Simultaneous Measurement of Swelling and Sorption in a

Ind. Eng. Chem. Res. 2005, 44, 2549-2560

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Simultaneous Measurement of Swelling and Sorption in a Supercritical CO2-Poly(methyl methacrylate) System Arvind Rajendran,† Barbara Bonavoglia,‡ Nicola Forrer,‡ Giuseppe Storti,‡ Marco Mazzotti,† and Massimo Morbidelli*,‡ Institute of Process Engineering, Sonneggstrasse 3, CH-8092 Zu¨ rich, Switzerland, and Institut fu¨ r Chemieund Bioingenieurwissenschaften, ETH Ho¨ nggerberg/HCI, CH-8093 Zu¨ rich, Switzerland

In this paper a novel method to simultaneously measure swelling and sorption of supercritical fluids in polymers in a commercially available setup is proposed. A purely gravimetric approach based on the use of a magnetic suspension balance is adopted to study the swelling/sorption behavior of poly(methyl methacrylate) in an atmosphere of CO2. The procedure to determine swelling and sorption involves two steps, one using pure CO2 and the other adding an inert to the system. From these two measurements, the swollen volume and the amount of CO2 sorbed in the polymer can be calculated on the basis of a number of assumptions whose validity is critically discussed. To test the reliability of the new protocol and to determine the recommended operating window, the obtained results are compared with measurements taken with a standard technique as well as literature data. It is concluded that the proposed technique works in a window of operating conditions that is system specific. This is due to a strong sensitivity of the adopted equations to the small effect of the inert on the sorption/swelling behavior of the system. 1. Introduction The problem of the environmental impact of wastewater during standard polymerization and polymer processing techniques has gained importance in the past decades and has promoted the quest for alternative solvents and procedures. One possible alternative is the use of supercritical fluids as solvents. Supercritical fluids are especially attractive because of their unique physical properties that can be tuned by slightly changing the operating conditions. Carbon dioxide, in particular, offers several advantages because it is readily available, cheap and clean and is considered to be a good plasticizer for many commercial polymers, which is an important property to be considered for processes such as purification, impregnation, and synthesis of porous materials.1,2 The development of these processes requires the understanding of the behavior of polymers in a CO2 environment, such as the sorption of CO2 in the polymer and the associated swelling of the polymer matrix.3-7 Several research groups have dealt in the past with the measurement of these two quantities.4,8,9 When a polymer is contacted with CO2, this is sorbed in the polymer matrix, thus causing the matrix to swell. Because sorption and swelling occur simultaneously, at least two independent measurements are needed to quantify both phenomena. Swelling can be measured by a variety of methods, e.g., optical measurements, waveguide spectroscopy, and special techniques, which involve the immersion of the swollen polymer in mercury to determine its volume.3,4,6,10 In the majority of the cases, the polymer sample to be studied is required to be fabricated into a defined geometrical shape, e.g., films, sheets, cylinders, etc. Sorption measurements are usually carried out in situ using a gravimetric technique * To whom correspondence should be addressed. E-mail: [email protected]. † Institute of Process Engineering. ‡ Institut fu ¨ r Chemie-und Bioingenieurwissenschaften.

or by removing the sample outside the cell and weighing it.3-5,7 Gravimetric techniques, when performed in situ at conditions where the weighed substance is immersed in a fluid, always yield the apparent mass because of the effect of buoyancy. To obtain the real mass of the substance, a buoyancy correction has to be made, for which the volume of the weighed substance and the density of the fluid phase should be known. Hence, the accuracy of the mass measurement depends on the accuracy with which the volume of the weighed sample is known. In particular, poly(methyl methacrylate) (PMMA)CO2 systems have been investigated by several groups3-5,7,9,11 exploring a similar range of conditions but using different techniques. The comparison of the results from these studies highlights many differences both in the qualitative and in the quantitative behavior of swelling and sorption. Strong inconsistencies can be found, and there exists a need for further experimental results. The present study aims at analyzing the swelling and sorption behavior of the PMMA-CO2 system. Two different approaches to measure swelling and sorption have been adopted. The first one, called the “twodensity” method, is purely gravimetric in nature, while the second one, called the “conventional” method, consists of a combination of visualization to measure swelling and gravimetry to measure sorption. The experimental procedures are described, and the results are presented. The reliability of the two-density method is discussed by comparison with the results of the conventional technique as well as with literature data. 2. Two-Density Method 2.1. Materials. PMMA in the form of an extruded rod was obtained from Maagtechnik, Du¨bendorf, Switzerland. The properties of the polymer are listed in Table 1. CO2 with a purity of 99.995% and argon with a purity

10.1021/ie049523w CCC: $30.25 © 2005 American Chemical Society Published on Web 10/19/2004

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Ind. Eng. Chem. Res., Vol. 44, No. 8, 2005

Table 1. Physical Properties of PMMA Used in This Work number-average molecular weight, Mn glass transition temperature, Tg bulk density, Fpoly 0

600 000 g/mol 105 °C 1.17 g/cm3

of 99.999% were obtained from Pangas AG, Luzern, Switzerland. 2.2. Experimental Setup. The gravimetric apparatus consisted of a Rubotherm magnetic suspension balance, with the provision to measure in situ the density of the fluid phase. The balance can be operated up to a pressure of 450 bar and a temperature of 250 °C with an absolute accuracy of 0.1 mg. The temperature is controlled to a precision of 0.1 °C using a heating jacket. The temperature of the fluid is measured with a thermocouple. The balance consists of a pressure chamber where the basket containing the polymer sample is housed. The basket and a titanium sinker, whose volume is calibrated, are connected to a metal suspension to which a permanent magnet is attached. The permanent magnet is magnetically coupled to the electromagnet connected to the control system. The control system measures the distance between the permanent magnet and the electromagnet, which provides the lifted mass. The balance is operated in two positions. In position 1, the metal suspension along with the basket containing the sample is lifted while the titanium sinker is at rest. In position 2, the metal suspension, the basket, and the titanium sinker are lifted. From the measurements in positions 1 and 2, the apparent weight of the sinker can be calculated. Because the volume and mass of the sinker are known, the density of the fluid can be calculated. A detailed description of the balance operation can be found elsewhere.12,13 2.3. Experimental Protocol. As mentioned above, the measurement of the sorption and swelling of the polymers in CO2 usually requires two different techniques. Because most techniques to measure swelling are based on visualization, which requires the assumption of isotropic volume expansion, a fabrication of the sample is required whereby the polymer is shaped into a regular geometrical form, e.g., disks, films, rods, etc. To overcome this limitation and to reduce the time required to perform two experiments (one each for the measurement of swelling and sorption), a new technique, which is purely gravimetric, is proposed. Initially, a weighed amount, around 1 g, of the polymer sample, mpoly 0 , is placed in the basket inside the balance. The chamber is then evacuated, and the weight of the sample in a vacuum, M1(0,T), is measured. The measured value is

