Johannes Peter Dürholt

Bayesian optimization (BO) is a promising strategy for accelerating gradient-elution liquid chromatography (LC) method development, but its practical success depends on several tightly coupled components. Here we report two main advances. First, for the Gaussian process (GP) surrogate models used within BO, we introduce a shape-aware gradient representation that compares gradient profiles directly through a Wasserstein-distance kernel, rather than through the pump-timetable coordinates used by standard representations. Second, we establish a robust automated acquisition and analysis workflow based on a trap phase that isolates gradient-driven elution and makes reliable closed-loop measurement possible. These are supported by three refinements: a flexible gradient domain with variable method duration and user-defined composition bounds, a window-relative sampler for monotonic gradient programs, and an adaptive reference point for multi-objective optimization. Across in silico and experimental datasets, Wasserstein-based representations generally predict separation quality more accurately than timetable-based approaches, especially when only a few training samples are available. This improved accuracy translates into more data-efficient singleand multi-objective optimization campaigns. Finally, we demonstrate the closed-loop framework in experimental case studies, where both single-and multi-objective campaigns improve upon a custom baseline method for a polymer-additive sample. Together, these results show that shape-aware gradient representations improve both GP predictive accuracy and BO sample efficiency, and that a flexible gradient domain, robust automated acquisition and analysis, and compatible sampling and optimization strategies enable effective closed-loop LC method development

Bayesian optimization (BO) is a promising strategy for accelerating gradient-elution liquid chromatography (LC) method development, but its practical success depends on several tightly coupled components. Here we report two main advances. First, for the Gaussian process (GP) surrogate models used within BO, we introduce a shape-aware gradient representation that compares gradient profiles directly through a Wasserstein-distance kernel, rather than through the pump-timetable coordinates used by standard representations. Second, we establish a robust automated acquisition and analysis workflow based on a trap phase that isolates gradient-driven elution and makes reliable closed-loop measurement possible. These are supported by three refinements: a flexible gradient domain with variable method duration and user-defined composition bounds, a window-relative sampler for monotonic gradient programs, and an adaptive reference point for multi-objective optimization. Across in silico and experimental datasets, Wasserstein-based representations generally predict separation quality more accurately than timetable-based approaches, especially when only a few training samples are available. This improved accuracy translates into more data-efficient singleand multi-objective optimization campaigns. Finally, we demonstrate the closed-loop framework in experimental case studies, where both single-and multi-objective campaigns improve upon a custom baseline method for a polymer-additive sample. Together, these results show that shape-aware gradient representations improve both GP predictive accuracy and BO sample efficiency, and that a flexible gradient domain, robust automated acquisition and analysis, and compatible sampling and optimization strategies enable effective closed-loop LC method development

Controlling the transport of thermal energy is key to most applications of metal–organic frameworks (MOFs). Analyzing the evolution of the effective local temperature, the interfaces between the metal nodes and the organic linkers are identified as the primary bottlenecks for heat conduction. Consequently, changing the bonding strength at that node–linker interface and the mass of the metal atoms can be exploited to tune the thermal conductivity. This insight is generated employing molecular dynamics simulations in conjunction with advanced, ab initio parameterized force fields. The focus of the present study is on MOF‐5 as a prototypical example of an isoreticular MOF. However, the key findings prevail for different node structures and node–linker bonding chemistries. The presented results lay the foundation for developing detailed structure‐to‐property relationships for thermal transport in MOFs with the goal of devising strategies for the application‐specific optimization of heat conduction.

The thermal conductivity is an important property of metal-organic frameworks (MOFs). For gas storage applications, a too low thermal conductivity might turn out to be a game-stopper. Conversely, for thermoelectric devices the thermal conductivity has to be low enough. The chemical and structural flexibility of MOFs provides handles for conveniently tuning thermal properties. Still, for realizing the full potential of these materials, a detailed understanding of the corresponding structure-to-property relationships is required. For achieving such an understanding, we employ quantum-mechanical and force-field based simulations to study heat transport processes in MOFs both in real as well as in reciprocal space. The former approach relies on analyzing the effective local temperature in different parts of the MOF during a non-equilibrium molecular dynamics simulation. This allows identifying specific elements and bonds within the MOF that act as heat-transport bottlenecks. For a variety of MOF structures we show that the main local inhibitor to heat flow is the bond between the metal ions in the nodes and the carboxylic oxygens in the linkers. Further computer experiments then allow assessing the impact of the strength of that bond and of parameters like the mass of the nodes, the length and density of the linkers, bonding motives, the network topology, etc.. Typically, we find that stronger bonds, lighter nodes, and longer and more dense linkers increase thermal transport. As an alternative approach, analyzing heat transport in reciprocal space enables us to connect the values of the thermal conductivity to the properties of phonons as the quanta of mechanical and thermal lattice energy. Of particular interest in this context is the impact of structural variations on quantities like phonon densities of states, group velocities, and phonon lifetimes, which all directly impact heat transport processes. An analysis of these quantities provides insight into the nature of the vibrations that most strongly impact thermal conductivities. Consistent with the results from the real-space analysis, we find that the group velocities of the relevant phonons are increased by lighter nodes and by an increased mode-linker coupling. Notably, the bonds between nodes and linkers are also a major source of anharmonicities, thus reducing phonon lifetimes and decreasing thermal conductivities. Finally, we show that phonon properties are also crucial for other parameters, like elastic constants, thermal expansion, and - by virtue of electron-phonon coupling - also charge transport.

