graphite oxide composites

Accepted Manuscript Pentadecane functionalized graphite oxide sheets as a tool for the preparation of electrical conductive polyethylene/graphite oxide composites Aline Guimont, Emmanuel Beyou, Pierre Alcouffe, Philippe Cassagnau, Anatoli Serghei, Gregory Martin, Philippe Sonntag PII:

S0032-3861(13)01100-2

DOI:

10.1016/j.polymer.2013.11.049

Reference:

JPOL 16637

To appear in:

Polymer

Received Date: 31 October 2013 Revised Date:

29 November 2013

Accepted Date: 30 November 2013

Please cite this article as: Guimont A, Beyou E, Alcouffe P, Cassagnau P, Serghei A, Martin G, Sonntag P, Pentadecane functionalized graphite oxide sheets as a tool for the preparation of electrical conductive polyethylene/graphite oxide composites, Polymer (2014), doi: 10.1016/j.polymer.2013.11.049. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Pentadecane functionalized graphite oxide sheets as a tool for the preparation of electrical conductive polyethylene/graphite

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oxide composites Aline Guimont,1) Emmanuel Beyou,*1) Pierre Alcouffe1), Philippe Cassagnau1), Anatoli

1)

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Serghei1), Gregory Martin,2) Philippe Sonntag2)

Ingénierie des Matériaux Polymères, CNRS UMR 5223, Université de Lyon, F-69003, France,

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Université Lyon1, Villeurbanne, F-69622 Lyon, France. 2)

Hutchinson S.A., Centre de Recherche, Rue Gustave Nourry, BP 31, 45120 Chalette-sur-Loing,

France

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*[email protected]

Abstract:

Covalent functionalization of pentadecane-decorated thermally reduced graphite oxide (GO) sheets

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has been studied as a tool for the preparation of polyethylene/GO composites exhibiting rheological and electrical percolation thresholds. It was accomplished through pentadecane based radical

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addition onto unsaturated bonds located on the GO sheets’ surface using dicumyl peroxide as hydrogen abstractor. This chemical functionalization influences solubility behaviour of the formed pentadecane grafted GO sheets in various solvents. Then, the compounding of the composites pentadecane grafted GO/PE was performed at a processing temperature of 140°C with 25, 20, 15, 10, 8 and 5 wt% loadings. Rheological and electrical percolation thresholds were found between 10 and 15 wt% for polyethylene/pentadecane functionalized graphene oxide composites while the composite graphite/PE at the same loading percentage did not reach any percolation threshold.

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1. Introduction For the past several years, much attention has been paid to the introduction of organic groups into carbon black, carbon nanotubes, silica and layered silicates by covalent bonding [1-6]. This enables

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the control of the dispersion of fillers in polymers and improves the properties of polymer nanocomposites [7].

Polyolefins, including polyethylene (PE) and isotactic polypropylene (iPP), are commercially the most important family of polymers with annual production exceeding 100 Mt [8]. Polyethylene

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(PE) is one of the most widely used commercial polymer due to the excellent combination of a low coefficient of friction, a good chemical stability and excellent moisture barrier properties [8, 9]. It is

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believed that incorporation of graphene sheets in a polyethylene matrix may lead to ultimate fibre reinforcement nanocomposites with significantly enhanced electrical and mechanical properties. Graphene is an atomically thin, 2-dimensional network of sp2-hybridized carbons that can be derived from naturally abundant, low cost graphite [10-12]. The fundamental properties of the

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single flat monolayer of graphite have been intensively investigated after the successful isolation of graphene layers by simple mechanical exfoliation [13-17]. Numerous strategies have been developped to control the dispersion of graphene sheets in polymer matrices. Top-down

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functionalization schemes are needed to create stable dispersions with chemical functionality in graphenes [18-20]. The classical approach involves aggressive oxidation of graphite according to

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the Hummers’ method [21] leading to the formation of graphite oxide (GO) as a starting material for the synthesis of processable graphene sheets. GO sheets are mostly described as built of pristine aromatic islands separated from each other by aliphatic regions that are highly oxygenated, bearing hydroxyl, epoxide, diol, ketone, and carboxyl functional groups [22]. As a result, GO platelets are hydrophilic and electrically insulating and their reduction to restore electrical conductivity results in graphene sheets [23]. When graphitic carbons are incorporated into PE, electrically and thermally conductive polymer composites can be produced having an interesting prospect for applications such as electromagnetic-reflective materials, static charge-dissipative materials and 2