M1(0,T) ) mmet + mpoly 0

(1)

where mmet is the mass of the lifted metal parts in the balance. Then the technique proceeds with the following two steps: (a) measurement of the apparent weight of the sample and the lifted metal parts after addition of CO2 to a desired pressure level, Pa; (b) addition of an inert to the existing CO2 environment up to a pressure level Pb (Pb > Pa) and measurement of the apparent weight of the sample and the lifted metal parts in the presence of the mixture (CO2 + inert). It is shown in the following that, under some specific assumptions, these experi-

ments give simultaneously the swelling and sorption of CO2 in the sample. After evacuation, the measurement cell in the balance is filled with CO2 to the desired pressure, Pa. Upon contacting the polymer, the CO2 solubilizes in the polymer matrix, thus causing it to swell. At equilibrium, the apparent weight of the metal parts and the swollen polymer is measured. The balance signal can be related to the relevant physical quantities by the following equation:

M1(Fa,T) ) mmet + mpoly + ms(Fa,T) - Fa[Vpoly(Fa,T) + 0 Vmet] (2) where M1(Fa,T) is the balance reading at the bulk fluid density Fa and temperature T, ms(Fa,T) is the mass of the CO2 sorbed in the polymer, Vpoly(Fa,T) is the volume of the swollen polymer at the operating conditions, and Vmet is the volume of the basket and the other lifted metal parts. The latter can be calculated by performing experiments without the polymer being present in the basket. The last term in the above equation, Fa[Vpoly(Fa,T) + Vmet], represents the buoyancy correction. Equations 1 and 2 can be combined to give

M1(Fa,T) - M1(0,T) ) ms(Fa,T) - Fa[Vpoly(Fa,T) + Vmet] (3) This equation contains three measurable quantities, M1(Fa,T), M1(0,T), and Fa, and two unknowns, ms(Fa,T) and Vpoly(Fa,T). Therefore, to calculate these two quantities, related respectively to the sorption and swelling, another independent equation is required. In the second experimental step, an inert gas is added to the existing CO2 environment until a pressure Pb is reached. Care has to be taken not to let any CO2 escape from the cell. To ensure this, a one-way valve is used at the gas dosing port. Because the balance setup does not allow for mixing within the cell, enough time has to be allowed until the balance signal and the density reach equilibrium conditions; that is, the fluid phase is homogeneous with no spatial gradients of concentration or temperature in the measurement cell. After equilibration, a measurement similar to that in step a is made, and under these conditions the apparent weight is given by

+ ms(Fb,T) - Fb[Vpoly(Fb,T) + M1(Fb,T) ) mmet + mpoly 0 Vmet] (4) where M1(Fb,T) is the balance signal at the bulk mixture density Fb and temperature T, while ms(Fb,T) and Vpoly(Fb,T) are respectively the mass of the sorbed gas in the polymer and the volume of the swollen polymer under these conditions. Inserting eq 1 in the above equation yields

M1(Fb,T) - M1(0,T) ) ms(Fb,T) - Fb[Vpoly(Fb,T) + Vmet] (5) where two new unknowns, ms(Fb,T) and Vpoly(Fb,T), are present.

Ind. Eng. Chem. Res., Vol. 44, No. 8, 2005 2551

Subtracting eq 3 from eq 5 and rearranging give the relationship

M1(Fa,T) - M1(Fb,T) b

a

- Vmet ) Vpoly(Fa,T) +

F -F ms(Fa,T) - ms(Fb,T) Fb - Fa

+

Fb [Vpoly(Fb,T) b a F -F Vpoly(Fa,T)] (6)

where the left-hand side consists of directly measurable quantities. The second term on the right-hand side is related to the difference in the amount of the sorbed gas in steps a and b, while the third term is related to the difference of the swollen volumes in steps a and b. At this point, if it can be assumed that the added inert neither changes the volume of the polymer nor dissolves in the polymer or displaces the CO2 that is sorbed in step a, and then the following relationships can be written:

ˆs ms(Fa,T) ) ms(Fb,T) ) m

(7a)

ˆ poly Vpoly(Fa,T) ) Vpoly(Fb,T) ) V

(7b)

These assumptions imply that the addition of the inert merely changes the bulk fluid phase density while it does not affect the polymer. Using these relationships, the number of unknowns in the system of the two equations (3) and (5) is reduced to two, namely, m ˆ s and V ˆ poly. By combining eqs 6 and 7, one can write an expression to calculate both the volume of the swollen polymer and the mass of sorbed CO2:

V ˆ poly )

M1(Fa,T) - M1(Fb,T) Fb - Fa

- Vmet

m ˆ s ) M1(Fa,T) - M1(0,T) + Fa[V ˆ poly + Vmet]

(8) (9)

from which swelling and sorption can be calculated as follows:

s)

V ˆ poly - Vpoly 0 Vpoly 0 q)

m ˆs mpoly 0

(10)

(11)

where Vpoly is the unswollen volume of the sample that 0 can be computed using reported density values for PMMA as listed in Table 1. In the above equations, V ˆ poly and m ˆ s refer to the measured value of the swollen volume and to the amount of the sorbed gas, respectively. Under the operating conditions where assumptions are made about the inert breakdown, the measured polymer volume obtained using eq 8 will, in fact, correspond to the right-hand side of eq 6. This value will hence be different from the real volume of the swollen polymer [Vpoly(Fa,T)] because of either the change in the volume of the swollen polymer or the change in the sorbed mass of the gas. It is worth noting that the denominator of the first term in eq 8 contains the difference Fb - Fa. Hence, it is important that the magnitude of this difference is larger than the accuracy with which the individual densities,

Figure 1. Calculated single-component solubility of CO2, argon, and helium in PMMA as a function of pressure at T ) 80 °C.

Fa and Fb, can be measured. If this criterion is not met, the accuracy with which Vpoly can be calculated will be low. This will further affect the accuracy with which the sorption can be calculated because in the buoyancy correction term Vpoly is scaled by the density, as can be seen from eq 9. Notably, the assumption of isotropic volume expansion of the polymer has never been made in the derivation of the procedure above. Hence, this can be used to measure the swelling of the polymer independent of its morphology, i.e., without resorting to casting the polymer into blocks or films. The key underlying assumption of this protocol is that the addition of the inert merely causes a change in the fluid density but does not influence the equilibrium between CO2 and the polymer. This is analyzed in the following. 2.4. Choice of the Inert. An ideal inert should satisfy the following criteria: (1) no solubility in the polymer, i.e., PMMA in the case under examination; (2) no effect on the CO2 fluid phase fugacity, which implies no effect on the CO2 sorption in the polymer; (3) significant effect on the fluid density (i.e., measurable density change). Two inert gases, helium and argon, were chosen as possible candidates. Their solubility in PMMA and their effect on the CO2 fugacity and on the density of the fluid phase have been estimated using suitable models. The fugacity of the pure gases was calculated using the Peng and Robinson equation of state (PR-EOS) using literature values for the pure-component paramenters14 and setting the interaction parameters to zero. The solubility of the different gases as a function of pressure in PMMA is shown in Figure 1. These were computed by multiplying the fugacity by a componentdependent solubility coefficient, which is estimated through a suitable empirical relation.15 It can be seen that the solubility of CO2 is much higher compared to those of both inerts. Among the inerts, Ar exhibits a higher solubility than He. Hence, for this criterion, He would be a better choice. The change in the fugacity and density of the bulk fluid phase upon addition of the inert was estimated using the PR-EOS. For evaluation of the performance against criteria 2 and 3 rather than a comparison of the absolute values of the fugacity and density, it is better to compare the change in these quantities induced by the inert addition, i.e., the pressure difference (Pb - Pa). A base case corresponding to pure CO2 at 80 °C and 100 bar was chosen as representative of the experimental

