Elisabeth Beyersmann
email: lisi.beyersmann@gmail.com

Deirdre Bolger

Chotiga Pattamadilok

Boris New

Jonathan Grainger

Johannes C Ziegler

Morphological processing without semantics: An ERP study with spoken words

Keywords: morphological processing, spoken word recognition, auditory lexical decision, event-related potentials (ERPs)

The time-course of morphological processing during spoken word recognition was investigated using event-related brain potentials (ERPs) in an auditory lexical decision task.

We compared three different types of French words: truly suffixed (e.g., pochette 'little pocket' = poche 'pocket' + diminutive suffix -ette), pseudo-suffixed (e.g., mouette 'seagull' = mou 'soft' + pseudo-suffix -ette) and non-suffixed target words (e.g., fortune 'fortune' = fort 'strong' + non-suffix -une). Suffixed (e.g., mouesse = mou + suffix -esse) and non-suffixed nonwords (e.g., mouipe = mou + non-suffix -ipe) were also tested. The behavioural results

showed that participants responded more slowly to non-suffixed words than to truly suffixed and pseudo-suffixed words, but there was no difference between these two suffixed conditions. Moreover, participants made more errors rejecting pseudo-suffixed nonwords than non-suffixed nonwords. In the ERP analyses, T0 was shifted to the end of the embedded stem or pseudo-stem. The ERP results revealed enhanced N400 amplitudes for non-suffixed words compared to truly suffixed and pseudo-suffixed words. Again, there was no difference between the truly and pseudo-suffixed conditions. In addition, we found an increased N400 amplitude for both pseudo-suffixed and non-suffixed nonwords than for words. The latency of the onset of this N400 effect varied between the three experimental conditions: the wordnonword difference occurred earliest in the truly suffixed condition, slightly later in the pseudo-suffixed condition and latest in the non-suffixed condition. Both behavioural and EEG data jointly suggest that spoken words with a genuine morphological structure and words with a pseudo-morphological structure are decomposed into morphemic sub-units. Moreover, the earlier appearance of the N400 effects in the truly suffixed condition indicates that morphological information is more readily available in words with a semantically transparent morphological structure.

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Spoken complex word recognition 4

Introduction

Several decades of research have examined automatic parsing mechanisms involved in the visual recognition of morphologically complex words. However, comparatively little work has focussed on the automatic mechanisms involved in decomposing spoken complex words.

The goal of the present study was to address this research gap by examining the early stages of morphological processing during spoken word recognition, using both behavioural data and event-related brain potentials (ERPs).

Morphological processing during visual word recognition

One of the key findings in the masked priming literature is that real suffixed (e.g. hunter) and pseudo-suffixed primes (e.g. corner) both facilitate the recognition of the embedded target word (e.g. hunter-hunt; corner-corn), relative to an orthographic control (e.g. cashew-cash)

(for reviews, see [START_REF] Amenta | Morphological processing as we know it: an analytical review of morphological effects in visual word identification[END_REF][START_REF] Rastle | Morphological decomposition based on the analysis of orthography[END_REF]. A common interpretation of these widely replicated findings is that both real suffixed words and pseudo-suffixed words are rapidly decomposed into their real or pseudo-morphemic subunits (hunt + er; corn + er)

during the initial stages of visual word recognition (e.g., [START_REF] Beyersmann | Morpho-orthographic segmentation without semantics[END_REF][START_REF] Longtin | Morphological priming without morphological relationship[END_REF][START_REF] Rastle | The broth in my brother's brothel: Morphoorthographic segmentation in visual word recognition[END_REF], whereas no such decomposition mechanism applies to words consisting of an embedded word and a non-morphemic ending (cashew, where ew is not an affix). The extent to which individual participants rely on morphological parsing during lexical processing can be modulated by individual differences in spelling and vocabulary (e.g., [START_REF] Andrews | Is morphological priming stronger for transparent than opaque words? It depends on individual differences in spelling and vocabulary[END_REF][START_REF] Beyersmann | Language proficiency and morpho-orthographic segmentation[END_REF]. However, what continues to be a matter of debate is how early or late morphological processing is influenced by semantics (e.g., [START_REF] Cavalli | Spatiotemporal Dynamics of Morphological Processing in Visual Word Recognition[END_REF]Feldman, Milin, Cho, Moscoso Del Prado Martin, & O'Connor, 2015;Feldman, O'Connor, & Moscoso del Prado Martin, 2009). Some studies have reported equal magnitudes of priming for truly and pseudo-suffixed words, suggesting that the initial stages of morphological processing are

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Spoken complex word recognition 6 semantically 'blind' (e.g., [START_REF] Beyersmann | Morpho-orthographic segmentation without semantics[END_REF][START_REF] Longtin | Morphological priming without morphological relationship[END_REF][START_REF] Rastle | Morphological decomposition based on the analysis of orthography[END_REF][START_REF] Rastle | The broth in my brother's brothel: Morphoorthographic segmentation in visual word recognition[END_REF]. Other studies have reported significantly increased magnitudes of priming in the truly suffixed compared to the pseudo-suffixed condition, suggesting that semantics modulate the very initial stages of visual word recognition (e.g., Schmidtke, Matsuki, & Kuperman, 2017). The latter view is consistent with parallel distributed processing theories (e.g., Gonnerman, Seidenberg, & Andersen, 2007;[START_REF] Plaut | Are non-semantic morphological effects incompatible with a distributed connectionist approach to lexical processing?[END_REF] according to which the reading system picks up on statistical regularities, such as the consistency with which the letters of a morpheme are mapped onto semantic representations.

Feldman

Whether or not the early stages of morphological processing are modulated by semantics may also depend on the nature and productivity of the morphological parsing system within specific languages. For instance, Semitic languages such as Hebrew and Arabic consist of divergent internal word structures, where stems and affixes are intertwined rather than concatenated linearly. Morphological priming effects in these languages are particularly robust compared to other Indo-European languages (e.g., Frost, Kugler, Deutsch, & Forster, 2005;[START_REF] Velan | Words with and without internal structure: what determines the nature of orthographic and morphological processing?[END_REF], suggesting that the degree of semantic influence on early morphemic parsing might vary between different languages.

Very useful in the context of this debate have been studies combining masked priming and high-temporal resolution recordings of event-related brain potentials (ERPs) to investigate the influences of orthography and semantics during morphological processing (e.g., [START_REF] Beyersmann | Semantic processing during morphological priming: An ERP study[END_REF][START_REF] Dominguez | Event-related brain potentials elicited by morphological, homographic, orthographic, and semantic priming[END_REF]Jared et al., 2017;[START_REF] Lavric | What do fully visible primes and brain potentials reveal about morphological processing[END_REF][START_REF] Morris | Semantic transparency and masked morphological priming: an ERP investigation[END_REF]Morris, Grainger, & Holcomb, 2008, 2013;Morris, Holcomb, & Grainger, 2008;[START_REF] Morris | Effects of lexical status and morphological complexity in masked priming: An ERP study[END_REF][START_REF] Royle | The temporal dynamics of inflected word recognition: a masked ERP priming study of French verbs[END_REF]. The majority of the reported ERP results have typically shown no difference between true

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Spoken complex word recognition 7 morphological and pseudo-morphological priming in earlier time windows (for converging evidence from MEG, see [START_REF] Lehtonen | Evidence for early morphological decomposition: Combining masked priming with magnetoencephalography[END_REF][START_REF] Lewis | The neural basis of obligatory decomposition of suffixed words[END_REF][START_REF] Solomyak | Evidence for early morphological decomposition in visual word recognition[END_REF]2010;but see Jared et al., 2017). However, when visible primes were used (e.g., [START_REF] Lavric | What do fully visible primes and brain potentials reveal about morphological processing[END_REF], morphological priming effects continued to be significant, whereas pseudo-morphological priming effects tended to be absent or reduced in the later time windows. Concurrent evidence is also reported by [START_REF] Lavric | Tracking hierarchical processing in morphological decomposition with brain potentials[END_REF], who carried out an unprimed lexical decision study, contrasting morphological (hunter), pseudo-morphological (corner), and non-morphological (cashew) target words. Results revealed a difference at about 190 ms between the non-morphological condition and the two morphological conditions (which showed no differentiation), reflecting greater negative amplitudes in central and posterior electrodes for the non-morphological condition. In addition, a difference was observed between the pseudo-morphological condition and the other two conditions at about 250 ms (which showed no differentiation), reflecting greater positive amplitudes in central and parietal electrodes in the pseudomorphological condition. In sum, these findings appear to suggest that complex printed words are initially decomposed based on a purely structural form of morphological analysis, whereas semantic constraints are only taken into account at later stages during morphological processing.

The sensitivity of the N400 component to morphological processes is also evidenced by studies contrasting inflected relative to simplex words. For instance, two Finnish unprimed lexical decision studies reported larger N400 amplitudes for inflected words compared to matched mono-morphemic words [START_REF] Lehtonen | Recognition of morphologically complex words in Finnish: Evidence from event-related potentials[END_REF][START_REF] Leinonen | Neurocognitive processing of auditorily and visually presented inflected words and pseudowords: evidence from a morphologically rich language[END_REF] for related evidence from MEG, see [START_REF] Vartiainen | Neural dynamics of reading morphologically complex words[END_REF].

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Spoken complex word recognition 8

Morphological processing during spoken word recognition

Unlike the rich literature on the morphological processing of printed words, we know comparatively little about its role in spoken word recognition. A number of studies have found that listeners show sensitivity to morphological information during spoken word recognition (e.g., [START_REF] Balling | Morphological effects in auditory word recognition: Evidence from Danish[END_REF]Emmorey, 1989;Gwilliams, Monahan, & Samuel, 2015;[START_REF] Marslen-Wilson | Morphology and Meaning in the English Mental Lexicon[END_REF][START_REF] Meunier | Frequency effects in auditory word recognition: The case of suffixed words[END_REF][START_REF] Wurm | Auditory processing of polymorphemic pseudowords[END_REF]. For instance, Emmorey (1989) carried out an auditory priming task showing that pseudo-prefixed words with bound stems produce priming (e.g. submit -permit) whereas phonologically related words do not (e.g. balloon -saloon). However, these findings were not replicated with suffixed words. A cross-modal priming study by [START_REF] Marslen-Wilson | Morphology and Meaning in the English Mental Lexicon[END_REF] revealed priming effects with truly suffixed (e.g. punishment-punish), but not pseudo-suffixed forms (e.g. casualty-casual), suggesting that morphological decomposition only applies to words with a genuine morphological structure (see also [START_REF] Meunier | Morphological decomposition and semantic integration in word processing[END_REF] converging evidence from spoken pseudoword processing). Consistent with these findings, it has been shown that the way listeners process prefixed words is affected by the transparency of the semantic relationship between the word constituents (e.g., [START_REF] Wurm | Auditory Processing of Prefixed English Words Is Both Continuous and Decompositional[END_REF][START_REF] Wurm | Auditory processing of polymorphemic pseudowords[END_REF][START_REF] Wurm | Conditional root uniqueness points: Psychological validity and perceptual consequences[END_REF]. Hence, these findings from spoken word recognition seem to provide very little support in favour of semantically "blind" morphological segmentation, a pattern typically seen in visual word recognition.

