In many growth models, economic growth arises from people creating ideas, and the long-run growth rate is the product of two terms: the effective number of researchers and their research productivity. We present a wide range of evidence from various industries, products, and firms showing that research effort is rising substantially while research productivity is declining sharply. A good example is Moore's Law. The number of researchers required today to achieve the famous doubling every two years of the density of computer chips is more than 18 times larger than the number required in the early 1970s. Across a broad range of case studies at various levels of (dis)aggregation, we find that ideas-and in particular the exponential growth they imply -are getting harder and harder to find. Exponential growth results from the large increases in research effort that offset its declining productivity.

Understanding the mechanisms of lithium-ion transport in polymers is crucial for the design of polymer electrolytes. We combine modular synthesis, electrochemical characterization, and molecular simulation to investigate lithium-ion transport in a new family of polyester-based polymers and in poly(ethylene oxide) (PEO). Theoretical predictions of glass-transition temperatures and ionic conductivities in the polymers agree well with experimental measurements. Interestingly, both the experiments and simulations indicate that the ionic conductivity of PEO, relative to the polyesters, is far higher than would be expected from its relative glass-transition temperature. The simulations reveal that diffusion of the lithium cations in the polyesters proceeds via a different mechanism than in PEO, and analysis of the distribution of available cation solvation sites in the various polymers provides a novel and intuitive way to explain the experimentally observed ionic conductivities. This work provides a platform for the evaluation and prediction of ionic conductivities in polymer electrolyte materials.

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The Materials Genome Initiative (MGI) advanced a new paradigm for materials discovery and design, namely that the pace of new materials deployment could be accelerated through complementary efforts in theory, computation, and experiment. Along with numerous successes, new challenges are inviting researchers to refocus the efforts and approaches that were originally inspired by the MGI. In May 2017, the National Science Foundation sponsored the workshop "Advancing and Accelerating Materials Innovation Through the Synergistic Interaction among Computation, Experiment, and Theory: Opening New Frontiers" to review accomplishments that emerged from investments in science and infrastructure under the MGI, identify scientific opportunities in this new environment, examine how to effectively utilize new materials innovation infrastructure, and discuss challenges in achieving accelerated materials research through the seamless integration of experiment, computation, and theory. This article summarizes key findings from the workshop and provides perspectives that aim to guide the direction of future materials research and its translation into societal impacts.

Fluoride ion batteries are potential “next-generation” electrochemical storage devices that offer high energy density. At present, such batteries are limited to operation at high temperatures because suitable fluoride ion–conducting electrolytes are known only in the solid state. We report a liquid fluoride ion–conducting electrolyte with high ionic conductivity, wide operating voltage, and robust chemical stability based on dry tetraalkylammonium fluoride salts in ether solvents. Pairing this liquid electrolyte with a copper–lanthanum trifluoride (Cu@LaF3) core-shell cathode, we demonstrate reversible fluorination and defluorination reactions in a fluoride ion electrochemical cell cycled at room temperature. Fluoride ion–mediated electrochemistry offers a pathway toward developing capacities beyond that of lithium ion technology.

The chemical design of polymers with target structural and/or functional properties represents a grand challenge in materials science. While data-driven design approaches are promising, success with polymers has been limited, largely due to limitations in data availability. Here, we demonstrate the targeted sequence design of single-chain structure in polymers by combining coarse-grained modeling, machine learning, and model optimization. Nearly 2000 unique coarse-grained polymers are simulated to construct and analyze machine learning models. We find that deep neural networks inexpensively and reliably predict structural properties with limited sequence information as input. By coupling trained ML models with sequential model-based optimization, polymer sequences are proposed to exhibit globular, swollen, or rod-like behaviors, which are verified by explicit simulations. This work highlights the promising integration of coarse-grained modeling with data-driven design and represents a necessary and crucial step toward more complex polymer design efforts.

