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Polymer 53 (2012) 4800e4805

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Polymer

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Two-dimensional Fourier transform rheological study on thermosensitivityof poly(N,N-diethylacrylamide) in aqueous solutions

Satu Strandman a,1, David G. Lessard a,1, Dagmar van Dusschoten b, Manfred Wilhelm c,Paula M. Wood-Adams d, Hans W. Spiess b, X.X. Zhu a,*

aDépartement de chimie, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal, Québec H3C 3J7, CanadabMax-Planck-Institut für Polymerforschung, Ackermannweg 10, Mainz D-55128, GermanycKarlsruhe Institut of Technology (KIT), Engesserstr. 18, Karlsruhe 76131, GermanydDepartment of Mechanical & Industrial Engineering, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada

a r t i c l e i n f o

Article history:Received 19 April 2012Received in revised form7 August 2012Accepted 11 August 2012Available online 17 August 2012

Keywords:Poly(N,N-diethylacrylamide)FT-rheologyThermosensitive polymers

* Corresponding author. Tel.: þ1 514 340 5172; faxE-mail address: julian.zhu@umontreal.ca (X.X. Zhu

1 S. Strandman and D.G. Lessard contributed equall

0032-3861/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.polymer.2012.08.028

a b s t r a c t

The phase transition of a thermo-responsive polymer, poly(N,N-diethylacrylamide) (PDEA) above itscritical overlap concentration (c*) has been studied by two-dimensional Fourier transform (FT) rheologyusing Large Amplitude Step Shear Oscillation (LASSO). This technique allows the separation of the linearand nonlinear contributions to different relaxation processes and the determination of their time scaleand amplitude through the time response of the shear stress after step strain experiments. The inter-chain interactions increase at the onset of the phase transition at 29 �C, indicated by an increased non-linear contribution at short relaxation times as compared to the single phase condition. During the phaseseparation of a concentrated solution above the phase transition temperature, the polymer-rich phasecan form a transient network created by the hydrophobic interactions between the collapsed polymerchains. The non-linear behavior of a phase-separated system well above the transition temperature (at33 �C) reflects the stretching of the bridging chain segments between larger aggregated domains and thecoalescence of aggregates broken during the step in strain. Relaxation time distributions have been fittedin the LASSO spectra by the nonlinear regularization (NLREG) technique and the relaxation times havebeen attributed with various linear and non-linear processes below and above the phase transitiontemperature.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Water-soluble polymers exhibiting a lower critical solutiontemperature (LCST) have been under intense research in recentyears [1]. Poly(N,N-diethylacrylamide) (PDEA, Scheme 1A) isa thermoresponsive polymer that can undergo a phase separationin an aqueous solution upon heating above its LCST (25e36 �C,depending on the molar mass of the polymer) [2e5]. PDEA-basedmaterials are potential candidates for biomedical [6] and techno-logical applications [7,8]. The behavior of polymer solutions at theirgel point has been widely studied by rheology [9], but the changesin mechanical properties at the phase transition temperature arenot well known. The phase transition of PDEA has earlier beencharacterized by different techniques such as turbidimetry [5,10],

: þ1 514 340 5290.).y to this work.

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differential scanning calorimetry [5,10], scattering methods [11e13], FTIR [14], NMR, [15,16], and rheology [13,17]. When thetemperature is increased above the critical temperature, thehydrophobic backbone and nonpolar groups of PDEA tend toassociate, leading to intra- and inter-molecular aggregation. Thisresults in the collapse of polymer chains (microphase separation)and often in the precipitation of the polymer from the solution(macrophase separation) [1]. The polymer-rich phase can forma colloidal suspension, precipitate, or form a gel, depending on theconcentration and molar mass of the polymer.

Rheologicalmeasurements onPDEA [13,17]have showna changeon the flow behavior occurring within a narrow temperature range.Below the LCSTand the critical overlap concentration, PDEAbehavesas a Newtonian fluid, but when heated above the LCST, non-linearflow behavior has been observed under similar shear conditions.Even for the concentrations as lowas 1.0wt-% (Mn¼360 000 g/mol),gel-like characteristics (storage modulus, G0 > loss modulus, G00)were observed at temperatures above the phase transitiontemperature, indicating intermolecular interactions [13]. This

Scheme 1. (A) Structure of PDEA. (B) A model describing the coileglobule transition ofPDEA above its critical overlap concentration c* upon heating.

