Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
pubs.acs.org/Macromolecules
Effect of Nanoparticle Organization on Molecular Mobility and Mechanical Properties of Polymer Nanocomposites Frantisek Ondreas,*,† Petr Lepcio,† Marek Zboncak,† Klara Zarybnicka,† Leon E. Govaert,‡ and Josef Jancar† †
Central European Institute of Technology, Brno University of Technology, Brno 61200, Czech Republic Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven NL-5600 MB, The Netherlands
‡
Downloaded via NOTTINGHAM TRENT UNIV on August 13, 2019 at 23:55:01 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
S Supporting Information *
ABSTRACT: Influence of nanoparticle (NP) spatial organization on relaxation and mechanical properties of polymer nanocomposites (PNCs) was investigated. For the first time, the properties of PNCs with various nanostructures at the constant chemical composition were related to their experimentally determined structural parameterseffective interfacial surface and interparticle distance. Segmental scale reinforcement active below and above glass transition was attributed to the immobilization and frustration of polymer segments caused by attractive polymer−particle interactions. A novel reinforcing mechanism of chain bound clusters related to their internal structure was revealed while negligible reinforcement from NP−NP interactions of contact aggregates was found. The mechanical response of PNCs was correlated with appropriate relaxation properties. It provided the first experimental proof that deformation yielding dynamics of PNCs is controlled by glass transition segmental mobility. Main features of various NP spatial organizations were characterized. Chain bound clusters showed the most significant reinforcement above the glass transition temperature (Tg). Moreover, the hierarchical nature of chain bound clusters caused broadening of the ductile response compared to other nanostructures and also to the neat matrix. The most pronounced enhancement of elastic modulus, yield stress, and creep durability was found for individually dispersed NPs. The acquired nanostructure−property relationships will provide a foundation for the future design of hierarchic and multidomain nanocomposites.
■
INTRODUCTION
significantly their amount in the nanocomposite which could have had a crucial influence on the final properties.16 However, the origin of this nanoscale reinforcing mechanism is still a matter of discussion.1,4,8,17−31 There is a decade-old dispute whether the reinforcement and viscoelastic features of PNCs such as the Payne effect originate from particle−particle interactions (preferring van der Waals interactions of progressive NPs aggregation17,18,31−34) or polymer−particle interactions (assuming immobilized polymer layer formation around NP surface with different properties from the bulk matrix1,4,5,19,20,25−27,29,30) which seems to be favored by the most recent works. Above Tg, polymer dynamics is frustrated by the vicinity of NPs and differs significantly from the unaffected dynamics of the bulk matrix.
Polymer nanocomposites (PNCs) hold a great promise as the next-generation lightweight functional materials with advanced and tunable mechanical properties.1−10 However, only a limited practical application of PNCs as structural components is currently found in the industry due to the insufficient control of the nanoparticle (NP) assembly, unknown nanostructure− property relations, and challenging production scale-up. While progress in NP self- and force-assembly have been reported over the last decade,5,11−14 nanostructure-property function linking the experimentally determined structural parameters with final nanocomposite properties has not been fully understood yet. There is a well described case represented by PNCs with grafted NPs where different mechanical response was found for various structuresfractals, strings, and dispersed NPs.15 However, the structures were fabricated by varying density and length of polymer grafts changing © XXXX American Chemical Society
Received: June 11, 2019
A
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
matrix were used to avoid the influence of graft−polymer interactions or altered crystallinity. The preparation protocol is described in detail in our previous study.14 Briefly, PNCs were solution blended in various solvents, dried at 140 °C to quantitatively remove the solvent, and pressure molded at 190 °C into sheets from which specimens were cut. Techniques. Dynamic mechanical analysis (DMA) was performed employing DMA RSA G2 (TA Instruments, USA) using a single cantilever geometry on specimens with dimensions of 30 × 5 × 1 mm. The thermomechanical history of samples was erased at 140 °C during 20 min before measurements. Temperature sweeps were performed in the temperature range from 140 to 90 °C with 1 °C step, at deformation amplitude of 0.05%, frequency of 1 Hz, without any additional axial force that could cause a complex response.40 Small amplitude oscillation shear measurements were conducted on an Ares G2 Rheometer (TA Instruments, USA) in the plate−plate geometry. Weak axial force was used in order to gently compensate gap position with respect to thermal expansion and retraction occurred during a test. Frequency sweeps from 0.01 to 20 Hz in temperature steps of 10 °C were performed for the temperature ranging from 200 to 150 °C. Standard deviation of DMA and rheology measurements did not exceed 5% as tested on standard specimens. Uniaxial tensile and creep measurements were measured utilizing a Zwick Roell Z010 (Zwick-Roell, CH) equipped with a 10 kN load cell. Dog-bone-shaped specimens were chosen for all mechanical measurements. The experiments were carried out at constant strain rates ranging from 10−5 to 10−1 s−1 at 60 and 80 °C. Creep measurements were performed at constant engineering stresses up to failure times of 4 × 105 s at 80 °C. Standard deviation of elastic modulus and yield stress was lower than 5 and 10%, respectively, as tested on standard specimens.
