Rapid High-Accuracy Quantitative Analysis of Water Hardness by Combination of One-Point Calibration Laser-Induced Breakdown Spectroscopy and Aerosolization

Abstract

Water quality should be tested to ensure it is acceptable for the healthy growth of plants and animals, and water hardness is one of the important testing indexes. Herein, a novel approach was proposed to achieve high accuracy and rapid quantitative analyses of water hardness by combining one-point calibration laser-induced breakdown spectroscopy (OPC–LIBS) and aerosolization. First, the water samples are aerosolized via the aerosol generation device and the LIBS spectra of aerosols are obtained. Then, a modified OPC–LIBS model is used to determine the elemental contents of the aerosols via LIBS spectra, in which the plasma temperature is calculated using the Multi-Element Saha–Boltzmann (ME–SB) plot. One suitable standard liquid sample (the concentrations of Ca, Mg, and Sr were 50 mg/L, 50 mg/L, and 500 mg/L, respectively) was selected to evaluate the quantitative performance of the modified OPC–LIBS. Then, the Ca and Mg concentrations in the three real water samples (from the Yangtze River, reservoir, and underground) were detected and quantified by the proposed method, and the quantitative results of three LIBS calibration methods were compared with that of inductively coupled plasma optical emission spectroscopy (ICP–OES). The average relative error of Ca and Mg found in the OPC–LIBS results was lower by 22.23% than the internal standard method and 14.50% lower than the external standard method. The method combining modified OPC–LIBS and aerosolization can achieve high-precision rapid quantification of water hardness detection, which provides a new path for rapid detection of water hardness and is expected to make online detection a reality in the water quality testing field.

1. Introduction

Water is an indispensable substance for the growth of plants and animals [1]. Water hardness is the total concentration of calcium (Ca) and magnesium (Mg) ions in water [2], and its testing is quite important to monitoring the quality of both industrial and domestic water [3]. The Chinese drinking water standards explicitly stipulate that the total hardness of drinking water should not exceed 450 mg/L [4], while the World Health Organization recommends an optimal drinking water hardness of 170 mg/L [5]. Long-term consumption of water with excessively low water hardness may increase the prevalence of diabetes [6] and heart disease [7]. Additionally, water with elevated levels of Ca and Mg may lead to gastrointestinal disturbances, such as diarrhea [8]. Industrial water of excessive hardness can lead to the formation of scale in boilers and other equipment, increasing the risk of equipment damage [9].

The main methods of water hardness testing include ethylene diamine tetra acetic acid titration (EDTA) [10], anodic stripping voltammetry (ASV) [11], ion chromatography [12], and inductively coupled plasma optical emission spectrometry (ICP–OES) [13]. The manual titration method involves the manual preparation of chemical reagents and performing titration measurements [14], which is time-consuming and carries the risk of secondary pollution. The ion chromatography method separates the ions in water using the ion exchange technique and then detects the concentrations of Ca and Mg ions using chromatography [15]. The anodic stripping voltammetry (ASV) method involves enriching the metal particles from the solution onto an electrode through processes like electrophoresis, then dissolving the target element into the electrolyte through an electrochemical reaction [16]. The concentration of the target element is determined by measuring the magnitude of the anodic stripping current [17]. ASV can lead to the formation of scale on the electrode over the long term, which can contaminate measurement accuracy and stability. ICP–OES [18] is a highly accurate method of testing water quality, but it relies on the specialized knowledge and expertise of operators. ZDS (Zero-Discharge Sampling) is a simple and fast method of estimating the total concentration of metal elements, but it cannot directly determine the specific content of elements like Ca and Mg in water. In summary, the methods discussed above all have their limitations and cannot meet the demands of online detection in industrial settings. Thus, a water hardness testing method that offers simple sample preparation procedures, ease of operation, and remote and rapid detection is urgently needed.

