research article particle size variation and prediction of...

Hindawi Publishing CorporationISRN Inorganic ChemistryVolume 2013 Article ID 194120 5 pageshttpdxdoiorg1011552013194120

Research ArticleParticle Size Variation and Prediction of Molecular Weight ofBi(III) Hydrolyzed Polymer Using Light Scattering Technique

N Priyadarshini M Sampath Shekhar Kumar and U Kamachi Mudali

Reprocessing RampD Division Reprocessing Group IGCAR Kalpakkam 603102 India

Correspondence should be addressed to Shekhar Kumar shekharigcargovin

Received 1 December 2012 Accepted 7 January 2013

Academic Editors K Y Choi and S Turmanova

Copyright copy 2013 N Priyadarshini et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The present paper gives an overview of the hydrolysis reactions up to colloid formation of Bi(III) in aqueous nitric acid mediumusing light-scattering measurements The hydrolysis products of Bi were polynuclear complexes such as dimers pentamers andthe most important is the hexameric species In the present investigation Bi3+ polymers were prepared by diluting differentconcentrations of Bi(NO

3)3sdot5H2O solutions to pH 1plusmn 01 by adding 01M NaOH solution as it starts to precipitates at pH 14 The

degree of polymerization was found to be 5-6 units Particle size measurements were performed and it has been found that particlesize increases at high concentration of Bi due to aggregation Refractive index measurements were also performed The molecularweight of hydrolyzed polymeric species of Bi was determined by using Debye plot and it was estimated as 1236 Da The secondvirial coefficient was found to be 624times 10minus3mLgminus1 Da The present investigation confirms that the predominant complex in thesolution has 5-6 Bi atoms

1 Introduction

Among numerous reactions that govern the chemical behav-ior of metal ions in aqueous medium the knowledge ofhydrolysis colloid formation and precipitation is of highestpriority In general metal ions in aqueous solutions form avariety of hydrolysis complexes such as mono- and polynu-clear hydroxospecies [1] The polynuclear complexes areformed followed by hydrolysis and in general it can berepresented as

119909M119899+ + 119910H2OlArrrArr [M

119909(OH)119910]

(119899119909minus119910)

+ 119910H+ (1)

The pH is the most governing factor where soluble hydrolysisspecies are present It is limited due to the formation ofcolloids or precipitation of hydroxides and oxides

Aqueous chemistry of Bi is primarily dominated by triva-lent complexes (Bi3+) [2] Bi(III) readily hydrolyzes in aque-ous solutions (p119870a = 151) and has high affinity to oxygenIn addition to that Bismuth is a strong Lewis acid and beginsto undergo hydrolysis at low pH values (pH sim 1) [3 4] TheBi3+ aqua ion [Bi(H

2O)119899]

3+ has been characterized using

many techniques which includes extended X-ray absorp-tion fine structure (EXAFS) and low angle X-ray scattering(LAXS) spectroscopy and concluded that 8 water moleculesare coordinated to Bi3+ But dynamic simulations showthat the number of coordinated water molecules is 9 (ie[Bi(H

2O)9]

3+) and is found analogous to structures foundamong lanthanides [5] Numerous studies on hydrolysis ofBi show that the predominant species at higher H+ concen-tration is Bi3+ It has been widely agreed that the hydrolyzedspecies of Bi are polymeric existing as dimers Bi

2O2

2+ pen-tamers Bi

5O5

5+ and the most important among them is thehexameric species Bi

6O6

6+ at moderate Bi concentrations(ge10minus2m) in acidic solutions with pH sim 2ndash5 Further hydrol-ysis over pH range of 4ndash6 leads to the formation of Bi

9

polynuclear complexes [6] Sedimentation equilibrium mea-surements indicate that there were 5 or 6 bismuth atoms inthe predominant complex present in solutions with approxi-mately 2 hydroxide ions bound per bismuth atom [7] SinceBi-Pb eutectic composition are heavy liquid coolant fornuclear reactors and several recent reactor prototypes usesteam-generationmodules in direct contact with liquidmetalcoolant Bi speciation under hydrothermal conditions is very

