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Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 19 >Page 1930001 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 19, 1930001 (2021)

Measurement of Molar Absorptivity of Low-Concentration Carbonate Aqueous Solution in Mid-Infrared Region

Meiting Zhang, Guangzhuang Cheng, Cuifeng Zhu, Xingzheng Shi, Xuefei Zheng, Chun Li, and Guang Yuan^*

Author Affiliations

College of Information Science and Engineering, Ocean University of China, Qingdao , Shandong 266100, China

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DOI: 10.3788/LOP202158.1930001 Cite this Article Set citation alerts

Meiting Zhang, Guangzhuang Cheng, Cuifeng Zhu, Xingzheng Shi, Xuefei Zheng, Chun Li, Guang Yuan. Measurement of Molar Absorptivity of Low-Concentration Carbonate Aqueous Solution in Mid-Infrared Region[J]. Laser & Optoelectronics Progress, 2021, 58(19): 1930001 Copy Citation Text

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Abstract

In this paper, the molar absorptivity of carbonate ions is calculated by measuring the infrared absorption spectra of 30-100 mmol/L low-concentration sodium carbonate aqueous solutions. The infrared absorption spectra of 30-100 mmol/L sodium carbonate aqueous solutions were measured using the infrared single attenuated total reflection (ATR) accessory based on zinc selenide. The simulated pure water ATR spectrum was used as the baseline to adjust the infrared absorption spectra of the sodium carbonate aqueous solutions. The Kramers-Kronig formula was used to calculate the refractive indices and extinction coefficients of the sodium carbonate solutions. Furthermore, the effective optical pathlengths and the molar absorptivities of the low-concentration sodium carbonate aqueous solutions were calculated. The calculated maximum molar absorptivity of carbonate ions is 2421.99 L/(mol·cm).

Keywords

baseline adjustment infrared absorption spectroscopy Kramers-Kronig relation molar absorptivity spectroscopy

A (k) = - l n \frac{I_{t}}{I_{0}} = ε (k) \cdot c \cdot L \cdot l g e

，（1）

A (k) = - l g R (k)

。（2）

\{\begin{matrix} {\hat{r}}_{S} = \frac{n_{1} c o s β_{i} - {\hat{n}}_{2} c o s {\hat{β}}_{t}}{n_{1} c o s β_{i} + {\hat{n}}_{2} c o s {\hat{β}}_{t}} \\ {\hat{r}}_{P} = \frac{{\hat{n}}_{2} c o s β_{i} - n_{1} c o s {\hat{β}}_{t}}{{\hat{n}}_{2} c o s β_{i} + n_{1} c o s {\hat{β}}_{t}} \end{matrix}

，（3）

\{\begin{matrix} {\hat{r}}_{S} = \sqrt[]{R_{S}} e x p (i \cdot θ_{S}) \\ {\hat{r}}_{P} = \sqrt[]{R_{P}} e x p (i \cdot θ_{P}) \end{matrix}

，（4）

\{\begin{matrix} l n {\hat{r}}_{S} = l n \sqrt[]{R_{S}} + i \cdot θ_{S} \\ l n {\hat{r}}_{P} = l n \sqrt[]{R_{P}} + i \cdot θ_{P} \end{matrix}

。（5）

A = \frac{A_{P} + 2 A_{S}}{3}

。（6）

d_{e} = \frac{d_{e S} + d_{e P}}{2}

，（7）

\{\begin{matrix} d_{e S} = \frac{n_{1}^{2} n_{2} c o s β_{i}}{(n_{1}^{2} - n_{2}^{2})} \times \frac{λ_{1}}{π \sqrt[]{n_{1}^{2} s i n^{2} β_{i} - n_{2}^{2}}} \\ d_{e P} = \frac{n_{1}^{2} n_{2} c o s β_{i}}{(n_{1}^{2} - n_{2}^{2})} \times \frac{2 n_{1}^{2} s i n^{2} β_{i} - n_{2}^{2}}{(n_{1}^{2} + n_{2}^{2}) s i n^{2} β_{i} - n_{2}^{2}} \times \frac{λ_{1}}{π \sqrt[]{n_{1}^{2} s i n^{2} β_{i} - n_{2}^{2}}} \end{matrix}

，（8）

\{\begin{matrix} R e f (x) = \frac{1}{π} P \int_{- \infty}^{\infty} \frac{I m f (x^{'}) d x^{'}}{x^{'} - x} \\ I m f (x) = - \frac{1}{π} P \int_{- \infty}^{\infty} \frac{R e f (x^{'}) d x^{'}}{x^{'} - x} \end{matrix}

，（9）

\{\begin{matrix} θ_{S} (k_{a}) = I_{S} + \frac{2}{π} P \int_{0}^{\infty} \frac{k \cdot l n {(R_{S})}^{1 / 2}}{k - k_{a}} d k \\ I_{S} = - 2 a r c t a n (\frac{\sqrt[]{{n_{1}}^{2} s i n^{2} β_{i} - n_{\infty}}}{n_{1} c o s β_{i}}) \end{matrix}

；（10）

\{\begin{matrix} θ_{P} (k_{a}) = I_{P} + \frac{2}{π} P \int_{0}^{\infty} \frac{k \cdot l n {(R_{P})}^{1 / 2}}{k - k_{a}} d k \\ I_{P} = - 2 a r c t a n (\frac{n_{1} \sqrt[]{{n_{1}}^{2} s i n^{2} β_{i} - {n_{\infty}}^{2}}}{{n_{\infty}}^{2} c o s β_{i}}) \end{matrix}

。（11）

\{\begin{matrix} n_{S} = n_{1} R e {[s i n^{2} β_{i} + {(\frac{1 - {\hat{r}}_{s}}{1 + {\hat{r}}_{s}})}^{2} c o s^{2} β_{i}]}^{1 / 2} \\ κ_{S} = - n_{1} I m {[s i n^{2} β_{i} + {(\frac{1 - {\hat{r}}_{s}}{1 + {\hat{r}}_{s}})}^{2} c o s^{2} β_{i}]}^{1 / 2} \end{matrix}

。（12）

\{\begin{matrix} n_{P} = R e {\{\frac{1 - {[1 - 4 \cdot {(\frac{1 - {\hat{r}}_{P}}{1 + {\hat{r}}_{P}})}^{2} \cdot s i n^{2} β_{i} c o s^{2} β_{i}]}^{\frac{1}{2}}}{2 \cdot {(\frac{1 - {\hat{r}}_{P}}{1 + {\hat{r}}_{P}})}^{2} \cdot \frac{c o s^{2} β_{i}}{{n_{1}}^{2}}}\}}^{1 / 2} \\ κ_{P} = I m {\{\frac{1 - {[1 - 4 \cdot {(\frac{1 - {\hat{r}}_{P}}{1 + {\hat{r}}_{P}})}^{2} \cdot s i n^{2} β_{i} c o s^{2} β_{i}]}^{\frac{1}{2}}}{2 \cdot {(\frac{1 - {\hat{r}}_{P}}{1 + {\hat{r}}_{P}})}^{2} \cdot \frac{c o s^{2} β_{i}}{{n_{1}}^{2}}}\}}^{1 / 2} \end{matrix}

。（13）

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Meiting Zhang, Guangzhuang Cheng, Cuifeng Zhu, Xingzheng Shi, Xuefei Zheng, Chun Li, Guang Yuan. Measurement of Molar Absorptivity of Low-Concentration Carbonate Aqueous Solution in Mid-Infrared Region[J]. Laser & Optoelectronics Progress, 2021, 58(19): 1930001

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