# Effect of purification method on the physico-chemical and optical properties of aqueous carbon dot dispersions analysed using generalised additive models

Enrique Manso, Christian Perruchot, Javier Tarrío-Saavedra, Salvador Naya, Alain Ponton

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## To cite this version:

Enrique Manso, Christian Perruchot, Javier Tarrío-Saavedra, Salvador Naya, Alain Ponton. Effect of purification method on the physico-chemical and optical properties of aqueous carbon dot dispersions analysed using generalised additive models. Journal of Materials Research and Technology, 2025, 39, pp.1627-1637. 10.1016/j.jmrt.2025.09.064. hal-05325724

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# Effect of purification method on the physico-chemical and optical properties of aqueous carbon dot dispersions analysed using generalised additive models

Enrique Manso<sup>a, ID</sup>, Christian Perruchot<sup>b</sup>, Javier Tarrío-Saavedra<sup>c</sup>, Salvador Naya<sup>c</sup>, Alain Ponton<sup>a, ID</sup>

## ARTICLE INFO

Keywords:

Carbon dots

Purification

Absorbance

Fluorescence

Statistical learning

Generalised additive models

Parametric regression

## ABSTRACT

We investigated the impact of purification method (dialysis versus ethanol precipitation) on the physico-chemical, optical, and rheological properties of glucose-derived carbon dots (CD) synthesised by ultrasonic treatment by combining a comprehensive experimental methodology and the utilisation of machine learning tools within the Artificial intelligence (AI) framework.

Supervised learning techniques such as nonparametric and semiparametric Generalised additive models (GAM) enabled to extract from optical spectra maximum intensity, wavelength of maximum intensity or full width at half maximum of absorbance or fluorescence revealing nonlinear CD dependence of these key parameters for dialysis and linear one for ethanol. The results demonstrated a more pronounced enhancement of an increase of maximum intensity, redshift and widening of both absorption and fluorescence optical peaks as well as viscosity for dialysed CD in comparison to the use of ethanol, which was associated to an improvement of purity and negative surface charge.

Structural and morphological analysis confirmed that dialysed CD exhibit a multi-layered structure with low crystallinity.

## 1. Introduction

Carbon dots (CD) are zero-dimensional carbon structures of nano-metric size with photoluminescent properties. They were first observed in 2004 during the purification of single-walled carbon nanotubes (SWCNT) [1]. CD exhibit a number of interesting chemical and physical properties, including a high surface area, the presence of diverse functional groups, excellent stability in aqueous dispersions, UV-visible absorption, photoluminescence, biocompatibility and non-toxicity [2], which enable their utilisation in a wide range of applications [3].

The synthesis of carbon dots has been a topic of extensive study since their initial discovery in 2004. The various synthesis techniques can be classified into two principal categories: top-down and bottom-up methods.

Top-down methods consist in breaking large carbonised materials such as graphene, graphene oxides or carbon nanotubes in order to yield

smaller structures by laser ablation [4,5], arc discharge [6], ultrasonic [7,8], chemical [9] and solvothermal [10,11] exfoliation. The primary issue with top-down methodologies is their limited applicability in large-scale production settings. This is due to the fact that they lead to lower quantum yields and the employment of costly, sophisticated equipment, in addition to toxic and uncontrollable conditions [3]. In contrast, bottom-up methods involve the synthesis of carbon dots from small organic precursors through the application of diverse chemical and physical techniques, including solvothermal reactions [12–14], microwave-assisted processes [15,16], thermal pyrolysis [17–19] or ultrasonic synthesis [20,21]. The use of bottom-up methods for CD synthesis is increasing due to the greater simplicity and lower cost and toxicity of these methods [3].

In comparison with other bottom-up methods, ultrasonic synthesis offers a low-temperature, and scalable route that does not necessitate the use of high-pressure vessels. The process has been demonstrated to

<footnote><sup>a</sup> Université Paris Cité, CNRS, Matière et Systèmes Complexes, F-75013, Paris, France</footnote>

<footnote><sup>b</sup> Université Paris Cité, CNRS, Interface Traitement Organisation et Dynamique des Systèmes, F-75013, Paris, France</footnote>

<footnote><sup>c</sup> Universidade da Coruña, MODES Group, CITIC, Mathematics Department, EPEF, Ferrol, Spain</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: alain.ponton@u-paris.fr (A. Ponton).</footnote>
provide rapid reaction kinetics. Furthermore, it can be performed with
simple equipment, thus reducing energy consumption and enabling
reproducible control over particle size distribution by controlling syn-
thesis parameters. These parameters include reaction time, temperature,
ultrasound power and frequency [22]. However, the majority of com-
mercial devices do not allow for tunable ultrasound frequency, and the
common heating of water due to prolonged sonication can compromise
the control of CD size and the achievement of monodisperse size
distributions.

The synthesis conditions and the selection of precursor have been
extensively studied in the literature [13,18,23,24]. However, another
crucial step in the synthesis of carbon dots is the purification of the CD in
order to isolate the nanoparticles from the precursors and other reaction
intermediates and by-products. The purification process is a key aspect
in obtaining CD dispersions that meet the requisite standards for theo-
retical research and applications [25]. In particular, an incomplete pu-
rification of CD can have a significant impact on their optical properties
due to the potential presence of residual organic moieties that may be
generated during the synthesis of CD, especially in bottom-up synthesis.
These moieties can possess fluorescent properties that can mask or alter
the properties of the resulting CD dispersions [26].