Laser-Induced Breakdown Spectroscopy (LIBS) has the characteristics of multi-elemental analysis, rapidity, and online, real-time, and in-situ operation, which offers great potential in water quality monitoring [19,20,21,22,23]. Because direct detection of water samples via LIBS led to plasma quenching, resulting in poor spectral stability and intensity [24], most studies of LIBS water quality analysis have used the strategy of transforming the form of water. Kumar et al. analyzed Mg, manganese (Mn), and chromium (Cr) by using a jet generated by an aerosolizer [25]. Liu et al. applied ultrasound suspension to hold droplets in the excitation focus for analysis; they found detection limits for cadmium (Cd) and lead (Pb) of 0.016 mg/kg and 0.028 mg/kg [26], respectively. Ma et al. utilized a substrate liquid-to-solid conversion method for sample pretreatment. The limits of detection (LODs) of Cr and Pb were 1.1 μg/L, and 4 μg/L [27], respectively. Extraction methods and substrate liquid-to-solid conversion techniques can achieve a high detection sensitivity, but they are complicated and time-consuming. Additionally, commonly used calibration methods in LIBS involving external and internal standards require the construction of calibration curves using samples of different concentration gradients, which significantly reduces the speed of quantitative analysis. Currently, few works have focused on the rapid testing of water hardness with LIBS. Thus, the current research focuses on how to rapidly obtain information on water hardness from the LIBS spectrum and achieve high-precision detection through a simple calibration model.

In this work, we propose a new method combining aerosolization with OPC–LIBS for rapid and high-precision testing of water hardness. We constructed an aerosol rapid generation device by which water samples are directly aerosolized. The laser is focused on the aerosol jet to obtain the LIBS spectra. A modified OPC–LIBS model based on the Multi-Element Saha–Boltzmann (ME–SB) plot is established to determine Ca and Mg contents, which requires a standard sample containing Ca, Mg, and strontium (Sr). The quantitative analysis was performed on the water samples from three different regions (Yangtze River, reservoir, and underground). Meanwhile, the results of the modified OPC–LIBS, external standard of LIBS, internal standard of LIBS, and ICP–OES were compared to evaluate the quantitative accuracy of the modified OPC–LIBS.

2. Experimental and Methods

2.1. Experimental Setup

A water quality monitoring device with LIBS based on the rapid aerosol generation system was constructed in this work. A schematic diagram is presented in Figure 1. The experimental setup comprised two main modules: the aerosol generation module and the LIBS detection module. The aerosol generation module was used to rapidly aerosolize water samples and then transport the aerosolized samples, a technique which is commonly used in analytical atomic spectrometry. Aerosolization is beneficial for the complete ionization of aqueous solutions. A Collison nebulizer (Huironghe Technology, China) was used as the aerosol generation device, and the flow rate at the outlet of the bottle was maintained at 1 L per minute (lpm). Subsequently, the aerosol passed through the drying tube and was transported to the LIBS system for spectroscopic detection. The drying tube exclusively mitigates humidity-induced signal fluctuations by absorbing water molecules, with no measurable impact on the transport or quantification of target ions. Moreover, after the aerosolized samples passed through the drying tube, the laser energy was no longer used for the evaporation of water, thereby improving the detection sensitivity. A laser (Quantel, CFR400, wavelength: 532 nm, pulse width: 7 ns, beam diameter: 7 mm, energy: 200 mJ, Orsay, France) was utilized to generate the plasma. The laser beam was expanded through a beam expander (Thorlabs, BE03-532, Newton, NJ, USA) and then focused by an aspherical lens (LBTEK, MAC1610-A, Shenzhen, China) to achieve stable excitation of the aerosol plasma. The laser propagation direction was orthogonal to the aerosol jet and aligned with its center. Plasma emission light was collected by a pair of flat-convex lenses with a focus of 50 mm, then transmitted to the end face of a bifurcated fiber (fiber diameter: 600 μm), which was attached to dual-channel fiber-optic spectrometers (Avantes, AvaSpec-ULS4096CL-EVO, wavelength range: 250-500 nm and 570-780 nm, Apeldoorn, The Netherlands).

