Diatom is a unicellular photosynthetic microalga that is found in diverse environments. These are decorated with siliceous cell walls called frustules. Diatoms have long been favoured by grazers such as microscopic protozoa and dinoflagellates. However, grazers typically remain intact in laboratory culturing and feed on diatom in culturing vessels and reducing biomass yield. The isolation and cultivation of diatoms in laboratories hamper diatoms’ diversity and vast industrial potential. Chitosan, a biopolymer, has been widely used with other polyelectrolytes to flocculate various organic and inorganic colloids at acidic pH. Dissolved chitosan (acidic pH) has been used in various natural water samples and wastewater system for dewatering. However, untreated chitosan flakes have never been evaluated in a heterogeneous natural water environment. Since diatoms have silica surfaces, we tested chitosan for diatom separation and optimized chitosan concentration and other parameters to obtain grazer-free diatom starter culture from raw water. We also elucidated the mechanism for chitosan flakes-mediated diatom flocculation through adsorption kinetics and molecular dynamic simulation analysis. The results of this study are statistically optimized and validated, with a significant R2 value of 0.99 for the proposed model.

  • Flocculation-based separation of diatoms from natural water samples is presented here.

  • The possibility of enrichment for less abundant diatom species is done by this method.

  • The method will reduce the labour associated with the serial dilutions and pure culture preparation.

Graphical Abstract

Graphical Abstract
Graphical Abstract

Diatoms are unicellular, photosynthesizing heterokont algae and are unique because of the siliceous cell wall (Ellegaard et al. 2016). Frustule – the diatom cell wall – has patterned nano-sized pores and mainly contains silica (Su et al. 2018). The cell wall proteins such as frustulin, pleuralin, and silaffin have been studied by Kroger et al. (1994, 1997, 1999). Diatoms are phytoplankton that usually floats on the surface and are frequently associated with algal blooms, which are also abundantly found attached to the stone surface (Wang et al. 2012). Earlier, the diatom studies were limited to academic research, mainly relating to morphological diversity studies or a nuisance for water reservoirs. However, progress has recently been made in biotechnological applications, where its use in bioremediation and biofuel generators has come to light. With the emergence of nanotechnology in the late 19th century, diatoms gained the world's attention. Richard Gordon introduced diatom nanotechnology to the globe in 1999 (Parkinson & Gordon 1999). Since then, several fields have tested various applications using live diatoms or frustules. Almost 12,000 research publications addressing diatoms or diatom frustules have been published in the past 10 years. However, the number is lower in comparison to its biotechnological potential. Recent studies on diatom frustules suggest that the siliceous cell wall has many applications due to its mechanical strength and porosity. Silicon is the main ingredient of diatom frustules, making it an ideal choice to fabricate organic solar cells, wherewith TiO2 frustules act as semiconductors (Jeffryes et al. 2011). Another advanced application of diatom frustules was explored in 2020, showing the haemostatic efficiency of frustules (Wang et al. 2021). Although promising, not a single commercial product is available in the market solely of diatom origin. So far, it has only been used for some rudimentary applications, such as matrix in water filtration capsules and an abrasive. Still, this glass dynamo is unexplored mainly because of cultivation and culturing constraints. Presently, a few algal culture collection centres offer researchers pure diatom species.

Most laboratory diatom cultivation studies involve pulling a defined amount of sample from a large reservoir and subsequently transfer into the enrichment growth medium. During these routine procedures, the authors noted the continuous reduction in the diatom population and reasoned that grazing by ciliates results in biomass loss. Also, there are similar observations from other researchers. Brook (1952) reported that Oxytricha (Protozoa) could eat up to 90 Nitzschia palea (diatom) in just 24 h. Wunsam et al. (2002) stated that grazers caused about 8% alteration in the diatom community. The study performed by Duarte et al. (2021) also reported the inferences of grazers during the diatom dilution experiments. No other technologies are introduced to mitigate the menace of grazers except the serial dilution technique.

Present limitations

Estimates of diatom species on water bodies range from 20,000 to 2 million. Every year, the number rises. However, the presence of grazers limits the enrichment and cultivation of diverse diatoms.

Several factors affect the isolation studies of diatoms.

