Optical constants of ethylene glycol over an extremely ... · PDF fileOptical constants of...

Optical constants of ethylene glycol over an extremely

wide spectral range

Elisa Sania,1,, Aldo Dell’Orob

aINO-CNR, Istituto Nazionale di Ottica, largo E. Fermi, 6, 50125 Firenze (Italy)bINAF Osservatorio Astrofisico di Arcetri, largo E. Fermi, 5, 50125 Firenze (Italy)

Abstract

Besides providing insights into the fundamental properties of materials, theknowledge of optical constants is required for a large variety of applications.In this work, for the first time to the best of our knowledge, an extremelywide spectral range from 181 to ∼54000 cm−1 has been explored for ethyleneglycol in the liquid phase, and optical constants in the whole range have beengiven. The approach we propose can also be applied to different fluids.

Keywords: Optical constants, Optical properties, Solar energy, Liquidphase, Ethylene glycol

Paper published on: Optical Materials Volume 37, November 2014,Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035

1. Introduction

The knowledge of the complex refractive index of materials is requiredin many fields and both for fundamental and applied research. The presentwork reports on the determination of optical constants (i.e. the real n andthe imaginary part k of the complex refractive index) of ethylene glycol in theliquid phase. Ethylene glycol is a fluid widely used in many industrial pro-cesses such as heating or cooling, chemical processes and thermal solar energysystems [1]. It is the main non-aqueous base fluid used for the preparation ofso-called nanofluids [1]-[12], as well as in mixed aqueous-non aqueous systems[13]-[15] for different thermal applications. Recently, it has been proposed as

1Corresponding author, email: [email protected]

Preprint submitted to Optical Materials February 19, 2015

2 EXPERIMENTAL SETUP

base fluid for novel direct solar absorbers [16] [17]. However, for a realisticassessment of the system performances when a direct interaction with light isrequired, both fundamental optical constants, including n, have to be char-acterized. The transmission spectrum and the k optical constant of liquidethylene glycol have been reported in the literature for the spectral range0.2-1.5 µm [18]. Some discrete infrared absorption peaks for glycol moleculesisolated in Ar or Xe matrices have been listed in [19] and for the liquid phasein [20]. Infrared transmittance spectra in limited spectral ranges have beenreported in [21] (300-1500 cm−1) and in [22] (∼450-3794 cm−1) but withoutgiving any optical constant. n has been measured by several Authors at thesingle wavelength of the sodium D line (0.5893 µm) [23]-[30] or at few dis-crete wavelengths in the range 0.22-0.58 µm ([31]). In this work, the opticalconstant k is obtained in an extremely wide wavelength range, from 0.185 µmto about 55 µm (∼ 54000-181 cm−1) from transmittance measurements. Theexperimental k spectrum is then used to calculate n in the whole investigatedrange by means of a Kramers-Kronig transform.

2. Experimental setup

The optical transmittance spectra of ethylene glycol (Aldrich ≥99%) havebeen measured over the considered spectral range by means of three differentexperimental setups: a ”Lambda 900” Perkin-Elmer dispersive spectropho-tometer for the range ∼54054-∼3333 cm−1 (0.185-3 µm), a Fourier trans-form ”Excalibur” Bio-Rad spectrometer with KBr optics for the wavenumberrange 5500-400 cm−1 (∼ 1.8-∼25 µm) and finally a Fourier transform ”Scimi-tar” Bio-Rad spectrometer with polyethylene windows and mylar beam split-ter for the range 420-181 cm−1 (∼24-∼55 µm). Except when differently spec-ified, the transmittance has been measured at different sample thicknessesusing a demountable variable-path cell composed by two optical windows andby a series of calibrated spacers. When the sample transmittance was toolow to have a detectable signal at the output, we assembled the cell withoutspacer as described in the following. We choose the cell window materialson the basis of their spectral transparency: CaF2 for the 0.185-3 µm range,KBr for ∼1.8-25 µm (available spacers from 50 to 350 µm) and polyethylenefor ∼24-55 µm (available spacers from 15 to 350 µm). Moreover, for the vis-ible range, where the ethylene glycol transmittance was very high, we usedalso quartz cuvettes with 5 and 10 mm path length to reduce the relativeuncertainty on k, as discussed in the following.


