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is reflected in GPC by the detection of a Gaussian distribution of molecular weights foreach sample as a function of time. The curve can be described by a number of termsdepending on the methods used to detect the sample eluted from the column. In this case,we used a refractive index detector that can not tell us anything about a polymer exceptwhen it comes off the column relative to pS of known molecular weight. This allows usto translate elution time (sometimes referred to as elution volume) into molecular weightin pS units.Conversion for sample X = 1 -Ratio for sample XRatio for standard/initial sampleArea under anisole peakArea under monomer peak= Ratio for sample X
8102103104105106107108Molecular WeightCBAFree-RadicalATRPGPC StandardType1.841.041.05Mw/MnABCFigure 2: Samples of refractive index responses for polystyrene standards and samplesprepared by ATRP and conventional free radical polymerization along with thecorresponding measured polydispersities (from K. Matyjaszewski, et al., Science, 1996,272, 866).To describe the curve further, the polymer sample can be treated in two differentways and each treatment yields a different value of molecular weight: a number average(Mn) and weight average (Mw) molecular weight. Mntends to be close to the peak of thecurve and Mwis skewed to the high end of the curve. If these two numbers were equal,there would be only one single spike at one molecular weight and Mw/Mnwould be one.Otherwise Mw/Mnis used as an indication of how far apart the two values are and hence,how broad the distribution is. Therefore, the closer Mw/Mnis to one, the narrower thedistribution of molecular weights and the more well-defined the sample is by Mn. Figure2 shows a typical GPC trace for polymers prepared by conventional free radicalpolymerization and ATRP as well as the standards used to calibrate the GPC and theircorresponding polydispersities for illustration.1H NMR spectra for vinyl polymers are similar to those of small molecules with afew exceptions. Because the linewidth of a given resonance is inversely dependent onsegmental flexibility, highly constrained segments of large molecules (such as the mainchain of a polymer) tend to have extremely broad lines. Signals corresponding to the sidechains tend to be narrower because they are usually less constrained. This means that a