Shear and elongational flow behavior of acrylic thickener solutions

15 Pages·2008·0.51 MB·English

RheolActa
DOI10.1007/s00397-008-0292-1
ORIGINAL CONTRIBUTION
Shear and elongational flow behavior of acrylic
thickener solutions
PartI: Effectofintermolecularaggregation
SaeidKheirandish·IlshatGuybaidullin·
WendelWohlleben·NorbertWillenbacher
Received:4February2008/Accepted:26April2008
©Springer-Verlag2008
Abstract We investigate the effect of hydrophobic ag- times are more than one order of magnitude lower
gregationinalkali-swellableacrylicthickenersolutions thanthelongestshearrelaxationtimes,suggestingthat
onshearandextensionalflowpropertiesattechnically aggregates cannot withstand strong flows and do not
relevant polymer concentrations using the commer- contributetotheelongationalviscosity.
cial thickener Sterocoll FD as model system. Appar-
ent molecular weight of aggregates in water is Mw ≈ Keywords Steadyshear·Oscillatorysqueezeflow·
108 g/mol and decreases by more than an order of Elongationalflow·CaBER·Acrylatethickener
magnitudeinethanol.Zeroshearviscosityη islowand
0
shearthinningisweakcomparedtothehighmolecular
weightoftheaggregates.Linearviscoelasticrelaxation Introduction
is described by the Zimm theory up to frequencies
of 104 rad/s, demonstrating that no entanglements are Abroadvarietyoftechnicallyorcommerciallyrelevant
presentinthesesolutions.Thisisfurthersupportedby materials like coatings, adhesives, pharmaceuticals, or
the concentration dependence of η0 and is attributed personal care products are formulated as complex,
tostrongassociationwithintheaggregates.Extensional multiphasefluids.Besidestheliquidcontinuousphase,
flowbehaviorischaracterizedusingthecapillarybreak- theseformulationsincludesolidcomponentslikeinor-
up extensional rheometry technique including high- ganic pigments and fillers or organic binder particles,
speedimaging.Solutionswithφ ≥1%undergouniform droplets of immiscible fluids, and active ingredients.
deformation and show pronounced strain hardening However, their flow behavior is often controlled by
up to large Hencky strains. Elongational relaxation so-called rheology control agents or thickeners in or-
der to provide the desired processing and application
properties.
In many technical processes, fluids are subject to
complex flow fields incorporating strong extensional
components. This is true not only for industrial coat-
S.Kheirandish·N.Willenbacher(B)
ing techniques like spraying, curtain coating, or blade
InstitutofMechanicalProcessEngineeringandMechanics,
UniversityofKarlsruhe,76128Karlsruhe,Germany coating, but also in filtration operations, fiber spin-
e-mail:[email protected] ning, food processing, inkjet printing, and application
of personal care, crop protection products, or deter-
PresentAddress:
gents.Accordingly,notonlyshearbutalsoextensional
S.Kheirandish
BorealisPolyolefineGmbH,St.-PetersStr.25, flowpropertiesofthecorrespondingcomplexformula-
4021Linz,Austria tionshavebeeninvestigatedintensivelywithrespectto
processing or application properties. For example, the
I.Guybaidullin·W.Wohlleben
effectofextensionalviscosityondropletformationand
BASFSE,PolymerResearch,
67076Ludwigshafen,Germany dropletsizedistributionhasbeeninvestigatedforcrop
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protectionformulations(Dexter1996)andwater-borne the midpoint diameter with time. The advantage of
coatings (Fernando et al. 2000). Even quantitative thismethodisitswideapplicabilitytovariouskindsof
relationships between effective elongational viscosity fluids with low viscosities below 100 mPa s. However,
and resulting droplet diameter have been derived for neither strain rate nor stress can be controlled exter-
differentsprayvalvegeometriesandatomizationcondi- nally,butoftenveryhightotalstrainscanbeachieved.
tions(Stelteretal.2000,2002).Extensionalflowprop- Variouspolymersolutionshavebeeninvestigatedusing
erties of paper coating colors have been characterized thistechniqueallforminguniformcylindricalfilaments,
with respect to their impact on coat weight (Kokko which homogeneously thin and finally break (Stelter
et al. 1999) and misting behavior (James et al. 2003). etal.2000,2002;Clasenetal.2006a,b;Bhardwajetal.
