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Study of temperature and concentration dependence of refractive index of liquids using a novel technique


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A simple and reliable method of measuring the refractive index of liquids is reported in the present paper. The technique was employed to study the temperature dependence of refractive index of water (at sodium D-line 589nm). By measuring the refractive index of water at different temperatures, the temperature coefficient of refractive index (dn/dT) was determined. In addition to this, refractive index of different solutions as a function of the concentration was studied. The results were compared with the results obtained from commercial refractometers and it was found that this technique is quite reliable and can be safely used in the study of the optical properties of any transparent liquids
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VOL.II, No.1, FEBRUARYR, 2006.
Subedi, D.P., Adhikari, D.R., Joshi, U.M., Poudel, H. N., Niraula, B.
Department of Natural Sciences,
Kathmandu University, Dhulikhel, Kavre, P.O. Box: 6250, Kathmandu, Nepal.
Corresponding Author E-Mail:
A simple and reliable method of measuring the refractive index of liquids is reported in
the present paper. The technique was employed to study the temperature dependence of
refractive index of water (at sodium D-line 589nm). By measuring the refractive index of
water at different temperatures, the temperature coefficient of refractive index (dn/dT)
was determined. In addition to this, refractive index of different solutions as a function of
the concentration was studied. The results were compared with the results obtained from
commercial refractometers and it was found that this technique is quite reliable and can
be safely used in the study of the optical properties of any transparent liquids
Refractive index is one of the most important optical properties of a medium. It plays
vital role in many areas of material science with special reference to thin film technology
and fiber optics. Similarly, measurement of refractive index is widely used in analytical
chemistry to determine the concentration of solutions. Recent studies [Schwartz 1999,
Olesberg 2000, Shlichta 1986] provide more detailed discussion on the concentration
mapping by the measurement of refractive index of liquids. Temperature coefficient of
refractive index can also be used to calculate thermal expansion coefficient [Miller 1975].
Several techniques are reported in literature for the measurement of concentration and
temperature dependence of refractive index of liquids [McPherson 1999, Garcia 1999,
Otalora 1999, Miyashita 1994]. The present paper reports a relatively simple and effective
technique, which can be used to measure the refractive index of the liquid at different
The absolute refractive index of a medium is the ratio of the speed of electromagnetic
radiation in free space to the speed of the radiation in that medium. The relative refractive
index is the ratio of the speed of light in one medium to that in the adjacent medium.
Refraction occurs with all types of waves but is most familiar with light waves. The
refractive index of a medium differs with frequency. This effect, known as dispersion,
lets a prism divide white light into its constituent spectral colors. For a given color, the
refractive index of a medium depends on the density of the medium, which on the other
hand is a function of temperature. By measuring the refractive indices at different
temperatures, the temperature coefficient of refractive index (dn/dT) can be determined.
A convenient formula for refractive index, n, can be obtained in the minimum deviation
case when a ray of light suffers deviation while passing through a prism. The deviation
produced by the prism depends on the angle of incidence. For a certain value of the angle
of incidence, the angle of deviation is minimum. If Dm denotes the angle of minimum
VOL.II, No.1, FEBRUARYR, 2006.
deviation for a given prism of refractive angle A, then the refractive index of the material
of the prism n is given by,
................ (1)
Equation (1) has been employed to calculate the refractive index of the liquids.
Experimental arrangement used in our study is depicted in Fig. 1. Specially constructed
hollow prism was used to measure the refractive index of liquids with the help of an
optical spectrometer. A monochromatic source of light (sodium lamp) was used and a
collimated beam was allowed to fall on one reflecting face of the liquid prism and the
angle of minimum deviation was determined for yellow light (at sodium Dline 589 nm).
Mean of two values were taken for each angle of minimum deviation. For the
measurement of refractive index at different temperature, the liquid was heated up to
80°C and poured into the hollow prism and the angle of minimum deviation was
measured at different temperatures of the cooling liquid. A thermometer was inserted in
the liquid avoiding the path of light being observed.
