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Optical constants of polyacrylamide solution in infrared spectral region
Accepted Manuscript Title: Optical constants of polyacrylamide solution in infrared spectral region Authors: Hanbing Qi, Xiaoxue Zhang, Minghu Jiang, Lu Yang, Dong Li PII: DOI: Reference:
S0030-4026(17)30947-6 http://dx.doi.org/doi:10.1016/j.ijleo.2017.08.055 IJLEO 59518
To appear in: Received date: Accepted date:
27-4-2017 7-8-2017
Please cite this article as: Hanbing Qi, Xiaoxue Zhang, Minghu Jiang, Lu Yang, Dong Li, Optical constants of polyacrylamide solution in infrared spectral region, Optik - International Journal for Light and Electron Opticshttp://dx.doi.org/10.1016/j.ijleo.2017.08.055 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Optical constants of polyacrylamide solution in infrared spectral region Hanbing Qia,b, Xiaoxue Zhanga, Minghu Jiangb, Lu Yanga, Dong Lia,b* a
School of Architecture and Civil Engineering, Northeast Petroleum University, Fazhan Lu Street, Daqing 163318, China
b
School of Mechanical Science and Engineering, Northeast Petroleum University, Fazhan Lu Street, Daqing 163318, China
Corresponding authors. Tel.: +86 459 6507763 E-mail: [email protected]
ABSTRACT Polyacrylamide (PAM) is a macromolecular polymer, and its solution is widely applied in oil exploitation, sewage treatment and paper making. Transmittance spectrum of PAM solution in the infrared wavelength region at normal incidence was investigated by an IRTracer-100 spectrometer, and the optical constants of PAM solution were obtained based on modelling transmittances combined with Kramers-Kronig (K-K) dispersion equation. The results show that the transmittance of PAM solution is higher than that of distilled water due to polyacrylamide. The transmission spectra shapes of PAM solution with different concentrations are similar in the wavelength range of 400-4000 cm-1, and it contains two strong absorption bands and two obvious peaks. The absorption index and refractive index of PAM solution all increased first and then decreased with the increase of concentration in the wavelength range of 2400-2800 cm-1. The absorption index and refractive index of PAM solution in the concentration range of 20-800mg/L are 3.42×10-3-9.13×10-3and 1.22-1.43, respectively.
Keywords: PAM solution; Transmittance spectra; Optical constants 1. Introduction As a linear polymer, polyacrylamide (PAM) has the amide group with high polar in its molecular structure, which results that it has the characteristics of hydrogen bonding and high reactivity. PAM solution is used in a very wide range of oil exploitation, sewage treatment and paper making [1-4]. The optical properties of PAM solution are often used in the concentration detection of PAM in oil field, and they are also a basis on the analysis of polymer-contained sewage by optical measurement [56]. However, there are limited researches about the optical properties of PAM solution. The optical constants are key parameters for determining the optical properties of PAM solution. The present techniques to calculate the optical constants of liquid like PAM solution are outlined as the inversion methods based on reflectance and transmittance spectra [7-9], the single reflectance method [10] and the single transmittance method [11-12], the spectroscopic ellipsometry [13-14], and the double-thickness transmittance method [15-16]. The inverse calculation process of the single reflectance method and the single transmittance method need to combine with Kramers-Kronig (K-K) dispersion equation [10-12]. For example, Jones and his co-workers [17] in National Research Council of Canada firstly proposed the single transmittance method combined with Kramers-Kronig (K-K). Zelsmann [18] measured optical properties of water in the spectral region extending from 25 cm-1 to 450 cm-1 by classical absorption techniques with a FTIR interferometer. From these experimental spectra, the optical constants n and k were calculated by
iteration using the Kramers-Kronig transformation, in which n and k is refractive and absorption index, respectively. Keefe et al [19-21] obtained the optical constants of some liquid matertials by Kramers-Kronig (K-K) dispersion equation, such as benzene-d1, toluene-d8 and n-pentane. Sani et al [22] used the k spectrum to calculate n by means of a Kramers–Kronig transform in an extremely wide wavelength range from 0.185μm to 55μm based on transmittance measurements. The single transmittance method combined with Kramers-Kronig (K-K) dispersion equation is used in a very wide range. Transmittance spectra of PAM solution in the infrared regions were investigated by an IRTracer-100 spectrometer. The optical constants of PAM solution were achieved by the single transmittance method combined with Kramers-Kronig (K-K) dispersion equation using the experimental results. 2. Experimental method The complex optical constants are defined by nˆ( ) n( ) ik ( )
（1）
All these quantities depend on the wavelength λ. The real part of the complex refractive index is the usual refractive index n and the imaginary part is the absorption index k. For the representation of a spectrum generally one uses a plot of the transmittance T versus wavenumber. T for a given sample thickness l is expressed as
T
I0 exp( l ) It
（2）
A l log10 (e) where α is the absorption coefficient of the sample. The corresponding absorption index k may be obtained from Eq. 2 by k ( )
( ) 4
（3）
The real part n(λ) is connected to the imaginary part k(λ) by the Principle of Causality by the Kramers-Kronig dispersion relations, which are given by n( ' ) n 2
0
X ( ) 2
k ( ' )sin(2 ' )d '
0
k ( ' ) 2
X ( ) cos(2 ' )d
0
X ( ) 2
X ( )sin(2 ' )d
0
（4a）
n( ' ) cos(2 ' )d '
（4b）
The total transmittance T of optical cell filled with liquid materials at normal incidence is as follows [23].
