J. of Supercritical Fluids 97 (2015) 6373

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The Journal of Supercritical Fluids

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Viscosity and density of poly(ethylene glycol) ancarbon dioxide at 353.2 K and 373.2 K at pressure

Masayuk MicMasaru W r.a,b

a Graduate Sch y, AramSendai 980-857b Graduate Sch UnivSendai 980-857

a r t i c l

Article history:Received 12 JuReceived in reAccepted 9 OcAvailable onlin

Keywords:Carbon dioxidePoly(ethylene glycol)ViscosityDensityMolecular weiFree volume v

een rexist, 8300 so

viscometer at 353.2 K and 373.2 K over the range of CO2 pressures from 5 MPa to 15 MPa. The densities ofCO2PEG solutions were calculated with the perturbed-chain statistical associating uid theory equationof state. From shear viscosity measurements, PEG 3000 and PEG 8300 were conrmed to be Newtonianand PEG 20000 was conrmed to be non-Newtonian. The viscosity reduction ratio for PEG solutionssaturated with CO2 was found to be independent of the PEG molecular weight (400 M 8300 g mol1).A simple equation is proposed that can correlate CO2PEG solution viscosity reduction ratio to within

1. Introdu

Poly(ethoxide as its20,000 g mothan 20,000oxide) or Pare hydrophgroups are Physical proroom temp(PEG 400) isis a crystalceutical ind

CorresponCenter of Supe6-11, Aoba-ku

E-mail add1 Present ad

tute of AdvancSendai 983-85

http://dx.doi.o0896-8446/ ghtiscosity model

0.08 in absolute units. The CO2PEG solution viscosities could be correlated with free volume models towithin 14% using the tted value of CO2 occupied volume.

2014 Elsevier B.V. All rights reserved.

ction

ylene glycol) or PEG, is a polymer that has ethylene repeating unit and a molecular weight that is less thanl1 [1]. For PEG that has a molecular weight greater

g mol1, the polymer is referred to as poly(ethyleneEO. In the polymer chain of PEG, methylene groupsobic whereas the ether oxygen and terminal hydroxyl

hydrophilic, which gives PEG its amphiphilic character.perties of PEG vary greatly with its molecular weight. Aterature, PEG that has a molecular weight of 400 g mol1

a liquid, while PEG 1500 is a waxy solid and PEG 6000line plastic. PEG is widely used in food and pharma-ustries due to its unique characteristic properties that

ding author at: Graduate School of Environmental Studies, Researchrcritical Fluid Technology, Tohoku University, Aramaki Aza Aoba 6-, Sendai 980-8579, Japan. Tel.: +81 22 795 5863.ress: smith@scf.che.tohoku.ac.jp (R.L. Smith Jr.).dress: Research Center for Compact Chemical System, National Insti-ed Industrial Science and Technology, Nigatake 4-2-1, Miyagino-ku,51, Japan.

include: (i) high solubility in both aqueous and organic solvents, (ii)no known immunogenicity, antigenicity and toxicity effects, and(iii) high exibility and hydration of the polymer chain [2].

Carbon dioxide (CO2) readily dissolves into PEG, while PEG ispractically insoluble in the vapor phase of CO2 [37]. A large amountof CO2 can be dissolved into PEG compared with other gases suchas propane and nitrogen [6]. Dissolution of CO2 into the PEG phasecauses a decrease in the melting point of PEG (ca. 20 K) [4,8,9],a signicant reduction in the PEG viscosity (5080%) [8,1012],a reduction in the CO2PEG interfacial tension [13], and swellingof the PEG [9,1416]. These characteristics of CO2PEG solutionshave been applied to particle formation processes [1719], biphasicreaction systems [20,21], membrane materials for gas separations[22,23].

Fundamental studies of CO2PEG solutions have been carriedout to understand the molecular interactions with microscopicand macroscopic methods. Using microscopic methods, the inter-action between CO2 and PEG was investigated by infrared (IR)spectroscopy [15,24], near-IR spectroscopy [14,16], and ab initiocalculations [16]. The IR peak of CO2 bending shift to lower wave-lengths in CO2PEG solutions indicates interaction between CO2and PEG [15]. The ab initio calculations show that the oxygen

rg/10.1016/j.supu.2014.10.0132014 Elsevier B.V. All rights reserved.i Iguchia,1, Yuya Hiragab, Kazuhiro Kasuyab, Takuatanabea,b, Yoshiyuki Satoa, Richard Lee Smith J

ool of Engineering, Research Center of Supercritical Fluid Technology, Tohoku Universit9, Japanool of Environmental Studies, Research Center of Supercritical Fluid Technology, Tohoku9, Japan

e i n f o

ly 2014vised form 9 October 2014tober 2014e 23 October 2014

a b s t r a c t

Few viscosity and density data have bmany vaporliquid equilibrium data poly(ethylene glycol) (PEG, M = 3000Viscosities of PEG 3000 and PEG 830d its solution withs up to 15 MPa

hael Aidab,,

aki Aza Aoba 6-6-11, Aoba-ku,

ersity, Aramaki Aza Aoba 6-6-11, Aoba-ku,

eported for CO2poly(ethylene glycol) solutions, even though in the literature. In this work, viscosity and density of pure0, 20,000 g mol1) at atmospheric pressure were measured.lutions with CO2 were measured with a torsional vibrating