To study the variation of refractive index of salt solutions as a function of concentration,
an electronic balance weighed salts and solutions of required concentrations were
prepared by dissolving the salts in 100 ml of water. Thus prepared solutions were filtered
before pouring into the hollow prism. The hollow prism was rinsed carefully after every
measurement. Solutions of lower concentrations (20%, 10%, 5%, 2.5% and 1.25%) were
made by diluting the solutions with equal volume of water.
Effect of Temperature on Refractive Index of Water
The refractive index of water as a function of temperature is depicted in Fig 2. The result
shows a linear dependence of refractive index of water on temperature in the range 30°C-
70°C. By applying data analysis program the experimental data were subjected to curve
fitting and the temperature coefficient of refractive index of water was found to be equal
to 1.853 × 104/C. For highly accurate measurements, the optical constants of the glass
container should also be taken in account because the light will pass through both the
solution and the container. According to the literature [Lukin 1993], the temperature
coefficient of refractive index of glass is of the order of 104/C. It is evident that very
small error can occur if the temperature dependence of the refractive index of glass is not
taken into account while measuring the temperature coefficient of refractive index of
Effect of Concentration
VOL.II, No.1, FEBRUARYR, 2006.
Fig.1 Experimental set-up for the measurement of refractive index by an optical
Refractive index of common salt solution as a function of concentration is depicted in
Fig. 3. For 20% solution, refractive index is as high as 1.358, which reduces to 1.331
when the solution is diluted to a concentration of 1.25%. With the decrease in
concentration, the density of the solution also decreases resulting a decrease in refractive
index. The results showed that the refractive index of the solution of concentration less
than 2.5% measures nearly the same as that of the pure water. The result indicated that the
effect of concentration on refractive index is dominant up to the concentration of 5%.
After that there is weak dependence of concentration of refractive index. Fig. 4 shows a
similar result for sugar solution. As the solubility of sugar is high, the measurements were
performed up to 40% concentration of the solution. The refractive index of the sugar
solution was found to be 1.387 for 40% solution. The value reduces to 1.332 when the
concentration was reduced to 2.5%. In contrast to the result of salt solution, the effect of
concentration is strong up to 20% concentration of the sugar solution. However, after this
value the dependence becomes weak.
Fig 5, 6 and 7 depict the dependence of refractive index of propanol_1, sucrose and
potassium chloride solution on their concentration respectively. A comparison is made
between the results obtained from our measurement and the values mentioned in literature
[]. It is evident that our results are in agreement with the literature
value so far as the nature of variation is concerned. Repeating the experiment checked the
value of refractive index of propanol_1 solution of 20% concentration with higher
deviation. Similarly, refractive index of sucrose solution of concentration 10% was
measured twice (indicated by error bar). In the same way for potassium chloride, the
experiment corresponding to 10% and 20% concentrations were repeated.
VOL.II, No.1, FEBRUARYR, 2006.
30 40 50 60 70 80
dn/dT = -1.853 x 10-4
Temperature (C)
Refractive index (n)
Fig 2 Temperature dependence of refractive index of water.
0 5 10 15 20
Common Salt Solution
Refractive index (n)
Concentration (%)
Fig. 3 Refractive index of sodium chloride solution as a function
f i
VOL.II, No.1, FEBRUARYR, 2006.
0 10203040
Refractive index (n)
Concentration (%)
Sugar solution
Fig. 4 Refractive index of sugar solution as a function o
its concentration expressed in percentage.
0 5 10 15 20 25 30 35 40 45
Current Technique (24C)
Literature value (20 C)
Refractive Index (n)
Concentration (%)
Fig. 5 Refractive index of Propanol_1 as a function of
concentration measured by the present technique and obtained
from literature.
VOL.II, No.1, FEBRUARYR, 2006.
Fig. 6 Refractive index of sucrose as a function of
concentration measured by the present technique and
obtained from literature.
