European Polymer Journal 47 (2011) 1300–1314

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European Polymer Journal

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Rheology of polyacrylate binders produced via catalytic chain transferpolymerization as an alternative to bitumen in road pavement materials

Gordon D. Airey a,⇑, Jasmin Wilmot b, James R.A. Grenfell a, Derek J. Irvine b,c,⇑,Ian A. Barker b,c, Jaouad El Harfi b,c

a Nottingham Transportation Engineering Centre, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdomb Department of Chemical and Environmental Engineering, Faculty of Engineering, University of Nottingham, University Park, Nottingham NG7 2RD,United Kingdomc School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

a r t i c l e i n f o

Article history:Received 13 December 2010Received in revised form 16 February 2011Accepted 1 March 2011Available online 6 March 2011

Keywords:PolymersBitumensPolyacrylatesRheologyThermal analysis

0014-3057/$ - see front matter � 2011 Elsevier Ltddoi:10.1016/j.eurpolymj.2011.03.002

⇑ Corresponding authors. Address: Nottinghamneering Centre, Pavement Research Building, UniveUniversity Park, Nottingham NG7 2RD, United Kin9513913; fax: +44 115 9513909 (G.D. Airey), tel.: +4+44 115 9514115 (D.J. Irvine).

E-mail addresses: gordon.airey@nottingham.ac.uk.irvine@nottingham.ac.uk (D.J. Irvine).

a b s t r a c t

Catalytic chain transfer polymerization has been successfully used to produce a range ofmethyl acrylate (MA) and butyl acrylate (BA) synthetic polymers of specific, targetedmolecular weights, with polydispersity index values in the range of 2–4.5. The rheologicalproperties of a subgroup of these synthetic binders consisting of four MA homo-polymersand one MA–BA co-polymer were then determined by means of oscillatory testing using adynamic shear rheometer (DSR). The rheological tests consisted of a combination of stress/strain amplitude and frequency sweeps using a standard 8 mm diameter parallel plate test-ing geometry. The rheological parameters of phase angle and complex, storage and lossmoduli were then shifted to form master curves at a reference temperature of 25 �C andisochronal plots at 0.1, 1 and 10 Hz. The rheological properties of the synthetic polymerswere also compared to those of standard road pavement bitumens. The results show thatit is possible to produce a range of synthetic polyacrylates with different rheologicalresponses by altering the reactant type, reactant concentration and polymerization condi-tions to match the rheological properties of road bitumens. All the polyacrylate bindersshowed a similar rheological profile with a unique viscoelastic response as representedby the phase angle master curves together with an upper limiting stiffness and intermedi-ate temperature/frequency ‘plateau’ region as shown in the complex modulus mastercurves. The results of the rheological examination of the binders showed that the key mate-rial property that influenced the performance of the polyacrylates in these specific applica-tion tests was glass transition temperature rather than molecular weight. Over this rangeof investigated molecular weights, it is the ratio between the two polymers which deter-mines the glass transition and as such determines the material properties. These findingssuggest that such sustainably sourced polyacrylate binders may allow for a move from pet-rochemical feed stocks to be made and allow for targeted road pavement design based onlocal climates, offering improved mechanical robustness.

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Transportation Engi-rsity of Nottingham,gdom. Tel.: +44 1154 115 9514088; fax:

k (G.D. Airey), dere-

1. Introduction

The efficient production of acrylic monomers fromrenewable resources such as lactic acid through dehydra-tion of the a-hydroxy group via acetoxylation (after con-version to the corresponding alkyl ester) provides anexciting opportunity to produce sustainable acrylic

G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314 1301

polymers on an industrial scale (see Fig. 1) and has beenthe subject of numerous patents and publications [1–6].

Previous studies have successfully shown that acrylicpolymers such as polyethyl acrylate (PEA) and polymethylacrylate (PMA) have rheological properties similar to thatof ‘soft’ (100/150 penetration grade) and ‘hard’ (10/20 pen-etration grade) road bitumens respectively and hence showpotential to provide a viable alternative to the exclusive useof fossil fuel derived bitumen in road pavement construc-tion [7,8]. These synthetic polymers, including low viscositypolybutyl acrylate (PBA), have also been successfullyblended with different bitumen grades to produce extendedbituminous binders and partially modified binders [9].

The polyacrylate binders which were investigated in theabove studies were all synthesized using atom transferradical polymerization (ATRP), a method of controlled freeradical polymerization widely used for academic and labo-ratory scale studies [10,11]. The aforementioned studies allconducted the polymerization reaction in the bulk (i.e. inthe absence of solvent) which was then quenched at a pre-defined time by diluting the resulting reaction mixturewith tetrahydrofuran. Finally the polymeric product wascollected via precipitation of this solution in hexane. Byconducting the polymerizations in this manner, isolation

Fig. 1. Two industrially viable synthetic routes to the production of n-alkyl acrylates from naturally derived lactic acid.

of polymeric materials which were used as the basis for arange of application test studies was successfully achieved.Furthermore, these tests have produced application resultsof sufficient interest that a more detailed molecular struc-ture/material property investigation has been undertaken.

ATRP allows very fine control over the polymers molec-ular weight (Mwt) and polydispersity index value (PDI)such that targeted molecular weights can be obtained witha high degree of consistency. In the previous study, ATRPwas conducted in bulk to ensure that the polymeric mate-rials isolated would have little reliance on raw materialsderived from petrochemical processes. Unfortunately, dueto the relatively intractable physical form of these low glasstransition temperature (Tg) materials, isolation of the poly-mer from un-reacted monomer necessitated the use of sol-vent in any case. Additionally, extreme increases inviscosity during the polymerization conducted in bulkcould lead to a non-efficient ATRP process. Furthermore,ATRP is currently not a commercially viable process, as itrequires considerable quantities of the metal complexeswhich result in the need for additional clean up stages forthe materials produced. Therefore, the basis of this studyis to begin a more rigorous structure/property relationshipfor these types of polyacylate binders by using a solvent toensure that the polymerization is well controlled through-out i.e. the high conversion, and thus the target structuresin terms of Mwt and PDI are obtained. A further aim wasto address the manufacture of these materials in a morecommercially viable manner. This latter target, combinedwith the fact that the initial ATRP materials produced inter-esting application results while not achieving low PDIs leadto a change in the polymerization method used for thisstudy. In this paper, catalytic chain transfer polymerization(CCTP) was chosen to produce the polyacrylate binders.This polymerization mechanism utilizes low spin cobaltcomplexes such as CoPhBF (bis-[(difluoroboryl)diphenyl-glyoximato]cobalt(II)) in ppm levels to exercise fine controlover the molecular weight of the polymer [12]. However,while ATRP can achieve PDIs in the region of 1.1 if practicedwell, CCTP will typically achieve broader molecular weightdistribution, often in region of 1.8–4.0. Furthermore, CCTPhas a great advantage over ATRP in that it has been success-fully used at full plant scale and has been commerciallyexploited in industrial processes [13–15].