Extensionalflowpropertiesdeterminetheatomization 2007).Inthesecases,thetensilestressisdirectlyrelated
of jet fuels (Chao et al. 1984) and the control of pre- to the surface tension of the fluid, the strain rate is
cisedropletdepositionininkjetprinting(Agarwaland defined by the change in the filament diameter, and
Gupta2002;TuladharandMackley2008). finally the extensional viscosity can be extracted as
Nevertheless, the determination of the elongational a function of total strain. On the other hand, even
viscosity of low viscosity fluids (like coatings, inks, Newtonian fluids (McKinley and Tripathi 2000) and
adhesives, or personal care products) with typical vis- also many commercially relevant complex fluids like
cosity values in the range of 10–1,000 mPa s is still an papercoating colors, adhesives,or cosmetic emulsions
experimentalchallenge.Varioustechniqueslikeporous exhibit non-uniform liquid bridges resulting in a fila-
mediaflow,opposingjetrheometry,four-rollmills,en- mentshapewithconcavecurvature.Inthesecases,the
trancepressurelossmeasurementsincapillaryrheome- calculated viscosity data are transient and/or apparent
tryincludingconvergingchannelfloworbubblegrowth values(Willenbacher2004).
and collapse measurements have been employed so Polymers and polyelectrolytes are widely used as
far (Macosko 1994). These different techniques cover thickenersforaqueousformulations(BraunandRosen
differentstrainrateandviscosityranges,butingeneral 2000). The dependence of extensional viscosity on
theflowkinematicsisnotpurelyextensional.Theflow polymerconcentrationandmolecularweight has been
canbetemporallyorspatiallyinhomogeneous,andonly studiedforvarioussynthetic(polyethyleneoxide,poly-
apparent extensional viscosities can be determined, acrylamide) and natural polymeric thickeners (xan-
comparison of data using different experimental tech- than,guargum)revealingadistinctdifferencebetween
niqueshavetobecomparedcautiously(Fergusonetal. flexible and stiff polymers. For the latter transient ex-
1997). In filament-stretching experiments (McKinley tensionalviscosityislower,strainhardeningislesspro-
and Sridhar 2002), a constant strain rate is imposed nounced(Dexter1996),andatsimilarrelaxationtimes,
on the fluid and the corresponding tensile stress is theirextensionalviscosityislowercomparedtoflexible
measured. Under certain constraints, the fluid forms a polymers (Stelter et al. 2002). Systematic data for the
slendercylindricalfilamentofuniformthickness,which shear and elongation rate dependence of the apparent
isuniaxiallystretched,andtheextensionalviscositycan Trouton ratio of cellulose solutions are also available
be determined as a function of strain rate and total (Kennedy et al. 1995). The characteristic relaxation
strain. However, this technique is typically used for time of cellulose solutions in filament-thinning exper-
fluidsintheviscosityrangewellabove1Pas(Bhardwaj iments was found to be strongly determined by the
etal.2007;Tripathietal.2006). highmolecularweightcomponentsandscaleswiththe
In this work, we use another filament-thinning (z+2)-average of the molecular weight distribution
technique, namely the capillary break-up extensional (Plog et al. 2005). Systematic studies regarding the
rheometry(CaBER;EntovandHinch1997;Bazilevskii effect of elasticity on the extensional flow properties
et al. 2001), in order to characterize the elongational ofpolymersolutionshavebeenperformedusingBoger
flowpropertiesofaqueousthickenersolutionsofalkali- fluids (Ng et al. 1996; Solomon and Muller 1996), and
swellable acrylate ester copolymers from emulsion it could be shown that even low concentrations of
polymerization. In a CaBER experiment, a fluid drop highmolecularweightpolymerscancausestrongstrain
is exposed to an extensional step strain, thus forming hardeningandyieldsTroutonratios(cid:4)3.
a liquid filament. Subsequent necking of that liquid The current work focuses on the class of acrylate
bridgeiscontrolledbythebalanceofcapillaryandvis- ester copolymers synthesized in a classical emulsion
coelastic forces. Large extensional strains are attained polymerization process and accordingly supplied as
as the filament undergoes thinning and finally breaks. highlyconcentrated,milky,aqueousdispersions(pH=
The only measured quantity is usually the change in 2–3.5). Typically, methacrylic acid (MAA), arylic acid
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(AA), and lower acrylates like ethylacrylate (EA) are Experimental
the main monomers used in commercial applications
(HagerandMartin1957;Miller1960).Thesethickeners Materials
are widely used in all kinds of water-borne coating
or adhesive formulations adjusted to pH values be- Sterocoll® FD (BASF SE, Ludwigshafen Germany)
tween 7 and 9. Upon neutralization, the weak acrylic is an alkali-swellable thickener for paper coating with
or methacrylic acid groups dissociate, thus solubilizing moderate thickening power. It is supplied as a highly
thepolymeranddevelopingtheirthickeningproperties concentrated, milky, aqueous dispersion with a solids
(Siddiqetal.1999).Thesethickenersareoftentermed contentof 25%,pH of2.2–2.6andis basedoncopoly-
alkali-swellable emulsion polymers (ASE). Their hy- merofethylacrylateand(meth)acrylicacidwithmolar
drophobically modified (HASE) counterparts belong ratioofacrylatetoacidsofabout1:1.
