domain: chim phys

text:
Jun Su

Tao Zhu

Thierry Pauporté

Ilaria Ciofini

Frédéric Labat
email: frederic.labat@chimie-paristech.fr

Improving the Heterointerface in Hybrid Organic-Inorganic Perovskite Solar Cells by Surface Engineering: Insights from Periodic Hybrid Density Functional Theory Calculations

A periodic hybrid density functional theory computational strategy is presented to model the heterointerface between the methylammonium lead iodide (MAPI) perovskite and titanium dioxide (TiO2), as found in perovskite solar cells (PSC), where the 4-chlorobenzoic acid (CBA) ligand is used to improve the stability and the band alignment at the interface. The CBA ligand acts as a bifunctional linker to efficiently connect the perovskite and the oxide moieties, ensuring the stability of the interface through Ti-O and Pb-Cl interactions. The computed density of states reveals that the perovskite contributes to the top of the valence band while the oxide contributes to the bottom of the conduction band with a direct bandgap of 2.16 eV, indicating a possible electron transfer from MAPI to TiO2. Dipole moment analysis additionally reveals that the CBA ligand can induce a favorable effect to improve band alignment and thus electron transfer from MAPI to TiO2. This latter has been quantified by calculation of the spin density of the reduced MAPI/CBA/TiO2 system and indicates an almost quantitative (99.94%) electron transfer from MAPI to TiO2 for the surface engineered system, together with an ultrafast electron injection time in the femtosecond timescale. Overall, the proposed DFT-based computational protocol therefore indicates that surface engineering and the use of a bifunctional linker can lead to a better stability, together with improved band alignment and electron injection in PSC systems.

INTRODUCTION

With excellent optoelectronic properties and potential for low-temperature device fabrication, organometal halide perovskites (AMX3) are extensively studied materials. 1 Since their very first combination with mesoporous TiO2 photoanode for visible-light conversion in photovoltaic cells by Myasaka et al. 2 , organometal halide perovskites AMX3 have attracted considerable attention as efficient light harvesters. In particular, organic-inorganic hybrid perovskite solar cells (PSC) have appeared as excellent potential candidates to produce clean energy, with easy fabrication, long charge carrier diffusion lengths and lifetimes, high absorption coefficient, solution processability and high photoconversion efficiencies (PCE). [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] These perovskites are composed of an organic cation A, a divalent metal cation M generally belonging to the fourth main group and a halide anion X, which are arranged in a rigid threedimensional network of corner-sharing MX6 octohedra. By varying the different possible combinations between these cationic and anionic species, bandgap tuning of the perovskite material is possible, thus allowing to readily modulate its light absorption for photovoltaic application. Although the M and X species can in principle be easily tuned in these structures, the A cation on the other hand fills the 12-fold coordinated cubo-octahedral space created by the inorganic metal halide octahedra, hence making its choice limited to either monovalent cations such as Cs + , Rb + or K + , or to the small organic methylammonium (MA + ) and formanidinium (FA + ) ions. 16 In particular, among the most studied hybrid perovskites for PSC application, the pioneering methylammonium lead iodide hybrid perovskite (MAPbI3, referred to as MAPI) still remains actively considered nowadays. 2,7,21 In a PSC, the perovskite layer 22 ensures light absorption and generates electron-hole charge carrier pairs which then dissociate into free charge carriers. The free excited electrons and holes diffuse within electron and hole transport layers (ETL and HTL) and are then collected by corresponding electrodes. 16 By optimizing the different components of PSC as well as by finely tuning their combination, their PCE has increased from 3.8 2 to 25.2% 23 during the last decade. 5,[7][8][9][10][11][12][13][14][15] Although PSCs are then now generally considered as one of the most promising devices for photovoltaic energy production, several points still remain critical however for realworld application, including mainly toxicity and long-term stability. For example, MAPI hydrolyzes in the presence of water, breaking the weak interaction between the inorganic and organic networks. [24][25][26] In addition, the commonly-used organic HTL for high PCE such as spiro-OMeTAD, P3HT or PTAA are expensive and sensitive to humidity, [27][28][29] and various alternatives such as transition-metal oxides or copper compounds have been explored. [30][31][32][33][34] The choice of the HTL and ETL is also critical for cell performances, since PSC rely on different interfaces which should all be adequately designed and matched to achieve high PCE, by reducing charge recombination losses and maximizing the open-circuit voltage, 35 hence implementing interfacial and surface engineering is particularly important in these systems. 16,36 One general possible strategy for surface engineering is the use of facile solution-based processes considering self-assembled monolayers (SAMs) of organic molecules [37][38][39] which can form thin, dense and stable layers able to modify the electronic structure of the metal oxide surface they are chemically attached to. In the PSC field, SAMs have already been proposed since they can potentially induce various favorable effects such as morphology modification, band alignment with the energy level of the photoexcited active layer, trap passivation and delay of charge recombination. 40,41 Among the available modeling tools, density functional theory (DFT) has already been widely used and shown to be a useful tool to predict the structural and electronic properties of key interfaces found in sensitized solar cells, [42][43][44][45][46][47][48][49][50][51] including the one formed between the MAPI perovskite and TiO2 in PSC. [52][53][54][55] While the works devoted to the investigation of the isolated components of this interface are numerous, [56][57][58][59] much fewer have focused on the investigation of the full interface, probably due to its complexity and to the associated high computational cost. For example, Yoshitaka et al. recently investigated the structural stability and the electronic structures of a series of low-indices surfaces of tetragonal MAPI, highlighting that the (110) and (001) terminations are expected to be stable, with shallow surface states that can act as efficient intermediates for hole transport to HTL. 60,61 The tetragonal MAPI (001) surface was also recently investigated, comparing the two possible MAI and PbI2 terminations, indicating that the MAI termination is relatively more favorable than the PbI2 one in equilibrium growth. 62 On the other hand, for the ETL, TiO2 is usually considered due to its wide bandgap and fairly transparent nature. 63 Although the rutile polymorph is the most stable one for large particles, nanoparticles preferentially form with the anatase variant which is commonly used in photovoltaic materials. 64,65 More precisely, the anatase (101) surface is thought to be the most stable surface orientation in such systems. [66][67][68][69] Finally, among the works devoted to the modeling of the full MAPI/TiO2 interface, 45,50,53,[70][71][72] De Angelis 53 et al. proposed the (110) surface of MAPI to preferentially grow on TiO2 due to better lattice matching, with the chloride atoms concentrating at the TiO2 interface. 70 In this article, we present a theoretical investigation of a modified MAPI/TiO2 interface that was first optimized experimentally. Indeed, we have studied the effect of SAMs of a series of para-substituted benzoic acid derivatives as TiO2/perovskite interfacial modifiers. 41 Among them, we have found that 4-chlorobenzoic acid (CBA) was the best candidate which improves markedly the power conversion efficiency (PCE) of the solar cells. Interfacial engineering with CBA enabled us to achieve a PCE of 21.3 % to be compared to 20.3% for the untreated cells (see Tables S1 andS2, Supporting Information). However, while interfaces play a key role in such cells, their experimental characterization at the structural and electronic levels still remains difficult. Consequently, modeling of such interfaces with appropriate computational methods is relevant for a better understanding of the basic working principles of PSC, and thus for the design of novel systems. We show here that the linking of perovskite and TiO2 moieties is enhanced by using the bifunctional CBA ligand. A model of the MAPI/CBA/TiO2 interface (Figure 1) has been built and its structural and electronic properties have been fully characterized at the periodic hybrid DFT level. The key electron injection process found at this interface has also been addressed. We show that SAMs can be efficiently used for surface engineering of the heterointerface found in PSC between MAPI and TiO2, due its bifunctional nature, acting both as a suitable spacer at the interface to improve its stability, but also imposing a favorable dipole moment to improve band alignment and thus electron injection in such systems. In the discussion, computational details are first presented in Section 2 while results obtained are discussed in Section 3. Finally, some conclusions are drawn in Section 4.

COMPUTATIONAL DETAILS

All calculations were carried out with the periodic Crystal17 code, which is based on a linear combination of atom-centered Gaussian orbitals and solves self-consistently both Hartree-Fock (HF) and Kohn-Sham equations. [73][74][75] Exchange and correlation energies were described using the global hybrid PBE0 functional, containing 25% of HF exchange. 76 Previous studies have shown that this functional can indeed provide reliable geometric and electronic properties of both TiO2 77 and MAPI 46 , that are the two building blocks of the interface targeted.