S. Strandman et al. / Polymer 53 (2012) 4800e4805 4801

transient network is broken down at high strain amplitudes andhigh oscillatory frequencies, leading to nonlinear behavior.Describing the viscoelastic material response under large defor-mations and thus, under nonlinear flow, is often difficult anddifferent relaxation processes cannot typically be differentiatedwithout performing multiple types of rheological experiments. Inmany applications, such as polymer processing, nonlinear condi-tions are common and hence, understanding the flow behavior isessential for each new class of materials [18].

Fourier transform (FT) rheology takes advantage of severaltechnological developments in rheology achieved in the recentyears [18e21]. This technique additionally improves the sensitivityvia oversampling [22] by a factor 3e10 and allows the observationand quantification of non-linear rheological phenomena. One ofthese techniques, large amplitude oscillatory shear (LAOS)[18,23,24] can measure and quantify the non-linear behavior ofpolymermelts and polymer solutions by shearing the sample in thedynamic mode at sufficiently high frequencies or strain amplitudesthat induce a non-linear shear flow. The response signal is acquiredand subsequently Fourier-transformed to obtain the relativeintensity and phase of the contributing odd harmonics of thefundamental frequency, which reflects the non-linearity of theresponse. This simple form of data analysis can be used to studyalmost any material in the non-linear regime, such as polymers,gels, asphalt, metals, ceramics and biofluids (such as blood andsaliva) [18]. Examples of stimuli-responsive systems that haverecently been studied by FT-rheology are biopolymer gels andsolutions based on chitosan [25], k/i-carrageenan [26,27], or starch[27], and soft thermosensitive poly(N-isopropylacrylamide) (PNI-PAM) microgel particles [28] or coreeshell particles with a PNIPAMshell [29,30].

For a better understanding of the higher harmonics, a moreadvanced non-linear rheology technique, large amplitude stepshear oscillation (LASSO), has been designed [18,31] and combinedwith 2-dimensional FT-analysis. This technique can measure non-linearity by combining the intensities of different harmonics asa function of relaxation times, allowing the correlation of relaxationtimes with the respective damping functions of certain rheologicalprocesses. The method consists of serial independent step-strainexperiments, the amplitudes of which follow a sinusoidal func-tion of time. The response is Fourier-transformed for each fixedwaiting time after the step, which results in a spectrum of therheological response for each of these waiting times. The timebehavior of each of these harmonics can be analyzed separatelyusing multi-exponential relaxation spectra. Assuming that therelaxation time constants are unaffected by shear steps (time-strainseparability which is often observed), this form of analysis willyield the relative contribution for each relaxation time to allharmonics, which directly gives quantitative information on thenon-linearity of all contributing processes. Although the molecularand theoretical interpretations are not always simple, it is possibleto correlate especially the slow relaxation modes such as stretch-ing, reptation, and orientation of the polymer chains or shear-induced breakdown and reformation of aggregates in morecomplex systems to the relaxation pattern of the harmonics. The

theoretical background has been discussed in details in the litera-ture [31,32].

Linear rheology gives insight on the phase transition tempera-ture of thermo-responsive polymers and the correspondingchanges in their rheological behavior, shown in our earlier study[13]. In the current study, our focus is on more highly entangledsystems over the very narrow temperature range where the phasetransition occurs. Therefore, the timeetemperature superpositionprinciple cannot be used as the polymer system changes uponincreasing temperature. LASSO has a shorter time lag and cantherefore be related to higher frequencies, and it improves thesensitivity to slow relaxation processes in comparison to otherrheological techniques, which is important for samples with lowviscosity. This technique allows the characterization of the non-linearity at the time scale of several orders of magnitude after theperturbation is applied. Here we have utilized LASSO to charac-terize the phase transition phenomena of a concentrated PDEAsolution occurring close to its LCST. A PDEA solution has beenstudied in an effort to investigate the non-linear flow behavior ofthermosensitive polymers and to understand the changes in therelaxation processes during the phase transition. The results of thisworkmay apply to related thermosensitive polymers in general andwe also show the use of the FT-rheology technique in the study ofpolymers with thermoresponsive behavior in solutions.

