Coverage Effects in Quartz Crystal Microbalance Measurements with Suspended and Adsorbed Nanoparticles.

Quartz crystal microbalance (QCM) biosensors often deal with nanoparticles suspended in the solvent at tens of nanometers above the resonator while being linked to some molecular receptor (DNA, antibody, etc.). This work presents a numerical analysis based on the immersed boundary method for the flow and QCM impedance created by an ensemble of spherical particles of radius R at varying surface coverage Θ and particle-surface gap distance Δ. The trends for the frequency Δf and dissipation ΔD shifts against Θ and Δ are shown to be determined by modifications in the structure of the perturbative flow created by the analytes. Simulations are in good agreement with a relatively large experimental database collected from the literature. Qualitative differences between the adsorbed (Δ ≈ 0) and suspended states (Δ > 0) are highlighted. In the case of adsorbed particles, deviations from the linear scaling Δf ∝ Θ are observed above Θ > 0.05 and largely depend on the specific analyte-substrate combination. Moreover, in general, ΔD(Θ) is not monotonous and usually presents a maximum around Θ âˆ¼ 0.2. In the case of suspended analytes, the agreement with the numerical results is quantitative, indicating that the predicted scalings are universal and determined by hydrodynamics. Up to high coverage, the suspended particles present Δf ∼ Θ and ΔD ∼ Θß, where ß ≈ 0.85 is not largely dependent on R. The present findings should help forecast molecular configurations from QCM signals and have implications on QCM analyses, e.g., in the case of suspended ligands (Δf ∝ Θ), it is safe to use Δf to build Langmuir isotherms and estimate equilibrium constants. Open questions on the transition from the suspended-to-adsorbed state are discussed.

Predicting the size and morphology of nanoparticle clusters driven by biomolecular recognition.

Nanoparticle aggregation is a driving principle of innovative materials and biosensing methodologies, improving transduction capabilities displayed by optical, electrical or magnetic measurements. This aggregation can be driven by the biomolecular recognition between target biomolecules (analytes) and receptors bound onto nanoparticle surface. Despite theoretical advances on modelling the entropic interaction in similar systems, predictions of the fractal morphologies of the nanoclusters of bioconjugated nanoparticles are lacking. The morphology of resulting nanoclusters is sensitive to the location, size, flexibility, average number of receptors per particle f̄, and the analyte-particle concentration ratio. Here we considered bioconjugated iron oxide nanoparticles (IONPs) where bonds are mediated by a divalent protein that binds two receptors attached onto different IONPs. We developed a protocol combining analytical expressions for receptors and linker distributions, and Brownian dynamics simulations for bond formation, and validated it against experiments. As more bonds become available (e.g., by adding analytes), the aggregation deviates from the ideal Bethe's lattice scenario due to multivalence, loop formation, and steric hindrance. Generalizing Bethe's lattice theory with a (not-integer) effective functionality feff leads to analytical expressions for the cluster size distributions in excellent agreement with simulations. At high analyte concentration steric impediment imposes an accessible limit value facc to feff, which is bounded by facc < feff < f̄. A transition to gel phase, is correctly captured by the derived theory. Our findings offer new insights into quantifying analyte amounts by assessing nanocluster size, and predicting nanoassembly morphologies accurately is a first step towards understanding variations of physical properties in clusters formed after biomolecular recognition.

Electromechanical Photophysics of GFP Packed Inside Viral Protein Cages Probed by Force-Fluorescence Hybrid Single-Molecule Microscopy.

Packing biomolecules inside virus capsids has opened new avenues for the study of molecular function in confined environments. These systems not only mimic the highly crowded conditions in nature, but also allow their manipulation at the nanoscale for technological applications. Here, green fluorescent proteins are packed in virus-like particles derived from P22 bacteriophage procapsids. The authors explore individual virus cages to monitor their emission signal with total internal reflection fluorescence microscopy while simultaneously changing the microenvironment with the stylus of atomic force microscopy. The mechanical and electronic quenching can be decoupled by ≈10% each using insulator and conductive tips, respectively. While with conductive tips the fluorescence quenches and recovers regardless of the structural integrity of the capsid, with the insulator tips quenching only occurs if the green fluorescent proteins remain organized inside the capsid. The electronic quenching is associated with the coupling of the protein fluorescence emission with the tip surface plasmon resonance. In turn, the mechanical quenching is a consequence of the unfolding of the aggregated proteins during the mechanical disruption of the capsid.

