domain: spi info

text:
Flora Estermann

Valérie Kaftandjian

Philippe Guy

Philippe Quetin

Philippe Delachartre

PWML Detection in 3D Cranial Ultrasound Volumes using Over-segmentation and Multimodal Classification with Deep Learning

Keywords: Deep Learning, Automatic Anomaly Detection, 3D Ultrasound Imaging, White Matter Injury, U-Net

Punctate white matter lesions (PWML) are the most common white matter injuries observed in preterm neonates. Automatic detection of these lesions could better assist doctors in diagnosis. Recent advances in deep learning have resulted in optimistic results on many MR biomedical image benchmark datasets, but few methods seem to tackle the detection of very small lesions in ultrasound images. In this paper, we propose a two-phase strategy. Firstly, we highlight the foreground information by aggregating the lesions in the ground truth along the coronal projection of the brain, then we train a segmentation network to detect PWML with the resulting oversegmented masks. Secondly, we introduce a novel deep architecture for multimodal classification, called 2.5D SC-Net, which is used to eliminate false alarms and improve specificity. Experimental results demonstrate the effectiveness of our method to detect PWML in ultrasound images, improving the recall by 15% compared to the best published models, while limiting the number of false alarms efficiently.

INTRODUCTION

Punctate white matter lesions (PWML) are responsible for neurodevelopmental sequelae in early childhood [START_REF] Nguyen | The brain's kryptonite: Overview of punctate white matter lesions in neonates[END_REF] [START_REF] De Bruijn | Neurodevelopmental consequences of preterm punctate white matter lesions: a systematic review[END_REF]. Currently, MRI is the gold standard for lesion detection, but this procedure is expensive and not always accessible. As ultrasound is routinely performed on newborns, this modality could be of real interest for the detection of lesions and allow more children with PWML to benefit from medical care.

Many papers present unsupervised approaches using CNNs for breast tumors classification [START_REF] Jiao | A parasitic metric learning net for breast mass classification based on mammography[END_REF], and brain tumor segmentation [START_REF] Liu | Refined-segmentation r-cnn: A twostage convolutional neural network for punctate white matter lesion segmentation in preterm infants[END_REF], but few methods seem to tackle the detection of very small lesions. On the other hand, on the side of supervised methods, research on automatic detection of PWML in MR images was first tackled by Mukherjee et al. [START_REF] Mukherjee | A fast segmentation-free fully automated approach to white matter injury detection in preterm infants[END_REF], who proposed a method that considers the correlation of pixels in 3D space. Besides, Liu et al. [START_REF] Liu | Trident segmentation cnn: A spatiotemporal transformation cnn for punctuate white matter lesions segmentation in preterm neonates[END_REF] proposed a spatiotemporal transformation structure in order to use the information between adjacent slices, which achieves higher performance than existing methods and consumes less computing resources than 3D CNNs. Despite the high contrast and low noise of MR images, the reported accuracy for the PWML detection task remains low with a Dice under 0.60 and a recall at 0.65. Finally, Erbacher et al. [START_REF] Erbacher | Priority u-net: Detection of punctuate white matter lesions in preterm neonate in 3d cranial ultrasonography[END_REF] started working on this task with cranial ultrasound (cUS) images and introduced a new model based on the 2D U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] and a soft attention model focusing on the PWML localization, called Priority U-Net, with the recall and the precision in the PWML detection task reaching 0.53 and 0.50 respectively.

As stated above, the detection and segmentation of PWML on cUS is extremely challenging. First, despite a higher resolution than MRI, US images are difficult to analyse because of their low contrast, the presence of speckle and the high variability related to the data acquisition process. Second, PWML are very tiny (in our dataset, the median volume of the lesions is less than 1mm 3 ), resulting in the lesion area being much smaller than the whole brain area, so the data imbalance problem between positive and negative pixels makes it a huge challenge for deep learning models to learn. Finally, the presence of numerous artifacts in the brain, very similar to true lesions in terms of gray levels, sometimes location or even shape, makes the distinction between true lesions and false alarms even more complicated. Recently, Dakak et al. [START_REF] Dakak | Deep learning-based defect detection in industrial ct volumes of castings[END_REF] developed an automatic approach to analyze discontinuities on industrial CT volumes by using a U-Net for segmentation followed by a classification network called CT-Casting Net. Although this paper does not discuss medical lesions, the common point is that discontinuities are very small and also similar to artefacts. Thus, it is expected that this 2-step approach can also be adequate in our present study.

In this work, we demonstrate that training the oversegmentation network with the expanded groundtruth helps to increase the number of detected lesions (higher recall). In addition, we introduce a novel architecture for multimodal classification, called 2.5D SC-Net, and show that performing a second stage of classification with more spatial context after segmentation improves the accuracy of the model by reducing the number of false alarms (higher precision). 2D predictions are then concatenated and compared to the 3D groundtruth for final assessment.

METHODOLOGY 2.1. Over-segmentation with Priority U-Net

Before training the model, the lesions in the ground truth are expanded by aggregating the foreground pixels within a 5slice sliding block along the coronal projection of the brain volume. It results in a label image with a higher percentage of foreground than the original label image, causing additional losses and helping to make training more effective.

Segmentation training is then performed on the modified ground truth with the Priority U-Net model (Fig. 1), which includes layers relying on 3D probabilistic maps derived from a spatial prior knowledge of PWMLs location and computed on the training dataset [START_REF] Erbacher | Priority u-net: Detection of punctuate white matter lesions in preterm neonate in 3d cranial ultrasonography[END_REF]. The output of the network usually includes many false positives, that will be removed during the next classification step.

Classification of PWML & False alarms

In parallel, we developed a novel multimodal classifier, called 2.5D SC-Net, trained on the joint fusion of the sagittal and coronal projections of the brain. Vignettes of size (32×32×2) centered on connected components (CC) from the 3D oversegmented mask are fed to the network as a 2-channel input (corresponding to each projection) to predict the class of the corresponding CC. The aim is to teach the network to differentiate true lesions from artifacts present in the brain, at a smaller scale but with more spatial context, while limiting the computational costs by using 2.5D instead of 3D volumes [START_REF] Liu | Trident segmentation cnn: A spatiotemporal transformation cnn for punctuate white matter lesions segmentation in preterm neonates[END_REF].

During training, features are extracted through convolutional blocks for each projection separatly, then joint fusion is performed by computing the weighted average on the flatten output of the feature extraction part of the network. Note that the weighting factors are fully learnt through the Weighted Average Layer (Fig 2).

During the testing phase, once the 3D intermediate mask is obtained after the first step of over-segmentation, 2D patches are extracted around the regions of interest (thumbnails from the image, centered around the connected com-ponents of the predicted mask) from the sagittal and coronal projections of the brain, concatenated and sent to the 2.5D SC-Net to identify the true PWML (Fig. 2). The intermediate mask is then corrected (i.e. the connected components predicted as false alarms are removed from the mask).

Class imbalance issue

As mentioned in the introduction, because the lesions are very small, the data imbalance problem between lesional pixels and background makes it a huge challenge for deep learning models to learn correctly. Therefore, the use of specific loss functions is considered to overcome this issue.

Self-Balancing Focal Loss: For a better training of the Priority U-Net, the Self-Balancing Focal Loss (SBFL) introduced by Liu et al. [START_REF] Liu | Trident segmentation cnn: A spatiotemporal transformation cnn for punctuate white matter lesions segmentation in preterm neonates[END_REF] is used in addition to the Dice Loss. The SBFL divides the whole loss into foreground loss and background loss part. It can automatically balance these losses and ultimately boosts the performance of the model.

SBF L 0 = -(1 -y pred ) × y pred × log(1 -y pred + ϵ) SBF L 1 = -y pred × (1 -y pred ) × log(y pred + ϵ) β = 0.4 × sum(SBF L 0 ) sum(SBF L 0 ) + sum(SBF L 1 ) + 0.5 SBF L = β × SBF L 1 + (1 -β) × SBF L 0
Where y pred is the intermediate output of the Priority U-Net and SBF L 0 and SBF L 1 are the focal loss of background and foreground pixels respectively. In order to segment PWML, we will focus on the segmentation of the lesion areas when balancing the loss of positive and negative samples. However, β should always be between 0.5 and 0.9 to ensure that the model does not only focus on the segmentation of positive areas. For that reason, we constrain β not to exceed 0.9 by applying a coefficient of 0.4 to the equation.

Weighted Cross-Entropy Loss: For the binary classification of the patches, we used the Weighted Cross-Entropy. Because our training dataset contained more negative than positive examples, but as we wanted to limit the trade-off between precision and recall, we performed a grid-search over 10 runs of 10-fold cross-validation and finally set α to 1.5.

EXPERIMENTS & RESULTS

Dataset

The 2D images are extracted from 54 reconstructed US brain volumes (including 29 with PWML) from 45 preterm babies whose mean age at birth was 31.6 ± 2.5 gestational weeks. In total, the dataset without preprocessing contains 414 lesions. The smallest lesion barely reaches 0.02mm 3 , while the largest is more than 41mm 3 . The median lesion size is 0.72mm 3 , which is extremely tiny. Besides, PWML have quite varied contrasts and do not really have specific shapes (punctate, ovoid or sometimes linear) 3. They are usually located in the center of hemispheres, near the lateral ventricles.

Data Preprocessing

As the acquisition process of the ultrasound images is performed manually by the pediatrician along the anterior/posterior axis of the brain, the brain scan does not always results in the same number of dynamic sequences (DICOM). In order to recover a complete volume, we completed this process by a reconstruction algorithm [START_REF] Martin | Automatic segmentation of the cerebral ventricle in neonates using deep learning with 3d reconstructed freehand ultrasound imaging[END_REF]. After that, a first preprocessing phase consists of extracting a sub-volume of size 128 × 128 × 128 in the top-right hemisphere, periventricular region of the brain for each patient.

In order to compare with MRI, a first filtering is performed on the size of the lesions for each volume to limit the number of lesions that are too small and to make the problem less complex. As a result, only 90% of the lesional volume is kept for each patient, which allows us to get rid of the tiniest lesions, that are usually not even visible in the MRI.

For the first over-segmentation step, lesions in the ground truth are expanded as described in the section 2.1, and 2D images of size 128 × 128 containing PWML are extracted along the coronal projection of the brain to train the Priority U-Net. Horizontal flipping is randomly applied with a probability of 0.5 for data augmentation.