64 M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373

Nomenclature

a shift factor or viscosity reduction ratioa0/sa1, a1b0, b1/K c/g ml1

c0/cm3 gd0/mPa sf H/mPa s k kij

kB/J K1

m M/g mol

Mn/g mMv/g moMw/g mp/MPa Sw T/K up/MPa uT/K Uc()/% Uc()/%

Uc()/% v/cm3 g

V/cm3

vf/cm3 g

vo/cm3 gwi

Greek symV/cm3

/J i/mPa s 0/mPa s/kg2 m/s1

/kg m3

/A /rad s

Superscrio

atom of PEGreveals a Le[16]. Using of CO2PEGequilibria ([4,8,9], dentensions [1being availawith pressuture [36,8that of PEGthat has a min PEG doesThe solubiliand 40 MPa

to be negligible for PEG of higher molecular weight. The density ofCO2PEG solutions decreases up to around 10 MPa [11,32], and thenslightly increases with CO2 pressure [11,13]. Due to the few datathat have been reported (M = 400, 600 and 2000 g mol1) [11,13,32],

sityders

have], 400

g moses wat prpreseeightn betionologtion

ed atwn adjustable parameters in Eq. (1)adjustable parameters in Eq. (2)polymer concentration in mixture

1, c1/cm3 g1 K1 adjustable parameters in Eq. (3) cmd1 gd1, d1, d2 adjustable parameters in Eq. (5)free volume fractionscaling value in Eq. (2) set equal to unitycoverage factorcorrection factor for binary segment interactionparameterBoltzmann constantnumber of segments per chain1 molecular weight

ol1 number average molecular weightl1 viscosity average molecular weight

the denwell unments[10,1220,000decreamuch in the ular wthat caapplica

Rheapplicareportas shool1 weight average molecular weightpressureswelling ratiotemperaturestandard uncertainty of pressurestandard uncertainty of temperaturecombined expanded uncertainty of viscosity

combined expanded uncertainty of visco-sitydensity productcombined expanded uncertainty of density

1 specic volumevolume1 free specic volume

1 occupied specic volumeweight fraction of component i

bolsvolume changedepth of pair potentialvolume fraction of component iviscosity

zero-shear rate viscosity4 s1 viscositydensity productshear ratedensity

segment diameter1 frequency

ptsatmospheric pressure

donates electrons to the carbon atom of CO2, whichwis acidbase type of interaction between CO2 and PEGmacroscopic methods, the thermodynamic properties

solutions have been reported that include vaporliquidVLE) [39,1416,2531], solidliquid equilibria (SLE)sities [11,13,32], viscosities [8,1012] and interfacial3]. Most research has focused on VLE with few reportsble for other properties. CO2 solubility in PEG increasesre and slightly decreases with an increase in tempera-,16,29]. The solubility of CO2 in PEG 200 is lower than

of higher molecular weight (ca. 400 g mol1). For PEGolecular weight above 400 g mol1, the CO2 solubility

not change much with the PEG molecular weight [4,6].ty of PEG 1500 in CO2 phase is below 0.05 wt% at 328 K

[15], so that PEG solubility in CO2 can be considered

(M 1500 ghigh molecurate dependweight fromin detail. InCO2PEG 2that PEG be

In this average m20,000 g mo3000 and PEThe objectCO2PEG 30ence of the

Viscositmeasured wthe torsionlating electThe viscomdensity valwork, atmo8300 were pressure dewere calculchain statisEoS is one othermodyncalculation2000 soluti

In PEG, ation of intrathe terminaminal grouof studies bonds in PE[45,46]. TheCO2 solubil[4,6], whichn-mers bettions with t2000 g mol

results withof higher mmation canEoS [44].

This wocalculate th behavior of CO2PEG solutions with pressure is not stilltood. For the viscosity of CO2PEG solutions, measure-

been reported for molecular weights of 200 g mol1

g mol1 [10,11], 600 g mol1 [10], 6000 g mol1 [8] andl1 [8]. The viscosity of PEG in the presence of CO2ith an increase in CO2 pressure and does not change

essures at higher than 20 MPa. However, PEG viscositynce of CO2 has not been reported for moderate molec-s (600 < M < 6000 g mol1) and the viscosity reduction

obtained with CO2 is of importance in technologicals.y of CO2PEG solutions is needed in many practicals. Shear viscosities of pure PEG and pure PEO have been

molecular weights from 200 g mol1 to 4 106 g mol1in Table 1 [3341]. At the lower molecular weight

mol1), PEG behaves as a Newtonian uid while PEG oflar weight behaves as a non-Newtonian uid. The shearence of viscosity for PEG that has an average molecular

2000 g mol1 to 20,000 g mol1 has not been studied the literature, measurements of CO2PEG 6000 and

0000 solution viscosities have been reported assuminghaves as a Newtonian uid [8].work, the rheological behavior of PEG that has

olecular weights of 3000 g mol1, 8300 g mol1 andl1 is veried. Subsequently, this work focuses on PEGG 8300 among the PEGs of moderate molecular weight.

ives in this work were to measure the viscosity of00 and CO2PEG 8300 solutions and to study the inu-

PEG molecular weight on solution viscosity.ies of CO2PEG 3000 and CO2PEG 8300 solutions wereith a torsional vibrating viscometer. The principle of

al vibrating viscometer is the dampening of an oscil-romechanical resonator immersed in the liquid [42,43].eter gives the viscositydensity product [43], so that aue is required to obtain the solution viscosity. In thisspheric densities of the pure PEG 3000 and pure PEGmeasured with a vibrating tube densimeter and high-nsities of CO2PEG 3000 and CO2PEG 8300 solutionsated using an equation of state based on the perturbed-tical associating uid theory (pc-SAFT EoS). The pc-SAFTf the models that has been widely applied to calculateamic properties of polymer systems [44]. The density

method was evaluated with measured values of PEGon with CO2 [32].lthough polymeric steric hindrances prevent the forma--hydrogen bonds, inter-hydrogen bonds form betweenl hydroxyl groups, and the hydrogen atom in the ter-p and the oxygen atom in the polymer chain. Resultsmade with IR spectroscopy show that the hydrogenG 2000 only form within the terminal hydroxyl groups

hydroxyl end groups of PEG have little inuence on theity in PEG of higher molecular weight (M > 200 g mol1)

is consistent with measured partition coefcients forween vapor and liquid phases [7,47]. For VLE calcula-he SAFT EoS for PEG that has a molecular weight above1, there is no distinct difference between calculation

or without the association term [6]. Therefore, for PEGolecular weight (M 2000 g mol1), hydrogen bond for-

be neglected in the VLE calculations with the pc-SAFT

rk examines models based on free volume theory toe viscosity reductions of PEG in the presence of CO2.