We introduce a coarse-grained approach for characterizing the long-timescale dynamics of ion diffusion in general polymer electrolytes using input from short molecular dynamics trajectories. The approach includes aspects of the dynamic bond percolation model [J. Chem. Phys. 1983, 79, 3133−3142] by treating ion diffusion in terms of hopping transitions on a fluctuating lattice. We extend this well-known approach by using short (i.e., 10 ns) molecular dynamics (MD) trajectories to predict the distribution of ion solvation sites that comprise the lattice and to predict the rate of hopping among the lattice sites. This yields a chemically specific dynamic bond percolation (CS-DBP) model that enables the description of long-timescale ion diffusion in polymer electrolytes at a computational cost that makes feasible the screening of candidate materials. We employ the new model to characterize lithium-ion diffusion properties in six polyethers that differ by oxygen content and backbone stiffness: poly(trimethylene oxide), poly(ethylene oxide-alt-trimethylene oxide), poly(ethylene oxide), poly(propylene oxide), poly(ethylene oxide-alt-methylene oxide), and poly(methylene oxide). Good agreement is observed between the predictions of the CS-DBP model and long-timescale atomistic MD simulations, thus providing validation of the model. Among the most striking results from this analysis is the unexpectedly good lithium-ion diffusivity of poly(trimethylene oxide-alt-ethylene oxide) by comparison to poly(ethylene oxide), which is widely used. Additionally, the model straightforwardly reveals a range of polymer features that lead to low lithium-ion diffusivity, including the competing effects of the density of solvation sites and polymer stiffness. These results illustrate the potential of the CS-DBP model to screen polymer electrolytes on the basis of ion diffusivity and to identify important design criteria.

Solid polymer electrolytes (SPE) have the potential to increase both the energy density and stability of lithium-based batteries, but low Li + conductivity remains a barrier to technological viability. 1, 2 SPEs are designed to maximize Li + diffusivity relative to the anion, while maintaining sufficient salt solubility.It is thus remarkable that polyethylene oxide (PEO), the most widely used SPE, exhibits Li + diffusivity that is an order of magnitude smaller than that of typical counter-ions, such as TFSI − , at moderate salt concentrations. 3, 4 Here, we show that Lewis-basic polymers like PEO intrinsically favor slow cation and rapid anion diffusion while this relationship can be reversed in Lewis-acidic polymers.Using molecular dynamics (MD) simulations, Lewis-acidic polyboranes are identified that achieve up to a ten-fold increase in Li + diffusivity and a significant decrease in anion diffusivity, relative to PEO. The results for this new class of Lewis-acidic SPEs illustrate a general principle for increasing Li + diffusivity and transference number with polymer chemistries that exhibit weaker cation and stronger anion coordination. Savoie, Webb, and Miller -2 PEO-based materials are among the most successful SPEs, with net conductivities on the order of 10 −4 − 10 −3 S · cm −1 at ambient temperature. 5,6 However, net conductivity actually overstates electrolyte performance, since only Li + typically participates in the electrode chemistries in lithium-based batteries (Fig. 1A). Measurements of the Li + transference number, T Li (the ratio of Li + conductivity to the total conductivity), show that anions are responsible for most of the conductivity in PEO, 7-9 and ion diffusivity measurements reveal that anion diffusivity is an order of magnitude larger than Li + diffusivity for common salts at typical concentrations. 3, 4 Most strategies for increasing T Li have focused on immobilizing the anion, 10-13 while the primary strategy for increasing overall diffusion rates has been to decrease the glass-transition temperature, T g , of the polymer. 5, 6 However, neither approach addresses the fundamental ion-polymer interactions that are responsible for asymmetric cation and anion conduction.The major finding of this work is that the low Li + diffusivity and high anion diffusivity that characterize PEO-based SPEs can be reversed to favor Li + conduction in Lewis-acidic polymers. In conventional SPEs based on polyethers and other Lewis-basic units, salt solubility is driven by strong cation-polymer interactions. 11,14,15 However, this preferential coordination of cations leads to both the high relative diffusivity of weakly coordinated anions and the low diffusivity of Li + (Fig. 1B). The trade-off between strong cation coordination and diffusivity suggests that the strategy of driving salt solubility with relatively stronger anion-polymer interactions and weaker cation-polymer interactions may enhance SPE performance. To investigate this trade-off, we present over 100 microseconds of MD simulations to charact...