The tablty of thn (oft) flm Lecture 2 Thermodynamc and tablty October 30, 2009 Ian Morron 2009
Revew of Lecture 1 The djonng preure a jump n preure at the boundary. It doe not vary between the plate. 1 G Π ( h) = A h T P σ σ,, 1, 2, N P h P 2π RR F y Π h dh R + R Force between 2 phere: 1 2 ( ) ( ) G(h) 1 2 y ( ) G h 1 Π ( h) = h 2 G 0 = σ σ σ = S 0 G ( ) ( ) = 0 0 l lv 3 h Curve 1 Stable Curve 2 Metatable Curve 3 - Untable Ian Morron 2009 14
Joah Wllard Gbb JOSIAH WILLARD GIBBS Born Feb. 11, 1839 Ded Apr. 22, 1903 PROFESSOR OF MATHEMATICAL PHYSICS IN YALE UNIVERSITY, 1871-1903 11-30-08 Ian Morron 2009 15
Gbb nterfacal phae Denty Interfacal Phae σ Dtance du = TdS pdv +σ da + μdn U = TS pv +σ A+ μ n p μ SdT Vdp + Adσ+ n dμ = 0 S dt V dp+ n dμ = 0 SdT Vdp+ ndμ = 0 dμ = dμ = dμ Dfferental of total energy Total energy Gbb-Duhem equaton For each bulk phae At equlbrum ( S S S ) dt ( V V V ) dp+ Adσ+ ( n n n ) dμ = 0 σ σ S = S S S V = V V V n = n n n σ σ σ Adσ + S dt V dp + nd μ = 0 σ Subtractng and renamng. Gbb adorpton otherm: Surface concentraton: n σ= = Γ μ A μ σ d d d μ Γ = n σ A -2 mol m Ian Morron 2009 16
Gbb urface phae F = C P+ 2 Gbb adorpton otherm: n σ dσ= dμ = Γdμ A The urface exce: Γ = n σ A -2 mol m For a 2-component ytem: Surface Surface Phae Phae dσ=γ1dμ 1+Γ2dμ2 wth the Gbb-Duhem relaton Xd 1 μ 1 + Xd 2 μ 2 = 0 G gve dσ=γ2dμ2 and the urface-exce concentraton G X 2 Γ 2 =Γ2 Γ1 X1 Dtance ndependent of the dvdng urface. Denty D Denty old Dtance Component 2 Component 1 2 component, 2 component, 2 phae 1 phae Ian Morron 2009 17
Interactng adorpton layer? Interfacal Phae Surface Phae Surface Phae Surface Phae Component 2 Component 2 Denty Denty Denty old Denty old Component 1 Component 1 σ Dtance Dtance Dtance Dtance 2 phae, 2 component 1 phae, 2 component Surface Phae Bulk h Phae Surface Phae X Γ =Γ Γ G 2 2 2 1 X1 X 1 and X 2 are no longer contant. They depend on h. ty Den old Component 2 Component 1 old Den ty h a new degree of freedom Dtance 1 lqud phae, 2 component Ian Morron 2009 18
du = TdS pdv + μ dn G = U - TS + pv ** Thermodynamc of thn flm* - 1 1 G Π ( h) = A h σ σ T, P, 1, 2, N r plate dg = SdT + VdP + μdn + A Ψ dσ AΠdh Ψ dσ =Ψ dσ +Ψ dσ plate j j j j = 1 j j (,,, σ, σ, ) (,,, σ, σ, ) GTPN h = AΠ TPN kdk+ G 1 2 1 2 h= h G = 1 1 2 2 h the free energy of Gbb model ncludng the adorpton at urface. r dg = d G μdn Ψ1dσ1 Ψ 2dσ2 = SdT + VdP + Ndμ + A( σ1dψ 1+ σ2dψ2) AΠdh = 1 = 1 A Gbb dd, we hall do, ubtract the unform properte of the bulk: V = k V k S = S Sk = S Vkk k k N = N N = N V n k k, k k k = μ ( σ Ψ + σ Ψ ) Π dg S dt Nd A 1d 1 2d 2 A dh = 1, r **Rowlnon and Wdom, Appendx 1 - Thermodynamc * Parallel plate. Ian Morron 2009 19
dg = S dt Ndμ A( σ1dψ 1+ σ2dψ2) AΠ dh = 0 = 1, r Thermodynamc of thn flm - 2 Snce the LHS a total dfferental, o the RHS, o 1 N Π = A h μ μ μ,, Ψ, Ψ h,,, Ψ, Ψ 1 2 1 2 1 N Π= dμ A h μ h a modfed σ,, Ψ1, Ψ2 Gbb equaton. dσ= dμ = Γdμ A n N A Π Γ = A μ h h, dh the exce adorpton due to djonng preure. Note that we do not know how much exce on ether plate! Ian Morron 2009 20
dg = S dt Ndμ A( σ1dψ 1+ σ2dψ2) AΠ dh = 0 = 1, r Thermodynamc of thn flm - 3 1 S Π = A h T 1 A μ,, Ψ, Ψ ( h= ) 1 2 Π S S = dh T h h, h, μ,, Ψ, Ψ If we know Π=Π( ht Ψ Ψ μ),, 1, 2, 1 2 the exce entropy due to djonng preure. We have (,,, σ, σ, ) (,,, σ, σ, ) GTPN h = AΠ TPN kdk+ G S S Vkk k = + 1 2 1 2 h= h So all the thermodynamc functon can be calculated. The ret tattcal mechanc, oft matter calng, etc Ian Morron 2009 21
1 G Π ( h) = A h σ σ Stablty of flm between parallel plate TP,, 1, 2, N Stable Sabewhen 2 G > 0 2 h dπ h d P P Untable: 1 G dh dh Π ( h) = A h Π ( h) < 0 Aumng all other thermodynamc value RTS. hh ( ) ( ) 0 = = 0 If the change n thckne not by a p, ( q ) tate at a hgher free energy o that: reverble path, then the (non-equlbrum) Π ( h) Π ( h) h non eq < h eq Some untable flm wll be table to fat eg e.g. Gbb-Marangon tablty a ncreae perturbaton: n lqud urface tenon wth expanon becaue urfactant adorpton low. Ian Morron 2009 22 Not preented durng Lecture 2.