T
Tg 2Tl 1 Rg Rg Rl Rg 2 Rl Rg RlTl 2
（5）
where Rg and Rl are the reflectance of glass and liquid materialslabs at normal incidence, respectively. ρg and ρl are the interface reflectance for surface between air and glass, and for surfacebetween liquid material and glass, respectively. kg and kl are theextinction coefficient of glass and liquid material, respectively. l and L are the thickness of glass slab and liquid material slab, respectively. λ is the wavelength.
The reflectance of glass and liquid material slabs at normal incidence are given by the following forms.
Rg g
(1 g ) 2 g e 1 l g e
Rl l
1 l e
8 k1l
（6）
8 k1l
(1 l ) 2 l e 2
8 k2 L
（7）
8 k2 L
The transmittance of glass and liquid material slabs at normal incidence are given as
Tg
(1 g )(1 l )e 1 l g e
Rl l
（8）
8 k1l
(1 l ) 2 l e 1 l e 2
4 k1l
8 k2 L
（9）
8 k2 L
where Tg and Tl are the transmittance of glass and liquid material slabs at normal incidence, respectively. The interface reflectance ρg and ρl are calculated based on Fresnel’s relations.
g
l
(ng 1)2 k g 2 (ng 1)2 k g 2
(nl ng )2 (kl k g )2 (nl ng )2 (kl k g )2
where ng and nl are the refractive index of glass and liquid material, respectively.
（10）
（11）
To solve the above expressions, a calculation procedure based on iteration technique was adopted as the following steps: 1) determine the assumed k values by Eq. (3); 2) calculate n by Eq. (4a); 3) calculate Rg , Tg , ρg of optical window by Eq. (6)(8)(10); 4) calculate Rl , Tl , ρl of liquid material by Eq. (7)(9)(11); 5) calculate the total transmittance T’ of three slabs system by Eq. (5) and analyze the calculation errors between measured value T and the calculated value T’. If the errors are rational, the k values calculation is finished, otherwise the assumed k values will be substituted by the new k values and then returns to 2). 3. Optical properties of PAM solution The concentration of PAM mother solution is 1g/L. After ripening it 24 hours, take it dilute into 10mg/L, 20mg/L, 30mg/L, 40mg/L, 50 mg/L, 60 mg/L, 70 mg/L, 80 mg/L, 90 mg/L, 100 mg/L, 200 mg/L, 300 mg/L, 400 mg/L, 500 mg/L, 600 mg/L, 700 mg/L, 800 mg/L, 900 mg/L, 1000 mg/L, respectively. The transmittance spectra of PAM solution were measured by IRtracer-100 in the wavelength range 400-4000cm1.
The material of optical window is zinc selenide. The path length is 0.025mm. The
transmittance spectra of PAM solution with different concentrations are shown in Fig.1. Fig.1. shows that the transmittance values of PAM solution with different concentrations are all higher than that of distilled water, which illustrates that the polyacrylamide containing in PAM solution results in its greater transmittance compared with water. The transmission spectra shapes of PAM solution with
different concentrations are similar in infrared wavelength region. It contains two strong absorption bands, 500-920 cm-1 and 2980-3680 cm-1. There are two obvious peaks at the 1882 cm-1 and 2627 cm-1 whose transmittance are greater than the nearby wavenumbers. An obvious trough at 2127 cm-1, its transmittance is less than the nearby wavenumbers. The reason of these peaks is as follows. The fundamental frequency absorption peaks are 3420 cm-1 (OH- stretching vibration), 1640 cm-1 (H2O deviational vibration), and 550 cm-1 (H2O swing vibration) in the infrared spectrum of water. A combination band at 2070 cm-1 is possibly produced by adding the two fundamental frequency variable angle vibration and swing together. So the trough at 2127 cm-1 is probably a combination band, and 500-920 cm-1, 1590-1700 cm-1 and 2980-3680 cm-1 are three fundamental frequency absorption peaks of water. 4. Optical constants of PAM solution The optical constants of PAM solution are obtained by the inversion model based on the experimental transmittance of PAM solution. Its concentrations are 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L, and the path length is 0.025mm. The absorption index k and refractive index n in the wavenumber range of 24002800 cm-1 are shown in Fig.2 and Table 1-2. Fig.2 shows the absorption index k and refractive index n in the wavenumber range of 2400-2800cm-1. The absorption index spectra of PAM solution with different concentrations are different, but the shapes are similar. The absorption index and refractive index of PAM solution all increased first and then decreased with the
increase of concentration in the wavelength range of 2400-2800 cm-1.The absorption index value decreased in the wavenumber range of 2400-2625cm-1, and it increased in the wavenumber of 2625-2800cm-1. The minimum values of absorption index of PAM solution with different concentrations are all at 2625cm-1. The absorption index of PAM solution at 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L are in the range of 3.68×10-3-8.7×10-3, 3.98×10-3-9.12×10-3, 4.21×10-3-9.13×10-3, 3.95×10-38.63×10-3 and 3.42×10-3-8.29×10-3, respectively. The refractive index values of PAM solution tended to be constant, and the spectra presented a smaller downtrend with the increase of wavenumber. The refractive index of PAM solution at 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L are in the range of 1.25-1.27, 1.35-1.37, 1.41-1.43, 1.32-1.34 and 1.22-1.24, respectively. 5. Conclusions The transmittance spectra of PAM solution in the infrared wavelength regions were measured. The transmittance of PAM solution is higher than that of distilled water due to polyacrylamide. The transmission spectra shapes of PAM solution with different concentrations are similar in the wavelength range of 400-4000 cm-1, and it contains two strong absorption band, 500-920 cm-1 and 2980-3680 cm-1, two obvious peaks at 1882 cm-1 and 2627 cm-1. The absorption index and refractive index of PAM solution all increased first and then decreased with the increase of concentration in the wavelength range of 2400-
2800 cm-1.The absorption index of PAM solution at 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L are in the range of 3.68×10-3-8.7×10-3, 3.98×10-3-9.12×10-3, 4.21×10-3-9.13×10-3, 3.95×10-3-8.63×10-3 and 42×10-3-8.29×10-3, respectively. The refractive index values of PAM solution tended to be constant, and the spectra presented a smaller downtrend with the increase of wavenumber. The refractive index of PAM solution at 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L are in the range of 1.25-1.27, 1.35-1.37, 1.41-1.43, 1.32-1.34 and 1.22-1.24, respectively. Acknowledgements The financial support provided by the Project Funded by PetroChina Innovation Foundation Grant No. 2015 D-5006-0605 and the Special funds for scientific research of Hei-Longjiang Education Department within the program Grant No. 2016YSFX-02 and the Natural Science Foundation of Hei-Longjiang through Grant No. JJ2016ZR0314 are gratefully acknowledged. References [1] H.J. Gong, G.Y. Xu, Y.Y. Zhu, et al, Influencing Factors on the Properties of Complex Systems Consisting of Hydrolyzed Polyacrylamide/Triton X-100/Cetyl Trimethylammonium Bromide: Viscosity and Dynamic Interfacial Tension Studies, Energy Fuels 23(1) (2009) 300-305. [2] J. Cao, Y.B. Tan, Y.J. Che, et al, Novel complex gel beads composed of hydrolyzed polyacrylamide and chitosan: An effective adsorbent for the removal of heavy metal from aqueous solution. Bioresour Technol 101 ( 2010) 2558-2561.
