Isabelle Baudino

According to his unpublished autobiography, James Northcote (1746-1831) had to change his painterly practice when John Opie (1761-1807) sensationally entered the London art scene in the 1780s. Deprived of vital portrait commissions, Northcote "betook himself from necessity to painting small historical and fancy subjects from the most popular authors of the day, as such subjects are sure of sale amongst the minor print dealers, being done in a short time and for a small price." 1 Apart from giving a retrospective account of an episode of the well-known rivalry among Georgian portrait painters, this quote points to the shaping of British eighteenth-century visual culture by and for the purpose of commerce. Reynolds's pupil is here conceding that turning to book illustration helped him compensate for the losses incurred by the arrival of the so-called "Cornish wonder" in the Metropolis. For decades indeed, visual artists had supplemented their income working in the print industry and their images had contributed to the success of texts in the British book market. Although book illustration was not new in the eighteenth century, technical improvements helped its development. As James Raven noted, one original feature of the flourishing London book tradeprecisely alluded to by Northcote in the above quotationwas that publishers commissioned works from painters and had them engraved in order to embellish their publications. 2 The capital's publishing booksellers were thus active art patrons who were able to promote their publications in glowing terms, flaunting the names of the finest artists on their books' title pages.

Samuel Wale (1714-1786) was one of these artists given that he was arguably one of the most prolific book illustrators of his time. 3 Far from limiting himself to one type of illustration, Wale was a protean draughtsman whose allegorical frontispieces were in demand to decorate all kinds of publications (from essays to novels, from magazines to prayer books, from Bible to poetry, travel narratives and dictionaries), and who designed hundreds of illustrative plates. In the 1750s, 1760s and 1770s, his name appeared on a monthly basis in the London press, in adverts for books and magazines to the point that it can be seen, without exaggeration, as a major selling point used by commercially-minded booksellers, and as a synonym for beautifullydesigned illustrations. Wale was particularly successful and influential in experimenting in a new kind of historical image, both instructive and pleasant, bringing together history and genre paintings. Getting his foot in the Knaptons' door undoubtedly helped him start a career in historical illustration: in 1747, he contributed an elegiac composition to the third edition of Rapin de Thoyras's History of England published by John and Paul Knapton. The composition shows Britannia, together with History and Time, lamenting the death of George I, the monarch to whom the book had originally been dedicated by Rapin. 4 Charles Grignion (1721-1810), who had been employed for engraving most of the decorative material of this edition, also engraved Wale's drawing which featured as a small historiated tailpiece at the end the last volume. Although limited, Wale's late involvement in this prestigious edition marked the beginning of a long-term creative partnership with Grignion.

Seventeen years after this first collaboration, Wale and Grignion took historical illustrations to a completely different level when Wale designed the frontispiece and sixty-four plates for Thomas Mortimer's New History of England, all engraved and embellished by Grignion. 5 In the press, they were advertised as "elegant Copperplates illustrating the most interesting Events recorded in the British Annals, together with Portraits at full Length of the Kings and Queens in the Habits of the Times". One plate accompanied each part issue, selling for six pence, and together they formed part of the booksellers' marketing strategy that aimed at enticing customers to buy regular instalments. 6 As stated in the advert, two kinds of illustrations were to be distinguished: thirty one full-page portraits of kings and queens on the one hand, and thirty three full-page historical scenes on the other hand, both stemming from long figurative traditions. The direct prototypes for portraits of British rulers in historical dress were the "heads" drawn by George Vertue (1684-1756) for the first and second editions of Rapin de Thoyras's History of England. Wale had certainly seen and studied those historical portraits, not only because he had himself contributed to the illustration of Rapin's classic but, because Vertue's heads had become so popular that they had been re-issued independently, copied and imitated. In fact, Wale's fulllength portraits were also presumably designed in order to depart from Vertue's standards and so as to avoid unwanted comparisons with Vertue's templates. His endeavour to give each king, or queen, a different face, attitude and costume, ten years before the publication of John Strutt's first works on dress history in 1774, and without borrowing from Vertue, resulted in a gallery of quite unremarkable, stiff, dolllike figures. On the contrary, Wale's historical scenes stood out because they considerably expanded in format from the historiated headpieces that had been published in Rapin's History of England before, and even more remarkably, because they expanded in scope from previous series of historical engravings such as The Life of Charles Ist published by Thomas and John Bowles in 1728. 7 Significantly, Samuel Wale had already completed a set of twenty-eight historical illustrations, in 1746 and 1747, for the sixth edition of John Lockman's New History of England. 8 This was an abridged version of Rapin's History of England, intended for young readers, and its plates were relatively basic, with very few characters involved in one action usually summed up by one gesture. And they did not satisfy the public, if we are to believe the apologetic advert issued in the London Evening Post acknowledging the disappointing quality of the engravings.9 In the absence of any original drawing by Wale, it is difficult to assess whether the deficiencies of Lockman's plates were to be blamed on the artist's lack of compositional skills, on the engravers' poor technique or on the didactic nature of the book itself. Anyhow, Wale did not consider his earlier plates fit for purpose when he undertook the illustration of Mortimer's book for he only re-used two of the designs he had made for Lockman's. In stark contrast, his drawings for Mortimer's New History of England were re-used as well as borrowed from by other artists, to illustrate other historical publications, until the end of the century. 10 Spanning the history of the British Isles from the coming of Christianity to the signing of the Bill of Rights, Wale's illustrations for Mortimer's New History of England portrayed characters and events he had never seen, and his thirty three images could thus be literally deemed works of fancy. Several of his original historical canvases were exhibited in London in the 1760s and 1770s and, even though their subjects were different from Philip Mercier's, Joshua Reynolds's or Thomas Gainsborough's fancy pictures, they did feature a similar combination of realism and distance. Wale's inventions were supposed to show real people from the past and to encourage viewers to imagine their likenesses and dresses, actions, words and feelings. He therefore had to design historical reconstructions appealing to a wide educated British public, for the surgeons, attorneys, clergymen, merchants, school masters and school mistresses that subscribed to the project.11 To do so, he mingled high and low pictorial conventions and designed plates that were hybrids between historical canvases and conversation pieces, thus falling under the definition of the fancy picture given by Martin Postle.12 This chapter discusses the in-betweenness of Wale's historical compositions, suggesting that like fancy pictures, their blend of fact and fantasy aroused the curiosity of viewers and elicited emotional responses that encouraged the artist and his contemporaries to engage with their national past.

