Michel Henry

« Phénoménologie

Frankfurt am Main Friedrich-Wilhelm Von Herrmann

V Klostermann

Beneath Time and Reflection: Husserl's Shadow in Michel Henry's non

Ever since The Essence of Manifestation (1963), Michel Henry's phenomenology developed itself in a tight dialogue with Husserl. This confrontation leads Henry, in 1995, to formulate the project of a « non intentional phenomenology » 2 , which finds its departure point in a quite simple question : is intentionalitythe key feature of consciousness and of lived experiences in Husserl's perspectiveable to ground itself, does it provide its own foundation ? If not, where is its condition of possibility to be found? Thus, instead of adopting a purely descriptive attitude towards intentional acts, Henry's gesture invites us to inquire into their origin and their inner ground, to submit them to a transcendental interrogation in order to discover « what ultimately makes them possible » 3 . This ambitious enterprise has known several moments since 1963 and has gone even further than the 1995 article, in Henry's latest phenomenological work, Incarnation (2000). A remarkable contribution to the debate is also brought by Material Phenomenology (1990). In order show the complexity and the incisiveness of Henry's project, it is nevertheless important to take into consideration its Husserlian background and roots. Indeed, hasn't Husserl himself explored the limits of intentionality? What is then the consistency and what is the status of the pre-(or non-) intentional in Husserl's phenomenology? Does Henry's non intentional phenomenology go entirely against Husserl, or is it, moreover, an attempt to save and justify a certain tendency that is present in Husserl's own phenomenological account of consciousness?

1

A previous version of the first half of this paper has been published in French, as the first part of « Michel

But first of all, for what reasons does Henry believe himself authorized to claim that intentionality could never find its ultimate phenomenological possibility in itself? A first element in order to answer this question is provided by the fact that intentionality designates the structure of a relationship to objects: therefore, it can very well describe and characterize the appearing of beings, but not its own appearing or its self-givenness. With this consideration, the heart of the problem has already been touched:

The question of intentionality is not that of its being but that of its appearing, and […] the question of how intentionality appears is that of knowing whether this appearing is homogeneous or identical to the appearing of beings, otherwise said, if the appearing of intentionality depends on intentionality itself. 4 This manner of questioning intentionality goes further than Heidegger's well known reproach in respect to the "indeterminacy" of the "being" of intentionality. By doing so, Heidegger's attempt to ground intentionality in a more original "transcendence", which is supposed to name its ontological ratio essendi 5 , is implicitly rejected as insufficient: for Henry, what Heidegger calls "transcendence" is equally unable to account for itself and, consequently, could not provide a satisfying foundation for intentionality. The second section of The Essence of Manifestation, baring the title "Transcendence and Immanence", has shown indeed that transcendence, understood as an act of "relating to…", can only ground itself in immanence. And Philosophy and Phenomenology of the Body, the contemporary work on Maine de Biran, has stated this in a particularly clear way:

More original than the phenomenon of transcendence, and somewhat prior to it, is the phenomenon of immanence, in which transcendence has its ultimate ontological condition of possibility. 6 This is why transcendence cannot provide the researched ground of intentionality, insofar as it does not fulfill the phenomenological requirement of being the principle of its own manifestation. Henry is fully conscious of how strong and radical this objection is when he writes: "This is the main and the strongest illusion of contemporary phenomenology: believing […] that transcendence is phenomenologically and ontologically autonomous" 7 .

Just like intentionality, transcendence requires a more original foundation. In order to accomplish it, one has to overcome the Heideggerian concern for the being of intentionality and hint instead at a deeper and more phenomenological level by interrogating its appearing, or the manner it is given to itself. And indeed, the appearing of intentionality cannot be that of beings or objects: intentionality is not an object, and supposing an intentional access to intentionality itself would necessarily lead to a regressus ad infinitum. It is why one needs to acknowledge that phenomenalisation cannot be univocal and homogeneous: "the categories that concern the how of givenness cannot be borrowed from the given itself" 8 . That is why the structure of appearing is necessarily dual, and one could not claim its unity or homogeneity, its "absolute indifference", without falling into an "ontico-phenomenological equivoque" (as Henry puts it in another famous article 9 ) that results from considering all phenomena as world-phenomena.

As we can see, the disclosure of the non intentional ground of intentionality requires the acknowledgment of the duality of appearing. Consequently, it becomes necessary to make room for a new kind of appearing, distinct from that of objects or beings, which could also be adequate for intentionality itself. Thus, it is according to the necessity of its own phenomenological foundation that intentionality reveals itself not to be the only principle of phenomenalisation; it is intentionality itself that unveils the limits of its own power of givenness, insofar as it unavoidably resists to an ontical or mundane appearing. The conclusion can therefore only be the following:

[…] intentionality is not a phenomenological concept fit to conceive intentionality. This means that intentionality does not accomplish its own revelation; the self-appearing of appearing is not the appearing of beings. 10 If there is, as shown by the case of intentionality, an appearing that is other than the ontical one, other than the appearing of beings, phenomenality can no longer be regarded as exclusively mundane or ontical, just as intentionality can no longer be the unique principle of appearing. It is thus necessary to abandon that which The Essence of Manifestation had called the "dogmatism of intentionality" 11 , dogmatism that sees in intentionality the "principle and unique criterion of phenomenality" 12 . In order to avoid this ontical drift of phenomenology, which reduces it entirely to a phenomenology of the object (and of the given, rather than of givenness), one has to face the most crucial phenomenological question, that of the appearing of appearingand, implicitly, that of the appearing of intentionality.

Husserl and the Impression as Primary Consciousness

But how could one subtract intentionality from its ontical deployment, how can one leave behind the level of objectifying intentionality? While engaging himself in such an enterprise, Henry is far from ignoring that this path has been outlined by Husserl himself: as he admits in his 1990 work, Material Phenomenology, "Husserlian phenomenology has not completely ignored the question of the self-givenness of intentionality" 13 . It is, more precisely, in his 1904-1905 Lectures on Inner Time-Consciousness, estimated by Henry as "an extraordinary text and probably the most beautiful of the century" 14 , that Husserl had attempted to go beyond objectifying intentionality by deepening the phenomenology of perception and stepping towards a phenomenology of inner time-consciousness. The question of the phenomenological origin of time had led Husserl to insist on the Urimpression as the "original source of all consciousness and all being" 15 , as an "absolute beginning", an original generation and creation without which consciousness "is nothing" 16 . Moreover, the crucial function of the Urimpression manifests, as Husserl puts it, the "enormous phenomenological difference" 17 that distinguishes it from all the other forms of consciousness (that are only its modifications or reproductions).

What is, more precisely, Husserl's goal in underlining the fact that the "primary consciousness" is an "impressional" 18 one? His polemic intention in the 1905 Lectures is to refute and avoid the derealization of time such as it inevitably occurs in the account of his master, Franz Brentano: for Brentano, the unity of (inner) time is granted by imagination, and this ultimately implies that time, outside the present moment, has no reality in itself. Quite the contrary, through his insistence on impression and on the mechanisms that allow its preservation, Husserl aims to prove that the reality of time is constantly provided and renewed. Quite remarkably, Henry's reading of the 1905 Lectures is somewhat symmetrical of Husserl's own criticism, insofar as it is driven by the same concern to avoid losing or weakening the reality of time; but instead of accepting Husserl's solutionaccording to which impression is the source of all intentionality -, Henry denounces the fact that, by inscribing impression within intentionality, Husserl destroys their difference and eventually produces the lack of reality he wanted to avoid 19 . Far from retaining the originarity of impression, its intentional recuperation can only provoke a leap into irreality.

In order to understand the reasons that lead Henry to claim that Husserl is unable to impede the relapse of phenomenological time into irreality, let us examine more thoroughly the enterprise of the 1905 Lectures. Paradoxically, it is precisely Husserl's effort to maintain the reality of the Urimpression within the perpetual flowing of time that will eventually produce what Henry estimates to be the unwanted result. The reason for this is the fact that the manner in which impression is preserved is dependent upon a first and genuine form of intentionality: namely, retention. Retention is itself an "original consciousness", for it is not an "image representation (Verbildlichung)" 20 of the past, but its intuition or its direct presentation: this is why Husserl can call it the "living horizon of the now" 21 . Husserl

19

Henry's detailed analysis of these Lectures is especially to be found in Phénoménologie matérielle (p. 30-50 in particular), but also in the conference "Phenomenological time and the living present", which is also from 1990 and was published for the first time in Auto-donation. Entretiens et conférences, Paris, Beauchesne, 2004, p. 45-62. emphasis on what distinguishes retention from commonly understood memory manifests indeed his will of preserving the impressional source of consciousness by granting to the consciousness of the past itself the characters of immediacy and intuitivity.

