solubility of hfc-134a, hcfc-142b, butane, and isobutane in low-density polyethylene at temperatures...

Fluid Phase Equilibria 232 (2005) 1–8

Solubility of HFC-134a, HCFC-142b, butane, and isobutane inlow-density polyethylene at temperatures from 383.15 to 473.15 K

and at pressures up to 3.4 MPa

Ming Wanga, Yoshiyuki Satoa, Toru Iketania, Shigeki Takishimaa,∗, Hirokatsu Masuokaa,Taku Watanabeb, Yoshihito Fukasawab

a Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japanb Packaging Products Division, Packaging Products Technology Department, Asahi Kasei Life& Living Corporation,

1-1 Hirata-nakamachi, Suzuka 513-8660, Japan

Received 20 August 2004; received in revised form 19 November 2004; accepted 2 December 2004

Abstract

red with av reased withd of state (S–LE reement witht isobutane,r ata andS factor.A , andH©

K

1

cplsa(1Gb

e,-ents.

lar2b,eth-

of

-per-redt goenge

0d

The solubility of HFC-134a, HCFC-142b, butane and isobutane in molten low-density polyethylene (LDPE) has been measuolumetric method at pressures up to 3.4 MPa and at temperatures of 383.15, 413.15, 443.15, and 473.15 K. The solubility incecreasing temperature and increasing pressure. The measured solubility was correlated with the Sanchez–Lacombe equationOS) and a temperature-dependent binary interaction parameter. In all cases, the calculated solubility was in reasonably good ag

he experimental data to within an average absolute deviation of 3.0, 5.1, 7.2, and 3.5% for HFC-134a, HCFC-142b, butane andespectively. The Henry’s constants,Kp, for butane and isobutane obtained in this work were in good agreement with the literature dtiel’s equation. A correlation for 1/Kp of fluorocarbons in LDPE was developed in terms of fluorocarbon critical compressibilityverage absolute deviations for the correlated 1/Kp were 2.7, 8.1, 1.3, 4.7, and 5.2% for CFC-11, CFC-12, HCFC-22, HFC-134aCFC-142b, respectively.2004 Elsevier B.V. All rights reserved.

eywords:Data and correlation; Solubility; Equation of state; Henry’s constant; Polyethylene; Fluorocarbon

. Introduction

Gas solubility in polymers is important in many pro-esses, especially in polymer foaming operations that usehysical blowing agents. In particular, low-density polyethy-

ene (LDPE) foam is widely used in industry as thermal in-ulators and shock absorbers. Chlorofluorocarbon blowinggents used for LDPE include CCl3F (CFC-11), CCl2F2CFC-12), CHClF2 (HCFC-22) and CClF2CClF2 (CFC-14). The solubilities of these gases have been reported byorski et al.[1]. Since the production of chlorofluorocar-ons was banned in 1997, replacements, such as CH2FCF3

∗ Corresponding author. Tel.: +81 82 424 7713; fax: +81 82 424 7713.E-mail address:[email protected] (S. Takishima).

(HFC-134a), CH3CClF2 (HCFC-142b), butane, isobutanand compressed gases such as N2 and CO2 have gained industrial interest and have come into use as blowing agSato et al.[2–5] have reported the solubility data of N2 andCO2 in molten polymers for the application to microcellufoams. However, solubility data of HFC-134a, HCFC-14butane and isobutane in LDPE are scarce. Moreover, mods are still lacking for reliable prediction of the solubilitygases in polymers.

Chaudhary and Johns[6] reported the solubility of isobutane in LDPE at pressures of 4–5.5 MPa and at tematures of 418–473 K. Their solubility data were scatteand extrapolation of the data to zero pressure did nothrough the origin. Maloney and Prausnitz[7] measured thHenry’s constants for butane in LDPE in temperature ra

378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2004.12.001

2 M. Wang et al. / Fluid Phase Equilibria 232 (2005) 1–8

from 397 to 573 K with a gas chromatographic method atatmospheric pressure. Several equations for Henry’s con-stants of solutes in LDPE[8–10] have also been proposed.The Henry’s constant data obtained through gas chromato-graphic methods at infinite dilution conditions can be usedto estimate gas solubility at higher pressures. However, asblowing agents are usually used at high pressures where thesolubility–pressure relation often deviates from Henry’s law,considerable error can occur and thus solubility data at highpressures are required for reliable design of foaming proc-esses.