It is no wonder that Samuel Wale's historical compositions attracted attention for they were made more striking than any other plate of the kind published before because of their beautiful and elaborate framing. Each scene was surrounded by winding foliage and undulating plants arranged in a series of scrolling raffle leaves and flowers. Because they were added around Wale's drawings on the copperplates, these distinctively Rococo frames were undoubtedly the work of Grignion who had been a pupil of Hubert-François Bourguignon, known as Gravelot (1699-1773). These embellishments were further enhanced by the exuberant lettering of the dedications inscribed below the images. Following from the frontispiece, whose dedicatee was George III, each historical scene was titled and dedicated to a different peerto some of the most powerful men in the kingdom, holding prestigious offices, to prominent Whigs whose patronage Mortimer was seeking. 13 Their names, inscribed in graceful swirling letters, may well have been penned by William Chinnery, one of the leading writing masters in London, with whom both Samuel Wale and Charles Grignion had worked on the illustration of the Book of Common Prayer. 14 Surrounded by those refined frames, the engravings were ennobled, presented like paintings, and there is evidence to suggest that at least three scenes were actually painted and later exhibited at the Royal Academy by Samuel Wale. 15 Although they drew in format and layout from conversations pieces, his illustrations were not unsimilar to reproductive prints made from history paintings for they had a textual source and were narrative compositions dedicated to noble historical characters. Each plate illustrated one emblematic episode from British history, or rather condensed a slice of history or a reign, into one single symbolical moment: for example King Henry II's reign is recorded through his argument with Thomas Becket and King John's is equated with the signing of the Magna Carta. Even a long process such as the Christianisation of Anglo Saxon England is summed up in the first plate, entitled St Austin preaching to King Ethelbert and Queen Bertha in the Isle of Thanet, in two movements: the king's outstretched arm willingly reaching for the cross held out by the missionary; the narrative dynamic of the picture is contained in the handing over of the cross suspended in mid air at the intersection of the diagonals. Whether Wale designed this representation and compiled his list of events alone, or did so with the help of the engraver, publishers and or author, is unknown. Yet we 13 As indicated on the title-page of the second volume of his New History of England, Thomas Mortimer was English vice-consul for the Austrian Netherlands when he wrote his book. He had been sent to Ostend to hold this diplomatic position on the recommendation of John Montagu, 4th Earl of Sandwich, who had himself become Secretary of State for the the Northern Department when George Grenville had replaced the Earl of Bute. See Christabel Osborne, 'Mortimer, Thomas (1730-1810) Ryland, 1758). My suggestion that Chinnery was employed for writing the dedications of Mortimer's plates can also be suuported by a comparison with his calligraphy in William Chinnery, Writing and Drawing Made Easy, Amusing and Instructive (Kingston-upon-Thames, Bellamy, 1750 ?). 15 See the Catalogues of the Royal Academy exhibition for the years 1769, 1774 and 1775. Since Samuel Wale's historical canvases are untraced, it is impossible to know their format but it can be assumed that they did not exceed the size of his surviving pictures which are conversation pieces.

have reasons to believe that Thomas Mortimer's choice of Samuel Wale and Charles Grignion was a well-informed one. Indeed the year before his New history of England was released, Mortimer, already a well-known writer on trade and finance, had published an interesting directory in which he listed the artists active in London, providing their addresses and some information on the genres in which they specialized, in order to make it easier for potential patrons to contact them. 16 This valuable survey is a direct offspring of the new exhibition culture, that flourished in the capital from 1760 and of which, Thomas Mortimer, being a member of the Society for the Encouragement of Arts, Manufactures and Commerce, was a strong advocate. The Directory offers an overview of the London artistic community before the incorporation of the Society of Artists of Great Britain in 1765, at a time when Francis Hayman (1708-1776), with whom Wale had worked, was celebrated as the country's most excellent history painter. In his Directory, Mortimer presents both Grignion and Wale as renowned specialists of history, history engraving for the first and painting for the latter. 17 Wale is also identified as a 'designer' that is to say, in the words of his friend John Gwynn (1713-1786), as an liberal artist, as a draughtsman with supreme "inventive power". 18 Mortimer may therefore well have entrusted Wale with the task of inventing the scenes taken from his history book, not least because the artist had already worked on a similar selection when he had been employed by Lockman.

However, Wale did not rely much upon this earlier work for Lockman and Mortimer's illustrations appear to have little in common. Both sets were of course intended for different readership groups and supposed to illustrate different texts. Moreover, Wale's new selection was not only drawn from Thomas Mortimer's narrative, but also, quite clearly, inspired by the list of fifty subjects made by the Knapton brothers when they had launched, with Robert Dodsley, the "English History Delineated" project in 1749. [START_REF][END_REF] In the wake of their 1747 edition of Rapin de Thoyras's History of England, precisely at the moment when Wale had become acquainted with them, John and Paul Knapton had planned to publish by subscription a set of fifty engravings illustrating episodes of English history from the landing of Julius Caesar to the presentation of the Bill of Rights to William and Mary. Although the "English History Delineated" eventually failed, and shrunk to the publication of six engravings two years later, 20 the list on which it was based provided an important benchmark for Wale who borrowed more than half of his new subjects from it. In addition, both the fifty subjects listed for the "English history delineated" and the thirty-three singled out in Mortimer's New History of England outline a similar visual historical panorama in which priority was not always given to obvious milestones.

