=394,932 g/mol. Carbon dioxide with the purity of 99.9% was obtained from Air Product Company. =199,597g/mol and M

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1 Optical Deterination of Supercritical CO -induced PMMA Swelling and Interrelated herodynaic Property Modeling Lihua Chen, Guiping Cao, Renhan Zhang, Feng He State Key Laboratory of Cheical Engineering, East China University of Science and echnology, Shanghai, 37, China Abstract: An optical deterination apparatus is applied to onitor in-situ the swelling behavior of glassy polyers(pmma) in the presence of supercritical carbon dioxide(scco ).his work provides swelling data for PMMA over a useful range of processing conditions (teperature fro 35K to 35K,and pressure up to 4MPa). he Sanchez-Lacobe equation of state (S-L EOS) has inherent ability to describe solvent (especially low olecular weight)-polyer syste. herefore, the PMMA raw data has been fitting into the pure coponent S-L EOS, which show the pressure, teperature and density characteristic paraeters are.38mpa, 898.4K and 6.7 kg -3 (suitable range:8-5mpa, 35-35K),respectively. Siilarly, the characteristic paraeters of CO which are 54.56MPa 33.38K 5. kg -3 (suitable range: 8-5MPa, 35-35K) can also be acquired.. he data of equilibriu swelling are then correlated with the scco - PMMA ixture systes S-L EOS. Results obtained here show that the teperature-independent binary interaction paraeter is.67, which can provide ixture S-L EOS odel to predict the solubility and swelling of CO in PMMA over wide range of pressure. he S-L EOS odeled curved agree well with the experient data. Keywords: PMMA; Supercritical carbon dioxide; Swelling; In-situ Optical deterination; Sanchez-Lacobe equation of state INRODUCION Carbon-dioxide, which has oderate critical teperature and pressure ( c =3.4 C, P c =7.38MPa), has shown several predoinant characteristic which are readily available, non-toxic, incobustible, cheically inert and environentally benign. High-pressure carbon-dioxide, especially supercritical carbon-dioxide (scco ) has becoe an excellent alternative of organic solvents. According to its unique physical property, scco has attracted wide attention in the field of acroolecular aterial during the last 5 years. Due to it is characterized by both swelling feature and diffusion in the polyer atrix, scco has been used successfully in polyer processing: e.g. icrocellular foaing [-], polyer synthesis, polyer odification [3-4], dye stuff and penetration of sall olecules such as edicine etc. he swelling of polyers involves either utual dissolution of two copletely iscible substances (solvent and polyer) or solution of the low-olecular-weight coponent into the polyer. Both cases result in increased obility of the polyer chain, which has been shown to odify reaction kinetics, iprove diffusion of sall olecules, and reduce polyer glass transition teperature ( g ).o ost of polyers, there are still short of underlying data used for scco -polyer processing. Wissinger and Paulaitis [8-9] have studied sorption and swelling of PMMA at the presence of CO up to MPa. Liu et al. [] easured swelling of PMMA with an optical cell still at relatively low pressure (8.3MPa). his paper studies the diffusion of CO in aorphous polyer(pmma) where crystallization effects induced by CO are inexistent,and therefore entire considerations are given to echanis of polyer swelling. In this work, experient pressure is extent fro 8MPa to 5MPa, eanwhile, we have applied the optical deterination apparatus with a high-definition digital caera in order to get a better investigation of swelling behavior. he interaction paraeter between CO and PMMA were regressed by fitting the swelling data to S-L EOS which are eployed to predict the both solubility and swelling ratio over a wider range of pressure and teperature in CO -PMMA syste. Nowadays, for the reason that there are still lack of systeatic research on the echanis of scco diffusion in polyer both at hoe and abroad, our work possess the value of practical applications as well as theoretical research. EXPERIMENAL SECION Material he poly(ethyl ethacrylate)(pmma) saple(lot.36) was obtained fro AOGLAS. GPC analysis gave the olecular weight of: M n =99,597g/ol and M w =394,93 g/ol. Carbon dioxide with the purity of 99.9% was obtained fro Air Product Copany. Specien preparation he stainless steel old, which had square holes ( ) inside filled with PMMA particles, was attached with releasing paper on both sides. he old was then sent into a press oulding achine where

teperature had been controlled at 8 o C for half an hour. After the old is taken out, PMMA speciens were cooled to the roo teperature so as to uncover the releasing paper attached on the old.