to the so-called associative thickeners which tend to Field flow fractionation (FFF) has been used to de-
form aggregates in aqueous solution. The rheological terminethemolecularweightofSterocollFDdissolved
behavior of these systems is therefore strongly con- inwateraswellasethanol.FFFseparatesaccordingto
trolled by the hydrophobic alkyl groups grafted onto thehydrodynamicdiameterintherangeof5to500nm,
thepolymerbackbone. corresponding to molar masses in the range 3 × 103
The shear rheological properties of these HASE- to 108 g/mol. This technique is widely used for analyt-
typethickenershavebeenstudiedintensively(English ical fractionation and determination of molar masses
et al. 1997; Abdala et al. 2004), mainly focusing on for colloids like lattices, polymers, and agglomerates.
the effect of chain length and concentration of the Themainapplicationsarecationicpolyelectrolytesfor
hydrophobic side groups, but also on the backbone paper manufacturing or flocculation agents in water
compositionaswellasoverallconcentrationandmole- treatment(Giddings1993;CölfenandAntonietti2000).
cular weight of the polymer. The aggregation of side The following experimental set-up has been used
chains has been proven by fluorescence spectroscopy here: the separation device is a flat channel (Con-
(Kumacheva et al. 1996). The strong shear-thinning senxus) about 0.35 mm high, 20 mm wide (conically
behaviorofHASE-typepolymersolutionsisattributed shapedduetotheasymmetriccross-flow),and300mm
tothebreakupofthesidechainaggregates.Intransient long. One flat side consists of a semipermeable mem-
extensionalflowexperiments,apronouncedmaximum brane (Amicon YM 10), where a constant part of the
oftheelongationalviscosityasafunctionofstrainrate carrierliquidisflowingthrough.Hereweusealinearly
is reported, and the viscosity drop at high strain rates rampedcross-flowof0.05–0ml/min.Thiscross-flowes-
is again attributed to the breakup of hydrophobic side tablishes a concentration gradient that is counteracted
chainsoftheaggregates(Kennedyetal.1995;Tanetal. by diffusion. Smaller colloidal polymers have higher
2000). diffusion coefficients, such that they experience the
Even in the absence of grafted hydrophobic side fasterelutionflowtowardsthecenteroftheflowchan-
chains, aggregation of polymer chains is an issue for nel.Typicalmigrationtimesinthechannelare1–40min
theseacrylicthickeners.Thesematerialsareassumedto (elutionflow0.5ml/min).Detectionbyrefractiveindex
bestatisticalcopolymers(e.g.,EAandAAmonomers), andmulti-anglelaserlightscattering(Wyatt,DawnEos
andiftheEAblocksarelongenoughtheyget“sticky” and R.I Optilab DSP) allows simultaneous determina-
or “blocky” and can cause intra- as well as intermole- tion of the distributions of absolute molar mass and
cular association. Accordingly, the existence of large radius of gyration. For FFF measurements, solutions
supramolecular aggregates has been clearly observed were diluted to a concentration of 0.5 g/L in 0.1 N
bystaticaswellasdynamiclightscatteringexperiments NaNO atpH=9.5–10.Forstaticlightscattering,sam-
3
(Daietal.2000;Wangetal.2005).Theunusualconcen- ples were diluted to a concentration series with 0.01–
tration dependence of the shear modulus G* also sug- 0.05 g/L in 0.1 N NaNO at pH = 9.5–10 and ethanol,
3
gested the relevance of aggregation for the thickening respectively. Independently determined refractive in-
propertiesofASE-typepolymers(Ngetal.2001).The dex increments of dn/dc = 0.149 mL/g against water
scopeofthispaperistocompareshearandelongational and dn/dc = 0.185 mL/g against ethanol were used for
flow properties of ASE-type thickener solutions. In dataevaluation.Inallcasessampleswerepurifiedusing
partI,wefocusontheaggregationphenomenon,which a 1.2-μm cellulose filter. Filtering is essential for FFF
istightlyrelatedtothesolventquality.Theforthcoming in order to remove dust and micron-sized impurities.
second part deals with the effect of crosslinking on Thesewouldelutein‘stericmode’fromtheFFFchan-
shearandextensionalflowproperties. nelandwouldmaskthesignalfromthethickener.
RheolActa
NaNO is a standard non-aggressive salt in the FFF Dynamic Material Testing (Ulm, Germany). In these
3
apparatus that partially screens the charges of the experiments, the sample is placed into a gap between
polyelectrolyte and thus reduces the inter- and in- two stainless steel plates. The lower one is supported
tramolecular electrostatic interactions. The fractiona- by a thin-walled quadratic copper tube carrying the
tion mechanism of the FFF channel is then a function piezoelementswhichexertthevibrationalmotionand
only of the hydrodynamic diameter, as desired for the pick-up the response signal. This lower part of the
determinationofmolarmassdistributions. device is surrounded by a double-walled cylinder al-
From static light scattering, we obtain M = 0.71 × lowingforcirculationofathermostatingfluid,andthe
w
108 g/moldeterminedintheconcentrationrange0.01– sample temperature is controlled with an accuracy of
0.05 g/L. In addition, light scattering yields an average ±0.1 ◦C. The upper boundary of the gap is a thick
radius of gyration of 275 nm. FFF yields M = 1.2 × metallid,whichprovidescompletesealingofthefluid.