2 ISRN Inorganic Chemistry

important to optimize the separation of Bi from concentratessuch as Cu Pb and Mo [8 9] Hence an attempt has beenmade to study the hydrolysis and polymerization reactions ofBi using light-scattering techniqueThe use of light scatteringto determine the molecular weight of polymers has increasedinterest because of the several advantages associated with thistechnique It provides a nondestructive analytical techniquefor probing structure and dynamics of polymeric solutionThe main aim of this study is to determine the particle sizeand its changes with change in concentration using dynamiclight scattering and weight average molecular weight of Bipolynuclear complexes by static light scattering

2 Theoretical

21 Dynamic Light Scattering Dynamic light-scatteringmea-surements measure the time dependence of scattered lightfluctuations that can be related to the translational diffusioncoefficient of the macromolecules In order to quantify thetime dependence the autocorrelation function 119866(120591) is calcu-lated from the product of two photon counts at time 119905 and119905 + 120591 such that 119866(120591) = ⟨119868(119905)119868(119879 + 120591)⟩ [10] The normalizedintensity autocorrelation function 119892(120591) is given by

119892

int(120591) =

⟨119868 (119905) 119868 (119905 + 120591)⟩

⟨119868 (119905) 119868 (119905)⟩

(2)

The intensity autocorrelation function is related to the fieldautocorrelation function 119892field(120591) by the Siegert relationship

119892

field= 1 + 119862

1003816

1003816

1003816

1003816

1003816

119892

int(120591)

1003816

1003816

1003816

1003816

1003816

2

(3)

where 120591 is the delay time and 119862 is the Siegert constant(experimental parameter of themeasuring device) For dilutedispersion of macromolecules 119892int(120591) becomes

119892

int(120591) = 119890

minusΓ120591

(4)

where Γ is the diffusion of particles under investigation Therelation between the diffusion coefficient (119863) and the param-eter Γ can be related by

119863 =

Γ

119902

2 (5)

where 119902 is the scattering vectorFrom the diffusion coefficient the hydrodynamic particle

radius 119877ℎcan be derived via the Stokes-Einstein relation

119877

ℎ=

119870

119861119879

6120587120578119863

(6)

where 119870119861is Boltzmannrsquos constant 119879 is the temperature and

120578 is viscosity of the solvent

22 Static Light Scattering Static light scattering (SLS) hasbeen widely used to determine the molecular weight of apolymer SLSmeasures the time-averaged scattering intensitythat can be related to the second virial coefficient and

molecular weight by constructing the Debye plot accordingto the equation

119870119862

119877

120579

= (

1

119872

119908

+ 2119860

2119862) (7)

where the optical constant 119870 = [2120587119899(119889119899119889119862)]

2119873

119860120582

4

∘ 119877120579is

the excess Rayleigh ratio119872119908is the weight average molecular

weight of the solute 119862 is the concentration (in gmL) 1198602is

the second virial coefficient120582119900is thewavelength of light used

119873

119860is Avogadrorsquos number and 119889119899119889119862 is the refractive index

increment due to the solute under a given set of solution con-ditions A positive value of 119860

2indicates repulsion between

molecules whereas a negative value indicates the presence ofintermolecular interactions The Debye plot is 119870119862119877

120579versus

concentration in gmL The intercept of the plot gives 1119872119908

and the slope is used to calculate the second virial coefficient[11 12]

23 Materials and Methods Bi(NO3)

3sdot 5H2O in crystalline

form was obtained from Glaxo laboratories (minimum assayof 980) Four different solutions of Bismuth were preparedby dissolving nitrate Bi(NO

3)

3sdot 5H2O in 1M nitric acid (AR-

Fisher assay of 69ndash71) to a concentration of 00064 0012100246 and 00367 gmLminus1 Bi(NO

3)

3sdot 5H2O is of AR grade

and used as such The resulting solutions were diluted bygradually adding 01MNaOH until slight turbidity occursThe pH of the solution was maintained as 1 plusmn 01 All thesolutions were prepared at room temperature Water used inthe experiments was ASTM Grade-I water (from a MilliporeSimplicity System with organic removal 182MΩcm) Sam-ples were weighed using Shimadzu (AUW220D) analyticalbalance with measurement uncertainty of plusmn001mg

24 Measurement of pH and Refractive Index The changes inthe pH of the solutions were monitored using Thermo Sci-entific Orion Star pH meter The glass electrode used for themeasurement was calibrated with buffer solutions of pH 401and 700 The accuracy of pH measurements was plusmn001 unitsRefractive index (119899

119863) of solutions of different concentration

of Bi was measured on Anton Paar RXA 156 refractometerequipped with integrated Peltier thermostat with standarddeviation of 2 lowast 10minus5 119899

