Nicolas Lebert

Nicolas Gay

Emmanuel Richaud
email: emmanuel.richaud@ensam.eu

Mechanical and macromolecular changes during thermal degradation of polyphenylsulfone

Polyphenylsulfone was thermally aged at temperatures corresponding to its processing and was mainly shown to undergo crosslinking as observed by measurements of average molar mass, rheometry and changes in glass transition temperature. Those experiments were completed by mechanical testing thin sample films at 250 and 280 °C. The same degradation mechanisms were observed and result in a strong decrease of ultimate strain accompanied by a slight decrease in elastic modulus and yield stress. Overall results were discussed using well know structure-properties relationships.

Introduction

Polysulfones form a wide family of thermoplastic polymers obtained by condensation of a diphenolate with a dihalogenated monomer [START_REF] Johnson | Poly(aryl ethers) by nucleophilic aromatic substitution. I. Synthesis and properties[END_REF] . These amorphous polymers belong to the high performances polymer familiy. The presence of aromatic ring induces relatively high glass transition temperature (typically around 200 °C) [START_REF] Sastri | Chapter 8 -High-temperature engineering thermoplastics: polysulfones, polyimides, polysulfides, polyketones, liquid crystalline polymers, and fluoropolymers plastics in medical devices -properties, requirements, and applications[END_REF] together with a high stability towards irradiations in comparison with aliphatic polymers [START_REF] Jahan | A comparative study of radiation effects in medical-grade polymers: UHMWPE, PCU and PEEK[END_REF] . In the same time, they benefit from a sub-glassy relaxation at around -100 °C i.e. well below the glass transition [START_REF] Naderi | Effects of chemical structure on gas transport properties of polyethersulfone polymers[END_REF] allowing a certain toughness.

PPSU can thus be envisaged for application such as aerospace and aeronautics (as skin of sandwich composites) [START_REF] Harizi | Mechanical behavior of carbon-reinforced thermoplastic sandwich composites with several core types during three-point bending tests[END_REF] , electrical component or medical devices [START_REF] Lisa | 3D printing of dental restorations: Mechanical properties of thermoplastic polymer materials[END_REF] where its aromatic behaviour and high Tg allow various kinds of sterilization process. Polysulfones display a very low Heat Release capacity during combustion can also be suitable for applications where flame retardant properties are required [START_REF] Lyon | Pyrolysis combustion flow calorimetry[END_REF] . This makes it one of the most technical thermoplastics on the market today.

PPSU are usually processed by injection moudling or extrusion but the need to manufacture parts with complex geometries makes it necessary to discuss on the possibility to investigate additive manufacturing (such as molten polymer filament layering 3-D printing) [START_REF] Schönhoff | 3D printing of dental restorations: Mechanical properties of thermoplastic polymer materials[END_REF] . During the additive manufacturing process by Fused Filament Fabrication for example, high temperature can lead to polymer degradation, breaking down polymer chains, weakening the finished part and leaving residue on the inside of the melt channel [START_REF] Gibson | Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing[END_REF] . This is the case even for high performances polymers where processing temperature in Fused Filament Fabrication or in Selective Laser Melting) can be narrow [START_REF] Luo | Controllable interlayer shear strength and crystallinity of PEEK components by laser-assisted material extrusion[END_REF] . The existence of a crosslinking mechanism will limit the diffusion of chains across interface [START_REF] Yang | Healing of thermoplastic polymers at an interface under nonisothermal conditions[END_REF] which may prevent the consolidation of FFF manufactured samples and the possibility to obtain acceptable mechanical properties [START_REF] Vaes | Semi-crystalline feedstock for filament-based 3D printing of polymers[END_REF] . There is also an increasing societal pressure to reuse such polymers, at least in the case of "closed loop" recycling for polymers scraps. The degradation induced during service life or processing may also limit the possibility to reprocess those polymers.

It arises the need to understand the effect of thermal degradation on the mechanical properties and the thermal stability of those materials. The thermal stability of aromatic polymers was already addressed in previous papers dealing with apparent modelling of the degradation [START_REF] Abate | Kinetics of the isothermal degradation of model polymers containing ether, ketone and sulfone groups[END_REF] but the fine understanding of macromolecular changes and their effect on mechanical properties remain an open question.

Finally, the aims of this paper are:

-to evaluate the thermal stability of PPSU in typical processing conditions in terms of temperature) -to investigate the macromolecular changes involved by the thermal degradation, -to propose some structure-properties relationships involved in the embrittlement of PPSU materials. For that purpose, we will address the degradation at 400 °C with some comparisons with samples degraded at lower temperatures. Even though additive manufacturing conditions is usually performed under atmospheric air, we will also investigate degradation under pure oxygen and under pure nitrogen, in order to investigate the purely "thermolytical" degradation processes (occurring in the bulk of polymer sample) and then the effect of oxygen (occurring in its surface). The knowledge of those two "extreme" behaviors is actually needed to describe the degradation in typical processing conditions under air.

Experimental

Materials

Several kinds of polysulfones (the structure of which being given in Fig. 1 ) were studied here, with a peculiar emphasis for PPSU.

Two kinds of PPSU samples (PPSU 1 and 2) were supplied as filament extruded by supplier for FFF purpose. Those latter were used as received. Some comparisons were performed with samples purified by refluxing in methanol during 24 h but only minor changes were observed so that PPSU's were used as received in the following.

For mechanical testing, PPSU filaments were pressed using a Gibitre laboratory press (2 min at 280 °C under 240 bars. Resulting films displayed a 50-60 μm thickness and then punched into 5B type dogbone specimens (according to ISO 527-2). Some complementary tests were done with several grades of polysulfones (all as received) given in Table 1:

Exposure conditions

Samples were either isothermally aged:

-in the cell of ThermoGravimetric Analysis device, either under nitrogen or oxygen atmosphere (see next paragraph), -in ventilated ovens at 250 °C (AP60, System Climatic Service) and 280 °C (UF160plus, Memmert).

Characterization methods

ThermoGravimetric analysis (TGA)

Experiments were performed using a Q50 apparatus (TA Instruments) driven by QSeries Explorer software. Two kinds of experiments were performed on about 15 mg samples placed in a platinum pans:

-continuous heating from room temperature to 700 °C either under inert (pure N 2 ) or pure O 2 atmosphere at a 10 °C min -1 rate, -isothermal ageing at 400 °C either under inert or pure O 2 atmosphere.

