Quartz crystal microbalance study of the kinetics of surface initiated polymerization

Surface initiated polymerization (SIP) is a valuable tool in synthesizing functional polymer brushes, yet the kinetic understanding of SIP lags behind the development of its application. We apply quartz crystal microbalance (QCM) to address two issues that are not fully addressed yet play a central role in the rational design of functional polymer brushes, namely quantitative determination of the kinetics and the initiator efficiency (IE) of SIP. SIP are monitored online using QCM. Two quantitative frequency-thickness (f-T) relations make the direct determination and comparison of the rate of polymerization possible even for different monomers. Based on the bi-termination model, the kinetics of SIP is simply described by two variables, which are related to two polymerization constants, namely a = 1/(k (p,s,app)-[M][R center dot](0)) and b = k (t,s,app)/(k (p,s,app)[M]). Factors that could alter the kinetics of SIP are studied, including (i) the molecular weight of monomers, (ii) the solvent used, (iii) the initial density of the initiator, (iv) the concentration of monomer, [M], and (v) the catalyst system (ratio among the ingredients, metal, ligands, and additives). The dynamic nature of IE is also described by these two variables, IE = a/(a + bt). Instead of the molecular weight and the polydispersity, we suggest that film thickness, the two kinetic parameters (a and b), and the initial density of the initiator and IE be the parameters that characterize ultra-thin polymer brushes. Besides the kinetics study of SIP, the reported method has many other applications, for example, in the fast screening of catalyst system for SIP and other polymerization systems.

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transformations of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was obtained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propagators were obtained.

Time-dependent density-functional calculations for optical spectra of Na-2 and Na-4 clusters

With the frame of the time-dependent local density approximation, an efficient description of the optical response of clusters has been used to study the photo-absorption cross section of Na-2 and Na-4 clusters. It is shown that our calculated results are in good agreement with the experiment. In addition, our calculated spectrum for the Na-4 cluster is in better agreement with experiment than the GW absorption spectrum.

TIME-DEPENDENT DENSITY FUNCTIONAL STUDY OF MULTIELECTRON TRANSFER IN Cq+-Na-4 COLLISIONS

The process of multielectron transfer from a Na-4 cluster induced by highly charged C6+, C4+, C2+ and C+ ions is studied using the method of time-dependent density functional theory within the local density approximation combined with the use of pseudopotential. The evolution of dipole moment changes and emitted electrons in Na-4 isobtained and the time-dependent probabilities with various charges are deduced. It is shown that the Na-4 cluster is strongly ionized by C6+ and that the number of emitted electrons per atom of Na-4 is larger than that of Na-2 under the same condition. One can find that the detailed information of the emitted electrons from Na-4 is different from the same from Na-2, which is possibly related to the difference in structure between the two clusters.