Rheology and Anomalous Flow Properties of Poly(ethylene-alt

Article pubs.acs.org/Macromolecules

Rheology and Anomalous Flow Properties of Poly(ethylene-altpropylene)−Silica Nanocomposites Klaus Nusser,† Gerald J. Schneider,*,† and Dieter Richter‡ †

Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS) at Heinz-Maier Leibnitz Zentrum, Lichtenbergstraße 1, 85747 Garching, Germany ‡ Forschungszentrum Jülich, Jülich Centre for Neutron Science (JCNS-1) & Institute for Complex Systems (ICS-1), Forschungszentrum Jülich, Jülich, Germany ABSTRACT: In this work, poly(ethylene-alt-propylene)−silica nanocomposites, constituting a model nanocomposite system with mostly nonattractive interactions, are studied by means of oscillatory shear rheology. Two different molecular weights were used in order to consider both the effect of nanoparticle presence on the relaxation of short as well as long polymer matrices. An increase of the particle fraction leads on the one hand to the observation of typical characteristics of colloidal rheology such as mechanical reinforcement and the formation of a particle gel. On the other hand and in the focus of our analysis, the increasing particle presence also directly affects the relaxation of the polymer chains. In particular, a shift of the polymer loss maximum in G″(ω) is found in the entangled matrices, whereas anomalous flow behavior is evidenced in the rheology data of highly filled short matrices. We succeeded to explain these macroscopic observations from the rheology experiments by considering small-angle neutron scattering and neutron spin echo results on the same samples, which yield detailed insight into the molecular circumstances responsible for the observed macroscopic property changes.

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INTRODUCTION Polymer nanocomposites constitute one of the most important material classes of the present, which is mostly due to their superior mechanical properties. In particular, by choosing the right recipe, the dynamic mechanical features can be adjusted within a wide application window. Unsurprisingly, plenty studies of different nanocomposite systems can be found in the literature.1−4 They document the very flexible applicability of nanocomposites and show evidence for reinforcement,5−7 viscosity reduction,8−10 gelation1,2,11 and other effects, which occur when a soft polymer matrix is mixed with a certain volume fraction of hard filler particles. Though interesting they may be, most of the studies chose a macroscopic method for the characterization of the composite systems, e.g., rheology or dielectric spectroscopy.12,13 This has necessarily resulted in a load of data sets. Unfortunately the microscopic, molecular insight into the matter has not been able to keep up with the vast literature pool of data. Undoubtedly, some very useful phenomenological models exist, which are able to describe different aspects of nanocomposite behavior (-the most common of them are summed up very nicely in ref 14). A lot of the underlying molecular views and assumptions of the models have not been experimentally confirmed, however. It was our goal to add some significant and basic experimental observations directly on the molecular scale to the existing potpourri of macroscopic data and, in this way, contribute to a deeper understanding of the molecular mechanisms, which lead to the remarkable © XXXX American Chemical Society

nanocomposite properties. To achieve this, we chose to start from a model system with mostly nonattractive polymer−particle interactions and investigate its properties in dependence of filler fraction Φ and chain molecular weight Mw. By means of small-angle neutron scattering and neutron spin echo experiments we have succeeded to give a thorough description of the molecular static and dynamic properties of the polymer chains in the presence of the nanoparticles.15−18 This way, it was possible to create a clear picture of the polymer dynamics and how the presence of nanoparticles affects it. Taking this information as our safe footing, we will now redirect our scale of observation from the truly microscopic scattering experiments to oscillatory shear rheology experiments on the same samples. This will enable us to correlate changes of the macroscopic mechanical properties with changes in the molecular dynamics, and thus help to identify the responsible mechanisms. After a very brief introduction into the model system under discussion and the rheology technique and theory, the results from rheology measurements will be presented. These results will be discussed in general first, before the focus will be shifted to a correlation of the rheology results with the scattering results presented earlier. Received: December 18, 2012 Revised: July 2, 2013