119863at 298K

25 Light-Scattering Measurements Both SLS and DLSexperiments were performed using Microtrac (NanotracULTRA) particle size analyzer Figures 1(a) and 1(b) representthe experimental light-scattering system used for the presentstudy The light source was a 780 nm 3mW diode laserAn external fiber-optic probe measuring 15m in length wasdipped inside a beaker containing the sample solution Theinterface between the sample and the probe is the sapphirewindow Initially it reflects the original laser back through thebeam splitter to a photodetector This signal which has thesame frequency as the original laser acts as a reference signaloffering heterodyne detection And then the laser passesthrough the sapphire window and is scattered by the particlesunder Brownian motion According to the Doppler effect

ISRN Inorganic Chemistry 3

Suspendedparticle

LaserScattered light from

particles

Reflected laser

Controlled reference is developed at the interface of the probe tip and fluid

Detector

(a)

(b)

Figure 1 (a) Schematics of the light-scattering system showing thedevelopment of controlled reference at the probe tip and fluid inter-face (b)Microtrac particle size analyzer with measurement range of08 nm to 64 120583m used for the present study

the laser is frequency shifted relative to the velocity of theparticle Light is scattered in all directions including 180∘backwards This scattered frequency shifted light is trans-mitted through the sapphire window to the optical splitterin the probe to the photodetector These signals of variousfrequencies combine with the reflected signal of unshiftedfrequency (controlled reference) to generate a wide spectrumof heterodyne difference frequencies The power spectrum ofthe interference signal is calculatedwith dedicated high speedFFT (Fast Fourier Transform) digital signal processor hard-wareThe power spectrum is then inverted to give the particlesize distributionThe schematic of the instrument is shown inFigure 1The scattered light was measured at an angle of 180∘Scattering experiments were performed at a temperature of27 plusmn 1

∘C The performance of the instrument was checkedwith the reference material (100 nm polystyrene microspheresuspended in water) prior to particle size measurementsTheuncertainty in the measurement was found to be plusmn1 nm

3 Results and Discussion

Figure 2 shows the comparison plot for varying particle sizeas the concentration of the solution varies The 119889

50values

range from 121 to 190 nm The details of each peak are givenin Table 1

The increase in particle diameter is due to aggregation ofsmaller particles as the concentration increasesThe polymer

0 200 400 600 800 10000

20

40

60

80

100

Chan

nel (

)

Size (nm)

Increasing concentration

0013 M (1213 nm)0025 M (1534 nm)

005 M (1604 nm)0076 M (1922 nm)

Figure 2 A comparison plot for intensity-averaged particle diame-ter (119889

50) variation with different concentration of polymeric Bi solu-

tions prepared in aqueous nitric acid medium

Table 1 Peak summary

Concentration(gmL)

Particle diameter(nm) Volume Width

00064 1213 977 54700121 1534 1000 51800246 1604 1000 81800367 1922 1000 2953

Table 2 Refractive indices for different concentration of Bi solu-tions

Wt concentration(gmLminus1) Refractive index RI increment

(dndC in mLgminus1)000634 133715001212 133750 00842002460 133866

is formed as a result of the condensation reaction between themonomeric speciesThe general equilibrium reaction is given

119899Bi3+ + 2119899H2OlArrrArr Bi

119899(OH)119899+2119899+ 2119899H+ (8)

Figure 3 shows the refractive index increment for differentconcentrations of Bi and the values are given in Table 2As the concentration increases the refractive index of thesolution also increases giving a positive slope 119889119899119889119862 =01304mL gminus1 This value has been used as an input for gen-erating the Debye plot Values of 436 gccminus1 and 19 wereassumed as particle density and particle refractive indexFigure 4 shows the Debye plot for different concentration ofBi It is a straight line with a positive slopeThe particles wereassumed spherical and ensured that the prepared solution


Table 3 Values of mean diameter KCRop and hydro-MW for different concentrations of Bi

Weight concentration (gmL) Mean diameter (120583m) KCRop (1Da) Hydro-MW000640 04530 827119864 minus 04 128119864 + 07

001212 00518 850119864 minus 04 191119864 + 08

002460 01262 885119864 minus 04 276119864 + 09

Table 4 Calculated parameters from the Debye plot

Substance Measured at 120582 = 780 nm

Bi (III) hydrouspolymer

119872

119908(Da) Second virial coefficient

119860

2(mLgminus1 Da)