TGA cell was continuously purged by a 50 ml min -1 gas flow. Results were analysed using TA Analysis software.

Differential scanning calorimetry

DSC experiments were conducted using a Q10 apparatus (TA Instruments) driven by QSeries Explorer. About 5 mg samples sealed in hermetic pas were subjected to 10 °C min -1 heating ramp under 50 ml min -1 nitrogen flow. Results were interpreted using TA Analysis software.

Sol gel analysis

Samples (about 50 mg) were immersed in THF. The presence of a gel (unsoluble part) was visually observed.

Gel permeation chromatography

Samples were analysed using a GPC system comprising a Waters HPLC apparatus (Waters 717 + apparatus) with a Styragel SE5 column with a tetrahydrofuran (THF) flow rate 1 ml min -1 . Detection was performed using a Waters 2414 Refractive Index (T detector = 40 °C). Apparatus was calibrated with unimolecular PS standards (supplied by Shodex).

Rheometry

Rheometric measurements were conducted using a DHR 20 rhetometer (TA Instruments). Samples were submitted to a 1% shear deformation at 400 °C under inert atmosphere supplied a 10 ml min -1 nitrogen flow. Plates diameter was 25 mm and gap was measured close to 1 mm.

Dynamical mechanical analysis

DMA tests were performed in tension mode using a Q800 apparatus (TA Instruments) controlled by QSeries Explorer. The samples were submitted to a 0.1% oscillatory strain at 10 Hz frequency and continuously heated at a 3 °C min -1 ramp. DMA cell was continuously purged with N 2 gas. Results were exploited with TA Universal Analysis software.

Tens ile tests

Tensile tests were conducted using an Instron 4301 at a 10 mm min -1 elongation rate equipped with a 100 N load sensor. Apparatus was driven by Bluehill software. 5 virgin or aged specimens (punched from virgin pressed films and then aged) were tested with a 2 mm width and a 10 mm initial length.

Results

The aim of this section is to investigate first the thermal stability of PPSU's. For that purpose, non-isothermal ageing will be performed. In order to be closer to the "real" processing and use conditions, isothermal ageing will be performed at 400 °C and lower temperatures. Ageing will be monitored mainly by macromolecular changes induced by degradation in order to establish links with changes in mechanical properties.

Gravimetric study

High temperature stability was first checked by non-isothermal TGA under nitrogen ( Fig. 1 a) and oxygen ( Fig. 1 b). We stress on the fact that non-isothermal tests offer a simple way to estimate the thermal stability of polymers but do not allow to perform lifetime prediction. The resulting curves are classically interpreted by measuring:

-the onset temperature (basically the temperature at which mass loss auto-accelerates), or the temperature corresponding to an "arbitrarily" fixed mass loss level (here 5, 10, 20 and 30%). We have chosen here to measure those latter values, which seemed to us more reliable than the simple "onset temperature value". -the char yield at 700 °C (possibly corresponding to a "pseudoplateau" as verified by isothermally maintaining samples at 700 °C during 20 min). The value measured at 700 °C at the end of the ramp ( η) is given in Table 2 .

Values are given in Table 2 for PPS and compared to those of other members of the aromatic polysulfone family.

PPSU isothermal ageing was thus performed in typical processing conditions, i.e. at 400 °C under nitrogen or oxygen. In fact, due to the existence of the so-called Diffusion Limited Oxidation effect, the polymer degradation for processing conditions must be close to degradation under nitrogen atmosphere in the bulk of thick samples and close to the degradation under oxygen for superficial layers. For that purpose, samples were in situ degraded in TGA cell. Results are presented in Fig. 3 .

Curves can be commented as follows:

-under inert atmosphere, PPSU degrades quite slowly even at 400 °C. PPSU 1 seems less stable than PPSU 2. The existence of mass loss means that some chain scissions occur, despite (as it will be seen later), crosslinking is also very important. -in presence of oxygen, mass loss kinetics display an autoaccelerated character suggesting the existence of an oxidation mechanism responsible of supplementary mass loss. The degradation of aromatic C -H into H 2 O, CO or CO 2 is a possible explanation but the investigation of those reactions goes out of the scope of the present work.

Samples were also continuously weighted for ageing at 280, 250, 220 and 200 °C under air. Here, PPSU 1 degrades slightly lower than PPSU 2, -at 220 °C and below, mass stayed constant (at least up to 10 0 0 h), -at 250 and 280 °C, a certain mass loss is observed indicating the existence of some chain scission process. Figure SI-1 depicts the case of ageing at 280 °C.

Macromolecular changes

To better understand the macromolecular changes occurring during ageing, degraded samples (either in oven or in situ in TGA cell) were analysed by DSC to measure the residual glass transition value. Data are given in Fig. 4 in the case of PPSU 1 filaments before and after ageing. Thermograms display the expected shape of amorphous polymers. Initial glass transition value is around 220 °C for unaged polymers in agreement with previous papers [START_REF] Liu | Design and synthesis of poly(arylene ether sulfone)s with high glass transition temperature by introducing biphenylene groups[END_REF] . For unaged PPSU, only the glass transition is visible at around 220 °C, this value being commented in the following section. Glass transition values (T g ) were determined for several exposure conditions and plotted versus time in Fig. 5 . Even though mass loss is observed (which is testimony of the occurrence of some chain scissions), T g mainly increases. It means either that PPSU undergoes additional polycondensation (involving chlorophenyl and phenolate chain end groups for example) or crosslinking, as it will be discussed in the following. Specifically, we observed the following trends:

-for ageing performed at 400 °C under N 2 or under O 2 , T g increases in both cases but at a slower rate in presence of oxygen than under inert atmosphere. According to Fig. 2 , mass loss is higher in presence of oxygen than under inert atmosphere.

