Fluid Phase Equilibria 246 (2006) 158–166

Measurement of gas solubility and diffusivity in polylactide

G. Li a,∗, H. Li a, L.S. Turng b, S. Gong c, C. Zhang c

a Department of Mechanical & Industrial Engineering, University of Toronto, Canadab Department of Mechanical Engineering, University of Wisconsin-Madison, United States

c Department of Mechanical Engineering, University of Wisconsin-Milwaukee, United States

Received 26 February 2006; received in revised form 25 May 2006; accepted 25 May 2006Available online 6 June 2006

Abstract

The solubilities of carbon dioxide and nitrogen in a polylactide melt were determined at temperatures from 180 to 200 ◦C and pressures up to28 MPa using a magnetic suspension balance (MSB). Both Sanchez–Lacombe (SL) and Simha–Somcynsky (SS) equations-of-state (EOS) wereapplied to predict the amount of volume swelling in the polylactide (PLA)/gas mixture due to gas dissolution. With the proper prediction of volumeswelling from both SS-EOS and SL-EOS, the “corrected solubility” was determined based on the experimentally measured “apparent solubility”from the MSB. After measurement of the gas sorption curve in the PLA melt, the theoretical sorption model based on Fick’s second law wasa©

K

1

ipltfcsdccfiispPwah

0d

dopted to extract the diffusion coefficients of carbon dioxide and nitrogen in polylactide at both 180 and 200 ◦C.2006 Elsevier B.V. All rights reserved.

eywords: Solubility; Diffusion coefficient; Equation-of-state; PLA; Carbon dioxide; Nitrogen

. Introduction

Polylactide (PLA) is a bio-based polymer with commercialmportance in the plastics industry [1]. PLA is an aliphaticolyester produced by either ring-opening polymerization ofactide or condensation polymerization of lactic acid monomershat are produced from renewable resources such as corn via aermentation process [1,2]. Due to its biodegradability and bio-ompatibility, PLA has been used for biomedical applicationsuch as sutures [3], tissue engineering scaffold [4–7], and drugelivery devices [8] for many years, mostly in the form of aopolymer of PLA and polyglycolide (PGA). The prohibitiveost of PLA limited its application mainly to the biomedicaleld until the 1980s. In recent years, PLA has gained much

nterest because it is being commercially produced on a largecale from biomass such as corn at a much more reasonablerice by companies such as NatureWorksTM LLC [1]. Therefore,LA has found applications in areas such as fast food serviceare, grocery and composting bags, mulch films, electronics,

nd controlled release matrices for fertilizers, pesticides, anderbicides. It is foreseeable that PLA can become an alterna-

tive to traditional commodity plastics for everyday applications[9].

As an emerging technique and a form of green chemistry, theadvantages of using supercritical fluids in polymer science (i.e.,polymer synthesis and polymer processing) have been reviewedby several authors [10–13]. Especially in the microporous poly-mer formation process, supercritical fluids were extensivelyused as physical blowing agents, which are currently replac-ing conventional organic blowing agents (i.e., environmentallyhazardous materials) [14–16]. Recently, there has been a strongtrend on the development of supercritical fluids technology dur-ing the biodegradable material fabrication process in both theacademic and industrial fields [17–19]. For example, Mooney etal. fabricated highly porous macrocellular PLA foams for tissueengineering scaffold with the aid of high pressure CO2 to avoidusing harmful organic solvents [17,18]. In 2002, a new techniquebased on supercritical fluid technology was invented to incor-porate biologically active materials into a biodegradable PLAmatrix for controlled drug release [19]. With the aid of supercrit-ical fluids, especially supercritical CO2, the application of PLAin the biomedical field has seen tremendously improved success.

∗ Corresponding author. Tel.: +1 416 978 0947; fax: +1 416 978 0947.E-mail address: gmli@mie.utoronto.ca (G. Li).