For the second classification step, sagittal and coronal patches of size 32 × 32 are extracted from the original volumes and used to train the 2.5D SC-Net (Fig. 2), including various examples with real lesions, artifacts/false alarms and normal examples. Random affine transforms (rotation, shearing, scaling, and translation) and flipping were employed for data augmentation.

Experimental Setup

The proposed pipeline was implemented in Python 3.9 with Keras and TensorFlow backend. All the models were trained and tested with GPU. For each model, we performed a 10fold cross validation with 3 patients in the validation set and 22 patients in the training set.

The Priority U-Net was trained for 25 epochs with the Self-balancing Focal Loss and the Dice Loss, whereas the 2.5D SC-Net was trained for approximately 20 epochs using the Weighted-binary Cross-entropy Loss. The batch size is 4 for the segmentation network and 32 for the classification network. The initial learning rate was fixed at 10e-1 with the Adam optimizer and automatically decreased by a factor 0.1 when validation loss did not improved after 10 epochs.

Results

Table 1: Final results of the proposed approach (Priority U-Net with Highlighted Foreground + 2.5D SC-Net) compared to state-of-the-art algorithms. All these results are the medians of 10-folds cross-validation (± std).

Model Recall Precision Dice (TP)

U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] 53.41 (± 12) 54.12 (± 13) 49.31 (± 15)

Priority U-Net [START_REF] Erbacher | Priority u-net: Detection of punctuate white matter lesions in preterm neonate in 3d cranial ultrasonography[END_REF] 58 To quantitatively assess the quality of the PWML detection produced by the target pipeline, we employed 3 criteria to evaluate each model : the Recall and the Precision for the detection task but also the Dice on true positives (TP) to get an overview of the segmentation ability of the model. For each of these metrics, the value closer to 1 the better. The quantitative results are shown in Table 1. Note that the high variability in results may be explained by the limited number of patients available for each validation fold. The evolution of the results after training the Priority U-Net with the expanded labels (HF for highlighted foreground) seems to support the fact that expanding the size of the lesion groundtruth during training actually helps the segmentation network to detect more PWML and smaller objects in general, significantly increasing the recall from 58 to 73%. After performing classification with the proposed 2.5D SC-Net, the precision improves from 48 to 56%, which compensates for the degradation observed with the over-segmentation. Besides, the Dice also increases from 53 to 59%. Please note that the network optimization was more focused on the detection task, and improvements are currently under study for the segmentation task.

In addition, we also show that giving more spatial context as a 2-channel input and implementing joint fusion in the multimodal classifier architecture also helps to preserve the recall because when classification was performed with the CT-Casting Net on a single projection, the recall dropped from 73 to 69% after classification, whereas it decreases by less than 1% with the 2.5D SC-Net.

As a result, our model achieves better performances for PWML detection in US images compared to other methods, with a higher sensitivity to very small lesions.

DISCUSSION AND CONCLUSION

In this paper, we first preprocessed the label images to get a higher percentage of foreground, before training a network to perform an over-segmentation of the original lesions. This first step was followed by a second step of multimodal classification to limit the number of missclassified artifacts in the brain. Our work shows that expanding the groundtruth allows a better detection of very small lesions such as PWML in US images. We also demonstrate that focusing on the lesions at a smaller scale and with more spatial context helps to improve the specificity of the model as well. At the end of the proposed pipeline, we reach a higher recall and precision (72% and 56% respectively) than those obtained with other stateof-the-art techniques.

Many previous studies have focused on MRI-based lesion detection, and very few have addressed problems on a scale as small as PWML. While relatively few have conducted this task on US images, this work highlights once again the possibility of detecting brain lesions through ultrasound imaging.

Nevertheless, we anticipate that results might be improved by enriching the database with more patients, or exploiting even more spatial context using 3D methods or attention modules. Improvements on the segmentation results are currently under study and will be the object of future works as well.

Fig. 1 :

 1 Fig. 1: Full pipeline : The over-segmentation of PWML with the Priority U-Net improves the recall but produces many false positives. A second stage of classification allows us to differentiate true lesions from false alarms and improves the precision of the intermediate output.2D predictions are then concatenated and compared to the 3D groundtruth for final assessment.

Fig. 2 :

 2 Fig. 2: Classification of PWML/False Alarms with 2.5D SC-Net. The classification helps to differentiate between actual lesions and other brain artifacts at a smaller scale. 2 projections of the brain (sagittal and coronal) are given as a 2-channel input to the network. The previous mask obtained after the over-segmentation is corrected with the output of the classification.

Fig. 3 :

 3 Fig. 3: PWML examples from the Brain US Dataset (Top row : US images. Bottom row : groundtruth masks). PWML have varied contrasts and shapes, and are often difficult to distinguish from peripheral vessels or arteries in cross-section.

ACKNOWLEDGMENTS

This work was supported by the LABEX CELYA (ANR-10-LABX-0060) operated by the French National Research Agency (ANR) and the University of Lyon, within INSA Lyon.

COMPLIANCE WITH ETHICAL STANDARDS

The data from human subjects used in this work were obtained and treated in line with the principles of the Declaration of Helsinki. Approval was granted by the Ethics Committees of the institutions involved in creating the PWML database, from which these data were accessed. The authors have no relevant financial or non-financial interests to disclose.


Viet Cong

Hervé Di Phan

Cédric Benedetto

Didier Sauzeat

Simon Lesueur

Pouget

Phan

Hervé Di Benedetto
email: herve.dibenedetto@entpe.fr

Cédric Sauzéat

Didier Lesueur

Simon Pouget

B H Di Benedetto

Influence of hydrated lime on linear viscoelastic properties of bituminous mastics

Keywords: Linear viscoelastic behavior, Hydrated lime, Mastic, Bitumen, Complex shear modulus, Rheological modeling

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Many studies were carried out on mastics (i.e. blends of bitumen and only finest aggregates part, called filler) [START_REF] Palade | Linear viscoelastic behavior of asphalt and asphalt based mastic[END_REF][START_REF] Delaporte | Linear viscoelastic properties of bituminous materials: from binders to mastics (with discussion)[END_REF][START_REF] Delaporte | Linear viscoelastic properties of bituminous materials including new products made with ultrafine particles[END_REF];L i a oa n dC h e n2011; [START_REF] Van Rompu | New fatigue test on bituminous binders: experimental results and modeling[END_REF]Wangetal.2013;[START_REF] Mannan | Experimental investigation on rheological properties of recycled asphalt pavement mastics[END_REF][START_REF] Riccardi | Development of simple relationship between asphalt binder and mastic based on rheological tests[END_REF][START_REF] Santagata | Fatigue and healing properties of bituminous mastics reinforced with nano-sized additives[END_REF][START_REF] Jiang | Evaluating the mastic distribution of asphalt mixtures based on a new thickness threshold using 2D image planers[END_REF]. It is generally admitted that the mastic and not the bitumen is the real glue that bonds the larger aggregates inside the bituminous mixtures. Then a better understanding of thermomechanical behavior of mastic should help to establish a rational link between the behavior of bitumen and bituminous mixtures. Furthermore, the effect of filler can be more easily studied in mastic than in bituminous mixtures. The important role 2 Experimental procedures and materials

Dynamic shear rheometer (DSR)

Tests were performed using a dynamic shear rheometer (DSR) (Physica MCR 501), which is shown in Fig. 1. The DSR tests were performed on cylindrical specimens of mastic or bitumen sandwiched between two plates, classically called "plate-plate" DSR geometry. The applied torque and the rotation angle were continuously measured. During tests, the temperature of the sample was ensured with a thermal chamber.

In this investigation, the tested cylindrical sample (diameter 4 mm and thickness 1.5 mm) was placed in the DSR at 40 °C and cooled for 2 h before testing. Three or four repetition tests were performed for each material. A sinusoidal rotation was applied and the corresponding torque was measured. Shear strain γ(t) and shear stress σ(t) could then be obtained. They are written in complex notation in Eq. (1):

σ(t)= σ 0 e iωt and γ(t)= γ 0 e i(ωt-ϕ) (1)
where σ 0 and γ 0 are the amplitude of shear stress and shear strain, respectively. ϕ is the phase lag.

The complex shear modulus G * can be calculated as follows:

G * (ω) = σ 0 e iωt γ 0 e i(ωt-ϕ) = G * e iϕ = G 1 + iG 2 = G * cos ϕ + i G * sin ϕ (2)
where |G * |, G 1 ,a n dG 2 represent, respectively, the norm, the real part and the imaginary part of G * . Samples were loaded at different frequencies (f ) and temperatures (T ) as indicated in Table 1. The selected maximum strain amplitude that was selected for each T is also indicated in Table 1. This amplitude was selected to remain within the linear domain.

Tested materials

One bitumen and five mastics were studied. A 35/50 penetration grade bitumen (called B3550) was tested and the same bitumen was used to prepare the mastics that have different fractions of HL and limestone. The filler and HL content were chosen within the range used in bituminous mixture containing 5.1% bitumen and 8% filler in total mass (either containing only limestone filler, or 6.75% limestone filler and 1.25% HL, or 5.5% limestone filler and 2.5% HL). The composition in mass and the volume of the tested materials and their name are given in Table 2. A reference name is assigned M3550-5.1 (indicating the penetration grade bitumen and bitumen content in corresponding mixture) followed by information on the HL content: 0, 1.25, 2.5, vol(1.25%) or vol(2.5%). As indicated previously, presented study is part of a wider research on thermomechanical behavior of bituminous mixtures containing HL. Considering the lower density of HL (2.24 g/cm 3 ) than the one of limestone filler (2.8 g/cm 3 ), the substitution of limestone filler with the same mass leads to an increase of the global volume of filler. In order to differentiate effects of mass and volume, two mastics with the same volume of fine particles were produced with only limestone filler. The mastic named M3550-vol(1.25%) has the same filler volume fraction as M3550-5.1-1.25 (which is 35.6%) and M3550-vol(2.5%) has the same filler volume fraction as M3550-5.1-2.5 (which is 36.5%).

The figure (1, 2, 3 or 4) following the material name indicates the replicated test number.

3 Experimental results for G * For each material, it can be considered, as a first approximation, that data are situated on a unique curve when changing f and T . Then the time-temperature superposition principle (TTSP) can be applied to the materials.

The master curves at a reference temperature Tref equal to 15 °C, are plotted in Fig. 3 for |G * | (upper) and ϕ (lower). It presents |G * | (in log scale) and ϕ, respectively, as a function of the equivalent frequency (a T f ,wherea T is the shift factor presented in next section).

