Journal of Membrane Science Membrane ...

Journal of Membrane Science 315 (2008) 82–92

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Membrane characterization by microscopic methods: Multiscale structure Y. Wyart a , G. Georges b , C. Deumie´ b , C. Amra b , P. Moulin a,∗ a Université Paul Cézanne Aix Marseille, Département Procédés Propres et Environnement (DPPE-CNRS-UMR 6181), Europˆ ole de l’Arbois, BP 80, Bat. Laennec, Hall C, 13545 Aix en Provence cedex 04, France b Université Paul Cézanne Aix Marseille, Institut Fresnel, Campus de Saint Jérˆ ome, av. Escadrille Normandie 13397 Marseille Cedex 20, France

a r t i c l e

i n f o

Article history: Received 8 October 2007 Received in revised form 30 January 2008 Accepted 9 February 2008 Available online 16 February 2008 Keywords: AFM SEM White light interferometry Roughness Porosity

a b s t r a c t A great number of studies have been carried out to obtain a better understanding of membrane fouling so as to be able to limit its effects. The parameters studied are many and can be classified into membrane structure parameters (porosity, roughness, pore size, pore shape, pore size distribution) and membrane/effluent coupling parameters (material, surface charge, hydrophobicity, etc. . .). In the case of the membrane structure parameters, three types of techniques can be used: displacement techniques, tracer retention techniques and microscopic techniques. In this paper, first microscopy observation methods are reviewed, and then the potential of three different techniques is studied. Scanning Electron Microscopy (SEM) provides information on surface porosity and layer thickness. The pore sizes measured with this technique were in agreement with the membrane cut off values given by the manufacturers. Atomic Force Microscopy (AFM) and White Light Interferometry (WLI) provide surface RMS roughnesses that depend on the observation scale. The RMS roughnesses that were obtained ranged between 100 and 4000 nm. For 4 unused ceramic membranes of different cut-offs and for 3 different scan sizes, the passage from one scan size to another is continuous in terms of information provided. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Membrane processes are the industrial processes whose development has been the fastest (12% growth per year) but membrane filtration is impeded by a major drawback: membrane fouling. The fouling can be either reversible or irreversible, depending on whether the membrane can be regenerated or not. This phenomenon entails a reduction in the production, a decline in the permeate flux, and a possible reduction in the performance of the membrane in terms of selectivity. Either a backwashing or a chemical wash will thus be necessary for the membrane to recover its initial performances. A great number of studies have been carried out in order to gain a better understanding of this phenomenon of membrane fouling so as to be able to limit its effects [1–3]. The parameters studied are many and can roughly be classified into: membrane structure parameters (porosity, roughness, pore size, pore shape, pore size distribution) and membrane/effluent coupling parameters (membrane material, surface charge, hydrophobicity, etc. . .). Only membrane structure parameters will be considered in this paper. The previous studies carried out in this domain have focused on three types of techniques: displacement techniques [4,5], techniques of tracers’ retention and microscopic techniques [4,6]. The displacement tech-

∗ Corresponding author. Tel.: +33 4 42 90 85 01; fax: +33 4 42 90 85 15. E-mail address: [email protected] (P. Moulin). 0376-7388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2008.02.010

niques require high pressures as they are used on membranes with pore sizes of about 10 nm (ultrafiltration). The tracer retention techniques have been widely used, especially for defining membrane cut-offs. Polyethylene glycols and proteins are the most often used tracers in the case of ultrafiltration, but they are sensible to operating conditions. Advances in the study of membrane structure have been made possible thanks to microscopic techniques such as Scanning Electron Microscopy (SEM) [7], Transmission Electron Microscopy (MET) [8], near-field microscopy (Atomic Force Microscopy, (AFM) [9]) and Scanning Tunnelling Microscopy (STM) [10]). Among these various techniques, the most widely used are SEM and AFM. The SEM applications are varied and focus on membrane structure characterization [11], hollow fiber membrane fabrication [12] and the study of the fouling process [13]. Hwang and Lin [14] used observations made using SEM to qualify the nature of the pores of 3 microfiltration membranes with a cut-off of 0.1 ␮m. They also observed the fouling of these membranes after filtration of a solution containing model particles of polymethyl methacrylate (mean diameter = 0.4 ␮m). The major drawback of this technique is the sample preparation by gold metallization, which entails a less accurate pore size determination. Atomic Force Microscopy (AFM) is a quite recent technique dating back from 1986 [15]. It was first used in 1988 to study the structure of polymeric membranes [16]. This technique can be used in three different modes: contact [17], non-contact [18] and tapping mode [19] and can be applied to all membranes, from microfiltration to reverse osmosis [20–22], for organic [23,24]

