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The dissolution of polymer-coated, controlled-release urea fertilisers by means of a simple, Fickian diffusion-based model is described. This is in contrast to prior contributions that invoke non-Fickian mechanisms or take a more quantitative view. Within a quasi-static approximation, simple expressions for the granule radius and release profile as a function of time are obtained in terms of experimentally accessible parameters. Predictions compare well with available experimental data, although the full model is required to capture the gradual saturation of released urea in the late stages of the process. If scaled appropriately, a wide range of experimental data for different coatings turn out to collapse onto what for all intents and purposes can be called a universal curve. This suggests that extensive experimental testing can be avoided if the properties of the coating are known beforehand.

Recently, Maassen et al. measured an appreciable pH difference between the bulk solution and the solution in the lumen of virus-like particles, self-assembled in an aqueous buffer solution containing the coat proteins of a simple plant virus and polyanions. [Maassen, S. J.; et al. Small 2018, 14, 1802081] They attribute this to the Donnan effect, caused by an imbalance between the number of negative charges on the encapsulated polyelectrolyte molecules and the number of positive charges on the RNA binding domains of the coat proteins that make up the virus shell or capsid. By applying Poisson-Boltzmann theory, we confirm this conclusion and show that simple Donnan theory is accurate even for the smallest of viruses and virus-like particles. This, in part, is due to the additional screening caused by the presence of a large number of immobile charges in the cavity of the shell. The presence of a net charge on the outer surface of the capsid we find in practice to not have a large effect on the pH shift. Hence, Donnan theory can indeed be applied to connect the local pH and the amount of encapsulated material. The large shifts up to a full pH unit that we predict must have consequences for applications of virus capsids as nanocontainers in bionanotechnology and artificial cell organelles., Comment: 31 pages, 4 figures, 1 TOC figure

We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means of molecular dynamics simulations. It appears that the impact of shear flow is subtle and highly non-trivial, even in the absence of hydrodynamic interactions between the particles. The presence of shear flow can both increase and decrease the percolation threshold, depending on the criterion used for determining whether or not two particles are connected and on the Péclet number. Our approach opens up a route to quantitatively predict the percolation threshold in nanocomposite materials that, as a rule, are produced under non-equilibrium conditions, making comparison with equilibrium percolation theory tenuous. Our theory can be adapted straightforwardly for application in other types of flow field, and particles of different shape or interacting via other than hard-core potentials.

The presence of deposits of alpha-synuclein fibrils in cells of the brain are a hallmark of several α-synucleinopathies, including Parkinson’s disease. As most disease cases are not familial, it is likely that external factors play a role in disease onset. One of the external factors that may influence disease onset are viral infections. It has recently been shown that in the presence of SARS-Cov-2 N-protein, αS fibril formation is faster and proceeds in an unusual two-step aggregation process. Here, we show that faster fibril formation is not due to a SARS-CoV-2 N-protein-catalysed formation of an aggregation-prone nucleus. Instead, aggregation starts with the formation of a population of mixed αS/N-protein fibrils with low affinity for αS. After the depletion of N-protein, fibril formation comes to a halt, until a slow transformation to fibrils with characteristics of pure αS fibril strains occurs. This transformation into a strain of αS fibrils subsequently results in a second phase of fibril growth until a new equilibrium is reached. Our findings point at the possible relevance of fibril strain transformation in the cell-to-cell spread of the αS pathology and disease onset.

Cowpea chlorotic mottle virus (CCMV) is a widely used model for virus replication studies. A major challenge lies in distinguishing between the roles of the interaction between coat proteins and that between the coat proteins and the viral RNA in assembly and disassembly processes. Here, we report on the spontaneous and reversible size conversion of the empty capsids of a CCMV capsid protein functionalized with a hydrophobic elastin-like polypeptide which occurs following a pH jump. We monitor the concentrations of T = 3 and T = 1 capsids as a function of time and show that the time evolution of the conversion from one T number to another is not symmetric: The conversion from T = 1 to T = 3 is a factor of 10 slower than that of T = 3 to T = 1. We explain our experimental findings using a simple model based on classical nucleation theory applied to virus capsids, in which we account for the change in the free protein concentration, as the different types of shells assemble and disassemble by shedding or absorbing single protein subunits. As far as we are aware, this is the first study confirming that both the assembly and disassembly of viruslike shells can be explained through classical nucleation theory, reproducing quantitatively results from time-resolved experiments.

