Supplementary Information
Effect of Graphene Nanoplatelets on the Mechanical and Gas Barrier Properties of Woven Carbon Fibre/Epoxy Composites
Xudan Yao1*, Thomas P. Raine1, Mufeng Liu1, Muzdalifah Zakaria2,Ian A. Kinloch1, Mark A. Bissett1*
1 Department of Materials, Henry Royce Institute and National Graphene Institute, University of Manchester, Oxford Road, Manchester M13 9PL, UK.
2 Petronas Research Sdn. Bhd, Lot 3288 & 3289, Off Jalan Ayer Itam, Kawasan Institusi Bangi, 43000 Kajang, Selangor Darul Ehsan, Malaysia
*Email: xudan.yao@manchester.ac.uk, mark.bissett@manchester.ac.uk
S1. Filtration effect of direct resin infusion
Initially, GNPs were mixed with the epoxy through vacuum mixing using a SpeedMixer (Fig.
S1a). Mixing conditions were set up as shown in Table S1. Afterwards, the hardener was added for further mixing under halved mixing times (Table S1), the mixture (Fig. S1b) was then applied to the carbon fibres through vacuum assisted resin infusion (Fig. S1c). After curing under the heating cycle (Fig. S2), the composite was achieved. The resultant sample shows that a large fraction of GNPs were filtered and stayed in the infusion mesh, as shown in Fig. S1d, rather than being distributed throughout the composite.
Table S1 Vacuum mixing parameters.
Stage 1 Stage 2 Stage 3
Speed (1/min) 0 800 2000
Vacuum (mbar) 5 5 5
Time for mixing GNP with resin
(min)
2 3 5
Time for mixing
hardener (min) 1 1.5 2.5
Fig. S1. Images of the (a) vacuum mixer, (b) mixed resin with 1 wt. % GNP after vacuum
mixing, (c) vacuum assisted resin infusion procedure and (d) the cured panel with a large amount of GNPs filtered and left in the infusion mesh.
Fig. S2. Cure cycle of the composite.
S2. Comparison of sample fabrication methods
As the direct resin infusion resulted in a severe filtration effect, wet lay-up and spray coating methods were developed, with corresponding cross-section optical microscope images shown in Fig. S3. Regarding the wet lay-up method, the mixture (Fig. S1b) was applied on to carbon
fibres manually, followed with vacuum bagging. However, the cross-section optical microscope image shows multiple visible voids (Fig. S3c). In order to solve this problem, after the wet lay-up procedure, resin infusion was conducted in place of simple vacuum bagging, however, this also resulted in visible voiding (Fig. S3d). In comparison, the control sample (Fig. S3a) and composites manufactured by spray coating GNPs (Fig. S3b) showed no visible defects on the cross-section areas. As a result, the spray coating method was selected for further investigations in this work.
Fig. S3. Optical microscope images of the cross-section area of: (a) control sample made
through resin infusion, (b) sample spray coated with 1 wt. % GNP followed by resin infusion, (c) sample made through wet lay-up and (d) sample made through wet lay-up followed with
resin infusion with 1 wt. % GNP.
S3. Carbon fibre volume fraction
Carbon fibre volume fractions (Vf) of the composites were evaluated through calculation based on the thickness (d) of the composites, density of the carbon fibre (ρf=1.76 g/cm3), layer number (n=8) and area weight (Aw=199 g/m2) of the fabric:
Vf=n Aw
ρfd (S1)
The resultant fibre volume fractions (Vf) and thicknesses of both eight layer (8L) and three layer (3L) composites are summarised in Fig. S4. The carbon fibre volume fraction of 8L composites tend to be lower than the 3L ones, due to increased interfaces where resin rich areas are formed, as shown in Fig. S4c. For both 8L and 3L composites, as the GNP loading increases, the fibre volume fraction tends to decrease. Considering the rule of mixtures, the Vf
was then used to normalize the mechanical properties of the composites according to:
Xn=X×Vfav
Vf (S2) where X and Xn represent the original and normalized composite properties, Vf represents the fibre volume fractions of the specific sample, and Vfav represents the average fibre volume fraction of samples with various GNP loadings [1,2].
Fig. S4. Thickness and fibre volume fraction of the (a) eight layer and (b) three layer CFRP
composites with different loadings of GNPs spray coated onto CFs. (c) Cross sectional optical microscope image of the 8L composites with resin rich area marked by arrows.
S4. Mechanical and gas barrier properties of the composites
Table S2: Normalized tensile and gas barrier properties of composites with different GNP loadings.
Sample No.
Tensile strength, σt
(MPa)
∆σt (%)
Tensile modulus, Et
(GPa)
∆Et (%)
CO2 permeability, P (x10-16 mol.m/
(m2·s·Pa))
∆P (%)
1 322.3±15.4 32.5±0.1 3.0±0.2
2 311.8±7.4 -3.2 32.4±0.3 -0.4 2.7±0.1 -9.8
3 319.8±4.4 -0.8 31.4±0.7 -3.5 2.5±0.4 -16.7
4 318.6±9.2 -1.1 31.8±1.0 -2.3 2.5±0.2 -17.5
5 306.9±7.5 -4.8 32.3±1.3 -0.7 1.3±0.2 -55.8
6 295.0±6.1 -8.5 31.6±0.7 -2.8 1.2±0.1 -61.0
Table S3: Normalized flexural properties of composites with different GNP loadings under four-point bending.