Of course, auditory word studies differ from printed word studies in one important aspect. As discussed earlier, semantically blind processing of printed words is typically observed in masked priming paradigms that tap into the early, initial stages of word recognition. In contrast, auditorily presented stimuli are very difficult to mask. As a result, evidence for the morphological processing of spoken words mainly comes from lexical decision tasks using overtly presented primes or no primes, whose behavioural outcome may reflect both early and later, more strategic, stages of word recognition, and therefore provide

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Spoken complex word recognition 9 little insight into the automatic, online processes of word recognition. One solution to this problem is the recording of ERPs to more closely monitor how morphological processes unfold over time.

Auditorily presented inflected words typically elicit larger N400 amplitudes than mono-morphemic words [START_REF] Leinonen | Neurocognitive processing of auditorily and visually presented inflected words and pseudowords: evidence from a morphologically rich language[END_REF][START_REF] Leminen | Spatiotemporal dynamics of the processing of spoken inflected and derived words: A combined EEG and MEG study[END_REF], thus replicating what is seen in the visual modality (e.g., [START_REF] Lehtonen | Recognition of morphologically complex words in Finnish: Evidence from event-related potentials[END_REF][START_REF] Leinonen | Neurocognitive processing of auditorily and visually presented inflected words and pseudowords: evidence from a morphologically rich language[END_REF][START_REF] Vartiainen | Neural dynamics of reading morphologically complex words[END_REF]. Moreover, illegal derived nonwords elicit a larger wide-spread negativity than existing derived words and legal derived nonwords at ∼300 ms after suffix onset [START_REF] Leminen | Time course of the neural processing of spoken derived words: an event-related potential study[END_REF]. This larger negativity (resembling the N400) in the illegal nonword condition was interpreted as reflecting a more difficult lexical-semantic integration of the morpheme constituents. A comparable pattern of ERP results was described by [START_REF] Leminen | Neural dynamics of inflectional and derivational morphology processing in the human brain[END_REF], showing that derived words produced an enhanced mismatch negativity (MMN) 130-170 ms after suffix onset compared to their derived nonword counterparts (see also Ettinger, Linzen, & Marantz, 2014, for related evidence from MEG). However, although these studies clearly demonstrate that morphological information influences spoken word recognition, they do not address the important question of whether the processing of spoken complex words is largely determined by semantic transparency, as several behavioural studies would suggest (e.g., [START_REF] Marslen-Wilson | Morphology and Meaning in the English Mental Lexicon[END_REF][START_REF] Wurm | Auditory Processing of Prefixed English Words Is Both Continuous and Decompositional[END_REF][START_REF] Wurm | Auditory processing of polymorphemic pseudowords[END_REF], or if form-based morphological segmentation mechanisms operate independently of semantics, as repeatedly reported in the visual domain (e.g., [START_REF] Amenta | Morphological processing as we know it: an analytical review of morphological effects in visual word identification[END_REF][START_REF] Beyersmann | Morpho-orthographic segmentation without semantics[END_REF][START_REF] Dominguez | Event-related brain potentials elicited by morphological, homographic, orthographic, and semantic priming[END_REF][START_REF] Rastle | Morphological decomposition based on the analysis of orthography[END_REF][START_REF] Rastle | The broth in my brother's brothel: Morphoorthographic segmentation in visual word recognition[END_REF][START_REF] Royle | The temporal dynamics of inflected word recognition: a masked ERP priming study of French verbs[END_REF][START_REF] Stockall | A single route, full decomposition model of morphological complexity: MEG evidence[END_REF]. The goal of the present study was to address this question using an auditory lexical decision task and ERP recordings to uncover how auditory morphological processes unfold over time.

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Spoken complex word recognition 10

The present study

Our study was conducted in French, comparing three different item types: truly suffixed words (e.g., pochette 'little pocket', consisting of the stem poche 'pocket' + diminutive suffix -ette), pseudo-suffixed words (e.g., mouette 'seagull', consisting of the pseudo-stem mou 'soft', where the pseudo-suffix -ette is homophonous to the real diminutive suffix) and nonsuffixed words (e.g., fortune 'fortune', containing the embedded word fort 'strong' followed by a non-suffix ending 'une'). To our knowledge, this is the first ERP study contrasting the auditory processing of truly suffixed and pseudo-suffixed words.

If it is indeed the case that morphological decomposition in the auditory modality is largely determined by semantics, we would expect to see (i) a reduction of the N400 amplitude for truly suffixed words relative to the pseudo-suffixed and non-suffixed conditions, and (ii) a greater "word-advantage" for truly suffixed words (i.e. shorter response latencies, lower error rates, and reduced N400 amplitudes relative to their corresponding nonwords) than for pseudo-suffixed and non-suffixed words. Behaviorally, this pattern should be reflected in faster and more accurate responses in the truly suffixed condition compared to the pseudo-suffixed and non-suffixed conditions, because access to the affix and the stem typically "bolsters" word responses (Gwilliams et al., 2015).

If however morphological processing operates independently of semantics (as Lavric et al., 2012's findings suggest), we would expect the N400 amplitudes for truly and pseudosuffixed words to pattern together (e.g., pochette and mouette) and differ from the nonsuffixed condition (e.g., fortune). In other words, the presence of an affix in the truly suffixed and pseudo-suffixed word conditions should lead to a reduction of the N400 amplitude, relative to the non-suffixed control. Moreover, a word-advantage (i.e., a reduction in N400 amplitude) should be evident for both truly suffixed and pseudo-suffixed words relative to their corresponding nonword counterparts, whereas no such difference would arise between non-suffixed words and their corresponding nonword controls. Given that the behavioural

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Spoken complex word recognition 11 responses in an unprimed lexical decision paradigm represent the end point of the lexical decision process, it is impossible to clearly tease apart early form-based vs. later semantic influences on the observed response latencies or error rates (which is precisely why we combined behavioural measures with the recordings of ERPs in this study). That is, the behavioural component of the morpheme facilitation effect may emerge for both truly suffixed and pseudo-suffixed words [START_REF] Lavric | Tracking hierarchical processing in morphological decomposition with brain potentials[END_REF], or alternatively only for truly suffixed words [START_REF] Rastle | Morphological and semantic effects in visual word recognition: A time-course study[END_REF].

In addition to the word trials, two sets of pseudo-suffixed and non-suffixed nonwords were included in the lexical decision task. For each word (e.g. mouette), we created a corresponding pseudo-suffixed nonword (by replacing the ending with a suffix, e.g. mouesse,

where -esse is a real French affix) and a corresponding non-suffixed nonword (by replacing the ending with a non-suffix, e.g. mouipe, where -ipe is not an affix). As such, we obtained item triplets with an identical word stem (e.g., mou) at word onset. If auditorily presented complex nonwords are decomposed into morphemic subunits just like words are, we would expect to see a "morpheme interference effect" [START_REF] Caramazza | Lexical access and inflectional morphology[END_REF][START_REF] Taft | Lexical storage and retrieval of prefixed words[END_REF] for pseudo-suffixed compared to non-suffixed nonwords. That is, nonwords consisting of stems and suffixes (e.g., mouesse) should be harder to reject and therefore elicit an enhanced N400 amplitude compared to nonwords consisting of stems and non-suffixes (e.g., mouipe).

Generally, the N400 effect for morphologically complex words occurs later in the auditory modality than in the visual modality, and response latencies are overall slower than in the visual modality (for a direct comparison of suffixed inflected word processing in the visual and auditory modalities, see [START_REF] Leinonen | Neurocognitive processing of auditorily and visually presented inflected words and pseudowords: evidence from a morphologically rich language[END_REF]. Moreover, the N400 in the auditory modality is more spread out than the N400 in the visual modality (e.g., see the auditory modality, we expected to observe a relatively late emergence of the N400 effect and overall slower response times than standardly reported in the visual modality.

Method

Participants

Twenty-eight healthy, native French-speaking volunteers (16 females, 12 males) participated in this study for monetary reimbursement. Their ages ranged from 18 to 46 years (mean age = 23.8, SD = 6.8). All were right-handed, with normal or corrected or corrected-to-normal vision and none reported any neurological or language impairment. All participants were university students and gave written consent. Ethics approval was obtained from the Institutional Review Board of Aix-Marseille University.

Materials

Fifty-one French pseudo-suffixed target words (e.g. mouette), were selected from the Lexique database [START_REF] New | Lexique 2: A new French lexical database[END_REF]. The pseudo-suffixed target words were selected such that the whole word never shared any semantic relationship with the embedded pseudo-stem (mou). In addition, we chose 51 truly suffixed target words (e.g. pochette),

where whole word and stem (poche) always shared a semantic relationship. The truly and pseudo-suffixed target words shared the exact same suffixes (and thus the exact same final string of phonemes). Finally, a third set of 51 non-suffixed items was selected from Lexique (e.g. fortune), which consisted of an embedded word (fort) and a meaningless non-morphemic ending (-une). Given that the items were presented auditorily, we ensured that the pronunciation of the stem did not change in the embedded context. All 153 target words were nouns.

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Spoken complex word recognition 13

The three sets of targets words were matched as closely as possible on written word frequency, spoken word frequency, number of letters, number of phonemes, number of syllables, orthographic neighbourhood (orthographic N), phonological neighbourhood (phonological N), orthographic Levenshtein distance 20 (old20), phonological Levenshtein distance 20 (pld20), ending length and uniqueness point (UP). Semantic relatedness values between whole words and their embedded words (e.g. mouette and mou) were extracted using the Latent Semantic Analysis Web facility (http://lsa.colorado.edu; [START_REF] Landauer | A solution to Plato's problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge[END_REF]. This analysis revealed that semantic relatedness values in the truly suffixed condition (0.24) were significantly higher than those in both the pseudo-suffixed (0.11) and the nonsuffixed conditions (0.11), but the pseudo-suffixed and non-suffixed conditions did not differ (see Figure 1). Crucially, a close inspection of the 20 nearest semantic neighbours of our target words showed that the results were highly inaccurate, presumably due to a bug in the French corpus analysis. We therefore applied the Latent Semantic Analysis model [START_REF] Landauer | A solution to Plato's problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge[END_REF] to a lemmatised corpus of 1.2 Go of French books, which replicated the results of the Latent Semantic Analysis Web facility (i.e. the semantic similarity between words and their embedded stems was significantly higher for truly suffixed words [0.54] than for pseudo-suffixed words [0.29], and 0.28 for non-suffixed words [0.28]). The mean item characteristics for each condition and p-values for the critical comparisons are reported in Appendix A.

