GPC if the sample were monodisperse.
STEP 1. I found it easiest to drop the DRI vs. Ve data into Origin one cocktail at a time. Origin has a nice
feature for scanning along a dataset, as shown by the arrow below.
So, I just read the Ve value for each peak and associate it with the M values supplied by the calibration
standard vendors. Of course, the biggest M value is the lowest Ve (assuming the GPC is working in size
exclusion mode, which is the case here).
STEP 2. I like Origin for making the M vs Ve calibration plot.
7.0
6.5
6.0
5.5
log10M
5.0
4.5
4.0
3.5
3.0
2.5
2.0
15
20
25
30
35
40
Ve/mL
Of course, Origin is good at fitting this, too (but maybe not—read on!). You can try various polynomial
fits.
7.0
B
Polynomial Fit of Data1_B
Upper 95% Confidence Limit
Lower 95% Confidence Limit
Upper 95% Prediction Limit
Lower 95% Prediction Limit
6.5
6.0
5.5
log10M
5.0
4.5
4.0
3.5
3.0
2.5
2.0
15
20
25
30
35
40
Ve/mL
In this case, I show a fifth-order polynomial. Origin computes confidence and prediction limits, too. The
arrows are discussed below.
Confidence limit: If you did the experiment 100 times, 95 of them would fall between the green
confidence limit lines drawn.
Prediction limit: You have a 95% chance that the next measurement would fall between the blue
prediction lines.
Of course, Origin provides all kinds of info about the fit, as shown on the next page. The most important
are the equation of fit, uncertainties in the various parameters to that equation, and the confidence
interval data. These are highlighted in the box below.
[11/23/2008 20:51 "/Graph1" (2454793)]
Polynomial Regression for Data1_B:
Y = A + B1*X + B2*X^2 + B3*X^3 + B4*X^4 + B5*X^5
Parameter
Value
Error
t-Value Prob>|t|
--------------------------------------------------------------------------A
184.88389
27.54607 6.71181 <0.0001
B1
-30.96298
5.38691 -5.74782 <0.0001
B2
2.13122 0.41545 5.12995 1.00793E-4
B3
-0.07323 0.0158 -4.63561 2.74872E-4
B4
0.00125 2.96308E-4
4.22659 6.41816E-4
B5
-8.53934E-6
2.19452E-6
-3.89121 0.0013
--------------------------------------------------------------------------R-Square(COD)
Adj. R-Square
Root-MSE(SD)
--------------------------------------------------------------------------0.99949 0.99933 0.02822 22
---------------------------------------------------------------------------
N
Parameter
LCI
UCI
--------------------------------------------------------------------------A
126.48888
243.27889
B1
-42.38271
-19.54326
B2
1.25051 3.01192
B3
-0.10672 -0.03974
B4
6.24228E-4
0.00188
B5
-1.31915E-5
-3.88718E-6
--------------------------------------------------------------------------ANOVA Table:
--------------------------------------------------------------------------Degrees of
Sum of Mean
Item
Freedom Squares Square F Statistic
--------------------------------------------------------------------------Model 5
24.85808 4.97162 6240.8574
Error
16
0.01275 7.96624E-4
Total
21
24.87082
--------------------------------------------------------------------------Prob>F
--------------------------------------------------------------------------<0.0001
--------------------------------------------------------------------------Fit and Residual data have been saved into Data1 worksheet.
STEP 3. Put the calibration results back into Excel because it’s easier to calculate in that program than it
is in Origin.
Best Fit Results
Value
Error
Value
Error
A
184.88389
27.54607
184.88389
27.54607
B1
-30.96298
5.38691
-30.96298
5.38691
B2
2.13122
0.41545
2.13122
0.41545
B3
-0.07323
0.0158
-0.07323
0.0158
B4
0.00125
2.96E-04
0.00125
2.96E-04
B5
-8.54E-06
2.19E-06
-8.54E-06
2.19E-06
Enter a Ve in mL
Best fit M
15 <--This cell is defined to be Ve
4.07E+09 <--This cell reads: =10^(M3+M4*Ve+M5*Ve^2+M6*Ve^3+M7*Ve^4+M8*Ve^5)
You can put any value you wish into Ve. For Ve = 25 mL, you get M = 3110….BUT THIS IS TOO LOW.
SOMETHING IS WRONG! Drawing arrows on the calibration clearly shows that Ve of 25 corresponds to
104.3  20,000. The problem is that Origin is not reporting out the data to the precision it uses internally
to compute the plot. This is actually the worst mistake I have seen Origin make. Maybe it has been
fixed in later versions.
This figure shows the plot YOU generate from Origin’s printed fit compared to the one ORIGIN generates
using the better numbers it has internally:
14
12
log10M
10
8
6
4
2
0
15
20
25
30
Ve/mL
35
40
45
So,that’s the hazard of trusting someone else for software. In the bad old days, we had our own
polynomial fit routine, which undoubtedly would have done this right. Today, we have Google, which
quickly leads us to a program named POLYSOLVE: http://www.arachnoid.com/polysolve/index.html
PolySolve produces these results, which seem more accurate as a reasonable M is found at Ve=25:
Best fit results from POLYSOLVE: http://www.arachnoid.com/polysolve/index.html
179.76398827770200000
A
-29.90223290944740000
B1
2.04508951275564000
B2
-0.06979938640524170
B3
0.00118523157897783
B4
-0.00000802259892519
B5
Ve
25
Best fit M from POLYSOLVE
25650
Nice of POLYSOLVE to provide so many significant figures, even though it fails to provide error
estimates. We could probably use those from Origin as a guide, but let’s just do the uncertainty
graphically to get an idea. The arrow drawn in the Origin figure with confidence limits shown above
gives us a low estimate of 104.3  20,000. Another arrow drawn to the upper confidence limit comes
closer to 104.5  30,000.
In consideration of the POLYSOLVE result, we might quote out, for Ve = 25 mL, M = 25,650 ± 5000.
Almost 20% uncertainty! GPC is one of those experiments that is more precise than accurate.