2 teperature had been controlled at 8 o C for half an hour. After the old is taken out, PMMA speciens were cooled to the roo teperature so as to uncover the releasing paper attached on the old. he next step was to reove the sticky aterial around speciens and to check the flaw of the surface such as bubble, irregularity, etc. he PMMA speciens were selected for further use. 3 Optical deterination syste High-definition digital caera (SP-35) was obtained fro Olypus Corporation. Continuous zoo icroscope (XZ series) was obtained fro Shanghai Yongheng Opitical Instruent Copany; herostatic Bath was obtained fro Shanghai Precise Instruent Copany. Optical deterination apparatus (HPR-E), shown in Figure, constructed of 36 stainless steel. eperature of the apparatus was aintained by an autoatic control unit in conjunction with a therocouple. he cell was wrapped with insulating aterials to create unifor heating in the cell. he pressure within the cell was onitored using an output pressure transducer. High pressure CO was introduced into the cell using a single-cylinder syringe pup (DZB-A), obtained fro Beijing Xiebo ransission echnology Research Institute. 4 Experiental Approach PMMA speciens were placed in the vacuu oven (5 o C) for ore than hours after being annealed in an inert atosphere for about 8 hours. At the beginning of each run, the cell was thoroughly cleaned with acetone, exposed for an hour to ensure acetone had entirely volatilized. hen a PMMA specien, taken out fro the vacuu oven, was fixed up on the glass stage, which was in thickness, inside the cell. Adjusts its position and ake sure that the side face of specien ( ) was exactly opposite the digital caera and icroscope. he glass stage, where specien was placed, has two ain functions: the first is to distinguish a specien fro the stage. he second is to eliinate the error occurred after focus re-adjustent. he effect of the functions is shown in Figure. Sapphire window Pressure controller P Heating eperature controller Polyer saple Sapphire window Light eitting diode Microscope Digital caera Glass flate Gas Exit Gas Entrance Gas resource Figure Optical deterination syste Figure Polyer specien lay on the glass plate(due to reversed iage, the real position differs fro it in the figure by 8 ) RESULS & DISCUSSION Data Analysis he optical deterination apparatus and a high-definition digital caera were introduced into the experient to record any changes of the polyer specien, in situ, during its swelling in the scco. Copared to other approaches (easure the thickness after depressurization), real-tie optical deterination can avoid the inaccuracies caused by foaing of the polyer which induced by escaping gas fro the swelled specien as well as pressure relief. he ratio of equilibriu swelling can be exained further in ter of the swelling ratio defined as ξ = V / V () Where, V is the volue of the specien at equilibriu state and V is the initial volue of the polyer. Assue that the polyer specien is isotropic, that is to say, length L b is identical with width L c in the swelling procedure. hus the volue of the polyer specien is defined as V = L L L = L L () a b c a b

3 he volue change of the polyer specien can be reflected fro the real-tie iage caught by digital caera. he initial state and equilibriu swelling state of polyer specien are shown in Figure 3 and Figure 4, respectively. Figure 3 Initial status of polyer specien (ZOOM Figure 4 Equilibriu swelling status of polyer x) specien (ZOOM x) Each polyer specien is easured through iaging processing software for six ties, and the confidence intervals of easured values within 95% fiducial probability are calculated so as to reove the value outside that intervals.hen, that group of values are averaged to obtain the length L b of the specien. Eventually, the equilibriu swelling radio can be calculated fro Equation () and (). Sanchez-Lacobe Equation of State. S-L EOS heory he Sanchez-Lacobe equation of state(s-l EOS), which was set up based on Flory-Huggins theory [-], is norally used for describing the phase behavior between acroolecular fluids and its ixture. S-L EOS is probably the ost widely used odel to describe CO solubility in various polyer systes, and is given by % ρ + P% + % ln( % ρ) + ( ) % ρ = (3) r Where, the reduced pressure P %, teperature % and density ρ% are defined as P% = P/ P, % = /, % ρ = ρ / ρ (4) Where, the characteristic paraeters P, and ρ can be obtained fro experiental PV data and the S-L EOS of pure coponents. he paraeter r is the nuber of lattice sites occupied by a olecule, which is related wo the other three paraeters and the olecular weight M of the pure coponent by r = MP /( R ρ ) (5) For polyer with long olecular chain, we can derive that: r and / r.for a ixture of a polyer and a penetrant, the characteristic paraeters can be calculated fro those for the pure coponents / r = φ/ r + φ/ r = φ/ r (6) Where φ i is the volue fraction of coponent i in the ixture, the subscript i= corresponds to the penetratant, i= to the polyer, and i= to the ixture. he polyer volue at equilibriu swelling is obtained fro the real-tie optical deterination. As the dilatant volue of the polyer is ainly caused by teperature, pressure and the swelling induced by dissolved CO, the voluetric fraction of penetrant in the polyer phase is given by φ = VCO / V = ρ /( ρξ) (7) he value of P can be deterined fro the pure coponent paraeters by P = φp + φp φφ Δ P (8) Δ P = P + P P (9) P = ψ P P () Where, ψ is the binary interaction paraeter, which shows the deviation of the ixture characteristic pressure fro the geoetric ean of the pure coponent characteristic pressures. he binary interaction 3

