An experimental approach for controlling confinement effects at catalyst interfaces

Catalysts are conventionally designed with a focus on enthalpic effects, manipulating the Arrhenius activation energy. This approach ignores the possibility of designing materials to control the entropic factors that determine the pre-exponential factor. Here we investigate a new method of designing supported Pt catalysts with varying degrees of molecular confinement at the active site. Combining these with fast and precise online measurements, we analyse the kinetics of a model reaction, the platinum-catalysed hydrolysis of ammonia borane. We control the environment around the Pt particles by erecting organophosphonic acid barriers of different heights and at different distances. This is done by first coating the particles with organothiols, then coating the surface with organophosphonic acids, and finally removing the thiols. The result is a set of catalysts with well-defined “empty areas” surrounding the active sites. Generating Arrhenius plots with >300 points each, we then compare the effects of each confinement scenario. We show experimentally that confining the reaction influences mainly the entropy part of the enthalpy/entropy trade-off, leaving the enthalpy unchanged. Furthermore, we find this entropy contribution is only relevant at very small distances (<3 Å for ammonia borane), where the “empty space” is of a similar size to the reactant molecule. This suggests that confinement effects observed over larger distances must be enthalpic in nature.

Designable materials help pinpoint the role of steric confinement in catalysis.     

Rheological Characterization of Computationally Synthesized Reactor Populations of Hyperbranched Macromolecules: Bivariate Seniority‐Priority Distribution of ldPE

Summary: Hyperbranched molecules like low‐density polyethylene (ldPE) adopt a huge variety of molecular architectures. Previous work has shown that it is possible to computationally synthesize these architectures and to characterize them according to radius of gyration. Here, a method is presented and applied on ldPE to characterize populations using rheological quantities in terms of comb‐shaped and Cayley tree structures. Interbranch segments are assigned seniority and priority values that quantify their behavior in relaxation and elastic deformation processes. New general‐purpose algorithms have been developed to derive the full bivariate seniority/priority distribution using a representation from the graph theory of branched architectures. This paper describes the computation of bivariate chain length/degree of branching distributions (CLD/DBD) using a Galerkin finite element method for two scission mechanisms: linear and topological scission. The DBD is calculated using pseudo‐distributions. Random scission is treated with fragment length and branch point redistribution functions as obtained from scission statistics of branched molecules, preferentially yielding short and long fragments. Reactor populations of ldPE architectures are then obtained using computational synthesis. The seniority and priority distributions calculated indeed prove to be an adequate characterization method. They show good comparison, although not a complete overlap, with size characterization using a variant of the radius of gyration. It was possible to calculate a full bivariate seniority/priority fraction distribution, but due to the limited sample size its surface was not smooth. Subsequent work has shown the consequences for the prediction of rheological properties.

Seniority/priority values for segments of molecules for one chain length/number of branch points combination.     

Stress analysis of thick-walled tube with step change in thermal expansion

The finite-element method of stress analysis is used to evaluate highly localized stress distributions in a thick-walled tube with a step change in temperature. Effect of gird size on stress calculated in the neighborhood of the temperature discontinuity is examined. A photoelastic analysis of the differential-thermal-expansion problem is also described. Comparison of the experimental and the calculated stress distributions shows good agreement. An approximate analysis which provides insight into the manner in which the thermal stresses develop is also included.     

A Fast Method to Compute the MSD and MWD of Polymer Populations Formed by Step‐Growth Polymerization of Polyfunctional Monomers With Identical Reactive Groups

A fast method is presented for the calculation of the MSD and the MWD of polymers obtained via step‐growth polymerization of polyfunctional monomers bearing identical reactive groups (i.e., systems of type “Afi”). Using this method, the complete distribution can be calculated rapidly, not just the statistical averages of the polymer population such as or . The computed MSD and MWD give more insight than these averages and can be compared to similar data measured on actual polymer systems. The low‐ and intermediate molecular size/weight part of the distribution curves are calculated using a recurrence scheme, while the high‐molecular tail (large and very large polymers) of the distributions is derived from an asymptotic approximation of the associated generating functions.

     

A Fast Method to Compute the MSD and MWD of Polymer Populations Formed by Step‐Growth Polymerization of Polyfunctional Monomers Bearing A and B Coreactive Groups

General step‐growth polymerization systems of order 2 are considered, i.e., systems of type “AfiBgi”, and a fast algorithmic method is presented to compute, at a given degree of conversion, the MSD and the MWD. The complete distribution is calculated; not just statistical averages of the polymer population such as or . For the computation of the low‐ and intermediate size/weight parts of the distribution curves, a set of recurrence relations is used. The high‐molecular size/weight parts of the curves (right tails) are computed using an accurate approximation derived from generating functions. In a previous paper, we applied our method to general order‐1 systems, i.e., systems of type “Afi”.

     

A molecular model for cohesive slip at polymer melt/solid interfaces

A molecular model is proposed which predicts wall slip by disentanglement of polymer chains adsorbed on a wall from those in the polymer bulk. The dynamics of the near-wall boundary layer is found to be governed by a nonlinear equation of motion, which accounts for such mechanisms on surface chains as convection, retraction, constraint release, and thermal fluctuations. This equation is valid over a wide range of grafting regimes, including those in which interactions between neighboring adsorbed molecules become essential. It is not closed since the dynamics of adsorbed chains is shown to be coupled to that of polymer chains in the bulk via constraint release. The constitutive equations for the layer and bulk, together with continuity of stress and velocity, are found to form a closed system of equations which governs the dynamics of the whole "bulk+boundary layer" ensemble. Its solution provides a stick-slip law in terms of the molecular parameters and extruder geometry. The model is quantitative and contains only those parameters that can be measured directly, or extracted from independent rheological measurements. The model predictions show a good agreement with available experimental data.     

Negative resistance and local charge-density-wave dynamics

Charge-density-wave (CDW) dynamics is studied on a submicron length scale in NbSe(3) and o-TaS(3). Regions of negative absolute resistance are observed in the CDW sliding regime at sufficiently low temperatures. The origin of the negative resistance is attributed to the different forces that the deformed CDW and quasiparticles feel: the force on the CDW is merely caused by a difference of the electric potentials, while the quasiparticle current is governed by a difference of the electrochemical potentials.