E Dundar

P Boulet

C Wexler

L Firlej

Ph Llewellyn

B Kuchta

Heterogeneous melting of methane confined in nano-pores

HAL is

I. INTRODUCTION

Since the discovery of nucleation reaction in the early 1930s [1][2] , the influence of nanoscale structure on the thermodynamics properties of the nano-systems has been studied. The recent rapid progress in the synthesis and processing of materials with tunable nanometer scale structures has resulted in the need to define rigorously the thermodynamics for the nanoscale systems. In particular, the issue of characterization of structural transformations of such small objects is an area of intense investigation [3][4][5][6][7][8][9][10] . It is well known that the nanosystems exhibit properties significantly different from their bulk analogs. In particular, the position of coexistence lines depends on the size and shape of the nano-objects and the phase diagrams are redefined. This is a consequence of the fact that nanosystems are characterized by high surface-to-volume ratio; the surface atoms are weakly bonded and their contribution to the latent heat is smaller. Consequently, the surface usually transforms at lower temperature than the bulk and the whole transition may happen smoothly over a large (but finite) range of temperatures. This observation suggests that at the nanoscale there is no temperature of melting (or any other structural change) in the conventional sense: the structural (phase) changes are gradual and phases are no longer distinguishable. ______________________________________________ a) Current email : Ege.Dundar@vub.ac.be b) Author to whom correspondence should be addressed. Electronic mail: : bogdan.kuchta@univ-amu.fr

The nano-objects exhibit continued transformations because their small size naturally favors larger amplitude of fluctuations. In addition, the fluctuations' amplitude is location-dependent, due to the heterogeneity of any nano-system. Consequently, the overall behavior of the system is not uniform but space-dependent. The nanoobjects also exhibit some features typical for second order critical behavior; however, the inherent limitation of the correlation length results in a lack of a real critical behavior.

Nano-porous materials define a particular environment for studies of nano-objects' properties. Not only they naturally define the nanosize limits of the matter confined in the pores but they also introduce an additional external force field due to the interaction with the pore walls. This field is not uniform, it depends on the wall heterogeneity and its strength decreases with a distance from the walls. Therefore, the interactions within each layer of the confined system are different from each other and depend on the layer position. The competition between the external heterogeneous forces and the intermolecular interactions is a key factor that modifies the properties of any confined nano-system.

Atomistic numerical simulations offer a possibility to precisely account for heterogeneity and fluctuations in nanoporous system. The amplitude of the fluctuations depends on the system size and their evolution in space reflects directly the characteristics of the potential energy surface (PES) explored by the microscopic configurations during the simulations. In this way, the existence of metastable states is often revealed, even ones with short lifetimes that may be difficult to detect experimentally. This unique possibility is a consequence of the system size. Bulk systems may be trapped at low temperatures in a part of the configurational space due to the low probability of transitions into other equivalent volume of the configurational space. In nano-systems, the transitions between different configurations are easier due to the larger amplitude of fluctuations.

The structural transformations of methane confined in pores have been studied numerically for many years.

Miyahara and Gubbins 3 already gave the general analysis of methane melting in slit pores. The melting was studied in pores of different shape [4][5][6][7] ; few examples of the solid-solid (hexagonal-tetragonal) transformations in slit pores were also reported 6,7 . In all cases, the common observed feature was a dependence of the transformation mechanism on the pores size. The strength of the adsorbate-adsorbent interaction was another important parameter defining the transition temperature 8,9 .

we analyze its influence on the mechanism of structural transformations in such nano-confined system. Two particular situations are discussed: first, the melting transition of methane confined in 3 and 4 nm carbon slitshaped pores; second, the melting of methane confined in 2.8 nm pores formed by square channels of the SURMOF structure. The mechanism of melting in slit and square pores is then compared, and the correlation between the nano-dimension and heterogeneity and discussed in details. Finally, we discuss the simulated transformations in the context of the existing experimental information 10 .

II. NUMERICAL METHODOLOGY

The pore structures studied in this paper are shown in Fig. 1. Two parallel graphene walls form the slitshaped carbon pores. We do not modeled multilayer graphene walls because their contribution is below 10% of the total interaction energy. We have studied two pore sizes: z = 3 nm and z = 4 nm, where z is defined as the distance between the centers of the carbon atoms in the graphene sheets forming the pore. In the xy plane, the pores are virtually infinite and modeled using periodic boundary conditions. The xy box dimensions (4.26 x 4.92) nm 2 are commensurate with the graphene structure. However, the wall structure was homogeneous. The effect of the corrugation of graphene surface has been estimated to be very small compared to the mean interaction energy. In addition, the choice of homogeneous walls allows one to exclude any influence of the wall heterogeneity on the melting transformation. The SURMOF possesses one of the largest pores reported so far for MOFs. For the longest molecular linker (PPDC 11 ), the size of the channel is 2.85 x 2.85 nm 2 and the structure has P4 symmetry. In our calculations, the channels have been modeled as infinitely long, again using periodic boundary conditions. The paper by Liu et al. 11 have described the details of the SURMOF structure in the paper. The position of the atoms of the SURMOF structure used in our simulation are included in the supplementary material.

The computational modeling was based on grand canonical Monte Carlo (GCMC) simulations implemented in our own code, extensively tested and validated [12][13][14][15] . The carbon slit-shaped framework and SURMOF structure were assumed rigid during simulations. All interatomic interactions were modeled using the Lennard-Jones (6-12) potential. The CH 4 molecules were considered as super-atoms (united atom model, UA).

