Daniel R Bortz

César Merino

Ignacio Martin-Gullon

CARBON NANOFIBERS ENHANCE THE FRACTURE TOUGHNESS AND FATIGUE PERFORMANCE OF A STRUCTURAL EPOXY SYSTEM

Keywords: A. Nano composites, A. Carbon nanotubes, A. Polymer matrix composites (PMCs), B. Fatigue, B. Fracture toughness

This study investigates the monotonic and dynamic fracture characteristics of a discontinuous fiber reinforced polymer matrix. Specifically, small amounts (0-1 wt%) of a helical-ribbon carbon nanofiber (CNF) were added to an amine cured epoxy system.

The resulting nanocomposites were tested to failure in two modes of testing; Mode I fracture toughness and constant amplitude of stress tension-tension fatigue. Fracture toughness testing revealed that adding 0.5 and 1.0 wt% CNFs to the epoxy matrix enhanced the resistance to fracture by 66 and 78%, respectively. Fatigue testing at 20 MPa peak stress showed a median increase in fatigue life of 180 and 365% over the control by the addition of 0.5 and 1.0 wt% CNF, respectively. These results clearly demonstrate the addition of small weight fractions of CNFs to significantly enhance the monotonic fracture behavior and long-term fatigue performance of this polymer. A discussion is presented linking the two behaviors indicating their interdependence and reliance upon the stress intensity factor, K.

Introduction

Epoxy systems are widely used to bind laminates of glass or carbon fiber or to suspend particulate or fibrous fillers to create advanced multifunctional composite materials in which a high specific strength is required. Carbon nanomaterials offer remarkable properties and discontinuous carbon nanotube (CNT) and carbon nanofiber (CNF) reinforcement of epoxy matrices has shown potential to augment a variety of physical and mechanical properties resulting in truly multifunctional composite materials.

Recent reviews by Spitalsky et al. [START_REF] Spitalsky | Carbon nanotube-polymer composites: Chemistry, processing, mechanical and electrical properties[END_REF] and Ma et al. [START_REF] Ma | Dispersion and functionalization of carbon nanotubes for polymer-based nanocomposites: A review[END_REF] highlight the latest advancements.

Understanding the monotonic and dynamic mechanical properties of structural epoxy reinforced with CNTs and CNFs will lend itself to the engineering of these advanced materials. In regard to the mechanical performance of these composites, interfacial adhesion between the matrix and reinforcing phase is essential [START_REF] Bai | Evidence of the reinforcement role of chemical vapour deposition multi-walled carbon nanotubes in a polymer matrix[END_REF][START_REF] Weisenberger | Enhanced mechanical properties of polyacrylonitrile/multiwall carbon nanotube composite fibers[END_REF]. From a micromechanics of materials point of view, in which the matrix and reinforcing phase act as heterogeneous entities acting upon each other, shear stress build-up along the length of the interface is the mechanism responsible for stress transfer from the matrix to the fiber [START_REF] Jones | Mechanics of composite materials[END_REF]. Inadequate fiber-matrix bonding is often cited as the explanation for unsatisfactory mechanical results.

When the stress intensity associated with an applied load exceeds the critical level needed to propagate a crack (K Ic ), energy is dissipated through fracture. Fracture toughness enhancements (and the mechanisms which govern them) through the addition of various micro and nano-sized particles in epoxy polymers are well cited in the literature [START_REF] Fiedler | Fundamental aspects of nanoreinforced composites[END_REF][START_REF] Gojny | Carbon nanotube-reinforced epoxy-composites: Enhanced stiffness and fracture toughness at low nanotube content[END_REF][START_REF] Johnsen | Toughening mechanisms of nanoparticle-modified epoxy polymers[END_REF][START_REF] Kim | Fracture toughness of the nano-particle reinforced epoxy composite[END_REF][START_REF] Ma | Effects of silane functionalization on the properties of carbon nanotube/epoxy nanocomposites[END_REF][START_REF] Nakamura | Effect of particle size on the fracture toughness of epoxy resin filled with spherical silica[END_REF][START_REF] Rafiee | Fracture and fatigue in graphene nanocomposites[END_REF][START_REF] Wetzel | Epoxy nanocomposites-fracture and toughening mechanisms[END_REF][START_REF] Zunjarrao | Characterization of the fracture behavior of epoxy reinforced with nanometer and micrometer sized aluminum particles[END_REF][START_REF] Palmeri | Sacrificial bonds in stacked-cup carbon nanofibers: Biomimetic toughening mechanisms for composite systems[END_REF]. Specifically, Gojny et al. [START_REF] Gojny | Carbon nanotube-reinforced epoxy-composites: Enhanced stiffness and fracture toughness at low nanotube content[END_REF] have demonstrated low concentrations of CNTs to increase the fracture resistance of an epoxy resin by approximately 25%. More recently, Palmeri et al. [START_REF] Palmeri | Sacrificial bonds in stacked-cup carbon nanofibers: Biomimetic toughening mechanisms for composite systems[END_REF] have used the same CNF used in this work to demonstrate fracture toughness enhancements of 45-80% in epoxy blends. Other work [START_REF] Ma | Effects of silane functionalization on the properties of carbon nanotube/epoxy nanocomposites[END_REF] though, has shown CNT reinforcement to negatively impact the fracture toughness of epoxy. It was shown that fracture resistance was only improved through surface functionalization with 3-glycidoxypropyltrimethoxysilane.

The fatigue failure of epoxy is the result of an initial reduction in stiffness due to the initiation of microscopic cracks at stress concentrating defects such as pores or material inhomogenities. Repeated loading causes these cracks to grow and accumulate until ultimately, a runaway crack leads to rapid, catastrophic failure. The literature has indicated that the addition of rubber [START_REF] Manjunatha | The tensile fatigue behaviour of a GFRP composite with rubber particle modified epoxy matrix[END_REF], metal [START_REF] Wetzel | Epoxy nanocomposites-fracture and toughening mechanisms[END_REF], silica [START_REF] Manjunatha | The tensile fatigue behaviour of a silica nanoparticle-modified glass fibre reinforced epoxy composite[END_REF] and more recently CNTs [START_REF] Grimmer | High-cycle fatigue of hybrid carbon nanotube/glass fiber/polymer composites[END_REF][START_REF] Zhang | Suppression of fatigue crack growth in carbon nanotube composites[END_REF][START_REF] Zhang | Heterogeneity in epoxy nanocomposites initiates crazing: significant improvements in fatigue resistance and toughening[END_REF][START_REF] Rafiee | Enhanced mechanical properties of nanocomposites at low graphene content[END_REF] and graphene [START_REF] Rafiee | Fracture and fatigue in graphene nanocomposites[END_REF][START_REF] Rafiee | Enhanced mechanical properties of nanocomposites at low graphene content[END_REF] positively influence fatigue life and fatigue crack propagation rates when dispersed in epoxy matrices. Grimmer and Dharan [START_REF] Grimmer | High-cycle fatigue of hybrid carbon nanotube/glass fiber/polymer composites[END_REF] suggested that the addition of CNTs to a glass fiber epoxy composite resulted in the adsorption of strain energy through the creation of nanoscale cracks in tension-tension fatigue testing.

It was observed that CNTs had a marked effect in high-cycle fatigue testing corresponding to low applied stress amplitudes. In this region, fatigue life was enhanced by 2.5 times over the non CNT-modified sample. Although the phenomena of crazing is not typically observed in epoxies due to its high crosslink density, Zhang et al. [START_REF] Zhang | Heterogeneity in epoxy nanocomposites initiates crazing: significant improvements in fatigue resistance and toughening[END_REF] provided SEM evidence of amido-amine-functionalized multiwall carbon nanotube (MWCNT) induced craze zones in fatigue crack propagation testing. It was argued that reinforcement was due in part, to the energy dissipative plastic deformation of the craze fibrils. In another report [START_REF] Zhang | The effect of carbon nanotube dimensions and dispersion on the fatigue behavior of epoxy nanocomposites[END_REF], the same group suggested that geometrical considerations and quality of dispersion are directly linked to fatigue improvements in MWCNT composite epoxy. It was maintained that reducing diameter, increasing length and bettering the dispersion of MWCNTs significantly reduced the rate of fatigue crack propagation. Rotary bending fatigue tests at low stress magnitudes also suggested MWCNTs to improve fatigue life in epoxy [START_REF] Yu | Fracture toughness and fatigue life of MWCNT/epoxy composites[END_REF]. Other reports have linked MWCNTs to significant increases in the fatigue life of thermoplastics such as PMMA [START_REF] Bortz | Fatigue performance of multiwall carbon nanotube composite PMMA and ABS[END_REF][START_REF] Marrs | Multiwall carbon nanotubes enhance the fatigue performance of physiologically maintained methyl methacrylate-styrene copolymer[END_REF][START_REF] Marrs | Augmentation of acrylic bone cement with multiwall carbon nanotubes[END_REF]. To this regard, it was the aim of this study to test the effect of the addition of small amounts (≤ 1.0 wt%) of CNFs on the fracture resistance and fatigue performance of a structural epoxy system.