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Figure 2. Calculated change in the CO2 fugacity in a mixture CO2 + inert as a function of Pb - Pa at T ) 80 °C and Pa ) 100 bar.

Figure 3. Calculated change in the density for a mixture CO2 + inert as a function of Pb - Pa at T ) 80 °C and Pa ) 100 bar.

conditions that were to be investigated. The effect of inert addition, starting from an initial condition with pure CO2 at a pressure Pa ) 100 bar to different final pressures Pb, is considered. The results are summarized in Figures 2 and 3. It can be seen from Figure 2 that, under the conditions considered for the comparison, the addition of He and Ar to CO2 changes the fugacity in opposite directions. The addition of He to CO2 causes the fugacity to increase, whereas the addition of Ar causes it to decrease. Considering its absolute value up to Pb - Pa ) 60 bar, the change in fugacity caused by Ar addition is larger than the one caused by He, while at conditions Pb - Pa > 60 bar, the opposite occurs. Hence, for this criterion, He would be a better inert up to Pb - Pa ) 60 bar and Ar would be a better choice if Pb - Pa > 60 bar, although in this case the difference between the two is marginal. The most important of these criteria, from the point of view of the measurement procedure, is the third one because this determines the accuracy in the estimation of V ˆ poly. From Figure 3, one can see that the addition of Ar as compared to He causes a much larger increase in the density, though changing the fugacity to comparable levels. On the basis of the combination of these two criteria, Ar would be a better candidate. In conclusion, though Ar has a larger solubility in PMMA than He, its solubility in PMMA is still much smaller than that of CO2 and, moreover, it performs considerably better than He when considering the

Figure 4. Experimental evaluation of the influence of argon addition levels on the measured swelling. Error bars represent the calculated measurement errors.

change in the fluid phase density, while affecting the CO2 fugacity in a comparable way. Hence, Ar was chosen as the inert for all of the measurements. 2.5. Results. Swelling and sorption measurements were carried out at 80 °C using the protocol described above. It has to be noted that the level to which Ar is to be added is a key step in the experimental procedure. Additions of small amounts of Ar could lead to a situation where the density change is too low, causing a large experimental error in the calculation of the swollen volume, whereas the addition of large quantities of Ar could alter the fugacity of CO2 and, moreover, lead to significant solubilization of Ar in the polymer. Hence, experiments were performed to study the influence of the effect of different Ar addition levels to determine the appropriate operating conditions. The results are summarized in Figure 4, where the calculated swelling and the corresponding error bars as a function of the amount of the inert added, in terms of the difference (Pb - Pa), are shown for three different values of Pa. The error bars have been calculated from a theoretical error analysis of the measurement that is reported in Appendix A.2.1. There appears to be no significant trend in the change of the measured value of swelling with respect to the addition of the inert. However, it is worth noting that, for all three cases, the greater the value of Pb - Pa, the smaller the error bar. The reason for this can be understood by considering the expressions used to calculate the error on V ˆ poly (eq A-7). The error on V ˆ poly is a function of ∆Fa, ∆Fb, and Fb - Fa. Because ∆Fa and ∆Fb are approximately proportional to Fa and Fb, respectively (cf. eq A-4), the overall error is proportional to the values of Fa/(Fb - Fa) and Fb/(Fb - Fa). This implies not only that the error bar becomes smaller as the difference Pb - Pa increases but also that, for a given Pb - Pa value, the error bar becomes smaller as Pa increases. After these preliminary experiments that give an idea about the proper level of argon addition, swelling and sorption characteristics were investigated in the pressure range 50-180 bar. The data are reported in Table 2 and plotted in Figures 5 and 6. For the experiments where different levels of argon were added, the swelling and sorption values corresponding to the highest values of Pb are considered, because they correspond to the smallest error. From Figure 5, it can be seen that swelling raises with pressure from 50 bar up to 140 bar and then goes through a maximum. From Figure 6, it


Figure 7. Photograph of the polymer disk arrangement. The polymer is indicated with dotted lines.

Figure 5. Experimental results for the CO2-induced swelling of PMMA at 80 °C obtained using the two-density method.

Figure 8. Sketch of the experimental setup for the visualization of swelling.

Figure 6. Experimental results for the sorption of CO2 in PMMA at 80 °C obtained using the two-density method. Also shown are the values obtained if the effect of swelling on the buoyancy correction is neglected. Table 2. Values of Swelling and Sorption Calculated Using the Two-Density Method at 80 °C Pa, bar

Pb, bar

swelling, %

sorption, g/g of polymer

50.0 50.0 50.0 70.0 70.0 103.0 103.0 103.0 103.0 108.0 140.0 140.0 140.0 162.2 162.2 182.0 182.0 182.0

54.0 59.0 68.0 80.0 102.0 114.0 114.0 128.0 151.0 134.0 151.0 189.0 210.0 206.4 235.0 202.0 222.0 282.0

6.44 ( 5.05 5.82 ( 2.33 5.59 ( 1.35 9.11 ( 2.45 10.23 ( 1.07 16.57 ( 3.49 11.87 ( 3.34 13.81 ( 1.66 13.96 ( 1.10 11.73 ( 1.65 18.75 ( 6.21 16.00 ( 1.66 15.57 ( 1.27 16.48 ( 2.15 14.24 ( 1.53 13.93 ( 7.86 14.92 ( 4.13 12.02 ( 1.80