The CH 4 -CH 4 Lennard-Jones parameters were CH4 = 3.730 Å and CH4 = 148.0 K. In slit pores, for methane-wall interactions, the Steele 10-4 potentials already tested in [START_REF] Nicholson | Computer Simulation and the Statistical Mechanics of Adsorption[END_REF][START_REF] Razak | [END_REF] were employed. Parameters describing fluid-solid interactions were obtained using the Lorentz-Berthelot mixing rules. The parameters for the framework atoms of SURMOF were obtained from the Universal Force Field (UFF). The interactions were cut-off beyond 15 Å. As the united atom representation of the CH 4 molecule is isotropic, electrostatic forces were not considered in the simulations. Periodic boundary conditions were employed in the directions parallel to graphene walls for carbon slit-shape pores, and in all direction in SURMOF simulations. Adsorption isotherm points were calculated by averaging the number of adsorbed molecules per unit cell of the material for a given chemical potential (P) and temperature T. The ideal gas model was applied. To characterize the mechanism of structural transformations within the adsorbed gas, we use two parameters: the 6 order parameter (to distinguish between the ordered solid-like structure and the disordered liquid layer) and the radial distribution function g(r). The 6 order parameter is defined as 18 (1) and is able to characterize structural 6-fold symmetry of the center-of-mass lattice positions by measuring the average bond order within a plane layer. Here the azimuthal angle k defines an orientation of a vector ("bond") between centers of mass of each nearest-neighbor pair in a layer 18 . The index k runs over the total number of 5 nearest-neighbor bonds N b in the adsorbed layer. 6 is equal to 1 if the structure represents ideal hexagonal (solid) order, and 0 if the structure is disordered (liquid). In this study, we analyze it separately for each adsorbed layer j.

The second function used to characterize the state of the adsorbed layer is the radial distribution function g(r). The 2-dimensional version of g(r) are calculated inside each layer adsorbed in the slit pores. These correlations help to identify the nature of the various phases, from very ordered solid-like phase to more disordered (liquid crystal or liquid-like) phases.

III. RESULTS

A. Adsorption mechanism and layering transition at T = 90 K.

At T = 90 K the adsorption of methane layers in slit pores is very regular because the adsorbent slit model has regular graphene-like walls. The isotherm of adsorption is step-wise (Fig. 2a); each subsequent layer is very stable and well ordered. However, any new layer formation is preceded by increased amplitude of structural and energy fluctuations, which indicate a destabilization of the adsorbed system before the new layer starts to form. In fact, for each layer, an optimal density exists that stabilizes the total adsorbed system. Such mechanism of layering transitions can be easily inferred from both the energy and the number of molecules fluctuations (Fig. 2b). The final filling of the pore (similar to capillary condensation) is also initiated by large fluctuations, especially, of the number of the adsorbed molecules. It is interesting to observe that the energy fluctuations show a global decreasing tendency with increased pressure. This is the direct consequence of the increasing contribution of the methanemethane interaction energy to the total energy of the adsorbed system. The final state of methane in the filled pore is characteristic for solid ordered arrangement in the contact layer. This is confirmed by the radial distribution function: the in-layer radial distribution function shows (Fig. 2c) that each layer has a different structure: the contact layer is solid, due to the ordering action of the strong interaction with the pore wall, whereas the third layer is, at least partially, liquid. This heterogeneity of the adsorbed system is the key feature determining the mechanism of melting. It will be discussed below in the following part of this paper.

It is important to emphasize that the mechanism of melting in pores may be studied at any stage of pore filling, even in partially filled pores. This means that any particular mechanism of melting is always defined for particular thermodynamic path. In this paper, we analyze the melting in completely filled pore, that is, for thermodynamic conditions where the external pressures is higher than the pressure required for the last vertical jump observed on the isotherm curve (Fig. 2ad). The adsorption mechanism is modified when the pore geometry changes from slit-shaped to square like.

Although the dimensions of square channels in SURMOF ( x = y = 2.85 nm) are close to the 3 nm slit pore, the change of pore geometry results in the increase of the energy of adsorption, due to the cumulative contributions coming from all walls. This leads to filling of the pore at pressures lower than in the slit pore: at the same thermodynamic conditions (T = 90 K, pressure = 0.002 bar) which in a slit pore at 90 K allows the adsorption of only the first layer, SURMOF pore is completely filled (Fig. 2d). The mechanism of methane adsorption in SURMOF is also different: (i) the adsorption of the first layer of atoms is rapid, (ii) the second layer adsorb more gradually, and (iii) filling of the central part of the pore rapidly follows the formation of the second layer. Globally, the density of the methane adsorbed in SURMOF is higher than its density in the slit pores. This is a consequence of stronger attractive interaction in the tetragonal pore as compared with the slit one. It is worth remembering that it happens at much lower pressure of the external gas than the filling of the slit pores. Therefore, the thermodynamic path in this case is different from the one used in the slit pores.

B. Melting of methane confined in 3 nm and 4 nm slit pores

At low temperatures (T < 90 K) methane adsorbed in slit-shaped pores has a well-defined layered structure (Fig. 3). However, the layers in the middle of the pore show different properties depending on the pore size. The 3 nm filled pore contains four well defined layer adsorbed on each pore wall (Fig. 3a). In the pore 4 nm wide, a fluid-like structure in the central part of the pore does not show localized layer distribution (Fig. 3b). In both systems, the first two layers are ordered, with center of molecules' mass forming a hexagonal pattern; therefore, their state can be qualified as solid. This is confirmed by calculation of the 6 ordered parameter (close to 1) and the solid-like character of the radial distribution function g(r) (Figs. 4 and2c, respectively). These similar nano-metric systems show important differences in the way they melt (Fig. 4). In both 3 nm and 4 nm pores, the central part of the pore has lower melting temperatures. This general feature is a consequence of the interaction of methane molecules with the confining pore walls. It induces an additional ordering of molecules in layers closer to the pore wall and, at the same time, the wall interaction is not affecting the central part of the pore. In 3 nm pores, all layers melt continuously. The melting of the second layer is shifted by -5 K (towards lower temperature) with respect to contact layer. In 4 nm pores, the contact layer and the second layer exhibit a discontinuous transformation, characteristic for 3D bulk systems; their melting temperature (~ 105 K) is close one to each other and higher than the bulk melting temperature (~ 90 K). The difference comes partially from our choice of the melting thermodynamic path. The 3 nm pore is filled at lower pressure than the 4 nm one.