A

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Mc(T = −15 °C) = 3120 g/mol, assuming a temperature independent Me/Mc = 2.6. Therefore, from a molecular point of view, it is clear that PEP3k is above the entanglement molecular weight and almost exactly at the critical molecular weight Mc. On the other hand, if we would select a polymer with a molecular weight far below the entanglement molecular weight, most likely effects caused by the finite length becomes more important. In case of PEP3k, our previously obtained small-angle neutron scattering data showed that PEP3k can be treated with Gaussian chain statistics, even though the scattering experiment already reveals a first signature of finite length effects, such as a structure factor which shows that the molecular weight needs to be taken into account to describe the experimental results correctly.15 We note that in case of polymers with a sufficiently high molecular weight, such as PEP50k, taking into account the chain length is usually not necessary. Therefore, even in comparison with Me, PEP3k can be considered to be at the optimum compromise between an entangled polymer and an oligomer. In summary, we consider the low (PEP3k) and high (PEP50k) molecular weight polymers as representatives of unentangled and entangled polymers. The silica nano fillers were obtained from Nissan Chemical (trade name: ORGANOSILICASOL Tol-St), and will be referred to as “ST” particles in this work. According to supplier information, the particle diameter is DST ≈ 10−15 nm, the silica surface is partially modified with short hydrocarbons not specified further. Approximately 20% of the OH surface groups have been replaced, which suffices to render the particle hydrophobic. The silica are supplied in a stable toluene solution at a filler fraction of Φ = ΦST ≈ 30 vol %. All necessary particle parameters for evaluation purposes were determined separately in adequate experiments, which are detailed in refs 15 and 16. Both PEP and the particle surface layer consist of hydrocarbons. Thus, a mostly nonattractive particle−polymer interaction is realized and the PEP−ST system constitutes a model nanocomposite with nonattractive interactions. The only attractive forces are due to van der Waals attraction. The nanocomposites were obtained by means of solution mixing in toluene. After stirring for 48 h, the samples were first evaporated in air for 12 h and then dried in a vacuum oven for 48 h at T = 50 °C. To our knowledge, for the particular combination of PEP and silica this leads to a good dispersion of silica in the melts, minimizing agglomeration. For the rheology measurements, the dry samples were vacuum molded in a Teflon mold to yield well-defined plates of a diameter of 8 mm and a thickness of approximately 1 mm. A complete list of sample compositions and nomenclature is given in Table 2. Note by

EXPERIMENTAL SECTION

Materials. The model nanocomposite used in this work consists of poly(ethylene-alt-propylene) (=PEP) as an apolar polymer matrix, into which hydrophobically modified silica nanoparticles from Nissan Chemical are added as filler component. In this way, we avoid permanent chain adsorption. Two pairs of deuterated and hydrogenated PEP samples with different molecular weights, h-PEP3k, d-PEP3k and h-PEP50k, d-PEP50k, were chosen as the soft matrix component. These PEP polymers were synthesized from parent polyisoprenes, h- and d-PI, by catalytic hydration (deuteration) using a conventional Pd/BaSO4 catalyst. The corresponding polyisoprenes were prepared by anionic polymerization of isoprene (isoprene-d) monomer, with tert-butyllithium as initiator and benzene as polymerization solvent. The obtained microstructure consists of 75% cis1,4, 18% trans-1,4, and 7% 3,4 units for the PI50k and of 65% cis-1,4, 29% trans-1,4, and 6% 3,4 units for the PI3k, which was verified by NMR spectroscopy. The weight-average molecular weights of the PI50k polymers were determined by low angle laser light scattering in heptane. The numberaverage molecular weight of the h-PI3k sample was obtained from 1H-NMR measurements using the 9 protons of the t-butyl initiator group as internal reference. Size exclusion chromatography (SEC) on the d-PI3k and h-PI3k in THF revealed almost identical elution volumes. The molecular weight of the d-PI3k is then derived from the number-average molecular weight of the h-PI3k obtained by NMR multiplied by the ratio of the molecular weights of the monomeric units, 76/68. The polydispersity of all PIs were determined by SEC in THF relative to polystyrene standards. After saturation, all PEP materials were remeasured by SEC revealing no detectable change in polydispersity. For the h-PEP materials complete saturation was verified by the disappearance of the vinyl protons in the 1H NMR spectra. Complete saturation was also assumed for the d-PEP polymers since they were prepared identically. The average molecular weights of the final PEP polymers were then recalculated by the simply adding D2 or H2 per repeat unit. The characteristics of all PEP polymers are summarized in Table 1. These molecular weights correspond to

Table 1. Molecular Characteristics of PEP Polymers sample

Ma (g/mol)