The primary methods for the purification of CD include dialysis [20, 27–30], centrifugation [31–33] and chromatography [18,34,35]. Other methods that have been used in recent years include filtering [8,36], liquid-liquid extraction [37,38], electrophoresis [39,40] or separation by precipitation [41]. Additionally, research has been performed with the aim of optimising existing methods such as dialysis [42], comparing the efficacy of different purification methods for the same synthesis of CD [8] and combining different purification methods [43]. Furthermore new purification methods have been explored to separate CD as a function of their degree of carbonisation or surface chemical properties such as ultracentrifugation with a hydrophilicity gradient [44], gradient extraction [45] or cloud point extraction [46]. Nevertheless, further research is required to optimise the purification process and develop a comprehensive methodology for determining the most efficient purification method for CD in different synthesis conditions. In addition, a statistical analysis of the data for prediction is necessary.

In order to gain a deeper understanding of the efficiency of different
purification techniques for carbon dots on their properties, we have
employed a straightforward bottom-up one-step ultrasonic synthesis of
CD using glucose as the precursor. Additionally, we have investigated
two established purification methods either by dialysis or by changing
the continuous phase from water to ethanol to make salts and remaining
glucose precipitate. The objective was to determine the most efficient
method for the purification of CD by measuring and comparing different
physical properties deeply analysed by statistical and machine learning
techniques.

## 2. Materials and methods

### 2.1. Materials and chemicals

D-(+)-glucose was purchased from Sigma Aldrich as well as MgSO4 anhydrous. The 0.5–1 kDa MWCO Biotech CE dialysis membranes were acquired from Spectrum Labs. While the 0.22 µm PES syringe filters were procured from Sartorius.

### 2.2. Synthesis of CD from glucose

The synthesis of CD was performed using a one-step bottom-up ultrasonic method [20,41]. In accordance with the synthesis protocol, 50 mL of a 1 mol/L D-(+)-glucose aqueous solution was mixed with 50 mL of 1 mol/L NaOH aqueous solution. The resulting solution was introduced into a Transsonic TI-H-5 ultrasonic bath from Bioblock Scientific and submitted to ultrasonication at a frequency of 25 kHz and maximum intensity (400 W) for a period of 4 h, yielding in the formation of a dark

red-brownish dispersion.

### 2.3. Purification of CD

#### 2.3.1. Purification with ethanol

The first purification method involved the precipitation of the re-
sidual salts and excess glucose in the CD dispersion by changing the
continuous phase from water to ethanol. In the initial stage of the pro-
cess, the pH was adjusted to a neutral value of 7 by the addition of HCl.
Subsequently, pure ethanol was added to the aqueous dispersion of CD
in a volumetric ratio of 5:1 and MgSO4 was added until the salt exhibited
free flow (approximately 45 g per 100 mL of water), thereby completely
removing the water from the mixture. The obtained orange dispersion
was then stored for 24 h, to allow the precipitation of the salts and
glucose, after which it was filtered by gravity. Finally, the ethanol was
evaporated in a rotary evaporator at 55–60 °C and 200 mbar and the
sample was diluted to 100 mL with pure water, ultrasonicated for 15 min
at 25 kHz and 400 W to break up possible aggregates and filtered with a
0.22 µm PES syringe filter to eliminate large carbonised structures. The
concentration was determined by the dry extract method in an oven at
60 °C observing a yield of ~50 % in mass compared to the initial mass of
glucose.

#### 2.3.2. Purification by dialysis

The second purification method employed was a dialysis method. The CD dispersion obtained was also neutralised to pH 7 using HCl and subsequently diluted to a concentration five times that of the initial concentration. The diluted dispersion was dialysed using a 0.5–1 kDa MWCO Biotech CE dialysis membrane for a period of 24 h, after which it was concentrated to 100 mL by rotary evaporation at 55–60 °C and 75 mbar and ultrasonicated for 15 min at 25 kHz and 400 W in order to break down any potential aggregates. The final dispersion was filtered using a 0.22 µm PES syringe filter to remove any residual large carbonised structures. The concentration was determined by the dry extract method in an oven at 60 °C, with a yield of approximately 12 % in mass compared to the initial mass of glucose.

A comparison between the two aforementioned purification methods
can be observed in Fig. 1.

## 2.4. Zeta potential determination

The zeta potential was determined by measuring the electrophoretic mobility of the CD in an aqueous dispersion at a concentration of 0.015 wt % CD and different pH values (4–11) using the Zetasizer Nano ZS device from Malvern Panalytical. Zeta potential was determined from electrophoretic mobility by applying the Henry equation, in which the Henry's function is fixed to a value of 1.5 according to Smoluchowski approximation for aqueous media with a moderate concentration of electrolytes [47].

The pH was controlled by the addition of HCl and NaOH to the CD dispersion samples. All measurements were performed in triplicate to ensure repeatability.

## 2.5. Ultraviolet (UV)-visible absorption spectroscopy

UV-visible light absorption measurements were performed using a JASCO V-630 double beam spectrophotometer in the wavelength range of 260–900 nm. Aqueous dispersions of CD were studied at different concentrations (0.001–0.2 wt % for CD purified with ethanol and 0.001–0.015 wt % for CD purified by dialysis) at constant pH (~6 in pure water). All measurements were performed at 25 °C. To ensure repeatability, all measurements were performed in triplicate with a standard deviation lower than 4 % for the maximum absorbance. Pure water was used as the reference solution.
<figure><img src="image_4.png" /><figcaption>Fig. 1. Schematic representation of the purification of CD dispersions by the two employed methods.</figcaption></figure>

## 2.6. Fluorescence measurements

Photoluminescent emission measurements were performed using a FS5 spectrofluorometer, manufactured by Edinburgh Instruments. Emission scans were performed in the UV-visible range using a 1 nm bandwidth for excitation and a 2 nm bandwidth for emission. Aqueous dispersions of CD were studied at various concentrations (0.001–1 wt % for CD purified with ethanol and 0.001–0.2 wt % for CD purified by dialysis) at constant pH (~6 in pure water). All measurements were performed at 20 °C. Emission spectra measurements following excitation at the wavelength at which maximum emission is observed were performed in triplicate to ensure repeatability with a standard deviation lower than 6.5 % for the maximum emission intensity. Pure water was used as reference.

