Molecular weight of polymers Molecular weight of polymers
Transcription
Molecular weight of polymers Molecular weight of polymers
Molecular weight of polymers Molecular weight of polymers Light scattering Light scattering Electromagnetic radiation 대기중에 부유하고 있는 입자상 물질에 빛을 조사하면 입자상 물질에 의해 빛이 산란하 게 된다. 물리적 성질이 동일한 입자상 물질의 빛을 조사하면 산란광의 양은 질량 농도에 비례하게 된다. 이러한 원리를 이용하여 산란광의 양을 측정하고 그 값으로부터 입자상 물질의 양을 구하는 방법이다 Transmission Reflection Absorption Scattering - transmission: transmitted radiation passes through the medium unaltered. - absorption: energy from the incident beam is taken up, resulting in: (1)heating, (2) re-emitting at another wavelength (fluorescence, phosphorescence), (3)supporting chemical reactions. - scattering: scattering is non-specific, meaning the incident radiation is entirely re-emitted in all direction with essentially no change in wavelength. Scattering results simply from the optical inhomogeneity of the medium. - reflection: scattering at the surface of a matter (not considered here) - Scattering center = small volumes of material that scatters light. ex. individual molecule in a gas - If the radius of the scattering center, a, is much smaller than the wavelength of the incident light (a < 0.05λo, less than 5% of λo); → When the oscillating electric field of the incident beam interacts with the scattering center, it induces a synchronous oscillating dipole, which re-emits the electromagnetic energy in all directions.(Rayleigh scattering) - ex. dissolved polymer coils of moderate molar mass radiated by VISIBLE light 88 89 Molecular weight of polymers Molecular weight of polymers Light scattering Light scattering : point scattered, d<<λ Rayleigh scattering A. The intensity of scattered light or turbidity() is depend on : For ideal polymer solution The incident radiation is entirely reemitted in all direction with essentially no change in wavelength (Iθ1 = Iθ2) a. size b. concentration For non-ideal polymer solution Light Scattering Data Processing c. polarizability Kc /R d. refractive index e. angle Slope=2A 2 f. solvent and solute interaction Intercept=1/M 90 Concentration, c : Rayleigh ratio (small particles) K : a system constant that depends only the solvent properties c : concentration M : MW 91 Molecular weight of polymers Molecular weight of polymers Light scattering Light scattering RGD(Rayleigh-Gans-Debye) scattering: In case of polymer (a /20, Rayleigh limit), there is inference between scattered light from the different part of the same molecule → Correction by scattering factor P(θ) is necessary Effect of particle size on intensity distribution 330 320 310 300 340 3502.0 0 10 20 1.5 60 70 0.5 280 270 80 0.0 90 260 Iθ1 ≠ Iθ2 (P1 ≠ P2) 100 250 Different part of more extended domain (B) produce scattered light which interferes with that produced by other part (A) constructive or destructive 240 230 220 210 40 50 1.0 290 30 110 200 190 For larger particles, intensity is reduced at all angles except zero. 180 170 160 120 130 140 150 : Rayleigh ratio (small particles) : Rayleigh ration (large particles) : : scattering factor (<1), function of size and shape of scattering volume Small Particles Large Particles Now we start seeing the angle dependence of the scattered light ! Correction by P(θ) 92 93 Molecular weight of polymers Molecular weight of polymers Light scattering : Zimm Plot Light scattering : Zimm Plot To get Mw, we do two extrapolations. First, plotting Kc/Rθ as a function of sin2(θ/2) at constant c gives a straight line with the following slope and intercept: For random coil polymer Final Rayleigh equation for random coil polymer Kc 1 R c 0 θ θ 0 M w Next we plot the intercepts of the plots as a function of concentration. The resulting plot should be a straight line with : 94 95 Molecular weight of polymers Molecular weight of polymers Light scattering : Zimm Plot Light scattering : Zimm Plot Plot Kc/Rθ vs sin2(θ/2)+kc, where k is a constant. k is chosen to spread out the plot and give equal weights to each variable - There will be experimental points at all grid points except along the lower line (the θ = 0 line) and the left-most line (the c = 0) line. - Connecting all the grid lines and extrapolating to the lowerleft corner, the intercept point gives the molecular weight (intercept = 1/MW). The lines labeled θ1, θ2,… are lines at constant θ with The lines labeled c1, c2,… are lines at constant concentration with 1 Mw Double extrapolation 96 97 Molecular weight of polymers Molecular weight of polymers Light scattering : Zimm Plot Light scattering : Zimm Plot c c c5 c1 c2 3 4 θ4 θ3 Measured at various θ & c θ=0 θ6 θ5 c=0 θ2 θ1 Extrapolated to θ=0 kc1 kc2 kc3 kc4 kc5 sin2(θ1/2) = kc (at θ=0) 98 sin2(θ2/2) Measured at various θ & c Extrapolated to c=0 =sin2(θ/2) (at c=0) sin2(θ3/2) sin2(θ4/2) sin2(θ5/2) sin2(θ6/2) 99 Molecular weight of polymers Molecular weight of polymers Light scattering : Zimm Plot Light scattering : Zimm Plot -3 c=0 c1 c5 c2 c3 c4 3.5x10 θ6 -3 θ3 θ2 θ1 θ=0 -3 2.5x10 Measured at various θ & c Kc/R θ4 0.845 3.0x10 θ5 Extrapolated to c=0 & θ=0 c 0.50 2.0x10 -3 Mw = 704k Rg = 35.8 nm -3 1.0x10 Mw 1.203 mg/mL -3 1.5x10 1 1.013 -4 3 2 A = 4.26 x 10 cm ·mol/g -4 5.0x10 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 2 100 sin () + 100c 101