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Materials Letters

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

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, Haimei Xie a

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

ARTICLE INFO

ABSTRACT

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

The size-dependent mechanical properties and the edge effect of the tangential interface between graphene 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 experiments. 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 decreasing 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 as flexible 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 transmission 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 properties of graphene, and these experimental studies have mainly focused on small-sized graphene samples that are a few to dozens of microns in length [4-6]. The studies on the interfacial performance of graphene on the macro- to micro-scales and the size effects on the performance are insufficient. Therefore, it is necessary 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 interface 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

* Corresponding authors. E-mail addresses: tju_ylkang@tju.edu.cn (Y. Kang), daniell_q@hotmail.com (W. Qiu).

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 parameters, 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 parameters 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 (L1 = 1 cm) to micro (L7 = 50 ^m) scales, as shown in Fig. 1

(a), and the width of graphene is identical (W = 2 mm). The gra-phene sheet is produced by CVD method (chemical vapor deposition) 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 in Fig. 1

(b). PET is a flexible substrate that is able to undergo a large deformation, as shown by its stress-strain curve provided in Fig. 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.

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/).

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.)

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 1.2 ^m in diameter, focused through a 50 x objective lens. Considering 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 in Fig. 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 50 ^m-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 cm-1 per % (PET strain). This peak shift process is similar to that reported for the 10,000 ^m-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 cm-1 per % 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, corresponding to the black and red vertical axes shown in Fig. 1(d).

To intuitively compare the strain field information obtained from the graphene with different sizes, Fig.2 depicts the contour maps of the strain field of the longest (L1) and shortest (L7) gra-phene during the loading process. The strain field 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 strain field 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 region around the edge of graphene and the strain gradually increases 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 L1 and L7 by comparing Fig. 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. 3 provides the variations of strain along the centerline 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 in Fig. 1(d). In the first 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. 2. Contour maps of the strain field of (a) the longest 10,000 ^m-long graphene (L1) and (b) the shortest 50 ^m-long graphene (L7) 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.

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 sufficiently strong. In the third stage (when the PET strain is more than 2%), the curves of graphene strain in both Fig. 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. Comparing Fig. 3(a) with (b), the evolution of the three bonding states at the interface, independent of the size of graphene, is identical, and the demarcation points between 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. As Fig. 3 shows, when the PET strain is more than 2%, the

maximum strain of 10,000 ^m-long graphene is 1.013%, while that of 50 ^m-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', lc, [13,14] then the ratio of the critical length to total length, lc/l, is defined as the 'relative critical length', 8, which can represent the extent that the interface is influenced by the edge effect, where the smaller the 8, the smaller the extent. From Fig.3, lc for 10,000 ^m-long graphene is 2000 ^m, and 8 is 0.2, while lc for 50 ^m-long graphene is 40 ^m, and 8 is 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. 3. Variations of the strain along the centerline of (a) the longest 10,000 ^m-long graphene (L1) and (b) the shortest 50 ^m-long graphene (L7) 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 X is used and the data for locations X e [-0.5, 0] are measured and the values of the data for locations X e [0, 0.5] are symmetric).

Table 1

The interfacial mechanical parameters of graphene with seven different lengths.

Graphene Failure Stiffness of Critical Relative Maximum in-

length l strength of interface length lc critical terfacial

(nm) interface ¿max (%) (nm) length » shear stress

¿m (%) Tmax (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

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 the flake element is established based on the force analysis of an element of graphene [12]. Supposing the deformation of graphene to be elastic, a = Ee, the relationship between the interfacial shear stress, t, and the normal stress, s, can be determined as:

da _ Ede _ t

dx ~ dx ~~ t (1)

where e is the normal strain in graphene, E is the Young's modulus and t is the thickness of the graphene. Herein, we take E = 1 TPa as the Young's modulus and t=0.34 nm as the thickness of graphene [16,17]. The maximum interfacial shear stress, Tmax, of 10,000 ^m-long graphene is 0.004 Mpa while the Tmax of 50 ^m-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 performance 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 mechanical parameters, are included in Table 1, where the deformation parameters, such as the failure strength and stiffness of interface, are size-independent, while the critical length, relative critical length and maximum interfacial shear stress are size-dependent.

The relative critical length, 8, is considered as a dimensionless parameter that deserves investigation. When the length of gra-phene is less than 2000 ^m, 8 decreases 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 2000 ^m, 8 is a constant, showing the degree is stable regardless 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 2000 ^m is classified as graphene on a macroscopic level.

4. Conclusion

between graphene and a PET substrate. The experiments on graphene 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 significantly decreases with an increase of the graphene length. However, the ultimate stiffness and failure strength of the interface are size-independent.

Acknowledgments

This work was financially supported by the National Basic Research Program of China (2012CB937500) and the National Natural Science Foundation of China (11227202 and 11272232). The experiment was supported by Nanjing JCNO Technology.

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Hence, we experimentally investigated the size-dependent mechanical properties and edge effect of the tangential interface