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Solubility of Hydrofluorocarbon (HFC-134a, HFC-152a) and Hydrochlorofluorocarbon (HCFC-142b) Blowing Agents in Polystyrene.


Solubilities of blowing agents (HFC-134a, HCFC-142b, and HFC-152a) in polystyrene (PS) were measured at temperatures from 348 to 473 K and pressures up to 3.2 MPa with a volumetric method. For all conditions, the solubility of the blowing agents in PS decreased with increasing temperature. At a given temperature and pressure, the solubility of HFC-134a, HFC-152a, and HCFC-142b in PS increased in that order. Solubilities could be correlated with the Sanchez-Lacombe equation of state with temperature-dependent binary interaction parameters to within 3.4% average relative percent deviation. The temperature dependence of the Henry's constants, [K.sub.p], for the blowing agents were found to have a linear relationship between ln(1/[K.sub.p]) and [([T.sub.c]/T).sup.2], where [T.sub.c] is the critical temperature of the blowing agent.


Chlorofluorocarbons (CFC-11 and CFC-12) have been used as physical blowing agents for industrial foaming processes for a number of years until they were banned in 1997 by the Montreal Protocol. Alternative blowing agents, such as hydrochlorofluorocarbons, hydrofluorocarbons, and hydrocarbons have been suggested as replacements since their ozone depletion potential is much less. However, solubility data required for process applications is lacking, which makes it difficult for practitioners to evaluate their performance or possible substitution.

Data on gas solubility, such as [N.sub.2] and [CO.sub.2] used for microcellular foam productions, in polymer melts have been reported by several investigators [1-3]. However, solubility data for blowing agents such as fluorocarbons are still needed. Gorski et al. [4] reported on the solubility of CFC-l 1, CFC-12, HCFC-22, and CFC-114 in seven polymers. Daigneault et al. [5] measured solubility of HCFC-142b, HFC-134a, HFC-125 and isopropanol in polystyrene at 40-200[degrees]C. Garg et al. [6] reported on the solubility of HFC-152a in molten polystyrene at temperature 135[degrees]C and 160[degrees]C and pressures up to 17 MPa. Wong et al. [7] reported solubility of HFC-134a in polystyrene at temperature 30-120[degrees]C and pressures up to 3.5 MPa. In these data, however, there are inconsistencies as described below. The objective of this study was to determine the solubility of fluorocarbon and chlorofluorocarbon blowing agents in polystyrene and to develop a method for solubility correlation.



Polystyrene (PS) ([bar{M}]w = 1.87 x [10.sup.5], [bar{M}]w/[bar{M}]n = 2.67, = 373.6 K) was obtained from Mitsui Toatsu Chemicals, inc. (Yokohama). The PS was frozen in liquid introgen and was ground to obtain from 0.1 mm to 0.25 mm particles after sieving. HFC-134a (1, 1, 1, 2-tetrafluoroethane, purity [greater than] 99.8%) was supplied by Daikin Industries, Ltd. (Osaka). HCFC-142b (1-chloro- 1, 1-difluoroethane, purity [greater than] 99.5%) and HFC-152a (1,1-difluoroethane, purity [greater than] 99.5%) were purchased from Asahi Glass Co. (Tokyo).


A volumetric method similar to that used by Gorski et al. [4] was used in this work. In the volumetric method, the system pressure and temperature are measured, and the amount of solute gas in the polymer at equilibrium is found by a mass balance on the solute in a sorption cell.

