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Chapter 12. Light scattering (determination of

MW without calibration)

Electromagnetic radiation ? ???? ????? ??

- ? ?? ??
- transmission transmitted radiation passes

through the medium unaltered. - absorption energy from the incident beam is

taken up, resulting in (1)heating, (2)

re-emitting at another wavelength (fluorescence,

phosphorescence), (3)supporting chemical

reactions. In this discussion, we assume that

radiation heating is negligible. Other

absorption effects are specific to the particular

medium, and will also not be considered here. - scattering scattering is non-specific, meaning

the incident radiation is entirely re-emitted in

all direction with essentially no change in

wavelength. Scattering results simply from the

optical inhomogeneity of the medium. - reflection scattering at the surface of a matter

(not considered here)

- Now we focus on the light scattering.
- Application of Light Scattering for Analysis
- Classical Light Scattering (CLS) or Static Light

Scattering (SLS) - Dynamic Light Scattering (DLS, QELS, PCS)
- CLS
- ?? Scattering center small volumes of material

that scatters light. ? individual molecule in

a gas. - Consequences of the interaction of the beam with

the scattering center depends, among other

things, on the ratio of the size of the

scattering center to the incident wavelength

(?o). Our primary interest is the case where

the radius of the scattering center, a, is much

smaller than the wavelength of the incident light

(a lt 0.05?o, less than 5 of ?o). This

condition is satisfied by dissolved polymer coils

of moderate molar mass radiated by VISIBLE light.

When the oscillating electric field of the

incident beam interacts with the scattering

center, it induces a synchronous oscillating

dipole, which re-emits the electromagnetic energy

in all directions. Scattering under these

circumstances is called Rayleigh scattering.

The light which is not scattered is transmitted

, where Is and It are the

intensity of the scattered and transmitted light,

respectively.

- Oscillating electric field of incident beam

interacts with scattering center, induces a

synchronous oscillating dipole, which re-emits

electromagnetic energy in all directions.

Rayleigh scattering? ?? ???? ??? ?? ??? ?? ???

(1cos2?)? ????, scattering center? observer???

??(r)? ??? ???.

- 1944, Debye

- Rearrange

Constant, K

?o ?????, dn/dc refractive index

increment no ??? refractive index, p???,

c????g/mL

I? is inversely proportional to ?o. Shorter

wavelength scatters more than longer

wavelength Assume system is dilute, the net

signal at the point of observation is sum of all

scattering intensities from individual scatterer

- no multiple scattering (scattered light from

one center strike another center causing

re-scattering, etc.).

- Two ways to access the light scattering

information experimentally - Turbidimeter (or spectrophotometer)
- Light scattering

1. Turbidimeter experiment (Transmitted light

intensity, It is measured)

Solution is dilute, so higher order concentration

terms can be ignored.

Procedure Measure t at various conc. ? Plot Hc/T

vs. c (straight line) ? Determine M from

intercept, 2nd virial coeff., B from slope

2. Light Scattering experiment (measure I? at

certain ? and r)

?6? ?4? ??

??? ??? ? 5 (?/20) ??? ??? ??? Rayleigh

limit

?-condition?? ???0.

lt??gt For polydisperse sample, Turbidity (?? light

scattering) is contributed by molecules of

different MW. Define ti ??? Mi? ?? ???? ??

turbidity ?

??? turbidity? light scattering???? ?? ????

weight-average MW??.

Rayleigh-Gans-Debye (RGD scattering) when the

scattering centers are larger than Rayleigh limit

Different part of more extended domain (B)

produce scattered light which interferes with

that produced by other part (A) - constructive or

destructive

Distribution is symmetrical for small particles

(lt?/20). For larger particles, intensity is

reduced at all angles except zero.

Contributions from two scattering centers can be

summed to give the net scattering intensity.

The result is a net reduction of the scattered

intensity

P? "shape factor" or "form factor"

Always P? lt 1, function of size and shape of

scattering volume. Now we start seeing the

angle dependence of the scattered light !

- p(?) decreases with ?.
- p(?) decreases more for higher MW.

Effect of MW and Chain Conformation on P?, and on

measured MW at 90o.

