Vincent Goudard
email: goudard@lam.jussieu.fr

JOHN, THE SEMI-CONDUCTOR: A TOOL FOR COMPROVISATION

This article presents "John", an open-source software designed to help collective free improvisation. It provides generated screen-scores running on distributed, reactive web-browsers. The musicians can then concurrently edit the scores in their own browser. John is used by ONE, a septet playing improvised electro-acoustic music with digital musical instruments (DMI). One of the original features of John is that its design takes care of leaving the musician's attention as free as possible.

Firstly, a quick review of the context of screen-based scores will help situate this research in the history of contemporary music notation. Then I will trace back how improvisation sessions led to John's particular "notational perspective". A brief description of the software will precede a discussion about the various aspects guiding its design.

INTRODUCTION 1.1 From traditional to graphical score

The score is generally considered as a tool for the composer to create a musical work for an interpreter. It describes the expected sonic result and prescribes the gestures to perform [START_REF] Bhagwati | Notational Perspective and Comprovisation[END_REF] . It thus stands as mnemonic mean to keep track of what is independent from the context of the performance [START_REF] Bayle | Musique acousmatique : propositions[END_REF] and often, is assimilated to the artwork itself in Western musical tradition.

Scores fulfill yet many other functions. It allows in particular to transpose the musical time into a visual space, enabling the composer to arrange musical elements "out of time" in order to produce pieces that could not be conceived without this visual support [START_REF] Canonne | Improvisation Collective Libre et Processus de Création : Création et Créativité au Prisme de la Coordination[END_REF] .

If the Western notational system invented by Guido d'Arezzo in the 11 th century has continuously evolved, improving with new symbols and techniques until the early [START_REF] Bhagwati | Notational Perspective and Comprovisation[END_REF] Eric Maestri proposes the terms "phonographic" and "ergographic" to describe both these aspects [14]. [START_REF] Bayle | Musique acousmatique : propositions[END_REF] Acknowledging here that the interpretation belongs to the contextual. 20 th century, the technological and cultural revolutions that followed subverted both the means of production and the range of musical expression, now extended to noise and the whole sound spectrum.

We can notice the development of so-called "graphic scores" [START_REF] Clay | Inventing Malleable Scores: From Paper to Screen Based Scores[END_REF] in the middle of the 20 th century, that reflects this musical evolution for which the traditional notation is insufficient. For reasons that might seem opposite, the graphic score helped to push both the limits of what was possible to "fix" in a composition -by specifying it entirely on a synthesis system, and the limits of what it was conceivable to vary -the part entrusted to the performer's interpretation. The scores for Iannis Xenakis' Mycene Alpha and Earle Brown's December 1952 highlight both these directions (see Figure 1).

This apparent opposition between a totally fixed work and a work that is totally subject to the performers' creativity seems more like the outcome of complementary approaches that aimed at exploring the new sound and musical domains, in their manifestations as well as in their potentialities, whether reified or fantasized.

Within this continuum of possibilities between fixed work and free improvisation, that Sandeep Bhagwati called "comprovisation" in [1], various notational perspectives can be considered. The various purposes of musical representation hitherto integrated in the traditional score gain independence and take a variable importance, adapting to the musical work and the performance contexts. The score defines the playing field, which is not necessarily linear and which, thanks to the possibility of producing animated images in real time, is no longer necessarily fixed.

Screen Scores

The increasing availability of digital devices led to the development of several applications meant for the creation of scores on-screen. As Lindsay Vickery notes in [20]:

These developments suggest a trend, particularly amongst young composers whose practice has developed exclusively on computer, to take the logical step to present notated materials on screen. Cat Hope summarizes the main features offered by this new medium with the following terms in [10]: scrolling, permutative, transformative, generative and networking capabilities of the digital medium.

Using computer graphics for the purposes of musical representation seems a medium of choice to enrich the possibilities of writing graphic scores. Especially, the fluidity of adaptation of the virtual medium makes it possible to envisage multiple "views" of the same score according to the contexts for which it is intended. Thus the composition, the performance, or the analysis of a musical work do not necessarily require the same representations. In terms of musical performance, we can add a distinction between the interpretation of a score by a human and a machine, these two types of "interpreters" affording relatively different abilities. [START_REF] Couprie | EAnalysis: developing a sound-based music analytical tool[END_REF] A notable exception is the contribution of Georg Hajdu [9] who proposes the concept of "disposable music" to qualify musical forms "that rely on a lesser degree on fully notated scores, such as "comprovi-

In the same way that digital technologies have atomized the musical instrument by decoupling its various constituents (gestural controller, mapping, synthesis, etc. becoming modular), they have also atomized the score into its various functions, supporting composition, performance or analysis. It is then necessary to specify which use case is at play and Cat Hope defines for this purpose the term "screen-score" as the medium presented to the musicians for a performance in [11]:

Screen-scores are notated music compositions devised to be performed; and are not to be confused with visual representations of music or the musical interpretation of visual art.

The concept of screen-scores has been investigated in depth by several authors, composers and musicologists, (in papers by Winkler [18], Clay [3] or Lee [12]) who discussed the advantages and drawbacks of using digital technologies for musical representation, both in its technical aspects and in its musicological consequences. Lindsay Vickery offers a very detailed review in [17] of critical latencies allowing an instrumentalist to read musical material displayed in real time and provides advices on what the composer should pay attention to when composing with this medium.

These studies offer relevant and valuable descriptions to the composer who wishes to work with screen-scores. However, it seems that they can be supplemented by a different approach to the score than those considered in most of the literature, in which the point of view is often that of the composer. The design of a screen-score system is consequently polarized by the central importance of the score, itself considered as a prerequisite for musical performance, a situation that also reflects a strong tradition of Western classical music [START_REF] Couprie | EAnalysis: developing a sound-based music analytical tool[END_REF] .

In the case of ONE's performances (Figure 2), which are based on a practice of free improvisation devoid of prior composition, the focus moves towards the instrumentalist's side. The central element is not the score but the listening and understanding of sound and other musicians. The score (if it is still possible to call it so) often emerges after the improvisation sessions and its presence should not be at the expense of mutual attention. From this perspective, it is possible to envisage that the musician him/herself adapts the musical representation to his/her own needs, depending on the parts s/he has to play, her/his personal preferences, the various movements of the score, etc.

