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The slope of this (and final) plot is 3.85
⋅
10
-6
, and according to the equation
above, it equals (16
π
2
R
G
2
/3
λ
2
)(1/M
w
). Inserting known values for
λ
(wavelength = 474 nm) and M
w
(just found), we obtain in this case R
G
= 57
nm.
In conclusion, these 4 steps, involving 4 sets of linear regressions, easily
provide M
w
, A
2
and R
G
. Such a procedure can easily be entered into a
spreadsheet or data program. It is strongly recommended to include the 4
graphical representations. In real life experimental data may fluctuate due to
random and systematic errors. Analysis of the plots may indicate which
measurements must be rejected – or repeated. In any case, automated
procedures should include determination of the uncertainty of the estimates.
6.2.7. The Zimm diagram.
A student once asked if ‘sim’ had something to with mobile phones, certainly
being unaware of the famous polymer scientist Bruno Zimm, who devised the
diagram for analyzing light scattering data. In such a diagram, where all data
are combined in a single figure, data are presented as plots of Kc/R
θ
as a
function of a combined parameter: sin
2
(
θ
/2) + kc, where k is an arbitrary
constant selected to spread the data in the diagram in a convenient way. In
the example below k = 10.000:
y = 3.85E-06x + 5.05E-06
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
0.0000 0.2000 0.4000 0.6000 0.8000 1.0000
sin
2
(
!
/2)
(Kc/R
!
)
c
=0