小体象中的非均匀成核 门玉梅，刘亚伟，白冬生，张现仁 北京化工大学， 有机无机复合材料国家重点实脸蜜
小体系中的非均匀成核 门玉梅，刘亚伟，白冬生，张现仁 北京化工大学， 有机无机复合材料国家重点实验室
我的研究兴趣 纳米材料的合成机理 酸好8容参 40383632302826242220181620263036404650 Zhang,Cao Wang,J.Phys.Chem.C 2008,112,2943 生物膜和跨膜输运 0.64 125s 214 320 Li,Zhang Wang,Biophys.J.2010,98,2554 Yue and Zhang,Soft Matter 2011,7,9104 相变与成核 Our recent results will be represented here
纳米材料的合成机理 生物膜和跨膜输运 相变与成核 Our recent results will be represented here …. 我的研究兴趣 40 38 36 32 30 28 26 24 22 20 18 16 20 26 30 36 40 46 50 Zhang, Cao & Wang, J. Phys. Chem. C 2008, 112, 2943 Li, Zhang & Wang, Biophys. J. 2010, 98, 2554 Yue and Zhang, Soft Matter 2011, 7, 9104
均匀成核：generally occurs in the interior of a uniform substance 非均匀成核：forms at preferential sites such as phase boundaries or impurities. 2啊
均匀成核: generally occurs in the interior of a uniform substance 非均匀成核: forms at preferential sites such as phase boundaries or impurities
成核研究的困难： 1.成核热力学 In an open system,a critical nucleus corresponds to a saddle point in functional space,which makes the numerical solution unstable. ------Constrained lattice density functional (LDFT)theory! 2.成核动力学 Molecular dynamics(MD)is computationally inefficient because nucleation is an activated process and occurs relatively seldom. ------Microsecond molecular dynamics and kinetic LDFT! 201 ×。=0 X0=2 10 01 0 0 15 20
成核研究的困难: 1. 成核热力学 In an open system, a critical nucleus corresponds to a saddle point in functional space, which makes the numerical solution unstable. ------Constrained lattice density functional (LDFT) theory! 2. 成核动力学 Molecular dynamics (MD) is computationally inefficient because nucleation is an activated process and occurs relatively seldom. ------Microsecond molecular dynamics and kinetic LDFT!
L.成核动力学 1)Constrained lattice density functional(LDFT)theory 2)Nucleation in a infinitely long pore 3)Capillary liquid bridges in AFM:Formation,rupture, and hysteresis 4)How nanoscale seed particles affect vapor-liquid nucleation 5)Nucleation in a pore with one-open end
I. 成核动力学 1) Constrained lattice density functional (LDFT) theory 2) Nucleation in a infinitely long pore 3) Capillary liquid bridges in AFM: Formation, rupture, and hysteresis 4) How nanoscale seed particles affect vapor-liquid nucleation 5) Nucleation in a pore with one-open end
Constrained LDFT To stabilize a nucleus,we introduced a suitable constraint in the framework of the LDFT Volume constraint E=2+2'=kT>[e,In p:+(1-p.)In(1-p.)] 0, P,∈vapor -号∑∑Pp,+∑AA-+g-Σx1-们 p,∈liquid Surface constraint E=2+2'=kT∑[p,lnp,+(I-p)ln(l-p】 [0. P,∈vapO -受∑∑P.P+∑A(-)+N-∑】= P,∈surface 0, p,∈liquid Men,Zhang and Wang,Phys.Rev.E 2009,79,051602
Constrained LDFT • To stabilize a nucleus, we introduced a suitable constraint in the framework of the LDFT – Volume constraint – Surface constraint ( ) [ ] 2 [ ln (1 )ln(1 )] i i 0 i i i i a i i a ff i i i i i ∑ ∑ ∑ ∑ ∑ − + − + − = Ω + Ω′ = + − − ρ ρ + ρ φ µ κ χ ε ρ ρ ρ ρ N L E kT ( ) [ ] 2 [ ln (1 )ln(1 )] i Si 0 i i i i a i i a ff i i i i i ∑ ∑ ∑ ∑ ∑ − + − + − = Ω + Ω′ = + − − ρ ρ + ρ φ µ κ χ ε ρ ρ ρ ρ Ns E kT liquid vapor i i i ∈ ∈ ⎩ ⎨ ⎧ = ρ ρ χ , , 1 0 liquid surface vapor i i i Si ∈ ∈ ∈ ⎪ ⎩ ⎪ ⎨ ⎧ = ρ ρ ρ χ 0, 1, 0, Men, Zhang and Wang, Phys. Rev. E 2009, 79, 051602
Nucleation in a infinitely long pore using the constrained LDFT,one can obtain the nucleation barrier and the morphology of critical nuclei 400 a =2.5 -●-adsor. 300 0- desor bulk -■-adsor. 200 -0- desor. 100 a000 033 3.2 3.1 3.0 -2.9 2.8 Chemcial potentialμ Men,Zhang,and Wang,Phys.Rev.E.79,051602(2009)