Hydrodynamics induce superdiffusive jumps of passive tracers along critical paths of random networks and colloidal gels.

We present a numerical study on the effect of hydrodynamic interactions (HI) on the diffusion of inert point tracer particles in several fixed random structures. As expected, the diffusion is hampered by the extra hydrodynamic friction introduced by the obstacle network. However, a non-trivial effect due to HI appears in the analysis of the van-Hove displacement probability close to the percolation threshold, where tracers diffuse through critical fractal paths. We show that the tracer dynamics can be split up into short and long jumps, the latter being ruled by either exponential or Gaussian van Hove distribution tails. While at short time HI slow down the tracer diffusion, at long times, hydrodynamic interactions with the obstacles increase the probability of longer jumps, which circumvent the traps of the labyrinth more easily. Notably, the relation between the anomalous diffusion exponent and the fractal dimension of the critical (intricate) paths is greater than one, which implies that the long-time (long-jump) diffusion is mildly superdiffuse. A possible reason for such a hastening of the diffusion along the network corridors is the hydrodynamically induced mobility anisotropy, which favours displacements parallel to the walls, an effect which has already been experimentally observed in collagen gels.

Quantitative description of the response of finite size adsorbates on a quartz crystal microbalance in liquids using analytical hydrodynamics.

Despite being a fundamental tool in soft matter research and biosensing, quartz crystal microbalance (QCM) analyses of discrete macromolecules in liquids so far lack a firm theoretical basis. Quite often, acoustic signals of discrete particles are qualitatively interpreted using ad hoc frameworks based on effective electrical circuits, effective springs and trapped-solvent models with many fitting parameters. Nevertheless, due to its extreme sensitivity, the QCM technique pledges to become an accurate predictive tool. Using unsteady low Reynolds hydrodynamics we derive analytical expressions for the acoustic impedance of adsorbed discrete spheres. The present approach is successfully validated against 3D simulations and a plethora of experimental results covering more than a decade of research on proteins, viruses, liposomes, and massive nanoparticles, with sizes ranging from a few to hundreds of nanometers. The agreement without fitting parameters indicates that the acoustic response is dominated by the hydrodynamic propagation of the particle surface stress over the resonator. Understanding this leading contribution is a prerequisite for deciphering the secondary contributions arising from the relevant specific molecular and physico-chemical forces.

Load Impedance of Immersed Layers on the Quartz Crystal Microbalance: A Comparison with Colloidal Suspensions of Spheres.

The analytical theories derived here for the acoustic load impedance measured by a quartz crystal microbalance (QCM), due to the presence of layers of different types (rigid, elastic, and viscous) immersed in a fluid, display generic properties, such as "vanishing mass" and positive frequency shifts, which have been observed in QCM experiments with soft-matter systems. These phenomena seem to contradict the well-known Sauerbrey relation at the heart of many QCM measurements, but here, we show that they arise as a natural consequence of hydrodynamics. We compare our one-dimensional immersed plate theory with three-dimensional simulations of rigid and flexible submicron-sized suspended spheres and with experimental results for adsorbed micron-sized colloids, which yield a "negative acoustic mass". The parallel behavior unveiled indicates that the QCM response is highly sensitive to hydrodynamics, even for adsorbed colloids. Our conclusions call for a revision of existing theories based on adhesion forces and elastic stiffness at contact, which should, in most cases, include hydrodynamics.

Boundary conditions derived from a microscopic theory of hydrodynamics near solids.