ACCEPTED MANUSCRIPT semiconductor layers in high voltage cables [24-25]. The most common method to synthesize polyolefin/graphene (oxide) hybrid materials is based on the use of melt and solvent blending techniques. Recently, Wang et al. [26] compared the properties of high density polyethylene

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(HDPE)/graphite nanosheets (GN) and HDPE/carbon black (CB) nanocomposites prepared by melt mixing and they showed that GN-filled HDPE nanocomposites exhibited very low percolation threshold (ca. 6 wt%) as compared with that of HDPE/CB (ca. 22 wt%). In addition, Macosko et al. [27] showed that thermally reduced graphene oxide (TRG) was well exfoliated in functionalized

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LLDPE while phase separated morphology was observed in the un-modified LLDPE. At less than 3 wt% of TRG, it was shown that electrical conductivity of the un-modified LLDPE was higher

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than that of the functionalized ones suggesting phase segregation between graphene and PE, and electrical percolation within the continuous filler-rich phase [27].

Solution mixing of the graphene oxide filler with chlorinated polyethylene compatibilizers followed by melt mixing of the solution mixed masterbatches with high-density polyethylene was also utilised by Chaudhry et al. [28] to generate PE/GO composites. It was found that

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compatibilizer with higher chlorination content interacted with polar graphene oxide surface more effectively thus leading to better filler dispersion in the composites. Other strategies can be based on the grafting of organic groups or PE onto the GO sheets to improve filler dispersion in the PE

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matrix. Kuila et al [29] prepared dodecyl amine-modified graphene (DA-G)/linear low density

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polyethylene (LLDPE) nanocomposites through solution mixing and field emission scanning electron microscopy analysis revealed homogeneous dispersions of graphene layers in the nanocomposites. Lin et al. [30] obtained PE/GO composites through the grafting of maleic anhydride functionalized polyethylene (MA-g-PE) onto aminopropyltriethoxysilane (APTES) coated GO sheets. Recently, Guimont et al. [19] developed two routes to covalently graft PE chains onto the surface of GO sheets via a radical grafting approach in presence of benzoyl peroxide and a cycloaddition [2+1] using azide end functionalized PE. The chemical modification of graphite and GO sheets through the use of free radical initiators is a promising route. Typically, peroxides are

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polymer chain (180-200 Å2).

Herein, the grafting of alkyl chains (average cross-sectional area = 20-40 Å2) onto GO is studied in order to improve the grafting ratio in comparison with PE and to ensure a good compatibility

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between GO and the polyethylene matrix when preparing PE/GO composites. Experiments assess the thermal decomposition of dicumyl peroxide (DCP) at 200°C in presence of pentadecane as a

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hydrocarbon substrate and GO sheets. The grafting reaction and the as-prepared pentadecane grafted GO/PE composites at different loading percentages are discussed with the help of FTIR, DRX, TGA, AFM and SEM images. Both rheological and electrical percolation thresholds are also determined.

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2. Experimental 2.1. Materials

Graphite powder was kindly provided by TIMCAL Graphite & Carbon (4 µm in size). GO was

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synthesized from graphite powder using the Hummers’ method [21]. A C/O atomic ratio of 2.22 was determined by elemental analysis. Pentadecane, potassium permanganate (KMnO4), sodium

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nitrate (NaNO3), concentrated sulfuric acid (H2SO4) and N-methylpyrrolidone (NMP) were all purchased from Aldrich. Dicumyl peroxide (DCP, Sigma-Aldrich-France; 98 % pure) was used as hydrogen abstractor.

1,4-dioxane (Sigma-Aldrich-France; 99 % pure), dimethylformamide (DMF, Sigma-AldrichFrance; 99 % pure), and heptane (Sigma-Aldrich-France; 99 % pure) were used as solvents. The polymer matrix used in this study is a commercial LDPE brand FinatheneTM (Fina Chemicals, Belgium, Mw=90000g/mole; density = 0.92 g.cm-3).

