Efficient sampling of reversible cross-linking polymers: Self-assembly of single-chain polymeric nanoparticles

We present a new simulation technique to study systems of polymers functionalized by reactive sites that bind/unbind forming reversible linkages. Functionalized polymers feature self-assembly and responsive properties that are unmatched by systems lacking selective interactions. The scales at which the functional properties of these materials emerge are difficult to model, especially in the reversible regime where such properties result from many binding/unbinding events. This difficulty is related to large entropic barriers associated with the formation of intra-molecular loops. In this work we present a simulation scheme that sidesteps configurational costs by dedicated Monte Carlo moves capable of binding/unbinding reactive sites in a single step. Cross-linking reactions are implemented by trial moves that reconstruct chain sections attempting, at the same time, a dimerization reaction between pairs of reactive sites. The model is parametrized by the reaction equilibrium constant of the reactive species free in solution. This quantity can be obtained by means of experiments or atomistic/quantum simulations. We use the proposed methodology to study self-assembly of single--chain polymeric nanoparticles, starting from flexible precursors carrying regularly or randomly distributed reactive sites. During a single run, almost all pairs of reactive monomers interact at least once. We focus on understanding differences in the morphology of chain nanoparticles when linkages are reversible as compared to the well studied case of irreversible reactions. Intriguingly, we find that the size of regularly functionalsized chains, in good solvent conditions, is non-monotonous as a function of the degree of functionalization. We clarify how this result follows from excluded volume interactions and is peculiar of reversible linkages and regular functionalizations.Comment: to appear in The Journal of Chemical Physic

Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces

At the heart of the structured architecture and complex dynamics of biological systems are specific and timely interactions operated by biomolecules. In many instances, biomolecular agents are spatially confined to flexible lipid membranes where, among other functions, they control cell adhesion, motility and tissue formation. Besides being central to several biological processes, \emph{multivalent interactions} mediated by reactive linkers confined to deformable substrates underpin the design of synthetic-biological platforms and advanced biomimetic materials. Here we review recent advances on the experimental study and theoretical modelling of a heterogeneous class of biomimetic systems in which synthetic linkers mediate multivalent interactions between fluid and deformable colloidal units, including lipid vesicles and emulsion droplets. Linkers are often prepared from synthetic DNA nanostructures, enabling full programmability of the thermodynamic and kinetic properties of their mutual interactions. The coupling of the statistical effects of multivalent interactions with substrate fluidity and deformability gives rise to a rich emerging phenomenology that, in the context of self-assembled soft materials, has been shown to produce exotic phase behaviour, stimuli-responsiveness, and kinetic programmability of the self-assembly process. Applications to (synthetic) biology will also be reviewed.Comment: 63 pages, revie

Large-N_f behavior of the Yukawa model: analytic results

We investigate the Yukawa model in which $N_f$ fermions are coupled with a scalar field $\phi$ through a Yukawa interaction. The phase diagram is rather well understood. If the fermions are massless, there is a chiral transition at $T_c$: for $T < T_c$ chiral symmetry is spontaneously broken. At $N_f=\infty$ the transition is mean-field like, while, for any finite $N_f$, standard arguments predict Ising behavior. This apparent contradiction has been explained by Kogut et al., who showed by scaling arguments and Monte Carlo simulations that in the large-$N_f$ limit the width of the Ising critical region scales as a power of $1/N_f$, so that only mean-field behavior is observed for $N_f$ strictly equal to infinity. We will show how the results of Kogut et al. can be recovered analytically in the framework of a generalized $1/N_f$ expansion. The method we use is a simple generalization of the method we have recently applied to a two-dimensional generalized Heisenberg model.Comment: Talk presented at XXIIIrd International Symposium on Lattice Field Theory, 25-30 July 2005, Trinity College, Dublin, Irelan