0.048 ( 0.004 0.048 ( 0.002 0.048 ( 0.001 0.071 ( 0.003 0.072 ( 0.001 0.117 ( 0.007 0.108 ( 0.007 0.111 ( 0.000 0.111 ( 0.003 0.112 ( 0.004 0.154 ( 0.021 0.145 ( 0.006 0.144 ( 0.005 0.158 ( 0.009 0.149 ( 0.007 0.149 ( 0.037 0.154 ( 0.020 0.140 ( 0.009

can be observed that sorption exhibits a trend similar to that of swelling; i.e., it rises with pressure up to 162 bar and then falls when the pressure is increased further. From Table 2, it can be noted that the error on sorption is smaller than that on swelling. The reason for this can be understood from the expressions used to calculate the error bars given in Appendix A.2.2. In Figure 6, the sorption values that one would obtain by assuming no swelling are also shown. The difference

between the curves shows the effect of omitting the polymer swelling on the buoyancy correction for the calculation of sorption. This clearly demonstrates that this difference would be negligible at lower pressure values but becomes significant at higher pressures, as expected. 3. Conventional Method Because the results obtained with the two-density method have to be validated and literature data for PMMA are not consistent with each other, a set of experiments using the conventional method, i.e., using two independent measurement techniques for swelling and sorption, were carried out. 3.1. Materials and Experimental Setup. For direct visualization, a cathetometer with an accuracy of 0.01 cm is used to determine the swelling of a polymer disk housed in a view cell. The view cell is a cylinder and has a volume of 50 cm3. Circular sapphire windows, which are orthogonal to the axis of the cylinder, are mounted at its two ends. The view cell is immersed in a thermostated water bath and is equipped with a pressure transducer and a thermocouple. For the sorption measurements, the Rubotherm balance whose operation is described in the previous section is used. 3.2. Experimental Procedure. 3.2.1. Swelling by Visualization. The same polymer rod as that used in the two-density measurements is annealed at 120 °C to relieve the stresses formed during the industrial extrusion process. The annealed rod is then machined to form a circular disk with a diameter d0 )1.7 cm and a thickness t0 ) 0.05 cm. The thickness is chosen so as to provide enough mechanical strength while at the same time limiting the characteristic diffusion length. Because stresses could be generated during the machining process, the disk was annealed again at the same condition, i.e., at 120 °C. It was found that if this annealing was not performed, when subjected to a CO2

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environment the disks tended to deform in a particular direction, i.e., anisotropically. The disk was fixed to a brass holder with a screw of diameter dscrew ) 0.13 cm to prevent the disk from floating away during CO2 dosing (see Figure 7). The brass holder along with the disk was placed in the cell parallel to its axis. The whole setup is then arranged to have the disk perfectly horizontal to avoid gravityinduced deformations. With this arrangement and given the fact that the cathetometer can be moved on a horizontal plane, the only characteristic length that could be measured was the diameter of the disk. The final setup is shown in Figure 8. After pressurization of the cell with CO2, the change in the diameter of the disk was measured until equilibration. To calculate the volume of the swollen disk, in addition to the diameter, its thickness is also required. Because the current setup does not allow the independent measurement of the thickness, isotropic volume expansion was assumed, i.e.

d(F,T) - dscrew t(F,T) ) d0 - dscrew t0

(12)

where d(F,T) and t(F,T) are the diameter and thickness of the swollen disk at a density F and temperature T, respectively. The swelling is therefore calculated using the following expression:

s)

Vpoly(F,T) - Vpoly 0 Vpoly 0

π [d(F,T)2 - dscrew2]t(F,T) 4 ) -1 π 2 [d0 - dscrew2]t0 4 (13)

By substitution of eq 12 into eq 13, the final expression for the calculation of the swelling is obtained:

s)

[

]

d(F,T) - dscrew d2(F,T) - dscrew2 -1 d0 - dscrew d02 - dscrew2

(14)

It is worth noting that, because the diameter of the screw is much smaller compared to that of the disk, its effect on the calculated swelling value is negligible. 3.2.2. Sorption by Gravimetry. The procedure to measure the sorption by gravimetry is the same as that in step a of the two-density method. Because a single value of the density is considered in each measurement, the superscript a is omitted in the following equations. At equilibrium conditions, the balance signal is again given by eq 3, which includes two unknown quantities, ms(F,T) and Vpoly(F,T). However, in this case, the value of Vpoly(F,T) can be computed independently using the as follows: measured swelling and the value of Vpoly 0 met ] ms(F,T) ) M1(F,T) - M1(0,T) + F[Vpoly 0 (1 + s) + V (15)

From the above expression sorption, q can be calculated as follows:

q ) ms(F,T)/mpoly 0

(16)

When experiments are performed at different pressures, the complete sorption isotherm can be measured. In the case where the pressure in the balance does not exactly match the pressure at which the swelling

Table 3. Values of Swelling Measured Using the Conventional Method T, °C

P, bar

s, %

T, °C

P, bar

s, %

50

29 48 72 83 95 119 131 147 182 191 37 60 81 113 132 154 180 187 214 243

4.67 7.43 11.77 14.41 16.61 19.78 20.38 21.59 22.80 23.41 4.67 8.74 11.76 16.39 18.37 20.36 21.36 21.97 23.18 24.82

80

20 46 51 79 107 126 148 162 197 231 244

3.04 5.23 6.15 9.69 12.35 15.05 17.00 18.39 21.79 22.19 23.21

65

Table 4. Values of Sorption Measured Using the Conventional Method T, °C

P, bar

q, g/g

T, °C

P, bar

q, g/g

50.0

54 78 95 116 128 135 150 176 189 64 90 116 136 153 175 193 207 237

0.0999 0.1377 0.1650 0.1886 0.1981 0.2065 0.2155 0.2256 0.2307 0.0799 0.1161 0.1501 0.1685 0.1819 0.1969 0.2059 0.2138 0.2277

80

50 103 108 162 183 207 238

0.0479 0.1082 0.1146 0.1663 0.1786 0.1916 0.2049

65

measurements are available, the value of swelling at the required pressure is obtained by interpolating the swelling data through a polynomial fit. 3.3. Results. Using the conventional approach, measurements were made at three different temperature levels, namely, 50, 65, and 80 °C, up to a pressure of 200 bar. The measurements at 80 °C were performed for comparing the data with the results of the twodensity method, while the experiments at 50 and 65 °C were carried out to have a significant comparison with previous literature data. The results of the swelling and sorption measurements are reported in Tables 3 and 4 and are shown in Figures 9 and 10, respectively. At all three temperatures investigated, both swelling and sorption increase monotonically with pressure. At a given pressure, swelling and sorption increase with decreasing temperature. From these results, it is possible to calculate the partial molar volume of CO2 in the polymer matrix. For this, only the data corresponding to the rubbery state of the polymer can be considered. Because sorption of a fluid changes the glass transition temperature, Tg, of a polymer, the values reported by Condo and Johnston16 for the Tg of CO2-swollen PMMA have been used to select experimental data among those in Table 3 that correspond to a rubbery state of the polymer.


Figure 9. Experimental results for the CO2-induced swelling of PMMA at three different temperatures obtained from the conventional method.

