Ultrasoft Particles Research Articles

Phase separation dynamics in a symmetric binary mixture of ultrasoft particles.

Phase separation plays a key role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The interaction among these aggregates is soft, i.e., they can significantly overlap at a small energy cost. From a computer simulation point of view, these complex macromolecular aggregates are generally modeled by soft particles. The effective interaction between two particles is defined via the generalized exponential model of index n, with n = 4. Here, using molecular dynamics simulations, we study the phase separation dynamics of a size-symmetric binary mixture of ultrasoft particles. We find that when the mixture is quenched to a temperature below the critical temperature, the two components spontaneously start to separate. Domains of the two components form, and the equal-time order parameter reveals that the domain sizes grow with time in a power-law manner with an exponent of 1/3, which is consistent with the Lifshitz-Slyozov law for conserved systems. Furthermore, the static structure factor shows a power-law decay with an exponent of 4, consistent with the Porod law.

Ultrasoft platelet-like particles stop bleeding in rodent and porcine models of trauma.

Uncontrolled bleeding after trauma represents a substantial clinical problem. The current standard of care to treat bleeding after trauma is transfusion of blood products including platelets; however, donated platelets have a short shelf life, are in limited supply, and carry immunogenicity and contamination risks. Consequently, there is a critical need to develop hemostatic platelet alternatives. To this end, we developed synthetic platelet-like particles (PLPs), formulated by functionalizing highly deformable microgel particles composed of ultralow cross-linked poly (N-isopropylacrylamide) with fibrin-binding ligands. The fibrin-binding ligand was designed to target to wound sites, and the cross-linking of fibrin polymers was designed to enhance clot formation. The ultralow cross-linking of the microgels allows the particles to undergo large shape changes that mimic platelet shape change after activation; when coupled to fibrin-binding ligands, this shape change facilitates clot retraction, which in turn can enhance clot stability and contribute to healing. Given these features, we hypothesized that synthetic PLPs could enhance clotting in trauma models and promote healing after clotting. We first assessed PLP activity in vitro and found that PLPs selectively bound fibrin and enhanced clot formation. In murine and porcine models of traumatic injury, PLPs reduced bleeding and facilitated healing of injured tissue in both prophylactic and immediate treatment settings. We determined through biodistribution experiments that PLPs were renally cleared, possibly enabled by ultrasoft particle properties. The performance of synthetic PLPs in the preclinical studies shown here supports future translational investigation of these hemostatic therapeutics in a trauma setting.

Glass quantization of the Gaussian core model.

We use the replica method to study the dynamical glass transition of the Gaussian core model, a system of ultrasoft repulsive spheres interacting via a Gaussian potential, focusing on low temperatures and low-to-moderate densities. At constant temperature, an amorphous glassy state is entered upon a first compression but this glass melts as the density is further increased. In addition to this reentrant transition, a second, smooth transition is discovered between a continuous and a discretized glass. The properties of the former are continuous functions of temperatures, whereas the latter exhibits a succession of stripes, characterized by discontinuous jumps of the glassiness parameters. The glass physics of ultrasoft particles is hence richer than that of impenetrable particles for reasons that can be attributed to the ability of the former to create and break out-of-equilibrium clusters of overlapping particles.

Pair-correlation functions and freezing transition in a 2D binary mixture of ultrasoft colloidal particles interacting via Hertzian potential

Density functional theory (DFT) of freezing and hypernetted chain (HNC) integral equation theory has been used to investigate the nature of pair-correlations and the freezing transitions in a binary mixture of ultrasoft colloidal particles confined to a two-dimensional (2D) plane. The particles of the system interact via Hertzian type model potential with varying softness. The accuracy of the pair-correlations obtained by HNC theory has been tested by performing NVT Monte Carlo (MC) simulation. The partial pair correlation functions of the mixture are found to exhibit non-monotonous behaviour whose nature depends on the softness of the potential and composition. Pair-correlations obtained by solving the HNC integral equation theory have been used in DFT to determine the freezing parameters of fluid-substitutionally disordered triangular solid. The constant pressure phase diagrams in the composition-temperature plane are found to be narrow spindle types.

Freezing of a soft-core fluid in a one-dimensional potential: appearance of a locked smectic phase

ABSTRACT We investigate the phase behaviour of a two-dimensional colloidal model system of ultra-soft particles on a substrate which varies periodically along one spatial direction. Our calculations are based on mean-field density functional theory for a system of particles interacting via an ultra-soft potential, that is, the generalised exponential model with index four (GEM-4). For suitable substrate periodicities (with commensurability parameter p = 2), we find a succession of phase transitions from a modulated liquid to a locked smectic and then to a locked floating solid phase. The appearance of a locked smectic phase is consistent with earlier theoretical predictions and experiments for freezing of more repulsive systems on structured surfaces (with p = 2). However, the present ultra-soft system does not display re-entrant melting. We here investigate the details of the density distributions of the different phases, thereby supplementing earlier work on GEM-4 systems with p = 1 [Phys. Rev. E 101, 012609 (2020)]. Interestingly, the observed succession of phase transitions can be triggered through different paths along which physical control parameters are changed.