In other words, crosslinking occurs under nitrogen and possibly under oxygen (since a gel fraction was observed) but is delayed due to oxidation processes. Interestingly, the increase is higher for PPSU than for example PEKK aged in the same conditions [START_REF] Choupin | Mechanical performances of PEKK thermoplastic composites linked to their processing parameters[END_REF] . It suggests that biphenyl groups contribute to crosslinking reaction. -The same is observed at 250 °C and 280 °C under air: T g continuously increases for PPSU fibers (2 mm diameter). The differences between thin films and fibers are relatively weak.

Usually, an increase in T g means that macromolecular mobility decreases. In a case of a thermoplastic polymer, it suggests that molar mass increases either because crosslinking and/or because of post polycondensation (condensation reactions are reported to occur in solvent at temperatures ranging from 130 to 250 °C [START_REF] Johnson | Poly(aryl ethers) by nucleophilic aromatic substitution. I. Synthesis and properties[END_REF] and it is recognized here that we do not know if they also occur at higher temperatures or if chain ends might be degraded first). Gel Permeation Chromatography experiments were performed in order to monitor the changes in Average molar masses. According to Fig. 6 , the maximum of the chromatogram is shifted towards higher elution times, which is in agreement with an increase in average molar mass. It can be seen that the broadness of the chromatogram (linked to the polydispersity index) also increases. Some values are given in Table SI-1 of SI.

Under the assumption of random chain scission and/or crosslinking [START_REF] Saito | On the effect of high energy radiation to polymers: I. Cross-linking and degradation[END_REF] , changes in average molar mass are given by:

1 M n - 1 M n 0 = ( s -cond ) -x (1) 1 M w - 1 M w 0 = s -cond 2 -2 x ( 2
)
in the case of a crosslinking mechanism leading to tetrafunctionnal nodes, or

1 M w - 1 M w 0 = s -cond 2 -x ( 3
)
in the case of a crosslinking mechanism leading to trifunctionnal nodes.

The exploitation of M n and M w changes showed that s -cond 0 and x 0, which suggests that both mechanisms co-exist. In the absence of evidence of tri-or tetrafunctionnal nodes, we did not deepen the quantitative analysis using Eqs (1) -(3) .

To better understand the nature of macromolecular changes and discuss on the existence either of polycondensation or crosslinking, rheometric measurements for PPSU in molten state were performed ( Fig. 7 ). The following changes were observed: at early exposure time, the loss modulus G'' is higher than the storage (elastic) one G'. This latter progressively increases and becomes higher than G''. Such a behaviour is characteristic of the formation of a gel [ 17 , 18 ]. The same occurs for PEES and PES. Very interestingly, the gel times are higher for both PEES and PES than for PPSU polymers as it will be discussed later. Consistently with TGA experiments under nitrogen ( Fig. 3 ), PPSU 1 degrades faster than PPSU 2. The existence of crosslinking was also confirmed by sol gel analysis: aged samples (either in oven in situ in TGA cell) were immersed in tetrahydrofuran. An insoluble fraction characteristic of a polymeric network was observed. The analysis of residual soluble fraction ( Fig. 6 ) also displays an interesting feature: chromatograms are progressively shifted towards high elution times meaning that molar mass progressively increases.

Changes in mechanical properties

To understand the consequences of ageing on mechanical properties in a first simplified approach, we performed ageing tests on thin films aged at 250 and 280 °C after several time intervals. In such ageing conditions, films could be aged without undergoing geometrical changes unacceptable in terms of mechanical testing meanwhile "macromolecular changes" (estimated for example from Fig. 5 ) are consistent with those of filaments investigated in this work.

Stress strain curves are overlapped in Fig. 8 . They call for the following comments:

-for unaged samples, a certain plastic deformation is observed with an average ultimate strain higher than 100%, -after ageing, ultimate elongation is progressively decreased. A certain plastic deformation remains, however possible, -elastic modulus and yield stress does not display significant changes, within the experimental incertitudes.

DMA analyses were conducted in the aim of establishing macromolecular changes and mechanical properties. PPSU displays two main transitions characteristic of its amorphous behaviour:

-a sub-glassy transition ( γ relaxation) located at around -100 °C ( Fig. 10 ) and associated to a local mobility ( Fig. 10 ). This one is common with other polysulfones such as PES (explaining why those glassy polymers actually display a plastic behaviour) but less intense meaning that the responsible groups are in lower concentration in PPSU than in PES and in PEES which is in line with the interpretation of Aitken et al. [START_REF] Aitken | Dynamic mechanical behavior of polysulfones[END_REF] according to which this relaxation would be due to either diphenyl sulfones or sulfones groups.

-the α-relaxation associated to T g -above T g , there is almost no rubbery plateau, as expected for a polymer with short chains [START_REF] Rudin | The elements of polymer science & engineering chapter 4mechanical properties of polymer solids and liquids[END_REF] . During ageing, the main changes in the α relaxation domain are consistent with a predominant crosslinking behaviour: T g increases meanwhile a rubbery plateau appears due to the increase of molar mass ( Fig. 11 ).

Discussion

The aim of this section is to explain the observed changes and make a link between all the observations obtained in this multiscale study. For that purpose, we will:

-discuss on the macromolecular changes, -comment the glass transition changes in link with molar mass changes, -discuss on the effect of macromolecular mobility on embrittlement.

On the mechanisms of degradation

To better discuss on the possible degradation mechanisms, we started from the reported values of bond energies available for example in the case of bisphenol A polysulfone [ 21 , 22 ] which were confirmed by a machine learning based quantum approaches for repetitive units close to PPSU [23] and other polysulfones (see Supplementary data). It seems clear that, for PPSU, the Ar-SO 2 bond still is the weakest bond in PPSU (Fig. 12).

At high temperatures, a chain scission mechanism is expected to occur in particular for the Aromatic ring -sulfur bond which seems the weakest link of polymer backbone (as assumed by Rambogin et al. [START_REF] Ramgobin | Thermal degradation and fire behavior of high performance polymers[END_REF] ):

Table 3

Calculation of Glass transition for several polysulfones and comparison with literature data (0, 1 and 2 correspond to the occurrence of groups in considered polymers).

