Dimethyl ether’s plasticizing effect on carbon dioxide solubility in polystyrene

Dimethyl ether’s plasticizing effect on carbon dioxide solubility in polystyrene

Polymer 97 (2016) 95e103 Contents lists available at ScienceDirect Polymer journal homepage: www.elsevier.com/locate/polymer Dimethyl ether’s plast...

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Polymer 97 (2016) 95e103

Contents lists available at ScienceDirect

Polymer journal homepage: www.elsevier.com/locate/polymer

Dimethyl ether’s plasticizing effect on carbon dioxide solubility in polystyrene S.H. Mahmood a, C.L. Xin b, P. Gong a, J.H. Lee a, G. Li a, C.B. Park a, * a b

Microcellular Plastic Manufacturing Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, Canada College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 March 2016 Received in revised form 29 April 2016 Accepted 6 May 2016 Available online 7 May 2016

The solubility of carbon dioxide (CO2) and dimethyl ether (DME) blends in polystyrene (PS) is studied as a function of the temperature and the pressure. The solubility was measured by means of the gravimetric method and a visualizing dilatometer which determined the swollen volume to compensate for the buoyancy change due to swelling. The solubility of the blend gases for the ternary PS/CO2/DME system is also predicted by the Simha-Somcynsky (SS) equation of state (EOS). The theoretical prediction of the blend solubility was in agreement with the experimental results. Adding DME to PS not only decreased the pressure required to dissolve CO2 in PS but the effects of plasticization were also observed. The remarkable plasticization effect due to the presence of DME increased the CO2 solubility via an increased free volume of PS. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Solubility Co-blowing agent Simha-Somcynsky equation-of-state Ternary system Plasticization

1. Introduction Thermoplastic foams, which have cellular core structures, are created by the phase separation of polymer/gas mixtures. Under high pressure, a polymer/gas system’s total Gibbs free energy decreases as gas is dissolved in the polymer matrix up to the solubility limit. This process typically swells the polymer volume [1,2]. Thus, the thermal and physical properties are changed [3e7]. For example, the glass transition temperature (Tg) is reduced due to the plasticization effect of the dissolved gas. The concentrated gas within the polymer matrix causes the Tg depression of a polymer/ gas mixture. As the diluents’ concentration is increased, regression in the Tg becomes more pronounced. This is due to an increase in the inter-chain distance and in the polymer segment’s mobility, which increases the free volume [8]. This degree of swelling and the solubility is a sensitive function of the pressure and the temperature. Therefore, a sudden pressure or temperature alteration induces a thermodynamic instability within the polymer/gas mixture, which would result in foaming of the polymer when the degree of the instability is high enough to overcome the bubble nucleation barrier and when enough gas is available to promote

* Corresponding author. E-mail address: [email protected] (C.B. Park). http://dx.doi.org/10.1016/j.polymer.2016.05.018 0032-3861/© 2016 Elsevier Ltd. All rights reserved.

bubble growth. As such, the solubility of the gas in the polymer is a critical parameter in controlling the phase separation and, eventually, the foam morphology. Numerous past theoretical studies have been conducted on binary polymer/gas systems to determine the solubility of gas in the polymer [9e11]. Their fundamental data have helped researchers to achieve the desired foam structure by optimizing the processing conditions based on the solubility data. The foam structure is typically characterized by the cell size, the cell density, the expansion ratio, and the open-cell content. A certain combination of these structural parameters allowed the foamed plastics to be effectively used in the structural, packaging, automotive, and sports industries [12,13]. Although binary systems have been used to produce polymeric foams in numerous commodity applications, a ternary system further enabled us to fabricate a more complex foam structure for specific functionalities. Gong et al. used a ternary polystyrene (PS)/ CO2/pentane system to produce PS foams with a small cell size and a large expansion ratio (17-fold) for thermal insulation [14]. CO2 was used to create a large bubble density, and pentane was used to achieve a large expansion ratio. Zhang et al. used a ternary PS/CO2/ water system to produce PS foams with bimodal cell morphology [15,16]. Lee et al. used a ternary low-density polyethylene (LDPE)/ CO2/butane system to produce LDPE foams with open-cell morphology [17,18]. However, unlike the binary systems, accurate

