Rheological Evidence of Physical Cross-Links and Their Impact in

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Rheological Evidence of Physical Cross-links and Their Impact in Modified Polypropylene Yan Li, Zhen Yao, Zhenhua Chen, Shaolong Qiu, Changchun Zeng, and Kun Cao Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie400809z • Publication Date (Web): 15 May 2013 Downloaded from http://pubs.acs.org on May 20, 2013

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Industrial & Engineering Chemistry Research

Rheological Evidence of Physical Cross-links and Their Impact in Modified Polypropylene Yan Lib,c,d , Zhen Yaob*, Zhen-hua Chenc,d, Shao-long Qiub, Changchun Zeng c,d*, Kun Caoa,b* a

State Key Laboratory of Chemical Engineering, Zhejiang University, Hangzhou 310027, China

b

Institute of Polymerization and Polymer Engineering, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, China

c

d

High Performance Materials Institute, Florida State University, Tallahassee, FL 32310, USA

Department of Industrial and Manufacturing Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA

AUTHOR INFORMATION Corresponding Author *Changchun Zeng Tel.: +1 850 410 6273 Fax.: +1 850 410 6342 E-mail addresses: [email protected]

*Kun Cao and *Zhen Yao

ACS Paragon Plus Environment

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Tel.: +86 571 87951832 Fax.: +86 571 87951832 E-mail addresses: [email protected] ; [email protected]


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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 (PPg-NH2). By varying the stoichiometric ratio of maleic anhydride grafted polypropylene (PP-gMAH) and ethylene diamine (EDA), a series of modified PPs with different degree of branching and side-group polarity were prepared. Extensive rheological studies were conducted after baseline characterization of the chemical and molecular structure of these materials using Fourier Transfer Infrared Spectroscopy (FTIR) and size exclusion chromatography (SEC), respectively. The results strongly suggest the presence of physical cross-links in a majority of the materials studies herein, which significantly impacts their rheological behaviors. The physical cross-links can be argued to be in the form of phase separated domains and hydrogen bonding, which has been reported in the literatures. KEYWORDS: polypropylene, long chain branching, physical cross-links


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1. INTRODUCTION Isotactic polypropylene (iPP) is one of the leading and fastest-growing polyolefins because of their attractive properties, such as high melting point, low density, excellent chemical resistance and high tensile strength etc.1 However, linear PPs possess low melt strength, which limits their uses in processes involving substantial elongational flow such as thermoforming, film blowing, extrusion coating, blow molding and foaming.1,2 Introducing long chain branching (LCB) into the molecular structure of PP, either through in-reactor polymerization or post-reactor treatment, has proven effective to overcome this shortcoming.2-11 Among the approaches for LCB introduction, reactive coupling of PP chains by small linker molecules11,12 is advantageous in several aspects, e.g., easy implementation and flexibility in controlling the branching structure.1316

Taking advantage of the high reactivity of the imidization reaction, a number 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 of the PPs, e.g., molecular weight, branching degree and density of the function groups, can be tailored.6,9,17 Aside from the topological change, the imidization reaction may also alter the local polarity within the molecules as a result of the incorporation of high polarity linkages. The disparity in polarity may lead to phase separation, and the phase-separated domains may serve as physical cross-links leading to potentially significant changes of mechanical and rheological properties of these materials. To the best of our knowledge, these issues have not been discussed in literatures, although physical cross-links have been observed in several polymers containing highly polar groups, e.g. hydroxyl18-19, carboxyl20-22, anhydride23,24 and ionic groups25, and the influences of such structures were well documented. More recently, formation of inhomogeneoity or microphase separation by grafting polar monomer (pentaerythritol triacrylate, PETA) onto other


