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Probing Flexural Properties of Cellulose Nanocrystal-Graphene Nanomembranes with Force Spectroscopy and Bulging Test Sunghan Kim, Rui Xiong, and Vladimir V. Tsukruk Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01079 • Publication Date (Web): 05 May 2016 Downloaded from http://pubs.acs.org on May 7, 2016

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Probing Flexural Properties of Cellulose Nanocrystal-Graphene Nanomembranes with Force Spectroscopy and Bulging Test †

†

†

Sunghan Kim , Rui Xiong , and Vladimir. V. Tsukruk ,* †

School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (USA)

Abstract The flexural properties of ultrathin freely standing composite nanomembranes from reduced graphene oxide (rGO) and cellulose nanocrystals (CNC) have been probed by combining force spectroscopy for local nanomechanical properties and bulging test for global mechanical properties. We observed that the flexural properties of these rGO-CNC nanomembranes are controlled by rGO content and deformational regimes.

The nanomembranes showed the enhanced mechanical properties due to

the strong interfacial interactions between interwoven rGO and CNC components. The presence of weak interfacial interactions resulted in time-dependent behavior with the relaxation time gradually decreased with increasing the deformational rate owing to the reducing viscous damping at faster probing regimes close to 10 Hz. We observed that the microscopic elastic bending modulus of 141 GPa from local force spectroscopy is close to the elastic tensile modulus evaluated from macroscopic bulging test, indicating the consistency of both approaches for analyzing the ultrathin nanomembranes at different spatial scales of deformation. We showed that the flexible rGO-CNC nanomembranes are very resilient in terms of their capacity to recover back into original shape.

Keywords: reduced graphene oxide (rGO), cellulose nanocrystals (CNC), atomic force microscopy, bulging test, flexural rigidity, nanomembrane resiliance

* Corresponding Author E-mail: [email protected], Phone: 404-894-6081, Fax: 404-385-3112 ACS Paragon Plus Environment

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Introduction Ultrathin nanomembranes have the potential to serve for various flexible functional devices due to their excellent mechanical strength, efficient loading transfer, and peculiar elastic properties.1,2,3,4 Although the fundamental mechanical properties of the nanocomposite membranes have been studied and discussed,5,6,7 there is still a lack of understanding for their flexural properties such as a flexural rigidity and a resilience.

Resilience and flexural rigidity are two critical factors which should be

simultaneously considered in order to effectively and physically identify the flexural properties.

The resilience represents a material’s capacity to be restored from a

deformed state to its original state and the normalized flexural rigidity indicates a resistance to applied bending forces.

By considering both the resilience and

flexural rigidity, it is possible to suggest the most promising materials and structures for applications within the demands of wearable electronics and bio-inspired soft devices. 8 , 9

The mechanical property of nanomembranes can be enhanced by

adding various reinforcing components in soft matrices.5,6,7

Among these

components, functionalized cellulose nanocrystals (CNC) and graphene oxides (GO) in particular received much attention as functional reinforcing nanomaterials. The 2D GO component is flexible and strong having high elastic modulus of about 200 GPa 10 and the 1D CNC component has the superior mechanical strength with elastic modulus about 150 GPa. 11

Their use results in significantly increased

strength and robustness, make them cost effective and lightweight, and render them highly adaptable and potentially biocompatible.12,13,14,15,16

For instance, CNC components were used for the fabrication of functional solar cell structures by tuning their morphological and chemical composition.17 Shelled CNCs were exploited for the construction of highly porous microcapsules. 18

The

antimicrobial nanomembranes with enhanced mechanical properties were developed by adding carboxylated CNCs to the polymer matrix.19 On the other hand, flexible and strong GO materials were used as a matrix to fabricate functional nanomembranes due to its high aspect ratio, low oxygen permeability, high surface area, and exceptional processibility.16,20 potential

functionalized

material

to

GO has already been considered as a generate

functional

biocompatible

nanomembranes when combined with silk fibroin, peptides, and cellulose


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21 , 22

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GO-based nanomembranes possess excellent mechanical

properties with high values of elastic modulus and mechanical strength.22,23 The reduced GO (rGO) nanomembranes might also facilitate high electrical conductivity, optical transparency, and thermal conductivity.24,25,26

Although the fundamental mechanical properties of rGO-CNC nanomembranes have been measured and discussed,26,27 there is still a lack of data for their flexural properties such as a flexural rigidity and a resilience.