## 2.7. Shear viscosity

Shear viscosity measurements were performed using a Haake Mars II torque-controlled rheometer from Thermo Scientific using a titanium cone-plate geometry with a 52 µm gap, a 1° cone angle and 60 mm diameter. Temperature control was achieved by means of a Peltier device. Shear viscosity was measured in a shear rate range from 350 to 500 s⁻¹ by applying rotational shear to the dispersion until a steady state was achieved. Measurements were performed for CD aqueous dispersions at different concentrations of CD (0–5 wt %) at a constant temperature of 25 °C. The average values of Newtonian viscosity were determined as the average of the measured shear viscosity values in the range of 350–500 s⁻¹ for each sample with a standard deviation lower than 0.5 %.

## 2.8. Chemical, structural and morphological characterisation of dialysed carbon dots

Fourier-transformed infra-red (FTIR) measurements were performed on the CD powder using a ThermoFisher Nicolet 8700 device. Approximately 1 % of the CD powder was grinded together with KBr and a pellet was prepared by applying around 8 tonnes of force. The measurement was performed in transmission mode, with a pellet of pure KBr employed for background reference. X-ray photoelectron spectroscopy (XPS) measurements were conducted using a Thermo K-Alpha⁺

spectrometer fitted with a monochromated Al-Kα X-ray source (1486.6 eV). To perform the measurements, the CD dispersion droplets were dried on an ITO-glass surface until a homogeneous layer was obtained. X-ray diffraction (XRD) measurements were performed using an Empyrean diffractometer from Panalytical, equipped with a copper X-ray source with a Kα value of 1.54 Å. The 2θ values were recorded between 4° and 60° for the CD powder. Atomic force microscopy (AFM) measurements were carried out using an Asylum MFP-3D device from Oxford Instruments in contact mode. In order to facilitate the measurement process, 0.1 wt % CD aqueous dispersion was dried on a mica surface. The height distribution of the CD was obtained by measuring 64 nanoparticles and analysing the height profile along different lines using the software Gwyddion. High-resolution transmission electronic microscopy (HR-TEM) measurements were performed using a JEOL ARM device operating at 80 kV. A droplet of the CD aqueous dispersion, with a concentration of 0.5 wt % was dried on a formvar grid for HR-TEM measurement. The size distribution was obtained by measuring a total of 44 nanoparticles. The diameter of the nanoparticles was determined by measuring the area of the nanoparticles using the software ImageJ and assuming a perfect circular shape for all particles observed by HR-TEM.

## 2.9. Statistical and machine learning techniques

In context of statistical learning and machine learning, regression analysis is a part of supervised learning techniques that allows for the prediction of the value of a quantitative variable Y as a function of one independent variable X (simple regression) or as a function of Xᵢ predictors, with i = 1, 2, ..., n. The utilisation of parametric regression facilitates the determination of the nature of the dependence, as a function of interpretable parameters. These later in turn provide information about the studied physico-chemical process [48]. The parametric regression can be linear or nonlinear and can be noted as

$$y_i = m(t_i) + \epsilon_i, \quad (1)$$

being m the regression model, yᵢ the estimates of the response variable, tᵢ the values of the predictor and εᵢ the error values (difference between real value of the response and estimates) with i = 1, 2, ..., n. When m is parametric, we could provide the M = {mθ(·)/θ ∈ Θ} definition, where θ is the vector of parameters belonging to subset Θ, which is defined in
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In this work, the relationship between response variables and predictors is strongly nonlinear, a factor which hinders the establishment of a simple and unique type of nonlinear regression model. Consequently, alternative, more flexible semiparametric models are employed in the domain of nonparametrics, machine learning and artificial intelligence. Therefore, the so-called Generalised additive models (GAM) are applied [49]. They provide an alternative to parametric regression assuming the unique hypothesis consisting of the Y variable depending on $X_i$ in a smooth way is valid. They are based on the fitting of basis of splines. This type of models enables the visualisation of the effect of each $X_i$ variable on the Y response variable. In this way, the GAM model can contribute to the characterisation of the type of effect (linear or nonlinear) of each $X_i$ variable. This information could be useful to estimate and fit the appropriate parametric model.

We can estimate the response variable as a function of covariates, qualitative variables and their interactions through the estimation of the corresponding smooth effects on the response. A general expression of GAM models is, for instance,

$$g(\eta) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + f_1(X_3) + f_2(X_4) + f_{12}(X_3, X_4), \quad (2)$$

where $g(\eta)$ is the fitting of a function of the response variable to predict ($\eta$ is the mean of the response variable Y), $X_1$ and $X_2$ are predictors included in a linear way (parametric approach) by the estimation of $\beta_i$, whereas $f_1, f_2$, and $f_3$ are the smooth effects (nonparametric approach) of the $X_3, X_4$, and $X_3$ and $X_4$ interaction, respectively. The ability to incorporate both parametric and semiparametric effects is the key advantage of utilising GAM semiparametric models. The estimation of these smooth effects is achieved through the implementation of thin plate splines and cubic regression splines and an estimation of these parameters through the utilisation of the REML algorithm [49].

In this study, GAM models allow us to analyse the absorption and fluorescence spectra as a function of wavelength and CD concentration and to estimate accurately optical parameters of CD aqueous dispersions. Moreover, we are able to estimate the dependence of these parameters as a function of CD concentration and method of CD purification.