Additional dispersion effects were accounted for through the empirical D3 correction. 78 Allelectron basis sets have been used for the CBA ligand and the methylammonium (MA + ) moieties. More precisely, for MA atoms, (31/1) contractions were used for H, while (631/31/1) contractions were employed for both C and N atoms. For CBA atoms, (511/1), (621/21/1), (7311/311/1), (8411/411/1) and (86311/6311) contractions were considered for H, C, N, O and Cl atoms, respectively. On the other hand, pseudopotentials were considered for all the other atoms. For Ti and O of TiO2, Durand and Barthelat large-core pseudopotentials with associated (1/1/41) and (31/31) contractions corresponding to 4 and 6 explicit electrons, respectively, were chosen. 79,80 Finally, for Pb and I, small core fully relativistic pseudopotentials developed at the Stuttgart University were selected, with 22 explicit electrons described using a (8811/1188/611/1) contraction scheme for Pb, and 25 explicit electrons described using a (8811/661/61) contraction scheme for I. 81 Reciprocal space was sampled using a shrinking factor of 2, corresponding to 4 k points in the irreducible Brillouin zone. Numerical DFT integration was performed considering 99 radial points and 1454 angular points, ensuring an error on the integrated electron density lower than 10 -5 |e-| per unit cell. The Coulomb and exchange series were truncated with threshold values of 10 -7 , 10 -7 , 10 -7 , 10 -9 , and 10 -27 .

Cell parameters of the lattice as well as atomic positions of a selected fragment of atoms (see below) were relaxed during geometry optimizations. Convergence was determined from the root-mean-square and absolute value of the largest component of the forces and displacements, considering default values. 75 Interface formation was energetically characterized by considering two quantities:

-adhesion energy, which is the energy gained by forming the interface, computed as:

Eads = E(MAPI/CBA) + E(TiO2) -E(MAPI/CBA/TiO2) (1)
where E(MAPI/CBA) and E(TiO2) are the total energies of the optimized MAPI/CBA slab and TiO2 supercell slab models, respectively, and E(MAPI/CBA/TiO2) is the total energy of the MAPI/CBA/TiO2 interface -specific adhesion energy, which is the adhesion energy per unit surface area, calculated as:

βads = Eads/S ( 2
)
where S is the surface area of the MAPI/CBA/TiO2 interface model. 82 The electron injection time was evaluated by considering a simplified orbital-based model derived from the original Newns-Anderson proposal for adsorbates on surfaces 83 , which was already successfully applied to dye-sensitized solar cells 51,84 . In this approach, only the evaluation of the broadening (Δ, in meV) of the donor level of the perovskite sensitizer when it is adsorbed on the TiO2 surface is required to compute the injection time (, in fs) according to:

τ=658/Δ (3)
More details regarding this methodology are available in Ref. 85 for instance. 85

RESULTS AND DISCUSSION

The models:

A MAPI/CBA/TiO2 interface was built starting from converged surface models of its two building blocks: the TiO2 oxide and the MAPI perovskite. A (2x2) supercell model of the anatase TiO2-(101) surface with 8 layers, corresponding to 8 O-Ti-O trilayers with 96 atoms and lattice parameters a=14.981 Å, b=11.088 Å and =109.7 was selected for the oxide part.

For MAPI, although both MAI-and PbI2-terminated (110) surfaces can exist, the former is known to be stable 61 and is expected to more easily bind to the TiO2 surface than the latter. A 3-PbI2 layers (110) slab was therefore obtained from the tetragonal MAPI bulk system with space group I4/mcm, resulting in a 2D lattice with lattice parameters a, b and  of 12.343 Å, 12.555 Å and 90.0, respectively. Consequently, a large mismatch between the lattice parameters of the 2D lattices of the TiO2 and MAPI slabs was obtained. The bifunctional nature of the CBA ligand was exploited by considering its carboxylate part to bind to TiO2 in a bridging bidentate mode, while its Cl atom was oriented towards the Pb atoms of MAPI close to the TiO2 substrate. By substituting all I -of the last layer of the MAPI surface with Cl atoms, Pb-Cl bonds were then created and the charge neutrality of the resulting unit cell was ensured by removing all H + of the last layer of MA moieties of MAPI. The final interface model was obtained by modifying the MAPI slab lattice to the values of the TiO2 supercell, resulting in an interface model with P1 symmetry, 328 atoms and 3876 atomic orbitals per unit cell. The lattice was then fully-relaxed, and all atoms but the lower 6 bottom layers of the TiO2 substrate were allowed to relax. In addition, to more clearly highlight the role of the TiO2 substrate in the MAPI/CBA/TiO2 interface, and especially on its electronic properties, we also considered adsorption of CBA on a MAI-terminated MAPI (110) slab with 3-PbI2 layers, considering a 1:1 substitution ratio between I -and Cl atoms. We note here that the CH3NH2 layer formed in contact with the CBA ligands is relevant for PSC application, since the CH3NH3 + ion in MAPI is well-known to readily deprotonate in the presence of water. In addition, chlorine atoms have already been shown to tend to concentrate at the TiO2 interface. 71 Figures 2c and 2d present resulting structures of both models after geometry optimization.

Structural and energetic features:

Table 1 summarizes the main structural features of the optimized lattices of the different building blocks and interface models considered, while Table 2 reports For MAPI/CBA, band dispersion can be noticed at the top of the valence band (VB) and at the bottom of the conduction band (CB). This can be related to the interaction of the CBA ligand with MAPI through its Cl atoms. In addition, the top of the VB and the bottom of the CB are mainly composed by the MAPI perovskite in which I -has been substituted with Cl in a 1:1 ratio. Compared to the clean MAPI (110) surface therefore, this leads to a band gap increase Furthermore, both band structures present direct band gaps at , highlighting a possible favorable and efficient photoexcitation of the heterointerface.

Band edge movements upon interface creation can also be qualitatively rationalized from the dipole moments components along the normal direction to the surface plane of the interface according to the Poisson equation 41 :

∆V = 𝑁 𝑠 𝜇𝑐𝑜𝑠𝜃 𝑎 𝜀 𝑟 𝜀 0
where Ns is the surface dipole density, μ the dipole moment, θa the tilt angle of the dipole with respect to the surface normal. εr is the dielectric constant, and ε0 is the permittivity of free space. A step in the local vacuum level ΔV can be obtained and qΔV, with q the elementary charge, can then modify the work function and the band edges of the interface. In particular, a positive value of ΔV would enhance the charge transfer to TiO2 while a negative one would reduce it. From the values reported in Table 3, for CBA/TiO2, the positive value suggests a charge transfer to the TiO2 surface. 41 As for MAPI/CBA, the value of the dipole moment pointing towards MAPI in the chemistry notation is negative, indicating that CBA may block electron reflow to MAPI. Furthermore, it can be noticed that a positive value is also obtained for MAPI/CBA/TiO2, thus highlighting that CBA can potentially enhance the electron transfer from MAPI to TiO2. To better clarify this point, electron injection from MAPI to TiO2 has been analyzed using an approach that we have developed notably for dye-sensitized solar cells 42,43 and quantum-dot sensitized solar cells 44 . More precisely, the spin density of the reduced MAPI/CBA/TiO2 system has been computed and the corresponding isodensity plot is shown in Finally, based on the Newns-Anderson model and the computed electronic structure of the MAPI/CBA/TiO2 system, the electron injection time is estimated to be 24 fs, indicating an ultrafast electron injection. This result is in good agreement with a previously-reported estimate based on a coupling matrix elements approach for the bare MAPI/TiO2 interface 86 where an injection in the femtosecond time scale has been obtained. We note that controversial experimental results are available regarding the electron injection time with values reported both in the picosecond [START_REF] Marchioro | Physical Chemistry of Interfaces and Nanomaterials[END_REF] or sub-picosecond [START_REF] Ponseca | [END_REF]89 timescales, preventing a more rigorous comparison between experimental and computed data.

CONCLUSIONS

In this article, a periodic hybrid density functional theory computational strategy has been presented to model the heterointerface between the MAPI perovskite and TiO2, as found in PSC, in which the CBA ligand has been used to improve the stability and the band alignment at the interface. The CBA ligand has been selected to act as a bifunctional linker to efficiently link the perovskite and the oxide moieties, ensuring stability of the interface through Ti-O and Pb-Cl interactions. The computed density of states revealed that the perovskite contributes to the top of the valence band while the oxide contributes to the bottom of the conduction band with a direct bandgap of 2.16 eV, indicating a possible electron transfer from MAPI to TiO2. Dipole moment analysis additionally revealed that the CBA ligand can induce a favorable effect to improve band alignment and thus electron transfer from MAPI to TiO2. This latter has been quantified by calculation of the spin density of the reduced MAPI/CBA/TiO2 system and indicated an almost quantitative electron transfer from MAPI to TiO2 for the surface engineered system, together with an ultrafast injection time in the femtosecond timescale. Overall, the proposed DFT-based computational protocol therefore indicated that by surface engineering with a bifunctional linker such as CBA, a better stability, together with improved band alignment and electron injection, could be obtained for PSC systems. Work is in progress to design novel PSC systems with enhanced efficiency based on these guidelines.