1236 624119864 minus 03

0005 001 0015 002 00251337

13372

13374

13376

13378

1338

13382

13384

13386

13388

Refra

ctiv

e ind

ex

Wt concentration (g mL )

Figure 3The 119889119899119889119862 curves obtained for different concentration ofBi(III) solution (1198772 = 09827)

was free of impurities The molecular weight of the polymerwas determined as 1236Da from the intercept of the plot Sec-ond virial coefficient was determined as 624119864minus03mLgminus1DaThe positive value of119860

2shows that the overall net interactive

force is repulsive between the solute species and hence stablein the aqueous nitric acid medium The positive value of thesecond virial coefficient shows a positive Δ119866 for polymerchain interpenetration which leads to steric stabilizationTheresulting stabilization could be the result of positive Δ119867 ornegative Δ119878 where positive enthalpy reflects the release ofbound solvent and negative entropy reflects the loss of con-figurational freedom as the polymer chains interpenetrateAt this condition the dispersion is sterically stabilized Thusnitric acid is found to be a good solvent medium The valuesof KCRop mean diameter and hydro molecular weight ofeach concentration are given in Table 3 With increasingconcentration of Bi the degree of polymerization increasesThe calculated parameters from the Debye plot are given inTable 4 The results show that Bi undergoes hydrolysis at lowpH and forms polymers with more than 5 units

0005 001 0015 002 0025000082

000083

000084

000085

000086

000087

000088

000089

Wt concentration (gmL)

KCR

op (1

Da)

Figure 4 Debye plot for various concentrations of Bi3+ with 1198772 of09834

4 Conclusion

A new approach was applied to interpret the hydrolyticbehaviour of Bi using light-scattering technique X-raydiffraction centrifugation electrophoretic and tyndallomet-ric studies reported the different species of Bi present in aque-ousmediumThe present investigation attempts to determinethe molecular weight of the hydrolyzed species It was shownthat the particle size increases due to increased aggregation ofsoluteThis shows that polymerization of Bi strongly dependson concentration The second virial coefficient has also beendetermined and the positive value shows that there is repul-sion between the molecules making the polymeric solutionstable The weight average molecular weight of polymers ofBi(III) formed in aqueous nitric acid medium has confirmedthat the hydrolyzed species has 5-6 atoms of Bismuth

References

[1] N TorapavaHydration solvation and hydrolysis of multichargedmetal ions [Doctoral thesis] 2011

[2] F A Cotton G Wilkinson C A Murillo and M BochmannAdvanced Inorganic Chemistry John Wiley amp Sons New YorkNY USA 1999

[3] R Luckay I Cukrowski J Mashishi et al ldquoSynthesis stabilityand structure of the complex of bismuth(III) with the nitrogen-donor macrocycle 14710-tetraazacyclododecane The role ofthe lone pair on bismuth(III) and lead(II) in determining co-ordination geometryrdquo Journal of the Chemical SocietymdashDaltonTransactions no 5 pp 901ndash908 1997


[4] V Stavila R L Davidovich A Gulea and K H WhirmireldquoBismuth(III) complexes with aminopolycarboxylate and poly-aminopolycarboxylate ligands chemistry and structurerdquo Coor-dination Chemistry Reviews vol 250 no 21-22 pp 2782ndash28102006

[5] J Naslund I Persson and M Sandstrom ldquoSolvation of thebismuth(III) ion by water dimethyl sulfoxide NN1015840 dimethyl-propyleneurea and NN-dimethylthioformamide An EXAFSlarge-angle X-ray scattering and crystallographic structuralstudyrdquo Inorganic Chemistry vol 39 no 18 pp 4012ndash4021 2000

[6] C F Baes and R E Mesmer The Hydrolysis of Cations JohnWiley amp Sons New York NY USA 1976

[7] R S Tobias and S Y Tyree ldquoStudies on hydrolyzed bismuth(III)solutions II Light scatteringrdquo Journal of the American ChemicalSociety vol 82 no 13 pp 3244ndash3249 1960

[8] D Gorse-Pomonti and V Russier ldquoLiquid metals for nuclearapplicationsrdquo Journal of Non-Crystalline Solids vol 353 no 32ndash40 pp 3600ndash3614 2007