2.2. Methods

Modified OPC–LIBS: The basic idea of the OPC–LIBS is to correct the Boltzmann plot of the unknown sample by using one matrix-matched standard sample, which was proposed by Cavalcanti et al. [28]. Compared with calibration-free LIBS (CF–LIBS), OPC–LIBS obtains higher quantitative accuracy by using one standard sample. The detailed steps of OPC–LIBS will not be repeated here, and the main steps of the modified OPC–LIBS we proposed are as follows:

(a)

First, instead of the Boltzmann plot, the ME–SB plot is used to calculate plasma temperature by the LIBS spectrum of the standard sample. The ME–SB plot, proposed by Aguilera et al., is a method of calculating the plasma temperature by utilizing the atomic spectral lines in plasma emissions [29]. Since its algorithm uses the known content values of elements in the sample, the calculated plasma temperature is quite accurate.

An ME–SB plot is derived from the following four equations:

$$I_{ki}=G{N}_a^I{A}_{ki}{g}_k{\displaystyle \frac{e^{-\frac{E_k}{K_{B}T}}}{U^I}}$$

(1)

$$I_{mn}=G{N}_a^{II}{A}_{mn}{g}_m{\displaystyle \frac{e^{-\frac{E_m}{K_{B}T}}}{U^{II}}}$$

(2)

$$N_a=N_a^I+N_a^{II}=C_{a}N$$

(3)

$$S={\displaystyle \frac{N_a^{II}}{N_a^I}}={\displaystyle \frac{{2\left(2\pi m_e{K}_{B}T\right)}^{\frac{3}{2}}}{N_e{h}^3}}{\displaystyle \frac{U^{II}}{U^I}}{e}^{-{\displaystyle \frac{E_{ion}}{K_{B}T}}}$$

(4)

where $I_{ki}$ is the line intensity of the atoms; $I_{mn}$ is the line intensity of the ions; $N_a$ is the number density of the species a; $N_a^I$ is the atomic number density of the species a; $N_a^{II}$ is the ionic number density of the species a; $N$ is the total number density of all species; $C_a$ is the concentration of the species a; $G$ is the gain factor; $A$ is the transition probability; $g$ is the degeneracy; $U$ is the partition function; $E_k$ and $E_m$ are the energy of the upper level; $E_{ion}$ is the first ionization energy; $T$ is the plasma temperature; $N_e$ is the electron density; $h$ is the Planck constant; $K_B$ is the Boltzmann constant; and $m_e$ is the electron mass.

Combining Equations (3) and (4), we get:

$$N_a^I={\displaystyle \frac{1}{1+S}}{N}_a={\displaystyle \frac{1}{1+S}}{C}_{a}N$$

(5)

Considering Equations (1), (2), (4) and (5), we can obtain a linear equation:

$$y^{\mathrm{*}}=m{x}^{\mathrm{*}}+q_s$$

(6)

$$\left\{\begin{array}{c}m=-{\displaystyle \frac{1}{K_{B}T}}\\ q_s=\mathit{ln}\left(GN\right)\end{array}\right.$$

(7)

$$x^{\mathrm{*}}=\left\{\begin{array}{cc}{E}_k\hfill & \hfill atomic line\\ E_m+E_{ion}& \hfill ionic line\end{array}\right.$$

(8)

$$y^{\mathrm{*}}=\left\{\begin{array}{c}ln\left({\displaystyle \frac{I_{ki}}{A_{ki}{g}_k}}\right)-ln\left({\displaystyle \frac{C_a}{1+S}}{\displaystyle \frac{1}{U^I}}\right) atomic line\\ ln\left({\displaystyle \frac{I_{mn}}{A_{mn}{g}_m}}\right)-ln\left({\displaystyle \frac{C_a}{1+S}}{\displaystyle \frac{1}{U^I}}\right)-ln\left({\displaystyle \frac{2{\left({2\pi m}_e{K}_{B}T\right)}^{\frac{3}{2}}}{N_e{h}^3}}\right)\hspace{1em}\hspace{1em}ionic line\end{array}\right.$$

(9)

where the electron density $N_e$ can be determined by the Stark broadening of the H_α line according to Ref. [30] and $S$ can be calculated by the Equation (4). The plasma temperature $T$ should be calculated iteratively due to the explicit dependence of y* on $T$ in Equation (9) [31].

When the concentration of the species is known, the ME–SB plot can be drawn via Equation (6), and the points representing the spectral lines of all the elements are in a straight line, similar to the Saha–Boltzmann plot. Specifically, the values of x* and y* are calculated from spectral line intensities and related atomic data by Equation (8) and Equation (9), respectively. Then, we can obtain the slope m and the intercept $q_s$ through linear fitting in the ME–SB plot. $T$ can be calculated from m via Equation (7).

