Mathilde Orselly

Julien Devemy

Agathe Bouvet-Marchand

Alain Dequidt

Cédric Loubat

Patrice Malfreyt

Molecular Simulations of Thermomechanical Properties of Epoxy-Amine Resins

All-atom molecular dynamics (MD) simulations were performed with the CHARMM force field to characterize various epoxy resins, such as aliphatic and bisphenol-based resins. A multistep cross-linking algorithm was established, and key properties such as density, glass temperature, and elastic modulus were calculated. A quantitative comparison was made and was proven to be in good agreement with experimental data, with average absolute deviations between experiments and molecular simulation comprised between 2% and 12%. Additional findings on structure-property relationships were highlighted such as the effect of the cross-linking rate and oligomerization of the resin.

INTRODUCTION

Epoxies are some of the most prominent thermosetting polymers valued nowadays due to their wide range of applications. This class of polymers is of interest for instance for structural components in aerospace applications, as well as electronics packaging or various types of coatings. This is made possible by their interesting versatility. The final material can be easily modulated by the chemical structure of the epoxy or the nature of the hardener, responsible for the striking thermal and mechanical properties of the resulting material. 1 Therefore, it is of great importance to be able to characterize them and comprehend the influence of the structural network on their properties. Aside from the usual experimental testing, computational chemistry has proven to be a great asset in this task. Indeed, predictive simulations are playing an increasing role in understanding the atomistic origin of the properties of polymers as well as in speeding up the process of selecting materials, thus complementing experiments in the search for tailored materials. However, one of the greatest challenges is to be able to reproduce reliably the physical, mechanical, and thermodynamic properties of such materials from atomistic models. Molecular dynamics (MD) has proven to be a powerful method to generate equilibrated atomistic configurations on which macroscopic properties are averaged. [START_REF] Li | Molecular Scale Simulations on Thermoset Polymers: A Review[END_REF] One of the first steps to reproduce thermosetting polymers in molecular simulations is to be able to cross-link the monomers, making it possible to characterize the polymeric material. Two approaches are typically used for the crosslinking of the monomers: a "back-mapping" procedure [START_REF] Komarov | Highly Cross-Linked Epoxy Resins: An Atomistic Molecular Dynamics Simulation Combined with a Mapping/Reverse Mapping Procedure[END_REF][START_REF] Gavrilov | Thermal Properties and Topology of Epoxy Networks: A Multiscale Simulation Methodology[END_REF][START_REF] Guseva | Crosslinking Mechanisms, Structure and Glass Transition in Phthalonitrile Resins: Insight from Computer Multiscale Simulations and Experiments[END_REF][START_REF] Prasad | Coarse -Grained Molecular Dynamics Simulation of Crosslinking of DGEBA Epoxy Resin and Estimation of the Adhesive Strength[END_REF] and a "reactive" one. [START_REF] Gavrielides | Model of the DGEBA-EDA Epoxy Polymer: Experiments and Simulation Using Classical Molecular Dynamics[END_REF][START_REF] Radue | Molecular Modeling of Cross-Linked Polymers with Complex Cure Pathways: A Case Study of Bismaleimide Resins[END_REF][START_REF] Bandyopadhyay | Molecular Modeling of Crosslinked Epoxy Polymers: The Effect of Crosslink Density on Thermomechanical Properties[END_REF][START_REF] Fan | Material Properties of the Cross-linked Epoxy Resin Compound Predicted by Molecular Dynamics Simulation[END_REF][START_REF] Nouri | A Molecular Dynamics Investigation on Mechanical Properties of Cross-Linked Polymer[END_REF][START_REF] Li | Molecular simulations of crosslinking process of thermosetting polymers[END_REF][START_REF] Shokuhfar | The Effect of Cross-linking Density on the Mechanical Properties and Structure of the Epoxy Polymers: Molecular Dynamics Simulation[END_REF][START_REF] Gissinger | Modeling chemical reactions in classical molecular dynamics simulations[END_REF][START_REF] Gissinger | AHeuristic Method for Reactive Molecular Dynamics[END_REF] The former is based on the cross-linking of coarse-grained monomers and then the all-atom model is later back-mapped in lieu of the coarse grains, while the latter already considers an all-atom model and the cross-linking is done between the experimental reactive pairs. These crosslinking methods can also be single or multiple steps but exhibit the same topology overall. [START_REF] Jang | Comparison of Crosslinking Algorithms in Molecular Dynamics Simulation of Thermosetting Polymers[END_REF] Regarding the epoxy systems investigated by molecular simulations, the most extensive research effort was found in resins resulting from the cross-linking between the diglycidyl ether of bisphenol F (DGEBF) and diethyl toluenediamine (DETDA), [START_REF] Bandyopadhyay | Molecular Modeling of Crosslinked Epoxy Polymers: The Effect of Crosslink Density on Thermomechanical Properties[END_REF][START_REF] Nouri | A Molecular Dynamics Investigation on Mechanical Properties of Cross-Linked Polymer[END_REF][START_REF] Li | Molecular simulations of crosslinking process of thermosetting polymers[END_REF][START_REF] Tack | Thermodynamic and Mechanical Properties of Epoxy Resin DGEBF Crosslinked with DETDA by Molecular Dynamics[END_REF][START_REF] Varshney | A Molecular Dynamics of Epoxy-Based Networks: Cross-Linking Procedure and Prediction of Molecular and Material Properties[END_REF] triethylenetetramine (TETA) [START_REF] Fan | Material Properties of the Cross-linked Epoxy Resin Compound Predicted by Molecular Dynamics Simulation[END_REF][START_REF] Yu | Multiscale Modeling of Cross-linked Epoxy Nanocomposites to Characterize the Effect of Particle Size on Thermal Conductivity[END_REF][START_REF] Choi | The Glass Transition and Thermoelastic Behavior of Epoxy-based ?anocomposites: A Molecular Dynamics Study[END_REF][START_REF] Yu | Multi-scale Modeling of Cross-linked Epoxy Nanocomposites[END_REF] or diethylenetriamine (DETA), [START_REF] Schichtel | Modeling Thermoset Polymers Using an Improved Molecular Dynamics Crosslinking Methodology[END_REF] especially in the fields of modern aeronautics. The cross-linking of the diglycidyl ether of bisphenol A (DGEBA) resin was also widely studied with different hardeners, such as isophorone diamine (IPDA), [START_REF] Wu | Atomistic Molecular Modelling of Crosslinked Epoxy Resin[END_REF][START_REF] Wu | Atomistic Molecular Simulations of Structure and Dynamics of Crosslinked Epoxy Resin[END_REF][START_REF] Wang | Glass Transition Investigations on Highly Crosslinked Epoxy Resins by Molecular Dynamics Simulations[END_REF] trimethylene glycol di-p-aminobenzoate (TMAB), [START_REF] Lin | Molecular Simulation of Cross-Linked Epoxy and Epoxy-POSS Nanocomposite[END_REF] diethyltoluenediamine (DETDA), [START_REF] Gavrilov | Thermal Properties and Topology of Epoxy Networks: A Multiscale Simulation Methodology[END_REF][START_REF] Jeyranpour | Comparative Investigation of Thermal and Mechanical Properties of Cross-linked Epoxy Polymers with Different Curing Agents by Molecular Dynamics Simulation[END_REF][START_REF] Clancy | Molecular Modeling for Calculation of Mechanical Properties of Epoxies with Moisture Ingress[END_REF][START_REF] Demir | A Robust and Reproducible Procedure for Cross-linking Thermoset Polymers using Molecular Simulation[END_REF] triethylenetetramine (TETA), [START_REF] Jeyranpour | Comparative Investigation of Thermal and Mechanical Properties of Cross-linked Epoxy Polymers with Different Curing Agents by Molecular Dynamics Simulation[END_REF] ethylenediamine (EDA), [START_REF] Gavrielides | Model of the DGEBA-EDA Epoxy Polymer: Experiments and Simulation Using Classical Molecular Dynamics[END_REF] diaminodiphenyl sulfone (DDS), [START_REF] Liu | Multiscale Simulation Study on the Curing Reaction and the Network Structure in a Typical Epoxy System[END_REF] methylenedianiline (MDA), [START_REF] Chang | Investigation of Hygroscopic Properties in Electronic Packages Using Molecular Dynamics Simulation[END_REF] poly(oxopropylene) diamines (POP), [START_REF] Jang | Comparison of Crosslinking Algorithms in Molecular Dynamics Simulation of Thermosetting Polymers[END_REF][START_REF] Soni | Effect of Cross-linker Length on the Thermal and Volumetric Properties of Cross-linked Epoxy Networks: A Molecular Simulation Study[END_REF][START_REF] Sirk | Bi-modal Polymer Networks: Composition-Dependent Trends in Thermal, Volumetric and Structural Properties from Molecular Dynamics Simulation[END_REF] 4,4′-methylenebis(cyclohexylamine) (MCA), 33 diethylenetriamine (DETA), [START_REF] Shokuhfar | The Effect of Cross-linking Density on the Mechanical Properties and Structure of the Epoxy Polymers: Molecular Dynamics Simulation[END_REF][START_REF] Arab | Glass Transition Temperature of Cross-linked Epoxy Polymers: a Molecular Dynamics Study[END_REF][START_REF] Arab | Molecular Dynamics Simulation of Cross-Linked Epoxy Polymers: the Effect of Force Field on the Estimation of Properties[END_REF][START_REF] Langeloth | The Glass Transition in Cured Epoxy Thermosets: A Comparative Molecular Dynamics Study in Coarse-Grained and Atomistic Resolution[END_REF] and polyetheramine JEFFAMINE D-230. [START_REF] Masoumi | A study of Thermomechanical Properties of the Cross-linked Epoxy: An Atomistic Simulation[END_REF][START_REF] Fan | Molecular Dynamics Predictions of Thermomechanical Properties of an Epoxy Thermosetting Polymer[END_REF][START_REF] Chowdhury | Epoxy Resin Thermo-mechanics and Failure Modes: Effects of Cure and Cross-linker Length[END_REF][START_REF] Patil | Free Volumes and Structural Relaxations in Diglycidyl Ether of Bisphenol-A Based Epoxy-Polyether Amine Networks[END_REF] To the best of our knowledge, novel epoxy resins based on the diglycidyl ether of vanillyl alcohol (DGEVA), diglycidyl ether of 1,4-butanediol (DGEBU), triglycidyl ether of phloroglucinol (PHTE), 4,4′-methylenebis(2,6-diethylaniline) (MDEA), m-xylylenediamine (MXDA), 4,4′-methylenebis(2isopropyl-6-methylaniline) (MMIPA), tetraethylenepentamine (TEPA), and 4,7,10-Trioxa-1,13-tridecane diamine (TTDA)

have not yet been studied by molecular simulations. Due to the broad variety of chemical structures, a comparison between experimental and simulation results on several key properties such as density, glass transition temperature, and elastic moduli is made possible.