This paper presents the solubility of HFC-134a, HCFC-142b, butane, and isobutane in LDPE. The solubility foreach system was measured at temperatures from 383.15 to473.15 K at intervals of 30 K and at pressures below 3.4 MPa.The solubility was correlated with the Sanchez–Lacombeequation of state (S–L EOS) with a temperature-dependentbinary parameter. The temperature dependence of theHenry’s constants for the blowing agents was alsoexamined.

2. Experimental

2.1. Materials

edb int asg FC-1 erep sahiG urity> Co.L ogent

2

ea-s dureo ed ex-pm briuma poly-m intro-d meo bout4 thes wasa thet suret car-r , and4

The solubility,S(g gas/g polymer), was evaluated for eachcell by the following equation:

S = mS − [MSP(Vsys− Vp)/ZSRT ]

mp(1)

wheremS is the mass of solute introduced in a cell,MS isthe molar mass of the solute,R is the gas constant,ZS is thecompressibility factor of the solute,Vsys is the inner volumeof the sorption cell including the tubing, andmp is the mass ofpolymer.Vp is the volume of polymer phase at equilibrium,which was estimated from the following equation:

Vp(T, P, S) = mp vp(T, 0, 0) Sw(T, P, S) (2)

wherevp(T, 0, 0) is the specific volume of the polymer atzero pressure that was obtained from the Tait equation withparameters reported by Rodgers[14] according toPVTdatareported by Zoller[15]. The Sw(T, P, S) is the swelling ofthe polymer, which was calculated with S–L EOS[12,13]asfollows:

Sw(T, P, S) = (1 + S)vS–L

p (T, P, S)

vS–Lp (T, 0, 0)

(3)

wherevS–Lp (T, 0, 0) is specific volume of pure polymer at

zero pressure calculated with the S–L EOS,vS–Lp (T, P, S) is

the specific volume of the polymer phase estimated with theS q.( in-c fromts lcu-l y foreu nabe[ andW

s lesst mentw sureds rrori

3

3

2b,bp leds mers ubil-i dis-s arlyw l.%i this

LDPE (Tm = 382.7 K, MFR = 2.3 g/10 min) was suppliy the Asahi Kasei Company. A sample film (0.05 mm

hickness) of LDPE was frozen in liquid nitrogen and wround to obtain 0.1–0.25 mm long flakes by sieving. H34a (purity >99.8%) and HCFC-142b (purity >99.5%) wurchased from Daikin Industries Ltd. (Osaka), and Alass Co. (Tokyo), respectively. Butane and isobutane (p99.5%) were obtained from Sumitomo Seika Chemicalstd. (Osaka). All gases used were degassed at liquid nitr

emperatures.

.2. Solubility measurements

The solubility of the blowing agents in LDPE was mured with a volumetric method. The apparatus and procef measurement are described briefly here since a detaillanation is available in a previous publication[11]. In thisethod, the system pressure and temperature at equilire measured, and the amount of solute dissolved in theer can be obtained by a mass balance on the soluteuced in a sorption cell with pre-determined inner voluf the system. Four sorption cells (each inner volume a2 cm3) were filled with the LDPE flakes (ca. 16 g) andolutes were loaded into the sorption cells at 373 K thatbout 10 K lower than the melting point of LDPE. Then,

emperature of the system was kept at 388 K for 3 h to enhat the LDPE thoroughly melted. The experiments wereied out at temperature levels of 383.15, 413.15, 443.1573.15 K.

–L EOS, andS is the solute solubility obtained with E1). Since Sw varies with the solubility and the S–L EOSludes a binary interaction parameter that is determinedhe experimental data, it is necessary to solve Eqs.(1)–(3)imultaneously. The following equations were used to caate compressibility factors because of their high accuracach substance. The EOS of Tillner-Roth and Baehr[16] wassed for HFC-134a; the EOS of Fukushima and Wata

17] was used for HCFC-142b; the EOS of Miyamotoatanabe[18,19]was used for butane and isobutane.The uncertainty of the temperature measurement wa

han±0.05 K, and the uncertainty of pressure measureas less than 0.03% F.S. The uncertainty in the meaolubilities is estimated to be within 4.0% including the en the polymer swelling estimation.