Modelling receding contact lines on superhydrophobic surfaces

We use mesoscale simulations to study the depinning of a receding contact line on a superhydrophobic surface patterned by a regular array of posts. In order that the simulations are feasible, we introduce a novel geometry where a column of liquid dewets a capillary bounded by a superhydrophobic plane which faces a smooth hydrophilic wall of variable contact angle. We present results for the dependence of the depinning angle on the shape and spacing of the posts, and discuss the form of the meniscus at depinning. We find, in agreement with [17], that the local post concentration is a primary factor in controlling the depinning angle, and show that the numerical results agree well with recent experiments. We also present two examples of metastable pinned configurations where the posts are partially wet.Comment: Revised version accepted for publication in Langmui

Capillary filling in microchannels patterned by posts

We investigate the capillary filling of three dimensional micro-channels with surfaces patterned by posts of square cross section. We show that pinning on the edges of the posts suppresses, and can halt, capillary filling. We stress the importance of the channel walls in controlling whether filling can occur. In particular for channels higher than the distance between adjacent posts, filling occurs for contact angles less than a threshold angle \sim 55 deg., independent of the height of the channel.Comment: To appear in Phys. Rev.

Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections

We investigate a two-dimensional classical $-vector model with a generic nearest-neighbor interaction$W(\bsigma_i\cdot \bsigma_j)$in the large-N limit, focusing on the finite-temperature transition point at which energy-energy correlations become critical. We show that this transition belongs to the Ising universality class. However, the width of the region in which Ising behavior is observed scales as$1/N^{3/2}$along the magnetic direction and as 1/N in the thermal direction; outside a crossover to mean-field behavior occurs. This explains why only mean-field behavior is observed for$N=\infty$Comment: 34 pages, 1 figur

Virial coefficients and osmotic pressure in polymer solutions in good-solvent conditions

We determine the second, third, and fourth virial coefficients appearing in the density expansion of the osmotic pressure of a monodisperse polymer solution in good-solvent conditions. Using the expected large-concentration behavior, we extrapolate the low-density expansion outside the dilute regime, obtaining the osmotic pressure for any concentration in the semidilute region. Comparison with field-theoretical predictions and experimental data shows that the obtained expression is quite accurate. The error is approximately 1-2% below the overlap concentration and rises at most to 5-10% in the limit of very large polymer concentrations.Comment: 26 pages, 4 figure

Steric interactions between mobile ligands facilitate complete wrapping in passive endocytosis

Receptor-mediated endocytosis is an ubiquitous process through which cells internalize biological or synthetic nanoscale objects, including viruses, unicellular parasites, and nanomedical vectors for drug or gene delivery. In passive endocytosis the cell plasma membrane wraps around the "invader" particle driven by ligand-receptor complexation. By means of theory and numerical simulations, here we demonstrate how particles decorated by freely diffusing and non-mutually-interacting (ideal) ligands are significantly more difficult to wrap than those where ligands are either immobile or interact sterically with each other. Our model rationalizes the relationship between uptake mechanism and structural details of the invader, such as ligand size, mobility and ligand/receptor affinity, providing a comprehensive picture of pathogen endocytosis and helping the rational design of efficient drug delivery vectors.Comment: Updated version of the manuscript. Accepted for publication in PR

Spherically averaged versus angle-dependent interactions in quadrupolar fluids

Employing simplified models in computer simulation is on the one hand often enforced by computer time limitations but on the other hand it offers insights into the molecular properties determining a given physical phenomenon. We employ this strategy to the determination of the phase behaviour of quadrupolar fluids, where we study the influence of omitting angular degrees of freedom of molecules via an effective spherically symmetric potential obtained from a perturbative expansion. Comparing the liquid-vapor coexistence curve, vapor pressure at coexistence, interfacial tension between the coexisting phases, etc., as obtained from both the models with the full quadrupolar interactions and the (approximate) isotropic interactions, we find discrepancies in the critical region to be typically (such as in the case of carbon dioxide) of the order of 4%. However, when the Lennard-Jones parameters are rescaled such that critical temperatures and critical densities of both models coincide with the experimental results, almost perfect agreement between the above-mentioned properties of both models is obtained. This result justifies the use of isotropic quadrupolar potentials. We present also a detailed comparison of our simulations with a combined integral equation/density functional approach and show that the latter provides an accurate description except for the vicinity of the critical point.Comment: Phys. Rev. E, accepte