4 paraeter is coonly assued to be unity when coponents are non-polar. he value of the ixture characteristic teperature,, is given by φp φp = P / + () In order to deterine the aount of penetrant sorbed into the polyer, the cheical potential of the penetrant in the pure phase is set equal to the cheical potential of the penetrant in the ixture μ, p = μ, () hat equality is based on the assuption that there is no polyer in the fluid phase. his assuption is generally valid except for certain fluoropolyers and silane polyers. he cheical potential of the penetrant in the pure phase is % ρ P% ( % ρ) ln( % ρ) ln % ρ μ, p = Rr (3) % % % ρ % ρ r While cheical potential of the penetrant in the penetrant-polyer ixture is % ρ P% ( % ρ) ln( % ρ ) ln % ρ μ, = R ln φ + φ + % ρ( M / ρ ) χφ + r [ ] (4) % % % ρ % ρ r Where, ρ% is given by equation 3.he paraeter χ is defined as χ =Δ P /( R) (5) he weight fraction of the penetrant, ω, and the close-packed volue fraction of the penetrant, φ, in the ixture, have the following relationship: ω = φ/ ( φ + φ( ρ / ρ) ) (6) If experient solubility data is available, and if the characteristic paraeters of the penetrant and polyer are specified, the binary interaction paraeter ψ can be deterined by iniizing the objective function: N (, pi ( ), i ( ) ) (7) i= s = μ μ Where N is the nuber of data points available. hen, the solubility of CO in polyer over a wide range of teperature and pressure can be predicted through S-L EOS.. Evaluation of Characteristic Paraeters of S-L EOS he pure coponent characteristic paraeters were obtained by fitting the PV experiental data into the S-L EOS using a non-linear least-squares analysis. here are several sets of characteristic paraeters coonly used in the literature are listed in the able : able CO characteristic paraeters reported in literature, K P, MPa ρ, kg -3 r range, K P range, MPa Ref [3] [4] [5] he facts that characteristic paraeters differ fro each other are probable caused by the different ranges of teperature and pressure used in regressing PV data, or by the diversity atheatical eans to estiate the characteristic paraeter. Due to the teperature and pressure ranges can not satisfy the experiental needs, it's necessary to re-calculate the CO characteristic paraeter. CO PV data (8-5MPa, 35-35K), obtained fro NIS [6], are used to regress the CO characteristic paraeter which listed in following table. able Sanchez-Lacobe CO Characteristic Paraeters, K P, MPa ρ,kg -3 r range, K P range, MPa Figure 5 shows a coparison of the calculated and experiental PV data for CO. Owing to a inor change of pressure will cause the great changes in density, the difference between odeled values and experiental values in the near supercritical region were greater than those far above the supercritical point. he standard variation of density is: N σ = ( ρ ρ ) /( N ) =.7kg ρ i= SL(i) -3 NIS 4

-3 Figure 5 CO density coparasion between NIS and S-L EOS calculated values ( σ ρ =.7kg ) Likewise, PMMA characteristic paraeter can be calculated by the sae approach.

5 -3 Figure 5 CO density coparasion between NIS and S-L EOS calculated values ( σ ρ =.7kg ) Likewise, PMMA characteristic paraeter can be calculated by the sae approach. As opposed to the CO syste, the PMMA data are scarce in the particular region. Although the teperature ranges used in this research (35-35K) are under the glass transition teperature, yet PMMA, plasticized by CO s penetration, are in a state of rubbery. hus the characteristic paraeters used in this paper were deterined by experient data of PMMA above the glass transition teperature. Zoller and Walsh [7] have reported experiental PV for PMMA in the teperature range fro 3 to 3.4 and in the pressure range fro to kg c for intervals of kg c. herefore, the ait equation was fit to the data, and was used to interpolate with respect to the teperature and pressure ρ P = cln + (8) ρ bexp( b ) Where, ρ is the density at pressure P and teperature ; ρ is the density at pressure P =. MPa and the sae teperature ; and c, b and b are constants. hese constants were deterined for PMMA in the region above g by non linear regression of the data of Zoller and Walsh. he resulting values are shown in able 3 able 3 Paraeters for PMMA in the ait equation(> g ) b, MPa b, K - c P range, MPa range, K Where, the standard variation of density between experiental and calculated by ait equation is -3 σ ρ =.4 kg.figure 6 shows the fit of the ait equation to the experiental data for PMMA above g. able 4 S-L EOS PMMA Characteristic Paraeters(> g ), K P, ρ, range, P range, MPa MPa kg -3 K Figure 6 PMMA density coparison between ait Figure 7 PMMA density coparison between ait -3-3 Equation and experiental value ( σ ρ =.4 kg ) Equation and S-L EOS ( σ ρ =.77 kg ) Where, sybols represent Zoller and Walsh s data and solid lines are the values calculated by the ait equation. Evidently, the data above g atch the lines quite well. he PV data (35-35K 8-5MPa), obtained by interpolation, are substituted into S-L EOS to estiate the PMMA characteristic paraeter listed in able 4. he coparision of PMMA density (35-35K 8-5MPa) between regressions fro the S-L EOS with those -3 fro ait equation is shown in Figure 7, whose standard variation of density is =.77 kg. σ ρ 5