Figure 1 :

 1 Figure 1: Schematic of the MAPI/CBA/TiO2 interface.

Figure 2 :

 2 Ball and stick representation of the (a) MAPI(110) surface, (b) the MAPI-slab with all iodide atoms on one surface replaced by chloride atoms, (c) MAPI/CBA unit cell and (d) MAPI/CBA/TiO2 interface unit cell. The solid yellow line represents the unit cell. Red, light grey, white, green, purple, dark grey, blue and grey spheres correspond to O, Ti, H, Cl, I, Pb, N and C atoms, respectively. The relaxed and frozen parts considered for the geometry optimization of the MAPI/CBA/TiO2 interface are indicated in Figure 2(d).

  selected resulting distances. The optimized a and b cell parameters of the MAPI/CBA/TiO2 interface model are close to those of the TiO2 supercell considered, with values of 14.821 Å and 11.003 Å, together with a γ angle of 108.0°. Compared to the TiO2 supercell lattice, a small shrinking of all lattice parameters is therefore obtained when going from the TiO2 supercell to the MAPI/CBA/TiO2 interface, with shrinking values of -1.07, -0.77 and -1.55 %, respectively for the a, b and γ parameters. From the data reported in

Figure 3

 3 presents the computed band structures, as well as the total and projected density of states (TDOS and PDOS) of the MAPI/CBA/TiO2 and MAPI/CBA interfaces.

from 2 .

 2 97 to 3.39 eV. When considering the MAPI/CBA/TiO2 interface on the other hand, the band gap decreases to 2.16 eV mainly due to the TiO2 contribution at the bottom of the CB. In fact, the band structure and DOS analysis of the MAPI/CBA/TiO2 interface reveals that the top of the VB is mainly due to MAPI while the bottom of the CB is mainly due to TiO2, suggesting a possible electron transfer from the perovskite to the oxide from an energetic viewpoint, which is in line with the working principles of PSC mentioned above. Furthermore, it should be noted that the CBA ligand does not contribute to the valence or conduction bands close to the band gap region. Here, we note that no spin-orbit coupling effects have been taken into account in these calculations, but these have previously been quantified and shown to further reduce the above-mentioned band gap values of about 1.1 eV.46

Figure 3 :

 3 Figure 3: (left) Band structure and (right) total and projected density of states (TDOS and PDOS) of the (top) MAPI/CBA and (bottom) MAPI/CBA/TiO2 interfaces. k-points used for the band structure are:  (0, 0, 0), Y (0, 1/2, 0), M (1/2, 1/2, 0) and X (1/2, 0, 0).

Figure 4 .

 4 It is clear that the computed spin density is mainly delocalized over the TiO2 part, with a 99.94% contribution of the added electron on the TiO2 substrate. This value is a quantification of the injection efficiency of the photogenerated electrons and indicates an almost quantitative electron transfer from MAPI to TiO2 through the CBA ligand.

Figure 4 :

 4 Figure 4: Spin density of the reduced MAPI-CBA-TiO2 interface system (excess of alpha electron is indicated in yellow), isosurface contour value: |0.00271| a.u.

Table 2 ,

 2 both Ti-O and Pb-Cl bonds can be evidenced, the CBA ligand acting with two complementary features to ensure interface stability between the perovskite and the oxide. The first feature corresponds to its bifunctional linker nature: a bridging bidentate mode is involved between the CBA carboxylate moiety and TiO2, while strongly distorted PbI5Cl octohedra can be evidenced between MAPI and CBA. Here, we note that Pb atoms both interact with Cl atoms and the deprotonated CH3NH3 + groups in the layer in contact with CBA. The same conclusion can be drawn in the MAPI/CBA case. The second feature is the ability of CBA ligands to lay on the TiO2 substrate, with computed tilting angles with respect to the surface normal of 30.0, 38.6, 38.6 and 46.9° for the four CBA molecules of the MAPI/CBA/TiO2 interface model unit cell for instance. In particular, favorable H + / interactions between the dissociated H + of the carboxylate groups of CBA adsorbed on the TiO2 substrate and the benzene ring of the CBA ligands tend to further improve interface stability by building a favorably organized CBA-TiO2 interface for the binding of MAPI. This can be related to the rigid nature of the CBA ligand. The computed adhesion energy of the MAPI/CBA/TiO2 model further confirms these conclusions, with a computed value of 3.45 eV, corresponding to a specific adhesion energy of 0.02 eV/Å 2 , indicating a stable interface formation. We note that this value is in line with the 0.04 eV/Å 2 value recently reported by Mosconi et al. for a similar interface based on the same surface orientations,70 as well with those obtained with other orientations.72

Table 1 :

 1 Lattice parameters a, b (in Å) and γ (in degrees) as well as computed band gaps (Eg, in eV) for selected systems involved in the interface model construction. Adhesion energy (Eadh, in eV) and specific adhesion energy (, in eV•Å -2 ) of the MAPI/CBA/TiO2 interface are also

	given.
		MAPI (110)	CBA/MAPI (110)	TiO2 (101)	MAPI (110)/CBA/TiO2 (101)
	a	12.343	12.343	14.981	14.821
	b	12.555	12.555	11.088	11.003
	γ	90.00	90.00	109.74	108.03
	Eg	2.97	3.39	5.03	2.16
	Ead	--	--	--	3.45
	β	--	--	--	0.02

Table 2 :

 2 Selected distances (in Å) between Pb, N and Cl atoms of the MAPI/CBA and MAPI/CBA/TiO2 systems.

		dN/Pb				dCl/Pb				dTi/O
	MAPI/CBA	3.35	3.71	4.03	5.47	2.62	2.63	4.74	5.56	-	-
		8	0	2	2	7	2	9	6
	MAPI/CBA/TiO	3.45	3.95	4.68	5.42	2.51	2.55	5.06	5.66	2.17
	2	7	7	6	4	7	3	3	9

Table 3 :

 3 Dipole moments components along the surface normals (z, in Debye) of the CBA/TiO2, MAPI/CBA and MAPI/CBA/TiO2 systems.

	Systems	z
	CBA/TiO2	0.89
	MAPI/CBA	-0.88
	MAPI/CBA/TiO2 0.61

ACKNOWLEDGMENTS J. S. and T. Z. acknowledge the CSC for Ph.D. scholarship. The authors acknowledge the use of computational resources at Très Grand Centre de Calcul (TGCC) provided by GENCI through project A0050810135. IC and FL thank the ITN program COSINE (Grant agreement ID 765739) for support.


Lison Fanuel

Simone Dalla

Barbara Tillmann

Temporal regularities benefit maintenance in aging

Keywords: Working memory, Maintenance, Refreshing, Aging, Temporal regularities

Sidonie Calingoula, Caroline Vignand and Constance Massie

Music cognition research has provided evidence for a benefit of temporally regular structures on various processes, such as perception [START_REF] Schwartze | Temporal regularity effects on pre-attentive and attentive processing of deviance[END_REF], learning [START_REF] Hoch | Regularity of unit length boosts statistical learning in verbal and nonverbal artificial languages[END_REF][START_REF] Selchenkova | The influence of temporal regularities on the implicit learning of pitch structures[END_REF] and, more recently, in episodic memory [START_REF] Hickey | Memory in time: Neural tracking of low-frequency rhythm dynamically modulates memory formation[END_REF][START_REF] Johndro | Temporal predictions provided by musical rhythm influence visual memory encoding[END_REF], working memory and short-term memory (Fanuel, Portrat, Tillmann, & Plancher, 2018;[START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF]. Previous research has suggested that maintenance in working memory relies on two distinct mechanisms: verbal rehearsal and attentional refreshing [START_REF] Camos | Attentional and non-attentional systems in the maintenance of verbal information in working memory: The executive and phonological loops[END_REF]. While verbal rehearsal allows for maintenance of verbal information via the phonological loop described in Baddeley's model [START_REF] Baddeley | Working memory[END_REF][START_REF] Baddeley | Exploring the articulatory loop[END_REF], attentional refreshing is viewed as a domain-general mechanism relying on attention [START_REF] Camos | What is attentional refreshing in working memory?: What is attentional refreshing?[END_REF]. Attentional refreshing (also referred to as refreshing) can be described as a brief thought to an item that is no longer perceptually present [START_REF] Johnson | MEM: Mechanisms of recollection[END_REF]. Recent results have provided evidence that attentional refreshing in young adults can benefit from a temporally regular structure [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF]). An isochronous tone sequence presented during the retention interval benefited to memory performance (in comparison to a silent retention period), suggesting that temporal regularities benefit maintenance in memory. As the benefit was not observed with a non-isochronous rhythm but persisted under concurrent articulation impeding verbal maintenance mechanism, temporal regularities were proposed to benefit attentional refreshing. There is consistent and compelling evidence that attentional refreshing is impaired in the elderly (Fanuel, Plancher, et al., 2018;[START_REF] Hoareau | Reconciling two computational models of working memory in aging[END_REF][START_REF] Jarjat | Aging Influences the Efficiency of Attentional Maintenance in Verbal Working Memory[END_REF][START_REF] Johnson | Second thoughts versus second looks: An age-related deficit in reflectively refreshing just-activated information[END_REF][START_REF] Loaiza | The influence of aging on attentional refreshing and articulatory rehearsal during working memory on later episodic memory performance[END_REF][START_REF] Plancher | Under which conditions can older participants maintain information in working memory?[END_REF]. Our study investigated whether older adults can also benefit from an auditory temporally regular structure presented during maintenance and whether their cognitive capacities can affect the potential benefit of temporal regularities on maintenance in shortterm memory.