In the particular case where the instruments are digital and programmable, the use of a networked score system finally offers the possibility of delegating certain parameters of the instrument to an outsourced control supported by the score. In a situation of improvisation, the negotiation between this automated control and the choice of the musician implies a mediation that I will discuss later.

sation" or laptop performance". However, even as "disposable" as it is, the score plays here again a prior role to the performance and remains central to the attention, differing from our approach.

TENOR'18

Proceedings of the 4th International Conference on Technologies for Music Notation and Representation

Improvisation in ONE -birth of a notation

The seven musicians of ONE6 are all deeply involved in the field of computer music with varying specialities applying in the fields of instrumental practice, composition, instrument making, research in music sciences and education. All of us practice digital musical instruments of which we built the software parts and sometimes also the hardware parts, to some extent. At the origin of our collaboration, there was no other project than that of attempting the experiment of playing a sound-based music together with such heteroclite digital instruments, without grid, without music theory, without prior agreement on the form and content. Several improvisation sessions were opportunities to discover our sounds, our playing styles, our musical vocabulary. These moments of rehearsal were and foremost the occasion of anarchic performances, guided only by the thread of our listening, to confront, to merge, to burst, to collide spaces, objects, soundtracks, along with moments of discussion and adjustments of our musical setup.

These sessions were also subject to classic improvisation exercises: searching for timbral fusion and counterpoints, fugal passages among musicians, accompanying a soloist, working on the pianissimo nuances, or playing "in the style" of a piece we knew. Eventually, audio recordings allowed us to play back the sometimes long and uninterrupted improvisations to extract interesting ideas.

The issue of large musical movements appeared before ONE's first public concert. The lack of a score structuring the concert's duration led us to follow a narrative scenario inspired by a novel by Jules Verne. Thus, the concert consisted of a series of chapters, simply identified by intertitles in lieu of exotic and imaginary soundscapes to be explored.

Little by little, these experiences gave rise to the emergence of a more atomic musical vocabulary representing atmospheres and movements collectively defined, that we named "karmas" [START_REF] Favreau | L'acousmographe 3[END_REF] . The various moments of play and discussion brought us to the development of other conceptual objects that were partly implemented in the form of a software nicknamed "John, the semiconductor".

The origin of John's development is related to the desire to find a way to structure musical time in different movements within the perspective of freely improvised concerts of fairly long duration. Another motivation lies in the ability to vary the improvisations so as not to always repeat the same textures and formal structures such as sequences of ascending-descending cycles.

In addition, we were looking for ways to stimulate the exploration of unusual combinations and musical ideas pushing us out of our "comfort zone". The proposal to mathematically divide time into sequences to allow all possible ensembles of solo, duet, trio, up to the tutti, was the first impetus for the development of a score generator able to automatically produce such distributions.

As the opinions diverged within the band on the balance between rules and absence of rules, a key principle did find a ground of agreement: John is a semi-conductor. This means that scores created using John are just a proposition that each member of the group is free to follow or not, depending on the musical context that only takes shape during the very moment of the performance. Listening remains the primary rule of the game, prevailing over a blind follow-up of the score. In particular, the articulation between the different parts of the score, whether they are tiled or disjointed, or the act of playing when not supposed to, etc. is left to the appreciation of each musician.

This principle has the direct consequence of a streamlined design whose purpose is to allow each player to situate oneself within the score at a glance, without monopolizing her/his attention to the detriment of the other musicians. The goal is therefore very different from the one pursued in other screen-based musical notation systems such as those explored in works involving (extreme) sight-reading [8].

Essentially, John allows collective time management, whether during rehearsals, composition, or performances, providing a shared representation support. A brief description of the software to capture its outline will precede a discussion of the different aspects related to this group management.

individual. In the same way the musical interpretation of a karma (as we define it) is subject to the actions of the musicians and any accident, bifurcation with respect to the score will prevail on the musical evolution more than the score itself.

ABOUT JOHN

John relies on a client / server architecture, in which each musician is visualizing a client interface in a web browser, on which s/he can act. This interface comes in two parts, a score generator on the one hand and an interactive visualization of the score on the other hand.

Score generator

The score generator makes it possible to very quickly create musical propositions by specifying only global constraints:

• overall duration of the score;

• minimum and maximum number of players;

• minimum and maximum duration of blocks;

• a list of karmas that identify a particular mood according to a common vocabulary established by the musicians during improvised practice sessions; • nuances from pianississimo to fortississimo.

Once these constraints are specified, the score generator produces a random proposition that respects these conditions, that is composed of a sequence of time blocks associated with a karma and a nuance. This proposal can then be adjusted in the editing / viewing interface.

Interactive visualization

This interface represents blocks on a timeline. It consists of a reduced global view on one hand, giving a shared overview of the whole score, and a zoomed local view, located above the global view. On the global view is a playhead that is common and synchronous to all clients (in red on Figure 3), as well as a window (in blue on Figure 3) defining the time span displayed in the local view. This window is defined individually by each musician on their client and is typically ranging from ten seconds to a few minutes depending on the temporal granularity of the score and the preference of each.

All controls are accessible in all clients, so that anyone can edit the score: generating a new score, moving and changing the duration of the blocks and their content (karma and nuance), starting playback, changing the playback speed, moving the playhead to start at a given moment of the score. These changes will be immediately reported to all other John's clients.

The user can also define local parameters which will only affect her/his own client interface: the various tracks visibility, the duration of one's local view and the synchronization (or not) of one's local view to the reading cursor with the link toggle-button.

Implementation details

After a first version developed with Max 8 , the application was brought to reactive HTML5 using the Meteor framework [START_REF] Goudard | Mapping modulaire de processus polyphoniques[END_REF] . This allows collective editing on any platforms (including mobile platforms) connected to a LAN, via a simple web browser. The visualization was implemented using the D3.js library [START_REF]Disposable Music[END_REF] . Scores are saved in JSON format as a list of events with a unique identifier, a track index, a start time, a duration, and a number of properties such as karma and nuance. During playback, time and score events are sent as MP messages [9] over the network using OSC 11 .