This paper presents a study of the structure/propertyrelationships relating to the rheological characteristics ofa range of polyacrylate binders of specifically designedmolecular structure and composition. As such, it detailsthe development of these polymeric binders and relatestheir molecular weight and glass transition characteristicsto their rheological performance at a range of experimentalconditions relative to the rheological properties of stan-dard road bitumens. The range of materials synthesisedand tested contain examples of both homo and co-poly-mers of the chosen acrylate monomers.

2. Materials

All materials were used as purchased without furtherpurification unless otherwise stated. A total of nineteen

1302 G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314

synthetic polymers (thirteen methyl acrylate, five butylacrylate and one copolymer of methyl acrylate and butylacrylate) were produced using CCTP following the experi-mental basis outlined by Evan Roberts et al. [16]. High pur-ity methyl acrylate (MA), butyl acrylate (BA), deuteratedchloroform (CDCl3) and Toluene were purchased fromAldrich. The catalytic chain transfer agent (CTA) bis-[(diflu-oroboryl)diphenylglyoximato]cobalt(II) (CoPhBF) was sup-plied by DuPont. The free radical initiator 2,20-azobisisobutyronitrile (AIBN) was supplied by WakoChemicals USA Inc., and was recrystallized twice frommethanol prior to use.

2.1. Typical homo-polymer synthesis

The production of the MA and BA based binders fol-lowed a general procedure with only monomer type, andthe relative concentrations of the chosen monomer, CoPh-BF and AIBN being altered. As an example, the productionof material 1 (Table 1, entry 1) is presented. A 50 mL two-necked round bottomed flask equipped with a magneticstirrer bar was charged with methyl acrylate (10 mL,9.6 g, 0.11 mol), toluene (20 mL), CoPhBF (2 mg, 3.2 �10�6 mol) and AIBN (0.5 w/w%, 48 mg) prior to sealing.The flask was deoxygenated via a 15 min nitrogen spurgeand then immersed in an oil bath at 65 �C for 4 h. Yieldswere determined gravimetrically after precipitation inhexane followed by drying in a vacuum oven at 50 oC.8.2 g (85 %); 1H NMR (CDCl3, 300 MHz) at 25 �C: d = 1.4–1.6, 1.6–1.8, 1.9–2.0 (m, 2H, CH2CHC@OOCH3); 2.2–2.4(m, 1H, CH2CHC@OOCH3); 3.7 (s, 3H, CH2CHC@OOCH3);Tg (inflection) 17.5 �C; Mn = 58300, Mw = 162600, PDI = 2.8.

2.2. Typical co-polymer synthesis

A 50 mL two-necked round bottomed flask equippedwith a Schlenk tap and a magnetic stirrer bar was chargedwith methyl acrylate (7.5 mL, 7.2 g, 8.3 � 10�2 mol), butylacrylate (2.5 mL, 2.2 g, 1.75 � 10�2 mol), toluene (20 mL),CoPhBF (2 mg, 3.2 � 10�6 mol) and AIBN (0.5 w/w%,48 mg) prior to sealing. The flask was deoxygenated via a15 min nitrogen spurge and then immersed in an oil bathat 65 �C for 4 h. Co-polymer ratios were determined bylooking at the ratio of methyl groups present in the samplefrom MA and BA (3.65 and 0.94 ppm respectively). Thepolymer was recovered in the same manner as thehomo-polymer. A 77:23 MA:BA co-monomer ratio wasfound in the isolated polymer. 8.3 g (88%); 1H NMR (CDCl3,300 MHz) at 25 �C: d = 0.94 (m, 3H, CH2CHC@OOCH2CH2CH2CH3); 1.4–1.7 (m, 13.6H, CH2CHC@OOCH3,CH2CHC@OOCH2CH2CH2CH3); 2.3 (broad s, 4.3H,CH2CHC@OOCH3, CH2CHC@OOCH2CH2CH2CH3); 3.7 (s,9.8H, CH2CHC@OOCH3); 4.0–4.1 (m, 2H, CH2CHC@OOCH2CH2CH2H3); Tg (inflection) 3.9 �C; Mn = 117800,Mw = 239400, PDI = 2.0.

3. Rheological testing

The rheological properties of the synthetic polymerswere measured using a Bohlin CVOR rheometer supplied

by Malvern Instruments. Measurements were performedin a dynamic oscillatory mode using parallel plate geome-try (8 mm diameter plates with a 2 mm testing gap) and acirculating fluid temperature control system. Two types oftest were performed on the polyacrylate binders. Initially,the linear viscoelastic (LVE) stress and strain limits forthe different polyacrylate binders were determined bymeans of amplitude sweeps undertaken at 5 and 20 �C ata loading frequency of 1 Hz. The stress sweeps consistedof ramping the applied torque from its lowest level toeither its highest level or to a point where the materialhad experienced significant mechanical damage. The stresssweeps were then used to determine the limit of the LVEresponse based on the point where complex modulus(G⁄) had decreased to 95% of its initial value as prescribedby Anderson et al. [17].

Once the linearity limits were established, the syntheticpolymers were subjected to dynamic oscillatory frequencysweeps performed within the region of LVE response. Thefrequency sweep tests were performed under controlledstrain loading conditions using frequencies between 0.1to 10 Hz at 5 �C temperature intervals between 5 and60 �C at a strain level of 0.2% for the synthetic polymers.

The test samples were prepared by using a hot-pourmethod whereby the polymers were heated up to 135 �Cand then carefully poured onto the lower base plate ofthe 8 mm diameter geometry. The upper plate was thenlowered to the required testing gap of 2 mm plus an addi-tion 50 lm. Excess binder that had been squeezed out be-tween the plates was trimmed flush to the edge of theplates using a hot spatula and the gap was further closedby 50 lm to achieve the required testing gap as well as aslight bulge around the circumference of the testing geom-etry (periphery of the test specimen) [18].

The rheological properties of the binders were analyzedin terms of their complex shear modulus (G⁄), phase angle(d), storage modulus (G0) and loss modulus (G0 0) at differenttemperatures and loading frequencies. A combination ofrheological master curves at a reference temperature of25 �C, isothermal and isochronal plots, and shift factorfunctions were used to model and represent the rheologi-cal behavior of the synthetic polymers.