-Figure 1 -For each word target, a pseudo-suffixed and a non-suffixed target nonword were created (306 nonwords in total). Pseudo-suffixed nonwords included the same stem but different affix, such that the whole letter string was not a word (e.g., for mouette, we selected the pseudo-suffixed nonword mouesse). The suffixes of the word targets were 'recycled' in the nonword targets by changing suffixes between different stems. Non-suffixed nonwords included the same stem with a non-morphemic ending (e.g. for mouette, we selected the non-

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Spoken complex word recognition 14 suffixed nonword mouipe). The non-morphemic endings of the nonwords were identical to the non-morphemic endings of the non-suffixed words. Only a few phonemes had to be changed in the nonwords to maintain the pronounceability of the letter string, and to match syllable structure. Three counterbalanced experimental lists were created using a Latin square design, such that every embedded word only occurred once in each list (e.g. mouette, mouesse and mouipe all occurred in different experimental lists, in order to avoid repetition of the embedded word mou within lists and therefore within participants).

Auditory targets were produced with the OS X Speech Synthesizer, using the French male voice 'Thomas'. The naturalness of the synthesized files was checked by two independent French native speakers. The speaking rate was set to 180 words per minute. All stimuli had a bit rate of 705 kbps. Auditory files were edited to ensure that any silence at the beginning and end of each item was removed. The mean stimulus duration across all items was 628ms. The mean durations per word-type and condition are presented in Table 1. A list of all items is presented in Appendix B.

-Table 1 -

Procedure

Stimuli were presented using experimental software EPrime 2.0 (Psychology Software Tools, Pittsburgh, PA). Participants were tested individually in a Faraday cage. Each trial consisted of a fixation cross which appeared in the centre of an LCD computer screen for 1000 ms, followed by the auditory target. The inter-trial interval was 1000 ms. If participants did not respond after 3 seconds had elapsed, the experiment proceeded automatically to the next trial.

The auditory target words were presented via headphones binaurally. Participants were instructed to decide as quickly and accurately as possible if the presented items were real French words or not. Participants responded by pressing one of two different response buttons. The right hand was used to respond YES and the left hand was used to respond NO.

Stimuli were presented in randomized order. All participants completed the three

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Spoken complex word recognition 15 experimental lists, but in randomised order (i.e. six possible list orders were created, which were assigned to 4 or 5 participants each). The ERP cap installation time (prior to testing) took between 20-30 minutes per participant. Each experimental list took approximately 10 minutes to complete (30 minutes in total).

Results

ERP recording and Pre-processing

ERPs were recorded using the Biosemi Active2 system at a sampling rate of 2048Hz. Sixtyfour electrodes were arranged on the participants' scalps using the 10-20 placement system.

Four additional electrodes were used to record vertical and horizontal eye movements (vEOGs and hEOGs, respectively). Two electrodes were positioned on the right and left mastoids; the left mastoid served as reference during recording. Throughout EEG acquisition, electrode impedance was kept below 20kΩ.

Processing of EEG data was carried out using the EEGLAB toolbox [START_REF] Delorme | EEGLAB: an open source toolbox for analysis of singletrial EEG dynamics including independent component analysis[END_REF]. The acquired EEG was down-sampled to 512Hz offline and a second-order Butterworth band-pass filter (0.1Hz -40Hz) was applied. The data were re-referenced to the average of the right and left mastoids. Noisy electrodes were detected in a semi-automatic manner by observing the electrode spectra and by calculating the kurtosis for each channel;

those channels with a kurtosis value exceeding 5 (z-score) were considered for rejection.

Ocular movements were corrected with Independent Component Analysis (ICA) by calculating the infomax ICA algorithm [START_REF] Bell | An information-maximization approach to blind separation and blind deconvolution[END_REF] on the 64 scalp electrodes.

To facilitate the calculation of clean ICA components, intervals of signal presenting very large noise exceeding 75µV were detected automatically and removed from the continuous data before ICA calculation. Those components corresponding to eye artefacts were identified via component topography, spectra and time course and only those components corresponding

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Spoken complex word recognition 16

to eye artefacts were removed; this generally corresponded to the first component. After ICA correction, those electrodes rejected due to noise were interpolated using spherical spline interpolation. The continuous data were then segmented into individual trials using the end of the embedded stems or pseudo-stems (e.g. the end of mou in mouette) as T0 1 . For each trial a pre-stimulus interval of 200ms was defined to ensure the same baseline activity for all word types. With T0 at the offset of the embedded stems, a post-stimulus interval of 700ms was defined. The pre-stimulus interval served as baseline, and baseline correction was carried out for all trials. Those trials in which the participants' reaction times fell outside the lower and upper limits of 200ms and 3000ms, respectively, were automatically rejected. Noisy trials were detected semi-automatically. Firstly, those epochs with activity exceeding a limit of ±75µV were removed. Linear drift was assessed and instances of drift exceeding 10µV were marked after which the remaining epochs were assessed using kurtosis, applying a limit of 5 (z-scores).

Five participants were excluded from the study due to the large number of trials rejected because of high error rates, extreme reaction times, or noisy EEG data. In addition, twelve words in the non-suffixed condition were incorrectly classified as non-morphological as they consisted of pseudo-stem + pseudo-suffix (highlighted with an asterisk in Appendix B) and were therefore excluded from behavioural and ERP analyses. Table 2 summarizes the total number of epochs retained after data cleaning as well the average proportion of epochs rejected across participants.

-Table 2 -

Statistical analyses

Behavioural analyses

1 In an earlier version of our manuscript the continuous data were segmented using the onset of the auditory target as T0, while using the same baseline. These earlier analyses led to similar but later effects, which are reported in the supplementary materials.

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Spoken complex word recognition 17

Lexical decisions to word and nonword targets were analysed as follows. Reaction times and error rates were analysed separately. Incorrect responses were removed from the reaction time (RT) analysis (7.7% of all data). Inverse RTs (-1000/RT) were calculated for each participant to correct for RT distribution skew and used throughout the analyses (Kliegl, Masson, & Richter, 2010). RTs and error rates are presented in Tables 3 and4 (see below)

and were analysed for each participant.

We used linear mixed-effect modelling to perform the main analyses [START_REF] Baayen | Analyzing linguistic data: A practical introduction to statistics using R[END_REF][START_REF] Baayen | Mixed-effects modeling with crossed random effects for subjects and items[END_REF]. Fixed effects, random effects, and random slopes were only included if they significantly improved the model's fit in a backward stepwise model selection procedure. Models were selected using chi-squared log-likelihood ratio tests with regular maximum likelihood parameter estimation. The model was refitted after excluding data-points whose standardised residuals were larger than 2.5 in absolute value (see [START_REF] Baayen | Analyzing linguistic data: A practical introduction to statistics using R[END_REF], which led to the removal of 1.6% of the nonword data and 2.4% of the word data. Trial order was included to control for longitudinal task effects such as fatigue or habituation.

Experimental list order was included as a covariate, in order to examine whether or not the observed effects would be modulated by number of exposures to the embedded word. In addition, we included word properties (i.e., subtitle word frequency, number of phonemes, number of syllables, phonological Levenshtein distance 20 (PLD20), uniqueness point (UP), and semantic relatedness proportion (LSA)) for both whole words (i.e. target words) and embedded words as covariates in the word analyses, to control for item specific differences across target words. The subtitle word frequencies were extracted from the film subtitle corpus in Lexique based on 52 million French words [START_REF] New | The use of film subtitles to estimate word frequencies[END_REF], coming from a variety of films, and then transformed using the Zipf scale (Van Heuven, Mandera, Keuleers, & Brysbaert, 2014). In addition, the duration of the embedded stem or pseudo-stem (in ms) was added as a covariate in the analyses to control for

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Spoken complex word recognition 18 differences in stimulus length. All continuous variables were centered and the lmer default coding for treatment contrasts (i.e., in alphabetical order) was used for the item type variable.

Word targets and nonword targets were first analysed separately, followed by a combined analysis. In the word data, factor item type was a 3-level factor (truly suffixed, pseudo-suffixed, non-suffixed), whereas in the nonword data, factor item type was a 2-level factor (suffixed, non-suffixed). Linear mixed-effects model as implemented in the lme4 package [START_REF] Bates | lme4: Linear mixed-effects models using Eigen and S4. R package version 1[END_REF] in the statistical software R (Version 3.0.3; RDevelopmentCoreTeam, 2008) were fitted using the above described model selection procedure. P-values were determined using the lmerTest package (Kuznetsova, Brockhoff, & Christensen, 2014).

Error analyses followed the same logic as the RT analyses. We applied a binomial variance assumption to the trial-level binary data using the function glmer as part of the Rpackage lme4.

Words.

In the reaction time analyses, the final linear mixed-effect model included five fixed effects factors (item type, list order, whole-word frequency, embedded word frequency, embedded word duration), random intercepts for participants and items, and random slopes for list order by participants. A significant effect of item type showed that participants responded more slowly to non-suffixed words than to truly suffixed words (t = 3.89, p < .001) and pseudo-suffixed words (t = 3.39, p < .001). The difference between the truly suffixed and the pseudo-suffixed condition was not significant (t = 0.53, p = .598). There was also a marginal main effect of list order (Χ 2 (1) = 3.28, p = .070) showing that participants responded gradually more slowly in the second and third experimental list compared to the first list. In addition, the analyses revealed a significant main effect of whole-word frequency (Χ 2 (1) = 22.54, p < .001) showing that participants responded faster to high frequency words, as well

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Spoken complex word recognition 19 as a significant main effect of embedded word frequency (Χ 2 (1) = 6.85, p = .009), showing that participants responded slower to targets with embedded high frequency words than to targets with embedded low frequency words (see Figure 2). The interactions between wholeword frequency and item type as well as the interaction between embedded word frequency and item type were not significant (Χ 2 (2) = 2.24, p = .326; Χ 2 (2) = 0.96, p = .619). To examine whether or not semantics influenced the activation of the embedded word, we tested the interaction between embedded word frequency and LSA semantic overlap, which turned out to be non-significant (Χ 2 (1) = 2.05, p = .152). Finally, there was a significant main effect of embedded word duration (Χ 2 (1) = 42.23, p < .001), showing that response times increased with increasing stimulus durations. No other effects were significant.

