and High-Pressure Capillary Column Inverse Gas Chromatography

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Macromolecules 2004, 37, 10134-10140

Probing Multicomponent Thermodynamic Effects by Low- and High-Pressure Capillary Column Inverse Gas Chromatography John M. Zielinski,* Roderick Fry,† and Michael F. Kimak Air Products and Chemicals, Inc., 7201 Hamilton Blvd., Allentown, Pennsylvania 18195 Received July 15, 2004; Revised Manuscript Received October 6, 2004

ABSTRACT: The capillary column inverse gas chromatography (CCIGC) technique has been applied from ambient pressure to ∼1100 psia to measure partition and diffusion coefficients in ternary systems containing poly(vinyl acetate) (PVAc). The ambient pressure experiments examined the effect of water and methanol on the thermodynamic interactions between toluene and PVAc. Toluene interactions with PVAc were unaffected by the presence of methanol but were greatly suppressed in the presence of water. A newly developed high-pressure CCIGC capability was benchmarked with the binary system vinyl acetate monomer (VAM) and PVAc, using an inert gas, i.e., helium, as the high-pressure carrier gas by comparing the data measured with traditional low-pressure CCIGC measurements. Variable-temperature, highpressure CCIGC experiments were subsequently performed with VAM using carbon dioxide and ethylene as the carrier gases. The VAM-PVAc partition coefficients were found to decrease appreciably in the presence of CO2 and ethylene while the diffusion coefficients exhibited a marked increase in VAM diffusion rates.

Introduction The sorption of solvents into polymers, even at low solvent partial pressures, can drastically alter the matrix glass transition temperature and the molecular mobility within polymer-solvent systems. Swelling a polymer with a high-pressure gas serves to plasticize the material in much the same way that organic solvents do and has similar effects on molecular mobility. In addition to the increase in molecular diffusion rates, the presence of a component can appreciably affect the thermodynamic interactions between the other constituents within the system. In the case of a devolatilizing unit, a nontoxic chemical species that both increases the molecular transport rate of the contaminant to be removed and simultaneously reduces the partition coefficient between the contaminant and the matrix material would be considered an ideal devolatilization facilitator as long as it can be easily extracted from the system. As a highly soluble fast diffusing small molecule, carbon dioxide is often a natural candidate for such a devolatilization aid. Since the use of high-pressure or supercritical conditions continues to be explored as a simple means of manipulating polymer properties and facilitating polymer processing, the development of experimental techniques able to measure multicomponent thermodynamic and transport data at pressures and temperatures of industrial importance is extremely valuable. Particularly, many novel polymer synthesis schemes involve the use of supercritical media. Capillary column inverse gas chromatography (CCIGC) has served as such a tool since its initial application to polymer systems. CCIGC is a versatile tool for high-throughput collection of partition and diffusion coefficient data for multiple solvents within a polymer of interest. In addition to the infinite dilution regime for which it was initially developed,1-7 CCIGC has already been ex† Present address: Department of Chemistry, The Pennsylvania State University. * To whom correspondence should be addressed.

tended to the finite concentration regime,8-10 where (1) polymer-solvent VLE and diffusion data can be examined at finite solvent concentrations and (2) the effects of one solvent (present in finite concentration) on the partition and diffusion coefficient of another solvent (present in trace quantities) can be readily examined. The capillary column inverse gas chromatography (CCIGC) experiment provides a valuable method of obtaining solubility and diffusivity data for polymerpenetrant systems. Conventional methods for measuring phase equilibria and diffusion coefficients, e.g., gravimetric and volumetric techniques, rely on bulk equilibration. These methods, however, become very difficult to apply to polymer-solvent systems when the solvent is present in vanishingly small amounts. The low diffusivity value, characteristic of polymer-solvent systems, is at the origin of the experimental difficulties encountered with classical techniques. As a consequence, only a small amount of diffusivity data for polymer solutions in the highly polymer concentrated region is available in the literature. This region, however, is of primary interest in the polymer industry, particularly in the manufacture of polymer films that often must be free of volatile matter for environmental and safety reasons. In addition, standard gravimetric and volumetric techniques have been developed to examine binary systems. Extension of these techniques to investigate vapor-liquid equilibria (VLE) and transport processes within multicomponent polymeric systems has been experimentally challenging. Although the applicability of CCIGC has been repeatedly demonstrated at infinite dilution1-7,11-19 and finite concentrations,8-10 the technique has thus far only been applied at ambient pressures and only in limited studies in the finite concentration regime. Furthermore, the ability to perform high-pressure chromatography measurements has seen limited exposure within the literature,20,21 and CCIGC experiments investigating the effects of a solubilized gas on phase equilibria and transport properties of a solvent have never been reported. With the increasing application of supercritical