A pronounced effect of NPs on mechanical properties is usually reported in close vicinity and above glass transition temperature (Tg).1,19,21,27,29,30 It was expected that this effect diminishes as the temperature drops below Tg.29 However, a significant influence of NPs was reported also below Tg.2,3,5,6,35 Jancar et al.2,3 investigated the influence of NPs on strain hardening and softening dynamics at various particle sizes, thermal histories, NP concentration, strain rates, and temperatures below Tg. Temperature and particle size-dependent increase of yield stress and elastic and strain hardening modulus was found as well as a significant influence of NPs on deformation dynamicsactivation energy and volume and strain softening overshoot. Hashemi et al.5 investigated the influence of NP−polymer interaction strength on the mechanical properties of silica NPs functionalized with 2ureido-4-pyrimidinone moieties strongly interacting with the PMMA matrix via hydrogen bonds. These interactions reminiscent of physical crosslinks were beneficial for the NP dispersion and elastic modulus and yield stress were significantly enhanced below Tg. Dorigato et al.6 found NP concentration and surface modification-dependent increase of elastic modulus, yield stress, stress and strain at break, and specific tensile energy at break of polylactide (PLA)/SiO2 PNCs below Tg. Cheng et al.35 found 130% increase of elastic modulus of PVAc/SiO2 PNC below Tg. They directly determined the increase of Young modulus of the interfacial layer compared to the bulk matrix below Tg. The phenomenon was explained by disturbed chain packing at the interface. Pseudo-brush stretched conformation was suggested to take place for polymer segments in the immediate vicinity of the NP surface.35,36 Despite recent advances,1−3,7,8,11,15,35,37−39 no experimental study focused on the NP spatial organization influence on PNC properties below and above Tg and their connection to the molecular relaxation at constant chemical composition has been published yet. The present study focuses on the influence of NP spatial organization on relaxation and mechanical properties. The results are related to NP volume fraction and experimentally determined structural parameterselement size and interelement distance. The term “element” used in this study refers to the basic NP structural entity interacting with the polymer matrix (Figure S1). That is, either an individually dispersed NP, a chain bound cluster, or a contact aggregate.14 Direct comparison among individually dispersed NPs, chain bound clusters, and contact aggregates at constant composition was utilized to investigate reinforcing mechanisms in PNCs below and above Tg. For the first time, direct experimental connection between the relaxation dynamics and mechanical properties of PNCs is reported. Nanostructureproperty function was proposed to aid the design of future lightweight PNC materials.
■
■
RESULTS AND DISCUSSION The structural analysis of the investigated PMMA/SiO2 system is only briefly recalled here as it has been described in detail in our previous study14 that focused on structure development of PNCs during solution blending. Solid-state PNCs were examined by USAXS and transmission electron microscopy (TEM) image analysis, and the data was combined with indirect rheological evidence from the solution blending step. Minor extension and modification are commented in the Supporting Information. We note that in the current study, the root mean square value was selected to represent the element diameter (Figure S2).The investigated samples covered three principal NP organizations. Acetone series featured individually dispersed NPs with gradual formation of small aggregates with increasing NP volume fraction evidenced by the increase of mean element size. Chain bound clusters (i.e., NPs intertangled with polymer chains) prepared from the acetone−toluene 1:1 mixture preserved an unchanged element size up to 5 vol %. The following slight increase in size was probably caused by the connection of neighboring clusters. The internal structure of chain bound clusters was previously interpreted from indirect rheological evidence and formation kinetics and will be recalled below in data interpretation. Contact aggregates of constant size were present in toluene series. The total interfacial surface area of NPs per unit volume of PNCs (m2/m3) labeled as the effective interfacial area, Seff, was calculated from the real element concentration and dimensions determined from the TEM image analysis. Details of the image analysis, interelement distance calculation, discussion about 2D data interpretation of the 3D situation, and comparison of the interelement distances to the model data41,42 are described in ref 14 and Supporting Information. Note that this parameter, Seff, does not correlate to the specific surface area expressed in
EXPERIMENTAL PART
Materials. The commercial grade poly(methyl methacrylate) (PMMA) Plexiglas 8N (Evonik, Germany) with Mn = 50 kg·mol−1, Mw/Mn = 1.9, and Tg = 112 °C was used as matrix. The PMMA contains 5−7% of isotactic, 50−52% of syndiotactic, and 41−52% of atactic chain sequences, all apparently randomly distributed along each chain, as determined by nuclear magnetic resonance analysis provided by the supplier (Evonik, GE). Colloidal bare silica NPs dispersed in isopropanol with a particle diameter of 20 ± 4 nm were supplied under the commercial name IPA-ST (Nissan Chemicals, JP). All solvents were in p.a. purity grade (Lachner, CZ). No grafting or surface functionalization of ceramic SiO2 NPs and glassy PMMA B
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 1. Dependence of ΔTg on (A) volume fraction and (B) effective interfacial surface area of elements (individual NPs, clusters, or aggregates) divided by the reciprocal value of interelement distance of various PNCs.
g/m2. It is believed that this parameter can represent the real element surface accessible for interfacial interactions with surrounding polymer chains. Interelement distance was calculated from the TEM image analyses and refers to the real interelement distances in the final nanocomposites. The combined parameter of these two structural variablesthe effective interfacial area divided by the interelement distance reflects the amount of the immobilized and frustrated polymer chains with regard to their spatial organization. Conveniently, it can indicate a possible percolation of the affected polymer layer as will be discussed later in the text. The dependences of the element diameter, interparticle distance, effective surface area, and effective surface area divided by interelement distance on NP volume fraction are shown in Figure S2. Individually dispersed NPs have the largest interfacial element surface and the shortest interelement distance. Therefore, they can modify the largest extent of surrounding chains. The induced mobility retardation and reinforcement clearly originate from attractive polymer−particle interactions that form an affected polymer layer around the NPs. It is assumed that this layer consists of two partsimmobilized and frustrated polymers.1 The immobilized layer represents tightly adsorbed polymer segments at the NP surface with highly retarded dynamics. Polymer segments connected or intertangled with the immobilized ones form an adjoining layer of frustrated polymer whose dynamics is also retarded but less than that in the immobilized layer. NPs in chain bound clusters are closely packed into bundles without a direct NP−NP contact as the interphase is mediated by inserted polymer chains immobilized by strong adsorption.43−47 These so-called bridging chains,22−24 which interact with multiple NPs at once, differ from the chains at the cluster−matrix interface as they are tightly confined between several NPs. Such clusters behave as independent entities dispersed in a polymer matrix.14 This system could be considered as a hierarchical structure with a two-level hierarchy. This material has two contributions to the final propertieselement−polymer interfacial interactions and intraelement NP−polymer-bridged nanostructure which contributes to intrinsic stiffness of the cluster. Contact aggregates have the lowest effective surface and their internal structure consists of van der Waals particle−particle interactions. This type of NP organization has also two contributions to the final properties arising from the low element−polymer interface and the particle−particle interactions inside the aggregates. Though the experimental structures were not the ideal representatives of the individual structural types, it was supposed that the structure polydispersity had only a minor effect on the final thermomechanical properties.