The experimental apparatus is shown in Fig. 1 and consisted of four sets of a sorption cell (about 42 [cm.sup.3] each), a solute cylinder (about 40 [cm.sup.3]), and a pressure sensor to obtain four solubility data, simultaneously. The sorption cells were filled with PS powder of known mass (about 22 g each) and were sealed with metal o-rings. After evacuation by means of a rotary vacuum pump, gas was loaded into the solute cylinders and was then introduced into the sorption cells. After a given period of time, the gas remaining in the filling tubes was recovered in the solute cylinders using liquid nitrogen. The amount of gas introduced (about 0.5-2.5 g) was determined by measuring the difference in the solute cylinder mass before and after filling the sorption cell. Mass measurements were made to a resolution of [pm]0.1 mg and an accuracy of [pm]1.0 mg with a balance (Mettler Toledo, AT400). The solubility, S [g-gas/g-polym.]. was evaluated by following relation:

S = [([m.sub.i] - [m.sub.f]) - [frac{MP([V.sub.system]}]-[{[V.sub.polymer]){ZRT}]]/[m.sub.p] (1)

where [m.sub.i] and [m.sub.f] are the mass of the solute cylinder before and after the filling, M is the molar mass of the gas, R is the gas constant, Z is the compressibility factor of the gas, and [m.sub.p] is the mass of polymer. The second term on the right-hand side of [E.sub.q] 1 is the amount of gas in the gas phase of the sorption cell under equilibrium at temperature T and pressure P. The system volume, [V.sub.system] is the inner volume of the sorption cell including a valve, pressure sensor, and tube, and [V.sub.polymer] is the polymer volume. In this work, the gas compressibility factor was obtained from the equation of state of Tillmer-Roth and Baehr [8], Fukushima and Watanabe [9], and Outcalt and McLinden [10] for HFC-134a, HCFC-142b, and HFC-152a, respectively. The system volume was calibrated by making PVT measurements of carbon dioxide at 323.2 K and was corrected with coefficient of linear expansion of SUS3O4 (16.9)x [10.sup.-6] [K.sup.-1]) [11]. Accuracy of the system volume was estimated to [pm]0.01 [cm.sup.3]. The polymer volume was calculated with sample mass (accuracy: [pm] 1.0 mg) and specific volumes measured with a PVT apparatus [12]. The quantity of dissolved gas can be appreciable and usually leads to polymer swelling. [V.sup.polymer] was corrected for the swelling, Sw, estimated with the Sanchez and Lacombe equation of state (S-L EOS) [13, 14] as described later. Details of the correction were described in the Appendix.

Four sorption cells were fixed on a brass plate (10 mm in thickness) in a thermostated air bath to achieve high temperature stability with fluctuations estimated to be no more than [pm]0.05 K. Temperature was measured to within [pm]0.05 K with a temperature indicator (Hart Scientific, 1502) and a platinum resistance thermometer (Netsushin, NSR-300) inserted into the brass plate. The thermometer as well as the indicator was calibrated against an intelligent standard thermometer (Kaye Instruments, X0860, accuracy: [pm]0.01 K). Pressures were measured by using pressure sensors (Bourns Inc., ST3110 10, F.S. 1.7 MPa and 3.4 MPa, accuracy: [pm]0.4 kPa and [pm] 1.0 kPa, respectively) calibrated against a quartz crystal pressure transducer (Paroscientific, Inc., 31K, F.S. 7 MPa, accuracy: 0.01% F.S.). The calibration of the pressure sensors ranged between 323 and 473 K and was carried out periodically.

In this work, PS powder was used to reduce the equilibration time even at lower temperatures, because the diffusion time period of the powder was shorter than that of a pellet. Therefore, the measurements were carried out from lower to higher temperatures to keep the short diffusion time period of the powder below the glass transition temperature. For the samples prepared, equilibrium required approximately 24 h at 348 K and 6 h at 473 K. The uncertainty of solubility on pressure, gas amount, inner volume of the cell, and polymer volume measurements is estimated to be [pm]0.15%, [pm]0.7%, [pm]0.5%, and n0.7%, respectively. The uncertainty on the other factors (temperature and polymer amount measurements) is less than [pm]0.1%. Total uncertainty of the solubility is estimated to be [pm]2.2% not including the uncertainty of the polymer swelling estimation.



Experimental results are shown in Figs. 2-4 and Tables 1--3, Solid symbols denote uncorrected solubilities and open symbols denote solubilities that were corrected for polymer swelling with the S-L EOS. The swelling correction for all conditions was less than 8.3% of the original solubility. The solubility of each blowing agent increased proportionally with pressure and decreased with temperature. This behavior is exhibited for many polymer and condensable gas systems.