Y. Wyart et al. / Journal of Membrane Science 315 (2008) 82–92

as well as inorganic [25,26] membranes. However, using contact mode AFM can damage reverse osmosis membranes [17,22,27]. This technique makes it possible to represent no conducting surfaces with a resolution of the order of the nanometer in either dry or wet environments [28–31]. Therefore, using AFM makes it possible to avoid drying the sample under vacuum. The AFM measurements give access to the roughness, pore size, pore density and pore size distribution of a membrane [32]. They can also provide information on the surface electrical properties of a membrane, its fouling potential towards a specific colloid [33] and its filtration performance as a function of its roughness [34]. All this can help to predict fouling without process measurements [35–37]. Vrijenhoek et al. [38] characterized 4 commercially available polyamide composite membranes for surface morphology, surface chemical properties and surface charge. Contact AFM measurements allowed them to show that the rougher the membranes, the more colloid particles deposited on them. Some drawbacks of the AFM technique were pointed at: due to the size of AFM scanning probe tips, there are some limitations to the scanning depth; also, AFM may distort membrane pore size due to rounded corners near pore entrance [39]. Boussu et al. [40] compared the results obtained using contact and non-contact mode AFM. It was concluded that when comparing surface roughnesses for different membranes the same AFM method and the same scan size must be used. Boussu et al. [40] also tested tapping mode AFM to characterize membranes with respect to their hydrophobicity, using phase shift measurements. Norberg et al. [41] performed bench-scale tests on membranes used for the treatment of brackish surface water. They evaluated membrane roughness by contact AFM (Root Mean Square roughness, RMS), surface charge by measuring the zeta potential and hydrophilic character by measuring the contact angle. Based on these results, 4 RO membranes (13.1 nm < RMS roughness < 67.4 nm) with a good resistance to fouling were selected for use in the pilot study. Al-Jeshi and Neville [42] studied the influence of the length of soaking time on RO membranes. Using contact mode AFM, they showed that surface roughness increased by 35% after 2 h of soaking in a NaCl solution at pH 4.3. Contrary to SEM, AFM can be used in an aqueous environment [43]. However, the observations are made on small surfaces and depend on the size and shape of the tips used. The information obtained using AFM are often confronted to the results obtained with electron microscopy techniques in order to better understands the fouling mechanism. With this in view, Elimelech et al. [44] used the contact mode AFM/SEM coupling to demonstrate the influence of the roughness of RO membranes on fouling by a colloidal suspension of silica. They compared the fouling behavior of cellulose acetate and polyamide composite membranes, the former being smoother than the latter. Results showed a higher permeate flux and a slower flux decline for the cellulose acetate membranes (the smoothest) compared to those for the polyamide composite membranes. For polysulfone membranes, Kim et al. [19] obtained with SEM smaller pore size than with tapping AFM. To determine pore size, AFM is more precise than SEM which needs a sample preparation step of gold metallization [45–47]. Hirose et al. [48] and Warczock et al. [49] studied by SEM and AFM the relationship between the skin layer surface structure of, respectively, RO and NF membranes and their filtration performances. It was shown that the roughest membranes provided the best performances in terms of flux, the flux increases quasi-linearly with the roughness. Although SEM and AFM are the two most popular techniques for characterizing membrane structure and fouling, there are other techniques that can be used for the same purpose. Koyuncu et al. [50] showed that the roughness values obtained by