3 TRANSMITTANCE

3. Transmittance

The spectral transmittance of the liquid τ(ν), with ν wavenumber, canbe expressed as a simple function of the spectral absorption coefficient α(ν)as

τ(ν) = exp(−α(ν) · x) (1)

where x is the liquid thickness. However, the transmittance T we measureis the total transmittance of the layered system window-liquid-window, im-mersed in air. At each interface (air-window, window-liquid) the light ispartially reflected and partially transmitted. Let’s we consider, for simplic-ity, that the window has no absorption in the considered spectral range.Under the hypotheses of absence of scattering and negligible coherent effects[32], the total transmittance T can be expressed as a function of τ and ofreflectances R1 and R2 at the interfaces as follows [33]:

T = (1−R1)2(1−R2)

2τ

[1 +

2R1R2

1−R1R2

+ (R1 +R2)2τ 2 + S(τ 4)

](2)

in this expression, S(τ 4) is the sum of contributions with powers of τ higherthan four. The terms with powers of τ are generated by multiple passesthrough the liquid due to multiple reflections. If they are negligible comparedto other terms, the total transmittance T is proportional to the transmittanceτ of the liquid sample. The reflectances R1 (at the air-window interface) andR2 (at the window-liquid interface) are given by [34]:

R1 =(nw − 1)2

(nw + 1)2(3)

R2 =(nw − n)2 + k2

(nw + n)2 + k2(4)

with nw real part of the refractive index of the window and n, k opticalconstants of the liquid. The optical constant k(ν) is connected to α by [32]:

k =α(ν)

4πν(5)

Eqs. 3 and 4 assume, for the medium surrounding the cell, optical constantsnm = 1 and km = 0.


3 TRANSMITTANCE

If we acquire two transmittance spectra T1 and T2 at two different thick-nesses x1 and x2 of the liquid, α can be directly obtained from the expression:

α(ν) = − 1

x2 − x1

lnT2(ν)

T1(ν)= − 1

∆xln

T2(ν)

T1(ν)(6)

without requirement of a prior knowledge of optical properties of the windowand with no need of a fitting procedure for n, k, as it would be required usinga single transmittance measurement and Eqs. 2-5.

The possibility to obtain α from two independent trasmittance measure-ments relies on the experimental error on a single trasmittance and how muchthe considered trasmittance values differ each other. The smaller is α, themore T1 and T2 must be different, i.e. the larger the difference of thicknesses|x2−x1| = |∆x| should be. A simple analysis of the error propagation showsthat, in the hypothesis here fulfilled that the error on the thicknesses is neg-ligible respect to |∆x|, the obtained value of α is at least twice as large as itserror, if α itself is larger than 2

√2ϵ/|∆x|, where ϵ is the relative uncertainty

of transmittance. This condition is fulfilled simply when

|T1 − T2|T2

> 2√2ϵ (7)

In the determination of α we checked this condition and, in the spectralregions where it was not satisfied, we took as upper limit for α its standarderror.

In the range 0.185-3.00 µm we acquired the transmittance spectra at sev-eral cell thicknesses from 50 to 350 µm, and we kept as α to be used in furthercalculations the value obtained by averaging the result of Eq. 6 for several(x1, x2) couples. Moreover, as in the spectral range from about 0.3 µm to1.1 µm wavelength the trasmittance was very high and near to 100% alsowith the largest available spacer, to reduce as much as possible the spectralinterval of uncertainty of α discussed above, additional transmittance mea-surements were carried out, with a different cell model allowing much longerpath lengths of 5 and 10 mm. The spectral resolution is 5× 10−3 µm in therange 0.185-0.860 µm and varies from 7 × 10−3 to 2 × 10−2 µm at longerwavelengths. The relative uncertainty ϵ of transmittance values is 0.5%.

For the Mid-Infrared range (5500-400 cm−1 wavenumbers, ∼1.8-∼25 µmwavelength), the transmittance fell to zero in a large part of the spectrumeven with the thinnest spacer available for KBr windows (50 µm). Thus, we


3 TRANSMITTANCE

used the demountable cell without spacer. This allowed to measure the trans-mittance for a very thin layer of liquid. Similarly to the method describedin [33], we took several measurements at different tightening levels of thecell nuts (i.e. at different sample thicknesses). The spectral resolution is 4cm−1. The relative uncertainty on transmittance is between 0.05% and 0.3%depending on the spectral region. For the determination of α, Eq. 6 requiresonly the knowledge of the thickness difference ∆x among two measurements,which was inferred as follows: for each considered couple of Mid-IR measure-ments, ∆x was chosen to match, in the regions of spectral superposition ofthe Mid-IR and UV-Vis-NIR instruments, the value of α determined by theUV-Vis-NIR measurements.

