1Chapter 4Molecular Weight and Molecular Weight Distribution华南理工大学童真mczatongscut.edu.cn2Significance and difficultiesz Birth certificate of polymer, = k Mz high molecular weight, 10000 Dal/molz property Tg= TgoK/Mz PolydisperseMW: water 18, benzene 78PE？Mn1 Dalton = (atomic weight of C)/12 NA34.1. Statistics of Molecular Weight of Polymers4 n: the total moles of macromolecules, w: total mass For i species, molecular weight Mi,mole ni, mass mi, mi= niMi Mole fraction of iNi,Weight fraction Wi, ii,nn mm= = ii,=iinmNWii1, 1= = NW4.1.1 Molecular weight averages5iiniiiii1=nMM NMWnM2ii iiiiiiiwmM nMM WMmnM= Number average molecular weightWeight average molecular weightViscosity average molecular weight()1 ii, =M WM KM w1, = =M M n1, =M Mn w0.5 1,5105平衡沉降A 102106光散射法A 103沉降平衡A 5104小角X射线衍射A 102沉降速度法A 103稀溶液粘度法R 102凝胶渗透色谱法R 10314z Special group at one or both ends of polymerz Determine the mass m and end-group n number of the polymerz M = m/nz limitation: definite molecular structure, M 0, good solvent, 1= 0, solvent, 1= z measured at different T, plot A2against T, determine temperature22z Tricaprotatecellulose in DMFz Poly(-methylstyrene) in benzene23z Measurement:z Solid theoretical foundation without other assumptions;z Absolute methodz Simple equipment, key point is the membrane and sensitive pressure measurementz Limitation: high Mn, low low Mn, leakage of the membrane24z Comparison of colligative methodssolution properties of 1% polymer with M = 2000015 cm solventOsmotic pressure210-3 oCFreezing point depression110-3 oCBoiling point elevation410-3mmHgVapor pressure loweringValueColligative property25z Instrument: Osmomat 090, Gonotec, Germanylower part: solvent, upper part: solutionseparated by membranemeasuring degree of vacuum in the lower part 0.1 mmHgMn: 100002X106Dol26Transmission lightIncident lightScattered lightrz Dipole in electromagnetic field vibrates at the same frequency scattering sourcez The electron polarization induces dipoles in atoms, molecules, particles 4.2.3 Light scattering27z Rayleigh scatteringa molecule with polarization degree in vacuumin yz plan42210142016sinIIr =I0I2142220242016sinIIr =()()4422 2 2 201 042 420088sin sin 1 cosII Irr =+=+()42240042081cosIIr =+42210142016sinIIr =in xy plan0: wavelength in vacuumFor daylight I1+ I2with I0/2For idea gas of molecules -blue sky28z Scattering in liquid: difference in polarization degree 000142AM nnNC = = and 0 : dielectric constant of solution and solvent = n 2, n : diffractive index, = NAC/M : molecule number in unit volume( )04=For infinitely dilute solutions(n/C)0: increment of n for infinite dilute solutions 29z Rayleigh ratio for daylight2202(1 co s )IRrI=+z Rayleigh ratio for perpendicularly polarized light20IRrI=R KMC=Optical constant：222040A04 nKnNC=()422042081cosIIr =+from000142AM nnNC = = = NAC/MFor dilute solution30z Incident light I0: perpendicularly polarizedz Scattering intensity I at distance r from per unit volume of solution:2200400A() 224nRTI= n CINr C /C : osmotic pressure of solutionz Density and concentration fluctuation in a liquid induces light scatteringz Einstein electromagnetic scattering theory-concentration fluctuation related to chemical potentials z If scattering object smaller than /20, no interference among scattered light312211, 2 = + = + CRT AC RT ACMCM22200420024112AnInCINr CA CM= +Rayleigh ratio：20IRrI=Optical constant：222040A04 nKnNC=212=+KCACRMTherefore32z Using an organic solvent with known Rto determine r2/I0z Measure n/ Cindependentlyz Measure I, determine Mfrom the intercept and A2from the slopez If the incident light is unpolarized212=+KCACRM2202(1 )=+IRrcon ICKCR1M2slope 2= A20IRrI=33()ii900iii wiiCCMRKCMKCMKCCKC WM KCM= =Light scattering weight average molecular weightz 1/04,z MCz Limitatione.g., PIB in benzeneiiiCWC=00nC34null0OB ,()2sin2rrssr= =nullnullnulliLight path difference :()2211-3 = +gPqRz If scattering object larger than /20, interference must be taken into account-Debye theoryDebye theory interference factorScattering vector4sin2 =nqA BCOsnullnull0sdetector35()2 W12KCA CRMP=+2111-= + + +xxxSeries expansion:2222g22 W1161sin232KC nR ACRM= + + +2222g216() 1 sin32= +nPR2gR: squared average radius of gyration36z Zimm Plot2 W 012KCACRM=+2222g2 WC01161sin32KC nRRM =+ + null2222g22 W1161sin232KC nR ACRM= + + +Plot against CPlot against sin2/2Result from LS: Mw, A2, 3701. CY202. sin2CY 03. Y04. YC222g216slope =3nRslope = 2A2=KCYR2sin2+aCC1C2C3C41