Through this, an evaluation of the performance and the reliability of general atomistic force fields and the capacity of simulation methods to reproduce the thermomechanical properties of these resins is carried out. Indeed, predicting the physical, mechanical, and thermodynamic properties of resins by using full atomistic models remains challenging because of the complexity of the interactions involved and the algorithm needed to post-treat the data. Such molecular simulations can open the way to interpreting the thermomechanical properties of resins on the basis of their structure and the molecular interactions involved.

In order to establish this comparison, a cross-linking algorithm was first made based on previous studies using the reactive method. [START_REF] Gavrielides | Model of the DGEBA-EDA Epoxy Polymer: Experiments and Simulation Using Classical Molecular Dynamics[END_REF][START_REF] Radue | Molecular Modeling of Cross-Linked Polymers with Complex Cure Pathways: A Case Study of Bismaleimide Resins[END_REF][START_REF] Bandyopadhyay | Molecular Modeling of Crosslinked Epoxy Polymers: The Effect of Crosslink Density on Thermomechanical Properties[END_REF][START_REF] Fan | Material Properties of the Cross-linked Epoxy Resin Compound Predicted by Molecular Dynamics Simulation[END_REF][START_REF] Nouri | A Molecular Dynamics Investigation on Mechanical Properties of Cross-Linked Polymer[END_REF][START_REF] Li | Molecular simulations of crosslinking process of thermosetting polymers[END_REF][START_REF] Shokuhfar | The Effect of Cross-linking Density on the Mechanical Properties and Structure of the Epoxy Polymers: Molecular Dynamics Simulation[END_REF][START_REF] Gissinger | Modeling chemical reactions in classical molecular dynamics simulations[END_REF][START_REF] Gissinger | AHeuristic Method for Reactive Molecular Dynamics[END_REF] This was followed by several procedures to ensure the reliability of the properties obtained, thus making it possible to enlighten key properties of materials and their relationship to their structure. To some extent, this study also aims at evaluating the transferability of the molecular models on resins not yet investigated by molecular simulations.

The paper is organized as follows. Section 2 describes the experimental and computational procedures. Section 3 presents the main results of this work in terms of density, glass transition temperature, and Young's modulus of various epoxy-amine resins. We conclude in Section 4.

EXPERIMENTAL AND SIMULATION METHODS

Experimental Details. 2.1.1. Hardeners and Resins

Studied. Various epoxy resins are studied, exhibiting a large panel of thermomechanical properties. These resins are widely used in industry. The formulations presented in this study include the compounds DGEBA, DGEBF, DGEBU, PHTE, and DGEVA as well as the hardeners IPDA, DETA, EDA, TEPA, TTDA, MDEA, MMIPA, and MXDA. DGEVA and PHTE can be derived from bio-based raw materials and were synthesized by Specific Polymers. These components are presented in Figure 1. The average number of repeating units (n) of DGEBA (Sika, Biresin CR170) was determined by 1 H NMR (Figure 2). Table 1 gives for the epoxies studied the degree (n) of oligomerization of the resin, the resin:hardener ratio, the molecular weight of the constitutive repeat unit, and the empirical density (detailed in the following subsection) as well as the number of atoms present and the size of the box for the simulations.

2.1.2. Determination of the Experimental Density and Glass Transition Temperature. The measurement of density has been performed on materials fully cured using a Ohaus density determination kit for a scale. Density determination is performed by Archimedes' principle. The density of the material is determined with the aid of a liquid whose density ρ 0 is known (water was used as an auxiliary liquid here). The solid is weighed in air (A) and then in the auxiliary liquid (B). The density ρ can be calculated from the two weights as follows ρ = [A/(A -B)](ρ 0ρ L ) + ρ L with ρ 0 being the density of the auxiliary liquid and ρ L the air density (0.0012 g/cm [START_REF] Komarov | Highly Cross-Linked Epoxy Resins: An Atomistic Molecular Dynamics Simulation Combined with a Mapping/Reverse Mapping Procedure[END_REF] ). The temperature of the auxiliary liquid was measured and taken into account in all density determinations. DSC analyses were performed by using a Mettler Toledo DSC instrument. Samples having masses of approximately 10 mg were placed in 100 μL aluminum pans with pierced lids under a nitrogen atmosphere. The applied heating rate was 10 °C min -1 under a nitrogen atmosphere. The thermal behavior of the samples was investigated using two repeated heatingcooling cycles. The following thermal procedure was used: first ramp from -60 to 250 °C and then from 250 to 25 °C. The glass transition temperature (T g ) was determined from the second heating curve.

2.2. Computational Details. The CHARMM general force field (CgenFF) [START_REF] Vanommeslaeghe | CHARMM General Force Field: A Force Field for Drug-Like Molecules Compatible with the CHARMM All-Atom Additive Biological Force Fields[END_REF][START_REF] Vanommeslaeghe | Automation of the CHARMM General Force Field (CGenFF) I: Bond Perception and Atom Typing[END_REF][START_REF] Vanommeslaeghe | Automation of the CHARMM General Force Field (CGenFF) II: Assignment of Bonded Parameters and Partial Atomic Charges[END_REF] is used to describe the intra-and intermolecular interactions of the thermosetting polymers. This class I force field has the following functional form:

U k r r k k n k k r r q q r R r R r ( ) ( ) cos( ) 1 ( ) ( ) 4 2 r ij ijk n n ijkl n i j ij ij ij ij
6 ij ij 0 Ä Ç Å Å Å Å Å Å Å Å Å Å Å Å Å i k j j j j j j y { z z z z z z i k j j j j j j y { z z z z z z É Ö Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ = + + [ + + ] + + + + (1)
For completeness, it is worth noting that force field parameters are usually denoted using σ rather than R min , the relationship between the two being

R 2 min 1/6 = .
Additionally, the CHARMM force field presents an additional component in the form of the Urey-Bradley term, which consists of a harmonic potential as a function of the distance between the nonbonded atoms 1 and 3 of a 1-2-3 angle.

The Lennard-Jones parameters between pairs of different atoms are obtained from the Lorentz-Berthelot combination rules, in which ϵ ij values are calculated by using the geometric mean and R min values by using the arithmetic mean. The cutoff distance for the van der Waals interactions is set to 8.0 Å, while the particle-particle particle mesh (PPPM) method with an accuracy of 1.0 × 10 -4 and a cutoff of 8 Å is considered for the long-range electrostatic interactions. For both the Lennard-Jones and Coulombic interactions, a force-switching function was applied between 8 and 10 Å.

Establishing the Cross-Linking Algorithm.

In the scope of this work, a multistep reactive cross-linking algorithm was used and is described in Figure 3, where the statistical NVT and NPT ensembles refer to the canonical and isothermal-isobaric ensembles, respectively. It includes the following steps, where the sequence of 3 + 4 + 5 steps was repeated until a predefined conversion rate was acquired (here 95% in accordance with the experimental conversion obtained after curing).

1. Stoichiometric packing of the unreacted monomers into a box of predefined density using Packmol. [START_REF] Martínez | A Package for Building Initial Configurations for Molecular Dynamics Simulations[END_REF] The parameters (type, bond, angle, dihedral, charges) are those of the reacted mixture. 2. Relaxation of the initial mixture with an NPT ensemble during 500 ps at 300 K. 3. NPT simulation at 300 K to relax the system. 4. NVT simulation at 900 K to allow the quick movement of the atoms while searching for unreacted pairs within a defined cutoff distance. At each time step, the interatomic distances between unreacted pairs are calculated. The simulation was stopped once a pair was found within 2 Å. 5. Creation of the bonds for two pairs that are in agreement with the distance conditions. Additionally, a second cutoff of 3 Å was applied to allow the formation of multiple bonds per loop and to quicken the process. 6. Updating of the parameters for the pairs that did not react. 7. Quick NPT relaxation at 300 K on the fully cross-linked system during 1 ns. 8. NPT simulation during 2 ns at 600 K to further relax the system, following a ramp from 300 to 600 K for 1 ns. 9. Last NPT simulation during 2 ns at 300 K to obtain a fully relaxed system, following a ramp from 600 to 300 K for 1 ns.

This cross-linking algorithm was designed without regard to the actual polymerization reaction kinetics. Experimentally, the curing temperature of such systems is below 200 °C. However, here the cross-linking was done partially at 627 °C (above the thermal decomposition temperature). The need for a higher temperature was driven by the appeal of a quick rearrangement of the atoms within the span of the MD simulations. Additionally, a buck pair_style was used for the unreacted pairs. Only the attractive term of the Lennard-Jones potential (1/r 6 ) was used. Reactive pairs are thus attracted to one another in order to facilitate bond creations. Without this potential between reactive pairs, the acquisition of a highly cross-linked resin as depicted in this work would be very timeconsuming. Additionally, the cutoff range was chosen in agreement with Figure 4. Radial distribution functions, shown in Figure 4, were calculated on an uncured mixture of DGEBA +IPDA and DGEVA+MXDA between the reactive carbon of the epoxy resin and the reactive nitrogen of the amine hardener. The first maxima are close to 3.7 and 4.1 Å, respectively. This is why a cutoff of 2-3 Å is deemed relevant when it comes to the compromise between computational efficiency and the resulting cross-linked resins. Too high of a cutoff guarantees faster cross-linking but can also lead to the formation of metastable resins where bonds cannot come back to their equilibrium value (∼1.45 Å). Experimentally, primary amines go through an addition reaction with the epoxide groups to form by ring-opening a hydroxyl group and a secondary amine. The secondary amine can further react with an epoxide to form a tertiary amine and an additional hydroxyl group. A hydroxyl-epoxy addition can also occur but less frequently. This last step was ignored during the simulated cross-linking, as well as the difference in reactivity of the primary and secondary amines.

All potential reactive sites were activated equally by removing the hydrogen atoms from the amine of the curing agent and hydrating the oxygen atoms from the epoxide and thus opening up the oxirane. The force field parameters (bonds, angles, dihedrals, impropers, partial charges) were thus adjusted to take into account this reacted structure. This change was revoked for the molecules that did not react at the end of the cross-linking procedure (see step 6 in the list).

The sequence 7 + 8 + 9 in the list was the postcure annealing process performed to fully relax the system. Using a high-temperature annealing period after cross-linking increases the density due to the fact that this addition of thermal energy can disrupt metastable configurations and allow finding lower energy configurations closer to global minima. It was successfully demonstrated that the thermal agitation produced higher density configurations, even though the original densities had already plateaued with the first NPT equilibration. [START_REF] Schichtel | Modeling Thermoset Polymers Using an Improved Molecular Dynamics Crosslinking Methodology[END_REF] Eight simulation boxes were hence created for each system containing the reacted form of the liquid mixture. They differ in their structure and the initial positioning of the molecules as to produce a statistical sample. The multistep cross-linking procedure depicted in Figure 3 was used to polymerize the resins at a conversion rate of 95% of the reactive end groups. The use of a high temperature of 900 K and a cutoff value of 2-3 Å grants a high rate of conversion while staying true to the interatomic distances. The full procedure can last between 6 and 20 ns.