M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373 65

Table 1Available literature for the rheological behavior of molten poly(ethylene glycol) and poly(ethylene oxide).

M range/g mol1 Range Rheological behavior Source

Mw/103 3 1 ad s1

1.0 6.318.6a 0 17.5340a

22.0 292 500 610, 932 11004000

a Value of M

The concepphenomenaume theoryTurnbull eq[51,52]. Thefree volume

Gerharddissolved Cmixture in has not beeapplies theCO2PEG 3compares th

Free volthat is deteoccupied voviscosity [5of CO2 in fr

2. Materia

2.1. Materi

Poly(eth3000 300lar weight oChemical Inular weightIndustries, 0.2 wt% for 20000 as deIn all experLtd.) were uspheric viscunder redu

2.2. Atmosp

2.2.1. ShearStatic an

at atmosphRheoStress ing of 0.10560 mm andspacing of and a cone aand stabilitshear stress

Static sh353.2 K to 38300 and PEthousand s

e saty med

erfored i

from low

gh shparat

(k = 00 anal).

New as aatess obt

[61]tives

+ a0 0 iseters

Viscoosph

ger vvalue.07% ate fred twhighigh tolevel1, Suorrepiric)

=

H isMn/10 /s /r

0.21.5 5300

66 M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373

(f)

(h)

(j)(k)

Fig. 1. Schema ) regu(g) measurem

less than 0.1formed in dlow to high The combinwere estimPEG 8300 (M

Atmosphempirical e

1000o

= vo

Parametersdensity dat

2.4. Viscosi

2.4.1. ViscoViscositi

were measuity sensor cHydramotioenergy lossconnected by a regula(D500, ISCOmeasured wature was mNetsushin) calibrated bwall of the samples wathat could b

cosit000 res fp

(a)

(b)

(c)

(e)

(k)

(d)

tic diagram of the viscosity measurement apparatus: (a) carbon dioxide cylinder; (bent cell; (h) electrical heater; (i) temperature probe; (j) rocking stand; (k) valves.

kg m3 over a 1 min interval. Measurements were per-uplicate and each series of measurements included thetemperature and the high to low temperature segments.

VisPEG 3pressued expanded uncertainties with a level of 0.95 (k = 2)ated to be 1.4 kg m3 for PEG 3000 and 1.6 kg m3 forethods S1 and Table S1, Supplementary material).eric density data were correlated with the following

quation:

= c0 + c1 T (3)

in Eq. (3), c0 and c1, were determined by tting thea.

ty of CO2PEG solutions

sity measurementes of PEG 3000 and PEG 8300 in the presence of CO2red with the apparatus as shown in Fig. 1. The viscos-

onsisted of a torsional vibrating viscometer (XL7-100N,n) that gives the viscositydensity product in terms of

or loss factor [64]. The measurement cell (70 ml) wasto a gas pressure line. Pressure of CO2 was controlledtor for measurements at 5 MPa and by a syringe pump) for measurements at high pressures. Pressure wasith an online pressure gauge (KDM30, Krone). Temper-easured by a platinum resistance thermometer (Pt100,in the wall of the cell. Temperature of the solution wasy measuring the difference between the inside and thecell (Methods S2, Supplementary material). Mixing ofs carried out by gentle and slow rocking of the apparatuse rotated by hand.

at room tem343.2 K to the viscomspheric viscwas purgedwas pressufactor weredetermineda time periosolutions wcell near hosolution. Mthree-day p

The refeset equal toat the referof the Stabiues from thexpanded uto be 4.0% 10 MPa andtary materiwere estimods S1 and

The viscmined fromthe followin

= ()

T(i)

(g)

lator; (c) syringe pump; (d) chiller; (e) pressure sensor; (f) viscometer;

y measurements were made at 353.2 K and 373.2 K forand at 353.2 K for PEG 8300 over the range of CO2rom 0 MPa to 15 MPa. The PEG was loaded into the cellperature and then heated up to temperatures abovemelt the PEG. After the PEG was completely melted,eter was mounted to a ange on the cell, and atmo-osities were measured at given temperatures. The cell

by pressurized CO2 several times, and then the systemrized up to the desired conditions. Values of the loss

recorded continuously and nal reported values were after the change of the loss factor was within 0.001 overd of a few hours. Time for equilibration of the CO2PEGas reduced by slowly rocking the cell and by placing therizontal position to enhance the dissolution CO2 into theeasurements for each sample were carried out within aeriod.rence condition for the viscositydensity product was

353.15 K and 0.1 MPa. The viscositydensity productence condition was determined from measured valuesnger viscometer for PEG 3000 and from measured val-e rheometer for PEG 8300. For PEG 3000, the combinedncertainties with a level of 0.95 (k = 2) were estimatedfor atmospheric conditions, 4.6% for 5 MPa, 4.7% for