The glass transition temperature was used as a probe to investigate the mobility changes in PNCs. The dependence of the difference between the glass transition temperature of PNCs and the neat PMMA, ΔTg, on the filler volume fraction for different dispersion states is shown in Figure 1A. An increase of Tg was found for all PNCs investigated. Attractive PMMA−SiO2 interactions were expected due to the hydrogen bonding between ester groups of PMMA and surface silanol groups of silica NPs.48 The greatest increase of Tg was recorded for PNCs with individually dispersed NPs. The NP content dependence of ΔTg exhibits an initial rapid increase compared to the neat PMMA followed by a weak growth at higher concentrations. A clustered system showed a gradual rise of Tg with increasing NP volume fraction. The lowest ΔTg was found in PNCs with aggregated NPs. The dependence of ΔTg on the effective interfacial area divided by the interelement distance revealed a two-step growth that, independent of structure, consists of initial rapid growth at low effective surface and large interelement distance followed by flat gradual increase (Figure 1B). The critical point was reached at ΔTg of approximately 5 °C. It corresponds well to the work of Hamieh et al.49 who found that Tg increase for syndiotactic PMMA adsorbed onto the silica surface equals approximately 5 °C. This suggests that the dynamics of almost all polymer chains was already affected at the critical point that is found at the interelement distance equal to two times the affected layer thickness (Figure S2). Both the immobilized and frustrated polymer layer originate from NP−polymer interactions. Saturation of the immobilized polymer layer can only be reached at very high NP volume fraction due to the typical layer thickness being approximately 1−3 nm,1,50,51 which is far less than the interelement distances determined in our samples (Figure S2). On the other hand, the frustrated polymer layer corresponds to the area characterized by distorted molecular dynamics of the whole chain caused by chain connectivity of its immobilized segments or by entanglement with its neighbor. According to our findings, its thickness is approximately 23 nm. Therefore, at the critical point where the interelement distance equals to two times the affected layer thickness, all macromolecules are already frustrated. Further increase of NP volume fraction or interfacial surface only increases the amount of immobilized segments. Though their dynamics is retarded more than that of the frustrated polymer layer, and their volume is relatively small and only minor increase of ΔTg is achieved above the critical point. The macroscopically determined Tg is not sensitive enough to such local changes in the chain dynamics and the final results are rather a volume average with a dominant response from the frustrated polymer C
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 2. Dependence of reptation time of PNC with various particle organization at 190 °C on (A) volume fraction and (B) effective interfacial surface area of elements divided by reciprocal value of interelement distance. (C) Dependence of zero shear rate viscosity on volume fraction of PNCs with various particle organization fitted by eq 1.
The dependence of the reptation time on the filler volume fraction revealed significant differences between various nanostructures (Figure 2A). However, the reptation time of various nanostructures fell onto a single curve when plotted against the interfacial surface area divided by the interelement distance. Moreover, it shows analogical features (critical point) as the glass transition temperature dependence further supporting the previous conclusions (Figure 2B). The correlation between this parameter and the relaxation response of PNCs on various time and length scales in transient and terminal regions supports the theory that it is a versatile and physically meaningful variable capable of characterizing the PNC inner structure. These experimental results are in a good agreement with the molecular modeling conclusions52 claiming that the prolongation of the reptation time originates not only from the extension of the primitive path of the chain contour length but also because chains must reptate through several domains of slower dynamics near the element surface. The internal structure of clusters was neglected in the calculation of the interfacial surface and they were treated as compact entities. Because the data collapsed onto the same curve as the dispersion of individual NPs, it seems that the bridging chains were unable to contribute significantly to the determined reptation time within the investigated volume fraction, temperature, and frequency range. The zero shear viscosity was evaluated by fitting the viscosity shear rate dependence with the Cross model.53 The filler volume fraction dependence of the relative zero rate viscosity of PNCs with various NP spatial organizations is shown in Figure 2C. The viscosity of nanocomposite fluids, if considered as a suspension of colloidal-size particles in polymer liquid, can be addressed by the modified Einstein−Stokes equation38,54−57
layer. Emamy et al.39 simulated the effect of NP size, NP− polymer interaction strength, and interparticle distance on the relaxation dynamics and Tg of PNCs. They determined three principal regions of Tg changes in attractively interacting PNCs by considering interparticle distance relative to coil dimensions as the governing parameter. Contact aggregates at low concentrations (below 5 vol % including) belong to the dilute region with an interelement distance much longer than gyration radius (Rg). Little increase of Tg found for these samples is then caused by decoupling of interfacial polymer dynamics from the polymer matrix. Shortening the interparticle distance to the dimensions of Rg should cause bridging of interfacial chains resulting in higher increase of Tg. The further shortening up to the segmental scale should tilt the response to the interfacially dominated regime where interfacial zones overlap due to the high NP concentration. The most pronounced increase of Tg can be found in this region. Individually dispersed NPs over the whole concentration range and chain bound clusters at higher concentrations (above 5 vol % including) should belong to the interfacially dominated regime while chain bound clusters with lower NP amount (below 5 vol %) affiliate to the bridging regime according to the Tg increase. However, their structural dimensions lie in the dilute regime according to the study (Figure S3). The discrepancy could be caused by the fact that the study considers only the immobilized layer as a zone with reduced dynamics. If the whole affected layer, that is, interfacial immobilized and frustrated layer combined, was considered as the region with slowed dynamics, better match with the model would be found. The presence of NPs altered the melt rheology response of the investigated PNCs by determining their processability and practical applicability. Reptation time, modulus of the rubbery plateau, and the thermal dependence of the zero-shear viscosity were evaluated as the representative rheological parameters.
ηr,0 = 1 + 2.5 kϕ + Pϕ D
(1) DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 3. Dependence of (A) elastic and (B) plateau composite modulus on volume fraction. Dependence of (C) elastic and (D) plateau composite modulus reduced to the matrix modulus and appropriate continuum micromechanics model on effective interfacial surface area of elements divided by the reciprocal value of interelement distance.