JOHN IN PRACTICE

Generative composition

The score generator saved a lot of time during the rehearsals, giving us an immediate possible musical structure like an empty shell. As arbitrary as it is, its main function is to stimulate the musical performance with the most minimal prescription: play (or don't). Thus the proposals are often tried as they come before being adjusted collectively according to what members of the band find interesting or not. We can then evolve this musical structure, with apparently more efficiency than if we were to start out from nothing.

Distributing participation

The fact that John explicitly proposes a distribution of playing time among each musician has led to situations of performance that we would not necessarily have tried, especially in reduced configurations (solo and duet), each of us having a tendency to play too readily to actually leave room for these minimal configurations to settle.

Moreover, having "out of the game" moments makes it possible to better anticipate one's appearances. Indeed, digital musical instruments often have a "meta" dimension [START_REF] Hope | The DECIBEL Scoreplayer -A Digital Tool for Reading Graphic Notation[END_REF] and more generally a huge number of settings. These planned moments of rest make it possible to better manage the time we have to reach less accessible settings.

Tight synchronisation

At a micro-temporal level, synchronisation is impeded by the lack of idiomatic rules [START_REF] Lee | Real-Time Music Notation, Collaborative Improvisation, and Laptop Ensembles[END_REF] . In particular, the absence of pulse or metric system makes the synchronization among musicians ever more difficult as their number increases and often deprives freely improvised musical forms from clear and tight transitions in large ensembles.

The conductor, when there is one, provides accurate cues, beats, and potential directions for play. Beside the ethical issues raised by the role of a leader in an [START_REF] Freeman | Extreme sight-reading, mediated expression, and audience participation: Real-time music notation in live performance[END_REF] https://cycling74.com/ 9 http://meteor.com/ 10 https://d3js.org/ 11 Open Sound Control: http://opensoundcontrol.org [START_REF] Hope | The DECIBEL Scoreplayer -A Digital Tool for Reading Graphic Notation[END_REF] That is, it can be totally reconfigured during the performance to offer a whole other set of sounds, processes and playing modes. [START_REF] Lee | Real-Time Music Notation, Collaborative Improvisation, and Laptop Ensembles[END_REF] such as chord grids, time signature, scales, etc. improvisation band, raised by Canonne in [2], entrusting the conducting to a person14 remains limited by the fact that s/he can only act in the present, and that it requires the almost permanent attention of the musicians, to the detriment of the attention they could bring to their peers. In this respect, the representation offered by John condenses in a certain way the score and the conductor in a single visual medium. The animated score ("scrolling score" in our case) offers indeed visual cues that indicate the simultaneity of several musical events, and its scrolling under the playhead allows a precise synchronization among the musicians at transitions.

Visual support for musical landmarks

Despite the availability of analysis tools [START_REF] Magnusson | Algorithms as Scores: Coding Live Music[END_REF] and a certain lexicon to describe sound and musical objects in electroacoustic music [START_REF] Magnusson | Scoring with Code: Composing with algorithmic notation[END_REF] , there is no standard of prescriptive notation for digital musical instruments. The lack of a unanimous vocabulary, the singular nature of the instruments and the tremendous sound palette they provide can make it a nightmare to identify and discuss what has just been played during a long improvisation session (somehow failing here to use the word "rehearsal"). A minimal score such as that proposed by John facilitates this identification and allows to re-work specific moments after a long performance. The reduction that symbolic notation carries out on the complex sonic outcome of a performance allows everyone to quickly find one's way in the temporal space of an improvisation, faster than it would if we had to refer to the sound recording.

An ecology of attention

Free electroacoustic improvisation involves strong musicians' attention to other musicians, to their instrument and, obviously, to sound. In this respect, digital instruments often present the additional drawback, as compared to acoustic instruments, of capturing some of the visual attention due to the frequent presence of a screen, many interaction parameters, and an interface sometimes lacking tactile feedback or touch marks that would allow to access them without needing to look at them. Furthermore, digital musicians will often prepare their instrumentarium just prior to the performance with a chosen set of ad-hoc musical elements [START_REF] Mim | Les Unités Sémiotiques Temporelles -Éléments nouveaux d'analyse musicale[END_REF] (when not recoding the whole thing) which further complicates a perfect knowledge of the ergonomics of the instrument, which would do without the visual.

John's design has been driven by an economy of cognitive load for musicians. Being able to partly customize one's visualization interface thus does not mean to add more visual data to it, but to see only what is necessary for one to gain collective awareness.

A score for humans and for (digital) instruments

During the score playback, the server sends data to clients as events begin or end (Figure 4). This information can be used by the musician's instrument (according this DMI is connected to the network). But, as John is only a "semiconductor", it may as well be subject to the musician/client approval to allow some flexibility in the way the musician sticks to the score. Thus, it could have been devised that a specific karma recalls a corresponding preset of sounds in the musician's instrument, suitable for the karma's mood. But if the musician is still playing a previous other karma, s/he probably will not want this notification to automatically change the preset before s/he finishes one's current phrase. This "loose control" makes John's usage a little different from traditional sequencers.

Showing the score?

Being able to read the interactions among the musicians in improvisation performances can contribute to the performance overall appreciation. Yet with DMIs, the spatial and energy decoupling between the instrumentalist's gestures and the resulting sound energy and location (on a possibly remote loudspeaker) confuses this reading. Screen-scores systems allow to share the score display with the audience more easily than printed scores and could help in this situation with the risk however, that it may "detract from the dramatic performative aspects of the work" among other reasons suggested by Cat Hope in [11]. Although John's score was never shown directly to the audience for this very reason, it has been used to control visual effects and lightings, meant both for stage design purpose and for helping listening and understanding of the music [START_REF] Schaeffer | Traité des objets musicaux[END_REF] . [START_REF] Schaeffer | Traité des objets musicaux[END_REF] Examples include switching spotlights on musicians supposed to play, changing light hue according to the karmas, projecting aggregated sound waves as traces of the score, synching video, etc.

PERSPECTIVES

It has been acknowledged by the members of ONE that John was helping our creative process. However, there remains open issues like collective synchronization over rhythmic passages. Especially, anticipating a dynamic process is no trivial task and would probably require specific tools for that purpose, such as the animations proposed by Ryan Ross Smith in [19].