Conformation MW (g/mol) RG (nm) P(90o) MW(90o)

Random coil

Polystyrene 51K 8 0.98 51K

Polystyrene( ? condition) 420K 19 0.95 400K

PMMA 680K 36 0.70 480K

Polyisoprene(70 cis) 940K 48 0.56 530K

Spherical

Bovine serum albumin 66K 3 1.00 66K

Bushy stunt virus 10700K 12 0.98 10500K

Rod shaped

Poly- -benzyl-L-glutamate 130K 26 0.91 118K

Myosin 493K 47 0.74 365K

DNA 4000K 117 0.35 1400K

Final Rayleigh equation for random coil polymer

? ?? ?? ??

Case 1 ??0

Plot Kc/R? vs. c y-??1/M, ???2A2

Case 2 c?0

Plot Kc/R? vs. sin2(?/2) y-??1/M, ???

(16p2/3M?2) rg2

Three information!

??? ?? ?? (1) ??? ??? ???? R???. (2) Kc/R? vs.

c, Kc/R? vs. sin2(? /2) plot ??. (3) ? 0 ? c

0 ? extrapolate.

Kc/R? vs. sin2(? /2)

Kc/R? vs. c

Zimm plot

??? ? ?? ???. ? ? extrapolated points

Cases

1. Small polymers ????? ??. (Horizontal line)

Zimm plot for PMMA in butanone ?o546 nm, 25?, no

1.348, dn/dc 0.112 cm3/g

- ?? ???? ??? ???. - Mw ? A2 ?? ?? - ???? ?? ???.

2. Small polymers in ?-solvent ?? ? ?? ??? ??.

Zimm plot of poly(2-hydroxyethyl methacrylate) in

isopropanol ?o436 nm, 25?, no 1.391, dn/dc

0.125 cm3/g

?-solvent A20? ?? ??, ???-???, ???-????? ?????

???? ??, ????? ?? ??.

- Calculated values Mw 66,000 g/mol
- A2 0 mol

cm3/g2 - - Kc/R? at small angles fall mostly below the

horizontal line plotted through the points from

medium and large angles.

3. Larger polymers in good solvent ?? ? ??? ??.

Zimm plot of polystyrene in toluene ?o546 nm,

25?, no 1.498, dn/dc 0.110 cm3/g

- ??? ? 2x105 ??? ??, Kc/R? ? ?? ??? (A2??)?

???. - Athermal Condition - No effect of

temperature on polymer structure

4. Polymers in poor solvent A2 ? ??? ? (? ???

? ? ??. ? ?? ?? ?? ??)

Zimm plot of polybutadiene in dioxane ?o546 nm,

25?, no 1.422, dn/dc 0.110 cm3/g

- - ?????? ??? ?? (nonlinear).
- - ?? microgel, ??, aggregate? ?? ? ?? ??.
- Curve-fitting? ??? ??.
- ???? ??? ???? ??.
- ??? ??? good solvent???
- ???? ??? ? ??.

Stand-alone vs. On-line MALS

- ltStand-alone modegt
- Stand-alone mode LS instrument is used itself.

- Zimm plot ? ?? M, A2, R?? ??

- ltOn-line modegt
- LS instrument is used as a detector for a

separator. - c0 ?? ??.
- ? slice? ?? Kc/R? vs. sin2(?/2) ???? ??,

y-?????? ??? (M), ???????? rg? ??. y-??1/M,

????? (16p2/3M?2) rg2 - ? slice? monodisperse??? ???? ?????? ????? ??.

??? ?? ???? ??? (?????? ? ?????? ???).

- Average Molecular Weights
- No-average Mn(Sci)/(S(ci/Mi))
- Wt-average MwS(ci Mi)/ S(ci)
- Z-average Mz S(ci Mi2)/S(ci/Mi)
- Average Sizes (mean square radii)
- No-average ltrg2gtn S(ci/Mi)ltrg2gti/S(ci/Mi)
- Wt-average ltrg2gtw S(ciltrg2gti)/Sci
- Z-average ltrg2gtzS(ciMiltrg2gti)/S(ciMi)

Light scattering instruments MALLS (Multi Angle

Laser Light Scattering) I? is measured at 15

angles (1) Stand-alone mode Measure scattered

light at different angles for different

concentrations ? Make a Zimm plot ? Determine M,

B, Rg

Assuming each slice is narrow distribution, Mw ?

Mi Average M can be calculated. It is therefore

very important to have a good resolution.

