Polymer Solutions: Physical Properties and their Relations I (Thermodynamic Properties: pVT data and miscellaneous properties of polymer solutions)

1686 Pages·2010·10.57 MB·English

by  Ch. Wohlfarth (auth.)

Landolt-Börnstein
Numerical Data and Functional Relationships in Science and Technology
New Series / Editor in Chief: W. Martienssen
Group VIII: Advanced Materials and Technologies
Volume 6
Polymers
Subvolume D
Polymer Solutions
Part 2
Physical Properties and their Relations I (Thermodynamic Properties:
PVT-Data and Miscellaneous Properties of Polymer Solutions)
Editors: M.D. Lechner, K.F. Arndt
Author: Ch. Wohlfarth
ISSN 1619-4802(Advanced Materialsand Technologies)
ISBN 978-3-642-02889-2 SpringerBerlin HeidelbergNew York
eISBN 978-3-642-02890-8
LibraryofCongressCataloginginPublicationData
ZahlenwerteundFunktionenausNaturwissenschaftenundTechnik,NeueSerie
EditorinChief:W.Martienssen
Vol.VIII/6D2:Editors:M.D.Lechner,K.F.Arndt
Atheadoftitle:Landolt-Börnstein.Addedt.p.:Numericaldataandfunctionalrelationshipsinscienceandtechnology.
TableschieflyinEnglish.
IntendedtosupersedethePhysikalisch-chemischeTabellenbyH.LandoltandR.Börnsteinofwhichthe6thed.beganpublicationin1950undertitle:
ZahlenwerteundFunktionenausPhysik,Chemie,Astronomie,GeophysikundTechnik.
Vols.publishedafterv.1ofgroupIhaveimprint:Berlin,NewYork,Springer-Verlag
Includesbibliographies.
1.Physics–Tables.2.Chemistry–Tables.3.Engineering–Tables.
I.Börnstein,R.(Richard),1852-1913.II.Landolt,H.(Hans),1831-1910.
III.Physikalisch-chemischeTabellen.IV.Title:Numericaldataandfunctionalrelationshipsinscienceandtechnology.
QC61.23502'.1262-53136
Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,
reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmor inotherways,andstorageindatabanks.Duplicationofthis
publicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermis-
sionforusemustalwaysbeobtainedfromSpringer-Verlag.ViolationsareliableforprosecutionactunderGermanCopyrightLaw.
SpringerisapartofSpringerScience+BusinessMedia
springeronline.com
©Springer-VerlagBerlinHeidelberg2010
PrintedinGermany
Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,that
suchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
ProductLiability:Thedataandotherinformationinthishandbookhavebeencarefullyextractedandevaluatedbyexpertsfromtheoriginalliterature.
Furthermore,theyhavebeencheckedforcorrectnessbyauthorsandtheeditorialstaffbeforeprinting.Nevertheless,thepublishercangivenoguarantee
forthecorrectnessofthedataandinformationprovided.Inanyindividualcaseofapplication,therespectiveusermustcheckthecorrectnessbyconsulting
otherrelevantsourcesofinformation.
Coverlayout:ErichKirchner,Heidelberg
Typesetting:AuthorsandRedaktionLandolt-Börnstein,Heidelberg
SPIN:12253043 63/3020-543210–Printedonacid-freepaper
Preface of the editors
Polymersbelongtoanessentialmaterialgroupwithmanyapplicationsnotonlyforpolymermanufacturersbutalsoin
physics,chemistry,medicineandengineeringtechniques.Thepresentedvolume“Polymers”withseveralsubvolumes
connectsacompletedatacollectionwithshortbutprecisedescriptionsofthedifferentquantitiesandtheirsignificances.
Theexperimentaldeterminationofthephysicalquantitiesisgivenaswellastheinfluencetootherphysicalquantities.
Thisvolumecouldhelptochoosethebestmaterialforallkindsofapplicationsalsoforthoseoneswhicharenotmen-
tionedinpolymermaterialbooks.Landolt-Börnstein“Polymers”isfocusedonpolymersinitsdifferentformsofrepre-
sentationsandphenomena,e.g.solids,melts,solutions.Thedifferentchaptersofthisvolumearewrittenbyexcellent
scientists.Thedataareevaluatedandweighted.
Thetargetgroupandpotentialusersarephysicists,chemists,materialscientistsandengineersinuniversitiesandin
theindustry.Thebookisintendedforthosewhoworkonpracticalproblemsinthepolymerfieldandwhoareinthe
needofnumericaldataonpolymerproperties.