Group Y gi (K kg mol -1 ) PSU PPSU PES PEES -Ar-SO 2 -Ar- 111 1 0 1 1 -Ar-C(CH 3 ) 2 -Ar- 87 1 0 0 0 -O-Ar-O- 47.5 0 1 0 1 -Ar- 35 0 1 0 0 > SO 2 32.5 0 1 0 0 -O- 4 2 0 1 0 -Ar-Ar- 85 0 1 0 0 Calculated T g ( °C) 199 226 222 215 Theoretical T g ( °C)
190 [START_REF] Richaud | Diffusion-controlled radiochemical oxidation of bisphenol A polysulfone[END_REF] 217-220 [START_REF] Dorf | Effect of the main process parameters on the mechanical strength of polyphenylsulfone (PPSU) in ultrasonic micro-moulding process[END_REF] 223-230 [ 29 , 30 ] 205-220 [ 31 , 32 ] Despite this primary reaction leading to chain scission, crosslinking seems the most prominent reaction. A possible explanation is the following: either chain end radical reacts by coupling or addition with an aromatic ring to give a tetrafunctional or a trifunctional node. According to some authors, the trifunctional crosslinking is favored, at least in the case of high temperature irradiation induced crosslinking [START_REF] Zhen | The effect of chain flexibility and chain mobility on radiation crosslinking of polymers[END_REF] . Another possibility is that radical isomerizes and give "middle chain" alkyl radicals reacting to give a tetrafunctional node. This complexity explains why we did not try to discuss our data using Eqs. (1) -3 .

According to Scheme 1 and 2 , the concentration in chain scission s would be equal to the concentration in crosslink, leading to an increase of both M n and M w until the formation of an unsoluble gel. Using now Eq. ( 1) -3 , it seems at least clear that the appearance of a gel means that x is higher than s/4 or maybe s/2 depending on the crosslinking mechanism.

The exact nature of mechanisms for ageing under air (including the contribution of oxygen) remains a grey area. On one side, TGA measurements at 400 °C clearly evidence that oxygen accelerates degradation. On the other side, the difference between very thin films and "thick" filaments are minor ( Fig. 5 ). Moreover, it can be noted that under pure oxygen, PPSU 2 degrades faster than PPSU 1 meanwhile under inert atmosphere and under air, PPSU 1 degrades faster. In other words, oxygen would play a minor role for the investigated ageing conditions.

The comparison of T g increase in PEKK (see [START_REF] Choupin | Mechanical performances of PEKK thermoplastic composites linked to their processing parameters[END_REF] ) and PPSU ( Fig. 5 ), in char yield for PPSU vs other polysulfones ( Fig. 2 a) and in kinetics of gelation of PPSU vs PES and PEES ( Fig. 7 ) suggests that, in a certain extent, the presence of biphenyl group favors the crosslinking despite its "rigidifying role" on chain dynamics (as it will be developed in the next paragraph). DMA result show that the γ relaxation is almost unchanged with ageing. According to [START_REF] Aitken | Dynamic mechanical behavior of polysulfones[END_REF] , this relaxation is due to sulfones or bibenzyl sulfone groups suggesting that these latter are not degraded during ageing meanwhile biphenyl groups would be the principal site of crosslinking. This remains to be firmly established in future works.

On the glass transition values

The glass transition values for unaged polymers can easily described in terms of structure properties relationships such as those proposed by Van Krevelen [START_REF] Van Krevelen | Properties of Polymers. Their correlation With Chemical structure; Their numerical Estimation and Prediction from Additive Group Contributions[END_REF] :

T g = 10 0 0 Y gi M UCR ( 4
)
Where M UCR is the molar mass of the whole repetitive unit (i.e. the monomer) and Y gi the contribution of elementary groups (sulfones, aryl…) to T g . The contribution of common constitutive groups is well-known for elementary groups (e.g. sulfones, ethers, aromatic ring) but grey zones remain on their values when they are combined together in the case of aromatic polymers. For example, the direct use of the set of values given in [START_REF] Van Krevelen | Properties of Polymers. Their correlation With Chemical structure; Their numerical Estimation and Prediction from Additive Group Contributions[END_REF] did not allow to predict the glass transition observed for PPSU (this work) and PSU for example [START_REF] Richaud | Diffusion-controlled radiochemical oxidation of bisphenol A polysulfone[END_REF] . We thus employed the following approach:

1 PES and PESU are the two most documented members of the family of aromatic polysulfones. The contribution for Ar-SO 2 -Ar, Ar-C(CH 3 ) 2 -Ar and > O are given in Van Krevelen's monograph [START_REF] Van Krevelen | Properties of Polymers. Their correlation With Chemical structure; Their numerical Estimation and Prediction from Additive Group Contributions[END_REF] and allow a nice agreement between experimental and theoretical values 2 In the case of polyether ether sulfone, the only possibility to reconcile experimental and theoretical values is to increase the contribution for O-Ar-O (from 37.4 to 47.5 K kg mol -1 ) 3 In the case of PPSU, using the contribution of Ar and SO 2 groups given in Van Krevelen's monograph, and 47.5 K kg mol -1 for O-Ar-O, the only possible agreement can be obtained by increasing significantly the Y gi contribution for biphenyl group (from 70 to 85 K kg mol -1 ), highlighting the positive effect of this group on rigidity.

Calculations are summarized in Table 3 .

During ageing however, average molar mass values are modified because of chain scission and/or crosslinking. Molar mass and T g are correlated by the Fox Flory formula based on the assumption that free volume comes from chain ends [START_REF] Fox | Second-order transition temperatures and related properties of polystyrene. I. Influence of molecular weight[END_REF] :

T g = T g - k F F M n ( 5
)
k FF is a priori unknown for PPSU but it can be shown that it is directly proportional to T g ∞ [START_REF] Richaud | Radiochemical ageing of poly(ether ether ketone)[END_REF] :

k FF ∼ a • T g∞ [START_REF] Lisa | 3D printing of dental restorations: Mechanical properties of thermoplastic polymer materials[END_REF] Making for example comparisons between PC for which: (T g ∞ ) PC = 434 K and (k FF ) PC = 187 K kg mol -1 , and PPSU, for which (T g ∞ ) PPSU ∼510 K, it gives (k FF ) PPSU ∼220 K kg mol -1 . According to Fig. 13 , experimental data fit well with the "Fox Flory " linear regression based on those calculations.