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white light interferometry (scanned area = 64 ␮m2 and 0.05 mm2 ) were higher than those obtained by tapping mode AFM (scanned area = 100 ␮m2 ). This can be accounted for, to some extent, by the fact that membrane surface roughness increases with increasing scan size, until a critical scan size of 250,000 ␮m2 is reached. The area that can be scanned by AFM is relatively small, well below this critical value, and so the results obtained using this technique can be misleading [50]. Today, new characterization techniques, as Confocal Scanning Laser Microscopy (CSLM) [51–56], provide a 3D representation of the membranes and of their fouling. By means of a fluorescent contrast agent, this non-destructive technique reveals the presence in the porous structure of defects that do not propagate to the membrane surface. This is a clear advantage of CSLM over SEM, which provides only 2D representations. Ferrando et al. [57] and Zator et al. [58] developed this technique to characterize the fouling of flat microfiltration membranes with fluorescent probes. This technique provides information on the fouling at the surface of the membrane and also inside the porous matrix as well as on the origin of the fouling and on the quantification of the blocked pore surface. However, the resolution of this technique is low, and thus it has so far been applied only to microfiltration. Another technique, also using fluorescence labelling, was developed by Hugues et al. [59] to give a 3D representation of flat membranes fouling. With this optical technique – namely two-photon femtosecond near infrared non-linearoptical imaging – they were able to show the influence of the concentration of a yeast fouling solution on the cake formation. The use of modern synchrotron radiation sources provides 3D visualization of the membranes using 2D images. Remigy and Meireles [60] applied this technique – which does not require any membrane preparation – to study the influence of the nature of the polymer (polysulfone or PVDF-HFP) for hollow fiber membranes. They were able to describe the geometry of the pores and the 3D architecture of the hollow fibers. However, using 2D images to obtain this 3D representation requires quite advanced data processing software and this technique is limited to the study of microfiltration membranes. Each microscopic technique has its advantages and disadvantages. We are going to compare the information obtained on ceramic membranes as a function of the cut-off using three different techniques: SEM, WLI and AFM. The range of membranes studied goes from the mere membrane support to ultrafiltration membranes. In particular, it will be shown that the roughness values depend on the scan size and that the passage from one scan size to another provides continuous information on the roughness. This not only confirms the importance of the scan size but also shows that some coherence exists between the surface roughness values obtained using two different techniques. This study was performed on unused ceramic membranes that had not been fouled. Previous studies had already showed the influence of the roughness–fouling relationship [34,38].

2. Material and methods Surface analysis can be done with different tools, each one with its own specificity with regard to the conditions of use and to the information it provides. In our study, we used a Scanning Electron Microscope (SEM), a White Light Interferometer (WLI) and an Atomic Force Microscope (AFM). In this section, the operating principle of each tool will be presented, so that the complementarity of the three techniques can be better understood. This study deals with the investigation of three ceramic membranes (cutoffs: 300 kDa, 0.1 and 0.45 ␮m) and the corresponding support. The membranes, supplied by Novasep Company, are 27 channels tubular KERASEP membranes with a TiO2 /ZrO2 skin. The membrane samples were obtained using a diamond saw and only the plane part of the channels was used.

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Fig. 1. Schematic drawings of a classical (a) and an interference (b) optical microscope.

2.1. Scanning Electron Microscopy JEOL JMS-6320F is a high-resolution scanning electron microscope with a cold field emission source and an in lens detection. It can be used from 0.5 to 30 kV with a resolution of 1.2 nm at 15 kV and 2.5 nm at 1 kV. High resolutions at low accelerating voltages are possible with this instrument thanks to its objective lens design. A secondary electron detector is integrated into the bore of the lens and the specimen can be brought up into the lens field. Working distances (WD) of as short as 2 mm are possible. The microscope is also fitted with a Noran Voyager EDX system with a light element X-ray detector (15 mm WD) and an Autrara Back Scatter Detector. There is also a second conventional secondary electron detector below the lens, which gives more topographic images. Magnifications of 25× to 650,000× (at 8 mm WD) are possible. The membranes, obtained by sawing with a diamond blade, were covered by a 2 nm gold layer to be analyzed. Fig. 2. Schematic drawing/diagram of an atomic force microscope.

2.2. Interferential optical microscopy 2.3. Atomic force microscopy Optical microscopy in classical configuration (Fig. 1a) provides images of the sample observed, with lateral magnification and resolution depending on the objective used. The axial dimensions are lost: the contrast between two imaged points depends only on the difference of reflection from the surface at these points, and not on their axial distance. More advanced systems, such as the confocal microscope [61] or the optical profilometer [62], make it possible to overcome this limit. In this study, an optical profilometer is used, operating with a Mireau interference objective (Fig. 1b). The images of the surface and a waveform generated by the reflection from a reference plane are superimposed. In these conditions, the imaging system acquires interference fringes. The source used is white, and the acquisition of several successive interferential images by moving the objective along its z-axis allows the reconstruction of the surface wave phase [63]. It is then possible to reconstruct the tridimensional profile of the object measured. Using the optical ˚ image sizes of 900 ␮m × 900 ␮m profilometer Talysurf CCI 3000 A, (×20 objective, lateral resolution = 0.75 ␮m) were obtained with a video camera providing images with 1024 × 1024 points. The ˚ However, difficulties expected vertical resolution is about 0.1 A. arise in the reconstruction of the profiles of too rough surfaces. It is always possible to reconstruct the non-measured points, if they are not too many, by interpolating with the nearby pixels. After the measurement, the images obtained can be numerically processed. For example, it is possible to flatten the curved surfaces by subtraction from a mean surface, to reveal the roughness properties. It is also possible to extract the roughness parameters of the sample, which was one of the aims of this study.