2. Experimental part

2.1. Polymer synthesis and characterization

N,N-diethylacrylamide was synthesized by using acryloyl chlo-ride (97%) with diethylamine in methylene chloride, followed bya distillation under vacuum affording a clear liquid. The polymerswere synthesized by free radical polymerization in water usingammoniumpersulfate as the initiator and subsequently fractionated[4,5]. Molar masses of the polymers were determined by a Waterssize exclusion chromatography (SEC) system using three Ultra-styragel columns in tetrahydrofuran (THF). Monodisperse poly-styrene standardswere used for themolarmass calibration [5]. Twopolymerswere used in this study: PDEA-600K (Mn¼ 600,000 g/mol,Mw/Mn ¼ 1.5) and PDEA-16K (Mn ¼ 16,000 g/mol, Mw/Mn ¼ 2.6).Cloud points representing the phase transition temperatures weredetermined by turbidimetry at a heating rate 0.1 �C/min and definedas the point of 50% of transmittance [5]. The cloud points of PDEA-600K and PDEA-16Kweremeasured tobe 29 and 32 �C, respectively.

2.2. LASSO setup

LASSO measurements were performed on a controlled strainARES rheometer (Rheometric Scientific). The instrument wasequipped with two different transducers covering the torque rangefrom 2 � 10�6 to 0.2 Nm. PDEA aqueous solutions were sheared ina 25-mm cone and plate geometry with a cone angle of 0.02 rad. Amultiple step strain experiment with the step amplitude followinga sinusoidal pattern [31] (Fig. 1A) was controlled externally usinga homemade Labview routine on a separate computer equippedwith a 16-bit analog-to-digital/digital-to-analog (ADC/DAC)converter PCI-MIO-XE10 card (National Instruments). Details of theexperimental methods were described previously [31]. Therheometer was placed on an antivibrational marble table to avoidrecording noise; the circulating bath and hoses were isolated fromthe marble table to minimize the vibrations from these sources. Toavoid dehydrationduring the long LASSOexperiments, a home-builtaluminumvapor trap was utilized. The viscosity increased less than10% during a one-day measurement using the cone and plate withthevapor trap. Furthermore, fresh sampleswerepreparedeveryday.

Torq

ue (a

.u.)

Time

A

{

Strain

B

Torq

ue (a

.u.)

Step number

t

Tor

que

(a.u

.) Time

γ

γ

0

Δ

Δ

Fig. 1. (A) Scheme of the LASSO experiment where the imposed strain (g0, indicatedwith an arrow) follows a sinusoidal curve (gray line), and the multiple relaxationpattern (exponential-type decay peaks in solid line) displays the torque as a function oftime. The inset shows an enlargement of a single relaxation peak after the fast imposedstrain, where Dt corresponds to the time between subsequent steps. (B) Torqueintensity as a function of step number at 3 different times after the step was applied, at18 ms (-), 28 ms (C) and 38 ms (:).

S. Strandman et al. / Polymer 53 (2012) 4800e48054802

Below the phase transition temperature, no thixotropy orrheopexy was noticed for aqueous PDEA solutions. Above it, thesamples appeared unstable for the first 10 min after which theyreached a steady state. To ensure a good reproducibility for theLASSO experiments above the phase transition temperature,several cycles were inspected to verify that no change of propertieswith time occurred. Experiments showing sustained variation withtime were rejected to ensure reliability.

The distribution of relaxation times (l) is broad, as is commonfor polymer solutions, and therefore the averaging procedure usesa low number of averages at short relaxation times to adequatelysample the fast relaxation processes, followed by a higher numberof averages to reduce the data set size and to further increase thesignal-to-noise ratio, enabling measurements at extremely lowtorque (in the range of 10�7 Nm). Without this kind of procedurethe amplitudes of the faster relaxation times would be under-estimated [31].

