Exceptions to Fourier's Law at the Macroscale.

The usual basis to analyze heat transfer within materials is the equation formulated 200 years ago, Fourier's law, which is identical mathematically to the mass diffusion equation, Fick's law. Revisiting this assumption regarding heat transport within translucent materials, performing the experiments in vacuum to avoid air convection, we compare the model predictions to infrared-based measurements with nearly mK temperature resolution. After heat pulses, we find macroscale non-Gaussian tails in the surface temperature profile. At steady state, we find macroscale anomalous hot spots when the sample is topographically rough, and this is validated by using two additional independent methods to measure surface temperature. These discrepancies from Fourier's law for translucent materials suggest that internal radiation whose mean-free-path is millimeters interacts with defects to produce small heat sources that by secondary emission afford an additional, non-local mode of heat transport. For these polymer and inorganic glass materials, this suggests unique strategies of heat management design.

The ergodicity question when imaging DNA conformation using liquid cell electron microscopy.

Assessing the ergodicity of graphene liquid cell electron microscope measurements, we report that loop states of circular DNA interconvert reversibly and that loop numbers follow the Boltzmann distribution expected for this molecule in bulk solution, provided that the electron dose is low (80-keV electron energy and electron dose rate 1-20 e- Å-2 s-1). This imaging technique appears to act as a "slow motion" camera that reveals equilibrated distributions by imaging the time average of a few molecules without the need to image a spatial ensemble.

Volatile Droplets on Water are Sculpted by Vigorous Marangoni-Driven Subphase Flow.

The shapes of highly volatile oil-on-water droplets become strongly asymmetric when they are out of equilibrium. The unsaturated organic vapor atmosphere causes evaporation and leads to a strong Marangoni flow in the bath, unlike that previously seen in the literature. Inspecting these shapes experimentally on millisecond and submillimeter time and length scales and theoretically by scaling arguments, we confirm that Marangoni-driven convection in the subphase mechanically stresses the droplet edges to an extent that increases for organic droplets of smaller contact angle and accordingly smaller thickness. The viscous stress generated by the subphase overcomes the thermodynamic Laplace pressure. The oil droplets develop copious regularly spaced fingers, and these fingers develop spike-shaped and branched treelike structures. Unlike this behavior for single-component (surfactant-free) oil droplets, droplets composed of two miscible (surfactant-free) organic liquids develop a rim of the less volatile component along the droplet perimeter, from which jets of monodisperse smaller droplets eject periodically due to the Rayleigh-Plateau instability. When evaporation shrinks droplets to µm size, their shapes fluctuate chaotically, and ellipsoidal shapes rupture into smaller daughter droplets when subphase convection flow pulls them in opposite directions. The shape of the evaporating oil droplets is kneaded and sculpted by vigorous flow in the water subphase.

Solid-body trajectoids shaped to roll along desired pathways.

In everyday life, rolling motion is typically associated with cylindrical (for example, car wheels) or spherical (for example, billiard balls) bodies tracing linear paths. However, mathematicians have, for decades, been interested in more exotically shaped solids such as the famous oloids1, sphericons2, polycons3, platonicons4 and two-circle rollers5 that roll downhill in curvilinear paths (in contrast to cylinders or spheres) yet indefinitely (in contrast to cones, Supplementary Video 1). The trajectories traced by such bodies have been studied in detail6-9, and can be useful in the context of efficient mixing10,11 and robotics, for example, in magnetically actuated, millimetre-sized sphericon-shaped robots12,13, or larger sphericon- and oloid-shaped robots translocating by shifting their centre of mass14,15. However, the rolling paths of these shapes are all sinusoid-like and their diversity ends there. Accordingly, we were intrigued whether a more general problem is solvable: given an infinite periodic trajectory, find the shape that would trace this trajectory when rolling down a slope. Here, we develop an algorithm to design such bodies-which we call 'trajectoids'-and then validate these designs experimentally by three-dimensionally printing the computed shapes and tracking their rolling paths, including those that close onto themselves such that the body's centre of mass moves intermittently uphill (Supplementary Video 2). Our study is motivated largely by fundamental curiosity, but the existence of trajectoids for most paths has unexpected implications for quantum and classical optics, as the dynamics of qubits, spins and light polarization can be exactly mapped to trajectoids and their paths16.

Phosphorescent extensophores expose elastic nonuniformity in polymer networks.