From the aspect of PLA commercial application develop-ment, the use of supercritical fluids is a very attractive tech-nology in the manufacturing of PLA-based commodity prod-ucts. The microcellular structure obtained through supercritical

378-3812/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2006.05.030

G. Li et al. / Fluid Phase Equilibria 246 (2006) 158–166 159

fluid assisted processing techniques improves the properties ofthe foamed part as well as saving material, thereby loweringthe production cost significantly which is the main constrainton the development of PLA-based commodity products. Inaddition, enhanced polymer foam processing with the aid ofsupercritical fluids has many advantages [13] as compared toconventional polymer processing. For example, the plasticiz-ing effect of the dissolved supercritical fluids in polymer meltsmay reduce the viscosity of the polymer melts without increas-ing the processing temperature, which can significantly enhancethe processability of the polymer. This is especially helpfulduring the processing of thermosensitive polymers like PLA[13].

As a fundamental study of PLA processing with the aid ofsupercritical fluids, this paper investigates the thermodynamicproperties of supercritical fluids in the PLA melt; i.e., the sol-ubility and diffusivity of supercritical fluids in the PLA meltat certain processing conditions. The solubility and diffusivityinformation of the supercritical fluids in the PLA melt are crucialparameters for the effective design of PLA processing param-eters with the presence of supercritical fluids, especially in thebiomedical, drug delivery, and packaging fields.

2. Theoretical background

The accurate measurement of solubility and diffusivity ofsacpedgesmStPlmmhmtiatplwcd[

mm

sured weight gain Wg versus time t) during the gas dissolutionkinetic process [29,33]. In this paper, a magnetic suspensionbalance was used to measure the sorption uptake curve of super-critical fluids – i.e., CO2 and N2 – in the PLA melt. BothSanchez–Lacombe (SL) and SS-EOS were used separately topredict the volume swelling for an accurate determination of thesolubility. Fick’s second law was applied in this study for theextraction of the diffusion coefficient from the sorption curve,which was obtained from MSB.

3. Experimental

3.1. Materials

Polylactide (PLA) (NatureWorksTM, PLA 3001D, Mn =6.6 × 105) was purchased in pellet form from NatureWorksTM

LLC. Carbon dioxide (Coleman grade, 99.99% purity) and nitro-gen (extra dry grade, 99.98% purity) were obtained from BOC,Canada. All chemicals were used as received.

3.2. Thermal analysis

Differential scanning calorimetry (DSC) analysis of PLA wasconducted with a DSC Q10 (TA instrument). The sample wasscanned between 40 and 200 ◦C at a heating rate of 10 ◦C/min.T ◦sm2ui33

ma

upercritical fluids in molten polymers has always been anttractive and challenging research topic for plastic foam pro-essing researchers. A variety of experimental methods wereroposed for the purpose of measuring the solubility of differ-nt gases in polymer melts [20–24]. For instance, the pressureecay method was employed by Sato et al. [20,21] to investi-ate the solubility of CO2 and N2 in PP, HDPE, and PS. Thelectrobalance method was employed by Wong et al. [22] totudy the solubility of CO2 in PS and PVC. In addition, theagnetic suspension balance (MSB) method was employed byato [22,25–27], Areerat et al. [23], and Li et al. [24] to measure

he gas solubility of CO2 and N2 in PS, PVAc, HDPE, PBS, andPO. Due to the swelling of the polymer melt during gas disso-

ution, consideration of the swollen volume of the polymer–gasixture was necessary to obtain an accurate solubility measure-ent. The swelling phenomenon is especially significant when

igh pressure is applied and more gas is dissolved into the poly-er melt. Therefore, the equation of state (EOS) was used for

he theoretical prediction of the swollen volume in the solubil-ty determination [23–30]. The Simha–Somcynsky (SS) EOS,long with five other theoretical equations-of-state (includinghe Sanchez–Lacombe EOS), have been extensively tested forolymers and oligomers by Rodgers [31]. SS-EOS shows excel-ent capabilities for describing polymer melt pvT data over aide range of temperatures and pressures. Moreover, the appli-

ation of the SS-EOS in the multicomponent fluid system to pre-ict the mixture’s pvT information has been previously studied32].