For the LASSO experiments with PDEA solutions (Fig. 1A), threeto five sinusoidal cycles each consisting of 21 shear steps wereapplied with a waiting time between consecutive steps rangingfrom 10 s for samples with short relaxation times to 100 s for thesample above the phase transition temperature. The time ofimposed strain is short, 25 ms. The total time needed for a LASSOexperiment varied from 10 min to 3 h. The data were saved asa continuous stream of data points. The data sets were rearrangedinto a two-dimensional array for each delay after a step in strain,and the signal was subsequently processed through a discretecomplex Fourier transform. Here, the magnitudes of the cosinetransformed signal are shown. The theory behind LASSO and the

details on the Fourier transform have been described in our earlierpaper [31] and have thus not been repeated here. The nonlinearregularization technique, NLREG [33], was used for continuousspectral analysis to yield relaxation time spectra that allow the fullcomparison between the G1 (linear) and G3 (non-linear processes)relaxations.

3. Results and discussion

3.1. Interpretation of LASSO results

LASSO is a multiple step strain experiment where the stepsfollow a sinusoidal pattern. The resulting torque is recorded andplotted as a function of time. A typical plot is shown in Fig. 1A,where the strain signal follows a stepped sine wave and the torquesignal after each step follows a multi-exponential decay. The stepsin strain are imposed as fast as possible (e.g. in 25 ms) to minimizethe relaxation of the polymer solution during them. The data setshave been rearranged into a two-dimensional array for each timeafter a shear step (Fig. 1B), and the signal was subsequently Fourier-transformed. For a linear response, the resulting pure sine wave istransformed into a single peak, which we refer to as G1 or thefundamental harmonic. For a non-linear response, higher, oddharmonics are observed.

Even harmonics of the fundamental are usually not observed inLASSO or LAOS (large amplitude oscillatory shear) experimentsbecause the appearance of the second harmonic and all other evenharmonics of the fundamental implies symmetry of the underlyingstress and strain tensors. In fact, the behavior resulting in suchasymmetry is rareormostlyabsentbecause isotropicmaterialsbehavethe same way when sheared clockwise and counterclockwise. Tech-nical problems such as cone slips, air bubbles, mechanical backlash ofthe rheometer, or edge fractures may generate an even harmonicbecause the response in the two directions might be different. Thepresence of the even harmonic is often a fingerprint to identify inap-propriate experimental conditions, or poor sample preparation. In ourcase, no significant even harmonicswere observed (typically less thanor equal to 10�4 e 10�5 relative to the fundamental).

LASSO is very sensitive towards the non-linearity arising fromthe construction or disruption of different interactions, such ashydrophobic interactions in phase-separated thermoresponsivesystems, under shear. This can provide better understanding of themicroscopic structure and mechanisms that are relevant to thestress relaxation process occurring in these polymer systems.Various effects can be differentiated, and their respective timescales can be determined. Chain stretching during the step in strainhas a hardening effect which results in an increasedmodulus, whilechain orientation results in a softening effect and a decreasedmodulus [31,32]. These processes have opposite effects on thehigher harmonics; therefore, the decrease of the third harmonicover time is related to the softening effect, while a positive slope inthe third harmonic is related to strain hardening. Both stretchingand orientation can occur when applying large enough strains tohighly entangled polymers. The relaxation of a stretched chain in anentangled polymer solution occurs faster than the other relaxationmodes such as the re-orientation.

A LASSO graph consists of harmonics (Gi) of the stress relaxationfunction. Fig. 2A shows the stress relaxation curves for a 15 wt-%solution of PDEA-600K below its phase transition temperature,represented by the first to the seventh odd harmonics (G1 e G7). Asmentioned above, the first harmonic is related to the linearcontribution to the response, whereas higher odd harmonics areonly generated after a non-linear response to an applied shear step[31]. The first harmonic is typical for the scaling law behavior of theunderlying relaxation process. The intensity of the higher

0.1

1

10

100

1000

0.1 10.1

1

10

100

1000

AG

i(t,0) (

Pa)

G1

G3

G5

G7

B

Gi(t,

0) (Pa

)

Time after step (s)

G1 ( 0=0.33) G3 ( 0=0.33) G1 ( 0=2.00) G3 ( 0=2.00)

Δ

Δ

Δ

Δ

γ

γ

γ

γ

γγ

Fig. 2. Stress relaxation curves of the Fourier-transformed harmonic response ofPDEA-600K at 27 �C (A) at a constant step strain magnitude Dg0 ¼ 2.00 correspondingto the odd harmonics (G1, G3, G5, and G7), (B) corresponding to the first and thirdharmonics at two different magnitudes, Dg0 ¼ 0.33 and 2.00. Symbols are used todistinguish the curves and do not represent the true density of data points.