Figure 11. Plot of corrected swelling vs CO2 concentration in the swollen polymer used to evaluate the partial molar volume of CO2 in PMMA. Points correspond to experimental data. Curves correspond to the straight line fit of the experimental data: (‚‚‚) 50 °C; (- - -) 65 °C; (s) 80 °C. Table 5. Estimated Partial Molar Volumes of CO2 in PMMA T, °C

V h CO2, cm3/mol

T, °C

V h CO2, cm3/mol

50.0 65.0

37.97 41.53

80.0

43.08

volume can be obtained by combining eqs 13, 16, 17, and 19:

V h CO2 ) Vpoly 0

Figure 10. Experimental results for the sorption of CO2 in PMMA at three different temperatures obtained from the conventional method.

The partial molar volume of CO2 in the polymer-CO2 system is defined as

V h CO2 )

( ) ∂Vpoly ∂nCO2

(17)

P,T,npoly

At constant T and npoly, the differential of the volume of the polymer, dVpoly, can be written as

dVpoly )

( ) ∂Vpoly ∂nCO2

dnCO2 + P

( ) ∂Vpoly ∂P

dP

(18)

nCO2

By substitution of the definition of the partial molar volume and introduction of the isothermal compressibility of the gas-polymer system, βpoly ) -(∂ ln Vpoly/ ∂P)T,nCO2, eq 18 becomes

h CO2 dnCO2 - βpolyVpoly dP dVpoly ) V

(19)

Now, assuming that βpolyVpoly = βpoly Vpoly 0 0 , i.e., the product of the compressibility and the polymer volume of the gas-polymer system do not change with the sorption of CO2, an expression for the partial molar

(

)

d Vpoly + βpoly 0 P ) dnCO2 Vpoly 0 MWCO2 d dq Fpoly 0

(s + βpoly 0 P) (20)

where MWCO2 is the molecular weight of CO2 and Fpoly 0 is the density of the pure polymer (cf. Table 1). However, in the literature, it is customary to express the sorbed concentration of CO2 in the swollen polymer, C, in cm3(STP)/g of polymer. Accordingly, eq 20 can be written as

V h CO2 ) 22410

d (s + βpoly 0 P) dC

(21)

For the calculation of V h CO2, βpoly was taken to be 2.566 0 -5 -1 9 × 10 bar . It can be shown that, under the considered operating conditions, the contribution of the term poly βpoly 0 P to the sum s + β0 P is minor (less than 2%) and therefore the effect of a possible inaccuracy in the quite arbitrary assumption βpolyVpoly = βpoly Vpoly is anyway 0 0 reduced. The plot of s + βpoly 0 P vs C for the three investigated temperatures is shown in Figure 11, where the data of the three different temperature values have been fitted with a straight line passing through the origin. The linearity of the plots suggests that for a given temperature V h CO2 is independent of the CO2 concentration, C, and the corresponding estimated values are reported in Table 5. Note that these values are close to the partial molar volume of CO2 typically encountered in rubbery polymers and in several organic liquids, i.e., 46 cm3/ mol.8,17 The temperature dependence of V h CO2, i.e., the decrease of V h CO2 with decreasing temperature, is also in agreement with previous literature results.17 These observations about the behavior of V h CO2 indicate that

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Figure 12. Comparison of the swelling results obtained by using the two-density and conventional methods at 80 °C.

Figure 13. Comparison of the sorption results obtained by using the two-density and conventional methods at 80 °C.

the swelling and sorption data measured in this study are consistent. Finally, it should be noted that, because V h CO2 remains fairly constant for rubbery polymers up to medium pressures, eq 20 can be easily integrated, leading to the following relationship between sorption, q, and swelling, s:

q)

MWCO2 s + βpoly 0 P V h CO2 Fpoly

(22)

0

This can be used to obtain quick estimates of swelling and sorption through measurements of either swelling or sorption. Note that in this case the temperature dependence of V h CO2 should be taken into account. The relationship given in eq 22 is accurate only for rubbery polymers and only up to a certain system-dependent pressure value. Above this threshold, V h CO2 decreases because of an unfavorable elastic contribution to the Gibbs free energy.18 Hence, in this region, eq 22 cannot be directly used anymore. 4. Discussion 4.1. Comparison between the Two-Density Method and the Conventional Method. The comparison of the results obtained using the two methods at 80 °C is illustrated in Figures 12 and 13. The swelling measured by the two methods exhibits good agreement up to a pressure of 140 bar. Beyond this pressure, the trends diverge, with the swelling measured by the two-

density method being lower than that measured by the conventional method and, therefore, clearly incorrect. A similar trend is observed in the case of sorption. The trend measured by the new method is unusual and has been observed neither in this work nor in the literature. This means that the difference in the volume measured in the two-density and conventional methods arises because of the fact that the inert does affect the system either by changing the mass of the sorbed gas or by changing the volume of the polymer system. To investigate this, the experimental procedure used in the two-density method was implemented again using the visualization setup. The view cell was first charged with CO2 up to a pressure of 180 bar because this is the pressure level where the two methods exhibit the largest difference. After equilibration, the diameter of the disk was measured, and then argon was charged in steps to reach the different values of Pb reported in Table 2. At each pressure level, the diameter of the disk was measured again. In none of these experiments could a measurable change in volume be observed. This observation seems to indicate that the differences in the measured values of swelling and sorption by the two methods is due to the change in the mass of the sorbed gas. This effect can be quantified using eq 6. In particular, the experiment corresponding to Pa ) 182 bar and Pb ) 282 bar, which corresponds to the largest difference in the measured swelling between the two methods, is considered. By substitution of the measured values on the left-hand side, the value of Vpoly(Fb,T) at Pa ) 182 bar obtained by interpolation from the results of the conventional method and the detection limit of the cathetometer for the term Vpoly(Fb,T) - Vpoly(Fa,T) ) 0.0045 cm3, the value of the quantity [ms(Fa,T) ms(Fb,T)]/(Fb - Fa) can be estimated. For the experimental conditions considered, this value is equal to -0.148 cm3, which corresponds to 14% of Vpoly(Fb,T) at Pa ) 182 bar. Further, the value of ms(Fa,T) - ms(Fb,T) at the same conditions corresponds to -0.0069 g, which is about 4% of the ms(Fa,T) value measured by the conventional method. It is evident that, though the magnitude of the change in the amount of the sorbed gas is minor, the impact it has on the measured volume is significant. This is due to the fact that the effect of the change in the sorbed amount is amplified by the term Fb - Fa, which in this case is 0.0466 g/cm3. Hence, it can be concluded that the differences in the measurement of the swelling and sorption between the two methods arise from the change in the amount of the sorbed gas caused by the addition of the inert. To conclude, the new method gives the possibility of measuring the sorption and swelling in a reliable way up to certain system-specific conditions. From the comparison of the two methods presented in this work, one can define the operating window where the twodensity method can be applied reliably for the system CO2-PMMA. It is seen that the technique yields good results up to about 150 bar, beyond which the estimation of the swelling and hence of the sorption becomes significantly different from the values that have been obtained by the conventional method. This is due to the fact that beyond this threshold the inert is sorbed by the polymer by an extent that, although modest, is sufficient to strongly affect the estimated values of CO2 sorption and swelling. Although, in principle, an inert better than argon could be found, it is clear that an


Figure 14. Comparison of the swelling results obtained by using the conventional method and those reported in the literature. The symbols refer to the results obtained in this work: (‚‚‚) Liau and McHugh at 58.1 and 68.0 °C;3 (- - -) Wissinger and Paulaitis at 58.8 °C;4 (s) Fehrenbacher et al. at 60 °C.6 The vertical lines indicate the pressures at which the polymer undergoes glass transition (data obtained from Condo and Johnston16).