where ηr,0 is the relative zero shear viscosity, 2.5 is the analytically determined Einstein coefficient, H is the second virial coefficient, also known as the Huggins coefficient, which characterizes the interparticle interactions, and k is the parameter that characterize the effective hydrodynamic volume of particles influenced by the interaction with polymer chains.38,54−57 Values of k ranging from large positive to large negative were reported previously.14,57 Adsorption of polymer segments onto the surface of particles increases their hydrodynamic size and, in turn, the value of k. The second virial term was neglected due to the very low NP concentrations. A significant discrepancy was found between the intrinsic viscosity and the Einstein’s value of 2.5 derived for noninteracting particles, as characterized by the k parameter. PNCs with individually dispersed NPs exhibited the highest k value (15) due to the largest interface area. The k value (11) of PNCs with chain bound clusters was close to the value of PNCs with individually dispersed NPs. The lowest k value (5) was found for PNCs with contact aggregates, but their k value still differed significantly from the Einstein coefficient. This effect was ascribed to the adsorption of polymer segments onto smaller aggregates that have still relatively large surface area. The thickness of the affected polymer layer was calculated by means of eq 2 h=
3
3Vk −r 4π
respectively. The obtained affected layer thickness suggests that every NP influences dynamics of approximately 2 coils in the direction perpendicular to the NP surface. This means that chain dynamics of all polymer chains is affected by NPs below the interparticle distance of approximately 46 nm. It corresponds to about 0.5 vol % filler loading for individually dispersed NPs and 3 vol % for chain bound NP clusters (Figure S2). The PNCs with chain bound clusters had the highest particle interaction coefficient (P value = 497) due to the interparticle interactions mediated by strongly adsorbed chains in closely packed clusters. The lowest P value (21) was found for PNCs with individually dispersed NPs because of their largest interelement distances and the absence of clusters. PNCs with aggregated NPs exhibited an intermediate P value (139). The existing volume replacement continuum mechanics models58−63 for the composition dependence of the elastic or plateau modulus were not able to describe the dependence of the relative moduli on the NP volume fraction (Figure 3A,B). Therefore, an additional reinforcement mechanism was considered. The dynamics of polymer chains in rubbery plateau regime, approximately 75 °C above the Tg, was retarded by the attractive NP−polymer interactions. Affected chains reached several orders of magnitude longer relaxation times when compared to the unaffected bulk. These results are in good agreement with numerous studies published before.1,4,8,27−30,64−66 However, a significant enhancement of elastic modulus (approximately 50% increase at 1 vol % of individually dispersed NPs) was also found approximately 35 °C below Tg. Obviously, the introduction of the immobilized “glassy” fraction present above Tg in the vicinity of NPs due to energetically shifted glass transition29 could not explain the reinforcement below Tg. The presence of NPs leads to a disturbed segmental packing with reduced dynamics. The directly adsorbed immobilized segments retard the dynamics further in the frustrated polymer layer through chain connectivity and entangled macromolecules. The affected chains undergo divergent structural relaxations upon cooling,
(2)
where h is the thickness of the affected polymer layer, V is the element volume, k is the above mentioned effective hydrodynamic volume parameter, and r is the element radius. Radii determined by image analysis of TEM snapshots were used (average radius of 15 nm for series of individually dispersed NPs and 22 nm for series with chain bound clusters as their internal structure was neglected).14 The thickness of the frustrated polymer layer was approximately the same for various NP spatial organizations23 ± 1 nm for PNCs with individually dispersed NPs and chain bound clusters, E
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 4. Strain rate dependence of (A) yield stress and (B) reduced yield stress to the distance from glass transition on the strain rate of the neat PMMA and PMMA/1 vol % SiO2 PNCs with various NP spatial organization measured in tension at 80 °C.
volumes of PNCs did not change compared to the neat PMMA. PNCs with individual NPs exhibited the most pronounced increase of the yield stress while aggregates exhibited the lowest. Ductile yielding represents a process of polymer segments rearranging under external deformation creating a new structure that can carry the stress. The rearranging dynamics of the affected segments demands greater deformational energy compared to the unaffected one. It was shown that the glass transition temperature reflects the influence of NPs on the segmental scale mobility. Therefore, the observed yielding dynamics changes could be related to the distance between the temperature of testing and the glass transition. This approach was already successfully adopted to explicate the dependence of polyamide mechanical properties on humidity,69 where water molecules increased chain mobility, and, therefore, decreased the mechanical performance. In the present study, the glass transition temperature and the yield stress increased due to the reduced segmental mobility of affected polymer chains around the NPs. The dependence of the yield stress reduced by the distance between testing and glass transition temperature is shown in Figure 4B. The dependence felt onto a single curve common for the neat PMMA matrix and the PNCs independent of NP spatial organization. It confirms that the molecular mobility at the segmental scale controls the yielding process of PNCs. Quite different situation was found at 60 °C (Figure 5) when compared to 80 °C. The ductile yielding did not control the response over the whole strain rate range and significant differences between various NP spatial organizations were found. Tensile curves of various materials at 10−3 s−1 and 60 °C are shown in Figure S4. While the neat PMMA showed preyield failure, it still followed the ductile yielding regime
resulting in a different molecular packing and position on the energy landscape67 with different relaxation times compared to the neat matrix. Therefore, more energy and longer time is needed to pull out the segments with affected dynamics from their energy minima which results in the enhanced mechanical properties of PNCs above and also below Tg. An important structural difference arose when the normalized moduli (reduced to the matrix modulus and appropriate continuum micromechanics model for expressing the extent of additional molecular scale reinforcement beyond the prediction of the micromechanics models68) were related to the experimentally determined structural parameter of the effective interfacial area divided by the interelement distance (Figure 3C,D). The normalized modulus dependence below Tg revealed that for individually dispersed NPs, a saturation caused by the “percolation” of frustrated chains has been reached even at the lowest investigated volume fraction. Chain bound clusters, on the other hand, showed a gradual increase of the normalized modulus above certain critical point of the effective interfacial area divided by the interelement distance (Figure 3C). Clearly, a more pronounced reinforcement above Tg was found for chain bound clusters compared to the individually dispersed NPs and contact aggregates (Figure 3D). Unlike for contact aggregates, where only the abovementioned segmental scale reinforcing mechanism was found suggesting negligible benefit from particle−particle interactions, there is another mechanism present in chain bound clusters which originates in the internal cluster structure. Inside the clusters, NPs are bonded by highly affected bridging chains with greatly retarded molecular dynamic and packing. Cheng et al.35 directly observed domains that bridged neighboring NPs with enhanced stiffness when mapped their PVAc/SiO2 PNCs using band excited atomic force microscopy. Unfortunately, the precise molecular structure and dynamics of the polymer chains within the clusters has not been experimentally characterized by the presented article nor by any other published work known to authors. Considering a different deformation of the polymer chains in the bulk matrix, in the vicinity of NPs, and in the inner structure of clusters, PNCs can exhibit a complex macroscopic response consisting of these contributions. The strain rate dependence of the yield stress of PMMA/SiO2 PNCs containing 1 vol % at 80 °C is shown in Figure 4A. The mechanical response was controlled by the ductile flow regime for all materials investigated in the whole strain rate range at 80 °C. The crossover between α and α + β regime remained localized near the strain rate of 10−3 s−1. Moreover, slopes of yield stress−strain rate dependence and related activation
Figure 5. Strain rate dependence of the yield stress of the neat PMMA and PMMA/1 vol % SiO2 PNCs with various NP spatial organization measured in tension at 60 °C. F
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 6. Dependence of time to failure on (A) load and (B) reduced load to the distance from glass transition of the neat PMMA and PMMA/1 vol % SiO2 PNCs with various NP spatial organizations measured in tensile creep at 80 °C.