Conventional measurements

of these properties is a challenging task especially for nanoscale membranes with thicknesses below 100 nm.

Thus, atomic force microscope (AFM) experiments

were exploited to evaluate the flexural properties at nanoscale.

Specifically, the

relation between applying load and deflection of freely suspended ultrathin nanomembranes on microscopic apertures can be determined by using force spectroscopy measurements. 28,29,30

Castellanos-Gomez et. al. reported that the

flexural properties of the freely suspended mica nanosheets can be determined by using an AFM bending test.31 Sridi et. al. used force-distance measurements to determine the bending (flexural) rigidity of freely suspended nickel-coated graphene oxide sheets.32 Alternatively, the deformational behavior can be characterized by using a bulging test.

For instance, Jiang et. al. measured the microscopic deflection

of polymer nanomembranes with a gold nanoparticles.29

However, the practical

measurements of the flexural properties in terms of both resilience and bending stiffness have not been analyzed for these different types of experiments concurrently.

In the present study, the flexural properties of freely suspended ultrathin rGO-CNC nanomembranes are investigated by using both force spectroscopy and a bulging experiment concurrently for comparative analysis of local and global mechanical behavior. The flexural rigidity of rGO-CNC nanomembranes was determined from the bulging tests by using a flexural model with clamped boundary conditions.

In

order to clarify the effect of residual surface stresses and time-dependent behavior on the flexural properties, the residual stress of rGO-CNC nanomembranes has been examined and dynamic measurements have been conducted. We confirmed that both the AFM bending test and the bulging test produce consistent and


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comparable characteristics.

5

Moreover, we demonstrated that laminated rGO-CNC

nanomembranes possess high resilience in comparison with other common engineering materials. Experimental section rGO-CNC fabrication process.

CNCs were prepared from microcrystalline cellulose

(MCC) by sulfuric acid hydrolysis.33

The PEI was used to modify the CNC by

following the procedure listed in the literature.34 Briefly, 1 mL of CNC suspension (1 wt%) was mixed with 2 mL of PEI solution (1 wt%, M w=25 000), following by stirring continuously for 1 h at room temperature.

The pH was adjusted to 1.5 with

concentrated HCl to enhance the ionic interactions between CNC and PEI.

After 10

min, the mixture was centrifuged at 14000 rpm for 10 min and washed with ultrapure water to remove free PEI, using the same centrifugation conditions. Finally, the PEI-modified CNC suspension was diluted to 0.3 wt%.

After the chemical

modification, around 10% weight fraction of PEI was introduced onto the surface of CNCs, which is determined by calculating the atom mass ratio from the X-ray photoelectron spectroscopy (XPS).26 Graphene oxide (GO) was prepared by using the Hummer’s method.35 Then, GO was dispersed in methanol by solvent exchange using centrifugal.

GO was

dispersed with concentration of 0.05 and 0.3 wt%, which were determined to take GO weight contents of 52.5 and 71.6 wt%, respectively.

For spin assisted-layer by

layer (SA-LbL) assembly, a sacrificial layer (about 200 nm) of cellulose acetate (CA) was deposited on silicon wafer (cut to 20 mm × 20 mm).

Then, the CNC aqueous

solution (0.3 wt%) and graphene oxide suspension with desired concentration were alternatively spun on the substrate (3000 rpm, 30 s) until the desired thickness (around 60 nm) was reached.

The reduction of the nanomembrane was conducted

with HI solution (57 wt%) at room temperature for 10 min. 36

The rGO weight

content was calculated from the each GO weight content by applying the degree of reduction of GO.26 The nanomembranes were released from the silicon wafer by dissolving the CA layer in acetone according to usual procedure.

37

The

nanomembranes were picked up by TEM grids and cleaned silicon wafers after they were transferred to DI water.