Figure 15. Comparison of the sorption results obtained by using the conventional method and those reported in the literature. The symbols refer to the results obtained in this work: (‚‚‚) Liau and McHugh at 58.1 and 68 °C;3 (- - -) Wissinger and Paulaitis at 58.8 °C;4 (-‚-) Chang et al. at 50 °C;5 (s) Shieh et al. at 52 °C.7 The vertical lines indicate the pressures at which the polymer undergoes glass transition (data obtained from Condo and Johnston16).

upper beyond for the application of the two-density method would most likely remain. 4.2. Comparison with the Literature Data. As discussed earlier, there is a discrepancy in the swelling and sorption data presented in the literature. Hence, it is important to compare the present data with the ones available in the literature in the vicinity of the experimental conditions that have been used in the present study. This is discussed below with reference to Figures 14 and 15, where the symbols correspond to data measured in this work and the curves to different sets of literature data. Because the behavior of the polymer below the glass transition depends on the thermal history of the sample, comparisons between different studies below Tg have to be performed with caution. However, for completeness, the following discussion compares the different results over the entire pressure range. To differentiate the region where the polymer exists in the glassy and rubbery states, in both Figures 14 and 15, a vertical line is drawn corresponding to the pressure at which the glass transition occurs for the different temperatures.

4.2.1. Swelling. Liau and McHugh3 used a visualization method to measure the swelling of a cylindrical rod of PMMA at 41.8, 58.1, and 68.0 °C. As shown in Figure 14, their data (dotted curves) and the data obtained in this work exhibit a similar temperature dependence; i.e., swelling decreases with increasing temperature. The swelling values of the two studies are consistent with each other up to a pressure of 50 bar, namely, until PMMA is in the glassy state. At pressures higher than 50 bar, the swelling data of Liau and McHugh are significantly lower. This could be due to the thickness of the considered sample, which was too large to achieve equilibrium in a sufficiently short period of time as discussed in refs 4 and 11. Note that the partial molar volumes calculated from the latter set of data are in the range of 4-19 cm3/mol, which is much lower than the about 45 cm3/mol that is estimated in the present study and in several other studies on rubbery polymers.8 Wissinger and Paulaitis4 used a visualization technique to measure the swelling of a film of a polymer suspended on a hook. The dilation of the length of the film that is perpendicular to the ground was measured. The reported swelling curves are shown in Figure 14 (broken curves). It is seen that these data, which have been measured at 58 °C, fall nicely between the swelling values measured at 50 and 65 °C in the present work up to a pressure of 80 bar. Beyond 80 bar, the swelling values are larger than ours. This can be explained by considering that, in the work of Wissinger and Paulaitis, it was found that the CO2 concentration of 45 cm3(STP)/g of polymer reduces the PMMA Tg to 58 °C, which is the temperature value where the swelling data were measured. Because in these conditions the concentration of CO2 is equal to 45 cm3(STP)/g of polymer at P ) 50 bar, when the polymer is no longer in the glassy state, the polymer chains have increased mobility, and this can cause sagging of the polymer film under its own weight, thus explaining the large swelling values measured at higher pressures.11 This explanation is further supported by the fact that V h CO2 calculated from their data lies in the range of 30-78 cm3/mol. These estimates were made for the conditions where the polymer is in a rubbery state. The variation of Tg with the sorbed concentration of CO2 reported by Wissinger and Paulaitis was used to determine whether the polymer is rubbery or glassy. At conditions close to the concentration at which the polymer changes from a glassy to a rubbery state, V h CO2 is close to 43 cm3/mol. However, at higher concentrations, the value of V h CO2 increases up to 78 cm3/mol. The data of Fehrenbacher et al.6 at 60 °C, which were measured using waveguide spectroscopy, are shown by the continuous curve in Figure 14. Their results, obtained in a range where PMMA is rubbery, agree with the data obtained in this work because they fall exactly between the data at 50 and 65 °C. 4.2.2. Sorption. Liau and McHugh3 use a barometric technique to measure the sorption data, which are shown by the dotted line in Figure 15. At both 58 and 68 °C, the reported sorption values are higher than those obtained in this work, and in addition, at higher pressures they exhibit an opposite trend with respect to temperature; i.e., sorption increases with temperature instead of decreasing. In a barometric technique, sorption is obtained through the following equation:

ms ) min - (Vcell - Vpoly)F

(23)

2558


where min is the mass of the gas initially filled in the system, Vcell is the volume of the barometric cell, F is the density of the gas, and Vpoly is the volume of the swollen polymer, which was determined independently. The value of swelling hence affects the sorption through eq 23. For a given sorption experiment, where the pressure in the system is measured at equilibrium, an underestimation of Vpoly would lead to a corresponding underestimation of the sorption. It was discussed that the swelling data of Liau and McHugh could be underestimated because of insufficient equilibration times. Under these circumstances, one would expect that the sorption data would be underestimated as well. However, the results show an opposite trend; i.e., the sorption is larger even though the swelling data were smaller. Wissinger and Paulaitis4 used a gravimetric technique to measure the sorption on a film of PMMA. The same apparatus as that used for swelling was used, but the hook was replaced with a spring. The comparison of these data with those obtained in this work is similar to that of the swelling data. As shown by the broken curve in Figure 15, the agreement is good up to a pressure of 80 bar, beyond which the values of Wissinger and Paulaitis are higher than ours. In a gravimetric system, the measured sorption is a function of the volume of the swollen polymer, as shown in eq 2. Hence, an overestimation of the swelling, such as that evidenced in Figure 14, leads to an overestimation of the sorption. Accordingly, it is possible that the larger swelling values, plausibly arising from sagging of the polymer, as discussed in the previous section, are responsible for the higher sorption values in Figure 15. Chang et al.5 use swelling as a means of measuring the sorption. They base their observation on the fact that, for rubbery polymers, the swelling and sorption are similar and hence the measurement of one value yields also the other. This observation was tested for silicone rubber at 35 and 50 °C, and it was found that the swelling values and the corresponding sorption values fit within 6% of each other. The sorption values at 50 °C, which are represented by the dotted-line curve in Figure 15, are much larger than the ones obtained in this work. In the work of Chang et al., for the PMMA case, it is not mentioned explicitly whether the measurements for swelling and sorption were performed or whether only the swelling experiments were performed. However, even considering that these values correspond to swelling values, they seem to be larger than our swelling data. Shieh and Liu7 do not perform an in situ measurement of sorption. The polymer sample is saturated with CO2 in a pressure cell. After equilibration, the pressure is released within 20 s; the polymer is taken out of the cell and weighed in a balance. The reported sorption values are much smaller than those measured in this work, as indicated by the continuous curve in Figure 15. The quick depressurization, in principle, should not have a major influence on the measurements because a polymer sample with a characteristic diffusion time for CO2 on the order of thousands of seconds has been used. However, the comparison with the other experimental data indicates that significant desorption of CO2 occurs even in such a short time. 5. Conclusion Swelling and sorption characteristics of the PMMACO2 system under supercritical conditions have been