. Results and discussion

.1. Experimental results

Experimental solubility data for HFC-134a, HCFC-14utane, and isobutane in LDPE are listed inTables 1–4andlotted inFigs. 1–4, respectively. In these figures, the unfilymbols denote apparent solubilities without the polywelling correction and the solid symbols denote the solties that were corrected for the polymer swelling due toolved solutes. The polymer swelling varied almost lineith an increase in the solubility. It reached about 50 vo

n the butane system at 383.15 K and 1.455 MPa, and

M. Wang et al. / Fluid Phase Equilibria 232 (2005) 1–8 3

Table 1Solubility of HFC-134a in LDPE

Temperature(K)

Pressure(MPa)

Solubility withoutswelling correction(g gas/g polymer)

Solubility withswelling correction(g gas/g polymer)

383.15 0.335 0.0060 0.00610.727 0.0133 0.01361.089 0.0195 0.02011.602 0.0299 0.0314

413.15 0.373 0.0057 0.00570.815 0.0126 0.01271.226 0.0185 0.01921.823 0.0285 0.0300

443.15 0.414 0.0054 0.00550.903 0.0122 0.01251.364 0.0179 0.01872.038 0.0280 0.0296

473.15 0.453 0.0053 0.00540.989 0.0121 0.01241.500 0.0178 0.01852.256 0.0279 0.0296

caused 10% difference between corrected and uncorrectedsolubilities.

The solubilities shown inFigs. 1–4 increased withincreasing pressure and decreasing temperature. The solu-bility isotherms for all the solutes examined were almostlinear at high temperatures. However, at low temperatures,Flory–Huggins type[20] isotherms can be observed; namely

Table 2Solubility of HCFC-142b in LDPE

Temperature(K)

Pressure(MPa)



383.15 0.270 0.0191 0.01930.436 0.0307 0.03130.581 0.0447 0.04570.857 0.0703 0.07251.228 0.112 0.1181.525 0.154 0.163

413.15 0.324 0.0177 0.01790.514 0.0290 0.02950.719 0.0405 0.04151.065 0.0635 0.06571.584 0.0989 0.1042.017 0.134 0.144

443.15 0.388 0.0162 0.01640.618 0.0263 0.0269

4

Table 3Solubility of butane in LDPE

Temperature(K)

Pressure(MPa)



383.15 0.373 0.0415 0.04200.521 0.0620 0.06320.805 0.108 0.1111.077 0.171 0.1791.193 0.203 0.2131.386 0.275 0.2921.455 0.302 0.322

413.15 0.529 0.0382 0.03890.752 0.0559 0.05721.192 0.0989 0.1031.632 0.155 0.1651.837 0.184 0.1992.203 0.247 0.2732.347 0.270 0.302

443.15 0.698 0.0352 0.03601.005 0.0531 0.05501.624 0.0902 0.09572.260 0.138 0.1522.601 0.164 0.1843.185 0.215 0.2513.447 0.232 0.277

473.15 0.871 0.0326 0.03341.266 0.0495 0.05162.075 0.0827 0.08912.923 0.124 0.1403.427 0.147 0.170

Table 4Solubility of isobutane in LDPE

Temperature(K)

Pressure(MPa)



383.15 0.380 0.0301 0.03050.709 0.0611 0.06260.944 0.0869 0.09011.119 0.108 0.1131.383 0.150 0.1581.525 0.175 0.187

413.15 0.501 0.0280 0.02850.976 0.0558 0.05771.326 0.0792 0.08321.571 0.0963 0.1022.032 0.133 0.1462.240 0.156 0.172

443.15 0.639 0.0260 0.02661.258 0.0511 0.05351.731 0.0724 0.07722.048 0.0864 0.09332.765 0.125 0.1403.025 0.141 0.160

473.15 0.795 0.0240 0.02461.542 0.0474 0.0499

0.865 0.0368 0.03781.292 0.0569 0.05941.937 0.0884 0.09432.500 0.119 0.130

73.15 0.451 0.0150 0.01520.719 0.0244 0.02491.006 0.0340 0.03501.508 0.0521 0.0546
2.280 0.0804 0.08662.979 0.101 0.118
2.142 0.0669 0.07212.535 0.0784 0.0860


Fig. 1. Solubility of HFC-134a in LDPE.

Fig. 2. Solubility of HCFC-142b in LDPE.

the solubility increases exponentially with pressure. The sol-ubility of HCFC-142b in LDPE (Fig. 2) was much higher thanthat of HFC-134a (Fig. 1). The solubility of butane (Fig. 3)was 20–80 wt.% higher than that of isobutane (Fig. 4) overthe range of conditions examined.

The solubilities of the CFC-11, CFC-12, and HCFC-22in LDPE were estimated from graphical data reportedby Gorski et al. [1] and are compared with those ofHFC-134a, HCFC-142b, butane and isobutane measuredin this work at 413 K inFig. 5. In this figure, solubilities

Fig. 3. Solubility of butane in LDPE.

