To Make a Good Infrared Spectrum in NaCl Aqueous Solution Where Lambert-Beer’s Law is Not to be Obeyed

Meng YAO; Hai-shui WANG

doi:10.3964/j.issn.1000-0593(2021)01-0065-06

Journals >Spectroscopy and Spectral Analysis >Volume 41 >Issue 1 >Page 65 > Article

Spectroscopy and Spectral Analysis
Vol. 41, Issue 1, 65 (2021)

To Make a Good Infrared Spectrum in NaCl Aqueous Solution Where Lambert-Beer’s Law is Not to be Obeyed

Meng YAO and Hai-shui WANG

Author Affiliations

School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, China

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DOI: 10.3964/j.issn.1000-0593(2021)01-0065-06 Cite this Article

Meng YAO, Hai-shui WANG. To Make a Good Infrared Spectrum in NaCl Aqueous Solution Where Lambert-Beer’s Law is Not to be Obeyed[J]. Spectroscopy and Spectral Analysis, 2021, 41(1): 65 Copy Citation Text

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Fig. 1. FTIR spectra of NaCl aqueous solutions(0, 2%, 4%, …, 28%, 30%, step 2%)

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Fig. 2. The difference spectra between NaCl aqueous solution(2%, 6%, …, 26%, 30%, step 4%) and pure water, respectively

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Fig. 3. The subtraction spectra between A_16%and different A^16%(c₁, c₂)
a: ΔA_16%(14%, 18%); b: ΔA_16%(12%, 20%); c: ΔA_16%(10%, 22%); d: ΔA_16%(8%, 24%); e: ΔA_16%(6%, 26%); f: ΔA_16%(4%, 28%); g: ΔA_16%(2%, 30%)

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Fig. 4. The subtraction spectra between A_16%and different A_h_16%(c₁, c₂)
a: ΔA_h_16%(14%, 18%); b: ΔA_h_16%(12%, 20%); c: ΔA_h_16%(10%, 22%); d: ΔA_h_16%(8%, 24%); e: ΔA_h_16%(6%, 26%); f: ΔA_h_16%(4%, 28%); g: ΔA_h_16%(2%, 30%)

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Fig. 5. The subtraction spectra between A_c and A_hc(2%, 30%)
a: ΔA_h4%; b: ΔA_h_6%; c: ΔA_h_8%; d: ΔA_h_10%; e: ΔA_h_12%;f: ΔA_h_14%; g: ΔA_h_16%; h: ΔA_h_18%; i: ΔA_h_20%; j: ΔA_h_22%;k: ΔA_h_24%; l: ΔA_h_26%; m: ΔA_h_28%

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Fig. 6. The fitting regression coefficient-c curves
(a): a^-c curve; (b): b^-c curve

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Fig. 7. The real spectra (dashed line) and corresponding hybrid spectra (dotted line) of NaCl aqueous solutions
a: A_5% and A_h_5%(2%, 30%); b: A_13% and A_h_13%(2%, 30%);c: A_15% and A_h_15%(2%, 30%); d: A_19% and A_h_19%(2%, 30%);e: A_23% and A_h_23%(2%, 30%); f: A_25% and A_h_25%(2%, 30%)

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编号	A_c	$A_{c_{1}}$	$A_{c_{2}}$	${\hat{A}}_{16 %}$ (c₁, c₂)= $\hat{a} A_{c_{1}}$ + $\hat{b} A_{c_{2}}$ + $\hat{e}$
1	A_16%	A_14%	A_18%	${\hat{A}}_{16 %}$ (14%, 18%)=0.585 6×A_14%+0.414 1×A_18%-3.47×10^-4
2	A_16%	A_12%	A_20%	${\hat{A}}_{16 %}$ (12%, 20%)=0.556 6×A_12%+0.443 1×A_20%-1.33×10^-5
3	A_16%	A_10%	A_22%	${\hat{A}}_{16 %}$ (10%, 22%)=0.507 7×A_10%+0.490 9×A_22%-6.01×10^-4
4	A_16%	A_8%	A_24%	${\hat{A}}_{16 %}$ (8%, 24%)=0.501 9×A_8%+0.496 7×A_24%+4.29×10^-4
5	A_16%	A_6%	A_26%	${\hat{A}}_{16 %}$ (6%, 26%)=0.477 1×A_6%+0.530 9×A_26%+4.58×10^-4
6	A_16%	A_4%	A_28%	${\hat{A}}_{16 %}$ (4%, 28%)=0.479 6×A_4%+0.524 5×A_28%+3.44×10^-4
7	A_16%	A_2%	A_30%	${\hat{A}}_{16 %}$ (2%, 30%)=0.484 2×A_2%+0.516 6×A_30%-3.17×10^-5

