Competition between deformation and free volume quantified by 3D image analysis of red blood cell.

Cells in living organisms are subjected to mechanical strains caused by external forces like overcrowding, resulting in strong deformations that affect cell function. We study the interplay between deformation and crowding of red blood cells (RBCs) in dispersions of nonabsorbing rod-like viruses. We identify a sequence of configurational transitions of RBC doublets, including configurations that can only be induced by long-ranged attraction: highly fluctuating T-shaped and face-to-face configurations at low, and doublets approaching a complete spherical configuration at high, rod concentrations. Complementary simulations are used to explore different energy contributions to deformation as well as the stability of RBC doublet configurations. Our advanced analysis of 3D reconstructed confocal images of RBC doublets quantifies the depletion interaction and the resulting deformation energy. Thus, we introduce a noninvasive, high-throughput platform that is generally applicable to investigate the mechanical response of biological cells to external forces and characterize their mechanical properties.

Surface tension measurement and calculation of model biomolecular condensates.

The surface tension of liquid-like protein-rich biomolecular condensates is an emerging physical principle governing the mesoscopic interior organisation of biological cells. In this study, we present a method to evaluate the surface tension of model biomolecular condensates, through straighforward sessile drop measurements of capillary lengths and condensate densities. Our approach bypasses the need for characterizing condensate viscosities, which was required in previously reported techniques. We demonstrate this method using model condensates comprising two mutants of the intrinsically disordered protein Ddx4N. Notably, we uncover a detrimental impact of increased protein net charge on the surface tension of Ddx4N condensates. Furthermore, we explore the application of Scheutjens-Fleer theory, calculating condensate surface tensions through a self-consistent mean-field framework using Flory-Huggins interaction parameters. This relatively simple theory provides semi-quantitative accuracy in predicting Ddx4N condensate surface tensions and enables the evaluation of molecular organisation at condensate surfaces. Our findings shed light on the molecular details of fluid-fluid interfaces in biomolecular condensates.

Computational design of anisotropic nanocomposite actuators.

This paper presents a theoretical investigation of the design of a new actuator type made of anisotropic colloidal particles grafted with stimuli-responsive polymer chains. These artificial muscles combine the osmotic actuation principle of stimuli-responsive hydrogels with the structural alignment of colloidal liquid crystals to achieve directional motion. The solubility of the stimuli-responsive polymer in the neutral state, its degree of polymerization, the salt concentration, and the grafting density of the polymer chains on the surface of the colloidal particles are investigated and identified as important for actuator performance and tunability. The computational results suggest that the proposed mechanically active material matches or exceeds the performances of natural muscles and provide the guidelines for the realization of artificial muscles with predetermined actuation properties.

Impact of poly(ethylene glycol) functionalized lipids on ordering and fluidity of colloid supported lipid bilayers.

Colloid supported lipid bilayers (CSLBs) are highly appealing building blocks for functional colloids. In this contribution, we critically evaluate the impact on lipid ordering and CSLB fluidity of inserted additives. We focus on poly(ethylene glycol) (PEG) bearing lipids, which are commonly introduced to promote colloidal stability. We investigate whether their effect on the CSLB is related to the incorporated amount and chemical nature of the lipid anchor. To this end, CSLBs were prepared from lipids with a low or high melting temperature (Tm), DOPC, and DPPC, respectively. Samples were supplemented with either 0, 5 or 10 mol% of either a low or high Tm PEGylated lipid, DOPE-PEG2000 or DSPE-PEG2000, respectively. Lipid ordering was probed via differential scanning calorimetry and fluidity by fluorescence recovery after photobleaching. We find that up to 5 mol% of either PEGylated lipids could be incorporated into both membranes without any pronounced effects. However, the fluorescence recovery of the liquid-like DOPC membrane was markedly decelerated upon incorporating 10 mol% of either PEGylated lipids, whilst insertion of the anchoring lipids (DOPE and DSPE without PEG2000) had no detectable impact. Therefore, we conclude that the amount of incorporated PEG stabilizer, not the chemical nature of the lipid anchor, should be tuned carefully to achieve sufficient colloidal stability without compromising the membrane dynamics. These findings offer guidance for the experimental design of studies using CSLBs, such as those focusing on the consequences of intra- and inter-particle inhomogeneities for multivalent binding and the impact of additive mobility on superselectivity.

Excluded volume interactions and phase stability in mixtures of hard spheres and hard rods.

