Ind. Eng. Chem. Res. 2007, 46, 3849-3851
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Effect of Molecular Weight on the Surface Tension of Polystyrene Melt in Supercritical Nitrogen H. Park,† C. B. Park,‡ C. Tzoganakis,† and P. Chen*,† Department of Chemical Engineering, UniVersity of Waterloo, 200 UniVersity AVenue, Waterloo, Ontario, Canada N2L 3G1, and Microcellular Plastics Manufacturing Laboratory, Department of Mechanical and Industrial Engineering, UniVersity of Toronto, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8
This paper presents experimental results on the effect of molecular weight on the surface tension of polystyrene melt in supercritical nitrogen. The surface tension was determined by the axisymmetric drop shape analysisprofile (ADSA-P) method, for which a high-pressure and high-temperature cell was used to form pendant drops of the polystyrene melt. For two monodisperse polystyrenes of Mw ∼ 100 000 and 400 000 and one polydisperse polystyrene, a linear relationship was found between surface tension and temperature and between surface tension and pressure within a temperature range of 170-210 °C and a pressure range of 500-2000 psi. With an increase in pressure or temperature, the surface tension of all three polystyrenes decreases. Monodisperse polystyrene of a higher molecular weight has a higher surface tension by 6-9 mJ/m2 under all experimental conditions. The surface tension dependence on temperature and on pressure is more significant for the higher molecular weight polystyrene. For the polydisperse polystyrene, high surface tension values seem to be related predominantly to its high molecular weight portion of polystyrene molecules. An empirical equation, the Mecleod relation, was used to relate surface tension with the density difference between the polymer and supercritical nitrogen satisfactorily. Introduction Surface tension is one of the most important physicochemical properties for polymeric materials in many engineering processes, such as foaming, suspension, wetting, and blending.1 However, experimental determination of the surface tension of a high viscosity polymer has been difficult at high temperatures and pressures during the experiment.2 The effect of molecular weight on polymer properties and processing has been well documented in the literature. Limited studies have been reported on the effect of polymer molecular weight on surface tension.3,4 There has been no report on the molecular weight effect on the surface tension of polymers of high molecular weight in a supercritical fluid. Supercritical fluids, such as carbon dioxide and nitrogen, have been widely used as foaming agents in the production of microcellular polymer foams.5,6 Although the amount of a supercritical fluid dissolved in the polymer is small, it can result in dramatic changes in physicochemical properties, such as the glass transition temperature, viscosity, solubility, and surface tension.7 There are many methods to measure surface tension. Among them, the pendant drop method has many advantages because of its simple setup and versatile applications.8-10 The pendant drop method has been used extensively for low molar mass liquids, liquid crystals, and polymers.11-13 Although the pendant drop method is theoretically simple, research on the surface tension of polymers in a supercritical fluid has been limited because of experimental difficulties in handling high-viscosity polymer melts under high temperature and high pressure.14,15 The primary objective of this study is to investigate the effect of the molecular weight on the surface tension of polystyrene melt in supercritical nitrogen. The surface tension is measured as a function of temperature and pressure in monodisperse * To whom correspondence should be addressed. E-mail: p4chen@ uwaterloo.ca. † University of Waterloo. ‡ University of Toronto.
polystyrenes of two different molecular weights and a polydisperse polystyrene. A recently designed high-temperature and high-pressure sample cell is employed in the surface tension measurement to obtain a wide range of experimental conditions. Using the set of surface tension data obtained, an empirical equation approximating the surface tension of polystyrene in supercritical nitrogen as a function of temperature and pressure is developed. Experimental Details Materials. Polydisperse polystyrene was obtained from Dow Chemical Company. Two monodisperse polystyrenes were obtained from Polyscience Inc. Table 1 shows the molecular weight information of these polystyrenes. Nitrogen (critical pressure ) 492 psi, critical temperature ) -147 °C) at 99.99% purity was purchased from PRAXAIR (Danbury, CT). Surface Tension Measurement. The surface tension of polystyrene in nitrogen was measured at different temperatures, from 170 to 210 °C, within a wide range of pressures, from 500 to 2000 psi. To achieve these experimental conditions, a high-temperature and high-pressure sample cell was used. This optical viewing cell consisted of a cylinder of stainless steel, which was heated by an electrical band heater. The cylinder was hollow, with an inner diameter of 30 mm and length of 25 mm. Two optical-quality sapphire windows (Meller Optics, Inc.) permitted the illumination and observation of the pendant drop formed by a sample polymer melt. The experimental setup was tested for its accuracy and reproducibility with a range of polymer-gas combinations, and the details of this setup and validation for the surface tension measurement were described in a recent publication.16 The technique of axisymmetric drop shape analysis-profile (ADSA-P)17,18 was used for image analysis and parameter estimation. Surface or interfacial tensions were obtained by fitting the Laplace equation of capillarity to the acquired shape and dimensions of axisymmetric menisci.19 The value of surface
10.1021/ie070311j CCC: $37.00 © 2007 American Chemical Society Published on Web 04/27/2007
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Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007
Table 1. Polystyrene Molecular Weightsa
b
polystyrenes (PS)
supplier
Mwb [g/gmol]
Mnc [g/gmol]
Mw/Mn
polydisperse PS high molecular weight monodisperse PS low molecular weight monodisperse PS
Dow Chemcials Polyscience Inc. Polyscience Inc.