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polymer, e.g., polylactic acid (PLA) had also been reported. Although not directly justified from rheology, its influence on crystallization suggests the existence of inhomogeneity.26 In this work, we set out to investigate the possible presence of the phase-separated structures in the modified PPs, their formation, and impact on the rheological properties. The employed samples were a series of LCBPPs prepared by supercritical carbon dioxide (scCO2) assisted reactive extrusion of PP-g-MAH and ethylene diamine with varying ratios for controlling extent of reaction and degradation,15 and an amine grafted polypropylene (PP-g-NH2) prepared via a solution process.27 The study was divided into two sections: (I) detailed structural characterization were conducted to examine the major differences between the modified samples (molecular weight, molecular weight distribution, gel content etc.), which form the basis to deconvolute various factors when interpreting the rheological response of these materials; (II) both linear, nonlinear shear rheometry and extension rheometry were then conducted, and the results strongly suggest that the rheological behavior of the modified PPs can be affected by both long chain branches (LCBs) and physical cross-links present.

2. EXPERIMENTAL SECTION 2.1. Materials PP-g-MAH (MAH content, 0.3 wt%) was from Ningbo Nengzhiguang New Material Co., Ltd, China. Ethylenediamine (EDA) was purchased from Hangzhou Changqing Chemical Reagent Co., Ltd, China. The 1, 2, 4-trichlorobenzene (TCB) and 2, 6-di-t-butyl-4-methylhenol (BHT) were purchased from Acros.

2.2. Sample preparation The LCBPPs were prepared via reactive extrusion assisted with scCO2, using a custom designed co-extrusion twin screw extruder (D = 20 mm; L/D = 48) operated at 180 oC and 150


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rpm.15 Table 1 shows the formulations and process parameters for preparing the LCBPPs. First, PP-g-MAH raw materials was vacuum dried at 80 °C for at least 12 h to remove the residual ungrafted MAH before use. Then PP-g-MAH was fed from the screw feeder. At a feed rate of 70 g/min, the residence time was about 3 min. Two independent piston pump injection systems were used for the delivery of EDA and CO2. The delivery pressure and rate could be controlled separately. The extrudate was cooled in a water bath and pelletized. Table 1 Amine grafted PP (PP-g-NH2) was synthesized using a solution process. In a typical process, 40 g PP-g-MAH was dissolved in 1500 g of xylene at 130 oC. Subsequently, a 10-fold excess of EDA was added and the mixture was stirred for at least 6 hours. After the imidization reaction, the product was precipitated in acetone and washed with a large amount of ethanol to remove the unreacted EDA. The samples were then dried at 80 oC under vacuum for 18 hours.

2.3. Structural characterization 2.3.1 Gel content determination The gel contents of the PP-g-MAH and modified samples were determined following ASTM D2765-84 using boiling xylene as the extraction solvent. All samples had a gel content value of zero.

2.3.2 Size-exclusion chromatography (SEC) Size exclusion chromatography (SEC, Viscotek 350A, Vicotek Ltd.) was performed at 150 °C using a TSK-gel column (GMHHR-H(S) HT, 300×7.8 mm). The SEC was equipped with a triple detection system: a refractive index detector, a four-capillary differential viscometer detector and light scattering detector. PP-g-MAH and modified samples were dissolved in TCB stabilized with 5×10-4 g ml-1 BHT at 150 oC for 4 h prior to analysis.


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2.3.3 Fourier transform infraed (FTIR) spectroscopy FTIR (Nicolet 5700, Thermo Ltd) was performed in a spectral range from 400 to 4000 cm-1 at a resolution of 2 cm-1. Data were collected as average of 32 scans.