w
108g/molinaqueoussolutionandM =4.6×106g/mol Theinstrumentoperatesataconstantforceamplitude,
w
inethanolbothmeasuredataconcentrationof0.5g/L. and from the ratio of the dynamic displacement of
TheseFFFresultsdirectlyprovetheexistenceofaggre- the lower plate (amplitude ∼5 nm) with and without
gatesinaqueoussolutionandtheirbreakupinethanol, fluid, the complex squeeze stiffness K* of the fluid is
whichisattributedtoanimprovedsolubilityoftheEA obtainedwhichisdirectlyrelatedtothecomplexshear
sequences. modulus G* assuming no-slip boundary conditions
Solutions of Sterocoll FD prepared for rheologi- (Kirschenmann 2003):
cal measurements were stirred at room temperature
(cid:2)(cid:3) (cid:4)
for 48 h and adjusted to the desired pH by slowly
3πR4 ρω2d2
adding 1 N NaOH. Polymer concentration was de- K∗ = G∗ 1+ +... (1)
2d3 10G∗
termined thermo-gravimetrically after neutralization.
Subsequently, samples were equilibrated for at least
24 h prior to testing. No further change of pH and where ρ is the fluid density, R (here 10 mm) is the
viscositywasobservedwithin3months. radius,anddistheheightofthegap.Thedenominator
in Eq. 1 is a series expansion taking into account the
inertia of the fluid in the gap. The determination of
Methods
G* strongly depends on the exact knowledge of d,
which is determined by calibration using Newtonian
Rotationalrheometry
liquids with viscosities between 1 and 2,000 mPa s.
Gap heights between 15 and 100 μm have been used
A rotational rheometer Haake RS100 (Thermo Elec-
here. Additional contributions of finite compressibil-
tron)equippedwithacone-platemeasuringcell(diam-
ity of the fluid can be safely neglected for the soft
eter d = 40 mm, cone angle α = 0.01 rad) was used
(G* < 1,000 Pa) polymer solutions investigated here,
to perform steady shear as well as small amplitude
but samples have to be degassed carefully in order
oscillatory shear experiments. The latter experiment
to avoid artificial compressibility from entrapped air.
covered the frequency range from 0.01 to 100 rad/s.
Moduli G(cid:8) or G(cid:8)(cid:8) in the range from 0.1 Pa to 10 kPa
Strain sweeps at ω = 3.14 rad/s were performed prior
areaccessiblewiththeset-updescribedhere.
toeachfrequencysweepinordertoidentifythelinear
viscoelastic response regime. All oscillatory shear ex-
perimentswere performedin a stress-controlled mode
Capillarybreak-upextensionalrheometry
and the critical stress of transition from linear to non-
linearresponsevariedbetween0.2and1Pa,depending
In a CaBER experiment (Bazilevskii et al. 2001;
on polymer concentration. This corresponds to critical
EntovandHinch1997),afluiddropisplacedbetween
strain amplitudes between 4% and 20%. Tempera-
twoplatesandsubsequentlyexposedtoanextensional
ture was controlled at T = 20 ± 0.2 ◦C using a fluid
step strain thus forming a liquid filament. A CaBER
thermostat.
1 (Thermo Electron) extensional rheometer was used
here, equipped with plates of diameter d = 6 mm.
c
Oscillatorysqueezeflow Plate separation was changed from L = 6 mm to
ini
L = 16 mm within 40 ms. This choice of parame-
fin
Oscillatory squeeze flow experiments were performed ters ensured that the initial filament diameter directly
usingapiezo-drivenaxialvibrator(Crassousetal.2005; after the plate separation stops was always around
Kirschenmann 2003) customized at the Institute for 1–1.5 mm for the fluids investigated here, and thus,
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capillary forces dominate over gravitational forces1 Resultsanddiscussion
and the subsequent necking of that liquid bridge is
controlled by the balance of capillary and viscoelastic Shearrheology
forces. The only measured quantity during filament
necking is the change in the midpoint diameter D(t) We have prepared aqueous solutions of Sterocoll FD
withtime,whichismonitoredusingalasermicrometer. withconcentrationsof0.7–5%anddifferentpHvalues
Deformationofafluidelementattheaxialmidplaneof between 6.5 and 9.5. Viscosity of these solutions ex-
the bridge is purely uniaxial. Large extensional strains hibitsamaximuminthepHrangearound8–9,andthe
are attained as filament thins and finally breaks. The results presented below focus on this pH range, which
theoretical basis for the capillary thinning of fluid fila- is also typical for many technical applications of such
mentshasbeendiscussedthoroughly(EntovandHinch thickeners.