Angular Dependence of Kc / R?(?? high molecular

weight DNA)

Effect of Particles/Gels on Light Scattering

Measurement Note the delicacy of extrapolation to

zero angle from larger distances.

- DALLS (Dual Angle) I?? is measured at 15o and

90o - LALLS (Low Angle) I? is measured at one low

angle (assume ?? 0) - Static mode measure LS at a few c ? Plot Kc/R?

vs. c ? Determine M and B from intercept and

slope. - On-line mode determine Kc/R? for each slice (

calculate M). Considering each slice is

narrow distribution, let Mw ( Mi, from which

average MW's can be calculated (as learned in

chapter 1). It is therefore again very

important to have a good resolution.

- RALLS (Right Angle)
- I? is measured at 90o.
- Simple design
- Higher S/N ratio, Application is limited to

cases where P? is close to 1 (e.g., less than

200K of linear random polymer) - RALLS combined with differential viscometer

(commercially available from Viscotek, "TRISEC")

ltTRISEC ?? ??gt Assume P? 1 and A2 0.

Determine Mest.

? is determined by differential viscometer, and

M determined in step 2.

Calculate new MW by

Go to step 2. Repeat until Mest does not change.

ltLight scattering experiment? ??? ???gt

?? K? B? ??? ?? parameter? ?? ?? ??. ???

??? ?? ? ?? ??? ??.

- n ??? refractive index
- dn/dc Specific refractive index increment
- B 2nd virial coefficient (Static mode??? B? ???

?? ??? ? ?? ??? Static mode? ??).

1. ??? Refractive Index ?? ?? ??? ?? RI ??? ???

??.

?? ??? ??? (R?? ???? ?)

Solvent RI R? x 106 cm-1

Carbon disulfide 1.6207 57.5

a-chloronaphthalene (140 oC) 1.5323 52.8

1,2,4-Trichlorobenzene (135 oC) 1.502 35.7

Chlorobenzene 1.5187 18.6

o-Xylene (35 oC) 1.50 15.5

Toluene 1.49 14.1

Benzene 1.50 12.6

Chloroform 1.444 6.9

Methylene chloride 1.4223 6.3

Carbon tetrachloride 1.46 6.2

Dimethyl formamide 1.43 (589 nm) 5.6

Cyclohexane 1.425 5.1

Cyclohexanone 1.4466 4.7

Methyl ethyl ketone 1.38 4.5

Ethyle acetate 1.37 4.4

THF 1.41 4.4

Acetone 1.36 4.3

Dimethyl sulfoxide 1.478 (589 nm) 4.1

Methanol 1.33 2.9

Water 1.33 1.2

- Except where otherwise noted, all measurements

made at ? 632.8 nm and T23 oC. RI at 632.8 nm

calculated by extrapolation from values measured

at other wavelengths. - Extrapolation? ?? reference Johnson, B. L.

Smith, J. "Light Scattering from Polymer

solutions" Huglin, M. B. ed., Academic press, New

York, 1972, pp 27

2. Specific refractive Index, dn/dc

- ???? ?? ? ?? (Polymer Handbook, Huglin, ed.,

Light Scattering from Polymer Solutions, Academic

Press, 1972) - ???? ?? ? ?? ?? ??? ?? ??
- Conventional method
- DRI? ??
- ? ?? ?? ???? (n2-n1)? ?? (recommended conc. 2,

3, 4, 5 x 10-3 g/mL) ? (n2-n1)/c2 vs. vs. c2?

plot ? zero concentration?? extrapolate ? dn/dc?

intercept? ? ? ???.

For concentration ranges generally used, the

refractive index difference, n2-n1, is a linear

function of concentration. In other words,

(n2-n1)/c2 is constant. ? (n2-n1)/c2 vs. c2 ????

???0.

This means that (n2-n1) needs to be measured for

only one or two different concentrations. If

(n2-n1)/c2 shows no significant dependence on c,

then dn/dc can be obtained by averaging

(n2-n1)/c2 values

- SEC/RI? ??
- ?? ?? ?? ??

?? dn/dc? ?? ????? ???? kR? ??

- ???? ??? ?? ?? ? ?? ?? estimate? ? ?? ??.
- extrapolate to desired wavelength

?? 2) polymer? ??? refractive index? ??

estimate

???? n2? polymer? partial specific volume

mL/g??. ?? n2 ? 1.