2.4. Rheological Characterization 2.4.1 Shear rheology Shear rheological measurements were conducted on a Stress-controlled rotational rheometer (Rheostress 6000, ThermoHaake co.) in a nitrogen environment using 20 mm-diameter parallel plates with a gap of 1 mm. Testing specimens were prepared by compression molding at 180 oC. Small amplitude oscillatory measurements were carried out at 180-220 oC with a frequency range from 0.1 to 628 rad/s. A small strain amplitude (1 %) was used to ensure that measurements were done in the linear viscoelastic (LVE) regime. Creep tests were performed at 180 oC following Gabriel.28 Small shear stresses between 2 and 5 Pa should be adopted to warrant linear viscoelastic response. At sufficiently long time (2500 s ~ 4000 s), the deformation rate approaches to steady state and the zero shear viscosity can be determined according to:

η0 = lim t →∞

t

(1)

J (t )

in which J(t) is the compliance of samples. Stress relaxation was measured at 180 oC under a series of step strains (γ = 0.3 – 6). System response time was less than 0.1 second in all measurements. Corrections were made following Stadler29 to take into account of the non-uniform sample deformation in parallel plate geometry. The damping function h(γ) was quantified using the following equation:

h ( γ ) = G ( γ , t ) G ( t ) (t > λK )

(2)


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where G(γ,t) is the relaxation modulus at a particular strain. G(t) is the equilibrium modulus, which is the relaxation modulus in the linear regime at time greater than a experimentally determined critical value λK.30 In our study all samples 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 extensional viscosity was measured using a MARS III rheometer (ThermoHaake co.) equipped with a Sentmanat extensional rheometer (SER) universal testing platform (SERHV-H01 model, Xpansion Instruments). The system was discussed in detail.31,32 Constant strain rate experiments were run at several elongational rates between 0.03 to 3 s-1 at 180 oC. Rectangular testing specimens of dimension 19 mm×10 mm×0.3 mm were prepared by pressing the samples at 180 oC. The strain-hardening factor χ was used to quantify the degree of strainhardening according to

χ=

ηE+ ( tmax , ε&) 3η + ( tmax )

(3)

where ηE+ is the extensional stress growth coefficients, η+ is the shear stress growth coefficients, ε& is the elongational rate, and tmax is time when the strain achieve the maximum value.

3. RESULTS AND DISCUSSIONS 3.1. Verification of PP modification by imidization reaction A series of modified PPs with increasing NH2/MAH ratio (R) were prepared as detailed in the experimental section, and their structures were characterized by FTIR (Figure 1a). The spectrum of PP-g-MAH was included as reference. The absorption bands at 1780 cm-1 (strong) and 1865 cm-1 (weak) were associated with the asymmetric and symmetric C=O stretching vibrations of


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the cyclic anhydride, respectively.33 The intensities decreased rapidly with the increase of R. This was concomitant with the appearance of a new peak 1705 cm-1 (and arguably a minute shoulder at 1773 cm-1), which was associated with the imide structure formed.6,9 For PP-g-NH2, two additional bands were present (1635 cm-1 and 1565 cm-1), which were assigned to the N-H bending vibration of amine.33 The MAH contents and degree of conversion were calculated by normalizing the area intensity of the anhydride peak (1780 cm-1) against that of the internal reference peak (1165 cm-1, characteristic of the CH3 group). As shown in Figure 1b, the conversion increased with increasing R and reached completion when R ≥ 1. Figure 1

3.2. Characterization of the microstructure of the modified PPs The aforementioned FITR analysis was consistent with the occurrence of the imidization reaction and formation of imide structure in the modified PPs. Moreover, the modified PPs were expected to possess different structures, which Scheme 1 schematically illustrates. When R < 1 (LCBPP1), low LCB content and un-reacted MAH group are anticipated. The LCB increased as R increased and reached the maximum when R approached to 1, the stoichiometric ratio for the imidization reaction. This was the case for LCBPP2. Upon further increase of R, dangling imide links started to form because abundant diamine molecules competed for the limited MAH supply. This reduced the degree of coupling and degree of long chain branching, as was the case for LCBPP3 and LCBPP4. Note this was accompanied by the incorporation of more polar amine groups into the polymer structure. Furthermore, in the presence of large excess of the diamine (R >> 1), amine-grafted polypropylene (PP-g-NH2) would result by transforming all MAH groups into pendant imide links with terminal amine moiety. Thus the modified PPs possessed distinctly