The concept of local and global view could probably be generalized to other shareable parameters. For example, being able to start a local playback in order to practice or prepare one's instrument on one's own. Similarly, it would be useful to work on another score than the ones loaded on others' clients. This de-synchronization raises however issues of versioning conflicts.

John's porting to a web technology is partly motivated by the possibility of future concerts involving a large number of musicians and where ever musician would be able to see his part with a simple web-browser. More developments will be needed to achieve such a performance, but there should not be technological locks.

Overall, computer-based scores give way to many possible interactions during performance time. Maybe the score should be considered as a collective instrument, which every musician and possibly the audience too, could play.

Figure 1 .

 1 Figure 1. Extracts from December 1952 by E. Brown (top) and Mycène Alpha by I. Xenakis (bottom).

Figure 2 .

 2 Figure 2. The members of ONE with their digital musical instruments.

Figure 3 .

 3 Figure 3. Snapshot of John's client interface.

Figure 4 .

 4 Figure 4. Receiving data in a Max instrument.

A notorious example is the rondeau "Ma fin est mon commencement" (14 th century) from Machaut in which the two voices are each other's retrograde.

… that is, using graphic signs other than the usual symbols of the conventional notation of notes on a staff.

Performance except: https://youtu.be/lBVNwGeTxFA

The relationship with this Indian concept is distant, but it does include an appealing meaning that echoes how we view them in performance: the set of actions represented by the karma influences the future of the

such as using Walter Thomson's Soundpainting or in a composition like John Zorn's Cobra.

Such as E-Analysis[START_REF] Couprie | EAnalysis: developing a sound-based music analytical tool[END_REF] or the GRM Acousmographe[START_REF] Favreau | L'acousmographe 3[END_REF].

In the work of Schaeffer[START_REF] Schaeffer | Traité des objets musicaux[END_REF], Bayle[START_REF] Bayle | Musique acousmatique : propositions[END_REF] or MIM[START_REF] Mim | Les Unités Sémiotiques Temporelles -Éléments nouveaux d'analyse musicale[END_REF] among others.

In an informal discussion, Thor Magnusson used the term "pregramming" for this particular work that precedes a concert.

Acknowledgments

This work was partly carried out within a doctoral program supported by the Collegium Musicae 19 . ONE is produced by Puce Muse 20 . Also, I would like to thank my colleagues from ONE for their valuable collaboration in the development of John : Laurence Bouckaert, Pierre Couprie, Hugues Genevois, Jean Haury, György Kurtág Jr. and Serge De Laubier.


Yang Fu

Gabriel Fodorean

Patrick Navard

Edith Peuvrel-Disdier

Study of the partial wetting morphology in PLA/PBAT/PA ternary blends: Case of composite droplets

Keywords: Ternary polymer blends, morphology, spreading coefficient, interfacial tension

The prediction of the morphology of ternary polymer blends requires a good knowledge of the values of the three interfacial tensions. We selected three polymers, either biobased or biodegradable, PA, PBAT and PLA and we accurately measured their interfacial tensions using the retraction method, varying the molar mass or inverting the phases. The following values of interfacial tensions were obtained:

= 3.3±0.7mN/m, = 5.6±0.3mN/m and = 3.0±0.4 mN/m. These values were used to calculate the spreading coefficients giving rise to two negative coefficients and one coefficient close to zero. Ternary blends with various compositions, two different levels of viscosity for the PBAT, different processing conditions were prepared. There was a very good agreement between the predictions of the spreading theory, when using the values of interfacial tensions in the right order of magnitude, and the observed morphologies, whatever the polymer serving as a matrix. When the PLA or PBAT was chosen as the matrix, the ternary blend morphology was composed of composite droplets, presenting a partial wetting morphology, dispersed in the polymer matrix. This morphology was observed whatever the composition, the viscosity level of the PBAT phase and the processing conditions. A further calculation of the free energy confirmed this morphology. The formation process of this semi-encapsulated morphology was observed during blending.

Introduction

Blending different polymers in order to obtain controlled supramolecular structures/morphologies able to provide improved properties has been studied and applied long ago. [START_REF] Paul | Polymer Blends[END_REF][START_REF] Martuscelli | Polymer Blends: Processing, Morphology, and Properties[END_REF][START_REF] Paul | Polymer blends: Formulation in Polymer blends: Formulation[END_REF][START_REF] Thomas | Characterization of Polymer Blends: Miscibility, Morphology and Interfaces[END_REF] Although several polymer pairs can be miscible [START_REF] Coleman | Specific Interactions and the Miscibility of Polymer Blends[END_REF] , most blends are formed by two, sometimes more, polymers which are phase separated in their fluid state. The obtained structures are then due to a combination of thermodynamic and kinetic aspects where the major parameters at stake are the interfacial tension between polymers (expressing the free energy barrier between them), the rheological properties of the individual polymers (mostly having an effect on the kinetics of morphology changes) and the processing conditions (controlling the morphology evolution and the final size). Binary blends can display a morphology composed of a matrix and a dispersed phase or a bi-continuous morphology.

Ternary blends can obviously display a much richer diversity of morphologies. Guo and co-workers [START_REF] Guo | [END_REF] were the first to use the expression of the free energy where they calculated (where stands for the interfacial area between the two phases, for their interfacial tension) for all possible morphologies of the same composition, allowing to predict the lowest free energy morphology at equilibrium. Another approach using the notion of spreading coefficient 7 ( ) was proposed by Hobbs and co-workers 8 and further developed by the group of Favis 9 considering the three spreading coefficients characterizing an A/B/C ternary blend:

Eq. 1

Four possible morphologies can be described by combining the different signs for the three spreading coefficients, as shown in Figure 1.

Figure 1: Four possible equilibrium morphologies for a ternary polymer blend, with a minor phase C and two major phases A and B, and their relations to the respective signs of the spreading coefficients, according to reference 9 .

The advantage of this approach is that the knowledge of the interfacial properties is enough to predict the morphology.