It is noteworthy that there are only few data corresponding to T g above 225 K which can be justified as follows: according to Eq. ( 3) , the appearance of a gel corresponds to a crosslink concentration x gel ∼1/M w0 ∼0.033 mol kg -1 . Using now Eqs (1) and ( 5) :

T g -T g0 = k FF • ( x + cond -s ) [START_REF] Lyon | Pyrolysis combustion flow calorimetry[END_REF] So that, if crosslinking predominates: T g -T g0 ∼k FF .x so that (T g ) gel ∼T g0 + 6 K, in agreement with the here above observation.

On the embrittlement mechanisms

During ageing the following trends are observed:

1 there is almost no change of yield stress. This result is quite surprising in a first approach since it is well known that [START_REF] Kambour | Correlations of the dry crazing resistance of glassy polymers with other physical properties[END_REF] :

σ y = C ( T g -T ) (8)
Where σ Y is the yield stress, T g the glass transition temperature and T the temperature at which samples are mechanically tested.

In other words, changes in T g should result in change in σ y . This is for example well verified in the case of physical ageing of polyamides by water diffusion where the presence of water induces both a decrease in T g and in σ y [START_REF] Gac | Yield stress changes induced by water in polyamide 6: Characterization and modeling[END_REF] . Here, despite a clear crosslinking, σ y remains almost constant within the timescale of embrittlement. Let us fist note that according to initial values of σ y and T g , the Kambour parameters (C in Eq. ( 8) ) should be around 0.3 MPa K -1 . According to Fig. 5 , T g increases by less than 5 °C Scheme 1. Possible primary chain scission event. 2 The slight decrease in elastic modulus is also to be discussed. From a theoretical point of view, elastic modulus of amorphous glassy polymers depends on the density of cohesive energy and the occurrence of sub glassy relaxations.

Here, it seems that sub glass relaxations are hardly changed by ageing suggesting that the small elastic modulus decrease would come from the disappearance of very cohesive groups and possibly their conversion into less cohesive ones. [START_REF] Jahan | A comparative study of radiation effects in medical-grade polymers: UHMWPE, PCU and PEEK[END_REF] The other main visible effects of ageing are the decrease in ultimate strain. It seems consistent with the fact that the appearance of crosslink nodes seems to decrease the capability of polymer to reach high stretching ratio (identically for example to elastomers). PPSU seems to stay partly ductile (in the conditions of mechanical tests) which is consistent with the fact that the relaxation associated to sub glassy transition does not vanish during ageing ( Fig. 11 a).

Conclusion

This paper deals with the thermal degradation of PPSU in rubbery conditions. The degradation was shown to induce a major crosslinking, in particular in processing conditions (as observed in particular by rheometric measurements). The overall crosslink-ing occurring during thermal degradation and the various processing steps limits the possibility of multiple recycling steps of those polymers (even if it the degradation at lower temperatures should also be investigated to fully conclude). It seems that the presence of bibenzyl groups favors this crosslinking, as illustrated by some comparisons of crosslinking kinetics in molten state with other aromatics polymers. From a mechanical point of view, PPSU loses a great part of its plasticity but never gets totally brittle. The exact nature of mechanisms (observed at molecular scale) remains open together with a more detailed understanding of structure-stability relationships involved in the stability of polysulfones, in particular with the influence of synthesis methods and end chain nature on chemical stability [START_REF] Perng | Thermal degradation mechanism of poly(arylene sulfone)s by stepwise Py-GC/MS[END_REF].

Declaration of Competing Interest

We hereby confirm that we have no conflict of interest with the paper

Fig. 1 .

 1 Fig. 1. Structure of investigated polymers: polyphenyl sulfone PPSU (a), polysulfone PES (b), Polyetherether sulfone (PEES) (c), bisphenol A polysulfone PESU (d).

Fig. 2 .

 2 Fig. 2. Non-isothermal TGA of polysulfones under nitrogen (a) or oxygen (b).

Fig. 3 .

 3 Fig. 3. Gravimetric study at 400 °C under inert ( , ) or pure O 2 atmosphere ( •, •). Open symbols correspond to PPSU 1 and closed ones to PPSU 2.

Fig. 4 .

 4 Fig. 4. DSC thermograms of PPSU 1 aged at 280 °C under air.

Fig. 5 .

 5 Fig. 5. T g changes of PPSU 1 and 2 after several ageing conditions: 400 °C (a), 280 (b) and 250 °C (c). NB: opens symbols correspond to thin samples aged under air (at 250 and 280 °C) or samples aged under pure O 2 (400 °C) meanwhile closed symbols correspond to thick samples (filament) aged under air (250 and 280 °C) or thick samples aged under pure N 2 (400 °C).

Fig. 6 .

 6 Fig. 6. GPC Chromatograms of PPSU 1 aged at 280 °C under air ( symbols correspond to PS calibration).

Fig. 7 .

 7 Fig. 7. Changes of storage and loss modulus of PPSU 1 (a), PPSU 2 (b), PES (c), PEES (d) at 400 °C under inert atmosphere.

Fig. 8 .

 8 Fig. 8. Stress strain curves for PPSU 1 aged at 280 (a) and 250 °C (b) under air.

Fig. 9 .

 9 Fig. 9. Changes of ultimate strain for PPSU 1 aged at 280 (a) and 250 °C (b) under air.

Fig. 10 .

 10 Fig. 10. Dynamical mechanical analysis of polysulfones in the low temperatures domain.

Scheme 2 .

 2 Scheme 2. Possible crosslinking mechanism by addition (a) or coupling (b).

Fig. 11 .

 11 Fig. 11. Dynamical mechanical analysis of polysulfones (virgin and aged at 280 °C) in the low (a) and high (b) temperatures domain.

Fig. 12 .

 12 Fig. 12. Estimation of some Bond Dissociation Energies in PPSU.

Fig. 13 .

 13 Fig. 13. Fox Flory plot of virgin and degraded PPSU's (straightline corresponds to theoretical Fox Flory plot: T g = 236 -220/M n ).

Table

  Description of polysulfones materials used in this work for comparison purposes.