1997). Having only the change in filament diameter as The linear viscoelastic properties of the solutions
a function of time, D(t), strain rate ε˙, tensile stress τ have beencharacterized using smallamplitude oscilla-
E
andapparentextensionalviscosityη canbecalculated tory shear and squeeze flow thus covering a frequency
E
according to following simplified equations (McKinley rangeofaboutsevendecades.Theresultsforsolutions
andTripathi2000): with different polymer concentrations at pH = 8 are
showninFig.1a,b.Thisisthefirstanalysisofthelinear
2 dD(t)
ε˙ =− (2) viscoelasticrelaxationofASE-typethickenersolutions
D(t) dt
in such a broad frequency range, which allows for a
robustcomparisontomodelpredictions.
2σ All G(cid:8), G(cid:8)(cid:8) data show the same pattern, at low fre-
τ = (3)
E D(t) quencies a terminal relaxation regime is found with
G(cid:8) ∼ ω2 and G(cid:8)(cid:8) ∼ ω, which switches over to a scal-
σ ing regime covering more than four decades on the
ηE =−dD(t) (4) frequency axis. For both moduli, the same scaling ex-
dt ponent is found, which varies between 0.585 and 0.6
Where σ is the surface tension of the fluid. The for the different solutions. This is the characteristic
time directly after cessation of the motion of the plate Zimm relaxation behavior and no crossover in G(cid:8) and
is defined as t = 0, and the corresponding filament G(cid:8)(cid:8) is observed. This important finding clearly reveals
diameter D has been used to calculate the Hencky thatdespitethepolymers’highmolecularweightentan-
0
strainε(t): glements do not contribute to the stress relaxation of
(cid:3) (cid:4) these solutions even at concentrations well above the
ε(t)=2ln D0 (5) overlap concentration c∗, and particularly also above
D(t) typical concentrations at which these thickeners are
In addition to the determination of the midpoint use√d in commercial formulations. We estimate c∗ ≈
diameter D(t), the full filament shape during the thin- 1 / N ≈ 0.1%, where N is the degree of polymeriza-
tion of the aggregates, and according to scaling theory
ning and necking process was monitored here for se-
onsetofentanglementisexpectedtooccuraround10c∗
lected samples using a high-speed camera (Fastcam
for polyelectrolytes in solutions of high ionic strength
1024PCIPhotron)taking1,000images/sataresolution
of 1,024×1,024 pixel equipped with a macro zoom (Dobrynin et al. 1996) similar as for neutral polymers.
Here entanglements are not observed even at higher
objective (Eneo Verifokal B 45 Z03 MV-MP, focal
concentrations,andweassumethisisduetointra-and
length 45–160 mm) and additional intermediate rings
intermolecular “sticky” contacts among hydrophobic
allowingfor0.3–1-foldmagnification.Illuminationwas
EAsequenceswithintheaggregates.
done with a white LED from the back. With this set-
For a quantitative analysis of our data, G(cid:8) and G(cid:8)(cid:8)
up,filamentthinningcouldberesolveddownto10μm.
werefittedusingtherelaxationfunctionfromtheZimm
All CaBER experiments were performed at ambient
theory(RubinsteinandColby2003):
temperature.
(cid:3) (cid:4) 1 (cid:3) (cid:4)
η t − /3ν t
G(t)= sφ exp − (6a)
λ λ λ
1This can be estimated by the so-called Bond number Bo = 0 0 z
ρgD(t)2/4σ (see,e.g.,AnnaandMcKinely2001)withtheaccel-
erationofgravityg,Bo<0.2forafilamentdiameterof1.5mm, whereηs isthesolventviscosityandφ thevolumefrac-
σ =35mN/m,andρ=1,000kg/m3. tion of the polymer. The dynamic mechanical moduli
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a b
c
(cid:8) (cid:8) (cid:8)(cid:8)
Fig.1 aStoragemodulusG vs.angularfrequencyforSterocoll cStorageandlossmodulusG andG vs.angularfrequencyfor
FD solutions with different polymer concentrations at pH=8. a Sterocoll FD solution with polymer concentration 3 vol% at
The frequency ranges in which data have been obtained by pH=8. Lines: Fit of the Zimm model to the experimental G(cid:8)
(cid:8)(cid:8)
oscillatoryshearandsqueezeflow,respectively,areindicatedby (solid lines) and G (dashed lines) data (for fit parameters see
arrows. b Loss modulus G(cid:8)(cid:8) vs. angular frequency for Sterocoll Table1).Insert:ShearmodulusG(t)usedtofittheZimmmodel
FD solutions with different polymer concentrations at pH=8. totheexperimentalG(cid:8)andG(cid:8)(cid:8)dataaccordingtoEqs.6aand6b
can be calculated from this relaxation spectrum using To enhance the efficiency and accuracy of the inte-
theFerry’srelations(Ferry1980): gralcalculation,afiniteelementmethodintroducedby
(cid:5)∞ NobileandCocchini(2001)wasusedtocalculateG(cid:8)(ω)
G(cid:8)(ω)=ω G(t)sin(ω·t)dt andG(cid:8)(cid:8)(ω).