[3] H. Saboorian-Jooybari, M. Dejam, Z.X. Chen, Heavy oil polymer flooding from laboratory core floods to pilot tests and field applications:Half-centurystudies, Journal of Petroleum Science and Engineering. 142 (2016) 85-100. [4] P. Raffa, A.A. Broekhuis, F. Picchioni, Polymeric surfactants for enhanced oil recovery: A review, Journal of Petroleum Science and Engineering. 145 (2016) 723733. [5] F.A.A. Momani, B. Ormeci, Measurement of polyacrylamide polymers in water and wastewater using an in-line UV–vis spectrophotometer, Journal of Environmental Chemical Engineering. 2 (2014) 765-772. [6] F. Baldi, F. Bignotti, I. Peroni, S. Agnelli, T. Riccò, On the measurement of the fracture resistance of polyacrylamide hydrogels by wire cutting tests, Polymer Testing. 31 (2012) 455-465. [7] R. Islam, D.R. Rao, Optical constants of polycrystalline ZnSe/CdSe alloy films, Opt. Mater.7 (1997) 47-50. [8] M.A. Khashan, A.M. El-Naggar, A new method of finding the optical constants of a solid from the reflectance and transmittance spectrograms of its slab, Opt. Commun. 174 (2000) 445-453. [9] S.Y. El-Zaiat, M.B. El-Den, S.U. El-Kameesy, Y.A. El-Gammam, Spectral dispersion of linear optical properties for Sm2O3 doped B2O3-PbO-Al2O3 glasses, Opt. Laser Technol. 44 (2012) 1270-1276.
[10] J.M. Gonzalez-Leal, E. Marquez, A.M. Bernal-Oliva, J.J. Ruiz-Perez, R. JimenezGaray, Derivation of the optical constants of thermally-evaporated uniform films of binary chalcogenide glasses using only their reflection spectra, Thin Solid Films 317 (1998) 223-227. [11] A.P. Caricato, A. Fazzi, G. Leggieri, A computer program for determination of thin films thickness and optical constants, Appl. Surf. Sci. 248 (2005) 440-445. [12] V. Dhanasekaran, T. Mahalingam, J.K. Rhee, J.P. Chu, Structural and optical properties of electrosynthesized ZnSe thin films, Optik 124 (2013) 255-260. [13] C.M.I. Okoye, Theoretical study of the electronic structure, chemical bonding and optical properties of KNbO3 in the paraelectric cubic phase, Phys. BCondens. Matter., 15 (2003) 5945. [14] J. Kvietkov, B. Daniel, M. Hetterich, M. Schubert, D. Spemann, Optical properties of ZnSe and Zn0.87Mn0.13Se epilayers determined by spectroscopic ellipsometry, Thin Solid Films 455-456 (2004) 228-230. [15] D. Li, Q. Ai, X.L. Xia, Determined Optical Constants of ZnSe Glass from 0.83 to 21 µm by Transmittance Spectra: Methods and Measurements, Japanese J. Appl. Phys. 52 (2013) 046602. [16] D. Li, Q. Ai, X.L. Xia, Measured optical constants of ZnSe glass from 0.83 μm to 2.20 μm by a novel transmittance method, Optik 124 (2013) 5177-5180.
[17] T.G. Goplen, D.G. Cameron, R.N. Jones, Absolute Absorption Intensity and Dispersion Measurements on Some Organic Liquids in the Infrared, Applied Spectroscopy 34(6) (1980) 657-691. [18] H.R. Zelsmann, Temperature dependence of the optical constants for liquid H2O and D2O in the far IR region, Journal of Molecular Structure 350 (1995) 95-114. [19] J.E. Bertie, Y. Apelblat, C.D. Keefe, Infrared intensities of liquids. Part XXIII. Infrared optical constants and integrated intensities of liquid benzene-d1 at 25℃, Journal of Molecular Structure 550-551 (2000) 135-165. [20] C.D. Keefe, J.K. Pearson, A. MacDonald, Optical constants and vibrational assignment of liquid toluene-d8 between 4000 and 450 cm-1 at 25℃, Journal of Molecular Structure 655 (2003) 69-80. [21] C.D. Keefe, S. Jaspers-Fayer, Infrared optical properties and Raman spectra of npentane and n-pentane-d12, Vibrational Spectroscopy 57 (2011) 72-80. [22] E. Sani, A. Dell’Oro, Optical constants of ethylene glycol over an extremely wide spectral range, Optical Materials 37 (2014) 36-41. [23] D. Li, Q. Ai, X.L. Xia, Double-thickness model of thermal radiation physical property measurement of semi-transparent liquid with transmission method, CIESCJ. 63 (2012) 123–129.