4. Physical/chemical characterization

4.1. Nuclear magnetic resonance (NMR)

All 1H NMR spectra were obtained in CDCl3 on a BrukerDPX-300 (300 MHz) spectrometer at 25 �C. Chemical shiftsare referenced against residual solvent signal (7.26 ppm).Analysis of the data was performed using the MestRe-Csoftware package from Mestrelab Research.

4.2. Gel permeation chromatography (GPC)

GPC was used to determine the molecular weight of thesynthetic polyacrylate binders utilising a refractive index(RI) detector with HPLC THF as the eluent. Samples wereprepared by dissolving 10 mg of polymer in 1 mL of HPLCTHF and passing them through a 0.2 lm filter in order to

Fig. 2. Typical GPC chromatogram of material 3 showing a mono-modal distribution where Mn = 37130, PDI = 3.30.

G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314 1303

remove any particulate contaminants. Analysis was per-formed at 40 �C with a flow rate of 1 mL/min throughtwo PolarGel-M columns calibrated between the range of580–377,400 Da with ten poly(styrene) narrow standards.All GPC equipment and standards were supplied by Poly-mer Laboratories (Varian Inc). GPC data was analysed usingthe Cirrus GPC Offline software package. A typical trace isshown in Fig. 2. The number average (Mn) and weight aver-age (Mw) molecular weight (Mn and Mw respectively) andPDIs of all synthetic polyacrylates are presented in Table 1.

4.3. Differential scanning calorimetry (DSC)

Glass transition temperature (Tg) points of the polymerswere determined using a Thermal Analysis TA InstrumentsQ2000 Differential Scanning Calorimeter (DSC) under anitrogen stream (50 mL min�1). Changes in heat flow wererecorded between �70 �C and 100 �C over two cycles. Ascan rate of 10 �C/min with a 10 min isotherm at eitherend of the temperature range was employed. The instru-ment was calibrated using indium metal standards sup-

Fig. 3. Change in heat flow associated with glass transition for material 3,depicting onset, inflection and offset temperatures. Measurements aretaken from the second cycle to avoid polymer memory artifacts.

plied by TA Instruments and has a quoted calorimetricprecision and reproducibility of ±0.05% and temperaturecontrol accuracy of ±0.1 �C. Analysis of the data was per-formed using Universal Analysis by TA and a series of re-peat measurements on a single polymer product showedthat the standard deviation from the mean Tg was±0.35 �C using this software. Unless otherwise stated, thesecond scan was used in order to neglect polymer process-ing history artifacts and values are representative of themean of three repeats. The DSC plot showing the onset,inflection point and the offset temperatures for bindermaterial 3 is shown in Fig. 3. Similar plots were producedfor the other synthetic polymers and the Tg’s for thesebinders are presented in Table 2.

5. Material synthesis

5.1. Binder design and synthesis

In the previous study [7], the target molecular weightfor the polyacrylate binders was set to be 35,000 Da(±3000). Thus the initial synthetic work for this paper con-centrated on achieving the same target molecular weightusing CoPhBF as the CCTP catalyst. Table 1 summarizesthe polyacrylate binders synthesized by CCTP using CoPh-BF at 65 �C in toluene by varying the concentration ofmonomer(s), CoPhBF and AIBN. The initial level of CTAagent used was 200 ppm as this has been shown to pro-duce dimer and trimer oligomers when methacrylates areadopted as the chosen monomer [19]. This experiment (Ta-ble 1 entry 1) showed that the acrylates are a monomerfamily that is less susceptible to CCTP control and a molec-ular weight of approximately 60,000 Da was achieved. Thiswas expected because the chain transfer constant (Cs) ofacrylate monomers is significantly lower than that ofmethacrylates (Cs (MA) = 0.008–0.022 � 103, Cs (BA) =0.7 � 103 and Cs (MMA) = 24–40 � 103 at 60 �C in bulkwith the methyl derivative of CoPhBF, bis-[(difluorobo-ryl)dimethylglyoximato]cobalt(II) (CoBF)) [20]. As a result,a structured series of experiments was conducted to

1304 G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314

examine the relationship between CTA concentration andmolecular weight for the two chosen acrylate monomers.Table 1 entries 1–5 define the molecular weight and PDI’srecorded as the CoPhBF concentration is increased for a setof polymerizations with a 0.5% w/w initiator loading withMA. A similar series was conducted where CoPhBF concen-tration is increased with BA. However, the resultant poly-mers from this BA study were found to exhibit physicalproperties that were inappropriate for the proposed appli-cation, more specifically their Tg’s were too low for them tobe viable as binders. Thus they have not been included inTable 1. Both series of experiments show that as the CCTagent concentration is increased, the molecular weightachieved is reduced as would be expected. However, themolecular weight reduction appears to reach a plateau,e.g. at approximately 32,000 Da, in the case of MA. It wasalso observed, that the molecular weight reduction wasnot identical for the two monomers chosen, again as a con-sequence of having differing chain transfer constants [20].The PDI’s observed were typically in the 2.5–3.5 regionwhich is characteristic of such a CCTP process and no sys-tematic reduction was recorded as the CTA agent level wasincreased. Table 1, entries 2, 6 and 7 shows that the molec-ular weights achieved are consistent over several repeatsand fall within the region of 52,000 ± 3500 Da.

The typical yield achieved in these initial experimentswas about 85%. The influence of initiator concentrationon the overall yield achieved was investigated to deter-mine if any improvement could be achieved without sig-nificantly affecting constituents of the isolated productobtained. The results of a series of experiments in whichthe initiator was introduced via a single addition at thestart of the experiment at 0.5, 1.0 and 2.0 %w/w levels forMA are shown in Table 1, entries 5, 8 and 9. These resultsshowed that a lower molecular weight material was pro-duced by increasing the initiator concentration. However,an associated PDI increase demonstrated that less controlover the polymerization was achieved. This is becausethere were two control mechanisms operating at higherAIBN levels i.e. termination occurring via both (a) CCTPchain transfer and (b) standard combination/dispropor-tionation. A further investigation involved the use of atwo-stage initiator addition where the synthetic methodwas as detailed in the experimental section but severalsmaller quantities of initiator/toluene solution were addedafter set time periods had elapsed. Table 1, entries 10 to 12detail the results from experimental repeats of entries 2, 6and 7 but using the two-stage initiator addition. The typi-cal gravimetric yield from these experiments was greaterthan 90%. However, they too exhibited multi-modal distri-butions inferring that the two competing mechanisms areboth operating under these conditions.

Finally a MA/BA co-polymer was synthesized (Table 1,entry 13) aiming to produce materials with intermediatecharacters to the homo-polymers discussed above, i.e. a re-duced, relatively low Tg coupled with a relatively highmolecular weight when compared to the homo-polymerbinders.

