Ind. Eng. Chem. Res. 1996, 35, 1115-1123
1115
Partition Coefficients and Polymer-Solute Interaction Parameters by Inverse Supercritical Fluid Chromatography Peter D. Condo,†,‡ Sheldon R. Sumpter,§,| Milton L. Lee,§ and Keith P. Johnston*,† Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712, and Department of Chemistry, Brigham Young University, Provo, Utah 84602
Inverse supercritical fluid chromatography (ISFC) is used to measure partition coefficients of five polar and nonpolar organic solids between supercritical CO2 and cross-linked poly(dimethylsiloxane) (PDMS) swollen with CO2. Polymer-solute interaction energies, which are determined from the partition coefficients, correlate with the heats of vaporization of the pure solutes. These interaction energies can be determined at ambient temperature for solutes that are too nonvolatile to study by inverse gas chromatography. Binary and ternary phase equilibria are modeled with lattice fluid theory including a term to account for the degree of polymer crosslinking. Experimental results indicate that solute adsorption on the support phase, which can be severe in packed columns, is negligible with the use of capillary columns. Introduction Compressed fluids, including supercritical fluids (SFCs), have been used in polymer separation and purification processes such as extraction and fractionation (Shim and Johnston, 1989, 1991a,b; Watkins et al., 1991; Hasch et al., 1993; McHugh and Krukonis, 1994; Xiong and Kiran, 1994). These fluids have also been utilized to facilitate impregnation of polymers with additives (Sand, 1986; Berens et al., 1988; Howdle et al., 1994) and to condition polymer membranes (Raymond and Paul, 1990; Pope and Koros, 1992). In the Unicarb spray painting process (Hoy and Donohue, 1990), supercritical CO2 is used as a thinner in place of hydrocarbons, to decrease VOC emissions by up to 75%. Several innovative processes have been developed which utilize compressed fluids in the production of polymeric materials such as microcellular foams (Cha and Suh, 1992; Dixon et al., 1993, 1994; Goel and Beckman, 1994), gels (Pradhan and Ehrlich, 1995), fibers (Matson et al., 1987; Lele and Shine, 1992; Dixon and Johnston, 1993; Dixon et al., 1993), and microparticles (Tom and Debenedetti, 1991; Dixon et al., 1993, 1994; Randolph et al., 1993). In extraction and impregnation processes involving polymers, the partitioning of a solute(s) between the polymer and fluid phases is a key property for design. In many of these processes, the polymer is insoluble in the compressed fluid, although exceptions to this generalization exist (Petersen et al., 1987; Tom and Debenedetti, 1992). In contrast to the limited solubility of most polymers in compressed fluids at moderate temperatures and pressures, compressed fluids may be appreciably soluble in some polymers (Wissinger and Paulaitis, 1987; Shim and Johnston, 1989; Briscoe and Zakaria, 1991; Garg et al., 1994). Most of the extraction and impregnation examples in the literature which utilize compressed fluids simply characterize the polymer product to determine if the extraction or impregnation was successful (Sand, 1986; McHugh and Krukonis, 1994). Fundamental studies to †
The University of Texas at Austin. Present address: 3M Center, St. Paul, MN 55144-1000. § Brigham Young University. | Present address: E. I. du Pont de Nemours Co., Inc., DuPont Agricultural Products, Global Technology Division, Experimental Station, Wilmington, DE 19800. ‡
0888-5885/96/2635-1115$12.00/0