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2.2. Grafting of pentadecane onto GO in presence of DCP 100 mg of GO in 3.5 mL of anhydrous 1-4 dioxane in a Schlenk-type reactor was sonicated for 1.5

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h using an ultrasonic bath. Then, 7.70 g (36.3 mmol) of pentadecane and 0.22 g (2.8 wt%, 0.8 mmol) of dicumyl peroxide were added and degassed by four freeze-pump-thaw cycles. Grafting reactions were carried out under constant stirring and heating at 200 °C under pressure for 6 hours,

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ensurering solvothermal reduction. At the end of the reaction, pentadecane grafted GO was centrifugated and further purified by centrifugation with THF as solvent. The solid material was

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collected, dried in vacuum at 80 °C for 48 hours and characterised.

2.3. Melt blending of pentadecane grafted GO with PE

The compounding of the composites pentadecane grafted GO/PE was performed in an intermeshing co-rotating twin-screw mini-extruder (ThermoFisher Haake-MiniLab) at a processing

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temperature of 140°C for 10 min at 100 rpm. The loadings of pentadecane grafted GO were 25, 20, 15, 10, 8 and 5 wt%. Then, the extrudates were pressed at 120 °C under 30 bar for 30 s and for 1 min under 100 bar forming 0.5 mm thick films (4 cm x 4 cm). For comparison, a graphite/PE

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2.4. Characterizations

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composite with a graphite loading of 25wt% was prepared using the same method.

FTIR spectra were recorded on a Nicolet FTIR 460 spectrometer using powder-pressed KBr pellets. Specimens for the measurements were prepared by mixing 1 mg of the sample powder with 150 mg of KBr and by pressing the mixture into pellets. The FTIR spectra were obtained at a resolution of 6.0 cm-1 at room temperature in a wavenumber range between 4,000 and 400 cm-1 and averaged over 70 scans.

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ACCEPTED MANUSCRIPT The powder X-ray diffraction (XRD) measurements were performed on a Siemens D500 diffractometer (Ni-filtered Cu KR radiation, 1.5405 Å). The d(0 0 2) basal spacings were calculated from the 2 θ values using the Bragg’s law. TGA analyses were carried out with a TA SDT Q600. Samples were heated at 5 °C.min-1 under

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helium flow (25 mL min-1).

Elemental analyses (EA) were carried out to determine the contents of C and O (analyzer: LECO SC144, Institut des Sciences Analytiques, Villeurbanne, France).

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Sonication was accomplished using an Elma S40 Ultrasonic apparatus (Sheller, 37 kHz, 140W). The powder conductivity measurements were carried out with a high voltage source-measure unit

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Keithley 237. The sieved powder (0.5 mm diameter) was introduced into a 1 cm internal diameter teflon ring capped with aluminum electrodes. The aluminum caps were compressed at 100 N (~2 MPa) between a two point electrode system.

Atomic Force Microscopy (multimode 8, Bruker) was used to characterize the morphology of

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pentadecane grafted GO. Pentadecane-grafted GO in a diluted DMF solution was deposited on a freshly cleaved mica wafer by spin coating and AFM images were obtained in a taping mode under ambient conditions.

Scanning electron microscopy (SEM) images were taken by a commercial FEI Quanta 250 FEG.

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The powder was deposited on silicon wafers and Pt metallized (8 nm tick). The PE-based

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nanocomposites films were polished by ultramicrotom using a diamond knife. The electrical conductivity of the films was measured using a Keithley 237 High-Voltage SourceMeasure Unit. The measurements were carried out in a two-point configuration by using a parallel plate geometry. The thickness of the sample was typically in the range of 0.5 mm while the area of the electrodes was 0.5 cm2. The conductivity was determined from the slope of the linear dependence between the measured current and the applied voltage. The viscoelastic measurements were carried out on the dynamic rheometer (ARES from TA) at the temperature T ≈ 140°C. Most of the rheological measurements were performed in an oscillatory 6

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3. Results and discussion

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3.1 Radical grafting of pentadecane onto GO sheets in presence of dicumyl peroxide

The oxygen-based polar groups located on the GO surface significantly alter the Van der Waals interactions between the GO sheets and lead to a range of more or less stable suspensions in water

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and organic solvents [35]. A strategy for enhancing the compatibility between GO sheets and polyethylene consists in functionalising the surface of GO with organic groups or polymers either