(b)

Second, the correction factor $P\left(\lambda \right)$ used in CF–LIBS for quantifying the unknown sample is calculated by:

$$P\left(\lambda \right)=Ag\cdot e^{-\Delta y}$$

(10)

$$\Delta y=y^{\mathrm{’}}-y^{\mathrm{*}}$$

(11)

$$y^{\mathrm{’}}=\left\{\begin{array}{c}-{\displaystyle \frac{E_k}{K_{B}T}}+q_s atomic line\\ -{\displaystyle \frac{E_m+E_{ion}}{K_{B}T}}+q_s ionic line\end{array}\right.$$

(12)

where the values of y′ are directly calculated using the above $q_s$ from the fitting line in the ME–SB plot. The values of y* are calculated by the measured intensities of spectral lines and related atomic data by Equation (9).

(c)

Third, CF–LIBS is performed to quantify the unknown sample by using the calculated $P\left(\lambda \right)$.

In this work, to quantify real water samples, we need to prepare two samples. One is a standard sample containing Ca, Mg, and Sr, and the other is a mixture of the unknown sample and a standard sample with a known Sr content. No sample pretreatment steps for further purification to avoid interferences in LIBS analysis are necessary. The plasma temperature T was first calculated using the spectrum containing Ca, Mg, and Sr lines from the standard sample via the ME–SB plot. Then, we can calculate the correction factor P(λ) using the calculated T and Equations (10)–(12). Next, we can perform the CF–LIBS with the calculated P(λ) on the LIBS spectra of the mixture and obtain the content ratios of Ca/Sr and Mg/Sr. Due to the Sr content in the mixture being known, the Ca and Mg contents can be derived using the ratios of Ca/Sr and Mg/Sr. Our modified OPC–LIBS algorithm was implemented on the MATLAB R2023a platform.

ICP–OES was used to quantify the Ca and Mg concentrations in the real water samples to evaluate the quantitative performance of LIBS analysis due to its quite high quantitative accuracy for aqueous solutions. But strict sample pretreatment is necessary for ICP–OES, and a series of standard solutions need to be prepared, in which the content of target elements varies on a gradient.

In this work, the limit of detection (LOD) was calculated using the 3σ criterion:

$$LOD=3\delta /k$$

(13)

where σ represents the standard deviation of the background radiation and k is the slope of the calibration curve.

2.3. Samples

To compare the quantitative performance of the above quantitative models, two different standard samples were purchased from the National Institute of Metrology: a mixed solution of potassium (K), Ca, sodium (Na), and Mg of 1000 mg/L (Standard Solution 1); and a solution of Sr of 1000 mg/L (Standard Solution 2). Standard Solution 1 was diluted into different concentrations by adding deionized water, named Sample Set 1. Then, Sample Set 1 was mixed with Standard Solution 2 in a 1:1 ratio to obtain Sample Set 2. The concentrations of elements in Sample Set 1 and 2 are listed in

Table 1. Element concentrations in samples.

Serial Number	Sample Set 1		Serial Number	Sample Set 2
	Mg (mg/L)	Ca (mg/L)		Mg (mg/L)	Ca (mg/L)	Sr (mg/L)
1	50	50	7	25	25	500
2	100	100	8	50	50	500
3	200	200	9	100	100	500
4	400	400	10	200	200	500
5	600	600	11	300	300	500
6	1000	1000	12	500	500	500

. Sample Set 1 was used for the external standard calibration method, while Sample Set 2 was used for the internal standard method [32] and OPC–LIBS. In this experiment, the analyte elements were Ca and Mg. Sr was selected as the internal standard element. Since the internal standard element is usually selected based on its chemical properties being similar to those of the analyte element, Sr was chosen. The line intensity of Sr II 407.77 nm was moderate in a concentration of 500 mg/L, ensuring that it was not influenced by self-absorption effects and its wavelength location was not affected by lines of other elements [33].