The nanomembranes were dried at room temperature


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before further characterization.

SEM and AFM imaging.

The surface morphology of rGO-CNC nanomembranes

was investigated by scanning electron microscopy (SEM) with Hitachi-3400SN with 10kV accelerating voltage.

The AFM images of rGO-CNC nanomembrane were

scanned by using an ICON AFM (Bruker). Soft tapping mode was used to obtain height AFM images of nanomembranes with minimum damages using the usual procedure

38 , 39

with silicon AFM tips (MicroMasch).

The AFM images of

nanomembranes were taken with scan size from 3 µm x 3 µm to 50 µm x 50 µm. The scan rates for obtaining images were selected between 0.5 Hz and 1 Hz.

The

thickness of nanomembranes was determined from the height histograms (NanoScope Analysis, Bruker).

Force-distance measurements.

Force-distance measurements were performed to

analyze the flexural property of rGO-CNC nanomembranes, which were freely suspended on the copper-TEM grids with circular apertures of 6 µm, 75 µm, and 600 µm.

The deflection sensitivity of the AFM tip was obtained by conducting force-

distance experiment on a sapphire substrate.

The spring constant of the AFM tip

was determined by using the thermal tune method.40 The radius of the AFM tip was obtained by deconvoluting the images on 20 nm gold nanoparticles.41 The forcedistance curves were obtained with various ramp rates of 0.2, 0.4, 0.6, 0.8, 1.0, 2.0, 4.0, 6.5, and 10 Hz. Bulging test.

To determine the deflection of rGO-CNC nanomembranes with

uniformly applied hydrostatic pressure, the bulging tests were performed with the custom-developed set-up and procedure as introduced earlier.29,42 The pressuredeflection curves were collected with the freely suspended nanomembranes on the 600 µm diameter of the single aperture grid. By measuring a height difference of the glass column, the hydrostatic pressure was controlled with an accuracy of ± 5 Pa. The pressure-deflection curves were collected by using the optical interference setup with a He-Ne laser (632.8 nm).

The images of interference patterns (Newton rings)

were collected, and analyzed using the custom made Fringe analysis software package.22,26,29


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Methodology of the deformational measurements The flexural properties of thin films have been widely determined by characterizing the load-deflection behavior at different experimental setups.29,31, 43

The AFM

bending experiment is usually selected as a method to collect load-deflection curves in a non-destructive manner at nanoscale.28, 44

To analyze nanomembrane

deformation, the general flexural model of the nanomembranes could be defined for membranes freely suspended across circular openings with a different diameter as explored in this study (Figure 1).

The governing equation of the flexural deformation of a circular membrane under point load can be used in the general form

45

:

d 1 d dw Q [ (r )]   r dr r dr dr D

(1)

where r is the radius between the center of a plate and a loading point, w is the deflection of a film, D is the flexural rigidity, and Qr is the shear force on a film.

Figure 1. SEM images of the rGO-CNC nanomembranes suspended over the apertures on TEM grids with a diameter of (a) 6 µm, (b) 75 µm, and (c) 600 µm.

Clamped boundary conditions are usually applied to the flexural model analysis of the composite nanomembranes because of strong adhesion between the


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nanomembranes and the solid support at the edges of apertures.29,46 Under these conditions, the shear forces can be defined as:

Qr   where P is the loading force.

P 2r

(2)

After integration of the original governing equation (1),

the equation of the membrane deflection can be expressed as:

w

P C r2 (r 2 ln r  r 2 )  1  C2 ln r  C3 8rD 4

(3)

where Ci is constants of integration. With the determined constants, the complete form of the equation for film deflection is:

w

P r (2r 2 ln  a 2  r 2 ) 16D a

where a is the radius of the apertures.

(4)

All constants in these equations can be

determined by the boundary conditions of the flexural model as presented in Table 1.

