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1、地址：英士楼218 电话：62784740 手机：13661380017 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 and DG
2、f 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 (异相) nucleation,Estimate the
3、critical nucleus size,For primary nucleus,For secondary nucleus,平衡熔点Tm0的测定方法,Gibbs-Thomson方程：,Hoffman-Weeks方程：,Hoffman JD, Weeks JJ. J. Res. Natl. Bur. Std. (U. S.) 1962, 66A, 13-28.,熔融线,熔融线,结晶线,Hoffman-Weeks 和Gibbs-Thomson方程的联系,Hoffman-Weeks曲线的斜率, 等于熔融线和结晶线的斜率之比。,Thermodynamics of Crystallization:
4、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 of “Impurities” o
5、n 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 connection,Note:,For poly
6、mer blends,polymer/small molecule,polymer/polymer,2. Linear Growth of Polymer Crystallization,Temperature dependence of linear growth rate (线生长速度),Temperature dependence of the radial growth rate u of spherulites in isotactic polystyrene (left), polyamid 6 (center) and poly(tetramethl-p-silpheylene
7、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 rate,Avrami指数n,= 空间维
8、数 + 时间维数,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 expanding circular waves, what is
9、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 ?,heter
10、ogeneous,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不随时间而变）,设新相在母相中成核，并经过一段孕育期以后长大成球状,新相半径,一个新相体积,d时间间隔内成核的相数目为：,则这些新相长大到时间t时的转变体积：,不同时间内形核的相在时间t的转变总体积：,为扩张体积，重复计算,已转变的体积不能再成核 新相长大到相互接触时，不能继续长大,（真正的转变体积）,在d时间内有,2. I随时间而变,Avrami方程：,当I随t而减小，3 n4 当I随t而增大，n4,