2π RR 2π RR F y R h dh F y h dh F y h dh 1 2 1 2 ( ) 2 π Π( ) ( ) Π( ) ( ) Π( ) p r r R1+ R2 n Ω y y y Stablty of flm between convex bode F y The change n force wth dtance : = gπ ( y ) Stablty of the equlbrum : df < 0 Hence: Π ( y ) > 0 dy < ( ) 0 If the change n thckne not tby a reverble path, then df df df non eq eq the (non-equlbrum) tate or dy dy dy at a hgher force o that: df non eq < > gπ( y) e.g. If the collon of charged partcle more rapd than the tme for the urface charge to equlbrate, the dperon may appear to be more table than t really. But, nteracton between convex urface are more lkely to be at equlbrum than parallel plate. Ian Morron 2009 Not preented durng Lecture 2. 23
Component of djonng preure What overlap? Electromagnetc feld from the random, quantum fluctuaton of electron n all the three phae. (Dperon force.) Statc electrc feld from charged urface. Interacton between molecule or polymer adorbed on the urface. Layered tructurng of olvent molecule, olute molecule or dpered phae. Ian Morron 2009 24 Not preented durng Lecture 2.
Expermental evdence Derjagun, B.V.; Rabnovch, Y.I.; Churaev, N.V. Drect meaurement of molecular force Nature, 272, 313 318, 1978. r Frt drect meaurement were reported n 1951. Frt Englh report n 1954. Quartz, platnum, gold n ar. Gla thread n water. Gla thread n water. = 2 π ( ) 12 u F rr 1 2 Rabnovch, Ya.I.; Derjagun, B.V.; Churaev, N.V. Drect meaurement of long-range urface force n ga and lqud d meda. Adv. Collod Interface Sc., 16, 63 78, 1982. Ian Morron 2009 Not preented durng Lecture 2. 25
Polymolecular adorbed layer? Water on mca Intal After collape Thee dtance are much larger than Debye length. For example: 0.1 N LCl on polhed damond wa 75 nm at 900 dyne/cm 2. The Debye length hould be about 1 nm. Nor t van der Waal force becaue of the extreme entvty to the dolved component. Derjagun, B.; Kuakov, M.; Lebedva. Range of molecular l acton of urface and polymolecular olvate (adorbed) layer. C.R. Acad. Soc. URSS, 1939, 23(7), 671-673. 300 nm Ian Morron 2009 Not preented durng Lecture 2. 26
Polywater Rabnovch, Y.I.; Derjagun, B.V. Interacton of hydrophobzed flament n aqueou-electrolyte oluton. Collod Surf., 30, 243 251, 1988. Ian Morron 2009 Not preented durng Lecture 2. 27
Polywater Ice-nne Ice-nne a fctonal materal conceved by wrter Kurt Vonnegut n h novel Cat' Cradle. It uppoed to be a more table polymorph of water than common ce (Ice I h ) whch ntead of meltng at 0 Celu (32 Fahrenhet), melt at 45.8 C (1144 F) (114.4 F). When ce-nne come nto contact wth lqud water below 45.8 C (whch thu effectvely upercooled), t act a a eed crytal, and caue the oldfcaton (freezng) of the entre body of water whch quckly crytallze a ce-nne. A global catatrophe nvolvng freezng the Earth' ocean by mple contact wth cenne ued a a plot devce n Vonnegut' novel. (wkpeda.com) Future oberver wll chuckle quetly over Derjagun dcomfture centfc htory wll ee Derjagun a a great phycal chemt who ha domnated theory and experment n urface and collod cence for ffty year... Let the lat word on polywater be thoe of Derjagun: It wa not a matter of belef, t wa a matter of performng better experment. Pethca, B.A. Book revew: Polywater by F. Frank, MIT Pre: 1981. J. Collod Interface Sc., 21, 607, 1982. Bor Vladmrovch Derjagun, 1902 1994. Ian Morron 2009 Not preented durng Lecture 2. 28
Iraelachvl, J. Intermolecular and urface force, 2 nd ed.; Academc Pre: Amterdam; 1985. Jacob box Surface force apparatu: Two mca urface, atomcally mooth, accuracy to 1 Å. At the 10 Å cale flud properte, uch a relaxaton tme, can be 10 10 tme greater than n the bulk. Djonng preure only mentoned twce n th (terrfc) book, once wth negatve Hamaker contant and once wth electrotatc repulon.) Ian Morron 2009 Not preented durng Lecture 2. 29