Thevolumeissubdividedinto
Nomenclature,Definition,Structure,andArchitectureofPolymers
PolymerSolidsandPolymerMelts
PolymerSolutions
ApplicationofPolymersandincludesThermodynamicProperties,Diffusion,Permeation,GasSolubility,Miscibility,
CrystallographicStructures,MechanicalProperties,ElectromagneticProperties,OpticalProperties,SpectroscopicProp-
erties,andTransportProperties.
In2004theeditorinchief,W.Martienssen,introducedanewgroupVIII“AdvancedMaterialsandTechnologiesand
suggestedavolume“Polymers”.ThepresentedvolumeVIII/6D2“ThermodynamicProperties–PhaseEquilibria”is
thesecondofapproximately7subvolumes.TheeditorswishtoexpresshisthankstotheauthorCh.Wohlfarthforthis
excellent volume. The encouraging and never ending support of the former editor in chief W. Martienssen and of
R.Poerschke,K.SoraandR.MünzfromSpringer-Verlagiskindlyacknowledged.Thepublisherandtheeditorsare
confidentthatthisvolumewillincreasetheuseofthe"Landolt-Börnstein".
Thecompletevolume,includinglinkstotheoriginalcitations,isalsoavailableonline:youcannavigatethroughthe
electronicversionofthisvolumestartingfromtheSpringerMaterials–TheLandolt-BörnsteinDatabasewebsitewww.
springermaterials.com;simplyselectthevolumefromtheelectronic“Bookshelf”andjumpdirectlyintothePDFdata
fileofinterestorsearchforentriesbythepowerfulsearchengine.
Wewouldbegratefuliftheuserssendusanyerrors,misprints,omissionsandotherflaw.Anysuggestioniswelcome!
Osnabrueck,Dresden,December2009 TheEditors
Editors
Lechner,M.D.
InstitutfürChemie
UniversitätOsnabrück
Barbarastr.7
D-49069Osnabrück,Germany
e-mail:[email protected]
Arndt,K.F.
InstitutfürPhysikalischeChemieundElektrochemie
TechnischeUniversitätDresden
Bergstr.66B
D-01069Dresden,Germany
e-mail:[email protected]
Author
Wohlfarth,Ch.
InstituteofPhysicalChemistry
MartinLutherUniversity
Von-Danckelmann-Platz4
D-06120Halle(Saale),Germany
e-mail:[email protected]
Landolt-Börnstein Editorial Office
SpringerVerlagGmbH
Tiergartenstr.17,D-69221Heidelberg,Germany
e-mail:[email protected]
Internet
www.springermaterials.com
Contents
VIII/6 Polymers
SubvolumeD:PolymerSolutions
Part2:PhysicalPropertiesandtheirRelationsI(ThermodynamicProperties:PVT-DataandMiscellaneousPropertiesof
PolymerSolutions)
1. Introduction................................................................ 1
1.1. SelectionofData................................................................ 1
1.2. MeasurementMethods,PolymerCharacterization,Compositions.............................. 1
1.3. ArrangementofData ............................................................ 12
1.4. SubstancesandNomenclature...................................................... 12
1.5. Referencesfor1................................................................ 12
2. PVT-DataandVolumeChangesofPolymerSolutions................................... 14
2.1. PVT-Data..................................................................... 14
2.2. DensitiesofMixturesandExcessVolumes ............................................ 30
2.3. PartialSpecificVolumesofPolymers ............................................... 118
2.4. Referencesfor2............................................................... 148
3. MiscellaneousThermodynamicProperties ..........................................157
3.1. SecondVirialCoefficients........................................................ 157
3.2. EnthalpiesofMixingandDilution.................................................. 399
3.3. SolubilityParameters ........................................................... 480
3.4. Referencesfor3............................................................... 496
4. PolymerList................................................................ 5
Introduction 1
Introduction
Data extract from Landolt-Börnstein VIII/6D2: Polymers, Polymer
Solutions, Physical Properties and their Relations I (Thermodynamic
Properties: PVT-data and miscellaneous properties of polymer
solutions)
1 Selection of Data
PVT-data, densities, excess volumes, second virial coefficients, enthalpies of mixing and solubility
parameters of polymer solutions are necessary quantities for understanding the physical behavior of
polymer solutions, for studying intermolecular interactions, and for gaining insights into the molecular
natureofmixtures.Theyareimportantcomplementstophaseequilibriumdataandtogetherbuildthebasis
foranydevelopmentsoftheoreticalthermodynamicmodels.However,thedatabaseforpolymersolutionsis
still modest in comparison with the enormous amount of data for low-molecular mixtures. Basic informa-
tion on thermodynamic properties of polymers and polymer solutions can be found in the Polymer
Handbook [1999BRA1]. Especially, polymer partial specific volumes, second virial coefficients, and
polymersolubilityparametersfromtheliteratureupto1996aresummarizedtosomeextendinthisPolymer
Handbook. Additionally, there is a chapter on properties of polymers and polymer solutions in the CRC
Handbook of Chemistry and Physics, [2007LID1]. Enthalpy data of polymer solutions were especially
collected in [2006WOH1]. PVT-data of polymer solutions can also be found in [2005WOH1]. At least,
polymersolution data are availablefrom the DortmundDataBank[2006DDB1].