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by a ‘grafting to’ or a ‘grafting from’ approach. The “grafting to” approach is usually used for grafting polymers onto carbon based materials and requires the synthesis of a polymer with reactive groups [36] or the use of a radical precursor [32]. In the latter case, the general mechanism of free radical grafting of hydrocarbon chains onto unsaturated compounds detailed in the literature

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[37-40] seems to express a widespread view. The grafting reaction starts with hydrogen abstraction onto the hydrocarbon substrate by alkoxyl radicals generated from thermal decomposition of a peroxide. Then, the active species generated onto the hydrocarbon backbone react with unsaturated

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bonds located on the GO surface (scheme 1). Herein, the hydrogen abstraction onto pentadecane by DCP was conducted in presence of a suspension of GO in 1,4-dioxane at a temperature of 200°C to

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ensure both the thermal decomposition of DCP and the solvothermal reduction of GO in order to restore the electrical conductivity.

Scheme 1. Grafting of pentadecane onto GO sheets in presence of dicumyl peroxide including its solvothermal reduction

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latter ones are still present on the GO surface after treatment, as they are stable in these experimental conditions (scheme 1).

The amount of DCP (2.8wt%) in the feed was chosen according to our previous work on the synthesis of PMMA-grafted polyethylene in presence of dicumyl peroxide as hydrogen abstractor

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[43, 44]. Then, pentadecane-grafted reduced GO sheets were extracted by centrifugation with THF as solvent to remove unreacted pentadecane. First of all, the grafting of pentadecane onto GO was

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qualitatively evidenced by FTIR (Figure 1b) analysis and X-ray diffraction (Figure 2b). Fig. 1a

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compares the FTIR spectra of pristine GO before and after the grafting reaction with pentadecane.

Fig. 1. FTIR spectra of a) GO and b) pentadecane-grafted GO

The FTIR spectrum of the hydroxyl region of GO exhibits a strong and wide OH stretching vibration band in the range 3600-3100 cm-1 due to physisorbed water molecules and hydroxyl groups located on the GO surface (Fig 1a). Characteristic peaks of carboxyl (1700 cm-1), epoxy (1000 cm-1) and remaining graphitic sp2 (1620 cm-1) are also observed (Fig 1a). Pentadecane grafted GO shows the appearance of peaks in the range 2900-2800 cm-1 (Fig 1b) corresponding to C-H stretching vibrations of CH3, CH2 and CH groups in pentadecane while the OH stretching 8

ACCEPTED MANUSCRIPT vibration band is low and the peak due to carbonyl groups is absent. Moreover, an increase of the C/O ratio from 2.2 to 7.6 is observed by elemental analysis. Both analysis suggest successful grafting of pentadecane and incomplete solvothermal reduction. The product was also

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characterized by XRD. Figure 2 shows XRD spectra of GO (curve a) and pentadecane grafted GO (curve b). GO exhibits an hygroscopic behavior generated by the presence of oxygen functions on its surface and its interlayer distance strongly depends on its level of hydration [45]. The (002)

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diffraction peak of GO appears at 2θ=11.6° corresponding to a d-spacing of 7.6 Å (Fig 2a).

Fig 2. XRD patterns for a) GO and b) pentadecane-grafted-GO

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Compared with GO, pentadecane-grafted-GO exhibits a very small broad diffraction peak shifted

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to 25° (Fig. 2b) due to a poor order along the stacking direction and the presence of many free nanosheets, as discussed by Nethravathi [44] and Ma [46]. The formation of an amorphous structure after grafting suggests that the increase of the interlayer distance (from 3.5 Å for graphite to 7.6 Å for GO) reduces the attractive interactions between the layers which favours the functionalisation of the material. Thermogravimetric analysis was performed on the reaction product in order to gain a more quantitative picture of the extent of GO functionalization. The TGA traces for both the starting pure reactants and the pentadecane-grafted GO sheets are shown in Figure 3. 9

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Fig. 3. Thermogravimetric data obtained for a) pentadecane, b) GO, c) solvothermal reduced GO at 200°C in 1,4-dioxane/ pentadecane mixture, d) pentadecane-grafted GO under He

Pentadecane molecules completely decompose in the temperature range between 150 and 170 °C

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(Fig 3a). GO is thermally unstable and starts to lose mass below 100 °C but the major mass loss occurs at about 200 °C (Fig 3b). As discussed by Gao et al. [47] the pyrolysis of the labile oxygencontaining functional groups to yield CO, CO2, and steam may explain the weight loss at 200 °C.