312 000 400 000 100 000
120 000 377 000 96 000
2.60 1.06 1.04
a The data of the molecular weight of the polydisperse PS are from other researchers,32 and those of the monodisperse PS are from the manufacturers. Mw [g/gmol]: weight-averaged molecular weight. c Mn [g/gmol]: number-averaged molecular weight.
Table 2. Density Difference Data between Polystyrene and Nitrogen at Various Temperatures and Pressures in Units of grams per cubic centimetersa pressure (psi) temperature (°C)
500
1000
1500
2000
170 180 190 200 210
0.9623 0.9564 0.9504 0.9442 0.9380
0.9381 0.9328 0.9272 0.9216 0.9157
0.9147 0.9099 0.9049 0.8997 0.8943
0.8921 0.8878 0.8833 0.8786 0.8736
a Note: The density differences of nitrogen and polystyrene saturated with nitrogen are determined by the Sanchez and Lacombe equation of states as expressed here: F˜ 2 + P ˜ + T˜ [ln(1 - F˜ ) + (1 - 1/r)F˜ ] ) 0 where F˜ is the reduced density, P˜ is the reduced pressure, T˜ is the reduced temperature, and r is the number of sites occupied by a molecule.26 The reduced parameters are defined as P ˜ ) P/P*, F˜ ) F/F*, T˜ ) T/T*, and r ) MP*/ (RT*F*) where F is the density, P is the pressure, T is the temperature, M is the molecular weight, and R is the gas constant. It is worth noting that the density differences calculated here do not distinguish the three polystyrenes of different molecular weights within the limited significant digits. As shown in the results of this study, the key parameter influencing the surface tension here is molecular weight.
tension was generated as a fitting parameter20 after a least-square algorithm was employed to minimize the difference between experimental and theoretical drop profiles. During this procedure, the density difference between polystyrene and nitrogen was an input parameter,21-23 which was determined by the Sanchez and Lacombe (S-L) equation of state (EOS).24-27 The data of density difference between polystyrene and nitrogen at different temperatures and pressures are shown in Table 2. Results and Discussion Effect of Molecular Weight on the Surface Tension. The surface tension of polystyrene melts in supercritical nitrogen was measured at four different pressures, 500, 1000, 1500 and 2000 psi, and five different temperatures, 170, 180, 190, 200 and 210 °C. The equilibrium surface tension values of the polystyrenes in nitrogen were obtained from their time-dependent surface tension measurements under each set of conditions. The average of the surface tension values is taken as the equilibrium surface tension when the change in surface tension is less than 0.0001 mJ/(m2 s) for 1 h. Errors are on the order of 0.01 mJ/m2. The results are shown in Figure 1 for two monodisperse polystyrenes of Mw ∼ 100 000 and ∼ 400 000, along with a polydisperse polystyrene. The surface tension values are in a range similar to those of other studies.22 Monodisperse, rather than polydisperse, polystyrenes are used in investigating the effect of molecular weight on the surface tension. because the polydispersity of polystyrene might add an additional influence. Figure 1 shows that the higher molecular weight polystyrene has a higher surface tension under all pressure and temperature conditions tested. To quantify the temperature and pressure influence on the surface tension, a second-order linear regression model was used.28 From statistical investigations, we can propose the following equations for the two monodisperse polystyrenes.
Figure 1. Surface tension as a function of temperature for two monodisperse polystyrenes under four different pressures and for one polydisperse polystyrene under two different pressures. Closed symbols refer to the monodisperse polystyrene of a weight-average molecular weight of 400 000 g/mol; open symbols refer to that of a weight-average molecular weight of 100 000 g/mol. Crossed and asterisk symbols refer to the polydisperse polystyrene. The lower molecular weight polystyrene shows lower surface tensions. The polydisperse polystyrene has a weight-average molecular weight of 312 000 g/mol and has slightly higher surface tensions than those of the high molecular weight monodisperse polystyrene.