deviation from the bulk matrix that is preserved also below Tg. In good accordance to our data, Patukhov, et al.73 showed that the increase of creep failure times of polycarbonate/carbon nanotubes PNCs in the plasticity controlled regime is connected with the increase of the yield stress as a consequence of the reduced chain mobility.
whereas the embrittlement of the PNCs with aggregates was so extensive that they did not follow the ductile yielding regime. The PNCs with individually dispersed NPs also showed a preyield failure. They followed the ductile yielding at intermediate stain rates but showed rather brittle fracture or slow crack growth regime at fast and slow strain rates. The PNCs with clusters followed the ductile yielding. Moreover, the response showed a post-yield failure at certain strain rates. The increase of elongation of PNC with the nanostructure similar to our chain bound clusters was observed for the PLA/treated SiO2 system.6 The origin of this advanced behavior can be attributed to the hierarchical character of clusters that can represent structured inclusions of interacting chains and particles dispersed in the matrix endowing both intrinsic and extrinsic deformation processes to become active. Good durability performance is a critical parameter of a high-end material design. Advanced long-term mechanical performance of PNCs has been reported by several authors.70−76 The influence of the NP spatial organization on the plasticity-controlled creep failure regime was investigated. The tensile creep behavior of 1 vol % PNCs of various NP spatial organizations was compared with the neat PMMA matrix, Figure 6A. The comparison of the creep curves of various materials at 80 °C and loaded with 18 MPa is shown in Figure S5. The PNCs with individually dispersed NPs showed a shift of more than one order of magnitude to longer failure times than the neat PMMA. The PNCs with clusters showed a less but still improved durability, while aggregates showed only negligible enhancement. It seems that the particle−particle interaction cannot contribute to the creep durability and particle−polymer interactions are fully responsible for the prolongation of the failure times. Similarly to the yield stress dependence, the response originates from the rearrangement of polymer segments under external stimuli in the investigated plasticity controlled regime. In creep tests, constant engineering stress causes the system rearrangement and a gradual deformation until failure at a critical plastic strain.73,77 Longer time was needed to pull out the affected segments from their deeper energetic minima at constant energy input (load) to approach the critical plastic strain causing macroscopic failure. The dependence of the creep failure time on the load reduced to the distance between testing temperature and Tg (Figure 6B) merged the response of the neat PMMA and PNCs with various nanostructures. Therefore, the distance between the temperature of testing and the glass transition (Tg−T) can reflect the position on the energy landscape67 and control the thermally activated processes below Tg. It provides another proof that NPs not only increase the glassy fraction but also introduce frustrated polymer dynamics and chain packing
■
CONCLUSION A significant influence of NP organization on relaxation and mechanical properties was found. Influence of NPs on glass transition segmental scale and terminal zone reptation dynamics and elastic modulus below and plateau modulus above Tg were related to the experimentally determined structural parametersthe effective interfacial area and the interelement distance. The two step increase of Tg and segmental scale reinforcing mechanism active below and above glass transition were attributed to the presence of immobilized polymer segments in the vicinity of the NP surface and frustration of connected and intertangled chains. A unique reinforcing mechanism of chain bound clusters related to their internal structure was revealed while negligible reinforcement from NP−NP interactions of contact aggregates was observed. The adsorption of polymer segments onto the particle surface increased their hydrodynamic size that influenced the viscosity of PNC melts. The affected polymer layer length was calculated to be approximately 23 nm (∼4 Rg) for the investigated PMMA/SiO2 system. It was proposed that the immobilized layer forms only a minor part (approximately 1−3 nm) in the closest vicinity of the NP surface while the rest is formed by a polymer layer with frustrated dynamics. PNCs with chain bound clusters showed the highest particle interaction coefficient due to the strong interactions of particles in closely packed clusters mediated by the adsorbed chains. Mechanical response of PNCs was correlated with molecular dynamics. The dependence of the yield stress reduced by the difference between the temperature of testing and glass transition related to the strain rate for PNCs with various NP spatial organizations and neat PMMA felt onto a single master curve as well as the creep failure time related to the load reduced by the distance between the temperature of testing and glass transition. It was concluded that the deformation yielding dynamics of PNCs is controlled by the segmental mobility at the time and length scale of glass transition. The principal features of various NP spatial organizations were characterized. Chain bound clusters showed the most enhanced reinforcement above the glass transition temperature (Tg) originating from the highly affected bridging chains inside the clusters. Moreover, the hierarchical nature of chain bound clusters caused a broadG