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different LCB contents and functional groups. They served as the model system for subsequent studies. Scheme 1 To further probe the structural differences among the modified PPs, the molecular weights of the samples were measured by light scattering (Table 2) and molecular weight distribution by size exclusion chromatography (Figure 2). Figure 2

Comparing to the PP-g-MAH, the LCBPPs had higher molecular weights and narrower molecular weight distribution, a direct consequence of chain coupling by imidization. The increase in molecular weight was the most prominent for LCBPP2 (more than 80%), which was the result of the highest extent of coupling when R = 1.7 By contrast, PP-g-NH2 had comparable albeit slightly lower molecular weight and narrower molecular weight distribution than PP-gMAH, suggesting that PP-g-NH2 retained the linear structure after modification. The slight reduction in molecular weight may result from chain degradation, which occurred predominately in high molar weights fractions thereby reducing polydispersity.34 Table 2 Figure 3 shows the Mark-Houwink plots for the samples. A linear relationship was observed for PP-g-MAH and PP-g-NH2 with a single slop (α = 0.74), implying a linear structure. On the other hand, the LCBPPs deviated from the linear relationship with a clear reduction of slope at high molecular weight fractions, are indicative of the presence of most long chain branches (LCBs) in PP chains with high molecular weight.5 The degree of reduction correlated well with


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the branching degree, with the highest reduction being observed LCBPP2, the modified sample with the largest amount of LCBs. Figure 3 The number of long chain branches per 1000 monomer units (λ, or branching degree) was commonly used for the quantitative interpretation of LCBs and is defined as:

λ=

Bn ×1000 × M M M

(4)

where MM is the molar mass of the monomer unit and M is the molar mass of the polymer chain. The average number of branches per polymer chain (Bn) was calculated according to a model developed by Zimm and Stockmeyer for randomly branched polymers with a branch point functionality of 3:35

 Bn 0.5 4 Bn  g =  1 +  +  7  9π  

−0.5

(5)

where g is the ratio of the mean-square radius of gyration of a branched polymer to that of a linear polymer of the same molar weight. Normally, g decreased with the increase of branches degree and graft length.6 It can be calculated using the intrinsic viscosity ([η]) of the branched and linear polymers as follows:36  [η ] g = b  [η ]  l

  

1

ε

(6)

where ε is ~0.5 or 1.5 for systems with low and high branching degrees, respectively. For moderately branched systems, an average value of 0.75 is recommended.37,38 Thus λ values for the samples were calculated and summarized in Table 2. LCBPP2 had the highest degree of branching (λ = 1.9), while the other three LCBPPs had the same λ value (1.1). Long chain branching was not present in PP-g-NH2.


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In summary, there were distinct differences in the microstructures between the PP-g-MAH and the LCBPPs, e.g., molecular weights and LCBs, whereas the PP-g-NH2 possessed a similar structure (linear) and molecular weight characteristics as PP-g-MAH, but distinctly different side group chemistry. They were used as the model system for the rheological investigation in the following sections that follow.

3.3 Shear Rheology 3.3.1 Linear viscoelasticity by small amplitude oscillatory rheometry The linear viscoelastic properties were measured by using small amplitude dynamic oscillatory rheometry. Figure 4 shows the complex viscosity (η*) measured at 180 oC. The influence of LCBs was profound. Comparing to the PP-g-MAH, the LCBPPs exhibited significantly higher viscosity and stronger shear thinning behavior, particularly at low frequencies. Both effects were the most prominent in the sample with highest LCBs (LCBPP2). Figure 4 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 and LCBPP4, even though it had a molecular weight that was more than 40% higher, and the three polymers had the same branching degree (λ = 1.1). Furthermore, the linear PP-g-NH2 showed substantially higher viscosity than LCBPP1. We reason that these peculiarities to the physical cross-links present in these samples (R > 1). The remainder of the text discusses additional experimental evidence to support this argument. Figure 5 compares the frequency dependency of the storage (G') and loss moduli (G'') of the samples. A reference temperature of 180 °C was used for the data shift. At low frequencies