The solubility of HFC-134a reported by Wong et al. [7] obtained with an electrobalance method were 17% lower than values interpolated from data in this work (Fig. 2). The solubility data of HFC-134a and HCFC-142b reported by Daigneault et al. [5] obtained with a volumetric method were higher than values obtained in this work. For the case of HCFC-142b. their solubilities were 23% and 30% higher than our solubilities at 353 K and 0.5 MPa and 473 K and 2.5 MPa, respectively. For the case of HFC-134b, their solubilities were 67% and 156% higher than our solubility at 353 K and 1 MPa and 473 K and 2.5 MPa, respectively. The correlated data of Garg et al. [6] for HFC-152a was 60% and 11% higher than our interpolated data at 135[degrees]C and 1.5 MPa and 160[degrees]C and 2.5 MPa, respectively. Their data could not be shown in Figs. 2-4, because of large deviations from ours. These differences may be attributed to the polymer volume evaluation. In all methods of this work and the literature except Garg et al., poly mer volume is highly sensitive to the solubility (for example: 0.2% error in polymer PVT causes 0.7% error in the solubilities of this work). Other works did not mention specific volume of polystyrene, whereas the PVT of polystyrene was measured in this work. In the method of Garg et al., gas bubbles may have been present caused by the stirring, which may have led to their higher values, because it is hard to separate the bubbles from a highly viscous polymer solution.


Experimental solubility data were correlated with the Sanchez and Lacombe equation of state (S-L EOS) [13, 14]:

[tilde{P}] = -[[tilde{[rho]}].sup.2] - [tilde{T}] [ln(1 - [tilde{[rho]}]) + (1 - 1/r)[tilde{[rho]}]] (2)

[tilde{P}] = P/[P.sup.*], [tilde{[rho]}] = [rho]/[[rho].sup.*], [tilde{T}] = T/[T.sup.*], r = [MP.sup.*]/[RT.sup.*] [[rho].sup.*] (3)

where characteristic parameters, [P.sup.*], [[rho].sup.*], and [T.sup.*] of the S-L EOS for mixture are evaluated with the following mixing rules:

[P.sup.*] = [[sum].sub.t] [[sum].sub.j] [[phi].sub.i] [[phi].sub.j] [[P.sup.*].sub.ij] (4)

[[P.sup.*].sub.ij] = (1 - [k.sub.ij])[([[P.sup.*].sub.i] [[P.sup.*].sub.j]).sup.0.5] (5)

[T.sup.*] = [P.sup.*] [[sum].sub.i] ([[[phi].sup.0].sub.t] [[T.sup.*].sub.i]/[[P.sup.*].sub.i]) (6)

l/r = [[sum].sub.i] ([[[phi].sup.0].sub.i]/[[r.sup.*].sub.i]) (7)

[[[phi].sup.0].sub.i] = ([[phi].sub.i] [[P.sup.*].sub.i]/[[T.sup.*].sub.i])/ [[sum].sub.j]([[phi].sub.j] [[P.sup.*].sub.j]/[[T.sup.*].sub.j]) (8)

[[phi].sub.t] = ([w.sub.i]/[[[rho].sup.*].sub.i])/[[sum].sub.j] ([w.sub.j]/[[[rho].sup.*].sub.j]), (9)

In Eqs 4-9, [[T.sup.*].sub.i], [[P.sup.*].sub.i], [[[rho].sup.*].sub.i], and [[r.sup.0].sub.i] refer to the characteristic parameters of component i in the pure state and [k.sub.ij] is a binary interaction parameter determined by fitting the equation to the experimental data. The pure component parameters used are given in Table 4. The equilibrium between vapor and liquid phases is determined by equating the chemical potentials. [[mu].sub.i], of each component between the two phases. In the calculation of solubilities, it was assumed that the polymer was monodisperse and that it did not dissolve in the vapor phase. Thus the equilibrium condition is represented by the following equation:

[[[mu].sup.L].sub.1](T, p, [[[phi].sup.G].sub.1]) = [[[mu].sup.G].sub.1](T, P) (10)

where subscript 1 denotes component 1 (gas) and [[[mu].sup.G].sub.1] is simply the Gibbs potential of the gas phase. The chemical potential [[[mu].sup.L].sub.1] is given by Eq 43 of Reference 14.

