Gel Permeation Chromatography Polymers and Coatings Laboratory California Polytechnic State University Gel permeation chromatography (GPC) has become the most widely used technique for determination of molecular weight distributions. Gel permeation chromatography separates polymers on the basis of molecular size. The smaller polymers spend time travelling through the pores of the gel and are eluted later than the larger polymers which spend less time in the pores.thus elution volume i(or elution time) is proportional to molecular size. It can be shown that hydrodynamic volume is proportional to the product [η]m where [η] is the intrinsic viscosity and M is the molecular weight (see Allcock and Lampe, Contemporary Polymer Chemistry, 2nd ed., pp 398-403). A plot of log [η]m versus elution volume (or elution time) for a particular solvent, column, and instrument provides a universal calibration curve which can be used for any polymer in that solvent so long as the Mark-Houwink constants are known for the polymer-solvent pair. Such a calibration curve is obtained by determining the retention volumes (or times) of monodisperse polymer standards. Once the calibration is obtained, the gel permeation chromatogram of any other polymer can be obtained in the same solvent and the molecular weight distribution determine from the calibration. If the polymer to be analyzed is the same polymer as that used in obtaining the calibration, a plot of log M versus elution volume (or time) can be used. Calibration Below are given data of elution times (t) obtained in a GPC for monodisperse polystyrene standards in tetrahydrofuran (THF). The intrinsic viscosities for the solutions are also given. A plot of log [η] versus log M is shown below giving determination of the Mark- Houwink constants for polystyrene in THF. M t/s [n] log M log[n] 867000 298 206.7 5.938 2.3153 411000 314 125 5.6138 2.0969 173000 354 67 5.238 1.8261 98200 373 43.6 4.9921 1.6395 51000 399 27.6 4.7076 1.4409 19900 438 14 4.2989 1.1461 10300 468 8.8 4.0128 0.9445 5000 507 5.2 3.699 0.716 1
Mark-Howink Constant Determination for Polystyrene in THF 3 y = - 1.9335 + 0.7167x R = 1.00 log[n] = log K + a log M a = 0.72 K = 0.0117 2 log [n] 1 0 3 4 5 6 log M The universal calibration curve and plot of log M versus elution time based on these data are given below: 9 Universal Calibration 8 y = 16.5457-0.0339x + 1.965e-5x^2 R = 1.00 log ([n]m) 7 6 5 4 250 350 450 elution time/s 2
Polystyrene/THF Calibration 6.0 5.5 y = 10.7825-0.0199x + 1.157e-5x^2 R = 1.00 5.0 log M 4.5 4.0 3.5 250 350 450 elution time/s Unknown Analysis A polystyrene sample was analyzed using this same GPC. The chromatogram obtained is given below: 120 Polystyrene Unknown in THF 100 80 height 60 40 20 0 200 300 400 500 t/s Values of height were taken at various times were taken from this chromatogram (points shown on chromatogram) and the data are given below: 3
time/s height log M M height/m height*m 275 2 6.18498125 1.53E+6 1.31E-06 3062043 285 5 6.05077325 1.12E+6 4.45E-06 5620090 295 10 5.91887925 8.30E+5 1.21E-05 8296201 305 20 5.78929925 6.16E+5 3.25E-05 1231208 315 30 5.66203325 4.59E+5 6.53E-05 1377695 325 50 5.53708125 3.44E+5 0.000145 1722078 335 70 5.41444325 2.60E+5 0.00027 1817779 345 95 5.29411925 1.97E+5 0.000483 1870004 355 105 5.17610925 1.50E+5 0.0007 1575062 365 110 5.06041325 1.15E+5 0.000957 1264173 375 100 4.94703125 8.85E+4 0.00113 8851793 385 90 4.83596325 6.85E+4 0.001313 6168872 395 75 4.72720925 5.34E+4 0.001406 4001939 415 55 4.51664325 3.29E+4 0.001674 1807199 425 35 4.41483125 2.60E+4 0.001347 909702.3 435 15 4.31533325 2.07E+4 0.000726 310044.8 445 3 4.21814925 1.65E+4 0.000182 49575.89 Sum 870 0.010446 1.48E+08 Mn = Sum(heights)/sum(height/M) = 83284.52 Mw = Sum (height*m)/sum(heights) = 169721.2 Mw/Mn = 2.04 The M values in the table were obtained by using the calibration equation: log M = 10.7825-0.0199 t + 1.157 E-5 t 2 as obtained from the polystyrene calibration. The determination of the number average (M n ) and weight average (M w ) molecular weight from this data is also shown. The data are probably accurate to no more than two significant figures. The experimental values obtained are M w = 8.3x10 4 g/mol and M n = 1.7x10 5 g/mol. Values of height/m and height*m are determined and sums of the heights, height/m and height*m are obtained. The values of M n and M w are obtained from ratios of these sums. The polydispersity (M w /M n ) is also obtained. Curves of mass fraction and mol fraction versus M obtained from these data are given below. These are the true molecular weight distribution curves. The height was assumed to be proportional to (actually equal to) the mass of polymer. 4
