A colorimetric sensing method for direct determination of the adsorption capacity of colored cations in adsorbents
Introduction
Adsorption is widely used in industrial processes, including wastewater treatment and resource recovery1,2,3,4,5. As a crucial parameter of the adsorbent, adsorption capacity is generally indirectly analyzed through differences in adsorbate concentration before and after adsorption6,7. It typically utilizes advanced instrumentation, such as atomic absorption spectroscopy (AAS), inductively coupled plasma (ICP) chromatography, and ultra-performance liquid chromatograph coupled with a mass spectrometer (UPLC–MS), making the testing process complex and unable to assess adsorption capacity in situ1,8,9.
In a typical adsorption process, as adsorption progresses, the adsorbate, serving as a guest molecule or ion, transfers its characteristics to the adsorbent. For example, many adsorbed cationic pollutants are colored, and it was observed during the research that the color of the adsorbent deepens with the increased adsorption capacity of colored pollutants. Some studies have noted this phenomenon and developed colorimetric sensors to measure the concentration of aqueous cations10,11, with very few studies addressing the rapid assessment of a critical metric—adsorption capacity8,12,13,14. Considering the post-adsorption adsorbent displayed assembled properties that correlate with adsorption capacity15, in our previous work, we utilized radiation flux to determine the adsorption capacity of radiative U(VI) cation. Nonetheless, research on using colorimetric sensing to measure the adsorption capacity of colored cations is still in its early stages15.
Therefore, this study uses titanates as a model adsorbent and colored Co(II), Ni(II), Cu(II), and U(VI) as model adsorbates to successfully construct a colorimetric sensing method linking absorbance with adsorption capacity. This method, approaching from a solid-phase perspective and based on the intrinsic properties of the ions, allows for the rapid and accurate determination of adsorption capacity using a spectrophotometer. Additionally, we have integrated a set of standard color cards for simple, quick, and in situ comparison.
Results and discussion
Colorimetric properties of titanate after adsorption
A series of adsorbents with graded adsorption capacities for colored ions Co(II), Ni(II), Cu(II), and U(VI) were prepared, referencing adsorption thermodynamics in batch experiments. To facilitate subsequent model development, common thermodynamic models (Langmuir, Freundlich, Temkin) were employed to fit the thermodynamic data1,16,17, with results presented in Supplementary Table 2. Among these, the Langmuir model demonstrated superior fitting for adsorption thermodynamics, and its corresponding curves are shown in Fig. 1. This model will also be used in the construction of subsequent models.
Langmuir correlation for Co(II), Ni(II), Cu(II) and U(VI) adsorption isotherms.
Through the batch adsorption process, the colored cations are enriched on the adsorbent surface, causing the adsorbent to display the colors of the respective ions. Analyses using XRD, FTIR, and XPS before and after adsorption on the titanate model adsorbents confirmed the successful adsorption of Co(II), Ni(II), Cu(II), and U(VI), with details available in Supplementary Note 3 of the Supporting Information18,19,20. Figure 2a demonstrates titanate model adsorbents with varying Co(II) adsorption capacities, showing a deepening blue color with increased adsorption capacity. To explore the feasibility of a colorimetric sensing method for assessing adsorption capacity, UV–Vis spectroscopy was utilized to analyze the samples. As Fig. 2b–e illustrates, the pure titanate model adsorbents exhibit no light absorption signal in the visible region. However, after adsorption of different colored cations, charge transfer induced by the metal cations’ d/f orbitals leads to characteristic absorption in various bands (Table 1), which increases with adsorption capacity21. These phenomena indicate that the colorimetric sensing method can be fabricated and used to evaluate adsorption capacity.
a Picture of titanate model adsorbents after adsorption of Co(II), b–e UV–Vis spectra of titanate after adsorption of Co(II), Ni(II), Cu(II) and U(VI), respectively.