Table 1. Conditions of the deformational behavior for flexural model used in this study. Boundary conditions

Constants

w   at r  0

C2  0

dw  0 at r  a dr

C1 

w  0 at r  a

P (1  2 ln a) 4D

C3 

Pa 2 16D

The bending tests can be performed by using AFM cantilevers with different spring constants (Figure 2). While performing the bending test, the deflection of AFMcantilever (δ) can be detected by the photodiode detector in one direction (c2direction). With the value of δ, the loading force (P) can be determined by:

P  k 


(5)

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where k is the spring constant of AFM-cantilever.

9

The process by which the AFM-tip

approaches (moves toward) the sample involves an increase in the displacement of an AFM-scanner (z).

During these approaching processes, the membranes

deflection (w) can be calculated from:

w  z 

(6)

This common analysis has been used for study of GO-CNC nanomembranes and major results are discussed below.

Figure 2. The AFM bending test using the AFM tip: (a) overall setup of the bending test, (b) procedure of the bending test with experimental parameters used in the equations.

Results and discussion Morphology of rGO-CNC nanomembranes.

The laminated nanomembranes


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studied here were fabricated by using the spin-assisted layer-by-layer (SA-LbL) assembly (see Experimental).

All nanomembranes fabricated here are smooth and

uniform with the average microroughness lower than other graphene oxide based materials (Figure 3a-c).26, 47

The rGO(46 wt%)-CNC, rGO(64 wt%)-CNC, and

rGO(100 wt%) nanomembranes have the root-mean-square microroughness (Rq) of 4.8 ± 0.6 nm, 5.3 ± 1.0 nm, and 7.0 ± 0.8 nm (within 1 x 1 µm2), respectively. The edges of the nanomembranes on the silicon substrates were scanned by AFM in order to measure the thickness in the range of 40 to 60 nm (Figure 3d, e).

Figure 3. Topographical AFM images (z-scale: 200 nm) of rGO(64 wt%)-CNC nanomembranes suspended over the apertures with a diameter of (a) 6 µm, (b) 75 µm, and (c) 600 µm. (d) 2-D and (e) 3-D height images (z-scale: 400 nm) of rGO(64 wt%)-CNC nanomembranes on a silicon substrate. The surface profile shows the thickness of rGO(64 wt%)-CNC nanomembrane about 60 nm. (f) Thicknesses of different nanomembranes on a silicon substrate.

Analysis of flexural properties by AFM bending test.

In order to evaluate the flexural

properties of rGO-CNC nanomembranes, force- distance curves collected on freely suspended membranes were analyzed as described above.


Using the value of the

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spring constants (from 5.9 N/m to 8.2 N/m), the applied force for the bending test on rGO-CNC was calculated by eq. (5).

The load-deflection plots can be generated

using eq. (6) (Figure 4).

Furthermore, the bending stiffness of the nanomembranes can be characterized by the reciprocal of the gradient of the plotted deflection-load curves according to the known spring-against-spring model (Figures 4, 5).48,49,50

Figure 4. Deflection-loading curves of (a) rGO-CNC nanomembranes on the 6 µm aperture; (b) data for rGO(64 wt%)-CNC nanomembranes on the various size apertures: 6 µm, 75 µm, and 600 µm. Each curve of rGO-CNC nanomembranes was obtained at different location.

As apparent from these representative data, the loading-deflection plots show significant variation of the deformational properties for nanomembranes with different


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composition and the same nanomembrane of different diameter apertures.

After

analyzing data for nanomembranes fabricated here and some of them suspended on different apertures, we observed that the rGO (64 wt%)-CNC nanomembrane showed the highest effective bending stiffness on an 6 µm aperture (Figure 5a).

Figure 5. Effective bending stiffness of (a) the rGO-CNC nanomembranes on the 6 µm diameter aperture and for the rGO(64 wt%)-CNC nanomembranes on the various apertures (b).

As known, the introduced reinforcing components can facilitate effective stress redistribution in order to enhance the mechanical performance.

51

The

nanomembranes with different rod-like CNC components show different mechanical properties with increasing CNC content in 46 or 64 wt%-CNC nanomembrane


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causing increased strength.

13

Complete removal of stiff, high-aspect ratio CNC

component results in significant reduction of bending stiffness of nanomembranes with predominant flexible GO sheets.