4.6% for 15 MPa (Methods S1 and Table S1, Supplemen-al). For PEG 8300, the combined expanded uncertaintiesated to be 10.4% for 5 MPa and 13.7% for 10 MPa (Meth-Table S1, Supplementary material).osity of pure PEG and its solutions with CO2 were deter-

the measured product of viscosity and density usingg equation:

103 (4)

M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373 67

where () represents the viscositydensity product that wasobtained from the measured loss factor of the apparatus, and refers to either the measured density for pure PEG or to the calcu-lated density for CO2PEG solution as described in Section 2.4. ForPEG 3000, tviscosity watmospheri15 MPa (Mecombined e5 MPa and 1

Possiblechecked bygiven temp3000 viscosdays, whichThus, at thefound to ocing at 373.2three-day pindicates thPEG dependthe viscosittainties are caused by t

2.4.2. ViscoCalculat

on the mod

= d0 (c)d

where d0, dtration of pThe value olap as interpbelow 1. Thrange of 3unity for nodened as f

f = vfv0

= v

where v is and the occucan be rewrCO2polymfraction.

The shifat atmosphbe expresse

ap,c = mixopo

=[(1

where wCO2and the subtion and thatmospherito unity for ular weightweight largset equal to

to unity [53,57]. The method described in Section 2.6 was used tocalculate the values of wCO2 and v

opolymer/vmixture.

Gerhardt et al. proposed a free volume fraction for mixtures thatused the occupied specic volume of the mixture (vo,mixture) and the

c volon, thws:

= vvo

re = freeon usach

= i viixtur

ixture

vo

vi ise of c

charined

usin.15 K

fromes of

diff the analyn Eq.CO2 wolatio6].

lcula

bilitted f

CO2 = equs froity d2 sol

nsity

id dbed-coS)

waheri

purews:

(

pc-Sork a

by mospergy sityhe combined expanded uncertainties of the measuredith a level of 0.95 (k = 2) were estimated to be 4.0% forc conditions, 5.0% for 5 MPa and 10 MPa, and 5.6% forthods S1, Supplementary material). For PEG 8300, thexpanded uncertainties were estimated to be 10.6% for3.9% for 10 MPa (Methods S1, Supplementary material).

decomposition of PEG during the measurements was measuring the pure PEG viscosity after heating at aerature for the maximum period of time (3 d). The PEGity decreased by 1.9% after heating at 353.2 K for three

is lower than the uncertainty of the measurements. experimental conditions, negligible decomposition wascur. However, the viscosity of PEG 3000 after heat-

K and that of PEG 8300 after heating at 353.2 K for aeriod decreased by 14.7% and 9.7%, respectively, whichat decomposition can occur during the measurement ofing on the treatment or measurement conditions. Fories of CO2PEG 3000 at 373.2 K, the calculated uncer-probably underestimated due to composition variationshe measurement conditions.

sity calculationion of the viscosity reduction ratio or shift factor is basedied KelleyBueche equation as given by Eq. (5) [53]:

1 exp(

d2f

)(5)

1 and d2 are characteristic parameters, c is the concen-olymer in the mixture and f is the free volume fraction.f d2 refers to the numerical factor of free volume over-reted by Cohen and Turnbull [48,49], which should bee exponent of the polymer concentration (d1) is in the4 for entangled polymer systems and is set equal ton-entangled polymers [57]. The free volume fraction isollows [50]:

v0v0

(6)

the specic volume, and vf and vo are the free volumepied volume, respectively. For the case of vf vo, Eq. (6)itten as f = vf/v. Due to the lack of validation for vf vo iner solutions, this work used Eq. (6) for the free volume

t factor for scaling of the viscosity of the pure polymereric pressure to that of the CO2PEG solution (ap,c) cand with Eq. (5) as follows:

ture(T, p, w)

lymer(T, po)

wCO2 )

(vopolymervmixture

)] exp

(d2,mixturefmixture

d2,polymerfpolymer

)(7)

represents the weight fraction of CO2 in the polymer,scripts mixture and polymer refer to the CO2PEG solu-e pure PEG, respectively. The superscript o refers toc conditions. In this work, the value of d1 was set equalPEG 3000 that is less than its value for the critical molec-

of PEG (3400 g mol1) [65]. For PEG that has a molecularer than the critical molecular weight, the d1 value was

3. The values of d2,mixture and d2,polymer were set equal

speciequatias follo

fmixture

vo,mixtu

Theequati(fi) of e

fmixture

i =w

vm

fi =vm

wherevolum

ThedetermEq. (3)be 353mineddensitidensitywithinIn the 8300 ivo for extrapture [6

2.5. Ca

Solucalcula

100 wThe

weightsolubilthe CO

2.6. De

LiquperturSAFT Edensityatmosption toas follo

= o

Thethis wminedand atthe enuid denume of the mixture (vmixture) [53]. In the Gerhardt et al.e free volume fraction of the mixture was represented

f,mixture

,mixture= vmixture vo,mixture

vo,mixture(8)

wCO2 vo,CO2 + wPEG vo,PEG (9) volume fraction of the mixture for the KelleyBuecheed the volume fraction (i) and the free volume fractioncomponent in the mixture as follows [59]:

CO2 fCO2 + polymer fpolymer (10)

e(11)

vo,i,i

(12)

the specic volume and vo,i is the occupied specicomponent i.acteristic parameter vo for PEG 3000 and PEG 6000 was

by tting viscosity data and calculated densities fromg Eq. (7) when the reference condition was chosen to

and 0.1 MPa. Then, the value of d0 in Eq. (5) was deter- the viscosity at the reference condition. The measured

PEG 8300 were used for those of the PEG 6000, since theerence of PEG 6000 and PEG 8300 can be estimated touncertainty of the present measurements (Section 3.2).sis with the free volume fraction, the vo value for PEG