Networks and gels are soft elastic solids of tremendous technological importance that consist of cross-linked polymers whose structure and connectivity at the molecular level are fundamentally nonuniform. Pre-failure local mechanical responses are not understood at the level of individual crosslinks, despite the enormous attention given to their macroscopic mechanical responses and to developing optical probes to detect their loci of mechanical failure. Here, introducing the extensophore concept to measure nondestructive forces using an optical probe with continuous force readout proportional to deformation, we show that the crosslinks in an elastic polymer network extend, fluctuate, and deform with a wide range of molecular individuality. Requiring little specialized equipment, this foundational single-molecule phosphorescence approach, applied here to polymer science and engineering, can be useful to a broad science and engineering community.

Oil-on-water droplets faceted and stabilized by vortex halos in the subphase.

For almost 200 y, the dominant approach to understand oil-on-water droplet shape and stability has been the thermodynamic expectation of minimized energy, yet parallel literature shows the prominence of Marangoni flow, an adaptive gradient of interfacial tension that produces convection rolls in the water. Our experiments, scaling arguments, and linear stability analysis show that the resulting Marangoni-driven high-Reynolds-number flow in shallow water overcomes radial symmetry of droplet shape otherwise enforced by the Laplace pressure. As a consequence, oil-on-water droplets are sheared to become polygons with distinct edges and corners. Moreover, subphase flows beneath individual droplets can inhibit the coalescence of adjacent droplets, leading to rich many-body dynamics that makes them look alive. The phenomenon of a "vortex halo" in the liquid subphase emerges as a hidden variable.

Experimental Guidelines to Image Transient Single-Molecule Events Using Graphene Liquid Cell Electron Microscopy.

In quest of the holy grail to "see" how individual molecules interact in liquid environments, single-molecule imaging methods now include liquid-phase electron microscopy, whose resolution can be nanometers in space and several frames per second in time using an ordinary electron microscope that is routinely available to many researchers. However, with the current state of the art, protocols that sound similar to those described in the literature lead to outcomes that can differ. The key challenge is to achieve sample contrast under a safe electron dose within a frame rate adequate to capture the molecular process. Here, we present such examples from different systems─synthetic polymer, lipid assembly, DNA-enzyme─in which we have done this using graphene liquid cells. We describe detailed experimental procedures and share empirical experience for conducting successful experiments, starting from fabrication of a graphene liquid cell, to identification of high-quality liquid pockets from desirable shapes and sizes, to effective searching for target sample pockets under electron microscopy, and to discrimination of sample molecules and molecular processes of interest. These experimental tips can assist others who wish to make use of this method.

Biopolymer Filament Entanglement Softens Then Hardens with Shear.

It is unsatisfactory that regarding the problem of entangled macromolecules driven out of equilibrium, experimentally based understanding is usually inferred from the ensemble average of polydisperse samples. Here, confronting with single-molecule imaging this common but poorly understood situation, over a wide range of shear rate we use single-molecule fluorescence imaging to track alignment and stretching of entangled aqueous filamentous actin filaments in a homebuilt rheo-microscope. With increasing shear rate, tube "softening" is followed by "hardening." Physically, this means that dynamical localization first weakens from molecular alignment, then strengthens from filament stretching, even for semiflexible biopolymers shorter than their persistence length.

Response of vesicle shapes to dense inner active matter.

We consider experimentally the Takatori-Sahu model of vesicle shape fluctuations induced by enclosed active matter, a model till present tested only in the absence of collective motion because few enclosed bacteria were used to generate the desired active motion (S. C. Takatori and A. Sahu, Phys. Rev. Lett., 2020, 124, 158102). Using deformable giant unilamellar vesicles (GUVs) and phase contrast microscopy, we extract the mode-dependence of GUV shape fluctuations when hundreds of E. coli bacteria are contained within each GUV. In the microscope focal plane, patterns of collective bacteria flow include vortex flow, dipolar flow, and chaotic motion, all of which influence the GUV shapes. The Takatori-Sahu model generalizes well to this situation if one considers the moving element to be the experimentally-determined size of the collecively-moving flock.

Comment on "Following Molecular Mobility during Chemical Reactions: No Evidence for Active Propulsion" and "Molecular Diffusivity of Click Reaction Components: The Diffusion Enhancement Question".

We provide arguments why we consider as inaccurate two recent JACS Articles which disagree with our laboratory's report of boosted diffusion during the copper-catalyzed azide-alkyne cycloaddition (CuAAC) "click" reaction. In the first paper (DOI: 10.1021/jacs.1c09455), Fillbrook et al. claim that their diffusion NMR experiments offer no evidence for boosted diffusion, but we argue that their use of Gd3+-chelates to speed up NMR relaxations times is flawed conceptually, the authors interpreting Gd3+-chelates as inert. Actually, the same features that make gadolinium ions useful as contrast agents in magnetic resonance imaging render them unsuitable for diffusion NMR. Nonetheless, by correctly adjusting technical aspects of the measurements, we confirm boosted diffusion even in the presence of this MRI contrast agent. The second paper of which we are skeptical, by Rezaei-Ghaleh et al. (DOI: 10.1021/jacs.1c11754), makes comparisons to a reference state that is not physically meaningful.

