Rheological Evidence of Physical Cross-Links and Their Impact inModified PolypropyleneYan Li,‡,§,∥ Zhen Yao,*,‡ Zhen-hua Chen,§,∥ Shao-long Qiu,‡ Changchun Zeng,*,§,∥ and Kun Cao*,†,‡

†State Key Laboratory of Chemical Engineering and ‡Institute of Polymerization and Polymer Engineering, Department of Chemicaland Biological Engineering, Zhejiang University, Hangzhou 310027, China§High Performance Materials Institute, Florida State University, Tallahassee, Florida 32310, United States∥Department of Industrial and Manufacturing Engineering, FAMU−FSU College of Engineering, Tallahassee, Florida 32310, UnitedStates

ABSTRACT: This paper reports our investigation of the existence of physical cross-links in modified polypropylenes (PPs)containing long chain branches (LCBPPs) or amine moiety (PP-g-NH2). By varying the stoichiometric ratio of maleic anhydridegrafted polypropylene (PP-g-MAH) and ethylenediamine (EDA), a series of modified PPs with different degrees of branchingand side-group polarities were prepared. Extensive rheological studies were conducted after baseline characterization of thechemical and molecular structures of these materials using Fourier transform infrared (FTIR) spectroscopy and size exclusionchromatography (SEC), respectively. The results strongly suggest the presence of physical cross-links in a majority of thematerials studies herein, which significantly impacts their rheological behaviors. The physical cross-links can be argued to be inthe form of phase-separated domains and hydrogen bonding, which has been reported in the literature.

1. INTRODUCTION

Isotactic polypropylene (iPP) is one of the leading and fastest-growing polyolefins because of its attractive properties, such ashigh melting point, low density, excellent chemical resistance,and high tensile strength.1 However, linear PPs possess lowmelt strength, which limits their use in processes involvingsubstantial elongational flow such as thermoforming, filmblowing, extrusion coating, blow molding, and foaming.1,2

Introducing long chain branching (LCB) into the molecularstructure of PP, through either in-reactor polymerization orpostreactor treatment, has proven effective to overcome thisshortcoming.2−11 Among the approaches for LCB introduction,reactive coupling of PP chains by small linker molecules11,12 isadvantageous in several aspects, e.g., easy implementation andflexibility in controlling the branching structure.13−16 Takingadvantage of the high reactivity of the imidization reaction, anumber of research groups prepared long chain branched PPs(LCBPPs) using amine and maleic anhydride grafted PP (PP-g-MAH).6−11 By varying the NH2/MAH ratio R, the structure ofthe PPs, e.g., molecular weight, branching degree, and densityof the function groups, can be tailored.6,9,17

Aside from the topological change, the imidization reactionmay also alter the local polarity within the molecules as a resultof the incorporation of high polarity linkages. The disparity inpolarity may lead to phase separation, and the phase-separateddomains may serve as physical cross-links leading to potentiallysignificant changes of mechanical and rheological properties ofthese materials. To the best of our knowledge, these issues havenot been discussed in the literature, although physical cross-links have been observed in several polymers containing highlypolar groups, e.g. hydroxyl,18,19 carboxyl,20−22 anhydride,23,24

and ionic groups,25 and the influences of such structures werewell documented. More recently, formation of inhomogeneityor microphase separation by grafting a polar monomer

(pentaerythritol triacrylate, PETA) onto another polymer,e.g., polylactic acid (PLA), had also been reported. Althoughnot directly justified from rheology, its influence oncrystallization suggests the existence of inhomogeneity.26

In this work, we set out to investigate the possible presenceof the phase-separated structures in the modified PPs, theirformation, and their impact on rheological properties. Theemployed samples were a series of LCBPPs prepared bysupercritical carbon dioxide (scCO2) assisted reactive extrusionof PP-g-MAH and ethylenediamine with varying ratios forcontrolling the extent of reaction and degradation,15 and anamine grafted polypropylene (PP-g-NH2) prepared via asolution process.27 The study was divided into two sections:(i) detailed structural characterizations were conducted toexamine the major differences between the modified samples(molecular weight, molecular weight distribution, gel content,etc.), which form the basis to deconvolute various factors wheninterpreting the rheological response of these materials; (ii)both linear and nonlinear shear rheometry and extensionrheometry were then conducted, and the results stronglysuggest that the rheological behavior of the modified PPs canbe affected by both long chain branches (LCBs) and physicalcross-links present.

