1,5. Polymerization Rate,2,5.1 Macro kinetics (宏观动力学),1. Monomer Conversion and Rp,3,1. Direct sampling (直接取样) weight the polymer at different intervals. 2. Dilatometer method (膨胀计法) V C 3. Refraction index (折光指数法) e.g. n PVAc-nVAc=0.071 4. Spectroscopy (光谱法) MMA at 1630 cm-1。 5. Calorimetry (量热法) H C,Measurement of Rp,4,Typical Polymerization Rate Curves,Rp,C%,t,Induction：decomposition of initiator,Initial ：C% = 0 5-10，a low steady rate,Middle ：auto-acceleration C%= 5-10 70-90）,End：drop of rate (C% =70-90 100),5,5.2 Micro Kinetics (微观动力学),Ri in the range of 10-8 10-10 mol/L.s, where f is initiation efficiency,Kinetic equation: Rp vs concentration of reactants,Initiation,6,Propagation,Rp = 10-4-10-6 Ms; kp = 102-104 M-1s; M = 10-7-10-8 M; M=1-10 mol/L,R=Ri,Assuming identical activity of radicals with various length, so kp=kp,i .,7,Termination,kt = kt,c + kt,d,2 represents two radicals were consumed by one reaction (US),disproportionation,combination,8,Total polymerization Rate,The polymerization degree is so large, that the monomer consumed in the initiation reaction can be neglected, or RiRp.,R=?,9,Steady State (稳态),A steady-state is established early in the reaction. The concentration of radicals is very small (ca. 10-8 M) and nearly constant throughout.,Steady-state The concentration of radicals is constant or initiation rate is equal to termination speed.,R determined by initiation mode,10,Polymerization rate with different initiations,Initiator,Self-initiation of Styrene,ln(M0/M) t: low conversion; I and f are constant,11,Actual Polymerization rate,different initiation and termination reactions,The specific mechanism can be deduced by the parameters m and n,12,5.3 Influence of Temperature,Arrhenius Equation,For normal polymerization initiated by initiator: Ed 125 KJ/mol, Ep29 KJ/mol, Et 17 KJ/mol, so E=83 KJ/mol This corresponds to a two or three fold rate increase for a 10 oC temperature increase.,13,5.4 Autoacceleration(自动加速效应),PMMA polymerization in benzene solution at various concentrations.,at low concentrations (40%), the polymerization proceeds smoothly with no unusual effects.,at higher concentrations, a pronounced rate acceleration after partial conversion of monomer to polymer. The more concentrated the solution, the earlier the acceleration occurs.,14,Autoacceleration only occurs during polymerizations with high concentrations of monomer (i.e., little or no solvent). The reaction proceeds normally for a while, then suddenly the rate of polymerization goes up dramatically. The molecular weight of chains that grow during the accelerated period is substantially higher than that of chains that grew earlier.,15,Reasons and Explanation,Termination involves the reaction between two chain ends. The high viscosity hinders the diffusion of chains because of entanglements, so the rate of termination slows considerably. The initiation and diffusion of small molecular monomers is hardly affected by viscosity, so propagation proceeds as before. Once a low, steady state concentration of radicals gives way to increasing concentration, chains grow without termination, so the conversion is rapid and the MW is high. For neat monomer, often in cases where the polymer formed is a high Tg material, there can come a point at which even the diffusion of monomer is slow. The mixture has become a hard glass, and unreacted radicals become trapped inside. The reaction shuts down at less than 100% conversion. Note that autoacceleration can be dangerous because the exotherm of polymerization can be released suddenly, leading to a runaway reaction.,16,Conditions affecting autoacceleration,Temperature the higher the Tp, the lower the viscosity Monomer concentration the content of polymer Solvent good solvent in favor of the diffusion of polymer chain Tg of polymer The homogeneity of polymerization media homogeneous or heterogeneous,17,5.5 Typical Polymerization Rate Curves,A: Slow initiation-acceleration-drop (“S” shape) B: uniform rate C: fast initiation-drop,A,B,C,18,Bulk polymerization of MMA monitored by ESR spectroscopy,Shen J, Tian Y, Wang G. Makromol Chem 1991;192:2669.,19,6. Average Molecular Weight,20,Average Molecular Weight,Polymer consists of chains with a variable number of monomer units. Of the key parameters influencing the physical properties of polymers, the average molecular weight usually is the dominant factor, often influencing the other parameters. Control on the molecular weight is one of the most important topics of polymer synthesis,21,6.1 Kinetic Chain Length (动力学链长),kinetic chain length: ,How many propagation steps occur before the chain mechanism is stopped? The amount of monomer consumed by one active species from initiation to termination,Steady State,no chain transfer,22,kinetic chain length: , MI-0.5,23, - termination mode-polymerization degree,Combination Xn=2,Disproportionation Xn=,