40
40
12
12 11
11
9 8
water 10mg/L 20mg/L 30mg/L 40mg/L 50mg/L 60mg/L 70mg/L 80mg/L 90mg/L 100mg/L
7 2000
2100
2200
波数(cm-1)
20 10
T(%)
30
Transmittance (%)
T(%)
30
10 9
water 100mg/L 200mg/L 300mg/L 400mg/L 500mg/L 600mg/L 700mg/L 800mg/L 900mg/L 1000mg/L
8 2000
20
2100 2200 波数(cm-1)
2300
10 0
0 1000
2000
3000
0
4000
1000
2000
3000
Wavenumber (cm-1)
Wavenumber (cm-1)
(a) 0-100mg/L
(b) 100-1000mg/L
Fig.1. The transmittance spectra of PAM solution
1.0x10-2
20mg/L 80mg/L 100mg/L 400mg/L 800mg/L
8.0x10-3
k
0
6.0x10-3
4.0x10-3 2400
2500
2600
2700
2800
Wavenumber (cm-1)
1.44 1.40 1.36
n
Transmittance (%)
10
1.32 20mg/L 80mg/L 100mg/L 400mg/L 800mg/L
1.28 1.24 1.20 2400
2500
2600
2700
2800
Wavenumber (cm-1)
(a) Absorption index
(b) Refractive index
Fig.2. The optical constants of PAM solution
4000
Table1 The absorption index of PAM solution Wavenumber
k
Wavelength
（cm-1）
20mg/L
80mg/L
100mg/L
400mg/L
800mg/L
（μm）
2413 2432 2452 2471 2490 2509 2529 2548 2567 2587 2606 2625 2644 2664 2683 2702 2722 2741 2760 2779 2799
0.00870 0.00793 0.00722 0.00661 0.00607 0.00553 0.00502 0.00458 0.00427 0.00400 0.00377 0.00368 0.00373 0.00382 0.00400 0.00435 0.00483 0.00541 0.00616 0.00713 0.00828
0.00912 0.00852 0.00766 0.00689 0.00649 0.00612 0.00547 0.00487 0.00468 0.00456 0.00419 0.00398 0.00415 0.00432 0.00438 0.00467 0.00525 0.00582 0.00647 0.00746 0.00863
0.00913 0.00880 0.00799 0.00699 0.00654 0.00635 0.00570 0.00510 0.00491 0.00479 0.00442 0.00421 0.00438 0.00455 0.00461 0.00490 0.00561 0.00635 0.00678 0.00772 0.00907
0.00863 0.00781 0.00695 0.00652 0.00609 0.00551 0.00514 0.00478 0.00436 0.00406 0.00397 0.00395 0.00397 0.00402 0.00416 0.00444 0.00484 0.00567 0.00637 0.00712 0.00834
0.00829 0.00747 0.00672 0.00618 0.00575 0.00517 0.00460 0.00424 0.00402 0.00372 0.00343 0.00342 0.00353 0.00358 0.00372 0.00412 0.00463 0.00514 0.00590 0.00691 0.00800
4.14 4.11 4.08 4.05 4.02 3.99 3.95 3.92 3.90 3.87 3.84 3.81 3.78 3.75 3.73 3.70 3.67 3.65 3.62 3.60 3.57
Table 2 The refractive index of PAM solution Wavenumber
n
Wavelength
-1
（cm ）
20mg/L
80mg/L
100mg/L
400mg/L
800mg/L
（μm）
2413 2432 2452 2471 2490 2509 2529 2548 2567
1.26678 1.26355 1.26198 1.26103 1.26032 1.25981 1.25951 1.25938 1.25932
1.36740 1.36389 1.36208 1.36121 1.36064 1.35997 1.35947 1.35940 1.35948
1.42778 1.42428 1.42220 1.42127 1.42093 1.42033 1.41953 1.41940 1.41973
1.33693 1.33399 1.33216 1.33087 1.33038 1.33022 1.32969 1.32918 1.32933
1.23636 1.23323 1.23180 1.23100 1.23030 1.22973 1.22951 1.22947 1.22939
4.14 4.11 4.08 4.05 4.02 3.99 3.95 3.92 3.90
2587 2606 2625 2644 2664 2683 2702 2722 2741 2760 2779 2799
1.25927 1.25933 1.25946 1.25954 1.25957 1.25960 1.25957 1.25938 1.25895 1.25817 1.25655 1.25131
1.35929 1.35919 1.35941 1.35957 1.35944 1.35938 1.35942 1.35923 1.35865 1.35784 1.35623 1.35077
1.41957 1.41913 1.41932 1.41976 1.41955 1.41917 1.41931 1.41930 1.41848 1.41751 1.41600 1.41031
1.32960 1.32941 1.32923 1.32954 1.32978 1.32951 1.32931 1.32938 1.32897 1.32792 1.32634 1.32120
1.22928 1.22941 1.22961 1.22966 1.22962 1.22972 1.22974 1.22950 1.22907 1.22839 1.22679 1.22168
3.87 3.84 3.81 3.78 3.75 3.73 3.70 3.67 3.65 3.62 3.60 3.57
S0030-4026(17)30947-6 http://dx.doi.org/doi:10.1016/j.ijleo.2017.08.055 IJLEO 59518
To appear in: Received date: Accepted date:
27-4-2017 7-8-2017
Please cite this article as: Hanbing Qi, Xiaoxue Zhang, Minghu Jiang, Lu Yang, Dong Li, Optical constants of polyacrylamide solution in infrared spectral region, Optik - International Journal for Light and Electron Opticshttp://dx.doi.org/10.1016/j.ijleo.2017.08.055 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Optical constants of polyacrylamide solution in infrared spectral region Hanbing Qia,b, Xiaoxue Zhanga, Minghu Jiangb, Lu Yanga, Dong Lia,b* a
School of Architecture and Civil Engineering, Northeast Petroleum University, Fazhan Lu Street, Daqing 163318, China
b
School of Mechanical Science and Engineering, Northeast Petroleum University, Fazhan Lu Street, Daqing 163318, China
Corresponding authors. Tel.: +86 459 6507763 E-mail: [email protected]