Fig. 7 Refractive index of potassium chloride as a function of
Concentration measured by the present technique and obtained from
We have been able to design a hollow prism suitable for the measurement of refractive
index of transparent liquids. Experimental results showed that this technique could be
safely employed to study the dependence of refractive index of solutions on their
concentration as well as on the temperature. The temperature coefficient of refractive
index of water (in the range of 30-70°C) was determined and it was found that the value
is in agreement with the results obtained from other methods of measurement. A linear
dependence of refractive index of some solutions (common salt, sugar, propanol_1,
sucrose, potassium chloride) with their concentration was observed.
VOL.II, No.1, FEBRUARYR, 2006.
This work was supported by University Grant Commission (UGC) of Nepal under the
mini research project grant.
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protein crystal growth. Analytical Chemistry, 72, 4985.
3. Shlichta, P. J., 1986. Feasibility of mapping solution properties during the growth
of protein crystals. J. Crystal Growth, 76, 656.
4. Miller, A., Hussmann, E. K., McLaughlin, W. L., 1975. Interferometer for
measuring fast changes of refractive index and temperature in transparent liquids
Review of Scientific instruments, 46, 1635.
5. McPherson, A., Malkin, A. J., Kuznetsov, Y. G., Koszelak, S., Wells, M., Jenkins,
G., Howard, J., Lawson, G., 1999. Effects of microgravity on protein
crystallization: evidence for concentration gradients around growing crystals , J.
Crystal Growth, 196, 572.
6. Garcia-Ruiz, J. M., Novella, M. L., Otalora, F., 1999. Supersaturation patterns in
counter-diffusion crystallisation methods followed by Mach-Zehnder
interferometry, Crystal Growth, 196, 703-710.
7. Otalora F, Novella ML, Rondon D, Garcia-Ruiz JM, 1999. Growth of lysozyme
crystals under micro gravity conditions in the LMS (STS-78) mission Journal of
Crystal Growth, 196, 649.
8. Miyashita, S., Komatsu, H., Suzuki, Y., Nakada, T., 1994. Observation of the
concentration distribution around a growing lysozyme crystal, J. Crystal Growth,
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9. Lukin, O.V., Magunov, A. N., 1993. Temperature measurement of glass and
quartz plates by laser interferometry, Opt. Spectrosc., 74, 630.
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... At shock pressures of 13-25 GPa, LN 2 remained optically transparent, and shock response of refractive index (n LN 2 1 ) increased up to 27% of n LN 2 0 with increasing density, in this pressure range increasing shock temperature showed no major influence on n LN 2 1 . The data of n LN 2 1 refutes the prediction of dissociation > 17 GPa and 4000 K [51], also the relatively stable value of n LN 2 1 argues the statement made by groups reporting the negative influence on index of liquid with increasing temperature [58][59][60]62]. As a conclusion, while it is the intent of shock study to adjudge the static experiments [28,31,32] performed to measure the refractive index, it is noticed that below 29 GPa, a considerable change in the density was effective to drive the refractive index regardless of N 2 's initial phase. ...
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We report the equation of state and optical properties of shock-compressed liquid nitrogen (LN2) by using a two-stage light-gas gun at pressure up to 29 GPa. Laser velocimetry measurements were used to investigate the transparency and refractive index of shocked LN2 as a function of density. As the density increased with increasing pressure and temperature (13–25 GPa), the refractive index increased up to 27% of pre-shot index of LN2. Evidently, such extreme conditions had no major influence on molecules, and no such dissociation was observed up to 25 GPa. The polarizability slightly decreased and thus supported the existence of intact diatomic molecular nitrogen. At 29 GPa, shocked LN2 dissociated, showing that it probably changed to a highly reflecting fluid. Altogether, these experiments showed how the density affects the refractive index without any change in chemical bonding and allocates the condition at which the temperature-driven dissociation takes place.
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... In the frame of linear optics, this can be achieved by measuring the refractive index of the particles. For example, the refractive index is used to detect variations in the chemical or structural properties of living cells [3,4] or to determine the mixture fraction or temperature of droplets in chemical engineering applications [5][6][7]. ...