What is then Henry's discontent with Husserl's solution? His argument consists in asserting that, instead of preserving what is specific to impression, retention ineluctably transforms it into what it is not: that is, into intentionality. And indeed, even if he admits that time-consciousness has its genuine source in impression, Husserl does not hesitate to characterize it eventually through intentionality. It is true that the form of intentionality which is then at stake is different from object-intentionality: Husserl speaks (in § 39 of the 1905 Lectures) of a "longitudinal" intentionality in order to distinguish that which grants the unity of the stream of inner-time from the objectifying ("transversal") intentionality; but the ultimate result of this distinction, far from limiting the rights and powers of intentionality, consecrates its absolute reign. This means that even in the "obscure depths of the ultimate consciousness that constitutes the temporality of lived experiences" (as the Ideas I put it 22 ), what we find can still be described as an intentional process. Therefore, the § 85 of Ideas I can serenely state that "intentionality […] resembles to an intentional medium that ultimately carries all lived experiences, even those that are not intentional", that is, even "the sensual element that, in itself, is in no way intentional" 23 .

In the 1905 Lectures, the same universal signification is granted to intentionality when the unity of inner time-consciousness is considered to be the result of a special type of intentional constitution. Husserl is nevertheless well aware of the fact that this duplication, this splitting of intentionality risks to mask what is specific to the temporal stream of consciousness and what distinguishes it from object-intentionality; but he prefers to face this consequence rather than to attempt to get round it:

[…] it is within a unique consciousness-stream that the temporal immanent unity of the sound [that is, of the temporal object] and the unity of the stream of consciousness itself are constituted. As shocking (or even absurd at first) as it might seem to say that the stream of consciousness constitutes its own unity, this is how things stand. Furthermore, longitudinal intentionality makes it useless and pointless to question any further the appearing of the temporal stream or the way it is given: "the self-appearing of the stream does not require a second stream: as a phenomenon the stream constitutes itself" 25 ; otherwise said, the stream produces its own self-givenness. These considerations show that Husserl has clearly and directly faced the question of the appearing (or that of the self-givenness) of intentionality. But the response provided by his theory of a double intentionalityof an intentional constitution of the stream of consciousness itself, which is also the key to its appearingcannot satisfy Henry. Even if the 1905 Lectures exhibit a layer of consciousness which is deeper and more fundamental than object-intentionality, they fail to establish not only the autonomy, but also the consistency of the pre-intentional. Thus, what is held to be primordial (the impression) is finally diluted into what is only its modification (retention and longitudinal intentionality); what is constituent is reduced to what is constituted. And quite predictably, Husserl can only be disconcerted by this paradox: "the constituent and the constituted coincide, and though naturally they cannot coincide at all levels" 26 . Moreover, while submitting the stream of inner time-consciousness to a constitution that is fully intentionalin spite of the fact that its origin and source are to be found in the Urimpression -, Husserl does not only inevitably alter it, but he also produces the loss of its materiality and of its specific consistency. Even though the § 8 of the 1905 Lectures proceeds to a genuine hyletic reduction ("We will now 'unplug' all transcendent apprehension or thesis and welcome the sound as a purely hyletic given", it is here announced 27 ), the consideration of the hyletic level, that had precisely allowed revealing the Urimpression, will finally be submerged by the unexpected primacy of the "form of the stream" in respect to its matter 28 . In conclusion, quite surprisingly, the 1905 Lectures lead to a double victory which is little compatible with their departure program: that of intentionality on impression and that of form on hylé. Henry's enterprise is fundamentally driven by the wish to avoid and to repair this double loss: its aim is to recuperate both the impression and the hylé and, by doing so, to disclose the non intentional ground of intentionality. It is to this intention that responds, on one hand, the elaboration of a material phenomenology that does no longer accept the subordination of hyletics to noetics, stated by Husserl in § 86 of Ideas I. For, as Henry puts it, "when reduced to intentional noesis, the transcendental cannot truly be such, cannot act like an a priori condition of all possible experience, if this generally requires something fully different from it: sensation, impression" 29 . One can easily recognize here Henry's objection as previously encountered: in spite of the universality that Husserl grants to it far too easily, intentionality cannot be its own condition of possibility, it cannot account for its own manifestation, insofar as an irreducible difference separates the appearing of beings from its own appearing. In order to reach the foundation of intentionality, it is required to rethink the relationship between sensual ύλη and intentional μορφή. And by doing so, ύλη is no longer to be understood as a mere content, but as the authentic transcendental, as the genuine condition of possibility: "Matter", for a material phenomenology, does no longer designate the other of phenomenality, but its essence. Thus, material phenomenology is the phenomenology in a radical sense, insofar as […] it accounts for its self-givenness. 30 For Henry, the hylé does no longer have to respond to the question of meaning and to obey to the intentional morphé as sinngebend, as the privileged source of meaning. Insofar as it can account for its self-givenness, the impressional matter, the hylé, is phenomenologically autonomous. This cannot be stated, however, about intentionality itself, which, as previously seen, intrinsically depends on the pre-intentionalthat is, on impression.

From Impression to Life

On the other hand, it is legitimate to inquire, as Henry does it himself, into the "origin of the impression", and by doing so, one has eventually to acknowledge "the inescapable reference of a phenomenology of impression to a phenomenology of life" 31 , motivated by the fact that "the original appearing of impression is nothing else but that of life" 32 . But how is this referral phenomenologically justified? Henry insists on the fact that the connection between life and phenomenalization is far from being extrinsic or accidental. This means that "life is phenomenological in a primordial and fundamental sense" 33 : namely, life is the only source of phenomenalization. This means that "phenomenality has its original essence in the fact that life experiences itself in such a manner that this self-experience is the self-appearing of appearing" 34 . That is why the phenomenology of life is precisely the most radical kind of phenomenology: without life as intrinsically phenomenological, there is indeed no phenomenalization and no phenomenality. Likewise, without life, there is no intentionality: "intentionality is only possible as intentional life" 35 . To put it otherwise:

There is no intentionality, but only an intentional life. The task of a non intentional phenomenology is precisely to acknowledge the specific phenomenality of life, the pathetic self-affection that makes it possible as a life, in its radical heterogeneity to [...] intentionality. 36 The non intentional phenomenology that is here at stake can be equally characterized, as previously seen, as a material phenomenology of impression and self-affection, as a phenomenology of affectivity, but it is ultimatelyas it appears nowa phenomenology of life. Nevertheless, it is here that lays also its most considerable difficulty: if there is such heterogeneity, such an ontological and phenomenological distance between intentionality and the life that grounds it, how is this grounding relationship still possible and conceivable? Henry has certainly not avoided the question, but his attempts to solve it show precisely how delicate the conquest of the autonomy of the pre-(or non-) intentional is.

The Case of Reflection

The treatment of the question of reflection is a symptomatic example of this difficulty and will consequently allow us to prolong our inquiry into Henry's plea for a non intentional phenomenology 37 . What are the status and the consistency of reflective consciousness in respect to non-or pre-reflective consciousness? The Husserlian analyses can here as well function as a guide. We have seen that the 1905 Lectures grant a crucial role and position to the Urimpression, to the impressive consciousness within the temporal immanent stream of lived experiences, and that retention, as the intuitive (presentative) consciousness of the past, is the mechanism through which this original consciousness is preserved. Or it is precisely on the base of retention that reflection, that is, the retrospective glance that embraces the past phases of the consciousness stream, is possible. But this does not mean that the initialimpressionalphase of the stream becomes conscious only through the reflection that retention makes possible. "If it were conscious only through retention, it would be impossible to understand that which allows characterizing it as a now" 38 . Consciousness is not entirely reflective, even though reflection is the most fruitful methodological tool for its study: "the initial phase of the stream can only become an object after its passing by, thanks to retention and reflection" [START_REF] Husserl | Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein[END_REF] .

