Revisiting the strain-induced softening behaviour in hydrogels.

The strain-induced softening behaviour observed in the differential modulus K(T,γ) of hydrogels is typically attributed to the breakage of internal network structures, such as the cross-links that bind the polymer chains. In this study, however, we consider a stress-strain relationship derived from a coarse-grained model to demonstrate that rupture of the network is not necessary for rubber-like gels to exhibit such behaviour. In particular, we show that, in some cases, the decrease of K(T,γ) as a function of the strain γ can be associated with the energy-related contribution to the elastic modulus that has been experimentally observed, e.g., for tetra-PEG hydrogels. Our findings suggest that the softening behaviour can be also attributed to the effective interaction between polymer chains and their surrounding solvent molecules, rather than the breakage of structural elements. We compare our theoretical expressions with experimental data determined for several hydrogels to illustrate and validate our approach.

On the origin of the negative energy-related contribution to the elastic modulus of rubber-like gels.

We consider a coarse-grained polymer model in order to investigate the origin of a recently discovered negative energy-related contribution to the elastic modulus G(T) of rubber-like gels. From this model, we are able to compute an exact expression for the free energy of the system, which allows us to evaluate a stress-strain relationship that displays a non-trivial dependence on the temperature T. We validate our approach through comparisons between the theoretical results and the experimental data obtained for tetra-PEG hydrogels, which indicate that, although simple, the present model works well to describe the experiments. Importantly, our approach unveiled aspects of the experimental analysis which turned out to be different from the conventional entropic and energetic analysis broadly used in the literature. Also, in contrast to the linear dependence predicted by the traditional, i.e., purely entropic, models, our results suggest that the general expression of the elastic modulus should be of the form [Formula: see text], with w(T) being a temperature-dependent correction factor that could be related to the interaction between the chains in the network and the solvent. Accordingly, the correction factor allows the expression found for the elastic modulus to describe both rubber and rubber-like gels.

Ligancy effects on nucleation kinetics.

Nucleation of particles into crystalline structures can be observed in a wide range of systems from metallic and metal-organic compounds to colloidal and polymeric patch particles. Here, we perform kinetic Monte Carlo simulations to study the nucleation kinetics of particles with different ligancies z at constant supersaturation s. This approach allows one to determine several physico-chemical quantities as a function of s, including the growth probability P(n), the critical nucleus size n*, and the stationary nucleation rate Js. Our numerical results are rationalized in terms of a self-consistent nucleation theory where both n* and Js present a non-trivial dependence on s, but which can be determined from the values of effective z-dependent parameters.

Microrheology of semiflexible filament solutions based on relaxation simulations.

We present an efficient computational methodology to obtain the viscoelastic response of dilute solutions of semiflexible filaments. By considering an approach based on the fluctuation-dissipation theorem, we were able to evaluate the dynamical properties of probe particles immersed in solutions of semiflexible filaments from relaxation simulations with a relatively low computational cost and higher precision in comparison to those based on stochastic dynamics. We used a microrheological approach to obtain the complex shear modulus and the complex viscosity of the solution through its compliance which was obtained directly from the dynamical properties of a probe particle attached to an effective medium described by a mesoscopic model, i.e., an effective filament model (EFM). The relaxation simulations were applied to assess the effects of the bending energy on the viscoelasticity of the semiflexible filament solutions, and our methodology was validated by comparing the numerical results to the experimental data on DNA and collagen solutions.

On the relationship between the plateau modulus and the threshold frequency in peptide gels.

Relations between static and dynamic viscoelastic responses in gels can be very elucidating and may provide useful tools to study the behavior of bio-materials such as protein hydrogels. An important example comes from the viscoelasticity of semisolid gel-like materials, which is characterized by two regimes: a low-frequency regime, where the storage modulus G'(ω) displays a constant value Geq, and a high-frequency power-law stiffening regime, where G'(ω) ∼ ωn. Recently, by considering Monte Carlo simulations to study the formation of peptides networks, we found an intriguing and somewhat related power-law relationship between the plateau modulus and the threshold frequency, i.e., Geq∼(ω*)Δ with Δ = 2/3. Here we present a simple theoretical approach to describe that relationship and test its validity by using experimental data from a ß-lactoglobulin gel. We show that our approach can be used even in the coarsening regime where the fractal model fails. Remarkably, the very same exponent Δ is found to describe the experimental data.