Shift factors

The construction of master curves requires shift factor (a T ) values. These values are presented in Fig. 4 as a function of T . This figure shows a good repeatability of obtained a T values between the three or four replicates of each material. Moreover, a T values are very close for the six tested materials. This result confirms previous results from our team showing this parameter is fixed by the bitumen whatever granular skeleton [START_REF] Delaporte | Linear viscoelastic properties of bituminous materials: from binders to mastics (with discussion)[END_REF][START_REF] Olard | General '2S2P1D' model and relation between the linear viscoelastic behaviors of bituminous binders and mixes[END_REF][START_REF] Pouget | Modeling of viscous bituminous wearing course materials on orthotropic steel deck[END_REF][START_REF] Mangiafico | New method to obtain viscoelastic properties of bitumen blends from pure and reclaimed asphalt pavement binder constituents[END_REF]. The two constants C 1 and C 2 of the WLF (Williams, Landel and Ferry) [START_REF] Williams | The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids[END_REF]) equation (Eq. ( 3)), used to fit a T data, are indicated in Table 3

.W ehave log(a T ) =- C 1 (T -T ref ) (C 2 + T -T ref ) (3)

Modeling

Experimental results are modeled using the LVE model, 2S2P1D, which was developed at the ENTPE. This model is a generalization of the Huet-Sayegh model consisting of two spring elements, two parabolic creep and one dashpot. An analogical representation is given in Fig. 5. It is widely used to model the LVE behavior in 1D and 3D of any bituminous material: bitumens, mastics and mixtures.

G * 2S2P 1D (ω) = G 00 + G 0 -G 00 1 + δ(jωτ) -k + (j ωτ ) -h + (j ωβτ ) -1 (4)
where j 2 =-1 ω: radian frequency, ω = 2πf k,h: exponents such that 0 <k<h<1; δ: constant G 00 : static modulus when ω → 0; G 0 : glassy modulus when ω →∞ β: dimensionless constant, related to Newtonian viscosity η = (G 0 -G 00 )βτ τ : characteristic time, function only of T .

To obtain G * at any T , it is possible to use the TTSP. In this case, only one parameter τ 0 and the shift factor value are required to calculate τ values (Eq. ( 5)); one uses

τ(T)= a T (T )τ 0 (5)
where a T is the shift factor at T . τ 0 is equal to the τ value at the chosen T ref .I th a st o be highlighted that only seven constants (G 00 , G 0 , δ,h,k,β,τ 0 ) are required to entirely characterize the LVE properties at a given T . In this paper, a T was approximated by the 3) for tested materials: master curves of the complex modulus, norm (upper) and phase angle (lower).

WLF equation (Eq. ( 3)). Finally, the number of constants amounts to nine, including C 1 and

C 2 fitted at T ref = 15 • C.
Figures 2 and3 show that the 2S2P1D model fits rather well experimental results of all tested materials on the whole range of f and T . 2S2P1D constants for all samples are given in Table 3.

In Table 3, the constants k, h, δ and β are identical for the six tested materials. This result confirms conclusion obtained by previous authors [START_REF] Delaporte | Linear viscoelastic properties of bituminous materials: from binders to mastics (with discussion)[END_REF][START_REF] Delaporte | Linear viscoelastic properties of bituminous materials including new products made with ultrafine particles[END_REF][START_REF] Olard | General '2S2P1D' model and relation between the linear viscoelastic behaviors of bituminous binders and mixes[END_REF][START_REF] Yusoff | Modelling the rheological properties of bituminous binders using the 2S2P1D model[END_REF][START_REF] Pouget | Modeling of viscous bituminous wearing course materials on orthotropic steel deck[END_REF]) that these constants are only dependent on the crude oil origin of bitumen, regardless of the penetration. It is recalled that the same 35/50 bitumen was used to produce all the tested materials. τ 0 , which is also bitumen dependent, and the constants G 0 and G 00 depend on filler content and characteristics. Considering the accuracy of the experimental device, |G * | values below 300 Pa could not be obtained. As a consequence any value of G 00 below 100 Pa can fit the data in the same way. A value G 00 = 0 was then arbitrarily chosen for 2S2P1D simulations. This constant G 00 should be focused on in other studies.

Analysis of the results

Normalized curves and link between the behaviors of bitumen and mastics

In this section, normalized curves, initially proposed by Olard and[START_REF] Olard | General '2S2P1D' model and relation between the linear viscoelastic behaviors of bituminous binders and mixes[END_REF][START_REF] Di Benedetto | Linear viscoelastic behavior of bituminous materials: from binders to mixes[END_REF] are considered to compare the materials properties.

The normalized complex modulus G * nor is defined by Eq. ( 6):

G * nor = G * -G 00 G 0 -G 00 (6)
Thanks to this parameter, the LVE behavior of each material can be described without the influence of G 0 and G 00 .Asthevaluesδ,k,h and β are identical for the six tested materials (Table 3), a unique G * nor simulated 2S2P1D curve in complex planes (Black diagram and the Cole-Cole axes) is obtained for all materials.

G *

nor is plotted in the Black diagram and the Cole-Cole axes in Fig. 6. The master curves are given in Fig. 7.

Figure 6 shows that all curves are superimposed. In order to obtain the same value of τ 0 = 0.00053 in Fig. 7 Figure 7 shows that all data are superimposed, which is an important output. It should be highlighted that all master curves are identical when reference temperature is adjusted to obtain the same value of τ 0 . This result confirms that filler (and more generally aggregates) only influences G 0 , G 00 and τ 0 values. All other constants are inherited from the bitumen. 3) for tested materials: master curves of the normalized complex modulus, norm (upper) and phase angle (lower) with τ 0 = 0.00053.

Several studies performed at the ENTPE [START_REF] Olard | General '2S2P1D' model and relation between the linear viscoelastic behaviors of bituminous binders and mixes[END_REF][START_REF] Pouget | From the behavior of constituent materials to the calculation and design of orthotropic bridge structures[END_REF][START_REF] Mangiafico | Influence of reclaimed asphalt pavement content on complex modulus of asphalt binder blends and corresponding mixes: experimental results and modelling[END_REF] showed that it is possible to predict the LVE behavior of mastic or bituminous mixture from the LVE properties of the bitumen and vice versa. The equation describing the relationship, also called the ENTPE transformation or SHStS (for shift, homothety shift and time shift transformation), is

G * mastic (f, T ) = G 00_mastic + G * bitumen 10 α f, T -G 00_bitumen G 0_mastic -G 00_mastic G 0_bitumen -G 00_bitumen (7)
If the value for bitumen G * bitumen is known at a temperature (T ) and a frequency (10 α f ), Eq. ( 7) gives the value for mastic G * mastic at T and f . Only three constants need to be known: G 00_mastic , G 0_mastic and α (this constant depends on the formulation). The α value can be determined from the parameter τ of 2S2P1D model. If the TTSP is verified, Eqs. ( 8)and( 9) can be considered:

G * (f, T ) = G * fa T (T ), T ref (8) τ mastic = 10 α τ bitumen (9)
The values of α are given in Table 4 for each of the tested materials. As an example, the comparison between experimental results and values of prediction using the SHStS transformation (Eq. ( 7)) from B3550 to M3550-5.1-1.25 is showed in Fig. 8. This figure reveals that the transformation gives a successful prediction of mastic LVE behavior from bitumen behavior on the whole T and f range. The same conclusion is valid for the other tested materials.

Effect of HL and volume of fine particles content

As indicated before, the five mastics were prepared with the same bitumen. For two mastics M3550-5.1-1.25 and M3550-5.1-2.5, HL replaces a part of limestone filler keeping the same total mass of filler than mastic M3550-5.1-0. As the volumetric mass of HL is lower than the one of limestone filler, the volume of fine particles increases with HL content.

Then the results obtained for these three mastics does not allow differentiating the effects of the two parameters: the introduction of HL and the volume increase. In order to quantify the influence of these two effects, the results obtained for mastics containing the same volume of fine particles (only limestone filler or limestone filler and HL) were also analyzed. M3550-vol(1.25%) was compared with M3550-5.1-1.25 (volume fraction of filler 35.6%) and M3550-vol(2.5%) was compared with M3550-5.1-2.5 (volume fraction of filler 36.5%). The average values of the different duplicated tests for each material were used in the analysis.

The complex reinforcement coefficient R * introduced by Delaporte [START_REF] Delaporte | Effect of ultrafine particles on linear viscoelastic properties of mastics and asphalt concretes[END_REF][START_REF] Delaporte | Linear viscoelastic properties of bituminous materials including new products made with ultrafine particles[END_REF]i su s e dt oc o m p a r et h eG * two mastics on the whole range of considered T and f . R * is defined as the ratio between the G * of two mastics (X and Y ) at the equivalent frequency (f e = a T f ) when the TTSP is validated:

R * = G * masticX (f e ) G * masticY (f e ) (10)
R * is a complex number. Its norm and its phase angle can be considered thus:

R * = |G * masticX (f e )| |G * masticY (f e )| ϕ R = ϕ masticX -ϕ masticY (11)
As a T values of the bitumen and the five mastics are very close and can be considered as equal, the same values of fe are obtained for the same value of f and T for the six tested materials. Then G * bitumen and G * mastic are taken at the same T -f couples to calculate R * . Three groups of comparison are proposed: -Mastics having the same mass of filler but different contents of HL, which gives information on the effect of HL at constant mass of filler. The two concerned mastics are M3550-5.1-1.25 and M3550-5.1-2.5 with reference mastic M3550-5.1-0.

-Mastics with the same volume of fine particles but different contents of HL. The two concerned mastics are M3550-5.1-1.25 (with HL), with reference M3550-vol(1.25%) (without HL) for a volume of filler: V filler = 35.6% V tot , and M3550-5.1-2.5 (with HL), with reference M3550-vol(2.5%) (without HL) for a volume of filler: V filler = 36.5% V tot .