The theory of nonlocal isothermal hydrodynamics near a solid object derived microscopically in the study by Camargo et al. [J. Chem. Phys. 148, 064107 (2018)] is considered under the conditions that the flow fields are of macroscopic character. We show that in the limit of macroscopic flows, a simple pillbox argument implies that the reversible and irreversible forces that the solid exerts on the fluid can be represented in terms of boundary conditions. In this way, boundary conditions are derived from the underlying microscopic dynamics of the fluid-solid system. These boundary conditions are the impenetrability condition and the Navier slip boundary condition. The Green-Kubo transport coefficients associated with the irreversible forces that the solid exert on the fluid appear naturally in the slip length. The microscopic expression for the slip length thus obtained is shown to coincide with the one provided originally by Bocquet and Barrat [Phys. Rev. E 49, 3079 (1994)].

A general phenomenological relation for the subdiffusive exponent of anomalous diffusion in disordered media.

This work numerically investigates the diffusion of finite inert tracer particles in different types of fixed gels. The mean square displacement (MSD) of the tracers reveals a transition to subdiffusive motion MSD ∼ tα as soon as the accessible volume fraction p in the gel decreases from unity. Individual tracer dynamics reveals two types of particles in the gels: mobile tracers cross the system through percolating pores following subdiffusive dynamics MSDmob ∼ tαmob, while a fraction ptrap(p) of the particles remain trapped in finite pores. Below the void percolation threshold p < pc all the particles get trapped and α → 0. By separately studying both populations we find a simple phenomenological law for the mobile tracers αmob(p) ≈ a ln p + c where c ≈ 1 and a ∼ 0.2 depends on the gel type. On the other hand, a cluster-analysis of the gel accessible volume reveals a power law for the trapping probability ptrap ∼ (p/pc)-γ, with γ ≃ 2.9. This yields a prediction for the ensemble averaged subdiffusion exponent α = αmob(1 - ptrap). Our predictions are successfully validated against the different gels studied here and against numerical and experimental results in the literature (silica gels, polyacrylamide gels, flexible F-actin networks and in different random obstacles). Notably, the parameter a ∼ 0.2 presents small differences amongst all these cases, indicating the robustness of the proposed relation.

Nanoscale hydrodynamics near solids.

Density Functional Theory (DFT) is a successful and well-established theory for the study of the structure of simple and complex fluids at equilibrium. The theory has been generalized to dynamical situations when the underlying dynamics is diffusive as in, for example, colloidal systems. However, there is no such a clear foundation for Dynamic DFT (DDFT) for the case of simple fluids in contact with solid walls. In this work, we derive DDFT for simple fluids by including not only the mass density field but also the momentum density field of the fluid. The standard projection operator method based on the Kawasaki-Gunton operator is used for deriving the equations for the average value of these fields. The solid is described as featureless under the assumption that all the internal degrees of freedom of the solid relax much faster than those of the fluid (solid elasticity is irrelevant). The fluid moves according to a set of non-local hydrodynamic equations that include explicitly the forces due to the solid. These forces are of two types, reversible forces emerging from the free energy density functional, and accounting for impenetrability of the solid, and irreversible forces that involve the velocity of both the fluid and the solid. These forces are localized in the vicinity of the solid surface. The resulting hydrodynamic equations should allow one to study dynamical regimes of simple fluids in contact with solid objects in isothermal situations.

Application of the Eckart frame to soft matter: rotation of star polymers under shear flow.

The Eckart co-rotating frame is used to analyze the dynamics of star polymers under shear flow, either in melt or solution and with different types of bonds. This formalism is compared with the standard approach used in many previous studies on polymer dynamics, where an apparent angular velocity ω is obtained from the relation between the tensor of inertia and angular momentum. A common mistake is to interpret ω as the molecular rotation frequency, which is only valid for rigid-body rotation. The Eckart frame, originally formulated to analyze the infrared spectra of small molecules, dissects different kinds of displacements: vibrations without angular momentum, pure rotation, and vibrational angular momentum (leading to a Coriolis cross-term). The Eckart frame co-rotates with the molecule with an angular frequency Ω obtained from the Eckart condition for minimal coupling between rotation and vibration. The standard and Eckart approaches are compared with a straight description of the star's dynamics taken from the time autocorrelation of the monomer positions moving around the molecule's center of mass. This is an underdamped oscillatory signal, which can be described by a rotation frequency ωR and a decorrelation rate Γ. We consistently find that Ω coincides with ωR, which determines the characteristic tank-treading rotation of the star. By contrast, the apparent angular velocity ω < Ω does not discern between pure rotation and molecular vibrations. We believe that the Eckart frame will be useful to unveil the dynamics of semiflexible molecules where rotation and deformations are entangled, including tumbling, tank-treading motions and breathing modes.