Experimental

Materials

Resoltech 1800/1805 (Resoltech, Eguilles, France), a low viscosity liquid epoxy system was used as the matrix. The epoxy resin, a reaction product of epichlorhydine with bisphenol A and bisphenol F, was cured with an amine hardener, 1,2diaminocyclohexane. The mixing ratio was 100:17 parts by weight. GANF, a commercial grade, helical-ribbon CNF was supplied by Grupo Antolín Ingeniería (Burgos, Spain) and used as provided [START_REF] Martin-Gullon | Differences between carbon nanofibers produced using Fe and Ni catalysts in a floating catalyst reactor[END_REF][START_REF] Vera-Agullo | Evidence for growth mechanism and helix-spiral cone structure of stacked-cup carbon nanofibers[END_REF][START_REF] Vera-Agullo | Analytical pyrolysis as a characterization technique for monitoring the production of carbon nanofilaments[END_REF][START_REF] Weisenberger | The effect of graphitization temperature on the structure of helicalribbon carbon nanofibers[END_REF]. GANF is synthesized by the continuous floating catalyst method using natural gas and sulfur as feedstock and a nickel compound as catalyst at approximately 1100 °C. The resulting CNFs are highly graphitic with no presence of an amorphous carbon coating. Outer diameters are heterogeneous, with an average of approximately 60 nm and a pre-processing aspect ratio (length/diameter) above 100. Structurally, GANF is comprised of a continuous graphitic ribbon helically rolled about the axis of the fiber (Fig. 1). Earlier TEM evidence [START_REF] Vera-Agullo | Evidence for growth mechanism and helix-spiral cone structure of stacked-cup carbon nanofibers[END_REF] of unraveled fibers has confirmed their continuity and differentiates them from the discontinuous cones of the more common stacked-cup CNF morphology. Ribbons are arranged ~25° oblique to the axis of the fiber and composed of approximately 5 individual layers of graphene [START_REF] Vera-Agullo | Evidence for growth mechanism and helix-spiral cone structure of stacked-cup carbon nanofibers[END_REF][START_REF] Varela-Rizo | Highly crystalline graphene oxide nano-platelets produced from helical-ribbon carbon nanofibers[END_REF].

Sample preparation

After hand mixing, CNFs were dispersed in the epoxy resin using a high shear laboratory mixer (Silverson L4RT) at 7000 rpm for 15 minutes. The hardener was subsequently added and further mixed at 5000 rpm for 5 minutes. Dispersions were processed with 0.5 and 1.0 wt% CNF. A neat epoxy sample was similarly processed and used as a control. After mixing, the dispersions were poured into a silicone mold and degassed for 30 minutes at a vacuum approaching -1 bar. Individually cast test coupons, measuring 250 × 25 × 2.5 mm for tension-tension fatigue testing, 63.5 × 12.7 × 4 mm for Mode I fracture toughness testing and 30 × 12.7 × 3.2 mm for DMA characterization, 6 were released from the mold after 12 hours at 40 °C. Additional heating in air for 15 hours at 60 °C and 6 hours at 110 °C completed the cure cycle. Specimen surfaces were smoothed on a rotary polishing machine using 320 grit followed by 600 grit silicone carbide grinding paper. Transmitted light (100×, Nikon Eclipse E200) and highresolution transmission electron microscopy (TEM, JEOL 1020) verified dispersion.

Testing was conducted 7 days after curing.

For fracture toughness testing, a 1 mm wide sharpened notch was machined at the mid-specimen point in the single edge notched bend (SENB) coupons. A pre-crack was subsequently introduced by tapping a fresh razor blade placed normal to the machined notch (Fig. 2). As per the standard, the ratio between the length of the notch plus the precrack (a) and the width (W) was between 0.45 and 0.55 for each specimen.

Dynamic mechanical analysis

Dynamic mechanical analysis (DMA) was performed in single cantilever mode using a TA Instruments 2980. Temperature ramps were carried out from 20 to 175 °C at a scan rate of 2 °C/min. The specimens were subjected to 20 µm amplitude of deflection at 1 Hz. This provided a strain of approximately 0.03% and was well within the linear elastic region. The glass transition temperature, T g , was taken as the peak of the ratio of the storage modulus to the loss modulus (tan δ).

Fracture toughness testing

Mode I fracture toughness tests by the 3-point bending method (ASTM D 5045 [START_REF]Standard test methods for plane-strain fracture toughness and strain energy release rate of plastic materials[END_REF]) were performed using an Instron 3344 (Instron Corporation, Canton, MA, U.S.A.) equipped with a 2 kN load cell. Three SENB specimens from each group were loaded to failure at a crosshead rate of 10 mm/min. Load-deformation curves were recorded and the pre-crack length was measured post mortem by optical microscopy. Testing was conducted at room temperature (25 °C). The critical-stress-intensity (K Ic ) needed to propagate the crack was calculated by

K Ic P BW 1 2 f x , (1)
where P is max applied load, B and W are specimen thickness and width and x is the ratio of the previously described crack length a and specimen width W. The function f(x) is the second order polynomial found here [START_REF]Standard test methods for plane-strain fracture toughness and strain energy release rate of plastic materials[END_REF]. The critical strain energy release rate (G Ic ) was computed by integration of the load-deformation curve used in the determination of K Ic .

Fatigue testing and statistical analysis

Constant amplitude of stress tension-tension fatigue testing (ASTM D 3479M [START_REF]Standard test method for tension-tension fatigue of polymer matrix composite materials[END_REF]) was performed at room temperature (25 °C) using an Instron 8516 100 kN servohydraulic materials testing system (Instron Corporation, Canton, MA, U.S.A.). No bonded tabs were used, instead an emery cloth interface functioned to prevent slippage and introduce the load to the specimen. Each test coupon was sinusoidally cycled between minimum and maximum in-plane axial load until failure at a frequency, f = 5

Hz. The ratio of the minimum to maximum applied load was R = 0.1. The number of cycles to failure (N) was recorded for each test coupon. Static tensile tests were carried out at a displacement rate of 2 mm/min using identical specimen geometry.

It was assumed that the fatigue life was normally distributed and the variance of log (N) was constant over the entire range of testing. In addition, the data contained no run-outs or suspended tests. Therefore, the cycles to failure were analyzed by constructing log-normally distributed S-N curves transformed into linear form according to ASTM [START_REF]ASTM manual on fitting straight lines[END_REF][START_REF]Standard practice for statistical analysis of linear or linearized stress-life (S-N) and strain-life (ε-N) fatigue data[END_REF] and expressed as

Y A BX , ( 2
)
where Y is equal to log (N), X is the maximum value of constant-amplitude cyclic stress and A and B are constants for each sample and estimated by

ˆ A Y ˆ B X (3)
and

ˆ B X i X Y i Y i 1 k X i X 2 i 1 k . ( 4
)
Each test program involved two specimens tested at each of five stress amplitudes resulting in a replication of 50%. The variance in log (N) data was calculated by

2 Y i ˆ Y i i 1 k k 2 , ( 5
)
where ˆ Y i is the estimated fatigue life from the median S-N curve from Eq. ( 2) and k is the total number of test specimens from each test program (in this case, k = 10). Hyperbolic confidence bands taking into account all points on the median S-N curve were computed using

ˆ A ˆ B X 2F p 1 k X X i 2 X X i 2 i 1 k 1 2 , ( 6
)
where F p = 4.4590 and corresponds to P = 95%. The confidence intervals are not designed to predict the inclusion of individual data points. Rather, it is expected that 95% of the computed hyperbolic confidence bands will include Eq. ( 2) over the entire range of X used in the testing program.

Scanning electron microscopy

Fracture surfaces from randomly selected failed specimens in both modes of testing were sectioned, sputter coated with gold and examined using high-resolution scanning electron microscopy (SEM, JEOL JSM-840). Qualitative conclusions were drawn from the micrographs on the fracture characteristics, reinforcement mechanisms and interactions between the CNFs and matrix.

Results and discussion

Dispersion of CNFs and degree of cure

A qualitative analysis indicated that the high-shear mixing protocol provided a respectable CNF dispersion throughout the epoxy matrix (Fig. 3). Though some agglomerations were observed, TEM exploration illustrated that the filaments were typically isolated and well wet by the matrix. Examination also revealed that the preprocessing aspect ratio of the CNFs was lessened to some extent. Filament shortening due to high-shear mixing processes has been reported in other work and is often unavoidable in the dispersion process [START_REF] Andrews | Fabrication of carbon multiwall nanotube/polymer composites by shear mixing[END_REF].

DMA results indicate no significant affect to the final degree of cure by CNF inclusion. The mean (standard deviation) T g taken from the tan δ peak for the neat, 0.5 and 1.0 wt% CNF materials were shown to be 126.3 (0.1), 126.9 (0.5) and 126.8 (0.3) °C, respectively. These values agree well with the manufacture's [37] figure of 130 °C for the given cure times and temperatures used here.

Fracture toughness testing results

Results of fracture toughness testing for the neat epoxy matrix and two CNF composites (0.5 and 1.0 wt%) are shown in Fig. 4. Both toughness parameters indicative of resistance to fracture (K Ic ) and rate at which energy is absorbed by crack growth (G Ic )

were shown to significantly improve with increasing CNF concentration (Fig. 4a). The Examination of fracture surfaces by SEM revealed the neat epoxy group to have the classic smooth fracture surface (Fig. 5a) observed in highly crosslinked polymer systems [START_REF] Kinloch | The toughening of cyanate-ester polymers Part I Physical modification using particles, fibres and woven-mats[END_REF]. River marks leading to the initial site of crack growth were detected but substantial indications of plastic deformation in the control group were not noted.