Model development of colorimetric sensing method
The model relationship between adsorption capacity and absorbance is crucial for the colorimetric sensing method. Based on the phenomena observed in Fig. 2 and using the thermodynamic equilibrium state as a mediator, a model relationship can be constructed between the characteristic absorbance at the maximum absorption wavelength (A, a.u.) and the adsorption capacity (Q, mmol/g) of colored cations. This facilitates the implementation of colorimetric sensing for directly determining adsorption capacity in solid adsorbent. The following assumptions are made for this model:
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(1)
As depicted in Fig. 3a, the adsorption process of colored cations on titanates can be simplified to a one-dimensional process, where colored cations diffuse across the bulk solution and boundary layer into the adsorption layer in the vertical direction (z-direction) driven by a concentration gradient. As the concentration of colored cations is generally low, and the volume, bulk density, and density (ρ, g/cm3) of the adsorbent remain unchanged before and after adsorption.
Fig. 3: Model fabrication. 
a Schematic illustration of the modeled adsorption process of colored cations. b Relationship circle between Q and A under non-equilibrium conditions.
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(2)
The model utilizes thermodynamic equilibrium states to develop a colorimetric sensing model. According to Fig. 1, the adsorption isotherm is best approximated by the Langmuir model. In addressing the relationship between Q and A under non-equilibrium conditions (Fig. 3b), it is postulated that Q correlates with a hypothetical bulk solution equilibrium concentration (Ce, mmol/mL). This equilibrium concentration corresponds directly to the equilibrium adsorption capacity (Qe, mmol/g), allowing non-equilibrium Q to be equated to equilibrium Qe. Overall, this model is applicable for assessing adsorption capacity in non-equilibrium states.
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(3)
The boundary layer is thin, so the solution’s bulk concentration of each colored cation, Ce, is linearly related to the concentration at the bottom of the boundary layer (Ce,b, mmol/mL):
$$,{C}_{{{e,b}}}=g{C}_{{{e}}}+f$$(1)where g is a proportionality coefficient, and f (mmol/mL) is a concentration constant. Additionally, the thickness of the adsorption layer (d, cm) is consistently small, with the adsorption capacity at the adsorption layer interface, Qe,b, in equilibrium with Ce,b, and the average adsorption capacity within the adsorption layer, Qe, in equilibrium with Ce.
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(4)
The sample amount for UV–Vis spectroscopy testing is w (g), with a sufficiently large number of adsorbent samples, uniform sample preparation, and a random micro-orientation distribution. The direction of the incident light from the detection source on each material is considered to be vertical, with a consistent detection depth denoted by l (cm). Moreover, the illuminated area of the adsorbent, S’ (cm2/g), is directly proportional to the specific surface area, S (cm2/g), with the proportionality denoted by η, i.e., S’ = ηS.
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(5)
At the maximum absorption wavelength, the Beer–Lambert law is obeyed.
Based on these assumptions, the concentration of colored cations in the adsorption layer, CA (mmol/mL), can be expressed as
Therefore, the amount of colored cations, nA (mmol), illuminated by the detection light during the UV–Vis test can be obtained:
According to the Beer–Lambert assumption, there is a linear relationship between A and nA:
where a represents a related constant (mmol−1), and b is the test background. By setting s = awηρSmin22 and expanding Qe,b using the Langmuir model (Eq. (5)), Eq. (6) can be obtained:
where Qm (mmol/g) represents the maximum adsorption capacity of the adsorbent, and k (mL/mmol) denotes the Langmuir equilibrium adsorption constant. For intuitive understanding in subsequent modeling, we define a qualitative maximum saturation absorbance (Am, a.u.) in Eq. (7) and obtained Eq. (8):
By combining Eq. (8) with the Langmuir model (Eq. (5)), a relationship between Qe and A can be established:
In accordance with assumption (2), for determining the adsorption capacity under non-equilibrium conditions, it is presumed that there exists a hypothetical equilibrium concentration, which can also be regarded as an equilibrium state. Therefore, Qe in Eq. (9) can be denoted as Q:
This formula, referred to as the AQ (A–Q) model, establishes a colorimetric relationship linking absorbance to adsorption capacity. By utilizing the maximum absorbance of characteristic absorption by colored cations, the adsorption capacity can be rapidly estimated.