We model the behavior of a single colloid embedded in a cross-linked polymer gel, immersed in a viscous background fluid. External fields actuate the particle into a periodic motion, which deforms the embedding matrix and creates a local microcavity, containing the particle and any free volume created by its motion. This cavity exists only as long as the particle is actuated and, when present, reduces the local density of the material, leading to swelling. We show that the model exhibits rich resonance features, but is overall characterized by clear scaling laws at low and high driving frequencies, and a pronounced resonance at intermediate frequencies. Our model predictions suggest that both the magnitude and position of the resonance can be varied by varying the material's elastic modulus or cross-linking density, whereas the local viscosity primarily has a dampening effect. Our work implies appreciable free-volume generation is possible by dispersing a collection of colloids in the medium, even at the level of a simple superposition approximation.

Inspired by recent experiments on the spontaneous assembly of virus-like particles from a solution containing a synthetic coat protein and double-stranded DNA, we put forward a kinetic model that has as main ingredients a stochastic nucleation and a deterministic growth process. The efficiency and rate of DNA packaging strongly increase after tiling the DNA with CRISPR-Cas proteins at predesignated locations, mimicking assembly signals in viruses. Our model shows that treating these proteins as nucleation-inducing diffusion barriers is sufficient to explain the experimentally observed increase in encapsulation efficiency, but only if the nucleation rate is sufficiently high. We find an optimum in the encapsulation kinetics for conditions where the number of packaging signal mimics is equal to the number of nucleation events that can occur during the time required to fully encapsulate the DNA template, presuming that the nucleation events can only take place adjacent to a packaging signal. Our theory is in satisfactory agreement with the available experimental data.

Carbon nanotubes (CNTs) are stiff, all-carbon macromolecules with diameters as small as one nanometer and few microns long. Solutions of CNTs in chlorosulfonic acid (CSA) follow the phase behavior of rigid rod polymers interacting via a repulsive potential and display a liquid crystalline phase at sufficiently high concentration. Here, we show that small-angle X-ray scattering and polarized light microscopy data can be combined to characterize quantitatively the morphology of liquid crystalline phases formed in CNT solutions at concentrations from 3 to 6.5 % by volume. We find that upon increasing their concentration, CNTs self-assemble into a liquid crystalline phase with a pleated texture and with a large inter-particle spacing that could be indicative of a transition to higher-order liquid crystalline phases. We explain how thermal undulations of CNTs can enhance their electrostatic repulsion and increase their effective diameter by an order of magnitude. By calculating the critical concentration, where the mean amplitude of undulation of an unconstrained rod becomes comparable to the rod spacing, we find that thermal undulations start to affect steric forces at concentrations as low as the isotropic cloud point in CNT solutions.

Recently, three distinct, well-separated transient regimes were discovered in the dynamics of the volume expansion of shape-shifting liquid crystal network films in response to the switching on of an alternating electric field [Van der Kooij et al., Nat. Commun., 2019, 10, 1]. Employing a spatially resolved, time-dependent Landau theory that couples local volume generation to the degree of orientational order of mesogens that are part of a viscoelastic network, we are able to offer a physical explanation for the existence of three time scales. We find that the initial response is dominated by overcoming the impact of thermal noise, after which the top of the film expands, followed by a permeation of this response into the bulk region. An important signature of our predictions is a significant dependence of the three time scales on the film thickness, where we observe a clear thin-film-to-bulk transition. The point of transition coincides with the emergence of spatial inhomogeneities in the bulk of the film in the form of domains separated by regions of suppressed expansion. This ultimately gives rise to variations in the steady-state overall expansion of the film and may lead to uncontrolled patterning. According to our model, domain formation can be suppressed by (1) decreasing the thickness of the as-prepared film, (2) increasing the linear dimensions of the mesogens, or (3) their degree of orientational order when cross-linked into the network. Our findings provide a handle to achieve finer control over the actuation of smart liquid crystal network coatings.

Inspired by recent experiments on the spontaneous assembly of virus-like particles from a solution containing a synthetic coat protein and double-stranded DNA, (1) we put forward a kinetic model that has as main ingredients a stochastic nucleation and a deterministic growth process. The efficiency and rate of the packaging of the DNA turn out to strongly increase by introducing proteins onto the DNA template that are modified using CRISPR-Cas techniques to bind specifically at predesignated locations, mimicking assembly signals in viruses. Our model shows that treating these proteins as nucleation-inducing diffusion barriers is sufficient to explain experimentally observed increase in encapsulation efficiency, but only if the nucleation rate is sufficiently high. We find an optimum in the encapsulation kinetics for conditions where the number of packaging signals is equal to the number of nucleation events that can occur during time required to fully encapsulate the DNA template, presuming that the nucleation events can only take place adjacent to a packaging signal. Our theory is in satisfactory agreement with the available experimental data.SIGNIFICANCEThe rate and efficiency of the encapsulation of double-stranded DNA by synthetic coat proteins was recently found to be strongly enhanced by the presence of specifically positioned protein molecules on the DNA that mimic so-called packaging signals. We present a kinetic theory based on the initial stochastic nucleation and subsequent deterministic elongation of the protein coat with the aim to explain these findings. We find that equidistantly placed nucleation sites that also act as diffusion barriers on the DNA have profound and non-trivial effects, and they can either slow down or speed up encapsulation, depending on how fast nucleation is on the time scale of the elongation process. Our findings may contribute to the rational design of linear virus-like particles.