Upon the completion of the sorption uptake curve measure-ent, the diffusion coefficients of the gases in the polymerelt were determined from the sorption uptake curve (mea-

he melting temperature of the PLA sample was 171.6 C ashown in Fig. 1. Weight loss with increasing temperatures wereeasured using a TA thermogravimetric analyzer (TGA, TA-

960 SDT) from 20 to 600 ◦C with a heating ramp of 20 ◦C/minnder an argon atmosphere. As shown in Fig. 2, the correspond-ng temperatures for 1, 5, and 10% weight losses were 300.64,28.03, and 339 ◦C, respectively. While at a temperature of99.35 ◦C, nearly 99% of the PLA had been decomposed.

Based on the above thermal behaviors of PLA, the solubilityeasurement temperatures for PLA were determined to be 180

nd 200 ◦C.

Fig. 1. DSC thermogram of PLA.

160 G. Li et al. / Fluid Phase Equilibria 246 (2006) 158–166

Fig. 2. TGA thermogram of PLA.

3.3. Determination of Tait’s parameters and scalingparameters for SL-EOS and SS-EOS

Based on published pvT data of PLA by Sato et al. [34], theTait equation for PLA (Eq. (1)) was derived as follows,

Vsp = 0.7788 × e(7.8261×10−4T )(

1 − 0.0894

× ln

(1 + P

2.2262 × 103 × e(−4.7417×10−3T )

))(1)

where the temperature T is measured in ◦C and the pressure Pis measured in bar.

In this study, the SL-EOS and SS-EOS scaling parameters ofPLA were optimized from the published pvT data [34] so thateach of the EOS’s yielded the best pvT fitting compatibility [31].All scaling parameters (in both the SS-EOS and SL-EOS) foreach component are listed in Table 1.

3.4. Measurement of apparent solubility

The magnetic suspension balance (MSB) from RubothermGmbH was used for the measurement of the sorption of CO2

and N2 in the PLA melts. All of the details of the experimentalapparatus and operational procedures were described in previ-ous publications by Sato, Areerat and Li, etc. [23,24,26,28]. Ashort description is briefly recapped here. First, approximately0.5 g of PLA was prepared in the form of a round disk with adiameter of about 13 mm and a thickness of about 3 mm for thesorption measurement. The PLA disk sample was then carefullylocated in a 13 mm-diameter aluminum cup. By doing this, itwas assured that only one (top) surface of the PLA melt samplewould be exposed to the high pressure gas during the sorptionprocess and thus the valid assumption of one-dimensional diffu-sion can be made. The PLA melt samples were first weighedas W(0, T) from the balance readout at vacuum (P = 0) andtemperature (T) before the introduction of the high pressuregas into the absorption chamber. The high pressure gas wasthen introduced into the sorption chamber and maintained ata constant pressure (P). When the sorption of the gas in thepolymer melt finished and the saturation stage was achieved(i.e., no more weight changes could be observed), the apparentweight of the polymer melt sample saturated with gas could beobtained from the balance readout W(P, T) at pressure (P) andtemperature (T).

Hence, the amount of gas dissolved in the polymer melt sam-ple, Wg, was calculated by employing the following equation[24,26,29]:

W

wstadts

wX

X

Table 1Scaling parameters for substances in SS-EOS and SL-EOS

S

(

S )

(

ubstance P* (MPa) V* (cm3/g) T* (K)

a) SS-EOSPLA 916.4 0.7919 10711CO2 954.2 0.586 2960N2 384.3 0.9475 1226.9

ubstance P* (MPa) V* (cm3/g

b) SL-EOSPLA 561.5 0.7513CO2 720.3 0.6329N2 103.6 1.2447

g = W(P, T ) − W(0, T ) + ρCO2 (VB + VP + VS) (2)

here ρCO2 is the density of the gas which was measured initu using MSB [35]; VB the volume of the sample holder; VPhe volume of the pure polymer sample (without gas dissolutionnd swelling) at pressure P and temperature T, which can beetermined from the mass and specific volume (Vsp) based onhe Tait equation of PLA (Eq. (1)); and VS is the amount of thewollen volume due to the gas dissolution.