Over the last decades, different hypotheses have been proposed for the cognitive mechanisms underlying age-related decline in working memory [START_REF] Logie | Working memory and ageing[END_REF][START_REF] Luo | Aging and memory: A cognitive approach[END_REF]. The slowing-down theory proposes that in general the speed of cognitive processes (including working memory) declines with age [START_REF] Salthouse | Influence of processing speed on adult age differences in working memory[END_REF]. More specifically, the attentional resource theory makes the hypothesis that the amount of attentional resources available for cognitive processing declines with age [START_REF] Naveh-Benjamin | The Associative Memory Deficit of Older Adults: Further Support Using Face-Name Associations[END_REF][START_REF] Rabinowitz | A processing resource account of age differences in recall[END_REF], resulting in increased difficulties to perform highly demanding cognitive tasks, such as working memory tasks. Another account, the inhibition framework, proposes that older adults have less efficient inhibitory processes, leading to increased difficulties to deal with interference and block out irrelevant information from working memory [START_REF] Borella | Working memory and inhibition across the adult life-span[END_REF][START_REF] Hasher | Working memory, comprehension, and aging: A review and a new view[END_REF]. Finally, a combination of the attentional resources and inhibition approaches was proposed by Jacoby and colleagues [START_REF] Jacoby | A process dissociation framework: Separating automatic from intentional uses of memory[END_REF][START_REF] Jennings | Automatic versus intentional uses of memory: Aging, attention, and control[END_REF], who hypothesized that older adults are specifically impaired in controlled processing, but not in automatic processing.

A growing body of evidence has shown that age-related deficits in working memory could be due to impaired attentional refreshing. The first studies investigating a deficit of refreshing in aging have focused on explicitly instructed refreshing of just-presented information and its impact on longterm memory (e.g., [START_REF] Higgins | The consequence of refreshing for access to nonselected items in young and older adults[END_REF][START_REF] Johnson | Second thoughts versus second looks: An age-related deficit in reflectively refreshing just-activated information[END_REF]. In [START_REF] Johnson | Second thoughts versus second looks: An age-related deficit in reflectively refreshing just-activated information[END_REF], for example, words were presented sequentially, and they were either presented once, repeated or followed by a dot that instructed participants to think about the preceding word (i.e., to refresh it).

Each time a new word (or dot) was presented, participants read the new word aloud, or recalled the previous word aloud in the refreshing condition; response times were recorded. While older participants responded globally more slowly than did young adults, response times of both young and older adults benefited to the same extent from word repetition. In comparison to word repetition, response times in the refreshing condition increased for both young and older adults. Response times in the refreshing condition were slower for older adults than for young adults, highlighting a slowing down of refreshing in aging. Computational modelling of working memory performance in young and older adults [START_REF] Hoareau | Reconciling two computational models of working memory in aging[END_REF][START_REF] Plancher | Under which conditions can older participants maintain information in working memory?[END_REF] also supported the hypothesis of slowed-down refreshing in aging. Memory performance of older adults was best fitted by a model in which refreshing times for older adults are five times longer than for young adults. Impaired refreshing could further explain why older adults benefit less from refreshing opportunities than do younger ones [START_REF] Jarjat | Aging Influences the Efficiency of Attentional Maintenance in Verbal Working Memory[END_REF].

However, other studies provided evidence for a preservation of attentional refreshing in aging.

In [START_REF] Johnson | Second thoughts versus second looks: An age-related deficit in reflectively refreshing just-activated information[END_REF], memory performance was assessed after the presentation of the word list in a recognition task. Both age groups performed better for repeated words than for words that were presented once, and memory performance was better in the refreshing condition than in the other conditions, suggesting that both groups benefited from the refreshing opportunity. In line with this finding, other empirical evidence suggests that the attentional refreshing mechanism is still efficient in aging. In a retro-cue paradigm, older and young adults benefited to the same extent from a cue presented during the retention interval that indicated which item will be subsequently tested [START_REF] Souza | No age deficits in the ability to use attention to improve visual working memory[END_REF]. Attentional refreshing involves both initiation of refreshing and refreshing per se [START_REF] Johnson | Electrophysiological Correlates of Refreshing: Event-related Potentials Associated with Directing Reflective Attention to Face, Scene, or Word Representations[END_REF]. Because attentional refreshing is prompted by the cue, initiation is not necessary. This could explain the preserved benefit of older adults from refreshing in the presence of the retro-cue. Indicating the spatial location of the item that will be tested might guide attention toward this location and thus facilitate the initiation of refreshing of this specific item.

Providing guidance for attention could thus be a mean to improve refreshing in aging and overcome the impaired initiation of refreshing.

The Dynamic Attending Theory (DAT, [START_REF] Jones | Time, our lost dimension: Toward a new theory of perception, attention, and memory[END_REF][START_REF] Jones | Dynamic Attending and Responses to Time[END_REF][START_REF] Large | Pulse and Meter as Neural Resonance[END_REF], a theoretical framework initially proposed in music cognition research, suggests that attentional resources are not distributed continuously over time, but develop over cycles (implemented via neurocognitive oscillations, e.g., [START_REF] Fujioka | Internalized Timing of Isochronous Sounds Is Represented in Neuromagnetic Beta Oscillations[END_REF][START_REF] Fujioka | Beta and gamma rhythms in human auditory cortex during musical beat processing[END_REF][START_REF] Nozaradan | Tagging the Neuronal Entrainment to Beat and Meter[END_REF][START_REF] Nozaradan | Capturing with EEG the Neural Entrainment and Coupling Underlying Sensorimotor Synchronization to the Beat[END_REF].

The presence of temporally regular structures in the environment provides predictable cues which synchronize attentional cycles (i.e., via entrainment). Successful synchronization allows predicting the occurrence of future events (see [START_REF] Arnal | Cortical oscillations and sensory predictions[END_REF] for a review), thus improving the allocation of attentional resources at the expected time points. For example and among other empirical findings, Cutanda, Correa and [START_REF] Craik | Auditory temporal preparation induced by rhythmic cues during concurrent auditory working memory tasks[END_REF] presented sequences of seven tones during the retention interval of a Sternberg-like paradigm. The six first tones of the sequence were at a low pitch and presented either isochronously (with a sound onset asynchrony of 800 milliseconds), non-isochronously or only the first and seventh tones were presented. The last tone of the sequence, shorter and with a higher pitch, constituted the target tone and participants were instructed to press a key as soon as they detected this tone. Detection times were faster when the target tone was preceded by the isochronous sequence than when preceded by the non-isochronous sequence or no sequence. The regular temporal structure provided by the isochronous sequences allowed perceivers to implicitly use the regularity for developing temporal expectations about the occurrence of the last tone, resulting in an enhanced perceptual processing (see also [START_REF] Geiser | A Corticostriatal Neural System Enhances Auditory Perception through Temporal Context Processing[END_REF] for converging data with an intensity discrimination task).

Recent research investigating short-term memory has revealed that a temporally regular structure can also improve maintenance of to-be-remembered information, in particular, attentional refreshing [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF]). Yet, up to now, the beneficial effect of temporal regularities on maintenance was only investigated in young adults (Fanuel, Portrat, et al., 2018;[START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF]. In the present study, we investigated whether the beneficial effect of a temporally regular structure on maintenance in short-term memory extends also to older adults. To this end, the same experimental paradigm as in Plancher et al. (2018, Experiment 1) was used. Participants were instructed to memorize series of letters, maintain them over a retention interval of six seconds, and recall them. The retention interval was either silent or filled with an isochronous auditory rhythm. Previous research has suggested that spontaneous preferred tapping tempo might change over life span [START_REF] Mcauley | The time of our lives: Life span development of timing and event tracking[END_REF]. While the reported tempi increased from childhood to young adulthood, they were quite similar (around 630ms) for young adults and the elderly (60-74 years old; see [START_REF] Mcauley | The time of our lives: Life span development of timing and event tracking[END_REF]. Thus, we here used the same isochronous sequence with 1-second sound onset asynchrony, as did [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF]. As the benefit of the isochronous sequence during the retention interval in young adults was due to the temporal regularities rather than the mere presence of tones, we here focused directly on this comparison. If the temporal regularities improve the efficiency of refreshing even in aging, memory performance should be greater in the rhythm condition (i.e., with the isochronous sequence) than in the silence condition.

