11 Wyatt Technology Corporation 2009 All Rights
Reserved1Introduction to Light Introduction to Light
ScatteringScatteringWyatt Technology Corporation Wyatt Technology
Corporation, Santa Barbara California , Santa Barbara California22
Wyatt Technology Corporation 2009 All Rights Reserved2Lecture
Overview Light scattering and its uses Physics background Theory
Running an Experiment Data analysis33 Wyatt Technology Corporation
2009 All Rights Reserved3What is Light Scattering?
Innatureblueskyandcloudsredsunsets44 Wyatt Technology Corporation
2009 All Rights Reserved4What is Light Scattering?Inthe lab55 Wyatt
Technology Corporation 2009 All Rights Reserved5,Molarmass M,Size
rg,Secondvirialcoefficient A2Translationaldiffusion,coefficient Dt
-CanbeusedtocalculaterhW h a t ca n Lig h t S ca tte rin gMe a su
re ?For asolute insolution,: lightscatteringcandetermine66 Wyatt
Technology Corporation 2009 All Rights Reserved6Light and its
PropertiesLightisanoscillatingwaveofelectricandmagneticfields :
Polarization directionofelectricfieldoscillation2E I : Intensity77
Wyatt Technology Corporation 2009 All Rights Reserved7How does
Light Scatter?,. Whenlightinteractswithmatter
itcauseschargestopolarizeTheoscillatingcharges.
radiatelight,Howmuchthechargesmoveandhencehowmuchlight,radiates
dependsuponthe . matter spolarizability88 Wyatt Technology
Corporation 2009 All Rights Reserved8Index of Refraction
nThepolarizabilityofamaterialisdirectlyrelatedtoitsindexofrefractionn.Theindexofrefractionisameasureof.
thevelocityoflightinamaterial . .,e g speedoflight,Forsolutes
thepolarizabilityisexpressedasthespecific,refractiveindexincrement
dn/dc.nvacuumliquidvv 2scattered
,`
.|dcdnIdcdnE scattered99 Wyatt Technology Corporation 2009 All
Rights Reserved9Adding Light : Interference Incoherentsum
Coherentsum2 12221 totalI IE E I+ + 2 1222122 1 total terms crossI
IE EE E I+ + + + 10 10 Wyatt Technology Corporation 2009 All Rights
Reserved10How Light Scattering Measures M: coherent:
incoherent222total4 E E E I + 222 2total2 E E E I + (
)2scattered
,`
.|dcdnMc I 11 11 Wyatt Technology Corporation 2009 All Rights
Reserved11Isotropic ScatteringFor particles much smaller than the
wavelength of the incident light ( 10 nm16 16 Wyatt Technology
Corporation 2009 All Rights Reserved16Basic Light Scattering
PrinciplesPrinciple 1The amount of light scattered is directly
proportional to the product of the polymer molar mass and
concentration.Principle 2The angular variation of the scattered
light is directly related to the size of the molecule.(
)2scattered
,`
.|dcdnMc I 17 17 Wyatt Technology Corporation 2009 All Rights
Reserved17Basic Light Scattering EquationIn the Rayleigh-Gans-Debye
limit, the two light scatteringprinciples are embodied in the
equation: This equation also contains a correction due to
concentration c.The correction is due to coherent intermolecular
scattering, and contains information on the second virial
coefficient.18 18 Wyatt Technology Corporation 2009 All Rights
Reserved18Definition of Terms 1n0 solventrefractiveindexN A
Avogadro s numberl0 vacuum wavelength of incidentlightdn/dc- .spec
refractiveindexincrement( Excess . . ie ,)from thesolutealone. R
ayleighratio Theratioof the,scatteredandincident light
intensitycorrectedfor sizeof scatteringvolume. anddistancefrom
scatteringvolume( ) ( ) ( ) [ ] 2 12 McP A McP K R 2402024
,`
.|dcdnNnKA( ) R Molar massM19 19 Wyatt Technology Corporation
2009 All Rights Reserved19csolute concentration (g/ml)P() form
factor or scattering function.P( )relates theangular variation in
scattering intensity to the mean square radius rgof the
particle.The larger rg, the larger the angular variation.Note that
P(0) = 1.A2second virial coefficient, a measure of solute-solvent
interaction.Positive for a good solvent.Definition of Terms 2( ) (
) ( ) [ ] 2 12 McP A McP K R 20 20 Wyatt Technology Corporation
2009 All Rights Reserved20Running an Experiment1:CalibrationWhy?The
detectors output voltages proportional to the light scattering
intensities. The voltages must be converted to meaningful
units.How?1.Flow pure, filtered (0.02 m) toluene through the flow
cell.2. ASTRA software measures the voltages from the 90 and
lasermonitor photodiodes with the laser on and off (dark voltages).