In summary, the key conclusions from the syntheticprogramme are that CCTP can be successfully used to pro-duce polymers of specific molecular weights with PDI’s

which are in the region of 2.5–3.5. The typical level ofCoPhBF required to achieve the target molecular weightof 35,000 Da is in the region of 800–1600 ppm for MAand 1600–3200 ppm for BA. Furthermore, for MA theachieved batch to batch molecular weight repeatability isbetter than ±3500 Da. The overall gravimetric yield canbe successfully raised by the subsequent introduction ofadditional aliquots of initiator at set time through thecourse of the reaction but this strategy results in PDI’s ofgreater than 3.5 for the product. Furthermore CCTP canbe successfully used to produce a MA/BA statistical co-polymers of a particular Tg.

5.2. Relation of molecular structure to Tg

As would be expected from literature [21–23], and dueto the relative ability of each polymer to form closelypacked chains, the difference in Tg between homo-poly-mers of MA and BA was large. The homo-BA polymers pro-duced were observed to possess Tg’s typically in the regionof �40 to �50 �C, while homo-MA polymers exhibited Tg’sin the range of 15 to 20 �C. The large range of Tg’s withineach homo-polymer set was attributed to the range ofmolecular weights synthesized, materials post productionprocessing and experimental error in the analysis as dis-cussed in the experimental section. The MA–BA co-poly-mer (Table 2, entry 5) exhibited a single Tg of 3.9 �C(277.1 K). NMR analysis confirmed that the molar ratio ofMA:BA in the isolated co-polymer was 77:23 mol% hencethe mass fraction of MA and BA within the sample was cal-culated to be 0.692 and 0.308 respectively. The averageexperimentally obtained Tg (inflection) measurements forthe isolated BA and MA homo-polymers were typically re-corded to be �45 and 17 �C respectively. The fact that theco-polymer exhibits a single Tg transition in its thermo-gram which occurs (3.9 �C) between those of the homo-polymer materials, suggests that the material produced isa true random co-polymer. As previously mentioned, thelow Tg of homo-BA polymers excluded them from furthermaterials testing with regards to assessing their suitabilityas synthetic bituminous binders. It was felt that the sam-ples would not be able to afford any of the rheologicalcharacteristics of a composite material that would mimicthose of hard or soft grade bitumens used in road pave-ment construction. Instead, as a result of the combinedassessment of the molecular weight, Tg data and samplephysical forms, a selection of homo-MA and MA–BA statis-tical co-polymer materials were considered suitable to besubjected to rheological studies (Table 2) where the rheo-logical testing primarily focused on performance differ-ences based on molecular weight and Tg. It is clear that afurther study on how the PDI affects the Tg of these polyac-rylate materials is warranted. However, as this will requirethe application of other controlled polymerization routese.g. ATRP, RAFT, etc., this falls outside of the scope of thiswork which is focused on applying the commercially viableprocess of CCTP. CCTP is not able to yield the level ofmolecular weight distribution control required for suchan exercise, however, the effects of PDI on the Tg of thematerials used in this study is the subject of ongoing work.

G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314 1305

6. Linear viscoelastic rheological characterization

6.1. Time–temperature superposition

The dynamic oscillatory data generated from the DSRfrequency sweeps were plotted in the form of isothermalcurves and shifted according to the time–temperaturesuperposition principle (TTSP) or the method of reducedvariables to produce continuous rheological master curvesfor the 4 MA based binders and MA:BA co-polymer [24]. Anexample of the process for material 8 (Table 1, entry 8) isshown in Fig. 4. The smooth, continuous nature of the mas-ter curves indicates the applicability of TTSP to the syn-thetic binders and the ‘‘thermo-rheological simplicity’’ ofthe material. The shape of the complex modulus mastercurve is reminiscent of an amorphous polymer or possiblya partially crystalline polymer [24,25]. A typical polymermelt type rubbery plateau region can be identified be-tween the reduced frequency values of approximately0.001 to 1 Hz. This intermediate plateau region is charac-terized by a plateau modulus (G0

N) which is independentof both molecular weight and temperature [26]. Due tothe thermo-rheological simplicity of the synthetic polymerbinders and the limited temperature range (5 to 60 �C),only horizontal shifting is required to produce smoothmaster curves of G⁄, G0, G0 0 and d over the extended fre-quency domain. Similar master curves were produced forthe other synthetic polymers.

6.2. Shift factors

The horizontal shifting used to produce the mastercurves is based on the equivalency between frequency(time) and temperature. The temperature dependency of

1E+04

1E+05

1E+06

1E+07

1E+08

1E+09

1E-04 1E-03 1E-02 1E-01 1E+0

Co

mp

lex

Mo

du

lus

(Pa)

Reduced Freq

Fig. 4. TTSP shifting of complex modulus isotherms to produce a continuousmaterial 8.

the rheological behavior is represented by shift factorsand expressed as:

aT ¼fr

fð1Þ

where aT is the shift factor, f is the tested frequency and fr isthe reduced frequency at an arbitrarily chosen referencetemperature, which in the case of the synthetic polymersis 25 �C.

The experimentally determined shift factors associatedwith the horizontal TTSP shifting of the rheological param-eters (G⁄, G0, G0 0 and d) for polyacrylate binders can be mod-eled using an Arrhenius equation of the following form[24]:

log aT ¼�DH

2:303R1T� 1

T0

� �� �ð2Þ

where R is the universal gas constant, DH is the flow acti-vation energy and T0 is an arbitrarily selected referencetemperature, taken to be 25 �C (298 K) in this study. If lo-gaT is plotted against the reciprocal of temperature (in K),then the activation energy for each of the binders can bedetermined from both the slope (s) and intercept (i) of alinear fit to the data using the following equations [27]:

DH ¼ 2:303Rs ð3Þ

DH ¼ 2:303RT0i ð4Þ

The viscosity of the material is proportional to exp(DH/RT) [24]. It is generally accepted that the higher the activa-tion flow energy, the higher the chain stiffness [28]. Thepolyacrylate polymers with the higher DH values shouldtherefore generally have higher G⁄ values at particulartemperatures and loading frequencies. Examples of the

0 1E+01 1E+02 1E+03 1E+04

uency (Hz)

Mastercurve 5°C

10°C 15°C

20°C 25°C

30°C 35°C

40°C 45°C

50°C 55°C

60°C

complex modulus master curve at a reference temperature of 25 �C for

1306 G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314

relationship between the experimental shift factors andthe Arrhenius equation for material 8 and the co-polymer,material 13 (Table 1, entries 8 and 13) are shown in Fig. 5a.In addition to the two polyacrylate polymers, the relation-ship between experimental shift factors and the Arrheniusequation is also presented for a standard 40/60 penbitumen.