Quantitatively speaking, the lack of observed plastic deformation and a smooth fracture Crack growth is from bottom to top in both images.

Fatigue testing results

Raw loading and life data from the constant stress amplitude, tension-tension fatigue testing are listed in Table 1. Cyclic stress vs. lifetime (S-N) curves are shown in Fig. 6 and a summary of the log-normal fitting parameters is given in Table 2. Indicative the median fatigue life, as computed by Eq. ( 2), to increase by approximately 180 and 365% over the control with the addition of 0.5 and 1.0 wt% CNF respectively. The smallest improvement in median fatigue life was observed at the highest stress amplitude, 40 MPa. Here, a decrease of 15% in fatigue life was observed at 0.5 wt% CNF and an improvement of approximately 10% over the control was realized at 1.0 wt% CNF.

Estimated variance in the log-normal distribution of each population was shown to be reasonably consistent across the control ( ˆ 2 0.020) and CNF modified samples ( ˆ 2 0.5 wt% 0.035 and ˆ 2

1.0 wt% 0.013). Hyperbolic confidence bands corresponding to P = 95% were calculated by Eq. ( 6). Ultimately, these bands are expected to include the straight line from Eq. ( 2) 95 times out of 100. The inclusion of the confidence intervals illustrates the significance in the improvement of fatigue life at low applied stress amplitudes. At 20 MPa peak stress, the percent increase between the lower confidence band of the 1.0 wt% CNF modified epoxy and the upper band of the control still stands at approximately 105%. Beginning at approximately 33 MPa, the intervals overlap throughout the remainder of the higher applied peak stress amplitudes. between the neat and 1.0 wt% data but were omitted to avoid confusion. Hyperbolic confidence bands are as computed by Eq. ( 6).

Examination of fracture surfaces by SEM echoed the observations made from the fracture toughness specimens. A smooth, glasslike surface devoid of observable signs of plastic deformation was detected in the neat sample (Fig. 7a). River marks immediately surrounding and tracing back to the crack initiation site were common. The CNF pinning [START_REF] Wetzel | Epoxy nanocomposites-fracture and toughening mechanisms[END_REF][START_REF] Kinloch | The fracture of hybrid-particulate composites[END_REF][START_REF] Evans | The strength of brittle materials containing second phase dispersions[END_REF][START_REF] Green | Fracture of a brittle particulate composite[END_REF][START_REF] Lange | The interaction of a crack front with a second-phase dispersion[END_REF], pullout and void nucleation [START_REF] Kinloch | The toughening of cyanate-ester polymers Part I Physical modification using particles, fibres and woven-mats[END_REF][START_REF] Kawaguchi | The effect of particle-matrix adhesion on the mechanical behavior of glass filled epoxies. Part 2. A study on fracture toughness[END_REF][START_REF] Lee | Fracture of glass bead/epoxy composites: on micro-mechanical deformations[END_REF] and crack deflection [START_REF] Faber | Crack deflection processes--I. Theory[END_REF][START_REF] Faber | Crack deflection processes--II. Experiment[END_REF]. Crack pinning has by and large been dismissed as an operating toughening mechanism in nanocomposites due to the matter of size compatibility [START_REF] Johnsen | Toughening mechanisms of nanoparticle-modified epoxy polymers[END_REF]. Typical crack tip radii are dimensionally much larger than the nanometer-sized reinforcing phase.

Nevertheless, reports of such occurrences have surfaced [START_REF] Wetzel | Epoxy nanocomposites-fracture and toughening mechanisms[END_REF]. Fiber pullout, resulting from de-bonding of the fiber from the matrix causes fibers to bridge cracks in the wake zone behind the advancing crack tip. This mechanism has been characterized as the predominate mode of "overload failure" in fibrous nanocomposites [START_REF] Marrs | Augmentation of acrylic bone cement with multiwall carbon nanotubes[END_REF]. The phenomenon, illustrated in Fig. 7c, is to be expected owing to the fact that the interfacial shear strength between the matrix and fiber has been shown to be less than the tensile strength of the fiber [START_REF] Barber | Measurement of carbon nanotube-polymer interfacial strength[END_REF]. In some instances, crack bridging has been cited a dominant toughening channel [START_REF] Rafiee | Enhanced mechanical properties of nanocomposites at low graphene content[END_REF]. In other reports though, it has been modeled to provide little overall reinforcement value [START_REF] Fiedler | Fundamental aspects of nanoreinforced composites[END_REF]. Faber and Evans [START_REF] Faber | Crack deflection processes--I. Theory[END_REF][START_REF] Faber | Crack deflection processes--II. Experiment[END_REF] concluded that if the plane of a propagating crack could be altered in three dimensional space by the inclusion of a reinforcing particulate then a mixed-mode loading condition could result. The continual twisting and turning action of the crack front during fracture leads to mixed-Mode I, II and III loading and results in an increase in total fracture surface area (Fig. 7b). The energy absorbed by the creation of additional fracture surface area necessitates additional energy to be input to the system to continually drive crack growth (i.e., higher G Ic values) [START_REF] Kinloch | The toughening of cyanate-ester polymers Part I Physical modification using particles, fibres and woven-mats[END_REF][START_REF] Faber | Crack deflection processes--I. Theory[END_REF][START_REF] Faber | Crack deflection processes--II. Experiment[END_REF]. The qualitative observation of increased fracture surface area and quantitative increase in G Ic in this study appear to agree with the crack deflection theory proposed by Faber and Evans. Despite the inherit interdependence of the toughening mechanisms described above, it appears that the role of CNFs during crack propagation are to aid in deflecting the advancing crack and force growth to deviate from the existing fracture plane.

Palmeri et al. [START_REF] Palmeri | Sacrificial bonds in stacked-cup carbon nanofibers: Biomimetic toughening mechanisms for composite systems[END_REF] have reported a potentially new type of toughening mechanism for this variety of CNF. It was claimed, via supporting SEM and TEM evidence, that through the severing of the graphitic π-π interactions of the oblique graphene layers the fibers can either "discretely splay" or "continuously unravel." The authors maintained the sacrificial bonding during unraveling could then lead to the fiber's spanning of cracks and ultimately result in an increase in toughness. It is interesting to note the ability of the fiber to unravel it's graphene layers has been previously demonstrated, albeit not in a composite [START_REF] Vera-Agullo | Evidence for growth mechanism and helix-spiral cone structure of stacked-cup carbon nanofibers[END_REF]. The present study can neither confirm nor deny the phenomena's manifestation in the matrix.

Effect of stress intensity and agglomerations

Results from fatigue testing indicate substantial and significant enhancement to the fatigue life of epoxy by the inclusion of a CNF reinforcing phase. Despite the reported positive effects of CNF addition in the high-cycle, low-stress amplitude fatigue testing regime, results from high-stress amplitudes (30-40 MPa peak stress) showed less than ideal results. The nonuniformity of the fatigue life increase at high applied stress levels is believed to be the result of two effects: (1) breakdown of the CNF/matrix interface and (2) CNF agglomerations (Fig. 7d) detracting from the positive reinforcing effect of individually dispersed fibers. Both conditions have a significant dependence on the stress intensity factor, K. At low applied stress levels, the interfacial strength of the CNF/matrix bond is believed to dominate localized stresses surrounding the crack tip.

These stresses are effectively transferred from the weaker matrix and distributed in the form of small-scale straining of the stiffer CNFs, preserving the elastic deformation of the bulk composite. This enables the fibers to actively interface with the matrix, shielding it from the buildup of stress and slowing the rate of fatigue crack propagation. Other studies have shown a strong dependence of stress intensity range (ΔK) in fatigue crack propagation rate testing [START_REF] Zhang | Suppression of fatigue crack growth in carbon nanotube composites[END_REF][START_REF] Rafiee | Enhanced mechanical properties of nanocomposites at low graphene content[END_REF][START_REF] Marrs | Carbon nanotube augmentation of a bone cement polymer[END_REF]]. An order of magnitude reduction in fatigue crack growth rate was observed at low applied ΔK with the addition of 0.5 wt% MWCNTs to an epoxy matrix [START_REF] Zhang | Suppression of fatigue crack growth in carbon nanotube composites[END_REF]. At much higher ΔK values, a growth rate nearly identical to the neat matrix was evident. In this instance, the stress intensity surrounding the crack tip causes the CNF/matrix interface to break down. Ensuing crack propagation is ultimately the result of the localized stress intensity reaching the critical state, K c . Thus, at smaller K values the CNFs more readily accept the transfer of stress. As K increases, the probability of crack growth due to interfacial failure heightens. For example, if we assume a fatigue crack has been naturally initiated at a single edge of a test coupon through repeated cycling, the Mode I stress intensity at the crack tip is given as

K I aF a W , (7)
where σ is applied stress, a is crack length and W is coupon width [START_REF] Tada | The stress analysis of cracks handbook 3rd[END_REF]. Using Eq. ( 7) and assuming a reasonable crack length, a table containing applied stresses and corresponding stress intensity factors can be constructed (Table 3). In this instance the stress intensity at the crack tip in the low applied stress regime is much less than the critical value needed to propagate a crack (as indicated in fracture toughness testing). Beginning at approximately 30 MPa and continuing into the higher applied stress levels, K becomes exceedingly greater than the measured critical value. This example suggests that once a fatigue crack initiates in high stress amplitude fatigue testing, little can be done to delay crack growth on the account of K being much higher than the measured critical value.