Moreover, as expected, the effective bending

stiffness of the nanomembrane inversely depends on the diameter of the freely suspended membranes (Figure 5b).52

In order to verify the applicability of clamped boundary conditions, the load-deflection curves of circular type rGO-CNC nanomembranes under concentrated-load were analyzed by using analytical models of both clamped and supported boundary conditions.

53

These simulated data were compared with the experimental data

collected in order to conclude relevance of different models (see Figure S1 in the Supporting Information).

Smaller deviation between the clamped model and the

linear fit analysis both suggest that the clamped boundary conditions are most appropriated for the suspended nanomembranes studied in this work.

Furthermore, the flexural rigidity of a nanomembrane can be defined through geometrical parameters from eq. (4).

To measure the maximum deflection, the

loading force is applied at the center of the nanomembrane.

Using the loading

force data and the deflection of the nanomembranes measured with an AFM bending test, the flexural rigidity of the various nanomembranes can be determined (Figure 6).

As we observed, the rGO (64 wt%)-CNC nanomembrane showed the greatest flexural rigidity of 2.22 ± 0.15 X 10-12 Nm (Figure 6a). The measured flexural rigidity reminds similar for the different aperture diameters: for diameters of 6 µm, 75 µm, and 600 µm, the flexural rigidity is 2.22 ± 0.15 X 10-12 Nm to 2.37 ± 0.35 X 10-12 Nm, and to 2.71 ± 0.50 X 10-12 Nm, respectively (Figure 6b).

As known, in contrast to

the effective bending stiffness, flexural rigidity does not depend by the diameter of the suspended membrane, as was confirmed by our experiments (Figure 6b).49 Thus, the flexural rigidity can be used as a size-independent parameter in designing freely standing flexible microstructures of different sizes.


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Figure 6. Flexural rigidity of (a) the various rGO-CNC nanomembranes on the 6 µm diameter aperture, (b) the rGO (64 wt%)-CNC nanomembrane on the various apertures.

Then, as known, the residual stress is generated within freely standing nanomembranes while it is transferred and dried at room temperature.54 Generally, the presence of residual stress can affect the apparent mechanical properties of nanomembranes and their ultimate strength.29 In order to clarify its influence on the flexural properties, the residual stress was determined by analyzing the loaddeflection curves independently during approaching and retracting cycles (Figure 7).


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Figure 7. (a) Deflection-load curves of rGO(64 wt%)-CNC nanomembranes on the 600 µm diameter aperture in both approaching and retracting modes. Linearly fits of approaching and retracting data are shown by the dotted and dashed lines, respectively. (b) Schematic of the AFM retracting process with parameters used in the equations.

The deflection of the nanomembrane and the pulling force during the retraction process can be determined by using eqs (5) and (6), respectively.

As shown in

Figure 7a, the difference between the linear fits indicates the presence of the residual stress.

However, there is no statistically significant difference in the

effective bending stiffness derived from both the approaching and retracting modes that indicates that the role of the residual stresses in the evaluation of the overall flexural properties over the entire deformational regimes is negligible.

All the flexural properties of the rGO-CNC nanomembrane discussed above were derived from AFM testing performed at a nominal ramp rate of 2 Hz under assumption of the purely elastic deformational behavior, which is a common widely used approach .55,56,57 However, the potential viscoelastic behavior can render the


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apparent mechanical properties to be time-dependent.58,59 An understanding of the viscoelastic contribution is necessary for characterization of their time-dependent flexural properties.

Thus, we addressed this issue by collecting force-distance data

while applying different ramp rates during AFM testing.60,61

In fact, we observed that the effective bending stiffness of the nanomembranes was observed to be strongly time dependent (Figure 8a).

At the lowest probing range

(0.2–0.8 Hz), the nanomembranes showed the lowest values for effective bending stiffness.

Moreover, up to 4 Hz, the effective bending stiffness of all the

nanomembranes gradually increased with the ramp rate up to factor of two (Figure 8a).

Within the highest rates of 4–10 Hz probed here, the effective bending

stiffness decreased slightly or remains unchanged as the ramp rate increased, but in any case it remains much higher than that at the slowest deformation rate.