FromafitofEqs.6aand6btotheexperimentaldata,
0
(cid:5)∞
we determine the characteristic longest and shortest
G(cid:8)(cid:8)(ω)=ω G(t)cos(ω·t)dt (6b) relaxationtimesλ andλ ofthe representativeZimm
z 0
0 chainaswellasthescalingexponentν.
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Table1 ZimmanalysisofthelinearviscoelasticresponseofaqueousSterocollFDsolutionsofvariouspolymerconcentrationsφ at
pH=8
φ/% ηs/mPas λz/s λ0/10−10s Napp/106 b/Å ν
0.7 1.0 2.2±0.2 0.11±0.02 2.75±0.28 3.6±0.5 0.585±0.01
2.0 1.0 1.2±0.1 0.24±0.05 1.25±0.13 4.6±0.5 0.585±0.01
3.0 1.0 1.0±0.1 0.29±0.06 1.01±0.10 4.9±0.5 0.585±0.01
3.5 1.0 1.0±0.1 0.31±0.06 0.94±0.09 5.0±0.5 0.585±0.01
4.8 1.0 4.0±0.2 0.40±0.08 1.07±0.11 5.5±0.5 0.608±0.01
(cid:8) (cid:8)(cid:8)
ThesolventviscositygiveninthetablewasusedasinputparameterfortheanalysisoftheG,G data.Errormarginsgiveninthetable
areduetotheuncertaintyinreproducibilityofshearmodulusmeasurementsandthecorrespondingerrorpropagationwhencalculating
(cid:8) (cid:8)(cid:8)
thefitparametersandrelatedquantities.TherelativeerrorinG andG isestimatedtobe10%.
The shortest relaxation time λ is related to the random coil configuration (Muroga et al. 1999; Ortiz
0
lengthofaKuhnsegmentb accordingto and Hadziioannou 1999). Finally, N and hence the
app
product N ·b is independent of concentration, sug-
λ app
b3 =k T 0 (7) gesting that the aggregate size is roughly independent
B η
s ofconcentration.
and from the ratio of τ0 and τz we get the number of In Fig. 2, we show the zero shear viscosity η0 for
Kuhnsegments N : two dilution series adjusted to pH = 8 and pH = 9,
app
respectively. At pH = 9, the viscosity is slightly lower
(cid:3)λ (cid:4)1/3ν than at pH = 8, but in both cases η0 increases only
Napp = λz (8) weakly with concentration and a power law depen-
0 denceη ∼φ1.25±0.1 isfoundatconcentrationsφ>1%.
0
Of course, these are apparent values, because our This is in excellent agreement with predictions for
analysis is based on the simplified Zimm model orig- unentangled, semidilute solutions of neutral polymers
inally developed for linear polymer chains in dilute (Colby et al. 1994) and polyelectrolytes in the high-
solutions, but here we are only interested in relative salt limit (Dobrynin et al. 1996). The ionic strength of
changesofb and Napp withchangingsolventqualityor thesolutionsinvestigatedherehasnotbeencontrolled
polymerconcentration.
The values for λ , λ , ν, N , and b determined
0 z app
forsolutionswithdifferentpolymerconcentrationsad-
justedtopH=8arelistedinTable1.Theexponentν =
0.585±0.01 is as expected from the Zimm model for
polymers in good solvents. The Kuhn length b is also
essentiallyindependentofconcentrationandvariesbe-
tween4.6±0.5and5.5±0.5Å,andonlyatφ =0.7%
aslightlylowervalueof3.6±0.5Åisfound.Fromthe
bondlengthandanglesofanaveragemonomerunitwe
calculate that a Kuhn element represents 2–3 physical
monomerunitswithanaverageM of96g/molfora1:1
w
MAA/EA copolymer composition. The Kuhn length
b is calculated from the shortest measured relaxation
time, which is determined by local displacements of
shortchainsegments,andhence,itcanbeassumedthat
this quantity is hardly affected by interactions among
singlechainsoraggregates.Therefore,wethinkitisjus-
tifiedtocompareourdatawithindependentresultsfor
pure poly(MAA) obtained from X-ray scattering and
atomic force microscopy. For pure PMAA in aqueous
Fig.2 Zeroshearviscosityasafunctionofpolymerconcentra-
solution,valuesforb intherangeof6–8Åarereported
tionfortwodifferentpHvalues.Errorbarsrefertothestandard
intheliteratureinabroadrangeofdegreeofionization
deviationofresultsfromfivemeasurementsondifferentsamples
and across the transition from contracted to expanded fromthesamebatch
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Fig.3 aReducedzeroshear a b
viscosityη0vs.ethanol
contentφ ofthesolvent
Ethanol
mixture.Circles:puresolvent,
squares:solutionswith0.7%
polymerconcentrationbut
differentsolvent
compositions.Dataare
normalizedtowaterviscosity
inthecaseofthepure
solvent,forthesolutionto
theviscosityofthesolutionin
purewater.Errorbarsrefer
tothestandarddeviationof
resultsfromfive
measurementsondifferent
samplesfromthesamebatch.
