1,8. Measurement of rate coefficients,2,History,Up to the late 1980s termination and propagation rate coefficients were accessible only in their coupled form, kp/kt0.5 or individually via combination with pseudo flickering techniques like the rotating sector or spatially intermittent polymerization methods in combination with stationary polymerization measurements.The situation has dramatically improved with the invention of the pulsed laser polymerization (PLP) technique in the late 1980s. Since then, this technique has been extensively used to collate propagation and termination rate coefficients for various homo- and copolymerizations.,3,8.1 Methods for the Measurement of kd,Rd = fkd IThe concentration can be measured via any quantity to which it is directly proportional, such as a spectroscopic infrared (红外光谱) absorption that can be easily followed with reaction time.Infrared spectroscopy has been used extensively in the past to study the decay of organic peroxides in various reaction media.,4,8.2 Methods for the Measurement of kp,Pulsed Laser PolymerizationSize-Exclusion Chromatography (PLP-SEC),irradiated by a pulsed laser beam (5-20ns),Monomer photoinitiator, (solvent & transfer agents),MW of polymer produced by PLP:L0,n=nkpMt0,5,6,8.2 Methods for the Measurement of kp,Electron Spin Resonance Spectroscopy-Stationary Polymerization (ESR) (电子自旋共振),7,8.2 Methods for the Measurement of kp,Quenched Instationary Polymerization Systems (QUIPS),A photopolymerizable mixture passes through a capillary system, is irradiated at a specific location, and polymerizes in the capillary during a well-defined dark period until it drops into a quenching bath with an inhibitor(nitroxyl radicals). Measuring the chain length distribution by size-exclusion chromatography that allows determination of kp in accordance with the equation. L=kpMt0,8,8.3 Methods for the Measurement of ktr,Mayo method,The usual procedure for measuring the chain transfer constant CT involves determination of Xn for a range of T/M values and plotting the data as 1/Xn versus T/M, that is, a Mayo plot. The value of CT is then determined as the straight-line slope of this plot.,9,8.4 Methods for the Measurement of kt,Single Pulse Pulsed Laser Polymerization (SP-PLP),10,Applying pulsed laser-polymerization (PLP) in conjunction with infrared or near-infrared spectroscopic measurement of monomer conversion induced by a single laser pulse (SP-PLP) allows for the determination of the ratio of termination to propagation rate coefficients, kt/kp, in wide ranges of temperature; pressure; and monomer conversion.,11,8.5 Determining the Mode of Termination: Disproportionation versus Combination,Identification and quantification of chain ends are not simple as they give only small signals (relative to the rest of the polymer chain) in a spectroscopic analysis. This can be overcome to some extent by isotopic labeling of the initiator end groups by 14C or by using initiator fragments containing fluorine or phosphorus as NMR-sensitive molecules. The application of the matrix-assisted laser desorption ionization time-of-flight mass spectroscopy (MALDI-TOF-MS) to the problem of end-group analysis of polymers brought some promising results to this field of polymerization kinetics.,12,MALDI-TOF-MS,13,14,Some rate coefficients,15,9. Molecular Weight Distribution 分子量分布,16,How to know MWD?,From the experimental measurement Precipitation fractionation (沉淀分级) Gel permeation chromatograph/Size exclusion chromatograph (GPC/SEC 凝胶渗透色谱/体积排斥色谱) MALDI-TOFForm theoretical Analysis Statistical approach (统计方法) Kinetic approach （动力学法）,17,9.1. Distribution for disproportionation or chain transfer,Consider only chains whose growth is terminated by either disproportionation or chain transfer.Note that in both the cases, the number of chains produced is equal to the number of chain terminated.,18,Let p = probability of adding a monomer to a grow chain.,a polymer chain with the length n is formed by n-1 propagation steps and one chain stopping (termination or transfer) event of probability (1-p).So the probability of finding a chain of length n is:,number of chains of size n,total number of chains,Instantaneous number-fraction distribution,number-fraction distribution,19,weight-fraction distribution,weight of chains of length n: Wn=mnNn,weight of all chains : W=mN0,Initial number of monomers,MW of monomer,Since one termination results in one chain, so,20,Molecular weight distribution curve,21,Average molecular weight,according to definition:,22,Average molecular weight,according to calculation:,polydispersity index(多分散性指数), PDI,23,There are (n-1) different ways to form a chain of length n from the combination of two chains, so,9.2. Distribution for Combination,Consider a chain of length n formed by combining m monomers with (n-m) monomers. For chain of length m, here are (m-1) addition steps and 1 termination For chain of length (n-m), here are (n-m-1) addition steps and 1 termination Probability of finding a chain of length n is:,