Liquid crystal networks exploit the coupling between the responsivity of liquid crystalline mesogens, e.g., to electric fields, and the (visco)elastic properties of a polymer network. Because of this, these materials have been put forward for a wide array of applications, including responsive surfaces such as artificial skins and membranes. For such applications, the desired functional response must generally be realized under strict geometrical constraints, such as provided by supported thin films. To model such settings, we present a dynamical, spatially heterogeneous Landau-type theory for electrically actuated liquid crystal network films. We find that the response of the liquid crystal network permeates the film from top to bottom, and illustrate how this affects the timescale associated with macroscopic deformation. Finally, by linking our model parameters to experimental quantities, we suggest that the permeation rate can be controlled by varying the aspect ratio of the mesogens and their degree of orientational order when crosslinked into the polymer network, for which we predict a single optimum. Our results contribute specifically to the rational design of future applications involving transport or on-demand release of molecular cargo in liquid crystal network films.

We apply connectedness percolation theory to fractal liquids of hard particles, and make use of a Percus-Yevick liquid state theory combined with a geometric connectivity criterion. We find that in fractal dimensions the percolation threshold interpolates continuously between integer-dimensional values, and that it decreases monotonically with increasing (fractal) dimension. The influence of hard-core interactions is only significant for dimensions below three. Finally, our theory incorrectly suggests that a percolation threshold is absent below about two dimensions, which we attribute to the breakdown of the connectedness Percus-Yevick closure., Comment: 7 pages, 8 figures

We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of noninteracting line segments and disks in two spatial dimensions. These examples serve as models for electrical percolation of elongated and flat nanofillers in thin film composites. While the standard contact volume argument and extensions thereof in connectedness percolation theory yield accurate predictions for slender nanofillers in three dimensions, they fail to do so in two dimensions, making our test a stringent one. In fact, neither a systematic order-by-order correction to the standard argument nor invoking the connectedness version of the Percus-Yevick approximation yield significant improvements for either type of particle. Making use of simple geometric considerations, our new method predicts a percolation threshold of ${\ensuremath{\rho}}_{c}{l}^{2}\ensuremath{\approx}5.83$ for segments of length $l$, which is close to the ${\ensuremath{\rho}}_{c}{l}^{2}\ensuremath{\approx}5.64$ found in Monte Carlo simulations. For disks of area $a$ we find ${\ensuremath{\rho}}_{c}a\ensuremath{\approx}1.00$, close to the Monte Carlo result of ${\ensuremath{\rho}}_{c}a\ensuremath{\approx}1.13$. We discuss the shortcomings of the conventional approaches and explain how usage of the nearest-neighbor distribution in our method bypasses those complications.

Using lattice Boltzmann simulations we investigate the impact of the amplitude of concentration fluctuations in binary fluid mixtures prior to demixing when in contact with a surface that is preferentially wet by one of the components. We find a bicontinuous structure near the surface for an initial, prequench state of the mixture close to the critical point where the amplitude of concentration fluctuations is large. In contrast, if the initial state of the mixture is not near the critical point and concentration fluctuations are relatively weak, then the morphology is not bicontinuous but remains layered until the very late stages of coarsening. In both cases, it is the morphology of a depletion layer rich in the nonpreferred component that dictates the growth exponent of the thickness of the fluid layer that is in direct contact with the substrate. In the early stages of demixing, we find a growth exponent consistent with a value of 1/4 for a prequench state away from the critical point, which is different from the usual diffusive scaling exponent of 1/3 that we recover for a prequench state close to the critical point. We attribute this to the structure of a depletion layer that is penetrated by tubes of the preferred fluid, connecting the wetting layer to the bulk fluid even in the early stages if the initial state is characterized by concentration fluctuations that are large in amplitude. Furthermore, we find that in the late stages of demixing the flow through these tubes results in significant in-plane concentration variations near the substrate, leading to dropletlike structures with a concentration lower than the average concentration in the wetting layer. This causes a deceleration in the growth of the wetting layer in the very late stages of the demixing. Irrespective of the prequench state of the mixture, the late stages of the demixing process produce the same growth law for the layer thickness, with a scaling exponent of unity usually associated with the impact of hydrodynamic flow fields.