-Figure 2-

In the error analyses, the final linear mixed-effect model included two fixed effects factors (whole-word frequency, number of phonemes of the whole word), and random intercepts for participants and items. The results showed that participants made less errors responding to high frequency than low frequency words (z = 3.61, p < .001) and less errors responding to shorter than longer words (z = 2.56, p = .011).

-Table 3-

Nonwords.

In the reaction time analyses, the final linear mixed-effect model included one fixed effects factor (list order), random intercepts for participants and items, and random slopes for list order by participants. The results revealed a marginal main effect of list order (t = 1.72, p = .099), suggesting that participants were gradually able to more rapidly reject nonwords in the second and third experimental list compared to the first list. There were no other significant effects.

In the error analyses, the final linear mixed-effect model included two fixed effects factors (item type; list order), random intercepts for participants and items, and random slopes

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Spoken complex word recognition 20

for item type by participants. There was a significant effect of item type (z = 7.51, p < .001),

showing that participants made more errors rejecting suffixed nonwords than non-suffixed nonwords. There was also a significant main effect of list order (z = 4.84, p < .001), indicating that participants gradually made less errors in the second and third experimental list compared to the first list, which is consistent with the training effect seen in the reaction time data.

-Table 4-

Words vs. nonwords.

In the reaction time analyses, the final model included two fixed effects factors (lexicality; item type), their interaction, random intercepts for participants and items, and random slopes for lexicality by participants. Reaction time analyses revealed a marginal main effect of lexicality (Χ 2 (1) = 3.57, p = .059), suggesting that participants were on average faster at responding to words than to nonwords. There was also a significant interaction between lexicality and item type (Χ 2 (2) = 37.44, p < .001), suggesting that the "word-advantage" was greater in the truly suffixed and pseudo-suffixed conditions than in the non-suffixed condition (t = 6.47, p < .001; t = 6.51, p < .001), whereas the word-advantage was equally large in the suffixed and pseudo-suffixed conditions (t = 0.01, p < .992). No other effects were significant.

In the error analyses, the final model included two fixed effects factors (lexicality; list order), random intercepts for participants and items, and random slopes for lexicality by participants. The main effect of lexicality (z = 6.12, p < .001) showed that overall participants made more errors responding to words than to nonwords, which indicates that the lexicality main effect in the RT data is due to an accuracy-speed trade off. There was also a significant effect of list order (z = 2.08, p = .038), indicating that participants gradually made less errors in the second and third experimental lists compared to the first list.

ERP analyses

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Spoken complex word recognition 21

Response contingent analyses were performed on ERP data. Throughout the ERP analyses, T0 was shifted to the end of the embedded stem or pseudo-stem.

Words.

Figure 3 presents the scalp maps of the activity over time, from -200 to 700ms for each word condition; each scalp map presents the mean activity in a 100ms time window. In addition, a plot of the Global Field Power (GFP) of each condition was plotted from -200 to 700ms. The GFP is the spatial root mean square across all electrodes and provides a global measure of the electric activity at the level of scalp [START_REF] Skrandies | Global field power and topographic similarity[END_REF]. One of the main advantages of GFP is that it yields a general estimate of electric activity that does not suffer from spatial bias, from the variations in the latencies of peaks activity that can be observed across different electrodes [START_REF] Michel | EEG source imaging[END_REF]. Here, the GFP provides a clear picture of the difference and similarity in the time-course of activity for the truly suffixed (TS), pseudosuffixed (PS) and non-suffixed (NS) conditions. Both the scalp maps and the GFP plots of the three word conditions demonstrate the similarity between the truly suffixed and pseudosuffixed conditions over the entire trial, as well as the divergence of the NS condition activity at a later time window spanning 400 to 600ms.

-Figure 3 -To determine when and over which brain regions differences emerge, without having to define temporal windows or electrodes of interest a priori, the participant-level grandaverage ERP data were subjected to a permutation test with cluster-based correction [START_REF] Maris | Nonparametric statistical testing of EEG-and MEG-data[END_REF] for each pairwise comparison (TS vs. NS, PS vs. NS, TS vs. PS). This analysis was carried out using the Matlab toolbox, FieldTrip [START_REF] Oostenveld | FieldTrip: open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data[END_REF]. A cluster-corrected permutation test revealed that the NS-TS difference was statistically significant from 300-500ms and the NS-PS difference was statistically significant from 400-500ms, and that these differences were concentrated over central and parietal regions (Figure 4). The TS vs. PS comparison did not reveal any significant differences according to the permutation test.

-Figure 4 -

The effect of item type on the grand average ERP activity is further highlighted in Figures 5a, 5b, and 5c. Significant differences between the NS vs. TS and NS vs. PS comparisons emerged over central and posterior electrodes of the right and left hemispheres.

Figures 5a, 5b and 5c present a subset of these electrodes (C3, Cz, C4, P3, Pz, P4, PO3, POz, PO4). Taken together, the results of the spatio-temporal analysis (cluster-corrected permutation test) and the analysis of the ERP data suggest that non-suffixed words elicited a significantly greater negativity than both truly suffixed and pseudo-suffixed words over central and parietal electrodes from 300-500ms following stimulus onset. There were no significant differences between the truly suffixed and pseudo-suffixed conditions (Figure 5c).

-Figures 5a, 5b and 5c -

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Spoken complex word recognition 23

In addition, we investigated the possible variation of ERP amplitude as a function of word frequency and uniqueness point, which have been found to influence ERP amplitude and in particular N400 amplitude (e.g., Dufour, Brunellière, & Frauenfelder, 2013;[START_REF] O'rourke | Electrophysiological evidence for the efficiency of spoken word processing[END_REF]. We applied an ERP-image visualisation method developed by [START_REF] Delorme | Grand average ERP-image plotting and statistics: A method for comparing variability in event-related single-trial EEG activities across subjects and conditions[END_REF], which revealed no significant variation of ERPactivity as a function of spoken word frequency or uniqueness point.

Words vs. nonwords.

Grand-average ERPs at all electrodes comparing words and nonwords for each word type were calculated. As in the word analyses, T0 was shifted to the end of the embedded stem or pseudo-stem. To determine time windows presenting significant differences, three pairwise comparisons were carried out for each word type by applying a permutation test with FDR correction (p ≤ .05) on the grand-average ERP data: non-suffixed nonwords (nonword-NS) vs. suffixed nonowords (nonword-S), words vs. non-suffixed nonwords and words vs.

suffixed nonwords (see Figures 6,7, and 8). While the permutation test did not reveal any statistically significant differences between the two types of nonwords (nonword-NS vs.

nonword-S), it did reveal a significant difference between words and nonwords. The wordnonword difference emerged between 300-700ms in the truly suffixed and pseudo-suffixed conditions (Figures 6 and7) and between 400-700ms in the non-suffixed condition (Figure 8).

In addition, the statistical analysis revealed that in the non-suffixed and pseudo-suffixed conditions the difference between non-suffixed nonwords and words (e.g. fortaque vs.

fortune) emerged slightly earlier than the difference between suffixed nonwords and words (e.g. forteur vs. fortune).

-Figures 6,7, and 8 -To obtain insight into the spatial and temporal distribution of the word-nonword differences observed in the grand-average ERPs, a cluster-corrected permutation test (p≤ .025,

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Spoken complex word recognition 24 two-tailed) was carried out on the participant-level grand-average data (see Figure 9).

Consistent with the ERP results in Figures 6,7, and 8, the results revealed an enhanced negativity for nonwords compared to words across all word types, in a time window between 300 -700ms. This N400 effect was widely distributed, spanning frontal, central and parietal regions, for the truly-suffixed and pseudo-suffixed conditions in particular. Interestingly, the spatial-temporal analysis revealed that the latency of this late effect was not uniform across the three conditions (see Figure 9): its onset occurred earliest in the truly-suffixed condition (300ms after stimulus onset), second in the pseudo-suffixed condition (300-400ms after stimulus onset) and latest in the non-suffixed condition (400-500ms after stimulus onset).

Nonwords showed a sustained negative deflection across all item types (see Figures 6,7, and 8).

-Figure 9 -It is noteworthy, however, that the earlier difference observed for the nonsuffixed condition over the 0-200ms time window did not reach statistical significance within the two-tailed cluster-corrected permutation test, given the parameters set for its calculation (in particular, the requirement of a minimum of 3 electrodes to establish spatial adjacency). Only when we carried out statistical analysis for individual electrodes (p ≤ ≤ ≤ ≤ .05, fdr corrected) did we find a significant effect for a limited number of electrodes, which was concentrated over the left posterior region (see Figure 10).

-Figure 10 -

Discussion

The aim of the present study was to examine morphological processing during spoken word recognition using ERP recordings in combination with an auditory lexical decision task. To this end, truly suffixed words were compared to pseudo-suffixed and nonsuffixed words, and pseudo-suffixed to non-suffixed nonwords. T0 was shifted to the end of

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Spoken complex word recognition 25 the embedded stem or pseudo-stem throughout the ERP analyses. The results can be summarised as two key findings, which we discuss below.

First, both EEG and behavioural results clearly dissociate the two morphological conditions from the non-morphological condition, thus providing evidence for a robust morpheme facilitation effect. Participants responded more slowly to non-suffixed words than to truly suffixed and pseudo-suffixed words, but no difference was found between the two suffixed conditions. This is in line with previous evidence from spoken word recognition, demonstrating that auditorily presented morphologically complex words are easier to classify than non-suffixed words, because hypothetically, access to the affix and the stem facilitates word recognition (Gwilliams et al., 2015). In line with the behavioural findings, the ERP waveforms of the two suffixed conditions did not significantly differ from each other (see Figure 5c). The presence of an affix in the truly suffixed and pseudo-suffixed words led to a reduction in N400 amplitude relative to the non-suffixed control condition (see Figures 5a and5b), thus providing evidence for morphological processing operating independently of semantics [START_REF] Lavric | Tracking hierarchical processing in morphological decomposition with brain potentials[END_REF].

One explanation for this pattern of results is that the spoken word recognition system benefits from the principle of full decomposition combined with the principle of edge-aligned embedded word activation (Grainger & Beyersmann, 2017), suggesting that word recognition is facilitated when the whole letter string can be completely divided into potential constituent morphemes. For example, hunter can be parsed into hunt and er, corner can be parsed into corn and er, but for non-suffixed words like cashew the principle of full decomposition fails, because the edge-aligned embedded word (cash) cannot be combined with another morpheme Spoken complex word recognition 26 1999; [START_REF] Stockall | A single route, full decomposition model of morphological complexity: MEG evidence[END_REF][START_REF] Taft | Lexical storage and retrieval of prefixed words[END_REF]. Here we propose to extend the principle of full decomposition to spoken word recognition, as it unambiguously explains why the morpheme facilitation effect is observed in the truly suffixed and pseudo-suffixed conditions, but not in the non-suffixed control condition (for a related proposal on auditory prefixed word processing, see [START_REF] Wurm | Auditory Processing of Prefixed English Words Is Both Continuous and Decompositional[END_REF].