10.1021/ma048556k CCC: $27.50 © 2004 American Chemical Society Published on Web 12/01/2004

Macromolecules, Vol. 37, No. 26, 2004

Multicomponent Thermodynamic Effects 10135

Figure 2. Schematic of gas chromatograph setup for highpressure CCIGC experimentation.

Figure 1. Gas delivery unit for high-pressure CCIGC experimentation.

media to develop novel polymers and production methods, and the continued interest of using CO2 as an agent for enhancing molecular transport of small molecules in polymers,22-24 the development of high-pressure CCIGC techniques to measure data at polymer processing conditions is of significant industrial and academic relevance. In this work, we apply CCIGC to probe thermodynamic effects in ternary systems containing PVAc. Specifically, at ambient pressures we examine toluene/ PVAc interactions in the presence of water and methanol, while at elevated pressures we investigate the effects of CO2 and ethylene on the interactions of vinyl acetate monomer (VAM) with PVAc. The modifications to the standard CCIGC equipment required to perform high-pressure CCIGC experiments are highlighted. Experimental Section The experimental apparatus was fabricated from an HP 5890 series II supercritical fluid chromatography (SFC) unit. There are two main components to this system: (1) the gas delivery unit (Figure 1) and (2) the high-pressure chromatograph (Figure 2). The gas delivery unit contains a gas cylinder, three high-pressure gas regulators, a ballast tank, and a relief valve. The need for a second regulator (R2) was realized during experimentation with ethylene as the carrier gas. As long as a helium cylinder is in use, R2 is unnecessary. R1 is capable of delivering gas at constant pressure from a cylinder of gaseous helium, but a cylinder containing supercritical ethylene introduces complications. As a result, R1 was unable to deliver a constant pressure of ethylene, as evidenced by difficulties establishing a baseline in the CCIGC experiments. Insertion of R2 enables complete control over the delivery pressure of ethylene. The ethylene upstream of R2 is already in the gas phase, and therefore the regulator functions as expected in delivering a constant pressure of ethylene carrier. The third high-pressure regulator, R3, is used to deliver