# 3. Results and discussion

## 3.1. Zeta potential determination

The zeta potential determination results of CD dispersions purified both by dialysis and with ethanol (see Fig. 2 in which the error bars represent the standard deviation of average values obtained from three measurements) show that the CD possess a negative surface charge. This is due to the presence of oxygen-based functional groups on their

<figure><img src="image_6.png" /><figcaption>Fig. 2. Zeta potential of CD dispersion purified with ethanol or by dialysis at different pH values.</figcaption></figure>

surface, which originate from the oxygen-based functional groups of glucose (hydroxyl and ether) and functional groups obtained by oxidation of these groups (carbonyl and carboxyl groups). These oxygen-containing functional groups are schematically represented on Fig. 2. The negative surface charge seems to vary between the two purification methods, with values of -40.1 ± 2.8 mV and -5.6 ± 1.8 mV obtained for CD dispersions purified by dialysis and with ethanol, respectively, at pH ~6. The difference in zeta potential value can be attributed both to a higher purity of CD with a more negative surface charge in the case of CD purified by dialysis as well as to a sedimentation of the most polar CD (with a more negative surface charge due to the presence of polar functional groups such as hydroxyl or carboxyl groups) when purifying carbon dots by changing the continuous phase to ethanol due to a lower polarity of ethanol when compared to water media.

With regard to the effect of pH, a global tendency can be observed towards a decrease in surface negative charge at pH values below approximately 6 and an increase at higher pH. This may be related to the pKa of deprotonation of aromatic hydroxyl (pKa ~10-12) and carboxylic (pKa ~3-6) groups respectively [50].

## 3.2. Absorption and fluorescence of CD dispersions

The absorption spectra of CD at different concentrations for both purification methods can be found in Fig. 3 representing the absorbance (defined as -log(I/I₀) where I₀ and I are the intensity of the incident light and of the light after travelling through the sample, respectively) as a function of wavelength. This figure demonstrates the presence of an absorption peak at 270-290 nm increasing with the concentration of CD and a tail at 300-400 nm which can be attributed to $\pi \to \pi^*$ and $n \to \pi^*$ transitions of C=C and C=O groups present in the CD structure respectively. This observation is consistent with previous reports on glucose-based CD [20].

In order to properly analyse the absorption peaks of CD dispersions, the obtained spectra were fitted by a non-parametric generalised additive model in order to extract information such as the maximum absorbance, the wavelength at which this maximum is observed ($\lambda_{absorbancemax}$) as well as the full width at half maximum (FWHM) of the peaks, without the influence of the noise of the experimental results. For this purpose, two different variables (wavelength and CD concentration) are modelled in a non-parametric way, taking into account the existence of a non-linear interaction between the two variables to obtain a model function:

$$g(E[\text{Absorbance}]) = f(\text{Wavelength, CD concentration}) \quad (3)$$

where E is the expected value of the conditioned mean and the link (g) is the inverse function assuming that the absorbance follows a gamma distribution and the chosen basis functions are cubic regression splines with a basis dimension of 50 for the wavelength and 5 for the CD concentration using tensor product smoothing.

The three parameters (maximum absorbance, $\lambda_{absorbancemax}$, FWHM) were numerically determined from the fitted curves. The dependence of the maximum absorbance on CD concentration and purification method considering the interaction between both parameters was fitted by multivariate linear regression while $\lambda_{absorbancemax}$ and FWHM were analysed using GAM which also considers the interaction between the two parameters ($\lambda_{absorbancemax}$ and FWHM). The confidence bands obtained by adding and subtracting the double of standard deviation of the residuals are included in Fig. 4a-c.

As shown in Fig. 4a, the increase of maximum absorbance with CD concentration which can be due to an increased number of $\pi \to \pi^*$ and $n \to \pi^*$ transitions from C=C and C=O groups is linear with different slopes depending on purification method. The goodness of the fitting is confirmed from the fact that the model explains the 99 % of the overall variability of response feature. Both CD concentration and purification method have a significant effect on maximum absorbance (p-values
<figure><img src="image_7.png" /><figcaption>Fig. 3. Absorption spectra of CD purified a) with ethanol or b) by dialysis at different CD concentrations at a pH of ~6. Continuous lines represent GAM fits.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 4. Effect of CD concentration (pH ~ 6) and purification method on a) maximum absorbance, b) wavelength of maximum absorbance ($\lambda_{absorbancemax}$) and c) full width at half maximum (FWHM) of the absorption peaks of CD dispersions. Continuous lines represent a) linear and b) and c) GAM fits.</figcaption></figure>

deduced from t statistical test <0.05) with a higher effect for CD dispersions purified by dialysis (slope of 105.9 compared to 42.1 in the first equation of Table 1). Furthermore, the model fulfils the hypothesis of linear regression models, i.e. residuals can be assumed to be independent, homokedastic, and Gaussian (p-value <0.01) after application of the Breusch-Pagan (p-value = 0.9452), Durbin-Watson (p-value = 0.159), and Shapiro-Wilk (p-value = 0.6419) tests. Application of Ramsey regression equation specification error test (RESET) test validates the linear regression model as evidenced by the calculated p-value (0.1574).

The increase of CD concentration may also result in shorter distance and aggregation between different CD present in the dispersion, with the subsequent creation of new lower energy level transitions due to the overlap of the energy levels of $\pi\to\pi^*$ and $n\to\pi^*$ transitions of CD groups [15]. These lower energy level transitions can induce an increase of $\lambda_{absorbancemax}$ or a redshift and their great variety lead to a broadening of the peaks (FWHM) depending on the purification method as experimentally observed in Fig. 4b and Fig. 4c respectively. These new energy level transitions can also lead to a variation of the bandgap of the material. The optical bandgap of CD has been previously calculated by the tau plot [51], which represents $(\alpha h\nu)^2$ versus $h\nu$ where $\alpha$ is the absorption coefficient, $h$ is the Planck constant and $\nu$ is the light frequency. The optical bandgap of CD in dispersion at different concentrations is calculated as the intersection of the x-axis with the extrapolation of the maximum slope of the tau plot. As observed in Fig. S1, the bandgap decreases as CD concentration increases (from 4.43 to 4.38 at 0.001 wt % to 4.24 and 4.26 at 0.015 wt % for CD dispersions dialysed and