Here, catastrophic failure immediately follows crack initiation. Conversely, it is suspected that the CNFs play a greater role in the suppression of fatigue related damage in lower applied stress regimes.

Conclusions

The addition of helical-ribbon carbon nanofibers has been shown to significantly improve the fracture resistance and fatigue performance of a thermosetting epoxy system.

The present results suggest that the influence of CNFs and their underlying mechanism of reinforcement are strongly K-dependent. In low applied stress amplitude fatigue testing, strain energy is interfacilly transferred to the stronger CNFs due to the dominance of the interfacial strength over localized stresses. In high-stress amplitude fatigue and fracture toughness testing, interfacial strength is considered to be much less than the local stresses induced by increasing K near the crack tip. In this higher stress regime it is suspected that the CNFs function mainly to deflect propagating cracks. When the strain energy associated with loading overpowers interfacial strength, cracks form and propagate along the interface. The de-bonding action dissipates energy and ultimately incites deflection of the crack front. Ensuing mixed-mode loading (Modes I, II and III) from the deflecting crack results in the observed increase in fracture surface area. Ultimately, the energy absorbed through these actions detracts from the available energy needed for crack growth. Together, these mechanisms lead to the enhancements in critical-stress-intensity factor and the energy per unit area of crack surface at the initiation of fracture. However, the expectation of reinforcement at stress intensities beyond K Ic , as hypothesized to exist just after crack initiation in high-stress amplitude fatigue testing, is futile. Future work should examine more dispersive methods of incorporating CNFs to the matrix since the tendency of agglomerates in the high-applied stress regime is to incite crack initiation and accelerate propagation rates.

To summarize, the current results indicate the reinforcement of a structural epoxy system with CNFs has markedly heightened the materials resistance to fracture and significantly increased fatigue performance. Additionally, it has been shown that these conditions are strongly contingent on stress intensity.

Fig. 1 .

 1 Fig. 1. A typical helical-ribbon carbon nanofiber viewed in high-resolution transmission

Fig. 2 .

 2 Fig. 2. Machined notch and pre-crack generated by tapping a fresh razor blade.

Fig. 3 .

 3 Fig. 3. (a) Transmitted light micrograph of 1.0 wt% CNF modified epoxy and (b) high-

1. 0

 0 wt% CNF loading resulted in the largest increase in K Ic , i.e., from 0.improvement. The corresponding enhancement in G Ic over the neat sample at 1.0 wt% CNF was 144%. The 0.5 wt% CNF 100 μm 0.5 μm a bloading resulted in smaller gains, yet the improvements in K Ic and G Ic were still 66 and 121% greater than the control group.

Fig. 4 .

 4 Fig. 4. (a) Mode I fracture toughness (K Ic ) and fracture energy (G Ic ) for neat, 0.5 and 1.0

  with the relatively low measured toughness of the material (K Ic = 0Inspection of the 1.0 wt% CNF modified epoxy confirmed the group to display a much rougher fracture surface (Fig5b). The formation of such additional surfaces during fracture is common to matrices reinforced with micrometer-sized particles and indicative of crack deflection[START_REF] Kinloch | The mechanical properties and fracture behaviour of epoxyinorganic micro-and nano-composites[END_REF].

Fig. 5 .

 5 Fig. 5. Low-resolution SEM images of (a) a neat epoxy specimen illustrating the

  of superior fatigue performance, the composites present much flatter S-N curves and although fatigue life is augmented along the entire range of cyclic stress used in the testing, the addition of CNFs more significantly enhanced the fatigue life in the highcycle, low-stress amplitude regime. Testing at the 20 MPa peak stress amplitude showed

Fig. 6 .

 6 Fig. 6. Cyclic stress verses logarithmic scale of cycles to failure (S-N curves) for neat

Fig. 7 .

 7 Fig. 7. A series of SEM images documenting (a) the typically smooth fracture surface of

3. 4 .

 4 Toughening mechanisms The quantitative K Ic and G Ic data presented here clearly show CNFs to enhance the fracture toughness of epoxy. Well-documented claims regarding the mechanisms for fracture energy dissipation in particulate reinforced thermosetting polymers include crack a b c d

Table 1 .

 1 Fatigue loading and life data for all test programs.

	Table 1a		Table 1b		Table 1c
	Neat matrix	0.5 wt% CNF	1.0 wt% CNF
	N	ζ max (MPa) N	ζ max (MPa) N	ζ max (MPa)
	810	40.0	552	40.0	1 360	40.0
	1 774 40.0	1 077	40.0	1 466	39.9
	1 773 35.0	3 713	35.0	3 976	35.0
	3 272 35.0	7 233	35.0	4 830	34.9
	7 891 30.1	6 745	30.0	9 596	30.0
	12 141 30.0	15 553 29.9	27 821 29.9
	16 921 25.0	30 054 24.9	53 028 25.0
	17 455 25.2	35 248 24.9	65 001 25.0
	44 567 20.0	117 248 20.0	217 943 20.0
	46 724 20.0	178 170 19.9	253 109 20.0

Table 2 .

 2 Fatigue mean fit parameters (log values given for A and B).

	Material	A	B	Coefficient of	Estimated normal
				determination, R 2	population variance, ˆ
	Neat matrix	6.285 -0.080 0.986	0.141
	0.5 wt% CNF 7.247 -0.106 0.930	0.188
	1.0 wt% CNF 7.579 -0.112 0.983	0.114

Table 3 .

 3 Maximum cyclic stress and corresponding Mode I stress intensity at the crack tip, as computed by Eq.[START_REF] Gojny | Carbon nanotube-reinforced epoxy-composites: Enhanced stiffness and fracture toughness at low nanotube content[END_REF]. A crack length of 500 μm was assumed for this example.

	ζ max (MPa) K I ( MPa m	1 2 )
	10	0.45
	20	0.89
	30	1.34
	40	1.79
	50	2.23

Acknowledgments

Financial support for this work was provided in part by the Investigación en Nuevos Materiales para su Aplicación en la Industria Aeronáutica (NACAR) project through Grupo Antolín Ingeniería. We also thank Dr. Byung Chul Kim at the Korea Advanced Institute of Science and Technology for valuable discussions regarding fracture toughness testing.


Hanna Lönnberg

Linda Fogelström

Qi Zhou

Anders Hult

Lars Berglund

Eva Malmström

Investigation of the graft length impact on the interfacial toughness in a cellulose/poly(caprolactone) bilayer laminate

Keywords: microfibrillated cellulose grafted with polycaprolactone A, Polymer-matrix composites B, Interfacial strength B, Delamination

Interfacial adhesion between immiscible cellulose-polymer interfaces is a crucial property for fibrous biocomposites. To tailor the interfacial adhesion, the grafting of polymers from cellulose films was studied using ring-opening polymerization of -caprolactone. The poly( -caprolactone) (PCL) grafted cellulose was analyzed with FTIR, AFM and via water CA measurements. The graft length was varied by the addition of a free initiator, enabling tailoring of the interfacial toughness. Films of microfibrillated cellulose were grafted with PCL and hot-pressed together with a PCL film to form a bilayer laminate. Interfacial peeling toughness correlates very strongly with PCL degree of polymerization (DP). PCL grafts form physical entanglements in the PCL matrix and promote significant plastic deformation in the PCL bulk, thus increasing interfacial peeling energy.

INTRODUCTION

Cellulose in the form of high-strength nanofibers is the main load-bearing constituent in the cell wall of plant structures. The biosynthetic origin combined with exceptional physical properties and nanoscale lateral dimension makes cellulose a highly desirable constituent in new nanostructured material systems such as nanopaper, [START_REF] Henriksson | Cellulose Nanopaper Structures of High Toughness[END_REF] aerogels, 2 biofoams, [START_REF] Svagan | Biomimetic foams of high mechanical performance based on nanostructured cell walls reinforced by native cellulose nanofibrils[END_REF] and high-strength biocomposites.

Fibrous plant cells, typically 30 µm in diameter and several mm in length, are already used as reinforcement in biocomposite materials. [START_REF] Mohanty | biodegradable polymers and biocomposites. An overview[END_REF] Such systems are very complex, and their end properties are difficult to predict. However, one of the most important issues for fully taking advantage of the excellent mechanical properties of cellulosic plant fibers in composite materials, is the creation of a strong interfacial adhesion between the reinforcing fiber and the polymer matrix. [START_REF] Riedel | Natural fibre-reinforced biopolymers as construction materials. New discoveries[END_REF] Different approaches have been utilized to improve fiber dispersion as well as strengthen the interface between fiber and matrix e.g. fiber-surface modification attaching silanes, isocyanates etc. to the hydroxyl group on the surface of cellulose. 7, 8 There are also a number of studies on the improvement of the mechanical properties by grafting polymers to or from the cellulose surface.