The results in Fig. 5a show that the shift factors for theMA based polyacrylate polymers, as well as the co-poly-mer, follow the Arrhenius equation with R2 values of 0.96and 0.98 for material 8 and material 13 respectively. Thiscompares favourably with the R2 value of 0.99 for the roadbitumen. The activation energies of the five synthetic poly-mers (material 1 – 213 kJ/mol, material 3 – 171 kJ/mol,

R² = 0.9955

-4

-3

-2

-1

0

1

2

3

4

0.0029 0.003 0.0031 0.0032 0.00

Lo

g a

T

1/Temp

Material 8

Material 13

40/60 pen

Linear (Material 8)

Linear (Material 13)

Linear (40/60 pen)

R² = 0.9988

0

2

4

6

8

10

12

14

16

18

20

-30 -20 -10 0

(T -

T0)/

Lo

g a

T

T - T

Material 8

Material 13

40/60 pen

Linear (Material 8)

Linear (Material 13)

Linear (40/60 pen)

Fig. 5. Horizontal shift factors modeled for materials 8 and 13 as well as 40/60 ptemperature difference in terms of the WLF equation in (b).

material 6 – 207 kJ/mol, material 8 – 183 kJ/mol and mate-rial 13 – 146 kJ/mol) were found to be weakly correlatedwith Tg (increasing) but had no correlation with Mwt orPDI.

It is also possible to model the experimentally deter-mined shift factors using a Williams Landel Ferry (WLF)equation [29]:

log aT ¼ �c0

1ðT � T0Þc0

2 þ T � T0ð5Þ

where c01 and c0

2 are empirically fitted parameters, T is tem-perature and T0 is the reference temperature of 25 �C.Equation (5) can be rearranged into a linear form as shownin Equation (6) and depicted in Fig. 5b for material 8 and

R² = 0.9558

R² = 0.9755

33 0.0034 0.0035 0.0036 0.0037

erature (°°K)

R² = 0.9929

R² = 0.9534

10 20 30 40

0 (°C)

en bitumen using an Arrhenius equation in (a) and as a relationship with

G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314 1307

material 13 (Table 1 entries 8 and 13), as well as for the 40/60 pen road bitumen:

� T � T0

log aT¼ c0

2

c01

þ 1c0

1

ðT � T0Þ ð6Þ

The constants c01 and c0

2 can then be calculated with respectto the reference temperature from the slope and interceptof the straight line described in Equation (6) as follows:

c01 ¼�1s

ð7Þ

and

c02 ¼

is

ð8Þ

As would be expected from literature [24], the results inFig. 5b show an improved fit for the WLF equation (R2 val-ues of 0.99 and 1.00 for the polymeric materials 8 and 13respectively) compared to that found for the Arrheniusequation but a reduced fit (R2 of 0.95) for the 40/60 penbitumen. The accuracy of the Arrhenius and WLF equationsrelative to the experimentally determined shift factors formaterial 8 is shown in Fig. 6 where the WLF equation pro-vides a far superior fit to the experimental shift factor datacompared to the Arrhenius equation. This behavior differsfrom that generally found for petroleum bitumens wheretwo fits are usually needed due to the thermo-rheologicalcomplexity and bimodal rheology of bitumen [30]. For bitu-men, the WLF equation is preferred at temperatures abovethe Tg of the binder, while the Arrhenius equation is moreapplicable at temperatures below Tg and at high tempera-tures in the Newtonian region of rheological behavior [31].

-4

-3

-2

-1

0

1

2

3

4

0 10 20 30

Lo

g a

T

Tempe

Fig. 6. WLF and Arrhenius equation fits of experimentally de

6.3. Time dependency

The time dependency of the synthetic binders is shownin the form of master curves of complex modulus andphase angle in Fig. 7 and 8 together with the rheologicalproperties of a ‘soft’ (160/220 pen), ‘intermediate’ (40/60pen) and ‘hard’ (10/20 pen) bitumen.

The TTSP complex modulus master curves show thesame rheological profile for all the MA polymers with G⁄

approaching a upper limiting value at high frequenciesand demonstrating a distinctive plateau region at interme-diate to low frequencies. Although the plateau region is notinvariant with reduced frequency (faT), a value of the pla-teau modulus (G0

N) can be approximated by taking an aver-age of the upper and lower limits at either end of thenominally linear region in Fig. 7. The upper and lower lim-its for all four MA polymers are the same irrespective of themolecular weight of the MA based polyacrylate polymers:1.5 � 105 Pa < G0

N < 6 � 105 Pa. The co-polymer (material13) again has a distinctive plateau region but overall thestiffness of the material is lower than that of the group offour MA polymers: 8 � 104 Pa < G0

N < 3 � 105 Pa. The inter-mediate plateau region sits between two distinct regionscorresponding to a high frequency (or transition) regionand a low frequency (or terminal) region. The high fre-quency region can be clearly identified in Fig. 7, althoughonly a small portion of the terminal region can be seendue to the DSR testing being limited to an upper tempera-ture of 60 �C and a lower frequency value of 0.1 Hz. Rheo-logical data for polybutyl acrylate, polyethyl acrylate andpolymethyl acrylate, covering the two distinct terminaland transition regions as well as the intermediate plateauregion, can be found in previous studies [7,8,26].

In terms of a comparison with the standard penetrationgrade bitumens, Fig. 7 shows that the MA homo-polymers

40 50 60 70

rature (°°C)

Experimental Shift Factors

WLF Equation

Arrhenuis Equation

termined shift factors for material 8 synthetic binder.

1E+04

1E+05

1E+06

1E+07

1E+08

1E+09

1E-04 1E-03 1E-02 1E-01 1E+00 1E+01 1E+02 1E+03 1E+04

Co

mp

lex

Mo

du

lus

(Pa)

Reduced Frequency (Hz)

Material 1

Material 3

Material 6

Material 8

Material 13

160/220 pen bitumen

10/20 pen bitumen

40/60 pen bitumen

Fig. 7. TTSP complex modulus master curves of polyacrylate synthetic binders together with ‘hard’, ‘intermediate’ and ‘soft’ bitumen at a referencetemperature of 25 �C.

10

20

30

40

50

60

70

80

90

1E-05 1E-04 1E-03 1E-02 1E-01 1E+00 1E+01 1E+02 1E+03 1E+04 1E+05

Ph

ase

An

gle

(d

egre

es)

Reduced Frequency (Hz)

Material 1

Material 3

Material 6

Material 8

Material 13

160/220 penbitumen

10/20 pen bitumen

40/60 penbitumen

Fig. 8. TTSP phase angle master curves of polyacrylate synthetic binders together with ‘hard’, ‘intermediate’ and ‘soft’ bitumen at a reference temperature of25 �C.

