ChromeGate 3.3.2 Software Manual - KNAUER Advanced Scientific ...

282 SEC Option
single variable search can be used to find D2 using the following
equation.
M
w
b
b
�
��
�
/ M �
��
�
n �
��
F(
t)
exp( �D2
t)
dt
���
F(
t)
exp( D2t)
dt
�
� a
��
a
�
The usual range for D2 is between 0 and 1 inclusive. Therefore, golden
section search is used to find D2s value. For example, with a known
value for Mw/Mn the search routine would substitute 0.5 for D2. If the
equation is valid, both sides of the equation equal each other, the search
ends and D2 = 0.5. If the equation is not valid, then values of 0.25 and
0.75 are substituted for D2 to see if either can satisfy the equation. If
neither can solve the equation then the D2 value that is closest to
satisfying the equation is the direction the search should continue.
Once D2 is solved D1 can be solved directly using one of the following
equations.
M
n
�
�
a � b
F(
t)
Exp(
D t)
dt
a
D
1
b
F(
t)
dt
2
M
w
D
1
b
�
F t)
Exp(
�D
t)
dt
( 2
� a
b
F(
t)
dt
With D1 and D2 solved a calibration curve can be created over time.
Equations Broad Standard Method 2
The second method is to solve for a non-linear Molecular Mass
calibration curve. The curves equation has two unknown Mark-Houwink
constants K and A. It is these constants that must be solved before this
curve can be created. To implement method 2 a user must supply a
molecular number average Mn and Molecular Mass average Mw for a
single broad Molecular Mass distribution MWD standard. Also, the user
must supply a universal calibration curve �(t).
� �
M � K
1� A t
1
(
1 �
)
1� A
1
Given below is an equation with unknown � and �.
M
�
� �
1
� �
1�
A
�
1 1
�A
�A
� t)
���
( )
( 1 1
1
K
t
� � A 1 �
� 1 1
K
Now there are four unknowns K, A, �, and �.
A single variable search using the following equation is used to find �,
and that in turn will allow a direct calculation to find �.
�
�
a