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Using all-atom molecular dynamics simulations, we report the structure and ion transport characteristics of a new class of solid polymer electrolytes that contain biodegradable and mechanically stable biopolymer pectin. We simulate a highly conducting ethylene carbonate (EC) as a solvent for lithium-trifluoromethanesulfonimide (LiTFSI) salt containing different weight percentages of pectin. Our simulations reveal that the pectin chains reduce the coordination numbers of lithium ions around the counterions (and vice-versa) because of stronger lithium-pectin interactions compared to lithium-TFSI interactions. Further, the pectin is found to promote smaller ionic aggregates over larger ones, contrary to results typically reported for liquid and polymer electrolytes. We observe that the loading of pectin in EC-LiTFSI electrolytes increases the viscosity ($\eta$) and relaxation timescales ($\tau_c$), indicating higher mechanical stability and, consequently, the mean squared displacements, diffusion coefficients (D), and the Nernst-Einstein conductivity ($\sigma_{NE}$) decrease. Interestingly, while the lithium diffusivities are related to the ion-pair relaxation timescales as $D_+\sim \tau_c^{-3.1}$, the TFSI$^-$ diffusivities exhibit excellent correlations with ion-pair relaxation timescales as $D_-\sim \tau_c^{-0.95}$. On the other hand, the NE conductivities are dictated by distinct transport mechanisms and scales with ion-pair relaxation timescale as $\sigma_{NE}\sim \tau_c^{-1.85}$.

We investigate the effect of pectin on the structure and ion transport properties of the room-temperature ionic liquid electrolyte 1-n-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF$_6$]) using molecular dynamics simulations. We find that pectin induces intriguing structural changes in the electrolyte that disrupt large ionic aggregates and promote the formation of smaller ionic clusters, which is a promising finding for ionic conductivity. Due to pectin in [BMIM][PF$_6$] electrolytes, the diffusion coefficient of cations and anions is observed to decrease by a factor of four for a loading of 25 wt. % in pectin. A strong correlation between the ionic diffusivities (D) and ion-pair relaxation timescales ($\tau$) is observed such that D~$\tau^{-0.75}$ for cations and D~$\tau^{-0.82}$ for anions. The relaxation timescale exponents indicate that the ion transport mechanisms in pectin-[BMIM][PF$_6$] electrolytes are slightly distinct from those found in neat [BMIM][PF6] electrolytes. These findings suggest that pectin-based solid polymer electrolytes may offer improved properties for battery applications, including ionic conductivity, mechanical stability, and biodegradability., Comment: 18 pages, 5 figures

Nanoscale fluid transport is typically pictured in terms of atomic-scale dynamics, as is natural in the real-space framework of molecular simulations. An alternative Fourier-space picture, that involves the collective charge fluctuation modes of both the liquid and the confining wall, has recently been successful at predicting new nanofluidic phenomena such as quantum friction and near-field heat transfer, that rely on the coupling of those fluctuations. Here, we study the charge fluctuation modes of a two-dimensional (planar) nanofluidic channel. Introducing confined response functions that generalize the notion of surface response function, we show that the channel walls exhibit coupled plasmon modes as soon as the confinement is comparable to the plasmon wavelength. Conversely, the water fluctuations remain remarkably bulk-like, with significant confinement effects arising only when the wall spacing is reduced to 7 A. We apply the confined response formalism to predict the dependence of the solid-water quantum friction and thermal boundary conductance on channel width for model channel wall materials. Our results provide a general framework for Coulomb interactions of fluctuating matter in nanoscale confinement.

Based on a Hamiltonian that incorporates the elastic coupling between a tracer and active particles, we derive a generalized Langevin model for the non-equilibrium mechanical response of active viscoelastic biomatter. Our model accounts for the power-law viscoelastic response of the embedding polymeric network as well as for the non-equilibrium energy transfer between active and tracer particles. Our analytical expressions for the frequency-dependent response function and the positional autocorrelation function agree nicely with experimental data for red blood cells and actomyosin networks with and without ATP. The fitted effective active-particle temperature, elastic constants and effective friction coefficients of our model allow straightforward physical interpretation., 6 pages, 2 figures; supplemental material (16 pages, 5 figures) is appended

We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a Generalized Langevin Equation (GLE) for a general interacting many-body system. The resulting GLE includes i) explicitly the potential of mean force (PMF) that describes the equilibrium distribution of the system in the chosen space of reaction coordinates, ii) a random force term that explicitly depends on the initial state of the system, and iii) a memory friction contribution that splits into two parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general non-linear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme thus combines all desirable properties of the Zwanzig and Mori projection schemes. The non-linear memory friction contribution is shown to be related to correlations between the reaction-coordinate velocity and the random force. We present a numerical method to compute all parameters of our GLE, in particular, the non-linear memory friction function and the random force distribution, from a trajectory in reaction coordinate space. We apply our method to the dihedral-angle dynamics of a butane molecule in water obtained from atomistic molecular dynamics simulations. For this example, we demonstrate that non-linear memory friction is present and that the random force exhibits significant non-Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction coordinates that are general functions of all positions in the phase space of the underlying many-body system; this corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium behavior but also the correct dynamics of the coarse-grained system.