By ignoring the polymer’s swollen volume, VS, the measuredeight gain can be treated as the apparent solubility (Eq. (3)),apparent, which is less than the actual solubility:

apparent = W(P, T ) − W(0, T ) + ρgas(VB + VP)

mass of sample(3)

Mn S C Reference

66000 2025.7 537.81 This work44.01 1 1 [37]28.01 1 1 This work

T* (K) Reference

635.52 This work208.9 + 0.459T − 7.56 × 10−4T2 [27]159.0 [27]

G. Li et al. / Fluid Phase Equilibria 246 (2006) 158–166 161

3.5. Determination of corrected solubility

As shown in Eq. (2), in order to accurately measure the sol-ubility of the gas in the polymer melt, the swollen volume (VS)needs to be considered. Especially under the circumstance ofa high gas density and a large amount of swollen volume, thebuoyancy effect correction on the apparent solubility data issignificant. However, the swollen volume of a polymer–gas mix-ture is difficult to measure physically. As a result, VS is usuallyobtained from the total mass change of the polymer sample andthe specific volume of the polymer–gas mixture (Vsp,mix), whichis calculated using an EOS. The Vsp,mix of the polymer–gas mix-ture can be calculated by solving either the SS-EOS (Eqs. (4)and (5)):

pV

T= (1 − η)−1 + 2yQ2(1.011Q2 − 1.2045)

T(4)

( s

3c

)[ s − 1

s+ ln(1 − y)

y

]

= η − 1/3

1 − η+ y

6TQ2(2.409 − 3.033Q2) (5)

or the SL-EOS (Eq. (6)):

P = −ρ2 − T

[ln(1 − ρ) +

(1 − 1

)ρ

](6)

Te

X

3

gc

µ

wµ

pos

[

µ

a

µ

where Gm is the molar free energy of the polymer–gas mixture(Eq. (11)) [36].

Gm

RT= x1 ln x1 + x2 ln x2 + ln

y

s

+ s1 − y

yln(1 − y) + (s − 1) ln

e

z − 1

− c

[ln

υ(1 − η)3

Q

]− 3

2c1x1 ln

2πm1RT

(Nah)2

− 3

2c2x2 ln

2πm2RT

(Nah)2 + cyQ2(1.011Q2 − 2.409)

2T

+ c

ms

[(1 − η)−1 + 2yQ2(1.011Q2 − 1.2045)

T

](11)

In SL-EOS, Eqs. (12) and (13) are used to calculate the µG1 and

µP1, respectively [37,38].

µG1 = r0

1RT

[− ρ1

T1+ P1

ρ1T1+(

1

ρ1− 1

)

× ln(1 − ρ1) + 1

r01

ln ρ1

](12)

µ

prvrstraemX

3t

ttTEa

r

herefore, the corrected solubility, Xcorrected, with the buoyancyffect compensation can be obtained using Eq. (7):

corrected = Xapparent + ρgasVS

mass of sample(7)

.6. Determination of the theoretical solubility

According to the phase equilibrium theory, the solubility ofas in a polymer melt can be theoretically calculated using theriterion for phase equilibrium (Eq. (8)),

G1 = µP

1 (8)

here µG1 is the chemical potential of gas in the gas phase and

P1 is the chemical potential of gas in the polymer–gas solutionhase. Under the phase equilibrium condition, the mass fractionf the gas in the polymer–gas solution phase, i.e., the theoreticalolubility, Xtheory, can be calculated from solving Eq. (8).

Particularly, in SS-EOS, Eq. (9) was used to calculate the µG1

36],

G1 =

∫ ∞

v

(P − RT

V

)dV + (PV − RT )

+ RT ln

(P

kT

(N2

a h2

2πm1RT

)3/2)

(9)

nd Eq. (10) was used to calculate the µP1 in Eq. (8) [36],

P1 = Gm + x2

∂Gm

∂x1(10)

P1 = RT

[ln φ1 +

(1 − r1

r2

)φ2 + r0

1 ρP∗

1 + P∗2 − 2P∗

12

P∗1 T1

φ22

]