The second key finding, which is complementary to the first one, is that the reduction of the N400 amplitude in the truly suffixed relative to the non-suffixed condition emerged slightly earlier (from 300ms onwards; see Figure 5a) than in the pseudo-suffixed condition (from 400ms onwards; Figure 5b). This result is further enhanced by the fact that we also found an enhanced and sustained N400 amplitude for nonwords compared to words which varied between the three experimental conditions: the word-nonword difference occurred earliest in the truly suffixed condition (e.g., pochette vs.

pochure/pochique; Figure 6), slightly later in the pseudo-suffixed condition (e.g., mouette vs.

mouesse/mouipe; Figure 7) and latest in the non-suffixed condition (e.g., fortune vs.

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Spoken complex word recognition 28

The word-nonword differences in the two suffixed conditions (Figures 6 and7) emerged about the same time as the morphological effects in these conditions (Figures 5a and5b), presumably because of the linearity of the auditory input signal. Since the onset of every auditory stimulus (without exception) was always a word (e.g. mou in mouette, mouesse and mouipe), participants had to delay their lexical decisions as well as morphological processing until the final part of the input signal, which is likely why word-nonword differences and the effect of morphology coincided in these data.

With respect to the timing of ERP responses in visual versus auditory lexical decision, our study is only partially consistent with the results of ERP studies that have examined morphological processing in the visual modality. On the one hand, the reduction of N400 amplitude is comparable to results from visual word recognition, where semantically blind morphological segmentation mechanisms are typically found around 200-500 ms after stimulus onset (e.g., [START_REF] Beyersmann | Morpho-orthographic segmentation without semantics[END_REF][START_REF] Lavric | Tracking hierarchical processing in morphological decomposition with brain potentials[END_REF][START_REF] Longtin | Morphological priming without morphological relationship[END_REF][START_REF] Quémart | The role of form and meaning in the processing of written morphology: A priming study in French developing readers[END_REF][START_REF] Rastle | Morphological decomposition based on the analysis of orthography[END_REF][START_REF] Rastle | The broth in my brother's brothel: Morphoorthographic segmentation in visual word recognition[END_REF]. An additional aspect of our findings, which provides further insights into the nature of the morphological decomposition process, is that auditory lexical decision latencies decreased with increasing whole-word frequencies, but increased with increasing embedded word frequencies (see Figure 2). The interaction between embedded word frequency and LSA semantic relatedness was not significant, suggesting that embedded words were activated independently of whether or not they shared a semantic relationship with the whole word. The main effect of embedded word frequency is consistent with a growing body of evidence (e.g., Amenta, Marelli, & Crepaldi, 2015;[START_REF] Beyersmann | Language proficiency and morpho-orthographic segmentation[END_REF][START_REF] Beyersmann | Embedded Stem Priming Effects in Prefixed and Suffixed Pseudowords[END_REF][START_REF] Marelli | A database of orthography-semantics consistency (OSC) estimates for 15,017 English words[END_REF]Marelli, Amenta, & Crepaldi, 2015;[START_REF] Taft | What cross-morphemic letter transposition in derived nonwords tells us about lexical processing[END_REF], suggesting that embedded words are always activated independently of whether they are accompanied by an affix (as in farm + er or corn + er) or a non-affix (as in cash + ew). The activation of embedded words (e.g., cash) then generates lexical competition with the whole word (e.g., cashew), thus leading to an increase in response times across

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Spoken complex word recognition 30 conditions (Grainger & Beyersmann, 2017). As the left panel of Figure 2 shows, the greater the frequency of the embedded word, the greater the competition. Crucially, although the embedded word frequency effect was observed across all item types, our combined behavioural and ERP data clearly demonstrate a robust morpheme segmentation effect in the two morphological conditions compared to the non-affixed control. This indicates that differences between (pseudo-)affixed and non-affixed words might depend on factors that are not necessarily related to the stem. Instead, it seems to be the absence of a suffix in the nonsuffixed items that is driving differences in effect sizes across item types. The presence of a suffix in the truly and pseudo-suffixed words would have provided a boost in activation to the whole stimulus, thus leading to faster response times and reduced N400 amplitudes in these conditions.

Finally, the behavioural results showed that participants made more errors rejecting pseudo-suffixed nonwords than non-suffixed nonwords, thus replicating the classical morpheme interference effect [START_REF] Caramazza | Lexical access and inflectional morphology[END_REF][START_REF] Taft | Lexical storage and retrieval of prefixed words[END_REF]. The presence of the embedded morphemic unit increases the 'word-likeness' of the nonword, which as a result becomes harder to reject. The EEG data did not reveal a statistically significant difference between the pseudo-suffixed and non-suffixed nonword conditions. It is possible that the morpheme interference effects in the behavioural data reflect later post-lexical processing stages, which are not picked up in the ERP signal. In any case, it is worth noting that previous ERP studies have not always confirmed the morpheme interference effect for complex nonwords (e.g., [START_REF] Leinonen | Neurocognitive processing of auditorily and visually presented inflected words and pseudowords: evidence from a morphologically rich language[END_REF], suggesting that this effect may not be as robust as the morpheme facilitation effect that is typically seen in the word data.

In sum, the present data shed new light onto the mechanisms involved in the recognition of morphologically complex spoken words. Both the behavioural and ERP data concurrently suggest that not only words with a true morphological structure, but also words with a pseudo-morphological structure are decomposed into morphemic sub-units during

  et al., 2015; Feldman et al., 2009; Jared, Jouravlev, & Joanisse, 2017;

Figure 1

 1 Figure 1 in Perre, Midgley, & Ziegler, 2009). Given that all our stimuli were presented in

  The cluster-corrected permutation test simplifies the resolution of the multiple comparison problem by correcting at the level of clusters formed on the basis of spatio-temporal adjacency. To calculate the permutation distribution, 2000 random partitions were computed and only those samples with a permutation p-value below the critical cluster (p ≤ .05) were selected. Clusters were formed from these samples based on an adjacency criterion at the spatio-temporal level. Spatio-temporal adjacency was established on the basis of a minimum of 3 electrodes, and neighbouring electrodes were defined using the triangulation algorithm implemented in FieldTrip. Finally, those clusters with a Monte-Carlo p-value less than .025 (two-tailed test) were retained; a two-tailed test was carried out as we were interested in both negative and positive directions. The cluster-corrected permutation test was carried out for all time points (2ms time windows), however to facilitate visualisation, the results of the test are presented as topographies over time in 100ms time steps.

(

  cash + ?) to create an exhaustive decomposition of the full word. The principle of full decomposition has been previously described as a mechanism underlying visual word recognition and can account for a wide range of findings from visual lexical decision and masked priming (e.g.,Grainger & Beyersmann, 2017;[START_REF] Münte | Decomposition of morphologically complex words in English: Evidence from event-related brain potentials[END_REF]

  forteur/fortaque; Figure8). Thus, although the difference between the truly and pseudosuffixed conditions was not significant in the 300-400 ms time window, the permutation and word-nonword analyses appear to provide cumulative evidence for an effect of semantic transparency which is coupled with the semantically blind morphological parsing effect seen in the two morphological conditions with word stimuli. In other words, the here observed N400 appears to be a reflection of not just one, but two additive effects: a semantically blind morpheme facilitation effect and as well as a semantic transparency effect. The reason why these two effects emerge nearly simultaneously can be explained by the interplay between a purely form-based morphological parsing mechanism and the added influence of semantics. We hypothesise that both truly suffixed (e.g., hunt + er) and pseudo-suffixed words (e.g., corn + er) are exhaustively decomposed into morphemic sub-units (e.g., Rastle & Davis, et al., 2004), and that this decomposition process facilitates the activation of the corresponding whole words (hunter and corner) and the herewith associated lexical decision response. The morpheme facilitation effect therefore explains the processing advantage in the two morphological conditions compared to the non-suffixed condition. The semantic transparency effect on the other hand suggests that the semantic transparency of truly suffixed words provides an additional boost in activation to the whole word representation, which could be the cause of the earlier onset of effects seen with semantically transparent words. While semantically transparent complex words like hunter benefit from feedback connections from the semantic level to the lexical level, semantically opaque words like corner do not benefit from semantic support (Diependaele, Sandra, & Grainger, 2009; Grainger & Beyersmann, 2017). The spoken word recognition system might use semantic feedback to more efficiently evaluate the morphological segmentation process, which would explain why the N400 effect emerged slightly earlier in the truly suffixed condition, compared to the other two conditions. This complex interplay between the semantic transparency and morpheme facilitation effects also fits with the renowned complexity of the N400 component, with difficulty in processing and amount of semantic activation being two likely contributions to variations in N400 amplitude. The N400 component is commonly associated with semantic influences on word recognition (Holcomb & Neville, 1990), but is also thought to reflect word form processing difficulty (e.g., Perre et al., 2011) and orthographically guided lexical prediction (e.g., Kim & Lai, 2012; Laszlo & Federmeier, 2009) can also play a role.

  For instance,[START_REF] Beyersmann | Semantic processing during morphological priming: An ERP study[END_REF] reported a reduction of the N400 amplitude between 200-400 ms in the morphological condition but not in the semantic or orthographic control conditions.[START_REF] Lavric | ERP evidence of morphological analysis from orthography: A masked priming study[END_REF] found a reduced N400 amplitude between 340-460 ms in both the morphological and pseudo-morphological conditions, but not in the non-suffixed condition. On the other hand, our results deviate from visual word recognition studies in the sense that we did not observe any effects on earlier ERP components. For instance,Lavric and colleagues reported a study in which theycombined visual lexical decision with ERP recordings, showing an early difference from ~190 ms between suffixed and pseudo-suffixed words compared to non-suffixed words (Lavric et al., 2012). A masked primed lexical decision study by Morris et al. (2007) revealed an N250 effect which was significant in the truly suffixed but not in the pseudo-suffixed condition (see also Lavric, Clapp, & Rastle, 2007). In contrast, we did not witness any ERP components of readily available in visual compared to auditory word recognition, because the visual system can perform a quick initial form-based analysis of the letter string. In auditory word recognition, the acoustic signal unfolds in time and is more variable (e.g., depending on the speaker's voice and intonation) which may constrain the speed by which the listener is able to morphologically segment any given input signal. In addition, as Rastle (2018) pointed out, while printed morphemic sequences possess a high degree of regularity (e.g. the suffix -ed denotes the past tense), the phonetic forms of morphological units are considerably less consistent (e.g. the suffix -ed maps onto multiple sound sequences/Id/,/3d/, and/əd/). The inconsistency in sound-to-morpheme mappings is likely to provide a challenge to the morphological segmentation system in the auditory domain and thus offers an explanation for why the here observed morphological effects emerge comparatively later compared to the visual domain.