Single ion system
To further explore the feasibility of the AQ model, an analysis of the relationship between the absorbance of adsorbents and the adsorption capacity of colored cations was conducted. The results, as shown in Fig. 4, indicate that at low adsorption capacities, even minor increases in adsorption capacity can cause significant changes in absorbance. When the adsorption capacity nearly reaches saturation, the absorbance at the maximum wavelength remains essentially unchanged. The AQ model was applied to correlate the data related to colored cations Co(II), Ni(II), Cu(II), and U(VI). As demonstrated in Fig. 4 and Table 2, the relationship between colorimetric absorbance and adsorption capacity for these four ions exhibits a high degree of fit when assessed using the AQ model, with the corresponding AQ models and deviations presented in Eqs. (11)–(14) and Supplementary Table 3. This result suggests the powerful analysis of adsorption capacity by colorimetric properties by the proposed method. Notably, based on the parameter Am derived from the AQ model fitting and the quantitative relationship between Am and Qm (Eq. (7)), the maximum saturation adsorption capacity can be quickly analyzed, providing a powerful tool for evaluating adsorbent saturated performance (Supplementary Table 4).
a AQ model correlation for the data related to colored cations. b A set of standard color cards for Co(II).
Especially, considering the applicability of the colorimetric sensing method and the demand for in situ evaluation during field tests, a set of standard color cards was integrated, using the adsorption capacity of Co(II) and its corresponding color as an example. These color cards can be utilized for rapid analysis of adsorption capacity to assess the adsorption state of adsorbents. Compared to traditional methods based on liquid-phase concentration, this study offers a novel and convenient approach for the quick, in situ detection of adsorption capacity.
Complex water body experiments
In a real complex water body, multiple coexisting cations are commonly present, making it necessary to evaluate the sensor model’s performance under such conditions. A titanate adsorbent was used to adsorb a mixed solution containing 0.5 mmol/L Co(II) and 0.5 mmol/L Cu(II) for 2 h, and the adsorbed powder was used as the detection target. As shown in Fig. 5a, the UV–Vis spectra of the adsorbed titanate showed strong absorption peaks at 600 and 800 nm, corresponding to the adsorption of Co(II) and Cu(II), respectively. Using absorbance data and applying Eqs. (11) and (12), the adsorption capacities of Co(II) and Cu(II) were determined to be 0.454 and 0.586 mmol/g, respectively. Traditional liquid-phase detection methods measured the adsorption capacities of Co(II) and Cu(II) as 0.507 and 0.504 mmol/g, respectively. Although the accuracy slightly decreased in the mixed cation system, the colorimetric sensing method still maintained good accuracy and can serve as a reliable method for rapid real-time estimation.
a UV–Vis spectra and adsorption capacity of Co(II) and Cu(II) in coexisting cation system. b UV–Vis spectra and adsorption capacity of Co(II) in real wastewater system.
To further investigate the practical applicability of the colorimetric sensing method, a study was conducted using real cobalt-containing wastewater from a factory. As shown in Fig. 5b, in the real wastewater system, the actual adsorption capacity of titanate towards 0.509 mmol/L Co(II) ions was 0.450 mmol/g, while the adsorption capacity calculated using Eq. (11) was 0.504 mmol/g. This result indicates that the colorimetric sensing model remains effective in detecting Co(II) even in complex real wastewater systems.
Economic analysis and application prospects
This research is expected to provide a powerful tool for the fast evaluation of actual adsorption capacity, saturated adsorption capacity assessment, and determination of adsorption equilibrium. Given the colored cations mentioned in the text, many traditional pollutants (such as dyes) and emerging contaminants, like tetracycline and nimesulide in PPCPs, also possess colors, suggesting the potential broad interests of this study for colored pollutants23,24,25,26. Furthermore, considering the widespread application of transition metal doping in environmental catalytic materials and the inherent coloration of most transition metals27,28, which might induce differences in material absorbance upon doping, this model also promises applicability in assessing the content of doping elements. It is important to note that deconvolution is required to ensure accuracy during the testing of mixed-colored cations, particularly when peak overlap occurs. The model may not be applicable if the colorimetric characteristic peaks of the colored ions are too closely aligned.