The binary interaction parameter, [k.sub.ij], in Eq 5 was determined so as to minimize the relative deviations between experimental and calculated solubilities at each temperature. Correlation results are shown as solid lines in Figs. 2-4. The interaction parameters and correlation errors are listed in Table 5. The Sanchez-Lacombe EOS could correlate solubilities to within 3.4% average relative deviation. Temperature dependence on [k.sub.12] of each mixture is shown in Fig. 5. The [k.sub.12] varied almost linearly with temperature. This result is useful to interpolate or possibly extrapolate the solubilities at a given temperature. Correlation equations were formulated for these mixtures by using a least-squares method to determine a linear relationship between [k.sub.12] and the absolute temperature:

For HFC-134a + PS

[k.sub.12] = 0.1614 - 3.466 x [10.sup.-4]T[K] (11)

For HCFC-142b + PS

[k.sub.12] = 0.1045 - 2.550 X [10.sup.-4]T[K] (12)

For HFC-152a + PS

[k.sub.12] = 0.1294 - 2.889 X [10.sup.-4]T[K] (13)

Although PS was in its glassy state below its glass transition temperature of 373.6 K, linear relationships were obtained over a broad temperature range encompassing the glass transition temperature. The glass transition concentration of gases at 348 K estimated with Chow's method [15] was 0.046, 0.045, and 0.030 g-gas/g-polymer for HFC-134a, HCFC-142b, and HFC-152a, respectively. Though a portion of data at 348 K was obtained in the glassy state, the solubility isotherms did not exhibit dual-mode sorption behavior. Kamiya et al. [16] found that sorption isotherms depended on the sample history in [CO.sub.2] + glassy poly(vinyl benzoate) system. In spite of the glassy state, the first sorption isotherm did not show adsorption in microvoid space and linearly increased with pressure. The isotherms agreed with those extrapolated from higher pressures above the glass transition concentration. The reason that the linear correlation of [k.sub.12] was not affected by glassy state can be possibly attributed to polymer hysteresis.

The correction for polymer swelling to determine the actual solubilities was estimated with the S-L EOS.

The precise swelling definition is given in the Appendix. The maximum swelling value was 9.7 vol% at 348.2 K and 0.678 MPa for HCFC-142b.

The solubilities of CFCs [4] and [CO.sub.2] [1] in PS at 373 K are shown in Fig. 6. In Fig. 6, the solubility is given in units of [mol-gas/kg-polym.], because this ratio is useful for comparing blowing agents. The solubility of the blowing agents in PS at 373 K is in the order of CFC-11 [greater than] HCFC-142b [greater than] CFC-12 [geq] HFC-152a [greater than] HFC-134a [greater than] [CO.sub.2]. The order of solubility is similar to the order of the boiling point temperature of the blowing agents (see Table 1), except for CFC-12.

Henry's Constant

The temperature dependence of the Henry's constants was determined. Henry's constant, [K.sub.p] [kg MPa/[cm.sup.3] (STP)], was defined as follows:

[K.sub.p] = [lim.sub.s[rightarrow]0] ([f.sub.g]/s) (14)

where [f.sub.g] is fugacity of gas and s is solubility of gas [[cm.sup.3] (STP)/kg-polym.]. Henry's constant was evaluated by using S-L EOS with optimized [k.sub.ij].

Stiel and Harnish [17] found a linear relationship between ln(1/[K.sub.p]) and [([T.sub.c]/T).sup.2] for the solubility of various solutes in molten PS.