ethylene to the reference line of the thermal conductivity detector (TCD), and the relief valve is present to prevent overpressurization of the reference line. The ballast (B1) is in place to help absorb any fluctuations in the delivery of carrier pressure from R1 and is bypassed when flowing helium. The entire gas delivery system is enclosed in a N2 vented Lexan box for safety considerations while flowing the flammable ethylene carrier. The high-pressure chromatograph contains an injection assembly, programmable temperature controller with heating tape, needle valve flow restrictor, GC oven, pressure transducer, capillary column, back-pressure control valve (BPCV), and a TCD. The injection assembly employs a Rheodyne sixport valve for high-pressure injections onto the column. A 0.5 µL sample loop on the injection valve is purged with the solute, and an injection is made as this sample loop is turned onto the column. After the injection, the valve is returned to its original position, and the carrier continues to flow through the bypass loop of the six-port valve. The programmable temperature controller and heating tape are used to keep the tubing between the injection valve and the column at a constant temperature of 80 °C. This prevents broadening of the elution profiles, which would occur if a cold section of tubing were present downstream of the injection point. The needle valve flow restrictor, NV1, is used to make minor adjustments to the flow of carrier gas. The GC oven controls the temperature for the experiment and is never heated above 80 °C (maximum allowable working temperature for the BPCV). The pressure transducer is used, in conjunction with a series of valves, to measure the pressure drop across the column. In general, this pressure drop is less than 1% of the pressure upstream of the column. The capillary column is heated within the GC oven and may be used with any coatable stationary phase. The BPCV (100-1500 psia obtained from Varian Inc.) is the key addition for doing high-pressure CCIGC. This component consists of a diaphragm valve that is tightened as the upstream pressure is increased in order to maintain a constant flow over the column. The dead volume of the BPCV is 1.6 µL. A thermal conductivity detector was employed because of its ability to function with flammable carrier gases as well as helium and CO2. The flow rate is monitored using a digital gas flowmeter at ambient pressure which is corrected for expansion of carrier from column pressure to ambient. The carrier gas velocity is measured by injecting an inert gas and determining its retention time. The carrier gas velocity did not change over the length of an average CCIGC experiment. The fused silica capillary column used in the CCIGC system was supplied by Restek (Bellefonte, PA) and coated with a 10 µm thick coating of PVAc (Aldrich Chemical Co., 167 kDa weight-average molecular weight) at the Center for the Study of Polymer-Solvent Systems at Penn State University. The column was 1705 cm in length with an inner diameter of 0.053 cm. Toluene, methanol, methyl acetate, and vinyl acetate monomer (VAM) were obtained from Sigma Aldrich. For the carrier gases used in this study, helium (UHP Grade) and

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carbon dioxide (Instrument Grade) were purchased from AirGas while ethylene (Tri-gas UHP Grade) was acquired from Matheson.

Results and Discussion The advent of CCIGC experimentation has provided a reliable means by which to probe polymer-solvent thermodynamic interactions, diffusion rates, and plasticization effects. The ease with which a variety of solvents can be examined, along with the rapid means of data evaluation available, renders CCIGC a highthroughput means of experimentation compared to conventional techniques. In addition, this technique lends itself to examine both the infinite dilution regime, i.e., the pure polymer limit, which is notoriously difficult to probe by conventional gravimetric and volumetric techniques, and in the realm of finite solvent concentrations. While extending CCIGC technique to employ high-pressure gas carriers was of particular interest to us, we first confirmed that our experimental protocols were consistent with previous studies focused on VLE and diffusion measurements by performing studies at low pressures at both infinite dilution and finite concentration. Low-Pressure Infinite Dilution Measurements. The most commonly conducted CCIGC experiments are performed at ambient pressures with trace amounts of injected solute.6,7,11-18 This infinite dilution regime is readily examined as a function of temperature, and experiments can be performed with a standard gas chromatograph. The principle behind this experiment is based upon the distribution of a volatile solute between a mobile gas phase and a stationary polymer phase. In a typical CCIGC experiment, a trace amount of solute ( methanol > methyl acetate > VAM > toluene. These data compare well with literature values4,7,9 and suggest that our experimental protocols are sound. The utility of infinite dilution CCIGC experimentation is also depicted in Figure 5 where we complement some diffusion data for the system MeAc/PVAc with data measured using a quartz spring McBain gravimetric apparatus equipped with a position-sensing laser for monitoring spring displacement. The initial diffusion coefficients reported were measured at MeAc concentrations of approximately 10 wt % in the polymer phase. At this high MeAc loading, the mutual binary diffusion coefficient is approximately 2 orders of magnitude higher than that probed at infinite dilution by the CCIGC technique. This strong dependence of D on solvent concentration clearly illustrates why the initial drying of a polymeric solution is accomplished with ease while extracting the last few molecules of solute (or contaminant) from an essentially dry polymer film requires a great deal of effort. For completeness, the gravimetric sorption isotherms measured for MeAc/ PVAc are included in Table 1. Low-Pressure Finite-Concentration Measurements. The measurement of solubility and diffusivity


Figure 3. Ambient-pressure infinite-dilution partition coefficients vs temperature for methanol, methyl acetate, water, toluene, and vinyl acetate monomer in PVAc.