Nucleation in a infinitely long pore using the constrained LDFT，one can obtain the nucleation barrier and the morphology of critical nuclei -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 0 100 200 300 400 Nucleation barrier ∆Ω Chemcial potential µ w=2.5 adsor. desor. bulk adsor. desor. a Men, Zhang, and Wang, Phys. Rev. E. 79, 051602 (2009)
Capillary liquid bridges in AFM:Formation, rupture,and hysteresis With constrained LDFT,we can get the stable, metastable,and transition state in the formation and rupture process of capillary bridge -1600 a-o-h=9-●-h=8 -0-h=7-■一h=6 -2000 -a-h=5--h=4 -a-h=3-*-h=2 -女一h=1-+-h=0 0-0 -2400 00 -2800 (a)Constrained grand potential 线年4 as a function of liquid bridge size -3200 RH=90% w=0.950 女省-的草 -36001 0 5101520 2530 Radius of water bridge Men,Zhang,and Wang,J.Chem.Phys.131,184702(2009)
Capillary liquid bridges in AFM: Formation, rupture, and hysteresis • With constrained LDFT, we can get the stable, metastable, and transition state in the formation and rupture process of capillary bridge 0 5 10 15 20 25 30 -3600 -3200 -2800 -2400 -2000 -1600 Grand potential Radius of water bridge h=9 h=8 h=7 h=6 h=5 h=4 h=3 h=2 h=1 h=0 RH=90% wt=0.950 a (a) Constrained grand potential as a function of liquid bridge size Men, Zhang, and Wang, J. Chem. Phys. 131, 184702 (2009)
Capillary liquid bridges in AFM:Formation, rupture,and hysteresis 400 80 RH=90% 350 b 9200 40 W=0.950 -o-formation 300 100 0 -0-01 -e-rupture 250 200 40 RH=90% 1.21.62.0242.8 0-0-000-0 150 w=0.950 Tip-substrate distance/nm -80 a 100 -o-formation 23 一。-rupture -120 50 0 ● 160 01234 0 0 Tip-substrate distance/nm 200 5 6 0 2 4 6 8 10 12 1416 Tip-substrate distance Tip-substrate distance (b)and(c)show the corresponding energy barrier and capillary force as a function of tip-substrate distance. Men,Zhang,and Wang,J.Chem.Phys.131,184702(2009)
Capillary liquid bridges in AFM: Formation, rupture, and hysteresis 345678 0 50 100 150 200 250 300 350 400 1.2 1.6 2.0 2.4 2.8 0 100 200 Energy barrier/X10 -20J Tip-substrate distance/nm Energy barrier Tip-substrate distance formation rupture RH=90% wt=0.950 b (b) and (c) show the corresponding energy barrier and capillary force as a function of tip-substrate distance. 0 2 4 6 8 10 12 14 16 -200 -160 -120 -80 -40 0 40 80 01234 -4 -3 -2 -1 0 1 Force/nN Tip-substrate distance/nm Force Tip-substrate distance formation rupture RH=90% wt=0.950 c Men, Zhang, and Wang, J. Chem. Phys. 131, 184702 (2009)
How nanoscale seed particles affect vapor- liquid nucleation With constrained LDFT,the shape of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as input. 140 120 100 80 60 -2.8电m 40 u=.2.88 u=-2.89 u=-2.91 △ 4=-2.89 u=-2.87 20 μ=-2.90 ◇μ=-2.91 0 1500 3000 4500 nucleus volume,Vd homogeneous nucleation at different chemical potentials Liu and Zhang,J.Chem.Phys.2011,(accepted)
• With constrained LDFT, the shape of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as input. 0 1500 3000 4500 0 20 40 60 80 100 120 140 energy barrier, ∆Ω nucleus volume, Vd µ=-2.87 µ=-2.88 µ=-2.89 µ=-2.90 µ=-2.91 homogeneous nucleation at different chemical potentials Liu and Zhang, J. Chem. Phys. 2011, (accepted) How nanoscale seed particles affect vaporliquid nucleation