bApparentdegreeof
polymerizationNapptimes
Kuhnsegmentlengthb vs.
ethanolcontentφ in
Ethanol
thesolventmixture.Lineisto
guidetheeye.Forerrorbars,
seeTable2
explicitly, but electrical conductivity varies from 2 to expected for the corresponding polymer solutions if
10mS/cmasφincreasesfrom1%to5%,indicatingthe they were ideal solutions, since then solvent viscosity
highionicstrengthofthesolutions,whichisduetothe shouldbeaconstantpre-factorofthesolutionviscosity.
ions introduced during neutralization. Ionic strength In contrast, we observe that the viscosity maximum is
decreaseswithdecreasingpolymerconcentrationsince less pronounced and occurs at lower ethanol content
less NaOH is needed for neutralization; accordingly, as compared to the pure ethanol–water mixture. At
a weaker concentration dependence of viscosity is ob- ethanol fractions beyond 0.5, the viscosity decreases
served approaching η ∼ φ0.5 as expected for poly- even below that of the solution in pure water. But at
0
electrolytesinthelow-saltlimit(Fuoss1951;Dobrynin anethanolcontentbeyond0.6,thesolutionsgetturbid
etal.1996).Moreover,itisworthnotingthatthesteady andphaseseparate.Thiscanbeinterpretedasfollows:
shear viscosity of solutions of Sterocoll FD is similar at low ethanol concentrations, aggregates partly break
tothatofsolutionsoflinearacrylicacidhomopolymers due to an increased solubility of the EA groups, and
with about 50 times lower average molecular weight this counteracts the increase of the solvent viscosity
compared at similar polymer concentration and pH.2 and hence the viscosity maximum is less pronounced
This also indicates a compact structure of the aggre- compared to the solvent mixture. Furthermore, the
gates, which is presumably the reason for the absence solubilityoftheMAAgroupsdecreaseswithincreasing
ofentanglements. ethanol content; thus, the polymer coils shrink and
An appropriate means to vary solvent quality and thisadditionallycontributestothereductionofviscos-
hence the aggregation behavior of the copolymer is ity. At high enough ethanol concentrations, this effect
to add ethanol as a co-solvent to the polymer solu- makes the copolymer insoluble, and thus the solution
tions. In Fig. 3a, we compare the corresponding η gets turbid, finally leading to phase separation. Zimm
0
and in Fig. 3b the values of the product N ·b analysis shows that the product N ·b, which is a
app app
for a mixing series with 0.7% polymer concentration measureofthemolecularweightoftheaggregates,de-
(Table2).Itiswellknownthatethanol–watermixtures creases monotonically with increasing ethanol content
exhibit a distinct maximum in viscosity at a mixing and thus directly shows the break-up of aggregates,
ratio of about 1:1, which is due to structure forma- which is attributed to the enhanced solubility of EA.
tion based on H-bonds. A similar behavior would be This result is in line with the reduction of molecular
weightobservedinfieldflowfractionationexperiments
atmuchlowerpolymerconcentrations,whenreplacing
2PrivatecommunicationY.Matter,BASFSE,ISISLaboratory,
Straßbourg. waterbyethanolasasolvent.
RheolActa
Table2 ZimmanalysisofthelinearviscoelasticresponseofSterocollFD(φ=0.7%)dissolvedinwater–ethanolmixtureswithdifferent
ethanolconcentrationsφ
Ethanol
φEthanol/% ηs/mPas λz/s λ0/10−10s Napp/106 b/Å ν
0 1.0 2.2±0.2 0.11±0.02 2.75±0.28 3.6±0.5 0.585±0.01
20 2.1 1.8±0.2 0.60±0.02 0.93±0.09 4.9±0.5 0.585±0.01
40 2.8 1.8±0.2 1.00±0.20 0.70±0.07 5.3±0.5 0.585±0.01
50 2.8 1.8±0.2 2.80±0.28 0.39±0.04 7.4±0.5 0.585±0.01
60 2.5 1.4±0.2 5.20±0.52 0.24±0.02 9.4±0.5 0.585±0.01
(cid:8) (cid:8)(cid:8)
ThesolventviscositygiveninthetablewasusedasinputparameterfortheanalysisoftheG,G data.Forerrormargins,seeTable1.