The Ideas I reaffirm the crucial role of reflection for the phenomenological analysis by stating (in § 77) that "the phenomenological method operates entirely throughout reflective acts" [START_REF] Husserl | Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie[END_REF] . Nevertheless, the methodological importance of reflection does not involve that lived experiences are conscious only thanks to reflective acts: "Every I has (erlebt) its lived experiences. […] He lives them: this does not mean: he has them 'under his eye' " [START_REF] Husserl | Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie[END_REF] .

Reflection is by its own nature a modification of lived experiences, and this implies that, when examining consciousness, we will eventually reach a level of "absolutely non reflective lived experiences" which are ultimately "impressions (Impressionen)" 42 . But in spite of this, reflection remains crucial and indispensable for the phenomenological analysis of consciousness, and this epistemological function is due especially to the fact that it is only through reflection that the lived experiences will appear as belonging to the intentional life of one and the same I. This is why the I is always a reflection-I: there is no such egological dimension in the purely impressional consciousness. Thus, a tension emerges from the collision and concurrence between the necessity to acknowledge the pre-reflective (and the pre-intentional) constitution of the I in its full consistency and autonomy, and the teleology of knowledge in which the pre-reflective and the pre-intentional are always eventually inscribed.

What is Henry's position in respect to Husserl's view on the role of reflection? The manner in which Husserl grounds in reflection both the certainty of the I and the belonging relationship that connects its lived experiences to it is clearly unacceptable to him. As he does in the case of intentionality, Henry firmly stresses the distance and the heterogeneity between reflection and the pre-reflective life:

Each time when, through a reflectionmay it be natural or transcendental reflection -, conscious thought tries to grasp life and have an intuitive knowledge of it […], it is not the reality of life in its ''original presence'' that it discovers, but only the empty spot of its absence. 43 Manifestly, when Henry denies that life could be grasped through reflection, his aim is to take into account more seriously the fact that life constitutes itself before reflection. Just like intentionality, reflection cannot properly designate the self-appearing of life, the selfgivenness of lived experiences. The claim that reflection, as necessarily derived and posterior, cannot grant an access to a life that is pre-reflective in itself, leads Herny to finally challenge the role and status of retention itself (which, as previously seen, was regarded by Husserl as the intermediary link between impression and reflection). Retention is therefore no longer seen as a necessary mediation, but as the first fatal alienation of impressionthat is, as the irremediable loss of the original consciousness. But once again, this manner of deepening the distances produces the same difficulty: how is the constitution of the stream of consciousness to be analyzed and described, if all the modifications of impression are rejected? For the stream cannot simply consist in impressions: the life of consciousness is not a perpetual present or a mere actuality. It is though into such a Cartesian vision of consciousness that Henry unavoidably leaps, especially when he follows Husserl's identification of the original Zeitbewusstsein to a "feeling (Empfinden)" 44 . This indication is taken indeed very seriously: impressional consciousness is not a reflective consciousness but, precisely, an affective one, whose essence is self-affection, that is, a form of self-experience prior to all reflection. This rejection of reflection, however, has a heavy price, insofar as, in this fashion, no form of inactuality of consciousness is any longer conceivable: what becomes then of inner temporality itself? Is there still room for something like a stream of consciousness? For the stream of lived experiences, as Husserl puts it in the Ideen I, "can never consist in mere actualities (das Erlebnisstrom kann nie aus lauter Aktualitäten bestehen)" 45 . As temporal, consciousness is necessarily also inactual in a way. What is then the consistency of its relationship to the past and to the future, knowing that neither the past nor the future are accessible through impression? What can then replace the function of reflection, which, for Husserl, grants the fact that even inactual lived experiences can still be perceived or at least are "ready to be perceived (wahrnehmungsbereit)" 46 ? But perhaps it is the connection between temporality and consciousness itself that has been too easily taken for granted in Husserl's phenomenology. This suspicion expresses, in my view, the ultimate level of Henry's critical reading of Husserl. In the preparation notes for L'essence de la manifestation that were recently edited 47 , it becomes apparent to what extent Henry has questioned precisely the manner Husserl thinks the I in the horizon of time: for the author of Ideen I, indeed, the unity of egological life and the unity of immanent temporality are one and the same. For Henry, instead, the unity of the I is not the unity of time but the unity of life itself: it is within life or as living that the I is given to itself in the first place. Time does not come before, but after the I: the I does not raise from the reflective unification of immanent time, but it is time that is not unified unless it is lived by the I. This also explains why reflection, insofar as it necessarily deploys itself in the element of time, cannot be the primary experience and occurrence of the I.

It is thus towards an immanence deeper than that of inner time that Henry aims to lead the phenomenological analysis of lived experiences through both the criticisms of intentionality and of reflection. In this manner, the ambition of his project of a non intentional phenomenology reveals itself in all its magnitude: its ultimate objective is to question and untie the connection between inner experience and time experience. The claim that underlies such an attempt is that life is not essentially temporal: time is only a worldly, outer adjunction to life and does not belong to its intimate essence. The challenge will then be to provide a non temporal description and comprehension of the inner affective dynamics of life. Whether Henry's solutionaccording to which the affective modulations of life, while undoubtedly forming a unified series, can distinguish themselves from one another only through their valence, independently from their temporal position 48 is a viable one, is a question that would undoubtedly require an autonomous inquiry.

Claudia SERBAN

Université Toulouse 2 Jean Jaurès (France)

48

For a subtle and well developed analysis that challenges this claim, see Grégori Jean, Force et Temps. Essai sur le "vitalisme phénoménologique" de Michel Henry, Paris, Hermann, 2015, in particular p. 55-64 and p. 205-220.

20

  Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein(1893- 1917), p. 32.

  24

22

  Edmund Husserl, Husserliana III/1 : Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, vol. I : Allgemeine Einführung in die Phänomenologie, éd. par Karl Schuhmann, 1976, p. 191-192. 23 Edmund Husserl, Husserliana III/1 : Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, vol. I : Allgemeine Einführung in die Phänomenologie, p. 192.

25

  Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein (1893-1917), p. 83. 26 Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein (1893-1917), p. 83. 27 Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein (1893-1917), p. 25.

  's

	17	Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein (1893-
	1917), p. 45.
	18	Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein (1893-
	1917), p. 90.

Michel Henry, « Phénoménologie non-intentionnelle : une tâche de la phénoménologie à venir », p. 386.

Michel Henry, « Quatre principes de la phénoménologie », Revue de Métaphysique et de Morale, 1/ 1991, p. 3-26, p. 17.

Michel Henry, « Phénoménologie non-intentionnelle : une tâche de la phénoménologie à venir », p. 390.

Michel Henry, « Quatre principes de la phénoménologie », p. 13.

Michel Henry, « Phénoménologie non-intentionnelle : une tâche de la phénoménologie à venir », p. 392.

Michel Henry, L'essence de la manifestation, Paris, Presses universitaires de France, 1963, 1990², p. 62.12Michel Henry, « Phénoménologie non-intentionnelle : une tâche de la phénoménologie à venir », p. 387.13Michel Henry, Phénoménologie matérielle, Paris, PUF, coll. « Épiméthée », p. 32.

Michel Henry, Phénoménologie matérielle, p. 31.

Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein(1893- 1917), ed. by Rudolf Boehm, Den Haag, Martinus Nijhoff, 1966, p. 67.

Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein(1893- 1917), p. 100.

Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein(1893- 1917), p. 43.

Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein(1893- 1917), p. 80. The remark added into brackets is my own.

Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein(1893- 1917), p. 114.

Michel Henry, Phénoménologie matérielle, p. 25-26.

Michel Henry, Phénoménologie matérielle, p. 58.

Michel Henry, Incarnation. Une philosophie de la chair, Paris, Seuil, 2000, § 9.

Michel Henry, Incarnation, p. 84.

Michel Henry, « Phénoménologie non-intentionnelle : une tâche de la phénoménologie à venir », p. 393.

Michel Henry, « Phénoménologie non-intentionnelle : une tâche de la phénoménologie à venir », p. 397.