It is the aim of this book to provide an overview for the most important new data for densities, excess
volumes, second virial coefficients, enthalpies of mixing and solubility parameters of polymers of binary
polymersolutions.However,nodataarecollectedherefornon-equilibriumstatesbelowtheglasstransition
temperature.Nodigitizeddatafromgraphsinpapershavebeenincludedinthisdatacollection(but,anum-
berofauthorsprovidedtheirexperimental results what isgratefully acknowledged). No data are collected
forsolutionscontainingtwoormorepolymersortwoormoresolvents,andnosolutionsincludingsurfac-
tants,salts,polyelectrolytes,ordendrimersareincludedintothisbook.Atleast,olderdataoflessaccuracy
were omitted.
The finaldate for including data into this volumewas December, 31, 2008.
1.1 Measurement Methods, Polymer Characterization, Compositions
Thisvolumecontainsdataofbinarypolymersolutionsasafunctionoftemperature,pressure,andcomposi-
tion. In the tables, the subscript 1 always denotes the polymer (because, the data tables are sorted
alphabetically with respect to the polymer as first component of the solution) and subscript 2 denotes the
solvent.
pVT/density measurement for polymer solutions
TherearetwowidelypracticedmethodsforthepVT-measurementofpolymersolutions:Piston-dietechni-
que or confining fluid technique. Both were described in detail by Zoller [1995ZOL1]. In the piston-die
technique, the material is confined in a rigid die or cylinder, which it has to fill completely. A pressure is
appliedtothesampleasaloadonapiston,andthemovementofthepistonwithpressureandtemperature
changes is used to calculate the specific volume of the sample. There are commercial devices as well as
laboratory-builtmachineswhichhavebeenusedintheliterature.Intheconfiningfluidtechnique,themate-
rialissurroundedatalltimesbyaconfining(inert)fluid,oftenmercury,andthecombinedvolumechanges
of sample and fluid are measured by a suitable technique as a function of temperature and pressure. The
volumechangeofthesampleisdeterminedbysubtractingthevolumechangeoftheconfiningfluid.Precise
Landolt-Börnstein DOI:10.1007/978-3-642-02890-8_1
NewSeriesVIII/6D2 #Springer-VerlagBerlinHeidelberg2010
2 Introduction
knowledge of the pVT-properties of the confining fluid is additionally required. For both techniques, the
absolute specific volume of the sample must be known at a single condition of pressure and temperature.
Measurement of densities for polymer solutions is usually made today by U-tube vibrating densimeters.
Such instruments are commercially available.
Excess volumes attemperature Tand pressure p aredetermined by:
(cid:1) (cid:3)
VEspec ¼ Vspec(cid:2) w1V01;spec þ w2V02;spec ð1Þ
or
VE ¼ðx1M1 þ x2M2Þ=(cid:2)(cid:2)ðx1M1=(cid:2)1 þ x2M2=(cid:2)2Þ ð2Þ
where:
M , M molarmass ofpolymeror solvent
1 2
V specific volume ofthe polymer solution
spec
VE, VE molar orspecific excess volume
spec
V , V specific volume ofpurepolymer(1) and puresolvent(2)
01, spec 02, spec
w and w mass fraction of polymer(1) andsolvent (2) (definition seebelow)
1 2
x and x mole fraction ofpolymer (1) and solvent (2) (definition see below)
1 2
ρ densityof thepolymersolution
ρ ,ρ densityof purepolymer(1) orpure solvent(2)
1 2
The second term inEqs.(1) and (2)correspondsto theideal volume,Vid, ofthe polymer solution.