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solubility data for the ternary systems are scarce, and a fundamental understanding of the role of each gas within the ternary system is lacking. On the other hand, a number of gases have been used as blowing agents in the foam industry. Chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), hydrocarbons (HCs), and hydrofluorocarbons (HFCs) have been used due to their low diffusivity and high solubility for low-density foam processing. However, most of these commonly used blowing agents are environmentally hazardous, flammable, and/or expensive. For instance, CFC’s contribute heavily to the depletion of the stratospheric ozone layer, and the Montreal Protocol banned their production in 1996 [19]. HFCs, as replacement blowing agents, have zero ozone depletion potential (ODP), but its emission control was required by Kyoto Protocol due to their high global warming potential (GWP). HCs (zero ODP and low GWP) are highly flammable, and the recently developed hydrofluoroolefins (HFOs) are too expensive for industrial-scale usage. Due to aforementioned environmental reasons, carbon dioxide (CO2), which is less environmentally threatening and economically viable, has been used as a replacement. However, CO2 tends to be relatively less soluble in polymer compared with the previously noted blowing agents. This, in turn, affects the processing conditions to produce the desired cell morphology of the foam. As a consequence, the processing pressure required to dissolve the less soluble CO2becomes very high. Therefore, in order to circumvent this critical drawback of CO2’s low solubility, other highly soluble co-blowing agents are also blended together with CO2. Ethanol, 2-ethyl hexanol, dimethyl ether (DME), and acetone [20e23] are a widely used co-blowing agent with CO2 due to their high solubility in polymers. Also, these gases are less environmentally threatening and are more economically viable [24]. In particular, DME has an outstanding secondary blowing agent characteristic along with CO2 in that it has a zero ODP, a low GWP, and non-toxicity [25]. Most importantly, DME interacts favorably with PS [26]. Furthermore, DME has a lower boiling temperature (24.8  C) compared to other highly soluble blowing agents such as hydrocarbons and alcohols, so it will remain in a gaseous phase at most ambient temperatures during winter. Hence, the shrinkage of the blowing agent during cooling within PS foams will be much less for DME than for hydrocarbons and alcohols which can liquefy easily. Therefore, the PS foams blown with DME will have a less shrinkage problem in environments where temperature drops considerably. Despite their great potential, the literature describing the blend gases, which are limitedly used in industrial polymer-foam processes [15e18] is scarce. It contains no information on their solubility or on how they affect each other. Such information is vital to the design of an optimal polymer foam process because it provides the critical information such as the minimum pressure to be maintained to keep a single-phase polymer/blend-gas mixture in the processing system, and the location of cell nucleation inside the die lip [27,28]. In this study, the solubility of blend gases was experimentally and theoretically investigated in PS. A very interesting phenomenon regarding the co-blowing agent’s role in enhancing the solubility of the inherently low-soluble CO2 within the polymer was discovered. The solubility of CO2, determined using the SimhaSomcynsky (SS) equation-of-state (EOS) was observed to increase in the presence of DME. DME was found to act as a plasticizer by increasing the free volume within the PS. It appears that the PS swells with the dissolved DME and thereby the solubility of CO2 in PS increases. The changes in the CO2 solubility are analyzed as a function of the DME content. To further confirm DME’s plasticizing effect, the depression of the Tg caused by the dissolution of each gas was also observed.

2. Theoretical background Theoretical models have been created to describe the interactions between polymer and gas with a view to optimizing the processing conditions. Two of such models used in the past are the Sanchez-Lacombe (SL) equation-of-state (EOS) and the SimhaSomcynsky (SS) EOS [29,30]. The two models were compared to the experimental findings for a binary system in our earlier work, and the SS-EOS was found to be closer to the experimental results compared to the SL-EOS [11,31]. Both the models can be traced back to the Flory-Huggins model and both allow for the holes to allow for entropy generation within the lattice hole theory. But, unlike the SL-EOS, the SS-EOS also accommodates the entropic contribution of the each lattice. This is resulted due to the presence of an additional characteristic parameter such as the flexibility of the molecules and the total number of mers present in a molecule. These differences may have contributed in the similarity of the SS-EOS prediction with the experimental findings over the SL-EOS for the binary polymer/gas systems. The effectiveness of the SS-EOS for describing the polymer/gas mixtures was also observed for ternary polymerblend gas systems [26]. The experimentally measured volume swelling of polymer-blend gas mixtures was adequately described by the SS-EOS. Therefore, we used the SS-EOS in this work to predict the solubility of the blend gases in the ternary system. A detailed explanation of the ternary based SS-EOS is described in Ref. [32]. A brief description of the ternary model is presented here. The pressure - specific volume - temperature (PVT) behavior of the mixture was obtained by solving Eqs. (1) and (2) of the SSEOS as follows:

  h i ~V ~ 2y P Q 2  1:011Q 2  1:2045 ¼ ½1  h1 þ T T~

(1)

and

    h i s s  1 lnð1  yÞ h  1=3 y þ ¼ þ Q 2 2:409  3:033Q 2 3c s y 1h 6T~ (2) As required by the SS theory, the volume of the gas molecules should match those of the molar repulsion volume of polymer segment; this was achieved by adjusting the polymer segment size [33]. Hence, in line with the polymer/gas system we studied, the SS scaling parameters for the PS and the gases involved were obtained. Table 1 lists all the scaling parameters for each component. According to the classical thermodynamic theory, the chemical potential (m) for each gas component (1 or 2) is identical in all phases (that is, the vapor phase and the polymer/gas mixture phase) under equilibrium conditions [35,36]. Therefore, the criterion for the phase equilibrium in the ternary system can be expressed by Eqs. (3)e(5):

mV1 ðP; T; m1 Þ ¼ mP1 ðP; T; n1 ; n2 Þ

(3)

mV2 ðP; T; m2 Þ ¼ mP2 ðP; T; n1 ; n2 Þ

(4)

Table 1 Scaling parameters for the SS-EOS. Substance

P* (MPa)

V* (cm3/g)

T* (K)

Mn

s

c

Reference

PS CO2 DME

807.8 954.2 1318.9

0.96475 0.586 0.5508

16,044 2960 4025

190,000 44.01 46.07

7309 1 1

1142 1 1

[26] [34] [26]

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3.2. Materials

m1 þ m2 ¼ 1 and x1 þ x2 þ x3 ¼ 1

(5)

where mVi is the chemical potential of gas in the vapor phase and mPi is the chemical potential in the polymer phase, mi represents the composition of the vapor phase (gases blend), ni represents the composition of the polymer phase, and xi is the molar fraction of each component in the system at a pressure (P) and a temperature (T). The molar fractions of the two gases (x1 and x2) in this ternary system are the only two independent composition variables. The chemical potential of each component was derived in Ref. [32] and is depicted as follows:

m1 ¼ Gm þ ð1  x1 Þ

vGm vGm  x2 vx1 vx2

(6)

m2 ¼ Gm þ ð1  x2 Þ

vGm vGm  x1 vx2 vx1

(7)

m3 ¼ Gm  x1

vGm vGm  x2 vx1 vx2

(8)

Since x1 and x2 are the only independent variables, it was deduced that:

 x1  x1

vm1 vm3  vx1 vx1 vm1 vm3  vx2 vx2

 þ x2

  vm2 vm3 vm þ 3¼0  vx1 vx1 vx1

(9)

þ x2

  vm2 vm3 vm þ 3¼0  vx2 vx2 vx2

(10)



97

The molar Gibbs free energy of the ternary mixture (Gm) was determined based on the approach illustrated by Jain and Simha [37,38]. The expression for Gm in the polymer phase for the ternary mixture system is shown in Eq. (11):

Gm y 1y lnð1  yÞ ¼ x1 lnx1 þ x2 lnx2 þ x3 lnx3 þ ln þ s s y RT " # e v* ð1  hÞ3 3 2pm1 RT þ ðs  1Þln  c ln  x1 c1 ln z1 2 Q ðNa hÞ2

