结晶动力学和结晶热力学补充材料.pptx

结晶晶动力学和力学和结晶晶热力学力学补充材料充材料Estimate the critical nucleus size For primary nucleus For secondary nucleus平衡熔点平衡熔点T Tm m0 0的测定方法的测定方法Gibbs-Thomson方程：Hoffman-Weeks方程：Hoffman JD,Weeks JJ.J.Res.Natl.Bur.Std.(U.S.)1962,66A,13-28.熔融熔融线熔融熔融线结晶晶线Hoffman-Weeks 和和Gibbs-Thomson方程的联系方程的联系Hoffman-WeeksHoffman-WeeksHoffman-WeeksHoffman-Weeks曲线的斜率曲线的斜率曲线的斜率曲线的斜率 ,等于熔融线和结晶线的斜率之比。等于熔融线和结晶线的斜率之比。等于熔融线和结晶线的斜率之比。等于熔融线和结晶线的斜率之比。Thermodynamics of Crystallization:2.Melting point of Polymer mixtureChemical Potential of Polymer in amorphous phaseConsider a system of Polymer/Impurity mixture:Chemical Potential of one monomer unit of polymer in amorphous phasePolymer is compatible with impurity but cant co-crystallize with impurityEffects of“Impurities”on TmCondition of Phase EquilibriumSuperscript of C:Crystalline PhaseSuperscript of I:Amorphous PhaseEffects of“Impurities”on TmFor x2,x1=1For end-group effects:1=2/N,=0For copolymeralternating copolymer:PXA 1P:Probability of crystalline unit with sequential connection Note:For polymer blendspolymer/small moleculepolymer/polymer2.Linear Growth of Polymer CrystallizationTemperature dependence of linear growth rate(线生长速度线生长速度)Temperature dependence of the radial growth rate u of spherulites in isotactic polystyrene(left),polyamid 6(center)and poly(tetramethl-p-silpheylene siloxane)(right).Tf:equilibrium melting temperature.Surface nucleation on substrate with length L with a rate iLinear growth rate G:the growth rate of crystal perpendicular to the substratel:fold length;a:width of stem;b:thickness of the stem;g:substrate completion rateAvrami指数指数n生长类型均相成核n=生长维数生长维数+1异相成核n=生长维数生长维数三维生长三维生长(球状晶体球状晶体)n=3+1=4n=3+0=3二维生长二维生长(片状晶体片状晶体)n=2+1=3n=2+0=2一维生长一维生长(针状晶体针状晶体)n=1+1=2n=1+0=1=空间维数空间维数+时间维数时间维数Kinetics models of overall crystallizationn1.Free growth modelRvtb.new nucleus produced-homogeneousa.constant numbers of nucleus-heterogeneoust t+D+Dt tt tD Dt ttI*nucleation ratetPoissons raindrop problemIf raindrops fall randomly on a pond creating expanding 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 nKinetics models of overall crystallization-Avramin2.Impingement modelPPoisson distributionWhat is the chance that no wave reaches a given point P in space heterogeneoushomogeneousThe Avrami equation for 3DE(t):wave spreading area during tWhile t or v is very smallor1.Johnson-Mehl方程（方程（I、u不随时间而变）不随时间而变）设新相设新相在母相在母相中成核，并中成核，并经过一段孕育期一段孕育期以后以后长大成球状大成球状新相半径新相半径一个新相体积一个新相体积d时间间隔内成核的时间间隔内成核的相数目为：相数目为：则这些新相长大到时间则这些新相长大到时间t时的转变体积：时的转变体积：不同时间内形核的不同时间内形核的相在时间相在时间t的转变总体积的转变总体积：为扩张体积，重复计算为扩张体积，重复计算已转变的体积不能再成核已转变的体积不能再成核新相长大到相互接触时，不能继续长大新相长大到相互接触时，不能继续长大（真正的转变体积）在在d时间内有时间内有2.I2.I随时间而变随时间而变Avrami方程：方程：当当I随随t而减小，而减小，3 n4当当I随随t而增大，而增大，n4汇报结束谢谢大家!请各位批评指正