Fig. 4. Solubility of isobutane in LDPE.

Fig. 5. Comparison of solubilities of various blowing agents in LDPE at413 K.

are represented in units of mol gas/kg polymer, so thatthe information is convenient for practical foaming pro-cesses. The order of the solubilities in LDPE was foundto be: CFC-11 > butane > isobutane > HCFC-142b > CFC-12 > HCFC-22 > HFC-134a, and had a similar order to theorder of the normal boiling point temperature of the solutes[21]: CFC-11 (Tb = 296.81 K) > butane (272.66 K) > HCFC-142b (264.05 K) > isobutane (261.34 K) > HFC-134a(247.04 K) > CFC-12 (243.45 K) > HCFC-22 (232.14 K).However, the solubility of isobutane in LDPE was60–80 mol% higher than that of HCFC-142b, even thoughthese two solutes have similar boiling point temperatures.Furthermore, HFC-134a, whose normal boiling point ishigher than those of CFC-12 and HCFC-22, had the lowestsolubility in LDPE among the solutes examined. It can beconsidered that the interaction between solute and LDPEhad a significant effect on the solubility as well as thecondensability of the solutes themselves.

3.2. Correlation

The S–L EOS[12,13]can describe the solubility of manypolymer–gas systems. The S–L EOS is expressed as:

P = −ρ2 − T

[ln(1 − ρ) +

(1 − 1

r

)ρ

](4)


Table 5Characteristic parameters for S–L EOS and solute properties

Substance P* (MPa) ρ* (kg/m3) T* (K) Tca (K) ωa Reference for S–L

EOS parameters

LDPE 382.1 889.3 685 – – [18]HFC-134a 482.9 1802.9 329.4 374.26 0.326 [11]HCFC-142b 427.3 1561.3 367.7 410.30 0.231 [11]Butane 322 736 403 425.12 0.200 [13]Isobutane 288 720 398 407.85 0.186 [13]

a From[21].

whereP , ρ, andT are the reduced pressure, density and tem-perature, respectively, andr represents the number of latticesites occupied by a molecule. The reduced quantities are de-fined as:

P = P

P∗ , ρ = ρ

ρ∗ , T = T

T ∗ , r = MP∗

RT ∗ρ∗ (5)

whereP* , ρ* , andT* are characteristic pressure, density, andtemperature, respectively, andM is the molecular weight.The pure component characteristic parameters used are listedin Table 5. For mixtures, these parameters were determinedfrom pure component parameters using the mixing rules de-scribed below:

φi = wi/ρ∗i∑

j wj/ρ∗j

(6)

φ0i = φiP

∗i /T ∗

i∑j φjP

∗j /T ∗

j

(7)

1

r=

∑i

φ0i

r0i

(8)

T ∗ = P∗ ∑i

φ0i T

∗i

P∗i

(9)

m-nmely,with

thehe

=r0{− ρ

T+ P

ρT+

(1

ρ−1

)ln(1−ρ)+

(1

r0

)ln ρ

}(13)

µL1(T, P, wL

1) = RT

{ln φ1 +

(1 − r1

r2

)φ2 + r0

1ρX1φ22

}

+r01RT

{− ρ

T1+ P1v

T1

+ v

[(1 − ρ) ln(1 − ρ) + ρ

r01

ln ρ

]}(14)

X1 = (P∗1 + P∗

2 − 2P∗12)v

∗1

RT(15)

The binary interaction parameterkij was determined by mini-mizing the following objective function at each temperature:

OF =n∑i

∣∣∣∣∣Scali − S

expi

Sexpi

∣∣∣∣∣2

(16)

whereS(g gas/g polymer) is solubility of the blowing agentscorrected for polymer swelling. The optimized values ofkijare listed inTable 6.

The correlation results with S–L EOS are plotted withs rea datag highp pa-r tions( ta att4 per-a

c oft

k

T nt d tob tanea can beu beu

olid lines in Figs. 1–4. The correlated solubilities wepproximately linear with pressure, while the measuredradually deviated from linear pressure dependence atressures. To improve the fit of the data, another fittingameter is probably required. The absolute average deviaAADs) between the correlated and the experimental dahe same temperature are listed inTable 6. Overall AAD was.6%, but higher deviations were observed at lower temtures and higher pressures.