Consequently, the density in the 4 nm pore is a little bit bigger and this leads to the discontinuous melting of the two contact layers.

The mechanism of melting in the slit pores is determined by several parameters. First, the character of transformation is strongly dependent on the strength of wall attraction as analyzed above, and pointed out in the past 8,9,19 . The gradient of the attractive forces effectively acting on subsequent layers in the pores makes the adsorbed system heterogeneous and, in consequence, the mechanism of melting depends on the layer position.

Additionally, the melting mechanism depends on the thermodynamic path chosen for the transformation. As the density of the system varies between different paths, the choice of the path may affect the apparent mechanism of melting. Any path between the bulk coexistence curves and the capillary coexistence curve could be used 3 . Here we have chosen arbitrary a path following the line between those two limits. Below 100 K the structure of methane adsorbed in SURMOF pores is solid. The order in the xy planes is defined by P4 tetragonal symmetry (Fig. 6), whereas in xz and yz planes the order is hexagonal. The arrangement is not perfect, due to the system nano-metric size in xy plans and non-commensurability between the SURMOF framework and methane structure. This leads to minor deformations of the adsorbed structure, clearly observed in the density distribution shown in the Fig. 6. The average density distribution is nearly constant below melting temperature (estimated to be T m = 102 2 K). The constant density is a consequence of the ordered, solid-like structure, which does not change until the methane melts. However, contrary to the melting of bulk methane, the transitions in confined system is gradual. After 10% abrupt decrease of density at melting point, it then continues to decrease continuously from 17 molecules/nm 3 to 13 molecules/nm 3 by 180 K. The interaction of methane with the SURMOF framework determines the mechanism of melting. The gradual melting is a consequence of the nano-size of the pores in xy plane. The contact layers of methane are strongly localized by the framework corrugation up to the highest simulated temperature T = 180 K. Their density is unchanged up to 180 K, the highest simulated temperature. At the same time, the inside pore fluctuations of molecules increase with temperature (Fig. 6) and the density is lower towards the center of the pore. Consequently, the melted structure is strongly heterogeneous; the inside of the pore is liquid but the molecules in the contact layers stay in a solid-like state. Calculations of the 6 order parameter confirms this strong structural heterogeneity.

Obviously, it is the methane-framework interaction, which stabilizes this solid-like structure in a similar way as the first adsorbed layer in the slit-shaped pores is stabilized by methane-carbon interaction. The heterogeneous corrugation of the wall is the additional factor, which localizes the atoms in solid-like arrangement, because it limits the lateral fluctuations of the methane molecules.

IV. CONCLUSIONS

The mechanism of melting of fluid nanosystems depends on their size, shape and type of environment in which they are embedded. The nanopores define a particular class of environments in which the molecules of the adsorbed fluid interact strongly with the porous framework; in consequence, a large variety of fluid nanosystems can be formed inside the pores, with various geometries, and length scales comparable to the characteristic scales of the intermolecular interactions. The mechanism of melting in such structures is strongly influenced by the competition between the effect of the nanometric size (which lowers the melting temperature) and the interaction of the fluid with the confining pore walls. Depending on the strength of this interaction the final transition temperature of the fluid nanosystems may either increase or decrease 8,9 . Experimental observations 10 show that in nano-pores of the width smaller than 4nm the mechanism of melting is no longer similar to that observed in the bulk systems. This is a consequence of a strong heterogeneity of the adsorbed nano-fluid where each layer of adsorbed molecules shows different properties.

Specifically, the nano-structures composed of few molecular layers (therefore, having at least one dimension smaller than 4 nm) are very heterogeneous. Consequently, the temperature (and the mechanism) of system phase transition is not unique and vary in a function of the position within the nano-system. In general, melting in nano-systems cannot be described by global parameters; it must be analyzed locally, depending on the molecules of fluid position and the distance from all pore walls. The density distribution is a graphical way of the melting mechanism analysis. The locally defined order parameters provide another, quantitative description of the phenomena. This approach is qualitatively different from the analysis of melting in pores larger than 4 nm, for which the classical picture of melting point depression is typically observed 10 . The order parameter 6 is one of many possible ways to characterize local structures. The choice depends on the symmetry of the studied system.

In addition, the mechanism of melting in confined systems depends on the thermodynamic path chosen to transform the solid into the fluid. In pores, there are many possible choices depending on the number of adsorbed layers. The pressure may follow any path in the (P,T) plane at any stage of adsorption. In the completely filled pore, any path between the filling pressure and the saturation pressure can be chosen. In pores where the pore filling is observed well below the saturation pressure, there are many choices of the melting thermodynamic path. However, higher pressure means higher density of the confined system that, in turn, can lead to discontinuous melting and/or may produce a hysteresis. The heterogeneity of system is additional and the most important factor determining the mechanism of melting.

We have observed an evolution of the melting mechanism as a function of the pore size. It is discontinuous transformations within the contact layers in 4 nm slit pores to the totally continuous one in 3 nm pore. The type of the transformation depends on the density of the confined system, which is affected by the strength of the interactions with the walls and by the equilibrium external gas pressure. Exploring this added "dimensions" in the parameter space is very interesting but requires a significant additional effort beyond the scope of this manuscript.

Fig. 1 .