2. EXPERIMENTAL SECTION2.1. Materials. PP-g-MAH (MAH content, 0.3 wt %) was

from Ningbo Nengzhiguang New Material Co., Ltd., China.Ethylenediamine (EDA) was purchased from HangzhouChangqing Chemical Reagent Co., Ltd., China. 1,2,4-

Received: March 12, 2013Revised: April 18, 2013Accepted: May 15, 2013Published: May 15, 2013

Article

pubs.acs.org/IECR

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Trichlorobenzene (TCB) and 2,6-di-tert-butyl-4-methylphenol(BHT) were purchased from Acros.2.2. Sample Preparation. The LCBPPs were prepared via

reactive extrusion assisted by scCO2, using a custom-designedcoextrusion twin screw extruder (D = 20 mm; L/D = 48)operated at 180 °C and 150 rpm.15 Table 1 shows the

formulations and process parameters for preparing theLCBPPs. First, PP-g-MAH raw material was vacuum-dried at80 °C for at least 12 h to remove the residual ungrafted MAHbefore use. Then PP-g-MAH was fed from the screw feeder. Ata feed rate of 70 g/min, the residence time was about 3 min.Two independent piston pump injection systems were used forthe delivery of EDA and CO2. The delivery pressure and ratecould be controlled separately. The extrudate was cooled in awater bath and pelletized.Amine grafted PP (PP-g-NH2) was synthesized using a

solution process. In a typical process, 40 g of PP-g-MAH wasdissolved in 1500 g of xylene at 130 °C. Subsequently, a 10-foldexcess of EDA was added and the mixture was stirred for atleast 6 h. After the imidization reaction, the product wasprecipitated in acetone and washed with a large amount ofethanol to remove the unreacted EDA. The samples were thendried at 80 °C under vacuum for 18 h.2.3. Structural Characterization. 2.3.1. Gel Content

Determination. The gel contents of the PP-g-MAH andmodified samples were determined following ASTM D2765-84using boiling xylene as the extraction solvent. All samples had agel content value of zero.2.3.2. Size-Exclusion Chromatography (SEC). Size exclusion

chromatography (SEC; Viscotek 350A, Vicotek Ltd.) wasperformed at 150 °C using a TSK-gel column (GMHHR-H(S)HT, 300 × 7.8 mm). The SEC was equipped with a tripledetection system: a refractive index detector, a four-capillarydifferential viscometer detector, and a light scattering detector.PP-g-MAH and modified samples were dissolved in TCBstabilized with 5 × 10−4 g mL−1 BHT at 150 °C for 4 h prior toanalysis.

2.3.3. Fourier Transform Infrared (FTIR) Spectroscopy.FTIR spectroscopy (Nicolet 5700, Thermo Ltd.) wasperformed in a spectral range from 400 to 4000 cm−1 at aresolution of 2 cm−1. Data were collected as an average of 32scans.

2.4. Rheological Characterization. 2.4.1. Shear Rheol-ogy. Shear rheological measurements were conducted on astress-controlled rotational rheometer (Rheostress 6000,ThermoHaake Co.) in a nitrogen environment using 20-mm-diameter parallel plates with a gap of 1 mm. Testing specimenswere prepared by compression molding at 180 °C.Small amplitude oscillatory measurements were carried out at

180−220 °C with a frequency range from 0.1 to 628 rad/s. Asmall strain amplitude (1%) was used to ensure thatmeasurements were done in the linear viscoelastic (LVE)regime.Creep tests were performed at 180 °C following Gabriel.28

Small shear stresses between 2 and 5 Pa should be adopted towarrant linear viscoelastic response. At a sufficiently long time(2500−4000 s), the deformation rate approaches steady stateand the zero shear viscosity can be determined according to

η =→∞

tJ t

lim( )t0 (1)

in which J(t) is the compliance of samples.Stress relaxation was measured at 180 °C under a series of

step strains (γ = 0.3−6). System response time was less than 0.1s in all measurements. Corrections were made followingStadler29 to take into account the nonuniform sampledeformation in parallel plate geometry. The damping functionh(γ) was quantified using the following equation:

γ γ λ= >h G t G t t( ) ( , )/ ( ) ( )K (2)

where G(γ,t) is the relaxation modulus at a particular strain.G(t) is the equilibrium modulus, which is the relaxationmodulus in the linear regime at time greater than aexperimentally determined critical value λK.