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The overall weight loss of GO is about 55 %. As shown in Figure 3d, the amount of organic functionalities covalently attached to the GO sheets are degraded at 250-650 °C and the graft

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density of pentadecane was determined from the weight loss between 250 and 650 °C. Considering a weight loss of 1.6 wt% after subtracting the contribution of the solvothermal reduced GO at 200 °C in a 1,4-dioxane/pentadecane mixture (Fig 3c), the calculation gave a pentadecane graft density of 0.09 mmol/g. For comparison, Tessonnier [48] reported a value 4 times larger for the grafting of decane onto GO in the presence of butyllithium. In the latter case, the basic agent ensured grafting of decane either by C−C coupling or by C−O coupling following the Williamson reaction. However, this technique requires the removal of any adsorbed moisture.

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dispersion in a DMF/heptane immiscible mixture and compared to GO (Fig. 4).

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Fig. 4. Digital images of GO derivative based-dispersions in DMF/heptane 50/50 with a

concentration of 0.35 mg/mL a) GO, b) GO after a thermal treatment at 200°C in 1,4-dioxane/

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pentadecane mixture and c) pentadecane grafted GO

It is well known that the highly oxygenated surfaces of GO sheets lead to a range of solubility in water and organic solvent such as DMF [35]. As expected, the stability of GO in heptane is very poor and GO sheets moved immediately to the DMF phase and a rather stable dispersion was

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obtained (Fig. 4a). After the thermal treatment of GO at 200°C, it keeps a higher affinity for the polar phase because of the residual presence of some polar functions due to its incomplete reduction (Fig 4b). However, the grafting of pentadecane molecules onto GO changes its

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hydrophilicity. Indeed, when placed in the DMF/heptane mixture, the pentadecane grafted GO transferred to the non polar layer of heptane confirming the successful surface modification.

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Then, surface morphology of pentadacane grafted GO sheets was evaluated by using atomic force microscopy (AFM)

measurement.

Indeed, AFM

images can determine

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functionalization of graphene sheets is successfully realized [49]. The AFM measurement was carried out to visualize the pentadecane grafted GO sheets deposited on freshly cleaved mica by spin-casting (Fig 5).

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Fig. 5. AFM images of a) GO and b) pentadecane grafted GO and height profiles of c) GO and d)

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pentadecane grafted GO

As shown in Figs.5a and 5b, AFM images display individual graphene sheets with lateral

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dimensions of several micrometers. GO displays a thickness in the range 1-2nm and its surface is smooth with a few folds (Fig 5c). The introduction of pentadecane onto the GO surface makes it

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relatively coarse with the apparition of some protuberances displaying a height close to 2nm (Fig 5d). Moroever, the scanning electron microscopy (SEM) image of pentadecane grafted GO shows randomly aggregated thin large flakes with wavy wrinkles and the edges of the thin sheets seem curved (Fig 6).

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Fig. 6. SEM images of pentadecane grafted GO

3.2 Electrical properties of pentadecane grafted GO

Electrical conductivity is an important intrinsic property of graphene and the functionalization may

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break the conjugation network through the conversion of sp2 into sp3 bonds. So, it is important to measure the electrical conductivity after the grafting step. The powder electrical conductivities for

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GO, pentadecane-grafted GO and graphite under low compaction are compared in Fig 7.

Fig. 7. Powder electrical conductivity of a) GO and b) pentadecane-grafted GO c) GO after a thermal treatment at 200°C in 1,4-dioxane/ pentadecane mixture and d) graphite

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than the electrical conductivity of highly compact grains (c = 104-105 S.m-1) because of a lower contact between the grains [51, 52]. The improved conductivities of GO (after the thermal treatment at 200°C in dioxane/pentadecane mixture with no peroxide (Fig 7c)) and pentadecane grafted GO (Fig 7b) indicate the reduction of GO sheets in the synthesis process. However, it does

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undergoe the change into sp2 ones during the reduction step.