In the Far Infrared (FIR) (420-181 cm−1, ∼24-∼55 µm) we used a slightlydifferent cell model, able to mount polyethylene windows and equipped withthinner spacers than the previous one. Transmittance measurements weretaken at different thicknesses, analogously to the UV-Vis-NIR case, and αwas analogously calculated. The minimum available thickness was 15 µm.

In the infrared, the spectra we acquired (Figure 1) are in good agreementwith published transmittance data ([22], available from ∼450 to 3794 cm−1

and [21] from 400 to 1500 cm−1). In the region 300-400 cm−1 our results showa better agreement with [20], which lists a weak transmittance minimum at360 cm−1, rather than [21], observing instead two weak minima at 430 and330 cm−1.

Once α(ν) was obtained as described for the whole investigated range, wecalculated the optical constant k(ν) from Eq. 5. The experimental values of kversus the wavenumbers, for the whole investigated range, are plotted in redcolor in Figure 2. The obtained k values in the range ∼6670-∼45000 cm−1

(1.40-0.22 µm) well agree with the data in [18], while some discrepancies canbe found around 50000 cm−1. Table 1 lists at the third column the values ofk at some discrete wavelengths.

Table 1: Optical constants at some discrete wavenum-bers. Bold fonts mark relative maxima and minima inthe n and k spectra. Maxima are identified by ∩ andminima by ∪.

Wavenumber n k Wavelengthcm−1 µm


3 TRANSMITTANCE

182.0±0.5 0.09± 0.02 ∼55342.0±0.5 1.47± 0.01 ∪ 0.053±0.007 ∼29418±2 1.48± 0.01 0.042±0.005 ∪ ∼24501±2 1.48±0.01 ∩ 0.07±0.01 ∼20519±2 1.46±0.01 0.09±0.01 ∩ ∼19545±2 1.45±0.01 0.07±0.01 ∼18599±2 1.44±0.01 0.073±0.006 ∩ ∼17741±2 1.42±0.01 ∪ 0.041±0.006 ∼13832±2 1.45±0.01 0.018±0.003 ∪ ∼12854±2 1.48±0.01 ∩ 0.048±0.007 ∼11.7865±2 1.45±0.01 0.08±0.01 ∩ ∼11.6872±2 1.45±0.01 0.07±0.01 ∪ ∼11.5883±2 1.41±0.01 0.11±0.02 ∩ ∼11.3897±2 1.38±0.01 0.038±0.006 ∼11.1952±2 1.44±0.01 0.011±0.002 ∪ ∼10.51025±2 1.54±0.01 0.08±0.01 ∼9.71043±2 1.44±0.02 0.18±0.03 ∩ ∼9.61054±2 1.38±0.02 ∪ 0.13±0.02 ∼9.51065±2 1.40±0.01 0.09±0.01 ∪ ∼9.41076±2 1.44±0.02 ∩ 0.12±0.02 ∼9.31086±2 1.36±0.02 0.18±0.03 ∩ ∼9.21097±2 1.28±0.02 ∪ 0.09±0.01 ∼9.11137±2 1.378±0.004 0.010±0.002 ∪ ∼8.81192±2 1.407±0.004 ∩ 0.022±0.003 ∼8.41203±2 1.404±0.004 0.026±0.004 ∩ ∼8.31232±2 1.404±0.004 0.018±0.003 ∪ ∼8.11254±2 1.407±0.004 0.021±0.003 ∩ ∼7.91283±2 1.411±0.004 0.017±0.003 ∪ ∼7.81308±2 1.417±0.004 ∩ 0.023±0.004 ∼7.61330±2 1.413±0.005 0.028±0.004 ∩ ∼7.51352±2 1.412±0.005 0.026±0.004 ∪ ∼7.41370±2 1.411±0.005 0.031±0.005 ∩ ∼7.31381±2 1.410±0.005 0.030±0.005 ∪ ∼7.21406±2 1.405±0.005 0.034±0.005 ∩ ∼7.11446±2 1.398±0.005 0.028±0.004 ∪ ∼6.91457±2 1.395±0.005 0.031±0.005 ∩ ∼6.81475±2 1.385±0.004 ∪ 0.019±0.003 ∼6.7