When described by a low-dimensional reaction coordinate, the rates of protein folding are determined by a subtle interplay between free-energy barriers and friction. While it is commonplace to extract free-energy profiles from molecular trajectories, a direct evaluation of friction is far more elusive, and one typically evaluates it indirectly via memoryless reaction rate theories. Here, using memory-kernel extraction methods founded on a generalised Langevin equation (GLE) formalism, we directly calculate the memory-dependent friction for eight fast-folding proteins, taken from a published set of large-scale molecular dynamics protein simulations. Our results reveal that, contrary to common expectation, friction is more important than free energy barriers in determining protein folding rates, particularly for larger proteins. We also show that proteins fold in a regime where the finite decay time of friction significantly reduces the folding times, in some instances by as much as a factor of 10, compared to predictions based on memoryless friction., Comment: 10 pages, 4 figures

Signatures of solvated excess protons in infrared difference absorption spectra, such as the continuum band between the water bend and stretch bands, have been experimentally known for a long time, but the theoretical basis for linking spectral signatures with the microscopic proton-transfer mechanism so far relied on normal-mode analysis. We analyze the excess-proton dynamics in ab initio molecular-dynamics simulations of aqueous hydrochloric acid solutions by trajectory-decomposition techniques. The continuum band in the 2000 - 3000 cm$^{-1 }$ range is shown to be due to normal-mode oscillations of temporary H$_3$O$^+$ complexes. An additional prominent peak at 400 cm$^{-1}$ reports on the coupling of excess-proton motion to the relative vibrations of the two flanking water molecules. The actual proton transfer between two water molecules, which for large water separations involves crossing of a barrier and thus is not a normal mode, is characterized by two characteristic time scales: Firstly, the waiting time for transfer to occur in the range of 200 - 300 fs, which leads to a broad weak shoulder around ~100 cm$^{-1}$, consistent with our experimental THz spectra. Secondly, the mean duration of a transfer event of about 14 fs, which produces a rather well-defined spectral contribution around 1200 cm$^{-1}$ and agrees in location and width with previous experimental mid-infrared spectra.

Saliva is primarily composed of water, but additionally includes a variety of organic and inorganic substances such as salt, proteins, peptides, mucins, virions, etc. The presence of such solutes affects the evaporation time of respiratory droplets that are sedimenting in air, and thereby the airborne transmission of infections. From solutions of the coupled heat-conduction and water-diffusion equations within the droplet and in the ambient vapor phase, we find that the solute-induced water vapor-pressure reduction considerably slows down the evaporation process and dominates the solute-concentration dependence of the droplet evaporation time. The evaporation-induced solute-concentration gradient near the droplet surface, which is accounted for using a two-stage evaporation model, is found to further intensify the slowing down of the drying process. On the other hand, the presence of solutes is found to reduce evaporation cooling of the droplet, which causes a slight decrease in the evaporation time. Overall, the first two effects are dominant, meaning that the droplet evaporation time increases in the presence of solutes. The solute-concentration dependence of the water diffusivity inside the droplet does not significantly change the evaporation time. Finally, crust formation on the droplet surface is found to increase the final equilibrium size of the droplet., 40 pages, 8 figures

Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with rigorous theoretical arguments, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids; as a consequence, its origin is non-local in time. Concomitantly, the molecules experience Brownian forces that display persistent correlations and long-lasting memory. A critical test of the generalised Stokes-Einstein relation, mapping the friction of single molecules to the viscoelastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield novel insights into vitrification mechanisms and the intriguing mechanical properties of soft materials.

