The kinetics of styrene emulsion polymerization

A study has been carried out on the kinetics of persulfate-initiated emulsion polymerization of styrene in the presence of an anionic (oleate) or mixed anionic-nonionic emulsifier. In both cases it appears that Smith-Ewart kinetics are obeyed, i.e., there is a constant-rate period up to 40–50% conversion, during which there is a concomitant constant molecular weight development. The sharp increases in molecular weight with conversion reported by Grancio and Williams appear to be an artifact resulting from the use of an impure emulsifier (Triton X-100), which acts as a chain transfer agent to reduce the molecular weight by approximately an order of magnitude. Hence there does not appear to be any kinetic justification for assuming an inhomogeneous swollen latex particle (“core-shell” morphology), and normal thermodynamic considerations should still apply to this swelling phenomemon.     

Chemistry of polybutadiene—iron carbonyl systems

The treatment of polybutadienes with iron carbonyls results in formation of polymers containing tricarbonyl(conjugated diene)iron units [C₈H₁₂Fe(CO)₃] and also results in geometrical isomerization of free double bonds. Heating of the iron carbonyl-containing polymers gives ferromagnetic products with enhanced thermal stability. The incorporation of iron carbonyl groups into the polymer is favored by basic solvents and high temperatures, the geometrical isomerization by acidic solvents and low temperatures. Steric factors are powerful in determining the rate of isomerization.     

Zur Röntgenbeugung an kleinen kohärenten Kristallbereichen

Relations for the angle intervals of incident and reflected X-rays in the case of diffraction have been derived for coherent single crystals of very small dimensions. For thin layers using kinematical theory of diffraction one gets explicite expressions which can also be deduced as limiting case from the relations of dynamical theory. In this case the behaviour of the rays is entirely analogous to their behaviour at diffraction by large perfect single crystals. For an isometric small crystal the quantitative connections are dependent on the concrete experimental arrangement. The principal possibilities for measuring these angle intervals of diffraction by diffractometry are considered and compared with regard to their information contents. For some practically important examples applying diffractometric investigations, the consequences are discussed resulting when considering the coherence length contributions. The possibility is evaluated to determine such a contribution experimentally by registering the rocking curve at constant angle 2⊖.     

Strain relaxation in the epitaxy of La2/3Sr1/3MnO3 grown by pulsed-laser deposition on SrTiO3(001)

With a Curie point at 370?K, the half-metal (La_0.7Sr_0.3)MnO₃ (LSMO) is one of the most interesting candidates for electronic devices based on tunnel magnetoresistance. SrTiO₃ (STO) is up to now the best substrate for the epitaxy of suitable thin films of LSMO. The pseudocubic unit cell of rhombohedral LSMO has a parameter a _LSMO such that (a _STO ? a _LSMO)/a _LSMO = +?0.83% (where a _STO is the parameter of cubic STO) and an angle of 90.26°. As strained growth is tetragonal, relaxation implies recovery of both the pseudocubic parameter and of the original angle. In the LSMO layers that we prepare by pulsed-laser deposition, we show that these two processes are quite independent. The angular distortion is partially recovered by twinning in films 25?nm thick, while recovery of the parameter never occurs in the thickness range that we explored (up to 432?nm). A relaxation, however, takes place above a thickness of 100?nm, associated with a transition from two-dimensional to three-dimensional columnar growth. It is accompanied by chemical fluctuations. Our magnetic measurements exhibit Curie temperatures and magnetic moments very close to the bulk values in those layers where the crystal parameter is strained but the angle partially relaxed.     

An almost sure invariance principle for stationary ergodic sequences of Banach space valued random variables

Summary In this paper we establish an almost sure invariance principle with an error termo((t log logt)^1/2) (ast) for partial sums of stationary ergodic martingale difference sequences taking values in a real separable Banach space. As partial sums of weakly dependent random variables can often be well approximated by martingales, this result also leads to almost sure invariance principles for a wide class of stationary ergodic sequences such as ø-mixing and -mixing sequences and functionals of such sequences. Compared with previous related work for vector valued random variables (starting with an article by Kuelbs and Philipp [27]), the present approach leads to a unification of the theory (at least for stationary sequences), moment conditions required by earlier authors are relaxed (only second order weak moments are needed), and our proofs are easier in that we do not employ estimates of the rate of convergence in the central limit theorem but merely the central limit theorem itself.     

The speed of biased random walk on percolation clusters

 We consider biased random walk on supercritical percolation clusters in ℤ². We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive. Received: 20 November 2002 / Revised version: 17 January 2003 Published online: 15 April 2003 Research supported by Microsoft Research graduate fellowship. Research partially supported by the DFG under grant SPP 1033. Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley. Mathematics Subject Classification (2000): 60K37; 60K35; 60G50 Key words or phrases: Percolation – Random walk     

Equitable resolvable coverings

In an earlier article, Willem H. Haemers has determined the minimum number of parallel classes in a resolvable 2‐(qk,k,1) covering for all k ≥ 2 and q = 2 or 3. Here, we complete the case q = 4, by construction of the desired coverings using the method of simulated annealing. Secondly, we look at equitable resolvable 2‐(qk,k,1) coverings. These are resolvable coverings which have the additional property that every pair of points is covered at most twice. We show that these coverings satisfy k < 2q ? , and we give several examples. In one of these examples, k > q. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 113–123, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10024