[9] S L Chryssoulis and J McMullen ldquoMineralogical investigationof gold oresrdquo inDevelopments in Mineral Processing D A Mikeand B A Wills Eds Elsevier Philadelphia Pa USA 2005

[10] R Pecora Dynamic Light Scattering Plenum New York NYUSA 1985

[11] J Bloustine V Berejnov and S Fraden ldquoMeasurements ofprotein-protein interactions by size exclusion chromatographyrdquoBiophysical Journal vol 85 no 4 pp 2619ndash2623 2003

[12] B J Berne and R Pecora Dynamic Light Scattering with Appli-cation in Physics Chemistry and Biology John Wiley amp SonsNew York NY USA 1976

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Analytical ChemistryInternational Journal of


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Organic Chemistry International

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important to optimize the separation of Bi from concentratessuch as Cu Pb and Mo [8 9] Hence an attempt has beenmade to study the hydrolysis and polymerization reactions ofBi using light-scattering techniqueThe use of light scatteringto determine the molecular weight of polymers has increasedinterest because of the several advantages associated with thistechnique It provides a nondestructive analytical techniquefor probing structure and dynamics of polymeric solutionThe main aim of this study is to determine the particle sizeand its changes with change in concentration using dynamiclight scattering and weight average molecular weight of Bipolynuclear complexes by static light scattering

2 Theoretical

21 Dynamic Light Scattering Dynamic light-scatteringmea-surements measure the time dependence of scattered lightfluctuations that can be related to the translational diffusioncoefficient of the macromolecules In order to quantify thetime dependence the autocorrelation function 119866(120591) is calcu-lated from the product of two photon counts at time 119905 and119905 + 120591 such that 119866(120591) = ⟨119868(119905)119868(119879 + 120591)⟩ [10] The normalizedintensity autocorrelation function 119892(120591) is given by

119892

int(120591) =

⟨119868 (119905) 119868 (119905 + 120591)⟩

⟨119868 (119905) 119868 (119905)⟩

(2)

The intensity autocorrelation function is related to the fieldautocorrelation function 119892field(120591) by the Siegert relationship

119892

field= 1 + 119862

1003816

1003816

1003816

1003816

1003816

119892

int(120591)

1003816

1003816

1003816

1003816

1003816

2

(3)

where 120591 is the delay time and 119862 is the Siegert constant(experimental parameter of themeasuring device) For dilutedispersion of macromolecules 119892int(120591) becomes

119892

int(120591) = 119890

minusΓ120591

(4)

where Γ is the diffusion of particles under investigation Therelation between the diffusion coefficient (119863) and the param-eter Γ can be related by

119863 =

Γ

119902

2 (5)

where 119902 is the scattering vectorFrom the diffusion coefficient the hydrodynamic particle

radius 119877ℎcan be derived via the Stokes-Einstein relation

119877

ℎ=

119870

119861119879

6120587120578119863

(6)

where 119870119861is Boltzmannrsquos constant 119879 is the temperature and

120578 is viscosity of the solvent

22 Static Light Scattering Static light scattering (SLS) hasbeen widely used to determine the molecular weight of apolymer SLSmeasures the time-averaged scattering intensitythat can be related to the second virial coefficient and

molecular weight by constructing the Debye plot accordingto the equation

119870119862

119877

120579

= (

1

119872

119908

+ 2119860

2119862) (7)

where the optical constant 119870 = [2120587119899(119889119899119889119862)]

2119873

119860120582

4

∘ 119877120579is

the excess Rayleigh ratio119872119908is the weight average molecular

weight of the solute 119862 is the concentration (in gmL) 1198602is

the second virial coefficient120582119900is thewavelength of light used

119873

119860is Avogadrorsquos number and 119889119899119889119862 is the refractive index

increment due to the solute under a given set of solution con-ditions A positive value of 119860

2indicates repulsion between

molecules whereas a negative value indicates the presence ofintermolecular interactions The Debye plot is 119870119862119877

120579versus

concentration in gmL The intercept of the plot gives 1119872119908

and the slope is used to calculate the second virial coefficient[11 12]

23 Materials and Methods Bi(NO3)

3sdot 5H2O in crystalline

form was obtained from Glaxo laboratories (minimum assayof 980) Four different solutions of Bismuth were preparedby dissolving nitrate Bi(NO

3)

3sdot 5H2O in 1M nitric acid (AR-

Fisher assay of 69ndash71) to a concentration of 00064 0012100246 and 00367 gmLminus1 Bi(NO