+ r01RT

[− ρ

T1+ P1

ρT1+(

1

ρ− 1

)ln(1 − ρ) + 1

r01

ln ρ

]

(13)

The methodology for determining the solubility was pro-osed based on the assumption that the EOS was capable of accu-ately computing the theoretical solubility (Xtheory) and swollenolume (VS) of the polymer–gas mixture. Therefore, the cor-ected solubility (Xcorrected) and theoretical solubility (Xtheory)hould be identical. Based on this methodology, the approacho calculate the theoretical solubility and to determine the cor-ected solubility with different EOSs (SS-EOS and SL-EOS)re proposed and explained in Fig. 3. The interaction param-ters (δe and δv for SS-EOS and k12 for SL-EOS) were opti-ized to minimize the difference between the Xcorrected and thetheory.

.7. Determination of the diffusion coefficients of gases inhe PLA melt

After the sorption curve (measured weight gain Wg versusime t) was obtained from MSB, Fick’s second law was usedo describe the kinetic process of gas sorption in the PLA melt.he analytical solution to Fick’s second law equation is given inq. (14) with the proper boundary and initial conditions associ-ted with the isobar, isothermal, and single side sorption of the

162 G. Li et al. / Fluid Phase Equilibria 246 (2006) 158–166

Fig. 3. Flow chart of the procedures to obtain the optimum interaction parame-ters and the solubility.

polymer disk sample [33]:

Wg(t) − Wg(0)

Wg(∞) − Wg(0)= 1 − 8

π2

∞∑n=0

1

(2n + 1)2

× exp

[−(2n + 1)2π2Dt

4L2

](14)

where L is the thickness of the polymer disk sample and Wg(t)is the weight of polymer–gas mixture at time t. For the deter-mination of diffusivity (the mutual diffusion coefficient) of gasinside of the polymer matrix, the numerical solution of the diffu-sion equation (Eq. (14)) was adopted so that the output from Eq.(14) fit the experimental sorption curve for the whole sorptionprocess. By minimizing the difference between the theoreticalresults and the experimental sorption curve, the diffusivity ofthe gas in the PLA melt could thus be determined [26,29].

The following four assumptions were made to determine thegas diffusivity:

• Assumed Fick’s second law was valid.• Assumed one-dimensional diffusion into the polymer sample

sheet with all diffusion substances entering through a singleface plane.

• Treated the diffusion coefficient, D, as being independent ofgas concentration during each stepwise gas sorption process.

•

4

4

ssti

Fig. 4. Volume swelling ratio of PLA–CO2 and PLA–N2 at: (a) 180 ◦C and (b)200 ◦C.

swollen volume of the polymer–gas mixture (VS) and the vol-ume of the pure polymer sample (VP), the volume swelling ratio,i.e., VS/VP, can be computed as SW (%).

The SW prediction of PLA with dissolution of CO2 and N2were calculated and shown in Fig. 4. It was obvious that the vol-ume swelling ratio increased with an increase of the dissolvedgas’s pressure. It is easy to understand that more gas will dissolvein the polymer melt under higher pressure, which increases thetotal occupied volume of the polymer–mixture system. FromFig. 4, it was also observed that the PLA–N2 mixture exhib-ited much less swollen volume as compared with the PLA–CO2mixture. Both SS-EOS and SL-EOS yielded almost the samevalue for the volume swelling ratio prediction on the PLA–N2mixture system at both 180 and 200 ◦C. Thus, there was nobig discrepancy between SS-EOS and SL-EOS in terms of thevolume swelling ratio predicted for the PLA–N2 mixture. Themaximum volume swelling ratio of the PLA–N2 mixture wasless than 4.34% at both 180 and 200 ◦C as shown in Table 2,no matter what EOS was applied. It is believed that the totalvolume could not expand significantly due to the very small

Assumed the thickness of the polymer disk, L, to be constantduring sorption (no swelling effect). Therefore, only sorptiondata at low pressures were used for the extraction of the dif-fusivity.