The key constraints and proposed resolutions are:

  • (1)

    During the collection to enrichment, the voracious protozoa and dinoflagellates eat up half of the diatom species, limiting the enrichment to only 2–3 species. Therefore, separating the protozoa before inoculating them into the growth medium can resolve the problem to a certain extent.

  • (2)

    For enrichment, several samples are withdrawn from the large water bodies. As a result, the species representatives are further diluted into the cultivation medium and do not appropriately represent the vast diversity. Henceforth, the experimental design should be devised, so that it first concentrates the diatoms from the large sample. Thereby it will increase the probability of enriching the diverse species.

The present study proposes a pre-inoculation approach to separate the grazers from the diatoms, which will overcome the above hitches.

Chitosan – biopolymer – is a naturally occurring linear polysaccharide composed of randomly scattered β-linked D-glucosamine and N-acetyl-D-glucosamine (Lubián 1989; Kumaran et al. 2021). Lertsutthiwong et al. (2009) reported chitosan as an effective bioflocculant for phytoplankton removal in outdoor shrimp culture tanks. Chitosan is insoluble above pH 6; some scanty reports suggest it as a clarifying agent for suspended solids above this pH range (Dong et al. 2014). Morrissey et al. (2015) have reported acidic chitosan to separate dewatered microalgae and cyanobacteria from the settling tank where polyampholyte was a primary flocculating agent. Divakaran & Pillai (2022) demonstrated the flocculation of three freshwater algae using chitosan. Applying chitosan in conjunction with other electrolytes or physical treatments for flocculation is not a new notion. Most articles have evaluated the chitosan's flocculation efficacy for a few pure algal cultures (Morales et al. 1985; Rashid et al. 2013; Xu et al. 2013; Lama et al. 2016; Corrêa et al. 2019). None has ever addressed the heterogeneous system like raw natural water, which contains myriad types of cells, particles, and other undefined materials, except for reports which include the dewatering of sludge as well as the removal of heavy metal ions from natural water systems (Pitakpoolsil & Hunsom 2013; Zhang et al. 2019). Borchert et al. (2021) have used chitosan to flocculate suspended silica and clay, exhibiting excellent potential as a flocculant. The diatoms and silica particles possess analogous surface charges, and the resemblance is the stimulus for the present research.

Here we report the simple method for chitosan-mediated quick flocculation of diatoms from natural water. The statistically supervised experiments show that 0.1 g of chitosan can efficiently settle an average of half a million diatoms from a 100 mL water sample within just 60 min. Also, we propose that the role of water bridges and hydrogen bonds developed between the silaffin (diatom surface protein) and chitosan is responsible for such specific flocculation and high flocculation efficiency. We also evaluated the adsorption kinetics and isotherms, where we observed chemisorption as the primary phenomenon for the adsorption.

Materials, samples, and sampling vials

Low-molecular-weight chitosan (from crab shells) was purchased from Sigma-Aldrich®.

The freshwater samples were collected from the lake, reservoirs, and rivers across the Charotar region, Gujarat, India (Supplementary Data S1). In addition, the marine water samples were collected from the Gulf of Khambhat (Gujarat, India). A customized 250 mL borosilicate glass bottle equipped with a screw cap at the bottom and a dispensing valve on the side was used for facilitating the floc settling and separation of supernatant. Standard f/2+ Si (Guillard 1975) medium was utilized to enrich and cultivate diatoms at 27 °C by adjusting the photoperiod at 12 h.

Method development

Chitosan is an inexpensive biopolymer often used to replace synthetic polyelectrolytes in wastewater treatments. Initially, 0.01, 0.1, and 0.5 g of chitosan flakes were dosed into 100 mL of freshly collected water samples in a separate bottle. The flakes were added immediately after collecting water and brought to the laboratory for further analysis. Simultaneously, the reference water sample (100 mL) was kept in a stoppered glass bottle. Then, the water and reactants were incubated for different time intervals to optimize gravitational settlement time, i.e., 60, 120, and 180 min. Each experiment is conducted in triplicates to optimize the time and reactant amount. The standard deviations and standard error were estimated using Origin Pro2022b.