To conclude on this methodological aspect, this method was employed to achieve the same degree of conversion as found experimentally within the time-limit constraints of the MD simulations. The accuracy of the structural, volumetric, and thermal properties of the resulting cross-linked polymer will be evaluated in the course of this paper.

Description of the MD Simulations.

The velocity-Verlet integrator was used to integrate the equations of motion using a time step of 1 fs. The SHAKE algorithm was applied to constrain the length of covalent bonds to hydrogen atoms to their equilibrium values. In order to control the temperature and pressure for NVT and NPT simulations, a Nose-Hoover thermostat and barostat were applied. [START_REF] Nosé | A Molecular Dynamics Method for Simulations in the Canonical Ensemble[END_REF] Unless stated otherwise, the MD simulations were performed at 300 K and 1 atm. The system was equilibrated during the first nanosecond, and data were acquired during the following nanosecond. Eight simulation boxes were used for each system. The molecular dynamics calculations were performed using the LAMMPS package. [START_REF] Plimpton | Fast Parallel Algorithms for Short-range Molecular Dynamics[END_REF]

RESULTS AND DISCUSSION

3.1. Measuring the Density. Before examining the density of cured resins, the uncured resins and hardeners were examined to appreciate the relevance of the CHARMM force field. Figure 5 shows that the majority of the monomers are included in the 5% domain, with a warning concerning the hardener EDA.

where k ≈ 320, ρ in kg/m 3 , and M a is in g/mol. M a is the average atomic mass of the polymer. This empirical relationship remains valid for most organic polymers (1.1 < ρ < 1.4 g cm -3 ). Unfortunately, the maximum error of up to 10% endangers a quantitative comparison, thus requiring the knowledge of the experimental density for a more refined comparison.

First, we observe that the agreement between empirical calculations (eq 2) and molecular simulation is good, with an average absolute deviation of 2.2%. The predicted values by molecular simulations also reproduce the variations in densities among the various resins. Other molecular models have also been shown to reproduce accurately the density for DGEBA/ IPDA [START_REF] Wu | Atomistic Molecular Simulations of Structure and Dynamics of Crosslinked Epoxy Resin[END_REF][START_REF] Wang | Glass Transition Investigations on Highly Crosslinked Epoxy Resins by Molecular Dynamics Simulations[END_REF] and DGEBA/DETA. [START_REF] Arab | Glass Transition Temperature of Cross-linked Epoxy Polymers: a Molecular Dynamics Study[END_REF] We can conclude that the CHARMM force field is able to yield simulated densities of epoxy-amine resins that match reasonably with experiments, even if this model is not exclusively designed for polymer and additives, unlike the COMPASS model. The good agreement between the different density values obtained by simulation and empirical calculations enables a validation of the choice of the force field and the methodology used to polymerize the cross-linked epoxy resins. The CHARMM force field can contribute for epoxy resins to the determination of a qualitative study but offers an error rate of up to 5.7% with the few experimental points. The simulated values reproduce well the variations between resins but give an underestimation of the density. On the other hand, the experimental density calculated with the Archimedes method can also present an underestimation of the real density of the polymer. Taking into account this bias, this first comparison of the density shows that the model and the methodology developed for the crosslinked epoxy resins perform well for this thermodynamic property. To go further in the validation of the methodology, we propose to extend the comparison to the glass transition temperature.

Assessing the Glass Transition

Temperature. Modeling of glass transition temperature is based on the dilatometry principle; the density decreases with an increase in the temperature. The glass transition temperature is then characterized by a break in this slope, showing a change in the relaxation speed of the material. It separates the vitreous from the rubbery states. The modeling procedure consists of heating the polymer at T g +200 K for 2 ns and cooling it at a rate of 20 K ns -1 down to T g -200 K. This cooling is done stepwise to retrieve the density of the equilibrated system at each plateau of temperature. The value of the ramp is a good compromise between the rapidity of the simulation and the accuracy of the results. As previously observed by Godey, 54 a transient region persists between the rubbery and vitreous states. This is relevant to the enlargement of the glass transition domain in a confined environment. [START_REF] Vignaud | Densification and Depression in Glass Transition Temperature in Polystyrene Thin Films[END_REF][START_REF] Lan | Methacrylate-Based Polymer Films Useful in Lithographic Applications Exhibit Different Glass Transition Temperature-Confinement Effects at High and Low Molecular Weight[END_REF] Region II is delimited by two temperatures, T 1 and T 2 , which correspond to a departure from the linear behavior of the free volume with respect to the temperature. Figure 7 shows the three regions obtained, and the glass transition temperature is conventionally taken as the intercept of the linear fits of region I and III (denoted as the green dashed line).

Usually, the coefficient of volumetric thermal expansion (CVTE) is adopted to determine the linear fit of the domains. Here, this coefficient is too noisy for the thermosets studied. A piecewise linear function is thus applied to fit the three domains accordingly; the script is provided by the Python library pwlf. [START_REF] Jekel | pwlf: A Python Library for Fitting 1D Continuous Piecewise Linear Functions[END_REF] This some automation to the fit of the domains, often very complicated and subjective to do. For each system, eight independent simulations are performed and the change in free volume is measured as a function of temperature.

However, in order to compare the simulated to the experimental values, the relation of Williams-Landel-Ferry (eq 3), which relies on the principle of time-temperature equivalence, is applied by using the empirical constants C 1 = 17.44 and C 2 = 51.6 K. It was deemed acceptable to use the universal constants because of the structure of the studied resins and the time constraint of using fitted constraints for each. [START_REF] Dudowicz | The Meaning of the "Universal" WLF Parameters of Glass-Forming Polymer Liquids[END_REF] In the scope of this work, several systems have been done both experimentally and by molecular simulations; this is mainly the case for the bio-based resins (DGEVA and PHTE). First, the correlation between these experimental and simulated glass transition temperatures is acceptable, with an average absolute deviation of 12%. The difference can be as minimal as 0.4% for PHTE/ IPDA and as important as 59.5% for DGEVA/DETA. Second, there is a disparity between experimental results if a comparison is made between values found in this work and those from references. As a matter of fact, a mean difference of ±11 K is found, with a disparity of up to ±27 K for the case of DGEBA/EDA. Nevertheless, the results in Figure 8 show a general great correlation between simulated and experimental data. The average absolute deviation is about 7.0% without taking into account the three identified outliers and 12.2% with. Indeed, the simulated values of the glass transition temperature are well within the error range of the experiments, which confirms the interest in using molecular simulations to predict this property. The tendency is surely well-preserved even though generic WLF coefficients are applied. In cases where the prediction is less efficient, a tuning of those coefficients might be of interest. However, it will require additional time-consuming simulations of various cooling speeds for each system. The gap between experimental and simulated results regarding the DGEVA/DETA, DGEBA/ Values with asterisks were obtained experimentally, while # indicates T α . The subscripts give the accuracy of the last decimal(s): i.e., 1.050 3 means 1.050 ± 0.003. EDA, and DGEBA/MMIPA systems has to be further investigated.

3.3. Finding Young's Modulus. Experimentally, Young's modulus is typically obtained by traction testing. The results are widely dependent on the stress-strain applied during the experiment. Nevertheless, these types of tests are normed, and the classic speed used is on the order of mm/min. However, it is practically impossible to measure the modulus at experimental strain rates in an MD system. One way to bypass this constraint is by using an innovative method based on the fluctuation of local density [START_REF] Klix | Glass Elasticity From Particle Trajectories[END_REF] inside the solid epoxy materials at equilibrium. Consequently, an NVT simulation is performed during 2 ns at 300 K for each system. The structural factor S is determined from the atomistic positions and is a function of the wave vector q. The following extrapolation in eq 4 is done to obtain the bulk and shear moduli, respectively B and G. The factor 2 is added here to take into consideration the two transversal directions compared to the expression established in ref 59 for a two-dimensional system (see the Supporting Information for a demonstration of the following expressions).

S q

TG S q T B G lim ( ) 2 lim ( ) 4/3

q q 0 0 = = + (4)
The first member of the equations is obtained graphically by linearly fitting the structure factor S and acquiring the intercept, which corresponds to the limit when the wave vector q to zero. A visual representation of this graphical method is found in Figure 9. However, the property of interest is Young's modulus. We suppose a homogeneous isotropic linear elastic material so that its elastic properties are uniquely determined by any two moduli. Thus, having moduli grants access to any other of the elastic moduli. The following equation is used to Young's modulus from the bulk and shear moduli computed previously: BG B G

9 3 = + (5)
the simulated Young's modulus determined here and a few experimental points taken from a previous experiment. [START_REF] Garcia | Mechanical Properties of Epoxy Networks Based on DGEBA and Aliphatic Amines[END_REF] As can be seen, the simulation fits roughly the few experimental data points, which is promising.

Knowing that the simulated values exhibit a significant correlation with an average absolute deviation of 2.7%, this seems like a fair assumption. This thus raises interest in the hope that this trend will be transferable to all modeled systems. However, a wider sample is needed in terms of experimental data sets and range of Young's moduli to positively conclude.

3.4. Influence of the Molecular Mass M n . One of the advantages of using MD simulations is to be able to straightforwardly customize the molecules used in the epoxy resins. As well as easily switching from one hardener to another, one can play with the possible oligomerization of the epoxies. The study done here enlightens the role that the molecular weight plays in the resulting thermomechanical properties of the resins. This investigation corresponds to a DGEBA+IPDA resin and includes six different oligomerizations of the DGEBA epoxy with values of n equal to 0.08, 0.32, 1, 3, 5, and 10 (see Figure 1). Values of n equal to 0.08 and 0.32 were taken from commercial references Sicomin, SR GreenPoxy 28 and Sika, Biresin CR170, respectively. Their population of n = 0, n = 1, etc. were determined by 1 H NMR. Otherwise, integer values of n were taken as a unique 2.

population. An additional experimental point at n = is proposed, corresponding to the Epikote 1004 commercial reference. This sample's density was experimentally measured, but a large amount of air was imprisoned inside the material, leading to an underestimation of the density.

A focus is made on the influence of the molecular mass on density, glass transition temperature, and Young's modulus (see Figure 11). Previous studies on DGEBA and Jeffamines show the link between the length of the cross-linker and the resulting properties. [START_REF] Chowdhury | Epoxy Resin Thermo-mechanics and Failure Modes: Effects of Cure and Cross-linker Length[END_REF][START_REF] Patil | Free Volumes and Structural Relaxations in Diglycidyl Ether of Bisphenol-A Based Epoxy-Polyether Amine Networks[END_REF] Similarly, this relationship is also displayed here: an increase in molecular mass causes an increase of the density and a decrease of the glass transition temperature and Young's modulus. This outcome can be explained first by the flexibility that the increase of the distance between cross-linking points brings, having a higher degree of oligomerization of the epoxies. By having this oligomerization, it is then easier to find a more relaxed structure, thus bringing the molecules closer together and increasing the density. The length of a cross-link is often one of the main focuses when it comes to tuning thermomechanical properties of materials. One could want to limit the brittleness of a material by lengthening a cross-link to bring some flexibility to a material, but it needs to be taken into account that this change is typically detrimental to the thermal stability. This study enlightens the dual effect of the cross-link length and how a middle ground needs to be reached when designing a new material, and how molecular simulations can help to that effect.