 1 Fig.1. Slit pore (left) and SURMOF (right) structures. The hydrogen, carbon and oxygen atoms are represented by light grey, grey and red colors, respectively. In the simulation, the slit walls are homogeneous without any corrugation.

Fig. 2 .

 2 Fig.2. Methane adsorption in a slit pore and in SURMOF (see Fig.1) at 90 K: (a) methane stepwise isotherm, showing subsequent layers formation in slit pores, (b) fluctuations (standard deviations from the average values) of energy and the number of adsorbed molecules in slit pores, (c) in-layer radial distribution functions: p = 0.09 bar (first 3 layers adsorbed on each wall in 3 nm slit pore), (d) methane adsorption in the SURMOF pore.

Fig. 3 .

 3 Fig. 3. (a) Mass density distribution in pore z = 3 nm, p = 0.11 bar; (b) mass density distribution in pore z = 4 nm, p = 0.11 bar, T = 90 K.

Fig. 4 .

 4 Fig.4. Melting in slit-shaped pores: left : z =3 nm, right : z = 4 nm. The 6 order parameter is calculated and traced separately for each layer.

C. Melting of methane confined in SURMOF 2 Fig. 5 .

 25 Melting of methane in SURMOF. Average methane density as a function of temperature. The open symbol show hysteresis on cooling the melted system.

Fig. 6 .

 6 Fig. 6. Melting of methane in SURMOF. Distribution of methane density in SURMOF pore. From left to right: 90 K, 105 K, 140 K, 180 K. The estimated melting temperature is 102 K.

ACKNOLEDGEMENTS

This work was partially supported by the Polish National Science Center (NCN, grant no. 2015/17/B/ST8/00099) and French National Research Agency ANR (grant NR-14-CE05-0009HYSTOR). CW acknowledges support from the donors of the American Chemical Society Petroleum Research Fund (52696-ND5).

SUPPLEMENTARY MATERIAL

See supplementary material for detailed SURMOF structure (x,y,z atomic positions) used in the simulation.


Svetlana Pinet

Johannes C Ziegler

F.-Xavier Alario
email: francois-xavier.alario@univ-amu.fr

Typing is writing: linguistic properties modulate typing execution

Typing is becoming our preferred way of writing. Perhaps because of the relative recency of this change, very few studies have investigated typing from a psycholinguistic perspective. In addition, and despite obvious similarities between typing and handwriting, typing research has remained rather disconnected from handwriting research. The current study aimed at bridging this gap by evaluating how typing is affected by a number of psycholinguistic variables defined at the word, syllable and letter levels. In a writing-to-dictation task, we assessed typing performance by measuring response accuracy, onset latencies -an index of response preparation and initiation -and interkeystroke intervals (IKIs) -an index of response execution processes. The lexical and sub-lexical factors revealed a composite pattern of effects. Lexical frequency improved response latencies and accuracy, while bigram frequency speeded up IKIs. Sound-spelling consistency improved latencies, but had an inhibitory effect on IKI. IKIs were also longer at syllable boundaries. Together, our findings can be fit within a framework for typed production that combines the previously developed theories of spelling and typing execution. At their interface, we highlight the need for an intermediate hierarchical stage, perhaps in the form of a graphemic buffer for typing.

Introduction

With the development of new information technologies, we might be giving up pens for keyboards. The cognitive impact of this (r)evolution is unknown [START_REF] Mikulak | Getting it in writing: Writing the Old-Fashioned Way May Enhance Learning and Memory[END_REF]. On the one hand, it is reasonable to assume similar linguistic representations and brain substrates for written production, whether it is handwritten or typed [START_REF] Purcell | A combined fMRI study of typed spelling and reading[END_REF]. On the other hand, cognitive models of typing [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF][START_REF] Rumelhart | Simulating a Skilled Typist : A Study of Skilled Cognitive-Motor Performance[END_REF] have remained somewhat disconnected from models of handwriting (e.g., [START_REF] Houghton | Normal and impaired spelling in a connectionist dual-route architecture[END_REF][START_REF] Rapp | The integration of information across lexical and sublexical processes in spelling[END_REF], with almost no attempts to make direct theoretical comparisons. Models of typing have been mainly concerned with the peripheral aspects of the typing process (i.e., response execution at the keystroke level) rather than its psycholinguistic components (i.e., response selection at the word level); the opposite is true for models of handwriting (Figure 1). Given the current interest in understanding motor planning (e.g. pre-motor, motor, monitoring, etc.) in the context of language production (for speech, see e.g., [START_REF] Bohland | Neural representations and mechanisms for the performance of simple speech sequences[END_REF][START_REF] Hickok | The architecture of speech production and the role of the phoneme in speech processing[END_REF], such a separation seems no longer tenable.

Figure 1: Prototypical models of spelling (adapted from [START_REF] Houghton | Normal and impaired spelling in a connectionist dual-route architecture[END_REF][START_REF] Rapp | The integration of information across lexical and sublexical processes in spelling[END_REF] and typing [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF] hierarchical dual-loop model, figure from [START_REF] Yamaguchi | Pushing typists back on the learning curve: revealing chunking in skilled typewriting[END_REF].

Psychonomic research on typing has mainly focused on execution processes. Quite precise mechanisms have been proposed for the correct retrieval and ordering of keystrokes prior to execution [START_REF] Rumelhart | Simulating a Skilled Typist : A Study of Skilled Cognitive-Motor Performance[END_REF]. Typically, these operate upon an already retrieved lexical representation. [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF] more recent model of typing (Figure 1) includes rather independent word and keystroke levels of processing: an "outer-loop" deals with language processing, while an encapsulated "inner-loop" produces a series of keystrokes from an input word. Consistent with this hypothesis, lexical frequency or Stroop-type interference do not appear to affect response durations or inter-keystroke intervals (IKIs) [START_REF] Baus | When does word frequency influence written production[END_REF][START_REF] Damian | Flexible and inflexible response components: a Stroop study with typewritten output[END_REF][START_REF] Logan | Stroop-Type Interference : Congruity Effects in Color Naming With Typewritten Responses[END_REF], whereas frequent letters, or bigram and trigram associations can speed up execution processes, depending on the typist's expertise (Behmer & Crump, n.d.).