<table><caption>**Table 1**
GAM fitting parameters and significance study for absorbance, $\lambda_{absorbancemax}$, and FWHM vs. CD concentration and purification method.</caption><tbody><tr><td colspan="4">Abs. = 0.109 + 42.1CD conc.·Pur. Met.[Ethanol] + 105.9CD conc.·Pur. Met.[Dialysed]; R<sup>2</sup> = 0.996</td></tr><tr><td>Parametric coefficients<br>(Intercept)</td><td>Estimate</td><td>t-value</td><td>p-value</td></tr><tr><td>CD conc: Pur. Met[Ethanol]</td><td>0.1090</td><td>6.082</td><td>5.10<sup>-4</sup></td></tr><tr><td>CD conc: Pur. Met[Dialysed]</td><td>42.08</td><td>17.094</td><td>5.75·10<sup>-7</sup></td></tr><tr><td></td><td>105.90</td><td>43.017</td><td>9.58·10<sup>-10</sup></td></tr><tr><td colspan="4">λ<sub>absorbancemax</sub> = 272.2 + f(CD concentration) Purification Method: R<sup>2</sup> = 0.81</td></tr><tr><td>A. Parametric coefficients<br>(Intercept)</td><td>Estimate</td><td>t-value</td><td>p-value</td></tr><tr><td>B. smooth terms</td><td>edf</td><td>F-value</td><td>p-value</td></tr><tr><td>f(CD conc): Pur. Met[Ethanol]</td><td>1.0000</td><td>4.0200</td><td>0.0918</td></tr><tr><td>f(CD conc): Pur. Met[Dialysed]</td><td>2.0620</td><td>14.7200</td><td>0.0040</td></tr><tr><td colspan="4">FWHM = 28.2 + f(CD concentration) Purification Method: R<sup>2</sup> = 0.83</td></tr><tr><td>A. Parametric coefficients<br>(Intercept)</td><td>Estimate</td><td>t-value</td><td>p-value</td></tr><tr><td>B. smooth terms</td><td>edf</td><td>F-value</td><td>p-value</td></tr><tr><td>f(CD conc): Pur. Met[Ethanol]</td><td>1.000</td><td>4.616</td><td>0.08441</td></tr><tr><td>f(CD conc): Pur. Met[Dialysed]</td><td>2.895</td><td>12.140</td><td>0.00929</td></tr></tbody></table>
purified with ethanol respectively) exhibiting an inverse correlation between the bandgap and $\lambda_{absorbancemax}$.

The increase of the two parameters ($\lambda_{absorbancemax}$ and FWHM) as a function of CD concentration is significantly different depending on the purification method. They are almost linear when CD are purified with ethanol (effective degrees of freedom, edf, equal to 1 in Table 1) but nonlinear sigmoid when purified CD are dialysed. In this later case, the significant effect of CD concentration on $\lambda_{absorbancemax}$ and FWHM is confirmed at 81 % and 83 % respectively by p-value <0.05. The F test is applied when testing the effect of smooth terms.

As observed in Fig. S2 in the supporting information, the emission spectra of the CD dispersions purified by the two methods are strongly dependent on the excitation wavelength not only in terms of emission intensity, which exhibits a maximum at a certain excitation wavelength ($\lambda_{excitationmax}$) and decreases when the wavelength deviates from this value, but also in the width of the peaks, observing a clear broadening of the peaks at higher excitation wavelengths as well as a redshift of the maximum of emission as the excitation wavelength is increased, as illustrated in Fig. S3. This dependency could be related to the size polydispersity of CD nanoparticles [52] as well as to a heterogeneous distribution of surface defects and functional groups with different energies [53].

These outstanding photoluminescent properties opening a wide range of applications have been the subject of intensive research for the past ten years [2] and are generally linked to three different mechanisms including quantum confinement effects, the presence of surface defects and the presence of fluorophore groups in their structure [54].

The concentration effect on the fluorescence of CD dispersions purified by both methods has also been studied. Fig. 5 illustrates the emission spectra at pH ~ 6, which was selected as the plateau of zeta potential to eliminate any potential pH-related interference during the measurements. The excitation wavelength was set to the wavelength at which the maximum emission was observed for each CD concentration (see Fig. S4a-b). The maximum excitation value was identified for each sample by measuring the emission spectra at different excitation wavelengths with a difference of 10 nm in excitation wavelength between measurements in a similar way as shown in Fig. S2.

As for UV-visible absorption measurements, a similar GAM model was also used to fit the fluorescence emission peaks at different CD concentrations. However, given that the emission spectra of CD dispersions are strongly dependent on the wavelength of excitation, the excitation wavelength at which the maximum of emission intensity is obtained at each CD concentration must be integrated as a third parameter into the modelling of fluorescence results. The resulting fitting model for the emission spectra as a function of emission wavelength and CD concentration can be expressed as a sum of two functions, a first one depending on the emission wavelength and CD concentration and a second one which only depends on the excitation wavelength at which the maximum of emission is obtained:

$$g(E[\text{Emission Intensity}]) = f_1(\text{Em. wavelength}, \text{pH}) + f_2(\lambda_{\text{excitationmax}}) \quad (4)$$

The basis functions are cubic regression splines for $f_1$ and Gaussian process splines for $f_2$ with a basis dimension of 50 for the wavelength, 8 for CD concentration for CD dispersions purified with ethanol and 7 for dialysed CD dispersions using tensor product smoothing and 4 for the maximum excitation wavelength.