- lt????gt
- dn/dc ? ??? ????? light scattering ??? ?? ??? ???

??? ?? ???? ???? ??. - Dn/dc ? ??? ????? ???? ??? ??. Dn/dc ? ???? ??.
- ??? dn/dc ?? ??. ???? ???? ?? ??? ??.

3. Virial Coefficient, B or A2

- ???? ?? ? ?? (? Polymer Handbook). ???? ?? ? ??

?? ??? ?? ?? (stand-alone Light scattering) - 2nd Virial Coefficient? Solute-Solvent

interaction? ??. - Polymer-solvent interaction, good solvent (the

higher, the better solvent). - 0 Unperturbed system
- - Polymer-polymer interaction, poor solvent.
- A2? ???? ?? A2 b M-a ? log A2 vs. log M?

??. ?? ???? ??, ? ???? ???. - dn/dc? A2? ???? ?? ???? S. Lee, O.-S. Kwon,

"Determination of Molecular Weight and Size of

Ultrahigh Molecular Weight PMMA Using Thermal

Field-Flow Fractionation/Light Scattering" In

Chromatographic Characterization of Polymers.

Hyphenated and Multidimensional Techniques,

Provder, T., Barth, H. G., and Urban, M. W. Ed.

Advances in Chemistry Ser. No. 247 ACS

Washington, D. C., 1995 pp93.

- Light scattering ??? ? ? ?? ?? ? ?? (concerns)
- ??? dn/dc, RI constant, A2? ??.
- As dn/dc increases, calculated MW decrease,

calculated mass decrease, and no effect on

calculated RG. - As RI constant increases, calculated MW

decreases, calculated mass increases, and no

effect on RG . - As A2 increases, calculated MW increases, no

effect on calculated mass, RG slightly increases. - Refractive Index Detector Calibration ? ????? ?

?? - RI Calibration constant inversely proportional

to the detector sensitivity. - Sensitivity of most RI detector is

solvent-dependent. - A calibration constant measured in a solvent may

not be accurate for other solvents. It is

recommended to use a solvent that will be used

most often (e.g., THF or toluene). - For RI calibration, only the RI signal is used.

Light scattering instrument calibration is not

needed. - Concentration of standards should be such that

the output of RI detector varies between about

0.1 - 1.0 V and should correspond to normal peak

heights of samples (For a Waters 410 RI at

sensitivity setting of 64, this corresponds

roughly to concentrations of 0.1 - 1.0 mg/mL. RI

output can be usually monitored by light

scattering instrument (e.g., channel 26 of DAWN). - Use NaCl in water as a standard for aqueous

system. - The RI calibration constant will change if you

change the sensitivity setting of the detector

So it is important to use the same sensitivity

setting of RI detector as that used when the

detector was calibrated.

- RI calibration preparation One Manual injector

with at least 2 mL loop, Five or more known

concentrations (0.1 - 1 mg/mL) of about 200 K

polystyrene in THF. - RI calibration Procedure
- Remove columns. Place manual injector with loop.
- Pump THF through a RI detector at normal flow

rate (about 1 mL/min). Purge both reference and

sample cells of detector until baseline becomes

flat stable. - Stop purging and wait till baseline becomes

stable. - Set up the light scattering data collection

software (enter filename, dn/dc, etc.) Enter 1 x

10-4 for RI constant (light scattering instrument

usually requires the RI constants to be entered).

Set about 60 mL for Duration of Collect . - Begin collecting data with ASTRA.
- Inject pure solvent first followed by stds from

low to high conc, and finish with pure solvent.

- Repeat the measurements if you want.
- Data Analysis (1)set baseline using signals from

pure solvent at the beginning and the end

(2)calculate each concentration as a separate

peak by marking exactly 1 mL as peak width (or 30

slices at 1 mL/min, 2 seconds of collection

interval).(3)calculate the mass of the peak

(4)plot the injected mass (y-axis) vs. calculated

mass (x-axis) (5)do linear regression on data by

forcing the intercept be zero (6)calculate RI

constant using RI constant slope x 1x10-4

- Chemical heterogeneity within each slice leads to

non-defined dn/dc ? Quantitation of chemical

heterogeneous samples is very difficult. - Limited sensitivity to low MW components.