Understanding the dynamical evolution of a percolating network during liquid–liquid demixing is crucial for many technological applications, including plastic electronics, such as organic photovoltaics, whose performance depends on the efficiency to transport the positive and negative charge carriers to the corresponding electrodes. The transport and collection of the charge carriers require sufficient asymmetry between the donor and acceptor phases by attaining a minimum concentration of the majority fluids in it, called the percolation threshold. We investigate demixing in symmetric binary blends on a substrate preferentially wet by one of the fluids from the perspective of such a percolation threshold to achieve directed and connectivity percolation. We also study the influence of the strength of the substrate interaction and the property of the blend right before the quench with respect to the critical point. It is commonly assumed that the bicontinuous morphology of a symmetric blend guarantees percolation, where the average concentration of the blend distinguishes the two phases. However, if the percolation threshold is larger than the average concentration, we find that percolating pathways grow monotonically and a percolating cluster forms only after a time lag. Furthermore, we find that this time lag is characterized by two universal kinetic regimes that can explain all our observations. The first regime is associated with the percolation threshold itself, which grows exponentially. The second regime displays an algebraic growth with an exponent of 1/3 and we argue that it must be associated with the direc- tional connectivity of the wetting phase to the substrate.

Tactoids are spindle shaped-droplets of a uniaxial nematic phase suspended in the co-existing isotropic phase. They are found in dispersions of a wide variety of elongated colloidal particles, including actin, fd virus, carbon nanotubes, vanadium peroxide and chitin nanocrystals. Recent experiments on tactoids of chitin nanocrystals in water show that electric fields can very strongly elongate tactoids even though the dielectric properties of the co-existing isotropic and nematic phases differ only subtly. We develop a model for partially bipolar tactoids, where the degree of bipolarness of the director field is free to adjust to optimize the sum of the elastic, surface and Coulomb energies of the system. By means of a combination of a scaling analysis and a numerical study, we investigate the elongation and director field's behavior of the tactoids as a function of their size, the strength of the electric field, the surface tension, anchoring strength, the elastic constants and the electric susceptibility anisotropy. We find that tactoids cannot elongate significantly due to an external electric field, unless the director field is bipolar or quasi bipolar and is somehow frozen in the field-free configuration. Presuming that this is the case, we find reasonable agreement with experimental data.

Liquid crystal networks combine the orientational order of liquid crystals with the elastic properties of polymer networks, leading to a vast application potential in the field of responsive coatings, e.g., for haptic feedback, self-cleaning surfaces, and static and dynamic pattern formation. Recent experimental work has further paved the way toward such applications by realizing the fast and reversible surface modulation of a liquid crystal network coating upon in-plane actuation with an AC electric field [Liu, Tito, and Broer, Nat. Commun. 8, 1526 (2017)10.1038/s41467-017-01448-w]. Here, we construct a Landau-type theory for electrically-responsive liquid crystal networks and perform molecular dynamics simulations to explain the findings of these experiments and inform on rational design strategies. Qualitatively, the theory agrees with our simulations and reproduces the salient experimental features. We also provide a set of testable predictions: the aspect ratio of the nematogens, their initial orientational order when cross-linked into the polymer network, and the cross-linking fraction of the network all increase the plasticization time required for the film to macroscopically deform. We demonstrate that the dynamic response to oscillating electric fields is characterized by two resonances, which can likewise be influenced by varying these parameters, providing an experimental handle to fine-tune device design.

We study by means of Monte Carlo simulations the internal structure of nematic droplets or tactoids formed by hard, rod-like particles in a gas of spherical ghost particles that act as depletion agents for the rods. We find that the shape and internal structure of tactoids are strongly affected by the size of the droplets. The monotonically increasing degree of nematic order with increasing particle density that characterizes the bulk nematic phase is locally violated and more so the smaller the tactoid. We also investigate the impact of an external quadrupolar alignment field on tactoids and find that this tends to make the director field more uniform, but not to very significantly increase the tactoid’s aspect ratio. This agrees with recent theoretical predictions yet is at variance with experimental observations and dynamical simulations. We explain this discrepancy in terms of competing relaxation times.