Figure 5. Comparison of methyl acetate/PVAc binary diffusion coefficients measured by infinite dilution CCIGC experimentation and by gravimetric sorption at 70 °C. These data illustrate the utility of CCIGC in measuring data at conditions unachievable by conventional experiments. The solid line is simply a guide for the eye. Table 1. Gravimetric Sorption Data for Methyl Acetate in PVAc: MeAc Weight Fraction vs Activity T ) 65 °C

Figure 4. Ambient-pressure infinite-dilution diffusion coefficients vs temperature for methanol, methyl acetate, water, toluene, and vinyl acetate monomer in PVAc.

parameters in polymer-solvent systems at finite concentrations is traditionally performed by gravimetric sorption25 or volumetric analyses.26 Chromatographic techniques have been used to probe polymer-solvent phase equilibrium characteristics since the early 1970s;1,8 however, application of the technique to the measure-

T ) 70 °C

ω1

P/P0

ω1

P/P0

0.2604 0.1976 0.1496 0.1172 0.0904 0.0724 0.0471 0.0272

0.7389 0.6283 0.5188 0.4227 0.3442 0.2802 0.2060 0.1103

0.0836 0.1074 0.1400 0.1841 0.2308 0.0110 0.0232 0.0399 0.0661

0.2842 0.3640 0.4541 0.5494 0.6354 0.0553 0.0947 0.1490 0.2326

ment of polymer-solvent mutual diffusion coefficients has only recently flourished.9-18 The expansion of CCIGC to finite concentrations has been accomplished8-10 by saturating the carrier gas with a volatile component and passing this saturated gas mixture through the capillary column, thereby equilibrating the polymer phase with a finite concentration of solvent. The carrier gas is typically doped with solvent vapor by passing it through an accurately temperaturecontrolled saturation vessel filled with liquid solvent. The temperature at which the liquid solvent is maintained regulates the partial pressure of solvent (P) in the gas phase of the capillary column, while the column temperature establishes the saturation vapor pressure (P0). The ratio of these two pressures, excluding nonideality considerations, determines the solvent activity. In general, the larger the value of P/P0, the greater will be the solvent loading in the polymer phase. Finite concentration experiments can be conducted by injecting a solute into a carrier gas stream that is saturated by the same solute or a completely different solvent. In the first case, the experimental results acquired are akin to traditional sorption experiments

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Figure 7. Toluene-PVAc partition coefficients, measured by CCIGC, in the presence of water at 80 °C (2) and methanol at 60 °C (4).19 Methanol does not affect the partitioning of toluene in PVAc, while water greatly hinders the interactions of toluene with PVAc.

Figure 6. Comparison of methanol/PVAc binary diffusion coefficients measured by infinite-dilution and finite-concentration CCIGC experimentation and by gravimetric sorption.

employing a binary polymer solvent pair, while the latter methodology opens the possibility of examining multicomponent effects, e.g., observing the effect that one solvent has on the thermodynamic interactions of another solvent with a polymer. In Figure 6 we compare methanol-PVAC mutual diffusion data measured by CCIGC as well as by gravimetric sorption (GS).27,28 As in Figure 5, the CCIGC data measured at infinite dilution nicely complement the finite concentration data. The concentration dependence of D for methanol-PVAc is clearly much weaker than that exhibited by the MeAc-PVAc system (Figure 5). This is expected on the basis of free volume theory29 due to the relative size of methanol vs MeAc. In addition, at the higher temperatures PVAc is appreciably above its glass transition temperature (Tg ∼ 30 °C) and therefore possesses ample free volume. Consequently, the additional free volume introduced by the methanol does not influence the molecular diffusion rate.29 An example of applying CCIGC at finite concentrations to probe multicomponent effects is depicted in Figure 7, where the effects of water and methanol on the toluene-PVAc partition coefficient are illustrated. Literature data from Surana19 reveal that the toluenePVAc partition coefficient is virtually unaffected by the introduction of methanol. In contrast, the addition of a small quantity of water into PVAc dramatically hinders the interactions of toluene with PVAc. This surprising result clearly illustrates that finite concentration CCIGC provides a valuable tool for examining multicomponent thermodynamic interactions. High-Pressure Infinite-Dilution Measurements. High-pressure CCIGC experiments are performed in much the same way as those at low pressures. In addition to the requirement of a back-pressure regulator for controlling the pressure and flow rate, the injection system must also be modified. The rubber septum found on typical chromatographs will not withstand high