Mn(exp)gtMn(true). The same concern with

differential viscometer experiments. - Limited Sensitivity of Light Scattering and RI

Detector

- g' values may be in error if each peak slice

contains both linear and branched polymer or

different types of long-chain branching g' will

be overestimated. - Quality of data is highly affected by the

presence of particles. - Lower limit of RG with MALS? ? 10 nm (about 100K

MW) - Inter-detector volume must be known accurately.

Comparison of online LS vs. viscometer

LS Viscometer

MWD Absolute Relative

need precise n and dn/dc Universal calibration must be valid or need M-H coefficient

independent of separation mechanism Independent of separation mechanism if M-H coefficients are used. Dependent on separation mechanism if universal calibration is used.

? distribution indirect from universal calibration direct, independent of separation mechanism

RG direct from MALS (limited to gt10 nm) indirect from universal cal. and Flory-Fox eqn. applicable to linear molecules only

Chain conformation MALLS RG vs. M plot ? vs. M plot (M-H coefficients can be obtained) RG vs. M plot.

Branching g obtained directly from MALS, indirectly from LALLS universal calibration g' obtained directly

heterogeneous samples limited because of dn/dc uncertainty directly applicable with univ. calib., but the change in dn/dc will affect DRI responses

Lower MW detectability 2K. depends on dn/dc and polydispersity as low as 300-400 has been reported

Response to particle contamination LALLS highly sensitive, MALLS less sensitive Insensitive

Information Content

Primary Secondary

LALLS M

MALLS M RG

PCS D Rh, M

Viscometer ? M, RG

Primary information high precision and accuracy,

insensitive to SEC variables, requires no SEC

column calibration.

ltSEC-VISC-LS instrumentgt

- Features
- MWD measured by LS
- IVD measured by Viscometer

- Both Viscometer and LS are insensitive to

experimental conditions and separation mechanism - No band broadening corrections are needed for Mw,

? , a, k, and g - Precise and accurate calculation of hydrodynamic

radius distribution, M-H constants, and Branching

distribution

- Dynamic light scattering (DLS, QELS, PCS)
- Classical light scattering "time-averaged

scattering intensity"? ?? ???? ??? ? scattering

center??? ?? ?? ?? ??? ? (algebraic summation).

- ??? algebraic summation? ??? ? ???? random??

array????, ?? phase relationship? scattering

volume dimension? ??? ?? ?? ??? ?????? ??

interference effect ?? average-out?? ??? ????

???. - Scattering volume dimension? ?? ???, ???? ??? ?

scattering center? ?? ?? ?? ?? ?? ??? interfere

(constructive or destructive) ???? ?? ???? ???

???? ???? ??? ?? ????. - ? ???? Brownian motion (diffusion) ? ?? ?? ?????

???? ???? ?? ?? ?? ????. ??? ???? ???? ??? ???

?? fluctuate??. - Fluctuate?? ??? ???? diffusion rate? ??

(diffusion rate? ???? ??? fluctuate). - nanometer ?? micron??? ??? ??? ???? ?? viscosity?

??? viscosity? ??? media? disperse?? ?? ?, ????

??? ?? ?? (fluctuation)? microsecond ??

millisecond??.

- A vertically polarized laser beam is scattered

from a colloidal dispersion. The

photomultiplier detects single photons scattered

in the horizontal plane at an angle ? from the

incident beam, and the technique is referred to

as "photon correlation spectroscopy (PCS) - Because the particles are undergoing Brownian

motion, there is a time fluctuation of the

scattered light intensity, as seen by the

detector. The particles are continually

diffusing about their equilibrium positions.

Analyzing the intensity fluctuations with a

correlator yields the effect diffusivity of the

particles. - Measured intensity, I vector sum of scattering

from each particle - Brownian motion motion caused by thermal

agitation, that is, the random collision of

particles in solution with solvent molecules.

These collisions result in random movement that

causes suspended particles to diffuse through the

solution. For a solution of given viscosity, ?,

at a constant temperature, T, the rate of

diffusion (diffusion coefficient) D is given by

the Stokes-Einstein equation, D(kT)/(6p?d),

where k Boltzman's constant, d equivalent

spherical hydrodynamic diameter. ??? diffusion

coefficient (D)? ?????? ?? ?? (?? ???)? ??? ? ??. - DLS??? ? ??? ??? ?? ?? ???? ??? ?? ??(t time

interval)?? ???? ??? ????. ???? ??? ???? ???