Sampl
e No. Flexural strength,
σf (MPa) ∆σf (%)
Flexural modulus, Ef
(GPa)
∆Ef (%)
1 491.5±14.0 39.4±0.6
2 530.0±9.6 7.8 41.1±0.7 4.3
3 450.7±24.7 -8.3 40.1±1.3 1.7
4 423.0±4.9 -13.9 39.6±1.1 0.6
5 371.8±15.9 -24.3 38.8±1.2 -1.4
6 321.8±9.8 -34.5 38.6±0.3 -2.0
S5. Validity of Nielsen's model
We have introduced Nielsen's minimum permeability model in the paper to analyse the permeability of the materials. The Nielsen's model has been recognized fitting accurately only with the gas permeability of composites when the filler loading is sufficiently high and the dispersion of the filler is assumed to be homogeneous. However, in this coating system, we realized that the Nielsen's theory is valid to describe the case. Hereby, the derivation of the Nielsen's equation is given, in addition to its application to the GNP coated CF reinforced epoxy composite.
A general accepted equation indicates that the permeability of a composite (P) is given by [3],
P = P01- Vf
τ (S3)
where P0 is the permeability of the matrix, τ is the tortuosity factor and is given by,
τ =da ds
(S4)
where da is the actual distance that a transport travels, and ds is the shortest distance that a transport has to travel (usually the thickness of a sample). Nielsen's model defines one case of the tortuous path and thus the tortuosity factor τ , that gives maximized paths of a penetrate (gas molecule) throughout the material, and therefore minimum permeability. We have the representative Nielsen's path (red path with an arrow) shown in Fig. S5a, with a representative volume element (RVE) created in the dashed box. From Figs. S5a-c, it shows the simplification of the RVE and finally the RVE in Fig. S5c is the Nielsen's case, where the volume fraction of the filler (Vg) is equal to t/T, where t is the average thickness of the flakes, and T is the thickness of the RVE. In Fig. S5, based on the RVE shown in the Figs. S5a-c, the actual distance (da) and the shortest distance (ds) of the path is given by,
da= T +l
2 (S5)
and ds= T
(S6)
where T is the thickness of the representative volume element (RVE), and l is the average length of the flakes. We can thereby substitute T with the average thickness of the flakes (t) and the volume fraction of the graphene nanoplatelets (Vg), since Vg=t/T. The tortuosity factor ( τ ) of Nielsen's model is then given by,
τ =da ds =
T +l 2 T =1+l
2 T =1+l 2 t Vg (S7)
where the effective aspect ratio of the nanoplatelets (s) is given by, s=l/t. Therefore, combining Eq. S3, Eq. S4 and Eq. S7, the permeability of the composite materials is given by,
P = P01- Vg 1+s
2 Vg
(S8)
Eq. S8 gives the same expression of Nielson's minimum permeability of a plate-like filler filled composite.
We can conclude from the derivation of Eq. S8 that the prerequisite of Nielsen's model is an infinite low end-to-end flake distance in the horizontal direction of the materials (perpendicular to the gas transport).
Fig. S5. (a) Standard RVE for a composite based on Nielsen's model; the red path with an arrow indicate the actual path of the penetrate. (b) Simplification of the RVE. (c) the RVE used in Nielsen's model; (d) the actual path (da) and the shortest path (ds) of Nielsen's model.
For a composite system where the filler loading of the GNPs is low, a homogeneous dispersion can give the case in Fig. S6a. In this case the Nielsen model is invalid to be used for the analysis of the permeability, since a gas molecule can miss many flakes throughout its path across the material. If we subjectively arrange the flake dispersion to a Nielsen case, then it has to be the Fig. S6b, where the in the horizontal direction, the flakes are distributed very close so that the gas molecule can always encounter a flake, making their path prolonged effectively and Vg can be analogous to t/T. However, this ideal case is unlikely to happen if low loading of GNPs is mixed into the matrix. Nevertheless, for the flakes coated on CF mats, it is likely to give us densely packed layers of GNPs, which is in Fig. S6c. The tortuosity path of Fig. S6c can be equivalent to the Nielsen's path of Fig. S6b.
In conclusion, with a coating technique, we use CF mats as the GNP carriers. We ended up obtaining many 'Nielsen layers' created throughout the materials. Even though the filler loading is low, the modelling still remains valid, because the tortuosity path is in agreement with Nielsen assumptions for the minimum permeability. This also explains the trend of the fitted curve gives correlation with the measured permeability results.
Fig. S6. Representative cases of 2D materials dispersed in a matrix at a low filler loading: (a) Homogeneous dispersion; (b) Specifically arranged Nielsen's case where the flakes can form layers where the end-to-end distance between flakes is infinitely low. (c) Analogy of coated
flakes using CF mats as a flake carrier, where the tortuous path created by the flakes can be analogous to Nielsen's case in (b).
References
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