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(terminal regime), all modified PPs show higher G' and reduced frequency dependence than PPg-MAH (aka, more solid-like or more elastic). Figure 5 The influence of the modification on the chain segmental relaxation was investigated by comparing the crossover frequency ωcr (i.e., frequency at which G' and G'' intersect), with Table 3 showing the results. Increasing LCBs led to a downward shift in crossover frequency or longer segmental relaxation time. Similar to the trend observed for viscosity, LCBPP3 and LCBPP4 had longer relaxation time (lower crossover frequency) than LCBPP1. Moreover, the linear PP-gNH2 had a relaxation time significantly longer than that of PP-g-MAH. Comparison of the behaviors of the PP-g-NH2 and the LCBPPs revealed important differences between LCBs and physical cross-links, and their impacts on the chain relaxation. At terminal regime, PP-g-NH2 behaved similarly to LCBPP3 and LCBPP4, and showed significantly lower frequency dependency (more solid-like with longer terminal relaxation time) than LCBPP1. However, the segmental relaxation of PP-g-NH2 was more rapid than that of LCBPP1 (higher crossover frequency in high frequency regime). It follows that the physical cross-link increased the network density and slowed the terminal and chain segmental relaxation to different degrees.25,39 The impact is much more prominent on the terminal relaxation of polymer chain. Table 3 It is known from literature that thermorheology is highly sensitive to LCBs. Thus the thermorheological properties of the materials were studied (Figure 6) by exploiting Van Gurp’s plot (vGP plot, the phase angle as a function of the magnitude of the complex modulus at different temperatures)40,41, which has proven useful for evaluating the thermorheological complexity of long chain branched polymers.3,42 For PP-g-MAH, LCBPP1, LCBPP3, LCBPP4,


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the data measured at different temperatures superimposed, suggesting thermorheological simplicity (Figure 6a). By contrast, the curves for either LCBPP2 or PP-g-NH2 at different temperatures did not superimpose (Figure 6b). Because of the constraints imposed by the LCBs in the former43 and the physical cross-links in the latter40, the chain relaxation did not obey the time-temperature superposition (TTS) principle. Instead in this time-temperature window, multiple relaxation processes were present and those processes had different temperature dependencies.3,42,44 The vGP plot was also useful for elucidation of change of elasticity resulting from “rheological percolation”.45 A phase angle approaching to 90° at low G* would suggest a material response dominated by viscous flow. On the other hand, the decrease of phase angle with decreasing G* is an indication of increasing elasticity and tendency to form a percolated structure. Smaller phase angle (δ) indicates stronger material elasticity. As shown in Figure 6, whereas the PP-g-MAH had constant δ in terminal region (close to 90o), all modified samples exhibited reduced phase angles (δ). The reduction of the phase angle, and therefore, the material elasticity, were in the following order: LCBPP2 > PP-g-NH2 ≈ LCBPP4 ≈ LCBPP3 > LCBPP1 > PP-g-MAH. While the reduction of phase angle was observed in long chain branched PPs,3 the enhanced elasticity in the linear PP-g-NH2 can only be rationalized by the presence of the physical cross-links, as LCBs were absent from the system. The physical cross-links likely were also present in LCBPP3 and LCBPP4, albeit to a lesser degree. The responses of these two LCBPPs were from the combined effects of LCBs and physical cross-links. Figure 6


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3.3.2 Zero shear viscosity Zero-shear viscosity (η0) is a fundamental rheological property that is highly sensitive to the change of molecular structure.46-48 The values for the different samples at 180 oC were measured by creep tests