Influence of the Conversion Rate.

In the same spirit, a study on the influence of the conversion rate was done to enlighten another facet of the complexity of the structureproperty relationship (Figure 12). In the scope of this work, a DGEBA/IPDA resin was studied with various curing rates of 30%, 50%, 70%, and 90%. When it comes to conversion rate, this link has been shown previously on Jeffamine systems. [START_REF] Chowdhury | Epoxy Resin Thermo-mechanics and Failure Modes: Effects of Cure and Cross-linker Length[END_REF] First, a slight decrease in density was observed here while it was not the case for the Jeffamine systems. This could be explained by the fact that an increase in cross-links could further constrain the system. The limited opportunity for monomers to be optimally stacked could lead to an increase in free volume and thus result in a decrease in density. Second, the trend regarding the glass transition temperature and Young's modulus is coherent with that of the Jeffamine systems. The link between the structure and the resulting properties is more readily accessible than for the density observations. Since a low conversion rate accounts for fewer cross-links, it is coherent to have a higher elastic response for this material. Similarly, less thermal energy is needed to go from a rigid amorphous thermoset to a more flexible one when fewer covalent bonds are present.

CONCLUSION

This work enlightens a broader study of the modeling of highperformance materials such as epoxy thermosets in terms of the chemical structure and thermomechanical properties. Novel resins were investigated, including bio-based ones, both experimentally and by molecular dynamics. The implementation of a "reactive" cross-linking allows for the creation of a highly cross-linked resin, of up to 99%. The use of the CHARMM force field, usually reserved for biomolecules, was proven to be suitable for these thermosetting resins. Indeed, this work exhibits a good correlation between experimental and simulated results for a variety of resins with backbones fluctuating from aliphatic to aromatic. Thermomechanical properties in the name of density, Young's modulus, and glass transition temperature were measured. In order to acquire these properties by simulation, innovative methodologies and post-treatment of the data were performed and compared with the experimental data to fully implement a robust and generalized approach for each property studied. The most compelling comparison is found in the glass transition temperature, as it is the property with the most data points both experimentally and by molecular simulation. Also, the novelty of this work resides in the large range of glass transition temperatures covered by the resins studied. Overall, because of the consistency with the experimental data, with average absolute deviations between experiments and molecular simulation comprised between 2% and 12%, it is possible to conclude that all of the methods presented are transferable and successful. Thus, it is possible to efficiently determine the density, the glass transition temperature, and Young's modulus for epoxy thermosets by atomistic methods. From an industrial point of view, the development of these methods is the starting point of a more ambitious goal. The definition of these first properties allows a quick characterization of a system and an evaluation if it is interesting for an experimental study according to the targeted specifications. As well as being a predicting tool, this investigation demonstrates the interest in using molecular simulations to extract important structural analyses, often difficult to obtain experimentally. Atomistic simulations will thus have a crucial role in the structureproperty understanding of materials by visualizing the system and acquiring key properties. Building from this, other types of resins such as polyurethanes are currently being considered and studied with this approach.

■ ASSOCIATED CONTENT * sı Supporting Information

Figure 1 .

 1 Figure 1. Molecular representation of the epoxy resins (a-e) and of the hardeners (f-m). Carbon, oxygen, nitrogen, and hydrogen atoms are shown in gray, red, blue, and white, respectively. (n, o) Snapshots of cross-linked systems, where orange and gray phases represent respectively the epoxy resins and hardeners.

Figure 2 .

 2 Figure 2. Depiction of the meaning of n in terms of the oligomerization of DGEBA.

Figure 3 .

 3 Figure 3. Multistep reactive cross-linking algorithm.

Figure 4 .

 4 Figure 4. Radial distribution functions of uncured resin DGEBA +IPDA (red) and DGEVA+MXDA (green) between the reactive carbon of the epoxy resin and the reactive nitrogen of the amine hardener.

Figure 6

 6 Figure 6 reports the values of density of different epoxyamine resins obtained from experimental measurements, empirical calculations, and atomistic simulations. Results taken from other works are given inTable 2. An empirical power law was taken into account to provide a qualitative comparison for resins where the experimental density was not present at room temperature. This relation can be used to describe the density of linear and network polymers according to their average atomic mass (M a ) and constitutive repeat unit (CRU) as stated in eq 2 53 M ) a 2/3 3 = ×

Figure 5 .

 5 Figure 5. Comparison of experimental and simulated densities of the uncured resins and hardeners. The dotted red lines correspond to a deviation of 5% from the experimental value.

Figure 6 .

 6 Figure 6. Comparison of the simulated, empirical, and experimental densities. Results taken from other works are given inTable 2.

Figure 7 .

 7 Figure 7. Free volume of DGEBA+IPDA with respect to the temperature. The glass transition temperature is considered as the middle vertical line (green dashed line).

Figure 8 .

 8 Figure 8. Comparison of simulated and experimental glass transition temperature T g . Results taken from other works are given in Table2.

Figure 9 .

 9 Figure 9. Graphical extrapolation of the structure factors.

Figure 10 .

 10 Figure 10. Comparison of the simulated with the experimental Young's modulus. Results taken from other works are given in Table2.

Figure 11 .

 11 Figure 11. Influence of the molecular weight on the thermomechanical properties of a DGEBA/IPDA system.

Figure 12 .

 12 Figure 12. Influence of the conversion rate on the thermomechanical properties of a DGEBA/IPDA system.

Table 1 .

 1 Description of the Characteristics of Resins and Hardeners Studied, Breaking down the Chemical Structure of the Repeat Unit: Composition, Mass, and Expected Density a

	resin	hardener	n	R:H ratio	mass of CRU (g/mol)	density (g/cm 3 ) (eq2)	no. of atoms	side of the box (Å)
	DGEBU	IPDA	0.32	2:1	574	1.040	7938	41.9
	DGEBA	DETA	0.32	5:2	2368	1.141	11267	48.7
	DGEBA	EDA	0.32	2:1	924	1.145	10919	47.8
	DGEBA	IPDA	0.32	2:1	1034	1.117	12701	50.5
	DGEBA	MMIPA	0.32	2:1	1174	1.128	14240	52.6
	DGEBA	MXDA	0.32	2:1	1000	1.152	11729	49.1
	DGEBA	TEPA	0.32	7:2	3404	1.137	11639	49.2
	DGEBA	TTDA	0.32	2:1	1084	1.129	13106	50.8
	DGEBF	IPDA	0	2:1	1008	1.140	12150	49.8
	DGEVA	DETA	0	5:2	1616	1.174	11500	48.5
	DGEVA	IPDA	0	2:1	734	1.134	8910	44.1
	DGEVA	MDEA	0	2:1	874	1.146	12900	50.3
	DGEVA	MXDA	0	2:1	700	1.187	9800	45.7
	PHTE	IPDA	0	3:4	1686	1.119	12900	50.3
	PHTE	MDEA	0	3:4	2106	1.136	15750	54.1
	PHTE	MXDA	0	3:4	1584	1.186	11100	48.0

a Calculated from eq 2 as the number of atoms present and the size of the box for the simulations.

Table 2 .

 2 Compiled Simulated and Experimental Data Sets for Cross-Linked Resins at 95% Confidence a

		density (g/cm 3 )	T g (°C)			E (GPa)
	system	exptl	sim	exptl	sim	exptl	sim
	DGEBU/IPDA		1.050 3	60 47	55 8			2.23 11
	DGEBA/DETA	1.178	1.111 3	119, 48 132, 49 142*	123, 34 133 10	2.55 11	48	2.57 14
	DGEBA/EDA		1.125 3	70, 50 118, 7 115 51	62 3 , 117 7			2.79 15
	DGEBA/IPDA	1.135	1.084 5	150*, 155, 48 159 49	149 21 , 158 25	2.65 5 48	2.56 13
	DGEBA/MMIPA	1.118	1.075 3		136 7			2.19 20
	DGEBA/MXDA	1.185	1.124 3		101 10			3.41 24
	DGEBA/TEPA		1.102 2	126 48	125 24	2.34 13	48	2.43 23
	DGEBA/TTDA		1.116 2	69 47	84 8			2.14 6
	DGEBF/IPDA		1.102 4		129 10			1.92 16
	DGEVA/DETA		1.179 2	79*	32 10			2.57 13
	DGEVA/IPDA		1.154 6	97, 52 107*	89 8			3.99 26
	DGEVA/MDEA		1.144 4	104*	98 13			3.23 18
	DGEVA/MXDA		1.219 3	74*	75 9			3.41 24
	PHTE/IPDA		1.108 5	225*, #	226 15			3.99 33
	PHTE/MDEA		1.104 6	117*	132 8			3.71 29
	PHTE/MXDA		1.202 5	176*	170 10			4.88 18
	a

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domain: scco shs info.info-cr

text:
Olivier De Casanove

Nicolas Leleu

Florence Sèdes
email: florence.sedes@irit.frnicolas.leleu@ut-capitole.fr

Applying PDCA to Security, Education, Training and Awareness Programs

Keywords: PDCA, Information Systems Security, Awareness, SETA, Guidelines

Security standards help to create security policies, but they are often very descriptive, especially when it comes to security awareness. Information systems security awareness is vital to maintain a high level of security. SETA programs (Security Education, Training and Awareness) increase information systems security awareness and play an important role in finding the strategic balance between the prevention and response paradigms. By reviewing the literature, we identify guidelines for designing a SETA program following a PDCA (Plan Do Check Act) cycle.

Introduction

Defining security awareness and more specifically its goals is a challenging task. This leads to a diversity of approaches and Tsohou et al. [START_REF] Tsohou | Investigating Information Security Awareness: Research and Practice Gaps[END_REF] conclude their paper saying that it creates frustration among security experts; this could be a reason why security awareness remains an issue. In this paper we will consider that the objective of security awareness is to reduce the share of security incidents caused by humans. To decrease the proportion of security incidents caused by well-meaning users, we need to educate them. As stated in [START_REF] Wilson | Building an Information Technology Security Awareness and Training Program[END_REF] "Accountability must be derived from a fully informed, welltrained and aware workforce." To promote a security culture, we can use security, education, training and awareness programs (SETA programs). "SETA programs aim to provide employees with the knowledge and motivation necessary to comply with security policies when confronted with a security risk" [START_REF] Silic | Using Design-Science Based Gamification to Improve Organizational Security Training and Compliance[END_REF]. Some information system security standards define objectives for promoting a security culture and for raising awareness. Two of the most famous standards addressing this concern are the ISO/IEC 27000 family [START_REF]framework[END_REF] and the NIST Cybersecurity Framework [START_REF] Stine | Framework for Improving Critical Infrastructure Cybersecurity[END_REF]. Unfortunately, information system security standards are very descriptive [START_REF] Barlette | The Adoption of Information Security Management Standards: A Literature Review[END_REF]. They set goals to reach, but rarely provide process or methodology on how to reach them; there is a need for guidelines. We propose to apply the Plan Do Check Act (PDCA) method to SETA programs to fulfil this need.