The three parameters (maximum emission intensity, $\lambda_{emissionmax}$, FWHM) were numerically determined from the fitted curves. Their dependence on CD concentration and purification method was fitted by GAM considering the interaction between both parameters with confidence bands obtained by adding and subtracting the double of standard deviation of the residuals.

As illustrated in Fig. 6a, a discernible increase of the maximum emission intensity is evident by increasing CD concentration until a maximum critical concentration (0.05 wt % for dialysed CD and 0.2 wt % for CD purified with ethanol). Therefore, a reduction of the maximum emission intensity is observed. The effect of CD concentration is truly nonlinear (the model explains the 98 % of the intensity variability) and significant (p-value <0.05) as shown in Table 2. This quenching can be attributed to a combination of two effects. An inner filter effect due to a reabsorption of the emitted light by the own carbon dots dispersion [55] which exhibits absorption within the range of the emission, and as previously discussed, this absorption increases at higher CD concentrations due to the redshift and widening of the absorption peak. The second phenomenon is the emergence of exciton annihilation due to shorter distances between the CD or even aggregation at higher concentrations of CD leading to an increase in nonradiative recombination and subsequent decrease of fluorescence intensity [15].

Furthermore, CD concentration in the whole studied range and purification method have also a significant (p-values deduced from t or F test <0.05) nonlinear effect (edf close or greater to 2) on $\lambda_{emissionmax}$ and FWHM (see Fig. 6b-c), explaining ≥ 90% of the overall information of the response variables (high goodness of fit). The mechanism responsible for this redshift and widening of the fluorescence peaks may be the same as that observed for absorption peaks, resulting from the overlapping of the energy levels of $\pi\to\pi^*$ and $n\to\pi^*$ transitions creating new lower energy level transitions [15]. If the CD concentration is limited to 0.25 wt%, we put in evidence that the greater increase in $\lambda_{emissionmax}$ and FWHM is still visible for CD purified by dialysis. This increase is exponential in nature, in contrast to the linear increase observed for the CD purified by ethanol (see insets of Fig. 6b-c).

All the above results show that fluorescence measurements as a function of CD concentration for CD dispersions obtained by both methods of purification present several differences. Firstly, the critical concentration for maximum emission is observed at a lower CD concentration for dialysed CD. Furthermore, the emission intensity at CD concentrations below this critical concentration is also higher for the dialysed CD (see Fig. 6a). This, combined with a higher $\lambda_{emissionmax}$ and

<figure><img src="image_9.png" /><figcaption>Fig. 5. Effect of CD concentration (pH ~ 6) on emission spectra of CD purified a) with ethanol or b) by dialysis. Continuous lines represent GAM fits.</figcaption></figure>
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 6.** Effect of CD concentration (pH ~ 6) and purification method on a) maximum emission intensity b) wavelength of maximum emission and c) FWHM of emission of CD dispersions. Continuous lines represent GAM fits.</figcaption></figure>

FWHM observed for the dialysed CD dispersion, seems to confirm a higher purity of the dialysed CD dispersion and therefore a higher real concentration of CD in the dispersion. However, it can also be observed how the maximum emission observed at concentration above the critical concentration is higher for the CD dispersion purified with ethanol (at 0.2 wt %) than for the CD dispersion purified by dialysis (at 0.05 wt %), which could be due to the presence of small organic moieties that also have an influence in the fluorescence of the CD dispersions purified with ethanol.

### 3.3. Shear viscosity

The linear variation of the shear stress of CD dispersions purified with ethanol or by dialysis as a function of shear rate at varying CD concentrations and at 25 °C (Fig. S5 in the supporting information) demonstrates that the dispersions exhibit Newtonian behaviour at least up to 5 wt %. The relative Newtonian viscosity (Newtonian viscosity of CD dispersion determined by the slope of the linear fitting of

<caption>**Table 2**</caption>

GAM fitting parameters and significance study for emission intensity, $\lambda_{emissionmax}$, and FWHM vs. CD concentration and purification method.

<table><caption>Intensity = 69559 + f(CD concentration)Purification Method: R<sup>2</sup> = 0.98</caption><thead><tr><th></th><th>Estimate</th><th>t-value</th><th>p-value</th></tr></thead><tbody><tr><td>A. Parametric coefficients<br>(Intercept)</td><td>69559</td><td>28.74</td><td>5.13·10<sup>-9</sup></td></tr><tr><td>B. smooth terms</td><td>edf</td><td>F-value</td><td>p-value</td></tr><tr><td>f(CD conc):Pur. Met[Ethanol]</td><td>3.466</td><td>134.63</td><td>&lt;2.10<sup>-16</sup></td></tr><tr><td>f(CD conc):Pur. Met[Dialysed]</td><td>3.951</td><td>53.81</td><td>1.23·10<sup>-6</sup></td></tr></tbody></table>

<table><caption>λ<sub>emissionmax</sub> = 452.3 + f(CD concentration)Purification Method: R<sup>2</sup> = 0.90</caption><thead><tr><th></th><th>Estimate</th><th>t-value</th><th>p-value</th></tr></thead><tbody><tr><td>A. Parametric coefficients<br>(Intercept)</td><td>452.3</td><td>113.1</td><td>&lt;2.10<sup>-16</sup></td></tr><tr><td>B. smooth terms</td><td>edf</td><td>F-value</td><td>p-value</td></tr><tr><td>f(CD conc):Pur. Met[Ethanol]</td><td>1.843</td><td>25.03</td><td>8.17·10<sup>-5</sup></td></tr><tr><td>f(CD conc):Pur. Met[Dialysed]</td><td>2.506</td><td>35.65</td><td>1.13·10<sup>-5</sup></td></tr></tbody></table>