Favis and coworkers 10 also proposed to take into account the contribution of the phase elasticity in the interfacial tension under shear and to consider this dynamic interfacial tension in order to estimate the minimum free energy of the blend.

In order to test the reliability of the models, various ternary blends were investigated to change of the interfacial tension balance and to obtain the different morphologies. [11][12][13][14][15][16][17][18][19][20][21][22][23][24] The models derived from Guo and Hobbs have successfully predicted the morphologies in ternary blends in most situations 12,[24][25] where the large values of spreading coefficients or high contrast of free energy are the main factors that determine the type of morphology.

However, if the interfacial effect is weak (for example in particular in the case of partial wetting, Figure 1.a), these models may no longer provide a correct prediction. All factors which can play a role on the kinetics of the morphology development such as the viscosity, the elasticity, the compatibilization (reactive compatibilizers…), any reticulation process, the sequence of introduction may affect the obtained morphology. The viscosity ratio and the mixing parameters should better control the size of the domains.

A large attention has been devoted to the understanding of the physical origin and the characteristics of the core-shell morphology of composite droplets imbedded in another polymer matrix (Figures 1.b and 1.c). Studies have concerned the variety of structures which could be obtained in the composite droplets, 26 the determination of the droplet size, of the relative thickness of the shell and their relative variation, [26][27][28][29] their effect on the dynamic rheological behavior of the blend in comparison to the binary blend 14,30 and of course the relationship with the mechanical properties. 17,[20][21][22][23][31][32][33][34] More recently, a focus was given on partial wetting morphologies, 9,[35][36] where droplets of one polymer are located at the interface of the two other polymers (Figure 1.a), compared to a complete wetting of the interface by the third phase (Figure 1.d). The coarsening of these two types of morphologies in the case of co-continuous morphologies was investigated. [START_REF] Ravati | 38 Zolali AM and favis BD[END_REF] A recent paper reported on the use of partially wetting droplets to compatibilize and toughen co-continuous ternary blends. 38 Very few studies concern the mechanisms governing the evolution of the morphology. Reignier et al. 11 showed the coalescence of core-shell droplets with time. Valera et al. 13 showed the different steps leading to a core-shell morphology when the third polymer (dispersed phase) was introduced in the pre-mixed binary blend.

Interfacial tension thus plays a very important role in the control of the hierarchal morphology of ternary blends. This means that the measurement of this parameter is critical. Several methods have been proposed in order to measure the interfacial tension between two molten polymers. A possibility is to calculate it from surface tensions or solubility parameters. 39 Another method classically used was proposed by Wu 40 and relates the interfacial tension to the surface tension of two polymers and and to their polar and dispersive terms. The advantage of these two calculation methods is their apparent simplicity and the ease of measuring the needed parameters.

However, due to their poor accuracy, they can only give a rough estimation of interfacial tensions. 41 Another way is to balance the interfacial tension with another force which effect will be easy to measure, like in the thread breaking or drop retraction methods or methods based on the rheological response of the blend. 40,[42][43][44] The drop retraction method, used in this work, is based on the measurement of the kinetics of drop relaxation after the drop has been deformed by a flow in the form of an ellipsoid with axis L and D.

The deformability parameter of this ellipsoid is time dependent and defined as:

Eq. 4

Assuming that the only driving force for the drop retraction is the interfacial tension and in the case of a very small initial deformation, Taylor 45 predicted that the deformability parameter has a decreasing exponential form (Equation 5) characterized by a drop relaxation time  (Equation 6).

Eq. 5

Eq. 6

is the initial deformability parameter at t = 0 s of the considered relaxation process, p is the viscosity ratio between the dispersed phase and the matrix, is the radius of the drop at the end of relaxation procedure, is the viscosity of the matrix and is the interfacial tension. The first measurement of the interfacial tension using this method was performed by Luciani. 39 The limit of validity of the model was evidenced experimentally by Assighaou et al. 46 Measuring the interfacial tensions is not an easy task since the different methods are indirect, fraught with potential artefacts. As an example, selecting in the literature three polymer couples, it is possible to find a very wide range of interfacial tension values. For example, the interfacial tension of PMMA/PS is reported to be between 0.25 to 3.1 mN/m, 10,18,[47][48][START_REF] Elmendorp | A Study on Polymer Blending Microrheology[END_REF][START_REF] Friedrich | [END_REF][51][52][53] the one of PA66/PS between 6.8 and 20 mN/m 12,[54][55][56] and the one of PLA/PBAT between 0.5 and 22 mN/m. [57][58][59][60] It is not always easy to understand the reasons leading to such large discrepancies. The problem is that no prediction of blend morphology can be made if the measured value of the interfacial tension between the two polymers varies by a factor five to ten.

The aim of this work was thus to investigate the morphology of a ternary bio-based and biodegradable blends composed of poly(butylene adipate-co-terphthalate) (PBAT), polyamide (PA) and polylactide (PLA) of different compositions. The morphology prediction implied to measure with the best possible accuracy the three interfacial tensions. The drop retraction method was used exchanging the nature of the polymer forming the drop and varying the viscosity level of the PBAT in order to improve the accuracy of the measurements. Attention was paid to the partial wetting morphology observed for some compositions. We were interested in the blend composition range giving rise to composite droplets presenting a partial wetting morphology in complement to the cocontinuous morphologies studied by the group of Favis. 47 The effect of different parameters such as, the blend composition, the exchange of the polymer matrix, the viscosity level of the PBAT phase and the processing parameters, on the blend morphology was investigated in order to test the reliability of the model prediction. A last part was devoted to the formation process of the partial wetting morphology during blending. Polyesters and polyamide being sensitive to humidity, they were dried at 80°C in a vacuum oven for at least four hours prior to any use of the polymers in the molten state (compounding, compression molding and rheometry).

Blend preparation

The melt blending of the polymers was performed in two different mixing devices of different sizes.

An internal mixer (Haake Rheocord 600P, ThermoFischer, Karlsruhe, Germany) was used to prepare 50 g of sample. The product from the internal mixer was then ground (grinder M50/80, Hellweg Maschinenbau GmbH & Co KG, Roetgen, Germany) prior the next forming step. A micro-compounder (Haake Minilab II, ThermoFischer, Karlsruhe, Germany) was also used to prepare the blends using only an amount of 5 g. It is equipped with two counter-rotating screws of 15 mm diameter. The screws constitute the mixing zone and they can be connected to a recirculation circuit including a parallelepiped tank allowing the matter to pass several times through the screws.