In fact, the list of events selected by Samuel Wale in Thomas Mortimer's New History of England, includes no coronation nor any marriage and only one battle scene (Cressy) ; presumably battles as complex developments were quite impossible to represent on a single-page format and required the skills of specialized battle painters. Moreover, if Wale had represented all the coronations, royal marriages, or even glorious military victories, that were necessarily mentioned in Mortimer's text, he would have given to the public a series of very similar pictures, of repetitive compositions that would not have raised much interest. He thus favoured uncommon episodes that were likely to whet the curiosity of the public. His search for novel and strange subjects is best exemplified in the only two royal deaths he chose to illustrate, that of King Edward the Martyr (believed to have been murdered by order of his stepmother) and of King William II (supposedly killed in a hunting accident). Like William Hogarth (1697-1764) or Francis Hayman, Samuel Wale's aesthetic pursuit was guided by a search for novelty and he approached variety in Addisonian terms as a stimulant of imaginative pleasures. 21 In order to display the most diverse and varied scenes, Wale paid careful attention to the scenery and to the design of buildings, furnishings and dresses. Although he did not have many sources readily available on costumes, he avoided uniformity by differentiating Saxon and early medieval loose tunics or cloaks from late medieval tighter fitting garments; for early modern men and women, he shortened cloaks, introduced hoses and embroidered jackets and went on to produce Tudor and Stuart dresses that Georgians would have found quite convincing. The lack of accuracy and inevitable anachronism of his costumes was somehow compensated by the care he gave to the depiction of furnishings and, most importantly, of buildings. Wale was indeed a skilled architectural draughtsman whose views of St Paul's or Vauxhall were much admired. Building on his success and experience, he designed historical plates that were heedful re-creations of styles prompting viewers to imagine the tastes of past centuries. His sequence of evocative period pieces were designed to please the eye but also to instruct, and to help the public to get a sense of historical depth. Wale's pictures offered a visual rendering of the historical narrative presented in the text and therefore contributed to the perception of historical chronology, a topical concern at the time. 22 Yet, for all the variety of events, characters, dresses and times they offer, Wale's illustrations are remarkably unified by their domestic perspective. Most often placing the viewer near the pictured space, as was done in fancy pictures, his compositions emphasize family settings and relations in the manner of conversation pieces. For instance, in St Austin preaching to King Ethelbert and Queen Bertha in the Isle of Thanet, Wale presented the conversion of England to Christianity as peaceful and homely. Queen Bertha is sitting beside the King, and a faithful dog is quietly lying next to the royal couple. The movement of the queen's right arm, underlining the transmission of the metonymic cross, can be interpreted as a reference to the part played by the Merovingian Christian princess in enabling Augustine's mission. Hatching is used to shed light upon the action and to enhance the chiaroscuro effect. In the shaded foreground, two kneeling characters with their backs to the viewera fearful child clinging to its mother's cloakfurther inscribe this religious and political event in a family circle. This contrasts with a previous representation that had been published in Richard Verstegan's Restitution of Decayed Intelligence in 1605, 23 and which shows the king alone, sitting on a throne under a canopy, facing the Christian missionary holding a processional banner; Ethelbert has two advisers by his side and Augustine is heading a group of monks. Women and children are absent and, the direct confrontation of royal and Christian emblems gives an altogether more contentious vision of the conversion seized in its political and religious dimensions. Samuel Wale probably knew this engraving either from an edition of Verstegan or from its re-use in both the French and English editions of Rapin de Thoyras, 24 and nonetheless opted for a more domestic rendition of this and other events. In his second plate, Alfred makes a collection of laws and divides the kingdom into counties, the topic is legal and administrative; yet composition shows a plausibly medieval interior with the Christian king, surrounded by clerics. Alfred is holding a book of laws open while pointing to a map of the English counties which happens to be held by a child. Both man and child look out from the room represented towards the source of light, an apt metaphor for the encouragement given to the acquisition of knowledge with the development of book writing and the organisation of schools during Alfred's reign. Whereas the chiaroscuro and the lifted curtain dramatize the action, the child who could stand as an allusion to schooling at court, embodies a diminutive and domestic approach to history. Even the frontispiece, dedicated to King George III, mingles allegory and everyday life showing Queen Charlotte, together with young princes George and Frederick, in the company of allegorical figures. Although she seems eager to meet History and Libertywho are being introduced to her by Britanniathe queen is primarily depicted as a mother holding the hand of her youngest son and, in a most realistic way, encouraging the eldest to walk forward. With her left hand suspended behind prince George's back, the queen looks as though she had just been walking down a corridor with her sons ; the portrait lacks poise but captures the instant in a lively vignette.

Depicting monarchs and princes in their domestic surroundings, these illustrations approached the past from a private perspective. Understating nobility and decorum, they ran the risk of narrowing the lessons of history to a series of anecdotes. However their tone is neither sarcastic nor satirical, and they do encourage viewers to see private virtues as tokens of public morality. In the plate entitled The Insolent behaviour of Dunstan to King Edwy on the day of his coronation, Bishop Dunstan is shown grabbing the King's clothes and trying to drag the young man out of a room. Behind Edwy, two women are visibly appalled: the younger, with her right hand on her heart, is moved and saddened whereas the older lifts her hands in shock and anger. Mortimer's text clarifies the situation telling the story of a deeply enamoured young King who, on the day of his coronation, had retired to Aethelgiva's apartment, to enjoy a conversation with her and her mother with all good intentions, and who was dragged forcibly back to the ceremony by the insolent bishop whom he later banished. 25 Placed at the centre, in a position reminiscent of Hercules between vice and virtue, King Edwy is holding back his body, obviously resisting to follow the bishop on what he believes to be the wrong path; he is even brandishing his sceptre towards the bishop who is holding his crosier. Behind the clash of emblems, viewers were to feel that the loving prince had been offended and to understand that he was a good monarch who rightfully opposed the clergyman's misuse of power. Inversely, they were to see in private vices the manifestations of public failings. Wale's penultimate historical scene relates events that took place during James II's reign. Entitled Remarkable instance of Col. l Kirk's cruelty and villany, it shows a couple in a bedroom whose window opens onto a gruesome scene of hanging. Whereas the man points to the scene with a satisfied grin on his face, the woman looks horrified; she seems to be losing sense and consciousness, holding on to his robe with her right hand and removing her cap with an uncontrolled gesture of her left hand. Mortimer's text helps elucidate the situation in a note in which he explains that Colonel Kirke had promised a lady that he would spare the life of her father (or husband) if she bestowed her favours upon him ; but after spending the night with her, he showed her, the next morning, the man she loved hanging from the gibbet. 26 Wale does not take advantage of this potentially salacious subject and his treatment, devoid of any satirical or erotic understones, aims at exposing the sheer immorality of Colonel Percy Kirke. What could appear to our eyes as a trivialization of history was in fact based on the work of a most celebrated historian, on David Hume's History of England,27 to which Mortimer refers in his note. Drawing from Hume, Mortimer directly connects Kirke's behaviour, and his role in the pacification campaign that followed Monmouth's rebellion, to the arbitrariness of the regime he served.

Published in the age of sensibility, Mortimer's New History of England contained innumerable sentimental anecdotes and his readers were expected to gain moral awareness through feelings and emotions. Sharing the same sentimental perspective, Wale's sequence of images tended to bring to the fore female characters and heroines, such as Elizabeth Woodville (1437-1492), wife of King Edward IV. She is portrayed twice and, in both instances, she is represented as a mother, first, before her marriage with the king, when she was still Lady Elizabeth Grey, imploring the restitution of her deceased husband's lands for her sons; then, after the king's death, as queen dowager, having to part with another son, the Duke of York. Although set against the backdrop of the War of the Roses, Elizabeth Woodville at the feet of Edward ye 4th, does not show the widow of a Lancastrian supporter petitioning the Yorkist king for her sons to be given what was owing to them but rather a sentimental encounter with a family twist. Here a young man is falling in love with a woman in the presence of the latter's mother and of the children she has had from a previous marriage. Although modest, Elizabeth's posture is reminiscent of the sinner Mary Magdalene's when she is greeting the risen Christ in the Noli me tangere trope, and of its appropriation in popular visual culture. 28 This visual allusion draws upon an ironic reading of the "touch me not" in this tactile encounter: his hand on his heart, the King is obviously touched and also touching the hand of Elizabeth. His slightly unstable position leads the viewer to imagine that he is about to come closer to help her get back up on her feet. Moved by the "fair suppliant", the king is also to be regarded as a generous prince, who unlike his brother Richard III, protected the widow and the orphans.