	Name	supplier	ref	Informations
	PES	Sigma Aldrich	191,094-50G
	PES	Sigma Aldrich	191,094-50G
	PSU	Sigma Aldrich	428,302-100G	M n = 16.0 kg mol -1
	PSU	Sigma Aldrich	182,443-5G	M n = 22.0 kg mol -1
	PEES	Sigma Aldrich	440,965-250G

Table 2

 2 Characteristics temperature for degradation and char yield ( η) for polysulfones.

	Atmosphere		PPSU 1	PPSU 2	PSU 1	PSU 2	PES 1	PES 2	PEES
	N 2	T 5%	508	521	487	495	489	513	521
		T 10%	530	543	496	505	517	534	539
		T 20%	555	561	505	513	541	552	554
		T 30%	568	571	511	519	555	563	564
		η (%)	43	47	29	29	38	41	41
	O 2	T 5%	484	478	478	489	478	469	501
		T 10%	525	526	494	505	500	496	527
		T 20%	553	552	509	518	530	532	546
		T 30%	567	564	518	525	545	546

Acknowledgements

Dr Jorge Peixinho is gratefully acknowledged for helping with rheometric measurements.

Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi: 10.1016/j.polymdegradstab.2021. 109 812.


Vincent Rialle

Annick Vila

Yves Besnard

HETEROGENEOUS KNOWLEDGE REPRESENTATION USING A FINITE AUTOMATON AND FIRST ORDER LOGIC: A CASE STUDY IN ELECTROMYOGRAPHY

Keywords: Medical expert systems, Heterogeneous knowledge representation, Finite automata, Electromyography

In a certain number of situations, human cognitive functioning is difficult to represent with classical artificial intelligence structures. Such a difficulty arises in the polyneuropathy diagnosis which is based on the spatial distribution, along the nerve fibres, of lesions, together with the synthesis of several partial diagnoses. Faced with this problem while building up an expert system (NEUROP), we developed a heterogeneous knowledge representation associating a finite automaton with first order logic. A number of knowledge representation problems raised by the electromyography test features are examined in this study and the expert system architecture allowing such a knowledge modeling are laid out.

Introduction

The various kinds of knowledge and reasoning used in expert systems (ES) have been carefully analyzed and classified over several years [START_REF] Clancey | Heuristic Classification[END_REF][START_REF] Keravnou | Deep and Shallow models in medical expert systems[END_REF][START_REF] Sowa | Conceptual structures: information processing in mind and machine[END_REF]. Nevertheless some types of knowledge remain difficult to represent by means of classical structures (production rules, frames, semantic nets, etc.) commonly used in expert systems. We were faced with this kind of problem while building up an expert system for the electrophysiological diagnosis of neuropathies (NP). The first version of knowledge about NP included in our system was described in 1987 [START_REF] Vila | Are expert-systems an aid for diagnosing neuropathies ?[END_REF].

Several projects have already been completed in the field of artificial intelligence applied to electromyography (EMG). The MUNIN system [START_REF] Andreassen | MUNIN -An expert system for EMG[END_REF][START_REF] Andreassen | MUNIN -On the case for probabilities in medical expert systems -a practical exercise[END_REF] is one of the major realizations. This project is based on a neo-bayesian approach of the inferential process. The reasoning framework is constituted with a probabilistic causal network in which each node has a concurrent conditional probability table. The main task of the system is to calculate probabilities of terminal nodes (illnesses) when some test result values are fed into the network.

The PC-KANDID system was developed in Prolog by A.Fuglsang-Frederiksen's team [START_REF] Fuglsang-Frederiksen | PC-KANDID: An expert system for electromyography[END_REF][START_REF] Ronager | An EMG expert assistant in clinical neurophysiology (PC-KANDID)[END_REF]. The system is founded on a logical rule based inference, without uncertainty management, and on an interactive cycle: planning -test -diagnosis. It covers most EMG diagnoses. NEUREX [START_REF] Reggia | Plausible Reasoning During Neurological Problem Solving: The Maryland NEUREX Project[END_REF], an application of the Parsimonious Covering Theory, is intended to be a general framework for neurological localization and diagnosis. A first outline of an expert system designed for electromyography: MYOSYS, in Prolog language, was outlined in our laboratory by D. Ziebelin [START_REF] Vila | Experimental EMG expert system as an aid in diagnosis[END_REF] in 1984. In contrast to the former systems, which deal with wide fields, the ADELE system [START_REF] Blinowska | Building an expert system in electrodiagnosis of neuromuscular diseases: prototype system[END_REF] is an expert system devoted to the diagnosis of a single disease: the carpal tunnel syndrome. The MYOLOG system [START_REF] Gallardo | Artificial Intelligence in the electromyographic diagnosis of cervical roots and brachial plexus lesions[END_REF] realized in Prolog is intended for the diagnosis of cervical radiculopathies and branchial plexus neuropathies, from spontaneous and voluntary muscular activities and clinical data. A system resulting from a neural network and an augmented transition network has been developed in Lisp by P.P. Jamieson [START_REF] Jamieson | Symbolic analysis of electromyographic data[END_REF]. Finally, we should mention the increasing use of artificial neural nets to classify patients into predetermined groups of pathologies [START_REF] Schizas | Artificial neural net algorithms in classifying electromyographic signals[END_REF].

We do not intend to present a new EMG expert system. Our goal is to expose an artificial intelligence modeling problem in a particular field of medical knowledge and practice. The choice of concepts described in this study is based on 2 major reasoning features that lead to NP diagnosis: this diagnosis is based, on one hand, on spatial distribution of lesions along the nerve fibres and, on the other hand, on synthesis of the different local diagnoses (at the nerve segment level, then at the whole nerve level).