(12) was set equal to that for PEG 6000. The value ofas set equal to 0.589 cm3 g1 which was obtained byn of the crystalline density to absolute zero tempera-

tion of CO2 solubility in PEG

ies of CO2 in PEG 3000 and PEG 8300 at 353.2 K wererom an empirical equation as follows:

1.602 p 3.236 102 p2+2.387 104 p3 (13)ation was obtained by tting data of PEG molecularm 1500 g mol1 to 8000 g mol1 [4,6,8]. All CO2PEGata could be correlated with Eq. (13) to within 2% ofubility value (Fig. S2, Supplementary material).

calculation of CO2PEG solutions

ensities of CO2PEG solutions were calculated with thehain statistical associating uid equation of state (pc-for non-associating systems [67]. The mixture liquids estimated from the measured density of pure PEG atc pressure (o) and the density ratio of CO2PEG solu-

PEG (/o), which was calculated by the pc-SAFT EoS

o

)(14)

AFT EoS parameters for the pure components used inre given in Table 2. The PEG parameters were deter-tting high-pressure densities of pure PEGs [68], and VLEheric densities of benzenePEG solutions [69] becauseparameter of the EoS tends to be insensitive to the liq-

[44]. In general, pure parameters were simultaneously

68 M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373

Table 2Pure component parameters in the pc-SAFT EoS for poly(ethylene glycol), benzene and carbon dioxide.

Substance m /A /kB/K

Poly(ethylenBenzenec

Carbon diox

a Experimenb Calculatio on anc Values rep

Table 3Values of kij foEoS.

M/g mol1

1500 3000 6000 8300

determinedPure paramselected binchosen as awithout ttFurther inforesults are material (Ta

The binamixtures w

CO2PEG =

CO2PEG =

where kij iparameter were determand PEG 603000 and PEtions are shthe VLE calcinto the vap

2.7. Parame

Adjustabdetermined

f (Y) =n

i=1

(

where Y refand Uc(Y) isn is the numrefer to calc

Correlatand average

Bias = 100

ARD = 100

Measu(ethyles; ol1, es of r bars

(Sup

ults and discussion

mospheric viscosity of PEG

tic and dynamic shear viscosities at 353.2 K for the PEGs ofnt molecular weights are shown in Fig. 2. PEG 3000 and PEGere found to behave as Newtonian uids, while PEG 20000

und to be non-Newtonian. Shear viscosities of PEG 3000 at and 373.2 K were found to be independent of the shear

Fig. S11, Supplementary material). Shear viscosities of PEG decreased at shear rates above 50 s1, which agrees with the

of Trml et al. [38]. Shear viscosities of PEG 20000 couldelated with Eq. (1) to within 0.2% in ARD and less than 0.1%

value with parameters 0 = 27,640 mPa s, a0 = 1.9296 106e glycol) 44.749M 3.0608 234.87 2.4653 3.6478 287.35

idec 2.0729 2.7852 169.21

tal densities of pure PEG taken from Zoller and Walsh [68].ns with the value of kij set equal to zero. Experimental data for the liquid compositiorted by Gross and Sadowski [67].

r poly(ethylene glycol) and carbon dioxide systems for the pc-SAFT

kij ARD wPEG/% Bias wPEG/% Source

0.0191 0.55 0.05 [4]0.0210 0.36

M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373 69

Table 4Atmospheric viscosities and densities of poly(ethylene glycol) 3000 measured with the different viscometers.a

T/K /mPa s /kg m3

Un-dried

Rheometer Torsional vibrating Stabinger

343.2 165.1 353.2 135.4 126.5b 126.5 363.2 104.7 99.55 98.38373.2 84.97 79.37 78.46

a Standard uncertainties are uT = 0.1 K for the rheometer and torsional vibrating viscometer, and 0.02 Kwith a 0.95 level of condence (k = 2) are Uc() = 10.4% for the rheometer, 4.0% for the torsional vibrating vi(Supplementary material).

b Measured value with the Stabinger viscometer.

Fig. 3. Atmospmolecular wei+, Parivalko etlation of Teramuncertainties o

Table 4 at atmosphPEG 3000 mresented by+0.1% with a relative dwork and f2816 g molfrom the repsities of PEGmeasured w

Fig. 4. Relativ3000. Symbolster; down triasymbols, un-dmated combin

iquid ence o

3000heric zero-shear rate viscosities of poly(ethylene glycol) of different

Fig. 5. Lthe pres[32]; ,ghts at 353 K: , This work; , Cruz et al. [72]; , Kukova et al. [8]; al. [36]; , Teramoto et al. [37]; , Trml et al. [38]; line, corre-oto et al. [37]. Error bars represent estimated combined expandedf the zero-shear rate viscosity (Supplementary material).

shows measured viscosities and densities of PEG 3000eric pressure of this work. The viscosities of un-driedeasured with the Stabinger viscometer could be rep-

Eq. (2) within an ARD of 0.3% and bias less thanparameters b0 = 4.0732 and b1 = 3147.1. Fig. 4 showseviation plot for PEG 3000 viscosities measured in thisor literature values [72]. The literature values (Mw =1, wH2O = 0.7 wt%) shown in Fig. 4 were estimatedorted kinematic viscosities [72] and the measured den-

3000 in this work. The viscosities of un-dried PEG 3000ith the different viscometers were in accordance with

e deviation plot for atmospheric viscosities of poly(ethylene glycol): circles, Stabinger viscometer; diamonds, cone and plate rheome-ngles, torsional vibrating viscometer; , reported values [72]; lledried sample; unlled symbols, dried sample. Error bars represent esti-ed expanded uncertainties of the viscosity (Supplementary material).