Focusing on the smalland seemingly trivialpicture, Wale actually connects his contemporaries to their ancestors, bringing historical characters closer to viewers not only spatially but emotionally. While undermining historical forces, he nonetheless elicits a sympathetic understanding of the lessons of history. His sentimental perspective may play down traditional male heroism but it promotes politeness instead. In keeping with the view that history is part of a polite education, expressed by Mortimer in his Preliminary Discourse,29 Wale's pictorial history conforms to the polite norm. This shows up clearly in The Black Prince waiting on ye King of France, his prisoner, a plate dedicated to one of the most memorable English victories of the Hundred Years' War. Rather than showing a confused depiction of the opposing armies (as attempted in the plate of the battle of Cressy), Wale chose to illustrate the aftermath of the 1356 battle of Poitiers, and more precisely the moment when the victorious English prince invited his prisoner, King John II of France, in his tent. In front of surprised servants and soldiers, King Edward III's son is pictured standing, handing a goblet on a plate to his vanquished enemy who is comfortably seated, with all the honours due to his rank. The embarrassment of the French king is expressed in the contradictory movement of his hands (reaching for the goblet with his right hand and refusing it with the left). As indicated by Mortimer, the story of the benevolent treatment of the defeated French king by the English young prince was taken from Froissart's Chronicles,30 but it certainly had a renewed currency in the years directly following the end of the Seven Years' War. Portrayed as a polite and respectful host, Edward has left his helmet lying on the floor as the only metonymic allusion to the campaigns, sieges and raids he had led. His attitude is not soldier-like and rather invokes that of magnanimous heroes, ancient and modern. With his foot forward, his outstretched arm and his hair seemingly tied back in an anachronistic eighteenth-century fashion, the Black Prince closely resembles the portrait of General Amherst painted by Francis Hayman to celebrate British magnanimity in triumph. 31 The vision of Britain that emerges from Wale's sequence of historical illustrations is not only flattering but restorative. While subscribing to the general ideological agenda of eighteenth-century whiggism, Wale primarily aimed for consensus. This is best demonstrated in his evolving representations of King Charles I: For Lockman, Wale had composed a sensational execution scene showing the king kneeling at the block and the executioner holding up an axe about to fall on Charles's nape; he replaced this undignified portrayal of the king by a moving farewell scene for Mortimer. His Charles Ist taking leave of his children is showing an affectionate father, bringing his younger son close to him, stoically giving his last advice to three of his children. The composition is clearly borrowed from the engraving of the same title made for the Bowles brothers' Life of Charles Ist in 1728. Wale adapted the large horizontal composition to the vertical size of the book page, thus bringing the four characters even closer to one another ; he kept from the original the anachronistic introduction of the Duke of York, and the strong resemblance between the king and his son, which David Solkin has convincingly interpreted as an allusion to their shared attempts at arbitrary rule. 32 But Wale noticeably turned Princess Elizabeth towards the viewer, thus displaying her grief and her tears made visible through the handkerchief she is using to wipe them away.

Like fancy pictures, Samuel Wale's historical illustrations were remarkably popular in the eighteenth century, so much so that they kept being re-used and reissued long after the artist's death. As pleasant historical reconstructions, they were fanciful visual arrangements that borrowed from both high and low genres. In a manner similar to fancy pictures, they played on distance to trigger emotions, staging a series of imagined historical encounters that encouraged Wale and his contemporaries to consider historical Britons as real people whose feelings they could share. Pieced together, his illustrations did outline the progressive coming of age of a sovereign Protestant nation, homeland of Parliamentary monarchy and civic liberties, but without being closely tied to party-oriented historical writing. Wale's plates primarily stemmed from the emergence of that visual culture defined by Peter de Bolla for they offered new modalities for the visualization of history. 33 Showing the past as an image, or as a sequence of images that could be shared by men and women across the British territories, they made history more accessible to a wider public. Pushing the past further than any engraved series published in his days and, at the same time, pulling the nation's ancestors towards the present, they affected the way in which eighteenth-century viewers felt they could engage with the past and reinvent it so as to turn the page on historical traumas. The persistence of his imagery in projects such as Robert Bowyer's "Historic Gallery", or even in nineteenthcentury historical imagination, testifies to its role in the cultural construction of the nation.

  ', rev. Anne Pimlott Baker, Oxford dictionary of national biography(Oxford, 2004) http://www.oxforddnb.com/view/article/19357 [accessed 29 July 2016]. The dedications inscribed below Wale's illustrations show that Mortimer, who was hoping for a consulship, was seeking support among the Whigs who had opposed Bute and this sheds light upon his being published by Isaac Fell who was a 'zealous anti-Ministry bookseller and editor'. See Michael F. Suarez, S.J., '"This necessary knowledge ": Thomas Chatterton and the ways of the London book trade', in Nick Groom, ed., Thomas Chatterton and Romantic culture (Basingstoke, 1999), p.98. 14 See The Book of Common Prayer: the Liturgy of the Church of England ; illustrated in fifty nine historical and explanatory sculptures, engraved by Messrs. Ravenet, Grignion, Scotin, Canott, Walker and W. Ryland. Published according to Act of Parliament May 1st 1755 by Edwd. Ryland (London:

See 'James Northcote's Autobiography', British Library Add MS 47792, p.14.

James Raven, The Business of Books: booksellers and the English book trade,1450-1850 (New Haven and London, 2007), p.253.

For details on Samuel Wale's career, see Isabelle Baudino, "Samuel Wale (1714-1786), a Foundation Member of the Royal Academy," The British ArtJournal, vol. XVIII, n°3 (2017) p.60-72.

[John Lockman], A New History of England, by Question and Answer. Extracted from the most celebrated English historians, particularly Mr Rapin de Thoyras, for the entertainment of our youth of both sexes. The sixth edition, corrected and improved. Adorned with thirty-two copper-plates, representing the most remarkable occurrences, and the heads of all the kings and queens (London, Astley and Baldwin, 1747). There are thirty-two illustrations in the volume: one frontispiece, three plates of heads and twenty-eight historical scenes.

See London Evening Post, issue 3014, 26-28 February 1747.