Deciphering the dynamics of star molecules in shear flow.

This work analyses the rotation of star polymers under shear flow, in melts, and in good solvent dilute solution. The latter is modeled by single molecule Brownian hydrodynamics, while melts are modeled using non-equilibrium molecular dynamics in closed (periodic) boxes and in open boundaries. A Dissipative Particle Dynamics (DPD) thermostat introduces pairwise monomer friction in melts at will, in directions normal and tangent to the monomer-monomer vectors. Although tangential friction is seldom modeled, we show that it is essential to control hydrodynamic effects in melts. We analyze the different sources of molecular angular momentum in solution and melts and distinguish three dynamic regimes as the shear rate [small gamma, Greek, dot above] is increased. These dynamic regimes are related with the disruption of the different relaxation mechanisms of the star in equilibrium. Although strong differences are found between harmonic springs and finitely extensible bonds, above a critical shear rate the star molecule has a "breathing" mode with successive elongations and contractions in the flow direction with frequency Ω. The force balance in the flow direction unveils a relation between Ω and the orientation angle. Using literature results for the tumbling of rings and linear chains, either in melt or in solution, we show that the relation is general. A different "tank-treading" dynamics determines the rotation of monomers around the center of mass of the molecule. We show that the tank-treading frequency does not saturate but keeps increasing with [small gamma, Greek, dot above]. This is at odds with previous studies which erroneously calculated the molecular angular frequency, used as a proxy for tank-treading.

The entropy of a complex molecule.

Entropy is a central concept in the theory of coarse-graining. Through Einstein's formula, it provides the equilibrium probability distribution of the coarse-grained variables used to describe the system of interest. We study with molecular dynamics simulations the equilibrium probability distribution of thermal blobs representing at a coarse-grained level star polymer molecules in melt. Thermal blobs are characterized by the positions and momenta of the centers of mass, and internal energies of the molecules. We show that the entropy of the level of description of thermal blobs can be very well approximated as the sum of the thermodynamic entropy of each single molecule considered as isolated thermodynamic systems. The entropy of a single molecule depends on the intrinsic energy, involving only contributions from the atoms that make the molecule and not from the interactions with atoms of other molecules.

Open boundary molecular dynamics of sheared star-polymer melts.

Open boundary molecular dynamics (OBMD) simulations of a sheared star polymer melt under isothermal conditions are performed to study the rheology and molecular structure of the melt under a fixed normal load. Comparison is made with the standard molecular dynamics (MD) in periodic (closed) boxes at a fixed shear rate (using the SLLOD dynamics). The OBMD system exchanges mass and momentum with adjacent reservoirs (buffers) where the external pressure tensor is imposed. Insertion of molecules in the buffers is made feasible by implementing there a low resolution model (blob-molecules with soft effective interactions) and then using the adaptive resolution scheme (AdResS) to connect with the bulk MD. Straining with increasing shear stress induces melt expansion and a significantly different redistribution of pressure compared with the closed case. In the open sample, the shear viscosity is also a bit lowered but more stable against the viscous heating. At a given Weissenberg number, molecular deformations and material properties (recoverable shear strain and normal stress ratio) are found to be similar in both setups. We also study the modelling effect of normal and tangential friction between monomers implemented in a dissipative particle dynamics (DPD) thermostat. Interestingly, the tangential friction substantially enhances the elastic response of the melt due to a reduction of the kinetic stress viscous contribution.

A multiblob approach to colloidal hydrodynamics with inherent lubrication.