3)

3sdot 5H2O is of AR grade

and used as such The resulting solutions were diluted bygradually adding 01MNaOH until slight turbidity occursThe pH of the solution was maintained as 1 plusmn 01 All thesolutions were prepared at room temperature Water used inthe experiments was ASTM Grade-I water (from a MilliporeSimplicity System with organic removal 182MΩcm) Sam-ples were weighed using Shimadzu (AUW220D) analyticalbalance with measurement uncertainty of plusmn001mg

24 Measurement of pH and Refractive Index The changes inthe pH of the solutions were monitored using Thermo Sci-entific Orion Star pH meter The glass electrode used for themeasurement was calibrated with buffer solutions of pH 401and 700 The accuracy of pH measurements was plusmn001 unitsRefractive index (119899

119863) of solutions of different concentration

of Bi was measured on Anton Paar RXA 156 refractometerequipped with integrated Peltier thermostat with standarddeviation of 2 lowast 10minus5 119899

119863at 298K

25 Light-Scattering Measurements Both SLS and DLSexperiments were performed using Microtrac (NanotracULTRA) particle size analyzer Figures 1(a) and 1(b) representthe experimental light-scattering system used for the presentstudy The light source was a 780 nm 3mW diode laserAn external fiber-optic probe measuring 15m in length wasdipped inside a beaker containing the sample solution Theinterface between the sample and the probe is the sapphirewindow Initially it reflects the original laser back through thebeam splitter to a photodetector This signal which has thesame frequency as the original laser acts as a reference signaloffering heterodyne detection And then the laser passesthrough the sapphire window and is scattered by the particlesunder Brownian motion According to the Doppler effect


Suspendedparticle


particles

Reflected laser


Detector

(a)

(b)






50values



0 200 400 600 800 10000

20

40

60

80

100

Chan

nel (

)

Size (nm)


0013 M (1213 nm)0025 M (1534 nm)

005 M (1604 nm)0076 M (1922 nm)





Concentration(gmL)


00064 1213 977 54700121 1534 1000 51800246 1604 1000 81800367 1922 1000 2953



(dndC in mLgminus1)000634 133715001212 133750 00842002460 133866



119899(OH)119899+2119899+ 2119899H+ (8)





001212 00518 850119864 minus 04 191119864 + 08

002460 01262 885119864 minus 04 276119864 + 09




119872


119860

2(mLgminus1 Da)

1236 624119864 minus 03

0005 001 0015 002 00251337

13372

13374

13376

13378

1338

13382

13384

13386

13388

Refra

ctiv

e ind

ex






0005 001 0015 002 0025000082

000083

000084

000085

000086

000087

000088

000089


KCR

op (1

Da)


4 Conclusion


References























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Suspendedparticle


particles

Reflected laser


Detector

(a)

(b)






50values



0 200 400 600 800 10000

20

40

60

80

100

Chan

nel (

)

Size (nm)


0013 M (1213 nm)0025 M (1534 nm)

005 M (1604 nm)0076 M (1922 nm)





Concentration(gmL)


00064 1213 977 54700121 1534 1000 51800246 1604 1000 81800367 1922 1000 2953



(dndC in mLgminus1)000634 133715001212 133750 00842002460 133866



119899(OH)119899+2119899+ 2119899H+ (8)





001212 00518 850119864 minus 04 191119864 + 08

002460 01262 885119864 minus 04 276119864 + 09




119872


119860

2(mLgminus1 Da)

1236 624119864 minus 03

0005 001 0015 002 00251337

13372

13374

13376

13378

1338

13382

13384

13386

13388

Refra

ctiv

e ind

ex






0005 001 0015 002 0025000082

000083

000084

000085

000086

000087

000088

000089


KCR

op (1

Da)


4 Conclusion


References























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




001212 00518 850119864 minus 04 191119864 + 08

002460 01262 885119864 minus 04 276119864 + 09




119872


119860

2(mLgminus1 Da)

1236 624119864 minus 03

0005 001 0015 002 00251337

13372

13374

13376

13378

1338

13382

13384

13386

13388

Refra

ctiv

e ind

ex






0005 001 0015 002 0025000082

000083

000084

000085

000086

000087

000088

000089


KCR

op (1

Da)


4 Conclusion


References























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




















Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

research article particle size variation and prediction of...

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