Ln(1/[K.sub.p]) = 6.859 + 2.706[([T.sub.c]/T).sup.2] (15)

where [T.sub.c] is critical temperature of the solute. Henry's constants for gases in PS obtained in this work, carbon dioxide [1], and Stiel and Harnish's equation are shown in Fig. 7. Eq 15 was developed to represent Henry's constants for many hydrocarbon vapors and Freons such as R-11, R-12, R-22, and etc. Henry's constants obtained in this work, however, deviated from Eq 15, and each gas required a separate correlation. The correlations determined were:

ln(1/[K.sub.p]) = 6.361 + 2.114[([T.sub.c]/T).sup.2] HFC - 134a + polystyrene (16)

ln(1/[K.sub.p]) = 6.847 + 2.371[([T.sub.c]/T).sup.2] HCFC - 142b + polystyrene (17)

ln(1/[K.sub.p]) = 6.732 + 2.306[([T.sub.c]/T).sup.2] HFC - 152a + polystyrene (18)

Equations 16-18 can represent the temperature dependence of the Henry's constant to within 0.9% average relative deviation.


Solubility of HFC-134a, HCFC-142b, and HFC-152a in polystyrene was measured at temperatures from 348 to 473 K and pressures up to 3.2 MPa with a volumetric method. The solubility of these gases in creased approximately linearly with increasing pressure and decreased with increasing temperature. The amount of HFC-134a, HFC-152a, and HCFC-142b in PS increased in that order. The Sanchez-Lacombe EOS could correlate solubilites to within 3.4% average relative deviation. The binary interaction parameter in the Sanchez-Lacombe EOS linearly varied with temperature. Henry's constants for each gas plotted as ln(1/[K.sub.p]) versus [([T.sub.c]/T).sup.2] were found to be linear.


The correction of polymer swelling due to gas dissolution is required to obtain the gas solubility. We used the swelling estimated with the S-L EOS to correct the solubility, because it is hard to measure the polymer swelling of molten polymer. Since absolute values of polymer specific volume are not accurately represented by the S-L EQS ([pm]0.0033 [cm.sup.3]/g) as reported by Rodgers (20), we used relative volume change of polymer estimated with the S-L EOS:

[V.sub.polymer] = [V.sub.polymer][(T,O).sub.exp] x Sw(T, P, S) (A-1)

where [V.sub.polymer] [(T,O).sub.exp] is volume of polymer at zero pressure obtained from the PVT experiment, and Sw(T, P, S) is the swelling due to gas dissolution as follows:

Sw(T, P, S) = (1 + S)[frac{[nu](T, P. S)}{[nu](T, O, O)}] (A-2)

In Eq A-2, [nu](T, O, O) is specific volume of pure polymer at zero pressure estimated with the S-L EOS. The [nu](T, is the specific volume of the mixture estimated with the S-L EOS combined with interaction parameter, [k.sub.12], optimized by fitting the solubility. Since Sw varies with the solubility. it is necessary to solve simultaneously Eqs 1, A-1, and A-2. The solubility was determined from successive substitution of S obtained from Eq 1 into Eq A-2.

In the carbon dioxide + poly(vinyl acetate) system at temperatures of 313.2 and 323.2 K and pressures up to 9 MPa, the swelling estimated with the S-L EOS combined with optimized [k.sub.ij] by fitting the solubility accurately represented the experimental data of Takishima et aL [21] to within an average relative deviation of 3.5%.


[f.sub.g] = Fugacity of gas, MPa.

[k.sub.ij] = Interaction parameter defined in Eq 5.

[K.sub.p] = Henry's constant, kg MPa/[cm.sup.3] (STP).

M = Molar mass, g/mol.

[bar{M}]n = Number average molar mass, g/mol.

[bar{M}]w = Weight average molar mass, g/mol.

m = Mass of sample cylinder, g

[m.sub.p] = Mass of polymer, g.

n = Number of data.

P = Pressure; MPa.

R = Gas constant(=8.314),J/(mol.K).

r = Number of site occupied by a molecule.