The PS used in this study was obtained from Americas Styrenics (Styron 610). It has a molecular weight (Mw) of 1.9  105 g/mol, a specific gravity of 1.04 g/cm3, and a melt flow index of 10 g/10-min. Carbon dioxide (Coleman grade, 99.99% purity) and DME (99.8% purity) were obtained from Linde Canada. 3.3. Experimental procedure PS pellets were weighed as W (0,T) from the balance readout at vacuum (P ¼ 0) and T of the MSB. The blowing agent was then introduced at a pre-set pressure into the MSB. A desired pressure was insured by means of a syringe pump (Teledyne Isco 260D). Once the sorption of the gas in the polymer was completed, and the saturation stage was reached, identified by a lack of weight gain in the saturated polymer melt, the weight gain was recorded, and the pressure was increased by means of a syringe pump. During this time, the weight of the gas dissolved in the polymer melt was noted on the MSB readout: W (P,T) at P and T. Hence, the amount of gas dissolved in the polymer melt sample, Wg, was calculated by using the following equation:

Wg ¼ WðP; TÞ  Wð0; TÞ þ rgas ðVB þ VP þ VS Þ

where rgas is the density of the gas, which was obtained in situ using a MSB, VB is the volume of the sample holder, VP is the volume of the neat polymer (without gas) at pressure P and temperature T. The latter was obtained from the mass (mP) and the specific volume (vsp) of the polymer sample; and the VS is the swollen volume of the polymer melt due to gas dissolution. By ignoring the polymer’s swollen volume, the measured weight gain can be treated as the apparent solubility, Xapparent, as follows:

Xapparent ¼

WðP; TÞ  Wð0; TÞ þ rgas ðVB þ VP Þ mP

(11)

3. Experimentation 3.1. Experimental setup The apparent solubilities of the pure and the blend gases were measured using a magnetic suspension balance (MSB) from Rubotherm GmbH. Fig. 1 shows a schematic of the MSB used. The details of this equipment can be found in Ref [30,39]. The volume swelling of the polymer/gas-blend was experimentally found in our previous work [26] using in-house PVT visualization equipment, details of which can be found in Ref. [1].

(13)

Hence, the corrected solubilityXcorrected, compensated for the buoyancy effect in Eq. (12), can be obtained as follows:

Xcorrected ¼ Xapparent þ

3 2pm2 RT 3 2pm3 RT  x2 c2 ln  x3 c3 ln 2 2 2 ðNa hÞ ðNa hÞ2 "   cyQ 2 1:011Q 2  2:409 þ þ c ð1  hÞ1 2T~ #  2yQ 2 1:011Q 2  1:2045 þ T~

(12)

rgas VS mP

(14)

The volume swelling of the polymer/gas mixture was obtained via the experimental approach discussed by Li et al. [1]. A brief description of the experimental process is mentioned here. A weighted pellet of PS was attached to a mounting tip. The sample was calibrated at the beginning of each experiment to determine the pixel size in x and y orientation, with regard to the XY stage movement of the CCD camera. The images of the polymer/gas mixture sessile drop were captured by the CCD camera at a prescribed interval under isothermal conditions. Each pressure level was maintained until saturation was reached. The saturation time was deduced by comparing the volume expansion for each pressure and temperature. Once the volume of the polymer/gas mixture had ceased to increase, saturation was assumed, and the pressure level was increased to a desired pressure value. The swollen volume was then determined by comparing the final equilibrium volume of the polymer/gas mixture with the initial volume of the polymer sample. The swelling ratio was hence determined as follows:

Sw ¼

    V T; P; teq V T; P; teq ¼ VðT; P; tin Þ mP vsp

(15)

where V(T,P,teq) is the measured equilibrium polymer/gas mixture

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Fig. 1. A schematic of the magnetic suspension balance [29].

volume at temperature T, pressure P, and equilibrium time teq, and V(T,P,tini) is the (initial) volume of the pure PS sample calculated at T and P, which is simply the specific volume multiplied by its mass. The specific volume of the pure PS sample, vsp, is modeled based on the well-known Tait Equation [40] using the measured PVT data of PS at various temperatures and pressures (shown in Fig. 2). The Tait Equation for the PS resin (Styron 610) is modeled as function of T and P as follows:

vsp ¼ 0:9442  eð9:191710 þ

4



  1  0:0894  ln 1 

P 3 1:0774  103  eð3:445110 TÞ

(16)

