Colloid chemistry chapter 3 effect of curvature

PowerPoint Presentation 1 Dr Ngo Thanh An Email ngothanhan@gmail com COLLOID CHEMISTRY Chapter 3 – Effect of curvature 1 Effect of radius on equilibrium Assume a droplet in vapor, using Young Laplace[.]

COLLOID CHEMISTRY Chapter – Effect of curvature Dr Ngo Thanh An Email: ngothanhan@gmail.com 1 Effect of radius on equilibrium Assume a droplet in vapor, using Young-Laplace equation: P P l  P v   In general, dG  SdT  VdP dG l  S l dT  V l dP l dG v  S v dT  V v dP v At equilibrium, we have conditions: dG(L)= dG(V) S Assuming Pv = const, v   S l dT V v dP v  V l dP l S v  l dT  V l dP l Effect of radius on equilibrium d P  d P l  P v  dP l d    l v  S dT l dP  d    l V P P l  P v    T S l  v S v  l d  dT  l  l   V  V To V l   v l S  T dT To T d  dT   To Gibbs – Thomson coefficient T   To  T     Effect of radius on equilibrium T   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!!! Nucleation G GS  GV 4r   r Gv G: overall excess free energy between a small solid particle of solute and the solute in the solution GS: excess free energy between the surface of the particle and the bulk of the particle GV: volume excess free energy: the excess free energy between a very large particle (r = ) and the solute in the solution Gv: free energy change of the transformation per unit volume GS: a positive quantity: (enlargement of area need supplying work, that means, work is negative  dG = - dA > 0) GV: a negative quantity: (increase of volume generate work, that means, work is positive  dG = - dA < 0) : interfacial tension between the developing crystalline surface and the supersaturated in which it is located 2 Nucleation dG 8r  4r Gv 0 dr rc  Gcrit 2 Gv 16 4rc2   3 Gv  Nucleation p' RT RT p' Gv vvapour dP   d ln P  ln o v v p po  molarvolume   Mw 16 v 2 Gc  [ RT ln S ]2 2 rc   Gv 2M w  RT ln S 2v p' RT ln o p Droplet in gas Pressure 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 outside of the liquid phase????? Convex meniscus (r > 0): the centre is inside of the liquid phase???? Droplet in gas Pressure  2   1 dP dP" dP ' d   2d    r  r Phase condition: d G" d G ' P ' 2V "  Po RTr  P'  P o and equilibrium vapor pressure is higher for a droplet than a flat surface ln Droplet in gas Kelvin Equation Pressure P' 2V" ln o  P RTr Implication of Kelvin Equation: 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 A droplet in equilibrium with its vapor is unstable All droplets are of uniform radius, r* , pressure is P' , Is this system stable? Droplet in gas Temperature dG ' dG" S 'dT  V 'dP ' S "dT  V "dP" Assume P’ = const S'  S"dT  V "dP" 0 where S'  S"  2  dP" dP' dP" d    r  T H vap  To T 1  r r  2  dT  V "d   0 r   0 r H vap T T 2V " ln  To H vap r T < To Bubble in liquid Pressure  V' RT  2  V "  V ' d dP"  dP"  d ln P"  V' V' V'  r  as"isthe gas ln P" 2V '  Po RTr P"  Po Bubble in liquid Temperature H dT  V "dP" 0, T RT V"  ; P"  2  dP" d    r  T T 1  r r T T 1  r r H dT   T T To R  2 P '  0 r r 2 P" P ' ; r  2  d   0  r  H  2  dT  R d ln  P '   0   T  r  T To r 0 Bubble in liquid Temperature  2   P'  T  T0 R  r   ln TTo H  P'      T  To for bubbles to exist