In both mixing pieces of equipment, the different components of the blend were introduced simultaneously in the mixer. Most blends were prepared in the internal mixer. The microcompounder was used to investigate the morphology developed in the ternary blends, since samples can be taken at various steps of the mixing process in an easy manner.

Rheological measurements

Rheological measurements were performed with a controlled-strain rheometer (ARES, TA Instruments, Delaware, USA). All measurements were performed in a cone-and-plate geometry The zero shear viscosities are reported in Table 1.

Scanning electronic microscopy (SEM)

The morphologies of the blends were observed by scanning electronic microscopy (SEM, Philips XL 30 ESEM) using the back-scattered electron mode and an accelerating voltage around 15 kV.

Observations were performed on cryo-fractured cross-sections of samples prepared for rheometry.

Cross-section surfaces were systematically polished in order to obtain flat surfaces with a roughness parameter close to 1 m and then coated with Au/Pd (deposit thickness around 10 nm). This procedure made it possible to distinguish the different polymers even in the case of the ternary blends.

Interfacial tension determination based on drop retraction

The drop retraction method implies the in-situ follow-up of the relaxation of a deformed drop. The diameter sample was allowed. The gap relatively to the drop dimension was large enough to ensure that the drop deformation or relaxation was not influenced by the wall vicinity. 61 Droplets were slightly deformed to ensure that the relaxation only took place via the iso-volumetric retraction of the droplet toward the spherical shape. Relaxation data were only considered valid when the deformability parameter was small enough (typically starting from 0.2). 46 The measurement of the two dimensions (major and minor axis) of the projected droplet was preferred to the determination of the true length of the major axis from the volume conservation knowing the radius of the drop after retraction (R 0 ) and the measurement of the minor axis. The deformation of the drop being very small, the interfacial tensions determined from direct measurements (projected length) or from corrected values were very close and within the error bars on these measurements. All values of interfacial tensions were determined from indirect measurements of the dimensions of the drops.

Results and Discussions

Interfacial tension

In order to compare morphologies to the theory based on the spreading coefficients, the interfacial tensions of the three couples must be known. A full description of the methodology followed to measure the interfacial tension of PLA/PBAT will be given in the following paragraph. The same procedure was followed for the two other couples but the results will be given without a full description.

Interfacial tension of PLA/PBAT blend

As mentioned in the introduction, very different values are reported on PLA/PBAT blends. [57][58][59][60] The interfacial tension was measured by the drop retraction method. All experiments were conducted at 180 °C.

Measurements were performed on droplets of PLA in PBAT 1 matrix, on the reverse system with droplets of PBAT 1 in PLA matrix, on droplets of PLA in the lower viscosity PBAT 2 matrix and on the reverse system on droplets of PBAT 2 in PLA matrix. Figure 3 shows an example of a PBAT 1 drop relaxation in PLA and Figure 4 depicts the time evolution of the drop deformability during the last relaxation stage plotted on a semi-log scale. The relaxation follows an exponential decay with a characteristic time (Equation 5) used to determine the interfacial tension (Equation 6). or PBAT 2 and PBAT 1 or PBAT 2 in PLA. As expected, the results show that there is no effect of the molar mass of PBAT as well as no effect of which polymer is acting as the drop. The mean value of the PBAT/PLA interfacial tension, as averaged over all the obtained results, is 3.3  0.7 mN/m.

Interfacial tension of PA/PBAT and PA/PLA blends

The fact that the PA copolymer was viscoelastic was considered to choose the polymer forming the droplet phase for the drop retraction experiments. Several authors investigated the effect of the viscoelastic character of the droplet or the matrix relatively to the case of two Newtonian fluids. 62 The relaxation of a lowly deformed viscoelastic droplet imbedded in a Newtonian matrix was reported to follow an exponential decay with a relaxation time similar to a blend with two Newtonian phases, 63 whereas a longer relaxation process was reported in the case of a Newtonian droplet in a viscoelastic fluid. 64 In order to limit the effect of viscoelasticity, the PA copolymer was chosen as the droplet phase. The retraction of PA droplets was measured in the PLA matrix and in both PBAT polymers.

When the drop retraction test was conducted on the PA drop in PBAT 2 , a different phenomenon was observed while deforming the PA drops: the drops did not deform along the shear direction as for the other cases but along the vorticity axis as shown on Figure 56. The orientation of objects along the vorticity axis is a common feature which usually occurs when the dispersed phase is solid 65 or fluid [66][67][68] . When the dispersed phase is solid, orientation of elongated objects along the vorticity axis is due to the elasticity of the suspending medium. 65 For fluid systems, such phenomena are taking place when the elasticity of the dispersed phase is much larger than the one of the matrix [66][67][68] which is the case for PA drops in PBAT 2 . The direction of deformation has no influence on the retraction kinetics after cessation of flow and allows to measure the interfacial tension. The mean interfacial tension values based on the retraction method for the three polymer couples PLA/PBAT, PLA/PA and PBAT/PA are reported in Table 3.

Prediction of the morphology of ternary blends

Using the values of the interfacial tensions given in Table 2, it is possible to calculate the values of the spreading coefficient:

Considering error bars on the interfacial tension values, appears slightly negative but could also be slightly positive, while the other two spreading coefficients are clearly negative.

According to the spreading model, there are two possible morphologies as illustrated in Figure 1 which will depend whether is above or below zero. When the three spreading coefficients are negative, which seems to be the case here, the PA drops are situated at the interface between the PLA and PBAT 1 phases in a partial wetting situation (see in Figure 1.a). However, if is above zero, then the PA droplets should be encapsulated by the PBAT phase (see Figure 1.d). To check if the spreading approach can predict the most probable morphology, two ternary blends of composition 60PLA/27PBAT/13PA were firstly prepared with the two PBAT polymers and examined by SEM. Figure 6 shows an example of morphology in the case of PBAT 1 grade. The black inclusions standing for the phase PA are mainly located at the interface between the dark gray phase (PBAT 1 ) and the white PLA phase. This is in agreement with the partial wetting morphology predicted by the spreading coefficients with all three negative coefficients. PA phase seems to have a preferential affinity with the PBAT phase, sign that is close to zero.