Assessing the structural properties of large proteins is important to gain an understanding of their function in, e.g., biological systems or biomedical applications. We propose a method to examine the mechanical properties of proteins subject to applied forces by means of multiscale simulation. We consider both stretching and torsional forces, which can be applied independently of each other. We apply torsional forces to a coarse-grained continuum model of the antibody protein immunoglobulin G (IgG) using Fluctuating Finite Element Analysis and identify the area of strongest deformation. This region is essential to the torsional properties of the molecule as a whole, as it represents the softest, most deformable domain. We subject this part of the molecule to torques and stretching forces on an atomistic level, using molecular dynamics simulations, in order to investigate its torsional properties. We calculate the torsional resistance as a function of the rotation of the domain, while subjecting it to various stretching forces. We learn how these obtained torsion profiles evolve with increasing stretching force and show that they exhibit torsion stiffening, which is in qualitative agreement with experimental findings. We argue that combining the torsion profiles for various stretching forces effectively results in a combined force-torque spectroscopy analysis, which may serve as a mechanical signature for the examined molecule., Comment: 11 pages, 9 figures

While the structure of a multitude of viral particles has been resolved to atomistic detail, their assembly pathways remain largely elusive. Key unresolved issues are particle nucleation, particle growth, and the mode of genome compaction. These issues are difficult to address in bulk approaches and are effectively only accessible by the real-time tracking of assembly dynamics of individual particles. This we do here by studying the assembly into rod-shaped viruslike particles (VLPs) of artificial capsid polypeptides. Using fluorescence optical tweezers, we establish that small oligomers perform one-dimensional diffusion along the DNA. Larger oligomers are immobile and nucleate VLP growth. A multiplexed acoustic force spectroscopy approach reveals that DNA is compacted in regular steps, suggesting packaging via helical wrapping into a nucleocapsid. By reporting how real-time assembly tracking elucidates viral nucleation and growth principles, our work opens the door to a fundamental understanding of the complex assembly pathways of both VLPs and naturally evolved viruses.

While the structure of a variety of viruses has been resolved at atomistic detail, their assembly pathways remain largely elusive. Key unresolved issues in assembly are the nature of the critical nucleus starting particle growth, the subsequent self-assembly reaction and the manner in which the viral genome is compacted. These issues are difficult to address in bulk approaches and are effectively only accessible by tracking the dynamics of assembly of individual particles in real time, as we show here. With a combination of single-molecule techniques we study the assembly into rod-shaped virus-like particles (VLPs) of artificial capsid polypeptides, de-novo designed previously. Using fluorescence optical tweezers we establish that oligomers that have pre-assembled in solution bind to our DNA template. If the oligomer is smaller than a pentamer, it performs one-dimensional diffusion along the DNA, but pentamers and larger oligomers are essentially immobile and nucleate VLP growth. Next, using real-time multiplexed acoustic force spectroscopy, we show that DNA is compacted in regular steps during VLP growth. These steps, of ∼30 nm of DNA contour length, fit with a DNA packaging mechanism based on helical wrapping of the DNA around the central protein core of the VLP. By revealing how real-time, single particle tracking of VLP assembly lays bare nucleation and growth principles, our work opens the doors to a new fundamental understanding of the complex assembly pathways of natural virus particles.

Conductive thin films are industrially applied from display units to sensors. For many applications, current thin films struggle with a lack of transparency to light and of mechanical flexibility. Conductive nanowires and polymers in appropriate combinations could circumvent these two issues. In order to shed light on the impact of manufacturing conditions on the properties of conducting thin film, we report on structure, conductivity and transmission experiments involving spin-coated silver nanowire and polymer latex mixtures. Surprisingly, we find the nanowires to predominantly orient either parallel or perpendicular to the centripetal force, thus forming a conductive network. The conductivity of this network is enhanced by relying on bilayer rather than monolayer films, which show a better transmittance than indium tin oxide films do in a broader wavelength range.

By means of replica exchange molecular dynamics simulations we investigate how the length of a silk-like, alternating diblock oligopeptide influences its secondary and quaternary structure. We carry out simulations for two protein sizes consisting of three and five blocks, and study the stability of a single protein, a dimer, a trimer and a tetramer. Initial configurations of our simulations are beta-roll and beta-sheet structures. We find that for the triblock the secondary and quaternary structures upto and including the tetramer are unstable: the proteins melt into random coil structures and the aggregates disassemble either completely or partially. We attribute this to the competition between conformational entropy of the proteins and the formation of hydrogen bonds and hydrophobic interactions between proteins. This is confirmed by our simulations on the pentablock proteins, where we find that, as the number of monomers in the aggregate increases, individual monomers form more hydrogen bonds whereas their solvent accessible surface area decreases. For the pentablock beta-sheet protein, the monomer and the dimer melt as well, although for the beta-roll protein only the monomer melts. For both trimers and tetramers remain stable. Apparently, for these the entropy loss of forming beta-rolls and beta-sheets is compensated for in the free-energy gain due to the hydrogen-bonding and hydrophobic interactions. We also find that the middle monomers in the trimers and tetramers are conformationally much more stable than the ones on the top and the bottom. Interestingly, the latter are more stable on the tetramer than on the trimer, suggesting that as the number of monomers increases protein-protein interactions cooperatively stabilize the assembly. According to our simulations, the beta-roll and beta-sheet aggregates must be approximately equally stable.

