Existence and equilibration of global weak solutions to Hookean-type bead-spring chain models for dilute polymers

We show the existence of global-in-time weak solutions to a general class of coupled Hookean-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum for the Navier-Stokes equation and a nonnegative initial probability density function for the Fokker-Planck equation, which has finite relative entropy with respect to the Maxwellian of the model, we prove the existence of a global-in-time weak solution to the coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the absence of a body force, the weak solution decays exponentially in time to the equilibrium solution, at a rate that is independent of the choice of the initial datum and of the centre-of-mass diffusion coefficient.Comment: 86 page

Energieeinsparung in der Chloralkalielektrolyse Abschlussbericht

The conventional way to study current and potential distributions in membrane-based electrolysis cells for alkali-metal chlorides is by mathematical modelling. These studies have provided valuable clues as to possible ways of saving energy, one of which consists in an optimisation of electrode structure. In the present study electrolysis cells equivalent to technical-scale electrolysers in terms of the relevant process parameters were examined at four different heights for cell voltage and component voltages (anode and cathode potential, potential difference between anode and cathode). Furthermore, measurements were performed on the NaCl distribution in the anode region and on potential differences within electrode structures. The results of this work clearly show that anode structure has an influence on cell voltage. This means that it will now be possible to increase voltage by 70 mV at 3 kA/m"2 and 90 C relative to the present state of the art. It was also shown that constructional improvements of the anode region lead to an almost complete equalisation of NaCl concentration in the anode region, even at current densities of up to 6 kA/m"2. (orig./MM)Bisher erfolgten Untersuchungen von Strom - und Potentialverteilung in Chloralkalielektrolysezellen nach dem Membranverfahren nur durch mathematische Modellierung. Aus diesen Arbeiten ergeben sich wichtige Hinweise auf moegliche Energieeinsparungen insbesondere durch Optimierung der Elektrodenstrukturen. Jetzt wurde in Elektrolysezellen, die in ihren verfahrenstechnisch relevanten Parametern den technischen Elektrolyseuren entsprachen, in vier verschiedenen Hoehen die Zellspannung und die Teilspannungen (Anoden- und Kathodenpotential, Spannungsabfall zwischen Anoden und Kathode) gemessen. Ausserdem konnten Messungen der NaCl-Konzentrationsverteilung im Anodenraum und die Spannungsabfaelle in den Elektrodenstrukturen vorgenommen werden. Im Ergebnis der Arbeiten konnten eindeutige Einfluesse der Anodenstrukturen auf die Zellenspannung ermittelt werden. Dadurch ist es moeglich, Spannungsverbesserungen bis zu 70 mV bei 3 kA/m"2 und 90 C gegenueber dem jetzigen technischen Standard zu erreichen. Weiter konnte durch konstruktive Verbesserung des Anodenraumes praktisch eine Egalisierung der NaCl-Konzentration im Anodenraum, auch bei Stromdichten bis 6 kA/m"2, nachgewiesen werden. (orig./MM)Available from TIB Hannover: F97B1330+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEBundesministerium fuer Bildung, Wissenschaft, Forschung und Technologie, Bonn (Germany)DEGerman

Data: Temperature Driven Transformation of the Flexible Metal-Organic Framework DUT-8(Ni)

These are the raw data of "Temperature Driven Transformation of the Flexible Metal-Organic Framework DUT-8(Ni)" DUT-8(Ni) metal-organic framework belongs to the family of flexible pillared layer materials. The desolvated framework can be obtained in the open pore form (op) or in the closed pore form (cp), depending on the crystal size regime. In the present work, we report on the behaviour of desolvated DUT-8(Ni) at elevated temperatures. For both, op and cp variants, heating causes a structural transition, leading to an new, crystalline compound, containing two interpenetrated networks. The state of the framework before transition (op vs. cp) influences the transition temperature: the small particles of the op phase transform at significantly lower temperature in comparison to the macroparticles of the cp phase, transforming close to the decomposition temperature. The new compound, confined closed pore phase (ccp), was characterized by powder X-ray diffraction and spectroscopic techniques, such as IR, EXAFS, and positron annihilation lifetime spectroscopy (PALS). Thermal effects of structural cp to ccp transitions were studied using differential scanning calorimetry (DSC), showing an overall exothermic effect of the process, involving bond breaking and reformation. Theoretical calculations reveal the energetics, driving the observed temperature induced phase transition.This work was financially supported by DFG (Deutsche Forschungsgemeinschaft) under contracts FOR 2433 and in project numbers 448809307, 464857745 (AT 289/1-1 and KA 1698/41-1) and 419941440. PP and JDE used high performance computing facilities of ZIH Dresden. The EXAFS experiments were conducted at the BL11S2 of Aichi Synchrotron Radiation Center, Aichi Science & Technology Foundation, Aichi, Japan (Proposal No. 2020D5036). We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out using beamline P02.1 at PETRA III. ZH acknowledges the support from the Swedish Research Council Formas (2020- 00831). J.D.E. is supported by a Ramsay Fellowship from the University of Adelaide