Similar partial wetting morphologies were also found with the PBAT 2 grade. This was surprising since the PBAT 2 had a much lower viscosity than the PBAT 1 . The factor was estimated for both PBAT grades in order to determine which phase should be the matrix in the composite droplet. 69 The viscosity values were considered at a mean shear rate of 25 s -1 corresponding to the condition 50 rpm in the internal mixer. Values smaller than one were obtained in all cases, confirming that PBAT is the matrix for the investigated range of volume fraction and whatever the viscosity level of the PBAT phase. The effect of the mixing conditions was further investigated in the case of the 60PLA/20PBAT 2 /20PA blend by varying the rotation speed (30 to 100 rpm), the temperature (170 to 190°C) or the mixing time (8 to 20 min). The type of morphology was in all cases well predicted by the spreading model.

The spreading theory is correctly predicting the observed morphologies of the PLA/PBAT/PA ternary polymer blends. This is in agreement with other works [24][25]27 We found a good agreement between the morphologies of the ternary blends based on PLA, PBAT and PA, using the interfacial tensions that we tried to measure with accuracy. mN/m). This means that interfacial tensions need to be determined with care in order to be in the right order of magnitude. The good agreement between the different morphologies of the ternary blends obtained while exchanging the matrix and the spreading coefficient theory confirms that the interfacial tensions which were measured are in the right order of magnitude.

Interpretation of the morphology based on thermodynamic aspects

As mentioned, the morphology of the ternary blend 60PLA/27PBAT 1 /13PA shown on Figure 6 is a partial wetting one. PA is forming droplets which are scattered all over the interface between PBAT and PLA. This is the situation represented on Figure 8A. An alternating morphology, PBAT encapsulated by a continuous outer layer of PA (full wetting), was tested. The question was to know why the PA phase could not form a stable layer around PBAT, as depicted on Figure 8B. Although the spreading theory was showing that the morphology A (Figure 8A and Figure 1.a) was the most favorable one, the calculation of the free energy of the morphologies for these two cases was performed. According to Guo and co-workers [START_REF] Guo | [END_REF] , the free energy is (where stands for the interfacial area between two phases, for their interfacial tension), considering that the contribution of the partial molar free energy is the same for these two cases since they have the same composition. It is thus possible to compute the free energy of these two cases A and B:

where R PBAT is the radius of PBAT drops (same in both cases), n is the number of PBAT drops and k is the volume ratio between PA and PBAT. Assuming that n = 10, the relative value of E A and E B are:

The result shows that the free energy of morphology A is lower than that of B. It confirms that morphology A representing a partial wetting morphology is also the more favorable one from the thermodynamic point of view for this polymer system.

Dynamic aspects of morphology development

 ij ij A  ij A ij 
In order to see how the blend morphology was transformed from the three polymers macroscopically separated (mm range) into a more intimate structure (shown on Figure 6), samples were collected during the mixing operation (dead stop experiments) in the recirculation zone of the micro-compounder (transitional zone between two successive passages of the blend in the twin screw zone). The reservoir being larger than the zone driving the mix, there is a sudden enlargement of the lateral dimension and thus the establishment of an extensional flow perpendicular to the flow direction. Samples were collected in this diverging zone. The visual aspect of the tree-like pattern at the entrance of the reservoir is due to the PBAT/PA inclusions elongated along the flow direction. A closer look at this morphology shows that every branch of this tree-like pattern is composed by PBAT and PA phases (Figure 9.b) due to their affinity (lowest interfacial tension of the three couples, Table 2). In the complex flux introduced by the micro-compounder, once a PA inclusion meets a PBAT inclusion, they are staying together. Then the elongated PA threads break at the interface of PLA and PBAT by rupture mechanism or Rayleigh instabilities depending on flow rate and time. In some favorable situations, this last mechanism should give a very regular distribution of PA droplets at the interface between PLA and PBAT phases, as reported by Ravati et al. 35,[START_REF] Ravati | 38 Zolali AM and favis BD[END_REF] .

Conclusion

A first part of this paper was dedicated to the determination of interfacial tensions using the drop retraction method varying the molar mass of the PBAT and inverting the phases. No effect of the Different morphologies were obtained which were in agreement with the prediction of the spreading coefficient theory. This shows that the determined interfacial tensions were at least in the right order of magnitude. The sensitivity of the morphology to the variation of the interfacial tension of PBAT/PLA, while keeping the two others constant, was examined. In fact the interfacial tension needs to be in a certain range of values which is quite large.

In blends where the PLA or the PBAT was the matrix, a partial wetting morphology was obtained, sometimes with a very regular distribution of drops of nearly the same size along the interface of the two other polymers. In this case of partial wetting morphology, a free energy calculation confirms its occurrence, compared to the case of a complete wetting where a thin layer of one polymer is covering the interface of the droplet formed by the other phase. The type of morphology was in all cases determined by the interfacial tension balance. This was also true in the case of the partial wetting morphology, even when the PBAT viscosity level was much lower than the other phases.

Observations of the process formation of composite droplets with a partial wetting morphology tend to show that this morphology results from the elongation and rupture of coupled filaments of PBAT and PA.

Provided that a reliable measurement of interfacial tensions is made, this set of results, added to the several other ones already published, shows that morphologies of ternary blends can be reasonably theoretically predicted, at least when no kinetic effect is slowing down the formation of the thermodynamically stable structure.

Tables:

  3051D) noted PLA from NatureWorks, Minnetonka, MN, USA, poly(butylene adipateco-terephthalate) (Ecoflex FBX 7011) noted PBAT from BASF, Ludwigshafen, Germany and a copolyamide (Plastamid HX2656), noted PA, from Arkema, Serquigny, France were chosen as components of the ternary blend due their respective immiscibility. Two batches of PBAT were investigated, PBAT 1 (Newtonian viscosity of 3250 Pa.s at 180 °C) and PBAT 2 (Newtonian viscosity of 150 Pa.s at 180 °C).