S. Strandman et al. / Polymer 53 (2012) 4800e4805 4803

harmonics with respect to the first harmonic provides a quantifi-cation of the degree of the non-linearity. The absolute value of thethird harmonic (G3) is the most intense of all the other harmonics.The intensities of the fifth (G5) and the seventh (G7) harmonics areweak and they will not be further analyzed. The ratio G3/G1 isa simple measure of the degree and type of the non-linearity.

Rheological behavior and the relaxation processes in a polymersolution depend strongly on the molar mass of the solute. Shortpolymer chains relax much faster than the long ones due to fewerentanglements, leading frequently to a Newtonian response even atlarge strains. In comparison, when a step strain is applied to thesolution of a polymer with high molar mass or high concentration(c> c*, critical overlap concentration), the initial stress is higher andthe time required for returning to the initial state is alsomuch longer.The entanglements of long polymer chains allow the sample to storeelastic energy temporarily and result in a non-linear flow behaviorthat can be quantified by LASSO. According to our earlier study, c* ofPDEAwithMn¼ 360,000 g/mol is between 5 and 10 wt-% [12]. Sincec* decreases with increasing molar mass, at 15 wt-% in solution,PDEA-600K would be well above the c* and hence, chain entangle-ments are expectedevenbelow thephase transition temperature. Onthe contrary, PDEA-16K is expected to be below its c* at 15 wt-%. Asa consequence, for the PDEA-16K solution, the modulus of the thirdharmonic (G3) representing the non-linear contribution is close tothe resolution limit of the instrument below the phase transitiontemperature (data not shown) and therefore, the focus of ourdiscussionwill be on PDEA-600K at constant concentration,15wt-%.

3.2. Effect of strain magnitude

As expected, there was a strong effect of the step strainmagnitude (Dg0) on the non-linearity of the flow. When a complex

fluid is exposed to a sudden step in strain, its response is in generalnon-linear which is represented by the 3rd and higher harmonics.As shown in Fig. 2B, at the strain magnitude Dg0 ¼ 0.33, theintensity of the third harmonic (G3) of PDEA-600K is less than 1% ofthe fundamental response (G1), indicating that the sample behavesmore or less linearly. As expected, the G1 is nearly independent ofthe strain magnitude within the error, while the intensity of thethird harmonic (G3) increases up to 17 times when the strain Dg0 isincreased from 0.33 to 2.0. Hence, the sample behaves in a morenon-linear manner at this strain magnitude and, therefore, thisstrain (Dg0 ¼ 2.0) was chosen for the further experiments.

3.3. Effect of temperature

Temperature obviously plays amajor role in the flow behavior ofthermosensitive polymers. When the sample is heated close to theLCST, random coils start to crumple, which leads to a decrease in thehydrodynamic volume of the polymer. This was confirmed bya sharp decrease both in viscosity and in loss modulus of the PDEAsolutions, which is more pronounced at low concentrations (belowc*) with fewer interchain interactions [13]. Further heating abovethe transition temperature gives compact particles (globules) thataggregate to larger particles until a colloidally stable population isobtained which may coalesce into a transient network particularlyat such high concentrations as in our work (Scheme 1B) [34].Methods such as dynamic and static light scattering have demon-strated this coileglobule transition [35e37]. The local polymerconcentration increases above the LCST due to phase separation,resulting in interconnections between aggregates of polymerchains in the concentrated phase [8] and increased viscosity [13].While at low temperatures the water molecules surrounding thepolymer are bound to it and to each other via hydrogen bonds, athigher temperatures they are released, which allows associativecontacts between the exposed hydrophobic regions [1] of the N,N-diethylacrylamide residues. PDEA does not contain a hydrogenbond donor group and it is slightly more hydrophobic than a well-known thermo-responsive polymer PNIPAM. Due to strongerinteractions between the polymer chains and their aggregates,a higher degree of non-linearity in flow is expected above the phasetransition temperature.