Plan Do Check Act

The Deming wheel (figure 1), also called continuous improvement wheel is a concept that illustrates the PDCA principle. It was made popular by William Edwards Deming. It aims to improve and optimise the gains and reduce the losses of products, processes or services. In the PDCA technique, the slope represents process improvement, the turning wheel continuously cycles Plan Do Check Act and thus climbs the hill, increasingly optimising the product, process or service with the aim of achieving the desired objective. Deming's representation also contains a wedge, it represents the quality system resulting from the previous improvement processes, the experience acquired which prevent the processes from going back. It must imperatively follow the upward movement of the wheel to avoid stagnating or even regressing. In other words, beyond the visual metaphor, it is necessary each time to improve the way of proceeding by avoiding repeating the errors of the past. We believe this tool can help design better SETA programs. With PDCA, we can limit the risk of failure, avoid repeating the same mistakes and provide guidelines.

Fig. 1. Deming's Wheel illustration

In this paper, we will extract guidelines from the literature to promote a security culture and raise awareness thanks to SETA programs. We do not seek to provide an exhaustive literature review but rather a useful compilation of SETA practices. These guidelines are presented in four sections, each section corresponds to a step in the PDCA cycle. Then, we discuss the future of SETA programs and security awareness. Finally, we conclude.

Plan the SETA Program

A SETA program is designed to make people adopt safe behaviours. People will still make mistakes even if they behave safely, but if we are successful, they will make fewer. The most effective way to change security behaviours is to make people adopt a security culture [START_REF] Solms | From policies to culture[END_REF]. To adopt a new culture, it is advised to generate an intrinsic motivation [8]. In other words, SETA programs should increase empowerment, which is a strong lever to increase security awareness [START_REF] Dhillon | Current directions in IS security research: towards socioorganizational perspectives[END_REF]. A SETA program designed to generate intrinsic motivation is more likely to be successful over a long period of time. To design such a program, we need to identify four elements: the source of the message, Erreur ! Utilisez l'onglet Accueil pour appliquer title au texte que vous souhaitez faire apparaître ici. 3 the type of message, the media of the message and the target of the message. Making the right choice decrease the risk of failing the SETA program.

The Source

First, we need to understand who is the source of the message [START_REF] Solms | From policies to culture[END_REF]. Depending on its hierarchical level, the program will not have the same degree of complexity. For instance, if the message is from executives, the objective will be to teach non-technical ideas, for example how to have good digital hygiene? As executives have less understanding of the production environment than team leaders, their messages should not be about technical matters. It is the role of the team leaders to translate the nontechnical messages into technical messages that are relevant to what their team is facing. For example, the team leader can turn the previous non-technical message into how to use the shared mailbox safely?

The type of message

There are two forms of communication that the SETA program should adopt [8] [2]:

• Persuasive communication/education: it answers the question "why" in the user's mind. It should increase people's insight and motivation. • Active participation/training it answers the question "how" in the user's mind. It should develop skills and competences.

Both are equally important; people will not be satisfied if the only reason given for improving security is "just do it" and they cannot do anything if they do not know how.

A good program is a combination of active training and persuasive communication [8].

There are five themes to conduct a security awareness campaign [START_REF] Kajzer | An exploratory investigation of message-person congruence in information security awareness campaigns[END_REF]: deterrence, morality, regret, incentive or feedback. They are defined as follows:

• Deterrence messages associate sanction to a bad action. This assumes that people are rational and will choose the best option for them, which will not be the one with the expected penalty. Empirical evidence that SETA programs are suitable for deterrence messages can be found in [START_REF] D'arcy | User Awareness of Security Countermeasures and Its Impact on Information Systems Misuse: A Deterrence Approach[END_REF]. This finding is confirmed by the literature review [START_REF] Abraham | Information Security Behavior: Factors and Research Directions[END_REF]. Lowry et al. [START_REF] Lowry | Proposing the control-reactance compliance model (CRCM) to explain opposing motivations to comply with organisational information security policies[END_REF] advise staying careful when using this theme, as deterrence messages create reactance and can "result in unintended negative consequences" [START_REF] Lowry | Proposing the control-reactance compliance model (CRCM) to explain opposing motivations to comply with organisational information security policies[END_REF].

• Morality messages attempt to evoke our own moral principles to avoid bad decisions. Empirical evidence that moral reasoning has an impact on security behaviour can be found in [START_REF] Myyry | What levels of moral reasoning and values explain adherence to information security rules? An empirical study[END_REF]. The authors also argue that appropriate punishment activities are important for moral reasoning to be effective. Punishment activities obviously cannot be carried out during a SETA program. • Regret messages assume that people can anticipate the emotional consequences of their choices before making a decision. This anticipation would encourage people to make the right choice. Empirical evidence of the positive effect of regret on security behaviour is found in [START_REF] Bulgurcu | Information Security Policy Compliance: An Empirical Study of Rationality-Based Beliefs and Information Security Awareness[END_REF] but is not distinguished from deterrence or morality. No significant evidence is found in [START_REF] Wright | Focusing on what might happen and how it could feel: can the anticipation of regret change students' computing-related choices?[END_REF]. • Incentive messages assume that giving rewards for doing the right thing helps people improve their behaviour. This can be seen as the opposite of regret messages. Empirical studies show that rewards for compliance with security policies and procedures are not associated with the individual's perceived mandatoriness of the established set of policies and procedures [START_REF] Boss | If someone is watching, I'll do what I'm asked: mandatoriness, control, and information security[END_REF] or with compliance [START_REF] Pahnila | Employees' Behavior towards IS Security Policy Compliance[END_REF]. A survey also concludes that rewards do not directly influence security behaviour [START_REF] Abraham | Information Security Behavior: Factors and Research Directions[END_REF]. However, [START_REF] August | Network Software Security and User Incentives[END_REF] finds theoretical evidence of positive effects on security behaviour and [START_REF] Bulgurcu | Information Security Policy Compliance: An Empirical Study of Rationality-Based Beliefs and Information Security Awareness[END_REF] finds empirical evidence that the incentive has a positive effect. Financial rewards also have a positive effect on security behaviour according to [START_REF] Goel | Can financial incentives help with the struggle for security policy compliance?[END_REF]. • Feedback messages assume that people will change their behaviour if they receive feedback on their actions, this can be positive or negative reinforcement. In [START_REF] West | The Psychology of Security[END_REF],

West explains that classical feedback mechanisms do not work in information systems security; the consequence of a bad action is often delayed, and the consequence of a good one is not to be under attack. In other words, nothing happens. Reinforcement learning is therefore not effective in this context.

In [START_REF] Mayer | Motivating Users to Consider Recommendations on Password Management Strategies[END_REF], the authors compared the effectiveness of different themes for a password policies awareness campaign to a control group and they found no significant difference between the groups' willingness to comply. They suggest that, on a motivate public, theme does not matter.

2.3

The media

There are different media for conveying a SETA program and choosing the right one is an important decision.

The choice of media depends on multiple factors, seven have been identified in [START_REF] Wilson | Building an Information Technology Security Awareness and Training Program[END_REF]:

• The population we are targeting: we will not use the same media if the targeted audience is computer literate or if it is not, for example. • The why or the how: some media are more suited for persuasive communication, and others for active participation. [START_REF] Wilson | Building an Information Technology Security Awareness and Training Program[END_REF] lists the possible media according to the question they answer. [START_REF] Albayram | Comparing the Effectiveness of Text-based and Videobased Delivery in Motivating Users to Adopt a Password Manager[END_REF] suggests that video-based communication is more effective than text-based communication to answer the question "why" (the objective of the study was motivating users to adopt password managers) • The price: [START_REF] Wilson | Building an Information Technology Security Awareness and Training Program[END_REF] details which media are cheap and which are expensive.

• Ease of use: How easy is it to access, deploy, update and maintain the SETA program? • Scalability: Can the material be used for different sized audiences and in different locations? • Support: Will support for the program be internal or external? Is it easy to find help to use the material? • Accountability: Which statistics can be used to measure the effectiveness of the program? How comprehensive are these measures?

As mentioned in the previous subsection 2.2, we need to use media that allow us to answer the question of how (active training) and why (persuasive communication).

2.4

The target

Finally, a SETA program should be audience-specific. Unfortunately, little work has been done to study the relationship between public types and other factors, such as the theme of a SETA program. However, one paper finds that there might be a correlation between personality traits and the effectiveness of a theme [START_REF] Kajzer | An exploratory investigation of message-person congruence in information security awareness campaigns[END_REF]. The most relevant advice found regarding the public is to divide the population by groups of interest. This recommendation is found several times in the literature, regardless of the study publication date [START_REF] Bauer | Prevention is better than cure! Designing information security awareness programs to overcome users' non-compliance with information security policies in banks[END_REF] [25] [START_REF] Wilson | Building an Information Technology Security Awareness and Training Program[END_REF].

Summary

To plan a SETA program we should assess available resources, understand who is the source of the message, what message we want to communicate, how we want to promote it and who is the target. If these attributes are identified, we decrease the risk of failing the campaign.

Do the SETA Program

During the Do step, we apply the choices made in the previous step and we conduct the SETA program. When we carry out the program, the most important thing is the public's willingness to participate [START_REF] Khan | Information Security Awareness Campaign: An Alternate Approach[END_REF]. Security gamification is a tool "to strengthen employees' motivations to encourage learning, efficacy, and increased employee compliance with organisational security initiatives" [START_REF] Silic | Using Design-Science Based Gamification to Improve Organizational Security Training and Compliance[END_REF]; we can therefore use it to design a successful SETA program. Guidelines on how to properly implement gamification are provided [START_REF] Silic | Using Design-Science Based Gamification to Improve Organizational Security Training and Compliance[END_REF]. Yet, as shown by [START_REF] Ophoff | Using Gamification to Improve Information Security Behavior: A Password Strength Experiment[END_REF] and [START_REF] Baxter | Applying Basic Gamification Techniques to IT Compliance Training: Evidence from the Lab and Field[END_REF], gamification in the context of security awareness does not always hit. Providing social interactions during a session increases the effectiveness of the SETA program and triggers positive changes in security behaviour [12] [26] [27] [28] [7]. This argument seems to demonstrate that e-learning is not appropriate since there are no interactions. On the other hand, Kävrestad et al. [START_REF] Kävrestad | Users perception of using CBMT for informationsecurity training[END_REF] [START_REF] Kävrestad | Evaluation of Contextual and Game-Based Training for Phishing Detection[END_REF] show that e-learning could be effective if "information [is] presented in short sequences to the learner. It should also include a practical element and be of direct relevance to the user's intention." [START_REF] Kävrestad | ContextBased MicroTraining: A Framework for Information Security Training[END_REF] Organised SETA programs in short sessions is a good practice, even if we are not doing e-learning [START_REF] Thomson | Information security awareness: educating your users effectively[END_REF]. At the end of the program, giving gifts is a good way to spread our message and reinforce the commitment [START_REF] Thomson | Information security awareness: educating your users effectively[END_REF].