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Complete dissolution of the active pharmaceutical ingredient (API) is critical in the manufacturing of liquid-filled soft-gelatin capsules (SGC). Attenuated total reflectance UV spectroscopy (ATR-UV) and Raman spectroscopy have been investigated for in-line monitoring of API dissolution during manufacturing of an SGC product. Calibration models have been developed with both techniques for in-line determination of API potency. Performance of both techniques was evaluated and compared. The ATR-UV methodology was found to be able to monitor the dissolution process and determine the endpoint, but was sensitive to temperature variations. The Raman technique was also capable of effectively monitoring the process and was more robust to the temperature variation and process perturbations by using an excipient peak for internal correction. Different data preprocessing methodologies were explored in an attempt to improve method performance.
Optimal storage of carbon dioxide (CO2) in aquifers requires dissolution in the aqueous phase. Nevertheless, transfer of CO2 from the gas phase to the aqueous phase would be slow if it were only driven by diffusion. Dissolution of CO2 in water forms a mixture that is denser than the original water or brine. This causes a local density increase, which induces natural convection currents accelerating the rate of CO2 dissolution. The same mechanism also applies to carbon dioxide enhanced oil recovery. This study compares numerical models with a set of high pressure visual experiments, based on the Schlieren technique, in which we observe the effect of gravity-induced fingers when sub- and super-critical CO2 at in situ pressures and temperatures is brought above the liquid, i.e., water, brine or oil. A short but comprehensive description of the Schlieren set-up and the transparent pressure cell is presented. The Schlieren set-up is capable of visualizing instabilities in natural convection flows; a drawback is that it can only be practically applied in bulk flow, i.e., in the absence of a porous medium. All the same many features that occur in a porous medium also occur in bulk, e.g., unstable gravity fingering. The experiments show that natural convection currents are weakest in highly concentrated brine and strongest in oil, due to the higher and lower density contrasts respectively. Therefore, the set-up can screen aqueous salt solutions or oil for the relative importance of natural convection flows. The Schlieren pattern consists of a dark region near the equator and a lighter region below it. The dark region indicates a region where the refractive index increases downward, either due to the presence of a gas liquid interface, or due to the thin diffusion layer, which also appears in numerical simulations. The experiments demonstrate the initiation and development of the gravity induced fingers. The experimental results are compared to numerical results. It is shown that natural convection effects are stronger in cases of high density differences. However, due to numerical limitations, the simulations are characterized by much larger fingers.
This book gives background information why shale formations in the world are important both for storage capacity and enhanced gas recovery (EGR). Part of this book investigates the sequestration capacity in geological formations and the mechanisms for the enhanced storage rate of CO2 in an underlying saline aquifer. The growing concern about global warming has increased interest in geological storage of carbon dioxide (CO2). The main mechanism of the enhancement, viz., the occurrence of gravity fingers, which are the vehicles of enhanced transport in saline aquifers, can be visualized using the Schlieren technique. In addition high pressure experiments confirmed that the storage rate is indeed enhanced in porous media. The book is appropriate for graduate students, researchers and advanced professionals in petroleum and chemical engineering. It provides the interested reader with in-depth insights into the possibilities and challenges of CO2 storage and the EGR prospect. © Springer International Publishing Switzerland 2016. All rights reserved.
Many workers have published various methods to measure refractive index of various liquids. Mostly, the measurement results are not traceable to SI units. A novel method is developed at CSIR-NPL, India (NPLI) to measure refractive of index of liquids using gauge blocks, metrological microscope and displacement laser interferometer. A vessel with flat bottom is chosen to hold the liquid under test. A pair of gauge blocks of different lengths is fixed in the vessel. The vessel is arranged under a vertically movable microscope. A calibrated displacement laser interferometer is attached to the microscope stage. The microscope is focused to the surface of gauge block before poring liquid. After poring liquid in the vessel, the microscope is moved vertically to regain the focussed image of surface of submerged gauge blocks. The measurement method is simulated mathematically. The refractive index of liquid medium is calculated using this mathematical model. Refractive index of water, isopropyl alcohol is measured. Various error contributing sources are identified. The measurement uncertainty is evaluated.