Partialspecific volumes ofpolymers
The totalspecificvolume ofthe polymer solution,V , can bewritten as
spec
Vspec ¼ w1V1;spec þ w2V2;spec ð3Þ
The partial specific volumesof polymer (1) and solvent(2), V , V , arecalculated by
1, spec 2, spec
(cid:4) (cid:5)
Vi;spec ¼ @m@Vmspec ði¼1;2Þ ð4Þ
i p;T;mj6¼i
where:
m totalmass of thepolymersolution
m ,m mass of polymer (1) or solvent (2)
1 2
Inthecaseofthebinarypolymersolution,thepartialspecificvolumeofthepolymercanalsobecalculated
using the tangentrule from Gibbs-Duhem equation:
(cid:4) (cid:5) (cid:4) (cid:5)
V1;spec ¼Vspec(cid:2)w2 @@Vwsp2ec p;T¼Vspecþð1(cid:2)w1Þ @@Vwsp1ec p;T ð5Þ
Forpracticalreasons,oftentheso-calledapparentpartialspecificvolumeofthepolymer,V * ,isapplied.
1, spec
Eq. (3) isthen written as
Vspec ¼w1V1(cid:3);spec þ w2V02;spec ð6Þ
Thisapparentpartialspecificvolumenowcontainstheeffectsofnonidealmixingofboththepolymerand
thesolvent.Substitutingthespecificvolumesofpolymersolutionandsolventbyexperimentallymeasured
densities, it isreadilyfound that
V(cid:3) ¼(cid:2)2(cid:2)w2(cid:2) ð7Þ
1;spec w1(cid:2)2(cid:2)
The relation between apparent and exact partial specific volume is found from Eq. (5) when Eq. (6) is
appliedfor thetotalspecificvolume.
(cid:4) (cid:5) (cid:4) (cid:5)
@V(cid:3) @V(cid:3)
V1;spec ¼V1(cid:3);spec(cid:2)w1w2 @1w;s2pec p;T¼V1(cid:3);specþw1w2 @1w;s1pec p;T ð8Þ
DOI:10.1007/978-3-642-02890-8_1 Landolt-Börnstein
#Springer-VerlagBerlinHeidelberg2010 NewSeriesVIII/6D2
Introduction 3
Inpractice,however,thedifferenceisverysmallandcanbeneglectedifthepolymerconcentrationiskept
low (w < 0.01). Therefore, most values reported in the literature are V * -values, since extrapolation
1 1, spec
accordingto Eq. (8) isusually omitted.
Sometimes, theexcess quantity, V E= V – V , isgiven in theliterature.
1 1 01
Determinationofsecondvirialcoefficients,A
2
Theosmoticvirialcoefficientsaredefinedviatheconcentrationdependenceoftheosmoticpressure,π,ofa
polymersolution, e.g., [1974TOM1]:
(cid:6) (cid:7)
p 1
¼RT þA2c1þA3c21þ... ð9Þ
c1 Mn
where:
A , A second,thirdosmotic virial coefficient
2 3
c (mass/volume) concentration ofpolymer (1)
1
M number-averagemolarmass ofthe polymer
n
R gas constant
T (measuring)temperature
The vapor pressure depression of the solvent in a binary polymer solution Δp = p s - p , is expressed at
2 2 2
temperature Tas:
(cid:6) (cid:7)
(cid:2)p2 ¼Vm2c1 1 þA2c1þA3c21þ... ð10Þ
p2 Mn
where:
p partial vapor pressure ofthe solvent(2)
2
p s saturation vapor pressure ofthe pure liquid solvent (2)
2
V molarvolumeof thepureliquidsolvent(2)
m2
The freezing point depression,Δ T , isgiven by:
SL 2
(cid:6) (cid:7)
1
(cid:2)SLT2 ¼ESLc1 þA2c1þA3c21þ... ð11Þ
Mn
The boilingpoint increase, Δ T , isgiven by:
LV 2
(cid:6) (cid:7)
1
(cid:2)LVT2 ¼ELVc1 þA2c1þA3c21þ... ð12Þ
Mn
where:
E ebullioscopicconstantof thesolvent
LV
E cryoscopic constantof thesolvent
SL
Δ T freezing point temperature differencebetweenpure solventand solution
SL 2
Δ T boiling point temperaturedifference between solution andpure solvent
LV 2
Scattering methods enable the determination of A viathe common relation:
2
Kc1RðqÞ¼1MwPzðqÞþ2A2QðqÞc1þ... ð13Þ
where:
K a constant that summarizesthe optical parameters ofa scattering experiment
M mass-average relative molarmass ofthe polymer
w
P(q) z-average ofthe scatteringfunction
z
q scattering vector q¼4(cid:3)(cid:4)sin(cid:5)
2
Q(q) function for the q-dependence ofA
2
R(q) excess intensity of thescattered beam atthe value q
λ wavelength
θ scattering angle
Landolt-Börnstein DOI:10.1007/978-3-642-02890-8_1
NewSeriesVIII/6D2 #Springer-VerlagBerlinHeidelberg2010
4 Introduction
Dependingonthechosenexperiment(light,X-rayorneutronscattering),theconstant,K,istobecalculated
from different relations. For experimental and theoretical details please see the corresponding textbooks
[1972HUG1,1982GLA1, 1986HIG1, 1987KRA1, and 1991CHU1].