Earlier seminal research on copy-typing also assessed the influence of lexical and sublexical properties and reported for example effects of word frequency on typing performance (e.g., [START_REF] Gentner | Lexical, Sublexical, and Peripheral Effects in Skilled Typewriting[END_REF][START_REF] Inhoff | Word frequency during copytyping[END_REF][START_REF] Viviani | Motor templates in typing[END_REF][START_REF] West | Hierarchy of Stroking Habits at the Typewriter[END_REF]. However, copy-typing involves some specific perceptual and cognitive mechanisms (e.g., visual letter identification) that are not present in spontaneous typing or typing to dictation, which may reduce the generalizability of the previously reported effects [START_REF] Bonin | Written object naming, spelling to dictation, and immediate copying: Different tasks, different pathways?[END_REF][START_REF] Nottbusch | Syllabic Sructures in Typing: Evidence from Deaf Writers[END_REF][START_REF] Will | Linguistic units in word typing: Effects of word presentation modes and typing delay[END_REF]. [START_REF] Bonin | Written object naming, spelling to dictation, and immediate copying: Different tasks, different pathways?[END_REF] compared different handwriting tasks and suggested that dictation was more sensitive to sublexical variables than copying; in typing, very few studies explored other production tasks [START_REF] Baus | When does word frequency influence written production[END_REF][START_REF] Bertram | Cascaded processing in written compound word production[END_REF][START_REF] Will | Linguistic units in word typing: Effects of word presentation modes and typing delay[END_REF].

Concurrently, handwriting research has followed a different path. Since [START_REF] Van Galen | Handwriting : Issues for a psychomotor theory[END_REF] seminal psychomotor theory, handwriting research typically focused on psycholinguistic processing stages at the expense of motor components, perhaps because of the difficulty to precisely track execution processes in handwriting. Dual-route frameworks of spelling are well established [START_REF] Houghton | Normal and impaired spelling in a connectionist dual-route architecture[END_REF][START_REF] Rapp | The integration of information across lexical and sublexical processes in spelling[END_REF]. Data from neuropsychological cases favor the existence of both lexical and sublexical processing routes, their parallel activation and integration in a "graphemic buffer", as well as the existence of feedback connections from the grapheme level to both pathways (see Figure 1). Supporting the dual-route spelling framework are also numerous reports about the influence of lexical (e.g., word frequency) and sublexical (e.g., sound-spelling consistency) variables on handwriting latencies across multiple task settings [START_REF] Bonin | The determinants of spoken and written picture naming latencies[END_REF][START_REF] Bonin | Written object naming, spelling to dictation, and immediate copying: Different tasks, different pathways?[END_REF][START_REF] Bonin | Do Phonological Codes Constrain the Selection of Orthographic Codes in Written Picture Naming[END_REF][START_REF] Delattre | Written spelling to dictation: Soundto-spelling regularity affects both writing latencies and durations[END_REF] although see [START_REF] Roux | The interaction between central and peripheral processes in handwriting production[END_REF]. However, lexical and sublexical factors also affect whole word durations (lexicality in Roux et al., 2013, regular-ity in citealpDelattre2006) and finer measures of response execution (inter-letter intervals and stroke durations; e.g., bigram frequency in Afonso, Álvarez, & Kandel, 2015;[START_REF] Kandel | For a psycholinguistic model of handwriting production: testing the syllable-bigram controversy[END_REF][START_REF] Roux | The interaction between central and peripheral processes in handwriting production[END_REF] While spelling models are well suited to account for the effects on response selection, they are not sufficiently specified in order to account for the effects on response execution.

In the present study, an attempt was made to bridge the gap between models of typing and handwriting by investigating the effects of several linguistic properties on different levels of typing performance and to interpret the results at the cross-roads of both frameworks. We asked skilled typists to write words to dictation and measured response onsets, individual IKIs, and overall accuracy. Onset latency was considered an index of response preparation and movement initiation of the first keystroke (i.e. mostly "outer-loop"; [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF], whereas IKI was taken as an index for response execution processes ("inner-loop").

We manipulated lexical and sublexical properties at various psycholinguistic levels. At the word level, lexical frequency was manipulated. At the syllable level, we investigated the effects of sound-spelling consistency. Between syllables, we investigated whether pure orthographic syllable boundaries were processed differently from phono-graphic syllable boundaries. Finally, at the letter level, we manipulated the frequency with which two letters co-occur (bigram frequency) and the consistency of the onset. Following previous research on handwriting and typing, we hypothesized that word frequency should preferentially affect word retrieval processes, bigram frequency should preferentially affect execution processes, and sound-spelling consistency might affect different processing levels.

Method

Participants Thirty-five skilled typists were recruited through campus advertisement on the basis of self-assessment criteria such as regular typed note-taking in classes. Five participants were excluded because they did not reach 70% accuracy in the task. Thus, we report data from 30 university students (7 males; mean age = 20.5 [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], all French native speakers). They had an average typing experience of 8.7 years and spent on average 3.5 hours a day typing.

75% of them took notes on their computer during classes.