Mw/Mn

h-PEP3k d-PEP3k h-PEP50k d-PEP50k

2980 3400 48900 49800

1.04 1.04 1.02 1.02

Table 2. Sample Nomenclaturea

a

Number-average molecular weight Mn for PEP3k, weight-average molecular weight Mw for PEP50k polymers. Mw/Mn represents the polydispersity index. the radii of gyration of Rg(T = 150 °C) = 1.93 ± 0.03 nm (h-PEP3k), Rg(T = 150 °C) = 8.33 ± 0.03 nm (h-PEP50k), as determined by small-angle neutron scattering.15 In order to understand the particular selection of the polymer melts the entanglement molecular weight Me or the related critical molecular weight Mc needs to be introduced. Below Mc the viscosity of polymers depends on M1, above on M3.4, where M represents the molecular weight.19 In the case of PEP, Me and Mc are related by Mc/Me(T = 100 °C) = 2.6.20 For PEP, Fetters et al. report Me(T = 140 °C) = 2280 g/mol,21 and thus, Mc = 5928 g/mol. Therefore, by considering just rheological experiment, at the first glance, it becomes evident that PEP3k represents the short and PEP50k the entangled polymer melt. However, we want to note that the comparison with Me deserves some attention. For example, Fetters et al. report a temperature dependent Me.20 Of course, a slight change of Me does not affect PEP50k. However, the molecular weight of PEP3k is very close to Me and therefore we would like to figure out, whether it is really below or above Me at the temperatures measured. In the literature Me(T = 24 °C) = 1475 g/mol is given.21 When we linearly extrapolate Me to one experimental temperature (T = −15 °C), as introduced later, Me(T = −15 °C) = 1200 g/mol or

sample

ΦSi [vol %]

ratio h/d-PEP

PEP3k-ST0 PEP3k-ST6 PEP3k-ST35 PEP3k-ST50 PEP50k-ST0 PEP50k-ST1 PEP50k-ST6 PEP50k-ST18 PEP50k-ST35 PEP50k-ST50

0 6 35 50 0 1 6 18 35 50

52/48 52/48 52/48 52/48 52/48 52/48 52/48 52/48 52/48 52/48

PEP50k denotes the Mw ≈ 50 kg/mol polymer matrix and PEP3k the Mw ≈ 3 kg/mol matrix. All values refer to room temperature of T = 25°C. The h/d ratios of protonated vs. deuterated components are given in vol/vol. a

the way that the combination of protonated and deuterated chains is not usual in rheology experiments, because there are no advantages resulting from it. In contrast to that, an adequate combination of protonated and deuterated chains is essential for the scattering experiments we performed (cf. refs 15−18), and we chose to use exactly the same samples in both experimental techniques in order to ensure perfect comparability. B

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METHODS: RHEOLOGY

For un-cross-linked melts the permanent elastic contribution Gelastic is 0. The terminal behavior for ω → 0 generated by equation eq 2 is that characteristic of viscous flow with G″(ω) ∝ ω and G′(ω) ∝ ω2. The ansatz originally proposed by Baumgaertel et al. for the spectrum reads

All samples were characterized by means of dynamic mechanical spectroscopy. The measurements were performed on a strain-controlled Rheometric Sci. ARES system operated in the dynamic mode using 8 mm parallel plates. Sample loading took place at room temperature of 25 °C for the PEP50k samples and at −15 °C for the PEP3k samples because of their very low viscosity. The gap between the parallel plates was adjusted to about 1 mm initially and varied with temperature to keep the normal force constant. The shear experiments were conducted with a shear amplitude of 0.5% well in the linear viscoelastic regime of the samples. For data treatment the software Rheometric Scientific software (Orchestrator) was used. The measurements were conducted in a temperature range from T = −25 to +25 °C (PEP50k) and T = −45 to −15 °C (PEP3k) and a frequency range from ω = 0.1 to 500 rad/s. The temperature stability was approximately 0.1 °C. From the rheology measurements at different temperatures master curves were constructed using the 2-dimensional time temperature shifting (TTS) option of the Rheometric Scientific Software (Orchestrator). The reference temperature T0 was taken to be 25 °C for all PEP50k curves and −15 °C for the PEP3k curves. The horizontal shift factors aT and vertical shift factors bT were determined accordingly. The validity of the Williams−Landel−Ferry relationship22 employed in the procedure

log aT = log

− C1(T − T0) τ(T ) = τ(T0) C 2 + (T − T0)

