an experimental investigation on the tangential interfacial properties of graphene size effect

An experimental investigation on the tangential interfacial propertiesof graphene: Size effect Chaochen Xua, Tao Xueb, Jiangang Guoa, Yilan Kanga,n, Wei Qiua,n, Haibin Songa, a Tianjin K

An experimental investigation on the tangential interfacial properties

of graphene: Size effect

Chaochen Xua, Tao Xueb, Jiangang Guoa, Yilan Kanga,n, Wei Qiua,n, Haibin Songa,

a

Tianjin Key Laboratory of Modern Engineering Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China

b

Center for Analysis and Test, Tianjin University, Tianjin 300072, PR China

a r t i c l e i n f o

Article history:

Received 20 August 2015

Received in revised form

18 September 2015

Accepted 21 September 2015

Available online 25 September 2015

Keywords:

Graphene

Size effect

Edge effect

Interface

Raman spectroscopy

a b s t r a c t

The size-dependent mechanical properties and the edge effect of the tangential interface between gra-phene and a polyethylene terephthalate substrate (PET) are investigated The interfacial mechanical parameters of graphene with seven different lengths are measured by in-situ Raman spectroscopy ex-periments New phenomena are observed, such as the existence of the edge effect in the interfacial stress/strain transfer process, and the length of the edge of the interface can be affected by the size of graphene Additionally, the interfacial shear stress exhibits a size effect, with its value significantly de-creasing with an increase of the length of graphene However, the ultimate stiffness and failure strength

of the interface are size-independent as they are constant regardless of the length of graphene

& 2015 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND

license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1 Introduction

Varisized graphene materials have been widely applied to the

new domain of microelectronic devices, such asflexible electronic

components, ultra-sensitive strain sensors and battery electrodes

[1–3] The quality and performance of these devices are often

limited by the mechanical properties and the deformation

trans-mission efficiency of the interface between graphene and the

substrate or surrounding material However, there have only been

a few experimental studies on the interfacial mechanical

proper-ties of graphene, and these experimental studies have mainly

fo-cused on small-sized graphene samples that are a few to dozens of

microns in length [4–6] The studies on the interfacial

perfor-mance of graphene on the macro- to micro-scales and the size

effects on the performance are insufficient Therefore, it is

neces-sary to experimentally measure the interfacial properties of

multi-sized graphene and systematically analyze any size effects

Herein, we focus on the size effect of graphene, and investigate

the size-dependent mechanical properties of the tangential

in-terface between multi-sized graphene and PET substrate In-situ

Raman spectroscopy measures the whole-field deformation of

graphene that is subjected to a uniaxial tensile load The edge

effect existing in the interfacial stress/strain transfer process and the evolution of the three bonding states at the interface, that is adhesion, slide and debond, are discussed The mechanical para-meters, such as shear strength, ultimate stiffness and failure strength of the graphene/PET interface with different sizes, are also provided We use experiments to analyze how these para-meters and the interfacial edge effect are controlled by the size of graphene

2 Materials and methods

To explore the size effect of graphene, seven graphene/PET specimens are designed The lengths of graphene range from the macro (L1¼1 cm) to micro (L7¼50μm) scales, as shown inFig 1

(a), and the width of graphene is identical (W¼2 mm) The gra-phene sheet is produced by CVD method (chemical vapor de-position) and is physically adsorbed on the PET substrate by Van der Waals forces at the interface, and these forces guarantee that the graphene can be deformed simultaneously as the PET substrate

is subjected to a uniaxial tensile displacement-controlled loading process by an ingenious micro-loading device, as shown inFig 1

(b) PET is aflexible substrate that is able to undergo a large de-formation, as shown by its stress–strain curve provided inFig 1(c),

in which the elastic region ranges from 0% to 2.5% The whole loading process is conducted in this elastic region to ensure linear loading and uniform deformation throughout the substrate

Contents lists available atScienceDirect

journal homepage:www.elsevier.com/locate/matlet

Materials Letters

http://dx.doi.org/10.1016/j.matlet.2015.09.088

0167-577X/& 2015 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

n Corresponding authors.

E-mail addresses: tju_ylkang@tju.edu.cn (Y Kang),

daniell_q@hotmail.com (W Qiu).

Materials Letters 161 (2015) 755–758

The wavenumber of the characteristic peaks in the Raman

spectrum is related to the lattice deformation, and the peak shift

can reflect the strain of a specific material The strain information

of porous silicon [7–9], carbon nanotubes [10,11] and graphene

[12] has been measured accurately using in-situ Raman

spectro-scopy In the Raman spectrum of monolayer graphene, the

2D-Raman peak will shift to lower or higher positions under tensile or

compressive load, termed as a red-shift or blue-shift, respectively

Hence, this shift is traced to measure the strain of graphene in this

experiment (hereafter, the 2D-Raman peak position will be termed

peak position for short) The Raman spectra are obtained through

a Renishaw-inVia system with a 633 nm and 0.23 mW He–Ne laser

as the excitation source The spot size of the laser is approximately

1.2μm in diameter, focused through a 50 objective lens

Con-sidering the symmetry of the specimen, the mapping area is a

quarter of the entire graphene area, which can be seen by the

red-shaded region inFig 1(b)