<table><caption>FWHM = 100.428 + f(CD concentration)Purification Method: R<sup>2</sup> = 0.95</caption><thead><tr><th></th><th>Estimate</th><th>t-value</th><th>p-value</th></tr></thead><tbody><tr><td>A. Parametric coefficients<br>(Intercept)</td><td>100.428</td><td>53.47</td><td>2.10<sup>-13</sup></td></tr><tr><td>B. smooth terms</td><td>edf</td><td>F-value</td><td>p-value</td></tr><tr><td>f(CD conc):Pur. Met[Ethanol]</td><td>2.187</td><td>52.61</td><td>5.03·10<sup>-6</sup></td></tr><tr><td>f(CD conc):Pur. Met[Dialysed]</td><td>3.003</td><td>50.35</td><td>3.51·10<sup>-6</sup></td></tr></tbody></table>

experimental data and divided by the viscosity of water at 25 °C) is shown (Fig. 7) to increase as a function of CD volume fraction (deduced from the CD concentration and a volumetric mass of 2.26 g/mL). The fitting of experimental data by classical Einstein model for diluted suspensions of rigid spheres without hydrodynamic interactions (dashed black line in Fig. 7) is inadequate. This deficiency can be attributed to the lamellar shape of CD with an aspect ratio of 8, as it will be later discussed during the study of the chemical, physical and morphological characterisation of CD. The dependence of interacting particles dispersion viscosity on the volume fraction ($\phi$) can be expressed as [56]:

$$ \frac{\eta_{disp.}}{\eta_{water}} = 1 + [\eta]\phi + k'_{H}[\eta]^2\phi^2 \quad (5) $$

where $\eta_{disp.}$ and $\eta_{water}$ are the viscosity of the dispersion and pure water respectively, $k'_{H}$ is the Huggins coefficient with a value of one when only hydrodynamic interactions are present not observing any attractive or repulsive interactions between the nanoparticles, and $[\eta]$ is the intrinsic viscosity of the nanoparticles which can be estimated as a function of their aspect ratio ($r_p$) by the following phenomenological equation:

$$ [\eta] = 2.5 + \frac{32(r_p - 1)}{15\pi} \left(1 - \frac{1}{r_p}\right) \left(1 - \frac{0.075}{r_p}\right) \quad (6) $$

Considering an aspect ratio of 8, an intrinsic viscosity of 6.7 can be estimated and, by applying this value in equation (5), it is possible to

<figure><img src="image_13.png" /><figcaption>**Fig. 7.** Relative Newtonian viscosity of CD dispersions purified with ethanol or by dialysis as function of CD concentration (25 °C). Comparison with theoretical models.</figcaption></figure>
model the CD concentration dependence of the viscosity (dotted green line in Fig. 7) showing a better agreement of the model to the experimental results compared to the Einstein model. The intrinsic viscosity of dispersions can also be determined as the limit of the reduced viscosity ($\eta_{red.}$) of the dispersion when nanoparticle concentration tends to zero.

$$[\eta] = \lim_{\phi \to 0} \left( \eta_{\text{red.}} = \frac{\eta_{\text{disp.}} - \eta_{\text{water}}}{\eta_{\text{water}} \phi} \right) \qquad (7)$$

By considering CD concentrations lower than 1 vol %, a value of intrinsic viscosity of 7.3 can be obtained for dialysed CD dispersions, which is in good agreement with the value of 6.7 obtained from the aspect ratio of the nanoparticles. For CD dispersions purified with ethanol a much lower value of 0.5 is deduced which could be related to the lower purity of CD dispersions purified by this method. Additionally, it is important to note that the increase in relative Newtonian viscosity is more pronounced for CD dispersions purified by dialysis, which again confirms a higher true concentration of CD in dispersion and therefore a higher purity.

In conclusion, the results obtained from the analysis on the zeta potential, absorption and fluorescence properties, and shear viscosity have clearly demonstrated that the dialysis process improves the degree of purification and the polarity of CD, which makes this purification process a better candidate for the purification of the studied glucose-based CD dispersions.

### 3.4. Chemical, structural and morphological characterisation of dialysed carbon dots

In order to gain a better understanding of the properties of dialysed CD, a series of chemical, structural and morphological studies have been performed.

The FTIR spectrum of CD powder obtained from CD dispersion purified by dialysis (Fig. 8) displays several peaks corresponding to the different oxygen-based functional groups generated during the CD synthesis from glucose. The wide band at ~3400 cm⁻¹ is a common characteristic peak of –OH hydroxyl groups. The peak observed at ~1050 cm⁻¹ and the shoulder found at ~1270 cm⁻¹ can be linked to the asymmetric and symmetric stretching of C–O–C groups. The peak at ~1400 cm⁻¹ is related to the stretching vibration of COO⁻ carboxylic groups. Additionally, the three peaks observed at approximately 1590, 1700 and 1760 cm⁻¹ are indicative of potential stretching vibrations of C=O and C=C groups. Finally, the stretching vibration of sp³ C–H bonding can be discerned at approximately 2930 and 780 cm⁻¹ [20, 57].

The XPS results (Fig. S6 in the supporting information) show good agreement with the observations acquired by FTIR.

High resolution C1s spectrum reveals the presence of four different carbon species. The peak centred at 285.00 eV is associated to C–C/C–H bonds and the peak at 286.47 eV can be related to both C–O–C and C–OH bonds. Lower intensity peak at 288.19 eV can be attributed to C=O and carboxylate groups. Finally, the lowest intensity peak at 289.56 eV

<figure><img src="image_14.png" /><figcaption>Fig. 8. FTIR spectrum of powder CD purified by dialysis.</figcaption></figure>

suggests the presence of few carboxyl groups. Furthermore, an elemental analysis was performed on the XPS spectrum, revealing the presence of 63.3 % of carbon which forms the core of the CD and 29.3 % of oxygen, derived from functionalisation. This indicates an approximate carbon-to-oxygen ratio of 2:1. Additionally, the sample contained low amounts of sodium (7.1 %) resulting from the NaOH employed during CD synthesis and a residual quantity of nitrogen (<0.3 %).