Thermodynamic data from the ultracentrifuge experiment can be obtained either from the sedimentation
velocity (sedimentation coefficient) or from the sedimentation-diffusion equilibrium since the centrifugal
forces arebalancedbytheactivitygradient.The determinationofsedimentation anddiffusioncoefficients
yields the virial coefficients by:
(cid:4) (cid:5) (cid:4) (cid:5)
D (cid:1) (cid:3) 1
1(cid:2)V1;spec(cid:2)2 ¼RT þ2A2c1þ3A3c21þ... ð14Þ
s M1
Sedimentation-diffusion equilibrium inan ultracentrifuge also gives a virial series:
(cid:4) (cid:5) (cid:4) (cid:5)
!2hD(cid:1)1(cid:2)V1;spec(cid:2)2(cid:3) @@lnhDc1 ¼RT M11þ2A2c1þ3A3c21þ... ð15Þ
where:
D diffusion coefficient
h distance from the center of rotation
D
s sedimentation coefficient
ω angular velocity
Bothequationsarevalidformonodispersepolymersonly.Forallpolydispersepolymers,differentaverages
wereobtainedforthesedimentationandthediffusioncoefficientswhichdependontheappliedmeasuring
modes and the subsequent calculations. The averages of M correspond with averages of D and s and are
1
mixed ones that have to be transformed into the desired common averages. For details, please see the
reviews [1975FUJ1, 1991MUN1, and 1992HAR1].
Inthediluteconcentrationregion,thevirialequationisusuallytruncatedafterthesecondvirialcoefficient
which leads to a linear relationship. A linearized relation over a wider concentration range can be con-
structed if the Stockmayer-Casassa relation between A and A isapplied:
2 3
(cid:4) (cid:5)
2
A3Mn ¼ A22Mn ð16Þ
Thesecondvirialcoefficientdependsonmolarmass.Forflexible,nonassociatingpolymers,asimplescal-
ingrelationcan be applied:
A2 ¼(cid:6)Mw(cid:2)(cid:7) ð17Þ
The constants α and βhave tobe fitted toexperimentaldata, e.g.[1994FET1].
Experiments using polydisperse polymers characterized by molar mass distribution functions (what is the
common situation in older literature) lead to A -values depending on the experimental method applied.
2
EspeciallyA -valuesfromosmometryandlightscatteringcandiffer considerablysincetheyrepresentdif-
2
ferentaverageswithrespecttothemolarmassdistributionfunction.Averagesofthesecondvirialcoefficient
obtained from measurements based on colligative properties, Eqs. (9–12), are double mass averages
whereasclassicallightscatteringmeasurementsgivedoublez-averagesofA ,fordetailssee[1971YAM1].
2
Z1 Z1
A(cid:3)2 ¼ AijwðMiÞwðMjÞdMidMj ¼hA2iw;w ð18Þ
i¼0 j¼0
(cid:4) (cid:5) Z1 Z1
1 2
AL2S ¼ Mw AijMiMjwðMiÞwðMjÞdMidMj ¼hA2iz;z ð19Þ
i¼0 j¼0
InthetableofChapter3.1,onecaneasilydistinguishbetweenA -valuesfromosmometryandlightscattering,
2
sinceinthefirstcaseM -valuesareusuallygiventocharacterizethepolymerwhereasinthelattercaseM -values
n w
areprovidedasthesemolarmassaveragesaretheexperimentalresultsobtainedfromEq.(9)orEq.(13).
DOI:10.1007/978-3-642-02890-8_1 Landolt-Börnstein
#Springer-VerlagBerlinHeidelberg2010 NewSeriesVIII/6D2