Five protein crystallisation experiments were performed within the Advanced Protein Crystallisation Facility (APCF) during the Life and Microgravity Spacelab (LMS) mission (orbiter mission STS-78). The objectives of these experiments were concentrated on the technical and phenomenological aspects of protein crystallisation in the APCF. High nucleation flux has been observed in all experiments due to early homogenisation of the salt concentration inside the protein chamber because of its shortness. Crystal size (length) shows a linear dependence on the square root of time between two crossovers related to an initial transient period during nucleation and to the depletion of protein concentration. Maximum growth rates of up to 50μm/h were observed slightly after nucleation. Crystal movement has been observed at average rates of 3.6μm/h (maximum rate of 20μm/h). The movement of different crystals is correlated suggesting that the mechanism responsible for movements operates at a length scale larger than the growth reactor, such as residual accelerations or g-jitters. The interferometric data recorded during the experiment have been used to reconstruct concentration gradients inside the protein chamber. Some technical problems in the laser prevented the reconstruction of time gradients. This problem is tackled by fitting spatial gradients to profiles obtained by simulation. X-ray diffraction showed the crystals were of very good quality, with an average limit of resolution of 1.25Å. The use of flat capillaries reduces the number of crystal handling and mounting steps. Very low mosaicity values were found (10–20arcsec). Mosaicity is shown to be an inhomogeneous and anisotropic property, the central part of the crystals (which grew at a faster rate) accumulating the domains having higher mosaicity. Large differences in mosaicity were found for peaks at the same resolution in the same crystal observed from different orientations. This anisotropy must be due to differences in the width of domain peaks or in their relative position in reciprocal space.
A double-beam interferometer has been designed for detecting changes of refractive index in transparent liquids associated with the absorption of ionizing radiation energy, due to short electron beam pulses from an accelerator. The response time of the interferometer is less than 0.2 μsec, and refractive index changes of the order of 10−7 can be measured, corresponding to a temperature change of ∼10−3 °C and an absorbed dose in water of ∼350 rad. The interferometer can be used as either a real-time or integrating radiation dosimeter, if the temperature coefficient of the refractive index (dn/dT) is known for the irradiated liquid in the temperature region of interest.
This paper summarizes the feasibility of using optical techniques for mapping the convection, temperature, and solute concentration in the solution around a growing protein crystal. Convection can be mapped by a variety of techniques which measure either refractive index differences, displacements, velocity, or solute optical absorption. For protein crystal growth, however, ordinary schlieren and interferometric techniques are marginally sensitive and most displacement marking techniques unsuitable; therefore, phase-contrast schlieren, ultraviolet solute absorption, and laser anemometry appear to be the most feasible. Mapping of temperature and concentration by the absorption-interferometric technique appears to be quite feasible for protein solutions because of their low dn/dC. Finally, the monitoring of protein crystal growth rates appears to be feasible by double-exposure holography or birefringence.
The optical path length distribution of the solution around a growing lysozyme crystal was observed in situ using a Michelson interferometer of the reflection type. From the interferograms, a concentration profile around a growing crystal and the growth rate were obtained and thus, we could evaluate the diffusion coefficient of the lysozyme molecules to be 1.59 × 10-10 m2/s. The measurement of the viscosity of the solution rendered it possible to estimate the Stokes radius of the diffusing entities which coincided with the crystallographic size of a lysozyme molecule.