The prototypical pillared layer MOFs, formed by a square lattice of paddle-wheel units and connected by dinitrogen pillars, can undergo a breathing phase transition by a “wine-rack” type motion of the square lattice. We studied this behavior, which is not yet fully understood, using an accurate first principles parameterized force field (MOF-FF) for larger nanocrystallites on the example of Zn₂(bdc)₂(dabco) [bdc: benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)], and found clear indications for an interface between a closed and an open pore phase traveling through the system during the phase transformation [J. Keupp and R. Schmid, Adv. Theory Simul., 2019, 2, 1900117]. In conventional simulations in small supercells this mechanism is prevented by periodic boundary conditions (PBCs), enforcing a synchronous transformation of the entire crystal. Here, we extend this investigation to pillared layer MOFs with flexible side-chains, attached to the linker. Such functionalized (fu-)MOFs are experimentally known to have different properties with the side-chains acting as fixed guest molecules. First, in order to extend the parameterization for such flexible groups, a new parameterization strategy for MOF-FF had to be developed, using a multi-structure force based fit method. The resulting parameterization for a library of fu-MOFs is then validated with respect to a set of reference systems and shows very good accuracy. In the second step, a series of fu-MOFs with increasing side-chain length is studied with respect to the influence of the side-chains on the breathing behavior. For small supercells in PBCs a systematic trend of the closed pore volume with the chain length is observed. However, for a nanocrystallite model a distinct interface between a closed and an open pore phase is visible only for the short chain length, whereas for longer chains the interface broadens and a nearly concerted transformation is observed. Only by molecular dynamics simulations using accurate force fields can such complex phenomena can be studied on a molecular level.

The prototypical pillared layer MOFs, formed by a square lattice of paddle-wheel units and connected by dinitrogen pillars, can undergo a breathing phasetransition by a “wine-rack” type motion of the square lattice. We studied this notyet fully understood behavior using an accurate first principles parameterized forcefield (MOF-FF) for larger nanocrystallites on the example of Zn 2 (bdc) 2 (dabco) [bdc:benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)] and found clear indi-cations for an interface between a closed and an open pore phase traveling throughthe system during the phase transformation [Adv. Theory Simul. 2019, 2, 11]. Inconventional simulations in small supercells this mechanism is prevented by periodicboundary conditions (PBC), enforcing a synchronous transformation of the entirecrystal. Here, we extend this investigation to pillared layer MOFs with flexibleside-chains, attached to the linker. Such functionalized (fu-)MOFs are experimen-tally known to have different properties with the side-chains acting as fixed guestmolecules. First, in order to extend the parameterization for such flexible groups,1a new parametrization strategy for MOF-FF had to be developed, using a multi-structure force based fit method. The resulting parametrization for a library offu-MOFs is then validated with respect to a set of reference systems and shows verygood accuracy. In the second step, a series of fu-MOFs with increasing side-chainlength is studied with respect to the influence of the side-chains on the breathingbehavior. For small supercells in PBC a systematic trend of the closed pore volumewith the chain length is observed. However, for a nanocrystallite model a distinctinterface between a closed and an open pore phase is visible only for the short chainlength, whereas for longer chains the interface broadens and a nearly concerted trans-formation is observed. Only by molecular dynamics simulations using accurate forcefields such complex phenomena can be studied on a molecular level.

Molecular simulations reveal that mesoporous metal–organic frameworks display large volumetric negative thermal expansion, which has a considerable effect on mechanical stability, outlining an alternative application for these ultra-porous materials.

Most conventional materials display expansion upon heating, so there is considerable interest in identifying materials that display the opposite behavior, negative thermal expansion (NTE). In the current study, seven mesoporous metal-organic frameworks (MOFs) of varying topology and composition, which exhibit outstanding porosity, were investigated using molecular simulation for temperature-induced contraction. We find exceptional NTE for the most porous MOFs and a correlation between the coefficient of NTE and porosity. The large molecular subunits of the MOFs were further studied to find they intrinsically display NTE, corresponding to terahertz vibrational modes. As a result, NTE has a considerable effect on the mechanical properties of these MOFs and is an important consideration for understanding the mechanical stability of new extremely porous materials.

Recently the possibility of using electric fields as a further stimulus to trigger structural changes in metal-organic frameworks (MOFs) has been investigated. In general, rotatable groups or other types of mechanical motion can be driven by electric fields. In this study we demonstrate how the electric response of MOFs can be tuned by adding rotatable dipolar linkers, generating a material that exhibits paralectric behavior in two dimensions and dielectric behavior in one dimension. The suitability of four different methods to compute the relative permittivity κ by means of molecular dynamics simulations was validated. The dependency of the permittivity on temperature T and dipole strength μ was determined. It was found that the herein investigated systems exhibit a high degree of tunability and substantially larger dielectric constants as expected for MOFs in general. The temperature dependency of κ obeys the Curie-Weiss law. In addition, the influence of dipolar linkers on the electric field induced breathing behavior was investigated. With increasing dipole moment, lower field strength are required to trigger the contraction. These investigations set the stage for an application of such systems as dielectric sensors, order-disorder ferroelectrics or any scenario where movable dipolar fragments respond to external electric fields.