γ(Mw ∼ 100 000, polydispersity ∼ 1) ) 25.0362 0.0448T - 0.0068P + (1.97 × 10-5)TP(R2 ) 0.99) (1) γ(Mw ∼ 400 000, polydispersity ∼ 1) ) 43.5497 0.0942T - 0.0120P + (3.91 × 10-5)TP(R2 ) 0.99) (2) where γ is the surface tension of polystyrene in supercritical N2, in millijoules per squared meter, T is the temperature in degrees celsius, and P is the pressure in pounds per square inch. Note that the second-order terms in T and P are absent; statistically, γ is linearly related to T and P. There is an interaction term in TP, indicating that γ dependence on T or P is affected by P or T, respectively. Comparison between the above two equations indicates that polystyrene of a higher molecular weight has a stronger temperature and pressure dependence of surface tension than polystyrene of a lower molecular weight. The cross interaction between temperature and pressure effects is also more significant for the higher molecular weight polystyrene. Effect of Polydispersity on the Surface Tension. Similar to its monodisperse counterparts, the polydisperse polystyrene demonstrates three trends of surface tension variation: The surface tension decreases with increasing temperature and pressure, and the temperature dependence of surface tension is less pronounced at higher pressure (Figure 1). It is noticed that the polydisperse polystyrene has a higher surface tension than the monodisperse polystyrene of Mw ∼ 400 000, even though its molecular weight, both weight-average and number-average, is below 400 000. In a polydisperse polymer, a wide distribution of molecular weights exists; thus, it may not be surprising that a portion of polystyrene molecules possesses a molecular weight greater than 400 000. This large molecular weight portion of polystyrene molecules may contribute more influentially to a
Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007 3851 Table 3. Parameters in the Macleod Equationa
Acknowledgment
polystyrenes (PS)
Macleod’s index (n)
constant (C)
polydisperse PS high molecular weight monodisperse PS low molecular weight monodisperse PS
4.5 ( 0.3 4.7 ( 0.1
3.5 ( 0.03 3.4 ( 0.01
4.8 ( 0.2
3.0 ( 0.01
a The parameters were obtained from the generalized Macleod equation, γ ) C(∆F)n, where γ is the surface tension, C a constant, ∆F the density difference between polymer and surrounding fluid, and n Macleod’s index. The standard errors are obtained at a 95% confidence level.
high surface tension. In other words, high surface tension values are mainly derived from polystyrene molecules of high molecular weights. This conclusion is also consistent with the fact that the surface tension of monodisperse polystyrene of Mw∼ 400 000 is greater than that of Mw ∼ 100 000. Relationship between Surface Tension and Density. The relation between surface tension and density has been expressed by the generalized Macleod equation:
γ ) C(∆F)n
(3)
where γ is the surface tension of the polymer, C is an empirical constant, ∆F is the density difference between the polymer and its surrounding fluid, and n is Macleod’s index. Table 3 shows the results of the fit of eq 3 to the experimental data. The values of Macleod’s indices obtained for the three polystyrenes are ranged from 4.5 to 4.8, similar to Wu’s results.30 These values are slightly higher than those of polystyrene in carbon dioxide; the lower molecular weight monodisperse polystyrene has a higher Macleod’s index. A detailed mechanistic study of the molecular weight effect on surface tension is currently underway. Dee and Sauer31 have shown that density profiles between vapor and liquid phases depend on the molecular weight of polymers. Polymers of a higher molecular weight have a steeper change in the density profile at the interface, indicating that high molecular weight polymers have a narrower interface. This may be related to higher surface tensions of polystyrenes with higher molecular weights. However, because of the small interfacial width, on the order of nanometers, detailed structural investigations have been difficult so far. More research will be needed, perhaps by combining experimental studies with theoretical modeling. Summary A set of the surface tension data of two monodisperse polystyrenes of Mw ∼ 100 000 and Mw ∼ 400 000 and one polydisperse polystyrene in supercritical nitrogen at various temperatures and pressures was successfully obtained. Within the experimental temperatures of 170-210 °C and pressures of 500-2000 psi, a linear dependence of surface tension on temperature and pressure was found. As the pressure or temperature increases, the surface tension of all three polystyrenes decreases. The slope of surface tension changes when temperature is decreased with increasing pressure. It has been found that the high molecular weight monodisperse polystyrene has a higher surface tension, by 6-9 mJ/m2, than the low molecular weight monodisperse one. The surface tension dependence on temperature, as well as on pressure, is stronger for the monodisperse polystyrene of higher molecular weight. For the polydisperse polystyrene, high surface tension values may be influenced more by high molecular weight portions of polystyrene molecules.