-Mastics without HL having different volumes of filler. The two concerned mastics are M3550-vol(1.25%) having a volume of filler of 35.6% and M3550-vol(2.5%) having a volume of filler of 36.5%, with reference M3550-5.1-0 (volume of filler of 34.7%).

|R * | and ϕ R of mastics containing the same mass of filler are presented as a function of equivalent frequency (f e )i nF i g .9. This figure shows that the mastic made with HL (but also with higher volume of fine particles) exhibits a higher |G * | than the one produced without HL (|R * | is always greater than 1 on the whole range of considered T and f ). At (15°C;10 Hz), which is used in the French pavement design method, the reinforcement is approximately 22% (|R * |=1.22) with M3550-5.1-1.25 and approximately 36% (|R * |= 1.36) with M3550-5.1-2.5. The parameter ϕ R is always negative. This indicates that the phase angle is reduced for mastics with HL filler (having the same total mass of filler). Meanwhile this reduction is rather small (less than 3°for most of the data). It may be seen that stiffening effects are T -f dependent as was already observed [START_REF] Delaporte | Linear viscoelastic properties of bituminous materials: from binders to mastics (with discussion)[END_REF][START_REF] Lesueur | The mechanisms of hydrated lime modification of asphalt mixtures: a state-of-the-art review[END_REF][START_REF] Wortelboer | Rheological properties of bitumen/filler mixtures[END_REF]Phanetal.2016Phanetal. , 2017)). It is more pronounced at low f and/or high T . Almost no effect exists at high f /low T ,as|R * |=1andϕ R = 0. The influence of the HL with constant volume of filler is presented in Fig. 10.A g a i n , the |R * | values are always greater than 1 and increase when the equivalent frequency f e decreases (high T /low f ). The same conclusion than the one proposed for mastics at constant mass of filler (Fig. 9) can be drawn. Meanwhile, the stiffening effect is much less pronounced when volume of filler is maintained constant. For 1.25% of HL (M3550-5.1-1.25) the |R * | value is very close to 1 (and ϕ R close to 0) on the whole T -f range, indicating no effect of HL. For 2.5% of HL (M3550-5.1-2.5) the |R * | values are greater than 1.25 for f e lower than 1, which confirm HL effect when increasing HL content. Then the change in volume induced by the lower volumetric mass of HL can only partly explain stiffening for higher percentage of HL. At (15 °C; 10 Hz) the reinforcement is close to 8% (|R * |=1.08) with 1.25% of HL and 15% (|R * |=1.15) with 2.5% of HL. ϕ R values, which are mainly negative, are smaller than 2°for most of the data, indicating a small effect on this parameter.

Test results focusing on volume of filler effects without HL are presented in Fig. 11.The reinforcement effect by increasing the volume of filler is observed on the whole T -f range: |R * | is always greater than 1 and ϕ R is always negative (except for some data at high T ). At 15°C and 10 Hz, this effect is close to 14% (|R * |=1.14) when volume of filler increased from 34.7% to 35.6% and 18% (|R * |=1.18) when volume of filler increased from 34.7% to 36.5%.

As shown before (Fig. 6), the master curves of the G * nor of all tested materials are superimposed. This result indicates than only three constants of 2S2P1D model are different for the materials, namely τ 0 , G 0 and G 00 . The accuracy of the experimental device would not allow one to obtain G 00 . The obtained values for τ 0 (at 15 °C) and G 0 are plotted as a function of the volume of filler in Fig. 12, for the five mastics. This figure reveals that both parameters G 0 and τ 0 increase with HL and volume of filler content. The influence of each effect can be clearly identified.

Conclusions

The study presented in this paper aimed at evaluating the influence of HL on the LVE behavior of mastic. Five mastics produced with the same mass of filler or the same volume but with and without HL and the used bitumen were tested with a DSR. The influence of HL on LVE properties is quantified on a wide range of T and f by means of R * . From the obtained results and performed analyses, the following remarks can be made:

-The TTSP was verified as a first approximation for the six tested materials. The a T values are very close for the six tested materials.

-The LVE behavior is correctly simulated with 2S2P1D model on the whole range of tested T and f .

-G * nor presents superimposed curves for the six tested materials in the Cole-Cole and the Black axes. This result confirms that normalized Cole-Cole and Black curves are fixed by the bitumen.

-The transformation SHStS proposed by University of Lyon/ENTPE yielded successful predictions of mastic LVE behavior from bitumen LVE behavior.

-The reinforcement effect of HL on LVE behavior of mastics was observed and quantified. This reinforcement effect is T -f dependent, it is much more pronounced at high T and/or low f . It should be underlined that, if mass is kept constant, volume of filler increases when limestone is replaced by HL. This volume increase can explain a large part of the observed stiffening effect when introducing HL at constant mass of filler. The introduction of HL at constant volume of filler has nearly no effect for HL content of 1.25%, but starts to be slightly visible for a HL content of 2.5%.

Fig. 1

 1 Fig. 1 (a, left) DSR apparatus used for tests; (a, right) close-up on a sample; (b) scheme giving the size of the samples

Figure 2

 2 Figure 2 presents data and 2S2P1D model simulations (presented further) for the three or four replicates on the six materials in the Cole-Cole axes (a) and in the Black diagram (b).For each material, it can be considered, as a first approximation, that data are situated on a unique curve when changing f and T . Then the time-temperature superposition principle (TTSP) can be applied to the materials.The master curves at a reference temperature Tref equal to 15 °C, are plotted in Fig.3for |G * | (upper) and ϕ (lower). It presents |G * | (in log scale) and ϕ, respectively, as a function of the equivalent frequency (a T f ,wherea T is the shift factor presented in next section).

Fig. 2

 2 Fig. 2 Experimental data and 2S2P1D simulation curves (constants given in Table 3) for tested materials: Cole-Cole axes (upper); Black diagram (lower).

Fig. 3

 3 Fig. 3 Experimental data and 2S2P1D simulation curves (constants given in Table3) for tested materials: master curves of the complex modulus, norm (upper) and phase angle (lower).

Fig. 4

 4 Fig. 4 Shift factors a T and WLF fitting equation (Eq. (3)).

Fig. 5

 5 Fig. 5 Analogical representation of 2S2P1D model (Olard and Di Benedetto 2003; Di Benedetto et al. 2007).

Fig. 6

 6 Fig. 6 Experimental data for normalized complex modulus and 2S2P1D simulation curve (constants given in Table 3) for tested materials: Cole-Cole axes (upper); Black diagram (lower).

  , different T ref are chosen for each material (T ref = 10.99 • Cf o r B3550, T ref = 15 • C for M3550-5.1-0, T ref = 16.52 • C for M3550-5.1-1.25, T ref = 17.57 • C for M3550-5.1-2.5, T ref = 16.28 • C for M3550-vol (1.25%), T ref = 17.57 • C for M3550vol (2.5%)).

Fig. 7

 7 Fig. 7 Experimental data and 2S2P1D simulation curve (constants given in Table3) for tested materials: master curves of the normalized complex modulus, norm (upper) and phase angle (lower) with τ 0 = 0.00053.

Fig. 8 Table 4

 84 Fig. 8 Prediction of mastic M3550-5.1-1.25 LVE behavior from DSR tests on corresponding bitumen B3550 using a SHStS transformation.

Fig. 9

 9 Fig. 9 Complex reinforcement coefficient R * at T ref = 15 • C for mastics containing the same mass of filler but different HL contents: Norm (left) and phase angle (right).

Fig. 10

 10 Fig. 10 Complex reinforcement coefficient R * at T ref = 15 • C obtained with a reference mastic having the same volume of filler but different HL contents: Norm (left) and phase angle (right).

Fig. 11

 11 Fig. 11 Complex reinforcement coefficient R * : Norm (left) and phase angle (right) for mastics without hydrated lime (effect of the increase of volume of fine particles) at T ref = 15 • C.

Fig. 12 τ

 12 Fig. 12 τ 0 and G 0 as a function of volume of filler (%)

Table 1 T

 1 , f and strain amplitude used for DSR tests

	T (°C) 60504030 15	10 0 -10-12.9-16.5

γ (%) 3 1 1 0.30.3 0.10.10.03 0.01 0.01 f (Hz)0.03; 0.119; 0.475; 1.89; 7.54; 30 0.01; 0.038; 0.144; 0.548; 2.08; 7.9; 30

Table 2

 2 Tested materials: name and composition

	Material	% in mass				% in volume
		Bitumen Limestone	HL	Total of	Bitumen Limestone	HL	Total of
			filler		filler		filler		filler
	B3550	100	0	0	0	100	0	0	0
	M3550-5.1-0	40.2	59.8	0	59.8	65.3	34.7	0	34.7
	M3550-5.1-1.25	40.2	50	9.8	59.8	64.4	28.6	7	35.6
	M3550-5.1-2.5	40.2	40.1	19.7 59.8	63.5	22.6	13.9 36.5
	M3550-vol(1.25%) 39.2	60.8	0	60.8	64.4	35.6	0	35.6
	M3550-vol(2.5%)	38.3	61.7	0	61.7	63.5	36.5	0	36.5

Table 3

 3 2S2P1D and WLF constants for the tested samples (Reference temperature 15 °C)

	Material	Sample G *

a Chosen arbitrarily due to lack of accuracy of the experimental device Equation (

4

)givesG * at a fixed T :


Johanne Pirkin-Benameur

Denis Bouyer

Damien Quemener
email: damien.quemener@umontpellier.fr

Self-oscillating polymer membranes with chemically fueled pore size oscillation mediated by pH-responsive polymer

Keywords: Self-oscillating membrane, pH oscillator, stimuli-responsive membrane, polydopamine, pH-sensitive polymer

Soft-matter materials research has considerably evolved in the last decades, mainly by promoting responsive polymer systems. Up to now, the dynamic behavior in materials was always reached by the action of an outside trigger (pH, light, etc..). This constraint has been relieved in a new class of materials that experienced selfoscillation. In this work, the self-regulating pH cycles caused by a chemical oscillator will induce autonomous pH-sensible polymer chain movements at the membrane interface, causing continuous pore-size oscillation cycles and thus a self-oscillating flux. This work involved the functionalisation of polyethersulfone commercial membranes to achieve pore size oscillations. The pH-sensitive polymer, poly(methacrylic acid) (PMAA), was obtained by deprotection of poly(tert-butyl methacrylate) (PtBuMA) synthesized by RAFT polymerization. To adapt this functionalisation to all types of commercial membranes, a thin layer of polydopamine (PDA) was deposited on the top of the membrane, which then allows a Michael-thiol-ene reaction between PDA and thiolfunctionalised PMAA, obtained from prior aminolysis of PtBuMA. The functionalisation steps were characterized by XPS, SEM, water contact angle, and permeability measurements. Membranes were then placed in a filtration system containing a chemical pH oscillator to control the PMAA chain conformation through the pH cycle. Water permeation analysis showed a dependence between permeability and PMAA conformation, leading to the conclusion that there is indeed a continuous oscillation in membrane pore size.