1308 G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314

are approximately equivalent to the ‘hard’ and ‘intermedi-ate’ bitumens, while the co-polymer is closer to the ‘soft’bitumen.

The viscoelastic response of all five polymers (as repre-sented by the d master curves in Fig. 8) all show a doubletransition from increasing elastic response at low to inter-mediate frequencies, followed by an increase in viscous re-sponse from intermediate to high frequencies and then a

further switch to increasing elastic response at high fre-quencies. This viscoelastic response differs from the rela-tively simple response associated with road bitumens,which consists of a continuous transition from viscous re-sponse at low frequencies to elastic response at high fre-quencies. The complex modulus and phase angle mastercurves for the MA polymers show a general increase inG⁄ (vertical translation at constant frequency or horizontal

1E+04

1E+05

1E+06

1E+07

1E+08

1E+09

-20 30 80 130 180

Co

mp

lex

Mo

du

lus

(Pa)

0.1 Hz

1 Hz

10 Hz

10

20

30

40

50

60

70

80

90

-20 30 80 130 180

Ph

ase

An

gle

(d

egre

es)

Temperature (°°C)

Temperature (°C)

0.1 Hz

1 Hz

10 Hz

0.1 Hz

1 Hz

10 Hz

Fig. 9. TTSP extended (a) complex modulus and (b) phase angle isochronal plots at 0.1, 1, and 10 Hz together with isolated experimental data points at 1 Hzof material 8 synthetic binder.

G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314 1309

translation to lower frequencies) and a related horizontaltranslation of d to lower frequencies with increasingmolecular weight. This trend can also be related to the flowactivation energy [28]. It is important to note that the rhe-ological correlation with Mwt would not apply across acry-late types and that DH and/or Tg would probably be abetter indicator of rheological response when all five poly-mers are considered [8].

Although the rheological profiles of the synthetic poly-mers are similar, there is a distinct difference between theposition of the complex modulus and phase angle mastercurves of the four pure MA based synthetic polymers com-pared to the MA:BA co-polymer. In general, material 13demonstrated a ‘softer’ more viscous behavior as shownby a lower complex modulus master curve in Fig. 7 andthe position of the phase angle master curve to the rightof the other four master curves in Fig. 8. This rheological

behavior is expected due to the presence of the lower vis-cosity butyl acrylate (23%) in the co-polymer (material 13).This ‘softer’ rheological behavior was also confirmed by thelower values of DH and Tg for material 13.

6.4. Temperature dependency

It is arguably more desirable to relate the physical andphysicochemical properties of the synthetic polymers totheir rheological properties as a function of temperaturerather than frequency (or time). This can be accomplishedby transposing the time dependent rheological data totemperature dependent data using the master curves andshift factor functions. To undertake this task, the WLFequation with fitted c0

1 and c02 constants for each of the rhe-

ological parameters (G⁄, d, G0 and G0 0) was used togetherwith the 25 �C reference temperature master curves to

1310 G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314

generate extended isochronal plots at three loading fre-quencies of 0.1, 1 and 10 Hz. Examples of the extendedcomplex modulus and phase angle isochronal plots areshown in Fig. 9a and b for material 8. It is important to notethat with the use of TTSP and the fitted WLF equations, therheological data points are not extrapolated outside themeasured data obtained from the dynamic oscillatory tem-perature-frequency tests. Experimental data points takenfrom each of the test temperatures at a frequency of 1 Hz

1E+04

1E+05

1E+06

1E+07

1E+08

1E+09

-20 0 20 40

Co

mp

lex

Mo

du

lus

(Pa)

Tempe

Fig. 10. Predicted complex modulus isochronal plots at

10

20

30

40

50

60

70

80

-20 0 20 40

Ph

ase

An

gle

(d

egre

es)

Tempe

Fig. 11. Predicted phase angle isochronal plots at 1 H

have been included in Fig. 9a and b to confirm the validityof the calculation procedure.

The rheological properties of the five polyacrylatesynthetic binders in terms of complex modulus and phaseangle isochronal plots at a frequency of 1 Hz are shown inFigs. 10 and 11.

The range of temperatures for the five polymers differfrom each other due to the procedure used to predict theisochrones but generally cover the temperature range from

60 80 100 120

rature (°°C)

Material 1

Material 3

Material 6

Material 8

Material 13

1 Hz for different polyacrylate synthetic binders.

60 80 100 120

rature (°C)

Material 1

Material 3

Material 6

Material 8

Material 13

z for different polyacrylate synthetic binders.

G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314 1311

approximately 0 �C to 90 �C. As already seen in Fig. 7 and 8,the isochronal plots in Fig. 10 and 11 show a distinct sep-aration of the rheological behavior of the four MA basedpolymers compared to the softer MA:BA co-polymer.Although only the temperature dependent rheological dataat 1 Hz has been shown, similar plots were produced at 0.1and 10 Hz with the rheological data simply being trans-lated to lower and higher temperatures as illustrated inFigs. 9a and b.

7. Rheological indices

Parameters taken from the temperature dependent rhe-ological curves produced at different frequencies (0.1, 1and 10 Hz) were used in an attempt to relate the rheologyof the synthetic polymers to their physical and physico-chemical properties. A total of fifteen rheological indiceswere defined from the phase angle, storage and loss mod-ulus isochrones as depicted in Fig. 12. Some of these indi-ces have fundamental rheological meaning while otherscan be considered to be simply empirical in nature. Therheological indices are grouped into temperatures relatingto particular rheological responses (e.g. balance of elasticand viscous response corresponding to TG 0=G0 0 and Td =45�)and the magnitude of the rheological parameters (e.g.G0 0peak and dpeak). As the rheological properties and there-fore the indices are frequency (time) dependent as wellas temperature dependent, the indices have been deter-mined for the binders at 0.1, 1, and 10 Hz but for brevityhave only been presented in Table 3 at a loading frequencyof 1 Hz. In addition to the rheological indices, the molecu-lar weights, activation energies and glass transition tem-peratures have also been included in Table 3.

1E+04

1E+05

1E+06

1E+07

1E+08

1E+09

-10 0 10 20 30

Sto

rag

e/L

oss

Mo

du

lus

(Pa)

Tempe

Tδ=45° Tδ=45°

δTδpeak

TG′=G′′

TG′′peak

G′′G′=G′

′

G′′G′=G′

′TG′=G′′

G′′peak

Fig. 12. Rheological parameters from phase angle, storage and

7.1. Rheological relationship with glass transition

The glass transition temperature can be considered tocorrespond to the rheological testing conditions (tempera-ture and loading frequency) where G0 0 is a maximum (peak)[25,32]. It is important to note that Tg defined in this man-ner is strongly dependent on testing frequency with an in-crease in Tg with increasing frequency. Similar effects canbe observed in calorimetric experiments as a function ofheating and cooling rates with an increase in Tg withincreasing heating rate.