3 Results and discussion

To quantitatively establish the relationship between the shift of

the peak position and the strain of graphene,Fig 1(d) depicts the

evolution of the peak position of 50μm-long graphene at the

central point of the graphene strip with increasing PET strain An

obvious red-shift of the peak position occurs during loading The

process of the peak shift can be divided into three stages termed

the linear stage, the nonlinear stage, and the stable stage The

slope of the linear stage is 40 cm1per % (PET strain) This peak

shift process is similar to that reported for the 10,000μm-long

graphene in Ref.[12] This reference reports that the bonding state

of the interface in the linear stage (the initial loading PET strain of

0.5%) is adhesion, which means the graphene tightly adheres to

the PET by the Van der Waals force and the strain of graphene and

PET is identical Therefore, the slope of 40 cm1per % can now be used to establish the linear relationship between the shift of the peak position and the strain of graphene as one-to-one, corre-sponding to the black and red vertical axes shown inFig 1(d)

To intuitively compare the strain field information obtained from the graphene with different sizes,Fig.2depicts the contour maps of the strainfield of the longest (L1) and shortest (L7) gra-phene during the loading process The strainfield of graphene in the vertical direction is uniform during the loading process, which means the interfacial edge effect upon the deformation caused by the top and bottom edges of graphene can be ignored However, the strainfield in the horizontal direction is not uniform at each level of PET strain after loading The gradually changing colors in the contour maps suggest the existence of the strain gradient re-gion around the edge of graphene and the strain gradually in-creases from 0% at the edge until it stabilizes in the central region This phenomenon indicates that the interfacial edge effect, caused

by the left and right edges of the graphene upon the deformation along the loading direction, exists throughout the whole loading process Besides, there is a huge difference in the length of the strain gradient region of graphene L1and L7by comparingFig 2(a) with (b), that is, the degree to which the interface is influenced by the edge effect varies with the length of graphene Therefore, the interfacial mechanical behaviors are susceptible to the size of graphene

To further explore the size-dependent interfacial mechanical behaviors,Fig 3provides the variations of strain along the cen-terline of the longest (L1) and shortest (L7) graphene for PET tensile strains of 0–2.5% during the loading process The evolution of the strain across the entire graphene can be divided into three stages

as observed for the center point of graphene inFig 1(d) In thefirst stage (when PET strain is less than 0.5%), the strain of the entire graphene, except for the edge, equals the strain of PET Hence, the deformation in the substrate completely transfers to the graphene

Fig 1 (a) Sketch of the seven graphene/PET specimens with different lengths (not to scale) (b) Schematic diagram of the experimental setup (micro-Raman system and graphene/PET specimen, not to scale) (c) Stress–strain curve of the PET substrate (d) The strain at the central point of the graphene strip as a function of PET strain during the loading process The shaded regions in (d) indicate the adhesion (red), slide (white) and debonding (blue) stages (Inset shows the 2D characteristic peak in the Raman spectrum of graphene before loading.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

C Xu et al / Materials Letters 161 (2015) 755–758 756

on its surface, so the interface is in the adhesion bonding state In

the second stage (when the PET strain is between 0.5% and 2%), the

graphene strain is less than the PET strain Hence, only part of the

deformation is transferred, so the slide begins between the

gra-phene/PET interfaces because the Van der Waals force is not

suf-ficiently strong In the third stage (when the PET strain is more

than 2%), the curves of graphene strain in bothFig 3(a) and (b) do

not change even as the PET strain keeps increasing Hence, no

deformation can be transferred and the interfaces totally debond

in the tangential direction ComparingFig 3(a) with (b), the

evo-lution of the three bonding states at the interface, independent of

the size of graphene, is identical, and the demarcation points

be-tween these bonding states are the PET strain values of 0.5 and 2%

The critical PET strain at which the interface begins to debond is

defined as the failure strength of the interface, and hence the two

graphene interfaces have the same failure strength, that is 2% The

maximum strain that can be transferred to the graphene before

the interfacial failure is defined as the ultimate stiffness of the

interface AsFig 3shows, when the PET strain is more than 2%, the

maximum strain of 10,000μm-long graphene is 1.013%, while that

of 50μm-long graphene is 0.998% Therefore, the ultimate stiffness

of the interface is hardly affected by the size of graphene The variations of strain along the centerline of graphene with two different lengths are both composed of two areas at every PET strain These are the central region, where the strain is stable, and the edge region, which is controlled by the interfacial edge effect that exhibits the strain gradient However, the lengths of the edge region are different depending on the size of graphene If the length of this edge region, in which the graphene strain rises from 0% to approximately 90% or 100% of the plateau value, is defined as the‘critical length’,l c,[13,14]then the ratio of the critical length to total length,l l c/, is defined as the ‘relative critical length’,ϑ, which can represent the extent that the interface is influenced by the edge effect, where the smaller the ϑ, the smaller the extent From Fig.3, l cfor 10,000μm-long graphene is 2000μm, and ϑis 0.2, whilel cfor 50μm-long graphene is 40μm, and ϑis 0.8 Therefore, the longer the graphene, the smaller the relative critical length, and hence the smaller the extent that the interface is influenced