This work presents an intermediate resolution model of the hydrodynamics of colloidal particles based on a mixed Eulerian-Lagrangian formulation. The particle is constructed with a small set of overlapping Peskin's Immersed Boundary kernels (blobs) which are held together by springs to build up a particle impenetrable core. Here, we used 12 blobs placed in the vertexes of an icosahedron with an extra one in its center. Although the particle surface is not explicitly resolved, we show that the short-distance hydrodynamic responses (flow profiles, translational and rotational mobilities) agree with spherical colloids and provide consistent effective radii. A remarkable property of the present multiblob model is that it naturally provides zero relative mobility at some finite inter-particle distance. In terms of mutual friction, this divergent force accurately represents the "soft" lubrication regime of spherical colloids and permits to resolve the increase of the solution viscosity up to moderately dense systems with volume fraction up to about 0.50. This intermediate resolution model is able to recover highly non-trivial (many-body) hydrodynamics using small particles whose radii are similar to the grid size h (in the range [1.6 - 3.2] h). Considering that the cost of the embedding fluid phase scales such as the cube of the particle radius, this result brings about a significant computational speed-up. Our code Fluam works in Graphics Processor Units and uses Fast Fourier Transform for the Poisson solver, which further improves its efficiency.

Brownian dynamics without Green's functions.

We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions "on the fly." Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

Multiparametric modulation of magnetic transduction for biomolecular sensing in liquids.

The recent COVID19 pandemic has remarkably boosted the research on in vitro diagnosis assays to detect biomarkers in biological fluids. Specificity and sensitivity are mandatory for diagnostic kits aiming to reach clinical stages. Whilst the modulation of sensitivity can significantly improve the detection of biomarkers in liquids, this has been scarcely explored. Here, we report on the proof of concept and parametrization of a novel biosensing methodology based on the changes of AC magnetic hysteresis areas observed for magnetic nanoparticles following biomolecular recognition in liquids. Several parameters are shown to significantly modulate the transducing capacity of magnetic nanoparticles to detect analytes dispersed in saline buffer at concentrations of clinical relevance. Magnetic nanoparticles were bio-conjugated with an engineered recognition peptide as a receptor. Analytes are engineered tetratricopeptide binding domains fused to the fluorescent protein whose dimerization state allows mono- or divalent variants. Our results unveil that the number of receptors per particle, analyte valency and concentration, nanoparticle composition and concentration, and field conditions play a key role in the formation of assemblies driven by biomolecular recognition. Consequently, all these parameters modulate the nanoparticle transduction capacity. Our study provides essential insights into the potential of AC magnetometry for customizing biomarker detection in liquids.

Hamiltonian adaptive resolution simulation for molecular liquids.

Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.

Monte carlo adaptive resolution simulation of multicomponent molecular liquids.

Complex soft matter systems can be efficiently studied with the help of adaptive resolution simulation methods, concurrently employing two levels of resolution in different regions of the simulation domain. The nonmatching properties of high- and low-resolution models, however, lead to thermodynamic imbalances between the system's subdomains. Such inhomogeneities can be healed by appropriate compensation forces, whose calculation requires nontrivial iterative procedures. In this work we employ the recently developed Hamiltonian adaptive resolution simulation method to perform Monte Carlo simulations of a binary mixture, and propose an efficient scheme, based on Kirkwood thermodynamic integration, to regulate the thermodynamic balance of multicomponent systems.

The Stokes-Einstein relation at moderate Schmidt number.

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

Boosting the efficiency of transient photoluminescence microscopy using cylindrical lenses.

Transient Photoluminescence Microscopy (TPLM) allows for the direct visualization of carrier transport in semiconductor materials with sub nanosecond and few nanometer resolution. The technique is based on measuring changes in the spatial distribution of a diffraction limited population of carriers using spatiotemporal detection of the radiative decay of the carriers. The spatial resolution of TPLM is therefore primarily determined by the signal-to-noise-ratio (SNR). Here we present a method using cylindrical lenses to boost the signal acquisition in TPLM experiments. The resulting asymmetric magnification of the photoluminescence emission of the diffraction limited spot can increase the collection efficiency by more than a factor of 10, significantly reducing acquisition times and further boosting spatial resolution.