Wale's illustrations were re-used in no fewer than nine different pictorial histories over the course of nearly thirty years.

Mortimer, New History of England, vol. 1, unpaginated list of subscribers.

In his seminal study, Postle gives the following definition: "The fancy picture was a nebulous, multifaceted and ambiguous genre, inhabiting a hinterland between real and ideal, fact and fantasy, high art and common life". See Angels and Urchins: the Fancy Picture in 18th-century British Art, exhibition catalogue, Djanogly Art Gallery, University of Nottingham 28March-4 May, 1998, Kenwood House, Hampstead London 14 May-9 August 1998 (London, 1998), p.9.

See Mr. [Thomas] Mortimer, The Universal Director; or, the nobleman and gentleman's true guide to the masters and professors of the liberal and polite arts and sciences; and of the mechanic arts,

On the Addisonian aesthetic register and its centrality in British artistic culture, see Ronald Paulson, The Beautiful, Novel and Strange: Aesthetics and Heterodoxy(Baltimore, 1996).

See Thomas Salmon, The Chronological Historian(London, Mears, 1723).

[Richard Verstegan], A Restitution of Decayed Intelligence: in antiquities. Concerning the most noble and renowned English nation (Antwerp, Bruney, 1605), p.144.

See [Paul] Rapin de Thoyras, Histoire d'Angleterre, contenant ce qui s'est passé depuis l'invasion de Jule Cesar jusqu'à la conquête des Normans, vol. 1 (The Hague, Alexandre de Rogissart, 1724), p.147 ; The History of England written in French by Mr. Rapin de Thoyras. Translated into English with additional notes by N. Tindal M. A. Vicar of Great Waltham in Essex, 2 nd ed. (London, James, John and Paul Knapton, 1732), vol.1 p.45.

Mortimer, New History of England, vol.1, p.84.

Mortimer, New History of England, vol. 2,

David Hume, The History of England, from the invasion of Julius Caesar to the revolution in1688, vol.6 (London, Millar, 1762), p.384. For Hume, the "maid" had actually pleaded for the life of her brother.

See for instance the frontispiece of Measure for measure drawn by Louis Du Guernier (1687-1716), in The works of Mr. William Shakespear, in nine volumes: with his life, by N. Rowe Esq; dorn'd with cuts (London: Tonson et al., 1714) p.203.

Mortimer, New History of England, vol.1, p.1.

Mortimer, New History of England, vol.1, p.593.

The painting made by Francis Hayman for Vauxhall Gardens has been lost but is known thanks to a modello: The Surrender of Montreal to General Amherst, 1760-1761, oil on canvas, 70.8 x 91.4 cm, Fredericton: Beaverbrook Art Gallery. See David Coke and Alan Borg, Vauxhall Gardens: a History(New Haven and London, 2011), p.128-131.

Solkin, "The English Revolution", p.274.

See Peter de Bolla, The Education of the eye: painting landscape and architecture in eighteenthcenturyBritain (Stanford, 2003), p.4.


A Allaoui

S V Hoa

M D Pugh

The electronic transport properties and microstructure of carbon nanofibre/epoxy composites

Keywords: A. Polymer Matrix-Composites, Carbon Nanofibres B. Electrical Properties, Microstructure D. Impedance Spectroscopy

Carbon nanofibres (CNF) were dispersed into an epoxy resin using a combination of ultrasonication and mechanical mixing. The electronic transport properties of the resulting composites were investigated by means of impedance spectroscopy. It was found that a very low critical weight fraction (p c = 0.064 wt %) which may be taken to correspond to the formation of a tunneling conductive network inside the matrix. The insulator-to-conductor transition region spanned about one order of magnitude from 0.1 to 1 wt %. Far from the transition, the conductivity increased by two orders of magnitude. This increase and the low value of the conductivity were explained in terms of the presence of an epoxy film at the contact between CNF. A simple model based on the CNF-CNF contact network inside the matrix was proposed in order to evaluate the thickness of that film.

INTRODUCTION

Carbon nanofibres (CNF) are hollow cylinders with diameters around one hundred nanometers and lengths of a few tens of microns giving high aspect ratios (length/diameter > 100). CNF are the cheaper counterpart of carbon nanotubes (about 3 to 500 times cheaper respectively when compared to multi-wall (MWNT) or single-wall carbon nanotube (SWNT)). They have a larger diameter (2 to 100 times respectively compared to MWNT or SWNT) and are less crystalline (with a kind of cup-stacked or stacked coins structure), while keeping acceptable mechanical and physical properties (Young modulus ~500 GPa, tensile strength ~3 GPa, electrical conductivity ~10 3 S/cm, thermal conductivity ~1900 W.m -1 .K -1 ). They are expected to be a promising nanofiller for the preparation of composites with multiple enhanced properties. Many studies related to the enhancement of the mechanical properties of an epoxy matrix by the introduction of CNF have been conducted [START_REF] Miyagawa | Thermo-physical properties of epoxy nanocomposites reinforced by carbon nanotubes and vapor grown carbon fibers[END_REF][START_REF] Gauthier | Reinforcement effects of vapour grown carbon nanofibres as fillers in rubbery matrices[END_REF][START_REF] Lee | Characterization of carbon nanotube/nanofiber-reinforced polymer composites using an instrumented indentation technique[END_REF][START_REF] Zhong | Graphitic carbon nanofiber (GCNF) polymer materials. I. GCNF epoxy monoliths using hexanediamine linker molecules[END_REF][START_REF] Xu | Mechanical property characterization of a polymeric nanocomposite reinforced by graphitic nanofibers with reactive linkers[END_REF][START_REF] Miyagawa | Effect of oxygen plasma treatment on mechanical properties of vapor grown carbon fiber nanocomposites[END_REF][START_REF] Choi | Mechanical and physical properties of epoxy composites reinforced by vapor grown carbon nanofibers[END_REF]. Some studies were dedicated to the electrical properties of CNF/epoxy composites [START_REF] Gibson | Formulation and evaluation of carbon nanofiber-based conductive adhesives[END_REF][START_REF] Kotaki | Electrically conductive epoxy/clay/vapor grown carbon fiber hybrids[END_REF][START_REF] Choi | Mechanical and physical properties of epoxy composites reinforced by vapor grown carbon nanofibers[END_REF][START_REF] Fukushima | Graphite nanoplatelets as reinforcements for polymers : structural and electrical properties[END_REF][START_REF] Lafdi | Effect of functionalization on properties of polymeric nanocomposites[END_REF][START_REF] Allaoui | Effect of the preparation method on the electrical properties of carbon nanofibre/epoxy nanocomposites[END_REF] and a general review of the properties of CNF-based composites has been published [START_REF] Tibbetts | A review of the fabrication and properties of vapor-grown carbon nanofiber/polymer composites[END_REF]. Because of their high aspect ratio and of van der Waals attractive interactions arising at the nanoscale, CNFs are tangled and form aggregates of different sizes which makes their homogeneous dispersion inside the matrix one of the main hurdles. For this reason, most of the research work published so far on the electrical properties of CNF-based composites focused on relatively high loadings, usually higher than 2 wt %, and aimed to obtain a high conductivity without determination of the critical weight fraction at which the system becomes conductive. In the literature, different preparation methods have been used to disperse CNF inside an epoxy resin and they led to different levels of electrical conductivity of the composites. The use of ultrasonication [START_REF] Choi | Mechanical and physical properties of epoxy composites reinforced by vapor grown carbon nanofibers[END_REF][START_REF] Fukushima | Graphite nanoplatelets as reinforcements for polymers : structural and electrical properties[END_REF] gives a higher level of conductivity, up to 1.2 x 10 -2 S/cm at 10 wt % loading [START_REF] Choi | Mechanical and physical properties of epoxy composites reinforced by vapor grown carbon nanofibers[END_REF], compared to mechanical mixing [START_REF] Gibson | Formulation and evaluation of carbon nanofiber-based conductive adhesives[END_REF][START_REF] Kotaki | Electrically conductive epoxy/clay/vapor grown carbon fiber hybrids[END_REF] giving rise to a maximum conductivity of 2 x 10 -5 S/cm at 8 wt % loading [START_REF] Gibson | Formulation and evaluation of carbon nanofiber-based conductive adhesives[END_REF]. Almost no data were published for CNF loading lower than 1 wt %. In the present paper, a method combining ultrasonication and mechanical mixing was used to prepare composites at different weight fractions, from 0.066 to 9 wt %, and their electrical properties were investigated by impedance spectroscopy. A complete picture of the electrical properties of a CNF/epoxy composite is given, including the vicinity of the insulator-to-conductor transition and the region far from the transition.