studied. A new measurement technique has been introduced. This technique, purely gravimetric in nature, measures simultaneously the sorption and swelling, and it does not assume isotropic expansion and, hence, has the advantage that it could be used on systems without the need to fabricate the polymer sample in any regular shape. A second approach considered involves the use of a conventional technique, i.e., swelling measurement by direct visualization and sorption measurement by gravimetry. The results obtained with the latter technique have been compared with literature data obtained with similar methods. A critical discussion of the various results allows one to draw conclusions about the behavior of the PMMA-CO2 system in the ranges of P ) 0-250 bar and T ) 50-80 °C. Finally, the swelling and sorption values measured by the two different methods at 80 °C indicated that, beyond about 150 bar, the new technique yielded underestimated values of the swelling and sorption as compared to the conventional technique. However, at pressures up to 150 bar, the results from the two methods were in good agreement, thereby showing that the new technique could be used at low and moderate pressures to obtain quick and reliable estimates of the swelling and sorption. It has been found that the inaccuracy of the data obtained with the new technique originated from a strong sensitivity of the method to small sorption of the inert. Acknowledgment We acknowledge the technical help of Christian Rohrbach. The financial support of the Federal Office for Education and Research (BBW, Bern, Switzerland; Contract No. EC-G1RD-CT-2002-00676), sponsor in the frame of the EU research program “Growth/Innovative Products”, and partial funding from the Swiss National Science Foundation (SNF) under Grant SNF 20-6798902 are gratefully acknowledged. Appendix: Error Analysis A.1. Density. The equation for calculating the density of the fluid phase is the following:

F)

msinker - M2(F,T) + M1(F,T)

(A-1)

Vsinker

where M1(F,T) and M2(F,T) correspond to the signal of the balance in positions 1 and 2, while Vsinker and msinker are the calibrated volume and mass of the sinker, respectively. The measurement error of the density is defined as

{(

) [ ] (

]

2 2 ∂F ∂F ∆msinker + ∆M1(F,T) + sinker ∂M1(F,T) ∂m 2 2 0.5 ∂F ∂F ∆Vsinker (A-2) ∆M2(F,T) + sinker ∂M2(F,T) ∂V

∆F )

[

)]

where ∆msinker and ∆Vsinker are the errors with which the mass and volume of the sinker are known and ∆M is the accuracy of the balance itself. Using eq 1, the following relationship describing the measurement error on the density is obtained:

∆F )

[(

) ( ) (

∆msinker Vsinker

2

+2

∆M Vsinker

2

+

∆Vsinker F Vsinker

)]

2 0.5

(A-3)


From the calibration certificate of the balance, it is known that

∆msinker ) 0.00001 g

The measurement error associated with the sorption measurement is given by

∆m ˆs)

(

Vsinker ) 4.37993 cm3 ∆V

sinker

) 0.00219 cm

3

By incorporation of this information in eq A-3 and by recognition of the fact that the contributions from the first and second terms are small compared to the third term, the error on the density can be approximated as follows:

∆F = 0.0005F

(A-4)

A.2. Two-Density Method. A.2.1. Swelling. The equation to calculate the volume of the polymer in the two-density method is given by eq 8

M1(Fa,T) - M1(Fb,T) b

a

F -F

- Vmet

(

[(

∂V ˆ poly ∆M ∂M1(Fa,T)

∂V ˆ poly ∆Fb ∂Fb

) ( 2

) ( 2

+

∂V ˆ poly ∆M ∂M1(Fb,T)

∂V ˆ poly + ∆Fa ∂Fa

) ( 2

)

2

[(

)]

2 0.5 ∂V ˆ poly + ∆Vmet met ∂V (A-6)

) (

)

∆M 2 V ˆ poly + Vmet b 2 + ∆F + a F -F Fb - Fa V ˆ poly + Vmet a 2 ∆F + (∆Vmet)2 Fb - Fa b

(

)

]

∆V ˆ

[(

) (

)

]

(A-7)

)

A.2.2. Sorption. The expression used for determining the sorption is given by eq 9

ˆ poly + Vmet] m ˆ s ) M1(Fa,T) - M1(0,T) + Fa[V

) ( 2

+

+

)]

2 0.5 ∂ms ∆Vmet met ∂V (A-10)

ˆ poly + 1.8696)0.0005Fa]2 + (Fa∆V ˆ poly)2 + ∆m ˆ s = [[(V a 2 0.5 (0.0057F ) ] (A-12) A.3. Conventional Method. A.3.1. Swelling. In the case of the conventional method, the error related to swelling is described by the following expression:

∆s )

[(

∂s ∆d(F,T) ∂dfin

) ( 2

+

)]

∂s ∆d0 ∂din

2 0.5

(A-13)

where ∆d(F,T) ) ∆d0 ) 0.01 cm corresponds to the accuracy of the cathetometer. The equation can be rewritten in the following way:

∆s )

(

{(

3d(F,T)2 - 2d(F,T) dscrew - dscrew2

) )

2

0.01

d03 + dscrew3 - dscrew2d0 - d02dscrew

-

+

2

3d02 - dscrew2 - 2d0dscrew

(d03 + dscrew3 - dscrew2d0 - d02dscrew)

0.01 2

}

0.5

[d(F,T)3 + dscrew3 - d(F,T)2dscrew - dscrew2d(F,T)]2

(A-14)

0.5

2 0.0001 2 V ˆ poly + 1.8696 b ) 2 b + 0.0005F + F - Fa Fb - Fa 2 0.5 V ˆ poly + 1.8696 a 0.0005F + 0.000032 (A-8) Fb - Fa

(

∂ms ∆Vpoly ∂V ˆ poly

)

2

which, when the value for dscrew ) 0.13 cm is inserted, becomes

The volume of the metal parts was determined by using an empty basket and was found to be Vmet ) 1.8696 cm3 with ∆Vmet ) 0.0057 cm3. Therefore, from eq 7, the measurement error on V ˆ poly (in cm3) is given by poly

+

∂ms ∆M ∂M(0,T)

Because the contribution from ∆M is small compared to the other terms and is not a function of Fa, the error on m ˆ s (in g) can be approximated as

+

where ∆Fa and ∆Fb are calculated from eq A-3. When the expressions for the partial differential terms are introduced, eq A-6 reduces to