Materials

Word frequency and consistency can only be manipulated between words. Because IKIs depend greatly on bigram layout on the keyboard [START_REF] Gentner | Lexical, Sublexical, and Peripheral Effects in Skilled Typewriting[END_REF], we constructed material such that the same bigrams were associated with different word frequencies and consistencies. We restricted our search to 5 to 7 letter disyllabic nouns, with a frequency of at least 1 occurrence per million. From this set, we selected stimuli according to the bigrams they contained. Starting from a random seed of three words, we sampled the pool of words so that each new selected word had at least 80% of its bigrams in common with the already selected stimuli. We excluded emotionally loaded words and words containing written accents. The final stimuli set comprised 92 disyllabic words from the BRULEX database [START_REF] Content | BRULEX A computerized lexical database for the French language[END_REF], see Table 1), with 126 different bigrams, each appearing between one to 23 times (mean = 4, SD = 3.7) across words (see Table 2).

Word and bigram frequencies were log-transformed.

Variables

Mean Median SD Min-Max Q1-Q3 Word length 6.4 7 0.67 5-7 6-7 Word Frequency 1.9 1.7 1.48 0.03-5.9 0.5-3. [START_REF] New | Lexique 2: a new French lexical database[END_REF] and computed from BRULEX [START_REF] Content | BRULEX A computerized lexical database for the French language[END_REF]) (syllable boundaries excluded).

We computed consistency ratios (CRs) [START_REF] Ziegler | Statistical analysis of the bidirectional inconsistency of spelling and sound in French[END_REF] for each syllable by dividing the number of "friends" (words that share the same phonology and orthography for a given syllable) by the summed numbers of "friends" and "enemies" (words that share the same phonology for that syllable, regardless of their orthography), weighted by the frequency of each word (i.e. a token count). Initial Consistency was computed in the same way for the first phoneme-grapheme correspondence. Consistency cannot be defined at syllable boundaries. As a special test for the influence of phonological properties during typing of these segments, we compared IKIs within syllables to those at phono-orthographic ("s-t" in "jus-ti-ce"/"Zys-tis") and pure orthographic ("i-c" in "jus-ti-ce"/"Zys-tis") boundaries. Sound files were generated with Apple Macintosh's speech synthesizer (French voice:

"Thomas"). The pronunciations were informally checked for appropriateness.

Experimental procedure

Participants were seated in front of a laptop computer (2013 Dell XPS). Responses were recorded via an external keyboard modified to provide millisecond accuracy (DirectIN High Speed Keyboard PCB v2010, Empirisoft). On every trial, a 200ms-beep was played to alert participants of the upcoming auditory target, presented between 500 and 800 ms later (lag randomly picked for every trial from a uniform distribution). Participants were given 2,500 ms from the onset of the stimulus to type the whole word. No visual feedback of what was typed was given; stimuli were delivered binaurally through standard headphones. As all relevant events were auditory, participants were instructed to look at the keyboard throughout the experiment.

The experiment consisted of three blocked repetitions of the same items, separated by a short break. All stimuli were presented in each block in different randomized orders with the constraint that two consecutive items never started with the same letter.

Statistical analysis

We performed analyses on accuracy rates, and on chronometric measures of correct trials only. A trial was considered correct if all letters of the word were correctly typed and no backspace occurred within the course of the trial. Responses that were not completed before the time out were excluded from the analysis. All analyses were performed using linear regression mixed-effects models (lme4 package in R software, [START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF]). Latencies and IKIs were analyzed separately. Dependent variables were transformed to approximate a normal distribution according to the result of a Box-Cox test: RT were inverse-transformed and IKIs were log-transformed. Outliers were identified by visual inspection of a Q-Q plot and removed from the analysis. Accuracy rates were analyzed with the same model structures as latencies, but using logistic regression.

We allowed intercept and slopes to vary by subject for all variables, by item for latencies and accuracy rates, and by bigram for IKIs. A comparison between a model fitted with random effects by bigram or by item confirmed that the bigram structure was preferable (smaller Akaike Information Criteria value). The consistency ratio variable did not have a homogeneous distribution because many values were close to 1. To avoid giving a higher weight to such extreme value, we performed the analyses on subsets of the data by randomly sampling items within this extreme population. Models run over the whole item set produced the same results than those reported here. In addition to the predictors of theoretical interest, the statistical models included control variables. For latencies and accuracy rates, we included block number, word length, stimulus acoustic duration, and typing speed (mean IKI computed by participants over all correct trials). For IKIs, we included block number, position within the word, and hand alternation (whether both letters of a bigram are typed with the same hand or not). As the generation of p-values for this kind of analysis is debated [START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF], we took t-values to approximate z-values, and considered significant any value above 1.96. Confidence intervals were computed by adding/subtracting [1.96 x standard error] to predictor parameter estimates.

Results

One item was excluded because its accuracy was less than 50% across all subjects ("harnais"). Trials with incomplete but otherwise correct responses were also excluded (7.8% of the data).

Latencies

Latency analyses showed significant facilitatory effects of word frequency (β = -1.42E -05; Block number and typing speed both showed significant negative effects, while stimulus acoustic durations had a significant positive effect (see Table 3).

β

Accuracy rates

Correct responses occurred on 90.9% of the trials. Word frequency (β = 0.23; z = 3.2) had a significant positive effect and second syllable consistency (β = 0.63; z = 1.9) had a marginal positive effect. (Figure 2, middle row). Neither initial consistency (β = 0.60; z = 1.5), first syllable consistency (β = 0.12; z = 0.39), nor bigram frequency (β = -0.20; z = -0.8) had significant effects.

IKIs within syllables

Word frequency did not yield a significant effect (β = 0.0028; t = 1.23; CI = [-0.035; -0.013]).

The consistency ratio of the syllable the IKI belonged to had a significant positive effect (β = 0.062; t = 4.9; CI = [0.037; 0.087]); the higher the syllable consistency, the longer the IKI (Figure 2, bottom). Bigram frequency had a significant facilitatory effect (β = -0.055; t = -3.1; CI = [0.029; 0.083]). Block number and position within the word also had significant effects (see Table 4).