Figure 1 :Figure 10 .Figure 2 :Figure 3 :Figure 4 :Figure 6 :Figure 7 :Figure 8 :Figure 5a :Figure 5b :Figure 5c :Figure 9 :

 1102346785a5b5c9 Figure 1

Table 1 Table 1 :

 11 Mean item duration (in ms) for the whole stimulus and the embedded word within each condition.

		TS condition	PS condition	NS condition
		Mean duration of whole stimulus
	words	590	578	630
	pseudo-suffixed nonwords	618	603	608
	non-suffixed nonwords	681	649	691
		Mean duration of embedded word
	words	303	280	397
	pseudo-suffixed nonwords	296	280	293
	non-suffixed nonwords	299	277	298

Table 2 Table 2 :

 22 Summary of the total number of trials per condition and the average proportion of the trials retained over all 22 participants (n=22) for words, pseudo-suffixed nonwords and non-suffixed nonwords within the truly suffixed (TS), pseudo-suffixed (PS) and non-suffixed (NS) conditions. Standard deviations are presented in parentheses.

		TS condition	PS condition	NS condition
		Total Epoch Number (n=22)
	words	817	846	800
	pseudo-suffixed nonwords	884	854	894
	non-suffixed nonwords	934	926	930
		% Epochs Retained (n=22)
	words	70 (11.6)	72 (11.9)	64 (10.2)
	pseudo-suffixed nonwords	75 (15.3)	73 (13.1)	76 (12.4)
	non-suffixed nonwords	80 (10.7)	79 (11.9)	81 (11.8)
		Stimuli examples
	words	pochette	mouette	fortune
	pseudo-suffixed nonwords	pochure	mouesse	forteur
	non-suffixed nonwords	pochique	mouipe	fortaque

Table 3 Table 3 :

 33 Mean lexical decision times and error rates for word targets averaged across subjects. Standard deviations are shown in parentheses.

	Item type	Reaction times (ms)	Error rates (%)
	Truly suffixed	959 (74)	14.1 (6.4)
	Pseudo-suffixed	943 (70)	12.4 (8.7)
	Non-suffixed	1012 (84)	14.8 (8.9)

Table 4 Table 4 :

 44 Mean lexical decision times and error rates for nonword targets averaged across subjects. Standard deviations are shown in parentheses.

	Item type	Reaction times (ms)	Error rates (%)
	Pseudo-suffixed nonwords 1042 (114)	7.0 (7.8)
	Non-suffixed nonwords	1034 (95)	2.8 (5.3)

Acknowledgments

This research, carried out within the Labex BLRI (ANR-11-LABX-0036) and the Institute of Convergence ILCB (ANR-16-CONV-0002), has benefited from support from the French government, managed by the French National Agency for Research (ANR) and the Excellence Initiative of Aix-Marseille University A*MIDEX (ANR-11-IDEX-0001-02). This work was further supported by an ANR grant to JG (ANR-15-FRAL-0003-01, MORPHEME) and a Macquarie University Research Fellowship (MQRF) to EB.

 (2015). Must analysis of meaning follow analysis of form? A time course analysis.

Front Hum Neurosci,9,111. doi:10.3389 .730


Henri Gouin

Adiabatic waves along interfacial layers near the critical point Ondes adiabatiques le long des interfaces près du point critique

Near the critical point, isothermal interfacial zones are investigated starting from a non-local density of energy. From the equations of motion of thermocapillary fluids [1], we point out a new kind of adiabatic waves propagating along the interfacial layers. The waves are associated with the second derivatives of densities and propagate with a celerity depending on the proximity of the critical point.

Résumé

Près du point critique, les couches interfaciales sont modélisées à l'aide d'une densité d'énergie non locale. A partir des équations du mouvement des fluides thermocapillaires [1], nous mettons en évidence des ondes adiabatiques se propageant le long des couches interfaciales. Ces ondes associées aux dérivées secondes des densités se meuvent avec une célérité dépendant de la proximité du point critique.

Version française abrégée

Le modèle le plus simple permettant de considérer les couches capillaires et les phases comme un unique milieu continu, consiste à prendre en compte une énergie comme la somme de deux termes : le premier correspond à l'énergie du milieu supposé uniforme et de composition égale à la composition locale, le second est associé à la non uniformité du fluide et exprimé par un développement en gradient de la masse volumique qui est limité au second 1 ordre [START_REF] Van Der Waals | Thermodynamique de la capillarité dans l'hypothèse d'une variation continue de densité[END_REF][START_REF] Cahn | Free energy of a non-uniform system III[END_REF]. Ce modèle permet le prolongement au cas dynamique des études effectuées sur les systèmes en équilibre. L'énergie interne volumique du fluide est maintenant proposée sous la forme d'une densité α dépendant non seulement de grad ρ mais aussi de grad s où ρ et s notent respectivement la masse volumique et l'entropie spécifique. Les milieux associés appelés fluides thermocapillaires [START_REF] Casal | Equations of motions of thermocapillary fluids[END_REF] ont une densité d'énergie de la forme [START_REF] Casal | Equations of motions of thermocapillary fluids[END_REF]. Pour un fluide isotrope, l'énergie prend la forme (2) et l'équation du mouvement s'écrit sous les formes équivalentes [START_REF] Slemrod | Admissibility criteria for propagating phase boundaries in a van der Waals fluid[END_REF] ou [START_REF] Truskinovsky | Dynamics of non-equilibrium phase boundaries in a heat conducting non-linearly elastic medium[END_REF] dans lesquelles une entropie h et une température θ dites thermocapillaires explicitées en (4) font intervenir deux nouveaux vecteurs Φ and Ψ associés à la non homogénéité des zones interfaciales et donnés par [START_REF] Cahn | Free energy of a non-uniform system III[END_REF]. Une telle énergie interne associe dans les équations du mouvement et de l'énergie un tenseur des contraintes sphérique. Le cas des écoulements isentropiques associés à l'équation [START_REF] Rowlinson | Molecular theory of capillarity[END_REF] correspond à la conservation de l'énergie [START_REF] Gouin | Thermodynamic form of the equation of motion for perfect fluids of grade n[END_REF]. Les mouvements isothermes représentés par ( 9) et [START_REF] Gouin | Material waves of a fluid in the vicinity of the critical point[END_REF] ont comme cas particulier les équilibres isothermes entre phases. Il est alors possible d'étudier les profils des densités dans les équilibres unidimensionnels correspondant aux zones interfaciales planes. Le choix d'une énergie interne thermocapillaire de la forme [START_REF] Hadamard | Leçons sur la propagation des ondes et les équations de l'hydrodynamique[END_REF] associée à une énergie interne α du milieu supposé homogène ramène l'étude des zones interfaciales à l'analyse d'un système dynamique (12b), (12a) qui donne deux équations différentielles. L'analyse asymptotique de ce système au voisinage du point critique montre que la densité de masse pilote le système en ce sens que l'on est ramené à une décomposition dynamique représentée par le système (15b), (15a). L'intégration de ce système nous ramène simplement au cas d'un modèle ne faisant plus intervenir que grad ρ. On retrouve immédiatement dans (16), les résultats proposés par Rowlinson et Widom [START_REF] Rowlinson | Molecular theory of capillarity[END_REF] pour le profil de la masse volumique, l'épaisseur de la couche interfaciale et la valeur de la tension superficielle des interfaces fluides au voisinage du point critique. Il est maintenant possible d'étudier, dans les interfaces isothermes, les ondes d'accélération correspondant à des discontinuités faibles des mouvements isentropiques c'est-à-dire celles pour lequelles ρ, s, grad ρ et grad s sont continus à la traversée des surfaces d'onde. Un calcul à la Hadamard [START_REF] Hadamard | Leçons sur la propagation des ondes et les équations de l'hydrodynamique[END_REF] est proposé. Il prend en compte l'équation de conservation de la masse (18), l'équation du mouvement sous la forme (5) et la condition de Rankine-Hugoniot associée à l'équation du mouvement écrite sous la forme équivalente [START_REF] Truskinovsky | Dynamics of non-equilibrium phase boundaries in a heat conducting non-linearly elastic medium[END_REF]. Il permet alors d'obtenir un système (23), (25), (27) de trois équations linéaires et homogènes relatif aux discontinuités des dérivées secondes à travers les surfaces d'onde (paragraphe 4.1). La condition de compatibilité de ce système s'exprime par l'équation (28) qui donne ainsi la célérité de l'onde. La relation (15a) issue du système dynamique (14b), (14a) obtenu par l'analyse asymptotique du paragraphe 3, permet d'expliciter la relation liant les gradients d'entropie et de masse volumique. Nous la calculons pour la valeur de la masse volumique critique. Nous en déduisons la valeur explicite de la célérité des ondes d'accélération cisaillées dans les interfaces fluides. Cette célérité exprimée par la relation (29) dépend des conditions thermodynamiques du point critique et de l'importance des coefficients associés aux termes représentant l'inhomogénéité du fluide dans la zone interfaciale. Elle est proportionnelle à (T c -T 0 ) 2 où T 0 représente la valeur de la température dans les phases liquide et vapeur et T c note la température critique. Les ondes solitaires dans la direction normale aux zones interfaciales ne dépendent pas du gradient d'entropie. Il n'en est pas de même des ondes isentropiques d'accélération qui se meuvent le long des interfaces : le fait que l'énergie interne dépend non seulement du gradient de masse volumique mais aussi du gradient d'entropie fait appara ître un nouveau type d'onde qu'il est impossible de mettre en évidence dans les modèles plus simples ne faisant intervenir que le gradient de masse volumique. Ces ondes exceptionnelles au sens de Lax [START_REF] Boillat | Non linear hyperbolic fields and waves in[END_REF] nécessitent le cadre d'un modèle physique à au moins deux dimensions d'espace. Des expériences effectuées récemment dans des laboratoires embarqués dans des engins spatiaux et utilisant comme fluide test le gaz carbonique dans des conditions qui le placent au voisinage de son point critique semblent montrer l'existence de telles ondes [13] et justifieraient alors le bien fondé du modèle de fluides thermocapillaires.