4 REFRACTIVE INDEX

1595±2 1.407±0.002 (3.5±0.6)·10−3 ∪ ∼6.31653±2 1.409±0.003 0.005±0.002 ∩ ∼6.02271±2 1.425±0.002 (1.5±0.3)·10−3 ∼4.42859±2 1.448±0.004 ∩ 0.021±0.003 ∼3.52878±2 1.441±0.005 0.028±0.004 ∩ ∼3.472903±2 1.438±0.004 0.021±0.003 ∪ ∼3.442943±2 1.429±0.005 0.032±0.005 ∩ ∼3.42968±2 1.418±0.004 ∩ 0.018±0.003 ∼3.373008±2 1.431±0.002 0.008±0.001 ∪ ∼3.323212±2 1.457±0.007 ∩ 0.041±0.006 ∼3.113364±2 1.41±0.01 0.08±0.01 ∩ ∼2.973477±2 1.366±0.007 ∪ 0.040±0.006 ∼2.873854±2 1.404±0.002 (5.7±0.2)·10−4 ∪ ∼2.594007±2 1.408±0.002 (12.4±0.4)·10−4 ∩ ∼2.494371±2 1.412±0.002 (8.3±0.3)·10−4 ∩ ∼2.295000±2 1.416±0.002 (1.57±0.08)·10−4 ∼2.005378±4 1.417±0.002 (6.3±0.5)·10−5 ∪ ∼1.865705±5 1.418±0.002 (1.12±0.06)·10−4 ∼1.756035±5 1.419±0.002 (9.0±0.5)·10−5 ∼1.666361±4 1.420±0.002 (1.50±0.06)·10−4 ∩ ∼1.576689±4 1.420±0.002 (1.26±0.04)·10−4 ∩ ∼1.497016±4 1.420±0.002 (7.0±0.3)·10−5 ∼1.4214000±50 1.428±0.002 <6.4·10−8 ∼0.7121000±50 1.438±0.002 <4.3·10−8 ∼0.4826000±170 1.447±0.002 <3.5·10−8 ∼0.3830000±230 1.457±0.002 <1.4·10−7 ∼0.3334000±290 1.468±0.002 <6.4·10−7 ∼0.2938000±360 1.482±0.002 (9±4)·10−7 ∼0.2642000±440 1.498±0.002 (1.5±0.4)·10−6 ∼0.2446000±530 1.517±0.002 (3.4±0.4)·10−6 ∼0.2250000±630 1.540±0.002 (9.4±0.3)·10−5 ∼0.2054000±730 1.567±0.002 (4.9±0.1) · 10−4 ∩ ∼0.19

4. Refractive index


4 REFRACTIVE INDEX

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0

20

40

60

80

0

20

40

60

80

100

% T

rans

mitt

ance

Wavenumber (103 cm-1) %

Tra

nsm

ittan

ce

Figure 1: Acquired transmittance spectra in the range 181-1500 cm−1. The spectra re-spectively shown as red circles and black line have been acquired at two different samplethicknesses. For a better visual comparison with literature data, they are reported in thepicture with shifted ordinates and intentionally left with a small vertical gap.


4 REFRACTIVE INDEX

0.5 1.0 1.5 2.00.00

0.05

0.10

0.15

0.20

0.25

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

k

Wavenumber (103 cm-1)

k

n

n

2.0 2.5 3.0 3.5 4.0 4.5 5.00.00

0.05

0.10

0.15

0.20

0.25

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

k


k

n

n

5 10 15 20 25 30 35 40 45 50

0.0

0.1

0.2

0.3

0.4

0.5

0.6

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

k x

10-3


k

n

n

Figure 2: The optical constants n and k in the whole investigated range. The onlyspectral data available in the literature for optical constants [18] [31] are also plotted forcomparison, showing a fair agreement (blue circles in the lower picture). The infrared kbands are due to molecular vibration modes [20], [21].