3.4. Blowing agent blending The process of blowing agent blending was presented in our earlier work [26]. The molar volume of DME needed to obtain a desired blend with respect to the total volume of the experimental set up was obtained by means of the Peng-Robinson (PR) EOS. The total volume of the experimental setup, illustrated in Fig. 3, was obtained using a syringe pump and ethanol. Ethanol was chosen due to its high evaporation rate. The syringe pump was filled with ethanol, and its volume, under an isobaric condition, was noted from the pump’s read-out. The ethanol was then allowed to enter the rest of the experimental setup and the difference in the volume from the pump’s read-out was deemed to be the volume of the experimental setup. Details on the derivation of the EOS are in Ref. [41]. Table 2 shows the gases’ characteristic parameters for PREOS. The molar volume (m3/mol) of the desired blend concentration at different temperature and pressure values was measured using the PR-EOS, and its respective density was calculated by using Eq. (17).



 1  þ x2 MCO2 x M Vm 1 DME

(17)

where Vm is the molar volume of the blend, x1 and x2 are the volume concentration of DME and CO2, respectively, MDME and MCO2 are the molar masses of DME and CO2, respectively. The molar volume of DME-CO2 at 463 K based on the PR-EOS is shown in Fig. 4. Based on the molar volume obtained, the volume of DME needed to be pumped for the desired concentration was calculated using following equations,

mDME ¼ Fig. 2. PVT behavior of PS.

Vc : M Vm DME DME

(18)

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99

Fig. 3. Schematic of the blending setup along with the MSB.

Table 2 Characteristic parameter of blowing agents for the PR-EOS.

CO2 DME

Tc (K)

Pc (kPa)

U

304.2 400.1

7382 5240

0.2250 0.1891

cause the obtained theoretical prediction to deviate from the true results as the concentration of the secondary gas increases. It is for this reason that the concentration of secondary gas (DME) was kept relatively lower compared to CO2. The molecular interaction parameters between CO2 and PS (i.e., dPe;13 anddPv;13 ), as well as those between DME and PS (i.e., dPe;23 and dPv;23 ) were obtained separately in a binary system, and were applied in the ternary system. Similarly, the parameters describing the interaction between CO2 and DME (dPe;12 and dPv;12 ) were also calculated. Fig. 5 illustrates the relationship of these interaction parameters. After successful determination of all the interaction parameters, the SS-EOS was applied to determine the ternary system’s thermodynamic properties. Tables 3 and 4 show these interaction parameters. 4.2. Determination of the experimental solubility of CO2/DME blends in PS The solubility of the CO2/DME blend (90:10, 85:15 and 80:20, volume % in blend-gas reservoir) in PS was measured using the

Fig. 4. Molar Volume of DME-CO2 with varying DME concentrations at 463 K.

VDME ¼

mDME

rDME

(19)

Where mDME is the mass of DME, rDME is the density of DME, :DME is the molar fraction of DME, and Vc is the volume of the chamber. 4. Results and discussion 4.1. Measurement of the interaction parameters for the SS-EOS A ternary system consists of three types of molecular interactions: interactions between the two gases and the interactions between each gas and the polymer. Hence, three pairs of interaction parameters for three distinct components (CO2 is 1, DME is 2, and PS is 3) have to be determined in order to use the SS-EOS for the ternary mixture system. These parameter have been determined in our previous study [26]. It was assumed that the presence of two gases components did not affect the interaction of each individual gas with the polymer matrix. It is noted that this assumption may

Fig. 5. Phase equilibrium of ternary system CO2/DME blend and PS.