Engineering Micromechanics of Soft Porous Crystals for Negative Gas Adsorption

Framework materials at the molecular level, such as metal-organic frameworks (MOF), were recently found to exhibit exotic and counterintuitive micromechanical properties. Stimulated by host-guest interactions, these so-called soft porous crystals can display counterintuitive adsorption phenomena such as negative gas adsorption (NGA). NGA materials are bistable frameworks where the occurrence of a metastable overloaded state leads to pressure amplification upon a sudden framework contraction. How can we control activation barriers and energetics via functionalization of the molecular building blocks that dictate the frameworks’ 30 mechanical response? In this work we tune the elastic and inelastic properties of building blocks at the 31 molecular level and analyze the mechanical response of the resulting frameworks. From a set of 11 frameworks, we demonstrate that widening of the backbone increases elasticity, while elongation of the building blocks results in a decrease in critical yield stress of buckling. We further functionalize the backbone by incorporation of sp3 hybridized carbon atoms to soften the molecular building blocks, or stiffen them with sp2 and sp carbons. Computational modeling shows how these modifications of the building blocks tune the 36 activation barriers within the energy landscape of the guest-free bistable frameworks. Only frameworks with free energy barriers in the range of 800 to 1100 kJ mol–1 37 per unit cell, and moderate yield stress of 0.6 to 38 1.2 nN for single ligand buckling, exhibit adsorption-induced contraction and negative gas adsorption. Advanced experimental in situ methodologies give detailed insights into the structural transitions and the adsorption behavior. The new framework DUT-160 shows the highest magnitude of NGA ever observed for nitrogen adsorption at 77 K. Our computational and experimental analysis of the energetics and mechanical response functions of porous frameworks is an important step towards tuning activation barriers in dynamic framework materials and provides critical design principles for molecular building blocks leading to pressure amplifying materials<br /

Towards General Network Architecture Design Criteria for Negative Gas Adsorption Transitions in Ultraporous Frameworks

Critical design criteria for negative gas adsorption (NGA), a counterintuitive feature of pressure amplifying materials, hitherto uniquely observed in a highly porous framework compound (DUT-49), are derived by analysing the physical effects of micromechanics, pore size, interpenetration, adsorption enthalpies, and the pore filling mechanism using advanced in situ X-ray and neutron diffraction, NMR spectroscopy, and calorimetric techniques parallelized to adsorption for a series of six isoreticular networks. Aided by computational modelling, we identify DUT-50 as a new pressure amplifying material featuring distinct NGA transitions upon methane and argon adsorption. In situ neutron diffraction analysis of the methane (CD4) adsorption sites at 111 K supported by grand canonical Monte Carlo simulations reveals a sudden population of the largest mesopore to be the critical filling step initiating structural contraction and NGA. In contrast, interpenetration leads to framework stiffening and specific pore volume reduction, both factors effectively suppressing NGA transitions.</p

CCDC 2003151: Experimental Crystal Structure Determination

Related Article: Simon Krause, Jack D. Evans, Volodymyr Bon, Irena Senkovska, Sebastian Ehrling, Paul Iacomi, Daniel D. Többens, Dirk Wallacher, Manfred S. Weiss, Bin Zheng, Pascal G. Yot, Guillaume Maurin, Philip L. Llewellyn, François-Xavier Coudert, Stefan Kaskel|2020|ChemRxiv|||doi:10.26434/chemrxiv.12619064,Related Article: Simon Krause, Jack D. Evans, Volodymyr Bon, Irena Senkovska, Sebastian Ehrling, Paul Iacomi, Daniel M. Többens, Dirk Wallacher, Manfred S. Weiss, Bin Zheng, Pascal G. Yot, Guillaume Maurin, Philip L. Llewellyn, François-Xavier Coudert, Stefan Kaskel|2020|Chemical Science|11|9468|doi:10.1039/D0SC03727C

CCDC 2003152: Experimental Crystal Structure Determination

Related Article: Simon Krause, Jack D. Evans, Volodymyr Bon, Irena Senkovska, Sebastian Ehrling, Paul Iacomi, Daniel D. Többens, Dirk Wallacher, Manfred S. Weiss, Bin Zheng, Pascal G. Yot, Guillaume Maurin, Philip L. Llewellyn, François-Xavier Coudert, Stefan Kaskel|2020|ChemRxiv|||doi:10.26434/chemrxiv.12619064,Related Article: Simon Krause, Jack D. Evans, Volodymyr Bon, Irena Senkovska, Sebastian Ehrling, Paul Iacomi, Daniel M. Többens, Dirk Wallacher, Manfred S. Weiss, Bin Zheng, Pascal G. Yot, Guillaume Maurin, Philip L. Llewellyn, François-Xavier Coudert, Stefan Kaskel|2020|Chemical Science|11|9468|doi:10.1039/D0SC03727C