Michel Henry, « Phénoménologie non-intentionnelle : une tâche de la phénoménologie à venir », p. 397.

For a further treatment of this question, see my paper : « Conscience impressionnelle et conscience réflexive : Husserl, Fink et les critiques phénoménologiques », Revue philosophique de la France et de l'étranger, n° 4/2012, p. 473-493.

Edmund Husserl, Husserliana III/1 : Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, vol. I : Allgemeine Einführung in die Phänomenologie, p. 166 and 167.

Michel Henry, Incarnation, p. 105.

Edmund Husserl, Husserliana X : Zur Phänomenologie des inneren Zeitbewusstsein(1893- 1917), p. 107.

Edmund Husserl, Husserliana III/1 : Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, vol. I : Allgemeine Einführung in die Phänomenologie, p. 73.

Edmund Husserl, Husserliana III/1 : Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, vol. I : Allgemeine Einführung in die Phänomenologie, p. 95.

Michel Henry, « Notes préparatoires à L'essence de la manifestation : la subjectivité », presented by Grégori Jean, Revue internationale Michel Henry, n° 3, 2012, p. 93-215.


Diana Nelli
email: nelli@fisica.unige.it

Christine Mottet
email: christine.mottet@univ-amu.fr

Riccardo Ferrando
email: ferrando@fisica.unige.it

Interplay between interdiffusion and shape transformations in nanoalloys evolving from core-shell to intermixed structures †

Nanoalloys are often grown or synthesized in non-equilibrium configurations whose further evolution towards equilibrium can take place through complex pathways. In this work, we consider bimetallic systems with tendency towards intermixing, namely AgAu, PtPd and AuCu. We analyze their evolution starting from non-equilibrium initial configurations, such as phase-separated core@shell ones, by means of Molecular Dynamics (MD) simulations. These systems present some differences, since AuCu bulk alloys make ordered phases at low temperature whereas AgAu and PtPd remain in solid solution. Moreover, Cu, Au and Ag have similar cohesive energies whereas Pt is much more cohesive than Pd. We consider both truncated octahedral and icosahedral initial shapes in the size range between 2 and 3 nm. For each AB system, we consider both A@B and B@A core@shell starting configurations. The evolution is characterized by monitoring the time-dependent degree of intermixing and the evolution of the shape. The simulations are performed up to temperatures close to the melting range. The approach to thermodynamic equilibrium is monitored by MD simulations and compared with the equilibrium chemical configurations obtained by Monte Carlo simulations.

Introduction

Alloy nanoparticles (referred to as nanoalloys in the following) are very often experimentally produced in out-of-equilibrium configurations. [START_REF] Ferrando | Structure and Properties of Nanoalloys[END_REF] Nanoalloy structures are characterized by geometric shape and chemical ordering, the latter being the pattern in which the atomic species are distributed. In general, non-equilibrium effects can occur both in shape and in chemical ordering.

Non-equilibrium trapping into metastable geometric shapes is found in elemental metallic nanoparticles [START_REF] Baletto | [END_REF]3 and in nanoalloys. [START_REF] Ferrando | Structure and Properties of Nanoalloys[END_REF] Well-known examples include the trapping into the icosahedral motif at large sizes, 4,5 the formation of tetrahedral structures in the gas phase 6 and in wet-chemistry synthesis, 7 the template growth of decahedral structures, 8 and the formation of triangular leaflets. 9 Also non-equilibrium effects on chemical ordering are observed both in wet-chemistry synthesis and in gas-phase growth experiments. In particular, here we are interested in the formation of phase-separated core@shell structures in nanoalloys that are miscible at equilibrium. In the synthesis by chemical reduction, both co-reduction and successive reduction methods [10][11][12] can lead to the formation of core@shell nanoalloys 13 in miscible systems.

In co-reduction, the metal with higher redox potential aggregates first, thus forming the cores of the nanoparticles, while the atoms of the second metal can subsequently aggregate to form the shells, as shown for the AgPd system. 10 AgPd presents a clear tendency to form solid solutions, 14 but in co-reduction experiments both Ag@Pd and Pd@Ag nanoparticles have been formed. 10 In PtPd, a variety of Pt@Pd, Pd@Pt and intermixed structures have been synthesised in co-reduction and successive reduction experiments. [15][16][17][18][19][20][21] Other highly miscible systems in which core@shell nanoalloys have been obtained by wet-chemistry methods are AuPd and AuCu. 22,23 In gas-phase experiments, the formation of B-rich (AB)@B nanoalloys, where the minority element A is always concentrated at the center of the nanoparticle, has been observed in AgAu, PtPd and PtNi. [24][25][26] The origin of this type of nonequilibrium chemical ordering has been rationalized by the depletion of the minority element in the metal vapour. The depletion takes place in the first stages of the nucleation of the nanoparticles, so that AB nanoalloys are initially formed and then covered by the majority atoms in the later stages of growth. 24 Ag@Au nanoalloys have been produced in the gas phase by subsequent aggregation in helium droplets, 27 whereas in wet-chemistry synthesis experiments, intermixed, Ag@Au and Au@Ag nanoalloys have been produced. 9,28 Non-equilibrium structures are expected to naturally evolve towards equilibrium. Therefore, the core@shell nanoalloys made of miscible metals should transform into some kind of intermixed chemical ordering if they are let evolve for sufficiently long times. At present, very little is known about the evolution pathways of these nanoalloys.

In this paper we simulate the evolution of AgAu, PtPd and AuCu nanoparticles from core@shell initial configurations by Molecular Dynamics (MD) simulations. All these systems are highly miscible, so that core@shell configurations of both types (B@A and A@B) are expected to be out of equilibrium.

AgAu, PtPd and AuCu are chosen because they are representative of different trends.

As regards macroscopic samples, in both AgAu 29 and PtPd 30,31 there is evidence in favour of the formation of solid solutions for all compositions, without evidence of miscibility gaps 31,32 or of the stabilization of ordered phases. On the other hand, in AuCu, there is strong miscibility with the formation of ordered phases 33 around different compositions, such as the L1 0 phase at equicomposition and the L1 2 phase at 1:3 and 3:1 compositions.

These systems differ also in the lattice mismatch between the elements, which is negligible in AgAu (0.2%), small in PtPd (0.9%) and very large in AuCu (11.4%) (see for example Ref. 34 ). In addition, the difference in bulk cohesive energy per atom (

E coh ) is small in AuCu (E Au coh -E Cu coh = 0.32 eV), intermediate in AgAu (E Au coh -E
Ag coh = 0.86 eV) and large in PtPd (E Pt coh -E Pd coh = 1.95 eV). [START_REF] Kittel | Introduction to Solid State Physics[END_REF] In order to check the approach to equilibrium at different temperatures, the results of the MD simulations are compared to those of Monte Carlo (MC) simulations of the equilibrium chemical ordering in the truncated octahedral (TO) and icosahedral (Ih) structures.

Model and methods

The nanoparticles are modelled by a many-body atomistic force field developed within the second-moment approximation to the tight-binding model, [START_REF] Cyrot-Lackmann | [END_REF][37][38] also known as Gupta potential. 39 Form and parameters of the potential are available in Ref. 40,41 for AgAu and PtPd and in Ref. 42 for AuCu. These force fields have been favourably tested against experiments and Density-Functional Theory calculations for AuCu and PtPd in previous works in our group. 25,42,43 For AgAu, our model predicts correctly the tendency of these metals to form solid solutions, with some Ag enrichment of the surface layer. This generally agrees well with the experimental results for nanoparticle sizes of a few nm, 32 while for small sizes DFT calculations have shown that charge-transfer effects, not included in the Gupta model, can counterbalance to some extent this trend towards Ag surface segregation, especially in icosahedral structures. 44 In our MD simulations, the classical equations of motion are solved by the velocity Verlet algorithm [START_REF] Allen | Computer Simulation of Liquids[END_REF] with a time step of 5 fs. In all cases, the duration of the simulations is of 10 µs. The simulations are made at constant temperature, keeping temperature constant by an Andersen thermostat [START_REF] Andersen | [END_REF] whose collision frequency is chosen in such a way that diffusive properties of atoms are not altered. 47 Simulations are made at different temperatures, whose range depends on the system. For each temperature, we perform at least three independent simulations, if not otherwise specified.