3. ASTRA then computes the calibration constant.21 21 Wyatt
Technology Corporation 2009 All Rights Reserved21Why? detector
sensitivities vary. each detector views adifferent scattering
volume. scattered light is refracted. only the 90 detector is
calibrated.Running an Experiment2:NormalizationHow?1. Fill flow
cell with isotropic scatterer in actual solvent to be used.2. ASTRA
software measures voltages for each angle and:a. Determines
refraction angle from solvent index of refraction.b. Determines
angle and scattering volume corrections.c. Normalizes each
corrected detector voltage signal to the 90 detector.22 22 Wyatt
Technology Corporation 2009 All Rights Reserved22Online Data
Collection ( RecordR ayleighratiovaryingangle 3or 18angles)for
miniD AWN or D AWN andmeasuring .concentration23 23 Wyatt
Technology Corporation 2009 All Rights Reserved23Online Data
Analysis( ) ( ) ( )21 2R K McP A McP ] ]. 1 Perform fit of angular
datatoretrieveM andrg.. 2 . A ssess qualityof fit usingaD
ebyeplot22 Wyatt Technology Corporation All Rights ReservedDefine
Peaksdetector 11 gfedcbtime (min)8.0 10.0 12.0 14.0 16.0 18.0
20.0relative scale0.00.51.01 1 2 2 3 3 4 4 5 5Batch Data
CollectionRecordR ayleighratiovarying- ( ) angle 3or 18 angles for
miniDAWN or DAWN- ( concentration multipleinjectionsof known c).
excess scatteringsolvent scattering+ detector offsetC1C2C3C4C525 25
Wyatt Technology Corporation 2009 All Rights Reserved25Batch Data
Analysis( ) ( ) ( )21 2R K McP A McP ] ]. 1 Perform globalfitof
datatolightscatteringequationtoretrieveM , rg,andA2.. 2 A ssess
qualityof fitusingaZ imm. plotWeight average molar mass (2.019
0.001) e+5 g/molZ-average rms radius 16.7 0.1 nmSecond virial
coefficient A2(4.100 0.010) e-4 mol mL/gsin(theta/2) + kc-0.5 0.0
0.5K*c/R(theta)-65.0x10-65.2x10-65.4x10-65.6x10-65.8x10-66.0x10
decreasingangle decreasingconcentration26 26 Wyatt Technology
Corporation 2009 All Rights Reserved26A Zimm Plot of BSAusing
Online Concentration DetectionZimm plotsin(theta/2) + kc-0.5 0.0
0.5K*c/R(theta)-51.52x10-51.54x10-51.56x10-51.58x10-51.60x10-51.62x10D
e f i n e P e a k sL SgfedcbU VgfedcC Rgfedcd R Igfedcbt i m e ( m
i n )1 0 . 0 1 5 . 0 2 0 . 0 2 5 . 0relative scale0 . 00 . 51 . 01
1 2 2 3 3 4 4 5 5 6 6RILSMw:. 662 kDaA2: . 1142 x 10-4/ mol mLg227
27 Wyatt Technology Corporation 2009 All Rights
Reserved27Measurements on Unfractionated Samples: Obtain. 1 -
Weight averaged: molarmass. 2 - z averaged: meansquareradius. 3. 3
- z averaged: rmsradiusii iWcM cMi ii iigzM cM c rr22radius square
meanaverage - z2zr28 28 Wyatt Technology Corporation 2009 All
Rights Reserved28Whats Next Remainder of day hands-on experience
with hardware and softwarebatch lab experiment, real data! Summary
session bring questions!