Temperature dependence of thekij is shown inFig. 6andould be correlated satisfactorily with a linear functionemperature:

12 = a + bT (17)

he values ofaandbare listed inTable 7. The AADs betweehe correlated and the experimental solubility were foune 3.0, 5.1, 7.2, and 3.5% for HFC-134a, HCFC-142b, bund isobutane systems, respectively. These equationssed to interpolatek12 at other temperatures and also maysed to extrapolatek12.

P∗ =∑

i

∑j

φiφjP∗ij (10)

P∗ij = (1 − kij)(P

∗i P∗

j )1/2 (11)

where theP∗i , T ∗

i , ρ∗i , andr0

i denote the characteristic paraeters of componenti in the pure state,wi is the mass fractioof componenti, φ0

i andφi represent the close-packed volufraction of componenti before and after mixing, respectiveandkij is a binary interaction parameter to be adjustedexperimental solubilities.

At equilibrium, the chemical potential of a solute inpure gas phase,µG

1 , is equal to the chemical potential of tsolute in the polymer phase,µL

1:

µL1(T, P, wL

1) = µG1 (T, P, wG

1 = 1) (12)

where

µG1 (T, P, wG

1 = 1)


Fig. 6. Temperature dependence of interaction parameters,k12, in S–L EOS.

3.3. Henry’s constants

The temperature dependence of the Henry’s constants wasexamined using the measured solubility data. Henry’s con-stants,Kp (kg MPa/cm3 (STP)), is defined by the followingequation:

Kp = lims→0

(fg

s

)(18)

Table 6Binary interaction parameters for the S–L EOS and correlation deviations

Temperature (K) k12 AADa (%)

HFC-134a + LDPE383.15 0.0630 3.0413.15 0.0476 2.8443.15 0.0330 3.1473.15 0.0193 3.2

HCFC-142b + LDPE383.15 0.0231 7.9413.15 0.0100 4.4443.15 0.0007 4.0473.15 −0.0077 3.5

Butane + LDPE383.15 −0.0112 8.0413.15 −0.0164 7.9443.15 −0.0221 7.0

Fig. 7. Comparison of Henry’s constants for solutes in LDPE.

wherefg is the fugacity of a gas ands(cm3 (STP)/kg polymer)is the solubility of the gas. In the determination of Henry’sconstant, measured solubility data at low pressures were cor-related with S–L EOS at each temperature. Then, predictedvalues offg/swere extrapolated to zero solubility to obtainthe Henry’s constants,Kp. The obtained values of the Henry’sconstants are shown inFig. 7.

Stiel et al. [9] proposed a linear relationship betweenln(1/Kp) and (Tc/T)2 for non-polar solutes in molten LDPEas follows:

ln

(1

Kp

)= 7.649+ (2.057+ 1.438ω)

(Tc

T

)2

(19)

whereTc andω denote the critical temperature and the acen-tric factor of solutes, respectively, and the values used in thiswork are listed inTable 5. The Henry’s constants of butaneand isobutane in LDPE calculated with Eq.(19)showed goodagreement with the experimental results as shown inFig. 7.However, this equation gave poor results (not shown inFig. 7)for the polar solutes, HFC-134a and HCFC-142b.

The Henry’s constants 1/Kp for butane obtained in thiswork were 0.5% higher on average than those reportedby Maloney and Prausnitz[7] in the temperature range of383.15–473.15 K and they were 5.1% higher on average thanthose calculated with Eq.(19). The 1/Kp for the isobutaneso

e inE 11,C

473.15 −0.0245 4.8

Isobutane + LDPE383.15 −0.0074 4.4413.15 −0.0125 3.5443.15 −0.0176 4.0473.15 −0.0187 1.5∑ exp exp
a AAD = (100/n) iS
cali − Si |/Si , n= number of data.

Table 7Parameters for Eq.(17)and calculated deviations

System a b (×103 K−1) AADa (%)

HFC-134a + LDPE 0.258 −0.507 3.0HCFC-142b + LDPE 0.152 −0.341 5.1Butane + LDPE 0.046 −0.152 7.2Isobutane + LDPE 0.042 −0.130 3.5

a AAD = (100/n)∑

iScali − S

expi |/Sexp

i , n= number of data.

l

T inT forH

otc emssc ibil-

ystem could be estimated with Eq.(19) to within an AADf 1.9%.