If the SETA program happens in a company or in an industrial context, the session needs to have as little impact as possible on production; therefore we should communicate the plan to all stakeholders [12] [2]. This means the people we are training, but also their immediate superiors and other people they work with who are not involved in the program. During the session, the trainees will not be able to maintain production; everyone working with them must be prepared for the consequences.

Summary

A program is more likely to succeed if it offers human interaction. If the program happens in a company, attendees' coworkers should be warned that attendees will not be available to maintain production.

Check the SETA Program

In the check step, we should verify whether we have processes to monitor the effectiveness and efficiency of the SETA program. To evaluate our program, we need to collect data. They can be feedback, questionnaires or notes taken during the session. We identified three types of evaluation in the literature: measure of behavioural intention, knowledge oriented and ulterior incident rate. A non-exhaustive list of papers related to each category can be found in table 1.

• Measure of behavioural intention:

The assumption behind this type of evaluation is that system, method or tool use can be estimated using many other measures, and that the behavioural intention to use is a good estimator of actual usage. For example, if we run a campaign to promote password managers, the higher the user's intention to use them, the more successful the campaign is. • Knowledge oriented: This evaluation method posits that people who have less understanding of security concepts are more likely to be victims of an attack. Therefore, assessing the knowledge gained after the SETA program can be an indicator of the effectiveness of the program. • Ulterior incident rate: This method consists of measuring the incident rate ulterior to the campaign. For example, if we run a campaign against bad password management and the rate of incidents related to bad password management decreases after the campaign, we can consider the campaign successful.

EVALUATION METHODS REFERENCES

Measure of behavioural intention [34] [35] [36]* [START_REF] Shropshire | Personality, attitudes, and intentions: Predicting initial adoption of information security behavior[END_REF] Knowledge test [START_REF] Mayer | Motivating Users to Consider Recommendations on Password Management Strategies[END_REF] [38] [START_REF] Kruger | A prototype for assessing information security awareness[END_REF] [40] [START_REF] Mayer | On the systematic development and evaluation of password security awareness-raising materials[END_REF] Ulterior incident rate [START_REF] Wilson | Building an Information Technology Security Awareness and Training Program[END_REF] Table 1. Evaluation methods (* is a review)

Regardless of the solution we choose for evaluating our program, we need to think about automating the evaluation [START_REF] Wilson | Building an Information Technology Security Awareness and Training Program[END_REF] [START_REF] Kruger | A prototype for assessing information security awareness[END_REF]. Some SETA programs can be huge; the process of collecting the data and then interpreting it can be time consuming. Obviously, some types of data are better suited for automation than others. Hand notes of the session, open-ended questions and oral feedback need a human to interpret them; therefore this is difficult to process automatically. On the other hand, online questionnaires or at least multiple-choice questionnaires are easier to process automatically.

Summary.

We establish a process to evaluate our program. As the SETA program will grow, it will be harder to evaluate it without automation. Some evaluation methods are most suited for automation than others; this should be taken into consideration when choosing the method to evaluate our program.

Adjust the SETA program

During the Act phase (also known as Adjust phase), we establish a process to ensure we perform a review on a periodic basis to confirm the continuing applicability, adequacy, effectiveness and efficiency of the SETA programs. In the first place, we take in consideration the data collected in the previous section to improve our program. Then, we verify if the campaign is consistent with the new policies and environment. The IT environment is an ever-evolving place, it is important to check if the messages provided are not obsolete. If so, we need to update them or add new ones. Once we have our new program, we should consider launching a new campaign. This cycle is the single-loop learning of the prevention paradigm described in [START_REF] Baskerville | Incident-centered information security: Managing a strategic balance between prevention and response[END_REF]. Since we are considering SETA program as a continuous process, a new campaign should be launched on a regular basis. Exactly as it seems obvious to everyone to update their antivirus software, security culture must also be updated.

Summary.

The improvement process is in two parts: first improve the program based on the feedback, second verify if the messages are still up to date. A new campaign must be planned at the end of the previous one.

Discussion and Perspectives

SETA programs are an important aspect of security. It differs from other aspects of security by putting the user back at the centre of the information system. This is associated with the field of "Human-Centred Security and Privacy" (HCSP), see [START_REF] Renaud | Contemplating human-centred security & privacy research: Suggesting future directions[END_REF] for a brief overview of this field.

While many tools in information system security are automated, non-technical security measures are exceptions to this rule. The PDCA cycle permits at least to create a clear process which will facilitate the creation of a SETA program. We used the PDCA cycle because it is a widely used tool in the industry, but other continuous improvement tools should be studied, or created if needed, to better suit the needs of information system security. We seek, in future works, to develop a PDCA-based method for the implementation of organisational SETA work.

SETA programs have been researched extensively, but some aspects have been neglected. For example, how themes interact with other variables, like the target of a campaign, is not well studied in the literature. We want to extract other weaknesses in future works, thanks to techniques such as content analysis.

Khan et al. [START_REF] Khan | Information Security Awareness Campaign: An Alternate Approach[END_REF] identify that information systems security awareness lags behind other domains such as ecological or public health awareness. They propose to imitate techniques from other fields to improve information systems security awareness. For example, in public health, a reference model is the EPPM (Extended Parallel Process Model) [START_REF] Witte | Putting the fear back into fear appeals: The extended parallel process model[END_REF]. This model works well with messages fear-based (they are similar to deterrence-based messages), which are effective for SETA programs according to what we found in the literature (see subsection 2.2).

At the check step, we listed models allowing measuring the SETA campaign effectiveness (see table 1). The lack of common datasets makes it difficult to compare them together and to conclude if one is better than another. In addition, there is a need for reproducibility since the datasets are not public.

Conclusion

Security awareness is a major concern in information system security. To promote awareness, we use SETA program. However, there is a lack of methodology on how to implement them in the state of the art. This is the problem we try to address in this paper. By reviewing the literature, we identify guidelines for designing SETA programs following a PDCA cycle. The PDCA cycle allows us to be prescriptive and not just descriptive as many current standards do. In addition, PDCA facilitates the continuous improvement of awareness campaigns which, as every security tool, should stay updated.

We believe this work can help information system security actors to design better prevention programs but not only. This work can also be used by researchers who want to study the various topics related to prevention. They can find in this paper guidelines to create effective programs to convey messages, leading to more efficient prevention campaign and more significant results.

Erreur ! Utilisez l'onglet Accueil pour appliquer title au texte que vous souhaitez faire apparaître ici.


João Luca Monzo

Pedro Ferreira

Paula Abreu

Annette Szumski

Michael Böhm

John J V Mcmurray

Bertram Pitt

Karl Swedberg

Dirk J Van Veldhuisen

Nicolas Girerd

; João

John Vincent

Faiez Zannad

MD Patrick Rossignol
email: p.rossignol@chru-nancy.fr

Visit-to-visit blood pressure variation and outcomes in heart failure with reduced ejection fraction: findings from the Eplerenone in Patients with Systolic Heart Failure and Mild Symptoms trial

Keywords: heart failure, visit-to-visit blood pressure variability, prognosis, systolic blood pressure. ClinicalTrials

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

Introduction

Visit-to-visit office blood pressure variability (BPV) has been associated with several cardiovascular events (e.g. stroke, myocardial infarction, and cardiovascular mortality) [START_REF] Diaz | Visit-to-visit variability of blood pressure and cardiovascular disease and all-cause mortality: a systematic review and meta-analysis[END_REF][START_REF] Kronish | The Association Between Antihypertensive Medication Nonadherence and Visit-to-Visit Variability of Blood Pressure: Findings From the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial[END_REF][START_REF] Muntner | The relationship between visit-tovisit variability in systolic blood pressure and all-cause mortality in the general population: findings from NHANES III, 1988 to 1994[END_REF][START_REF] Muntner | Visit-to-Visit Variability of Blood Pressure and Coronary Heart Disease, Stroke, Heart Failure, and Mortality: A Cohort Study[END_REF][START_REF] Shimbo | Association between annual visit-to-visit blood pressure variability and stroke in postmenopausal women: data from the Women's Health Initiative[END_REF], independently of other cardiovascular risk factors. Both low and high BPV have also been associated with worse outcomes depending on the context and population (general population, chronic kidney disease, hypertension, diabetes, high risk population, heart failure, etc.) [START_REF] Chang | Visit-to-Visit Office Blood Pressure Variability and Cardiovascular Outcomes in SPRINT (Systolic Blood Pressure Intervention Trial)[END_REF][START_REF] Ferreira | Visit-to-visit blood pressure variation is associated with outcomes in a U-shaped fashion in patients with myocardial infarction complicated with systolic dysfunction and/or heart failure: findings from the EPHESUS and OPTIMAAL trials[END_REF][START_REF] Rossignol | Visit-to-visit blood pressure variability is a strong predictor of cardiovascular events in hemodialysis: insights from FOSIDIAL[END_REF][START_REF] Rossignol | Increased visit-to-visit blood pressure variability is associated with worse cardiovascular outcomes in low ejection fraction heart failure patients: Insights from the HEAAL study[END_REF][START_REF] Rothwell | Limitations of the usual blood-pressure hypothesis and importance of variability, instability, and episodic hypertension[END_REF][START_REF] Rothwell | Prognostic significance of visit-to-visit variability, maximum systolic blood pressure, and episodic hypertension[END_REF][START_REF] Vidal-Petiot | Visit-to-visit variability of blood pressure and cardiovascular outcomes in patients with stable coronary heart disease. Insights from the STABILITY trial[END_REF]. BPV can be influenced by several factors such as medication adherence, class of antihypertensive medication, intensity of blood pressure (BP) treatment, autonomic dysfunction and patient age [START_REF] Hong | Medication adherence and visit-to-visit variability of systolic blood pressure in African Americans with chronic kidney disease in the AASK trial[END_REF][START_REF] Kostis | Visit-to-visit blood pressure variability and cardiovascular death in the Systolic Hypertension in the Elderly Program[END_REF][START_REF] Mancia | Visit-to-Visit Blood Pressure Variability: An Insight Into the Mechanisms[END_REF].