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
(8) Kumar, S. K.; Ganesan, V.; Riggleman, R. A. Outstanding theoretical questions in polymer-nanoparticle hybrids. J. Chem. Phys. 2017, 147, 020901. (9) Mannov, E.; Schmutzler, H.; Chandrasekaran, S.; Viets, C.; Buschhorn, S.; Tölle, F.; Mülhaupt, R.; Schulte, K. Improvement of compressive strength after impact in fibre reinforced polymer composites by matrix modification with thermally reduced graphene oxide. Compos. Sci. Technol. 2013, 87, 36−41. (10) Chandrasekaran, S.; Sato, N.; Tölle, F.; Mülhaupt, R.; Fiedler, B.; Schulte, K. Fracture toughness and failure mechanism of graphene based epoxy composites. Compos. Sci. Technol. 2014, 97, 90−99. (11) Jouault, N.; Zhao, D.; Kumar, S. K. Role of Casting Solvent on Nanoparticle Dispersion in Polymer Nanocomposites. Macromolecules 2014, 47, 5246−5255. (12) Akcora, P.; Liu, H.; Kumar, S. K.; Moll, J.; Li, Y.; Benicewicz, B. C.; Schadler, L. S.; Acehan, D.; Panagiotopoulos, A. Z.; Pryamitsyn, V.; Ganesan, V.; Ilavsky, J.; Thiyagarajan, P.; Colby, R. H.; Douglas, J. F. Anisotropic self-assembly of spherical polymer-grafted nanoparticles. Nat. Mater. 2009, 8, 354−359. (13) Zhao, D.; Gimenez-Pinto, V.; Jimenez, A. M.; Zhao, L.; Jestin, J.; Kumar, S. K.; Kuei, B.; Gomez, E. D.; Prasad, A. S.; Schadler, L. S.; Khani, M. M.; Benicewicz, B. C. Tunable Multiscale Nanoparticle Ordering by Polymer Crystallization. ACS Cent. Sci. 2017, 3, 751− 758. (14) Lepcio, P.; Ondreas, F.; Zarybnicka, K.; Zboncak, M.; Caha, O.; Jancar, J. Bulk polymer nanocomposites with preparation protocol governed nanostructure: the origin and properties of aggregates and polymer bound clusters. Soft Matter 2018, 14, 2094−2103. (15) Kumar, S. K.; Jouault, N.; Benicewicz, B.; Neely, T. Nanocomposites with Polymer Grafted Nanoparticles. Macromolecules 2013, 46, 3199−3214. (16) Huang, Y.; Zheng, Y.; Sarkar, A.; Xu, Y.; Stefik, M.; Benicewicz, B. C. Matrix-Free Polymer Nanocomposite Thermoplastic Elastomers. Macromolecules 2017, 50, 4742−4753. (17) Clément, F.; Bokobza, L.; Monnerie, L. Investigation of the Payne effect and its temperature dependence on silica-filled polydimethylsiloxane networks. Part I: Experimental results. Rubber Chem. Technol. 2005, 78, 211−231. (18) Clément, F.; Bokobza, L.; Monnerie, L. Investigation of the Payne effect and its temperature dependence on silica-filled polydimethylsiloxane networks. Part II: Test of quantitative models. Rubber Chem. Technol. 2005, 78, 232−244. (19) Jouault, N.; Dalmas, F.; Boué, F.; Jestin, J. Multiscale characterization of filler dispersion and origins of mechanical reinforcement in model nanocomposites. Polymer 2012, 53, 761−775. (20) Kalfus, J.; Jancar, J. Immobilization of polyvinylacetate macromolecules on hydroxyapatite nanoparticles. Polymer 2007, 48, 3935−3937. (21) Jouault, N.; Vallat, P.; Dalmas, F.; Said, S.; Jestin, J.; Bouè, F. Well-Dispersed Fractal Aggregates as Filler in Polymer-Silica Nanocomposites: Long-Range Effects in Rheology. Macromolecules 2009, 42, 2031−2040. (22) Sarvestani, A. S.; Picu, C. R. Network model for the viscoelastic behavior of polymer nanocomposites. Polymer 2004, 45, 7779−7790. (23) Sarvestani, A. S.; Picu, C. R. A frictional molecular model for the viscoelasticity of entangled polymer nanocomposites. Rheol. Acta 2005, 45, 132−141. (24) Picu, C. R.; Sarvestani, A. S.; Palade, L. I. Molecular Constitutive Model for Entangled Polymer Nanocomposites. Mater. Plast. 2012, 49, 133−142. (25) Ciprari, D.; Jacob, K.; Tannenbaum, R. Characterization of polymer nanocomposite interphase and its impact on mechanical properties. Macromolecules 2006, 39, 6565−6573. (26) Tannenbaum, R.; Zubris, M.; David, K.; Ciprari, D.; Jacob, K.; Jasiuk, I.; Dan, N. FTIR characterization of the reactive interface of cobalt oxide nanoparticles embedded in polymeric matrices. J. Phys. Chem. B 2006, 110, 2227−2232.
ening of the ductile response compared to the other nanostructures and the neat matrix. The most pronounced enhancement of the elastic modulus, yield stress, and creep durability was found for individually dispersed NPs due to the largest effective surface and the smallest interelement distance. The presented nanostructure-property function of PNCs will provide a foundation for the design of the next-generation lightweight materials.