2

Introduction

Our century is filled with many issues, such as chemical pollution [START_REF] Persson | Outside the Safe Operating Space of the Planetary Boundary for Novel Entities[END_REF], which is partly caused by the lack of responsiveness of current materials. This problem and resource shortages are forcing us to develop materials with an improved lifespan, notably through new functionalities. Nature creates materials that meet this challenge, because of their advanced compositions and functions. Thus, one of the major challenges in the materials field is to reach the autonomy level of natural materials. Nowadays materials explored to mimic the nature include stimuli-sensitive systems [START_REF] Wei | Stimuli-responsive polymers and their applications[END_REF]. Several stimuli have been studied to that purpose such as temperature [START_REF] Roy | New directions in thermoresponsive polymers[END_REF], pH [START_REF] Dai | {pH}-Responsive polymers : synthesis, properties and applications[END_REF],

mechanical strength [START_REF] Davis | Force-induced activation of covalent bonds in mechanoresponsive polymeric materials[END_REF], biological triggers [START_REF] Colson | Biologically Responsive Polymeric Nanoparticles for Drug Delivery[END_REF], and electromagnetic fields [START_REF] Fernández-Nieves | Engineering colloids with optical and geometrical anisotropies: decoupling size monodispersity and particle properties[END_REF] for applications such as chromatography [START_REF] Terefe | Application of stimuli responsive polymers for sustainable ion exchange chromatography[END_REF], surface functionalisation [START_REF] De Groot | Switching transport through nanopores with pH-responsive polymer brushes for controlled ion permeability[END_REF], and sensor [START_REF] Gao | A wireless magnetoelastic biosensor for rapid detection of glucose concentrations in urine samples[END_REF]. pH being one of the most common variables for biological reactions [START_REF] Schmaljohann | Thermo-and pH-responsive polymers in drug delivery[END_REF][START_REF] Yang | Synthesis of pH-sensitive hollow polymer microspheres and their application as drug carriers[END_REF], pH sensitive polymers have found various applications, especially in biomedical field [START_REF] Zarrintaj | Thermo-sensitive polymers in medicine: A review[END_REF]. pH-sensitive membranes have also been developed due to the potential brought by this trigger such as stimuli-responsive permeation [START_REF] Qu | A pH-Responsive Gating Membrane System with Pumping Effects for Improved Controlled Release[END_REF], pore size change [START_REF] Yi | A pH-responsive PAA-grafted-CNT intercalated RGO membrane with steady separation efficiency for charged contaminants over a wide pH range[END_REF][START_REF] Chen | Stimuli-Responsive Two-Dimensional Supramolecular Polymers Based on Trinuclear Platinum(II) Scaffolds: Reversible Modulation of Photoluminescence, Cavity Size, and Water Permeability[END_REF], nanoparticle fractionation [START_REF] Ye | High-Flux pH-Responsive Ultrafiltration Membrane for Efficient Nanoparticle Fractionation[END_REF], or antifouling properties [START_REF] Ma | Preparation of an antifouling and easy cleaning membrane based on amphiphobic fluorine island structure and chemical cleaning responsiveness[END_REF]. The pH responsiveness was introduced either during the membrane formation [START_REF] Qiao | Enzyme immobilization on a pH-responsive porous polymer membrane for enzymatic kinetics study[END_REF][START_REF] Aissou | Asymmetric Solvent-Annealed Triblock Terpolymer Thick Films Topped by a Hexagonal Perforated Lamellar Nanostructure[END_REF][START_REF] Luo | pHresponsive poly(ether sulfone) composite membranes blended with amphiphilic polystyreneblock-poly(acrylic acid) copolymers[END_REF] or via a post functionalisation [START_REF] Ye | High-Flux pH-Responsive Ultrafiltration Membrane for Efficient Nanoparticle Fractionation[END_REF][START_REF] Ma | Preparation of an antifouling and easy cleaning membrane based on amphiphobic fluorine island structure and chemical cleaning responsiveness[END_REF][START_REF] Salehi | Improved performance of thin-film composite forward osmosis membrane with click modified polysulfone substrate[END_REF][START_REF] Kochameshki | Graphene oxide grafted poly(acrylic acid) synthesized via surface initiated RAFT as a pHresponsive additive for mixed matrix membrane[END_REF][START_REF] Deng | PH-Responsive Copolymer Films Prepared by Surface-Initiated Polymerization and Simple Modification[END_REF]. However, the limitation of these membranes, and materials in general, is that they must be "manually" activated and deactivated by triggering the corresponding stimulus [START_REF] Walther | Viewpoint: From Responsive to Adaptive and Interactive Materials and Materials Systems: A Roadmap[END_REF]. Materials that cross this boundary gains autonomy, whether it is by allowing self-protection [START_REF] Wong | Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity[END_REF], self-reporting [START_REF] Gossweiler | Mechanochemical activation of covalent bonds in polymers with full and repeatable macroscopic shape recovery[END_REF], selfhealing [START_REF] Chen | A thermally remendable cross-linked polymeric material[END_REF], regenerating [START_REF] White | Restoration of large damage volumes in polymers[END_REF], or controlled degradation ability [START_REF] Park | Thermally triggered degradation of transient electronic devices[END_REF].

A standalone promising feature in this category that has recently been reported is self-oscillation. It involves coupling a sensitive material with a chemical oscillator. A chemical oscillator is a network of chemical reactions in which the concentration of the products changes on a cyclic basis until the source of energy is exhausted.

When coupled to a material, continuous periodic variation of macroscopic properties such as its volume or its hydrophobic-hydrophilic balance is observed. Since the first self-oscillating materials developed by Yoshida [START_REF] Yoshida | Self-Oscillating Gel[END_REF], many works have been carried out with the Belouzov-Zhabotinsky (BZ) oscillator, such as self-walking gel [START_REF] Maeda | Self-Walking Gel[END_REF], self-oscillating gel for mass transports [START_REF] Yoshida | Self-oscillating surface of gel for autonomous mass transport[END_REF], soft actuators of organized self-oscillating microgels [START_REF] Suzuki | Soft actuators of organized self-oscillating microgels[END_REF] or self-oscillating chemoelectrical interface of solution-gated ion-sensitive field-effect transistor [START_REF] Sakata | Self-oscillating Chemoelectrical Interface of Solution-gated Ion-sensitive Fieldeffect Transistor Based on Belousov-zhabotinsky Reaction[END_REF]. This concept doesn't allow only to create new materials, but also to discover new possibilities with well-known polymer properties like lower critical solution temperature autonomously modulated by photo-regulation [START_REF] Yamamoto | Self-oscillation of polymer and photo-regulation by introducing photochromic site to induce LCST changes[END_REF]. Despite the accomplishments already reached, the self-oscillating field still has a high potential, with recent progress achieved to precisely control the mechanical oscillation [START_REF] Homma | Autonomous Nanoscale Chemomechanical Oscillation on the Self-Oscillating Polymer Brush Surface by Precise Control of Graft Density[END_REF][START_REF] Geher-Herczegh | Delayed Mechanical Response to Chemical Kinetics in Self-Oscillating Hydrogels Driven by the Belousov-Zhabotinsky Reaction[END_REF], or simply by getting even closer to what nature is capable of. Indeed, in all the biological phenomena, the cellular membrane is a wonderful model because of the astonishing possibilities of action, from formation to self-destruction, only triggered by the membrane environment. Being able to reach this complexity level would resolve most of the issues in the membrane field.

To achieve this objective, our group recently introduced the concept of self-oscillating filtration membranes [START_REF] Benoit | Self-Oscillating Membranes with Polymer Interface Synchronized with Chemical Oscillator to Reproduce Lifelike Pulsatile Flow[END_REF]. From an alumina membrane functionalized by a pH-sensitive polymer, pH oscillations in the filtration cell made it possible to obtain transmembrane flux oscillations. The principle relies on a change in conformation of a polymer chain as a function of the pH which leads to cycles of opening and closing of the membrane pores.

Here a new strategy is proposed to explore a universal method of introducing self-oscillation functionality to all types of membranes, in particular polymer membranes. The overall strategy is depicted in Figure 1. The principle is based on the synchronization between a pH oscillator, here Bromate-Sulfite-Ferrocyanide (BSF) and a membrane made pH-sensitive. To obtain this membrane, poly(methacrylic acid) (PMAA) was chosen as a pHsensitive polymer thanks to its pKa at 4.8 [START_REF] Benoit | Self-Oscillating Membranes with Polymer Interface Synchronized with Chemical Oscillator to Reproduce Lifelike Pulsatile Flow[END_REF]. PMAA is synthesized by Reversible Addition-Fragmentation Chain Transfer (RAFT) polymerization of tert-butyl methacrylate (tBuMA), followed by hydrolysis of the resulting PtBuMA. After aminolysis of the RAFT end group, the PMAA chains are terminated by a thiol function which will be used subsequently for their grafting onto the membrane. To make this grafting possible regardless of the type of membrane, a thin layer of polydopamine is first deposited. A Michael thiol-ene reaction between PMAA and polydopamine then allows membrane functionalisation. In the presence of the pH oscillator, cycles of change in the conformation of the PMAA chains allow for a cyclic change of the pore size and therefore of the transmembrane flux. In this work, the influence of the polydopamine deposition time and the PMAA molecular weight on the oscillation properties is particularly studied.

Materials

Tert-butyl methacrylate 98%, containing 200 ppm monomethyl ether hydroquinone as inhibitor (Sigma) was filtered through an inhibitor removing resin for 15 minutes before use. Azobisisobutyronitrile (Fluka) was used after two recrystallizations in methanol. 4-cyano-4-(phenylcarbonothioylthio)pentanoic acid (Sigma), 1-Hexylamine (Fluka, 99%), chlorohydric acid 37% in weight, (trimethylsilyl)diazomethane solution 2.0 M in diethyl ether (Sigma) dopamine hydrochloride (Sigma), tris glycine buffer solution 10x concentrate (Sigma), potassium bromate (Sigma), bromocresol green, dye content 95% (Sigma), potassium hexacyanoferrate(II) trihydrate (Sigma), sodium sulfite (Sigma), sulfuric acid 99.9% (Sigma), bovine serum albumine (Sigma), dextran from Leuconostoc with Mn= 6000 g.mol -1 , Mn= 70000 g.mol -1 , Mn= 100000 g.mol -1 , Mn= 200000 g.mol -1 , Mn= 500000 g.mol -1 , Mn= 2 000000 g.mol -1 (Sigma), were used as received. Commercial polyethersulfone membranes with MWCO = 100 kDa, 63.5 mm diameter (Millipore®, PBHK06210) were washed 1 h by immersion in MilliQ water with water being changed three times before use.