Molecules, the Ultimate Nanomotor: Linking Chemical Reaction Intermediates to their Molecular Diffusivity.

The intellectual community focused on nanomotors has recently become interested in extending these concepts to individual molecules. Here, we study a chemical reaction according to whose mechanism some intermediate species should speed up while others slow down in predictable ways, if the nanomotor hypothesis of boosted diffusion holds. Accordingly, we scrutinize the absolute diffusion coefficient (D) during intermediate steps of the catalytic cycle for the CuAAC reaction (copper-catalyzed azide-alkyne cycloaddition click reaction), using proton pulsed field-gradient nuclear magnetic resonance to discriminate between the diffusion of various reaction intermediates. We observe time-dependent diffusion that is enhanced for some intermediate molecular species and depressed for those whose size increases owing to complex formation. These findings point to the failure of the conventional Stokes-Einstein equation to fully explain diffusivity during chemical reaction. Without attempting a firm explanation, this paper highlights aspects of the physics of chemical reactions that are imperfectly understood and presents systematic data that can be used to assess hypotheses.

Mixed-Charge Nanocarriers Allow for Selective Targeting of Mitochondria by Otherwise Nonselective Dyes.

Targeted delivery of molecular cargos to specific organelles is of paramount importance for developing precise and effective therapeutics and imaging probes. This work describes a disulfide-based delivery method in which mixed-charged nanoparticles traveling through the endolysosomal tract deliver noncovalently bound dye molecules selectively into mitochondria. This system comprises three elements: (1) The nanoparticles deliver their payloads by a kiss-and-go mechanism - that is, they drop off their dye cargos proximate to mitochondria but do not localize therein; (2) the dye molecules are by themselves nonspecific to any cellular structures but become so with the help of mixed-charge nanocarriers; and (3) the dye is engineered in such a way as to remain in mitochondria for a long time, up to days, allowing for observing dynamic remodeling of mitochondrial networks and long-term tracking of mitochondria even in dividing cells. The selectivity of delivery and long-lasting staining derive from the ability to engineer charge-imbalanced, mixed [+/-] on-particle monolayers and from the structural features of the cargo. Regarding the former, the balance of [+] and [-] ligands can be adjusted to limit cytotoxicity and control the number of dye molecules adsorbed onto the particles' surfaces. Regarding the latter, comparative studies with multiple dye derivatives we synthesized rationalize the importance of polar groups, long alkyl chains, and disulfide moieties in the assembly of fluorescent nanoconstructs and long-lasting staining of mitochondria. Overall, this strategy could be useful for delivering hydrophilic and/or anionic small-molecule drugs difficult to target to mitochondria by classical approaches.

Reply to Comment on "Using NMR to Test Molecular Mobility during a Chemical Reaction".

Reports of boosted diffusion during chemical and enzymatic reactions have inspired a loyal community of scientists who find them so counterintuitive that they must be artifact. This second Comment on the subject by these authors is about technicalities of how to analyze data we deposited online regarding J. Phys. Chem. Lett. 2021 12, 2370 and Science 2020 369, 537. Now that their own data is also online, one apparent discrepancy can be resolved: we demonstrate that the authors' data agrees with ours because their first Comment on this subject reported only truncated short-time excerpts of the longer time series they deposited online (zenodo.org/record/4628353). This second Comment adds five additional objections, four of which are too technical to change the qualitative conclusion. The fifth objection errs because it omits recognizing intermediate states of the click reaction during which one reactant complexes with the catalyst to form an object of larger size. Elsewhere we analyzed in great detail the respective influences of boosted diffusion and this hydrodynamic effect (DOI: 10.26434/chemrxiv.14740563.v1). The factual evidence and reasoning in this Reply strongly support this laboratory's earlier conclusions regarding boosted diffusion during common chemical reactions.

Using NMR to Test Molecular Mobility during a Chemical Reaction.