Under many in vitro conditions, some small viruses spontaneously encapsidate a single stranded (ss) RNA into a protein shell called the capsid. While viral RNAs are found to be compact and highly branched because of long distance base-pairing between nucleotides, recent experiments reveal that in a head-to-head competition between an ssRNA with no secondary or higher order structure and a viral RNA, the capsid proteins preferentially encapsulate the linear polymer! In this paper, we study the impact of genome stiffness on the encapsidation free energy of the complex of RNA and capsid proteins. We show that an increase in effective chain stiffness because of base-pairing could be the reason why under certain conditions linear chains have an advantage over branched chains when it comes to encapsidation efficiency. While branching makes the genome more compact, RNA base-pairing increases the effective Kuhn length of the RNA molecule, which could result in an increase of the free energy of RNA confinement, that is, the work required to encapsidate RNA, and thus less efficient packaging.

When colloidal particles form a crystal phase on a spherical template, their packing is governed by the effective interaction between them and the elastic strain of bending the growing crystal. For example, if growth commences under appropriate conditions, and the circular crystal that forms reaches a critical size, growth continues by incorporation of defects to alleviate elastic strain. Recently it was found experimentally that, if defect formation is somehow not possible, the crystal instead continues growing in ribbons that protrude from the original crystal. Here we report on computer simulations in which we observe both the formation of ribbons at short interaction ranges and packings that incorporate defects if the interaction is longer-ranged. The ribbons only form above some critical crystal size, below which the nucleus is roughly spherically shaped. We find that the scaling of the critical crystal size differs slightly from the one proposed by the Manoharan group, and reason this is because the actual process is a two-step heterogeneous nucleation of ribbons on top of roughly circular crystals., 24 pages, 11 figures

The effect of the dispersed state of graphene is studied as a factor influencing the electrical percolation threshold of graphene/polystyrene nanocomposites. We find the percolation threshold of our nanocomposites, prepared with graphene dispersions with different thermodynamic stabilities, degrees of exfoliation, and size polydispersities, to range from 2 to 4.5 wt %. Connectedness percolation theory is applied to calculate percolation thresholds of the corresponding nanocomposites, based on the premise that size polydispersity of graphene platelets in the corresponding solutions must have a strong influence on it. Theory and experimental results agree qualitatively.

Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerisation reactions. One of the most important characteristic features in this kind of problem is the existence of a lag phase before self-assembly takes off, which is what we focus attention on. We study the associated lag time as a function of the system size and kinetic pathway. We find that the leading order stochastic contribution to the lag time before polymerisation commences is inversely proportional to the system volume for large-enough system size for all nine reaction pathways tested. Finite-size corrections to this do depend on the kinetic pathway.

Many single-stranded (ss) ribonucleic acid (RNA) viruses self-assemble from capsid protein subunits and the nucleic acid to form an infectious virion. It is believed that the electrostatic interactions between the negatively charged RNA and the positively charged viral capsid proteins drive the encapsidation, although there is growing evidence that the sequence of the viral RNA also plays a role in packaging. In particular, the sequence will determine the possible secondary structures that the ssRNA will take in solution. In this work, we use a mean-field theory to investigate how the secondary structure of the RNA combined with electrostatic interactions affects the efficiency of assembly and stability of the assembled virions. We show that the secondary structure of RNA may result in negative osmotic pressures while a linear polymer causes positive osmotic pressures for the same conditions. This may suggest that the branched structure makes the RNA more effectively packaged and the virion more stable.

The percolation threshold of single-walled carbon nanotubes (SWCNTs) introduced into polystyrene (PS) via a latex-based route has been reduced by using conductive surfactants. The use of the conductive polymeric latex, poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS), in conjunction with SWCNTs leads to conductive composites with loadings of both constituents below their own individual percolation thresholds. The high concentration of PEDOT:PSS in the final composites raises the concern that the composite conductivity is a result of the presence of the PEDOT:PSS alone. To elucidate the cooperative nature of the two conductive components, the contribution of the SWCNTs to the overall composite conductivity is investigated by replacing the original high-quality SWCNTs with SWCNTs of a lower quality. Percolation thresholds recorded for systems utilizing the lower quality tubes stabilized with nonconductive surfactants were over 2 wt % SWCNTs (4 times that of previously reported systems). The introduction of PEDOT:PSS was, once again, found to lower the percolation threshold (to 0.3 wt %) and to increase the ultimate conductivity up to the level of a pure PEDOT:PSS/PS blend. In the PS/PEDOT:PSS-SWCNT systems, the role of the SWCNT network is proposed to be limited to the formation of a template or scaffold on which a (more or less) continuous PEDOT:PSS layer deposits. The ultimate conductivity is therefore determined by the PEDOT:PSS alone.