S = Solubility, g-gas/g-polym.

s = Solubifity, [cm.sup.3] (STP)/kg-polym.

Sw = Volume swelling due to gas dissolution.

T = Absolute temperature, K.

V = Volume, [m.sup.3].

[upsilon] = Specific volume, [m.sup.3]/kg.

w = Mass fraction.

Z = Compressibility factor.

[phi] = Segment fraction.

[mu] = Chemical potential, J/mol.

[rho] = Density, kg/[m.sup.3].


b = Boiling point.

c = Critical value.

cal = Calculated value.

exp = Experimental value.

i,j = Component.


G = Gas phase.

L = Liquid phase.

O = Pure state.

* = Characteristic parameter.

[sim] = Reduced value defined in Eq 3.


The authors wish to thank Mr. T. Fukusako for his assistance with the experiments. This work was supported through a Grant-in-Aid for Scientific Research (A) (Project No. 09305053) by the Ministry of Education, Science, Sports and Culture, Japan and through the "Research for the Future" program (Project No. JSPS-PFTF 96P00401) by the Japan Society for the Promotion of Science.

(*.) Corresponding author. (email):; phone & fax: +81-824-24-7721.


(1.) Y. Sato, M. Yurugi. K. Fujiwara. S. Takishinia, and H. Masuoka, Fluid Phase Equilibria, 125, 129(1996).

(2.) Y. Sato, K. Fujiwara, T. Takikawa, Sumamo, S. Takishima, and H. Masuoka, Fluid Phase Equilibria, 162, 261 (1999).

(3.) J. G. Lee and R W. Flumerfelt, J. Appl. Polym Sci., 58, 2213 (1995).

(4.) R. A. Gorskl, R. B. Ramsey, and T. Dishart, J. Cellular Plastics, 22, 21 (1986).

(5.) L. E. Daigneault, Y. P. Handa, B. Wong, and L. M. Caron, J. Cellular Plastics, 34, 219 (1998).

(6.) A. Garg. E. Gulari, and C. W. Manke, Macromolecules. 27, 5643 (1994).

(7.) B. Wong, Z. Zhang, and Y. P. Handa, J. Polym. &L: Part B: Polyrn. Phys., 36, 2025 (1998).

(8.) R. Tiliner-Roth and H. D. Baehr, J. Phys. Chem Ref. Data, 23, 657 (1994).

(9.) M. Fukushima and N. Watanabe, Trans. of the JAR, 9, 247 (1992).

(10.) S. L. Outcalt and M. O. McLinden, J. Phys. Chem. Ref Data, 25. 605 (1996).

(11.) Japanese Industrial Standard, JIS-B8243, p. 166, Japanese Standards Association, Tokyo (1981).

(12.) Y. Sato, Y. Yamasald, S. Takishima, and H. Masuoka, J. Appl. Polym. Sci, 66, 141 (1997).

(13.) I. C. Sanchez and R H. Lacombe, J. Phys. Chem., 80, 2352 (1976).

(14.) I. C. Sanchez and R H. Lacombe, Macromolecules, 11, 1145 (1978).

(15.) T. S. Chow, Macromolecules, 13, 362 (1980).

(16.) Y. Kamiya, K. Mizoguchi, Y. Naito, and T. Hirose, J. Polym. Sci: Part B: Polym. Phys., 24, 535 (1986).

(17.) L. I. Stiel and D. F. Harnish, AIChE J., 22, 117 (1976).

(18.) R. C. Reid, J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids, 4th Ed., p. 656, McGraw-Hill, New York (1987).

(19.) ASHRAE Handbook, Fundamentals, chap. 17, American Society of Heating Refrigerating and Air-Conditioning Engineers, Inc., Atlanta (1993).

(20.) P. A. Rodgers, J. App. Polym. Sci, 46, 1061 (1993).

(21.) S. Takishima, K. Nakamura, M. Sasaki, and H. Masuoka, Sekiyu Gakkatshi, 33, 332 (1990).
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Date:Jun 1, 2000
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