EXPERIMENTAL

Materials

Heat treated graphitized CNF (Pyrograf III PR24LHT) with diameters in the range of 60-150 nm and lengths between 30 and 100 µm, were obtained from ASI (Figure 1). A low viscosity diglycidyl ether of bisphenol-A (DGEBA) epoxy resin (η ~ 0.7 Pa.s) with triethylenetetramine (TETA) hardener (Epofix, Struers) was used. The stochiometric ratio was 100:12 (w/w) epoxy resin:hardener.

Sample preparation

The as-received CNF powder contained many large clumps with sizes in the mm range.

Sieving as reported elsewhere [START_REF] Allaoui | Effect of the preparation method on the electrical properties of carbon nanofibre/epoxy nanocomposites[END_REF][START_REF] Allaoui | Dielectric properties of composites of multi-walled carbon nanotubes in a resin matrix[END_REF] was used as a standard debulking method. The CNF powder was manually pushed through a 0.5mm sieve. Carbon nanofibres were then dispersed in acetone in a concentration of 0.3 vol % using tip ultrasonication in pulse mode (30 pulses per minute) combined with mechanical mixing. The epoxy resin was diluted in acetone (1:4 in volume) and then added to the CNF solution. The mixture was again submitted to ultrasonication in pulse mode (30 pulses per minute) combined with mechanical mixing for 4 hours. Solvent was removed by heating under continuous mixing. A masterbatch containing 10 wt % of CNF was obtained in that way.

Composites with different CNF loadings ranging from 0.066 to 9 wt % were prepared by dilution of the masterbatch with the right amount of resin. The mixture was mixed under vaccum with a Thinky mixer at 2000 rpm. The hardener was added, the mixture was again mixed under vacuum, then cast into a mold and cured at 120 °C for two hours.

Disk-shaped samples with diameter 25 mm were obtained and polished down to a thickness around 1 mm.

Impedance spectroscopy

The electrical properties were investigated using a dielectric analyzer (TA Instrument DEA 2970) in ceramic parallel plate mode. All experiments were performed at room temperature and at testing frequencies ranging from 1 to 10 5 Hz. Nitrogen gas was used to provide an inert environment at a flowing rate of 500 ml/min. The sample was placed between two gold electrodes, a load (300 N) was applied and the thickness was measured with the built-in LVDT (linear voltage-displacement transducer) with a precision of 1 µm. A low amplitude sinusoidal voltage (V applied ) was applied and the current (I measured ) through the sample was measured. The AC conductivity is given by

RESULTS AND DISCUSSION

Microstructure

Light transmission optical micrographs at low magnification permitted the observation of the gradual formation of a complex network and the global homogeneity of the sample.

As the weight fraction increased, the aggregation appeared more refined and highly structured, as can be seen in Figure 2a. At a higher magnification (Figure 2b), the interconnected network of CNF is revealed. It can be observed that CNF have different lengths ranging from 1 to 10 microns. As previously reported [START_REF] Allaoui | Effect of the preparation method on the electrical properties of carbon nanofibre/epoxy nanocomposites[END_REF], when using mechanical mixing for dispersing CNF in epoxy, isolated aggregates with size around 30 microns remained. This size almost corresponds to the length of the CNF, as a consequence, it is difficult to break these aggregates without CNF breakage and length reduction. The effect of fibre breakage is to shift the CNF critical fraction at which the composite becomes conductor to higher values. In this work, the effect of fibre breakage is negligible compared to the beneficial effect of desaggregation as the critical fraction is reduced from 1 to less than 0.1 wt %. The better the dispersion the lower the critical fraction.

