山东大学：《物理化学》课程教学资源（讲义资料）8.8.2 Dynamic Properties of colloids

8.8.2 Dynamic Properties of colloids Out-class reading Levine pp 402-405 13.6 Colloids

8.8.2 Dynamic Properties of colloids Out-class reading: Levine pp. 402-405 13.6 Colloids

8.8.2 Dynamic properties of colloids (1) Brownian motion Robert Brown (1773-1858) Vitality? In 1827, the botanist Robert Brown published a study "a brief account on microscopic observation on the particles contained in the pollen of plant. He reported an irregular motion of pollen grains

(1) Brownian motion In 1827, the botanist Robert Brown published a study “A brief account on microscopic observation on the particles contained in the pollen of plant”. He reported an irregular motion of pollen grains. Vitality? 8.8.2 Dynamic properties of colloids

8.8.2 Dynamic properties of colloids (1)Brownian motion Wiener suggested that the brownian In 1903, Zsigmondy studied Brownian motion arose from molecular motion motion using ultramicroscopy and found T F∝ independent of the chemical nature of the Unbalanced particles collision from medum For particle with diameter> 5 um,no molecules Brownian motion can be observed Although motion of molecules can not be observed directly, the Brownian motion gave indirect evidence for it

In 1903, Zsigmondy studied Brownian motion using ultramicroscopy and found： For particle with diameter > 5 m, no Brownian motion can be observed. Wiener suggested that the Brownian motion arose from molecular motion. Unbalanced collision from medium molecules Although motion of molecules can not be observed directly, the Brownian motion gave indirect evidence for it. (1) Brownian motion 8.8.2 Dynamic properties of colloids r T  1 r   independent of the chemical nature of the particles

8.8.2 Dynamic properties of colloids (2) Diffusion and osmotic pressure 1905 Einstein proposed that D kRT rT f=frictional coefficient For spheric colloidal particles, XX Concentration gradient f= tnr Stokes'law Fickian first law for diffusion RT Einstein first law for D L6丌 r diffu uSIon D

(2) Diffusion and osmotic pressure x Fickian first law for diffusion Concentration gradient = dn dc D dt dx  = − 1905 Einstein proposed that: Lf RT f k T D = = B For spheric colloidal particles, f = 6r Stokes’ law f = frictional coefficient L r RT D 6 1 = Einstein first law for diffusion 8.8.2 Dynamic properties of colloids

8.8.2 Dynamic properties of colloids (2)Diffusion and osmotic pressure Atoms and molecules had long been theorized as the In 1908, Perrin found that, for gamboge constituents of matter. Albert Einstein published a sol with diameter of 0.212 um, n=0.0011 paper in 1905 that explained in precise detail how the motion that brown had observed was a result of the Pa.s. After 30s of diffusion the mean pollen being moved by individual water molecules diffusion distance is 7.09 cm s-I making one of his first big contributions to science This explanation of Brownian motion served as D、RT1 convincing evidence that atoms and molecules exist L tnr and moves constantly. which was further verified experimentally by Jean Perrin in 1908 He calculated Avgadro's constant from this equation Because of the Brownian motion osmotic pressure also originates L=6.5×10 Which confirms the validity of Einstein- RT Brownian motion equation

In 1908, Perrin found that, for gamboge sol with diameter of 0.212 m,  = 0.0011 Pas. After 30 s of diffusion, the mean diffusion distance is 7.09 cm s -1 . L = 6.5  1023 Because of the Brownian motion, osmotic pressure also originates RT V n  = Which confirms the validity of Einstein￾Brownian motion equation (2) Diffusion and osmotic pressure 8.8.2 Dynamic properties of colloids Atoms and molecules had long been theorized as the constituents of matter. Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules, making one of his first big contributions to science. This explanation of Brownian motion served as convincing evidence that atoms and molecules exist and moves constantly, which was further verified experimentally by Jean Perrin in 1908. L r RT D 6 1 = He calculated Avgadro’s constant from this equation

8.8.2 Dynamic properties of colloids (2)Diffusion and osmotic pressure 2Dt C E D r RT t D Z2x B 12x L nr L rnr Einstein-Brownian motion equation Xc x(C1-C2) The above equation suggests that if x could be determined using ultramicroscope, the diameter of the colloidal particle can be calculated. The dc=D C mean molar weight of colloidal particle can also dx x determined according to m