However, no relationship between TG 0 0peak and Tg wasfound, which may be partly attributed to the narrow rangeof the two sets of data (TG0 0peak between 3 and 9 �C, Tg be-tween 14 and 18 �C) as well as the frequency of 1 Hz usedto define the rheological index. In addition, no TG 0 0peak in-dex was determined for the co-polymer as this would haverequired DSR testing below 5 �C. It is possibly that a TG 0 0peak

value together with the Tg of 4 �C for material 13 wouldhave improved the correlation.

Another rheological index that may be correlated withTg is the temperature at the peak phase angle (Tdpeak).This parameter did include a value for material 13 anda correlation showing increasing Tg with increasing Tdpeak.Other correlations with increasing Tg were found for thetemperatures related to increasing values of TG 0=G0 0 orTd=45�.

7.2. Rheological relationship with molecular weight

An increase in molecular weight can be considered torelate to an increase in stiffness and elastic response in arheological material. Various rheological indices definedin Fig. 12 can be considered indicative of increased stiff-

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

40 50 60 70

Ph

ase

An

gle

(d

egre

es)

rature (°C)

Storage Modulus

Loss Modulus

Phase Angle

Tδ=45°

peak

Tδtrough

δtrough

G′′G′=G′′TG′=G′′

loss modulus isochronal plots at 0.1 Hz for material 8.

Table 1Reactant type, reactant concentration and GPC molecular weight data for the target polyacrylate binders.

Material/entry ref. Acrylate type Acrylate conc. (%) CoPhBFa (ppm) AIBNb (w/w%) Mnc (g mol�1) PDId

1 MA 100 200 0.5 58,300 2.82 MA 100 400 0.5 55900 2.43 MA 100 800 0.5 37100 3.34 MA 100 1600 0.5 32100 3.25 MA 100 3200 0.5 32500 3.06 MA 100 400 0.5 49900 2.57 MA 100 400 0.5 49300 2.98 MA 100 3200 1.0 25900 3.49 MA 100 3200 2.0 11500 4.6

10 MA 100 400 2 � 0.5e 38900 3.111 MA 100 400 2 � 0.5e 38800 3.012 MA 100 400 2 � 0.5e 41400 2.913 MA:BA 77:23 400 0.5 117,800 2.0

a Catalytic chain transfer agent (CTA).b Initiator.c Number average molecular weight from GPC 120.d Polydispersity from GPC 120.e Second 0.5 w/w% shot of AIBN added after two hours.

Table 2Glass transition temperatures of polyacrylates from DSC analysis.

Table entry Material ref. Mn (g mol�1) On-set Tg (�C) Inflection Tg (�C) End-set Tg (�C)

1 1 58,300 14.1 17.5 18.12 3 37,100 14.7 17.8 19.53 6 49,900 10.9 14.8 16.74 8 25,900 14.9 17.5 19.65 13 117,800 0.6 3.9 5.1

Table 3Rheological parameters for synthetic binders at 1 Hz as determined by DMA.

Parameter Material 1 Material 3 Material 6 Material 8 Material 13MA MA MA MA Co-polymer

TG0 0peak (�C) 8 3 9 5 –G0 0peak (MPa) 100 100 100 100 –TG0=G0 0 (�C)a 11 4 12 7 –G0 0G0=G0 0 (MPa)a 80 90 80 90 –Td=45� (�C)b 12 4 12 7 –TG0=G0 0 (�C)c 29 22 30 25 15G0 0G0=G0 0 (MPa)c 600 600 700 600 300Td=45� (�C)d 29 23 30 26 15TG0=G0 0 (�C)e – – – 91 94

G0 0G0=G0 0 (MPa)e – – – 40 25Td=45� (�C)f – – – 91 –Tdpeak (�C) 19 12 18 14 5dpeak (�) 69 72 74 71 72Tdtrough (�C) 51 45 54 45 37dtrough (�) 22 22 22 27 19Mn (gmol�1) 58,300 37,100 49,900 25,900 117,800DH (kJmol�1) 213 171 207 183 146Tg (�C) 17 18 15 17 4

a Low temperatures.b Increasing phase angles with temperature (low temperatures).c Intermediate temperatures.d Decreasing phase angles with temperature.e High temperatures.f Increasing phase angles with temperature (high temperatures).

1312 G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314

ness and elastic response (e.g. the temperature(s) at whichG0=G0 0 (TG0=G0 0 or Td=45�) or the magnitude(s) of G0 0 whereG0=G0 0 (G 0 0G0=G0 0)). There is some correlation of TG0=G0 0 with

Mwt for the four MA polymers but as mentioned previ-ously the correlation does not hold when the MA:BA co-polymer is added to the data set.

G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314 1313

7.3. Rheological relationship with activation energy

Finally, the rheological indices used for both Tg and Mwtcan be used to establish a relationship with DH. Althoughnot one of the physical or physicochemical propertieslisted in Tables 1 and 2, DH does provide a physicochemi-cal representation of the link between the rheological(flow) behavior of the material, external influences (tem-perature) and the physical and chemical structure of thepolymer. The correlations between DH and indices suchas TG 0=G0 0, Td=45� and Tdpeak are excellent with increases inactivation energy being associated with increases in thesetemperature indices.

8. Conclusions

A range of polymethyl acrylate and polybutyl acrylatesynthetic binders which targeted Mwts and PDIs withinan acceptable range (2–4.5) have been successfully pro-duced using CCTP processing, a more industrially viableprocess compared to ATRP. The synthetic polymers bindershave been produced by varying the acrylate type, composi-tion (monomer ratio in co-polymer), quantity of CoPhBFand percentage of AIBN initiator. This has resulted in arange of polyacrylate binders having different molecularweights, PDIs and glass transition temperatures.

A subset of four PMA and one PMA-co-PBA syntheticbinders were selected from the original nineteen polymerssynthesized for detailed rheological evaluation and charac-terization. PBA synthetic binders were not included in therheological study due to their low Tg values and physicalform (low viscosity elastomers). The rheological testingof the synthetic polymers was undertaken by means ofoscillatory shear tests using a DSR together with a parallelplate testing geometry within the LVE response of thepolymers. Testing was performed over a range of tempera-tures and loading frequencies and the rheological data ana-lyzed using a combination of data shifting techniques andparameter plots.