Electrical conductivity

The electrical conductivity, σ, as a function of frequency is plotted in Figure 3 for the composites at different CNF loadings. For each loading, at least three samples were tested and the reproductibility is good. As expected, the standard deviation is higher in the transition region. The unfilled epoxy resin showed a typical insulating behaviour with a frequency-dependent conductivity. The composite with 0.066 wt % has the same behaviour as the matrix with a shift of its conductivity about two orders of magnitude compared to the virgin resin. At 0.1 wt % loading, the behaviour of the composite became semi-conducting. The conductivity is independent of the frequency until an onset frequency, noted as f 0, at which it increased with frequency. From 0.1 to 1.2 wt %, the same behaviour was observed with a shift of f 0 to higher frequencies. This kind of behaviour was previously reported for carbon black composites [START_REF] Connor | Broadband AC conductivity of conductor-polymer composites[END_REF][START_REF] Zois | Electrical Properties and Percolation Phenomena in Carbon Black Filled Polymer Composites[END_REF] and is also described by universal scaling laws [START_REF] Dyre | Universality of ac conduction in disordered solids[END_REF]. A model was proposed by Connor et al. [START_REF] Connor | Broadband AC conductivity of conductor-polymer composites[END_REF] based on the fact that an additional contribution to conductivity comes from electrons in finite-size clusters with fractal nature that can be scanned at higher frequencies (higher than f 0 ). Percolation theory predicts power law scaling of conductivity, σ, and dielectric constant, ε, with frequency ω close to the transition region; σ α ω x and ε α ω -y . Different mechanisms [START_REF] Song | Experimental study of the three-dimensional AC conductivity and dielectric constant of a conductor-insulator composite near the percolation threshold[END_REF] (intercluster polarization (x=0.72, y=0.28), anomalous diffusion inside cluster (x=0.58, y=0.42)) have been proposed to explain the conduction behaviour. In our case, x takes values ranging from 0.45 to 0.65, and y takes values ranging from 0.17 to 0.25, for p in the range 0.23 to 0.8 wt %, and these values do not appear to correspond closely to the defined mechanisms. On the other hand, log σ is linear with p -1/3 , as can be seen in Figure 4, showing the possible preponderance of the tunneling conduction mechanism [START_REF] Connor | Broadband AC conductivity of conductor-polymer composites[END_REF]. For higher loadings (≥ 1.2 wt %), the onset frequency disappeared and the composite presented a conducting behaviour over the whole domain of frequency studied. The AC conductivity at 1 Hz is plotted as a function of wt % of CNF in Figure 5.

The electrical conductivity increased by seven orders of magnitude with the addition of 1.2 wt % of CNF into the epoxy resin. The data corresponding to the vicinity of the transition, that is from 0.1 to 1.2 wt %, was fitted to the universal scaling law [START_REF] Kirkpatrick | Percolation and conduction[END_REF][START_REF] Stauffer | Introduction to percolation theory[END_REF]:

σ = A (p -p c ) t ( for p < p c ) (1)
with σ, the electrical conductivity; A, a constant; p, the weight fraction of CNF; p c , the critical weight fraction of CNF, and t the critical exponent related to the dimensionality of the system. It was found that the critical weight fraction is 0.064 wt % and the exponent is 1.78, which is close to that of a three dimensional random system (t = 1.94) [START_REF] Stauffer | Introduction to percolation theory[END_REF]. This critical weight fraction corresponds to the formation of a tunneling conductive network. This is a network of aggregates that are close enough from each other (~1 nm) to allow for tunneling conduction between them. As an illustration of this aspect, the case of the composite with 0.066 wt % of CNF (thus p > p c ) has an insulating behaviour with a conductivity two orders of magnitude higher than that of the unfilled resin. It is also interesting to observe that the conductivity increased by two orders of magnitude after the transition and reached 5.5 x 10 -5 S/cm at 9 wt %.

A tunneling contact model

After the transition, for CNF loadings higher than 1.2 wt %, the electrical conductivity did not change significantly and was around 10 -6 S/cm, before increasing again by about two orders of magnitude. The value of the conductivity right after the transition is lower than expected, considering that the conductivity of the pure CNF powder at 10 vol % is around 1 S/cm as reported by the supplier and as measured by our own means. Similar conclusions were drawn in a previous study [START_REF] Allaoui | Comportement mécanique et électrique des enchevêtrements de nanotubes de carbone[END_REF]. In that study, the electrical conductivity of a network of multiwall carbon nanotubes (MWNT) was measured as a function of the volume fraction of MWNT. The electrical conductivity of MWNT/epoxy composites prepared with the same MWNT was also measured. The comparison of the results showed up to three orders of magnitude of difference of the extrapolated conductivity of the 100 vol % MWNT material. This discrepancy led to the conjecture that a thin film of epoxy was present at the contact between MWNT. When the thickness of that insulating film is sufficiently small (~1 nm), quantum mechanics laws state that the probability to find an electron on the other side of the film is non-zero and the electrons can cross this insulating barrier by "tunnel effect". We propose to evaluate the thickness of the epoxy film. We model the composite as a stacking of layers. The resistance of one layer is that of a network of parallel resistors. Each resistor has the same resistance, noted as R contact , and represents the contact between the CNF with an epoxy film in their vicinity along with the segment of CNF between contacts. The thickness of one layer is assumed to be equal to the distance between contacts, noted as λ. At least two assumptions are made. In each layer, the network is perfectly 3D random and all the contacts participate in the conduction (we do not take into account aggregation and dead-end branches: far from the transition, the latter may have a limited effect). All resistors have the same resistance, that is we do not take into account the distribution in diameter of the CNF or variation of epoxy film thickness. The resistance of a contact is the sum of R epoxyl , the resistance of an epoxy film with thickness s and surface area equal to that of a CNF-CNF contact, and of R CNFp, the resistance of the CNF portion between two contacts.

epoxyl CNFp contact R R R + = (5)
A schematic illustration of the model is given in Figure 6. We do not take into account the complexity of the contact surface and we approximate it by a square of side equal to the diameter of a CNF; 2 d S contact = . This means that all CNF are assumed to cross each other under a right angle and thickness variation along the section is neglected. Hence, with ρ tunnel the tunneling resistivity of the epoxy film (in Ω.cm 2 ). Even if we know that the resistance between two contacts, that is the resistance of a portion of CNF, is negligible compared to that of a contact (this makes sense, the conductivity along a CNF is 10 3 S/cm compared to the bulk conductivity of a network of CNF at 10 vol % around 1 S/cm), we will include this term in order to keep the generality of the model. As a consequence, the resistance of the CNF portion between two contacts is

φ σ λ σ π d R CNF d CNF CNFp 2 1 1 1 4 2 = = (7)
The combination of equations ( 4), ( 5), ( 6) and ( 7) led to the following expression for the electrical conductivity of the composite

CNF tunnel d d d φσ ρ π σ 2 1 1 1 16 2 + = (8)
The volume fraction of CNF was given by

1 1 -         + = CNF epoxy epoxy CNF p p ρ ρ φ
with ρ CNF = 2 g.cm -3 and ρ epoxy = 1.1 g.cm -3 the densities of CNF and epoxy, and p CNF and p epoxy the weight fractions of CNF and epoxy. An important research effort [START_REF] Sommerfeld | Elektronentheorie der metalle[END_REF][START_REF] Holm | Über den Widerstand dünnster fremdschichten in metallkontakten[END_REF][START_REF] Holm | Electric contacts: theory and application[END_REF][START_REF] Simmons | Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film[END_REF] was dedicated to the calculation of the tunneling resistivity based on quantum considerations. For low voltages, the Holm-Kirschstein [START_REF] Holm | Über den Widerstand dünnster fremdschichten in metallkontakten[END_REF][START_REF] Holm | Electric contacts: theory and application[END_REF] [START_REF] Simmons | Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film[END_REF] made refined calculations taking into account the true shape of the potential and not the approximate parabolic form assumed by Holm et al. [START_REF] Holm | Über den Widerstand dünnster fremdschichten in metallkontakten[END_REF][START_REF] Holm | Electric contacts: theory and application[END_REF]. He derived the following expression of the tunneling current density, J, in A.cm 2