30 In our study allsamples exhibited linear viscoelasticity when γ < 0.5, and G(t)(γ = 0.3) was considered as the equilibrium modulus.

2.4.2. Uniaxial Extensional Rheology. The uniaxial exten-sional viscosity was measured using a MARS III rheometer(ThermoHaake Co.) equipped with a Sentmanat extensionalrheometer (SER) universal testing platform (Model SER-HV-H01, Xpansion Instruments). The system has been discussed indetail.31,32 Constant strain rate experiments were run at severalelongational rates between 0.03 and 3 s−1 at 180 °C.Rectangular testing specimens of dimensions 19 mm × 10

Table 1. Summary of LCBPPs Prepared by scCO2 AssistedReactive Extrusion

samplePP-g-MAH(wt %)

R,NH2/MAH

temp(°C)

press.(MPa)

CO2(wt %)

LCBPP1 100 0.5 180 8 2LCBPP2 100 1 180 8 2LCBPP3 100 2.0 180 8 2LCBPP4 100 4 180 8 2

Figure 1. (a) FTIR spectra of the PP-g-MAH and modified samples. (b) Conversion of maleic anhydride vs the NH2/MAH ratio (R).

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mm × 0.3 mm were prepared by pressing the samples at 180°C. The strain-hardening factor χ was used to quantify thedegree of strain hardening according to

χη ε

η=

+

+t

t

( , )

3 ( )E max

max (3)

where ηE+ is the extensional stress growth coefficient, η+ is the

shear stress growth coefficient, ε is the elongational rate, andtmax is the time when the strain achieves its maximum value.

3. RESULTS AND DISCUSSION3.1. Verification of PP Modification by Imidization

Reaction. A series of modified PPs with increasing NH2/MAHratio (R) were prepared as detailed in the Experimental Section,and their structures were characterized by FTIR spectroscopy(Figure 1a). The spectrum of PP-g-MAH was included asreference. The absorption bands at 1780 (strong) and 1865(weak) cm−1 were associated with the asymmetric andsymmetric CO stretching vibrations of the cyclic anhydride,respectively.33 The intensities decreased rapidly with theincrease of R. This was concomitant with the appearance of anew peak at 1705 cm−1 (and arguably a minute shoulder at1773 cm−1), which was associated with the imide structureformed.6,9 For PP-g-NH2, two additional bands were present(1635 and 1565 cm−1), which were assigned to the N−Hbending vibration of amine.33 The MAH contents and degreeof conversion were calculated by normalizing the area intensityof the anhydride peak (1780 cm−1) against that of the internalreference peak (1165 cm−1, characteristic of the CH3 group).As shown in Figure 1b, the conversion increased withincreasing R and reached completion when R ≥ 1.3.2. Characterization of the Microstructure of the

Modified PPs. The aforementioned FTIR analysis wasconsistent with the occurrence of the imidization reactionand formation of imide structure in the modified PPs.Moreover, the modified PPs were expected to possess differentstructures, which Scheme 1 schematically illustrates. When R <1 (LCBPP1), low LCB content and unreacted MAH group areanticipated. The LCB content increased as R increased andreached the maximum when R approached 1, the stoichiometricratio for the imidization reaction. This was the case forLCBPP2. Upon further increase of R, dangling imide linksstarted to form because abundant diamine molecules competedfor the limited MAH supply. This reduced the degree ofcoupling and degree of long chain branching, as was the casefor LCBPP3 and LCBPP4. Note that this was accompanied bythe incorporation of more polar amine groups into the polymerstructure. Furthermore, in the presence of a large excess of thediamine (R ≫ 1), amine grafted polypropylene (PP-g-NH2)would result by transforming all MAH groups into pendantimide links with terminal amine moiety. Thus the modified PPspossessed distinctly different LCB contents and functionalgroups. They served as the model system for subsequentstudies.To further probe the structural differences among the