ABSTRACT Polyacrylamide (PAM) is a macromolecular polymer, and its solution is widely applied in oil exploitation, sewage treatment and paper making. Transmittance spectrum of PAM solution in the infrared wavelength region at normal incidence was investigated by an IRTracer-100 spectrometer, and the optical constants of PAM solution were obtained based on modelling transmittances combined with Kramers-Kronig (K-K) dispersion equation. The results show that the transmittance of PAM solution is higher than that of distilled water due to polyacrylamide. The transmission spectra shapes of PAM solution with different concentrations are similar in the wavelength range of 400-4000 cm-1, and it contains two strong absorption bands and two obvious peaks. The absorption index and refractive index of PAM solution all increased first and then decreased with the increase of concentration in the wavelength range of 2400-2800 cm-1. The absorption index and refractive index of PAM solution in the concentration range of 20-800mg/L are 3.42×10-3-9.13×10-3and 1.22-1.43, respectively.
Keywords: PAM solution; Transmittance spectra; Optical constants 1. Introduction As a linear polymer, polyacrylamide (PAM) has the amide group with high polar in its molecular structure, which results that it has the characteristics of hydrogen bonding and high reactivity. PAM solution is used in a very wide range of oil exploitation, sewage treatment and paper making [1-4]. The optical properties of PAM solution are often used in the concentration detection of PAM in oil field, and they are also a basis on the analysis of polymer-contained sewage by optical measurement [56]. However, there are limited researches about the optical properties of PAM solution. The optical constants are key parameters for determining the optical properties of PAM solution. The present techniques to calculate the optical constants of liquid like PAM solution are outlined as the inversion methods based on reflectance and transmittance spectra [7-9], the single reflectance method [10] and the single transmittance method [11-12], the spectroscopic ellipsometry [13-14], and the double-thickness transmittance method [15-16]. The inverse calculation process of the single reflectance method and the single transmittance method need to combine with Kramers-Kronig (K-K) dispersion equation [10-12]. For example, Jones and his co-workers [17] in National Research Council of Canada firstly proposed the single transmittance method combined with Kramers-Kronig (K-K). Zelsmann [18] measured optical properties of water in the spectral region extending from 25 cm-1 to 450 cm-1 by classical absorption techniques with a FTIR interferometer. From these experimental spectra, the optical constants n and k were calculated by
iteration using the Kramers-Kronig transformation, in which n and k is refractive and absorption index, respectively. Keefe et al [19-21] obtained the optical constants of some liquid matertials by Kramers-Kronig (K-K) dispersion equation, such as benzene-d1, toluene-d8 and n-pentane. Sani et al [22] used the k spectrum to calculate n by means of a Kramers–Kronig transform in an extremely wide wavelength range from 0.185μm to 55μm based on transmittance measurements. The single transmittance method combined with Kramers-Kronig (K-K) dispersion equation is used in a very wide range. Transmittance spectra of PAM solution in the infrared regions were investigated by an IRTracer-100 spectrometer. The optical constants of PAM solution were achieved by the single transmittance method combined with Kramers-Kronig (K-K) dispersion equation using the experimental results. 2. Experimental method The complex optical constants are defined by nˆ( ) n( ) ik ( )
（1）
All these quantities depend on the wavelength λ. The real part of the complex refractive index is the usual refractive index n and the imaginary part is the absorption index k. For the representation of a spectrum generally one uses a plot of the transmittance T versus wavenumber. T for a given sample thickness l is expressed as
T
I0 exp( l ) It
（2）
A l log10 (e) where α is the absorption coefficient of the sample. The corresponding absorption index k may be obtained from Eq. 2 by k ( )
( ) 4
（3）
The real part n(λ) is connected to the imaginary part k(λ) by the Principle of Causality by the Kramers-Kronig dispersion relations, which are given by n( ' ) n 2
0
X ( ) 2
k ( ' )sin(2 ' )d '
0
k ( ' ) 2
X ( ) cos(2 ' )d
0
X ( ) 2
X ( )sin(2 ' )d
0
（4a）
n( ' ) cos(2 ' )d '
（4b）
The total transmittance T of optical cell filled with liquid materials at normal incidence is as follows [23].
T
Tg 2Tl 1 Rg Rg Rl Rg 2 Rl Rg RlTl 2
（5）
where Rg and Rl are the reflectance of glass and liquid materialslabs at normal incidence, respectively. ρg and ρl are the interface reflectance for surface between air and glass, and for surfacebetween liquid material and glass, respectively. kg and kl are theextinction coefficient of glass and liquid material, respectively. l and L are the thickness of glass slab and liquid material slab, respectively. λ is the wavelength.