determine the important variables to be utilized in the design of extraction and impregnation processes are rare due to experimental challenges (Olesik et al., 1987). Both kinetic and thermodynamic issues are important (Berens et al., 1988; Shim and Johnston, 1989, 1991a,b). More studies are needed to provide a basis for efficient design of extraction and impregnation processes by control of such factors as selectivity in extraction and degree of loading in impregnation processes. Berens et al. (1988) used a gravimetric technique to study the kinetics and thermodynamics associated with solute impregnation of glassy polymers facilitated by pressurized CO2. They proposed that CO2 solubility in polymers can be appreciable and that CO2 can be an effective plasticizer for some glassy polymers. This idea has been examined both experimentally and theoretically, and a new concept of retrograde vitrification has been discovered (Condo et al., 1992, 1994). Plasticization of a polymer with CO2 was shown to increase solute diffusivities in polymers by a factor greater than 106, thus removing significant kinetic limitations to solute impregnation of the polymer (Kalospiros and Paulaitis, 1994). Shim and Johnston (1989, 1991a,b) used inverse supercritical fluid chromatography (ISFC) in a thermodynamic study of solute partitioning. Both the finite and infinite dilution concentration regimes were studied. In the finite concentration regime, a maximum in the solute sorption in the polymer was measured as a function of CO2 pressure. Interaction parameters determined at infinite dilution were used to calculate the phase behavior for the polymer-solute-SCF system over the entire composition range. Several experimental advancements in the ISFC technique were introduced by Shim and Johnston in order to determine thermodynamic properties. These include corrections for polymer swelling due to sorption of the compressed fluid, and for solute adsorption on the chromatographic support phase, in the packed columns. Several research groups have used lattice models to describe the thermodynamics of the ISFC system (Martire and Boehm, 1987; Shim and Johnston, 1989; Roth, 1992a,b). Martire and Boehm (1987) used lattice fluid theory for both the polymer and fluid phases. Yan and Martire (1992) have expanded their theoretical treat© 1996 American Chemical Society
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Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996
ment of chromatography to treat shape selectivity by incorporating solute shape as well as anisotropy of the stationary phase (e.g., liquid crystalline polymers). Roth (1992a,b) applied lattice fluid theory to Shim and Johnston’s experimental results for the poly(dimethylsiloxane) (PDMS)-CO2-naphthalene system. These models did not take into account the cross-linked nature of the polymer. All the experimental and theoretical ISFC studies described above consider only nonpolar solutes. The objective of this study is to advance the ISFC technique to provide for efficient and reliable determination of thermodynamic interaction energies for multicomponent systems consisting of polymer, SCF, and solute(s). Capillary columns are used in order to remove the serious problem of solute adsorption, which takes place on packed column support phases, particularly for polar solutes. Partition coefficients and polymer-solute interaction parameters are determined for polar as well as nonpolar solutes. The phase equilibrium thermodynamics of multicomponent systems is developed by using lattice fluid theory including a term to account for the cross-linked nature of the polymer. Theory The theory derived below is a generalization of lattice fluid theory (Sanchez and Lacombe, 1976, 1978) to multicomponent systems with the incorporation of the effects of polymer cross-linking (Panayiotou and Sanchez, 1992) and bond flexibility (Flory, 1956). Consider a system of N1 molecules each consisting of r1 segments, N2 molecules each consisting of r2 segments, ..., Nm molecules each consisting of rm segments, and N0 holes. Employing the mean-field and Flory approximations (i.e., large z), the number of system configurations is given by (Sanchez and Lacombe, 1976)
Ω)
( ) ∏( ) (δi/ωi)
N0 m
1
1 - F˜
i)1
Ni
φiF˜
(1)
where δi is the chain flexibility parameter (Flory, 1956; Gibbs and Di Marzio, 1958; Sanchez and Lacombe, 1976) and ωi is an attrition factor
( ) ( )
δi ) z
z-2 fi
(ri-2)fi
1 1 - fi