The effect of evaporation on droplet sedimentation times is crucial for estimating the risk of infection from virus-containing airborne droplets. For droplet radii in the range 100 nm < R < 60 ��m, evaporation can be described in the stagnant-flow approximation and is diffusion limited. Analytical equations are presented for the droplet evaporation rate, the time-dependent droplet size and the sedimentation time, including the significant effect of evaporation cooling. Evaporation makes the time for large droplets to sediment much longer and thus significantly increases the viral air load. Using recent estimates for SARS-CoV-2 concentrations in sputum and droplet production rates while speaking, a single infected person that constantly speaks without a mouth cover produces a total air load of more than 10^4 virions. In a mid-size closed room, this leads to a viral inhalation frequency of at least 2.5 per minute. Low relative humidity, as encountered inside buildings in winter and in airliners, speeds evaporation and thus keeps initially larger droplets suspended in air., New version contains estimate of number of virions sedimenting in air in steady state and effect of air-exchange rate in closed room

International audience; Nanofluidics has firmly established itself as a new field in fluid mechanics, as novel properties have been shown to emerge in fluids at the nanometric scale. Thanks to recent developments in fabrication technology, artificial nanofluidic systems are now being designed at the scale of biological nanopores. This ultimate step in scale reduction has pushed the development of new experimental techniques and new theoretical tools, bridging fluid mechanics, statistical mechanics, and condensed matter physics. This review is intended as a toolbox for fluids at the nanometer scale. After presenting the basic equations that govern fluid behavior in the continuum limit, we show how these equations break down and new properties emerge in molecular-scale confinement. A large number of analytical estimates and physical arguments are given to organize the results and different limits.

The structure and stability of strongly charged complex fibers formed by complexation of a single long semi-flexible polyelectrolyte (PE) chain and many oppositely charged spherical macroions are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures are determined by a competition between attraction between spheres and the PE chain (which favors chain wrapping around the spheres), chain bending and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as medium salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in a chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30nm, which appears to agree with the thickness observed in in vitro experiments on chromatin. We also find a macroion density of 5-6 per 11nm which agrees with the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic model, these findings suggest that chromatin-like structures should also be observable for PE-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge., Comment: 18 pages, 15 figures

Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low temperature / low force compact (folded) structure and a high temperature / high force molten (unfolded) structure. The influence of c on phase diagrams, critical exponents, melting, and force extension curves is derived analytically. For vanishing pulling force, only for the limited range of loop exponents 2 < c < 2.479 a melting transition is possible; for c, 19 pages, 14 figures, supplementary material

The adsorption of a single polymer to a flat surface in shear is investigated using Brownian hydrodynamics simulations and scaling arguments. Competing effects are disentangled: in the absence of hydrodynamic interactions, shear drag flattens the chain and thus enhances adsorption. Hydrodynamic lift on the other hand gives rise to long-ranged repulsion from the surface which preempts the surface-adsorbed state via a discontinuous desorption transition, in agreement with theoretical arguments. Chain flattening is dominated by hydrodynamic lift, so overall, shear flow weakens the adsorption of flexible polymers. Surface friction due to small-wavelength surface potential corrugations is argued to weaken the surface attraction as well., 6 pages, 4 figures

We present an overview of our understanding of electrostatic interactions between charged macromolecular surfaces mediated by mobile counter- and coions. The dichotomy between the weak and the strong coupling regimes is described in detail and the way they engender repulsive and attractive interactions between nominally equally charged macroions. We also introduce the concept of dressed counterions in the case of many-component Coulomb fluids that are partially weakly and partially strongly coupled to local electrostatic fields leading to non-monotonic interactions between equally charged macroions. The effect of quenched surface charge disorder on the counterion-mediated electrostatic interactions is analyzed within the same conceptual framework and shown to lead to unexpected and extraordinary electrostatic interactions between randomly charged surfaces with equal mean surface charge densities or even between effectively neutral macroion surfaces. As a result, these recent developments challenge some cherished notions of pop culture., 18 pages, 5 figures

Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic (Berezinskii-Kosterlitz-Thouless) geometric order, occurs in the phase diagram, in addition to the ordinary (compact) percolating phase and the non-percolating phase. It is found that no connection exists between, on the one hand, the onset of this geometric BKT behavior and, on the other hand, the onsets of the highly clustered small-world character of the network and of the thermal BKT transition of the Ising model on this network. Nevertheless, both geometric and thermal BKT behaviors have inverted characters, occurring where disorder is expected, namely at low bond probability and high temperature, respectively. This may be a general property of long-range networks., Added explanations and data. Published version. 4pages, 4 figures

We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The theory is designed to exactly reproduce the lowest order equilibrium averages of a stretched polymer, and treats the full complexity of the problem: the resulting dynamics include the coupled effects of long-range hydrodynamic interactions, backbone stiffness, and large-scale polymer contour fluctuations. Validated by Brownian hydrodynamics simulations and comparison to optical tweezer measurements on stretched DNA, the theory is highly accurate in the intermediate tension regime over a broad dynamical range, without the need for additional dynamic fitting parameters., 22 pages, 9 figures; revised version with additional calculations and experimental comparison; accepted for publication in Macromolecules