Synthesis and Membrane Functionalisation

RAFT Synthesis of poly(tert butyl methacrylate)

Tert-butyl methacrylate (tBuMA) is placed in a flask with DMF at [tBuMA]= 0.5g.mL -1 , and the number of moles of AIBN and CTA corresponding to the target molar mass. As an example, the target ratio for MnPMAA of 20000 g.mol -1 is = 5 and =141. The solution is then degassed with nitrogen in an ice bath for 30 minutes. The reaction was carried out for 24 h at 70 °C. The polymer is then precipitated twice in a cold methanol/water mixture 4:1(v:v) and dried at room temperature under vacuum for 24h.

Aminolysis of poly(tert-butyl methacrylate)

The aminolysis procedure reported by Whittaker and al. [START_REF] Whittaker | Synthesis of Monocyclic and Linear Polystyrene Using the Reversible Coupling/Cleavage of Thiol/Disulfide Groups[END_REF] was adapted as follows: in a flask, PtBuMa is dissolved at a concentration of 6.5 ml/g in THF and cooled in an ice bath. A large excess of hexylamine ( = 20) is cooled in an ice bath. The two solutions are placed in two separate flasks, before being degassed with nitrogen for 30 minutes in an ice bath. The hexylamine solution is added to the polymer solution by syringe under nitrogen flow. The reaction was carried out at room temperature for 20 hours. The polymer is precipitated in a methanol/water mixture 4:1 (v:v) and dried at room temperature under vacuum for 24h.

Deprotection of PtBuMA-SH

The protocol reported by Cazares-Cortes et al. [START_REF] Cazares-Cortes | Polymethacrylic Acid Shows Thermoresponsivity in an Organic Solvent[END_REF] was adapted as follows: aminolyzed PtBuMa is dissolved in dioxane at a concentration [PtBuMA-SH] = 83 mg.mL -1 . Under stirring, an excess of HCl ( = 10) is added dropwise, before allowing the reaction to reflux for 16 hours at 85°C. Approximately one third of the solvent was then evaporated on a rotary evaporator before precipitating the polymer in cooled diethyl ether.

Methylation of PMAA to poly(methyl methacrylate) (PMMA)

In order to check the molecular weight distribution of PMAA in organic medium and avoid its aggregation in water during its analysis, PMAA was methylated into poly(methyl methacrylate) (PMMA) before being characterized in Size Exclusion Chromatography in tetrahydrofuran. The protocol reported by Lacik et al. [START_REF] Lacík | SEC Analysis of Poly(Acrylic Acid) and Poly(Methacrylic Acid)[END_REF] was used and adapted as follows: PMAA is dissolved in a 1:1 (v:v) mixture of THF / water at a concentration of 5mg/mL and placed in a flask. Trimethylsyldiazomethane is then added dropwise with stirring until the yellow color is constant and no further off-gassing occurs. The flask is left to stir until the solution has completely decolored (7h). The solution was then placed in a beaker in the fume hood and left in the open air until the solvent had evaporated completely.

PDA coating on commercial membranes

The protocol reported by Lee et al. [START_REF] Lee | Mussel-inspired surface chemistry for multifunctional coatings[END_REF] was adapted as follows: in a first step, three 24 mm diameter membranes are cut from the 64 mm commercial membrane, before being washed for 1 hour in Milli-Q water. A pH = 8.5 solution is prepared using a 10: 1 Milli-Q water/tris glycine buffer solution. Dopamine is added to obtain a concentration of 0.1 mg.mL -1 . Membranes are then immersed 15 minutes directly to the dopamine solution under stirring (70 rpm). Once the reaction is complete, the membrane is washed directly with milli-Q water, then subjected to an ultrasound bath for 15 minutes, and stored in milli-Q water/ethanol 95:5 (v:v).

PMAA-SH grafting on PDA-coated membranes

A 10 -5 mol solution of PMAA is prepared in milli-Q water at pH = 8.5. The PDA-coated membrane is placed in the solution, and the reaction is carried out at 55°C for 2h. Once the reaction is complete, the membrane is rinsed with milli-Q water, subjected to an ultrasound bath for 15 minutes, and then stored in milli-Q water/ethanol 95 : 5 (v : v). UV-Vis Spectroscopy. Polymer solutions before and after aminolysis were prepared at the same concentration. The analysis was performed in a glass cuvette with the UvLine connect series 940 (SECOMAM) from 200 to 800 nm in absorbance.

Membrane characterization

Water Contact angle (WCA). The WCA analysis was conducted with the ILMS GBX and Digidrop GBX software. The membrane is dried in an oven, before being glued to a support prior the analysis. WCA was measured with a drop volume of approximately 1.7 µL. About 10 measurements are made before being averaged for each trial, and three trials are performed.

Scanning Electron Microscopy (SEM). SEM analyses were conducted using a Hitachi S-4500 (Tokyo, Japan) device operating at spatial resolution of 1.50 nm at 15 kV energy. The samples of 1cm x 0,5 cm were dried and coated with an ultrathin layer of electrically conducting platinum deposited by high-vacuum evaporation. Energy-dispersive X-ray spectroscopy analysis (EDX) was taken with Zeiss EVO HD15 microscope coupled with an Oxford X-MaxNSDD EDX detector. Surface porosity has been obtained from binarized SEM images using Image J ® software with = !" # $!% × 100.

Gravimetric analysis. Sample gain in weight after functionalization was estimated on samples dried for 1 h in a vacuum oven at 50°C, before being weighed with a Precisa XT 220 A balance.

Porosity measurement. Membranes were previously weighed after drying for 2h in a vacuum oven at 50°C, before being placed under ultrasound for 1 hour in a beaker of 1-butanol until no more bubbles escape from it. The membranes were then weighed directly after removal from the beaker and blotting excess of 1butanol from the membrane surface. The equation for measuring the porosity (P) is as follows [START_REF] Gu | Formation of poly(vinylidene fluoride) (PVDF) membranes via thermally induced phase separation[END_REF]:

)*%, = *-. --0 ,1 0 1 0 -. + *1 . -1 0 ,-0
with W1 = initial mass, W2 = mass after immersion in 1-butanol, ρ1 = polyethersulfone density (1.37 g.mol -1 ) and ρ2 = 1-butanol density (0.8 g.mol -1 ) Sieving curves. Dextran of different molecular weights were used to prepare aqueous solutions at a concentration of 1000 ppm. 10 ml was then poured into a dead end stirred filtration cell at 1 bar. The first 2mL of permeated water were discarded, and the next 4mL were taken as permeate solution. The last 4mL remaining in the filtration cell constituted the retentate solution. Membranes were washed 10 minutes in water under ultrasounds between each attempt. The solution signal was then analyzed by a Water 2414 refractive index detector.

Liquid-liquid porometry. It was conducted with PRM-2000-LL-R porometer from G.E.P.S. France.

Prior to the measurement, same amount of MilliQ water and 1-butanol was "mixed" and let to separate by decantation in order to saturate the two phases. The aqueous and organic phases were then stored separately.

Before the porometry experiment, the membrane was completely soaked into the aqueous phase before being placed in a porometer cell. Increasing pressure from 0 to 6 bar was applied on the organic phase side of the membrane to progressively replace the aqueous phase.

Zeta potential measurement. The surface charge (zeta potential) of the membrane was estimated using SurPASS electrokinetic analyzer (Anton Paar, GmbH, Graz, Austria) based on the streaming potential method.

Washed membrane samples were mounted in an adjustable gap cell and soaked in 1 mM KCl. The cell height was fixed at 100 mm. The electrolyte solution was circulated in the cell between two pieces of membrane. The zeta potential was calculated using the Helmholtz-Smoluchowski equation from the measured streaming current as a function of pH.

X-Ray photoelectron spectrometry (XPS). XPS was carried out with the ESCALAB 250 device from

ThermoElectron. The excitation source was the monochromatic source, Al Kα line (1486.6 eV). The surface analyzed has a diameter of 500 µm. Photoelectron spectra were calibrated in binding energy with respect to the energy of the C-C component of carbon C1s at 284.8 eV. pH analysis. The HI 5221 (Hanna) instrument was calibrated with pH 4, 7 and 9 buffer solutions.

Measurements were then recorded every second. Chemical resistance. Resistance of the membranes to the acidic and alkaline environments was estimated by comparing the initial water flux of the grafted membrane at 1 bar of pressure drop with the flux after an immersion of the membrane during 15 days at pH=3 for acidic condition, and pH=10 for alkaline condition.

Tensile test. Mechanical properties of the membrane were measured with a 5kN ProLine ZwickRoell universal testing machine and screw grips of 10kN. A 1x2cm sample membrane was cut and placed on the screw grip while still wet from the conservation solution. The measurement started with 2cm between the two screw grips.

Water permeation analysis and acquisition of oscillations

The 22 mm diameter membrane was placed into a homemade stainless steel 22 ml dead-end filtration cell. A 1L Amicon tank filled with MilliQ water was connected to the cell with adjustable pressure. Permeated water was measured using a balance connected to the S232 Data Logger software with a 0.599s time step acquisition. A conditioning step was applied to all membranes by applying a pressure drop of 4 bar during 30 minutes before any permeability measurement. SI28). The pH oscillator allows cyclic variations of the pH with wide and regular amplitude of oscillations between 3.5 and 6.5 under the membrane filtration conditions (Figure SI24). The targeted k0 value, which corresponds to the inverse of the residence time in the filtration cell, was 1.10 -3 s -1 .