Analysis of the lesions distribution along the nerves involves a spatial reasoning that may be either systematic or guided by heuristics. The highlighting of such heuristics, which is part of cognitive psychology [1], seems obviously more complex than the use of systematic reasoning. Nevertheless, the latter, even if described in propositional logic, would still be cumbersome with regards to the considered reasoning features. Therefore, the knowledge modeling solution we propose is heterogeneous: it is based on a finite automaton [START_REF] Hopcroft | Introduction to automata theory, languages and computation[END_REF][START_REF] Salomaa | Theory of automata[END_REF] used jointly with three other knowledge sources. First order logic is used in almost every part of the system : inference engine, finite automaton and production rules. The overall system is written in Prolog [START_REF] Brakto | Prolog Programming for Artificial Intelligence[END_REF][START_REF] Shapiro | The art of Prolog[END_REF][START_REF] Subrahmanyam | The software engineering of expert systems: Is Prolog appropriate[END_REF]. First we will briefly describe the main characteristics of an EMG examination. Then, we will lay out the general structure of the EMG knowledge leading to the diagnosis of neuropathies. A number of knowledge representation problems raised by the EMG test characteristics will be tackled and the choice of a heterogeneous knowledge representation using a finite automaton, as a solution to these problems, will be explained. Due to the number of knowledge sources, we will not describe them extensively but we will focus in greater detail on the description of the automaton and on the overall expert system architecture which make its use possible.

EMG principles

EMG consists of different suitable electrophysiological techniques aimed at studying the peripheral nerve system (PNS), muscles and neuromuscular junction. Neuropathies are diseases of the PNS and especially of the nerves innervating the face and limb muscles. Lesions detected by the EMG examination affect either axons of the fibres (axonal lesions) or myelin sheath (demyelinating lesions); if both structures are concerned, we call them mixed lesions. The neuropathy diagnosis is provided by the EMG examination of several nerves, mainly median and ulnar nerves for the upper limbs, peroneal and tibial nerves for the lower limbs.

The diagnosis activity involves 2 main steps, with a specific type of knowledge for each step. These two steps are as follows:

• Step A: successive tests are performed on each chosen nerve. The choice of nerves is made according to the patient's symptoms and signs. These tests are included into charts that have been standardized in our laboratory. They are chosen according to the clinical findings -i.e. the diagnosis hypotheses -, and to the nerve under study. The number of segments that we usually explore is variable: generally between 1 and 2 for sensitive fibres, and between 2 and 5 for motor fibres. For example, in the median nerve study, there are 2 stimulation points -palm and wristfor the sensory nerve conduction test, and 5 segments for the motor nerve conduction test. Electrophysiological parameters to be analyzed on the sensory and muscle action potentials are: a) sensory fibres: sensory action potential (SAP) and sensory nerve conduction velocity (SCV) on both segments; amplitude ratio of the SAP for the second segment. b) motor fibres:

-for the first segment: amplitude and distal latency of the compound muscle action potential (CMAP), -for the next four segments: amplitude of the CMAP, amplitude ratio of the successive CMAP, and motor nerve conduction velocity (MCV).

Each such examined nerve is given a diagnosis, whose process will be described below.

• Step B: the overall diagnosis is made up from the synthesis of the diagnoses for each nerve (local synthesis) and for the various nerves (overall synthesis).

corresponding semantic variables getting their values in sets such as {normal, decreased, very decreased} or {normal, increased, very increased}. These semantic variables are used as premises to the segment diagnosis rules (Fig. 3 not take into consideration, at this stage, the kind of lesion: axonal, demyelinating or mixed). The knowledge leading to the diagnosis of the nerve is based on the spatial distribution of the pathological segments along the nerve (Fig. 4).

In level 2 there are three possible kinds of pathologies, determined according to the following rules:

-focal neuropathy: several contiguous segments affected. Obviously, the consequence of this solution would be to considerably diminish the degree of intelligence of the system, since it is possible to deduce the answer from the state of the factual base.

only
A second solution would consist in representing all the possible figures in production rules such as: Nevertheless, this solution has two major drawbacks:

if seg 1 is V 1
-First: the number of possibilities for one nerve with n segments is 2 n . Since, first, n is comprised between 1 and 5 and, second, there are at least 20 couples of rachidian nerves likely to be analyzed,

we obtain an explosion of potential combinations, even in first order logic.

-Second: from a scientific or medical point of view these production rules have no interest since they are simple basic operation rules.

Finite automaton

Taking into account these knowledge representation problems, we made the choice of inserting in the knowledge base and in the inference engine an extremely simple and safe mechanism with regards to its principle as well as its recursive representation in first order logic: the finite automaton. This solution allows an almost immediate association between the list of segment statements and the nerve diagnosis.

Definition

A finite automaton consists of a finite set of states and a set of transitions which make it possible to move from one state to another when a symbol, from a predetermined set of input symbols, is fed into the automaton. The finite automaton is formally defined by a 5-tuplet (Q, Σ, δ, q 0 , F) in which Q is the finite set of states, Σ is a finite input alphabet, q 0 belongs to Q and designates the automaton initial state, F √ Q is the set of final states, and δ is the transition function associating each couple (q,a) of Q x Σ with an element p' of Q: δ(q,a) = q'.

With regards to our application, the finite set of states is Q = { start, n, f_a, f_b, m_f_a, m_f_b, d }.

The symbols n, f_a, m_f_a and d represent normal, focal, multiple focal and diffuse states respectively. These states are represented by large triangles in the transition diagram (Fig. 6). The symbols f_b and m_f_b (small triangles in the diagram) correspond to states which repeat a principal state and yet direct the analysis towards a new principal state.

The set of final states is: F = {n, f_a, f_b, m_f_a, m_f_b, d}.

As indicated in 3.2, the normal segments are symbolized by 0 and the affected ones by 1, hence:

Σ = { 0, 1 }.
For example, the following input chain : [0,1,0,1,0], called chain of segment states, reflects the state of a nerve whose second and fourth segments are affected, the three others being normal. Therefore the definition of an automaton for the analysis of a nerve is : (Q, ∑, δ, start, F).

The symbolic functioning is the following: the chain of segment states is read from left to right or from right to left (the direction is not important). Each reading of a new value from the input chain introduces a state transition from the previous state. For example, let n be the automaton state at a given time of the analyzing process, and let 1 be the new input value, then the automaton moves to the state f_a (i.e. δ(n,1) = f_a). The initial state, before the first input, is the start state. The final state (after the last input) corresponds to the nerve diagnosis. Since there are several transition possibilities (exactly 2) for every state, the automaton is called nondeterministic. The transitions defining the automaton and expressed in relational form, as in Prolog language, are shown in Figure 7. The automaton mechanism is expressed in the recursive predicate shown in The working memory allows result sharing between the different inference phases, i.e.:

-from phase 1 to phase 2: sharing of the electrophysiological parameters, -from phase 2 to phase 3: sharing of the diagnoses of segments, -from phase 3 to phase 4: sharing of the diagnoses of nerves.