Neutral or charged polymers that are densely end-grafted to surfaces form brush-like structures and are highly stretched under good-solvent conditions. We discuss and compare relevant results from scaling models, self-consistent-field methods and MD simulation techniques and concentrate on the conceptual simple case of planar substrates. For neutral polymers the main quantity of interest is the brush height and the polymer density profile, which can be well predicted from self-consistent calculations and simulations. Charged polymers (polyelectrolytes) are of practical importance since they are soluble in water. Counterion degrees of freedom determine the brush behavior in a decisive way and lead to a strong and non-linear swelling of the brush., 36 pages, 13 figures, Advances in Polymer Science (2005)-in press

We experimentally and theoretically consider highly condensed planar brushes made of charged polymers. Using x-ray reflectivity on polyelectrolytes which are anchored at the water-air interface, it is shown that such strongly stretched brushes show a slight but detectable height variation upon lateral compression. This stands in contrast to the well-accepted scaling relation in the so-called osmotic brush regime, which predicts the brush height to be independent of the grafting density. Similar effects are seen in simulations on highly compressed charged brushes. Scaling arguments which go beyond the linear approximation for the entropy of confined counterions and for weak chain-stretching are able to explain those findings on a semi-quantitative level., Comment: 18 pages, 6 figures

We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and the counterion-condensation process at polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction., Comment: 14 pages, 8 figures; shorter and revised version of Eur. Phys. J. E 12, 223 (2003)

We investigate numerically and on the scaling level the adsorption of a charged colloid on an oppositely charged flexible membrane. We show that the long ranged character of the electrostatic interaction leads to a wrapping reentrance of the complex as the salt concentration is varied. The membrane wrapping depends on the size of the colloid and on the salt concentration and only for intermediate salt concentration and colloid sizes we find full wrapping. From the scaling model we derive simple relations for the phase boundaries between the different states of the complex, which agree well with the numerical minimization of the free energy., Comment: 7 page, 11 figures

Similarly and highly charged plates in the presence of multivalent counter ions attract each other, leading to electrostatically bound states. Using Monte-Carlo simulations we obtain the inter-plate pressure in the global parameter space. The equilibrium plate separation, where the pressure changes from attractive to repulsive, exhibits a novel unbinding transition. A systematic and asymptotically exact strong-coupling field-theory yields the bound state from a competition between counter-ion entropy and electrostatic attraction, in agreement with simple scaling arguments., Comment: 4 pages, 4 figures

This chapter deals with various aspects related to the adsorption of long chain-like macromolecules (polymers) onto solid surfaces. Physical aspects of the adsorption mechanism are elaborated mainly at thermodynamical equilibrium. The basic features needed in modeling of this adsorption are discussed. We first discuss the adsorption of a single and long polymer chain to the surface. The surface interaction is modeled by a potential well with a long-ranged attractive tail. A simple mean-field theory description is presented and the concept of polymer "blobs" is used to describe the conformation of the chain at the surface. The thickness of the adsorbed layer depends on several polymer and surface parameters. Fluctuation corrections to mean-field theory are also discussed. We then review adsorption as well as depletion processes in the many-chain case. Profiles, changes in the surface tension and polymer surface excess are calculated within mean-field theory. Corrections due to fluctuations in good solvent are taken into account using scaling concepts. The proximal exponent is introduced in analogy to surface critical phenomena. The interaction between two surfaces with adsorbed polymer layers is discussed, and various cases leading to attractive and repulsive interactions are mentioned. Polyelectrolytes are of practical importance due to their water solubility; we give a short summary of recent progress in this rapidly evolving field. The behavior of grafted polymers, i.e., polymers which are anchored with one end to a solid substrate is also reviewed., Comment: 44 pages, 10 figures, review article to appear as a chapter in "Metal Oxides"

We formulate the non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of fluctuations and correlations are included by a loop-wise expansion around this saddle point. We show that the Poisson equation is obeyed at each order in the loop expansion and explicitly give the expansion of the Gibbs potential up to two loops. We then apply our formalism to the case of an impenetrable, charged wall, and obtain the fluctuation corrections to the electrostatic potential and counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. We also calculate effective interactions between charged particles, which reflect counter-ion correlation effects., Comment: 12 pages, 8 postscript figures

A field theory is presented for particles which interact via Coulomb and hard-core potentials. We apply the method to the one-component plasma (OCP) with hard cores, consisting of identical particles of fixed charge and diameter in a neutralizing background, and the symmetric two-component plasma (TCP) with hard cores, consisting of equal numbers of positively and negatively charged particles of identical size. We obtain exactly the first few coefficients of a systematic low-density expansion of the free energy for both models. The OCP coefficients go over to the classical Abe result in the high-charge (or small hard-core diameter) limit. The TCP, on the other hand, exhibits diverging coefficients in the high-charge limit, which is due to the formation of strongly bound ion-pairs., Comment: 8 pages, 6 postscript figures