∆V ˆ poly ) 2

2

+

ˆ poly)∆Fa]2 + (Fa∆V ˆ poly)2 + ∆m ˆ s ) [2(∆M)2 + [(Vmet + V a met 2 0.5 (F ∆V ) ] (A-11)

(A-5)

from which the following expression for the measurement error can be obtained:

∆V ˆ poly )

) (

∂ms ∆Fa ∂Fa

) ( 2

which can be rearranged to obtain

∆M1(F,T) ) ∆M2(F,T) ) ∆M ) 0.0001 g

V ˆ poly )

[(

∂ms ∆M ∂M1(Fa,T)

(A-9)

∆s )

(

{(

-

3d(F,T)2 - 0.26d(F,T) - 0.0169

d03 - 0.13d02 - 0.0169d0 + 0.0022 3d02 - 0.26d0 - 0.0169

)

2

0.01

0.01 (d03 - 0.13d02 - 0.0169d0 + 0.0022)2

+

)

2

[d(F,T)3 - 0.13d(F,T)2 - 0.0169d(F,T) + 0.0022]2

}

0.5

(A-15) A.3.2. Sorption. In the case of the conventional method, the error related to sorption is described by the following expression:

∆ms ) {2(0.0001)2 + {[Vmet + V0(1 + s)]∆Fa}2 + (Fa∆Vmet)2 + (FaV0∆s)2}0.5 (A-16) Because the contribution from ∆M is small compared

2560


to the other terms and is not a function of Fa, the error on m ˆ s (in g) can be approximated as

∆ms = {[1.8696 + V0(1 + s)]0.0005Fa}2 + (0.0057Fa)2 + (FaV0∆s)0.5 (A-17) considering that, in this case, the swollen volume is expressed as Vpoly ) V0(1 + s). Notation C ) concentration of the sorbed gas CO2 [cm3(STP)/g of polymer] CO2 ) [cm3(STP)/g of polymer] d ) diameter of the disk [cm] f ) fugacity [bar] M1 ) balance signal at measuring position 1 [g] M2 ) balance signal at measuring position 2 [g] Mn ) number-average molecular weight [g/mol] m ) mass [g] m ˆ s ) measured value of the sorbed gas by the two-density method [g] MW ) molecular weight [g/mol] n ) number of moles [mol] P ) pressure [bar] q ) sorption [g/g] s ) swelling T ) temperature [°C] t ) thickness of the disk [cm] V ) volume [cm3] V ˆ poly ) measured volume of the polymer by the two-density method [cm3] V h ) partial molar volume [cm3/mol] Greek Letters β ) isothermal compressibility [bar-1] ∆ ) error F ) density [g/cm3] Subscripts and Superscripts 0 ) state of the polymer a ) state of the polymer after step a in the two-density method b ) state of the polymer after step b in the two-density method basket ) basket fin ) final state of the polymer disk met ) metal parts in the balance poly ) polymer sinker ) sinker

Literature Cited (1) Cooper, A. Polymer synthesis and processing using supercritical carbon dioxide. J. Mater. Chem. 2000, 10, 207-234. (2) Tomasko, D. L.; Li, H. B.; Liu, D. H.; Han, X. M.; Wingert, M. J.; Lee, L. J.; Koelling, K. W. A review of CO2 applications in the processing of polymers. Ind. Eng. Chem. Res. 2003, 42 (25), 6431-6456. (3) Liau, I.; McHugh, M. Supercritical Fluid Technology; Elsevier Science Publishers: New York, 1985. (4) Wissinger, R.; Paulaitis, M. Swelling and Sorption in Poymer-CO2 Mixtures at elevated Pressures. J. Polym. Sci., Part B: Polym. Phys. 1987, 25, 2497-2509. (5) Chang, S.; Park, S.; Shim, J. Phase equilibria of supercritical fluid-polymer systems. J. Supercrit. Fluids 1998, 13, 113-119. (6) Fehrenbacher, U.; Jakob, T.; Berger, T.; Knoll, W.; Ballauff, M. Refractive index and swelling of thin PMMA films in CO2/MMA mixtures at elevated pressures. Fluid Phase Equilib. 2002, 200, 147-160. (7) Shieh, Y.; Liu, K. Solubility of CO2 in Glassy PMMA and PS over a Wide Pressure Range: The Effect of Carbonyl Groups. J. Polym. Res. 2002, 9, 107-113. (8) Fleming, G. K.; Koros, W. J. Dilation of Polymers by Sorption of Carbon-Dioxide at Elevated Pressures. 1. SiliconeRubber and Unconditioned Polycarbonate. Macromolecules 1986, 19 (8), 2285-2291. (9) Kamiya, Y.; Mizoguchi, K.; Naito, Y. Plasticization of Poly(Ethyl Methacrylate) by Dissolved Argon. J. Polym. Sci., Part B: Polym. Phys. 1992, 30 (10), 1183-1183. (10) Jacobs, M.; Kemmere, M.; Loos, T.; Keurentjes, J. Sorption and Swelling Behavior of Polymers in High-Density Gases. Experiments and Modeling. In HP 4th International Symposium on High-Pressure Technology and Chemical Engineering, Venice, 2002. (11) Zhang, Y.; Gangwani, K. K.; Lemert, R. M. Sorption and swelling of block copolymers in the presence of supercritical fluid carbon dioxide. J. Supercrit. Fluids 1997, 11 (1-2), 115-134. (12) Dreisbach, F.; Losch, H. W. Magnetic suspension balance for simultaneous measurement of a sample and the density of the measuring fluid. J. Therm. Anal. Calorim. 2000, 62 (2), 515-521. (13) DiGiovanni, O.; Doerfler, W.; Mazzotti, M.; Morbidelli, M. Adsorption of supercritical carbon dioxide on silica. Langmuir 2001, 17, 4316-4321. (14) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall International: New York, 1999. (15) Van Krevelen, D. W. Properties of Polymers; Elsevier Science Publishers: New York, 1990. (16) Condo, P. D.; Johnston, K. P. Retrograde Vitrification of Polymers with Compressed Fluid DiluentssExperimental Confirmation. Macromolecules 1992, 25 (24), 6730-6732. (17) Kamiya, Y.; Naito, Y.; Hirose, T.; Mizoguchi, K. Sorption and Partial Molar Volume of Gases in Poly(Dimethyl Siloxane). J. Polym. Sci., Part B: Polym. Phys. 1990, 28 (8), 1297-1308. (18) Shenoy, S. L.; Fujiwara, T.; Wynne, K. J. Quantifying Plasticization and Melting Behavior of Poly(vinylidene fluoride) in Supercritical CO2 Utilizing a Linear Variable Differential Transformer. Macromolecules 2003, 36, 3380-3385.

Received for review June 3, 2004 Revised manuscript received August 18, 2004 Accepted August 20, 2004 IE049523W

Simultaneous Measurement of Swelling and Sorption in a

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