The

difference of the rate dependent effective bending stiffness is statistically significant (see Figure S2 in the Supporting Information).

As a next step, the time-dependent

behavior of effective bending stiffness was analyzed in order to derive the relaxation time, τ, which is fundamental characteristic of molecular-segmental mobility of materials at different spatial scales.62

As known, the relaxation time of the nanomembranes can be calculated from the experimental data by using a modified Johnson model as:63



3 2

3UT 1  2  4 R E

t t   E     (1  )(1  e )    E0  

(7)

where 𝑈 is the loading rate, T is the temperature, R is the radius of the tip, ν is the Poisson’s ratio for the specimen, E∞ is the infinite modulus of a specimen, t is the time in seconds from the beginning of the deformational process. ratio was used as 0.3 for the elastic deformation.64


The Poisson’s

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Figure 8. (a) Effective bending stiffness and (b) relaxation time of rGO-CNC nanomembranes on the 6 µm diameter aperture at various ramp rates. Dashed curves show the non-linear fit of the relaxation time in ramp rates.

The analysis of experimental data shows that the relaxation time gradually decreases as the deformation rate increases (Figure 8b).

Specifically, the value of

relaxation time of rGO (46 wt%)-CNC is 137 msec while rGO (64 wt%)-CNC shows much faster relaxation time of 54 msec at the 0.2 Hz ramp rate.

Overall, the rGO

(64 wt%)-CNC nanomembrane possess the fastest relaxation times indicating the high ability to adapt the external stresses.

As known, the relaxation time is


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generally inversely proportional to the rate of local motion (group, molecular, segmental) in viscoelastic materials.65,66 In other words, the relaxation time reflects the nature of forced molecular motion; small-scale motions (group, molecular) are related to faster relaxation time while slower relaxation time implies large-scale motions (segmental, particular) with higher entanglement constraint.62,

66

The

balance of fast and slow molecular motions of different components (biopolymers, graphene oxides, and confined interphases) is a critical factor to determine the resulting viscoelastic property of materials.

In general, stiffer GO elements

exhibited shorter relaxation times, while the soft biopolymer elements showed relatively longer relaxation times.67

On the other hand, the rGO (46 wt%)-CNC

shows the most pronounced viscoelastic behavior among the nanomembranes (Figure 8b).

At the high ramp rates, the relaxation times of the rGO (46 wt%)-CNC

are very short, ranging from 2 ms to 10 ms.

However, the relaxation time

significantly increased up to 140 ms at slow deformational rate of 0.2 Hz.

These results confirm that, overall, the elastic solid properties of a material dominate at high-frequency ramp rates, whereas viscous behavior is more apparent under low frequencies. 68 , 69

With this understanding, it follows that the lower values for

effective bending stiffness shown at slower ramp rates are caused by the slow relaxation of intermixed components.

At the fast ramp rates, the dominant elastic

solid properties cause higher values for effective bending stiffness.58,65

Such

behavior is common for flexible soft materials but the relaxation times of bulkier components in GO-CNC nanomembranes are higher than in ultrathin films from common synthetic polymers.58

The bulging test.

To evaluate the flexural properties of the nanomembranes under

conditions of uniform macroscopic deformation, a bulging test can be conducted in accordance with the usual procedure.26, 70

For this test, steady increasing

hydrostatic pressure was applied to the selected nanomembrane fixed by sample holders on a substrate with an aperture diameter of 600 µm (Figure 9a).

As the

pressure increased, a nonlinear increase in the deflection of the nanomembrane was observed (Figure 9b).


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Figure 9. (a) The bulging test schematics with parameters for eq. (9) (b) Deflection of the series of the rGO-CNC nanomembranes on the 600 µm aperture vs applied pressure. (c) Flexural rigidity of rGO(64 wt%)-CNC nanomembrane as determined by bulging test and AFM.


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The flexural properties of the nanomembranes can be analyzed by using a uniformly loaded deflection model of circular film under clamped boundary conditions:45,71

4t 0 32 w3 p  2 w  4 2 D(1  v) r r t

(8)

where p is the uniform pressure, σ0 is the residual surface stress which can be ignored (see above). The analysis of the bulging test produced the values of the flexural rigidity of 2.47 ± 0.37 X 10-12 Nm for the selected rGO(64 wt%)-CNC nanomembrane.