Fig 2 Contour maps of the strain field of (a) the longest 10,000 μm-long graphene (L 1 ) and (b) the shortest 50 μm-long graphene (L 7 ) at six different levels of PET tensile strain applied in the horizontal direction during the loading process The list of numbers (left) shows the six different levels of PET tensile strain from 0% to 2.5%, and the bar legend (right) plots the relationship between the contour colors and the strain of the graphene The two contour maps are displayed as the same size for the purpose of facilitating the comparison and hence the lengths of graphene are normalized so that the distances along the graphene are expressed as fractional coordinates,X=x L/ , where L is the total length of specific graphene and X= ± 0.5 represents the left and right edges of graphene.

Fig 3 Variations of the strain along the centerline of (a) the longest 10,000 μm-long graphene (L 1 ) and (b) the shortest 50 μm-long graphene (L 7 ) at 13 different levels of PET tensile strain applied in the horizontal direction during the loading process (Inset) Schematic showing the locations of the sampling points along the centerline of graphene (the length of graphene is normalized, the fractional coordinate Xis used and the data for locations X∈ [− 0.5, 0 ] are measured and the values of the data for locations

C Xu et al / Materials Letters 161 (2015) 755–758 757

by the edge effect This phenomenon verifies the results from

numerical simulations reported in Refs.[4]and [15]

To explore how the interfacial stress transfer between the

graphene and substrate is affected by the size of graphene, the

force balance between the shear forces at the interface and the

tensile forces in theflake element is established based on the force

analysis of an element of graphene[12] Supposing the

deforma-tion of graphene to be elastic,σ=E ε, the relationship between the

interfacial shear stress, τ, and the normal stress, s, can be

de-termined as:

d

( ) whereεis the normal strain in graphene, E is the Young's modulus

and t is the thickness of the graphene Herein, we take E¼1 TPa as

the Young's modulus and t¼0.34 nm as the thickness of graphene

[16,17] The maximum interfacial shear stress,τmax, of 10,000μ

m-long graphene is 0.004 Mpa while the τmax of 50μm-long

gra-phene is 0.237 Mpa Therefore, the maximum interfacial shear

stress significantly increases as the graphene length decreases

To systematically discuss the size-dependent interfacial

per-formance of graphene, the experiments on the graphene with

seven different lengths are analyzed as described in the previous

section The experimental results, including five interfacial

me-chanical parameters, are included inTable 1, where the

deforma-tion parameters, such as the failure strength and stiffness of

in-terface, are size-independent, while the critical length, relative

critical length and maximum interfacial shear stress are

size-dependent

The relative critical length,ϑ, is considered as a dimensionless

parameter that deserves investigation When the length of

gra-phene is less than 2000μm, ϑdecreases as the graphene length

increases, which means the degree that the interface is affected by

the edge effect is reduced with an incremental change of the

graphene length However, when the length of graphene is more

than 2000μm, ϑis a constant, showing the degree is stable

re-gardless of any incremental change of the graphene length This

suggests that the dimensionless parameter serves as a scaling

factor to evaluate the interfacial edge effect of graphene As the

scaling factor tends toward being constant, the size of graphene

reaches the macroscopic scale and the interfacial edge effect is no

longer influenced by the size of graphene Therefore, with regard

to the graphene used in this experiment, the graphene longer than

2000μm is classified as graphene on a macroscopic level

4 Conclusion

Hence, we experimentally investigated the size-dependent

mechanical properties and edge effect of the tangential interface

between graphene and a PET substrate The experiments on gra-phene with seven different lengths show that the edge effect in the interface is affected by the size of graphene, and this size effect can be described by the scaling factor, that is, the relative critical length (defined as the ratio of the critical length to total length) This scaling factor decreases with an incremental change of the graphene length and tends toward being constant when the gra-phene reaches the macroscopic level Additionally, we show that the interfacial shear stress is size-dependent, and its value

sig-nificantly decreases with an increase of the graphene length However, the ultimate stiffness and failure strength of the inter-face are size-independent

Acknowledgments This work wasfinancially supported by the National Basic Re-search Program of China (2012CB937500) and the National Natural Science Foundation of China (11227202 and 11272232) The ex-periment was supported by Nanjing JCNO Technology

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Table 1

The interfacial mechanical parameters of graphene with seven different lengths.

Graphene

lengthl

(μm)

Failure

strength of

interface

m

ε (%)

Stiffness of interface

max

ε (%)

Critical length l c

(μm)

Relative critical length ϑ

Maximum in-terfacial shear stress

max

τ (Mpa)

50 2 0.998 40 0.80 0.237

100 2 0.988 70 0.70 0.158

200 2 0.988 116 0.58 0.089

800 2 1.000 280 0.35 0.055

2000 2 1.013 400 0.20 0.022

5000 2 1.013 1000 0.20 0.009

10,000 2 1.013 2000 0.20 0.004

C Xu et al / Materials Letters 161 (2015) 755–758 758