H(τ ) = Heτ ne + Hgτ −ng , τ0 < τ < τmax H(τ ) = 0, τ > τmax

He = represents the entanglement regime, whereas Hg = relates to the transition zone to the glassy relaxation. More sophisticated spectra have been suggested in the literature, but the BSW spectrum proved to yield good results for our data. Although the spectrum cut off times τ0 and τmax lack a strict physical significance, they can be connected with real physical quantities in the case of quite monodisperse linear polymers studied here. τ0 compares to the relaxation time of an entanglement segment and is the shortest relaxation time considered in the model. The longest considered relaxation time τmax on the other hand corresponds approximately to the disentanglement time τRep of a full chain (entangled melt) or the Rouse time τR (unentangled melt). According to ref 25, −ne is the slope of G″ in the entanglement region, and ng represents the slope toward the glass transition region. However, we want to emphasize that these parameters are just loosely connected with the molecular parameters, because they are not based on a molecular model. The parameter G0N is called the plateau modulus. In polymer nanocomposites, a dependence of the plateau modulus G0N(Φ) = G0N(Φ = 0)R(Φ) on the filler fraction Φ is usually observed.5,6,26 R(Φ) is the so-called reinforcement factor. At a certain critical filler fraction Φ* filler−polymer and/or filler−filler interactions may lead to the formation of a threedimensional network in the sample. We want to use the term network in its broadest meaning, i.e., referring to particle−particle, and/or polymer mediated systems. At the so-called gel point a connected network spanning the whole sample volume exists and the rheological behavior changes from melt-like to solid-like above a shortest network relaxation time τ*. Viscous flow no longer appears in the terminal regime, but the zero-shear viscosity and the longest system relaxation time τend diverge. In the recorded G′(ω) (or respectively G″(ω)) the influence can easily be seen in the slopes at low ω deviating from the undisturbed flow ω2 (ω1) behavior. To quantitatively include the possibility of gelation in the analysis, a gel relaxation contribution Hgel(τ) has to be added to the relaxation spectrum H(τ). For a critical gel, we define this contribution in accordance with the literature by a self-similar relaxation pattern:27

(1)

is not straightforward in filled polymer systems and will be investigated below. Independent of the applicability of TTS the relevant results could in all cases be extracted from the data at the measurement temperature alone so that all conclusions are independent of the validity of master curve construction.

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THEORETICAL BACKGROUND: RHEOLOGY For the description of the viscoelastic properties of polymers there exist some elaborate models that interconnect macroscopic observations from rheological experiments with the molecular structure and dynamics of polymer melts. For unentangled melts the Rouse model is the adequate molecular description.19 For the case of linear entangled polymer melts a very good description was achieved by an implementation of the tube model by Likhtman and McLeish.23 Their molecular analysis of the complex shear modulus includes all elementary processes from short scale Rouse dynamics to reptation, accounting also for contour length fluctuations, constraint release and longitudinal modes. It is our goal, however, to characterize changes in the rheology data induced by the addition of nanoparticles. There, it cannot be assumed a priori that a description in terms of standard polymer dynamical processes is justified. Therefore, we chose a phenomenological spectral approach, based on the well-known BSW model to get a parametrization of the effect of nanoparticle addition. The BSW model by Baumgaertel et al.24,25 is based on the fact that even a very complex relaxation process can always be described as a superposition of elementary relaxators with different characteristic relaxation times, in this case implemented as a continuous relaxation spectrum H(τ). In the dynamic mechanical experiments performed in the present work, the complex dynamic shear modulus G*(ω) = G′(ω) + iG″(ω) is measured and can be calculated from the spectrum via +∞

G′(ω) = Gelastic +

∫−∞ +∞

G ″ (ω) =

∫−∞

Hgel(τ ) = Sgel /Γ(n)τ −n

(4)

for τ* < τ < ∞. Γ(n) is the gamma function, the amplitude Sgel represents the gel stiffness and n is a relaxation exponent between 0 and 1. With this definition, the gel contribution to the storage and loss moduli can be written as:27 G′critgel (ω) =

G′′critgel (ω) tan(nπ /2)

= Sgel Γ(1 − n) cos(nπ /2)ωn (5)

for 0 τdecorr, diffusive motion with n = 1 is found. When we now add particles to the melt the mean square displacement is reduced over the whole time range, i.e. evidencing a reduced diffusion. Using additional simulations, we demonstrate interchain interactions are responsible for this reduction. Furthermore, in the composites with a high particle fraction, we observe subdiffusive behavior over the whole time region of the NSE experiment. For example, in case of Φ = 50%, we observe n = 0.75 ± 0.02. This value is larger than those reported by Vilgis et al. However, we want to emphasize that our experiments represent the average value of the whole polymer phase in the nanocomposite, whereas the calculations are related directly to the value of a single chain at a surface. On the basis of the theoretical calculations and the own experiments, it seems to be reasonable to analyze the intermediate range more in detail. For that purpose, we subtract the gel contribution G″corr (ω) = G″total (ω) − G″ gel (ω)