modified PPs, the molecular weights of the samples weremeasured by light scattering (Table 2) and the molecularweight distributions were measured by size exclusionchromatography (Figure 2).Compared to the PP-g-MAH, the LCBPPs had higher

molecular weights and narrower molecular weight distributions,a direct consequence of chain coupling by imidization. The

increase in molecular weight was the most prominent forLCBPP2 (more than 80%), which was the result of the highestextent of coupling when R = 1.7 By contrast, PP-g-NH2 hadcomparable albeit slightly lower molecular weight and narrowermolecular weight distribution than PP-g-MAH, suggesting thatPP-g-NH2 retained the linear structure after modification. Theslight reduction in molecular weight may result from chain

Scheme 1. Illustrations of the Structural Differences amongModified PPs Prepared by Varying the Stoichiometric Ratio(R) of PP-g-MAH and Ethylenediamine (EDA)

Table 2. Molecular Structure Parameters of PP-g-MAH andModified PPs

sample Mw (kg/mol) Mw/Mn λa

PP-g-MAH 202 2.9 0LCBPP1 338 2.8 1.1LCBPP2 367 2.5 1.9LCBPP3 236 2.5 1.1LCBPP4 226 2.4 1.1PP-g-NH2 201 2.5 n.d.b

aλ is the number of long chain branches per 1000 monomer units.bNot detected.

Figure 2. Molecular weight distributions of PP-g-MAH and modifiedsamples.

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degradation, which occurred predominantly in high molecularweight fractions, thereby reducing polydispersity.34

Figure 3 shows the Mark−Houwink plots for the samples. Alinear relationship was observed for PP-g-MAH and PP-g-NH2

with a single slope (α = 0.74), implying a linear structure. Onthe other hand, the LCBPPs deviated from the linearrelationship with a clear reduction of slope at high molecularweight fractions, which is indicative of the presence of mostlong chain branches (LCBs) in PP chains with high molecularweight.5 The degree of reduction correlated well with thebranching degree, with the highest reduction being observed inLCBPP2, the modified sample with the largest amount ofLCBs.The number of long chain branches per 1000 monomer units

(λ, or branching degree) was commonly used for thequantitative interpretation of LCBs and is defined as

λ =BM

M(1000)nM (4)

where MM is the molar mass of the monomer unit and M is themolar mass of the polymer chain.The average number of branches per polymer chain (Bn) was

calculated according to a model developed by Zimm andStockmeyer for randomly branched polymers with a branchpoint functionality of 3:35

π= + +

−

⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎤⎦⎥g

B B1

749

n0.5

n0.5

(5)

where g is the ratio of the mean-square radius of gyration of abranched polymer to that of a linear polymer of the same molarweight. Normally, g decreased with the increase of the degree ofbranches and the graft length.6 It can be calculated using theintrinsic viscosity ([η]) of the branched and linear polymers asfollows:36

ηη

=ε⎛

⎝⎜⎞⎠⎟g

[ ][ ]

b

l

1/

(6)

where ε is ∼0.5 or 1.5 for systems with low and high branchingdegrees, respectively. For moderately branched systems, anaverage value of 0.75 is recommended.37,38

Thus λ values for the samples were calculated andsummarized in Table 2. LCBPP2 had the highest degree ofbranching (λ = 1.9), while the other three LCBPPs had the

same λ value (1.1). Long chain branching was not present inPP-g-NH2.In summary, there were distinct differences in the micro-

structures between the PP-g-MAH and the LCBPPs, e.g.,molecular weights and LCBs, whereas PP-g-NH2 possessed astructure (linear) and molecular weight characteristics similar tothose of PP-g-MAH, but a distinctly different side groupchemistry. They were used as the model system for therheological investigation in sections 3.3 and 3.4.