Fig. 3A shows that the first harmonic of the modulus, G1,increases above the LCST for PDEA-600K. The increase in G1 and G3(Fig. 3B) upon heating from 27 to 29 �C arises from increasedinterchain interactions above c* at the onset of phase transition.This can be compared to what is observed for more dilute solutionswhere a decrease in modulus occurs when temperature isincreased just at the onset of phase transition. In addition, therelaxation times increase at 31 and 33 �C and the torque does notrelax completely even after a 100-s delay time. Such long relaxationtimes, above the phase transition temperature, probably stem fromthe high fluctuating local polymer concentration, as well as fromthe extensive entangling of chains and bridging between theaggregates. According to the tube model [38], several relaxationmodes, including Rouse relaxation and reptation, exist in a singlephase concentrated polymer solution such as ours below thetransition temperature.When the polymer chain is stretched by thestep strain, it relaxes with the Rouse time followed by a slowerdisentanglement by the reptation process [31]. The situation ismuch more complex in the phase-separated state when thefollowing factors will contribute to the stress relaxation behavior aswell as the previously mentioned mechanisms: breakup, coales-cence and deformation of aggregates, existence of the bridges chainsegments between aggregates, and the interfacial tension. Ingeneral, we expect that an imposed large-magnitude strain willstretch the bridging chains and deform and break the aggregates

Fig. 3. Influence of temperature on the LASSO behavior of PDEA-600K solution atDg0 ¼ 2.00 and T ¼ 27 �C (-), 29 �C (,), 31 �C (:), and 33 �C (D): the magnitude of(A) the first harmonic G1 and (B) the third harmonic G3, as well as (C) the intensityratio G3/G1.

S. Strandman et al. / Polymer 53 (2012) 4800e48054804

[39]. The stretched bridging chains will relax more slowly thanstretched chains in a simple polymer solution due to the largehydrodynamic volumes of the aggregates to which they belong.Additionally, deformed aggregates will resume their equilibriumshape with a time determined by their size, the interfacial tension,and the viscosity of the continuous phase (here mostly watercontaining very few polymer segments). Finally the coalescence ofaggregates will occur on yet another time-scale.

At 33 �C, we note that the absolute intensity of the thirdharmonic (G3) increases at short times i.e. the slope of the plot ispositive (Fig. 3B), while a decrease would be observed for a typicalstress relaxation process. This may be due to the stretching of thebridging chains [31] and/or coalescence of aggregates brokenduring the step in strain as such a positive slope indicates a stiff-ening of the system. Because these processes are comparativelyrapid, this effect is only observed at short times, while we observethe expected decrease in G3 with time and a negative slope. Abovethe LCST, the time for complete relaxation of stress is much longerdue to higher local polymer concentration in a phase-separatedsystem, and the stronger interpolymer interactions as well as theconnections between the aggregates leading to longer relaxationtimes. This behavior is similar to that observed by Serero et al. [40]with an aqueous solution of a telechelic associative polymer under

large magnitude step strain. At a critical strain (Dg0 approximately2) the transient network breaks apart very quickly followed bya slower relaxation process. The authors attributed this behavior tothe detachment of highly stretched chains from the network at theshort time followed by the slow relaxation of the less stretchedchains still attached to the network.

Fig. 3C shows the time dependence of G3/G1 at differenttemperatures. A higher value of this ratio corresponds to a higherdegree of non-linearity. At temperatures of 27, 29 and 31 �C, thesystem is more non-linear at short relaxation times. At 33 �C thedegree of non-linearity is low at short times and increases toa plateau at longer relaxation times. The data at 29 �C have been cutat 3 s (above which the noise is prominent) in order to expand thefigure. High non-linearity at short relaxation times at thistemperature, relative to 27 �C, probably stems from the increasedlocal concentration and thus increased intermolecular interactionsprior to actual phase transition and aggregation. The lower G3/G1ratio at 31 �C and furthermore at 33 �C at short relaxation timeslikely arises from the combined effects of breakup of large aggre-gates upon shear and their re-forming during the stress relaxationprocess. At 31 �C it appears that the breakup process dominatessince we do not see the characteristic increase in G3 with relaxationtimewhich would indicate a structural evolution leading to a stiffersystem. In comparison, at 33 �C it seems that both breakup andcoalescence of the aggregates occur causing the increase in G3 withrelaxation time and the very low degree of non-linearity at shorttimes. The stretched bridging chains may enhance the reforming ofthe aggregates. We note that G3/G1 at 33 �C reaches a plateau afterapproximately 1 s indicating that the shape of the relaxation curveis the same in both the linear (G1) and non-linear (G3) components.From this we can conclude that any structural changes imparted tothe system at a strain magnitude of 2.0 have completely returned totheir original state by 1 s.