Method validation

The separated floc was redissolved into 1 ml of sterile distilled water, and the cells were quantified using an improved Neubauer's chamber. Similarly, cells from clarified suspension were withdrawn and visualized under the light microscope (CH20i, Carl Zeiss) at 40× magnification. The diatoms and protozoa were visually counted and curated towards performing three individual observations, where two others recalculated the number from the same preparation. The mean values of three individuals were considered a single observation, and three such observations were made for each sample. Next, the same glass coverslips were dried at 40 °C in a hot air oven (Nova, India) for 60 min and analysed with a scanning electron microscope (SEM; JSM 7900F, JEOL). Before visualization, the glass coverslips were coated with tungsten in the sputtering unit for 20 s. The procedure will increase the electron conductivity of the sample. The SEM images were captured at different magnifications, and the size of enticed diatoms was measured with Fiji ImageJ analysis software (Schindelin et al. 2015).

Assays for the process parameter

The method's efficiency was evaluated for different water pH values, and the collected water samples had pH values of 6–9; then 0.1% of chitosan flakes were added into the water, and the recovered flocs were assayed in 60 min.

Furthermore, to evaluate the competence of the developed method for higher volumes, 1 g of chitosan flakes spiked into 1,000 mL of the water sample. Finally, the flocculation efficiency was estimated by calculating the diatom/protozoa numbers in flocs and supernatant.

In another experiment, diatom surface-associated polysaccharides (extracellular polymeric substances, EPS) were extracted from pure culture, and the flocculation efficiency was estimated. For each instance, the flocculation efficiency (FE) was calculated using Equation (1), where N represents the cell number and t sampling time.
formula
(1)

Next, the possible chitosan toxicity on diatom cells was evaluated by performing 0.4% trypan blue live-dead staining of the obtained flocs after 240 h of incubation. Also, we assessed the chitosan's efficiency for heterogeneous culture, where various diatom species were present.

Mechanism probing for diatom–chitosan interaction

Chitosan surfaces are irregular, and to predict their diatom adsorption efficiency, we performed an adsorption kinetic analysis at a constant temperature (30 °C). Next, 100 mL of sterile water taken into the stoppered borosilicate glass bottles and 100 mg of chitosan flakes were added to five independent bottles with fixed diatom cell numbers (1.025 × 105 cells/ml). The contact time was 15–60 min. After every 15-min interval, the supernatant and flocs were separated. Next, chitosan-enticed diatoms were separated by centrifugation (1000 rpm) and washing, and the cell concentration was estimated using an optimized spectrophotometric method (optical density measurement at 700 nm). Next, we used IsoFIT, an isotherm fitting tool for modelling the adsorption data using the method reported by Dave & Modi (2019).

Next, we determined the specific binding positions and affinities by performing molecular docking (MD) and molecular dynamic simulations (MDS) to predict the adsorption mechanism. We chose the abundantly expressed diatom surface marker silaffin (PDB ID 2NBI) as the receptor (De Sanctis et al. 2016). The ligand chitosan's chemical structures were obtained from PubChem (National Center for Biotechnology Information 2022). Next, we performed the MD analysis in Autodock vina 4.2 by the method reported by Kukol (2011).

Then, the energy-minimized chitosan–silaffin complex was simulated to mimic the natural environment using water as an explicit solvent at 30 °C at pH 8. For molecular dynamic simulation, we used Schrodinger, Desmond 2021–4 (Sanyanga et al. 2019).

The association predicted by the MDS analysis was validated by performing the FT-IR analysis of diatom cells, chitosan–diatom mixture (1:1), and chitosan. The sample preparation and processing were carried out by the method and the instrument reported by Dave & Modi (2018). Next, we analysed the obtained peaks using the Origin Pro2022b peak analysis command. Finally, we studied each peak for intensity, area, and full width at half maximum (FWHM).

Method optimization for chitosan-mediated diatom flocculation

In a closed laboratory culturing environment, where a raw water sample contains a prey-predator and other impurities, naturally, the growth opportunities shift towards predators. Therefore, the proposed method aims to pool the diatoms (prey) from the water sample to limit the weed and ease subsequent enrichment and cultivation. For that, we dosed various flakes in 15 distinct natural water samples. The water samples were collected from different sites and varied in composition, nutrition loading, and biodiversity. The supernatant (S) and flocs (F) were separated post-dosing. Figure 1 shows the SEM image of separated flocs with an average diameter of 300 μm, worth noting the absence of ciliates in flocs. The flakes-mediated floc is compact and robust compared to Al2(SO4)3 and amphoteric chitosan solution-derived flocs of microalgae, with a diameter ranging from 500 to 700 μm (Dong et al. 2014).
Figure 1

SEM of flocs after treating with 0.1 g of chitosan.