3.3. Shear Rheology. 3.3.1. Linear Viscoelasticity bySmall Amplitude Oscillatory Rheometry. The linear viscoe-lastic properties were measured by using small amplitudedynamic oscillatory rheometry. Figure 4 shows the complex

viscosity (η*) measured at 180 °C. The influence of LCBs wasprofound. Compared to PP-g-MAH, the LCBPPs exhibitedsignificantly higher viscosities and stronger shear thinningbehaviors, particularly at low frequencies. Both effects weremost prominent in the sample with the highest LCBs(LCBPP2).Several peculiarities were noted in the low frequency

response that did not arise from long chain branching. First,LCBPP1 had significantly lower viscosity than LCBPP3 andLCBPP4, even though it had a molecular weight that was morethan 40% higher, and the three polymers had the samebranching degree (λ = 1.1). Furthermore, the linear PP-g-NH2showed substantially higher viscosity than LCBPP1. We reasonthat these are peculiarities of the physical cross-links present inthese samples (R > 1). The remainder of the text discussesadditional experimental evidence to support this argument.Figure 5 compares the frequency dependency of the storage

(G′) and loss (G″) moduli of the samples. A referencetemperature of 180 °C was used for the data shift. At lowfrequencies (terminal regime), all modified PPs show higher G′and reduced frequency dependence than PP-g-MAH (that is,more solidlike or more elastic).The influence of the modification on the chain segmental

relaxation was investigated by comparing the crossoverfrequency ωcr (i.e., frequency at which G′ and G″ intersect),with Table 3 showing the results. Increasing LCBs led to adownward shift in crossover frequency or longer segmentalrelaxation time. Similar to the trend observed for viscosity,LCBPP3 and LCBPP4 had longer relaxation times (lowercrossover frequencies) than LCBPP1. Moreover, the linear PP-g-NH2 had a relaxation time significantly longer than that ofPP-g-MAH.

Figure 3. Mark−Houwink plots of PP-g-MAH and modified samples.

Figure 4. Complex viscosity vs angular frequency measured at 180 °Cfor PP-g-MAH and modified samples.

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Comparison of the behaviors of PP-g-NH2 and the LCBPPsrevealed important differences between LCBs and physicalcross-links, and their impacts on the chain relaxation. At theterminal regime, PP-g-NH2 behaved similarly to LCBPP3 andLCBPP4, and it showed significantly lower frequency depend-ency (more solidlike with longer terminal relaxation time) thanLCBPP1. However, the segmental relaxation of PP-g-NH2 wasmore rapid than that of LCBPP1 (higher crossover frequency inhigh frequency regime). It follows that the physical cross-linkincreased the network density and slowed the terminalrelaxation and chain segmental relaxation to differentdegrees.25,39 The impact is much more prominent on theterminal relaxation of the polymer chain.It is known from the literature that thermorheology is highly

sensitive to LCBs. Thus the thermorheological properties of thematerials were studied (Figure 6) by exploiting van Gurp’s plot(vGP plot, the phase angle as a function of the magnitude ofthe complex modulus (G*) at different temperatures),40,41

which has proved useful for evaluating the thermorheological

complexities of long chain branched polymers.3,42 For PP-g-MAH, LCBPP1, LCBPP3, and LCBPP4, the data measured atdifferent temperatures superimposed, suggesting thermorheo-logical simplicity (Figure 6a). By contrast, the curves for eitherLCBPP2 or PP-g-NH2 at different temperatures did notsuperimpose (Figure 6b). Because of the constraints imposedby the LCBs in the former43 and the physical cross-links in thelatter,40 the chain relaxation did not obey the time−temper-ature superposition (TTS) principle. Instead, in this time−temperature window, multiple relaxation processes werepresent and those processes had different temperaturedependencies.3,42,44

The vGP plot was also useful for elucidation of change ofelasticity resulting from “rheological percolation”.45 A phaseangle approaching 90° at low G* would suggest a materialresponse dominated by viscous flow. On the other hand, thedecrease of the phase angle with decreasing G* is an indicationof increasing elasticity and tendency to form a percolatedstructure. A smaller phase angle (δ) indicates stronger materialelasticity. As shown in Figure 6, whereas the PP-g-MAH had aconstant δ in the terminal region (close to 90°), all modifiedsamples exhibited reduced phase angles (δ). The reduction ofthe phase angle and, therefore, the material elasticity were inthe following order: LCBPP2 > PP-g-NH2 ≈ LCBPP4 ≈LCBPP3 > LCBPP1 > PP-g-MAH. While the reduction of thephase angle was observed in long chain branched PPs,3 theenhanced elasticity in the linear PP-g-NH2 can only berationalized by the presence of the physical cross-links, asLCBs were absent from the system. The physical cross-linkslikely were also present in LCBPP3 and LCBPP4, albeit to a

Figure 5. Master curves of (a) storage moduli (G′) and (b) loss moduli (G″) for PP-g-MAH and modified PPs.