We investigated by means of polarization microscopy the influence of a magnetic field on the shape and director field of nematic droplets in dispersions of plate-like colloidal particles. To interpret the experimental observations, we put forward a simple theory in which we presume strong anchoring and a sphero-cylindrical droplet shape. This model allows us to extract values for the interfacial tension and the splay elastic constant from the experimental data.

We report on two diaminotriazine-equipped naphthalene derivatives that bind reversibly to a single-stranded DNA template or "tape-measure molecule" via hydrogen bonding, yielding monodisperse double-stranded DNA hybrids with one strand consisting of a supramolecular naphthalene backbone. These assemblies have been investigated extensively, both experimentally and theoretically. The structure and the templated self-assembly process of the complex have been characterized with UV-vis spectroscopy, circular dichroism spectroscopy, molecular dynamics simulations, cryo-transmission electron microscopy, liquid atomic force microscopy, electrospray ionization mass spectrometry, light scattering, and 1H NMR and infrared spectroscopy. We have found that the DNA hybrid complexes have a right-handed helical arrangement stabilized by pi-pi interactions and hydrogen bonds. The hydrophilic hydroxyl group at the end of the ethylene glycol of the guest molecule suppressed both the nontemplated self-assembly of the naphthalene guest molecules and the further aggregation of the entire DNA hybrid complex. Through the use of a theoretical mass-action model for the templated self-assembly, the host-guest and guest-guest interaction energies were estimated by fitting to the spectroscopic data. The differently estimated values of the interaction energies and thermodynamic parameters vary within experimental error, showing the self-consistency of the model. From the obtained correlation between the positions of the guest molecules bound on the template, we have obtained a qualitative theoretical picture of the way in which the guests are physically distributed on the templates. For short templates, the templates are filled one-by-one, even at moderate fractions of bound sites. For larger templates, the templates first have alternating sequences of filled and empty sections, after which, at large fractions of bound sites, virtually all of the binding sites for all template lengths are filled.

We apply continuum connectedness percolation theory to realistic carbon nanotube systems and predict how bending flexibility, length polydispersity, and attractive interactions between them influence the percolation threshold, demonstrating that it can be used as a predictive tool for designing nanotube-based composite materials. We argue that the host matrix in which the nanotubes are dispersed controls this threshold through the interactions it induces between them during processing and through the degree of connectedness that must be set by the tunneling distance of electrons, at least in the context of conductivity percolation. This provides routes to manipulate the percolation threshold and the level of conductivity in the final product. We find that the percolation threshold of carbon nanotubes is very sensitive to the degree of connectedness, to the presence of small quantities of longer rods, and to very weak attractive interactions between them. Bending flexibility or tortuosity, on the other hand, has only a fairly weak impact on the percolation threshold.

By applying polymer scaling theory, we investigate the effects of steric interactions on the growth of a class of equilibrium polymers that require activation before polymerization can take place. The growth exponents that we obtain in dilute and semidilute solutions of such thermally activated supramolecular polymers are identical to those for isodesmic equilibrium polymers, but different from those of "living" supramolecular polymers that are chemically activated by reaction with an initiator. We also find that with increasing activation energy the crossover from the dilute to the semidilute regime shifts toward the polymerization transition and eventually merges with it, giving rise to nonclassical behavior in particular of the osmotic compressibility. It appears that steric interactions make the polymerization more co-operative in dilute solution, but less so in semidilute solution.