Atomic force microscopes are not optical microscopes. They use the mechanical interactions with a probe scanned parallel to the mean plane (xy) of the surface to be studied. The probe tip is mounted on the end of a cantilever (Fig. 2). As the tip gets in contact with the surface, the vertical deflection of the cantilever is measured by an optical system (a laser beam is bounced off the cantilever onto a dual element photodiode). A Q-Scope 250 (QUESANT) was used in this and two different scan sizes were investigated: 5 ␮m × 5 ␮m and 50 ␮m × 50 ␮m with a resolution of 512 × 512 points. It was tried to visualize the porosity of the membranes at different scales. We chose very sharp tips (ref CSC 12) whose characteristics are given in Fig. 3. The images obtained can be numerically processed. In particular, it is always possible to adjust the mean plane of the surface by subtraction of surfaces to correct the imperfections of the chosen scan size. It is then possible to extract the

Fig. 3. Characteristics of the tips used: ␮masch CSC12.


Fig. 5. Roughness spectrum obtained on a limited frequency window and frequency windows accessible by the various microscopy techniques.

Fig. 4. Profile h(x,y) obtained after microscopic measurement.

roughness parameters, or to directly process the profile data. This will be developed in the following paragraph.

The microscopy techniques, which were used, allow to obtain information at different scales. The two types of microscopes presented above provide a profile of each membrane surface: h(x,y) (Fig. 4). It is sampled during the measurement, with a sampling interval: L N

(1)

with L: size of the measured area; N: number of points on each x line (or column). It is then possible to extract roughness parameters, and in particular, the mean roughness Ra Ra =

1 h(nx, my) N2

(2)

n,m

= ()

S

d = 2 ()

() ¯ d

(4)

Rq is thus deduced by integration on the accessible window (Fig. 5). It is essential at this stage to notice that all these integrals are limited on finite intervals [64]. Indeed, given the experimental measurement conditions and the usual laws on Fourier transforms, the spatial pulsation bounds can be defined according to the scan size L and the number of considered points N [64]: ∈

N L

,

(5)

L

The definition of Rq is not an intrinsic definition but depends on the measurement conditions, that is to say on the scale at which the surface is observed. The microscopy techniques that were used led to different accessible frequency bandwidths (Fig. 5), depending on the [L, N] couple chosen. 3. Results and discussion

To compare surfaces more accurately, the surface roughness spectrum must be calculated: 42

to calculate the RMS roughness, Rq : Rq2 =

2.4. Comparing the techniques: multiscale analysis

x = y =

85

˜ )| 2 |h(

(3)

˜ spatial Fourier transform of where = (, y ): spatial pulsation; h: the h(x,y) profile; S = L2 : measured area. or even better its average on The bidimensional spectrum (), can be represented and allows the polar angle () where = ||,

3.1. In lens detection field SEM An in lens detection field SEM (Jeol JSM-6320F) was used to obtain for each membrane cross-section images of the membrane and images of its skin layer. The cross-section images (Table 1) provided information on the membrane structure. It could thus be seen that the three membranes studied were constituted of successive layers of different granulometries: a membrane support

Table 1 Cross-section images (300 kDa, zoom ×3000; 0.1 ␮m, zoom ×2000 and 0.45 ␮m, zoom ×600) and top views (300 kDa, zoom ×150,000; 0.1 ␮m, zoom ×30,000 and 0.45 ␮m, zoom ×5000) of the membranes Membrane cut-off

Cross-section

Top views

300 kDa

0.1 ␮m

0.45 ␮m

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Fig. 6. Black and white images of the membrane top views: 300 kDa (a, zoom ×150,000), 0.1 ␮m (b, zoom ×30,000) and 0.45 ␮m (c, zoom ×5000) and associated cumulative percentage of pore number according to pore size.