. Results and discussion

.1. Swollen volume prediction

With the dissolution of gas in the PLA melt during theorption process, the overall volume of the PLA–gas mixturewelled. In order to determine the amount of swollen volume dueo the gas dissolution, both SS-EOS and SL-EOS were adoptedn this study. From the EOS-based theoretical prediction on

G. Li et al. / Fluid Phase Equilibria 246 (2006) 158–166 163

Table 2Volume swelling prediction of PLA with dissolution of N2 at 180 and 200 ◦C

Pressure (MPa) SL-based volumeswelling (%)

SS-based volumeswelling (%)

180 ◦C3.48 0.39 0.446.97 0.88 0.94

10.44 1.34 1.4313.92 1.79 1.9217.41 2.22 2.4120.89 2.62 2.9124.38 3.02 3.4427.87 3.39 3.98

200 ◦C3.45 0.68 0.446.94 1.18 0.97

10.45 1.65 1.5113.93 2.09 2.0517.41 2.52 2.5920.90 2.93 3.1524.39 3.31 3.7327.88 3.69 4.34

amount of dissolved N2 in the PLA melts. It was also observedfrom Table 2 that there was no obvious temperature effect on thevolume swelling ratio prediction of the PLA–N2 mixture. ThePLA–N2 mixture showed almost the same swelling behavior atboth 180 and 200 ◦C.

However, when CO2 was introduced, the PLA–CO2 meltmixture exhibited much more swollen volume due to the largeamount of dissolved CO2 in the PLA melt as shown in Fig. 4 andTable 3. The maximum volume swelling ratio of the PLA–CO2mixture reached 31.3% when SL-EOS was applied at 27.89 MPaand 180 ◦C (Table 3). Also, it is quite obvious that the volumeswelling ratio of PLA–CO2 increases with an increase of pres-sure. It is believed that the volume swelling ratio of PLA–CO2is strongly dependent on the amount of dissolved CO2 gas. The

Table 3Volume swelling prediction of PLA with dissolution of CO2 at 180 and 200 ◦C

Pressure (MPa) SL-based volumeswelling (%)

SS-based volumeswelling (%)

180 ◦C3.47 3.22 2.366.94 6.68 4.81

10.44 10.28 7.2713.93 14.02 9.7817.42 17.93 12.4320.92 22.10 15.4322

2

111222

more CO2 gas molecules that are dissolved in the PLA melt, themore volume the gas molecules, and hence the overall mixture,will occupy. Unlike the PLA–N2 system, it was found that therewas a large discrepancy between the SS-EOS-based predictionand SL-EOS-based prediction on the volume swelling ratio forthe PLA–CO2 mixture. SS-EOS gave a lesser volume swellingprediction than SL-EOS, which was similar to previous find-ings [24]. Also the SS-EOS and SL-EOS gave different resultswhen predicting the temperature effect on the volume swellingratio for PLA–CO2. There is a significant temperature effect onthe volume swelling when SL-EOS is applied. It was believedthat there are significant differences in determining the appar-ent solubility of N2 and CO2. Therefore, the deviation may beconcealed on the theoretical volume swelling calculation resultsfrom the two EOS due to the very small values of N2 solubil-ity. Another reason is the relatively poor data correlation viaSS-EOS. The differences between SL-EOS and SS-EOS needto be further investigated. The validity of the different EOSs onvolume swelling prediction will be verified through the experi-mental measurement of pvT data for the polymer–gas mixture.

4.2. Gas solubility determination

With an SS-based or an SL-based swollen volume prediction,the solubility of CO2 and N2 in PLA at 180 and 200 ◦C wassuccessfully obtained on the basis of MSB-measured apparentsNCswEa

TS

P(

(

111222

(

111222

Tip

4.42 26.54 19.107.89 31.30 24.07

00 ◦C3.50 3.10 2.176.98 6.09 4.460.44 9.16 6.823.92 12.37 9.317.41 15.72 12.010.89 19.28 15.124.38 23.08 18.967.86 27.18 24.20

olubility. As shown in Fig. 5 and Table 4, the solubility of2 in PLA increases as the pressure increases. Compared withO2, the solubility of N2 in PLA was much less. The maximum

olubility of N2 in PLA can reach up to 0.0174 g gas/g polymerithin the pressure range of interest. Both SS-EOS and SL-OS provide reasonably good fitting results between Xcorrectednd Xtheory. There were no significant differences between the

able 4olubility of N2 in PLA

ressureMPa)