Introduction

To study capillary layers and bulk phases, the simplest model considers an energy as the sum of two terms: a first one corresponding to a medium with a uniform composition equal to the local one and a second one associated with the non-uniformity of the fluid [START_REF] Van Der Waals | Thermodynamique de la capillarité dans l'hypothèse d'une variation continue de densité[END_REF][START_REF] Cahn | Free energy of a non-uniform system III[END_REF]. The second term is approximated by a gradient expansion, typically truncated to the second order. A representation of the energy near the critical point therefore allows the study of interfaces of non-molecular size. Obviously, the model is simpler than models associated with the renormalization-group theory [START_REF] Domb | The critical point[END_REF]. Nevertheless, it has the advantage of extending easily well-known results for equilibrium cases to the dynamics of interfaces [START_REF] Slemrod | Admissibility criteria for propagating phase boundaries in a van der Waals fluid[END_REF][START_REF] Truskinovsky | Dynamics of non-equilibrium phase boundaries in a heat conducting non-linearly elastic medium[END_REF]. For equilibrium, Rowlinson and Widom [START_REF] Rowlinson | Molecular theory of capillarity[END_REF] pointed out that the model can be extended by taking into account not only the strong variations of matter density through the interfacial layer but also the strong variations of entropy. In dynamics, for an extended Cahn and Hilliard fluid, the volumic internal energy ε is proposed with a gradient expansion depending not only on grad ρ but also on grad s (ρ is the matter density and s the specific entropy) :

ε = f (ρ, s, grad ρ, grad s). ( 1
)
The medium is then called a thermocapillary fluid [START_REF] Casal | Equations of motions of thermocapillary fluids[END_REF]. Using an energy in the form (1), we have obtained the equations of conservative motions for nonhomogeneous fluid near its critical point [START_REF] Casal | Equations of motions of thermocapillary fluids[END_REF][START_REF] Gouin | Thermodynamic form of the equation of motion for perfect fluids of grade n[END_REF][START_REF] Casal | Non-isothermal liquid-vapour interfaces[END_REF]. The idea of studying interface motions as localized travelling waves in a multi-gradient theory is not new and can be traced throughout many problems of condensed matter and phase-transition physics [START_REF] Gouin | Material waves of a fluid in the vicinity of the critical point[END_REF]. In Cahn and Hilliard's model [START_REF] Cahn | Free energy of a non-uniform system III[END_REF], the direction of solitary waves was along the gradient of density [START_REF] Slemrod | Admissibility criteria for propagating phase boundaries in a van der Waals fluid[END_REF][START_REF] Gouin | Material waves of a fluid in the vicinity of the critical point[END_REF]. Here, adiabatic waves are considered and a new kind of waves appears. The waves are associated with the spatial second derivatives of entropy and matter density. For this new kind of adiabatic waves, the direction of propagation is normal to the gradient of densities. In the case of a thick interface, the waves are tangential to the interface and the wave celerity is expressed depending on thermodynamic conditions at the critical point.

Equations of thermocapillary fluid motions

The equations of motion are proposed in [START_REF] Casal | Equations of motions of thermocapillary fluids[END_REF][START_REF] Gouin | Thermodynamic form of the equation of motion for perfect fluids of grade n[END_REF][START_REF] Casal | Non-isothermal liquid-vapour interfaces[END_REF]. Due to the fact the fluid is isotropic, grad ρ and grad s are taken into account by their scalar products only. Let us denote β = (grad ρ) 2 , χ = grad ρ . grad s, γ = (grad s) 2 .

In variables ρ, s, β, χ, γ,

ε = g(ρ, s, β, χ, γ). (2)
The equations of thermocapillary fluids introduced two new vectors Φ and Ψ such that :

Φ = C grad ρ + D grad s, Ψ = D grad ρ + E grad s, (3)
with

C = 2 ε ,β , D = ε ,χ , E = 2 ε ,γ .
We denote

h = ε ,ρ -div Φ, θ = 1 ρ (ε ,s -div Ψ) . (4)
In the case of compressible fluids, scalars ε ,ρ and (1/ρ) ε ,s are the specific enthalpy and the Kelvin temperature. Look at two particular cases :

Conservative motions

We obtained [START_REF] Casal | Equations of motions of thermocapillary fluids[END_REF] the equation of motion in the form :

Γ = θ grad s -grad(h + Ω), ( 5
)
where Γ is the acceleration vector, Ω is the extraneous force potential. This equation is equivalent to the balance of momentum:

∂ ∂t (ρu) + div(ρ u ⊗ u -σ) + ρ grad Ω = 0 (6)
with σ j i = -(P -ρ div Φ) δ j i -Φ j ρ ,i -Ψ j s ,i where P = ρ ε ,ρ -ε (in the case of classical compressible fluids, P denotes the pressure) and u is the fluid velocity. For conservative motions, ds dt = 0, [START_REF] Rowlinson | Molecular theory of capillarity[END_REF] which is equivalent to the balance of energy ∂e ∂t

+ div (e -σ)u -div W -ρ ∂Ω ∂t = 0, (8)
with W = dρ dt Φ + ds dt Ψ and e = 1 2 ρu 2 + ε + ρΩ.

Isothermal motions

We obtained [START_REF] Casal | Equations of motions of thermocapillary fluids[END_REF] the equation of motion in the form :

θ = T 0 , (9)
Γ = -grad(µ + Ω), ( 10
)
where T 0 is constant and µ = ε ,ρ -s T 0 -div Φ is the chemical potential of the thermocapillary fluid.

3 Liquid-vapor interface near its critical point

The critical point associated with the equilibrium of two bulks of a fluid corresponds to the limit of their coexistence. The thickness of the interface increases as the critical point is approached and it becomes infinite when the interface itself disappears. As its critical point is approached, the gradients of densities are then smooth. In the following, we consider the case when

ε = ρ α(ρ, s) + 1 2 C (grad ρ) 2 + 2D grad ρ . grad s + E (grad s) 2 (11)
where α denotes the specific internal energy of the fluid in uniform composition (let α(ρ, s) be the analytic α as it might be given by a mean-field theory), C, D, E are constants and CE -D 2 > 0. If D = 0 and E = 0, we are back to the Cahn and Hilliard model of capillarity [START_REF] Cahn | Free energy of a non-uniform system III[END_REF]. If not, we deduce

h = h 0 -(C ∆ ρ + D ∆ s), θ = T - 1 ρ (D ∆ ρ + E ∆ s),
where h 0 ≡ α + ρ α ′ ρ and T ≡ α ′ s are respectively the specific enthalpy and the Kelvin temperature of the homogeneous fluid of matter density ρ and specific entropy s; we denote by µ 0 = ε ′ ρ -s T its chemical potential. At phase equilibrium, Eq. ( 9) is verified when T 0 is the temperature in the bulks. If we neglect the body forces, we obtain

D ∆ ρ + E ∆ s = ε ′ s -ρ T 0 , (12a) C ∆ ρ + D ∆ s = ε ′ ρ -s T 0 -µ 1 (12b)
where µ 1 is the value of µ 0 in the liquid and the vapor bulks.

To be in accordance with Rowlinson and Widom ([7] p. 253), we consider a representation of ρ α(ρ, s) in the form

ρ α(ρ, s) = B 2A 2 A(ρ -ρ c ) 2 + ρs 2 + ρs + A 2 B (T c -T 0 ) 2 + ρµ 1 + ρsT 0 (13
) where A and B are two positive constants associated with the critical conditions and s which is defined except to any additive constant is choosen such that s c = 0. System [START_REF] Boillat | Non linear hyperbolic fields and waves in[END_REF] yields

D ∆ ρ + E ∆ s = B A ρ (ρ -ρ c ) 2 + 2 B A 2 ρ 2 s + ρ (T c -T 0 ), C ∆ ρ + D ∆ s = 2 B (ρ -ρ c ) 3 + 2 B A ρ s (ρ -ρ c ) + B A (ρ -ρ c ) 2 s + 2 B A 2 ρ s 2 + s (T c -T 0 ) .
The equations of the coexistence curve at T = T 0 are associated with ∆ ρ = 0 and ∆ s = 0. They are as in [START_REF] Rowlinson | Molecular theory of capillarity[END_REF], A(ρ-ρ c ) 2 +ρs = 0 and ρs+ A 2 B (T c -T 0 ) = 0. In the bulks, near the critical point, the respective magnitudes of ρρ c and s with respect to

T c -T 0 are ρ -ρ c ∼ cte (T c -T 0 ) 1 2 , s ∼ cte (T c -T 0 ).
In one-dimensional problems, ρ = ρ(y), s = s(y). To consider the respective order of magnitude of the densities and the physical scales associated with the interfacial sizes, we look at the change of variables

T c -T 0 = ǫΥ, y = ǫ n Y, ρ(y) -ρ c = ǫ 1 2 R(Y ), s(y) = ǫ S(Y ),
where 0 < ǫ ≪ 1, and n is constant. The main part of system ( 12) leads to

ǫ -2n D ǫ 1 2 d 2 R dY 2 + E ǫ d 2 S dY 2 = ǫ B A ρ R 2 + 2 B A 2 ρ 2 S + Υρ (14a) ǫ -2n C ǫ 1 2 d 2 R dY 2 + D ǫ d 2 S dY 2 = ǫ 3 2 2 B R 3 + 2 B A ρ R S (14b)
Then n = -1 2 and in this asymptotic analysis, if ′′ denotes the second derivative with respect to the space variable y, system (12) yields the approximation

2 ρs = A 2 B (T 0 -T c ) -A (ρ -ρ c ) 2 , ( 15a
)
C ρ ′′ = 2 B (ρ -ρ c ) 3 + 2 B A ρs (ρ -ρ c ) (15b)
and consequently by elimination of s between (15b) and (15a), we obtain

C ρ ′′ = B (ρ -ρ c ) 3 -A (T c -T 0 )(ρ -ρ c ), (16)
and for planar liquid-vapor interfaces,

1 2 Cρ ′2 = √ B 2 (ρ -ρ c ) 2 - A 2 √ B (T c -T 0 ) 2 . ( 17
)
We are back to the classical van der Waals theory for mass density profile in the interfacial layer (see [START_REF] Rowlinson | Molecular theory of capillarity[END_REF], p.p. 250-251).

4 Weak discontinuity in conservative motions

Conditions of a weak discontinuity

In a fixed coordinate system, to describe the fluid motion, we refer to the coordinates x ≡ (x 1 , x 2 , x 3 ) as the particle position (Eulerian variables). We denote by z = t x the time-space variables; V ≡ 1 u is the time-space velocity. Let us consider a mobile surface Σ t defined in the physical space occupied by the fluid, we denote by g the celerity of Σ t , n its normal vector,

N = -g n ; v = N * V ≡ n * u -g
is the fluid velocity with respect to Σ t (-v is the celerity of Σ t with respect to the fluid) and n * is the transposed of n.

To Eq. ( 6) of motion, we have to add the equation of balance of mass

∂ρ ∂t + div(ρu) = 0, (18)
Eq. ( 7) of conservation of the entropy and relation (13).