Importance of non-affine viscoelastic response in disordered fibre networks.

Disordered fibre networks are ubiquitous in nature and have a wide range of industrial applications as novel biomaterials. Predicting their viscoelastic response is straightforward for affine deformations that are uniform over all length scales, but when affinity fails, as has been observed experimentally, modelling becomes challenging. Here we present a numerical methodology, related to an existing framework for amorphous packings, to predict the steady-state viscoelastic spectra and degree of affinity for disordered fibre networks driven at arbitrary frequencies. Applying this method to a peptide gel model reveals a monotonic increase of the shear modulus as the soft, non-affine normal modes are successively suppressed as the driving frequency increases. In addition to being dominated by fibril bending, these low frequency network modes are also shown to be delocalised. The presented methodology provides insights into the importance of non-affinity in the viscoelastic response of peptide gels, and is easily extendible to all types of fibre networks.

Influence of network topology on the swelling of polyelectrolyte nanogels.

It is well-known that the swelling behavior of ionic nanogels depends on their cross-link density; however, it is unclear how different topologies should affect the response of the polyelectrolyte network. Here we perform Monte Carlo simulations to obtain the equilibrium properties of ionic nanogels as a function of salt concentration Cs and the fraction f of ionizable groups in a polyelectrolyte network formed by cross-links of functionality z. Our results indicate that the network with cross-links of low connectivity result in nanogel particles with higher swelling ratios. We also confirm a de-swelling effect of salt on nanogel particles.

Universality in the morphology and mechanics of coarsening amyloid fibril networks.

Peptide hydrogels have important applications as biomaterials and in nanotechnology, but utilization often depends on their mechanical properties for which we currently have no predictive capability. Here we use a peptide model to simulate the formation of percolating amyloid fibril networks and couple these to the elastic network theory to determine their mechanical properties. We find that the time variation of network length scales can be collapsed onto master curves by using a time scaling function that depends on the peptide interaction anisotropy. The same scaling applies to network mechanics, revealing a nonmonotonic dependence of the shear modulus with time. Our structure-function relationship between the peptide building blocks, network morphology, and network mechanical properties can aid in the design of amyloid fibril networks with tailored mechanical properties.

Communication: Non-monotonic supersaturation dependence of the nucleus size of crystals with anisotropically interacting molecules.

We study the nucleation of model two-dimensional crystals formed from anisotropically interacting molecules using kinetic Monte Carlo simulations and the forward flux sampling algorithm. The growth probability P(n) of a cluster of n molecules is measured while the supersaturation s and interaction anisotropy of the molecules are varied, in order to gain insight into the nucleation mechanism. It is found that with increasing degree of interaction anisotropy the nucleus size (defined as the cluster size at which P(n) = 0.5) can increase with increasing s, with sharp jumps at certain s values. Analysis of the cluster shape reveals that nucleation in the system studied is of a non-standard form, in that it embodies elements of both the classical nucleation theory and the density functional theory frameworks.

Motion-induced inertial effects and topological phase transitions in skyrmion transport.

When the skyrmion dynamics beyond the particle-like description is considered, this topological structure can deform due to a self-induced field. In this work, we perform Monte Carlo simulations to characterize the skyrmion deformation during its steady movement. In the low-velocity regime, the deformation in the skyrmion shape is quantified by an effective inertial mass, which is related to the dissipative force. When skyrmions move faster, the large self-induced deformation triggers topological transitions. These transitions are characterized by the proliferation of skyrmions and a different total topological charge, which is obtained as a function of the skyrmion velocity. Our findings provide an alternative way to describe the dynamics of a skyrmion that accounts for the deformations of its structure. Furthermore, such motion-induced topological phase transitions make it possible to control the number of ferromagnetic skyrmions through velocity effects.

Amyloid Fibril Solubility.

It is well established that amyloid fibril solubility is protein specific, but how solubility depends on the interactions between the fibril building blocks is not clear. Here we use a simple protein model and perform Monte Carlo simulations to directly measure the solubility of amyloid fibrils as a function of the interaction between the fibril building blocks. Our simulations confirms that the fibril solubility depends on the fibril thickness and that the relationship between the interactions and the solubility can be described by a simple analytical formula. The results presented in this study reveal general rules how side-chain-side-chain interactions, backbone hydrogen bonding, and temperature affect amyloid fibril solubility, which might prove to be a powerful tool to design protein fibrils with desired solubility and aggregation properties in general.