Table 3. Rheology Properties of PP-g-MAH and ModifiedSamples

sample ωcr (rad/s) η0 (×103 Pa·s) Mb/Mw

PP-g-MAH 244 1.53 1.00LCBPP1 88 14 0.97LCBPP2 10 196 0.85LCBPP3 64 79 0.78LCBPP4 70 85 0.77PP-g-NH2 99 97 0.70

Figure 6. Phase angle as a function of the complex modulus for (a) PP-g-MAH, LCBPP1, LCBPP3, and LCBPP4 (simple) and (b) LCBPP2 and PP-g-NH2 (TTS breakdown). Solid, empty, and plus symbols represent data from 180, 200, and 220 °C, respectively.

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lesser degree. The responses of these two LCBPPs were fromthe combined effects of LCBs and physical cross-links.3.3.2. Zero Shear Viscosity. Zero shear viscosity (η0) is a

fundamental rheological property that is highly sensitive tochange in the molecular structure.46−48 The values for thedifferent samples at 180 °C were measured by creep tests45 andplotted as a function of molecular weight (Figure 7a). Todeconvolute the effects of molecular weight and chain topology,the measured values were further normalized against that of thelinear polymer with the same weight-average molecular weightη0(lin). η0(lin) was calculated from eq 7, a well-definedrelationship for linear PP at 180 °C.49

η = − + Mlog 15.4 3.5 log0 W (7)

η0/η0(lin) represents the net effect of the chain topology on thezero shear viscosity and is shown in Figure 7b. The rapidincrease of η0/η0(lin) when R was increased from 0 to 1 can beattributed to the increasing degree of long chain branching,which reached a maximum at R = 1 (LCBPP2). However, thecontinued increase of η0/η0(lin) in LCBPP3, LCBPP4, and PP-g-NH2 cannot be attributed to the LCBs, as the degree of longchain branching was lower in LCBPP3 and LCBPP4, and wasabsent in PP-g-NH2. Thus physical cross-links in these materialsplayed a significant role in affecting the zero shear viscosity.For a polymer with branching, Janzen and Colby50 developed

an empirical formula that correlates the molecular weightbetween branches (Mb) which are much larger than theentanglement molecular weight with the polymer zero shearviscosity and weight-average molecular weight.Mb can be calculated from eqs 8 and 9.

η = +γ⎡

⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥⎛⎝⎜

⎞⎠⎟AM

MM

MM

1s

0 bb

c

2.4w

b

/

(8)

γ= +

⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟⎤⎦⎥⎥

sB

MM

max 1,32

98

ln90

b

Kuhn (9)

η = +⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥AM

MM

10 ww

c

2.4

(10)

where Mc is the critical molecular mass for entanglement ofrandom branches, Mc = 2Me = 13 640 g/mol.46 Mw is the mass-

average molecular mass of PP-g-MAH. A is a parameter that canbe calculated from η0 and Mw of the linear polymer using eq 10,which was 1.13 × 10−5 in the present study. B is a constant, B =6; MKuhn is the Kuhn length, which was 187.8 g/mol for PP.44

Mb/Mw was calculated for each sample, and values aresummarized in Table 3. PP-g-MAH had an Mb/Mw value of 1,consistent with a linear morphology. When R was increased, theratio initially decreased, due to the fact that with the increasingdegree of branching the same amount of mass would have to bedistributed between more branch points. However, a reversedtrend was observed when R > 1. LCBPP3 and LCBPP4 hadlower degrees of branching than that of LCBPP2 but possessedlower Mb/Mw. Furthermore, PP-g-NH2 showed a ratio of 0.77,significantly lower than the predicted value for a linear polymer(Mb/Mw = 1). This discrepancy, however, provided directevidence of the presence of physical cross-links in thesesamples, which reduced Mb/Mw. Moreover, the perceived“abnormality” of Mb/Mw for these samples in fact suggests thatthe presence of such physical cross-links was substantial, andthey indeed behaved similarly to branching as discussed byTierney and Register.44 Whereas the lower ratios for LCBPP3and LCBPP4 were from the combined effects of LCBs andphysical cross-links, in PP-g-NH2 it was entirely due to thephysical cross-links.Thus far we have observed a series of phenomena in some of

