結(jié)晶動(dòng)力學(xué)和結(jié)晶熱力學(xué)補(bǔ)充材料

1、.,徐軍 地址：英士樓218 電話：62784740 手機(jī)Email：jun-,.,Process of Polymer CrystallizationTwo steps:,1. Nucleation (成核) process,Size,DG,0,embryo,super critic. size,stable,critical nucleus,DG = Gcrystal Gmelt , DG = DH TDS Gcrystal = Gbulk + SAs DG = Gbulk - Gmelt + SAs =DGf + SAs A is the suface area

2、 and DGf is the bulk free energy change.,Schematic representation of the change in free energy as a function of size illustrating the nucleation process,Types of crystal nuclei. (a) primary (初次), (b) secondary (二次), (c) tertiary (三次) nucleus.,Homogeneous (均相) and heterogeneous (異相) nucleation,.,Esti

3、mate the critical nucleus size,For primary nucleus,For secondary nucleus,.,平衡熔點(diǎn)Tm0的測定方法,Gibbs-Thomson方程：,Hoffman-Weeks方程：,Hoffman JD, Weeks JJ. J. Res. Natl. Bur. Std. (U. S.) 1962, 66A, 13-28.,熔融線,.,熔融線,結(jié)晶線,Hoffman-Weeks 和Gibbs-Thomson方程的聯(lián)系,Hoffman-Weeks曲線的斜率, 等于熔融線和結(jié)晶線的斜率之比。,.,Thermodynamics of Cr

4、ystallization: 2. Melting point of Polymer mixture,Chemical Potential of Polymer in amorphous phase,Consider a system of Polymer/Impurity mixture:,Chemical Potential of one monomer unit of polymer in amorphous phase,Polymer is compatible with impurity but cant co-crystallize with impurity,.,Effects

5、of “Impurities” on Tm,Condition of Phase Equilibrium,Superscript of C: Crystalline Phase,Superscript of I: Amorphous Phase,.,Effects of “Impurities” on Tm,For x2, x1=1,For end-group effects: 1=2/N, =0,For copolymer,alternating copolymer: PXA1,P: Probability of crystalline unit with sequential connec

6、tion,Note:,For polymer blends,polymer/small molecule,polymer/polymer,.,2. Linear Growth of Polymer Crystallization,Temperature dependence of linear growth rate (線生長速度),Temperature dependence of the radial growth rate u of spherulites in isotactic polystyrene (left), polyamid 6 (center) and poly(tetr

7、amethl-p-silpheylene siloxane) (right). Tf: equilibrium melting temperature.,Surface nucleation on substrate with length L with a rate i Linear growth rate G: the growth rate of crystal perpendicular to the substrate,l: fold length; a: width of stem; b: thickness of the stem; g: substrate completion

8、 rate,.,Avrami指數(shù)n,= 空間維數(shù) + 時(shí)間維數(shù),.,Kinetics models of overall crystallization,1. Free growth model,Rvt,b. new nucleus produced - homogeneous,a. constant numbers of nucleus- heterogeneous,t+Dt,t,Dt,t,I* nucleation rate,t,.,Poissons raindrop problem If raindrops fall randomly on a pond creating expandi

9、ng circular waves, what is the chance that the number of waves created by different raindrops which pass over a representative point P up to time t is exactly n?,Kinetics models of overall crystallization-Avrami,2.Impingement model,P,Poisson distribution,What is the chance that no wave reaches a given point P in space ?,heterogeneous,homogeneous,The Avrami equation for 3D,E(t): wave spreading area during t,While t or v is very small,or,.,1. Johnson-Mehl方程（I、u不隨時(shí)間而變）,設(shè)新相在母相中成核，并經(jīng)過一段孕育期以后長大成球狀,新相半徑,一個(gè)新相體積,d時(shí)間間隔內(nèi)成核的相