The reflectance of glass and liquid material slabs at normal incidence are given by the following forms.
Rg g
(1 g ) 2 g e 1 l g e
Rl l
1 l e
8 k1l
（6）
8 k1l
(1 l ) 2 l e 2
8 k2 L
（7）
8 k2 L
The transmittance of glass and liquid material slabs at normal incidence are given as
Tg
(1 g )(1 l )e 1 l g e
Rl l
（8）
8 k1l
(1 l ) 2 l e 1 l e 2
4 k1l
8 k2 L
（9）
8 k2 L
where Tg and Tl are the transmittance of glass and liquid material slabs at normal incidence, respectively. The interface reflectance ρg and ρl are calculated based on Fresnel’s relations.
g
l
(ng 1)2 k g 2 (ng 1)2 k g 2
(nl ng )2 (kl k g )2 (nl ng )2 (kl k g )2
where ng and nl are the refractive index of glass and liquid material, respectively.
（10）
（11）
To solve the above expressions, a calculation procedure based on iteration technique was adopted as the following steps: 1) determine the assumed k values by Eq. (3); 2) calculate n by Eq. (4a); 3) calculate Rg , Tg , ρg of optical window by Eq. (6)(8)(10); 4) calculate Rl , Tl , ρl of liquid material by Eq. (7)(9)(11); 5) calculate the total transmittance T’ of three slabs system by Eq. (5) and analyze the calculation errors between measured value T and the calculated value T’. If the errors are rational, the k values calculation is finished, otherwise the assumed k values will be substituted by the new k values and then returns to 2). 3. Optical properties of PAM solution The concentration of PAM mother solution is 1g/L. After ripening it 24 hours, take it dilute into 10mg/L, 20mg/L, 30mg/L, 40mg/L, 50 mg/L, 60 mg/L, 70 mg/L, 80 mg/L, 90 mg/L, 100 mg/L, 200 mg/L, 300 mg/L, 400 mg/L, 500 mg/L, 600 mg/L, 700 mg/L, 800 mg/L, 900 mg/L, 1000 mg/L, respectively. The transmittance spectra of PAM solution were measured by IRtracer-100 in the wavelength range 400-4000cm1.
The material of optical window is zinc selenide. The path length is 0.025mm. The
transmittance spectra of PAM solution with different concentrations are shown in Fig.1. Fig.1. shows that the transmittance values of PAM solution with different concentrations are all higher than that of distilled water, which illustrates that the polyacrylamide containing in PAM solution results in its greater transmittance compared with water. The transmission spectra shapes of PAM solution with
different concentrations are similar in infrared wavelength region. It contains two strong absorption bands, 500-920 cm-1 and 2980-3680 cm-1. There are two obvious peaks at the 1882 cm-1 and 2627 cm-1 whose transmittance are greater than the nearby wavenumbers. An obvious trough at 2127 cm-1, its transmittance is less than the nearby wavenumbers. The reason of these peaks is as follows. The fundamental frequency absorption peaks are 3420 cm-1 (OH- stretching vibration), 1640 cm-1 (H2O deviational vibration), and 550 cm-1 (H2O swing vibration) in the infrared spectrum of water. A combination band at 2070 cm-1 is possibly produced by adding the two fundamental frequency variable angle vibration and swing together. So the trough at 2127 cm-1 is probably a combination band, and 500-920 cm-1, 1590-1700 cm-1 and 2980-3680 cm-1 are three fundamental frequency absorption peaks of water. 4. Optical constants of PAM solution The optical constants of PAM solution are obtained by the inversion model based on the experimental transmittance of PAM solution. Its concentrations are 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L, and the path length is 0.025mm. The absorption index k and refractive index n in the wavenumber range of 24002800 cm-1 are shown in Fig.2 and Table 1-2. Fig.2 shows the absorption index k and refractive index n in the wavenumber range of 2400-2800cm-1. The absorption index spectra of PAM solution with different concentrations are different, but the shapes are similar. The absorption index and refractive index of PAM solution all increased first and then decreased with the
increase of concentration in the wavelength range of 2400-2800 cm-1.The absorption index value decreased in the wavenumber range of 2400-2625cm-1, and it increased in the wavenumber of 2625-2800cm-1. The minimum values of absorption index of PAM solution with different concentrations are all at 2625cm-1. The absorption index of PAM solution at 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L are in the range of 3.68×10-3-8.7×10-3, 3.98×10-3-9.12×10-3, 4.21×10-3-9.13×10-3, 3.95×10-38.63×10-3 and 3.42×10-3-8.29×10-3, respectively. The refractive index values of PAM solution tended to be constant, and the spectra presented a smaller downtrend with the increase of wavenumber. The refractive index of PAM solution at 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L are in the range of 1.25-1.27, 1.35-1.37, 1.41-1.43, 1.32-1.34 and 1.22-1.24, respectively. 5. Conclusions The transmittance spectra of PAM solution in the infrared wavelength regions were measured. The transmittance of PAM solution is higher than that of distilled water due to polyacrylamide. The transmission spectra shapes of PAM solution with different concentrations are similar in the wavelength range of 400-4000 cm-1, and it contains two strong absorption band, 500-920 cm-1 and 2980-3680 cm-1, two obvious peaks at 1882 cm-1 and 2627 cm-1. The absorption index and refractive index of PAM solution all increased first and then decreased with the increase of concentration in the wavelength range of 2400-
2800 cm-1.The absorption index of PAM solution at 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L are in the range of 3.68×10-3-8.7×10-3, 3.98×10-3-9.12×10-3, 4.21×10-3-9.13×10-3, 3.95×10-3-8.63×10-3 and 42×10-3-8.29×10-3, respectively. The refractive index values of PAM solution tended to be constant, and the spectra presented a smaller downtrend with the increase of wavenumber. The refractive index of PAM solution at 20mg/L, 80mg/L, 100mg/L, 400mg/L and 800mg/L are in the range of 1.25-1.27, 1.35-1.37, 1.41-1.43, 1.32-1.34 and 1.22-1.24, respectively. Acknowledgements The financial support provided by the Project Funded by PetroChina Innovation Foundation Grant No. 2015 D-5006-0605 and the Special funds for scientific research of Hei-Longjiang Education Department within the program Grant No. 2016YSFX-02 and the Natural Science Foundation of Hei-Longjiang through Grant No. JJ2016ZR0314 are gratefully acknowledged. References [1] H.J. Gong, G.Y. Xu, Y.Y. Zhu, et al, Influencing Factors on the Properties of Complex Systems Consisting of Hydrolyzed Polyacrylamide/Triton X-100/Cetyl Trimethylammonium Bromide: Viscosity and Dynamic Interfacial Tension Studies, Energy Fuels 23(1) (2009) 300-305. [2] J. Cao, Y.B. Tan, Y.J. Che, et al, Novel complex gel beads composed of hydrolyzed polyacrylamide and chitosan: An effective adsorbent for the removal of heavy metal from aqueous solution. Bioresour Technol 101 ( 2010) 2558-2561.