The initial core@shell structures of the MD simulations are chosen as follows. For all systems, we consider truncated octahedra of 586 atoms in which the shell has a thickness of 2 atomic layers, which corresponds to 140 and 446 atoms in the core and in the shell, respectively (see Fig. 1). Specifically, the surface is made of 272 atoms and the subsurface of 174 atoms. For each AB bimetallic system, both A@B and B@A initial configurations are considered, which correspond to the two different compositions A 140 B 446 and A 446 B 140 . For AuCu, in which there is a large lattice mismatch, we consider also an icosahedral structure of 561 atoms, with a shell of two layers, corresponding to 147 and 414 atoms in the core and in the shell, respectively. In this case, the surface is made of 252 atoms and the subsurface of 162 atoms. Also in this case, both core@shell types are considered, namely Au@Cu at composition Au 147 Cu 414 and Cu@Au at composition Au 414 Cu 147 . The icosahedral structure is considered because previous simulations of phase-separating systems with lattice mismatch have shown that the kinetics of the approach to equilibrium depend on the nanoparticle shape; 48 here we want to check whether this effect is also present in miscible systems.

MC simulations are performed in the canonical ensemble (constant temperature). Atomic displacements and exchanges between two atoms of different species are proposed and accepted according to a Metropolis sampling, 49 which insures to reach a Boltzmann distribution of the chemical configurations at equi-librium and at a given temperature. Atomic displacements are randomly proposed inside a sphere centered on the atomic position of the randomly selected atom to move. The maximum displacement amplitude varies with temperature, typically around 0.01 √ T d, d being the lattice parameter in Angstroms, which means from 0.8 Å at room temperature to 1.2 Å at 600 K. The number of atoms of each element remains constant in the cluster. Equilibrium configurations are determined at different temperatures, by slowly increasing or decreasing the temperature, typically 20 K by 20 K each 3000 macrosteps. Averages to characterize the equilibrium configurations are performed after 1000 macrosteps and integrated over 2000 macrosteps. Each macrostep consists of proposing either one displacement or one chemical exchange randomly to any atom of the cluster. We propose more displacements than exchanges. If M steps is the number of macrosteps, n dep and n ex the numbers of displacements and chemical exchanges per atom, the number of microsteps N steps is equal to:

N steps = M steps N atom n dep + n ex 2 . ( 1
)
We take n dep =10 and n ex =1. The total number of atoms in the cluster is N atom = 586 or 561, and therefore the number of microsteps is around 10 millions. We note that, at variance with MD simulations, our MC simulations are only able to equilibrate chemical ordering (including local relaxations) within a given structural motif, but they are not able to catch shape transformations.

Results

In the following, the approach to equilibrium chemical ordering is monitored by calculating the number of mixed nearest-neighbour bonds, and the number of surface and subsurface atoms of the minority component. Structural transformations are singled out by means of the Common Neighbour Analysis signatures, 50 as explained in Ref. 51

AgAu

In AgAu, the evolution towards intermixing takes place within the initial fcc motif without relevant shape changes. Only some surface rearrangements and the formation/disappearance of stacking faults are observed during the simulations. Interdiffusion takes place on average in an isotropic way. As the simulation temperature increases, the MD final configurations get closer and closer to the equilibrium chemical ordering, as shown by the comparison between MD and MC data for mixed nearest-neighbour bonds, and for the number of minority surface and subsurface atoms (see Fig. 2). Here, MD data are obtained by averaging the quantities over the last µs of the simulations.

On our MD time scale of 10 µs, an almost perfect equilibration is achieved at T = 675 K and T = 700 K for Ag 140 Au 446 and Ag 446 Au 140 , respectively, whereas for temperatures below 600 K interdiffusion is negligible. These results indicate rather similar interdiffusion rates for both compositions. We note that, as expected, the data in Fig. 2(b-c) show that Au and Ag atoms have a certain preference for subsurface and surface sites, respectively.

PtPd

The PtPd system is characterized on average by stronger cohesion and by considerably higher melting temperatures than both AgAu and AuCu, 34,[START_REF] Kittel | Introduction to Solid State Physics[END_REF] especially on the Pt-rich side. For this reason, we expect that diffusion processes are activated at higher temperatures than in AgAu and AuCu. As a consequence, the temperature ranges in which we simulate our systems are higher, up to 900 K for Pt 140 Pd 446 and to 1050 K for Pt 446 Pd 140 .

Equilibrium surface enrichment in Pd is found in our model and in other atomistic models, 25,52 and it is supported by the results of experiments and DFT calculations. 21,53 Our model also predicts subsurface enrichment in Pt, 25 in agreement with results in the literature. 54 As regards the evolution of the nanoparticle shapes, our simulations never show transformations from the fcc motif to decahedral (Dh) or Ih motifs. This is in agreement with the experimental evidence, since Dh and Ih structures are quite rarely observed in pure Pt 6 and pure Pd 55 nanoparticles, and in their nanoalloys. 25,56 In our simulations, only the formation of defects, such as islands on stacking fault sites 6 and twin planes, is observed.

If temperature is sufficiently high, the evolution of chemical ordering is quite significant, and, in the case of Pt 140 Pd 446 , it takes place by a somewhat unexpected two-stage process. This process is shown in Fig. 3, which reports (a-c) data and (d) snapshots of the evolution in a representative simulation at T = 900 K.

In the first stage of the evolution, which takes place in the interval 10-40 ns in our three simulations at 900 K, the Pt core does not change its shape, but shifts from a central to an off-center position, in which the geometric center of the Pt core is displaced by about 3.5 Å from the geometric center of the whole nanoparticle (see Fig. 3(c)). In this off-center position, some facets of the Pt core occupy the subsurface layer, i.e. they are covered by a Pdskin. 57,58 Correspondingly, the number of Pt-Pd bonds does not change at all, but the number of subsurface Pt atoms steadily increases (see Fig. 3(a,b)). This first transformation is accompanied by a relatively modest energy gain of about 5 eV, but the structure still remains quite far from the equilibrium chemical ordering.

The off-center displacement of the Pt core is caused exclusively by the motion of Pd atoms around it, to reach a conformation of the shell that allows a better rearrangement of Pd atoms around the Pt core, because of the freedom of surface Pd atoms to relax their positions.

In the second stage, which takes place gradually from about 100 ns onwards, we observe interdiffusion of Pt and Pd atoms, which finally leads to an almost complete dissolution of the Pt core into the Pd matrix. The number of Pt-Pd bonds strongly increases, together with the number of subsurface Pt atoms, and the geometric center of the Pt atoms finally becomes close to that of the whole nanoparticle (see again Fig. 3(a-c)). A few Pt atoms finally appear in the surface layer. The energy gain in the second stage is more substantial, of about 15 eV.

The whole evolution of the Pt core can be observed in Fig. 3(d).

At lower temperatures, the kinetics are slower and therefore the simulations reproduce only a part of the evolution observed at T = 900 K. Completion of the first stage may take about 1 µs and several µs at T = 800 and 750 K, respectively, while the second stage only just begins. At T = 700 K, even the first stage is not completed within the 10 µs time scale.

Pt@Pd and (PtPd)@Pd nanoparticles with off-center cores have been observed in several experiments. 15,[17][18][19]25,43 In these experiments, the nanoparticles have been grown in isotropic environments, so that the cause of the symmetry breaking leading to the off-center cores is not obvious. The mechanism revealed by our simulations could explain why these structures form, along with their long-lasting metastability.

In Pt 446 Pd 140 , the simulations show a progressive dissolution of the initial Pd core into the Pt matrix, which takes place on average in an isotropic way. In Fig. 4 we show (a-c) data and (d) snapshots of the evolution in a representative simulation at T = 1050 K. Pd atoms are able to move towards the nanoparticle surface, and, after a few ten ns, they begin to appear at the surface. At the end of the simulation, the majority of Pd atoms has reached the surface (see Fig. 4(b)). During this process, the energy of the nanoparticle progressively decreases. This kind of behaviour is very similar to the one observed in all simulations of AgAu, so that the pathway shown in Fig. 4(d) is qualitatively representative of the evolution of both Ag@Au and Au@Ag structures.