(14); dash linefor the EoS are

their uncerby about 1ture valuesthose of thimolecular w

3.2. Atmosp

MeasureTable 4. Meof dried PEThis indicatdensities is3000 were dby tting daARD and biues were obc0 = 6.8601 PEG 3000 a18500 [68]increased w

3.3. Density

DensitieSAFT EoS calculation solutions hof VLE dataeters for PDried Un-dried Dried

169.3 1085.6 1084.9127.9 1077.4 1077.099.52 1069.3 1069.079.45 1061.2 1061.1

for the Stabinger viscometer, and combined expanded uncertaintiesscometer and 1.0% for the Stabinger viscometer, and Uc() = 1.4 kg m3

densities of (a) poly(ethylene glycol) 2000, (b) 3000 and (c) 8300 inf carbon dioxide versus pressure. Symbols: , 2000 g mol1 at 374.3 K

g mol1 at 353.2 K; , 8300 g mol1 at 353.2 K. Lines: solid lines, Eq.s, the pc-SAFT EoS. Pure component parameters and the values of kij

given in Tables 2 and 3, respectively.tainties. The viscosity of un-dried PEG 3000 was lower% than that of dried PEG (wH2O = 0.2 wt%). The litera-

of the PEG viscosities [72] were about 12% larger thans work, which might be attributed to differences in theeight of PEG.

heric density of PEG

d atmospheric densities of PEG 3000 are shown inasured values of un-dried PEG 3000 agreed with thoseG 3000 within the uncertainty of the measurements.es the effect of 0.2 wt% water content in PEG 3000 on

below 1.4 kg m3. The parameters in Eq. (3) for PEGetermined as c0 = 6.8202 101 and c1 = 6.9762 104ta of both samples, using which the obtained values ofas were below 0.1%. For PEG 8300, ARD and bias val-tained as below 0.1% using the parameters in Eq. (3) as

101 and c1 = 6.8346 104. The measured values ofnd PEG 8300 were between values of PEG 1470 and PEG

(Fig. S12, Supplementary material), and the densitiesith the molecular weight of PEG.

of CO2PEG solutions

s of CO2PEG solutions were calculated from the pc-as shown in Fig. 5 along with literature data. Themethod for liquid mixture densities for CO2PEG 2000as been evaluated by Funami et al. [32]. Due to the lack

for PEG 2000CO2 system, binary interaction param-EG 1500CO2 were used in the density calculations.

70 M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373

Table 5Viscositydensity product, density and viscosity for poly(ethylene glycol) solutionssaturated with carbon dioxide at 353.2 K and 373.2 K.a

T/K p/MPa /kg2 m4 s1 /kg m3 b /mPa s

M = 3000 g m353.2 353.2 353.2 373.2

M = 8300 g m353.2 353.2

a Standard uuncertainties wand Uc() = 5.0for PEG 8300 (

b Calculated

Atmospherunderestimsity calculapressure waculated by tsolution de1.0% (Fig. S1tainty of th

Calculatwith pressupressures, tThis trend o400 solutionCO2 solubil

The denthe weight PEG (VPEG) follows (Me

CO2+PEGPEG

=

where V/Vin solution expansion otively largethe solution

The dencalculating mentary mCO2PEG 1up to 30 Mdecreased aswelling raPasquali et reported diincrease in Cing pressurincreasing pswelling rather studiesare needed

3.4. Viscosi

Viscositithe measursity with Edecreased w

iscosi of difrk: l1 at

red li equatd valu0 g mostimat

enta

O2 the at o

cositio ofempcosition rs (Men 34term. 2 Ker Pns arratuhe efeatmion r

caneights from 400 g mol1 to 8300 g mol1 as a function of the

fraction of CO2 in the PEG solution as follows:

exp5.7777 wCO2 1.7214 101 (wCO2 )

2

+6.3273 103 (wCO2 )3 (21)

(21) can represent the viscosity reduction ratio of CO2PEGol1

5.0 87.1395 1073.4 81.1810.0 61.4204 1070.0 57.4015.0 50.3371 1068.8 47.105.0 61.7483 1057.6 58.39

ol1

5.0 1078.72 1074.3 100410.0 781.124 1070.8 729.5

ncertainties are uT = 0.1 K and up = 0.1 MPa, and combined expandedith a 0.95 level of condence (k = 2) are Uc() = 2.0%, Uc() = 4.64.7%5.6% for PEG 3000, and Uc() = 10.413.7% and Uc() = 10.613.9%Supplementary material).

values with Eq. (14).

ic densities calculated directly by the pc-SAFT EoS wereated by 1% for both PEGs. Therefore, in the mixture den-tions used in this work, a density change ratio with CO2s adopted as a correction for atmospheric densities cal-he pc-SAFT EoS (Eq. (14)). The calculated CO2PEG 2000nsities agreed with the experimental values to within3, Supplementary material), and so the standard uncer-e solution density was estimated to be 1.0%.ed liquid densities for CO2PEG solutions decreasedre for values of up to about 1020 MPa. At higherhe calculated liquid densities increased with pressure.f density with pressure has been observed for CO2PEGs [11], and is probably due to the interplay between the

ity in PEG and the swelling of the PEG caused by CO2.sity change ratio with CO2 pressure was described byfraction of CO2 in the PEG (wCO2 ), the volume of pureand the volume change in the presence of CO2 (V) asthods S4, Supplementary material):

1(1 wCO2 )(1 + V/VPEG)

(20)

PEG is denoted as the swelling ratio (Sw). The decreasedensity at low pressure can be attributed to the volumef the PEG solution with dissolved CO2. Due to a rela-

amount of dissolved CO2 in the PEG at high pressure, density increased as pressure was increased.sity behavior at high pressure was investigated bythe swelling ratio with Eq. (20) (Fig. S14, Supple-aterial). In this work, the calculated swelling ratio for500 solutions increased monotonically with pressurePa, however, the rate of increase of the swelling ratiot pressures above 10 MPa. The behavior of calculatedtios at low pressure is in accordance with the study ofal. [9,15]. At high pressure (p > 10 MPa), Pasquali et al.