We evaluate critically the use of pulsed gradient spin-echo nuclear magnetic resonance to measure molecular mobility during chemical reactions. With raw NMR spectra available in a public depository, we confirm the boosted mobility during the click chemical reaction (Wang et al. Science 2020 369, 537-541) regardless of the order of magnetic field gradient (linearly increasing, linearly decreasing, random sequence). We also confirm boosted mobility for the Diels-Alder chemical reaction. The conceptual advantage of the former chemical system is that a constant reaction rate implies a constant catalyst concentration, whereas that of the latter is the absence of a paramagnetic catalyst, precluding paramagnetism as an objection to the measurements. The data and discussion in this paper show the reliability of experiments when one avoids convection, allows decay of nuclear spin magnetization between successive pulses and recovery of its intensity between gradients, and satisfies quasi-steady state during the time window to acquire each datum. Especially important is to make comparisons on the time scale of the actual chemical reaction kinetics. We discuss possible sources of mistaken conclusions that are desirable to avoid.

Response to Comment on "Boosted molecular mobility during common chemical reactions".

Günther et al report that their control experiment using randomized magnetic field gradient sequences disagreed with findings we had reported using linear gradients. However, we show that measurements in our laboratory are consistent using both methods.

Anatomy of cage formation in a two-dimensional glass-forming liquid.

As a glass-forming liquid is cooled, the dynamics of its constituent particles changes from being liquid-like to more solid-like. The solidity of the resulting glassy material is believed to be due to a cage-formation process, whereby the motion of individual particles is increasingly constrained by neighbouring particles. This process begins at the temperature (or particle density) at which the glass-forming liquid first shows signs of glassy dynamics; however, the details of how the cages form remain unclear1-4. Here we study cage formation at the particle level in a two-dimensional colloidal suspension (a glass-forming liquid). We use focused lasers to perturb the suspension at the particle level and monitor the nonlinear dynamic response of the system using video microscopy. All observables that we consider respond non-monotonically as a function of the particle density, peaking at the density at which glassy dynamics is first observed. We identify this maximum response as being due to cage formation, quantified by the appearance of domains in which particles move in a cooperative manner. As the particle density increases further, these local domains become increasingly rigid and dominate the macroscale particle dynamics. This microscale rheological deformation approach demonstrates that cage formation in glass-forming liquids is directly related to the merging of such domains, and reveals the first step in the transformation of liquids to glassy materials1,5.

Master curve of boosted diffusion for 10 catalytic enzymes.

Molecular agitation more rapid than thermal Brownian motion is reported for cellular environments, motor proteins, synthetic molecular motors, enzymes, and common chemical reactions, yet that chemical activity coupled to molecular motion contrasts with generations of accumulated knowledge about diffusion at equilibrium. To test the limits of this idea, a critical testbed is the mobility of catalytically active enzymes. Sentiment is divided about the reality of enhanced enzyme diffusion, with evidence for and against. Here a master curve shows that the enzyme diffusion coefficient increases in proportion to the energy release rate-the product of Michaelis-Menten reaction rate and Gibbs free energy change (ΔG)-with a highly satisfactory correlation coefficient of 0.97. For 10 catalytic enzymes (urease, acetylcholinesterase, seven enzymes from the glucose cascade cycle, and one other), our measurements span from a roughly 40% enhanced diffusion coefficient at a high turnover rate and negative ΔG to no enhancement at a slow turnover rate and positive ΔG Moreover, two independent measures of mobility show consistency, provided that one avoids undesirable fluorescence photophysics. The master curve presented here quantifies the limits of both ideas, that enzymes display enhanced diffusion and that they do not within instrumental resolution, and has possible implications for understanding enzyme mobility in cellular environments. The striking linear dependence of ΔG for the exergonic enzymes (ΔG <0), together with the vanishing effect for endergonic enzyme (ΔG >0), are consistent with a physical picture in which the mechanism boosting the diffusion is an active one, utilizing the available work from the chemical reaction.

Boosted molecular mobility during common chemical reactions.

Mobility of reactants and nearby solvent is more rapid than Brownian diffusion during several common chemical reactions when the energy release rate exceeds a threshold. Screening a family of 15 organic chemical reactions, we demonstrate the largest boost for catalyzed bimolecular reactions, click chemistry, ring-opening metathesis polymerization, and Sonogashira coupling. Boosted diffusion is also observed but to lesser extent for the uncatalyzed Diels-Alder reaction, but not for substitution reactions SN1 and SN2 within instrumental resolution. Diffusion coefficient increases as measured by pulsed-field gradient nuclear magnetic resonance, whereas in microfluidics experiments, molecules in reaction gradients migrate "uphill" in the direction of lesser diffusivity. This microscopic consumption of energy by chemical reactions transduced into mechanical motion presents a form of active matter.