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Table 3 SS-EOS interaction parameters for the binary systems (CO2/PS and DME/PS). Temperature 423 K

CO2 DME CO2 DME CO2 DME

463 K 483 K

de

dv

1.0809 0.9689 1.0875 0.9428 1.091 0.9384

0.9791 0.9847 1.0084 0.9854 1.006 0.9856

Table 4 SS-EOS interaction parameters for the blend blowing agents (CO2:DME in PS). Temperature 423 K 463 K 483 K

de dv de dv de dv

90:10

85:15

80:20

1.0686 1.0499 1.0312 1.0625 1.0364 1.0427

0.9984 0.9989

1.0656 0.9687

Fig. 7. Effect of the temperature on the solubility of the blend (90:10) in PS

experimental procedure mentioned in Section 3.3. In order to obtain the solubility of the blend gas in PS correctly, the swelling has to be accurately measured separately according to Eq. (14). The volume swelling of the PS/CO2/DME mixture was measured experimentally using an in-house dilatometer where the temperature, the pressure, and the blend-gas ratio were precisely controlled [26]. These data are now used to calculate the experimental solubility, which is shown in Fig. 6. The solubility of the blends in PS was found to be higher than that of pure CO2, as Fig. 6 shows. This is somewhat similar to our previous work that the solubility of CO2/N2 blend was higher than that of pure N2 [42]. It was observed that the blend solubility is proportional to the pressure for each blend, following the Henry’s Law [43,44]. The effect of the temperature on the solubility of the blend is depicted in Fig. 7 whose trend follows a typical Arrhenius Equation for each fixed blend. With an increase in the temperature, the blends’ solubility decreased. This solubility trends with respect to the pressure and the temperature are similar to those found in the earlier literature [11,19,29,31,45]. The experimental solubility of each blend gas in PS is mathematically modeled as a function of the temperature (Arrhenius

  509:95 C100:0 ¼ 0:272  Pexp  5:074 þ T

(20)

  727:15 C90:10 ¼ 0:274  Pexp  5:431 þ T

(21)

Equation) and the pressure (Henry’s Law) based on the data shown in Fig. 7. These models for pure CO2 and the CO2:DME blend ratio of pure 90:10 (in the blend-gas reservoir) are shown in Eqs. (20) and (21).where P is pressure (MPa) and T is temperature (K).

4.3. Determination of the theoretical solubility of CO2/DME blends in PS based on SS-EOS The theoretical solubility of the blend gas in PS was determined by using SS-EOS as discussed in Section 2. The validity of the SSbased ternary model was established in our earlier work [26]. The interaction parameters were measured and optimized for each system of the blend-gas and PS mixtures. These interaction parameters were then implanted in the SS-EOS to determine the theoretical solubility of the blend. These solubility data are shown as the solid line in Fig. 8. Instead of using the completely theoretical prediction from the EOS, the solubility could also be determined semi-empirically from Eq. (14) by using the swelling data from the SS EOS and the (experimentally obtained) apparent solubility (denoted as ‘SSCompensated’ in Fig. 8). Fig. 8 shows that the theoretical solubility and the semi-empirical solubility data are close to the experimental solubility, indicating that the SS-EOS is adequate in describing the CO2-DME blend-gas solubility in PS. The dependence of the theoretical (and semi-empirical) solubility on the temperature and the pressure was comparable to the case of the experimental solubility, and a similar model based on the Henry’s law and the Arrhenius Equation can also be derived.

  400:01 C100:0 ¼ 0:813Pexp  5:947 þ T Fig. 6. Experimental solubility of CO2/DME blend in PS as a function of the pressure at various ratios of the blend gas at 423 K.

(22)

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Fig. 8. Comparison of the experimental, semi-empirical, and theoretical solubility of CO2/DME blend in PS for the blend ratio of 90:10 in the reservoir (a) at 423 K, (b) at 463 K, and (c) at 483 K.

  764:36 C90:10 ¼ 0:205Pexp  5:266 þ T

(23)

where P is pressure (MPa) and T is temperature (K). Fig. 8 also shows that the solubility above 6.9 MPa must consider the volume swelling in that the difference between the corrected solubility and the apparent solubility is not negligible. Either theoretically or empirically measured swelling data should be used to determine the solubility accurately at elevated pressures.