9,10-12

The effect of chain entanglements on the interfacial toughness has been reviewed by Creton et al. [START_REF] Creton | Adhesion and fracture of interfaces between immiscible polymers: from the molecular to the continuum scale[END_REF] At high areal density of high molar mass polymer molecules crossing an immiscible interface, entanglements can be highly successful during interface separation and promote extensive plastic deformation in polymer regions surrounding the interface. As a consequence, significant improvement in the interfacial toughness can be achieved.

14

In the present study, we use the ideas reviewed by Creton et al. for fracture of interfaces between immiscible polymers, [START_REF] Creton | Adhesion and fracture of interfaces between immiscible polymers: from the molecular to the continuum scale[END_REF] and apply them to the equally immiscible interface between cellulose nanofibers and a polymer matrix. For this reason, we graft PCL chains of various chain lengths from the cellulose surface in a step towards molecular design of grafts for interfacial toughness. High interface toughness often enhances composites strength; however, low toughness of the fiber/matrix interface may also be advantageous in certain fibrous polymer composites. Extensive fiber pull-out is then promoted, and consumes considerable energy so that composite toughness is increased. 15 We have previously confirmed that ring-opening polymerization (ROP) is a versatile technique in order to covalently graft polymers directly from cellulose substrates, via a grafting-from approach. [START_REF] Lönnberg | Grafting of cellulose fibers with poly( -caprolactone) and Poly(L-lactic acid) via ring-opening polymerization[END_REF][START_REF] Lönnberg | Surface grafting of microfibrillated cellulose with poly( -caprolactone) -Synthesis and characterization[END_REF] Surface characterizations of the PCL-grafted substrates with different graft lengths, as well as various prefunctionalization of the cellulosic surfaces, have shown significant impact on the surface composition, the surface morphology as well as the hydrophobic properties. [START_REF] Lönnberg | Grafting of cellulose fibers with poly( -caprolactone) and Poly(L-lactic acid) via ring-opening polymerization[END_REF] In addition, for PCL-grafted nanosized cellulose, longer grafts gradually improved the dispersion in non-polar solvent and showed a gradual change in the thermal properties and in the crystallization behavior of the PCL grafts, which verified an increase in graft length with higher target DP, i.e., ratio of added monomer to initiator. Habibi et al. [START_REF] Habibi | Bionanocomposites based on poly( -caprolactone)-grafted cellulose nanocrystals by ring-opening polymerization[END_REF] studied nanocomposite materials reinforced with different compositions of PCL-grafted cellulose nanocrystals that were obtained via a grafting-from approach. They reported a significant improvement in mechanical properties of biocomposites based on PCL-grafted cellulose nanocrystals in comparison to neat cellulose nanocrystals. However, no investigation of the graft length impact on the mechanical properties was performed.

In the present study PCL of different molecular weights is grafted from a cellulose surface and thereafter we analyze the effect of graft length on the interfacial adhesion in a bilayer laminate. The aim is to investigate if chain entanglements across a PCL grafted cellulose fiber/ polymer matrix interface can be utilized to strengthen the interfacial toughness between the reinforcement and the matrix in a biocomposite material.

EXPERIMENTAL

Materials. ε-Caprolactone (ε-CL), benzyl alcohol, tin octoate (SnOct 2 ), tetrahydrofuran (THF), methanol (MeOH) and poly(ε-caprolactone) (PCL) (Sigma-Aldrich, MW 80 000 g/mol) were used as received. Microfibrillated cellulose films (MFC-films) were prepared according to a procedure described by Henrikssson et al. [START_REF] Henriksson | Cellulose Nanopaper Structures of High Toughness[END_REF] The MFC-films were dried in vacuum oven at 50 °C for 24 h prior to use.

Characterization. Nuclear magnetic resonance (NMR) spectra were recorded at 400 MHz on a Bruker AM 400 using CDCl 3 as solvent. The TMS signal was used as an internal standard. Fourier transform infrared spectroscopy (FTIR) was performed on a Perkin-Elmer Spectrum 2000 FTIR equipped with a MKII Golden Gate, Single Reflection ATR system from Specac Ltd, London, U.K. All spectra were normalized against a specific ATR crystal adsorption. Size exclusion chromatography (SEC) of the free, ungrafted, polymer formed was performed using a TDA Model 301 equipped with one or two GMH HR -M columns with TSK-gel (Tosoh Biosep), a VE 5200 GPC Autosampler, a VE 1121 GPC Solvent pump and a VE 5710 GPC Degasser, from Viscotek Corp. THF was used as the mobile phase (1.0 ml min -1 ). The measurement was performed at 35 °C. The SEC apparatus was calibrated with linear polystyrenes standards, and toluene was used as flow rate marker. Peel tests were performed on a dynamic mechanical analysis (DMA) TA-instrument Q800 equipped with a film fixture for tensile testing. The measurements were performed on rectangular laminates samples (20x4mm) at room temperature. The tests were performed in a controlled stressstrain mode with a preload force of 0.0010N and force ramp of 0.100N/min. The instrument set-up allowed for a maximum displacement of 20 mm. Four samples were used to characterize each PCL-MFC laminate. Atomic Force Microscopy (AFM) was performed using a Nanoscope III-a system (Digital Instruments) equipped with an EV-type vertically engaged piezoelectric scanner operating in tapping mode in air. Silicon AFM probes from Veccon (Nanosensors) were used with a resonance frequency of 275-348 kHz.

Synthesis of MFC-films grafted with PCL (MFC-PCL).

In total, six different samples of the MFC-films were prepared: blank and MFC-PCL with target DP 75, 150, 300, and 600.

The target DP was based on the amount of monomer, ε-CL, and the initiator, benzyl alcohol, added to the systems. The polymerizations were performed similarly to previously described procedures. 16, 17 Pre-dried MFC-films (2 pieces of 2*3 cm 2 and 1 piece of 2*1 cm 2 )

were immersed in ε-CL (12 g) and toluene (20 ml). Thereafter benzyl alcohol was added to the solution, corresponding to the targeted DP. To remove a majority of the remaining water, part of the solvent (15 ml) was distilled off before the catalyst, Sn(Oct) 2 (0.36 g), was added to the system under argon flow at 100 °C. The polymerizations were allowed to proceed16-18 h. Subsequently, the free PCL was dissolved in THF and precipitated in cold MeOH. In order to remove physically adsorbed but ungrafted PCL, the PCL grafted MFC films were thoroughly washed using soxhlet extraction in THF before characterization. The blank sample was treated in the same manner as the other samples with the exception that no catalyst was added in the ROP step.

Preparation of PCL-film and PCL-MFC bilayer laminates. PCL-films were prepared by

solvent casting from THF. The bilayer laminates of MFC-PCL films and PCL-films were prepared by hot-pressing at 120 °C, 2 min 1 unit pressure and then 5 min 4 unit pressure.

RESULTS AND DISCUSSION

In this study ring-opening polymerization (ROP) is performed to graft poly(εcaprolactone) (PCL) from a film of microfibrillated cellulose (MFC) derived from wood pulp. [START_REF] Henriksson | Cellulose Nanopaper Structures of High Toughness[END_REF] Subsequently, the PCL-grafted MFC films (MFC-PCL), are hot-pressed together with neat PCL film to form a PCL-MFC bilayer laminate. During the hot press stage the grafted molecules can diffuse across the interface.

In an attempt to gradually improve the interfacial peeling toughness of the PCL-MFC laminates the MFC-films were grafted with PCL to several different polymer lengths. We have previously demonstrated that the length of the polymer grafts, and the graft layer thickness, can be varied by the addition of a free (sacrificial) initiator (benzyl alcohol) to the polymerization mixture in a grafting-from approach, Scheme 1. 16, 17 The sacrificial initiator also gives rise to a free polymer that can be isolated and subsequently characterized.

The samples prepared in this study are outlined in Table 1. The molar masses of the ungrafted, free PCL formed during ROP were determined by SEC and 1 H NMR spectroscopy. The determined molar masses (M n ), and corresponding (DP), were found to be lower than the theoretical values. This is somewhat expected since the ROP is initiated both from the added free initiator as well as from available OH-groups on the cellulose surface. However, the estimated molar masses of the free PCL were found to increase with increasing monomer-to-initiator ratio, i.e. target DP, Table 1.

FTIR spectroscopy was used to compare the amount of grafted PCL on the MFC-film surfaces for the different targeted DPs, Figure 1. In agreement with the previous studies 16, 17 a gradually increasing peak intensity of the carbonyl peak (at 1725 cm-1) was observed for higher target DP, thus indicating that more polymer is bound to the surface when higher DPs were targeted, which is also in agreement with the results from the characterization of the free, ungrafted PCL analyzed via 1 H-NMR and SEC analysis.

Atomic force microscopy (AFM) was used to study the change in surface morphology due to grafting, Figure 2. The MFC-film shows a defined fibrillar structure, whereas the images of MFC-PCL reveal an increasingly more polymer-covered surface with less defined fibrillar structure. Thus, there is a good agreement between the results from the FTIR analysis and the AFM images that indicate a gradual increase of the grafted polymer layers, or graft lengths, on the MFC-film surfaces with higher target DPs.