4 REFRACTIVE INDEX

On the basis of the experimental value of k(ν) we calculated the corre-sponding values of the refractive index n(ν). Being n(ν) and k(ν) respec-tively the real and complex part of the complex refractive index m(ν) =n(ν) + ik(ν), they are related each other through the Kramers-Kronig rela-tionship:

n(ν) = n(∞) +2

πP

∫ ∞

0

ν ′k(ν ′)

ν ′2 − ν2dν ′ (8)

where P identifies the Cauchy’s principal part of the integral and n(∞) isthe value of the refractive index at high wavenumbers. In the usual practice,the constant value n(∞) is not known. Generally it is indirectly obtainedimposing, for a given wavenumber, that n is equal to a value already known.The integral in Eq. 8 has been numerically computed using the Maclaurin’sformula [36]. The uncertainty on n(ν) has been calculated propagating theexperimental uncertainty on k(ν).

The major technical limitation of the method based on the Kramers-Kronig relationship is that the integral in Eq. 8 should be calculated fromzero to infinity, or in other words the value of n at a given wavenumber couldbe computed only if k is know for all wavenumbers. Different approacheshave been discussed in the literature to overcome this issue [37]-[39]. Al-though this requirement is not experimentally possible, nevertheless it doesnot means that n(ν) cannot be computed with a satisfactory accuracy if kis know in an enough wide interval of wavenumbers around ν. Problems canoccur at the edges of the spectral interval for which a measure of k has beenpossible. In our case, the value of n(ν) for ν slightly larger than 181 cm−1 ora little less than 54000 cm−1, computed by means of Eq. 8, could be affectedby truncation errors depending on the values of k respectively below 181cm−1 and above 54000 cm−1. For the present work, as it has been motivatedby solar energy applications of ethylene glycol, the spectral range of maininterest for us is that of sunlight (0.3-2.5 µm wavelength, ∼ 34000-∼ 4000cm−1). Towards long wavelengths (low wavenumbers), the range of our mea-surements is consistently larger than the spectral interval of interest, thus wecould reasonably expect that truncations errors on this side will have a smallor negligible effect on n(ν) in this region[37]. In fact, at a given wavenumberν, the error ∆n due to the truncation of the integral in Eq. 8 for ν ′ < νc canbe estimated evaluating the integral from 0 to νc. For νc ≪ ν, it is simple toshow that

∆n ∼ 2

πkννcν2

(9)


4 REFRACTIVE INDEX

where k and ν are respectively the mean values of k and ν over the interval[0, νc]. Being νc = 181 cm−1, a conservative case is that ν ∼ 90 cm−1 andk ∼ 10−1, it turns out that ∆n ∼ 0.03 for ν = 200 cm−1, ∼ 0.004 at 500cm−1 and ∼ 0.001 at 1000 cm−1. For ν = 200 cm−1 the condition νc ≪ νused in Eq. 8 to approximate the denominator to ν2 is not fulfilled, so in thiscase the evaluation of ∆n is probably underestimated. Therefore we expectthat, for ν larger than 300/400 cm−1, ∆n is comparable or smaller than theuncertainty of n due to the measurement errors. At short wavelengths (highwavenumbers) we have a clear effect of truncation because the computed val-ues of n in the range 20000-45000 cm−1 result to be independent on ν whilefrom literature we know that in the same range n increases with wavenum-ber [31]. This clearly suggests the presence of a big spectral feature above54000 cm−1. The behavior of n is compatible with the increasing phase ofthe refractive index before a region of anomalous dispersion, correspondingto a peak of k. We explored the space of lorentzian peak solutions by fittingthe literature value of n in the range 20000-45000 cm−1. The best solutionconsists of a peak (A) around ∼ 100000 cm−1, and all compatible solutionsreproduce the values of n within an error of 2×10−3, while providing negligi-ble values of k in the same range. The increasing of the experimental k curvefrom ∼ 40000 cm−1 cannot be explained by the peak A, but it is reproducedby a much weaker peak (B) at ∼ 55000 cm−1, that in turn gives a negligiblecontribution to the values of n in the range 20000-45000 cm−1. Thus, peaksA and B together are able to reproduce in a satisfactory way both n and kin the range 20000-54000 cm−1. Such extrapolation of the k spectrum hasbeen used as input of Kramers-Kronig transform correcting the truncationerror at high wavenumbers, reproducing the correct behavior of n and allow-ing the correct determination of the zero point n(∞). More precisely, it wasobtained imposing n = 1.432 at ν = 17241.4 cm−1, as reported in [31], andconsidering the uncertainty on its value produced by the uncertainty on thek extension (i.e. ∆n = 2 · 10−3).

