Colloid chemistry chapter 7 kinetic properties of colloids

COLLOID CHEMISTRY Chapter – Kinetic properties of colloids Dr Ngo Thanh An Brownian motion Diffusion • Particles spontaneously diffuse from a region of higher concentration to a region of lower concentration until the concentration of the system is uniform throughout • Diffusion is a direct result of Brownian movement 2 Diffusion No of atoms crossing area A per unit time dn dc  DS dt dx Diffusion coefficient/ diffusivity Cross-sectional area Concentration gradient Matter transport is down the concentration gradient Fick’s I law A Flow direction  D is known as the diffusion coefficient (area per unit time)  The negative sign is because diffusion occurs in the direction of decreasing concentration 2 Diffusion Diffusion Sedimentation Sedimentation in gravitational fiel Let us represent the gravity, buoyant and drag forces by Fg , Fb and Fd , respectively Let the mass of the particle be m, and its velocity relative to the fluid be v The resultant force on the particle is Fg - Fb - Fd The acceleration of the particle is dv/dt Therefore, we can write the following force balance dv m  Fg  Fb  Fd dt Fg mg Sedimentation Sedimentation in gravitational fiel • By Archimedes’ principle, the buoyant force is the product of the mass of fluid displaced by the particle and the acceleration under gravity mg Fb  p where ρ is the density of the liquid and ρp is the density of the particle The drag force on the particle is given by Stokes’ law Fd 3vd 6vr Sedimentation Sedimentation in gravitational fiel • where μ is the viscosity of the liquid and d is the diameter of the particle dv    p    6vr   g   dt    p  m  If dv/dt = 0, we will have the terminal velocity, vt  p     mg     p   vt  6r Sedimentation Sedimentation in gravitational fiel m  r  2r g  p    dx vt   9 dt Sedimentation Sedimentation in centrifugal field Sedimentation Sedimentation in centrifugal field Sedimentation Equilibrium of Sedimentation and diffusi • Flux of diffusion (Fick I’s law): dC  DS dx Where: D: diffusion constant, x: distance • Flux of sedimentation dx CS (number of particles crossing unit area per second) dt Where: C: concentration; S: area Sedimentation Equilibrium of Sedimentation and diffusi At equilibrium: Where: dx dC CS  DS dt dx dx  dt D 2r g  p    9 RT 6rN A R dC r g  p   dx  T NA C V p g  p   dx  kT dC C Sedimentation Equilibrium of Sedimentation and diffusi  V p  p   gdx  dC    C kT   h  V p  p   g  dC    dx  C kT  Co  Ch  V p  p   gh  C h Co exp    kT   Osmosis Osmosis Osmosis Osmosis Osmosis