Contact angle (CA) against water was measured to investigate the change in hydrophobicity of the MFC-films as an effect of the grafting of PCL from the surface, Table 1. It can be observed that the PCL grafting increased the hydrophobicity of all MFCfilms. The MFC-PCL75 to MFC-PCL300 exhibits similar CA (91-94°), whereas a significantly higher CA was observed for the MFC-PCL600 (105°). Thus, all CAs of the PCL-grafted MFC-films are significantly higher than for both the reference materials, PCL and casted MFC-films. So despite the fact that the longer PCL grafts have a more smoothening effect on the surface morphology, observed with AFM, the higher surface coverage of hydrophobic PCL in combination with the present of surface roughness is accompanied by a higher hydrophobicity. The results are in good agreement with a previous study of PCL-grafted filter papers [START_REF] Lönnberg | Grafting of cellulose fibers with poly( -caprolactone) and Poly(L-lactic acid) via ring-opening polymerization[END_REF] where high surface coverage of PCL grafts, obtained after pre-functionalization and grafting with long PCL grafts, significantly increased the CA to 105° for the PCL-grafted filter paper surface.

The graft length impact on the interfacial toughness in a bilayer laminate of the PCL grafted MFC-films was evaluated in a peel test, using a DMA instrument. The MFC-PCL films with different target DPs were laminated against thin films of pure PCL-forming bilayer laminates, which thereafter were subjected to the peel test. Figure 3 presents the peeling energy as a function of displacement; the values are also reported in Table 1. As seen, the sample grafted with short PCL chains, MFC-PCL75, does not show any improvement of the interfacial adhesion as compared to the neat MFC-film. This suggests that albeit the hydrophobicity of the surface is increased, as verified by CA measurements, the grafts are too short to substantially affect the interfacial adhesion. The samples MFC-PCL150 to MFC-PCL600, however, require a significantly higher peeling energy. Since the energy is very high, plastic deformation in the PCL matrix is the only plausible explanation caused by significant contribution from chain entanglements. In addition, interfacial peeling toughness correlates very strongly with increasing chain length of PCL. This clearly demonstrates the importance of physical entanglements to promote plastic deformation in the PCL layer, and this represents the first study where the potential of this approach is demonstrated for cellulose-polymer interfaces. Herein the engineering of interfacial toughness at cellulose-polymer interfaces has been demonstrated and may be extended to other polymer systems. The demonstration is of great significance for cellulose biocomposite materials, since the laminate can be viewed as a model for fiber/matrix and nanofiber/matrix interfaces. Furthermore, we anticipate a highly durable interface bond in moist environments due to the grafted molecules and the corresponding physical entanglements in the interphase region.

CONCLUSION

In the present work, grafting impenetrable cellulose fiber surfaces with polymer chains was demonstrated as a tool for tailoring the interfacial adhesion in a bilayer laminate due to the formation of physical entanglements between chains in the matrix and on the surface. A grafting-from approach was utilized to covalently graft the MFC-films with PCL to different target DPs (MFC-PCL), controlled by the addition of a free initiator.

Characterization of the ungrafted PCL and PCL-grafted MFC films showed an increase in the molecular weight, and the graft layer thickness, with higher target DP. The MFC-PCL films were hot-pressed together with thin PCL-films to form bilayer laminates, which thereafter was subjected to peel tests in order to investigate the effect of graft length on the interfacial adhesion in the bilayer laminate. The peel test revealed a significant impact of the graft length on the interfacial adhesion, and an increase in the molecular weight of the PCL grafts required a gradually increase in the peeling energy for a delamination of the bilayer laminate. Thus, the formation of entanglements across the immiscible cellulose/PCL interface promotes plastic shear yielding in the bulk polymer layer and therefore dramatically enhances interfacial toughness of the immiscible interface studied.

Scheme Caption

Scheme 1. ROP of -CL from the MFC-film surface using benzyl alcohol as free initiator. The images are 1.5x1.5 µm 2 .

Figure 3. Interfacial peeling energy (toughness) of bilayer laminates prepared by joining MFC-PCL film with a PCL film.

Figure 1 .

 1 Figure 1. FTIR spectra of blank MFC-film and MFC-films grafted with different target DP

Figure 2 .

 2 Figure 2. AFM images of reference MFC-film (A), MFC-PCL150 (B), MFC-PCL600 (C).

  Scheme 1.

Table Caption Table 1 .

 Caption1 Characterization of ungrafted PCL formed during ROP of -CL, contact angle of the PCL grafted MFC-films, and results from the peel test of the bilayer laminate.

Table 1 .

 1

	Sample		SEC	NMR	CA	Peel test e	Peel test e
		Theo.MW a	Mn (PDI) b	Mn (conv) c	CA (std) d	Displacement f	Peeling
							energy (std)
		(g/mol)	(g/mol)	(g/mol, %)	(°)	(mm)
							(J/m 2 )
		(DP theo )	(DP SEC )	(DP NMR )
	MFC-film	-	-	-	67 (±2)	15.0	14.9 (4.2)
	MFC-PCL75	8700	7900 (1.2)	6700 (91)	91 (±1)	17,5	15,3 (4.4)
		(75)	(69)	(59)
	MFC-PCL150 17200	10000 (1.2)	7750 (93)	93 (±2)	20.0	41.7 (11.6)
		(150)	(88)	(68)
	MFC-PCL300 34300	12200 (1.3)	9700 (91)	94 (±1)	20.0	52.8 (11.8)
		(300)	(107)	(85)
	MFC-PCL600 68500

Acknowledgement. Swedish Agency for Innovation Systems (VINNOVA) and Swedish

Center for Biomimetic Fiber Engineering (BIOMIME) are thanked for financial support.

M. Ankerfors at Innventia AB, Sweden, is thanked for providing the MFC.


Marielle Henriksson

Linda Fogelström

Lars A Berglund

Anders Hult

Novel nanocomposite concept based on crosslinking of hyperbranched polymers in reactive cellulose nanopaper templates

Keywords: A. Nano composites, B. Fibre/matrix bond, B. Interface, D. Dynamic mechanical thermal analysis (DMTA), Cellulose nanofiber

Cellulosic fibers offer interesting possibilities for good interfacial adhesion due to the high density of hydroxyl groups at the surface. In the present study, the potential of a new nanocomposite concept is investigated, where a porous cellulose nanofiber network is impregnated with a solution of reactive hyperbranched polyester. The polymer is chemically cross-linked to form a solid matrix. The resulting nanocomposite structure is unique. The matrix surrounds a tough nanopaper structure consisting of approximately 20 nm diameter nanofibers with an average interfiber distance of only about 6 nm. The cross-linked polymer matrix shows strongly altered characteristics when it is crosslinked in the confined space within the nanofiber network, including dramatically increased Tg, and this must be due to covalent matrix-nanofiber linkages.

Introduction

Cellulose nanocomposites attract great interest. In the present paper, we add to their potential by utilizing a highly functional hyperbranched polymer matrix system in a cellulose nanopaper structure. The highly functional hyperbranched prepolymers, in combination with the large specific surface area of the hydroxyl-functional cellulose network, creates unprecedented nanofiber-matrix interaction. This adds a new synergistic characteristic to the well-known cellulose advantages. Cellulose is obtained from renewable resources, is of low cost, has high crystal modulus [START_REF] Sakurada | Experimental determination of the elastic modulus of crystalline regions in oriented polymers[END_REF] and potentially high tensile strength [START_REF] Joffe | Strength and adhesion characteristics of elementary flax fibres with different surface treatments[END_REF]. An important characteristic is the network-forming ability of cellulose nanofibers [START_REF] Favier | Nanocomposite materials from latex and cellulose whiskers[END_REF][START_REF] Favier | Polymer nanocomposites reinforced by cellulose whiskers[END_REF]. In addition to strong reinforcement effects on mechanical properties of polymers [START_REF] Samir | Review of Recent Research into Cellulosic Whiskers, Their Properties and Their Application in Nanocomposite Field[END_REF][START_REF] Berglund | Cellulose-based nanocomposites[END_REF], cellulose nanofibers strongly increase the thermal stability [START_REF] Favier | Nanocomposite materials from latex and cellulose whiskers[END_REF][START_REF] Favier | Polymer nanocomposites reinforced by cellulose whiskers[END_REF], decrease the thermal expansion [START_REF] Yano | Optically transparent composites reinforced with networks of bacterial nanofibers[END_REF], and improve the thermal conductivity [START_REF] Shimazaki | Excellent Thermal Conductivity of Transparent Cellulose Nanofiber/Epoxy Resin Nanocomposites[END_REF] of the polymer matrix. Transparent composites can be obtained due to the nanoscale of cellulose nanofibers [START_REF] Yano | Optically transparent composites reinforced with networks of bacterial nanofibers[END_REF][START_REF] Iwamoto | Optically transparent composites reinforced with plant fiber-based nanofibers[END_REF]. In the context of clear polymer coatings, nanocellulose reinforcement has the potential to preserve transparency and at the same time strongly improve mechanical properties.