Figure 8. Comparison between experimental and regressed elution profiles for vinyl acetate monomer (VAM) on a PVAc column at 1121 psia and 75 °C with a helium carrier at 7.4 cm/s.

pressures. Consequently, a high-pressure injection valve is employed by turning the sample injection into the flow path of the carrier gas. A typical elution profile observed in the infinite dilution regime is provided in Figure 8 for VAM injected into a helium carrier stream and passed through a PVAc column. The system pressure was 1121 psia, the temperature was maintained at 75 °C, and the carrier gas velocity was 7.4 cm/s. Included in the figure is the fit of experimental data with the CCIGC model (eqs 1 and 2), which illustrates the excellence by which these experimental curves can be represented. For this experiment the R and β values were 0.35 and 1.35, indicating a mild degree of asymmetry in the peak shape. Infinite dilution solubility and diffusivity data for VAM on PVAc with a helium carrier, over a range of pressures, were successfully obtained using the highpressure CCIGC method. Figure 9 demonstrates the independence of the VAM-PVAc partition coefficient with respect to helium pressure at 75 °C. Since helium is essentially insoluble in PVAc, it is expected that the solubility of VAM in PVAc remains constant even at



Figure 9. Infinite dilution partition and diffusion coefficients for vinyl acetate monomer in PVAc at 75 °C as a function of helium pressure. Since helium is presumed to be a noninteracting gas, no pressure dependence of K and Dp is expected. The slight reduction of Dp may be attributed to a mass transfer resistance.

elevated pressures. The slight decrease in D with increasing pressure, however, is most likely due to the formation of a mass transfer boundary since there are many more molecules of helium present to impede the migration of VAM to the polymer surface. The effect of the boundary increases as helium pressure increases, resulting in slightly reduced values for the polymer phase diffusion coefficient for VAM in PVAc. High-Pressure Finite-Concentration Measurements. In addition to the infinite-dilution data, highpressure measurements infinitely dilute in one component using a second solute in finite concentration as the carrier gas have been successfully obtained. In these experiments, ethylene and CO2 were employed as carrier gases, and their effect on the interaction of VAM with PVAc was explored. Since ethylene and CO2 both have a finite solubility in PVAc, the swelling of the coating had to be considered in the data analysis. By assuming isotropic swelling, the film thickness could be calculated from

[ (

τ ) R - R2 -

)]

MP + MCP πLFPP

1/2

(3)

Here, R is the internal radius of the uncoated capillary column, MP represents the mass of the polymer in the column, which is a constant value, MCP represents the mass of carrier gas in the polymer phase, which is dependent on pressure and temperature, and FPP is the mass density of the polymer phase. For this investigation, values of MCP and FPP were determined from correlations of experimental gravimetric sorption data. At the conditions of maximum carrier gas sorption, i.e., the highest pressures and lowest temperatures, the ethylene sorption was approximately 1 wt % while for CO2 it was ∼13 wt %. These values translate to a 3% and ∼15% increase in the film thickness, respectively. To ensure that the coating was stable at these temperatures and plasticization conditions, we periodically reverted back to using helium as the carrier gas and ensured that we could reproduce both our K and Dp values precisely. In Figure 10 we provide partition coefficient data for VAM-PVAc as a function of inverse temperature and carrier gas pressure. The effect of temperature is typical

Figure 10. Infinite dilution partition coefficients for VAMPVAc as a function of carrier gas pressure and temperature. The presence of finite concentrations of sorbed CO2 and ethylene reduces the VAM partition coefficients. The solid line is a correlation of all of the data using a helium carrier.