Figure 2 shows the values of n as a function of the wavenumber (blackline). The n values at some discrete wavelengths are listed in Table 1 (secondcolumn).

For operating purposes, e.g. the use of n in optical design and ray trac-ing software packages, it can be useful to give the obtained n in terms of aphenomenological expression. Thus we fitted n as a function of the wave-length λ with a four-parameter Sellemeier equation [40], using a least-squares


REFERENCES

algorithm:

n2 = 1 +0.01778 · λ2

λ2 − 9.02+

1.01887 · λ2

λ2 − 0.01028(10)

This equation is valid for λ expressed in µm and lying in the range 0.185-2.8µm.

It should be noticed that Sellmeier-type expressions are intrinsically lim-ited to spectral regions with no absorption. In fact, in the vicinity of absorp-tion peaks (corresponding to the zeros of denominators), Sellmeier equationsgive the unphysical result of diverging n values. If we relax the physical mean-ing of the equation used for fitting n(λ) and we accept to obtain a purelyphenomenological expression useful for analytically writing n in limited spec-tral ranges, it is possible to find, for instance, the following expression, validfor λ ∈ (3.4, 6.8) µm and reproducing n within its uncertainty:

n2 = 1 +0.6 · λ2

λ2 − 4.05+

12.55 · λ2

λ2 + 153.3− 60.1 · λ2

λ2 + 1008.2(11)

5. Conclusions

In conclusion, we have obtained the optical constant k(ν) of ethyleneglycol from transmittance measurements over a range as wide as from 181to ∼54000 cm−1. The Kramers-Kronig theory, in combination with an ad-hoc technique of extrapolation to avoid truncation errors at the edges of theexperimental spectrum, has been used to calculate the real part n(ν) of therefractive index. Limitations and tricks of this approach are discussed. TheSellmeier equation for n in the wavelength range 0.185-2.8 µm is given, aswell as a purely phenomenological polynomial expression for fitting n in therange 3.4-6.8 µm.

Acknowledgements

Authors are grateful to S. Barison and C. Pagura (CNR-IENI, Italy) forkindly supplying ethylene glycol.

References

[1] F.S. Javadi, R. Saidur, M. Kamalisarvestani, ”Investigating performanceimprovement of solar collectors by using nanofluids”, Renew. Sust. En-ergy Reviews, Volume 28 (2013), 232-245


REFERENCES REFERENCES

[2] J. A. Eastman, S. U. S. Choi, S. Li, W. Yu, L. J. Thompson, ”Anoma-lously increased effective thermal conductivities of ethylene glycol-basednanofluids containing copper nanoparticles”, Applied Physics Letters 78,718 (2001); doi: 10.1063/1.1341218

[3] M. P. Beck, T. Sun, A. S. Teja, ”The thermal conductivity of aluminananoparticles dispersed in ethylene glycol”, Fluid Phase Equilibria 260(2007) 275278

[4] M. Chopkar, S. Kumar, D.R. Bhandari, P.K. Das, I. Manna, ”Develop-ment and characterization of Al2Cu and Ag2Al nanoparticle dispersedwater and ethylene glycol based nanofluid”, Materials Science and En-gineering B 139 (2007) 141148

[5] Dae-Hwang Yoo, K.S. Hong, Ho-Soon Yang, ”Study of thermal conduc-tivity of nanofluids for the application of heat transfer fluids”, Ther-mochimica Acta 455 (2007) 6669

[6] J. Garg, B. Poudel, M. Chiesa, J. B. Gordon, J. J. Ma, J. B. Wang, Z.F. Ren, Y. T. Kang, H. Ohtani, J. Nanda, G. H. McKinley, G. Chen,”Enhanced thermal conductivity and viscosity of copper nanoparticlesin ethylene glycol nanofluid”, Journal of Applied Physics 103, 074301(2008); doi: 10.1063/1.2902483