The number of Pd atoms in the subsurface is always small (see Fig. 4(b)), indicating that their diffusion from the subsurface to the surface is relatively quick. At variance with the previous case of Pt 140 Pd 446 , there is no indication of a significant displacement of the core to off-center positions, as the distance between the geometric center of the Pd atoms and the geometric center of the whole nanoparticle oscillates during the simulation, and never exceeds 1.6 Å (see 4(c)). At lower temperatures the evolution is slower but of the same type as at T = 1050 K. Now we check whether the evolution of the nanoparticles during the MD simulations has brought them to the equilibrium chemical ordering. As shown in Ref., 43 in PtPd the equilibration of chemical ordering is much slower than that of nanoparticle shape, so that it is not warranted that it can be obtained on our time scale of 10 µs. In Fig. 5 we report the temperature dependent behaviour of the number of mixed nearest-neighbour bonds, and of the number of minority surface and subsurface atoms. Data in Fig. 5 clearly show that at the highest temperatures (900 K for Pt 140 Pd 446 and 1050 K for Pt 446 Pd 140 ) the chemical ordering obtained in the MD simulations is quite close to equilibrium, while it becomes progressively farther from equilibrium at lower temperatures.

AuCu

As explained in Section 2, the AuCu system exhibits relatively large lattice mismatch, therefore we may expect a different equilibration kinetics of chemical ordering in TO and Ih structures. 48 However, as we will see below, this will not be the only difference in the evolution starting from these structures.

Au 414 Cu 147

For Au 414 Cu 147 the initial structure is the Cu@Au Ih shown in Fig. 1(c-d). This is indeed a rather stable structure, since it evolves in the MD simulations by essentially keeping the Ih shape (with the formation of a few surface defects, especially at the highest simulation temperature). Therefore a direct comparison with MC data is straightforward in this case.

In Fig. 6 we report the number of mixed nearest-neighbour Au-Cu bonds and the numbers of Cu surface and subsurface atoms. Our MD simulations on the scale of 10 µs show a significant increase of intermixing for T ≥ 700 K. In fact, the number of mixed bonds increases from the value 408 of the perfect Cu@Au structure to 600 and more. This is mainly due to the displacement of the Cu atoms from the core to the subsurface layer, which corresponds to the reverse displacement of the Au atoms. On the other hand, the number of Cu atoms in the surface layer remains very limited.

The comparison between MD and MC data shows that MD simulations are not able to fully reach the equilibrium chemical ordering, even at the highest MD simulation temperature of 750 K. Note that for T > 750 K the structure enters the melting range.

Au 446 Cu 140

For Au 446 Cu 140 , the initial structure is the Cu@Au TO of Fig. 1(ab). The evolution of this structure is very different from that of the Ih Au 414 Cu 147 . In fact, for T ≥ 550 K the structure transforms into an Ih shape at some stage of the simulation in most cases. This happens at shorter and shorter times by increasing the temperature: a few µs at 550 K, ∼ 10 2 ns at 600 K and ∼ 10 ns at 650 K. The transformation is due to the superior energetic stability of the Ih motif for this composition. At 500 and 525 K (for which we have made only one simulation per temperature), and in one of the three simulations at 550 K, the structures stay within the TO motif till the end of the simulation.

In the following, we analyze whether the evolution of the chemical ordering depends on the shape of the nanoparticle.

First, we notice that in the simulations starting from the TO motif the evolution towards intermixing is much faster than in the simulations starting from the Au 414 Cu 147 icosahedron of section 3.3.1. This is evident in the range 500-600 K, where in Au 414 Cu 147 the number of mixed bonds stays essentially constant up to the end of the simulation (see Fig. 6(a)), while in Au 446 Cu 140 the number of mixed bonds almost doubles in 10 µs (see Fig. 7). This is a clear indication of the slower approach to equilibrium of chemical ordering in Cu@Au Ih than in Cu@Au fcc structures.

A striking confirmation of this fact is found in Fig. 7(a), in which the number of mixed bonds is plotted as a function of time in two simulations of Au 446 Cu 140 at 550 K. In one of these simulations, the cluster keeps the fcc structure till the end, while in the other simulation, a TO→Ih transformation takes place at t ≃ 4.7 µs. Once the transformation is accomplished, the evolution of chemical ordering essentially stops, with the number of mixed bonds keeping a constant value.

The slower diffusion of Cu atoms from the core of the Ih is due to the compression of inner sites in that structure. 59 The displacement of the small Cu atoms from the central part of the Ih, and, correspondingly, the displacement of the large Au atoms in their place, cause an increase of stress in the structure that partially counterbalances the driving force towards intermixing of the two metals. As a result, interdiffusion is more difficult in the Ih than in the fcc structures.

The blocking of chemical ordering evolution in Ih structures has some unexpected consequences. With increasing temperature, the TO→Ih transformation takes places more and more rapidly, so that the fast evolution of chemical ordering is mostly limited to the ever shorter time intervals of persistence of the fcc structure, and it is nearly blocked afterwards. Therefore, the increase of temperature does not produce a faster approach to equilibrium chemical ordering, but almost the opposite (see Fig. 7(b)). This is a quite surprising result of the interplay between interdiffusion and shape changes in determining the kinetics of approach to equilibrium. In Ih Au 147 Cu 414 (Fig. 8) one half of the structure is heavily distorted at the very beginning of the evolution (Fig. 8(b)), while the other half keeps its Ih shape. Immediately after (Fig. 8(c)), several Au atoms are ejected into the surface layer, but only in the distorted half, while no Au atoms appear on the surface of the Ih half. This is followed by a stage in which the distorted half becomes gradually less disordered (Fig. 8(d)), leading to the formation of a highly defective Ih, which gradually evolves into a multidecahedron 60,61 (not shown in the figure), and then to a Dh by mechanisms similar to those described in Ref. 61 In the evolution, transitions back and forth from decahedra to bidecahedra are frequently observed. Only in one simulation the defective Ih structure evolves back to a perfect Ih.

While the initial ejection of Au atoms to the surface is very fast, once the structure returns back to a more ordered shape, diffusion of Au becomes much slower.

At the end of the simulations (i.e. at t = 10 µs) at 600 K, about half of Au atoms is either in the surface or in the subsurface layers. In the simulations at T = 650 and 700 K, the observed evolution mechanisms is of the same type, but the final numbers of subsurface and surface Au atoms is larger.

In TO Au 140 Cu 446 (Fig. 9), the initial evolution leads to liquidlike structures, isotropically disordered on all sides (Fig. 9(b)). Correspondingly, the ejection of Au atoms to the surface layer is not one-sided as in Au 147 Cu 414 , but isotropic (Fig. 9(c)). The transition to liquid-like structures has been observed in previous simulations of phase-separating AuCo and AgNi nanoalloys evolving from intermixed configurations. 48 The liquid-like structures then transform back to solid structures (Fig. 9(d)), that are in all cases imperfect Ih, which then relatively quickly evolve into multidecahedra and finally into Dh (not shown in the figure). As in the previous case, transitions back and forth from decahedra to bidecahedra are frequently observed.

Conclusions

The evolution of AgAu, PtPd and AuCu from core-shell configurations towards intermixing occurs through quite different pathways.

In AgAu and PtPd, where lattice mismatch is negligible and small, respectively, the evolution takes place within the initial structural motif, which is the fcc truncated octahedron. Structural defects such as stacking faults are often formed, but the final nanoparticle shapes resemble the initial ones.

However, evolution of chemical ordering takes place by different pathways in Ag@Au, Au@Ag and Pd@Pt on one side, and in Pt@Pd on the other side.

In Ag@Au, Au@Ag and Pd@Pt, the core atoms exchange with the shell atoms to produce an isotropic diffusion by which intermixing gradually increases. As expected on the basis of cohesive energies, diffusion is faster in AgAu than in PdPt, so that in the latter system the typical onset temperatures for interdiffusion are significantly higher.