F A B C D c1 c2 E ½ x ½ x x c c dx dc ( ) 1 − 2  =              = −         = − ( ) 2 1 2 1 2 1 n xc1 xc2 x c1 c2 x c c D dx dc D ( ) 1 − 2  =      ( ) 2 ( ) 1 1 2 1 2 t x c c x c c D = − − − x = 2Dt r t L RT x 3 = Einstein-Brownian motion equation The above equation suggests that if x could be 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: M r L 3 3 4 = L r RT D 6 1 = (2) Diffusion and osmotic pressure 8.8.2 Dynamic properties of colloids

8.8.2 Dynamic properties of colloids (3 )Sedimentation and sedimentation equilibrium Mean concentration:(c-12 dc D)sedimentation equilibrium The number of colloidal particles diffusion Buoyant (c-)AchL 2 Di Diffusion force 丌=CRT Gravitational dn= rTdc orce b h The diffusion force exerting on each colloidal particle rTdc dc c-)AdhL cdhL

(3) Sedimentation and sedimentation equilibrium diffusion 1) sedimentation equilibrium Gravitational force Buoyant force a a’ b b’ c dh Mean concentration: (c - ½ dc) The number of colloidal particles: AdhL dc c ) 2 ( − Diffusion force:  = cRT d = RTdc The diffusion force exerting on each colloidal particle cdhL RTdc AdhL dc c Ad f d = − = ) 2 (  8.8.2 Dynamic properties of colloids

8.8.2 Dynamic properties of colloids (3 )Sedimentation and sedimentation equilibrium Heights needed for half-change of concentration he gravitational force exerting on each particle: systems Particle diameter △h 4 r/nm (0-P0)g 0.27 skI Highly dispersed 1.86 2.15m Au SOl Micro-dispersed 8.53 2.5cm InC LI Au sol (p-p°)(h2-h1)g RT Coarsely dispersed 186 0.2m uSo」 Altitude distribution Brownian motion is one of the important reasons for the stability of colloidal system

The gravitational force exerting on each particle: f g r ( )g 3 4 0 3 =   −  g d f = f h h g RT LV c c ln ( )( ) 2 1 0 2 1 =  −  − Altitude distribution systems Particle diameter r / 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 Heights needed for half-change of concentration Brownian motion is one of the important reasons for the stability of colloidal system. (3) Sedimentation and sedimentation equilibrium 8.8.2 Dynamic properties of colloids

8.8.2 Dynamic properties of colloids (3 )Sedimentation and sedimentation equilibrium 2r2( )g 7 2) Velocity of sedimentation Gravitational force exerting on a particle Times needed for particles to settle 1 cm 4 radius time 8=37(- po)8 10 um 5.9s When the particle sediments at velocity v μm 98s the resistance force is 100nm 16h f:= fv= 6tn 10 nm 68d When the particle sediments at a constant velocity 1 nm 19y g For particles with radius less than 100 nm sedimentation is impossible due to convection and vibration of the medium

2) Velocity of sedimentation Gravitational force exerting on a particle: f g r ( )g 3 4 0 3 =   −  When the particle sediments at velocity v, the resistance force is: f fv rv F = = 6 When the particle sediments at a constant velocity F g f = f  r   g v ( ) 9 2 2 0 − = radius time 10 m 5.9 s 1 m 9.8 s 100 nm 16 h 10 nm 68 d 1 nm 19 y Times needed for particles to settle 1 cm For particles with radius less than 100 nm, sedimentation is impossible due to convection and vibration of the medium. (3) Sedimentation and sedimentation equilibrium 8.8.2 Dynamic properties of colloids

8.8.2 Dynamic properties of colloids (4)ultracentrifuge: Centrifuge acceleration Sedimentation for colloids is usually a=o x o-xM very slow process. The use of a centrifuge C can greatly speed up the process by F=o2xM increasing the force on the particle far above that due to gravitation alone xMo=MvPpoox 1924, Svedberg invented ultracentrifuge the r.p. m of which can attain 100 160 For sedimentation with constant velocity thousand and produce accelerations of the order of 106g dc Mox(1-vpo)dx RT

(4) 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. 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 = r 2 Fc = xM r 2 Fc = xM F xM M v x b 2 0 r 0 2 = =   dt dx F Lf d = For sedimentation with constant velocity v dx RT M x c dc (1 )0 2 r   = − 8.8.2 Dynamic properties of colloids