This value is close (the same within standard deviation) to the

values of 2.72 ± 0.50 X 10-12 Nm, which was obtained from the AFM bending test (Figure 9c).

Thus, even though two deformational experiments were performed

with different physical models beneath and different loading conditions, they generate similar physical characteristics independently upon type of deformation (local bending or macroscopic bending).

Therefore, we can suggest that the

flexural rigidity of ultra-thin nanomembranes can be characterized consistently by applying these quite different experimental setups.

Comparison between elastic tensile modulus and elastic bending modulus.

As a

next step, the bending elastic modulus of rGO-CNC nanomembranes, Ebending, was determined from the AFM probing by using the equation:45

Ebending 

12(1  v )  t3 2

2r 2 ln

r  (a 2  r 2 ) a P 16w

(9)

As known, in the case of isotropic elastic material, the elastic bending modulus is equivalent to the elastic tensile modulus.

However, shear deformations during the

bending test might result in a progressive delamination of the laminated composites and causes reduction of the apparent values of the bending elastic modlus. 22,72,73 As we observed, in our case, the elastic bending modulus of 141 ± 26 GPa determined from these measurements is extremely high and only slightly lower than the elastic tensile modulus of 169 ± 33 GPa, obtained earlier from bulging tests.26 This result highlights strong bonding between flexible GO sheets and the rigid rodlike CNC components in the composite nanomembranes fabricated here.


The

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dense ionic interactions between components can be achieved by introducing the oppositely surface groups.

The introduction of CNC components, which are

positively charged due the presence of the PEI shell, can enhance the interfacial interactions with negatively charged GO sheets.

On the other hand, the hydrogen

bonding between CNC and GO components is one another critical interaction factor to strengthen the interfacial interactions.26

Moreover, the rGO sheets capable of

strong π-π interactions after removal of the oxygen functional groups during the reduction process.26 These enhanced interfacial interactions can facilitate further improving of the mechanical property of the rGO-CNC nanomembranes.

Comparative analysis of flexural properties of rGO-CNC nanomembranes.

To

compare the flexural properties of the rGO-CNC nanomembranes with other engineering materials, the normalized flexural rigidity of specific engineering materials can be directly compared along with their resilience values.

Resilience

and flexural rigidity are two critical factors which should be simultaneously considered in order to effectively and physically identify the mechanical properties. As known, resilience (Ur) can be calculated by:74

Ur 

 y2

(10)

2E

where σy is the yield strength and E is the Young’s modulus.

On the other hand, the

normalized flexural rigidity (D/t3) can be determined by:45

D E  3 t 12(1  v 2 )

(11)

The nanomembranes with 6 CNC-GO bilayers of total thickness of 30 nm show increment of 5 ± 2 nm per CNC-GO bilayer with the diameter of CNC component of 7 ± 2 nm.22,26

Thus, the flexural rigidity can be normalized to the thickness.

To

calculate the resilience and the normalized flexural rigidity of other materials, the values of yield strength and Young's modulus were taking the highest values reported the literature.

The highest yield strength of the rGO-CNC nanomembrane

in this study was obtained from the stress-strain curves from the bulging test.


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In the comparison of various materials’ flexural properties, the reference material was set as copper, which is widely used in a variety of engineering applications owing to its favorable strength and flexibility.75,76 In the coordinate system, which made by the copper as a reference feature (Figure 10), the left side of the plot represents less flexible (high resistance to bending force) materials while the right side indicates more flexible (low resistance to bending force) materials.

In contrast,

the upper region of the plot corresponds to the high resilience materials, while the bottom region covers materials with low resilience. Furthermore, the upper right quadrant includes materials with better flexural properties, including combined greater flexibility and high resilience. .26,2 9, 77,78,79,80,81, 82,83,84, ,85,86

The rGO-CNC nanomembrane has high resilience of about 1.5 MPa (10 times higher than copper), a value which is better than most of other engineering materials. Moreover, the relatively low flexural rigidity of 13 GPa for composite rGO-CNC materials is close to that in copper (15 GPa). Most metals and graphene have high resilience, but relatively low flexibility.