[7] P. Sharma, I-H. Baek, T. Cho, S. Park, K. B. Lee, ”Enhancement ofthermal conductivity of ethylene glycol based silver nanofluids”, PowderTechnology 208 (2011) 719

[8] W. Yu, H. Xie, X. Wang, X. Wang, ”Significant thermal conductivityenhancement for nanofluids containing graphene nanosheets”, PhysicsLetters A 375 (2011) 13231328

[9] W. Yu, H. Xie, L. Chen, Y. Li, ”Investigation of thermal conductivityand viscosity of ethylene glycol based ZnO nanofluid”, ThermochimicaActa 491 (2009) 9296

[10] H. Chen, Y. Ding, Y. He, C. Tan, ”Rheological behaviour of ethyleneglycol based titania nanofluids”, Chemical Physics Letters 444 (2007)333337



[11] M. J. Pastoriza-Gallego, L. Lugo, J. L. Legido, M. M. Pineiro, ”Thermalconductivity and viscosity measurements of ethylene glycol-based Al2O3nanofluids”, Nanoscale Research Letters 6 (2011) 221

[12] N. Jha, S. Ramaprabhu, ”Thermal conductivity studies of metal dis-persed multiwalled carbon nanotubes in water and ethylene glycolbased nanofluids”Journal of Applied Physics 106 , 084317 (2009); doi:10.1063/1.3240307

[13] P. K. Namburu, D. P. Kulkarni, D. Misra, D. K. Das, ”Viscosity of cop-per oxide nanoparticles dispersed in ethylene glycol and water mixture”,Experimental Thermal and Fluid Science 32 (2007) 397402

[14] D. P. Kulkarni , P K. Namburu , H. E. Bargar, D. K. Das, ”ConvectiveHeat Transfer and Fluid Dynamic Characteristics of SiO2 Ethylene Gly-col/Water Nanofluid”, Heat Transfer Engineering, 29 (2008) 1027-1035,DOI: 10.1080/01457630802243055

[15] M. P. Beck, Y. Yuan, P. Warrier, A. S. Teja, ”The thermal conduc-tivity of alumina nanofluids in water, ethylene glycol, and ethyleneglycol + water mixtures”, J. Nanopart. Res. 12 (2010)14691477 DOI:10.1007/s11051-009-9716-9

[16] E. Sani, L. Mercatelli, S. Barison, C. Pagura, F. Agresti, L. Colla, P.Sansoni, ”Potential of carbon nanohorn-based suspensions for solar ther-mal collectors”, Solar Energy Mat. Solar Cells 95 (2011) 29943000

[17] A. Moradi, E. Sani, M. Simonetti, F. Francini, E. Chiavazzo, P. Asinari,”Carbon-nanohorn based nanofluids for a direct absorption solar col-lector for civil application”, Journal Nanoscience Nanotechn., in press(2014)

[18] T. P. Otanicar, P. E. Phelan, J. S. Golden, ”Optical properties of liq-uids for direct absorption solar thermal energy systems”, Solar Energy,Volume 83 (2009) 969977

[19] H. Frei, T.-K. Ha, R. Meyer, H.H. Gunthard, ”Ethylene glycol: infraredspectra, ab initio calculations, vibrational analysis and conformations of5-matrix isolated isotopic modifications”, Chemical Physjcs 25 (1977)271-298



[20] W. Sawodny, K. Niedenzu, J. W. Dawson, ”The vibrational spectrumof ethylene glycol”, Spectrochimica Acta, 1967, Vol. 28A, pp. 799-806

[21] P. Buckley, P. A. Giguere, ”Infrared studies on rotational isomerism. I.Ethylene glycol”, Canadian Journal of Chemistry 45 (1967) 397-407

[22] Smith, A.L., The Coblentz Society Desk Book of Infrared Spec-tra in Carver, C.D., editor, The Coblentz Society Desk Book ofInfrared Spectra, Second Edition, The Coblentz Society:Kirkwood,MO, 1982, pp 1-24. Spectrum is available online at the NIST web-site: http://webbook.nist.gov/cgi/cbook.cgi?ID=C107211&Type=IR-SPEC &