2.4. Delay and Gate Width Parameter Optimization

To obtain optimal experimental results, the gate width and delay of the spectrograph were optimized. All of the experiment was carried out in the atmosphere, and the laser energy was set to 200 mJ with a frequency of 20 Hz. The 100 mg/L mixed solution of Ca and Mg solution was selected for the optimal experiment [34]. Every 10 spectra were averaged to one, and a total of 100 spectra were collected at each successive excitation. The optimization results for the delay of the Ca II 393.37 and Mg II 279.55 are shown in Figure 2. The spectral intensities of Ca II 393.37 and Mg II 279.55 decrease as the delay increases. The signal-to-noise ratio (SNR) of Ca II 393.37 and Mg II 279.55 at 3 μs were relatively high, which was the optimal delay in this experiment. The optimization of gate width is shown in Figure 3. It indicates that when the gate width exceeds 200 μs, the spectral intensity and SNR of Ca II 393.37 and Mg II 279.55 remain relatively constant. Thus, 200 μs was set as the gate width for this experiment.

3. Results and Discussion

3.1. Standard Calibration Models

The external standard calibration model: Sample Set 1 was tested by the experimental system and the calibration curves for Ca II 393.37 and Mg II 279.55 were built as shown in Figure 4a and b, respectively. The R² measurements of Ca II 393.37 and Mg II 279.55 were 0.9992 and 0.9991, respectively, and the LODs were 1.41 mg/L and 2.714 mg/L, respectively.

The internal standard calibration model: Sample Set 2 was tested by the experimental system and the internal standard calibration curves for Ca II 393.37 and Mg II 279.55 were built as shown in Figure 5a and b, respectively. The R² measurements of Ca II 393.37 and Mg II 279.55 were 0.9982 and 0.9993, respectively, and the LODs were 7.45 mg/L and 14.31 mg/L, respectively. The R² exceeded 0.99 of Ca II 393.37 and Mg II 279.55 in Figure 4 and Figure 5. The LODs of the internal standard were significantly lower than those of the external standard.

3.2. OPC–LIBS

To optimize the quantitative performance of OPC–LIBS, a simulated quantitative analysis was conducted to determine the suitable standard sample. The ME–SB plot of Ca, Mg, and Sr was established as shown in Figure 6. Three single-standard samples were prepared with different concentrations of Ca, Mg, and Sr, labeled as S-1 (50 mg/L, 50 mg/L, 500 mg/L), S-2 (200 mg/L, 200 mg/L, 500 mg/L), and S-3 (500 mg/L, 500 mg/L, 500 mg/L). Three tested samples were prepared with different concentrations of Ca, Mg, and Sr, labeled as T-1 (50 mg/L, 50 mg/L, 500 mg/L), T-2 (200 mg/L, 200 mg/L, 500 mg/L), and T-3 (600 mg/L, 600 mg/L, 500 mg/L). The sample contents and the final quantitative results are shown in

Table 2. Element concentrations in samples.

Test Samples Ca, Mg, Sr (mg/L)		Standard Samples Ca, Mg, Sr (mg/L)		Quantitative Results
				Ca (mg/L)	Mg (mg/L)
T-1	50, 50, 500	S-1	50, 50, 500	53.53	51.42
		S-2	200, 200, 500	53.62	50.61
		S-3	500, 500, 500	55.12	52.78
T-2	200, 200, 500	S-1	50, 50, 500	201.90	196.77
		S-2	200, 200, 500	202.27	193.67
		S-3	500, 500, 500	207.90	201.95
T-3	600, 600, 500	S-1	50, 50, 500	583.58	568.49
		S-2	200, 200, 500	584.65	559.56
		S-3	500, 500, 500	600.93	583.44

. The relative errors (REs) of Ca and Mg quantitative results are shown in Figure 7.

When using standard sample S-1, the REs of Ca in the three test samples were 7.06%, 0.95%, and 2.74%, and those of the Mg were 2.84%, 1.62%, and 5.25%. The results of Ca and Mg are better than S-2 and S-3. Therefore, the S-1 was the best choice as the single-standard sample for the modified OPC–LIBS.