In a secondary analysis of the high-dose versus low-dose losartan on clinical outcomes in patients with heart failure (HF) trial (HEAAL), a high BPV was found to be associated with poorer cardiovascular outcomes [START_REF] Rossignol | Increased visit-to-visit blood pressure variability is associated with worse cardiovascular outcomes in low ejection fraction heart failure patients: Insights from the HEAAL study[END_REF]. Conversely, in the ivabradine and outcomes in chronic heart failure trial (SHIFT), low BPV was associated with worse outcomes [START_REF] Bohm | Effect of Visit-to-Visit Variation of Heart Rate and Systolic Blood Pressure on Outcomes in Chronic Systolic Heart Failure: Results From the Systolic Heart Failure Treatment With the If Inhibitor Ivabradine Trial (SHIFT) Trial[END_REF]. Finally, in a recent analysis of patients with myocardial infarction and left ventricular dysfunction, heart failure or other high-risk features, there was a U-shaped relationship between BPV and outcomes, with an excess of mortality in both the high and the low BPV tertiles [START_REF] Ferreira | Visit-to-visit blood pressure variation is associated with outcomes in a U-shaped fashion in patients with myocardial infarction complicated with systolic dysfunction and/or heart failure: findings from the EPHESUS and OPTIMAAL trials[END_REF].

In order to characterize the relationship between visit-to-visit BPV and outcomes further in HFrEF, and to determine whether eplerenone might modulate the effects of BPV on prognosis, we analysed BPV in patients enrolled in the Eplerenone in Patients with Systolic Heart Failure and Mild Symptoms trial (EMPHASIS-HF).

Methods

Study population

The primary objectives, the protocol and the outcomes of the EMPHASIS-HF have been previously described in detail [START_REF] Zannad | Eplerenone in patients with systolic heart failure and mild symptoms[END_REF]. In brief, EMPHASIS-HF was a randomized, double-blind, placebo-controlled outcomes trial in patients with chronic systolic heart failure and mild symptoms. The study was conducted in accordance with the Declaration of Helsinki and approved by site ethics committees. All participants gave written informed consent to participate in the trial.

Outcomes

The primary outcome in this trial was a composite of death from cardiovascular causes or a first hospitalization for heart failure. We analysed the effect of systolic blood pressure coefficient of variation (SBP-CoV) on the primary outcome, as well as the effect of SBP-CoV on the two components of this composite. We also examined whether the effect of eplerenone on these outcomes was modified by SBP-CoV.

Visit-to-visit blood pressure variation

Blood pressure was measured at each visit after 5 min of rest in the seated position by a trained observer using a validated oscillometric semi-automated blood pressure machine with the appropriate cuff size.

During the site assessment visits, each site was confirmed to keep a certificate of calibration every 3-6 months and these were monitored during site visits. The clinic visits were timed to coincide with trough measurements. Three blood pressure measures were performed systematically and the average of these measures was recorded in the study dataset. Time interval between office visits was: screening, baseline, week 1, week 4, every three months for the first year and thereafter, every 4 months for the entire duration of the trial. Mean BP (systolic and diastolic) was calculated as the average of all post-baseline BP values up to and including first event or last BP measurement, whichever comes first. Only subjects with at least two visits and therefore two averaged (average of three measurements) systolic blood pressure (SBP) and diastolic blood pressure (DBP) values were included in the analysis. Standard deviation (SD) was calculated for HF hospitalization, CV death, and HF hospitalization/CV death events separately and included the same measurements as for mean BP. BPV was calculated as SBP coefficient of variation, that is, the ratio of the SD to the mean (SBP-CoV =SD/mean*100%). The correlation between mean SBP and SBP SD was modest.

There was almost no correlation between mean SBP and SBP coefficient of variation (SBP-CoV), and therefore, SBP-CoV was chosen for further analysis instead of SD being less dependent on the mean.

Statistical methods

Categorical data are presented as percentages, normally distributed continuous data as mean ± SD, and nonnormally distributed variables as median and interquartile range (IQR). Differences in means and proportions amongst SBP-CoV tertiles were analysed with one-way ANOVA tests and chi-square test, respectively.

Univariate and multivariate Cox proportional hazard regression models were used to model time-toevent for primary and secondary outcomes. Multivariate models include the following selected covariates: treatment, gender, age, diabetes, haemoglobin, estimated glomerular filtration rate, systolic blood pressure, myocardial infarction, body mass index and heart rate. Proportional hazards assumptions for dependent variables were visually assessed by plotting the log[-log(S(t))] function as a function of survival time (t), where S(t) represents the survival function. In the multivariate models, the adjustment covariates were chosen from demographic, clinical/pharmacological, and laboratory variables that were previously found to be clinically and prognostically relevant [START_REF] Collier | The impact of eplerenone at different levels of risk in patients with systolic heart failure and mild symptoms: insight from a novel risk score for prognosis derived from the EMPHASIS-HF trial[END_REF], with additional adjustment for treatment allocation (eplerenone or placebo). Estimated glomerular filtration rate was calculated by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation [START_REF] Levey | A new equation to estimate glomerular filtration rate[END_REF]. We assessed the prespecified SBP-CoV tertile by treatment interactions as well as SBP-CoV tertile by 3 SBP-category interactions in univariate and multivariate Cox models. The linearity assumption of the relationship between SBP-CoV and the log-hazard of outcome was assessed using restricted cubic splines with five knots equally spaced at the 0 th , 25 th , 50 th , 75 th and 100 th percentiles according to the Harrell's rule [START_REF] Harrell | Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis[END_REF]. The Wald test associated with the nonlinear component was statistically significant, and a nonlinear relationship was assumed regarding all the studied outcomes (p-value for linearity <0.001). A p-value less than 0.05 was considered as statistically significant.

No adjustment for multiplicity of testing was performed providing this is a hypothesis-generating study. All analysis was performed with the SAS software (SAS Institute Inc., Cary, NC, USA).

Results

Demographics and Clinical Characteristics

Patients were divided into SBP-CoV tertiles as follows: tertile 1 (T1) ≤6.0% (n=851), tertile 2 (T2) 6.1 -9.0% (n=790), and tertile 3 (T3) >9.0% (n=908). There was a significant trend to a higher number of blood pressure measurements from the lower to the upper tertile (p<0.001 for trend). The baseline characteristics of the three groups were similar except for the frequency of an ischemic etiology and higher body mass index (BMI), in T1 compared to T2 and T3. Overall, the mean number of blood pressure measures available was 6.4±3.2. The mean SBP at baseline was similar across tertiles (124.5±15.2 vs 125.1±17.0 vs 123.5±17.9 for lower, middle and upper tertiles, respectively; p=0.15), whereas DBP was lowest in the upper tertile of SBP-CoV (75.6±9.7 vs 75.2±10.0 vs 73.8±10.9 T1, T2 and T3, respectively; p<0.001) (Table 1).

We also explored clinical outcomes dividing patients in SBP-CoV quintiles (quintile 1 (Q1) ≤4.5%, n=493; quintile 2 (Q2) 4.5 -6.6%, n=500; quintile 3 (Q3) 6.7 -8.5%, n=489; quintile 4 (Q4) 8.6 -11%, n=502; and quintile 5 (Q5) >11%, n=476) and in tertiles of DBP coefficient of variation (DBP-CoV; tertile 1 (T1) ≤7.1%, n=826; tertile 2 (T2) 7.2 -11.5%, n=824; and tertile 3 (T3) >11.5%, n=810).

Clinical Outcomes

SBP-CoV was independently associated with worse outcomes. In particular, lower SBP-CoV was associated with a higher rate of the composite of cardiovascular (CV) death or HF hospitalization (HFH) (adjusted HR (T1 vs T2) 2.01, 95%CI [1.62-2.51]) and HFH (adjusted HR (T1 vs T2) 1.78, 95%CI [1.36-2.32]) (Table 2 & Fig. 1). Both low and high SBP-CoV were associated with CV death: adjusted HR T1 vs T2 2.48 (95%CI 1.81-3.39) and adjusted HR T3 vs T2 1.68 (1.24-2.29) (Table 2). These results were consistent also Finally, we determined the effect of DBP-CoV on outcomes. Lower DBP-CoV, but not higher, was associated with a higher rate of all studied outcomes (CV death and HFH adjusted HR (T1 vs T2) Content 6, that illustrates the interaction of systolic blood pressure coefficient of variation against other factors). The effect of eplerenone was consistent across all SBP-CoV tertiles (Table 2).

SBP-CoV and mean SBP interaction

SBP modified the relationship between SBP-CoV and the primary outcome (p for interaction = 0.049) and, particularly, HF hospitalization (p for interaction = 0.018) (Fig. 2 & see Table, Supplemental Digital Content 6, that illustrates the interaction of systolic blood pressure coefficient of variation against other factors). The worse outcomes associated with both low and high SBP-CoV were accentuated in people with a low (<110 mmHg) and high (>140 mmHg) mean SBP, compared to an SBP between 110 and 140 mmHg ("intermediate") (see Table, Supplemental Digital Content 7, that illustrates the prognostic associations between tertiles of mean systolic blood pressure and systolic blood pressure coefficient of variation).

Discussion

In HFrEF patients in EMPHASIS-HF, low SBP-CoV was associated with worse outcomes, whereas high SBP-CoV was associated with higher rate of cardiovascular death only. It also seemed that low and high SBP-CoV had stronger prognostic implications in the context of low and high SBP, with less of an "effect" of SBP-CoV when the SBP was within the range of 110 to 140 mmHg. SBP-CoV did not modify the favourable impact of eplerenone on outcomes.

Our findings differ from many prior investigations of SBP-CoV in other disease states where the majority of the studies reported a higher risk of adverse outcomes with higher rather than lower SBP-CoV [START_REF] Diaz | Visit-to-visit variability of blood pressure and cardiovascular disease and all-cause mortality: a systematic review and meta-analysis[END_REF]. Focusing specifically on HF, Rossignol and colleagues [START_REF] Rossignol | Increased visit-to-visit blood pressure variability is associated with worse cardiovascular outcomes in low ejection fraction heart failure patients: Insights from the HEAAL study[END_REF] also showed that higher visit-to-visit systolic BPV was associated with worse outcomes in the 3834 patients with HFrEF in HEAAL. On the other hand, in 6505 HFrEF patients in SHIFT [START_REF] Bohm | Effect of Visit-to-Visit Variation of Heart Rate and Systolic Blood Pressure on Outcomes in Chronic Systolic Heart Failure: Results From the Systolic Heart Failure Treatment With the If Inhibitor Ivabradine Trial (SHIFT) Trial[END_REF], lower SBP-CoV was associated with higher event rates, in keeping in with the present findings in EMPHASIS-HF.