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CONCLUSION In this work, two nanocomposite model systems with mostly nonattractive polymer−particle and particle−particle interactions were characterized by means of oscillatory shear rheology. Apart from the occurrence of typical effects in colloidal rheology like mechanical reinforcement and gelation above a critical filler fraction 0 < Φ* < 0.18, the main focus was directed toward the thorough detection of changes in the polymer relaxation. In order to achieve a correct molecular interpretation of those changes, the results from small-angle neutron scattering and neutron spin echo experiments were used and physically correlated with the rheology data. In the case of the entangled PEP50k matrix, we discussed the shift of the maximum in G″(ω) by the increasing geometrical confinement imposed on the polymer relaxation by the surrounding particle structure. In particular, the peak position ωmax and the tube diameter dapp derived from the neutron spin echo experiment are very similar, when pure reptation in the framework of the de Gennes model is assumed to connect ωmax and dapp, where the position of the regular polymer tube diameter is now taken by an apparent confinement length dapp, comprising the effects of surrounding chains and the confinement by the particle structure. In the case of the unentangled PEP3k chains, no reptationlike confinement on the mode relaxation of the chains was observed. This is due to the fact that the chain size Rg = 1.9 nm of these short chains is much smaller than the typical void sizes in the particle structure even at the highest filler fraction, with the average particle diameter being Dpart = 17 nm. Instead, it was shown that the particle structure significantly hinders the relaxation of interchain correlations. In short chain matrices, those correlations decay rather fast so that in our unfilled reference sample PEP3k-ST0 normal diffusion of uncorrelated chains was evidenced for times t > 55 ns. In contrast to that the mean square displacement of the center of mass was found to be anomalous up to times t ≫ τdecorr in nanocomposites with high particle filler fractions. From the observation point of view of oscillatory shear rheology, this anomalous center of mass diffusion appeared as a significant deviation from normal viscous flow behavior at shear frequencies ω < 2π/τR, where instead of the regular terminal regime G″ ∝ ωn with n = 1 a significantly lower flow exponent n = 0.69 was found. Summing up, both in nanocomposites with entangled and unentangled polymer matrices, the influence of the particle presence on the chain dynamics was resolved. In both cases, the particles act merely as geometrical obstacles, i.e., a kind of wide pore structure, to which the polymer motion is confined. The manifestation of this geometrical confinement turned out to be slightly different in both cases, however, due to the very different length scale ratios “polymer size/typical particle void size” in the two model systems. When in the entangled matrix even the internal chain relaxation was confined and thus slowed down, in the unentangled matrix only a hindrance on the interchain relaxation was imposed.

(17)

The resulting curve is depicted in Figure 8. We would like to note that in order to test the influence of this subtraction we

Figure 8. Loss modulus G″ of PEP3k-ST50 before (G″total) and after ″ ) subtraction of the gel relaxation contribution Ggel ″ . For (Gcorr comparison the data of PEP3k-ST0 are also shown (vertically shifted by a factor).

varied G″gel(ω) up to a point, where no visible deviations occur. For comparison, the uncorrected PEP3k-ST50 data and the (vertically shifted) PEP3k-ST0 data are also given in the graph. It can be seen that the onset of flow at ωmax is not shifted to a different frequency regarding the unfilled polymer melt. It is rather the case that the flow regime can no longer be characterized by normal viscous diffusion behavior, as indicated by the change of slopes from 0.93 ± 0.01 to 0.69 ± 0.01. Taking into account the fitting errors does only slightly change the exact value 0.69. This value refers to the best fit value. But any result within the fitting error leads to the same observation and in particular the same general physical conclusion. No gelsubtraction within the error bars is able (or even close) to reproduce the original slope of 0.93 from the unfilled melt. So clearly the slope in the region of viscous flow becomes smaller. In summary, the analysis of rheology and NSE data

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (G.J.S.) [email protected]. I

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank L. Willner for kindly providing the polymers and W. Pyckhout-Hintzen for introduction and technical support of the rheology experiments. K.N. acknowledges the financial support of the Evonik Stiftung.

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