In a previous study, an enzymatic pretreatment procedure was developed in order to facilitate preparation of cellulose nanofibers from wood pulp [START_REF] Henriksson | An environmentally friendly method for enzyme-assisted preparation of microfibrillated cellulose (MFC) nanofibers[END_REF][START_REF] Pääkkö | Enzymatic Hydrolysis Combined with Mechanical Shearing and High-Pressure Homogenization for Nanoscale Cellulose Fibrils and Strong Gels[END_REF]. These nanofibers were used as composite-material reinforcement [START_REF] Henriksson | Structure and Properties of Cellulose Nanocomposite Films Containing Melamine Formaldehyde[END_REF], and as cell wall reinforcement in polymer foams [START_REF] Svagan | Biomimetic foams of high mechanical performance based on nanostructured cell walls reinforced by native cellulose nanofibrils[END_REF]. Recently, we reported on high mechanical performance of cellulose nanopaper structures [START_REF] Henriksson | Cellulose Nanopaper Structures of High Toughness[END_REF] and related nanocomposites with a plasticized starch matrix [START_REF] Svagan | Biomimetic polysaccharide nanocomposites of high cellulose content and high toughness[END_REF]. It is important to investigate new types of polymer matrices for cellulose nanocomposites to extend their property range.

Polymer latexes and water-soluble polymers are the most commonly used matrices [START_REF] Samir | Review of Recent Research into Cellulosic Whiskers, Their Properties and Their Application in Nanocomposite Field[END_REF][START_REF] Berglund | Cellulose-based nanocomposites[END_REF], since they are conveniently combined with cellulose nanofibers dispersed in water. Polymerization routes are also interesting to explore. In the search for reactive monomers and prepolymers, processing criteria are critical. Since the present composites are prepared by impregnation of a nanofiber network, low viscosity is required for complete impregnation. The use of phenol formaldehyde of low molar mass [START_REF] Nakagaito | Novel high-strength biocomposites based on microfibrillated cellulose having nano-order-unit web-like network structure[END_REF], melamine formaldehyde [START_REF] Henriksson | Structure and Properties of Cellulose Nanocomposite Films Containing Melamine Formaldehyde[END_REF], acrylates and epoxies [START_REF] Yano | Optically transparent composites reinforced with networks of bacterial nanofibers[END_REF] has been reported. In the present study, a hyperbranched polymer is used since it has potential as a member of a new class of reactive matrix-forming molecules in nanofiber networks.

Hyperbranched polymers have a highly branched structure with a large number of endgroups [START_REF] Hult | Hyperbranched polymers[END_REF][START_REF] Malmström | Hyperbranched aliphatic polyesters[END_REF]. Consequently, the structure is usually globular with a high density of functional groups at the surface. The compact conformation leads to low viscosity and Newtonian rheology [START_REF] Magnusson | The effect of degree of branching on the rheological and thermal properties of hyperbranched aliphatic polyethers[END_REF]. During cross-linking, the kinetics can be very fast due to the high accessibility of functional groups. The resulting polymer network has a structure largely predetermined by the hyperbranched polymer. This is highly versatile since the center can have certain structural characteristics, whereas the surface functionality can be tailored to provide specific reactions or solubility properties. The globular structure precludes the entanglement mechanisms that linear polymers are subjected to, and enables the hyperbranched polymer to easily flow into the web of cellulose nanofibers, even at comparatively high molecular weights.

In the present study we investigate the potential of a new nanocomposite concept, where porous nanocellulose networks are impregnated by a solution of reactive hyperbranched polymers which is then subjected to thermal cross-linking. A hydroxyl-functional hyperbranched aliphatic polyester in methanol solution is used with a melamine-based curing agent (HMMM) [START_REF] Fogelström | Hard and flexible coatings based on nanoparticle-filled hyperbranched polymers[END_REF]. The preparation procedure involves solvent exchange of a nanocellulose hydrogel followed by polymer solution impregnation [START_REF] Nogi | Fiber-content dependency of the optical transparency and thermal expansion of bacterial nanofiber reinforced composites[END_REF]. This procedure offers great potential in that many different solvents are feasible and a range of polymers can be used, yet the potential advantages of a tough nanopaper structure are preserved.

Experiments and methods

Materials

The cellulose nanofibers are microfibrillated cellulose, MFC, provided by Innventia AB.

MFC was prepared from enzymatically pretreated bleached sulphite softwood pulp (Domsjö ECO Bright) by microfibrillation in a Microfluidizer, Microfluidics M-110EH, Microfluidics Inc [START_REF] Pääkkö | Enzymatic Hydrolysis Combined with Mechanical Shearing and High-Pressure Homogenization for Nanoscale Cellulose Fibrils and Strong Gels[END_REF]. Hyperbranched polymer Boltorn H30 was supplied by Perstorp Specialty Chemicals AB, and hexamethoxymethyl melamine (HMMM) by Becker Industrial Coatings AB, and TONE polyol 0301 was from Union Carbide. Texanol (2,2,4-trimethyl-1,3-pentanediol monoisobutyrate) and methanol were purchased from Sigma-Aldrich.

Preparation of MFC nanofiber films 0.4 g (dry weight) of MFC dispersion was diluted to 0.2 wt.-% and stirred for 48 h. Films of cellulose nanofibers were prepared by filtration. A glass filter funnel (7.2 cm in diameter) was used with a filter membrane, 0.65 µm DVPP, Millipore. The wet film was placed between two metal plates and dried at 55 °C for 48 h. The resulting thickness varied in the range of 60-70 µm between the prepared films.

Preparation of polymer matrix films

Boltorn H30 (3.25 g, 65 wt.-% of the dry weight) was added to a roundbottomed flask and preheated in an oven at 140 ºC until it melted. The flask was put in an oil bath at 60 °C and methanol (3.0 g) was added. The mixture was stirred. HMMM (0.75 g, 15 wt.-% of the dry weight) and TONE polyol 0301 (1.0 g, 20 wt.-% of the dry weight) were added and dissolved. A film-forming additive, Texanol, was added. Films were applied to Teflon substrates with a 200 µm frame applicator. The solvent was evaporated at room temperature for 2 hours and then at 50 °C over night. Subsequently, the films were cured at 140 °C for 20 minutes, and the resulting thicknesses were 40-60 µm.

Preparation of composites

Matrix solutions were prepared by adding Boltorn H30 (9.75 g) to a roundbottomed flask and preheated in an oven at 140 ºC until it melted. Methanol was added (135 mL, 85 mL and 50 mL for the 10 w/v%, 15 w/v%, and 30 w/v% matrix solution) and the flask was heated to 60 ºC, and stirred. HMMM (2.25 g) and TONE polyol 0301 (3 g) were added.

The filtered, wet cellulose nanofiber hydrogel films were subjected to solvent exchange where water was replaced by methanol. These films were then immersed in 30 ml of the matrix solution and kept in a vacuum desiccator for 24 h. The films were dried between metal plates at 55 °C for 24 h and then cross-linked at 140 °C and 10 MPa for 20 minutes. The nanofiber content was calculated from the final weight of the composite. The matrix solution concentrations were 30 w/v%, 15 w/v%, and 10 w/v% and resulted in composites with 33 wt.-%, 51 wt.-%, and 63 wt.-% cellulose nanofibers, respectively. This corresponds to volume fractions (V f ) of 0.26, 0.43 and 0.55, estimated from fiber weight fractions, measured density for the matrix=1090 kg/m 3 , assumptions of no porosity, and an estimated MFC density=1500 kg/m 3 . This estimation was performed based on the fact that the degree of order, and subsequently the density, is expected to be lower for MFC than for the cellulose crystal which has a density of 1570 kg/m 3 [22]. The composite film has a diameter of 70 mm and a thickness in the range of 80-230 µm, depending on composition.

Field emission scanning electron microscopy, FE-SEM

The microstructure of the composites was studied with S-4800 scanning electron microscope. The specimens were coated by gold using an Agar HR sputter coater. The surfaces of the composites and the fracture surfaces were analyzed at 2 kV acceleration voltage.

Density and porosity

An Archimedes scale was used for determination of density of the matrix and the cellulose nanofiber film. The density was calculated from sample displacement when immersed in mercury [START_REF] Baggerud | Measurement of volume fractions of solid, liquid and gas in kraft and CTMP paper at varying moisture content[END_REF]. The porosity was calculated assuming a cellulose density of 1500 kg/m 3 .

Tensile testing

Tensile tests of the films were performed with an Instron machine equipped with a 100 N or a 500 N load cell. Specimens were 5 mm wide and thicknesses were uniform and 50-230 µm depending on composition. Grip distance was 20 mm and testing was performed at a cross-head speed of 2 mm/min. Specimens were conditioned and tested at 50% relative humidity and 23 °C. Displacement was measured by Differential Speckle Photography (DSP) [START_REF] Ljungdahl | Transverse anisotropy of compressive failure in European oak -a digital speckle photography study[END_REF]. A pattern was prepared for the DSP by printer toner.

Data are based on at least 5 specimens. The toughness is defined as work-to-fracture, calculated from the area under the stress-strain curve.

Dynamic mechanical analysis, DMA

The DMA data were obtained with a TA Instruments Q800 in tensile mode. The grip distance was 10 mm and the heating rate was 2 °C min -1 . The specimens, 5 mm wide and with a thickness varying between 50 µm and 230 µm, were dried in a vacuum oven at 50 °C prior to analysis.

