Determination of dn/dc by Multi-Point RI Method
by Dr. Max Haney, Viscotek Corp.
IntroductionThe value of the polymer specific refractive index, dn/dc, is critical for accurate molecular weight calculations using a light scattering detector. This can easily be determined from a plot of RI detector peak area vs. sample concentration at fixed injection volume, or alternately from a plot of RI detector peak area vs. injection volume at fixed sample concentration. This method can be used either in GPC, or for direct injection modes. The slope yields an accurate determination of dn/dc and the graph provides a visual estimate of the precision of measurement and confirmation of the linear response of the RI detector.
Data required:•A method file. Specification must include refractive index of solvent and RI detector calibration.
•Two or more data files of the same sample run under the same flow rate conditions and solvent.
•The flow rate, sample concentrations, and injection volumes must be specified accurately in the run parameters of the data files. Any absolute error in these values (and the RI detector calibration) will reflect directly in the absolute accuracy of the determination of dn/dc.
Basic equation
of the RI Detector:The integrated peak area is related to five variables as follows.
[1] RI.Area = RI.Cal dn n0 dcV inj Conc
A sixth variable, flow rate, is implicit in the peak area definition.
[1a] RI.Area =ΔV&Simga;i RIi =Flow RateData Rate 60&Simga;i RIi
Units and Definitions:n0 is the refractive index of the solvent at the detector temperature.
RIi is the RI signal in mv at time ti.
ΔV is the flow volume increment, i.e., volume of solvent between data points in the detector.
Data Rate is the rate of data acquisition in points per second. Flow Rate is in mL/minute.
V.inj is the volume of sample injected in mL.
Conc is the concentration of the sample injected in units of g/mL, so the data file concentration (mg/mL) must be divided by 1000 before inserting in equation 1.
Procedure 1. Variable ConcentrationIf we fix the injection volume and inject samples of variable concentration, the RI peak area can be measured and plotted versus sample concentration. The slope of this plot determines value of a composite of variables as follows.
[2] Slope =ΔRI.Area = RI.Cal dnΔConc n0 dcV.inj
Assuming RI.Cal, n0, and V.inj are known a priori, the dn/dc is thereby calculated from the measured slope, i.e., the change in peak area per unit change in sample concentration.
Procedure 2. Variable Injection VolumeIf we fix the sample concentration and inject samples of variable volume, the RI peak area can be measured and plotted versus injection volume. The slope of this plot determines the variable composite as follows.
[3] Slope =ΔRI.Area = RI.Cal dnΔV.inj n0 dcConc
Assuming RI.Cal, n0, and Conc are known a priori, the dn/dc is thereby calculated from the measured slope, i.e., the change in peak area per unit change in injection volume.
click the image to enlarge
Figure 1: dn/dc Determination Using Variable Concentration |
Implementation in SoftwareThe procedures are best implemented through the existing feature of OmniSEC GPC software called Trend View.
DiscussionOf course, equation 1 can be used to determine a value for dn/dc from a single measurement of RI peak area. This can be done in OmniSEC by setting the dn/dc value to zero in the Method. The multi-point plot, though, has some distinct visual advantages over this single point method. One can inspect it to see if it behaves properly:
•Do all of the points fall on a straight line? Curvature would be suspicious. A single bad point could be eliminated.
•Does the line intercept the axes origin?
It is sometimes thought that one can determine dn/dc by this multi-point method by simply making dilutions of a solution of unknown concentration so that the relative ratios of the different concentrations are known, but not the absolute values thereof. This is not true. Both procedures require absolute values for sample concentrations and injection volumes.
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