Xapparent SL Xcorrected SL Xtheory SS Xcorrected SS Xtheory

a) 180 ◦C3.48 0.0020 0.0021 0.0023 0.0021 0.00206.97 0.0039 0.0043 0.0045 0.0043 0.00410.44 0.0057 0.0065 0.0066 0.0066 0.00613.92 0.0072 0.0086 0.0087 0.0087 0.00827.41 0.0086 0.0107 0.0107 0.0109 0.01030.89 0.0097 0.0127 0.0127 0.0130 0.01254.38 0.0107 0.0147 0.0146 0.0152 0.01487.87 0.0115 0.0165 0.0164 0.0174 0.0173

b) 200 ◦C3.45 0.0021 0.0023 0.0023 0.0022 0.00216.94 0.0041 0.0045 0.0045 0.0045 0.00420.45 0.0058 0.0068 0.0066 0.0067 0.00643.93 0.0072 0.0088 0.0087 0.0088 0.00867.41 0.0084 0.0108 0.0107 0.0109 0.01090.90 0.0094 0.0127 0.0127 0.0129 0.01324.39 0.0102 0.0145 0.0145 0.0150 0.01577.88 0.0108 0.0162 0.0164 0.0171 0.0184

he unit of solubility is (g gas)/(g polymer). The SL interaction parameter k12

s −0.0231 at 180 ◦C and −0.0032 at 200 ◦C separately. The SS interactionarameters are optimized as δe = 1.1722; δv = 1.0414 at both 180 and 200 ◦C.

164 G. Li et al. / Fluid Phase Equilibria 246 (2006) 158–166

Fig. 5. Solubility of CO2 and N2 in PLA at: (a) 180 ◦C and (b) 200 ◦C.

SS-EOS-based Xcorrected and the SL-EOS-based Xcorrected on thePLA–N2 system, which means that either the SS-EOS or SL-EOS could be applied to determine the solubility of the PLA–N2system without much deviation. Moreover, in Table 4, it wasclearly shown that the temperature did not affect the solubilityof N2 in PLA much at either 180 and 200 ◦C.

The solubility of CO2 in PLA was shown in Fig. 5 andTable 5 as well. Unlike in the PLA–N2 system, the swollenvolume is an outstanding factor in determining the CO2 solu-bility in PLA. The Xcorrected of CO2 is more than 200% that ofthe Xapparent at 27.89 MPa due to the buoyancy compensation.As shown in Fig. 5, for the PLA–CO2 system, the approachbased on the SL-EOS generated a better fitting between Xcorrectedand Xtheory, whilst there was a big deviation between Xcorrectedand Xtheory when the SS-EOS was adopted. In Table 5, it wasalso observed that the SS-EOS-based Xcorrected was less thanthe SL-EOS-based Xcorrected due to the lesser volume swellingratio prediction from SS-EOS. Therefore, it will be wiser to con-sider the error on the volume swelling ratio prediction generatedfrom the different EOSs when accurate solubility information

Table 5Solubility of CO2 in PLA

Pressure(MPa)

Xapparent SL Xcorrected SL Xtheory SS Xcorrected SS Xtheory

(a) 180 ◦C3.47 0.0213 0.0226 0.0229 0.0222 0.01926.94 0.0415 0.0468 0.0466 0.0453 0.0386

10.44 0.0596 0.0720 0.0713 0.0684 0.058313.93 0.0746 0.0980 0.0968 0.0909 0.078417.42 0.0865 0.1247 0.1236 0.1130 0.099720.92 0.0951 0.1525 0.1521 0.1352 0.123924.42 0.1009 0.1819 0.1824 0.1592 0.153327.89 0.1044 0.2131 0.2148 0.1880 0.1929

(b) 200 ◦C3.50 0.0189 0.0201 0.0191 0.0197 0.01746.98 0.0351 0.0397 0.0388 0.0385 0.0351