Figure 1

SEM of flocs after treating with 0.1 g of chitosan.

Close modal
Next, Figure 2 represents the number of diatoms separated by dosing 0.1 g of chitosan. A similar trend was seen in all studied water samples. A large floc was formed at a higher chitosan concentration (0.5 g), resulting in protozoa entrapment in the cavities. Hence, the method was optimized for 0.1 g of chitosan for 100 mL of raw water. Only the data for three representative natural water samples (numbers 1, 2, 3 from Supplementary Data S1) are summarized in Figure 2 to avoid repetitions of similar results.
Figure 2

Concentration (g) optimization assays for gravitational settlement by flocculant; on the second Y-axis, S represents the clarified solution, while F refers to flocs.

Figure 2

Concentration (g) optimization assays for gravitational settlement by flocculant; on the second Y-axis, S represents the clarified solution, while F refers to flocs.

Close modal

On average, there were 1.25 × 104 cells/mL when counted without any treatment. Post-flocculation, 5 × 104 cells/mL were observed in flocs exhibiting an average of 40% increase in the cell numbers. In a similar setup, Şirin et al. (2012) have reported only 15% flocculation for chitosan solution on microalgae Phaeodactylum tricornutum. We have obtained far better flocculation efficiency with the chitosan flakes.

Additionally, the cell counting was statistically supervised, and the standard deviation was never more than 5%, with a standard error of around 6.2%.

Assay parameters and method validation

Water pH

From the 15 water samples, three with pH in the range of 6.5–8.5 opted to evaluate the impact of water's pH, where the salinity of water sample 3 was 32 ppt. The data presented in Figure 3 show the chitosan's stability as a flocculant. No change was noted in the flocculation efficiency of chitosan within the studied pH range and salinity. The previous report suggested that 1% chitosan suspension (pH 1) can flocculate the Chlamydomonas reinhardtii, where authors have changed the pH of the medium besides using chitosan in a formulated water system (Lopez et al. 2016). Our method has the advantage of simplicity, and neither a chitosan pre-treatment nor a pH shift needed to achieve the diatom flocculation.
Figure 3

Effect of water's pH on chitosan-mediated flocculation of diatoms.

Figure 3

Effect of water's pH on chitosan-mediated flocculation of diatoms.

Close modal

Scale-up

Furthermore, no additional flocculants are required for separation. When tested for higher volumes (1 L), 1 g of chitosan displayed similar diatom loading (Figure 4). Initially, there was 6.9 × 104 cells/mL, which increased to 40% after flocculation, giving 1.7 × 105 cells/mL. Therefore, the designed process is also validated for higher volumes.
Figure 4

Scale-up studies for 1 L of volume.

Figure 4

Scale-up studies for 1 L of volume.

Close modal

Also, we evaluated the impact of EPS on the flocculation process. No significant changes in the flocculation efficiency were observed where previous reports suggested the negative influence of EPS on flocculation (Wilén et al. 2003).

Chitosan toxicity assay

In addition, we investigated the possible toxic effects of chitosan on diatom cells. However, even after 10 days of co-incubation (chitosan and diatoms), no adverse impact on cell viability is seen. Figure 5 shows the unstained metabolically active cells.
Figure 5

Vital stain with 0.4% Trypan blue (a) dead diatom cell or empty frustule stained blue (b–f) unstained cells displaying cellular content.

Figure 5

Vital stain with 0.4% Trypan blue (a) dead diatom cell or empty frustule stained blue (b–f) unstained cells displaying cellular content.

Close modal

Species abundance within flocs

In routine laboratory microalgae cultivation, a small sample volume is dosed into the cultivation or enrichment medium, where predators and other competitors outnumber the diatoms (Barra et al. 2014; Lundholm et al. 2018). Furthermore, the inadequate sample size may reduce the chances for less abundant species. For example, in the light microscopy analysis of raw water samples, only 1–2 diatoms can be observed in the microscopic field (Figure 6).
Figure 6

Diatom morphology typing in a raw water sample (1) at 40× magnification in a light microscope. (a and b) Pre-flocculation field of views (FOVs) and arrow points to the diatoms. (c) Post-flocculation microscopic analysis of supernatant displaying only grazers in FOV.