the samples that can be attributed to the presence of physicalcross-links therein. For example, the viscoelastic behaviors ofthe linear PP-g-NH2 resembled those of materials with cross-links, and were significantly different from those of the linearPP-g-MAH, even though both polymers had similar averagemolecular weights and molecular weight distributions. Whilethe exact structures and their formation mechanism of thephysical cross-links are not entirely clear and are worthy offurther investigation in their own merits, a plausible explanationis offered here. In PP-g-NH2, the pendant link (imide-amine)possessed high polarity and may phase separate from thenonpolar polypropylene matrix, resulting in formation ofmicrodomains that act as physical cross-links.18,20−25 Suchphase-separated structures also are likely to be also present inLCBPP3 and LCBPP4, although to a lesser extent due tosmaller amounts of the amine groups. Physical cross-links fromhydrogen bonds between carbonyl and amine groups may alsoexist in the LCBPPs. However, their contribution to theobserved change in the rheological properties is likely to be

Figure 7. (a) Weight-average molar mass dependence of the zero shear viscosity at 180 °C. The straight line is the calculated zero shear viscosity forlinear PPs, η0(lin) (by eq 7), as a function of molecular weight. The measured values for the modified PPs η0 (symbols in the figure, measured by creeptest) are higher than those for the linear PPs of the same molecular weight, as a result of the cross-links in these polymers. The arrows indicate thatthe actual zero shear viscosity is higher than the plotted value, because a steady state could not be obtained in these measurements. Confidence barsindicate an error of ±5% in the molecular weight. (b) Normalized zero shear viscosities η0/η0(lin) of modified PPs and the parent PP-g-MAH as afunction of the NH2/MAH molar ratio. Linear PPs have a constant normalized zero shear viscosity of 1, as indicated by the flat line in the figure.

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negligible due to the following facts: (i) the isolatedhomogeneously dispersed hydrogen bonds do not affect themelt elasticity;51,52 (ii) these hydrogen bond cross-links areinefficient unless they are enhanced by cooperativity byorganizing them in extended domains.21

To summarize, the linear rheological behaviors of the LCB-PPs are affected by LCBs, or a combination of LCBs andphysical cross-link structure, whereas the physical cross-linksfrom phase separation are primarily responsible for theobserved behavior differences between PP-g-NH2 and PP-g-MAH. To our knowledge, this is the first report on the effect ofamine functionalization on the polymer melt viscoelasticity.3.3.3. Nonlinear Relaxation Behavior. To further compre-

hend the behaviors of these materials, the investigation wasextended to the nonlinear viscoelastic regime. Figure 8 shows

the experimentally determined damping functions for PP-g-MAH and modified samples, and the predictions from theDoi−Edwards (DE) damping function and the Lodge equation.The DE prediction of h(γ) takes the following approximateform:53

γγ

=+

h( )1

1 0.2 2 (11)

The Lodge equation, which is based on the temporarynetwork model, predicts54

γ =h( ) 1 (12)

For PP-g-MAH, h(γ) showed a slightly weaker straindependence than the DE prediction, which was consistentwith previous reports and is related to the polydispersity of themolecular weight.55 The modified samples showed dampingbehaviors that significantly deviated from the DE prediction,suggesting the presence of a complex branching structure, e.g.,multipoint long chain branches along the backbone.30,56

With the increase of R, the damping functions exhibitedincreasingly weaker strain dependency, digressing further fromthe DE prediction and gradually approaching the Lodgeprediction. It is plausible that the damping mechanism issimilar to that for multiarm star chains57 and gels.58 The aminegroups of a single chain may be located in differentmicrodomains, thereby forming a huge transient network thatexhibits only weak damping.58