Based on the hypothesis that rhythm perception skills are likely to influence the processing of temporal regularity, interindividual variation in rhythm perception was evaluated with tasks of the Battery for the Assessment of Auditory Sensorimotor and Timing Abilities (BAASTA;[START_REF] Dalla Bella | BAASTA: Battery for the assessment of auditory sensorimotor and timing abilities[END_REF]. If rhythm perception is mediating the memory benefit from the regular sequence, then these abilities should modulate the effect of the isochronous rhythm on memory performance. Moreover, because aging has been associated with various cognitive changes, in particular in executive functions [START_REF] Valdois | Heterogeneity in the cognitive profile of normal elderly[END_REF][START_REF] Ylikoski | Heterogeneity of cognitive profiles in aging: Successful aging, normal aging, and individuals at risks for cognitive decline[END_REF], we investigated whether the cognitive capacities of older adults might mediate the potential benefit of the temporal regularities (if any) on maintenance in short-term memory. In particular, the effect of a temporally regular structure on maintenance in short-term memory might be modulated by the sensitivity to irrelevant information.

For each participant, we evaluated general cognition, executive functions including inhibition, shortterm memory and working memory. If one (or more) cognitive function(s) mediate(s) the benefit from the regular structure, then the performance in the associated neuropsychological evaluation should predict the potential benefit in the rhythm condition compared to silence. Because the presence of the tones can be considered as irrelevant information regarding the memory task [START_REF] Page | The irrelevant sound effect: What needs modelling, and a tentative model[END_REF], inhibition capacities can be expected to mediate the benefit of temporal regularities. We further investigated whether older adults benefited from the presence of a temporally regular structure to the same extent as younger adults. To do so, we contrasted the rhythm effect on memory performance for older and younger adults. We expected that the age-related deficit in inhibition processes might led to a smaller benefit of temporal regularities on maintenance in working memory for older adults than for younger ones.

Method

Participants

Forty participants (25 women) aged between 63 and 90 years (M = 72.13, SD = 6.57) voluntarily participated in the study. Sample size was determined based on our previous study [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF] investigating the effect of temporal regularities on maintenance in working memory with 20 young adults. Because of higher variability in cognitive profiles in the elderly as compared to younger adults [START_REF] Lindenberger | Variability in cognitive aging: From taxonomy to theory[END_REF], we doubled the amount of participants for the present study. They were recruited either in a retirement home or through social networks and were not selected relative to musical training. Participants did not report any sensory, cognitive, psychological or neurological disorders. The study was conducted in Lyon 2 university, which does not have an Institutional Review Board. Even though the study was not approved by an ethics committee, it was conducted in line with recommendations from Helsinki declaration, and participants gave written informed consent prior to the experiment.

Neuropsychological evaluation

Each participant completed several neuropsychological tests. A general measure of cognition was obtained with the Mini Mental State Evaluation (MMSE, [START_REF] Folstein | Mini-mental state": A practical method for grading the cognitive state of patients for the clinician[END_REF][START_REF] Kalafat | Standardisation et étalonnage français du "Mini Mental State"(MMS) version GRECO[END_REF] for the French version used in the present study). The MMSE scores confirmed that none of the participants was cognitively impaired (cut-off score of 27): M = 28.85 ± 1.10; range = 27-30). For a more detailed cognitive profile of the participants, memory and executive functions were also assessed. Short-term memory and working memory were measured with the forward and backward span tasks of the Wechsler Adult Intelligence Scale (WAIS, [START_REF] Wechsler | Wechsler adult intelligence scale-Fourth Edition (WAIS-IV)[END_REF], respectively. Speed processing and flexibility measures were provided by the Trail Making Test (TMT, [START_REF] Lezak | Neuropsychological assessment[END_REF], by calculating response times to perform the TMT-A and calculating the difference between response times in the TMT-A and TMT-B (furthered referred to as TMT B-A). Finally, the Stroop Victoria Test [START_REF] Stroop | Studies of interference in serial verbal reactions[END_REF][START_REF] Davidson | Stroop Interference, Practice, and Aging[END_REF][START_REF] Bayard | Test du Stroop Victoria-Adaptation francophone[END_REF] for the French version) provided a measure of inhibitory capacities distinguishing the inhibition of a dominant, highly interfering, response (i.e., the classical Stroop task comparing the naming of the color of dots versus naming the color of the ink of words of color) and the inhibition of an information that is producing weak interference (i.e., comparing the naming of the ink of dots versus neutral words, which do not refer to colors; [START_REF] Bayard | Test du Stroop Victoria-Adaptation francophone[END_REF]. Both measures of inhibition correspond to a ratio between the task involving inhibition (i.e., naming of words) and the control condition (i.e., naming of the color of the dots): the higher the score, the lower the inhibition capacities. The Hospital Anxiety and Depression Scale (HADS, [START_REF] Zigmond | The hospital anxiety and depression scale[END_REF][START_REF] Untas | Anxiété et dépression en hémodialyse: Validation de l'Hospital Anxiety and Depression Scale (HADS)[END_REF] for the French version) provided a general measure of anxiety and depression and the Geriatric Depression Scale (GDS, [START_REF] Yesavage | Development and validation of a geriatric depression screening scale: A preliminary report[END_REF][START_REF] Clement | Development and contribution to the validation of a brief French version of the Yesavage Geriatric Depression Scale[END_REF] for the French version) allowed for an elderly-specific assessment of depression. To ensure that participants did not suffer from depressive or anxiety symptoms that could interfere with working memory functioning [START_REF] Christopher | The impact of clinical depression on working memory[END_REF], inclusion criteria was to score below 8 to the HADS and below 10 at the GDS [START_REF] Mykletun | Hospital Anxiety and Depression (HAD) scale: Factor structure, item analyses and internal consistency in a large population[END_REF][START_REF] Yesavage | The Geriatric Depression Rating Scale: Comparison with other self-report and psychiatric rating scales[END_REF].

Insert Table 1 about here

Rhythm perception

After the neuropsychological evaluation, two sub-tests of the BAASTA [START_REF] Dalla Bella | BAASTA: Battery for the assessment of auditory sensorimotor and timing abilities[END_REF] were used to evaluate participants' rhythm perception (with isochronous sequences and with music; stimulus inter-onset interval and inter-beat interval = 600ms). Data were collected with a tablet LG G Pad 8.0. Participants first performed the Anisochrony Detection task with tones and then the Beat Alignment Test (BAT). The Anisochrony Detection task with tones consisted in the presentation of sequences of five tones that were either isochronous or not, depending on the inter-onset interval (IOI) between the penultimate and the last tone. Participants were asked to decide whether the sequence was regular or irregular. The threshold for detecting anisochrony was calculated using an adaptive method (see Dalla Bella et al., 2017 for more details). In the BAT, short musical excerpts were presented with an isochronous sequence of tones superimposed onto the music. The sequence of tones was either aligned to the musical beat or not. Participants we instructed to decide whether the isochronous sequence was aligned with the beat of the musical excerpt or not. Correct responses and false alarms were calculated and resulted in a sensitivity measure of beat alignment (i.e., d').

Experimental task

Material. Material and procedure were as described in [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF], except that the number of training trials was doubled to ensure correct understanding of instructions by the elderly participants. The experiment was programmed with OpenSesame 3.0 [START_REF] Mathôt | OpenSesame: An open-source, graphical experiment builder for the social sciences[END_REF].

Twenty-four sequences of six letters were created from a subset of letters including only bisyllabic consonants (i.e., all consonants except the "W" which is trisyllabic in French) and constituted the to-be-memorized material. A given letter was only presented once in a sequence. Acronyms and alphabetically ordered string were avoided. Each letter was equally presented over the entire experiment and at each serial position.

An isochronous rhythm was created using a woodblock tone of 58-ms duration. The tone was repeated six times with a sound-onset asynchrony (SOA) of 1000 ms.

Procedure (Figure 1). Each trial began with a black fixation cross displayed in the center of the white screen during 500 ms. Letters from a given sequence were then sequentially presented in black in a 60-pixels mono font in the center of a white screen. Each letter remained on the screen for 800 ms followed by 200 ms of blank. Participants were instructed to read the letters aloud when they appeared on the screen and to memorize them as best as they can. After the letters' presentation, the screen remained blank for 6000 ms, constituting the retention interval. This retention interval was filled with the auditory isochronous rhythm (Rhythm condition) in half of the experimental trials and remained without sound in the other half of the experimental trials (Silence condition). As in previous studies (Fanuel et al., 2018;[START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF], participants were asked to recall the letters aloud in their order of appearance after the retention interval. The experimenter wrote down the recalled sequence and asked participants for more details on the serial position if any doubt remained for the experimenter (i.e., if the participant recalled less than six letters, he/she was asked to explicit the position of the letters). A given letter in a sequence was considered as correctly recalled when it was recalled at the correct serial position. One point was attributed to each letter that was correctly recalled, leading to a serial recall score with a maximum of six points for each sequence.

Experimental conditions (rhythm, silence) were blocked and the order of presentation as well as the letter sequences assigned to each condition were counterbalanced across participants following a Latin square. Each experimental condition began with four training trials followed by 12 experimental trials.