Due to the important fact that the first discontinuities of ρ and s are not existing in thermocapillary mixtures, weak discontinuities of isentropic motions correspond to ρ, s, ∂ρ/∂x, ∂s/∂x, continuous through the wave surfaces. As in [START_REF] Hadamard | Leçons sur la propagation des ondes et les équations de l'hydrodynamique[END_REF], we denote by [ ] the jump of a tensorial quantity through a surface of discontinuity Σ t . The jump of a spatial derivative of a continuous quantity is colinear to the normal vector to the wave surface; as in Hadamard's tensorial framework, there exits two scalar fields λ 1 , λ 2 on Σ t , such that , where H is a 3-vector field on Σ t . Then,

∂ρ ∂z = 0 ⇒ ∂ ∂z ( ∂ρ ∂z ) * = λ 1 NN * ⇒ ∂ ∂x ( ∂ρ ∂x ) * = λ 1 nn * , (19a)
∂s ∂z = 0 ⇒ ∂ ∂z ( ∂s ∂z ) * = λ 2 NN * ⇒ ∂ ∂x ( ∂s ∂x ) * = λ 2 nn * , (19b)
[ Γ] = ∂u ∂z V = H N * V ≡ v H.
λ 2 NN * V + NΞ * ∂s ∂z * = 0 ⇔ N λ 2 v + ∂s ∂x H = 0 or, λ 2 v + ∂s ∂x H = 0. ( 22
)
From Rankine-Hugoniot condition associated to Eq. ( 6), we obtain the compatibility condition: [-g ρ u * + ρ n * uu * -n * σ] = 0, and the continuity of ρ, ∂ρ/∂x, s, ∂s/∂x, yields [ div Φ ] = 0 or [ C∆ρ + D∆s ] = 0 which is equivalent to

C λ 1 + D λ 2 = 0. (23)
Consequently, there exists a scalar field λ 3 on Σ t such that

∂ ∂x (C∆ρ + D∆s) = λ 3 n * . (24)
Equation of motion (5) yields

[ Γ ] = [ θ ] grad s -λ 3 n, or, ρ v H = -(Dλ 1 + Eλ 2 ) grad s -ρ λ 3 n.
By projection on the normal and tangent plane to Σ t and taking relation (21) into account, we obtain

D (n * grads) λ 1 + E (n * grads) λ 2 + ρ λ 3 = 0, , (25)
ρ v H = -(D λ 1 + E λ 2 ) grad tg s, (26)
where grad tg s denotes the tangential part of grads in Σ t . Elimination of H in the relation (26) comes from relation ( 22), and we get

D (grad tg s) 2 λ 1 + E (grad tg s) 2 -ρ v 2 λ 2 = 0. (27)
Consequently, we obtain the system (23), ( 25), (27) of three homogeneous linear equations with respect to the variables λ 1 , λ 2 , λ 3 . The compatibility of the three equations yields

ρ v 2 = (CE -D 2 ) (grad tg s) 2 C . (28)

Celerity of isentropic waves of acceleration

The temperature in liquid and vapor bulks is T 0 . Then relation (15a) yields grad A(ρρ c ) 2 + 2 ρ s = 0 ⇔ A(ρρ c ) grad ρ + grad ρs = 0.

The value ρ = ρ c of the matter density in the interface corresponds to the maximum value of grad ρ. The matter density ρ c is characteristic of the interfacial matter. For such a value, grad ρs = 0 and s = (A 2 /2Bρ c ) (T 0 -T c ).

Consequently, grad s

= A 2 2Bρ 2 c (T c -T 0 ) grad ρ, and
v 2 = (CE -D 2 ) A 4 (grad tg ρ) 2 (T c -T 0 ) 2 4 C B 2 ρ 5 c .

Due to relation (17), we obtain when

ρ = ρ c , C (grad tg ρ) 2 = A 2 2 B (T c -T 0 ) 2 , and consequently, v 2 = (CE -D 2 ) A 6 (T c -T 0 ) 4 8 C 2 B 3 ρ 5 c . (29)
In the interfacial layer, grad ρ is normal to iso-density surfaces. The isentropic waves of acceleration associated with a weak discontinuity shear the interfacial layer. The wave celerity which is proportional to (T c -T 0 ) 2 , vanishes at the critical point and can be calculated numerically by means of a state equation.

Results and discussion

Near the critical point, for thermocapillary fluids, the variation of matter density leads to the variations of entropy (see Eq. ( 15a)). This extension of Cahn and Hilliard fluids seems at first sight purely formal and at equilibrium yields same results as the classical van der Waals model does [START_REF] Van Der Waals | Thermodynamique de la capillarité dans l'hypothèse d'une variation continue de densité[END_REF]. In dynamics, motions in the normal direction to fluid interfaces (as solitary waves) are not involved in an additive dependance of the entropy gradient. In this paper, we see that the dependance of entropy gradient is necessary for isentropic waves of acceleration along the interfaces: the fact that the internal energy depends not only on the gradient of matter density but also on the gradient of entropy, yields a new kind of waves which does not appear in the simpler models. It is easy to see they are exceptional waves in the sense of Lax [START_REF] Boillat | Non linear hyperbolic fields and waves in[END_REF] and they appear only in, at least, two-dimension spaces. Recent experiments in space laboratories, for carbonic dioxide near its critical point have showed the possibility of such waves [13] and should justify the well-founded of the thermocapillary fluid model.

and consequently λ 1 =

 1 [ ∆ρ ] and λ 2 = [ ∆s ]. (20) From [V] = 0, we deduce ∂V ∂z = Ξ N * with N * = (-g, n * ) and Ξ = 0 H


Audrey Chapelle

Samuel Charlot

Véronique Conédéra

Justyna Jońca

Myrtil L Kahn

Katia Fajerwerg

Pierre Fau

Céline Combettes

Vincent Bley

Philippe Menini

V Conedera

J Jonca

Ph Ménini

Selective GAS sensor based on screen-printed ZNO nanorods

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

1) Context / Study motivation

Screen-printing processes offer many advantages in precise control of thickness and chemical composition of films, totally compatible with MEMS technology, and low-cost for large-scale production. This technic is widely used in the field of gas sensors since many years [START_REF] Prudenziati | Thick film technology[END_REF][START_REF] Menil | The thick film route to selective gas sensors[END_REF] but mostly used to elaborate thick films for heating resistance than sensing element based on semiconducting oxides.

Metal oxide thin film sensors have been widely used for gas sensing applications thanks to their sensitivity toward a large variety of gases [START_REF] Ding | Surface state trapping models for SnO2-based microhotplate sensors[END_REF], but they suffer from a lack of selectivity.

One method to overcome this problem consists in using a temperature modulation of the sensor, by changing the power consumption [START_REF] Burresi | Dynamic CO recognition in presence of interfering gases by using one MOX sensor and a selected temperature profile[END_REF][START_REF] Dufour | A new way to greatly improve metaloxide gas sensors selectivity[END_REF]. This kind of profile allows fast chemical reaction changes, and consequently fast gas sensitivities changes while maintaining the integrity of the material.

This work demonstrate the feasibility of well controlled films of a ZnO nanostructured sensing material deposited by screen printing technique on microhotplate and the sensing performances by using specific profile associated to the temperature and bias current modulation.

2) Description of sensor technology

The tested devices have been developed on an optimized microhotplate that can work at high temperature and low power consumption (500°C, 55mW). The platform consists of a silicon bulk on which a thermally resistive bilayer SiO2/SiNx membrane was grown. Afterwards, Ti/Pt metallization was realized by lift-off to define heating resistor and the sensing resistor. SiO2 passivation layer was previously sputtered in order to electrically isolate the two electrodes. Finally, the rear side of the bulk was etched to release the membrane in order to increase the thermal resistance and then to limit thermal dissipation (Figure 1).

ZnO nanorods sensitive material was prepared by an organometallic approach [START_REF] Jońca | Shapecontrolled ZnO nanostructures for gas sensing applications[END_REF]. ZnO ink was prepared with organic vehicle and thin films were deposited using an automatic DEK horizon screen-printing machine through a polyester mask. After deposition, the films were left 24h at room temperature and then annealed under ambient air at 500°C during 2 h.

Chips were then diced one by one using a diamond blade dicing method and packaged in TO-5 can, and then aluminum wires were wire-bonded between Pt metal pad on the microhotplate and the TO-5 pad in for electrical connections.

The response S (%) toward different gases is defined by the following equation ( 1):

( ) 100 % ×         - = air air gas R R R S (1)

3) Results / Conclusions / Perspectives

Screen printed ZnO nanorods thin films were analyzed using a classic SEM S4800 (Figure 2). After annealing at 500°C the morphology of the nanorods still remains the same; 200nm in length and 10nm in width.

According to previous study [START_REF] Dufour | A new way to greatly improve metaloxide gas sensors selectivity[END_REF], Figure 3 shows the profile that allows good reproducibility, fast stabilization and best sensing performances. This profile includes power (temperature) and sensing bias current changes. This profile generates a huge amount of information, thus only 3 gases at 1 concentration (CO [300ppm], NH3 [5ppm] and NO2 [0.2ppm]), 2 temperatures from the profile (500 and 200°C) and 2 bias current (1 and 10µA) will be considered.

The variation of the bias current leads to several phenomena. On the Figure 4, at 1µA (hatched surface), decrease the temperature increases the response to CO. The opposite is observed at 10μA. At 500°C (red surface) and whatever the bias current applied, there is no influence observed for NH3 and NO2 detection. However, at 200°C (blue surface) the response to NO2 is ten times increased with a higher current and an inversion of the signal occurs for NH3 at 10µA.

The principal component analysis (PCA) algorithm is a popular technique for reducing the dimensionality of data [START_REF] Tomchenko | Semiconducting metal oxide sensor array for the selective detection of combustion gases[END_REF]. Thus, PCA was performed using sensor responses for ZnO nanorods to each gas. Figure 5 displays a visual appraisal of the discrimination of each gas.

In conclusion, thin films of ZnO nanorods have been synthetized by an organometallic route and deposited by screen printing method onto the microsystems. Since the sensor temperature is not permanently at high operating temperature, sensor defects caused by diffusion and chemical reactions are less likely, the sensor lifetime may possibly be increased. Moreover, thanks to electrical control, the obtained sensor displays an enhanced selectivity toward CO, NH 3 and NO2 gases. Furthermore, this work highlights the potential application of a low cost sensor array based on several metal oxide sensors in discriminating toxic and pollutants gases leading to an effective way to achieve high selectivity.

Figure 1 :Figure 2 .Figure 3 .Figure 4 .Figure 5 .

 12345 Figure 1: Top view (left) and cross section (right) of the micromachined device

ACKNOWLEDGEMENTS:

This work was partly supported by the French RENATECH network in LAAS, CNRS, Toulouse.