The correlation of by-participant estimated effect sizes (i.e. random slopes) and typing speeds was significant for syllable consistency (r = 0.69, p = 2.2E -5) and bigram frequency (r = 0.43, p = 0.02), with effect sizes strongly consistent across participants (Figure 3).

Word frequency random slopes did not correlate with typing speeds (r = -0.25, p > 0.1).

Figure 3: Correlations of by-participant random slopes (in IKI analysis) for word frequency, consistency and bigram frequency with participants' typing speed.

IKIs at syllable boundaries

The analysis of syllable-boundary IKIs revealed no effect of word frequency, while boundary type had a significant effect: IKI was longer at pure orthographic (β = 0.064; t = 2.8; CI = [0.0182; 0.109]) and at phono-orthographic boundaries (β = 0.099; t = 4.6; CI = [0.0565; 0.142]) than within a syllable; IKI at phono-orthographic boundaries tended to be longer than at pure orthographic boundaries (Figure 4). Bigram frequency also had a significant negative effect (β = -0.043; t = -3.7; CI = [-0.0667; -0.0201]). These effects were observed over and above the contributions of control variables: block number, hand alternation, and absolute position within the word (see Table 5).

q q

Phono-Orthographic

Discussion

We assessed the effects of various variables on different processing levels involved in word typing: lexical frequency (word level), sound-spelling consistency (syllable level), orthographic vs. phono-orthographic syllable boundaries (cross-syllabic positions), and bigram frequency and onset consistency (letter Lexical frequency yielded a facilitatory effect on latencies and accuracy rates (word level), but not on IKIs (keystrokes). Bigram frequency had a facilitatory effect on IKIs, but had no effect on response latencies or accuracy rates. To the extent that latencies provide a measure of response selection, the lexical frequency effect points towards faster word retrieval with increasing word frequency. The bigram frequency effect on IKI points towards execution and inner-loop processes; hypothetically, frequent bigrams are typed more often, and the time between two keystrokes is reduced with practice and automaticity [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF], as attested by the significant correlation of individual bigram frequency effects with typing speed [START_REF] Behmer | Crunching big data with finger tips: How typists tune their performance toward the statistics of natural language[END_REF][START_REF] Gentner | Lexical, Sublexical, and Peripheral Effects in Skilled Typewriting[END_REF][START_REF] West | Hierarchy of Stroking Habits at the Typewriter[END_REF].

The absence of word frequency effect on IKI contrasts with previous observations in spoken word production [START_REF] Gahl | Thyme" and "Time" are not homophones: the effect of lemma frequency on ord durations in spontaneous speech[END_REF], but is consistent with previous typing reports [START_REF] Baus | When does word frequency influence written production[END_REF][START_REF] Bertram | Cascaded processing in written compound word production[END_REF]in handwriting, Delattre et al., 2006). It is also consistent with observations in graphemic buffer patients [START_REF] Hillis | The graphemic buffer and attentional mechanisms[END_REF], who showed sub-lexical errors in handwriting (e.g. letter substitutions, transpositions) that were insensitive to lexical factors (e.g. frequency). Together, all of the above observations support the central claim of previous typing models (e.g., [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF], which postulate distinct word and keystroke levels of processing.

Onset consistency does improve response latencies. This would be expected within dualroute models of spelling [START_REF] Houghton | Normal and impaired spelling in a connectionist dual-route architecture[END_REF][START_REF] Rapp | The integration of information across lexical and sublexical processes in spelling[END_REF], where consistency results in a processing advantage because both the lexical and sublexical routes yield the same output. Dual-route models also naturally explain the effects of word frequency on response latencies because the lexical route is frequency-sensitive. Thus, it appears that a dual-route architecture is a well-suited addition to capture "outer-loop" word retrieval processes in typing [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF].

Other aspects of our findings, however, might require additional assumptions. IKIs were longer at syllable boundaries than within syllables, replicating previous reports in typing [START_REF] Gentner | Lexical, Sublexical, and Peripheral Effects in Skilled Typewriting[END_REF][START_REF] Will | Linguistic units in word typing: Effects of word presentation modes and typing delay[END_REF] and handwriting [START_REF] Kandel | For a psycholinguistic model of handwriting production: testing the syllable-bigram controversy[END_REF]. Given that transitions between hierarchical levels take longer than within the same level [START_REF] Rosenbaum | Hierarchical control of 16 rapid movement sequences[END_REF], we would argue that syllables constitute such a level of processing in typing between words and keystrokes and could perhaps be implemented in the context of a graphemic buffer [START_REF] Hillis | The graphemic buffer and attentional mechanisms[END_REF]). This would be in line with theories of spelling [START_REF] Kandel | For a psycholinguistic model of handwriting production: testing the syllable-bigram controversy[END_REF][START_REF] Rapp | The integration of information across lexical and sublexical processes in spelling[END_REF], challenging [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF] two-level hierarchical organization.

Finally, syllable consistency had an inhibitory effect on IKIs -IKIs were longer for consistent than for inconsistent syllables -especially so in slower typists. This was unexpected, as dual-route models of spelling would always predict facilitatory effects of consistency (see above, onset consistency), inasmuch as they account for the effect at the outcome of word retrieval processes. Noticeably, opposite effects on latencies and IKIs have a precedent in both the typing and handwriting literatures. [START_REF] Snyder | The problem of serial order skilled typing[END_REF] observed facilitation of latencies, along with lengthened durations with increasing prime-target orthographic overlap. Previously, Van Galen (1990) had reported shorter retrieval but increased handwriting durations for words with repeated syllables. He suggested that repeated syllables yield shorter retrieval at the word level but repeated strokes cause extra processing load at a lower level. These precedents suggest an explanation for the unexpected consistency effect because consistent syllables have greater orthographic overlap with their consistent neighbors ("friends" words with the same spelling) than inconsistent syllables. Thus taking a chaining account perspective [START_REF] Snyder | The problem of serial order skilled typing[END_REF], one could argue that consistent syllables occur in different words and could therefore be associated with different motor programs, which might potentially create interference or uncertainty with respect to the motor program that would need to be executed.