In Pt@Pd, the evolution of chemical ordering takes place by two steps. Shell atoms are much more mobile than core atoms, also because of the much lower cohesion of Pd compared to Pt. These shell atoms gradually rearrange in such a way that the shell becomes asymmetric and the Pt core is displaced to a subsurface position, which, according to our model, is energetically more favorable than the symmetrically centered position. These off-center core positions are however metastable, so that they evolve at a later stage into intermixed configurations, that are initially somewhat asymmetric, and then progressively become symmetric. Pt@Pd nanoparticles with off-center cores have been observed in several experiments, 15,[17][18][19]25,43 which support the long-lifetime metastability of these configurations.

The AuCu system is characterized by a large lattice mismatch. At equilibrium, the larger Au atoms tend to enrich the surface, whereas Cu atoms enrich the subsurface layer, and in icosahedra, also the central part of the nanoparticle, where they can decrease the stress of the structure.

In Au 414 Cu 147 and Au 446 Cu 140 , icosahedral shapes are energetically more favorable than truncated octahedra, even for size 586 which is a geometric magic size for the TO. The initial truncated octahedral Cu@Au shapes therefore tend to transform into icosahedra, in which diffusion of Cu atoms from the core to the shell (and correspondingly of Au atoms from the shell to the core) is almost stuck. The TO→Ih shape transformation, and the corresponding stop of interdiffusion, takes place on shorter and shorter time scales as temperature increases. As a consequence, one finds a quite counterintuitive result -the approach to equilibrium chemical ordering is not accelerated by the temperature increase.

In Au 147 Cu 414 and Au 140 Cu 446 the initial Au@Cu structures present very high compression in the core, so that they evolve very quickly into disordered shapes. During the disordering process, several Au atoms are ejected to the nanoparticle surface to release the internal stress. In truncated octahedral Au 140 Cu 446 , the disordered structures are isotropic and liquid-like. In icosa-hedral Au 147 Cu 414 only half of the structure becomes disordered, and Au atoms are ejected only through the disordered part. In all cases, the nanoparticles eventually evolve into more ordered shapes, which are mostly decahedral. After this stage, the diffusion of Au atoms to the surface is considerably slowed down.

In conclusion, the evolution of these nanoparticles from initial core@shell configurations to their equilibrium intermixed chemical ordering arises from a complex interplay between interdiffusion of atoms and shape rearrangements, whose effects are especially exemplified by the highly non-trivial evolution pathways of Pt@Pd, Cu@Au and Au@Cu structures.

Fig. 1 (

 1 Fig.1 (a-b) Initial truncated octahedral structure of 586 atoms with core@shell chemical ordering: (a) shows its surface, whereas (b) shows a cross section. (c-d) Initial icosahedral structure of 561 atoms with core@shell chemical ordering: (c) shows its surface, whereas (d) shows a cross section.

Fig. 2

 2 Fig. 2 Simulation results for Ag 140 Au 446 and Ag 446 Au 140 . (a) Comparison between the number of Ag-Au nearest neighbour bonds at equilibrium (MC data) and at the end of the MD simulations. The MD data are averaged over the last µs of the simulations. (b) Comparison between equilibrium MC and MD data for the number of Ag surface and subsurface atoms in Ag 140 Au 446 . (c) Comparison between equilibrium MC and MD data for the number of Au surface and subsurface atoms in Ag 446 Au 140 .

Fig. 3

 3 Fig. 3 Evolution of truncated octahedral Pt 140 Pd 446 from a Pt@Pd configuration in a simulation at T = 900 K. Time evolution of (a) number of Pt-Pd nearest-neighbour bonds, (b) number of Pt surface (red) and subsurface (blue) atoms and (c) distance between the geometric center of Pt atoms alone and geometric center of the whole nanoparticle. (d) Representative snapshots from the simulation at different times. Pt and Pd atoms are coloured in grey and blue, respectively. Pd atoms are represented as small spheres to show the evolution of the Pt core.

Fig. 4

 4 Fig. 4 Evolution of truncated octahedral Pt 446 Pd 140 from a Pd@Pt configuration in a simulation at T = 1050 K. Time evolution of (a) number of Pt-Pd nearest-neighbour bonds, (b) number of Pd surface (red) and subsurface (blue) atoms and (c) distance between the geometric center of Pd atoms alone and geometric center of the whole nanoparticle. Note that the distances in (c) are much smaller than those in the corresponding Pt@Pd case (Fig. 3(c)) (d) Representative snapshots from the simulation at different times. Pt and Pd atoms are coloured in grey and blue, respectively. Pt atoms are represented as small spheres to show the evolution of the Pd core.

Fig. 5 (

 5 Fig. 5 (a) Number of mixed bonds in Pt 140 Pd 446 and Pt 446 Pd 140 . (b) Number of surface and subsurface Pt atoms in Pt 140 Pd 446 . (c) Number of surface and subsurface Pd atoms in Pt 446 Pd 140 . Equilibrium data according from MC simulations (small symbols) are compared to the MD data (big symbols) for the same quantities. The MD data are averaged over the last µs of the simulations.

Fig. 6

 6 Fig. 6 Simulation results for the Au 414 Cu 147 Ih structure. (a) Comparison between the number of Au-Cu nearest neighbour bonds at equilibrium (MC data) and at the end of the MD simulations. (b) Comparison between equilibrium MC and MD data for the number of surface and subsurface atoms. The MD data are averaged over the last µs of the simulations.

Fig. 7 (

 7 Fig. 7 (a) Time dependence of the number of Au-Cu bonds in two simulations starting from a Cu@Au TO of composition Au 446 Cu 140 . Simulation temperature is 550 K. In the first simulation (red curve) the structure remains in the TO motif till the end, while in the second simulation (blue curve) a TO→Ih transformation takes place between 4 and 5 µs. The black arrow indicates the moment at which the transformation occurs, which corresponds to a meaningful change in the time evolution of the mixed bonds. (b) Final number (averaged over the last µs of the simulation) of nearest neighbour Au-Cu bonds. Red squares correspond to simulations in which the structure remains in the TO motif, whereas blue diamonds correspond to simulations in which the TO→Ih transformation takes place at some stage. Note that more than 1000 Au-Cu nearestneighbour bonds are expected at equilibrium (see Fig.6(a)), a value which is significantly larger than those of the MD simulations.

3. 3 . 3

 33 Au 147 Cu 414 and Au 140 Cu 446 In both Au 147 Cu 414 and Au 140 Cu 446 the evolution of the initial Au@Cu structure is dominated by fast shape changes. These shape changes are caused by the strong positive pressure in the larger Au core atoms, which is quickly released by distortions of the nanoparticle shape. Even though the final structure is Dh for both Au 147 Cu 414 and Au 140 Cu 446 , the evolution pathways are quite different, especially in the first part of the simulations. Typical evolution sequences of the first part of simulations at T = 600 K are shown in Figs. 8 and 9.

Fig. 8

 8 Fig.8Shapshots from the initial part of a simulation of Au 147 Cu 414 at T = 600 K. In the top row, the cluster surface is shown, while in the bottom row, Cu atoms (brownish) are displayed as small spheres to show the structure of the Au core (in yellow).

Fig. 9

 9 Fig. 9 Shapshots from the initial part of a simulation of Au 140 Cu 446 at T = 600 K. In the top row, the cluster surface is shown, while in the bottom row, cross sections are given to show the degree of intermixing. Cu and Au atoms are coloured in brownish and yellow, respectively.

[START_REF] Ferrando | Structure and Properties of Nanoalloys[END_REF][START_REF] Baletto | [END_REF][3][4][5][6][7][8][9][10]

Acknowledgements

The authors acknowledge networking support from the International Research Network Nanoalloys of CNRS. DN and RF acknowledge financial support from the project "Understanding and Tuning FRiction through nanOstructure Manipulation (UT-FROM)" (grant 20178PZCB5), funded by MIUR within the program "Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2017", and from the Progetto di Eccellenza of the Physics Department of the University of Genoa.

Notes and references

Author Contributions

DN performed and analyzed the MD simulations. CM performed and analyzed the MC simulations. RF assisted in the analysis of the simulations and supervised the work. All authors contributed to the drafting of the paper.

Conflicts of interest

There are no conflicts to declare.