10.44 0.0500 0.0605 0.0589 0.0578 0.053413.92 0.0624 0.0819 0.0801 0.0771 0.072817.41 0.0723 0.1038 0.1023 0.0963 0.093920.89 0.0795 0.1262 0.1258 0.1161 0.118224.38 0.0845 0.1499 0.1509 0.1382 0.148227.86 0.0875 0.1752 0.1780 0.1656 0.1888

The unit of solubility is (g gas)/(g polymer). The SL interaction parameter k12

is −0.1403 at 180 ◦C and −0.1513 at 200 ◦C separately. The SS interactionparameters are optimized as δe = 1.0515; δv = 0.9945 at both 180 and 200 ◦C.

is required. Although the SS-EOS-based Xcorrected and the SL-EOS-based Xcorrected were different for the PLA–CO2 system,they showed the same trend: the solubility of CO2 in PLA isstrongly dependent on the temperature. With increasing tem-peratures, the solubility of CO2 in PLA decreased significantlyno matter what EOS was applied. The maximum solubility ofCO2 in PLA at 27.89 MPa was 0.2131 g gas/g polymer at 180 ◦Cand 0.1752 g gas/g polymer at 200 ◦C when the SL-EOS wasemployed.

4.3. Gas diffusivity determination

As described in the previous section, the sorption curves werefirst obtained from MSB to extract the diffusion coefficient ofgas (N2 and CO2) in the PLA melt. In Fig. 6, the sorption curvesfor N2 and CO2 during the pressure step from 6.9 to 10.5 MPawere used as an example to illustrate the procedure for extract-ing the diffusion coefficient. The diffusion coefficient was thenoptimized so that the sorption model (Eq. (14)) based on Fick’ssecond law fit the experimental sorption curve. Even thoughthere were some assumptions during the extraction of the diffu-sion coefficient from the sorption curve (i.e., one-dimensionaldiffusion and ignoring the swelling effect), the sorption modeldescribed the whole sorption process very well for both N2 andCO2. According to Fig. 7, the significant pressure effect on thediffusion coefficient could not be observed. This finding sup-ptipavt

orts our assumption at the beginning. In fact, Fig. 7 shows thathe diffusivity of both CO2 and N2 decreases somewhat with anncrease of gas pressure. Indeed, the hydrostatic pressure maylay a role in this decreased diffusivity through reducing thevailable free volume in the system. Other data that support thisiewpoint include CO2 diffusion in polyamide [39] and a gela-inized starch system [40]. However, temperature is a dominate

G. Li et al. / Fluid Phase Equilibria 246 (2006) 158–166 165

Fig. 6. Sorption curve of: (a) N2 and (b) CO2 in PLA at 180 and 200 ◦C.

factor on the diffusion coefficient. With the increase of temper-ature, the diffusion coefficient increased significantly. Betweenthe comparison of N2 and CO2, N2 exhibited a higher diffusioncoefficient.

Fig. 7. Diffusivity of N2 and CO2 in PLA at 180 and 200 ◦C.

5. Summary

In order to develop PLA-based products with supercriti-cal fluid processing techniques such as microcellular injectionmolding, an investigation of the solubilities and diffusion coef-ficients of carbon dioxide and nitrogen in polylactide melt werecarried out at 180 and 200 ◦C. Both SS-EOS and SL-EOS wereapplied to predict the amount of volume swelling in the PLA–gasmixture due to gas dissolution and to compensate for the buoy-ancy effect associated with the swelling during the solubilitydetermination. The theoretical sorption model based on Fick’ssecond law was adopted to extract the diffusion coefficients fromthe sorption curves. The experimental results exhibited signif-icant differences in the solubility of carbon dioxide and thatof nitrogen in PLA melts, with carbon dioxide solubility up to20% and nitrogen solubility up to 2%. At the same temperature,nitrogen exhibited higher diffusivity than carbon dioxide.

Acknowledgments

This project was financially supported by Auto 21, the Con-sortium for Cellular and Microcellular Plastics (CCMCP), andNSF DMI-0544729. Their financial support is greatly appreci-ated.

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