Estimate of interfiber distance and volume fraction modified matrix

The interfiber distance, s, is calculated according to equation (1) assuming continuous, unidirectionally oriented fibers and hexagonal packing [START_REF] Hull | An Introduction to Composite Materials[END_REF]. The real material consists of flexible nanofibers oriented random-in-the-plane, so the real distances have a wide distribution but the scale is the same. V f is the fiber volume fraction and r is the fiber radius.

r V s f ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 1 3 2 2 2 1 π (1)
The ratio of the volume fraction of modified matrix, V mm , to the total volume fraction matrix, V m, where V m =1-V f , is calculated from equation (2) [START_REF] Hull | An Introduction to Composite Materials[END_REF].

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + = 1 1 ) 2 ( 2 m m mm V r t r t V V (2)

Results and discussion

Structure

Images of the composites with a nanofiber volume fraction of 0.26 content, and porous neat cellulose "nanopaper" structures are presented in Figure 1. The surface of cellulose nanopaper reveals a fibrous structure, where the cellulose nanofibers are randomly distributed, see Figure 1a. The cross-section shows a layered structure, see Figure 1b.

The porosity of the nanopaper is 24%, based on density data (1140 kg/m 3 ). The FE-This is confirmed by x-ray diffraction [START_REF] Henriksson | Cellulose Nanopaper Structures of High Toughness[END_REF].

The porous cellulose nanofiber film is observed to absorb the uncured liquid matrix during impregnation and the nanofiber orientation distribution within the composites should therefore be similar to the nanofiber film with 100% cellulose. The composites surfaces are more featureless due to the presence of polymer matrix. The layered structure of the cross section can still be observed in the composites, see Figure 1c. The porosity is reduced, due to the addition of matrix as well as the hot-pressing.

Careful scrutiny still makes it possible to discern some porosity in the nanocomposite samples.

Mechanical properties

Free-standing specimens of the nanocomposite films were characterized by dynamic mechanical analysis (DMA) in tensile mode. As can be seen in Figure 2a, the storage modulus increased significantly with increased amount of cellulose nanofibers in the films, especially in the rubbery region above T g . There is a large difference between the pure polymer matrix and the nanocomposite film with a nanofiber volume fraction of V f =0.26. The storage modulus for cellulose V f =0.43, 0.55 and 1 increases in the anticipated order.

The peak in the tan δ curve, see Figure 2b, represents the matrix T g . For the polymer matrix reference sample, the glass transition occurs at 48 °C. The curve for the film with cellulose nanofiber V f =0.26 exhibits two peaks, so the matrix has two T g 's, at 48 °C and 92 °C. The latter could be due to a matrix phase chemically linked with nanofiber surfaces. Another contributing factor could be physically bound regions of polymer in the vicinity of the nanosized particles, in which the mobility of the polymer chains is strongly affected [START_REF] Tsagaropoulos | Dynamic Mechanical Study of the Factors Affecting the Two Glass Transition Behavior of Filled Polymers. Similarities and Differences with Random Ionomers[END_REF]. In the curve for the film with cellulose V f =0.43 the lower T g peak at 48 °C is still visible, but much smaller. The dominant second T g is in this curve slightly shifted upwards to 94 °C. At a cellulose nanofiber V f =0.55, the material no longer exhibits two T g 's and the remaining T g is now shifted all the way up to 119 °C. This is an increase of more than 70 °C, which is quite remarkable. The fact that the original tan δ peak for the matrix reference is lowered and widened in the nanocomposite curves is interesting. The decrease in peak height indicates a matrix structure with increased physical and chemical cross-links while the widening of the peak indicates an increased distribution of effective average molar mass between the physical and chemical cross-links. This is expected if a substantial fraction of the matrix is interacting with the nanofiber surfaces in the network.

It is useful to consider the approximate scale of the interfiber distances in these materials. We can for simplicity assume that all nanofibers have a diameter of 20 nm, are cylindrical, and oriented in the same direction. A certain matrix region close to the fiber surface is altered, and the thickness of this region is t. The shortest distance between nanofiber surfaces for the case of hexagonal fiber packing is denoted s, see Table 1. The thickness t is selected on the basis of an estimated diameter of the hyperbranched molecule of 3 nm, based on information in the literature [START_REF] Ihre | Synthesis, characterization, and 1 H NMR selfdiffusion studies of dendritic aliphatic polyesters based on 2,2bis(hydroxymethyl)propionic acid and 1,1,1-tris(hydroxyphenyl)ethane[END_REF].

Considering data for a 3 nm thick interphase region, the estimation of affected matrix fraction V mm /V m becomes as large as 24-84%. In order to put this into perspective the interfiber distance s and affected matrix fraction is also presented for fibers with 20 µm diameter. The nanoscale effect is substantial.

The Young's modulus and strength increase dramatically with increasing nanofiber content compared with the neat matrix (Figure 3, Table 2). The largest relative improvement in mechanical properties is observed for Young's modulus. The nanofiber composite with a volume fraction of 0.26 shows almost 900 times increase in 10 modulus compared with the neat matrix. The increase is even greater for the other composites. This is in agreement with the DMA results. The increase is due to the high modulus of the cellulose nanofiber network compared with the matrix material. The strength is also increased but more moderately. The great improvement in modulus and strength with addition of a cellulose nanofiber network is accompanied by decreased strain-to-failure.

Data for Young's modulus versus fiber content are presented in Figure 4a.

Conventional composite micromechanics modeling predictions for materials with discrete fibers are not applicable due to the network reinforcement. In Figure 4b, the data for ultimate tensile strength are presented as a function of nanofiber content. At a volume fraction of 0.55, the average strength is 108 MPa. This is similar to data for a porous cellulose nanopaper structure without matrix and V f =0.62 (106 MPa) [START_REF] Henriksson | Cellulose Nanopaper Structures of High Toughness[END_REF]. It seems that the high-T g matrix leads to premature failure at low strains. Interfiberslippage mechanisms are likely to have a positive effect on strain-to-failure [START_REF] Henriksson | Cellulose Nanopaper Structures of High Toughness[END_REF], and are hindered by the stiff matrix in this case.

Conclusions

A wood cellulose nanopaper template was impregnated by a hydroxyl-functional hyperbranched aliphatic polyester solution and polymerized to form a polymer network.

A strong increase in matrix T g of up to 71 °C is observed for the nanocomposites containing up to 55% by volume of about 20 nm diameter nanofibers. The reason is decreased molecular mobility in the geometrically confined polymer network, due to interactions with the cellulose nanofiber surfaces. Covalent matrix-nanofiber linkages are present since HMMM can react chemically with hydroxyl groups at the nanofiber surfaces. This suggests a new nanocomposite concept where a significant proportion of the confined polymer matrix is covalently attached to the cellulose nanofibers. Chemical stability is expected to be high in such materials since fiber-matrix interaction occurs through chemical bonding. The result also means that cellulose nanopaper templates are identified as a highly reactive reinforcement phase. This is a unique feature of cellulose nanopaper and contrasts with the properties of commonly used composites reinforcements such as polyethylene fibers, aramid fibers, carbon fibers, and carbon nanotubes.

Figure 1 .

 1 Figure 1. FE-SEM images of (a) film surface of 100% MFC, (b) fracture surface of

Figure 2 .

 2 Figure 2. DMA curve of nanocomposite films with V f =0 (black), 0.26 (red), 0.43 (blue), 0.55 (green) and 1 (grey, dashed) cellulose nanofibers; (a) storage modulus, (b) tan δ.

Figure 3 .

 3 Figure 3. Uniaxial stress-strain curves for cellulose nanocomposite films with V f =0

Figure 4 .

 4 Figure 4. Young's modulus (a) and ultimate tensile strength (b) as a function of

  Fig 1c

Table 1 .

 1 Effects of volume fraction nanofibers and fiber radius on the affected matrix fraction. Calculated according to equation (1), b Calculated according to equation (2).

	Tables
			diameter=20 nm	diameter=20 µm
	Volume fraction,	Thickness,	Interfiber	Affected matrix	Interfiber	Affected matrix
	V f	t [nm]	distance, s a [nm]	fraction, V mm /V m b	distance, s a [nm]	fraction, V mm /V m b
	0.26	3.0	17.4	0.24	17400	0.00021
	0.43	3.0	9.0	0.52	9000	0.00045
	0.55	3.0	5.7	0.84	5700	0.00073

a

Table 2 .

 2 Mechanical properties for cellulose nanofiber reinforced nanocomposites from the uniaxial tensile test in figure3. The samples are conditioned at 50% RH and 23 ºC. The values in parentheses are the sample standard deviations.

	Nanofiber volume fraction, V f	Modulus [GPa] Tensile strength [MPa]	Strain-to-failure [%]	Work to fracture [MJ/m 3 ]	Moisture content [%]
	0	0.0036 (0.0007) 6.1 (1.5)	23.3 (3.8)	0.8 (0.3) 4.0
	0.26	3.2 (0.5)	49.4 (4.8) 4.1 (1.2)	1.2 (0.3) 5.1
	0.43	6.7 (0.9)	85.0 (10.3) 2.7 (0.2)	1.4 (0.1) 4.4
	0.55	9.7 (1.6)	108 (17.7) 2.8 (0.3)	1.9 (0.4) 4.7
	1.0	13.9 (1.1)	213 (14.9) 6.6 (0.7)	9.4 (1.5) 8.3

Acknowledgements

Tom Lindström and Mikael Ankerfors, Innventia AB, Sweden, are acknowledged for kindly providing microfibrillated cellulose. The Swedish Research Council is gratefully acknowledged for financial support.