20
detector 2. This angular dependency of light scattering intensity is represented by the particle
scattering function
P
(
θ
)
in light scattering theory, see Equation [A.2-1].
Quantitative theories of
P
(
θ
) for the solute shape models of hard-sphere, random-coil,
and rigid-rod types have long been worked out and published.
4
For example, the
P
(
θ
) function
according to Debye’s theory for random coil polymers
5
gives:
[A.2-5]
( )
(
)
[
]
P
X
e
X
X
θ
=
− −
−
2
1
2
or,
[A.2-6]
( )
P
X
X
θ
= −
+
−
1
3
12
2
. . .
where,
[A.2-7]
2
2
sin
3
8
=
θ
λ
π
n
R
X
g
Equation [A.2-6] shows that it is the initial slope of the
P
(
θ
) function which is proportional to the
square of the polymer radius of gyration,
R
g
, value. In this manner a light scattering instrument
can be used to determine the
R
g
of the polymer samples.
Since there are two variables,
θ
and
C
in Equation [A.2-1], a double-extrapolation
procedure is used to obtain
M
w
as well as
R
g
and
A
2
. This is done by plotting
K
c
/R
g
versus sin
2
(
θ
/
2
) and
C
, known as the Zimm plot method.
6
SEC LIGHT SCATTERING DETECTOR
Potentially, the coupling of an on-line light scattering detector can give a very powerful
polymer characterization capability. Considerable efforts have been invested in the past two
decades or more in the attempt to develop an on-line light scattering detector for SEC to
achieve absolute molecular weight distribution determination of polymer samples. Earlier
commercial light scattering detectors for SEC were far less than satisfactory because of the lack
of detection precision.
7,8
The concentration of the polymer solution eluting from an SEC column
is extremely dilute. The polymer concentration level in an SEC effluent is typically an order of
magnitude less than the sample concentration commonly used in classical light scattering
experiments. The signal-to-noise of a light scattering instrument is the most important
consideration in the SEC detector application.
Viscotek’s choice of the 90° right angle in the light scattering instrument is for the reason
of optimum signal-to-noise performance in the SEC-LS detection. Compared to the other
scattering angles, the 90° scattering intensity is the least affected by the problems of stray-light,
5
P. Debye, Technical Report CR-637, Private Communication to Reconstruction Finance Corporation,
Office of Rubber Reserve (1945). Reprinted in “Light Scattering from Dilute Polymer Solutions”, (D.
McIntyre, and F. Fornick, eds.) pp. 139-147, Cordon and Breach, New York (1964).
6
B. H. Zimm, J. Chem. Phys.,
16
, 1093 (1948).
7
Grinshpun, O’Driscoll, and Rudin, ACS Symposium SER.,
245
, 273 (1984).
8
S. Kim, P. M. Cotts, and W. Volksen, J. Polymer Science, Part B: Polymer Physics,
30
, 177 (1992).