In this paper we study excluded volume interactions, the free volume fraction available, and the phase behaviour, in mixtures of hard spheres (HS) and hard rods, modeled as spherocylinders. We use free volume theory (FVT) to predict various physical properties and compare to Monte Carlo computer simulations. FVT is used at two levels. We use the original FVT approach in which it is assumed that the correlations of the HS are not affected by the rods. This is compared to a recent, more rigorous, FVT approach which includes excluded volume interactions between the different components at all levels. We find that the novel rigorous FVT approach agrees well with computer simulation results at the level of free volume available, as well as for the phase stability. The FVT predictions show significant quantitative and qualitative deviations with respect to the original FVT approach. The phase transition curves are systematically at higher rod concentrations than previously predicted. Furthermore, the calculations revealed that a certain asphericity is required to induce isostructural fluid-fluid coexistence and the stability region is highly dependent on the size ratio between the rods and the spheres.

Multiphase Coexistences in Rod-Polymer Mixtures.

Using recently derived analytical equations of state for hard rod dispersions, we predict the phase behavior of athermal rod-polymer mixtures with free volume theory. The rods are modeled as hard spherocylinders, while the nonadsorbing polymer chains are described as penetrable hard spheres. It is demonstrated that all of the different types of phase states that are stable for pure colloidal rod dispersions can coexist with any combination of these phases if polymers are added, depending on the concentrations, rod aspect ratio, and polymer-rod size ratio. This includes novel two-, three-, and four-phase coexistences and isostructural coexistences between dilute and concentrated phases of the same kind, even for the more ordered (liquid) crystal phases. This work provides insight into the conditions at which particular multiphase coexistences are expected for well-defined model colloidal rod-polymer mixtures. We provide a quantitative map detailing the various types of isostructural coexistences, which confirms an early qualitative hypothesis by Bolhuis et al. ( J. Chem. Phys. 107, 1997 1551).

Kinetic state diagrams for a highly asymmetric block copolymer assembled in solution.

Polymer self-assembly is used to form nanomaterials with a wide range of structures. While self-assembly of polymers in bulk has been thoroughly explored, the same process in solution remains widely used but partially unresolved, due to the formation of structures which are often kinetically trapped. In this paper we report kinetic state diagrams of polystyrene-b-poly(ethylene oxide) block copolymer in water by changing the solvent-switch assembly conditions. We study 36 different conditions for a single block copolymer, exploring three parameters: polymer concentration, temperature and rate addition of selective solvent. The data shows that polymer concentration plays an important role in determining which morphologies are accessible within a given set of experimental parameters and provides evidence that vesicles can evolve into particles with complex internal structures, supportive of recent mechanistic studies. Most importantly, the data shows a complex relationship between all parameters and the resulting kinetically trapped morphologies indicating that combined in situ and ex situ studies are required to gain a fundamental understanding of kinetically controlled block copolymer assembly processes.

Repulsive and attractive depletion forces mediated by nonadsorbing polyelectrolytes in the Donnan limit.

In mixtures of colloids and nonadsorbing polyelectrolytes, a Donnan potential arises across the region between surfaces that are depleted of the polyelectrolyte and the rest of the system. This Donnan potential tends to shift the polyelectrolyte density profile toward the colloidal surface and leads to the local accumulation of polyelectrolytes. We derive a zero-field theory for the disjoining pressure between two parallel flat plates. The polyelectrolyte is allowed to enter the confined interplate region at the cost of a conformational free energy penalty. The resulting disjoining pressure shows a crossover to a repulsive regime when the interplate separation gets smaller than the size of the polyelectrolyte chain, followed by an attractive part. We find a quantitative match between the model and self-consistent field computations that take into account the full Poisson-Boltzmann electrostatics.

From a eutectic mixture to a deep eutectic system via anion selection: Glutaric acid + tetraethylammonium halides.

In pursuit of understanding structure-property relationships for the melting point depression of binary eutectic mixtures, the influence of the anion on the solid-liquid (S-L) phase behavior was explored for mixtures of glutaric acid + tetraethylammonium chloride, bromide, and iodide. A detailed experimental evaluation of the S-L phase behavior revealed that the eutectic point is shifted toward lower temperatures and higher salt contents upon decreasing the ionic radius. The salt fusion properties were experimentally inaccessible owing to thermal decomposition. The data were inter- and extrapolated using various models for the Gibbs energy of mixing fitted to the glutaric-acid rich side only, which allowed for the assessment of the eutectic point. Fitting the experimental data to a two-parameter Redlich-Kister expansion with Flory entropy, the eutectic depth could be related to the ionic radius of the anion. The anion type, and in particular its size, can therefore be viewed as an important design parameter for the liquid window of other acid and salt-based deep eutectic solvents/systems.

Experimental Evidence for Algebraic Double-Layer Forces.