On the stress overshoot in cluster crystals under shear

Using non-equilibrium molecular dynamics simulations we study the yielding behaviour of a model cluster crystal formed by ultrasoft particles under shear. We investigate the evolution of stress as a function of strain for different shear rates, $\dot{\gamma}$, and temperatures. The stress-strain relation displays a pronounced maximum at the yielding point; the height of this maximum, $\sigma_\text{p}$, increases via a power law with an increasing shear range and tends to saturate to a finite value if the limit shear rate goes to zero (at least within the considered temperature range). Interestingly, this behaviour can be captured by the Herschel-Bulkley type model which, for a given temperature, allows us to predict a static yield stress $\sigma^{0}_\text{p}$ (in the shear rate tending to zero limit), a characteristic timescale $\tau_\text{c}$, and the exponent $\alpha$ of the above-mentioned power-law decay of the $\sigma_\text{p}$ at high shear rates. Furthermore, for different temperatures, the $\sigma_\text{p}$ can be scaled as functions of $\dot{\gamma}$ onto a single master curve when scaled by corresponding $\tau_\text{c}$ and ${\sigma}_\text{p}^{0}$. Moreover, for a given shear rate, $\sigma_\text{p}$ displays a logarithmic dependence on temperature. Again, the $\sigma_\text{p}{-}T$ curves for different shear rates can be scaled on a single logarithmic master curve when scaled by a corresponding fitting parameters.

Freezing of a soft-core fluid in a one-dimensional potential: Predictions based on a pressure-balance equation.

Using concepts from classical density functional theory, we investigate the freezing of a two-dimensional system of ultrasoft particles in a one-dimensional external potential, a phenomenon often called laser-induced freezing (LIF). In the first part of the paper, we present numerical results from free minimization of a mean-field density functional for a system of particles interacting via the GEM-4 potential. We show that the system does indeed display a LIF transition, although the interaction potential is markedly different from the cases studied before. We also introduce a suitably defined effective density within the potential wells ρ[over ¯]_{eff} as a control parameter of LIF, rather than the amplitude of the external potential as in the common LIF scenario. In the second part, we suggest a theoretical description of the onset of LIF which is based on the pressure-balance equation relating the pressure tensor and the external potential. Evaluating this equation for the modulated liquid phase at effective density ρ[over ¯]_{eff} and combining it with the (known) stability threshold of the corresponding bulk fluid, we can predict the critical effective density or, equivalently, the potential amplitude related to the onset of LIF. Our approach yields very good results for the model at hand and it is transferable, in principle, to other model systems.

Slow dynamics coupled with cluster formation in ultrasoft-potential glasses.

We numerically investigate the slow dynamics of a binary mixture of ultrasoft particles interacting with the generalized Hertzian potential. If the softness parameter, α, is small, the particles at high densities start penetrating each other, form clusters, and eventually undergo the glass transition. We find multiple cluster-glass phases characterized by a different number of particles per cluster, whose boundary lines are sharply separated by the cluster size. Anomalous logarithmic slow relaxation of the density correlation functions is observed in the vicinity of these glass-glass phase boundaries, which hints the existence of the higher-order dynamical singularities predicted by the mode-coupling theory. Deeply in the cluster glass phases, it is found that the dynamics of a single particle is decoupled from that of the collective fluctuations.

Ordered structures formed by ultrasoft, aspherical particles

ABSTRACTWe have applied the formalism of classical density functional theory to study the shape and the orientation of the density profiles formed by aspherical, ultrasoft particles. For simplicity we have considered particles with an elliptic shape, characterised by an aspect ratio λ. The 's are obtained via the minimisation of the grand-potential functional , for which we have used a mean-field format. The optimisation of is numerically realised in a free (i.e. unbiased) manner minimising the functional with respect to the density profile, which we have discretised in the unit cell of the lattice on 803 grid points. Keeping the temperature fixed and varying the chemical potential and λ, we have investigated the impact of these parameters on the density profile.

Non-monotonic variations of the nucleation free energy in a glass-forming ultra-soft particles fluid.