3.4. Fitting the experimental data

The relaxation curves shown in Fig. 3 corresponding to the firstand third harmonic of the modulus, G1 and G3, were fitted by theNLREG procedure [33] to Equation (1)

Gi�t� ¼

ZN

�N

Hi

�s�e�t=sdln

�s�

(1)

where s represents the relaxation time and Hi(s) the weightingfactor of the stress relaxation function of harmonic i. The resultingrelaxation time distributions are shown in Fig. 4. No meaningful fitwas obtained for the spectrum of G3 at 33 �C due to shape of thecurve shown in Fig. 3B.

At low temperatures, the processes with short relaxation timesare more important, while at high temperatures the maxima shifttowards longer relaxation times and the intensity of the weightedspectrum, sHi(s), is larger at all times. The short relaxation timebehavior (up tow1 s) at 27 and 29 �C are similar for both G1 and G3,suggesting the same origin of the linear and non-linear relaxationprocesses at this time scale and at these temperatures.We note thatthe low modulus values, especially at 27 �C, make the physicalmeaningfulness of the features of the spectra uncertain. Another,slower linear relaxation process (G1) is observed at w3 s at 27, 29and 31 �C. At 31 �C, we can distinguish two long time processes inG1 (the first atw3 s and the second atw50 s) as well as the shortertime process occurring at w0.7 s. If we consider this system abovethe phase transition temperature to be similar to an emulsion or animmiscible polymer blend then we expect 3 linear relaxationprocesses: the first due to the continuous phase (here a very dilute

Fig. 4. Weighted relaxation time spectra (sHi(s) vs. s) as fitted by the program NLREGfor G1 (A) and G3 (B) of LASSO experiments at different temperatures; 27 �C (-), 29 �C(,), 31 �C (:), and 33 �C (D). The insets show the rescaled spectra at the two lowesttemperatures.

S. Strandman et al. / Polymer 53 (2012) 4800e4805 4805

polymer solution), the second due to the chains in the dispersedphase (here a highly concentrated polymer-rich phase) and thefinal due to the shape relaxation of the dispersed phase which isdetermined by the particle size and the interfacial tension. Thenwemay attribute the relaxation peaks at w0.7, w3 and w50 s to theseprocesses, respectively, although further study may help to confirmthis.We also note that the shape of the relaxation spectrum fromG3is very different from the linear spectrum (G1) indicating differentorigins of the non-linear behavior as compared to the linearbehavior at 31 �C. At 33 �C, we find a very broad relaxation peak inG1 with a maximum at w9 s which likely represents the convolu-tion of two processes.

4. Conclusions

We have earlier shown the shear-thinning character, increasedviscosity, and gel-like properties of thermo-responsive PDEAsolutions above the phase transition temperature by standardrheological methods [13]. Here we have applied for the first timethe more sophisticated LASSO rheological experiment to study thenon-linear behavior of a concentrated PDEA solution in the courseof the phase transition at a narrow temperature range. During thephase separation, the polymer-rich phase can coalesce and forma network of entangled polymer chains, which is easily destroyedby shear force. Hence, the aggregation of PDEA could be describedthrough the formation of a transient network created by thehydrophobic interactions between the collapsed polymer chains,

yielding stronger non-linear flow effects. The non-linear behaviorof a phase-separated systemwell above the transition temperaturereflects the stretching of the bridging chains between largeraggregated domains and the coalescence of aggregates brokenduring the step in strain. The possible origins of different processesof the relaxation time spectra obtained by NLREG analysis havebeen discussed, although further studies of the highly complexsystem would be needed for more conclusive remarks. The workdemonstrates the potential of LASSO experiments and two-dimensional Fourier transform rheology in characterizing thenonlinear behavior of stimuli-responsive systems.

Acknowledgments

The financial support from the NSERC of Canada, CanadaResearch Chair, and FQRNT of Québec is greatly acknowledged. D.L.also wishes to thank DAAD of Germany for a travel grant.X.X.Z. thanks Alexander von Humboldt Stiftung for a scholarship.