( ) ( ) ( ) { } 2 1 2 1 025 . 1 exp ) 025 . 1 exp( 10 2 . 6 2 10 V s V s s J + - + - - × × = ϕ ϕ ϕ ϕ (10) where ( ) ( ) ( ) (
) is a more crude approximation. The thickness of the epoxy film is plotted in Figure 8 using the values of these fitting parameters and the assumed power law dependence with the volume fraction of CNF. It was found that the film thickness is in the range of 12-20 Å and decreases when the volume fraction of CNF increases. This thickness range corresponds to the size of a few epoxy molecules [START_REF] Liang | Investigation of molecular interactions between (10, 10) single-walled nanotube and Epon 862 resin/DETDA curing agent molecules[END_REF]. The difference in thickness between the two models was less than 2 Å and the trend was quite similar.

        - -       - - +       - Φ = 2 1 1 2 1 2 2 1 ln 75 . 5 2 s s s s s s s s s s s V r ε ϕ and Φ = r s ε 6 1 Φ +         - + Φ - = r r r s V s s s ε ε ε

CONCLUSIONS

In this study, carbon nanofibre-based composites were prepared using a method combining ultrasonication and mechanical mixing. The study of their electrical properties by impedance spectroscopy revealed a low critical weight fraction, p c = 0.064 wt %, corresponding to the formation of a tunneling conductive network. The transition region was quite large, spanning about one order of magnitude, from 0.1 to 1.2 wt %. In that region, the composites presented a conducting behaviour until an onset frequency at which their conductivity increased with frequency, that is an insulating behaviour. The onset frequency increased with CNF weight fraction and disappeared for p ≥ 1.2 wt %.

Far from the transition, the conductivity increased by two orders of magnitude. A simple model, based on the CNF-CNF contact inside the matrix and assuming the presence of an epoxy film in the vicinity of the contact, was proposed in order to evaluate the thickness of this film. It appears that the thickness corresponds to the size of a few epoxy molecules and decreased with CNF weight fraction. The decrease of the epoxy film may explain the two orders of magnitude increase in the conductivity observed far from the transition.

LIST OF CAPTIONS

  δ being the phase angle shift, e being the thickness and A the surface area of the sample.

  A composite sample of thickness e is a stacking of e/λ layers (the layers resistances are in series). The electrical resistance of the composite is number of contacts (in parallel) in one layer. Considering a composite sample of surface area S, the electrical conductivity is thus n being the number of contacts per unit volume in a three dimensional random fibre network which is given by[START_REF] Alkhagen | Nonlinear elasticity of fiber masses[END_REF] φ the volume fraction of fibres and d their diameter. The distance between contacts in a three dimensional random fibre network is given by[START_REF] Alkhagen | Nonlinear elasticity of fiber masses[END_REF]

s

  equation gives the tunnel resistivity in Ω.cm 2 being the film thickness in Å, Φ the work function of the metal in eV and ε r the relative permittivity of the film material. Simmons

  thickness s expressed in Å and the work function Φ in eV. The electroaffinity of the film material should be taken into account, but in the case of an insulator, it is assumed that it may be negligible compared to the work function. The voltage, V, is given by considering one electron carrying the elementary charge +e passing into the film of thickness s, surface area S contact and capacitance C V=e/C=e/(ε r ε 0 S/s) with ε r and ε 0 ~8.85 x 10 -12 F/m, the permittivity of respectively the film and vacuum. The tunneling resistivity is then obtained, resistivity was calculated using the relative permittivity of the epoxy ε r ~ 2.65, the work function of graphite [27] Φ = 4.62 eV and an average CNF diameter d = 100 nm. We assumed that the film thickness varies with the volume fraction of CNF following a power law dependence;β φ K s =. The experimental data were fitted to equation (8) with K and β as free parameters using the two different models for the tunneling resistivity;plotted in Figure7. The fitting curves are superimposed and the values of the fitting parameters are quite similar. The Simmons model is a refined version of Holm's model, the difference is the potential used to calculate the tunnel current, in Holm's model, there

Figure 1 -

 1 Figure 1 -Scanning electron micrograph of the carbon nanofibres.

Figure 2 -

 2 Figure 2 -Light transmission optical micrographs of the composites at different loadings of CNF ranging from 0.066 to 1.2 wt %. a) magnification 50X b) magnification 1600X.

Figure 3 -

 3 Figure 3 -Electrical conductivity of the composites at different CNF loadings as a function of frequency.

Figure 4 -

 4 Figure 4 -Logarithm of the conductivity as a function of p -1/3 . Solid line is a linear fit to the data.

Figure 5 -

 5 Figure 5 -Electrical conductivity of the composites at 1 Hz as a function of weight fraction of CNF. The solid line is a fit to the universal scaling law. (Inset: logarithm of conductivity as a function of logarithm of reduced weight fraction and fit to a line).

Figure 6 -

 6 Figure6-Sketch of the model adapted from[START_REF] Allaoui | Comportement mécanique et électrique des enchevêtrements de nanotubes de carbone[END_REF].

Figure 7 -

 7 Figure 7 -Electrical conductivity as a function of volume fraction of CNF. The solid line is a fit to equation (8).

Figure 8 -

 8 Figure 8 -Thickness of the epoxy film as a function of volume fraction of CNF.

Figure 1 -

 1 Figure 1 -Scanning electron micrograph of the carbon nanofibres.

Figure 2 -

 2 Figure 2 -Light transmission optical micrographs of the composites at different loadings of CNF ranging from 0.066 to 1.2 wt %. a) magnification 50X b) magnification 1600X.

Figure 3 -

 3 Figure 3 -Electrical conductivity of the composites at different CNF loadings as a function of frequency.

Figure 4 - 20 Figure 5 -

 4205 Figure 4 -Logarithm of the conductivity as a function of p -1/3 . Solid line is a linear fit to the data.

Figure 6 - 21 Figure 7 -

 6217 Figure 6 -Sketch of the model adapted from [21].

Figure 8 -

 8 Figure 8 -Thickness of the epoxy film as a function of volume fraction of CNF.

ACKNOWLEDGEMENT

Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) is appreciated.