Using molecular dynamics simulation, we study the impact of the degree of supercooling on the crystal nucleation of ultra-soft particles, modeled with the Gaussian core potential. Focusing on systems with a high number density, our simulations reveal dramatically different behaviors as the degree of supercooling is varied. In the moderate supercooling regime, crystal nucleation proceeds as expected from classical nucleation theory, with a decrease in the free energy of nucleation, as well as in the size of the critical nucleus, as supercooling is increased. On the other hand, in the large supercooling regime, we observe an unusual reversal of behavior with an increase in the free energy of nucleation and in the critical size, as supercooling is increased. This unexpected result is analyzed in terms of the interplay between the glass transition and the crystal nucleation process. Specifically, medium range order crystal-like domains, with structural features different from that of the crystal nucleus, are found to form throughout the system when the supercooling is very large. These, in turn, play a pivotal role in the increase in the free energy of nucleation, as well as in the critical size, as the temperature gets closer to the glass transition.

Glass Transitions in Monodisperse Cluster-Forming Ensembles: Vortex Matter in Type-1.5 Superconductors.

At low enough temperatures and high densities, the equilibrium configuration of an ensemble of ultrasoft particles is a self-assembled, ordered, cluster crystal. In the present Letter, we explore the out-of-equilibrium dynamics for a two-dimensional realization, which is relevant to superconducting materials with multiscale intervortex forces. We find that, for small temperatures following a quench, the suppression of the thermally activated particle hopping hinders the ordering. This results in a glass transition for a monodispersed ensemble, for which we derive a microscopic explanation in terms of an "effective polydispersity" induced by multiscale interactions. This demonstrates that a vortex glass can form in clean systems of thin films of "type-1.5" superconductors. An additional setup to study this physics can be layered superconducting systems, where the shape of the effective vortex-vortex interactions can be engineered.

Characterization of the structural collapse undergone by an unstable system of ultrasoft particles

Abstract The effective repulsion between macromolecules such as polymer chains or dendrimers is everywhere finite, implying that interaction centers can even coincide. If, in addition, the large-distance attraction is sufficiently strong, then the system is driven unstable. An unstable system lacks a conventional thermodynamics since, in the infinite-size limit, it eventually collapses to a finite-size cluster (for instance, a polymer dispersion undergoes irreversible coagulation when increasing the amount of dissolved salt beyond a certain limit). Using a double-Gaussian (DG) potential for demonstration, we study the phase behavior of a system of ultrasoft particles as a function of the attraction strength η . Above a critical threshold η c , the DG system is unstable but its collective behavior is far from trivial since two separate regions of the thermodynamic plane can be identified, based on the value taken by the average waiting time for collapse: this is finite and small on one side of the boundary, while presumably infinite in the other region. In order to make sense of this evidence, we consider a stable system of particles interacting through a DG potential augmented with a hard core (stabilized DG, or SDG potential). We provide arguments supporting the view that the boundary line of the unstable DG model is the remnant of the spinodal line of a fluid–fluid phase transition occurring in the SDG model when the hard-core diameter is sent to zero.

Tunable slow dynamics in a new class of soft colloids.

By means of extensive simulations, we investigate concentrated solutions of globular single-chain nanoparticles (SCNPs), an emergent class of synthetic soft nano-objects. By increasing the concentration, the SCNPs show flattening, and even reentrant behaviour, in the density dependence of their structural and dynamic correlations, as well as a soft caging regime and weak dynamic heterogeneity. The latter is confirmed by validation of the Stokes-Einstein relation up to concentrations far beyond the overlap density. Therefore SCNPs arise as a new class of soft colloids, exhibiting slow dynamics and actualizing in a real system the structural and dynamic anomalies proposed by models of ultrasoft particles. Quantitative differences in the dynamic behaviour depend on the SCNP deformability, which can be tuned through the degree of internal cross-linking.

Hopping and diffusion of ultrasoft particles in cluster crystals in the explicit presence of a solvent

We have investigated diffusion and hopping processes in a cluster crystal formed from mesoscopic, ultrasoft particles. In contrast to previous contributions we have explicitly included in our investigations the microscopic solvent by using a simulation scheme that takes the induced hydrodynamic interactions into account as faithfully as possible. In our investigations we first focused on the processes of migration of the ultrasoft particles. By evaluating dynamical correlation functions we were able to demonstrate that the presence of the solvent does indeed have an important impact on the diffusion and hopping processes of the particles: this applies in particular to the diffusive behaviour, to the angular orientation of the jump events and to the spatial extents of these events. In a second set-up we have added non-cluster-forming ultrasoft particles to the system, investigating thus the impact of the solvent and that of the mutual interaction of the two species of ultrasoft particles on their respective dynamic behaviours. Our investigations clearly demonstrate, beside the expected significant role that the solvent plays in this set-up, that diffusion and the jump processes show distinct differences for the two particle species.