■
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b01197. Element definition and schematic representation of NP spatial organizations; details to structural analysis including dependence of element diameter, interelement distance, Seff, and Seff divided by interelement distance on volume fraction of NPs; dependence of difference of PNCs Tg and matrix Tg divided by matrix Tg on interelement distance divided by the radius of gyration; and comparison of tensile and creep curves of the neat PMMA and PNCs with 1 vol % of SiO2 NPs (PDF)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Frantisek Ondreas: 0000-0003-3845-1766 Marek Zboncak: 0000-0002-6463-2985 Funding
Funding this work under grant number 18-17540S from Grant Agency of Czech Republic and internal BUT student grant STI-J-4204 is greatly acknowledged. Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Jancar, J.; Douglas, J. F.; Starr, F. W.; Kumar, S. K.; Cassagnau, P.; Lesser, A. J.; Sternstein, S. S.; Buehler, M. J.; Current, M. J. issues in research on structure-property relationships in polymer nanocomposites. Polymer 2010, 51, 3321−3343. (2) Jancar, J.; Hoy, R. S.; Lesser, A. J.; Jancarova, E.; Zidek, J. Effect of Particle Size, Temperature, and Deformation Rate on the Plastic Flow and Strain Hardening Response of PMMA Composites. Macromolecules 2013, 46, 9409−9426. (3) Jancar, J.; Hoy, R. S.; Jancarova, E.; Zidek, J. Effect of temperature, strain rate and particle size on the yield stresses and post-yield strain softening of PMMA and its composites. Polymer 2015, 63, 196−207. (4) Jancar, J. Review of the role of the interphase in the control of composite performance on micro- and nano-length scales. J. Mater. Sci. 2008, 43, 6747−6757. (5) Hashemi, A.; Jouault, N.; Williams, G. A.; Zhao, D.; Cheng, K. J.; Kysar, J. W.; Guan, Z.; Kumar, S. K. Enhanced Glassy State Mechanical Properties of Polymer Nanocomposites via Supramolecular Interactions. Nano Lett. 2015, 15, 5465−5471. (6) Dorigato, A.; Sebastiani, M.; Pegoretti, A.; Fambri, L. Effect of Silica Nanoparticles on the Mechanical Performances of Poly(Lactic Acid). J. Polym. Environ. 2012, 20, 713−725. (7) Chevigny, C.; Jouault, N.; Dalmas, F.; Boué, F.; Jestin, J. Tuning the Mechanical Properties in Model Nanocomposites: Influence of the Polymer-Filler Interfacial Interactions. J. Polym. Sci., Part B: Polym. Phys. 2011, 49, 781−791. H
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules (27) Sotta, P.; Albouy, P.-A.; Abou Taha, M.; Long, D. R.; Grau, P.; Fayolle, C.; Papon, A. Nonentropic Reinforcement in Elastomer Nanocomposites. Macromolecules 2017, 50, 6314−6322. (28) Merabia, S.; Sotta, P.; Long, D. R. A Microscopic Model for the Reinforcement and the Nonlinear Behavior of Filled Elastomers and Thermoplastic Elastomers (Payne and Mullins Effects). Macromolecules 2008, 41, 8252−8266. (29) Berriot, J.; Montes, H.; Lequeux, F.; Long, D.; Sotta, P. Gradient of glass transition temperature in filled elastomers. Europhys. Lett. 2003, 64, 50−56. (30) Tauban, M.; Delannoy, J.-Y.; Sotta, P.; Long, D. R. Effect of Filler Morphology and Distribution State on the Linear and Nonlinear Mechanical Behavior of Nanofilled Elastomers. Macromolecules 2017, 50, 6369−6384. (31) Bokobza, L. Natural Rubber Nanocomposites: A Review. Nanomaterials (Basel) 2018, 9, 12. (32) Witten, T. A.; Rubinstein, M.; Colby, R. H. REINFORCEMENT OF RUBBER BY FRACTAL AGGREGATES. J. Phys. II 1993, 3, 367−383. (33) Rong, W.; Pelling, A. E.; Ryan, A.; Gimzewski, J. K.; Friedlander, S. K. Complementary TEM and AFM force spectroscopy to characterize the nanomechanical properties of nanoparticle chain aggregates. Nano Lett. 2004, 4, 2287−2292. (34) Hager, J.; Hentschke, R.; Hojdis, N. W.; Karimi-Varzaneh, H. A. Computer Simulation of Particle-Particle Interaction in a Model Polymer Nanocomposite. Macromolecules 2015, 48, 9039−9049. (35) Cheng, S.; Bocharova, V.; Belianinov, A.; Xiong, S.; Kisliuk, A.; Somnath, S.; Holt, A. P.; Ovchinnikova, O. S.; Jesse, S.; Martin, H.; Etampawala, T.; Dadmun, M.; Sokolov, A. P. Unraveling the Mechanism of Nanoscale Mechanical Reinforcement in Glassy Polymer Nanocomposites. Nano Lett. 2016, 16, 3630−3637. (36) Schneider, D.; Schmitt, M.; Hui, C. M.; Sainidou, R.; Rembert, P.; Matyjaszewski, K.; Bockstaller, M. R.; Fytas, G. Role of Polymer Graft Architecture on the Acoustic Eigenmode Formation in Densely Polymer-Tethered Colloidal Particles. ACS Macro Lett. 2014, 3, 1059−1063. (37) Cassagnau, P. Melt rheology of organoclay and fumed silica nanocomposites. Polymer 2008, 49, 2183. (38) Anderson, B. J.; Zukoski, C. F. Rheology and Microstructure of Entangled Polymer Nanocomposite Melts. Macromolecules 2009, 42, 8370−8384. (39) Emamy, H.; Kumar, S. K.; Starr, F. W. Diminishing Interfacial Effects with Decreasing Nanoparticle Size in Polymer-Nanoparticle Composites. Phys. Rev. Lett. 2018, 121 (), DOI: 10.1103/ PhysRevLett.121.207801. DOI: 10.1103/physrevlett.121.207801 (40) Ondreas, F.; Jancar, J. Temperature, Frequency, and Small Static Stress Dependence of the Molecular Mobility in Deformed Amorphous Polymers near Their Glass Transition. Macromolecules 2015, 48, 4702−4716. (41) Zidek, J.; Kucera, J.; Jancar, J. Model of Random Spatial Packing of Rigid Spheres with Controlled Macroscopic Homogenity. Comput. Mater. Continua 2010, 16, 51−73. (42) Zidek, J.; Kucera, J.; Jancar, J. Nearest Particle Distance and the Statistical Distribution of Agglomerates from a Model of a Finite Set of Particles. Comput. Mater. Continua 2011, 24, 183−208. (43) Hooper, J. B.; Schweizer, K. S.; Desai, T. G.; Koshy, R.; Keblinski, P. Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions. J. Chem. Phys. 2004, 121, 6986−6997. (44) Hooper, J. B.; Schweizer, K. S. Contact aggregation, bridging, and steric stabilization in dense polymer-particle mixtures. Macromolecules 2005, 38, 8858−8869. (45) Hooper, J. B.; Schweizer, K. S. Theory of phase separation in polymer nanocomposites. Macromolecules 2006, 39, 5133−5142. (46) Hooper, J. B.; Schweizer, K. S. Real space structure and scattering patterns of model polymer nanocomposites. Macromolecules 2007, 40, 6998−7008.