Additionally, this study further calculated the economic costs of the developed technology. The colorimetric sensing method is simple, easy to learn, and requires low technical expertise. According to cost estimates (Supplementary Table 6), the cost per test using a UV–Vis spectrophotometer is only $0.088, while using a color card for estimation costs just $0.002 per test. The low cost of testing makes this method promising for widespread adoption in industrial production.
Above all, a universal colorimetric sensing method has been proposed based on the AQ model to evaluate adsorption capacity. For the first time, this method establishes a connection between the absorbance and adsorption capacity from a solid-phase perspective. Research on four randomly selected colored cations using this model has shown high concordance between calculated and actual results, enabling rapid and accurate determination of adsorption capacity with consistent effectiveness in complex water bodies. Additionally, a related set of standard color cards has been developed for colorimetric analysis, facilitating quick, in situ estimation of adsorption capacity during field operations and engineering projects. This research offers a new approach to rapid detection of adsorption capacity.
Methods
Synthesis of model adsorbents
Titanate model adsorbents were prepared using a hydrothermal method by mixing 1 g of anatase TiO2 with 60 mL of 10 mol/L NaOH aqueous solution and stirring for 90 min20. Subsequently, the mixture was transferred into a 100 mL stainless steel autoclave lined with polytetrafluoroethylene and subjected to hydrothermal treatment at 130 °C for 72 h. After cooling to room temperature, the product was washed with deionized water until the supernatant was nearly neutral and then dried at 60 °C for 12 h to obtain the titanate model adsorbent. Details on its characterization can be found in Supplementary Note 3 of the Supporting Information.
Characterizations
The chemical and binding states were analyzed using X-ray photoelectron spectroscopy (XPS, Thermo Scientific ESCALAB 250Xi). The functional groups present in the materials were identified through Fourier transform infrared spectroscopy (FTIR, Bruker Alpha II). The concentrations of ions were measured by inductively coupled plasma optical emission spectrometry (ICP-OES, Agilent 5110), and the absorbance of the samples was determined by ultraviolet–visible light spectroscopy (UV–Vis spectroscopy, Shimadzu UV-3600i Plus).
Batch experiments
Four typical colored cations, Co(II), Ni(II), Cu(II), and U(VI), were selected as model adsorbates for batch experiments.
The adsorption kinetics were determined by sampling at 5, 10, 20, 30, 60, and 120 min during the adsorption with an initial cation concentration of 0.8 mmol/L at 25 °C. The adsorption isotherms were tested using cation solutions with initial concentrations ranging from 0.1 to 3.2 mmol/L. Specifically, 40 mL of each solution at different concentrations was added to 50 mL polyethylene tubes, followed by the addition of titanate model adsorbent at a dosage of 1 g/L and ultrasonic mixing. The entire system was then immediately placed in a constant temperature shaker at 25 °C and agitated at 800 rpm for 2 h to reach adsorption equilibrium. The adsorbed titanate adsorbents were regenerated using 0.1 mol/L HCl and 0.1 mol/L NaOH for reuse. The regeneration and reuse process was repeated three times to verify the regeneration efficiency29.
The ion concentration in the solution was measured using ICP-OES, and the equilibrium adsorption capacity for each ion was calculated using Eq. (15):
where C0 (mmol/mL) represents the initial concentration of the adsorbates, Ce (mmol/mL) is the equilibrium concentration, V (mL) is the volume of the solution, and m (g) denotes the added mass of the adsorbent.
After adsorption, the titanate model adsorbent was centrifuged and placed in an oven, where it was dried at 60 °C for 12 h. The absorbance of the powder was then measured using UV–Vis spectroscopy with consistent test area for each material.
Complex water body experiments
The coexisting cation experiment was conducted using a mixed solution of 0.5 mmol/L Co(II) and 0.5 mmol/L Cu(II). Specifically, the titanate adsorbents were placed in the mixed solution for 2 h of adsorption, followed by centrifugation and drying. The absorbance of the powder was measured using UV–Vis spectroscopy, and the adsorption capacity was calculated based on the proposed colorimetric model.
For the real wastewater experiment, the wastewater was prepared according to the composition of wastewater from a production process at a new materials company in Hunan, China, as detailed in Supplementary Table 5. The procedure followed the same steps as in the coexisting cation experiment.
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