According to conventional wisdom, electric double-layer forces normally decay exponentially with separation distance. Here, we present experimental evidence of algebraically decaying double-layer interactions. We show that algebraic interactions arise in both strongly overlapping as well as counterion-only regimes, albeit the evidence is less clear for the former regime. In both of these cases, the disjoining pressure profile assumes an inverse square distance dependence. At small separation distances, another algebraic regime is recovered. In this regime, the pressure decays as the inverse of separation distance.

Design principles for metamorphic block copolymer assemblies.

Certain block copolymer assemblies in selective solvents undergo dynamic morphology transitions (metamorphism) on varying the solution temperature. Despite the great application potential, there is a lack of fundamental understanding of the relationship between copolymer composition and the thermally-induced metamorphic behavior. Herein this relationship is studied by applying Scheutjens-Fleer Self-Consistent Field (SF-SCF) theory to develop fundamental design principles for thermoresponsive diblock copolymers exhibiting metamorphic behavior. It is found that metamorphism is caused by variation in the degree of stretching of the lyophobic blocks in response to changes in solvency. An optimal lyophobic/lyophilic block length ratio interval 3.5 ⪅ fB ⪅ 5.5 is identified. Such a fB window allows switching between spheres, cylinders and vesicles as preferred morphologies, with relatively small changes in the lyophobic block solvency. The transition from spheres to cylinders and from cylinders to bilayers can be controlled by varying fB, the overall degree of polymerization of the diblock copolymer, and by choosing an appropriate lyophilic block. Empirical relationships are provided to establish a connection between the SCF-SCF predictions and experimental observations.

Correction: Directional-dependent pockets drive columnar-columnar coexistence.

Correction for 'Directional-dependent pockets drive columnar-columnar coexistence' by Álvaro González García et al., Soft Matter, 2020, DOI: 10.1039/d0sm00802h.

Directional-dependent pockets drive columnar-columnar coexistence.

The rational design of materials requires a fundamental understanding of the mechanisms driving their self-assembly. This may be particularly challenging in highly dense and shape-asymmetric systems. Here we show how the addition of tiny non-adsorbing spheres (depletants) to a dense system of hard disc-like particles (discotics) leads to coexistence between two distinct, highly dense (liquid)-crystalline columnar phases. This coexistence emerges due to the directional-dependent free-volume pockets for depletants. Theoretical results are confirmed by simulations explicitly accounting for the binary mixture of interest. We define the stability limits of this columnar-columnar coexistence and quantify the directional-dependent depletant partitioning.

Selective colloidal bonds via polymer-mediated interactions.

Regioselectivity in colloidal self-assembly typically requires specific chemical interactions to guide particle binding. In this paper, we describe a new method to form selective colloidal bonds that relies solely on polymer adsorption. Mixtures of polymer-coated and bare particles are initially stable due to long-ranged electrostatic repulsion. When their charge is screened, the two species can approach each other close enough for polymer bridges to form, binding the particles together. By utilizing colloidal dumbbells, where each lobe is coated with polymer brushes of differing lengths, we demonstrate that the Debye screening length serves as a selective switch for the assembly of bare tracer particles onto the two lobes. We model the interaction using numerical self-consistent field lattice computations and show how regioselectivity arises from just a few nanometers difference in polymer brush length.

(Homo)polymer-mediated colloidal stability of micellar solutions.

Despite their wide range of applications, there is a remarkable lack of fundamental understanding about how micelles respond to other components in solution. The colloidal stability of micellar solutions in presence of (homo)polymers is investigated here following a theoretical bottom-up approach. A polymer-mediated micelle-micelle interaction is extracted from changes in the micelle-unimer equilibrium as a function of the inter-micelle distance. The homopolymer-mediated diblock copolymer micelle-micelle interaction is studied both for depletion and adsorption of the homopolymer. The fluffy nature of the solvophilic domain (corona) of the micelle weakens the depletion-induced destabilization. Accumulation of polymers into the corona induces bridging attraction between micelles. In fact, both depletion and adsorption phenomena are regulated by the coronal thickness relative to the size of the added polymer. Penetration of guest compounds into the coronal domain of crew-cut micelles, with a narrower yet denser corona, is less pronounced as for starlike micelles (with a more diffuse corona). Therefore, crew-cut micelles are less sensitive to the effect of added compounds, and hence more suitable for applications in multicomponent systems, such as industrial formulations or biological fluids. The trends observed for the colloidal stability of crew-cut micelles qualitatively match with our experimental observations on aqueous dispersions of polycaprolactone-polyethylene glycol (PCL-PEO) micellar suspensions with added PEO chains.

Oil-in-water emulsions based on hydrophobic eutectic systems.