Guillaume Thouvenin

Blandine Prevost

Harriet Corvol
email: harriet.corvol@aphp.fr

The omicron wave modifies the COVID-19 paradigm in children with cystic fibrosis

Keywords: COVID-19, SARS-CoV-2, omicron variant, children, cystic fibrosis

Vaccination" by Rostad et al [START_REF] Rostad | Functional antibody responses to SARS-CoV-2 variants in children with COVID-19, MIS-C, and after two doses of BNT162b2 vaccination[END_REF]. The authors show in children that the BNT162b2 COVID-19 vaccine elicits higher neutralizing antibody responses than the infection itself with differences among the various SARS-CoV-2 variants.

The incidence of COVID-19 worldwide has been far lower in children than in adults until the appearance of the variant of concern B. 1.1.529 (Omicron). Omicron has been shown to cause a dramatic increase in pediatric infections and hospitalizations in comparison with the previous variants [START_REF] Taytard | More on BNT162b2 Covid-19 Vaccine in Children 5 to 11 Years of Age[END_REF][START_REF] Taytard | SARS-CoV-2 B.1.1.529 (Omicron) Variant Causes an Unprecedented Surge in Children Hospitalizations and Distinct Clinical Presentation Compared to the SARS-CoV-2 B.1.617.2 (Delta) Variant[END_REF]. The higher infectivity of this Omicron variant has been attributed to mutations in the spike glycoprotein-binding human ACE2, resulting in increased infectivity of nasal epithelial cells and ACE2-positive cells [START_REF] Viana | Rapid epidemic expansion of the SARS-CoV-2 Omicron variant in southern Africa[END_REF]. These alterations in virus conformation influence antibody neutralization and facilitate viral immune escape [START_REF] Viana | Rapid epidemic expansion of the SARS-CoV-2 Omicron variant in southern Africa[END_REF]. Although more contagious, the Omicron variant was shown to lead to less severe forms of COVID-19 [START_REF] Maslo | Characteristics and Outcomes of Hospitalized Patients in South Africa During the COVID-19 Omicron Wave Compared With Previous Waves[END_REF]. Although this was partly attributed to COVID-19 vaccines in adults, similar milder severity was described in children under 5 years old for whom no vaccine was available [START_REF] Wang | Incidence Rates and Clinical Outcomes of SARS-CoV-2 Infection With the Omicron and Delta Variants in Children Younger Than 5 Years in the US[END_REF].

During the first year of the pandemic, the incidence of SARS-CoV-2 infection in people with cystic fibrosis (pwCF) was shown to be low and far less than that expected in comparison with the general population [START_REF] Corvol | Cumulative Incidence and Risk Factors for Severe COVID-19 in French People with Cystic Fibrosis. Clinical infectious diseases : an official publication of the Infectious Diseases Society of America[END_REF][START_REF] Carr | Factors associated with clinical progression to severe COVID-19 in people with cystic fibrosis: A global observational study[END_REF]. Hypotheses were that pwCF use barriers such as wearing masks, frequent hand washing and social distancing in order to limit exposure and avoid infection. An international study during the first COVID wave in children with CF described a low incidence of infections that led to mild illness, especially in children with non-severe pre- [9]. In order to study the impact of the Omicron variant on children with CF, we looked at what is happening in our pediatric CF center since the surge of the Omicron variant. This observational study was approved by the local ethics committee of our institution, which waived the need for patients' consent (Study PED_COVID N°20200717191204).

A C C E P T E D M A N U S C R I P T existing lung disease
Seventy-six children with CF are currently followed in the pediatric CF center of the University Hospital Trousseau, Assistance Publique Hôpitaux de Paris (APHP) Paris, France.

Before the Omicron wave (2020-2021), only 7 (9%) children had been identified as infected by SARS-CoV-2 in our center; all remained asymptomatic and were diagnosed by a systematic assessment of SARS-CoV-2 serology (Table ). During the Omicron wave, 24 (32%) children were identified as infected from January to July 2022, 2 of whom were re-infections. Four children remained asymptomatic, all having received 2 doses of the BNT162b2 COVID-19 vaccine before the infection. Among the 24 children, 16 were older than 5 years, and 11 had received at least one dose of the vaccine. Symptoms at infection onset were similar to those described in the general population (Table ). Five children were hospitalized for COVID-19, and 2 required oxygen but not intensive care. This report emphasizes the high infection rate of the Omicron variant, even in a CF population used to applying barrier measures to avoid infections. Moreover, this surge of infections was unexpected given the previous low incidence of COVID-19 observed in pwCF [START_REF] Corvol | Cumulative Incidence and Risk Factors for Severe COVID-19 in French People with Cystic Fibrosis. Clinical infectious diseases : an official publication of the Infectious Diseases Society of America[END_REF][START_REF] Carr | Factors associated with clinical progression to severe COVID-19 in people with cystic fibrosis: A global observational study[END_REF]. Nevertheless, children with CF who were vaccinated developed mild forms of COVID-19 and/or remained asymptomatic. Interestingly, all asymptomatic CF patients during the Omicron wave were children who were vaccinated. This report supports efforts to expand vaccination against COVID-19 in childrenfor whom the BNT162b2 COVID-19 vaccine has been shown to be safe and to elicit high neutralizing antibody response [START_REF] Rostad | Functional antibody responses to SARS-CoV-2 variants in children with COVID-19, MIS-C, and after two doses of BNT162b2 vaccination[END_REF]10].

A C C E P T E D M A N U S C R I P T A C C E P T E D M A N U S C R I P T 9. Bain R, Cosgriff R,

Table. Children with cystic fibrosis diagnosed as infected by SARS-CoV-2 before and during the Omicron wave in a pediatric French CF center

A C C E P T E D M A N U S C R I P T

2 .

 2 Centre de Recherche Saint-Antoine (CRSA), Sorbonne Université, Paris 75012, France. *Corresponding author: Harriet Corvol, MD Pediatric Respiratory Department and CF Center, Hôpital Trousseau 26 avenue du Dr Netter, 75012 Paris, France Tel: (33) 1 44 73 67 18 Email: harriet.corvol@aphp.fr Running head: Omicron infection in children with cystic fibrosis We have read with interest the article "Functional Antibody Responses to Severe Acute Respiratory Syndrome Coronavirus 2 Variants in Children With Coronavirus Disease 2019, Multisystem Inflammatory Syndrome in Children, and After Two Doses of BNT162b2

  Zampoli M, et al. Clinical characteristics of SARS-CoV-2 infection in children with cystic fibrosis: An international observational study. J Cyst Fibros 2021; 20:25-30. 10. Walter EB, Talaat KR, Sabharwal C, et al. Evaluation of the BNT162b2 Covid-19 Vaccine in Children 5 to 11 Years of Age. N Engl J Med 2022; 386:35-46.

1 2 3

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Table . Children with cystic fibrosis diagnosed as infected by SARS-CoV-2 before and 1 during the Omicron wave in a pediatric French CF center 2 3 Before the Omicron Wave (2020-2021) During the Omicron Wave (2022)

 .

		1	Hospitalization duration (days): median (range) ICMJE DISCLOSURE FORM	0	5 (4;14)
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	Oxygen supplementation (n, %) Date: July 20, 2022 3 Your Name: Guillaume THOUVENIN 4		0	2 (11%)
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	In	8	Patients (n, % among the 76 children with CF followed in the center) Clinical characteristics Age (years): median (range) Age class (n) (<5 yrs / 5-11 yrs / > 11 yrs) Male (n, %) SARS-CoV-2 infection diagnostic A N U 7 (9%) 6.8 (4.6;14.1) 2/3/2 6 (86%) A N U S C R I P T 24 (32%) 9.7 (0.3;18) 11 (46%) 8/5/11 S C R I P T
			Positive systematic serology (n, %)	M M	7 (100%)	3 (12.5%)
		Positive PCR and/or antigenic test in nasopharyngeal swabs (n, %) Asymptomatic (n, %) Clinical presentation at infection onset Fever (n, %) Fatigue (n, %) Altered cough (n, %) Rhinorrhea (n, %) A C C E P T E D A C C E P T E D	0 7 (100%) 0 0 0 0	24 (100%) 4 (17%) 14 (58%) 13 (54%) 9 (38%) 10 (42%)
			Dyspnea (n, %)		0	5 (21%)
			Hospitalization (n, %)		0	4 (17%)

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