References

[1] Aseyev V, Tenhu H, Winnik FM. Adv Polym Sci 2011;242:29e89.[2] Ilavsky M, Hrouz J, Ulbrich K. Polym Bull 1982;7:107e13.[3] Marchetti M, Prager S, Cussler EL. Macromolecules 1990;23:1760e5.[4] Idziak I, Avoce D, Lessard D, Gravel D, Zhu XX. Macromolecules 1999;32:

1260e3.[5] Lessard DG, Ousalem M, Zhu XX. Can J Chem 2001;79:1870e4.[6] Sun Y, Qiu Z, Hong Y. Chin J Polym Sci 1992;4:311e8.[7] Kokufuta E. Adv Polym Sci 1993;110:157e77.[8] Schild HG. Prog Polym Sci 1992;17:163e249.[9] Winter HH, Mours M. Adv Polym Sci 1997;134:165e234.

[10] Liu HY, Zhu XX. Polymer 1999;40:6985e90.[11] Plestil J, Ilavsky M, Pospisil H, Hlavata D, Ostanevich YM, Degovics G, et al.

Polymer 1993;34:4846e51.[12] Itakura M, Inomata K, Nose T. Polymer 2000;41:8681e7.[13] Lessard DG, Ousalem M, Zhu XX, Eisenberg A, Carreau PJ. J Polym Sci Part B

Polym Phys 2003;41:1627e37.[14] Eggert M, Freitag R. J Polym Sci. Part A Polym Chem 1994;32:803e13.[15] Spevacek J, Geschke D, Ilavsky M. Polymer 2001;42:463e8.[16] Spevacek J, Hanykova L, Ilavsky M. Macromol Chem Phys 2001;202:1122e9.[17] Hrouz J, Ilavsky M. Polym Bull 1989;22:271e6.[18] Wilhelm M. Macromol Mater Eng 2002;287:83e105.[19] Wilhelm M, Maring R, Spiess HW. Rheol Acta 1998;37:399e405.[20] Wilhelm M, Reinheimer P, Ortseifer M. Rheol Acta 1999;38:349e56.[21] Hyun K, Klein CO, Wilhelm M, Cho KS, Nam JG, Ahn KH, et al. Prog Polym Sci

2011;36:1697e753.[22] Van Dusschoten D, Wilhelm M. Rheol Acta 2001;40:395e9.[23] Yziquel F, Carreau PJ, Tanguy PA. Rheol Acta 1999;38:14e25.[24] Daniel C, Hamley IW, Wilhelm M, Mingvanish W. Rheol Acta 2001;40:39e48.[25] Cho J, Heuzey MC, Hamdine M. Macromol Mat Eng 2007;292:571e81.[26] Hilliou L, Wilhelm M, Yamanoi M, Gonçalves MP. Food Hydrocolloids 2009;

23:2322e30.[27] Klein C, Venema P, Sagis L, van der Linden EJ. Non-Newtonian Fluid Mech

2008;151:145e50.[28] Carrier V, Petekidis G. J Rheol 2009;53:245e73.[29] Le Grand A, Petekidis G. Rheol Acta 2008;47:579e90.[30] Koumakis N, Pamvouxoglou A, Poulos A, Petekidis G. Soft Matter 2012;8:

4271e84.[31] Van Dusschoten D, Wilhelm M, Spiess HA. J Rheol 2001;45:1319e39.[32] Wagner MH, Rolón-Garrido VH, Hyun K, Wilhelm M. J Rheol 2011;55:495e

516.[33] Honerkamp J, Weese J. Rheol Acta 1993;32:65e73.[34] Chan K, Pelton R, Zhang J. Langmuir 1999;15:4018e20.[35] Wang X, Qiu X, Wu C. Macromolecules 1998;31:2972e6.[36] Wu C, Zhou S. Macromolecules 1995;28:5388e90.[37] Okada Y, Tanaka F. Macromolecules 2005;38:4465e71.[38] De Gennes PG. J Chem Phys 1971;55:572e6.[39] Han CK, Bae YH. Polymer 1998;39:2809e14.[40] Séréro Y, Jacobsen V, Berret JF, May R. Macromolecules 2000;33:1841e7.