[3] H. Saboorian-Jooybari, M. Dejam, Z.X. Chen, Heavy oil polymer flooding from laboratory core floods to pilot tests and field applications:Half-centurystudies, Journal of Petroleum Science and Engineering. 142 (2016) 85-100. [4] P. Raffa, A.A. Broekhuis, F. Picchioni, Polymeric surfactants for enhanced oil recovery: A review, Journal of Petroleum Science and Engineering. 145 (2016) 723733. [5] F.A.A. Momani, B. Ormeci, Measurement of polyacrylamide polymers in water and wastewater using an in-line UV–vis spectrophotometer, Journal of Environmental Chemical Engineering. 2 (2014) 765-772. [6] F. Baldi, F. Bignotti, I. Peroni, S. Agnelli, T. Riccò, On the measurement of the fracture resistance of polyacrylamide hydrogels by wire cutting tests, Polymer Testing. 31 (2012) 455-465. [7] R. Islam, D.R. Rao, Optical constants of polycrystalline ZnSe/CdSe alloy films, Opt. Mater.7 (1997) 47-50. [8] M.A. Khashan, A.M. El-Naggar, A new method of finding the optical constants of a solid from the reflectance and transmittance spectrograms of its slab, Opt. Commun. 174 (2000) 445-453. [9] S.Y. El-Zaiat, M.B. El-Den, S.U. El-Kameesy, Y.A. El-Gammam, Spectral dispersion of linear optical properties for Sm2O3 doped B2O3-PbO-Al2O3 glasses, Opt. Laser Technol. 44 (2012) 1270-1276.
[10] J.M. Gonzalez-Leal, E. Marquez, A.M. Bernal-Oliva, J.J. Ruiz-Perez, R. JimenezGaray, Derivation of the optical constants of thermally-evaporated uniform films of binary chalcogenide glasses using only their reflection spectra, Thin Solid Films 317 (1998) 223-227. [11] A.P. Caricato, A. Fazzi, G. Leggieri, A computer program for determination of thin films thickness and optical constants, Appl. Surf. Sci. 248 (2005) 440-445. [12] V. Dhanasekaran, T. Mahalingam, J.K. Rhee, J.P. Chu, Structural and optical properties of electrosynthesized ZnSe thin films, Optik 124 (2013) 255-260. [13] C.M.I. Okoye, Theoretical study of the electronic structure, chemical bonding and optical properties of KNbO3 in the paraelectric cubic phase, Phys. BCondens. Matter., 15 (2003) 5945. [14] J. Kvietkov, B. Daniel, M. Hetterich, M. Schubert, D. Spemann, Optical properties of ZnSe and Zn0.87Mn0.13Se epilayers determined by spectroscopic ellipsometry, Thin Solid Films 455-456 (2004) 228-230. [15] D. Li, Q. Ai, X.L. Xia, Determined Optical Constants of ZnSe Glass from 0.83 to 21 µm by Transmittance Spectra: Methods and Measurements, Japanese J. Appl. Phys. 52 (2013) 046602. [16] D. Li, Q. Ai, X.L. Xia, Measured optical constants of ZnSe glass from 0.83 μm to 2.20 μm by a novel transmittance method, Optik 124 (2013) 5177-5180.
[17] T.G. Goplen, D.G. Cameron, R.N. Jones, Absolute Absorption Intensity and Dispersion Measurements on Some Organic Liquids in the Infrared, Applied Spectroscopy 34(6) (1980) 657-691. [18] H.R. Zelsmann, Temperature dependence of the optical constants for liquid H2O and D2O in the far IR region, Journal of Molecular Structure 350 (1995) 95-114. [19] J.E. Bertie, Y. Apelblat, C.D. Keefe, Infrared intensities of liquids. Part XXIII. Infrared optical constants and integrated intensities of liquid benzene-d1 at 25℃, Journal of Molecular Structure 550-551 (2000) 135-165. [20] C.D. Keefe, J.K. Pearson, A. MacDonald, Optical constants and vibrational assignment of liquid toluene-d8 between 4000 and 450 cm-1 at 25℃, Journal of Molecular Structure 655 (2003) 69-80. [21] C.D. Keefe, S. Jaspers-Fayer, Infrared optical properties and Raman spectra of npentane and n-pentane-d12, Vibrational Spectroscopy 57 (2011) 72-80. [22] E. Sani, A. Dell’Oro, Optical constants of ethylene glycol over an extremely wide spectral range, Optical Materials 37 (2014) 36-41. [23] D. Li, Q. Ai, X.L. Xia, Double-thickness model of thermal radiation physical property measurement of semi-transparent liquid with transmission method, CIESCJ. 63 (2012) 123–129.