Although explanations have been suggested for an association between high SBP-CoV and worse outcomes [START_REF] Mancia | Visit-to-Visit Blood Pressure Variability: An Insight Into the Mechanisms[END_REF], the potential mechanisms underlying the association between low SBP-CoV and poor outcomes are still debated. In HFrEF low SBP-CoV may be related to classical factors involved in BP control as reduced cardiac output and myocardial contractile reserve, but also to intrinsic factors such as a blunted baroreflex sensibility [START_REF] Lanfranchi | Arterial baroreflex function and cardiovascular variability: interactions and implications[END_REF], impaired autonomic nervous system integrity [START_REF] Grassi | Diurnal blood pressure variation and sympathetic activity[END_REF] and altered circadian hormonal secretion [START_REF] Giles | Circadian variation in blood pressure and heart rate in nonhypertensive congestive heart failure[END_REF]. Collectively, the dysregulation of these pathways may identify sicker patients at higher risk of adverse events.

In the EMPHASIS-HF [START_REF] Zannad | Eplerenone in patients with systolic heart failure and mild symptoms[END_REF] eplerenone significantly reduced the risk of the primary outcome (composite of death from cardiovascular causes or HF hospitalization) by 37%. Although the mechanisms through which mineralocorticoid receptor antagonists are thought to provide cardiovascular protection, such as reduction in cardiac fibrosis and neurohormonal activation [START_REF] Tsutamoto | Effect of spironolactone on plasma brain natriuretic peptide and left ventricular remodeling in patients with congestive heart failure[END_REF][START_REF] Brown | Eplerenone: cardiovascular protection[END_REF], might also affect BPV, we found that eplerenone did not affect SBP-CoV and that effect of eplerenone was consistent across SBP-CoV tertiles.

Similarly, in the SHIFT trial [START_REF] Bohm | Effect of Visit-to-Visit Variation of Heart Rate and Systolic Blood Pressure on Outcomes in Chronic Systolic Heart Failure: Results From the Systolic Heart Failure Treatment With the If Inhibitor Ivabradine Trial (SHIFT) Trial[END_REF], a statistical interaction was found between mean SBP and SBP-CoV with regards to the primary outcome and HF hospitalization. While the effect modification was slight, low SBP-CoV was more likely to be associated with adverse outcomes in patients with both low and high SBP, while the SBP within the "normal" range showed less relevance, consistent with our findings. This "interaction" may be potentially attributable to two linked mechanisms: on the one hand, hypertension is a well-known risk factor for worse cardiovascular outcomes in most populations whereas, on the other, pump failure and poor contractile reserve may lead to a low SBP in the setting of left ventricular systolic dysfunction. This U-shaped relationship appeared to influence mainly HF hospitalizations that may be more susceptible to variations in blood pressure. In the EPHESUS trial [START_REF] Pitt | Eplerenone, a selective aldosterone blocker, in patients with left ventricular dysfunction after myocardial infarction[END_REF] patients were enrolled early after myocardial infarction (3 to 14 days after the index event) and SBP-CoV was also associated with outcomes

  exploring SBP variability SD (CV death and HFH adjusted HR (T1 vs T2) 2.43, 95%CI [1.97-3.01]; HFH adjusted HR (T1 vs T2) 2.25, 95%CI [1.75-2.90]; CV death adjusted HR T1 vs T2 2.43 (95%CI 1.83-3.24) and adjusted HR T3 vs T2 1.46 (1.09-1.95) (see Table, Supplemental Digital Content 1, that illustrates clinical outcomes in systolic blood pressure variability SD tertiles). To better depict the trend of the risk we also evaluated clinical outcomes in SBP-CoV quintiles. We showed an increase of risk for the composite of CV death or HFH (adjusted HR (Q1 vs Q3) 2.80, 95%CI [2.13-3.69]; adjusted HR (Q5 vs Q3) 1.49, 95%CI [1.12-1.99]) and CV death (adjusted HR (Q1 vs Q3) 3.33, 95%CI [2.40-4.81]; adjusted HR (Q5 vs Q3) 1.82, 95%CI [1.25-2.66]) in the lower and higher quintile, meanwhile only the lower quintile of SBP-CoV was associated with HFH (adjusted HR (Q1 vs Q3) 2.42, 95%CI [1.73-3.37]) (seeTable, Supplemental Digital Content 2, that illustrates clinical outcomes in systolic blood pressure coefficient of variation quintiles).

FIGURE 1 .

 1 FIGURE 1. "Spline" graphical representation of the prognostic implications of systolic blood pressure

FIGURE 2 .

 2 FIGURE 2. Interaction between mean systolic blood pressure (SBP) and systolic blood pressure coefficient

Table, Supplemental Digital Content 3, that

  illustrates clinical outcomes in diastolic blood pressure coefficient of variation tertiles). Models adjusted for confounding factors and for randomized treatment gave similar findings (

	1.51,
	95%CI [1.23-1.86]; CV death adjusted HR (T1 vs T2) 1.43, 95%CI [1.08-1.89]; HFH adjusted HR (T1 vs
	T2) 1.55, 95%CI [1.20-2.01]) (see

Table 2 & see Table, Supplemental Digital Content 4, that

 2 illustrates the prognostic associations of systolic blood pressure coefficient of variation adjusted for confounding factors).

	Univariate and multivariate sensitivity analyses that included patients with a minimum of three BP
	measures gave consistent findings (see Table, Supplemental Digital Content 5, that illustrates the
	prognostic associations of systolic blood pressure coefficient of variation in patients with 3 or more blood
	pressure measurements).
	The relationship between SBP-CoV and outcomes was not modified by eplerenone (p value for
	interaction=0.482) or hypertensive status (p value for interaction=0.484) (see Table, Supplemental Digital

TABLE 1 .

 1 Population characteristics by systolic blood pressure coefficient of variation tertiles

		Global
	Characteristics		T1: <6.0%	T2: 6.1-9.0%	T3: >9.0%	p-value
		population
			(N=851)	(N=790)	(N=908)
		(N=2.549)
	Age, years	68.67.6	68.47.8	68.57.5	69.07.6	0.170
	Male, n (%)	1988 (78)	662 (77.8)	619 (78.4)	707 (77.9)	0.956
	Hypertension, n (%)	1697 (66.6)	586 (68.9)	523 (66.2)	588 (64.8)	0.183
	Diabetes, n (%)	778 (30.5)	265 (31.1)	231 (29.2)	282 (31.1)	0.642
	AFib, n (%)	792 (31.1)	269 (31.6)	263 (33.3)	260 (28.6)	0.108
	PVD, n (%)	2 (0.1)	1 (0.1)	1 (0.1)	0 (0)	0.574
	COPD, n (%)	355 (13.9)	124 (14.6)	99 (12.5)	132 (14.5)	0.394
	Smoker, n (%)	260 (10.2)	82 (9.6)	85 (10.8)	93 (10.2)	0.578
	Previous MI, n (%)	1275 (50.0)	470 (55.2)	400 (50.6)	405 (44.6)	<0.001
	Ischemic HF, n (%)	1752 (68.8)	642 (75.5)	550 (69.6)	560 (61.8)	<0.001
	Hemoglobin, g/dL	13.81.6	13.81.6	13.91.5	13.81.5	0.063
	BMI, Kg/m 2	27.64.8	27.84.8	27.74.8	27.34.9	0.048
	SBP, mmHg	124.316.8	124.515.2	125.117.0	123.517.9	0.153
	DBP, mmHg	74.810.2	75.69.7	75.210.0	73.810.9	<0.001
	Heart rate, bpm	73.315.5	73.015.2	73.315.3	73.515.9	0.778
	Thiazides, n (%)	267 (10.5)	103 (12.1)	71 (9.0)	93 (10.2)	0.115
	SBP variability coef., %	7.94.1	3.81.7	7.40.8	12.23.0	<0.001
	SBP measures, n	6.43.2	5.43.1	6.93.0	6.83.1	<0.001
	Eplerenone allocation, n (%)	1284 (50.4)	413 (48.5)	399 (50.5)	472 (52.0)	0.350
	List of abbreviations: AFib, atrial fibrillation; BMI, body mass index; COPD, chronic obstructive pulmonary

disease; CV, cardiovascular; DBP, diastolic blood pressure; HF, heart failure; MI, myocardial infarction; PVD, peripheral vascular disease; SBP, systolic blood pressure; T, tertiles. T1, low SBP variability; T2, intermediate SBP variability; T3, high SBP variability.

The EMPHASIS-HF study was sponsored by Pfizer and the statistical analyses were performed by Pfizer. Dr. Karl Swedberg has received honoraria (modest) from AstraZeneca, Novartis, Pfizer and Servier.

in a U-shaped manner, but without interaction with SBP. The different settings and populations may explain these slightly different findings.

As with SBP-CoV, patients in the lowest third of DBP-CoV had the highest risk [START_REF] Diaz | Visit-to-visit variability of blood pressure and cardiovascular disease and all-cause mortality: a systematic review and meta-analysis[END_REF]. Noteworthy, a previous study conducted in a large HFrEF population showed that patients in the lower tertile of DBP-CoV had the worse outcome [START_REF] Bohm | Effect of Visit-to-Visit Variation of Heart Rate and Systolic Blood Pressure on Outcomes in Chronic Systolic Heart Failure: Results From the Systolic Heart Failure Treatment With the If Inhibitor Ivabradine Trial (SHIFT) Trial[END_REF], confirming our findings. This association is likely driven by similar pathophysiological mechanisms as above discussed for SBP-CoV.

Limitations

Some limitations of the present analysis should be acknowledged. Firstly, our analysis was post-hoc and exploratory. However, data were derived from a large randomized controlled trial, providing sufficient statistical power for reliable analysis of the relationships between SBP-CoV and risk. Second, our results were obtained in patients with HFrEF and mild symptoms and generalization to other patients with HF is not possible. Third, the mechanisms underlying the relationship between SBP-CoV and outcomes (especially for the association between low SBP-CoV and worse outcomes) are not completely understood and further studies are required. Fourth, a threshold systolic blood pressure value was used to determine entry into the trial, which may have influenced SBP-CoV of some extent [START_REF] Musini | Factors affecting blood pressure variability: lessons learned from two systematic reviews of randomized controlled trials[END_REF]. Fifth, because of the multicentric design of the study that encompassed end-points not primarily focused on blood pressure measurement, different devices for blood pressure measurement were used. Notwithstanding, all BP measurements were made using validated semi-automated blood pressure machines with calibration records monitored during every clinical research monitoring visit. Moreover, having different devices reduces the probability of a systematic error to occur, reinforcing the validity of our associations i.e. they were not affected by random fluctuations in the measurements. Finally, these findings are hypothesis generating only, as interactions tests are statistically weak and these tests were not adjusted for multiplicity.

Conclusion

In our cohort of HFrEF patients with mild symptoms both a low and high SBP-CoV and low DBP-CoV were associated with worse outcomes. SBP-CoV did not modify the effect of eplerenone and eplerenone did no modify SBP-CoV. Further studies are warranted to clarify the role of BPV in HF.

List of Supplemental Digital Content

Supplemental Digital Content 1.

CV deat h

Hazard ratio p for interaction = 0.363