45

and plotted as a function of molecular weight (Figure 7a). To de-convolute the

effects of molecular weight and chain topology, the measured values were further normalized against that of the linear polymer with the same weight average molecular weight η0(lin). η0(lin) was calculated from eq. 7, a well-defined relationship for linear PP at 180 oC.49

logη0 = −15.4 + 3.5LogMW

(7)

η0/η0(lin) represents the net effect of the chain topology on the zero shear viscosity and is shown in Figure 7b. The rapid increase of η0/η0(lin) when R was increased from 0 to 1 can be attributed to the increasing degree of long chain branching, which reached maximum at R = 1 (LCBPP2). However, the continued increase of η0/η0(lin) in LCBPP3, LCBPP4 and PP-gNH2 cannot be attributed to the LCBs, as the degree of long chain branching was lower in LCBPP3 and LCBPP4, and was absent in PP-g-NH2. Thus physical cross-links in these materials played a significant role in affecting the zero shear viscosity. Figure 7 For polymer with branching, Janzen and Colby50 developed an empirical formula that correlates the molecular weight between branches (Mb) which are much larger than the entanglement molecular weight with the polymer zero shear viscosity and weight average molecular weight. Mb can be calculated from eqs. 8 and 9.

  M 2.4   M  η0 = AM b 1 +  b    w    M c    M b 

s

γ

(8)


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 s = max 1, 3 + 9 B ln  M b γ  90 M kuhn  2 8

  

  M 2.4  η0 = AM w 1 +  w     M c  

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(9)

(10)

where Mc is the critical molecular mass for entanglement of random branches, Mc = 2Me = 13640 g/mol.46 Mw is the mass-average molecular mass of PP-g-MAH. A is a parameter that can be 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 summarized in Table 3. PP-g-MAH had an Mb / Mw value 1, consistent with a linear morphology. When R was increased, the ratio initially decreased, due to the fact that with the increasing degree of branching the same amount of mass would have to be distributed between more branch points. However, a reversed trend was observed when R > 1. LCBPP3 and LCBPP4 had a lower degree of branching than that of LCBPP2 but possessed a lower 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 direct evidence of the presence of physical cross-links in these samples, which reduced Mb / Mw. Moreover the perceived “abnormality” of Mb / Mw for these samples in fact suggests the presence of such physical cross-links were substantial, and they indeed behaved similarly to branching as discussed by Tierney et al.44 Whereas the lower ratios for LCBPP3 and LCBPP4 were from the combined effects of LCBs and physical cross-links, in PP-g-NH2 it was entirely due to the physical cross-links. Thus far we have observed a series of phenomena in some of the samples that can be attributed to the presence of physical cross-links therein. For example, the viscoelastic behaviors of the


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linear PP-g-NH2 resembled those of materials with cross-links, and were significantly different from those of the linear PP-g-MAH, even though both polymers had similar average molecular weight and molecular weight distribution. While the exact structures and their formation mechanism of the physical cross-links are not entirely clear and are worthy of further investigation in their own merits, a plausible explanation is offered here. In PP-g-NH2, the pendant link (imide-amine) possessed high polarity and may phase separate from the polar polypropylene matrix, resulting in formation of microdomains that act as physical crosslinks.18,20-25 Such phase separated structures also are likely to be also present in LCBPP3 and LCBPP4, although to a lesser extent due to smaller amount of the amine groups. Physical crosslinks from hydrogen bond between carbonyl and amine groups may also exist in the LCBPPs. However, their contribution to the observed change in the rheological properties is likely to be negligible due to the following facts: i) the isolated homogeneously dispersed hydrogen bonds do not affect the melt elasticity51,52, and ii) these hydrogen bond cross-links are inefficient unless they are enhanced by cooperativity by organizing them in extended domains.21 To summarize, the linear rheological behaviors of the LCB-PPs are affected by LCBs, or combination of LCBs and physical cross-links structure, whereas the physical cross-links from phase separation are primarily responsible for the observed behaviors differences between PP-gNH2 and PP-g-MAH. To our knowledge, this is the first report on the effect of amine functionalization on the polymer melt viscoelasticity.