Table 2 Summary of pore sizes obtained for each membrane Membranes

Pores number

Pores size at 90%

Mean pores size at 90%

Standard deviation (%)

300 kDa

1 2 3 4

Zoom 100,000 100,000 50,000 150,000

255 163 478 105

24 nm 33 nm 28 nm 33 nm

29.5 nm

17

0.1 ␮m

1 2 3 4

15,000 30,000 15,000 15,000

1106 282 1016 1112

0.095 ␮m 0.105 ␮m 0.110 ␮m 0.110 ␮m

0.105 ␮m

7

0.45 ␮m

1 2 3 4

5,000 15,000 5,000 15,000

705 92 662 71

0.450 ␮m 0.375 ␮m 0.450 ␮m 0.450 ␮m

0.430 ␮m

9


ensuring the mechanical resistance of the membrane, a pre-layer and a skin layer ensuring the membrane selectivity. With SEM it is also possible to observe the membrane skin layer (top views). Four cross-section images were taken for each membrane. Table 1 presents also for each membrane one of the 4 top view images. From those views, black and white images were obtained using the image processing software Image-J (Fig. 6). On these images, it was possible to distinguish the pores from the membrane material and thereby estimate the pore size using the image processing software. Fig. 6 gives the cumulative percentage of the number of pores as a function of the pore size for the three cut-offs studied. Similar results were obtained for the 4 images obtained for each membrane. In Fig. 6, it is interesting to note that the pore size that corresponds to 90% on the cumulative curve is nearly equal to the size of the molecule that shows 90% of the solute rejection. The molecular weight of such a molecule is usually called molecular weight cut-off. Hence the pore size that corresponds to 90% on the cumulative curve is used hereafter as a pore size that represents the membrane. Table 2 summarizes all the information gathered from Fig. 6. The results for the microfiltration membranes were obtained with different zooms (5000, 15,000 and 30,000). However, in view of the reproducibility of the results (standard deviation < 10%), this does not seem to have affected the pore size determination. The metallization step allows better visualization of the sample but in our study the pore size was affected by the deposition of a 20 A˚ conducting gold layer, whose thickness was negligible compared with the pore size. It can thus be concluded that the SEM technique used in our study provides reliable information on the pore size of the microfiltration membranes, even though they had been previously

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metallized. On the other hand, the results obtained for the ultrafiltration membrane were more scattered, with a standard deviation of about 17% despite a mean pore size (29.5 nm) in accordance with the indications of the manufacturer (20–30 nm). It seems that the smaller the pore size, the more the measurement is impaired by the metallization step. In other words, there were limitations to the use of Jeol JSM-6320F for the determination of ultrafiltration membrane pore size. These limitations were due to the thickness of the conducting deposit, which was no longer negligible compared with the pore size. Nevertheless, the SEM technique provided a good definition of the structure of the microfiltration and ultrafiltration membranes studied, in terms of layer thickness and pore size. 3.2. AFM and WLI Atomic force microscopy (512 points, 5 ␮m × 5 ␮m and 50 ␮m × 50 ␮m) and white light interferometry (1024 points, 900 ␮m × 900 ␮m) were used to obtain information of the topography of both the membranes and the support and to determine their roughness. Some results obtained with WLI are presented in Table 3. To allow for surface defects, a series of images was taken for each of the membrane samples. From these results, roughness spectra were determined and the RMS roughnesses for each of the membranes were calculated in the associated frequency band. The results obtained are gathered on Fig. 7 as well as the error bars which correspond to standard deviation of 5 measurements at different sample locations. It can be seen that for each sample the RMS roughness is high, comprised between 1000 and 4500 nm. Moreover, the higher the membrane cut-off, the higher the membrane

Table 3 Images obtained with WLI: 300 kDa, 0.1 ␮m and 0.45 ␮m Membrane cut-off

300 kDa

0.1 ␮m

0.45 ␮m

90◦ view

Top view

88


Fig. 7. Evolution of the roughness for each membrane with WLI.

roughness. This seems logical since the higher the membrane granulometry (and thus the more uneven the surface), the higher the roughness. To complete these results, observations on smaller scan sizes were performed using AFM. The membranes were scanned on two scan sizes (512 points, 5 ␮m × 5 ␮m and 50 ␮m × 50 ␮m). The observations made are, respectively, presented in Tables 4 and 5. The roughness spectra were then obtained to determine roughnesses in the associated frequency bandwidths (Fig. 8). The error bars of Fig. 8 correspond to standard deviation of 5 measurements at different sample locations. Each one of these bandwidths allows characterization of the membrane at a different scale. The first observation that can be made is that, whatever the membrane, the RMS roughness obtained for the 50 ␮m × 50 ␮m scan size is