Fluids of semiflexible ring polymers: effective potentials and clustering

We present a computational investigation of the structural properties of a fluid of semiflexible ring polymers. Stiffness is introduced by implementing intramolecular barriers. Because of these barriers, shrinkage of the rings is energetically unfavourable, and the ring size can exhibit a non-monotonic density dependence. At high concentrations the rings can swell and adopt open configurations that facilitate interpenetration and clustering. We obtain effective potentials between the centers-of-mass of the rings at infinite dilution, and explore their validity over the whole range of concentrations. Except for the limit of small rings, the effective fluid of ultrasoft particles provides a good description of the real system over a considerable range of densities, even above the overlap concentration. In particular the clustering behaviour predicted by the effective description is observed in the real system for a certain range of molecular masses. However, the effective description is incomplete. Inspection of the clusters of real rings reveals that these can arrange in a complex disordered phase formed by long columns of oblate rings, which are penetrated by bundles of elongated prolate rings. These anisotropic features of the real system are not captured by the standard effective approach, which only considers macromolecular centers-of-mass. This suggests the need to include the relative orientation between rings in the effective potentials.

Interfacial and wetting behaviour of phase-separating ultrasoft mixtures

We apply density functional theory to study the interfacial properties of a phase-separating binary fluid of ultrasoft particles, whose interaction potentials belong to the family of the so-called generalized exponential models (GEM). By using the formalism of the density functional theory within the mean-field approximation, we investigate the equilibrium density profiles for each component at the free interface as well as at a repulsive, flat wall. We show that the studied system can lead to first-order wetting transition which is characterized by a layering-like behaviour due to the clustering properties of GEM particles.

Hopping and microscopic dynamics of ultrasoft particles in cluster crystals

We have investigated the slow dynamics of ultrasoft particles in crystalline cluster phases, where point particles interact through the generalized exponential potential u(r) = e exp[−(r/σ)n], focusing on the cluster fcc phase of this model with n = 4. In an effort to elucidate how the mechanisms of mass transport depend on the microscopic dynamics and in order to mimic a realistic scenario in a related experiment we have performed molecular dynamics, Brownian dynamics, and Monte Carlo simulations. In molecular dynamics simulations the diffusion of particles proceeds through long-range jumps, guided by strong correlations in the momentum direction. In Monte Carlo and Brownian dynamics simulations jump events are short-ranged, reflecting the purely configurational nature of the dynamics. In contrast to what was found in models of glass-forming liquids, the effect of Newtonian and stochastic microscopic dynamics on the long-time relaxation cannot be accounted for by a temperature-independent rescaling of the time units. From the obvious qualitative discrepancies in the short time behavior between the three simulation methods and the non-trivial difference in jump length distributions, long time relaxation, and dynamic heterogeneity, we learn that a more complex modeling of the dynamics in realistic systems of ultrasoft colloids is required.

Chromosome aberration induction is dependent on the spatial distribution of energy deposition through a cell nucleus

The importance of the spatial distribution of energy deposition through the nucleus in determining the resultant chromosome rearrangements was investigated using fluorescent in situ hybridisation technique following either uniform or partial irradiation of HF19 human fibroblast cells with low-LET 1.5 keV ultrasoft X-rays. Irradiations were performed with and without a copper irradiation mask with a Poisson distribution of micron-sized holes immediately below the irradiation dish and the results are compared with previous results obtained following exposure to a Poisson distribution of alpha particles. For the same radiation quality, the spatial distribution of energy deposition within the nucleus was found to be important in determining the ultimate biological response, with an increased ratio of complex-to-simple aberrations observed for partial compared to uniform irradiation. Comparisons between low-LET ultrasoft X-rays and high-LET alpha particles indicate that the sub-micron clustering of damage along the alpha particle track is more important than just the total number of double-strand breaks produced.

Ground states of ultrasoft particles with attractions: a genetic algorithm approach

We analyse in detail the ground-state structure of model systems of athermal star polymers with an additional, tunable attraction that may result from dispersion or depletion forces. To perform a free, unbiased search in the space spanned by the crystal parameters, we employ genetic algorithms, which are enhanced with respect to previous versions in their ability to find stable structures that occupy very narrow basins of attraction in the energy landscape. Application of this method brings about a very large variety of ground states for star polymers with attractions, in particular for the case of intermediate functionalities and strong, short-range attractive forces.

Cluster-forming systems of ultrasoft repulsive particles: statics and dynamics

In this paper, we present a short review as well as novel results on a recently established counterintuitive phenomenon of cluster aggregation of particles that interact via purely repulsive interactions. We demonstrate how repulsion can lead to clustering provided that the interaction allows full particle overlaps and also displays negative Fourier components. The formation of crystals with average site occupancy that scales linearly with density, and which is in general a noninteger number, is demonstrated by means of density functional theory and Monte Carlo simulations. Noninteger average occupancy of lattice sites is sustained by incessant hopping processes in the crystal, which we observe and quantitatively analyze by means of Molecular Dynamics simulations. The simultaneous presence of relaxative dynamics on the single-particle and arrested dynamics on the collective level leads to an unusual interplay between the two and to novel scenarios of dynamical arrest in the cluster crystal.