Extensionalrheology before the filament breaks. Similar phenomena have
beenobservedforlowviscosity,weaklyelastic,aqueous
The extensional flow properties of the thickener solu- solutions of high molecular weight polyethylene oxide
tions have been characterized using the CaBER tech- (PEO; Oliveira et al. 2006). At all higher concentra-
nique.InFig.4,thetimedependenceofthenormalized tions,filamentsthinuniformlyuntiltheyfinallyvanish.
midpointdiameterisshownforthreedifferentpolymer There is no indication of any filament instability or
concentrations between 0.7% and 1%. The difference inhomogeneity in deformation within the optical res-
intheinitialdiameterdecayisnotverypronounced,but olution of our set-up. Figure 6 shows the evolution
thediameteratfailurestronglydecreasesandfilament of the midpoint diameter for polymer concentrations
lifetime increases with increasing polymer concentra- ≥1%.Anexponentialdecayofthefilamentdiameteris
tion.Moreover,high-speedimagingrevealsdistinctdif- observedoveranextendedperiodoftimeand D(t)/D
0
ferencesinbreak-upmechanisms,asshowninFig.5.At canbedescribedas:
0.7%polymerconcentration,filamentbreak-upoccurs (cid:6) (cid:7) (cid:6) (cid:8)
within 20 ms after the motion of the upper plate has D(t) D =exp −t 3λ (9)
0 E
stopped. In this short period of time, no homogenous
cylindrical fluid filament is formed. The liquid bridge The characteristic relaxatio(cid:6)n time λE is directly re-
is belly-shaped and break-up seems to be driven by lated to the strain rate ε˙ =2 3λ , which is constant
E
inertiaandgravity.Atpolymerconcentrations≥0.9%,
in this regime (cf. Eq. 2). Furthermore, this behavior
cylindrical fluid filaments are formed quickly and thin
corresponds to an exponential growth of the tensile
homogeneously. For the solution with 0.9% polymer
stress(cf.Eq.7).Intheterminalregimeofthefilament-
content, a beads-on-a-string instability (Goldin et al.
thinning process, the diameter decreases faster than
1969; Clasen et al. 2006a, b; Wagner et al. 2005) oc-
expected from a single exponential decay, resulting in
curs at a filament diameter of about 60 μm, shortly a downward curvature of the D(t)/D vs. time curves
0
in the semilog plot. The described behavior is typical
for weakly elastic polymer solutions. It has been ob-
served,e.g.,forpolyacrylamidesolutions(Stelteretal.
2002), polystyrene Boger fluids (Anna and McKinely
2001), or PEO solutions (Oliveira et al. 2006) and is
generally attributed to the strain hardening of these
solutionsrelatedtotheextensionofpolymercoils.The
rapidfilamentdecayintheterminalregimeisgenerally
attributed to the finite extensibility of the polymer
chains(Clasenetal.2006a,b).
Here we find that the maximum Hencky strain
ε at which the filaments break, and hence filament
max
lifetime increase substantially with increasing polymer
concentration. For further numerical analysis of the
results,wefitapowerlawtothe D(t)/D dataandthen
0
wecalculateε˙andηE,appanalyticallyaccordingtoEqs.2
and8.Thisavoidslargescatterinresults,whichwould
Fig.4 CaBERexperiments:reducedfilamentmidpointdiameter
be inferred from calculating the derivative of D(t)
for solutions with different polymer concentrations at pH = 8.
Dashedlinesindicateinitialslopeoftherespectivedata numerically. For the experimental data presented in
RheolActa
a b c
d e
Fig. 5 a–e Images of filaments from solutions with different failure(t=94ms)forpolymerconcentration0.9%.eLastimage
polymer concentrations at pH = 8. a–c Taken after 27, 29, and beforefailure(t=197ms)forpolymerconcentration1.0%
31 ms for polymer concentration 0.7%. d Last image before
Fig.6,thisisshowninFig.7a,b.Theself-selectedstrain at pH = 8, but at a slightly higher viscosity level. The
ratesintheCaBERexperimentsdecreasewithincreas- corresponding values for the ratio ηE,app(t = 0)/η0 and
ing polymer concentration and are in the range 1– ε areshowninFig.8.
max
20s−1.Foreachconcentration,thestrainrateincreases A comparison of characteristic relaxation times in
slightly with increasing total strain, but not more than shear and extensional flow is shown in Fig. 9 for both
50% even up to Hencky strains of about 5. The ratios concentration series at pH = 8 and pH = 9. Here we
oftheinitialvaluesofηE,appandthezeroshearviscosity havecalculatedthelongestrelaxationtimeinshearλS
for the different concentrations are between 1 and 2 accordingto:
and are thus slightly lower than the value of 3, which
G(cid:8)
is expected in the limit of linear response. However, λ = lim (10)
severe strain hardening is observed for all solutions. S ω→0 G(cid:8)(cid:8)ω
At the highest polymer concentration, the apparent Itisinterestingtonotethattherelaxationtimescal-
extensional viscosity increases exponentially almost culatedinthiswayaresystematicallylowerthanthose
until failure at ε =7.7. For lower concentrations, fromZimmanalysis.Atallinvestigatedconcentrations,
max
deviationsfromtheexponentialgrowthbehavioroccur λ isatleastafactorof10lowerthanλ .Atthelowest
E S
around ε ≈ 4 and ηE,app seems to level off at higher concentrationsthedifferenceisevenmorepronounced,
strain,butthisisrelatedtothenon-constantstrainrate. but in these cases the short extension relaxation time
Filamentthinningandbreak-upresultsareverysimilar is attributed to the occurrence of flow instabilities. At