One limitation of the current investigation is that language production was elicited through a dictation task. Dictation calls for specific auditory perceptual processes and might emphasize sublexical processes [START_REF] Bonin | Written object naming, spelling to dictation, and immediate copying: Different tasks, different pathways?[END_REF]. Thus, a general model of typing would need to be tested with different typed production tasks.

Overall, then, the present results call for a combination of the dual-route architecture for retrieval with a separated stage for execution ("inner loop"). They also suggest the need for a graphemic buffer involved in typing [START_REF] Hillis | The graphemic buffer and attentional mechanisms[END_REF][START_REF] Van Galen | Handwriting : Issues for a psychomotor theory[END_REF]. This buffer would constitute an additional level of hierarchical processing, complementing [START_REF] Logan | Hierarchical control of cognitive processes: the case for skilled typewriting[END_REF] dual-loop model. Many details of this buffer remain to be established (see also [START_REF] Will | Linguistic units in word typing: Effects of word presentation modes and typing delay[END_REF], for considerations regarding the impact of linguistic properties on typing execution); our results highlight the role of orthographic and phonological boundaries, as well as the competition between sequences to be typed (motivated by the unexpected syllable consistency effect). The relationship between this putative buffer and the inner-loop, where letter sequences are processed for execution, remains as an important target for future work.

t

  = -3.75; CI = [-2.16E -05; -6.74E -06]) and of initial phoneme consistency (β = -8.43E -05; t = -3.44; CI = [-1.32E -04; -3.63E -05]). The more frequent a word and the more consistent the first phoneme, the shorter the onset latency. First or second syllable consistency ratios had no significant effects, and neither did bigram frequency (β = 5, 60E -05; t = -0, 42; CI = [-3.20E -05; 2.08E -05]; see Figure 2, upper row).

Figure 2 :

 2 Figure 2: Dependent measures (in rows, respectively: reaction times, accuracy rates, and interkeystroke intervals (IKI)) by quintiles of predictors (in columns, respectively: word frequency, consistency and bigram frequency). Error bars correspond to mean standard error calculated by bootstrap. The distribution of each predictor is depicted along the x-axis.

Table 1 :

 1

	0

Stimuli characteristics provided by Lexique

[START_REF] New | Lexique 2: a new French lexical database[END_REF]

and

[START_REF] Planton | Processus centraux et périphériques en production écrite de mots: études comportementales, en neuroimagerie fonctionnelle et par stimulation magnétique transcranienne[END_REF]

, and computed from BRULEX

[START_REF] Content | BRULEX A computerized lexical database for the French language[END_REF]

.

Table 2 :

 2 Bigram characteristics provided by Surface database

Table 3 :

 3 Results of the latencies analysis. β represent the magnitude of the effect (slope of the regression model); t-values above 1.96 are considered significant. RTs were inversetransformed.

	SE	t	95%CI	(sig)

Table 4 :

 4 Results of the IKI analysis. β represent the magnitude of the effect (slope of the regression model); t-values above 1.96 are considered significant. IKIs were log-transformed.

		β	SE	t	95%CI	(sig)
	(Intercept)	5.65	0.178	31.7
	Word Frequency	0.00282	0.00228 1.23	-0.0350	-0.0132
	Consistency	0.0563	0.0137	4.10	-0.0178 -0.000384	*
	Bigram Frequency	-0.0552	0.0180 -3.07	0.0294	0.0832	*
	Position	-0.0241	0.00558 -4.32 -0.0904	-0.0200	*
	Block number	-0.009096 0.00444 -2.05	5.30	6.00	*
	Hand alternation	0.0751	0.0388	1.93 -0.00166	0.00729	(*)

Table 5 :

 5 Results of the syllable boundaries analysis. ß represent the magnitude of the effect (slope of the regression model); t-values above 1.96 are considered significant. IKIs were log-transformed. O: Orthographic boundaries. PO: Phono-orthographic boundaries. NO: Within syllable IKI.

	Not boundary
	Orthographic
		120	160	200	240
			Inter-Keystroke Interval (ms)
	Figure 4: Boxplot of subjects mean IKI (in ms) at syllable boundaries.
		β	SE	t	95%CI	(sig)
	(Intercept)	5.56	0.118	47.2
	Word Frequency	-0.00124 0.00134 -0.93 -0.00386
	Boundary (O/NO)	0.0635	0.0231	2.75	0.0182	0.109	*
	Boundary (PO/NO)	0.0992	0.0218	4.55	0.0565	0.142
	Bigram Frequency	-0.0434	0.0119 -3.66 -0.0667	-0.0201	*
	Position	-0.0178 0.00526 -3.39 -0.0281	-0.00752	*
	Block number	-0.00875 0.00399 -2.19 -0.0166 -0.000932	*
	Hand alternation	0.0856	0.033	2.6	0.0209	0.1502	*

Acknowledgements

We thank Elie Fabiani for her help in data collection. This work was supported by the European Research Council (FP7/2007-2013 Grant number 263575), the Ministère de l'Enseignement et de la Recherche (doctoral MNRT grant to Svetlana Pinet), the Brain and Language Research Institute (A*MIDEX grant ANR-11-IDEX-0001-02, LABEX grant ANR-11-LABX-0036), and the Federation de Recherche 3C (Aix-Marseille Universite).