Statistical analyses

Statistical analyses were computed using JASP 0.11.1 (JASP Team, 2019) with the default settings. In addition to classical frequentist statistics, bayesian statistics were computed. The bayesian factor (BF) associated to an effect is the resulting statistics of the comparison between all the models including this particular effect and all the models not including this effect [START_REF] Etz | JBS Haldane's contribution to the Bayes factor hypothesis test[END_REF]. Thus, it reflects the probability of the inclusion of this effect averaged across all candidate models.

When applicable, we will report the bayesian factor associated to an effect (BF), as well as the most probable model (i.e., the model that fits best the data) and its associated bayesian factor (BFM).

Importantly, a bayesian factor can give evidence towards the alternative hypothesis (H1) or towards the null hypothesis (H0). Following [START_REF] Lee | Bayesian cognitive modeling: A practical course[END_REF], a BF between 3 and 10 is considered as moderate support for the alternative hypothesis and BF above 10 are considered as a strong support for the alternative hypothesis. BF10 values between 1/3 and 1/10 and below 1/10 are considered as moderate support and strong support for null hypothesis, respectively. BF10 values between 1/3 and 3 are considered as ambiguous information (Etz et al., 2017;[START_REF] Lee | Bayesian cognitive modeling: A practical course[END_REF][START_REF] Wagenmakers | A practical solution to the pervasive problems of p-values[END_REF].

Results

Neuropsychological measurements

Results of all neuropsychological tests are reported in Table 1. Importantly, no indication of cognitive disorders was observed in our pool of participants (all MMSE scores were above or equal to 27), and none of the participants had anxiety or depression-related symptoms (HADS < 8 for both anxiety and depression sub-tests; GDS < 10).

BAASTA tasks

Concerning the BAASTA tasks, fewer data were acquired due to either participants who interrupted the task (N = 2 for the Beat Alignment Test, N=6 for the Anisochrony Detection with Tones) or technical reasons (N = 13): data of 25 participants were analyzed for the Beat Alignment Test (mean d' = 1.81, SD = 1.33) and 21 for the Anisochrony Detection with Tones (mean threshold = 78 ms -i.e., 13 % of the IOI -, SD = 27 ms). These results are consistent with previous data assessing rhythm perception in the elderly [START_REF] Bégel | Test-retest reliability of the Battery for the Assessment of Auditory Sensorimotor and Timing Abilities (BAASTA)[END_REF], mean age = 62.95, SD = 5.92, ranged between 50 and 76 years-of-age) with the Anisochrony Detection task with tones (first session: mean threshold = 13.67 % , SD = 3.27, second session: mean threshold = 12.92 %, SD = 2.86) and the Beat Alignment Test (first session: mean d' = 1.67, SD = 1.36 ; second session: mean d' = 1.82, SD = 1.49). Rhythm perception of the elderly did not seem to differ from young adults performance (mean age = 23.9 ± 4.1, mean threshold for anisochrony detection with tones about 10 % and mean d' for Beat Alignment Test about 2.10, Dalla [START_REF] Dalla Bella | BAASTA: Battery for the assessment of auditory sensorimotor and timing abilities[END_REF].

Serial recall

A one-way ANCOVA was performed on serial recall performance with experimental condition (Silence vs. Rhythm) as the within-participant factor and the MMSE score as a covariate to control for general cognition differences. The effect of condition was not significant (F(1, 38)=1.01, p=.32) and bayesian analyses showed moderate evidence for no effect of condition (BF = 0.32; M = 4.41, SD = 0.94 in the silence condition; M = 4.31, SD = 1.13 in the rhythm condition). 1 To investigate whether cognitive processes or perception abilities could mediate a potential effect of rhythm on maintenance in memory, correlation and regression analyses were performed with the difference in serial recall performance between the two experimental conditions (i.e., rhythmsilence) as dependent variable and the neuropsychological measures (MMSE, forward span, backward span, response time for TMT A, TMT B-A, inhibition score for dominant response and inhibition score for weakly-interfering information) as well as the rhythm perception performance (d' of beat alignment and anisochrony detection threshold). Stepwise multiple regressions were then conducted for each of the dependent variables with all neuropsychological measures as potential predictors to be included in the regression equation. 2 In the stepwise regression, predictor variables were entered into the regression equation one at a time based upon statistical criteria (i.e., p<.05). At each step in the analysis, the predictor variable that contributes the most to the prediction equation in terms of increasing the multiple correlation, R, is entered into the regression equation. When no additional predictor variables added further statistically significant contribution to the regression equation, the analysis stops.

1 To check for potential order effects, a two-way ANCOVA was performed with condition (Silence vs. Rhythm) as a within-participant factor, the order of block presentation (Silence-Rhythm vs. Rhythm-Silence) as between-participants factor, and the MMSE score as covariate. Neither main effects nor interaction were significant (F<1 for both main effects of condition and order, F(1, 37) = 1.835, p=.18, Condition*Order interaction), and BF either favored null hypothesis (BF = 0.29 for Condition main effect, BF = 0.29 for the Condition*Order interaction) or were ambiguous (BF = 0.49 for Order main effect).

2 Rhythm perception measures were not included in the regression analyses because of the missing data which reduced the data set. For completion only, we conducted also the correlation and regression analyses including only participants for whom all data (neuropsychological and rhythm perception measures) were available (N=20). The overall result pattern was confirmed, but with slight differences (see footnotes below) likely due to lower statistical power because of the drastic reduction of the sample size.

The difference in serial recall performance between the experimental conditions (i.e., rhythmsilence) was correlated only with the inhibition score for the weakly-interfering information (Pearson's r(38) =-.44, p<.001, BF = 10.02; note that the lower the score, the better the inhibition capacities). The other correlations were not significant (all p > .23) and were associated with either moderate evidence in favor of the null hypothesis (MMSE, Backward span, TMT B-A, Stroop score for highly interfering information, d-prime score for Beat Alignment Test) or with ambiguous information (Forward span, TMT A, threshold of anisochrony detection with tones; see Table 1). The regression analysis on the difference between memory performance in rhythm and silence conditions was performed to evaluate whether the inhibition score for irrelevant information was sufficient to predict the rhythm effect on memory performance or whether the inclusion of other neuropsychological measures could provide a better account. At step one of the analysis, the inhibition score for weakly-interfering information was entered into the regression equation, and it significantly predicted the rhythm effect on memory performance (F(1,36) = 7.97, p=.008). The contribution of the inhibition score for weakly-interfering information was significant (β=-0.77, t(36)=-2.82, p=.008) and accounted for about 18% of the variance of the memory performance difference rhythm-silence. As shown in the Figure 2, the presence of the rhythm elicited a positive effect on recall performance as compared to silence for older adults who had a lower Stroop score (i.e., high inhibition capacities). On the contrary, the presence of the rhythm impaired recall performance of older adults with a higher Stroop score (i.e., lower inhibition capacities). For detailed individual performance in Rhythm condition presented as a function of performance in the Silence condition, see Figure S1 in Supplementary material. Data were best fitted by the model including only inhibition score for weakly-interfering information (BFM = 6.99). No other measure entered into the equation at step two of the analysis, showing that the inhibition capacity for weakly-interfering information was the only significant predictor of the memory performance difference between rhythm and silence conditions. 3

Insert Figure 2

about here

Comparison with younger adults

To better understand whether aging influenced the beneficial effect of temporal regularities on maintenance in working memory, we compared the data from the older adults of the present study with data of younger adults (data from Plancher et al., 2018, experiment 1). Experimental designs of Plancher et al. (2018, experiment 1) and the present study were identical, except for neuropsychological evaluation and rhythm perception measures, which were not collected for the younger adults.

The twenty young adults of Plancher et al.'s study were non-musician students from Lyon.

Aiming for comparable educational background in the two populations and the largest N possible for both age groups, we selected a subset of older adults whose educational level matched the one of the young adults (i.e., 12 years of studies or more, corresponding to post-secondary education). Older adults were not selected based on their musical training but none of them were professional musician. This sub-sampling resulted in the following two participant groups : (1) 23 older adults (out of 40, i.e. A two-way analysis of variance (ANOVA) was performed with Condition (Rhythm, Silence) as within-participant factor and Age (Older, Younger) as between-participants factor. The main effect of 3 Analyses including only participants with data for the BAASTA showed that the correlation with the inhibition score for weakly-interfering information just failed to reach significance (p=.07), no other correlation was significant. No predictor factor entered into the regression equation (note that for inhibition score for weakly-interfering information, β=-0.81, t(18)=-1.93, p=.07).