Figure 6

Diatom morphology typing in a raw water sample (1) at 40× magnification in a light microscope. (a and b) Pre-flocculation field of views (FOVs) and arrow points to the diatoms. (c) Post-flocculation microscopic analysis of supernatant displaying only grazers in FOV.

Close modal
In contrast, the post-flocculation light microscopic and SEM analysis shows more than 20 diatom particles in a field of view (Figure 7). Figures 8(a) and 8(b) summarize the species abundance in selected raw water samples, where pre- and post-flocculation numbers of species are presented. More genera have revealed their presence in the floc, which was utterly missed in direct microscopy of natural water. This way, we can extract the diverse species in a small inoculation volume. Eventually, it will upshoot the tiny habitat into the enrichment medium.
Figure 7

SEM images of flocs obtained from the water sample displaying post-flocculation. Species abundance: (a) Orthoseira, (b) Stephanocyclus, (c) Aulacoseira, (d) Gogorevia, (e) Diadesmis, (f) Gomphonema, (g) Synedra, and (h) Nitzschia.

Figure 7

SEM images of flocs obtained from the water sample displaying post-flocculation. Species abundance: (a) Orthoseira, (b) Stephanocyclus, (c) Aulacoseira, (d) Gogorevia, (e) Diadesmis, (f) Gomphonema, (g) Synedra, and (h) Nitzschia.

Close modal
Figure 8

Species abundance in raw water samples. (a) SEM image of enriched diatom (Sample 3) cultivated in f/2 medium. (b) Pre- and post-flocculation genera abundance in the various water samples obtained from cell counting in 100 FOVs.

Figure 8

Species abundance in raw water samples. (a) SEM image of enriched diatom (Sample 3) cultivated in f/2 medium. (b) Pre- and post-flocculation genera abundance in the various water samples obtained from cell counting in 100 FOVs.

Close modal

Flocculants/adsorption mechanism prediction

The flocculation process involves the adsorption of biopolymer onto the particle's surface (Demir et al. 2020). Usually, chitosan adsorbing on a diatom may attach to another diatom particle's bare surface, forming bridges through patching and charge neutralization mechanisms. When flocculation and adsorption processes are correlated, tuning the process to obtain the desired floc characteristics is possible. Adsorption and flocculation must coincide with functioning rather than as an independent mechanism. They are practically inseparable phenomena that can be modelled through various theoretical and experimental approaches (Strand et al. 2001; Rasteiro et al. 2015).

Our research elucidates the mechanism for chitosan-mediated diatom separation using adsorption isotherm experiments and other in silico investigations such as MD and MDS. Silaffin (diatom surface protein) gave maximum binding affinities to −7.4 kcal/mol, exhibiting relatively strong binding. Additionally, this energy-minimized binding pose (from the docking study) was simulated at the system with a pH of 8 and a temperature of 30 °C to understand the chemistry behind the adsorption of diatoms on the chitosan surfaces. Figure 9 illustrates the root mean square deviation (RMSD) of a ligand and protein computed based on their interaction and initial structure. The system never attained an equilibrium evident from the fluctuated RMSD trajectories above 3 Å, far from reaching balance (Tilwani et al. 2022). Thus, the non-equilibrium bridging and the phase transition seem to be the primary flocculation mechanism for the chosen system (Strand et al. 2003).
Figure 9

The RMSD plot for silaffin and chitosan interaction.

Figure 9

The RMSD plot for silaffin and chitosan interaction.

Close modal
The chitosan–silaffin interaction mainly involves PRO276, VAL278, THR280, SER281, ALA283, SER285, GLN287, GLN290, GLU296, SER310, SER311, ARG312, PRO313, ASP315, and ARG346, and the majority are the polar residues with an average of 40% contact across the simulation time (Figure 10). Here, the –NH2 and –OH functional groups of the chitosan play a crucial role in forming the specific H-bond with the protein residues. Furthermore, according to our observations, Khnifira et al.’s (2021) report has also displayed the significance of the amine (NH2) group in Eriochrome black T dye adsorption.
Figure 10

Chitosan–silaffin surface chemistry.

Figure 10

Chitosan–silaffin surface chemistry.