Figure 11. Infinite-dilution diffusion coefficients for VAMPVAc as a function of carrier gas pressure and temperature. The extra free volume introduced by finite concentrations of sorbed CO2 and ethylene increase the VAM diffusion coefficients. The reduction of the apparent activation energy of diffusion with increasing pressure reflects the competition between polymer free volume loss with decreasing temperature and free volume gain due to increased carrier gas sorption with decreasing temperature.

of polymer-solvent systems; i.e., K decreases as temperature increases. However, the magnitude of K and the strength of its dependence on T are generally not known a priori. Similarly, the effect of introducing a finite concentration of either CO2 or ethylene into the polymer phase on the VAM-PVAc partition coefficient is not generally known a priori. Both CO2 and ethylene serve to depress the interactions of VAM with PVAc. In the case of CO2 it is observed that the greater the pressure, the lower the VAM-PVAc partition coefficient. The VAM-PVAc mutual binary diffusion coefficients are presented in Figure 11 as a function of inverse temperature and carrier gas pressure. As in Figure 4, the temperature dependence is Arrhenius in nature over the small temperature range investigated with smaller diffusion coefficients at lower temperatures. It is interesting to note, however, that the apparent activation energy for VAM diffusion decreases as the carrier gas pressure increases. The reason for the observed concentration dependence of the apparent activation energy is easily understandable when one realizes that there are two completing effects that influence the total free volume within the system. The first regards the reduction of the PVAc

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contribution to the total free volume as temperature is reduced, and the second is related to the increased sorption level (and corresponding increase in free volume contribution) of CO2 or ethylene at a fixed partial pressure when sample temperature is decreased. The addition of free volume to the stationary phase serves to increase the binary mutual diffusion coefficient (as is clearly seen in Figures 5 and 6), while the reduction of polymer free volume leads to lower diffusion coefficients (see Figure 4). The concentration dependence of the apparent activation energy is governed by these competing effects. As the partial pressure of the carrier is increased, the plasticization effect is expected to eventually dominate the temperature effect and lead to diffusion coefficients that increase with decreasing temperature! Finally, it should be noted that the apparent activation energy, which can be deduced from the slope of the Arrhenius plot given in Figure 11, is not the true activation energy for diffusion. The true activation energy must be evaluated at isosteric conditions, i.e., as a function of temperature with constant solvent concentration within the polymer phase. Summary The utility of CCIGC to probe multicomponent thermodynamic and transport effects has been clearly demonstrated in several examples. At ambient pressures and infinitely dilute conditions, CCIGC experiments have revealed that toluene interactions with PVAc are shown to be unaffected by the presence of methanol, while they are appreciably suppressed by water. The VAM diffusion coefficients measured within PVAc at high pressures in the presence of either CO2 or ethylene illustrate how competing free volume effects influence the apparent activation energy for diffusion. The relative influence of the plasticization of the polymer due to carrier gas loading and the loss of free volume due to temperature effects on the diffusion of VAM has been shown to vary depending on the partial pressure of carrier in the multicomponent system. Application of a newly developed high-pressure CCIGC capability to infinite dilution and finite concentration systems has been established, and the ability to effectively measure solubility and diffusivity data has been presented. This experimental method is easily extendable to applications involving a multitude of carrier gases, solutes, and stationary phases. The temperature limitation on the back-pressure regulator (∼80 °C) is the predominant limitation of the current HPCCIGC design. Establishing appropriate flow rates and pressures with a series of orifices of varying diameter would eliminate this limitation since they are generally capable of attaining much higher temperatures (∼250 °C). The solubility and diffusivity parameters from multicomponent polymer-solvent-solvent systems at high pressure have been successfully measured over a range of temperatures and pressures. The VAM diffusion coefficients measured within PVAc in the presence of either CO2 or ethylene illustrate how competing free