Specifically, graphene has the highest

resilience at 8.5 GPa, but its flexural rigidity is high at 92 GPa, signifying relatively high stiffness.79

87

In comparison, ceramics and single-wall nanotube (SWNT)

demonstrate poorer flexural properties, marked by low resilience and high flexural rigidity.

For example, SWNT shows low resilience at 11 kPa (130 times lower than

for rGO-CNC nanomembranes fabricated here) and high flexural rigidity at 92 GPa (7 times higher than for rGO-CNC nanomembranes).82

Most polymers and

polymer-composites attain relatively superior flexural properties, that is, high resilience and greater flexibility.

However, even though the flexibility of polymers is

greater than rGO-CNC nanomembrane, their resilience is much lower (Figure 10, pay attention to double log scales). Thus, the flexural properties of the rGO-CNC nanomembranes fabricated here are superior to other engineered materials in terms of both resilience and flexural rigidity.


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Figure 6. Comparison of flexural properties of various engineering materials in terms of resilience and normalized flexural rigidity (star-mark provides flexural properties of this work). All data are taken from current literature.26,29,77,78,79,80,81,82,83,84,85,86,87 Abbreviations: PS: polystyrene; PET: polyethylene terephthalate; PAH: polyallylamine hydrochloride; PSS: polysodium 4-styrenesulphonate; PMMA: polymethyl methacrylate; PPE: polyphenyl ether, SWNT/SWCNT: single-wall carbon nanotube; SF: silk-fibroin; GO: graphene oxide; rGO: reduced graphene oxide; CNC: cellulose nanocrystal; Si 3N4: silicon nitride.

In order to characterize the overall level of material’s flexural properties, we suggest a pertinent figure of merit (F.O.M.) to be defined as:

F .O.M 

Ur log( D / t 3 )

(12)

The proposed FOM characterize the optimal flexural material’s behavior (Figure 11). This characteristic can be identified by dividing the resilience by the normalized flexural rigidity including logarithm function, which is used for compensating the unit difference between the resilience and the normalized flexural rigidity.

Flexible

materials should be easily deformed (low flexural rigidity) but also can be easily restored to original shape from the deformed shape (high resilience). Thus, the higher FOM value represents better flexible performance with the rGO-CNC


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nanomembranes fabricated here showing the better performance than any other engineering material except graphene (monolayer) (Figure 11).

Monolayer

graphene is mechanically robust and flexible, however, monolayer graphene has limited applicability.88,89

Figure 7.

Comparison of FOM values of various engineering materials .

Conclusions In conclusion, the flexural properties of rGO-CNC nanomembranes were investigated by using both the AFM bending test and the bulging test in multiscale (micro and nanoscale).

The encapsulation of rigid cellulose nanocrystals results in

enhanced resilience of the composite nanomembranes, and the flexible graphene oxide monolayers facilitate the highly flexible nanomembranes with the increased robustness initiated by reduction of GO component due to enhanced interfacial interactions.

Two-component nanomembranes studied here show the time-

dependent behavior in the designated deformational rate with the relaxation time exceeding significantly those observed for conventional polymer films.

The elastic

bending modulus of the nanomembrane was found to be in a good agreement with


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the elastic tensile modulus, which indicates high interfacial bonding strength of GO sheets and CNC rod-like nanostructures.

Finally, the analysis of the practical

performance in the terms of flexural FOM indicates the rGO-CNC nanomembranes show high flexural properties with combined high resilience and high flexibility on top of their high mechanical strength.

These flexural properties of the rGO-CNC

nanomembranes can facilitate their exploration as flexible and wearable electronic devices, energy harvesting systems, ion and charge transfer membranes, and lightweight ballistic protection.

Acknowledgements This study was supported by the National Science Foundation CBET-1402712 and the Air Force Office of Scientific Research, FA9550-14-1-0269. The authors declare no competing financial interests.


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