4.4. Effect of the DME concentration on the change in the CO2 solubility in PS It should be noted that the compositions of the CO2 and DME molecules within the PS matrix are not the same as those in the reservoir for each particular blend-gas ratio. Irrespective of the CO2 and DME concentrations in the reservoir, the final concentrations of CO2 and DME in the PS matrix are determined thermodynamically from Eqs. (3) and (4). But the solubility measurements mentioned in the previous sections are made without specifying the individual blowing-agent solubility contributions or their effects on each other. Although the blend solubility of CO2 and DME at various reservoir compositions was measured, the measured data of the swelling and the solubility did not give any information about the individual gas solubility. So, the individual solubility of CO2 and DME in the PS matrix is determined for each composition, and the results are analyzed in this section. The individual solubility of the two gases within the blend can be obtained by analyzing the SS-EOS model for each ternary system. As Section 4.3 mentioned, the SS-EOS was found suitable to measure the blends’ solubility in PS and, hence, the SS-EOS was used to predict the DME’s and the CO2’s solubility individually as well. The ternary system with a different CO2 and DME ratio in the reservoir was obtained from the mass fractions, x1 and x2, obtained from Eqs. (9) and (10). The calculated data are shown in Fig. 9.

Fig. 9. Effect of DME solubility on the solubility of CO2 in PS.

It is of great interest to note that the theoretically predicted solubility of CO2 within the PS matrix was found to be almost proportional to the concentration of DME within the same PS matrix. This increment in the CO2 solubility was evident in all the measured temperature range. The results presented in Fig. 9 can also be depicted in the form of the solubility pressure, which is the minimum pressure required to maintain a single-phase polymer/ gas mixture for a dissolved gas content. Reducing this pressure can benefit the foaming process greatly because of the decreased resistance in the die. With an increased DME content, the solubility pressure decreases as illustrated in Fig. 10. Because of the stronger affinity and superior intermolecular forces between PS and DME [46], in contrast to PS and CO2, DME would cause a relatively higher

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~ P Q R si Sw T Ti* T~ vsp yi* Vi* ~ V xi X y z ni Fig. 10. Effect of the DME concentration in blend on the solubility pressure at 423 K.

volume swelling of the polymer/gas mixture [26]. This would increase the polymer’s free volume. This added free volume could then permit the CO2 molecules to penetrate further and to increase the CO2’s solubility. 5. Conclusion We investigated the solubility of CO2 and DME blends at varying volume concentrations (90:10, 85:15and 80:20) in PS. The experiments were carried out at temperatures of 423 K, 463 K and 483 K and at pressures ranging up to 20.68 MPa. The solubility was measured experimentally using both a gravimetric instrument and the PVT visualization system. Furthermore, solubility was also theoretically determined using the SS-EOS. The blends’ solubility increased incrementally with an increase in DME’s concentration. The SS-EOS was also used to determine the solubility of each gas within the polymer in a ternary system. Hence, we deduced through the SS-EOS, that the DME’s plasticizing nature caused the CO2’s solubility to increase in the PS matrix. Acknowledgments The authors are grateful for the financial support provided by the Industry members of the Consortium for Cellular and Microcellular Plastics, and the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (DG) 154279-2010. Nomenclature ci Gm h mi mP Mi N Na P Pi*

chain (molecule) flexibility; 3c is total external degrees of freedom attributed to a chain (molecule) molar Gibbs free energy for polymer/gas mixture [J$mol1] Planck’s constant 6.6260755 $ 1034 [J$s1] molar mass of segment (mer) of “i” component [g$mol1] mass of neat polymer [g] molecular weight of per molecule [g$mol1], M ¼ misi total number of molecules (s-mers) Avogadro’s number, 6.0221367$1023 pressure [Pa] characteristic pressure of component “i” [Pa], Pi* ¼ (qzεi*)/ (syi*)

h mVi mPi r

reduced pressure P/P* ~ 1 , dimensionless identity ðyVÞ gas constant, 8.3143 [J$(mol$K)1] number of mers per molecule of component “i” volume swelling ratio temperature [K] characteristic temperature of component “i” [K], Ti* ¼ (qzεi*)/(cK) reduced temperature T/T* specific volume [cm3$g1] characteristic volume per mer of component “i” [m3$mer1] characteristic volume of component “i” (m3$mol1) reduced volume V/V* mole fraction of “i” component in mixture system solubility (g of gas/g of polymer) occupied lattice site fraction 12,the lattice coordination number composition of the polymer phase for component “i” 21/6yQ1/3 dimensionless number chemical potential of gas in vapor phase [J$mol1] chemical potential of gas in the polymer melt [J$mol1] density of gas [g$cm3]

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