6 .3 Evaluating the binary interaction paraeter ψ of the ixture. he binary interaction paraeter ψ of the ixture was obtained by solving the resulting Equation 3 and siultaneously. After substituting the equilibriu swelling ratio into the equation, the value of the binary interaction paraeter ψ is deterined to be.67 by non-linear least-squares analysis. Figure 8 PMMA equilibriu swelling ratio Figure 9 PMMA equilibriu swelling ratio predicted coparison between S-L EOS and experiental at various teperature and pressure - values( σ μ = 6.7J ol ) - Figure 8 shows a coparison of equilibriu swelling ratio, whose standard variation isσ μ = 6.7J ol, between experiental points and S-L EOS s calculation. he close agreeent of the theoretical prediction to the easured physical properties of the CO -swellen polyer deonstrates the ability of the S-L EOS to effectively odel the swelling behavior of high pressure CO in an aorphous polyer. he extent of swelling increases with pressure but exhibits different trends with teperature. hus the isotheral equilibriu swelling ratio of PMMA induced by CO versus pressure is shown in Figure 9. During CO at the region slightly above the supercritical point, little increase in pressure can significantly enhance the extent of swelling. he volue of specien is suppressed when CO penetrating in to polyer at the high pressure, therefore, the swelling ratio change slowly at that region. CONCLUSION High-pressure optical deterination apparatus and high-definition digital caera were introduced for investigating in situ the swelling behavior of PMMA in contact with sc CO and finally. As the pressure increases at isotheral conditions, the specien expands correspondingly. However, the syste teperature exhibits a different trend against pressure. Both CO and PMMA s characteristic paraeters are obtained fro fitting PV experiental data into the S-L EOS. he binary interaction paraeter ψ, which was deterined to be.67, can be retrieved by substituting the equilibriu swelling ratio into S-L EOS. he S-L EOS was found to in good agreeent with experiental calculated variables and can be used as a predictive tool to obtain physical properties of the CO -PMMA syste. REFERENCES [] Satish K., Eric J., AIChE Journal, 4, 995, 357 [] Will S., Nandika D., Journal of Cellular Plastics, 4, 4, 9 [3] Alessandro G., Raffaella G., Macroolecules, 37, 4, 458 [4] Dong Q., Liu Y., Journal of Applied Polyer Science, 9, 4, 3 [5] Said-Galiyev E., Nikitin L., Industrial and Engineering Cheistry Research, 39,, 489 [6] Ireneo K, Febe V. Current Opinion in Solid State and Materials Science, 7, 3, 399 [7] Kazarian G, Eckert A.,Proceedings of the ACS Division of Polyeric Materials Science and Engineering, 75, 996,73 [8] Wissinger G., Paulaitis E., Industrial & Engineering Cheistry Research, 3(5), 99, 84 [9] Wissinger G., Paulaitis E., Journal of Polyer Science, Part B: Polyer Physics, 5, 987, 497 [] Liu D., Macroolecules, 38, 5, 446 [] Sanchez C., Lacobe H., he Journal of Physical Cheistry, 8(), 976, 35 [] Sanchez C., Lacobe H., Journal of Polyer Science Polyer Letters Edition, 5(), 977, 7 [3] Pope S., Sanchez C., Macroolecules, 4(8), 99, 779 [4] Kilpatrick K., Chang H,. Phase Equilibria, 3, 986, 49 [5] Hariharan R., Journal of applied polyer science, 5(), 993, 78 [6] National Institute of Standards and technology, [7] Zoller P,, Walsh J., Walsh W. Pennsylvania: echnoic publ. co., 995, 47 [8] Quach A,, Siha R., Journal of Applied Physics, 4(), 97, 459 6

7 [9] Beret S,, Prausnitz M., Macroolecules, 8(4), 975,536 7

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