Table 1. The binary linear regression equations between A_c and

A_{c_{1}}

A_{c_{2}}

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编号	F	r²	估计标准误差	$t_{\hat{a}}$	$t_{\hat{b}}$	$t_{\hat{e}}$
1	7.2×10⁸	1.000	1.7×10^-4	811	573	106
2	6.7×10⁸	1.000	1.8×10^-4	1 541	1 232	-4
3	2.8×10⁸	1.000	2.8×10^-4	1 273	1 243	119
4	2.3×10⁸	1.000	3.1×10^-4	1 504	1 516	75
5	1.4×10⁸	1.000	3.9×10^-4	1 399	1 553	64
6	1.2×10⁸	1.000	4.3×10^-4	1 528	1 727	43
7	6.9×10⁷	1.000	5.6×10^-4	1 371	1 507	-3

Table 2. The significance test of linear regression effect of the regression equations between A_16% and

A_{c_{1}}

A_{c_{2}}

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编号	A_c	$A_{c_{1}}$	$A_{c_{2}}$	A_hc(2%, 30%)= $\hat{a}$ A_2%+ $\hat{b}$ A_30%
1	A_4%	A_2%	A_30%	A_h_4%(2%, 30%)=0.930 3×A_2%+0.062 6×A_30%
2	A_6%	A_2%	A_30%	A_h_6%(2%, 30%)=0.855 2×A_2%+0.149 9×A_30%
3	A_8%	A_2%	A_30%	A_h_8%(2%, 30%)=0.772 5×A_2%+0.229 7×A_30%
4	A_10%	A_2%	A_30%	A_h_10%(2%, 30%)=0.696 5×A_2%+0.307 2×A_30%
5	A_12%	A_2%	A_30%	A_h_12%(2%, 30%)=0.622 1×A_2%+0.381 4×A_30%
6	A_14%	A_2%	A_30%	A_h_14%(2%, 30%)=0.546 6×A_2%+0.456 5×A_30%
7	A_16%	A_2%	A_30%	A_h_16%(2%, 30%)=0.484 2×A_2%+0.516 6×A_30%
8	A_18%	A_2%	A_30%	A_h_18%(2%, 30%)=0.396 9×A_2%+0.601 2×A_30%
9	A_20%	A_2%	A_30%	A_h_20%(2%, 30%)=0.311 6×A_2%+0.686 5×A_30%
10	A_22%	A_2%	A_30%	A_h_22%(2%, 30%)=0.266 1×A_2%+0.734 5×A_30%
11	A_24%	A_2%	A_30%	A_h_24%(2%, 30%)=0.194 5×A_2%+0.807 7×A_30%
12	A_26%	A_2%	A_30%	A_h_26%(2%, 30%)=0.144 0×A_2%+0.857 6×A_30%
13	A_28%	A_2%	A_30%	A_h_28%(2%, 30%)=0.072 66×A_2%+0.927 6×A_30%

Table 3. The hybrid spectra equations between A_hc and A_2%, A_30%

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c(w/v)/%	$\hat{a}$	$\hat{b}$	$\hat{a}$ + $\hat{b}$
4	0.930 3	0.062 6	0.992 9
10	0.696 5	0.307 2	1.003 7
16	0.484 2	0.516 6	1.000 8
22	0.266 1	0.734 5	1.000 6
28	0.072 7	0.927 6	1.000 3

Table 4. The relationship among c, regression coefficient

\hat{a}

and

\hat{b}

and

\hat{a}

\hat{b}

Meng YAO, Hai-shui WANG. To Make a Good Infrared Spectrum in NaCl Aqueous Solution Where Lambert-Beer’s Law is Not to be Obeyed[J]. Spectroscopy and Spectral Analysis, 2021, 41(1): 65

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