Atomic force microscopy (AFM) investigations have revealed that macromolecular crystals, during their growth, incorporate an extensive array of impurities. These vary from individual molecules to large particles, and microcrystals in the micron size range. AFM, along with X-ray topology, has further shown that the density of defects and faults in most macromolecular crystals is very high in comparison with conventional crystals. The high defect density is a consequence of the incorporation of impurities, misoriented nutrient molecules, and aggregates of molecules. High defect and impurity density, contributes to a deterioration of both the mechanical and the diffraction properties of crystals. In microgravity, access by impurities and aggregates to growing crystal surfaces is restricted due to altered fluid transport properties. We designed, and have now constructed an instrument, the observable protein crystal growth apparatus (OPCGA) that employs a fused optics, phase shift, Mach–Zehnder interferometer to analyze the fluid environment around growing crystals. Using this device, which will ultimately be employed on the international space station, we have, in thin cells on earth, succeeded in directly visualizing concentration gradients around growing protein crystals. This provides the first direct evidence that quasi-stable depletion zones formed around growing crystals in space may explain the improved quality of macromolecular crystals grown in microgravity. Further application of the interferometric technique will allow us to quantitatively describe the shapes, extent, and magnitudes of the concentration gradients and to evaluate their degree of stability.
We present experimental observation of the spatio-temporal pattern of supersaturation in counter-diffusion methods. These complex patterns were recorded by dynamical interferometric analysis using a Mach–Zehnder configuration. Tetragonal hen egg white lysozyme crystals were grown inside APCF (advanced protein crystallisation facility) reactors. Salt and protein diffusion profiles were obtained independently by performing duplicated experiments with and without protein in the protein chamber; salt gradients were observed directly while protein concentration profiles are computed from the differences in refractive index between the two experiments. As expected from computer simulations, the time evolution of supersaturation shows a maximum about 45 h after activation (although this value can change as a function of the starting conditions and the geometry of the reactor). Nucleation takes place before this maximum supersaturation is reached. This explains the trend of the growth rate versus time curves for experiments performed within APCF reactors (both on ground and in space) and in capillaries by the gel acupuncture technique. By using very low concentration agarose gel in the protein chamber, sedimentation and buoyancy effects are eliminated so that the effects of gravity on fluid dynamics and hence on the spatio-temporal evolution of supersaturation can be assessed. These results confirm experimentally the predicted behaviour of counter-diffusion systems and support their use in growing large high-quality protein single crystals.
Fiber optic Raman spectroscopy combined with a partial least-squares regression model was investigated as a means to monitor lysozyme concentration during crystallization in a hanging drop experiment in real time. Raman spectral features of the buffer and protein were employed to build the regression model. This model was used to calculate the compositional changes within the hanging drop. The use of fibre optic technology coupled with Raman spectroscopy, which is ideal for use with aqueous media, results in a powerful noninvasive probe of the changing environment within the solution. These preliminary findings indicate that solubility as well as supersaturation measurements can be made.
A temperature-insensitive method for measuring protein concentration in aqueous solutions using near-infrared spectroscopy is described. The method, which is based on identification of the net analyte signal of single-beam spectra, can be calibrated using a single protein absorbance measurement and is thus well suited for crystallization monitoring where the quantity of protein is limited. The method is applied to measurements of glucose-isomerase concentration in a sodium phosphate buffer that is actively varied over the temperature range of 4-24 degrees C. The standard error of prediction using the optimized spectral range of 4670-4595 cm(-1) is 0.12 mg/mL with no systematic trend in the residuals with solution temperature. The method is also applied to previously collected spectra of hen egg-white lysozyme and yields a standard error of prediction of 0.14 mg/mL. Spectra sampled at discrete wavelengths can also be used for calibration and prediction with performance comparable to that obtained with spectral bands. A set of four wavelengths are identified that can be used to predict concentrations of both proteins with a standard error less than 0.14 mg/mL.
Growth of lysozyme crystals under micro gravity conditions in the LMS (STS-78) mission
  • Novella F Ml Otalora
  • Rondon D Garcia-Ruiz
  • Jm
Otalora F, Novella ML, Rondon D, Garcia-Ruiz JM, 1999. Growth of lysozyme crystals under micro gravity conditions in the LMS (STS-78) mission Journal of Crystal Growth, 196, 649.