We gratefully acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), Canadian Foundation for Innovation (CFI), and Canada Research Chairs (CRC) Program. Literature Cited (1) Myers, D. Surfaces, Interfaces, and Colloids: Principles and Applications; VCH publishers Inc: New York, 1991. (2) Demarquette, N. R.; Kamal, M. R. Polym. Eng. Sci. 1994, 34 (24), 1823-1833. (3) Malson, R.; Jalbert, C. A.; Muisener, P. A. V. O.; Koberstein, J. T.; Elman, J. F.; Long, T. E.; Gunesin, B. Z. AdV. Colloid Interface Sci. 2001, 94, 1-19. (4) Jannasch, P. Macromolecules 1998, 31, 1341-1347. (5) Cooper, A. I. J. Mater. Chem. 2000, 10, 207-234. (6) Tomasko, D. L.; Li, H.; Liu, D.; Han, X.; Wingert, M. J.; Lee, L. J.; Koelling, K. W. Ind. Eng. Chem. Res. 2003, 42, 6431-6456. (7) Lee, M.; Park, C. B.; Tzoganakis, C. Polym. Eng. Sci. 1999, 39, 99-109. (8) del Rio, O. I.; Neumann, A. W. J. Colloid Interface Sci. 1997, 196, 136-147. (9) Rotenberg, Y.; Boruvka, L.; Neumann, A. W. J. Colloid Interface Sci. 1983, 93, 169-183. (10) Lau, W. W. Y.; Burns, C. M. J. Colloid Interface Sci. 1973, 45, 295-302. (11) Alexopoulos, A. H.; Puig, J. E.; Franess E. I. J. Colloid Interface Sci. 1989, 128, 26-34. (12) Song, B.; Springer, J. J. Colloid Interface Sci. 1996, 184, 77-91. (13) Anastasiadis, S. H.; Chen, J. K.; Koberstein, J. T.; Sohn, J. E.; Emerson, J. A. Polym. Eng. Sci. 1986, 26, 1410-1428. (14) Roe, R.-J.; Bacchetta, V. L.; Wong, P. M. G. J. Phys. Chem. 1967, 71, 4190-4193. (15) Wu, S. J. Phys. Chem. 1970, 74, 632-638. (16) Park, H.; Park, C. B.; Tzoganakis, C.; Tan, K. H.; Chen, P. Ind. Eng. Chem. Res. 2006, 45, 1650-1658. (17) Cheng, P.; Li, D.; Boruvka, L.; Rotenberg, Y.; Newmann, A. W. Colloids Surf. 1990, 43, 151-167. (18) Susnar, S. S.; Hamza, H. A.; Newmann, A. W. Colloids Surf. 1994, 89, 169-180. (19) Andreans, J. M.; Hauser, E. A.; Trucker, W. B. J. Phy. Chem. 1938, 42, 1001-1019. (20) Cheng, P.; Neumann, A. W. Colloids Surf. 1992, 62, 297-305. (21) Xue, A.; Tzoganakis, C.; Chen, P. Polym. Eng. Sci. 2004, 44, 1827. (22) Li, H.; Lee, L. J.; Tomasko, D. L. Ind. Eng. Chem. Res. 2004, 43, 509-514. (23) Funami, E.; Taki, K.; Murakami, T.; Kihara, S. Presented at the Polymer Processing Society Annual Meeting, 2006, paper no. SP2.18. (24) Sanchez, I. C.; Lacombe R. H. Macromolecules 1978, 11, 11451156. (25) Sanchez, I. C.; Lacombe, R. H. J. Phys. Chem. 1976, 80, 23522363. (26) Sato, Y.; Takikawa, T.; Takishima, S.; Masuoka, H. J. of Supercrit. Fluids 2001, 19, 187-198. (27) Sato, Y.; Yurugi, M.; Fujiwara, K.; Takishima, S.; Masuoka, H. Fluid Phase Equilib. 1996, 125, 129-138. (28) O’Neill, M. L.; Cao, Q.; Fang, M.; Johnston, K. P.; Wilkinson, S. P.; Smith, C. D.; Kerschner, J. L.; Jureller, S. H. Ind. Eng. Chem. Res. 1998, 37, 3067-3079. (29) Milton, J. S.; Arnold, J. C. Introduction to probability and statistics; McGraw-Hill Inc.: New York, 1995. (30) Wu, S. Polymer Interface and Adhesion; Marcel Dekker Inc.: New York, 1982. (31) Dee, G. T.; Sauer, B. B. AdV. Phys. 1998, 47 (2), 161-205. (32) Machell, J. S.; Greener, J.; Contestable, B. A. Macromolecules 1990, 23, 186-194.
ReceiVed for reView March 1, 2007 ReVised manuscript receiVed April 6, 2007 Accepted April 17, 2007 IE070311J
