Molecular weight distribution in emulsion polymerization. I. The homopolymer case

A model for evaluating the instantaneous degree of polymerization distribution of homopolymers produced in emulsion, based on the mathematics of the Markov chains, is developed. The model accounts for any number of active chains per particle, as well as for the two fundamental mechanisms of chain termination: mono- and bi-molecular, both by combination and by disproportionation. The core of the model is the so called subprocessmain process treatment, which allows us to correctly evaluate the degree of polymerization of the chains growing in the polymer particles, by distinguishing between the events experienced by the polymer chain which imply a change of its degree of polymerization (subject transitions) and those which imply only a change in the particle state (environment transitions). This is obtained by properly defining the one-step transition probability matrix of the relevant Markov process. Once this is done, the evaluation of the distribution of the degrees of polymerization reduces to a few simple operations among matrices. Explicit expressions for the instantaneous probability density functions and the relative cumulative distributions are obtained. The application of such relationships is facilitated by the numerical procedures reported in the Appendices. The results of the model developed in this work are in agreement with those of earlier models in the range of parameter values of practical interest. In the limit of very low molecular weights, only the model developed in this work provides the correct answer. Moreover, a much more significant result is its applicability to the case of emulsion copolymerization, as it is shown in Part II.     

GaSb and InAs: New Materials for Metal-Semiconductor Point-Contact Diodes

Metal-semiconductor point contact diodes have proved to be good detectors and mixers for radiation from the far-infrared to visible. Until now GaAs, InSb and InP are the most studied and used semiconductor materials for these devices. In this work we present the performance in the visible and infrared region for metal-semiconductor point-contact diodes with GaSb or InAs as the semiconductor layers. These two new materials have shown good characteristics.     

Existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods

Summary. Given a nonsingular matrix , and a matrix of the same order, under certain very mild conditions, there is a unique splitting , such that . Moreover, all properties of the splitting are derived directly from the iteration matrix . These results do not hold when the matrix is singular. In this case, given a matrix and a splitting such that , there are infinitely many other splittings corresponding to the same matrices and , and different splittings can have different properties. For instance, when is nonnegative, some of these splittings can be regular splittings, while others can be only weak splittings. Analogous results hold in the symmetric positive semidefinite case. Given a singular matrix , not for all iteration matrices there is a splitting corresponding to them. Necessary and sufficient conditions for the existence of such splittings are examined. As an illustration of the theory developed, the convergence of certain alternating iterations is analyzed. Different cases where the matrix is monotone, singular, and positive (semi)definite are studied. Received September 5, 1995 / Revised version received April 3, 1996     

Lagrange approach to the optimal control of diffusions

A new approach to the optimal control of diffusion processes based on Lagrange functionals is presented. The method is conceptually and technically simpler than existing ones. A first class of functionals allows to obtain optimality conditions without any resort to stochastic calculus and functional analysis. A second class, which requires Ito's rule, allows to establish optimality in a larger class of problems. Calculations in these two methods are sometimes akin to those in minimum principles and in dynamic programming, but the thinking behind them is new. A few examples are worked out to illustrate the power and simplicity of this approach.Research performed at the Mathematisches Seminar der Universität Kiel with support provided by an Alexander von Humboldt Foundation fellowship.     

Thienopyrrolyl dione end-capped oligothiophene ambipolar semiconductors for thin film- and light emitting transistors

The design, synthesis and structure-property investigation of a new thienopyrrolyl dione substituted oligothiophene material showing reduced band gap energy, low lying LUMO energy level and ambipolar semiconducting behaviour is described.     

Influence of n-hexanol and n-octanol on wetting properties and air entrapment at superhydrophobic surfaces

Superhydrophobic surfaces have recently attracted a lot of attention due to their self-cleaning properties. The superhydrophobic surfaces used in our studies were prepared using a mixed inorganic-organic coating. In order to check how short chain surface active agents affect the surface energy of such surfaces, their wettability (sessile drop technique) and the kinetics of the three phase contact formation were studied. It was found that with increasing concentrations of n-hexanol and n-octanol the surface energy of these surfaces was only slightly changed, i.e. a small decrease in contact angle values with increasing solution concentration was detected. Even for the most concentrated n-hexanol and n-octanol solutions, the contact angles were in the range 145-155° and the drop rolled off, indicating that the studied surfaces stayed superhydrophobic. Air bubbles, upon collision with such superhydrophobic surfaces, spread over the superhydrophobic surface within milliseconds in the studied solutions.     

Facile synthesis of non-ionic dimeric molecular resonance imaging contrast agent: its relaxation and luminescence studies

A bis-polyazamacrocycle, 10'-bis(acetamido)ethane-bis[1,4,7-tri(carboxymethane)-1,4,7,10-tetraazacyclododecane] (DO3A-AME-DO3A) was synthesized for application in magnetic resonance imaging. The efficacy of DO3A-AME-DO3A as non ionic magnetic contrast agent was tested by performing relaxometric studies on its gadolinium complex. The longitudinal relaxivity, r(1) and transverse relaxivity, r(2) values were found to be 5.84 mM(-1)s(-1) and 6.82 mM(-1)s(-1), per Gd(III) at pH 7.0, 37 °C. The luminescence properties of europium complex of DO3A-AME-DO3A were investigated in aqueous medium. The lifetime of Eu(2)-DO3A-AME-DO3A in water was found to be 0.786 ms. Emission and luminescence lifetime measurements on the europium complex of DO3A-AME-DO3A gives a hydration number of q = 1.9. The reaction enthalpy and entropy were found to be, ΔH(0) = -(6.2 ± 2) kJ mol(-1), ΔS(0) = - (1.8 ± 0.4) kJ mol(-1)K(-1), and K(Eu)(298) = (1.8 ± 0.1).     

Determination of Conformational Equilibria in Proteins Using Residual Dipolar Couplings

In order to carry out their functions, proteins often undergo significant conformational fluctuations that enable them to interact with their partners. The accurate characterization of these motions is key in order to understand the mechanisms by which macromolecular recognition events take place. Nuclear magnetic resonance spectroscopy offers a variety of powerful methods to achieve this result. We discuss a method of using residual dipolar couplings as replica-averaged restraints in molecular dynamics simulations to determine large amplitude motions of proteins, including those involved in the conformational equilibria that are established through interconversions between different states. By applying this method to ribonuclease A, we show that it enables one to characterize the ample fluctuations in interdomain orientations expected to play an important functional role.     

Poly(diol-co-citrate)s as novel elastomeric perivascular wraps for the reduction of neointimal hyperplasia

The synthesis of poly(diol-co-citrate) elastomers that are biocompatible with vascular cells and can modulate the kinetics of the NO release based on the diol of selection is reported. NO-mediated cytostatic or cytotoxic effects can be controlled depending on the NO dose and the exposure time. When implanted in vivo in a rat carotid artery injury model, these materials demonstrate a significant reduction of neointimal hyperplasia. This is the first report of a NO-releasing polymer fabricated in the form of an elastomeric perivascular wrap for the treatment of neointimal hyperplasia. These elastomers also show promise for other cardiovascular pathologies where NO-based therapies could be beneficial.