(ri-2)(1-fi)
; where ωi )
2eri-1 ri (2)
Here the chain flexibility parameter is derived for the general case of a semiflexible chain. δi is the number of internal configurations available to a semiflexible chain molecule of ri-mers in free space when fi(ri - 2) bonds in a type i molecule are in “flexed” or high-energy states and (1 - fi)(ri - 2) bonds are in a low-energy state (for example, gauche and trans states). In a completely filled lattice, δi is reduced by a factor of ωi caused by inter- and intramolecular interference (excluded volume). The fraction of occupied sites (or the reduced density), F˜ , is defined by m
riNi ∑ i)1 F˜ ) m
N0 +
∑ i)1
riNi
≡
rN N0 + rN
(3)
where N, xi, φi, and r are given by: m
N)
Ni; ∑ i)1
xi )
Ni m
Ni ∑ i)1
m
r)
∑ i)1
xiri
riNi
; φi )
(4)
riNi ∑ i)1 m
1
or
m
) r
φi
∑ i)1 r
(5)
i
The mean-field system energy E is a combination of inter- and intramolecular energies: m
E ) -rNF˜* +
Ni(ri - 2)fi∆i ∑ i)1
(6)
∆i is the increase in intramolecular energy that accompanies the “flexing” of a bond in a type i chain molecule. It is assumed for simplicity that this is a twostate molecule (z - 2 of high energy and 1 of low energy). The creation of a vacancy in component i requires an energy * ii. The creation of a vacancy in a multicomponent mixture requires an energy *. In a mean-field approximation: m
* )
∑ i)1
m m
∑ ∑φiφjXij j)1 i>j
φi* ij - kT
(7)
Xij ) (* ii + * jj - 2* ij)/kT
(8)
1/2 * ij ) ζij(* ii* jj)
(9)
The equilibrium number of flexed bonds is determined by finding the maximum term in the canonical partition function Ωe-E/kT to yield the familiar Boltzmann expression (Flory, 1956):
fi )
(z - 2) exp(-∆i/kT) 1 + (z - 2) exp(-∆i/kT)
(10)
When ∆i ) 0, fi ) (z - 2)/(z - 1) and δi ) z(z - 1)ri-2 for the case where the chain is fully flexible. The system volume, V, is given by:
V ) (N0 + rN)v*
(11)
We arbitrarily choose the nonlinear relation for v* (Panayiotou, 1986): m m
v* )
∑ ∑φiφjv*ij j)1 i)1
(12)
where v*ii is the characteristic segment volume of component i. A linear relation for v* has also been used extensively (Sanchez and Lacombe, 1976). For v* ij (i * j) we arbitrarily chose the combining rule as follows (Panayiotou, 1986):
(
)
1/3 1/3 v* + v* ii jj v* ij ) 2
3
(13)
We choose our mixing rules such that ri is the same in the pure state and in the mixture (Panayiotou, 1986). This leads to the following relation for the mass fraction
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1117
N0 (Panayiotou and Sanchez, 1992):
of component i
1
wi )
m
( )( )( )
(14)
F*j v* φj j
∑ j)1 F*
[
yi ) φir/ri
(15)
T ˜ and P ˜ are the reduced temperature and pressure given by:
and the specific closed-packed volume, v*sp, by
v*
T ˜ ) T/T*; T* ) */k
(23)
P ˜ ) P/P*; P* ) kT*/v* ) */v*
(24)
F˜ ) F/F*
(25)
(16)
m
F* ∑ j v* j φj j)1 The size parameter r is related to the molecular weight M by:
Mi MiP* i ) F*i v* F* kT* i i i
The three equation of state parameters T*, P*, and F*, which can be determined from experimental PVT data, completely characterize the pure components. In the case of an un-cross-linked or lightly cross-linked polymer, r2 f ∞, and the last term in the bracket is zero, and one obtains the familiar lattice fluid equation of state (Sanchez and Lacombe, 1976):
(17)
G ) GLF + GEL
(18)
µLF i kT
[ ∑( ) ( ) ∑( ) ]}
) ln φi + 1 -
ri r
(ri - 2) ln(1 - fi) +
GLF ) rN -F˜* + Pv*v˜ + kT (v˜ - 1) ln(1 - F˜) +
r
ln(2/z) - 1 ln F˜ + 1 +
+ r
m
φi
i)1
ri
ln
φi
m
φi
i)1
ri
+
ri
(ri -
The elastic contribution to the free energy is given by (Panayiotou and Sanchez, 1992):
kT
G
)
({
2N ∆τ ]} { Ve }
3 -kT ln Rs3exp - (Rs2 - 1) 2
[
N2
2
)
()[ ri
)
2(f-1)N2/f
(26)
[
m m
φjXij - ∑ ∑φjφkXjk] + ∑ j)1 k)1j>k
˜ 2 riv˜ P
]
m
∑
T ˜ v*j)1
φjv* ij - 1 -
riF˜ T ˜i
+ ln F˜ +
() 2
riz
(27)
The elastic contribution is given where i * 2:
µEL i
EL
m
+ riF˜[
ri(v˜ - 1) ln(1 - F˜) + ln
(19)
2) ln(1 - fi)
)]
1 F˜ ) 0 r
Chemical Potential. The lattice fluid contribution to the chemical potential of component i, µLF i , is obtained by differentiating the lattice fluid Gibbs free energy with respect to the Ni:
The lattice fluid contribution is given by:
1
(
[
F˜2 + P ˜ +T ˜ ln(1 - F˜) + 1 -
Gibbs Free Energy. It is assumed that one of the components in the system, namely, component 2 is a cross-linked polymer. Following Panayiotou and Sanchez (1992), it is assumed that the lattice fluid and elastic contributions to the Gibbs free energy are additive:
{
)]
(
The mole fraction of component i is given by
ri )
)
1 F˜ + r φ2F˜ 2 2 R - + 1 ) 0 (22) r2 s f
v*i φi
i
v* sp )
(
F˜2 + P ˜ +T ˜ ln(1 - F˜) + 1 -
r2
2
φ2 Rs -
2 f
+1
][ ∑ 2
m
v*j)1
]
φjv*ij - 1
(28)
Partition Coefficient. The partition coefficient, Ki, is defined as the ratio of the concentration of i in the polymer CiP, to that in the fluid, CiF
Ki ) CiP/CiF
(29)
(20) which may be rearranged to where Rs3 is the degree of swelling. The functionality of the cross-linking sites (f) is set equal to 3 in this study. The pre-cross-linked PDMS contains 1% vinyl groups which serve as cross-linking sites. The term Rs3 is, assuming no solvent present during cross-linking:
Rs3 )
rNv˜ v* v˜ v* V ) ) V0 r2N2v˜ 2v* φ2v˜ 2v* 2 2
(21)
Equation of State. The equation of state is obtained by differentiating the Gibbs free energy with respect to
Ki )
( )( ) yiP vF yiF vP
(30)
where vF and vP are the molar volumes of the respective phases. An expression for the mole fraction of component i in the fluid phase (yiF) may be obtained by solving the chemical potential expression (27) for φiF. Substituting the result into eq 15 to convert from segment fraction to mole fraction yields (Panayiotou, 1986; Martire and
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Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996
Figure 1. Schematic diagram of the supercritical fluid chromatographic equipped with time-split injection system: A, solute saturator; R, integral restrictor; S, Valco sampling valve.
Boehm, 1987; Sanchez and Rodgers, 1990):
F
yi )
() { rF ri
exp
µLF i kT
-1+
()
ln(1 - F˜F) - ln m m
2
riz
∑ ∑φj φk Xjk] k)1j>k F
F
riF˜F
ri +
T ˜i
F
r
the switching valve. A 20 ms time-split was used to inject only a small portion of the sample loop. The solutes studied were naphthalene (Aldrich 18450-0, 99+%), phenanthrene (Aldrich P1140-9, 98+%), pyrene (Aldrich P18551-5, 99+%), 2-naphthol (Aldrich 185507, 99%), and benzoic acid (Fisher A-65). The capillary column was coated with polymer using the static coating method (Kong et al., 1984; Condo, 1993). n-Pentane was chosen as the solvent for its ability to dissolve the polymer and its high volatility for ease of removal from the column. The polymer was cross-linked using 2,2′-azobis(2-methylpropane) (Wako, VR-160) (Condo, 1993). The azo compound was chosen as the cross-linking agent over more traditional peroxides in order to decrease polymer activity due to the cross-linking agent (Wright et al., 1982). In addition, SE-33 poly(dimethylsiloxane) contains 1% vinyl groups to facilitate cross-linking. The solute partition coefficient may be written from eq 29 as
- ri(v˜ F - 1) ×
K3∞ )
m
- ln F˜F - riF˜F[
[
˜F 2 riv˜ FP T ˜
F
v*
m
φjFXij ∑ j)1
]
φjFv*ij - 1 ∑ j)1
F
}
(32)
From the ISFC experiment the capacity ratio, k3∞, is obtained (Petersen and Helfferich, 1965)
k3∞ )
-
(ri - 2) ln(1 - fi)
( )( ) n3P∞ VF n3F∞ VP
(31)
Performing a similar manipulation on the chemical potential of component i in the polymer phase and substituting yiF and yiP into eq 30 yields the partition coefficient, Ki. Experimental Section The supercritical fluid chromatograph (Lee Scientific (Dionex) Model 501) was equipped with computercontrolled time-split injection and a flame ionization detector (FID) (see Figure 1). Oven temperature was maintained to within 0.1 °C, and pressure was controlled with a computer-controlled syringe pump. The pressure was measured at the column inlet with a pressure transducer (Sensotec, Model GM) which offers (0.03% accuracy. Measurements at column inlet and outlet indicate negligible pressure drop (