??? t? ?? ?, I(0)? I(t)? ??. ?? ?? ?? interval?

?? ???? I(0)? I(t)? ??? ? intensity product,

I(0)I(t)? ???? ltI2(0)gt, ? average of the square

of the instantaneous intensity ? ???? - ?? "I(0)?

I(t)? correlate????"?? ??. ???? ??? ???? ???

??? t? ? ?, I(0)? I(t)? ??? ??? ?? ??? - "I(0)?

I(t)? correlate???? ??" ?? "I(0)? I(t)?

un-correlate ????" ?? ??. ???? intensity

product, I(0)I(t)? ???? ??? ltI2gt, ? square of the

long-time averaged intensity? ??. ???? ??? ????

??? ??? t? ??? ??? ?? ?, "I(0)? I(t)? ?????

correlate????".

- Measured intensity, I vector sum of scattering

from each particle - Measure I at various time interval, ?,
- I(0) I(t) for short t ? correlated,

correlation decreases as ? increases. - I(0)? I(t)? ?????? Correlation? ??? ??? ? ??.

correlation? ??? ???? ?? average of the intensity

product, G(t)? ????. - ?? G(t)Anto correlation function

ltI(t)I(tt)gt average of the intensity product.

- ?? ???? t ? ???? ?? G(t)? ??.
- G(t) is high for high correlation, and is low for

low correlation. - High correlation means that particles have not

diffused very far during t. Thus G(t)

remaining high for a long time interval indicates

large, slowly moving particles. - The time scale of fluctuation is called "decay

time - Decay time is directly related with the particle

size. The inverse of decay time is the decay

constant, ?. - Usefulness of G(t) directly relatable to the

particle diffusivity - For monodisperse samples,

?? ?? ??? ?? ??? interval?? autocorrelation

function, G(t)? ???

G(t) vs. t? ???? ??? Exponential function? ????

G(t)? fit??.

Rh? ??, ??? ?? ???? Measure I(t) at various ? ?

G(t) ?

?? DLS ? ??? ???? diffusion? ?? ??? ?? ?? ??

dispersion ( ? 0.03)? ??? ???. ? volume

fraction of suspended spheres.

, where N Avogadro's no., M MW, Vh

hydrodynamic vol.). Infinite dilution D?? ??

???? ?? ? 0.005? ?? ??? ??.

???? f(a) distribution function, I(a,?)

scattering intensity function for RGD spheres.

PC? ??, normal?? log-normal distribution

function? G(t)? fit??.

?? Narrow, mono-modal distribution ??? ??,

"method of cumulant"? ??, ??? ?? ??? ? ??.

- ???? an nth moment of f(a).
- We see that DLS yields a somewhat unusual

average radius (the inverse "z-average", and one

which is quite highly sensitive to the presence

of outsized particles. - DLS uses a single exponential decay function, and

thus it does not give information on sample

polydispersity.

- ??
- RI values of medium and sample are needed for DLS

experiments. - RI 1.333 for water, and 1.5 - 1.55 for typical

polymers and proteins. - RI of sample is needed only when the intensity

weight needs to be converted to the volume weight

(e.g., for samples having broad distributions).

- Theory to convert the intensity to the volume

is only for solid particles. So the conversion

will not be accurate for samples such as

liposomes which are hollow inside. - For samples such as liposome, a value between 1.5

- 1.55 can be used as it is typical values for

polymers and proteins. - For samples having narrow distributions, only the

unimodal analysis is performed, and thus there is

no need to convert the intensity to the volume

. - RI value will not make any difference in the

average size data because only the RI of medium

is need for unimodal analysis.

DLS summary

- D depends on MW and conformation
- Diffusion coefficient distribution can be

obtained - D is independent on chemical composition. ?D can

be obtained without knowing chemical composition. - Concentration is not needed to determine D
- Input parameters (T, n, ? ) are easily measured.
- Concerns sensitivity, interference from

particulates, inconsistency, not very useful

for polydispersed or multi-modal distributions.

lt??gt Particle Size Conversion Table

Mesh size Approximate ?µ size

4 4760

6 3360

8 2380

12 1680

16 1190

20 840

30 590

40 420

50 297

60 250

70 210

80 177

100 149

140 105

200 74

230 62

270 53

325 44

400 37

625 20

1250 10

2500 5