M.L.Hackert (with figures from Precesion Detectors and Wyatt Tech.) - PowerPoint PPT Presentation

M.L.Hackert (with figures from Precesion Detectors and Wyatt Tech.) and

Define “ Raleigh Ratio ” as R q = (i q / I q )(r 2 / (1 + cos 2 q )), and thus R q = [2p 2 n o 2 (dn/dC) 2 / l 4 N o ] CM , or R q = KCM . Note: Different experimental methods yield different types of experimentally arrived at “Molecular Weights.” Light scattering yields a “weight average” molar mass – solutions must be scrupulously clean since dust will contribute to average as very large molecules.  C i M i y /  C i M i y-1  N i M i /  N i  C i /  (C i /M i ) Number Average M n y = 0 Osmotic Press / F.Pt.  N i M i 2 /  N i M i  C i M i /  C i Weight Average M w y = 1 Light Scatt. / Sed. Eq.  N i M i 3 /  N i M i  C i M i 2 /  C i M i 2 “Z” Average M Z y = 2 Sedimentation Equil.

 C i M i y /  C i M i y-1  N i M i /  N i  C i /  (C i /M i ) Number Average M n y = 0 Osmotic Press / F.Pt.  N i M i 2 /  N i M i  C i M i /  C i Weight Average M w y = 1 Light Scatt. / Sed. Eq.  N i M i 3 /  N i M i  C i M i 2 /  C i M i 2 “Z” Average M Z y = 2 Sedimentation Equil. Examples: Sample 1 - 98% major component M = 30,000 + 2% dimer M ~ 60,000 Mn = [98(30,000) + 2(60,000)] / 98 + 2 = (2,940,000 + 120,000) / 100 = 30,600 Mw = [98(30,000) 2 + 2(60,000) 2 ] / (98(30,000) + 2(60,000) = (88,200,000,000 + 7,200,000,000) / (2,940,000 + 120,000) = 95,400,000,000 / 3,060,000 = 31,176 (Mw/Mn) Polydispersity = 31,176 / 30,600 = 1.02 Sample 2 - 98% major component M = 30,000 + 2% aggregate M ~ 600,000 Mn = [98(30,000) + 2(600,000)] / 98 + 2 = (2,940,000 + 1,200,000) / 100 = 41,400 Mw = [98(30,000) 2 + 2(600,000) 2 ] / (98(30,000) + 2(600,000) = (88,200,000,000 + 720,000,000,000) / (2,940,000 + 1,200,000) = 808,200,000,000 / 4,140,000 = 195,217 (Mw/Mn) Polydispersity = 195,217 / 41,400 = 4.72

• Fractionate sample • Combine LS measurement with SEC (size excludion chromotography)