Fig. 6. VsolutionThis wo400 g moEq. (21);line, thethe tteand 830resent e(Supplem

other Ction inwith th

Visthe ratgiven tthe visreductweightbetwewas deat 353for othsolutiothe litesince tture trreduct353.2 Kular wweight

ap,c =

Eq.

fferent trends for the PEG 1500 swelling ratio with anO2 pressure: (i) monotonic increase of Sw with increas-

e up to 20 MPa [15] and (ii) small change of Sw withressure up to 25 MPa [9]. In this work, the calculated

tios at high pressure depended on pressure and so fur- on volumetric-related properties of CO2PEG solutions

in the future.

ty of CO2PEG solutions

es of CO2PEG solutions are given in Table 5 includinged viscositydensity product and the calculated den-q. (14). The measured viscosity of CO2PEG solutionsith an increase in CO2 pressure in a similar trend as

solutions tocosity ratioindependen

In Fig. 6tions at 35and the KelResults for Pthe Supplemof the molaorder of PEestimated fmated the The overesory might bty reduction ratio for dissolved carbon dioxide in poly(ethylene glycol)ferent molecular weight at temperatures between 347.8 and 353.2 K., 3000 g mol1 at 353.2 K; , 8300 g mol1 at 353.2 K. Literature: +,

347.8 K [11]; , 6000 g mol1 at 353.2 K [8]. Lines: black solid line,ne, Gerhardt et al. equation; blue line, KelleyBueche equation; solidion with the literature value of vo,CO2 ; dashed line, the equation withe of vo,CO2 to CO2PEG solution viscosities at 353.2 K (M = 3000, 6000l1). Parameters in the equations are given in Table 6. Error bars rep-ed combined expanded uncertainties of the viscosity reduction ratiory material).

PEG solutions [8,11]. At 15 MPa and 353.2 K, the reduc-CO2PEG solution viscosity by CO2 was 62% comparedf the pure PEG.y reduction ratio in the presence of CO2 is dened as

the CO2PEG solution viscosity to that of pure PEG at aerature. When there is no CO2 dissolution into the PEG,y reduction ratio is equal to unity. Fig. 6 shows viscosityatios of CO2PEG solutions for different PEG molecular

= 400, 3000, 6000 and 8300 g mol1) at temperatures7.8 K and 353.2 K. In Fig. 6, the CO2 solubility in the PEGined by calculation with the pc-SAFT EoS for PEG 3000

and for PEG 8300 at 353.2 K, and from the literatureEGs [5,8]. Although the viscosities of CO2PEG 20000e available at temperatures from 353. 2 K to 393.2 K inre [8], the reported values were excluded in the gure,fect of shear rate on PEG 20000 viscosity and tempera-ent of the samples are unknown (Fig. 3). The viscosityatio for dissolved CO2 in the PEG between 347.8 K and

be reduced to a simple curve for PEGs of different molec- within 0.08 of the ap,c value. The reduction in vis- caused by CO2 dissolution into PEG was found to bet of the PEG molecular weight., the viscosity reduction ratio for CO2PEG 3000 solu-3.2 K was predicted with the Gerhardt et al. equationleyBueche equation from parameters given in Table 6.EG 6000 and PEG 8300 solutions with CO2 are shown inentary material (Figs. S15 and S16). Calculated values

r occupied volume (vo M/cm3 mol1) was in decreasingG 6000 > PEG 3000 > CO2, which agrees with the orderrom the chemical structure. Both equations overesti-viscosity reduction by 40% for the CO2PEG solutions.timation of the viscosity reduction values by the the-e caused by large values of the calculated free volume

M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373 71

Table 6Characteristic parameters for free volume viscosity models for poly(ethylene glycol) 3000, 6000 and 8300, and carbon dioxide.

Substance d0/mPa s cmd1 gd1 vo/cm3 g1 ARD/% Bias/%

Poly(ethylene glycol) 3000 0.5595 0.7839 0.7 0.2Poly(ethylen 7Poly(ethylen 7a

Carbon diox

3 4

a Value set eb Values not

fraction of twas made w(Section 2.4ity data of C353.2 K witbe correlate6000 and 1Similar resuThe use of reduction rSupplemenconcluded tculation shocalculation effect on th

4. Conclus

New vis3000 g mol

373.2 K oveShear viscobehave as non-Newtovided by CO3000, 6000cosity redua given temcosity reduPEG solutioto 8300 g mhardt et al. oratio of thedata to withis used.