[23] A. M. Awwad,A. H. Al-Dujaili, H. E. Salman, ”Relative Permittivities,Densities, and Refractive Indices of the Binary Mixtures of Sulfolanewith Ethylene Glycol, Diethylene Glycol, and Poly(ethylene glycol) at303.15 K”, J. Chem. Eng. Data 2002, 47, 421-424

[24] A. Marchetti, C. Preti, M. Tagliazucchi, L. Tassi, G. Tosi, ”The N,N-Dimethylformamide + Ethane-I ,2-diol Solvent System. Dielectric Con-stant, Refractive Index, and Related Properties at Various Tempera-tures”, J. Chem. Eng. Data Vol. 36, No. 4, 1991, p. 365

[25] T. M. Aminabhavi, B. Gopalakrishna, ”Density, Viscosity, Refrac-tive Index, and Speed of Sound in Aqueous Mixtures of NJV-Dimethylformamide, Dimethyl Sulfoxide, NJV-Dimethylacetamide,Acetonitrile, Ethylene Glycol, Diethylene Glycol, 1,4-Dioxane, Tetrahy-drofuran, 2-Methoxyethanol, and 2-Ethoxyethanol at 298.15 K”, J.Chem. Eng. Data 1995, 40, 856-861

[26] L. Albuquerque, C. Ventura, R. Goncalves, ”Refractive Indices, Densi-ties, and Excess Properties for Binary Mixtures Containing Methanol,Ethanol, 1,2-Ethanediol, and 2-Methoxyethanol”, J. Chem. Eng. Data1996, 41, 685-688

[27] T. H. Baker, G. T. Fisher, J. A. Roth, ”Vapor Liquid Equilibrium andRefractive Indices of the Methanol-Ethylene Glycol System”, J. Chem.Eng. Data, Vol. 9, No. 1 (1964) 11-12



[28] E. T. Foggi, A. N. Hixson, A. R. Thompson, ”Densities and RefractiveIndexes for Ethylene Glycol-Water Solutions”, Analytical Chemistry,Vol. 27 (1955) 1609

[29] N. G. Tsierkezos, I. E. Molinou, ”Thermodynamic Properties of Water+ Ethylene Glycol at 283.15, 293.15, 303.15, and 313.15 K”, J. Chem.Eng. Data 43 (1998) 989-993

[30] H. El-Kashef, ”The necessary requirements imposed on polar dielectriclaser dye solvents”, Physica B 279 (2000) 295-301

[31] Wohlfarth, C., Wohlfarth, B., 1996. Optical Constants. Springer-Verlag,New York.

[32] C. F. Bohren, D. R. Huffman, 2004 Absorption and Scattering of Lightby Small Particles., Wiley

[33] Y. Kameya, K. Hanamura, ”Enhancement of solar radiation absorptionusing nanoparticle suspension” Solar Energy 85 (2011) 299307

[34] M. F. Modest, ”Radiative heat transfer”, Academic Press, 2003

[35] S.E. Stein, ”Evaluated Infrared Reference Spec-tra”, online paper available on the NIST website:http://webbook.nist.gov/chemistry/coblentz/

[36] Ohta K. Ishida H., ”Comparison Among Several Numerical IntegrationMethods for Kramers-Kronig Transformation”, Applied Spectroscopy,Vol 42 (1988), 952-957.

[37] J. P. Hawranek, R. N. Jones, ”The control of errors in i.r.spectrophotometry-V. Assessment of errors in the evaluation of opticalconstants by transmission measurements on thin films”, SpectrochimicaActa, Vol. 32A (1976) 99-109

[38] D. M. Roessler, ”Kramers - Kronig analysis of reflectance data: III.Approximations, with reference to sodium iodide”, Br. J. Appl. Phys.17 (1966) 1313 doi:10.1088/0508-3443/17/10/309

[39] K. F. Palmer, M. Z. Williams, B. A. Budde, ”Multiply subtractiveKramersKronig analysis of optical data”, Applied Optics, Vol. 37, (1998)2660-2673



[40] W. Sellmeier, ”Zur Erklarung der abnormen Farbenfolge im Spectrumeiniger Substanzen”, Ann. Phys. Chem. 143, 271 (1871)


Date post:	27-Mar-2018
Category:	Documents
Upload:	phungdung
View:	213 times
Download:	0 times

Optical constants of ethylene glycol over an extremely ... · PDF fileOptical constants of...

Documents