M massfr. mols mol fr 1.53E+06 0.0023 1.3E-06 0.0001 1.12E+06 0.0057 4.4E-06 0.0004 8.30E+05 0.0115 1.2E-05 0.0012 6.16E+05 0.023 3.2E-05 0.0031 4.59E+05 0.0345 6.5E-05 0.0063 3.44E+05 0.0575 0.00015 0.0139 2.60E+05 0.0805 0.00027 0.0258 1.97E+05 0.1092 0.00048 0.0462 1.50E+05 0.1207 0.00070 0.067 1.15E+05 0.1264 0.00096 0.0916 8.85E+04 0.1149 0.00113 0.1081 6.85E+04 0.1034 0.00131 0.1257 5.34E+04 0.0862 0.00141 0.1346 3.29E+04 0.0632 0.00167 0.1602 2.60E+04 0.0402 0.00135 0.1289 2.07E+04 0.0172 0.00073 0.0695 1.65E+04 0.0034 0.00018 0.0174 Polystyrene MW Distribution (mass fractions) 0.15 0.10 mass fraction 0.05 0.00 0e+0 4e+5 8e+5 1e+6 2e+6 Molecular Weight 5
Polystyrene MW Distribution (mol fractions) 2e-1 mol fraction 1e-1 0e+0 0e+0 2e+5 3e+5 4e+5 molecular weight If a polymer other than polystyrene had been studied, the universal calibration curve would have been used to obtain the molecular weight of each fraction using the Mark- Houwink constants. [η]m = (KM a )M = KM 1+a so M = ([η]m/k) 1/(1+a) where [η]m is obtained from the calibration curve at each elution time. Experimental You will use monodisperse polystyrene standards to obtain a universal calibration curve for the GPC. Make up solutions of approximately 0.5% by weight of the samples in THF. You can combine 3 different molecular weight standards in one solution. The instructor will instruct you in how to use the GPC. Determine the retention times and retention volumes for the standards. Using the known Mark-Houwink constants for PS in THF, make a universal calibration curve for the instrument. Make up 0.5% solutions of whatever polymer you are to analyze in THF. Run the GPC of the sample. The instructor will show you how to transfer the file to Excel for processing. Obtain M w, M n, the polydispersity index and plot the mol fraction and mass fraction distribution curves. Include copies of all relevant work and results in your notebook. See next page for details on operation of HP GPC system. 6
GPC Analysis Using the HP HPLC System 1. Make up a solution of your polymer in THF (approximately 0.5% by weight). If necessary, filter the solution through a 0.2 micron syringe filter. 2. Check solvent reservoir. If necessary, add HPLC-grade THF. Remove the cap from the solvent reservoir bottle so you can fit a plastic funnel in the top. Add THF until the bottle is nearly full. Do not overfill! Replace the cap and degas with helium for at least fifteen minutes. Allow the solution to sit for five minutes before starting pump. Check solvent waste bottle to be sure it is not too full. 3. Start HP Chemstation program. Turn on system and adjust flow rate to 2 ml per minute. Allow baselines of RI and UV/VIS detectors to stabilize. Be sure to flush the RI detector for at least five minutes then switch off flush. 4. Set up sample using software. Obtain a 50 microliter sample using the GPC syringe. Be sure you are using a syringe with a flat tip. Rinse the syringe twice with the sample and put the waste into a waste vial. Inject 50 microliters into the injection valve. With the syringe still in the valve, turn valve to start run. Remove the syringe and rinse twice with THF. 5. After all peaks are recorded, stop run (F8). Shut down the GPC if no one else will be using it that day. In any event, stop the pump unless you need to do another run. 6. Open GRAMS 32 and open the GPC file you just obtained (usually you want the ADC file -- this is the RI detector). Adjust the baseline using a two point fit, forcing points to data, zero and level, as shown by instructor. Export as Data, open Excel and paste file data into a new worksheet. 7. Examine the Excel data and remove unwanted data so only the peaks of interest remain. 8. Analyze the data to obtain M n, M w, the polydispersity, and the entire molecular weight distribution curve. Either the mass fraction or mole fraction (or both) can be plotted versus molecular weight. 7