Modeling of Bromide-Sulfite-Ferrocyanide (pH and ionic strength)

Bromate-sulfite-ferrocyanide (BSF) pH oscillator has been modeled as described in our previous work [START_REF] Benoit | Self-Oscillating Membranes with Polymer Interface Synchronized with Chemical Oscillator to Reproduce Lifelike Pulsatile Flow[END_REF]. The system of Ordinary Differential Equations (ODE) that described chemical reactions was numerically solved using finite element software: COMSOL Multiphysics® 5.4. A variable time step was used to improve the numerical resolution. The evolution of ionic strength (I) during pH oscillations was carried out by taking into account the following ionic species: Cations: Na + , H + , K + Anions: OH -, HSO4 -, SO4 2-, SO3 2-, HSO3 -, BrO3 -, Br -, HFe(CN)6 3-, Fe(CN)6 4- Ionic strength was calculated over time by the following equations:

Results and Discussion

Polymer Synthesis

Scheme 1 -Overview of the thiol-functionalized polymethacrylic acid (PMAA) synthesis by RAFT polymerization 9

RAFT synthesis of PtBuMA

In a first step, a thiolated pH sensitive PMAA was prepared by RAFT polymerization of tBuMA followed by its aminolysis and hydrolysis (Scheme 1). MAA was not polymerized directly as its corresponding PMAA polymer is not soluble in an organic solvent and hard to characterize in water due to its inclination to self-aggregate. The SEC curves of all PtBuMA polymers demonstrate distinct molecular weight distributions and low dispersity as expected from a controlled polymerization (Figure SI-1). PtBuMA was obtained with monomer conversions greater than 70% for all polymers (Table SI-1).

Aminolysis of PtBuMA

As previously explained, the grafting of PMAA onto the polymer membrane was carried out by a

Michael thiol-ene reaction on a deposited polydopamine top layer. For that, an aminolysis of the RAFT end group is required to yield a thiol group at the end of the PtBuMa chain (Scheme 1).

The aminolysis was characterized by UV-visible spectroscopy following the absorbance peak at 300 nm, related to the aromatic RAFT end group. A large decrease in the signal attests to the success of the reaction with a yield estimated up to 92% (Figure SI-2a, Table SI-1). The SEC curves before and after aminolysis (Figure

SI-2b

) demonstrate the integrity of the polymer after the reaction, although some slight chain-chain coupling was observed due to a thiol oxidation into disulphide.

Deprotection of PtBuMA from PMAA

The aminolyzed PtBuMA was then converted into PMAA by hydrolysis of the tert-butyl group. The completion of the reaction is shown by the disappearance of the tert-butyl signal in 1 H NMR (Figure SI-6).

The FTIR spectra of the polymers were carried out after each step (Figure SI-3). The PtBuMA and aminolyzed PtBuMA spectra are nearly identical as expected, since the very low concentration of the RAFT end group does not enable any detection. Peak at 2992 cm -1 is assigned to the C-H stretching of alkane, and 1735 cm - 1 to the C=O stretching of ester group. After hydrolysis, FTIR spectrum of the resulting PMAA shows the appearance of a peak at 3300-2500 cm -1 assigned to O-H stretching of the carboxylic acid group, as well as a peak at 1715 cm -1 corresponding to the C=O stretching of the carboxylic acid group, in agreement with the 1 H NMR.

As previously reported [START_REF] Benoit | Self-Oscillating Membranes with Polymer Interface Synchronized with Chemical Oscillator to Reproduce Lifelike Pulsatile Flow[END_REF], PMAA is difficult to characterize in aqueous SEC due to the presence of aggregates. To check the distribution of molecular weights after hydrolysis of the tert-butyl group, PMAA was methylated in poly(methyl methacrylate) (PMMA) and analyzed in THF SEC (Figure SI-4). A shift of the entire distribution toward lower molecular weights is observed, as expected, with a maintained low dispersity of 1.06.

Note that the secondary pic corresponds to a double molecular weight, which is due to thiol-thiol coupling, as explained before. The functionalisation of a commercial polyethersulfone membrane (PES) by the pH sensitive PMAA was mediated through the deposition of a thin polydopamine (PDA) layer, as described in Figure 2. This technique, already reported in the literature [START_REF] Chen | Mussel-Inspired Polydopamine Coating Enhances the Intracutaneous Drug Delivery from Nanostructured Lipid Carriers Dependently on a Follicular Pathway[END_REF], is very versatile and can be applied to all types of membranes without physicochemical constraints due to the ability of the PDA to stick anywhere. Polymer grafting was then performed simply by immersion of the PDA-coated membrane in a PMAA solution. This functionalisation process occurs in water under mild conditions, making any potential scale-up environmentally friendly. The functionalisation was indirectly characterized by the flux measurement (Figure 4a). A flux decrease is observed after each functionalisation step from virgin PES membrane to PDA-modified membrane to PMAAgrafted membrane. However, the decrease does not appear to be correlated with the molecular weight of the grafted PMAA and ranges from 10 to 60% for the same PDA deposition time (15 min).

Membrane functionalisation

An increase of the surface hydrophilicity was also observed after each step, illustrated by the decrease of the water contact angle (Figure 4b). If the trend is clear and constant, the water contact angle seems to be sample dependent, with a dependence more relying on the varying surface roughness rather than the results of the PMAA molecular weight for instance. Switching the water pH of the droplets from 7 to 3 did not provide a clear tendency. It is assumed that it is the result of two antagonist effect: an acidic pH below the PMAA pKa will result in the pore opening due to the polymer contraction. However, PMAA also became less hydrophilic at this pH, as did the membrane surface.

Each step of membrane modification has been characterized by SEM (Figure 4c-h Gravimetric analysis was carried out to estimate the weight of polymer deposited at the membrane surface after PDA coating and PMAA grafting (Table SI-3). As expected, a correlation between the PDA deposition time and the PDA quantity deposited is observed. Because PMAA is grafted onto the PDA layer, a direct link is observed between the quantity of PDA deposited and the yield of PMAA grafting. Interestingly, for the same PMAA grafting time, the grafted PMAA was 2.4 times higher when the deposited PDA was higher.

Here it is suspected that 18h PDA coating has increased surface roughness and thus the specific PDA surface available for PMAA grafting. Young moduli (tensile test) were measured to see if the PMAA grafting would have an impact, but it appears that the deposition is too thin to make any significant difference (Table SI-4).

The surface composition was characterized by XPS analysis (Figure . However, unless a sufficient PDA layer is deposited (18h), the elemental compositions (C, N, O and S) of the PDA coated membranes remain similar to the PES commercial membrane. This is a further proof that the PDA deposition time chosen (15 minutes) allows a very thin layer to be deposited, sufficient to be able to functionalize without drastically changing the chemical nature of the interface. The XPS data (Table SI -5) shows that the carbon and nitrogen concentrations in PMAA grafted membranes are similar than in the commercial membrane, but the oxygen concentration rises with the polymer grafting, which is in line with the theory. It also appears that the sulfur concentration decreases for all the grafted samples, proving that deposition on the PES membrane is taking place.

A measurement of the streaming potential was performed (Figure SI-7). A significantly different evolution of the calculated negative zeta potential is observed, attesting to the difference in surface chemistry.

However, a similar isoelectric point (IEP) at pH 3-3.5 for the three samples, in agreement with reported PES IEP [START_REF] Sadegh | Protein-polymer interaction: Transfer loading at interfacial region of PES-based membrane and BSA[END_REF], suggests that only a partial coverage of the membrane surface occurs.

pH-induced self-oscillating flux

In order to yield a self-oscillating behavior, a pH-sensitive polymer membrane is mounted into a dead- The pure water flux of the virgin PES membrane, the PDA coated membrane, and the PMAA grafted membrane were then measured at pH values above and below the PMAA pKa to assess its effect (Figure 5).

Whereas a slight increase in flux at basic pH is observed for commercial and PDA covered membranes, a clear flux decreases of 40% at pH=8 is measured when PMAA is grafted onto the membrane. Indeed, above PMAA pKa value, the polymer is in an expanded conformation which obstructs the pores and reduces their size. Since the dependence is inversed compared to the PDA coated membrane, it can be deducted that PMAA membrane is pH-sensitive and that a modulation of the pH results in a proportionate change in the water permeability. It should be noted that the tolerance of the membrane towards acidic and alkaline operating conditions was checked to avoid any misinterpretation. The water flux at ΔP = 1 bar of the virgin PES membrane and the PMAA grafted membrane was measured at pH 3 and 10 for 15 days without showing any significant change (JPES MEM, pH3=278±51 L.h -1 .m -2 ; JPES MEM, pH10=181±24 L.h -1 .m -2 ; JPMAA MEM, pH3=125±3 L.h -1 .m -2 ; JPMAA MEM, pH10=129±5 L.h -1 .m -2 ).

As explained before, autonomous cyclic pH change will be carried out thanks to the BSF chemical oscillator setup in the filtration cell. BSF is an oscillating network of chemical reactions, which can be summarized by a set of 7 reactions [START_REF] Benoit | Self-Oscillating Membranes with Polymer Interface Synchronized with Chemical Oscillator to Reproduce Lifelike Pulsatile Flow[END_REF] (Table SI- Figure 6b shows that there is a more or less pronounced decrease of the oscillation amplitude in time, with a variable intensity depending on the PMAA molecular weights. The PMAA chains remain hydrophilic all the time including below the pKa of the PMAA. However, as reported in literature, the grafted polymer onto the membrane surface may not be fully accessible to the bulk solution and some charges can remain avoiding a complete polymer collapsing over the cycles [START_REF] Schacher | Self-Supporting, Double Stimuli-Responsive Porous Membranes From Polystyrene-block-poly(N,N-dimethylaminoethyl methacrylate) Diblock Copolymers[END_REF]. It can be noted that the greatest decrease in amplitude was observed with MEM_PMAA16k. The oscillation periods represented in Figure 6c remain relatively stable over time, except for MEM_PMAA20k, for which a slight increase is observed over time. As the oscillation period depends on the oscillator mechanism, it is complex to analyse the evolutions. However, it appears that all the periods are shorter than for the BSF oscillator alone, which shows that the membrane participates in the oscillating system. The molecular weight of the grafted PMAA appears to modulate both the period and the amplitude, as summarized in Figure 7. When the two parameters are compared in Figure 7, it appears that both values increase with the molecular weight of PMAA, then decrease for PMAA20k, before increasing again at PMAA22k. A hypothesis is that a steric exclusion occurs between Mn= 16 000 g.mol -1 and 20 000 g.mol -1 . A large amplitude can be observed when the PMAA is located inside the pores. When the PMAA chain length is increased, the flux change, corresponding to the compact and extended conformations of PMAA in the pores, is larger. However, above a threshold value of PMAA molecular weight, some steric hindrance can occur, preventing grafting inside the pores and thus leading to a decrease in the flux oscillation amplitude. A second increase above 20 000 g.mol - 1 is also observed which can be explain by an obstruction of the pores from the membrane surface. If the hypothesis is correct, the pore size distribution for MEM_PMAA10k and MEM_PMAA20k would be significantly different. Indeed, MEM_PMAA10k would have a reduced pore size due to the presence of the polymer chains in the pores, whereas grafting of MEM_PMAA20k would have a lower pore size impact, being mostly located at the membrane surface. The sieving curves, carried out with dextran of different molecular weights, are presented in Figure 8. The sieving curves were measured for two grafted PMAA molecular weights, PMAA10k and PMAA20k.