A phenomenological theory is presented for the kinetics of the in vitro assembly and disassembly of icosahedral virus capsids in solutions of coat proteins. The focus is on conditions where nucleation-type processes can be ignored. We find that the kinetics of assembly is strongly concentration dependent and that the late-stage relaxation time varies as the inverse of the square of the concentration. These findings are corroborated by experimental observations on a number of viruses. Further, our theory shows that hysteresis observed in some experiments could be a direct effect of the kinetics of a high-order mass action law, not necessarily the result of a free energy barrier between assembled and disassembled states. © 2007 IOP Publishing Ltd

We synthesize two differently sized poly(methyl methacrylate-co-tert-butyl acrylate) latexes by emulsion polymerization and mix these with a sonicated single-walled carbon nanotube (SWCNT) dispersion, in order to prepare 3% SWCNT composite mixtures. We spin-coat these mixtures at various spin-speed rates and spin times over a glass substrate, producing a thin, transparent, solid, conductive layer. Keeping the amount of SWCNTs constant, we vary the weight fraction of our smaller 30-nm latex particles relative to the larger 70-nm-sized ones. We find a maximum in the electrical conductivity up to 370 S/m as a function of the weight fraction of smaller particles, depending on the overall solid content, the spin speed, and the spin time. This maximum occurs at 3-5% of the smaller latex particles. We also find a more than 2-fold increase in conductivity parallel to the radius of spin-coating than perpendicular to it. Atomic force microscopy points at the existence of lanes of latex particles in the spin-coated thin layer, while large-area transmission electron microscopy demonstrates that the SWCNTs are aligned over a grid fixed on the glass substrate during the spin-coating process. We extract the conductivity distribution on the surface of the thin film and translate this into the direction of the SWCNTs in it.

Spindle-shaped nematic droplets (tactoids) form in solutions of rod-like molecules at the onset of the liquid crystalline phase. Their unique shape and internal structure result from the interplay of the elastic deformation of the nematic and anisotropic surface forces. The balance of these forces dictates that tactoids must display a continuous variation in aspect ratio and director-field configuration. Yet, such continuous transition has eluded observation for decades: tactoids have displayed either a bipolar configuration with particles aligned parallel to the droplet interface or a homogeneous configuration with particles aligned parallel to the long axis of the tactoid. Here, we report the first observation of the continuous transition in shape and director-field configuration of tactoids in true solutions of carbon nanotubes in chlorosulfonic acid. This observation is possible because the exceptional length of carbon nanotubes shifts the transition to a size range that can be visualized by optical microscopy. Polarization micrographs yield the interfacial and elastic properties of the system. Absorbance anisotropy measurements provide the highest nematic order parameter (S = 0.79) measured to date for a nematic phase of carbon nanotubes at coexistence with its isotropic phase.

We present a statistical mechanical model based on the principle of mass action that explains the main features of the in vitro aggregation behavior of the coat protein of tobacco mosaic virus (TMV). By comparing our model to experimentally obtained stability diagrams, titration experiments, and calorimetric data, we pin down three competing factors that regulate the transitions between the different kinds of aggregated state of the coat protein. These are hydrophobic interactions, electrostatic interactions, and the formation of so-called “Caspar” carboxylate pairs. We suggest that these factors could be universal and relevant to a large class of virus coat proteins.

The conformational behavior of both uncharged and charged hyperbranched polymers (HBPs) in dilute solutions has been studied using Brownian dynamics simulations. A distinction has been made between two types of architectures: type 1, which is characterized by its degree of polymerization (N) and its number of generations (gmax), and type 2, which is characterized by its degree of polymerization (N) and its degree of branching (DB). The radius of gyration (Rg) of both uncharged and charged type 1 HBPs is strongly influenced by variation of g. For uncharged type 2 HBPs Rg is relatively insensitive to variation of DB, whereas for charged type 2 HBPs Rg is a decreasing function of DB. The values of the radii of gyration as determined in the simulations are well reproduced in mean-field calculations. Scaling of Rg with the Wiener index and N has been investigated and compared to data from literature. The radial mass distribution of a charged type 1 HBP exhibits an ordering of the monomers that is highly dependent on g; the radial mass distribution of a charged type 2 HBPs shows an ordering that is only weakly dependent on DB. These orderings manifest themselves via oscillations of the static structure factor.

Electrostatic interactions play a central role in the assembly of single-stranded RNA viruses. Under physiological conditions of salinity and acidity, virus capsid assembly requires the presence of genomic material that is oppositely charged to the core proteins. In this paper we apply basic polymer physics and statistical mechanics methods to the self-assembly of a synthetic virus encapsidating generic polyelectrolyte molecules. We find that (i) the mean concentration of the encapsidated polyelectrolyte material depends on the surface charge density, the radius of the capsid, and the linear charge density of the polymer but neither on the salt concentration or the Kuhn length, (ii) the total charge of the capsid interior is equal but opposite to that of the empty capsid, a form of charge reversal. Unlike natural viruses, synthetic viruses are predicted not to be under an osmotic swelling pressure. The design condition that self-assembly only produces filled capsids is shown to coincide with the condition that the capsid surface charge exceeds the desorption threshold of polymer surface adsorption. We compare our results with studies on the self-assembly of both synthetic and natural viruses., Comment: 41 pages, 4 figures