(47) Hall, L. M.; Jayaraman, A.; Schweizer, K. S. Molecular theories of polymer nanocomposites. Curr. Opin. Solid State Mater. Sci. 2010, 14, 38−48. (48) Van der Beek, G. P.; Stuart, M. A. C.; Fleer, G. J.; Hofman, J. E. SEGMENTAL ADSORPTION ENERGIES FOR POLYMERS ON SILICA AND ALUMINA. Macromolecules 1991, 24, 6600−6611. (49) Hamieh, T.; Toufaily, J.; Fadlallah, M.-B. Study of superficial properties of some polymers and oxides. Adv. Powder Technol. 2003, 14, 547−558. (50) Kim, S. Y.; Schweizer, K. S.; Zukoski, C. F. Multiscale Structure, Interfacial Cohesion, Adsorbed Layers, and Thermodynamics in Dense Polymer-Nanoparticle Mixtures. Phys. Rev. Lett. 2011, 107 (), DOI: 10.1103/PhysRevLett.107.225504. DOI: 10.1103/physrevlett.107.225504 (51) Cheng, S.; Carroll, B.; Lu, W.; Fan, F.; Carrillo, J.-M. Y.; Martin, H.; Holt, A. P.; Kang, N.-G.; Bocharova, V.; Mays, J. W.; Sumpter, B. G.; Dadmun, M.; Sokolov, A. P. Interfacial Properties of Polymer Nanocomposites: Role of Chain Rigidity and Dynamic Heterogeneity Length Scale. Macromolecules 2017, 50, 2397−2406. (52) Riggleman, R. A.; Toepperwein, G.; Papakonstantopoulos, G. J.; Barrat, J.-L.; de Pablo, J. J. Entanglement network in nanoparticle reinforced polymers. J. Chem. Phys. 2009, 130, 244903. (53) Cross, M. M. RHEOLOGY OF NON-NEWTONIAN FLUIDS - A NEW FLOW EQUATION FOR PSEUDOPLASTIC SYSTEMS. J. Colloid Sci. 1965, 20, 417. (54) Anderson, B. J.; Zukoski, C. F. Rheology and Microstructure of an Unentangled Polymer Nanocomposite Melt. Macromolecules 2008, 41, 9326−9334. (55) Anderson, B. J.; Zukoski, C. F. Rheology and Microstructure of Polymer Nanocomposite Melts: Variation of Polymer SegmentSurface Interaction. Langmuir 2010, 26, 8709−8720. (56) Mueller, S.; Llewellin, E. W.; Mader, H. M. The rheology of suspensions of solid particles. Proc. R. Soc. A 2010, 466, 1201−1228. (57) Kim, S. Y.; Zukoski, C. F. Super- and sub-Einstein intrinsic viscosities of spherical nanoparticles in concentrated low molecular weight polymer solutions. Soft Matter 2012, 8, 1801−1810. (58) Guth, E.; Gold, O. On the hydrodynamic theory of the viscosity of suspensions. Phys. Rev. 1938, 53, 322. (59) Guth, E. Theory of filler reinforcement. Appl. Phys. 1945, 16, 20. (60) Smallwood, H. M. Limiting law of the reinforcement of rubber. J. Appl. Phys. 1944, 15, 758. (61) Kerner, E. H. The elastic and thermoelastic properties of composite media. Proc. Phys. Soc. 1956, 69, 808. (62) Nielsen, L. E. GENERALIZED EQUATION FOR ELASTIC MODULI OF COMPOSITE MATERIALS. J. Appl. Phys. 1970, 41, 4626−4627. (63) Nielsen, L. E.; Landel, R. F. Mechanical Properties of Polymers and Composites; CRC Press: New York, 1994. (64) Schneider, G. J. Dynamics of nanocomposites. Curr. Opin. Chem. Eng. 2017, 16, 65−77. (65) Berriot, J.; Montes, H.; Lequeux, F.; Long, D.; Sotta, P. Evidence for the shift of the glass transition near the particles in silicafilled elastomers. Macromolecules 2002, 35, 9756−9762. (66) Mujtaba, A.; Keller, M.; Ilisch, S.; Radusch, H.-J.; Beiner, M.; Thurn-Albrecht, T.; Saalwächter, K. Detection of Surface-Immobilized Components and Their Role in Viscoelastic Reinforcement of Rubber-Silica Nanocomposites. ACS Macro Lett. 2014, 3, 481−485. (67) Debenedetti, P. G.; Stillinger, F. H. Supercooled liquids and the glass transition. Nature 2001, 410, 259−267. (68) Jancar, J.; Recman, L. Particle size dependence of the elastic modulus of particulate filled PMMA near its T-g. Polymer 2010, 51, 3826−3828. (69) Parodi, E.; Peters, G. W. M.; Govaert, L. E. Prediction of plasticity-controlled failure in polyamide 6: Influence of temperature and relative humidity. J. Appl. Polym. Sci. 2018, 135, 45942. (70) Bellemare, S. C.; Bureau, M. N.; Denault, J.; Dickson, J. I. Fatigue crack initiation and propagation in polyamide-6 and in polyamide-6 nanocomposites. Polym. Compos. 2004, 25, 433−441. I
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules (71) Jen, M.; Tseng, Y.; Wu, C. Manufacturing and mechanical response of nanocomposite laminates. Compos. Sci. Technol. 2005, 65, 775−779. (72) Takeda, T.; Shindo, Y.; Wei, Z.; Kuronuma, Y.; Narita, F. Fatigue failure and electrical resistance behaviors of carbon nanotubebased polymer composites under uniaxial tension-tension loading in a cryogenic environment. J. Compos. Mater. 2015, 49, 457−463. (73) Pastukhov, L. V.; Mercx, F. P. M.; Peijs, T.; Govaert, L. E. Long-term performance and durability of polycarbonate/carbon nanotube nanocomposites. Nanocomposites 2019, 4, 223−237. (74) Dorigato, A.; Pegoretti, A. Tensile creep behaviour of polymethylpentene-silica nanocomposites. Polym. Int. 2010, 59, 719−724. (75) Böger, L.; Sumfleth, J.; Hedemann, H.; Schulte, K. Improvement of fatigue life by incorporation of nanoparticles in glass fibre reinforced epoxy. Compos. Appl. Sci. Manuf. 2010, 41, 1419−1424. (76) Knoll, J. B.; Riecken, B. T.; Kosmann, N.; Chandrasekaran, S.; Schulte, K.; Fiedler, B. The effect of carbon nanoparticles on the fatigue performance of carbon fibre reinforced epoxy. Compos. Appl. Sci. Manuf. 2014, 67, 233−240. (77) Kanters, M. J. W.; Kurokawa, T.; Govaert, L. E. Competition between plasticity-controlled and crack-growth controlled failure in static and cyclic fatigue of thermoplastic polymer systems. Polym. Test. 2016, 50, 101−110.
J
DOI: 10.1021/acs.macromol.9b01197 Macromolecules XXXX, XXX, XXX−XXX