40
40
12
12 11
11
9 8
water 10mg/L 20mg/L 30mg/L 40mg/L 50mg/L 60mg/L 70mg/L 80mg/L 90mg/L 100mg/L
7 2000
2100
2200
波数(cm-1)
20 10
T(%)
30
Transmittance (%)
T(%)
30
10 9
water 100mg/L 200mg/L 300mg/L 400mg/L 500mg/L 600mg/L 700mg/L 800mg/L 900mg/L 1000mg/L
8 2000
20
2100 2200 波数(cm-1)
2300
10 0
0 1000
2000
3000
0
4000
1000
2000
3000
Wavenumber (cm-1)
Wavenumber (cm-1)
(a) 0-100mg/L
(b) 100-1000mg/L
Fig.1. The transmittance spectra of PAM solution
1.0x10-2
20mg/L 80mg/L 100mg/L 400mg/L 800mg/L
8.0x10-3
k
0
6.0x10-3
4.0x10-3 2400
2500
2600
2700
2800
Wavenumber (cm-1)
1.44 1.40 1.36
n
Transmittance (%)
10
1.32 20mg/L 80mg/L 100mg/L 400mg/L 800mg/L
1.28 1.24 1.20 2400
2500
2600
2700
2800
Wavenumber (cm-1)
(a) Absorption index
(b) Refractive index
Fig.2. The optical constants of PAM solution
4000
Table1 The absorption index of PAM solution Wavenumber
k
Wavelength
（cm-1）
20mg/L
80mg/L
100mg/L
400mg/L
800mg/L
（μm）
2413 2432 2452 2471 2490 2509 2529 2548 2567 2587 2606 2625 2644 2664 2683 2702 2722 2741 2760 2779 2799
0.00870 0.00793 0.00722 0.00661 0.00607 0.00553 0.00502 0.00458 0.00427 0.00400 0.00377 0.00368 0.00373 0.00382 0.00400 0.00435 0.00483 0.00541 0.00616 0.00713 0.00828
0.00912 0.00852 0.00766 0.00689 0.00649 0.00612 0.00547 0.00487 0.00468 0.00456 0.00419 0.00398 0.00415 0.00432 0.00438 0.00467 0.00525 0.00582 0.00647 0.00746 0.00863
0.00913 0.00880 0.00799 0.00699 0.00654 0.00635 0.00570 0.00510 0.00491 0.00479 0.00442 0.00421 0.00438 0.00455 0.00461 0.00490 0.00561 0.00635 0.00678 0.00772 0.00907
0.00863 0.00781 0.00695 0.00652 0.00609 0.00551 0.00514 0.00478 0.00436 0.00406 0.00397 0.00395 0.00397 0.00402 0.00416 0.00444 0.00484 0.00567 0.00637 0.00712 0.00834
0.00829 0.00747 0.00672 0.00618 0.00575 0.00517 0.00460 0.00424 0.00402 0.00372 0.00343 0.00342 0.00353 0.00358 0.00372 0.00412 0.00463 0.00514 0.00590 0.00691 0.00800
4.14 4.11 4.08 4.05 4.02 3.99 3.95 3.92 3.90 3.87 3.84 3.81 3.78 3.75 3.73 3.70 3.67 3.65 3.62 3.60 3.57
Table 2 The refractive index of PAM solution Wavenumber
n
Wavelength
-1
（cm ）
20mg/L
80mg/L
100mg/L
400mg/L
800mg/L
（μm）
2413 2432 2452 2471 2490 2509 2529 2548 2567
1.26678 1.26355 1.26198 1.26103 1.26032 1.25981 1.25951 1.25938 1.25932
1.36740 1.36389 1.36208 1.36121 1.36064 1.35997 1.35947 1.35940 1.35948
1.42778 1.42428 1.42220 1.42127 1.42093 1.42033 1.41953 1.41940 1.41973
1.33693 1.33399 1.33216 1.33087 1.33038 1.33022 1.32969 1.32918 1.32933
1.23636 1.23323 1.23180 1.23100 1.23030 1.22973 1.22951 1.22947 1.22939
4.14 4.11 4.08 4.05 4.02 3.99 3.95 3.92 3.90
2587 2606 2625 2644 2664 2683 2702 2722 2741 2760 2779 2799
1.25927 1.25933 1.25946 1.25954 1.25957 1.25960 1.25957 1.25938 1.25895 1.25817 1.25655 1.25131
1.35929 1.35919 1.35941 1.35957 1.35944 1.35938 1.35942 1.35923 1.35865 1.35784 1.35623 1.35077
1.41957 1.41913 1.41932 1.41976 1.41955 1.41917 1.41931 1.41930 1.41848 1.41751 1.41600 1.41031
1.32960 1.32941 1.32923 1.32954 1.32978 1.32951 1.32931 1.32938 1.32897 1.32792 1.32634 1.32120
1.22928 1.22941 1.22961 1.22966 1.22962 1.22972 1.22974 1.22950 1.22907 1.22839 1.22679 1.22168
3.87 3.84 3.81 3.78 3.75 3.73 3.70 3.67 3.65 3.62 3.60 3.57