volume effects influence the apparent activation energy for diffusion. The relative influence of the plasticization of the polymer due to carrier loading and the loss of free volume due to temperature effects on the diffusion of VAM has been shown to vary depending on the partial pressure of carrier in the multicomponent system. Acknowledgment. We gratefully acknowledge the financial support provided for R.F. by the Air Products and Chemicals, Inc./Penn State University Graduate Fellowship program. References and Notes (1) Gray, D. G.; Guillet, J. E. Macromolecules 1973, 6, 223-227. (2) Pawlisch, C. A.; Macris, A.; Laurence, R. L. Macromolecules 1987, 20, 1564-1578. (3) Pawlisch, C. A.; Bric, J. R.; Laurence, R. L. Macromolecules 1988, 21, 1685-1698. (4) Arnould, D.; Laurence, R. L. Ind. Eng. Chem. Res. 1992, 31, 218-228. (5) Arnould, D.; Laurence, R. L. ACS Symp. Ser. 1989, 391, 87106. (6) Romdhane, I. H.; Danner, R. P. AIChE J. 1993, 39, 625635. (7) Surana, R. K.; Danner, R. P.; Tihminlioglu, F.; Duda, J. L. J. Polym. Sci., Part B: Polym. Phys. 1997, 35, 1233-1240. (8) Price, G. J.; Siow, K. S.; Guillet, J. E. Macromolecules 1989, 22, 3116-3119. (9) Surana, R. K.; Danner, R. P.; Duda, J. L. Ind. Eng. Chem. Res. 1998, 37, 3203-3207. (10) Tihminlioglu, F.; Surana, R. K.; Danner, R. P.; Duda, J. L. J. Polym. Sci., Part B: Polym. Phys. 1997, 35, 1279-1290. (11) Xie, L. Q. Polymer 1993, 34, 4579-4584. (12) Bonifaci, L.; Carnelli, L.; Cori, L. J. Appl. Polym. Sci. 1994, 51, 1923-1930. (13) von Meien, O. F.; Biscaia, E. C.; Nobrega, R. AIChE J. 1997, 43, 2932-2943. (14) Muralidharan, V.; Tihminlioglu, A.; Antelmann, O.; Duda, J. L.; Danner, R. P.; De Haan, A. J. Polym. Sci., Part B: Polym. Phys. 1998, 36, 1713-1719. (15) Tihminlioglu, F.; Danner, R. P. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 1965-1974. (16) Tihminlioglu, F.; Danner, R. P.; Lutzow, N.; Duda, J. L. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 2429-2435. (17) Balashova, I. M.; Danner, R. P.; Puri, P. S.; Duda, J. L. Ind. Eng. Chem. Res. 2001, 40, 3058-3064. (18) Cai, W. D.; Ramesh, N.; Tihminlioglu, F.; Danner, R. P.; Duda, J. L.; de Haan, A. J. Polym. Sci., Part B: Polym. Phys. 2002, 40, 1046-1055. (19) Surana, R. K. Ph.D. Thesis, The Pennsylvania State University, 1997. (20) Alessi, P.; Kikic, I.; Cortesi, A. Ind. Eng. Chem. Res. 2002, 41, 4873-4878. (21) Alessi, P.; Cortesi, A.; Kikic, I.; Vecchione, F. J. Appl. Polym. Sci. 2003, 88, 2189-2193. (22) Cao, H. H.; Lin, G. X.; Jones, A. A. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 1053-1067. (23) Ghosh, A.; Chapman, W. G. Ind. Eng. Chem. Res. 2002, 41, 5529-5533. (24) Gupta, R. R.; RamachandraRao, V. S.; Watkins, J. J. Macromolecules 2003, 36, 1295-1303. (25) Duda, J. L.; Kimmerly, G. K.; Sigelko, W. L.; Vrentas, J. S. Ind. Eng. Chem. Fundam. 1973, 12, 133-136. (26) Lundberg, J. L.; Wilk, M. B.; Huyett, M. J. Ind. Eng. Chem. Fundam. 1963, 2, 37-43. (27) Kishimoto, A. J. Polym. Sci., Part A: Gen. Pap. 1964, 2, 1421-1439. (28) Vrentas, J. S.; Duda, J. L.; Hou, A. C. J. Polym. Sci., Part B: Polym. Phys. 1985, 23, 2469-2475. (29) Zielinski, J. M.; Duda, J. L. AIChE J. 1992, 38, 405-415.

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