Fig. 8. Evolution of the roughness obtained by AFM for 5 ␮m × 5 ␮m and 50 ␮m × 50 ␮m windows.

higher than that obtained for the 5 ␮m × 5 ␮m scan size. For the 50 ␮m × 50 ␮m scan size, the RMS roughnesses range between 300 and 3500 nm, whereas for the 5 ␮m × 5 ␮m scan size, they range between 100 and 2000 nm. It can also be seen that, whatever the scan size, the roughness increases with the membrane cut-off. This is in agreement with the results obtained by WLI. It is thus true

Table 4 Images obtained with AFM 5 ␮m × 5 ␮m: 300 kDa, 0.1 and 0.45 ␮m Membrane cut-off

300 kDa

0.1 ␮m

0.45 ␮m

45◦ view

Top view


89

Table 5 Images obtained with AFM 50 ␮m × 50 ␮m: 300 kDa, 0.1, 0.45 ␮m and support Membrane cut-off

45◦ view

300 kDa

0.1 ␮m

0.45 ␮m

Support

that the determination of the RMS roughness for a membrane is a function of the observation scale: therefore, no RMS roughness will be significant unless it is given with the value of the scan size. From these results, it was possible to compare the different techniques and the different observation scales. To do this, the

roughness spectrum of each membrane was plotted as a function of the spatial pulsation (Fig. 9). It should be noticed that, whatever the membrane, the roughness spectra overlap from one frequency bandwidth to another when the measurement technique and the scan size change (from WLI in 900 ␮m × 900 ␮m to AFM in

90


WLI (900 ␮m × 900 ␮m) and AFM (5 ␮m × 5 ␮m) experiments. This is of interest for the study of the membrane fouling phenomenon, where smaller scan sizes are required to characterize the porosity and roughness of the filtration cake at different scales. 4. Conclusion In this study, three microscopy techniques were applied to four unused ceramic membranes (300 kDa, 0.1 and 0.45 ␮m, support). With the field SEM technique, the structures of these membranes were studied at different levels. The cross-section images provided information on the number of layers that constitute the membranes and on the thickness of these layers. The top views allowed visualization of the skin layer of each membrane. With an image processing software, it was observed that the pore size corresponding to 90% on the cumulative curve of pore number is nearly equal to the size of the molecule that shows 90% of the solute rejection. Even though the results obtained were correct, this technique had limitations when applied to ultrafiltration membranes, because the membrane pore size was quite affected by the metallization step. The results obtained by white light interferometry and by atomic force microscopy show that the determination of the membrane roughness depends on the observation scale. The roughness of a membrane increases markedly with the observation scale. For an observation scale, the roughness increases with the membrane cut-off. However, there is a continuity between the different scan sizes for the determination of the RMS roughnesses, which will allow a multiscale study of the fouling process. This study is currently in progress and will be the topic of an upcoming paper. Acknowledgment The authors would like to thank Novasep society for technical support.

Nomenclature

Fig. 9. Roughness spectrum for each membrane: 300 kDa (a), 0.1 ␮m (b) and 0.45 ␮m (c), and support (d).

50 ␮m × 50 ␮m) and when the scale changes for a same technique (from a 50 ␮m × 50 ␮m to a 5 ␮m × 5 ␮m scan size). Globally, it can be noticed that there is a slight difference between the slopes of the roughness spectra of the various membranes, represented in logarithmic coordinates. Indeed, the slope absolute value increases slightly from the 300 kDa (slope-2.2) to the 0.1 ␮m membrane and to the 0.45 ␮m membrane (slope-2.4). With reference to previous works [64], a fractal dimension can be associated to the surface: D = (8 − ˛)/2, where ˛ is the absolute value of the spectrum slope. When ˛ decreases, the fractal dimension increases, which corresponds to a surface filling the space more (dense surface), therefore, being denser and less rough. This analysis confirms that the 300 kDa membrane is denser than the 0.45 ␮m one. However, this analysis is only global. Fig. 9 confirms that a RMS roughness given for a membrane must imperatively be given with the scan size since it influences the determination of the roughness. However, it is observed that there is a continuity in the determination of the roughness between the

h(x,y) (x,y) L S N m, n x, y Ra Rq

profile of the surface (m) spatial coordinates length and width of the area measured (m) area measured (m2 ) number of points per line and column on an image obtained by microscopy integers sampling interval along x and along y mean roughness (m) root mean square roughness (m)

Greek symbols roughness spectrum (m4 ) spatial pulsation (m−1 )

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