  (25 mm diameter and a 0.04 rad angle) at 180 °C under nitrogen environment. Disk-shape samples (thickness 1 mm, diameter 25 mm) were prepared by compression molding using a hot press (Carver M3853-0, Carver, Indiana, USA) at 180 °C, 25 MPa for 8 min. Angular frequency sweep measurements (from 10 2 to 10 -1 rad/s) were performed in the linear domain of viscoelasticity of the neat components. Care was taken to check the thermal stability of the polymers and the linear domain prior to frequency sweep measurements.

Figure 2

 2 Figure2shows the rheological behavior of the pristine polymers under small amplitude oscillatory shear.

Figure 2 :

 2 Figure 2: Small amplitude oscillatory shear data of the pristine polymers measured at 180°C: a. complex viscosity, b. storage modulus

  deformation of the droplet was performed in a transparent counter-rotating shear cell coupled to a transmission optical microscope. The sample consists in a sandwich of a small piece of polymer A between two polymer films of the matrix polymer B. The sandwich sample was then introduced in the shear cell at 180 °C, molten, stabilized in temperature (after 5 min) and squeezed to the nominal gap. The temperature was considered as homogeneous after 10 min of heating. The droplet phase imbedded in the matrix was deformed under the action of shear up to a certain deformation where the shear flow was stopped. The drop relaxation kinetics was monitored. The gap was fixed at 1000 m. The relaxation of 40 to 110 m radius drops was investigated. The relaxation kinetics of at least 6 to 10 drops per system was measured. Attention was paid to the following factors during these measurements. The temperature of the polymer in the transparent shear cell was controlled using 50 m diameter thermocouples. Only a few degrees difference between different locations in the 4 cm

Figure 3 :

 3 Figure 3: Relaxation of an ellipsoidal drop of PBAT 1 in the PLA in matrix after deformation under shear (flow direction is horizontal, vorticity axis is vertical). The drop radius is 83 µm.

Figure 4 :

 4 Figure 4: Time evolution of the deformability parameter in the case of Figure 3.

Figure 5 :

 5 Figure 5: Retraction of PA drops in PBAT 2 matrix after drop deformation. Deformation occurred along the vorticity axis (vertical), the flow direction being horizontal (indicated by the arrow). The radius of the drop is 106 µm.

Figure 6 :

 6 Figure 6: SEM micrography of a 60PLA/27PBAT 1 /13PA ternary blend prepared in the internal mixer: at 180°C, 50 rpm for 12 min. The black phase is PA, the dark gray phase is PBAT 1 and the light gray phase is PLA.

Figure 7 :

 7 Figure 7: Morphologies of the three blends: a. 60PLA/20PBAT 2 /20PA; b. 60PBAT 2 /20PA/20PLA and c. 60PA/20PLA/20PBAT 2 as seen by SEM and their respective model predictions (d. to f.). Blends were prepared in the internal mixer at 180°C, 80 rpm for 12 min.

Figure 8 :

 8 Figure 8: Two possible morphologies for the 60PLA/20PBAT/20PA blends.

Figure 9 .

 9 a shows a "tree-like" morphology which is generated in the elongational field at the entrance of the recirculation reservoir for a 60PLA/20PBAT 1 /20PA blend. a.b.

Figure 9 :

 9 Figure 9: Morphology pattern of the ternary blend 60PLA/20PBAT 1 /20PA at the diverging entrance of the recirculating reservoir in the micro-compounder (180°C, 80 rpm, 12 min): a. overall view; b. enlargement of a zone showing the twinning of PA (black) and PBAT (dark gray) phases.

16 molar

 16 mass was detected. Inverting the phases had no effect on the interfacial tension. The interfacial tensions between the three polymer couples are = 3.3±0.7mN/m, = 5.6±0.3mN/m and = 3.0±0.4 mN/m. Based on this, spreading coefficients were calculated, giving = -5.9mN/m, = -0.5mN/m, = -5.3mN/m, with one of them being very close to zero. Polymer blends composed of bio-based PLA and PA and biodegradable PBAT were prepared varying the composition, the processing parameters, the PBAT viscosity level and exchanging the matrix (60PLA/27PBAT/13PA, 60PBAT/2OPA/20PLA, 60PA/20PLA/20PBAT).

Table 1

 1 gives the different values of interfacial tensions for the four possible cases, i.e. PLA in PBAT 1

  Since a large range of interfacial tensions is reported in the literature for the polymer couple PLA/PBAT, one can wonder whether considering other values of interfacial tensions for this couple of polymers would lead the same prediction of the morphology. Considering the interfacial tensions of PA/PLA and of PA/PBAT as constant, it is interesting to note that an interfacial tension for PLA/PBAT between 2.6 and 8.6 mN/m would lead to the prediction of a partial wetting morphology (all spreading coefficients being negative), whereas an interfacial tension lower than 2.6 or larger than 8.6 would lead to an encapsulated morphology (one spreading coefficient being positive with encapsulation of PLA in

	PBAT phase if	.2.6 mN/m and encapsulation of PLA in PA phase if	.8.6

Table 1 :

 1 Newtonian viscosity at 180°C of the pristine polymers using the Carreau-Yasuda model

	Polymer	PBAT 1	PBAT 2	PLA	PA
	(Pa.s)	3250	150	1800	3300

Table 2 :

 2 Mean interfacial tensions of the PLA/PBAT couple as measured by the drop retraction method varying the molar mass of PBAT and inverting which polymer is the drop.

		PLA in PBAT	PBAT in PLA
	PBAT 1	3.4  0.8 mN/m	3.3  0.7 mN/m
	PBAT 2	3.6  0.8 mN/m	3.0  0.4 mN/m

Table 3 :

 3 Mean interfacial tension values of the three couples PLA/PBAT, PLA/PA and PBAT/PA

		Interfacial tension
	PA/PLA	5.6  0.3 mN/m
	PLA/PBAT	3.3  0.7 mN/m
	PBAT/PA	3.0  0.4 mN/m

Acknowledgements

This work was performed in the frame of the Industrial Chair on Bioplastics supported by Arkema, L'Oréal, Nestlé, PSA and Schneider Electric.