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8.8 Properties of colloids 8.8.1 Optical property of colloids 8.8.1 Tyndall effect and its applications (1) Tyndall effect 1857, Faraday first observed the optical properties of Au sol 1871, Tyndall found that when an intense beam of light is passed through the sol, the scattered light is observed at right angles to the beam. sol solution Dyndall Effect: particles of the colloidal size can scatter light. (2) Rayleigh scattering equation: The greater the size (V) and the particle number (v) per unit volume, the stronger the scattering intensity. light with shorter wave length scatters more intensively. 9 vV I I0 24 r 2 2 2 2 n n 1 cos n 2n 2 2 2 2 2 1 2 1 I K cV 2 4 Applications 1. Colors of scattering light and transition light: blue sky and colorful sunset 2. Intensity of scattering light: wavelength, particle size. Homogeneous solution? 3. Scattering light of macromolecular solution? 4. Determine particle size and concentration? Distinguishing true solutions from sols (3) Ultramicroscope Richard A. Zsigmondy 1925 Noble Prize Germany, Austria, 1865-04-01 - 1929-09-29 Colloid chemistry (ultramicroscope) principle of ultramicroscope 1): Particle size For particles less than 0.1 m in diameter which are too small to be truly resolved by the light microscope, under the ultramicroscope, they look like stars in the dark sky. Their differences in size are indicated by differences in brightness. The pictures are reproduced from the Nobel Prize report. 2) Particle number: can be determined by counting the bright dot in the field of version; 3) Particle shape: is decided by the brightness change when the sol was passing through a slit. Slit-ultramicroscope Filament, rod, lath, disk, ellipsoid 4) Concentration and size of the particles I K cV 2 4 For two colloids with the same concentration: I1 V12 2 I2 V2 For two colloids with the same diameter: I1 c1 I2 c2 From: Nobel Lecture, December, 11, 1926 8.8.2 Dynamic properties of colloids (1) Brownian Motion: 1827, Robert Brown observed that pollen grains executed a ceaseless random motion and traveled a zig-zag path. In 1903, Zsigmondy studied Brownian motion using ultramicroscopy and found that the motion of the colloidal particles is in direct proportion to Temperature, in reverse proportion to viscosity of the medium, but independent of the chemical nature of the particles. Vitality? For particle with diameter > 5 m, no Brownian motion can be observed. Wiener suggested that the Brownian motion arose from molecular motion. Although motion of molecules can not be observed directly, the Brownian motion gave indirect evidence for it. Unbalanced collision from medium molecules (2) Diffusion and osmotic pressure Fickian first law for diffusion dm dc DA dt dx x Concentration gradient Concentration gradient Diffusion coefficient 1905 Einstein proposed that: kBT RT D f Lf f = frictional coefficient For spheric colloidal particles, f 6r RT 1 D L 6r Stokes’ law Einstein first law for diffusion C c1 A c2 E D ½x B ½x F 1 1 1 m xc1 xc2 x(c1 c2 ) 2 2 2 (c1 c2 ) dc D D x dx dc (c1 c2 ) x dx (c1 c2 ) 1 D t x(c1 c2 ) 2 x x 2 Dt x RT t L 3r Einstein-Brownian motion equation x RT t L 3r The above equation suggests that if x was determined using ultramicroscope, the diameter of the colloidal particle can be calculated. The mean molar weight of colloidal particle can also be determined according to: 4 3 M r L 3 Perrin calculated Avgadro’s constant from the above equation using gamboge sol with diameter of 0.212 m, = 0.0011 Pas. After 30 s of diffusion, the mean diffusion distance is 7.09 cm s-1 L = 6.5 1023 Which confirm the validity of Einstein-Brownian motion equation Because of the Brownian motion, osmotic pressure also originates n RT V (3) Sedimentation and sedimentation equilibrium 1) sedimentation equilibrium diffusion Buoyant force Mean concentration: (c - ½ dc) Gravitational force b’ b a dh c The number of colloidal particles: a’ dc (c ) AdhL 2 Diffusion force: cRT d RTdc The diffusion force exerting on each colloidal particle Ad RTdc fd dc cdhL (c ) AdhL 2 The gravitational force exerting on each particle: fg 4 3 r ( 0 ) g 3 f g fd c1 LV ln ( 0 )( h2 h1 ) g c2 RT Altitude distribution c1 LV ln ( 0 )( h2 h1 ) g c2 RT Heights needed for half-change of concentration systems Particle diameter / nm h O2 0.27 5 km Highly dispersed Au sol 1.86 2.15 m Micro-dispersed Au sol 8.53 2.5 cm Coarsely dispersed Au sol 186 0.2 m This suggests that Brownian motion is one of the important reasons for the stability of colloidal system. 2) Velocity of sedimentation Gravitational force exerting on a particle: 4 3 f g r ( 0 ) g 3 When the particle sediments at velocity v, the resistance force is: f F fv 6rv When the particle sediments at a constant velocity 2 r 2 ( 0 )g v 9 fF fg 2 r 2 ( 0 )g v 9 Times needed for particles to settle 1 cm radius time 10 m 5.9 s 1 m 9.8 s 100 nm 16 h 10 nm 68 d 1 nm 19 y For particles with radius less than 100 nm, sedimentation is impossible due to convection and vibration of the medium. 3) ultracentrifuge: Sedimentation for colloids is usually a very slow process. The use of a centrifuge can greatly speed up the process by increasing the force on the particle far above that due to gravitation alone. revolutions per minute 1924, Svedberg invented ultracentrifuge, the r.p.m of which can attain 100 ~ 160 thousand and produce accelerations of the order of 106 g. Centrifuge acceleration: a x 2 Fc 2 xM r Fc xM r 2 Fb xM 0 M r v 0 x 2 2 dx Fd Lf dt For sedimentation with constant velocity c2 dc M r x c1 (1 v 0 )dx M r c RT (1 v 0 ) 2 ( x22 x12 ) 2 2 RT ln Therefore, ultracentrifuge can be used for determination of the molar weight of colloidal particle and macromolecules and for separation of proteins with different molecular weights. rotor light Quartz window balance cell Sample cell bearing To optical system The first ultracentrifuge, completed in 1924, was capable of generating a centrifugal force up to 5,000 times the force of gravity. Theodor Svedberg 1926 Noble Prize Sweden 1884-08-30 - 1971-02-26 Disperse systems (ultracentrifuge) Svedberg found that the size and weight of the particles determined their rate of sedimentation, and he used this fact to measure their size. With an ultracentrifuge, he determined precisely the molecular weights of highly complex proteins such as hemoglobin (血色素). Why does Ag sol with different particle sizes show different color? Out-class reading: Levine pp. 402-405 colloidal systems lyophilic colloids lyophobic colloids sedimentation Emulsion Gels