Conclusion

We showed that there are some scientific knowledge fields for which classical structures such as production rules, frames or semantic nets are not suitable. EMG is a typical example of such fields:

the physician performs a spatial reasoning from the distribution and number of abnormal segments.

Such a reasoning is without doubt the result of different procedures depending on the physician (competence, experience, etc.). We leave it to cognitive psychology to study human functioning in establishing such a diagnosis. Thus, the model we described is not a priori a human function model.

The synthesis diagnosis is set up by a finite automaton which repeats a sequential, spatial and numeric reasoning. This reasoning is rather similar to that of a beginner's or a very well organized but nervous person's.

The automaton stands among three other knowledge sources, whose functioning is supervised by an appropriate inference engine. The insertion of this automaton in the core of the expert system has notably influenced the architecture of the whole system. First order logic is used in the construction of the automaton as well as in the representation of knowledge of levels 1 and 3.

This solution allows a significant decrease of the number of production rules and of the system response time. The current version of the system does not use any probability or uncertainty weighting. A new version using an approximate reasoning is under study.

This heterogeneous knowledge representation is operational in the NEUROP expert system, written in Prolog and currently under evaluation in the EMG Laboratory of the teaching hospital of Grenoble.

Discussion

The paradigm of expert systems includes the idea that knowledge accumulated in a knowledge base should reflect the expert's knowledge as exactly as possible. Classical knowledge representation structures such as production rules, frames or semantic nets must allow an easy reading of this knowledge for maintenance and updating purposes. This legitimate point of view has contributed to the wide development of knowledge based systems. However, such an opinion is limited to knowledge that easily lends itself to a symbolic representation (such a feature does not in any way preclude the intrinsic knowledge complexity).

It is not so when the conceptual model cannot be easily translated into classical structures such as production rules, frames, semantic nets or mixed models combining two or three of these structures.

Even though it is not closely copied from these usual artificial intelligence structures, the automaton model is yet connected to the ES paradigm at least through its declarative form in first order logic.

Moreover, as indicated in point 5, this model could be considered as a small-scale production system. Particularly, there is a strong analogy between the transition relation set as shown in fig. 7 and a small knowledge base. Especially, this transition set could be easily altered by addition, modification or withdrawal of transitions, according to a possible knowledge improvement. This will in fact be the case in the next version of the automaton, when specialists include knowledge related to conduction blocks (null amplitude of a sensory or compound muscle action potential ) in the expert system.

Nevertheless the similitude to the ES paradigm remains limited. Indeed, there is no reason for affirming that the model constituted by the finite automaton reflects an expert's way of reasoning (it is difficult to imagine that an expert reasons as mechanically as the automaton does).

However, one major question raised from the adoption of a procedural knowledge representation in an expert system is: is it necessary to represent, with an absolute accuracy, the expert's way of reasoning? Is this accuracy not achieved in some cases at the cost of a considerable complication of the knowledge base?

The weakness that one could reproach the automaton model with is that it does not use any heuristic knowledge -a major attribute of human intelligence -: the way to achieve the synthesis diagnosis of a nerve is an absolutely systematic and exhaustive reasoning. However, this weakness is compensated by the relatively low number of nerve segments (5 maximum) which minimizes the advantage of heuristic rules.

It should also be observed that, to be understood, the automaton we have devised needs very few concepts about the theory of finite automata, and constitutes an elegant solution to the spatial reasoning knowledge representation. As far as they are concerned, the medical experts who participated in the knowledge base building consider the adoption of the notion of the finite automaton as a practical substitute to a human knowledge model whose conception is beyond their reach. This way, we can state that such a solution constitutes to some extent a contribution of artificial intelligence to the medical expertise modeling.

Fig. 4 .Fig. 5 . 4 . Problems of knowledge representation at level 2

 4542 Fig. 4. Examples of spatial distribution of lesions

1 Fig. 6 .

 16 Fig. 6. Transition diagram of the finite automaton n : normal state f_a, f_b : focal neuropathy d : diffuse neuropathy m_f_a, m_f_b : multiple focal neuropathy

Figure 8 .Fig. 9 .

 89 Figure 8.

  ).

	if	amplitude at the wrist	is	very decreased
			amplitude at the wrist
	and if	ratio:	amplitude at the palm is	normal
	and if	velocity at the wrist	is	normal or decreased
	then lesion of the segment	is	severe axonal
			_________
	if	amplitude at the wrist	is	normal
			amplitude at the wrist
	and if	ratio:	amplitude at the palm is	normal or decreased
	and if	velocity at the wrist	is	decreased
	then lesion of the segment	is	mild demyelinating

Fig. 3. Sample of diagnosis rules applied to a motor segment of the median nerve Level 2: Each segment whose diagnosis is different from the normal label is pathological (we do

Acknowledgements. This work has been supported by the REGION RHONE-ALPES via the Pôle

Rhône-Alpes de Génie Biologique et Médical under grant 509004/12 GBM.

Recording point

Muscle : Abductor Pollicis Brevis

Stimulation points

Knowledge description and representation

knowledge levels

These two stages of the examination lead to the three following levels of knowledge (Fig. 2):

Level 1 : analysis of one nerve segment (step A,1),

Level 2 : analysis of a total nerve (step A,2): synthesis of the segment analyses, Level 3 : analysis of the whole nerves (step B): synthesis of the nerve analyses.

Thus, both level 2 and level 3 correspond to the synthesis of the preceding level.

Utilization

The finite automaton described above simulates the knowledge of level 2. One can consider that it is in itself a small-scale system (inference engine + knowledge base) in which the motor is constituted by the recursive predicate automaton, and the knowledge base is represented by the transition set. Thus, the automaton insertion in the expert system takes place at the inference engine level as well as at the knowledge base level.

The system architecture includes 4 cooperating knowledge sources successively used through the 4 phases of the diagnosis process (Fig. 9). A special inference engine supervises the successive use of the knowledge bases. These knowledge bases communicate via a central working memory, as in the case of a blackboard.