We demonstrate that oil-in-water emulsions can be prepared from hydrophobic eutectic systems (ES). Light microscopy and dynamic light scattering show that droplets are formed and zeta potential measurements indicate sufficient stability against coalescence. We investigate whether Ostwald ripening occurs in these ES-in-water emulsions by following the droplet growth over time and comparing it with an emulsion comprising decane in water. At first sight, the Ostwald ripening rate of the ES-in-water emulsion is expected to be orders of magnitude larger than the ripening of the decane-in-water emulsion due to a much higher solubility of the dispersed phase. However, experimentally we find that the ES-in-water emulsion actually grows a factor of two slower than the decane-in-water emulsion. We attribute this to the two-component nature of the ES, since the growth rate is mainly set by the least-soluble component of the ES. Thus, ESs offer the advantage of creating liquid emulsions of solid components, while setting the emulsion stability through their composition.

Controlling the Spatial Distribution of Solubilized Compounds within Copolymer Micelles.

The solubilization of lyophobic compounds in block copolymer micelles has been extensively investigated but remains only partially understood. There is a need to understand the fundamental parameters that determine the spatial distribution of the solubilized compounds within the micelles. Controlling this feature is a key aspect in the design of drug delivery systems with tailored release properties. Using Scheutjens-Fleer self-consistent field (SF-SCF) computations, we found that solubilization is regulated by a complex interplay between enthalpic and entropic contributions and that the spatial distribution can be controlled by the concentration and solubility of the guest compound in the dispersion medium. Upon solubilization, a characteristic change in size and mass of the micelles is predicted. This can be used as a fingerprint to indirectly assess the spatial distribution. Based on these findings, we developed two experimental protocols to control and assess the spatial distribution of lyophobic compounds within block copolymer micelles.

A Single Thermoresponsive Diblock Copolymer Can Form Spheres, Worms or Vesicles in Aqueous Solution.

It is well-known that the self-assembly of AB diblock copolymers in solution can produce various morphologies depending on the relative volume fraction of each block. Recently, polymerization-induced self-assembly (PISA) has become widely recognized as a powerful platform technology for the rational design and efficient synthesis of a wide range of block copolymer nano-objects. In this study, PISA is used to prepare a new thermoresponsive poly(N-(2-hydroxypropyl) methacrylamide)-poly(2-hydroxypropyl methacrylate) [PHPMAC-PHPMA] diblock copolymer. Remarkably, TEM, rheology and SAXS studies indicate that a single copolymer composition can form well-defined spheres (4 °C), worms (22 °C) or vesicles (50 °C) in aqueous solution. Given that the two monomer repeat units have almost identical chemical structures, this system is particularly well-suited to theoretical analysis. Self-consistent mean field theory suggests this rich self-assembly behavior is the result of the greater degree of hydration of the PHPMA block at lower temperature, which is in agreement with variable temperature 1 H NMR studies.

Interactions between amphoteric surfaces with strongly overlapping double layers.

The entropic repulsion between strongly overlapping electrical double-layers from two parallel amphoteric plates is described via the Donnan equilibrium in the limit of zero electric field. The plates feature charge-regulation and the inter-plate solution is in equilibrium with a reservoir of a monovalent electrolyte solution. A finite electric potential and disjoining pressure is found at contact between the plates, due to a complete discharging of the plates. For low potentials, the decay of potential and pressure is fully governed by a characteristic length scale and the contact potential. Additionally, for large separations we find a universal inverse square decay of disjoining pressure, irrespective of the contact potential. The results of the Donnan theory show quantitative agreement with self-consistent field computations that solve the full Poisson equation.

Phase behaviour of colloidal superballs mixed with non-adsorbing polymers.

Inspired by experimental work on colloidal cuboid-polymer dispersions (Rossi et al., Soft Matter, 7, 4139 (2011)) we have theoretically studied the phase behaviour of such mixtures. To that end, free volume theory (FVT) was applied to predict the phase behaviour of mixtures of superballs and non-adsorbing polymer chains in a common solvent. Closed expressions for the thermodynamic properties of a suspension of hard colloidal superballs have been derived, accounting for fluid (F), face-centred cubic (FCC) and simple cubic (SC) phase states. Even though the considered solid phases are approximate, the hard superballs phase diagram semi-quantitatively matches with more evolved methods. The theory developed for the cuboid-polymer mixture reveals a rich phase behaviour, which includes not only isostructural F1-F2 coexistence, but also SC1-SC2 coexistence, several triple coexistences, and even a quadruple-phase coexistence region (F1-F2-SC-FCC). The model proposed offers a tool to asses the stability of cuboid-polymer mixtures in terms of the colloid-to-polymer size ratio.