Acknowled

The authof the Minisof this work

Appendix A

A.1. Pure pa

Pure parto the methit was assummolecular wof the molecimizing the

erg

, ,

PEG liquuid nzensolveter wwas phasentr

Xj /= i

X refEGs ampolue

Initiues o

effeas inal vaB = 2

ork w 44.7culate glycol) 6000 5.8594 0.771e glycol) 8300 1.1558 101 0.771ide n.d.b 0.589

0.6870.691

qual to PEG 6000. determined in this work.

he CO2PEG solutions. Prediction of viscosity reductionith value of vo,CO2 determined from the crystal density). The vo,CO2 was also determined by tting the viscos-O2PEG solutions (M = 3000, 6000 and 8300 g mol1) ath each equation (Table 6). The viscosity reduction couldd to within an ARD of 6.4% for PEG 3000, 9.2% for PEG4.2% for PEG 8300 using the Gerhardt et al. equation.lts were obtained with the KelleyBueche equation.tted vo,CO2 improved the prediction of the viscosityatio for the CO2PEG solutions (Figs. 6, S15 and S16,tary material). From the results in this study, it can behat the value of vo,CO2 for the viscosity reduction cal-uld be determined by tting viscosity data, while the

method for the free volume fraction seems to have littlee viscosity reduction ratio.

ions

cosity data for CO2PEG solutions are reported for1 and 8300 g mol1 of molecular weight at 353.2 K andr the range of CO2 pressures from 5 MPa to 15 MPa.sity measurements show that PEG 3000 and PEG 8300Newtonian uids whereas PEG 20000 behaves as anian uid. Comparing the viscosity reduction ratio pro-2 among PEGs of different molecular weights (M = 400,

and 8300 g mol1), it can be concluded that the vis-ction ratio is independent of PEG molecular weight atperature. A simple relationship can correlate the vis-ction ratio in terms of the weight fraction of CO2 inns for PEG molecular weight being from 400 g mol1

ol1 within 0.08 in absolute units. The equation of Ger-r KelleyBueche overestimates the viscosity reduction

CO2PEG solutions by up to 40%, but can correlate thein 14% when a tted value of the CO2 occupied volume

gement

ors would like to acknowledge partial nancial supporttry of Education, Science, Sports and Culture for support.

.

Levenb

f (m/M

wherein thethe liqfor benot disparamphase liquid using c

(YXi

)

wherepure PPEG coThe va1010.the val

Theeters was initiand /kthis w(m/M =ues calrameters of poly(ethylene glycol) for the pc-SAFT EoS

ameters (m, and ) of PEG were determined accordingod proposed by Gross and Sadowski [44]. In this work,ed that only segment number (m) is dependent on theeight and that it can be represented as a linear functionular weight. Pure parameters were determined by min-

following objective function (f(m/M, , /kB)) using the

to within 0the pure pa

Vericatby calculatpc = 4.6751 pc = 8.0639 pc = 5.53721et al. [73]. Tare denoted1.2 0.5

([66], for equations of Gerhardt et al. andKelleyBueche)(This work, for Gerhardt et al. equation)(This work, for KelleyBueche equation)

Marquardt method with numerical derivatives [62]:

/kB) =418i=1

(PEG,cal,i PEG,exp,i

Uc(PEG,exp,i)

)

+9

j=1

(wLPEG,cal,j wLPEG,exp,j

Uc(wLPEG,exp,i)

)

+8

k=1

(LC6H6+PEG,cal,k

LC6H6+PEG,exp,k

Uc(LC6H6+PEG,exp,k)

)(A1)

is the density of pure PEG, wLPEG is the PEG compositionid phase of benzenePEG mixture and LC6H6+PEG isdensity of benzenePEG mixture. In the calculationsePEG mixtures, it was assumed that the PEG doese into the vapor phase and that the binary interaction

as set equal to unity (kij = 0). The composition in liquiddetermined by the isofugacity of benzene in vapor andes. The derivatives of the parameters were obtained byal differences:

=YXi(1+),Xj /= i

YXi(1+),Xj /= i

2Xi(A2)

ers to the pure parameters, Y represents the density ofnd its mixture with benzene in the liquid phase, or thesition in the liquid phase in the benzenePEG mixture.of that represents the difference was set equal toal values of the pure parameters were estimated fromf diethyl ether reported by Gross and Sadowski [67].

ct of initial values on determination for the pure param-vestigated by using values reported by Martn et al. [28]lues. The obtained parameters (m/M = 44.927, = 3.057134.57) were slightly different from those values used inhen the initial values were set equal to diethyl ether49, = 3.0608 and /kB = 234.87). However, the ARD val-ed with these different parameters were in accordance

.02%. Thus, there is little inuence on initial values forrameters determined in this work.ion of the calculation with the pc-SAFT EoS was madeion for the critical point of methane (Tc = 191.4006 K,MPa and c = 0.14285), carbon dioxide (Tc = 310.2768 K,MPa and c = 0.13186) and benzene (Tc = 572.3948 K,

MPa and c = 0.13039) which were reported by Privathe critical temperature, pressure and reduced density

as Tc, pc and c, respectively.

72 M. Iguchi et al. / J. of Supercritical Fluids 97 (2015) 6373

Appendix B. Supplementary data

Supplementary material related to this article can be found,in the online version, at http://dx.doi.org/10.1016/j.supu.2014.10.01

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Viscosity and density of poly(ethylene glycol) and its solution with carbon dioxide at 353.2K and 373.2K at pressures up t...1 Introduction2 Materials and methods2.1 Materials2.2 Atmospheric viscosity of pure PEG2.2.1 Shear viscosity measurement and correlation2.2.2 Viscosity measurement and correlation

2.3 Atmospheric pure PEG density measurement and correlation2.4 Viscosity of CO2PEG solutions2.4.1 Viscosity measurement2.4.2 Viscosity calculation

2.5 Calculation of CO2 solubility in PEG2.6 Density calculation of CO2PEG solutions2.7 Parameter determination and evaluation

3 Results and discussion3.1 Atmospheric viscosity of PEG3.2 Atmospheric density of PEG3.3 Density of CO2PEG solutions3.4 Viscosity of CO2PEG solutions

4 ConclusionsAcknowledgementA.1 Pure parameters of poly(ethylene glycol) for the pc-SAFT EoSAppendix B Supplementary data

ReferencesReferences