It should be first mentioned that a weak reproducibility was observed when repeating the sieving curve measurements on different samples of the same membrane as illustrated by the large error bars obtained for the virgin PES membrane (Figure SI-28) [START_REF] Peinador | Liquid-liquid displacement porosimetry for the characterization of virus retentive membranes[END_REF]. To try to overcome its impact, the sieving curves were made on the same membrane for all the functionalisation steps (Figures 8). Liquid-liquid porometry (Figure 9) shows that the commercial membrane has an average pore size of 22 nm and a relatively large dispersity. The PDA deposition doesn't seem to affect significantly the pore size distribution.

However, when PMAA is grafted, the pore size distribution is shifted towards lower values in all cases, showing that PMAA grafting is decreasing the pore size with a higher shift towards lower pore size with increasing PMAA molecular weight, in agreement with the evolution of the water flux as previously discussed. However, for the membranes grafted with PMAA ≥ 20 000 g.mol -1 , a double distribution is observed with smaller pores as in the case observed with PMAA lower than 20 kg.mol -1 , but also with a remaining distribution of pore size from the initial PDA membrane. A hypothesis is that a partial steric exclusion of PMAA from the membrane pores appended leading to leave unfunctionalized a part of the initial pore size distribution. This is in agreement with the break in water flux amplitude trend observed in Figure 7 at this PMAA molecular weight. We didn't succeed in showing a clear shift of the pore size distribution from the sieving curves or from the porometry measurement when comparing the results at pH below and above the PMAA pKa (data not shown). To understand that observation, the expected pore size variation resulting from a pH below and above the PMAA pKa was estimated from the measured water flux variations according to the Poiseuille law (equation 1) (Table SI- [START_REF] Fernández-Nieves | Engineering colloids with optical and geometrical anisotropies: decoupling size monodispersity and particle properties[END_REF].

A pore size change of maximum 2.5 to 6.5% (0.4 to 1.5 nm) is expected which explains the difficulty to directly observe it following the pore size. It is however clearly visible in the flux measurement thanks to dependence of the flux to the fourth power of the pore radius. We can therefore conclude that water flux self-oscillations have been yielded without significantly alter the solute retention of membrane.

The BSF oscillator involves many ionic species whose concentration can vary with time depending on the oscillatory regime. Given our use of a weak polyelectrolyte (PMAA), the impact of ionic strength on water permeation results was checked. For this, the ionic strength of the oscillator (400 mmol.L -

Figure 1 -

 1 Figure 1 -General strategy carried out to produce self-oscillating polymer membranes

  For a water permeation under pH oscillations, aqueous feed solutions separated in two tanks entered premixed at the same flow rate into the dead end filtration cell (Figure SI28) (Tank 1: [KBrO3]0 = 75 mM and [sodium bromocresol green]0= 2.15 .10 -3 mM; Tank 2: [Na2SO3]0 = 70 mM, [K4Fe(CN)6]0 = 15 mM, [H2SO4]0 = 7.5 mM). BSF pH oscillator was set up in the filtration cell under pressure and the relative pH evolution was monitored by video acquisition of the solution color change thanks to a pH indicator (bromocresol) (Figure

Figure 2

 2 Figure 2 -a) Synthesis and coating of polydopamine onto polyethersulfone membrane followed by b) grafting of pH-sensitive PMAA chains through Michael thiol-ene reaction.

Figure 3 -Figure 4

 34 Figure 3 -Evolution of the flux of the PES membrane after PDA deposition (JPDA) compared to the flux of the virgin membrane (J0).

Figure 5 -

 5 Figure 5 -Water flux ratio at pH 8 and 3 of the commercial PES membrane (MEM), the membrane coated with PDA for 15 min (MEM PDA), and the membrane grafted with PMAA5k (MEM_ PMAA5k) at ΔP= 1 bar.

  [START_REF] Colson | Biologically Responsive Polymeric Nanoparticles for Drug Delivery[END_REF]. The cyclic predominance of certain reactions in the BSF oscillator leads to a modulation of the pH within a domain of residence time in the filtration cell. The residence time domain to observe the pH oscillations was previously estimated from the construction of a bifurcation diagram (Figure SI-21)[START_REF] Benoit | Self-Oscillating Membranes with Polymer Interface Synchronized with Chemical Oscillator to Reproduce Lifelike Pulsatile Flow[END_REF] and a k0 value of 10 -3 s -1 was targeted in this work, k0 being the inverse of the residence time in the filtration cell. The pH oscillations produced from a BSF oscillator for a k0 of 10 -3 s -1 have an average period of about 390 s after stabilization with a pH varying cyclically and continuously between 3 and 6.5 (Figure SI-22). PMAA pKa being around 4.8, then the pH oscillations will enable change of conformation of PMAA chains grafted on the membranes. Because of the inability to directly follow the pH change in a pressurized filtration cell, a colored indicator was used to visually track the pH oscillation. The BSF reaction alone was filmed and monitored by a pH-meter to see if the colored indicator is a reliable tracking system (Figure SI-23). It appears that the visual color change and the pH change match perfectly.

Figure 6 -

 6 Figure 6 -a) Self-oscillating flux of functionalized membranes synchronized with a BSF oscillator with the following conditions: [KBrO3]0 =75 mM, [Na2SO3]0 =70 mM, [K4Fe(CN)6]0 = 15 mM, [H2SO4] = 7.5 mM for T

2 )Figure 7 -

 27 Figure 7 -Average amplitude and period of water flux oscillations for each PMAA molecular weight

Figure 8 -

 8 Figure8-Sieving curve for •) PDA coated membrane ▲) grafted membrane with PMAA =10 000 g.mol -1 and ▼) grafted membrane with PMAA =20 000 g.mol-1

  It appears that the PDA deposition has not clearly shifted the sieving curve towards lower pore values as expected, which could be explained by a change in the surface properties (hydrophilicity, roughness) counterbalancing the pore size decrease. Grafting of PMAA has shifted the sieving curve to lower pore size, in agreement with the flux decrease observed previously. However, considering the error bars, the sieving curves as measured with the two PMAA molecular weights did not highlight a significant difference.

Figure 9 -

 9 Figure 9 -Liquid-liquid porometry results for PES commercial membrane, PDA-coated membrane (15 min) and membranes grafted with PMAA of different molecular weights.

  1 ) was reproduced by adding NaCl (0.4 mol.L -1 ) to water. As shown in Figure SI-25, the transition from pure water to salted water was not accompanied by a change in flux. In addition, a theoretical modeling of pH and ionic strength oscillations was performed (Figure and only a weak ionic strength oscillation is observed between 414 and 420 mmol.L -1 . Thus, we can conclude that the ionic strength imposed by the pH oscillator does not impact the water permeation results. The flux oscillations are therefore only the results of the expansion-contraction cycles of the PMAA inside the membranes pores.

  polymer membranes showing continuous periodic flux evolution have been successfully prepared. The flux oscillations were obtained by coupling a pH-sensitive polymer membrane to a pH oscillator (BSF). For this, PMAA was synthesized with different molecular weights and grafted onto a commercial PES membrane via an intermediate layer of PDA. Each stage of polymer manufacturing and membrane functionalisation has been precisely characterized. Secondly, the pH oscillator was stabilized in a filtration cell and brought into contact with the pH-sensitive membrane. The PMAA grafted onto the membrane responds almost instantaneously to changes in pH and oscillates between two chain conformations (extended and collapsed). Therefore, an autonomous and cyclic membrane pore size change was observed leading to the selfoscillation of the membrane water flux. Interestingly, although water flux is periodically modulated, the corresponding pore size change due to the pH modulation is estimated to be less than 6%, which has immeasurable impact on the solute retention of membrane. In addition, the amplitude of the flux cycles can be modulated by the molecular weight of the PMAA grafted onto the membrane until a threshold value of 20 000 g.mol -1 , above which a polymer exclusion from the pores was observed. In perspective to this work, the effect of flux oscillations on the challenging fouling phenomenon will be explored since a perpetual change of the membrane surface properties combined with an adhesion of retained species hampered by flux oscillations could offer a more sustainable alternative to the usual mechanical and chemical membrane cleanings. Bringing selfoscillating behaviour to a polymer filtration membrane represents a further step towards the design of autonomous membranes.Credit authorship contribution statementJohanne Pirkin-Benameur: Conceptualization, Methodology, Data curation, Writing -original draft, Writingreview & editing. Denis Bouyer: Conceptualization, Methodology, Data curation. Damien Quemener: Conceptualization, supervision, acquisition of funds, data curation, writing -review & editing.

  ). Although the top surface images do not show any real difference after functionalization steps, a thin layer of PDA and PMAA is

	well observed in the cross-section images. The EDX mapping (Figure SI-8) shows that PMAA is uniformly
	grafted with visible enrichment of carbon on the surface. The membrane bulk porosity was estimated from 1-
	butanol gravimetric analysis and a stable value around 77% is found for all membranes (porosity MEM = 77.5%;
	porosity MEM PDA 15 min = 77.7%; porosity MEM PMAA_10k = 77.2%). Since only a surface modification is performed
	on an asymmetric PES membrane, the overall porosity is in return not affected. On the contrary, the time of PDA
	deposition is found to change surface porosity, as measured by SEM image treatment (porosity MEM = 7.8%;
	porosity MEM PDA 15 min = 3.4%; porosity MEM PDA 1 h = 3.5%; porosity MEM PDA 18 h = 1.5%). Similar trend is
	observed with PMAA grafting, which reduces surface porosity (porosity MEM PMAA_22k (with PDA=15 min) = 2.3%), in
	agreement with a polymer coating/grafting.

Acknowledgements 20

The authors thank the Institut Universitaire de France (IUF) and the Agence Nationale de la Recherche (ANR) through the OsciMEM project (ANR-20-CE06-0013-01) for financial support. Valérie Flaud, Didier Cot, and Bertrand Rebiere are acknowledged for XPS, SEM, and EDX analysis.

Declaration of Competing Interest

The authors declare no conflict of interest.