Condition was significant and associated with a strong evidence for the effect (F(1,32) = 36.07, p<.001, η²p=.53, BF = 39,307), with better memory performance in the rhythm condition (M = 4.81, SD = 0.78) than in the silence condition (M = 4.41, SD = 0.90). The main effect of Age was not significant (F < 1; M = 4.71, SD = 0.83 for older adults, M = 4.51, SD = 0.67 for younger adults), but the inclusion of the Age factor in the model was highly probable (BF = 1,528). The interaction between Age and Condition was significant (F(1, 41) = 30.33, p<.001, η²p=.43, BF = 39307.81, Figure 3). As expected, for younger adults, performance was significantly better in the rhythm condition (M = 4.96, SD = 0.55) than in the silence condition (M = 4.05, SD = 0.88; p<.001), but not for the older adults (M = 4.69, SD = 0.93 in the rhythm condition, M = 4.73, SD = 0.81 in the silence condition; p = .769). Bayesian analyses highlighted that the model including Condition and Age main effects in addition to their interaction best fitted the data (BFM = 6,099). Comparison between younger and older adults confirmed that older adults benefited less than younger adults from the presence of temporal regularities during the retention interval.

Insert Figure 3 about here

Discussion

The present study aimed to investigate whether older adults can benefit from temporal regularities during short-term memory maintenance as previously observed for young adults. Related to the previously reported attentional deficit in aging (Fanuel, Plancher, et al., 2018;[START_REF] Hoareau | Reconciling two computational models of working memory in aging[END_REF][START_REF] Jarjat | Aging Influences the Efficiency of Attentional Maintenance in Verbal Working Memory[END_REF][START_REF] Johnson | Second thoughts versus second looks: An age-related deficit in reflectively refreshing just-activated information[END_REF][START_REF] Plancher | Under which conditions can older participants maintain information in working memory?[END_REF], we hypothesized an enhancement of attentional refreshing in the presence of an isochronous rhythm during the retention interval and investigated whether the cognitive capacities of older adults can affect the potential benefit of temporal regularities on maintenance in short-term memory. To address these questions, we contrasted the presence of an isochronous rhythm during the retention period to a silent retention interval. Serial recall performance of letters was measured to assess memory performance.

The isochronous rhythm during the retention interval did not benefit memory performance at the group level. The absence of benefit of temporal regularities on maintenance in older adults as a group contrasted with the previously reported benefit of temporal regularities on maintenance in younger adults [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF]. The benefit of temporal regularities on maintenance in younger adults might be due to some fine-tuned matching between refreshing rate and subdivisions of the isochronous rhythm [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF]. As attentional refreshing is slowed down in aging [START_REF] Hoareau | Reconciling two computational models of working memory in aging[END_REF][START_REF] Plancher | Under which conditions can older participants maintain information in working memory?[END_REF], the refreshing rate of older adults might not be as well tuned to the subdivision of the isochronous rhythm as it is the case for the young adults, thus decreasing the potential beneficial effect of temporal regularities on maintenance.

Our further investigations of the impact of an isochronous rhythm on memory performance by including the evaluation of cognitive functions and rhythm perception revealed an influence of participants' inhibitory capacities. More specifically, inhibitory capacities for weakly-interfering material predicted the difference in memory performance between the two conditions. Notably, memory performance of the participants with high inhibitory capacities for weakly-interfering material (as assessed by the Stroop Victoria subtest) seemed to benefit from the isochronous rhythm, while memory performance of the participants with lower inhibition capacities seemed impaired in the presence of the temporal regularities. No other measure of cognitive functions or rhythm perception was linked to a potential effect of rhythm on memory performance.

In line with previous findings in young adults [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF], the present study highlights that maintenance in short-term memory in older adults can be enhanced in the presence of temporal regularities, but this benefit depends on the inhibition profiles of the elderly participants.

Based on the Irrelevant Sound Effect [START_REF] Page | The irrelevant sound effect: What needs modelling, and a tentative model[END_REF], the auditory rhythm presented during the retention interval can be considered as an interfering stimulation, even though only with a low-level interference because the six tones were all identical and were presented in a predictable way. Older adults with good inhibition capacities might be more efficient in inhibiting the influence of sound occurrence per se, and thus be able to take advantage of the regular structure that guides attention over time and benefits to refreshing information. In contrast for older adults with lower inhibition capacities, the presence of tones might have thus constituted an irrelevant stimulation difficult to deal with and preventing them to benefit from temporal regularities.

In line with previous studies suggesting that short-term memory is not always altered in normal aging (e.g., [START_REF] Bopp | Aging and verbal memory span: A meta-analysis[END_REF][START_REF] Connor | Memory in Old Age: Patterns of Decline and Preservation[END_REF][START_REF] Peters | A multicomponent exploration of verbal short-term storage deficits in normal aging and Alzheimer's disease[END_REF][START_REF] Sekuler | Short-term visual recognition and temporal order memory are both well-preserved in aging[END_REF], memory performance of older adults was similar to the one of younger adults. Yet, temporal regularities benefited to older adults in a lesser extent than to young adults. As inhibition processes are proposed to be impaired in aging [START_REF] Borella | Working memory and inhibition across the adult life-span[END_REF][START_REF] Hasher | Working memory, comprehension, and aging: A review and a new view[END_REF], inhibition capacities might have contributed to the age difference in the benefit from temporal regularities on maintenance. Future studies should empirically investigate how the reduced benefit of temporal regularities in older adults as compared to younger adults is related to an age-related deficit of inhibition capacities, and in particular to weakly interfering material.

It is worth pointing out that inhibition capacities assessment consisted in measuring the time ratio between the response time of naming of color ink with and without interference. A higher ratio thus indicates that more time is necessary to inhibit irrelevant information. Older adults with lower inhibition capacities for irrelevant information thus needed more time to inhibit irrelevant information (i.e., tones). Because time sharing of attentional resources is at the core of working memory functioning [START_REF] Barrouillet | Time Constraints and Resource Sharing in Adults' Working Memory Spans[END_REF][START_REF] Barrouillet | Time and cognitive load in working memory[END_REF][START_REF] Barrouillet | On the law relating processing to storage in working memory[END_REF], the findings suggest that if more time is used for the inhibition of irrelevant stimuli like the tones' occurrence, then less time is available for attentional maintenance. One could thus argue that older adults who needed more time to inhibit the tones have less time for maintenance, and also not enough available time to benefit from the temporal regularities. This would also be consistent with the smaller benefit of temporal regularities for older adults in comparison to the benefit observed for young adults [START_REF] Plancher | Boosting maintenance in working memory with temporal regularities[END_REF]. Fewer attentional resources seem to be available to older adults than young adults [START_REF] Naveh-Benjamin | The Associative Memory Deficit of Older Adults: Further Support Using Face-Name Associations[END_REF][START_REF] Rabinowitz | A processing resource account of age differences in recall[END_REF]. If less attentional resources are available -either because they are used to process something else or because of an age-related reduction of the amount of attentional resources -, then synchronizing them to an externally regular structure might be more difficult, explaining why older adults benefit less from temporal regularities than do young adults and why older adults for whom inhibition takes more time do not benefit at all.

The DAT proposes that the presence of temporal regularities can facilitate and speed up cognitive processes, in particular for events occurring at the expected time points. As a temporally regular structure allows the perceiver to develop temporal expectations about the occurrence of future events, the allocation of increased attentional resources at expected points in time leads to faster processing of the event [START_REF] Jones | Temporal aspects of stimulusdriven attending in dynamic arrays[END_REF][START_REF] Sanabria | Rhythms that speed you up[END_REF]. In light of the slowing down proposal to explain age-related deficit in working memory [START_REF] Salthouse | Influence of processing speed on adult age differences in working memory[END_REF], the presence of a temporally regular structure may improve maintenance of older adults by speeding up the cognitive processes occurring at this moment. If refreshing one specific item requires less time, then more time is available for the refreshing of other items, resulting in improved memory performance.

The attentional refreshing mechanism can be separated into two distinct processes: the initiation of refreshing and the refreshing per se [START_REF] Johnson | MEM: Mechanisms of recollection[END_REF][START_REF] Johnson | Electrophysiological Correlates of Refreshing: Event-related Potentials Associated with Directing Reflective Attention to Face, Scene, or Word Representations[END_REF]. While refreshing per se relies on perceptual cortical areas (e.g., fusiform area for faces, parahippocampal area for scenes, [START_REF] Johnson | A brief thought can modulate activity in extrastriate visual areas: Top-down effects of refreshing just-seen visual stimuli[END_REF], the initiation of refreshing relies on frontal lobes that are known to be involved in executive functions [START_REF] Miyake | The unity and diversity of executive functions and their contributions to complex "frontal lobe" tasks: A latent variable analysis[END_REF] and more generally in attentional processes [START_REF] Foster | The cognitive neuropsychology of attention: A frontal lobe perspective[END_REF]. Numerous studies have provided evidences for a deficit of attentional refreshing in aging [START_REF] Hoareau | Reconciling two computational models of working memory in aging[END_REF][START_REF] Jarjat | Aging Influences the Efficiency of Attentional Maintenance in Verbal Working Memory[END_REF][START_REF] Johnson | Second thoughts versus second looks: An age-related deficit in reflectively refreshing just-activated information[END_REF][START_REF] Plancher | Under which conditions can older participants maintain information in working memory?[END_REF], and specifically hypothesized a deficit in the initiation of refreshing (Fanuel et al., 2018). It has been shown that external information in the memory environment can contribute to compensate impaired self-initiated processes [START_REF] Craik | On the transfer of information from temporary to permanent memory[END_REF][START_REF] Craik | Auditory temporal preparation induced by rhythmic cues during concurrent auditory working memory tasks[END_REF][START_REF] Luo | Aging and memory: A cognitive approach[END_REF]. In our present study, the auditory rhythm could have provided the environmental support for the initiation of attentional refreshing and thus benefit to maintenance.