The present work determined the intercept and slopq. (19) for each solute–LDPE system including CFC-FC-12, HCFC-22 according to Gorski et al.[1]:

n

(1

Kp

)= c + d

(Tc

T

)2

(20)

he values ofc andd, and the correlation errors are listedable 8. The AADs of 1/Kp were less than 1.0% exceptCFC-142b and isobutane.Eq. (19) written in terms of the acentric factor could n

orrelate Henry’s constant for fluorocarbon–LDPE systatisfactorily as shown inFig. 7. Zhong and Masuoka[22]orrelated Henry’ constants with the critical compress


Table 8Parameters in Eq.(20)and calculated deviations of Henry’s constant for solute–LDPE systems

Solute Tca Zc

a c d AADb (%)

HFC-134a 374.26 0.262 7.135 1.256 0.20HCFC-142b 410.30 0.274 7.589 1.813 2.40Butane 425.12 0.274 7.650 2.396 0.36Isobutane 407.85 0.278 7.672 2.320 1.28CFC-11[1] 471.10 0.283 7.700 2.172 0.62CFC-12[1] 385.10 0.280 7.543 1.990 0.82HCFC-22[1] 369.28 0.274 7.417 1.806 0.16

a From[21].b AAD = (100/n)

∑i|(1/Kcal

p,i ) − (1/Kexpp,i )|/(1/K

expp,i ), n= number of data.

Fig. 8. Henry’s constants for fluorocarbons in LDPE.

ity factor, Zc of solutes for polar solute–LDPE and polarsolute–PDMS systems. Their equation for LDPE did notwork well for the fluorocarbon systems examined here. Inthis work,Zc was used to correlate the intercept and slope ofEq. (20) for the fluorocarbons, and the results are plotted inFig. 8. The relationship developed for the correlation of theHenry’s constants was:

ln

(1

Kp

)= (29.260Zc − 0.700)

+ (38.401Zc − 8.598)

(Tc

T

)2

(21)

The AADs of 1/Kp for CFC-11, CFC-12, HCFC-22, HFC-134a, and HCFC-142b in LDPE from Eq.(21)were 2.7, 8.1,1.3, 4.7, and 5.2%, respectively, over the temperature rangefrom 380 to 500 K. Eq.(21)was also found to be the reliablefor the prediction of the 1/Kp of the fluorocarbons studied inthis work.

4. Conclusions

Solubilities of HFC-134a, HCFC-142b, butane, andisobutane in LDPE were measured at temperatures of383.15–473.15 K and pressures up to 3.4 MPa. The sol-u as-i pera-t E

was found to be: CFC-11 > butane > isobutane > HCFC-142b > CFC-12 > HCFC-22 > HFC-134a, which was similarto the order of normal boiling temperatures of the solutes.However, this order is not strictly obeyed due to some cases ofstrong solute-polymer interactions. The solubility data couldbe correlated satisfactorily with the Sanchez–Lacombe EOSand a temperature-dependent binary parameter. Binary inter-action parameters in the Sanchez–Lacombe EOS were foundto vary almost linearly with temperature. Henry’s constantswere obtained from the measured solubilities. The Henry’sconstants for butane and isobutane in this work were consis-tent with the prediction of Stiel et al. to within absolute aver-age deviations of 5.1 and 1.9%, respectively, while large de-viations were found for HFC-134a and HCFC-142b. Henry’sconstants for fluorocarbons could be satisfactorily correlatedwith a function in terms of the critical compressibility factor.

List of symbolsfg fugacity of solute (MPa)kij interaction parameter betweeni andj componentsKp Henry’s constant (MPa kg polymer/cm3 (STP))m mass of the sample cylinder (g)mp mass of polymer (g)M molar mass of the solute (g/mol)MFR melt flow rate (g/10 min)P pressure (MPa)r idRsSSTv

VZ

Gµ

ρ

φ

Sb boiling pointc critical point

bilities for all gases in LDPE increased with increng pressures and decreased with increasing temure. At 413 K, the order of the solubilities in LDP

number of segments in a molecule for lattice flugas constant (8.314 J/(mol K))solubility (cm3 (STP)/kg polymer)solubility (g gas/g polymer)

w swelling due to solute dissolutiontemperature (K)specific volume (m3/kg)volume (m3)compressibility factor

reek letterschemical potential (J/mol)density (kg/m3)volume fraction

ubscripts


i,j componentm melting point

Superscripts0 pure state* characteristic parameter∼ reduced valuecal calculated valueexp experimental valueG gas phaseL liquid phase

References

[1] R.A. Gorski, R.B. Ramsey, T. Dishart, J. Cell. Plast. 22 (1986)21–51.

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solubility of hfc-134a, hcfc-142b, butane, and isobutane in low-density polyethylene at temperatures...

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