The morphology of CD was studied by high-resolution (HR-TEM) imaging, which revealed the presence of a circular shaped CD (see Fig. 9a). The size distribution obtained by HR-TEM (see Fig. 9b) showed a lateral size diameter of 13.9 ± 6.6 nm. The inset image in Fig. 9a qualitatively indicates the presence of interplanar distances within some CD, suggesting the possibility of order. However, the crystallinity degree appears to be low.

AFM imaging (see Fig. 10) was used to study the three-dimensional morphology of CD. The height of the CD (1.7 ± 0.9 nm) was found to be approximately eight times lower than their lateral size, suggesting that the structure of our CD appears to be lamellar rather than spherical.

The lamellar structure was corroborated by XRD in Fig. 11 in which three pronounced peaks at the values of 2θ values of 6.6°, 18.4° and 38.0° were discernible. The peaks correspond to the diffraction peaks related to the interlayer distances d₀₀₁ of graphite oxide, d₀₀₂ of graphite and the d₁₀₀ distance of two carbon atoms on the same graphene layer respectively. The broad width of the peaks is evidence of the low crystallinity degree of the synthesized CD as observed by HR-TEM (see Fig. 9a). The interlayer distances were calculated by using Bragg’s law yielding values of d₀₀₁ = 1.3 nm, d₀₀₂ = 0.48 nm and d₁₀₀ = 0.24 nm. The value obtained for d₁₀₀ is in good agreement with the typical values of graphene layers of graphite (0.246 nm) as well as the values of d₀₀₁ interlayer distances close to 1.3 nm previously reported for graphite oxide in high humidity environments or in hydrated states [58–60]. This could be related to the high hygroscopicity observed for CD [61,62]. The value observed for the d₀₀₂ interlayer distance seems to be higher than the typical value for graphite of 0.355 nm [63]. Previously, interlayer distances exceeding 0.4 nm have been reported in expanded graphite [64,65], which exhibits higher oxidation degrees than pristine graphite.

In view of the morphological and crystalline structural results, namely a lateral size eight times larger than the height and the existence of two different interlayer distances between graphene layer crystalline structure, we propose for dialysed CD a multilayered structure with a low degree of crystallinity.

### 4. Conclusions

The synthesis of carbon dots (CD) was successfully achieved through a bottom-up, one-step ultrasonic method using glucose as the precursor, followed by purification by either ethanol or dialysis. The developed comprehensive methodology combining multiple experimental investigations with statistical modelling enabled to evaluate the impact of purification on physico-chemical, optical and rheological properties of aqueous CD dispersions. Absorbance and fluorescence spectra were analysed using non-parametric generalised additive models (GAM), to extract key optical parameters such as maximum intensity, wavelength at maximum intensity, and full width at half maximum. Dependence of these properties on carbon dot concentration has been established by GAM and multivariate linear regression with marked differences depending on purification method: approximately linear trends for ethanol-purified dispersions, and nonlinear behaviour for those purified by dialysis. We clearly demonstrated an increase of maximum intensity, redshift and widening of optical peaks as well as the increase of viscosity with a more pronounced enhancement for CD dispersion purified by dialysis. This could be related to both a higher purity and pH dependent negative charge derived from functional groups such as hydroxyl, carbonyl and carboxyl groups supported by zeta potential, Fourier-transformed infra-red, X-ray photoelectron spectroscopy and viscosity results. Morphological and structural analysis showed that dialysed CD
<figure><img src="image_15.png" /><figcaption>Fig. 9. a) High resolution transmission electron microscopy (HR-TEM) images of CD purified by dialysis and b) size distribution of CD purified by dialysis obtained by HR-TEM.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 10. a) AFM image, and b) height distribution of CD purified by dialysis.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 11. XRD spectrum of CD purified by dialysis.</figcaption></figure>

exhibit a multilayered structure with a low degree of crystallinity. Altogether, this work demonstrates that the purification process is a critical parameter for tuning the functional properties of carbon dots and should be considered a key element in their optimisation and application. The enhanced optical performance achieved through dialysis purification make these CD useful for fluorescence bioimaging, chemical sensing and optoelectronic device integration, where high purity and tunable emission are critical.

### CRediT authorship contribution statement

Enrique Manso: methodology, data acquisition, writing original draft, Christian Perruchot: measurements and analysis of XPS, Javier Tarrio and Salvador Naya: statistical analysis, Alain Ponton: writing,

review and editing, supervision.

### Data availability

Raw data are not publicly available to preserve individual privacy under the European General Data Protection Regulation.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Alain PONTON reports financial support was provided by National Centre for Scientific Research. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

The authors would like to thank Jean-Marc Di Meglio (Université Paris Cité, CNRS, Matière et systèmes complexes) for AFM measurements. Alexandre Chevillot (Université Paris Cité, CNRS, Interface traitement organisation et dynamique des systèmes) is acknowledged for his technical support to FTIR analysis. Guillaume Wang (Université Paris Cité, CNRS, Matériaux et phénomènes quantiques) is acknowledged for HR-TEM measurements.

CNRS is greatly acknowledged for financial support mobility under International research project (IRP) entitled COGAS: smart composite materials for selective adsorption and water purification. The work of Salvador Naya and Javier Tarrío-Saavedra is also supported by Ministerio de Ciencia e Innovación grants PID2020-113578RB-100 and PID2023-147127OB-100, and by the Xunta de Galicia (Grupos de
Referencia Competitiva ED431C-2020-14 and ED431C 2024/14, Centro de Investigación y Desarrollo del Sistema universitario de Galicia ED431G2019/01, and CITIC, research center with accreditation of excellence belonging to the CIGUS Network ED431G 2023/01), all of them through the ERDF.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jmrt.2025.09.064.

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