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not permit to restore the initial conductivity of graphite because a fraction of sp3 bonds does not

3.3 Viscoelastic properties of pentadecane grafted GO/PE composites As discussed by Macosko [23], the most economically method for dispersing particles into polymers is melt blending despite the thermal instability of most chemically modified graphene. Kim et al. [25] showed that the dispersion of graphene could not be improved by grafting maleic

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anhydride onto the PE matrix through melt compounding. Herein, the compounding of the pentadecane grafted GO/PE composites was performed at a processing temperature of 140°C with 25, 20, 15, 10, 8 and 5 wt% loadings. Then, the effect of pentadecane grafted GO loading on the

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shown in figure 8.

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viscoelastic behavior of the corresponding PE based composites was studied and the results are

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Fig.8. Viscolastic behavior (frequency dependence) of PE filled pentadecane grafted GO with

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loadings varying from 4.8 to 25 wt% : a)Variation of the storage modulus G’(ω) ; b) Variation of the absolute complex viscosity |η*(ω)|

It should be noted in Fig 8a that the storage modulus G’ becomes independent of frequency (G’∝ω0) at low frequency for pentadecance grafted GO content up to 15wt% accordingly to shear thinning behavior of the absolute viscosity (|η*|∝ω-1). This asymptotic behavior is typical of a solid-like response resulting from the formation of a network of filler–filler contacts [25, 53-56].

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pentadecane grafted GO (Fig 9).

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Fig.9. SEM images of cross-section films of pentadecane grafted GO/PE composites with different graphite based loadings: a) 5 wt% b) 15 wt% and c) 25 wt%

Indeed, we can observe a homogeneous dispersion of pentadecane grafted sheets into PE at a low

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content (5 wt%, Fig 9a) as well as isolated aggregates with lateral dimensions of several micrometers and thicknesses close to 100 nm. Moreover, petandecane grafted GO layers are oriented which may not favour the formation of a transversal percolation network (Fig 9a). In contrary, by increasing the pentadecane grafted GO content from 5 wt% to 15 wt%, graphite based

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aggregates sheets can bridge each other causing network percolation.

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Then, the electrical conductivity of the films was measured in a two-point configuration using a Keithley 237 High-Voltage Source-Measure Unit. The conductivity was determined from the slope of the linear dependence between the measured current and the applied voltage. Up to loadings of 10%w, the intensities of the electrical currents were below the resolution limit of the instrument, which corresponds to a resistivity value of 1014 Ωcm (Fig 10).

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Fig. 10 Resistivity of rGO-penta filled PE at different loadings

Starting with 15 wt%, a decrease in the resistivity was observed, indicating the formation of electrical percolation paths as a result of the inclusion of the rGO-penta fillers. With increasing the

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volume fraction of the fillers, a monotonic decrease in the resistivity was detected, which reached a value of ~105 Ωcm for a loading factor of 25 wt%. While it is difficult to give a sharp value for the percolation threshold of this composite material, it is clear that starting with a loading of 15 wt%,

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the samples begin to exhibit a significant electrical conductivity. This finding is in good agreement with the viscoelastic measurements showing a rheological percolation threshold close to 15wt%.

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The broadness of the insulating-conductive transition observed with increasing the concentration of the fillers was attributed to the rather irregular character of the rGO sheets.

4. Conclusions

In this study, nanocomposites reinforced with functionalised GO platelets were synthesized by melt compounding. First, pentadecane was covalently grafted onto the surface of GO sheets via a radical grafting approach using dicumyl peroxide as hydrogen abstractor at 200 °C. Qualitative evidence of pentadecane grafting was done by FTIR and X-ray diffraction patterns suggested a disordered 17

ACCEPTED MANUSCRIPT stacking of GO like sheets after the grafting procedure. A pentadecane graft density of 0.09 mmol/g was determined by TGA, giving stable suspension of GO sheets in heptane phase when immersing into a DMF/heptane biphasic solution. Then, dispersion of pentadecane grafted oxide sheets in PE

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by melt compounding was studied by linear viscoelastic measurements on composite melts and SEM images confirmed a rheological percolation threshold close to 15 wt%. Moreover, the resulting composites were electrically conductive at a pentadecane grafted GO sheets content up to 10 wt%. Further improvements are currently under study to improve the dispersion of pentadecane-

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grafted GO into PE matrix

Acknowledgments:

The financial supports from the French National Agency for Research (ANR-09-MAPR-0008) and the competitiveness cluster Plastipolis are acknowledged. We would personally like to thank Pierre

1 for their technical help.

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