The synthetic polymers tested were all found to be ther-mo-rheologically simple and demonstrated an equivalencybetween temperature and time (frequency) in terms oftheir rheological data. In addition, the rheological responseof the synthetic binders was found to cover the rheologicalproperties generally associated with ‘hard’, ‘intermediate’and ‘soft’ paving grade bitumens. Using TTSP, both anArrhenius equation and a WLF function were found toaccurately model the temperature dependence of the syn-thetic polymers allowing the flow activation energy of thepolymers to be determined as well the rheological data tobe transposed to the temperature domain.

The extended isochronal plots for the rheologicalparameters of d, G0 and G0 0 were used to define a numberof rheological indices that were then used to establish cor-relations with the physical and physicochemical propertiesof the polyacrylate subset. For the entire data set, consist-ing of the four MA polymers as well as the MA:BA co-poly-mer, the key material property that influenced therheological properties of the polyacrylates was glass tran-sition temperature. Additionally, there was some indica-

tion of a minor trend between some of the rheologicalindices and molecular weight. However, this was limitedto the four MA polymers and was manifest in the observa-tion that higher values of Mwt corresponded to increasedstiffness and elastic response.

Polyacrylate binders produced from sustainable sourcesfor use in road pavement manufacture provides an excitingopportunity to provide new composite materials withoutreliance on petrochemical feed stocks. Furthermore, thecorrect binder for a geographical region/climate can beeasily designed based upon Tg prediction and the knowl-edge of the ideal Tg from application tests. The wide scopefor structural changes to be implemented into these mate-rials means manufacturing a potential binder with signifi-cantly improved mechanical performance is a realpossibility. In addition, since there is only a minor relation-ship between materials performance as a bituminous bin-der and Mwt, the production of very high Mwt polymers(which are often favoured as they generally offer enhancedmechanical performance) should not affect the ability ofthe polyacrylate to act as a binder. The use of these mate-rials in enhancing road pavement robustness is the subjectof further large scale composite tests.

Acknowledgements

The authors acknowledge the support of the DICE initia-tive and the EPSRC for this project. The authors wish tothank Davide De Focatiis (The University of Nottingham)for his useful discussion on this work.

References

[1] Lilga MA, Werpy TA, Holladay JE. Preparation of an alpha, beta-unsaturated acids/esters e.g. acrylates useful in production of varietyof polymer materials, plastics, involves esterifying a carboxylic acidwith an alpha-hydroxy acid/ester. Lilga MA; Werpy TA; Holladay JE;Battelle Memorial Inst.

[2] Filachione EM, Lengel JH, Fisher CH. Ind Eng Chem 1945;37(4):388–90.

[3] Werpy TA, Lilga MA. Production of an acrylate by isolating acomposition comprising an ester compound and subsequentlyheating the composition. Battelle Memorial Inst (Batt).

[4] Alas M, Bouniot A, Redien P. Process for the preparation of opticallypure esters of lactic acid. 1988. p. 7.

[5] Kim J-H, Han J-Y, Lee S-W. Kongop Hwahak 2005;16(2):243–9.[6] Hottois D, Bruneau A, Bogaert J-C, Coszach P. Manufacture of lactic

acid esters. 2010. p. 23.[7] Airey GD, Mohammed MH, Fichter C. Fuel 2008;87(10–11):1763–75.[8] Airey GD, Mohammed MH. Rheologica Acta 2008;47(7):751–63.[9] Airey G, Mohammed M, Collop AC, Hayes CJ, Parry T. Road Materials

and Pavement Design 2008;9:13–35.[10] Kato M, Kamigaito M, Sawamoto M, Higashimura T. Macromolecules

1995;28(5):1721–3.[11] Wang JS, Matyjaszewski K. J Am Chem Soc 1995;117(20):5614–5.[12] Gridnev AA, Ittel SD. Chem Rev 2001;101(12):3611–59.[13] Wilfordbrown JH, Kirtley N, Irvine DJ, Wilford-Brown JH. Fully

recyclable sinks, bath tubs or shower bases|by supplying to spraymixing zone aqueous dispersion of benzoyl or lauryl peroxide, andpolymethacrylate in curable methacrylate coating. Imperial ChemInd Plc.

[14] Lynch JP, Irvine DJ, Beverly GM. Thermo-formable cast methylmethacrylate! polymer sheet|comprises syrup solution ofpolymethacrylate in curable monomeric methacrylate, curinginitiators, and cobalt chelate catalytic chain transfer agent.Imperial Chem Ind Plc; Ineos Acrylics UK Ltd.

[15] Beverly GM, Irvine DJ, Lynch JP. Composite extruded plasticfilm|comprising an acrylic polymer and strips of a plastic materialembedded with the acrylic polymer. Imperial Chem Ind Plc.

1314 G.D. Airey et al. / European Polymer Journal 47 (2011) 1300–1314

[16] Roberts GE, Heuts JPA, Davis TP. Macromolecules2000;33(21):7765–8.

[17] Anderson DA, Christensen DW, Bahia HU, Dongre R, Sharma MG,Antle CE, Button J. Binder Characterisation, 1994.

[18] Airey GD, Hunter AE. Proc Inst of Civil Engineers-Transport2003;156(2):85–92.

[19] Haddleton DM, Topping C, Kukulj D, Irvine D. Polymer1998;39(14):3119–28.

[20] Heuts JPA, Roberts GE, Biasutti JD. Aust J Chem 2002;55(6–7):381–98.

[21] Lendlein A, Schmidt AM, Langer R. Proc Natl Acad Sci USA2001;98(3):842–7.

[22] Ma QG, Wooley KL. Journal of Polymer Science Part a-PolymerChemistry 2000;38:4805–20.

[23] Ahn D, Shull KR. Langmuir 1998;14(13):3637–45.[24] Ferry JD. Viscoelastic properties of polymers. New York, 1980.

[25] Mezger TG. The Rheology Handbook: For rotational and oscillatoryrheometers. Hannover, 2002.

[26] Ahmad NM, Lovell PA, Underwood SM. Viscoelastic properties ofbranched polyacrylate melts. Polym Int 2001;50:625–34.

[27] Daga VK, Wagner NJ. Rheologica Acta 2006;45(6):813–24.[28] McKee MG, Unal S, Wilkes GL, Long TE. Branched polyesters: recent

advances in synthesis and performance. Prog Polym Sci2005;30:507–39.

[29] Williams ML, Landel RF, Ferry JD. J Am Chem Soc1955;77(14):3701–7.

[30] Lesueur D. On the thermorheological complexity and relaxationmodes of asphalt cements. J Rheol 1999;43:1701–4.

[31] Anderson DA, Christensen DW, Bahia HU. Associated Asphalt Tech1991;60:437–532.

[32] Kriz P, Stastna J, Zanzotto L. Road Materials and Pavement Design2008;9:37–65.