3.3.3 Nonlinear relaxation behavior To further comprehend the behaviors of these materials, the investigation was extended to the nonlinear viscoelastic regime. Figure 8 shows the experimentally determined damping functions for the PP-g-MAH and modified samples, and the predictions from the Doi-Edward (DE)


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damping function and the Lodge equation. The DE prediction of h(γ) takes the following approximate form:53 h (γ ) =

1 1 + 0.2γ 2

(11)

The Lodge equation, which is based on the temporary network model, predicts:54

h (γ ) = 1

(12)

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

Figure 8 With the increase of R, the damping functions exhibited increasingly weaker strain dependency, digressing further away from the DE prediction and gradually approaching the Lodge prediction. It is plausible that the damping mechanism is similar to that for multi-arm star chains57 and gels58. The amine groups of single chain may be located in different microdomains, thereby forming a huge transient network that exhibits only weak damping.58 Also notable is the difference of the response in linear and nonlinear regime. In the linear regime, LCBPP2, which had the highest LCBs, showed substantially higher elasticity than LCBPP3 and LCBPP4. In the nonlinear regime, however, the influences of the physical crosslinks were more profound, suggested by the significantly weaker damping functions in LCBPP3 and LCBPP4 than in LCBPP2. In fact, the effects of the physical cross-links were so substantial that the damping behavior of the linear PP-g-NH2 approached to the Lodge prediction.


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In summary, study on the nonlinear stress relaxation supports the notion of substantial presence of a gigantic transient network that is extensively cross-linked, which may result from multipoint chain branches, phase separation and hydrogen bonding.

3.4 Uniaxial elongational rheology Uniaxial extensional rheometry were conducted to probe the long relaxation time of the samples.59 Figure 9a and 9b showed the tensile stress growth coefficients of PP-g-MAH and modified materials measured at 180 oC. The solid lines represented the 3-fold of the shear stress growth coefficient. At initial stage, the uniaxial extensional viscosity of all samples was about three times the shear viscosity following the Trouton rule60, characteristic of linear viscoelasticity. The tensile stress growth coefficients of PP-g-MAH increased gradually with no clear “strain hardening”, typical of a linear polymer.61 By contrast, all modified samples displayed noticeable strain hardening, strongly suggesting the presence of multiple long chain branches per chain in these polymers.62 Figure 9c showed the strain hardening factors for the PP-g-MAH and modified samples as a function of strain rate. The extension rate dependence of the strain hardening factors is an indication of the strength of the network. A weak dependence implies the inability of the applied stress to disrupt the network to “soften” the material and therefore, a high network strength. For LCBPP1, LCBPP2 and LCBPP3, the strain hardening factor decreased with increasing strain rates, typical for polymers with low branching density.4,48 In comparison, the strain hardening factors for LCBPP4 and PP-g-NH2 remained nearly constant at low strain rate (< 1 s-1), suggesting considerable strength of the networks. As the LCBs in LCBPP4 were lower than in LCBPP2 and did not exist in the PP-g-NH2, the strength of the network must originate from the physical cross-links. The extensional measurements conducted herein not only further confirmed


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the existence of the physical cross-links, but also revealed that such cross-links may possess considerable strength. Still, under higher stress (when the strain rate is > 1 s-1 in the present study) these networks were readily destroyed, resulting in rapid softening of the materials.63-65

Figure 9

4. CONCLUSIONS In this study we synthesized a series of polypropylenes containing long chain branching and pendant amine groups by modifying maleic anhydride grafted polypropylene with ethylene diamine. Detailed structural and rheological characterizations were subsequently conducted. The investigation yielded several new findings: (1) substantial presence of physical cross-links in the linear PP-g-NH2 and some long chain branched PPs, which presumably arise from polarity disparity driven phase separation and hydrogen bonding, and (2) significant changes in the rheological properties of the samples resulting from the physical cross-links and/or the combined effects of physical-crosslinks and LCBs. Furthermore, the effects of the physical cross-links may be different in the linear and nonlinear regime.


