but still meets the requirements of the postulates, such as any mixture of solvents is also a solvent. These conditions are met by connecting the external solvent points with line segments for each material to form polygon solubility areas. An example of a two-dimensional solubility parameter diagram is shown in Figure 2 for poly(pheny1ene oxide)
AfN
oyso EtA
EutA
DMA el.40
AcPH CYH'ONE
PytA CVHOL.
?*
TVF
NITROB
M.c
F
EQC
wR.*TCEV
c!
BY ODCB
111p
.
ETB
;
w v *Tat
T
1-
HEX HEP
01-
,
:
,
MCVH ,
:
,
c
:
'YL
C514
CVH 1
,
,
,
1
,
,
,
,
,
,
,
,
,
,
,
,
cs: * I
Figure 1. Two-dimensional solubility parameter space with a single point characterizing the solvent power of each liquid.
m
PARTIALLY SOLUBLE
X INSOLUBLE
u
NM X
DMSO * EtA