Aging has also been related to changes in the use of cognitive strategies. Young and older adults do not use the same strategies (e.g., [START_REF] Dunlosky | Measuring strategy production during associative learning: The relative utility of concurrent versus retrospective reports[END_REF][START_REF] Duverne | Age-related differences in arithmetic problem-verification strategies[END_REF].

Older adults also make poorer choices amongst available strategies and are less efficient in executing the selected strategy [START_REF] Lemaire | Cognitive strategy variations during aging[END_REF]. In our study, the presence of temporal regularities might have benefited to short-term memory by helping older adults in the use of (maintenance) strategies. Using a retro-cue paradigm, [START_REF] Souza | No age deficits in the ability to use attention to improve visual working memory[END_REF] showed preserved attentional refreshing in aging when participants were explicitly instructed to use the retro-cue as a refreshing indication. With explicit instruction, older adults would use the same maintenance strategy as younger (i.e., refreshing) because they have an environmental support. In our study, no explicit instructions were given, neither about potential maintenance mechanism to use nor how to "use" the tones. Nevertheless, the auditory rhythm seems to have provided some form of environmental support for maintenance processes, which might have remained on an implicit level.

The hypotheses of an enhanced initiation of refreshing and a speeding up of refreshing thanks to temporal regularities are not mutually exclusive. Studies investigating the time needed for refreshing in aging [START_REF] Hoareau | Reconciling two computational models of working memory in aging[END_REF][START_REF] Johnson | Second thoughts versus second looks: An age-related deficit in reflectively refreshing just-activated information[END_REF][START_REF] Plancher | Under which conditions can older participants maintain information in working memory?[END_REF] did not distinguish the time necessary to initiate refreshing and the time required for refreshing per se. Providing external guidance for the allocation of attentional resources with temporal regularities can facilitate and fasten the initiation of attentional refreshing, which would result in more time available for refreshing per se and thus in improved memory performance. To test this hypothesis, further studies providing a time measurement of refreshing, distinguishing the initiation of refreshing and the refreshing per se, are necessary. This would allow us to distinguish whether the presence of a temporally regular structure prompts the initiation of refreshing or speeds up the refreshing per se in the elderly.

Overall, the present study revealed that the maintenance in short-term memory of older adults can benefit from the presence of temporal regularities under some conditions. The findings suggest an improvement of attentional refreshing in the presence of a temporally regular structure, notably with attentional refreshing benefitting from guidance of attention over time. It might be argued that the presence of temporal regularities benefited verbal rehearsal as the to-be-memorized material was verbal and the phonological loop was available for maintenance. However, support for the influence of the temporally regular structure on attentional refreshing has been previously provided, notably the benefit of the rhythm persisted under concurrent articulation for young adults (Plancher et al., 2018, Exp. 2).

Working memory is at the core of the cognitive system and its impairment with aging is assumed to mediate the effect of aging on cognition [START_REF] Salthouse | Influence of processing speed on adult age differences in working memory[END_REF]. Enhancing working memory of older adults might thus contribute to reduce the decremental effect of aging on general cognition. The potential beneficial effects of music and-music-like material on rehabilitation and cognitive stimulation has been previously shown in other cognitive domains [START_REF] Bigand | The Neurosciences and Music-V. Cognitive Stimulation and Rehabilitation[END_REF]. Future studies should provide a better understanding of the cognitive processes involved in the improvement of maintenance in working memory thanks to temporal regularities. Beyond the here observed influence of inhibition capacities, the tempo embedded in the temporal regularities (i.e., here implemented with the sound onset asynchrony in the sequence) and the individual differences in general temporal processing capacities (e.g., rhythm and beat perception and production) as well as their potential changes in aging might impact the benefit of temporal regularities on maintenance in memory. Future studies should extend the present findings to concrete applications aiming to improve working memory of older adults using musical and rhythmic training activities. Indeed, previous research has provided evidence for the link between musical training and memory performance (see [START_REF] Talamini | Musicians have better memory than nonmusicians: A meta-analysis[END_REF] for a review), even in the elderly [START_REF] Hanna-Pladdy | The Relation Between Instrumental Musical Activity and Cognitive Aging[END_REF]. Because working memory deficits have also been reported for various pathologies, such as dementia [START_REF] Kirova | Working memory and executive function decline across normal aging, mild cognitive impairment, and Alzheimer's disease[END_REF], strokes [START_REF] Martin | Measurements of auditory-verbal STM span in aphasia: Effects of item, task, and lexical impairment[END_REF] or schizophrenia [START_REF] Starc | Schizophrenia is associated with a pattern of spatial working memory deficits consistent with cortical disinhibition[END_REF], these applications could also be broadened to the clinical domain aiming at improving cognitive functions as well as the well-being of these populations.

Table 1. Overview of neuropsychological and perceptual evaluation and their correlation with the difference of memory performance between Rhythm and Silence condition. Descriptive statistics for the group of participants are reported for each score obtained by the participants in the neuropsychological and perceptual tests are reported (N = the number of participants whom completed each tests, M = Mean of the group, SD = standard deviation of the group, Min. = the minimum score, Max. = maximum score, Cut-off = cut-off used to decide whether a score is pathological or not). Pearson's correlations between difference of memory performance between Rhythm and Silence condition and neuropsychological and perceptual evaluations are also reported (df = degree of freedom, r = Pearson's r, p = p-values, BF = Bayesian Factor)

  57.5% of the initial sample) aged between 64 and 83 years-old (M = 71.31, SD = 4.68) with an educational level ranging between 12 and 17 years of study (M = 14.56, SD = 1.92) and (2) 20 younger adults aged between 20 and 29 years-old (M = 24.55, SD = 2.50) with an educational level ranging between 13 and 19 years of study (M = 15.8, SD = 1.44).

Figure 1 .

 1 Figure 1. Schematic representation of the experimental design. Each trial started with a fixation

Figure 1 .

 1 Figure 1. Memory performance difference between the two experimental conditions (ΔRhythm-

Figure 3 .

 3 Figure 3. Recall performance (with a maximum of six letters) presented as a function of the

*

and perceptual tests Descriptive statistics Correlation with Rhythm -Silence difference in memory performance

  . Significant correlations are flagged. **p<.01. NA stands for Not Applicable.

	Neuropsychological N	M	SD	Min.	Max. Cut-off df	r	p	BF
	General cognition
	MMSE	40	28.25	1.10	27	30	27	38	-0.167	.303	0.33
	Anxiety and Depression
	HADS -Anxiety	40	3.30	2.13	0	8	8	NA	NA	NA	NA
	HADS -Depression	40	3.38	1.18	0	8	8	NA	NA	NA	NA
	GDS	40	2.65	2.35	0	9	10	NA	NA	NA	NA
	Memory
	Forward span	40	5.73	1.18	4	9	NA	38	0.184	.255	0.37
	Backward span	40	4.58	1.15	2	8	NA	38	0.149	.360	0.30
	Executive functions
	TMT A	40	43.03	26.96	17	163	NA	38	0.191	.238	0.39
	TMT B-A	38	55.87	38	8	225	NA	36	-0.153	.359	0.30
	Stroop -highly interfering
		40	2.24	0.63	1.17	4.58	NA	38	-0.147	.366	0.29
	response inhibition
	Stroop -weakly interfering	40	1.38	0.33	0.93	2.3	NA	38 -0.443** .004	10.02
	information inhibition
	Rhythm perception
	Beat Alignment Test -d'	25	1.81	1.33	-0.25	4.37	NA	23	-0.074	.726	0.30
	Anisochrony Detection
		21	78	27	40.8	135	NA	19	0.047	.838	0.63
	with Tones -Threshold

This work was supported by a grant from Region Rhône-Alpes. It was conducted within the framework of the LabEx CeLyA ("Centre Lyonnais d'Acoustique," ANR-10-LABX-0060) and the LabEx Cortex ("Construction, Function and Cognitive Function and Rehabilitation of the Cortex," ANR-11-LABX-0042) of Université de Lyon, within the program "Investissements d'avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). All authors participated in drafting the manuscript and revising its intellectual content. Conception and design were managed by Gaën Plancher, Barbara Tillmann and Lison Fanuel, and data were analyzed by Lison Fanuel. The authors thank