3.3. Comparative Analysis of Quantitative Results with Real Samples

The three water samples (from the Yangtze River water, underground, and reservoir) were selected for testing with the three LIBS quantitative methods. The quantitative analysis of the real samples used the internal standard and external standard methods and their respective calibration curves built in Section 3.1 and Section 3.2. During OPC–LIBS analysis, S-1 was chosen as the single-standard sample for the OPC–LIBS. Standard Solution 2 was added to the real sample in 1:1, so the Sr content in the mixture was 500 mg/L. Then, the LIBS spectra of the mixture were obtained and the modified OPC–LIBS was performed to calculate the Ca and Mg concentrations in the real samples. The quantitative results of the three methods and ICP–OES are listed in

Table 3. The Ca and Mg concentrations in the three water samples (from the Yangtze River water, underground, and reservoir) with the three LIBS quantitative methods and ICP–OES.

Samples	Methods	Ca (mg/L)	Mg (mg/L)
Yangtze River water	ICP–OES	50.20	21.08
	External standard	38.19	27.71
	Internal standard	43.07	27.47
	OPC–LIBS	45.79	21.83
groundwater	ICP–OES	41.68	20.49
	External standard	34.53	27.47
	Internal standard	34.09	27.87
	OPC–LIBS	38.70	22.51
reservoir water	ICP–OES	19.74	2.74
	External standard	28.13	Not detected
	Internal standard	14.11
	OPC–LIBS	21.79

and the REs of the three methods compared to ICP–OES are shown in Figure 8.

It can be observed that the relative error (RE) of Ca in the Yangtze River water sample calculated by OPC–LIBS is 10.23%, lower than the external standard and internal standard by 8.43% and 13.68%, respectively. The RE of Mg by OPC–LIBS is 2.73%, which is lower than the external standard and internal standard by 8.42% and 13.24%, respectively. The RE of Ca is 8.42% by OPC–LIBS in the groundwater, which is lower than the external standard and internal standard by 8.42% and 13.24%, respectively. The RE of Mg by OPC–LIBS is 7.24%, which is lower than the external standard and internal standard by 26.82% and 19.61%, respectively. The RE of Ca is 14.55% by OPC–LIBS in reservoir water, which is lower than the external standard and internal standard by 27.96% and 5.45%, respectively. Mg was not detected in this experiment. From the overall results, the average relative error (ARE) of Ca and Mg in the three samples with the OPC–LIBS is 22.23% lower than the internal standard method and 14.50% lower than the external standard method. The main reasons were that the three real samples came from different regions and there were many other elements in the samples. The samples of the external standard method used deionized water to dilute the solution, which led to poorer quantitative results due to the mismatch between the calibration curve and the sample matrix. Therefore, the significant differences in the matrix between the calibration samples and the real test samples and the spectral signals of the samples fluctuated, leading to an impact on the quantification results of the external standard method. In contrast, the internal standard method, which involves the addition of an internal standard element, achieves a more harmonious matrix among the three samples. This consistency leads to better quantification results in the internal standard method than in the external standard method. The OPC–LIBS uses the ME–SB plot to accurately calculate the plasma temperature and eliminate the matrix effect to obtain the best results among the three quantitative models.

4. Conclusions

In conclusion, our study established a LIBS experimental platform based on an aerosol rapid generation device. The device is capable of rapidly converting aqueous solution samples into an aerosol state within a few seconds for excitation and detection. A modified OPC–LIBS using the ME–SB plot is proposed based on the characteristics of LIBS spectra by this device. The optimal composition of the single-standard sample for OPC–LIBS was determined as 50 mg/L for Ca, 50 mg/L for Mg, and 500 mg/L for Sr. After mixing the real samples with the Standard Solution 2 containing Sr in 1:1, the LIBS spectra were obtained, and then the modified OPC–LIBS was performed to calculate the concentrations of Ca and Mg in the real samples. The three real water samples (the Yangtze River water, groundwater, and reservoir water) were tested by the internal standard method, external standard, and the modified OPC–LIBS. The average relative error (ARE) of Ca and Mg in the three real samples by OPC–LIBS was 22.23% lower than the internal standard method and 14.50% lower than the external standard method. The above results indicate that the modified OPC–LIBS achieves high detection accuracy while significantly reducing the number of standard samples based on the plasma model. It is an efficient method for water hardness analysis, with great potential for widespread application in online water hardness monitoring.