Colloid chemistry - Chapter 3: Effect of curvature - Ngo Thanh An

Nội dung text: Colloid chemistry - Chapter 3: Effect of curvature - Ngo Thanh An

1. 1. Effect of radius on equilibrium Assume a droplet in vapor, using Young-Laplace equation: P = Pl − Pv =   In general, dG = −SdT +VdP dGl = −S l dT +V l dPl dGv = −S vdT +V vdPv At equilibrium, we have conditions: dG(L)= dG(V) (S v − S l )dT = V vdPv −V l dPl Assuming Pv = const, S v−l dT = −V l dPl
2. 1. Effect of radius on equilibrium T =   2 For a sphere T =   r Change to equilibrium as a function of radius expressed as an undercooling. Thus during nucleation, the phase diagram is altered. The actual equilibrium point is lower than that shown on the phase diagram due to curvature. There is always undercooling during homogeneous nucleation!!!
3. 2. Nucleation d G = 8 r − 4 r 2 G = 0 dr v 2 rc = Gv 3 2 16  4 rc Gcrit = 2 = 3 ( Gv ) 3
4. 3. Droplet in gas Convention Symbol “: is use to denote the phase on the concave side of a meniscus Symbol ‘: is use to denote the phase on the convex side of a meniscus Thus, for a droplet in a gas, symbol “ is for the liquid and ‘ for the gas For a droplet in gas, the centre is inside the liquid phase → this is the convex meniscus? 2 P = P" − P'= r Concave meniscus (r 0): the centre is inside of the liquid phase????
5. 3. Droplet in gas Kelvin Equation P' 2V" ln = Po RTr Implication of Kelvin Equation: 1. In a mist containing various droplet sizes, large droplets will grow at the expense of small and average droplet size will increase with time. Ostwald Ripening. 2. A droplet in equilibrium with its All droplets are of uniform radius, r*, vapor is unstable. pressure is P' , Is this system stable?  
6. 4. Bubble in liquid 2 V"−V ' −V ' RT d = dP" dP" − d ln P" r V ' V ' V ' as"isthegas P" 2V ' ln = − Po RTr P" Po
7. 4. Bubble in liquid 2 + P' T −T R 0 = ln r TT H P' o T To for bubbles to exist