Also notable is the difference of the response in linear andnonlinear regimes. In the linear regime, LCBPP2, which hadthe highest LCBs, showed substantially higher elasticity thanLCBPP3 and LCBPP4. In the nonlinear regime, however, theinfluences of the physical cross-links were more profound,suggested by the significantly weaker damping functions inLCBPP3 and LCBPP4 than in LCBPP2. In fact, the effects ofthe physical cross-links were so substantial that the dampingbehavior of the linear PP-g-NH2 approached the Lodgeprediction.In summary, study on the nonlinear stress relaxation

supports the notion of the substantial presence of a gigantictransient network that is extensively cross-linked, which mayresult from multipoint chain branches, phase separation, andhydrogen bonding.

3.4. Uniaxial Elongational Rheology. Uniaxial exten-sional rheometry was conducted to probe the long relaxationtimes of the samples.59 Figure 9a,b shows the tensile stressgrowth coefficients of PP-g-MAH and modified materialsmeasured at 180 °C. The solid lines represent the 3-foldchange of the shear stress growth coefficient. At the initial stage,the uniaxial extensional viscosities of all samples were about 3times the shear viscosities following the Trouton rule,60

characteristic of linear viscoelasticity. The tensile stress growthcoefficients of PP-g-MAH increased gradually with no clear“strain hardening”, typical of a linear polymer.61 By contrast, allmodified samples displayed noticeable strain hardening,strongly suggesting the presence of multiple long chainbranches per chain in these polymers.62

Figure 9c shows the strain hardening factors for the PP-g-MAH and modified samples as a function of strain rate. Theextension rate dependence of the strain hardening factors is anindication of the strength of the network. A weak dependenceimplies the inability of the applied stress to disrupt the networkto “soften” the material and, therefore, a high network strength.For LCBPP1, LCBPP2, and LCBPP3, the strain hardeningfactor decreased with increasing strain rates, typical forpolymers with low branching density.4,48 In comparison, thestrain hardening factors for LCBPP4 and PP-g-NH2 remainednearly constant at low strain rate (<1 s−1), suggestingconsiderable strength of the networks. As the LCBs inLCBPP4 were lower than in LCBPP2 and did not exist inPP-g-NH2, the strength of the network must originate from thephysical cross-links. The extensional measurements conductedherein not only further confirmed the existence of the physicalcross-links, but also revealed that such cross-links may possessconsiderable strength. Still, under higher stress (when the strainrate is >1 s−1 in the present study) these networks were readilydestroyed, resulting in rapid softening of the materials.63−65

4. CONCLUSIONSIn this study we synthesized a series of polypropylenescontaining long chain branching and pendant amine groupsby modifying maleic anhydride grafted polypropylene withethylenediamine. Detailed structural and rheological character-izations were subsequently conducted. The investigationyielded several new findings: (1) the substantial presence ofphysical cross-links in the linear PP-g-NH2 and some long chainbranched PPs, which presumably arise from polarity disparitydriven phase separation and hydrogen bonding, and (2)significant changes in the rheological properties of the samplesresulting from the physical cross-links and/or the combinedeffects of physical cross-links and LCBs. Furthermore, the

Figure 8. Long time damping function h(γ) for PP-g-MAH andmodified samples. The solid curves indicate the Doi−Edwardsprediction without independent alignment approximation. The dashedline is the prediction from the Lodge equation.

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effects of the physical cross-links may be different in the linearand nonlinear regimes.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: zeng@eng.fsu.edu (C.Z.); kcao@che.zju.edu.cn(K.C.); zyao@che.zju.edu.cn (Z.Y.). Tel.: (850) 410-6273(C.Z.); +86 571 87951832 (K.C., Z.Y.). Fax: (850) 410-6342(C.Z.); +86 571 87951832 (K.C., Z.Y.).NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by the National Natural ScienceFoundation of China (NSFC 50390097, NSFC 50773069, andNSFC 51173166), the Program for Changjiang Scholars andInnovative Research Team in University of China (No.IRT0942), the Specialized Research Fund for the DoctoralP rog r am of Highe r Educa t i on o f Ch ina (No .20110101110030), and the Center of Excellence in AdvancedMaterials (CEAM) award from the State of Florida, USA.

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