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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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Figure 2. Molecular weight distribution of the PP-g-MAH and modified samples.


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Figure 3. Mark-Hauwink plots of the PP-g-MAH and modified samples.


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Figure 4. Complex viscosity vs. angular frequency measured at 180 oC for the PP-g-MAH and modified samples.


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Figure 5. (a) Master curves of (a) storage modulus (G′) and (b) loss moduli (G˝) for the PP-gMAH and modified PPs.


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


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Figure 7. (a) Weight-average molar mass dependence of the zero shear viscosity at 180 oC. The straight line is the calculated zero shear viscosity for linear PPs η0(lin) (by equation (7)) as a function of molecular weight. The measured values for the modified PPs η0 (symbols in the figure, measured by creep test) are higher than those for the linear PPs of the same molecular weight, as a result of the crosslinks in these polymers. The arrows indicate that the actual zero shear viscosity is higher than the plotted value, because a steady state could not be obtained in these measurements. Confidence bars indicate 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 a function of 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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Figure 8. Long time damping function h(γ) for the PP-g-MAH and modified samples. The solid curves indicate the Doi-Edwards prediction without independent alignment approximation. The dashed line is the prediction from the Lodge equation.


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Figure 9. (a) and (b) Tensile stress growth coefficients ηE+ of PP-g-MAH and modified samples under different strain rates at 180 oC. The curve 3η+ showed the 3-fold of shear stress growth coefficient from steady shear start-up measurements at 0.01 s-1 and 180 oC; (c) The strainhardening factor as a function of strain-rate of PP-g-MAH and modified samples.


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Scheme 1 Illustrations of the structural differences among the modified PPs prepared by varying the stoichiometric ratio (R) of PP-g-MAH and ethylene diamine (EDA).


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Table 1 Summary of LCBPPs prepared by scCO2 assisted reactive extrusion PP-g-MAH

NH2/MAH

Pressure

CO2

wt%

R

C

MPa

wt%

LCBPP1

100

0.5

180

8

2

LCBPP2

100

1

180

8

2

LCBPP3

100

2.0

180

8

2

LCBPP4

100

4

180

8

2

Samples

Temperature o


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Table 2 Molecular structure parameters of the PP-g-MAH and modified PPs. Samples

Mw kg/mol

Mw/Mn

λa

PP-g-MAH

202

2.9

0

LCBPP1

338

2.8

1.1

LCBPP2

367

2.5

1.9

LCBPP3

236

2.5

1.1

LCBPP4

226

2.4

1.1

PP-g-NH2

201

2.5

n.d.b

a: λ is the number of long chain branches per 1000 monomer units b: not detected


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Table 3 Rheology properties of the PP-g-MAH and modified samples ωcr

η0

rad/s

×103 Pa·s

PP-g-MAH

244

1.53

1.00

LCBPP1

88

14

0.97

LCBPP2

10

196

0.85

LCBPP3

64

79

0.78

LCBPP4

70

85

0.77

PP-g-NH2

99

97

0.70

Samples

Mb/Mw


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Funding Sources National Natural Science Foundation of China (NSFC 50390097, NSFC 50773069, and NSFC 51173166) Program for Changjiang Scholars and Innovative Research Team in University of China (No.IRT0942) Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20110101110030) Center of Excellence in Advanced Materials (CEAM) award from the State of Florida, USA. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (NSFC 50390097, NSFC 50773069, and NSFC 51173166), the Program for Changjiang Scholars and Innovative Research Team in University of China (No.IRT0942), Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20110101110030), and Center of Excellence in Advanced Materials (CEAM) award from the State of Florida, USA.


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Rheological Evidence of Physical Cross-Links and Their Impact in

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