Close modal
Next, we surveyed the representative bond chemistries of –NH2 (chitosan) and SiO2 (frustule) by FT-IR analysis (Figure 11). Two intense bands representing SiO2 were observed: one around 1,098 cm−1 for asymmetric stretching vibration of Si–O–Si bonds assigning to SiO2 tetrahedra (Lyu et al. 2021) and the other at 469 cm−1 is an asymmetric bending vibration of Si–O–Si bonds. Hydroxide and amines (chitosan) can be bonded to the surface of silica materials through SiO–H···A (acceptor molecule) by forming hydrogen bonds at the external silanol sites (Grabowsky et al. 2009). The Si–O–Si bending of pristine diatoms gave a peak at 469 cm−1, while chitosan–diatom mixtures showed steep drops in peak intensity and broadened peaks. Thus, the peak shift observed at 478 cm−1 (inset Figure 11) is mainly due to the formation of hydrogen bonding of SiO···H–NH with chitosan; a relative peak shift was observed in the amine bending region of lone chitosan–frustule.
Figure 11

FT-IR analysis. Inset graph depicts the FWHM and peak intensity analysis for the selected peaks (478 cm−1).

Figure 11

FT-IR analysis. Inset graph depicts the FWHM and peak intensity analysis for the selected peaks (478 cm−1).

Close modal
Earlier in this section, we established that chemisorption could be a mechanism for diatom–chitosan interaction. The adsorption isotherm analysis for diatom–chitosan interaction follows the Langmuir isotherm (Supplementary Data S2), suggesting that the adsorbate adsorption is limited to one molecular layer, and the system attains equilibrium within 60 min (Figure 12). The computed value for the Langmuir constant is 5.11 × 104, indicating the higher interaction between the chitosan and the silaffin-containing frustules.
Figure 12

Adsorption kinetics study for chitosan–diatom.

Figure 12

Adsorption kinetics study for chitosan–diatom.

Close modal

Biopolymer – chitosan – is a conventional flocculant for water, wastewater treatment, dewatering/harvesting, and fermentation processes (Chen et al. 2003). Applying chitosan for only diatom separation in the raw water where other microalgae and grazers are present was the challenge for the current research (Kale & Karthick 2015). So far, the chitosan solution (pH 1) has been evaluated for the sedimentation of various microalgae from the cultivation vessels. Surprisingly, our observation noted very few other microalgal cells at the bottom. Nevertheless, this observation does not make sense scientifically, considering that several research articles cite chitosan solution for microalgae flocculation. It may be because all previous reports have been for defined culturing conditions such as specific medium, ion strength, and cell density, where chitosan can flocculate other non-siliceous microorganisms.

Furthermore, almost all the surveyed articles utilized other electrolytes or physical treatments specific to the particular research culture (Şirin et al. 2012). Therefore, contrary to our primary attempt to sediment diatoms with chitosan solution (pH 1–7), we have not seen any significant sedimentation. Consequently, we conclude that the modifications optimized in this study, such as using chitosan flakes instead of a soluble suspension, favour diatom sedimentation. Additionally, while other cited articles utilize spectrophotometric quantification, the observation method in this article relies on direct cell counting. The direct cell count presents a more specific view of the studied organisms. Here, the study does not focus on one or two genera but rather on the sedimentation of siliceous cells.

Diatom's biotechnological potential is still underutilized, and access to pure diatom culture is a crucial constraint. This diatom separation method would provide more ease in developing the inoculum for subsequent bioprocesses. Furthermore, without any complex pre-treatment or additional substances, chitosan flakes efficiently separate the siliceous diatoms leaving grazers and other competitors in the top layer.

With this, we report an easy, quick, reliable, and reproducible method for diatom separation from natural water. The earlier studies on title flocculants for microalgae demand specific chitosan pre-treatments. At the same time, here directly, the chitosan flakes were applied in the defined ratio of 1:1,000 (chitosan (g):water (mL)). The developed process is highly accurate and precise for diatoms while leaving microalgae and protozoa in the supernatant. This rapid (only 60 min) method will boost diatom pure culture studies, thereby filling a void in the availability of pure culture. Also, we elucidated the mechanism of chitosan–frustule interaction, where the formation of hydrogen bonds among silaffin and SiO2 of frustule with chitosan primary amines play a significant role in adsorption and flocculation. The chitosan–diatom adsorption process follows the Langmuir isotherm model.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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