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).

Coarse graining and adsorption in bottlebrush-colloid mixtures.

We study the adsorption properties in bottlebrush/colloid binary mixtures by combining scaling theories, theoretical predictions, self-consistent field computations (SCFC), and molecular dynamics simulations. In particular, we focus on adsorption in the case in which an attraction is set between the two species, by analysing the solution properties for a range of interactions and the size ratio between colloids and bottlebrushes, in the case in which colloids are smaller than the macromolecules. We show that the onset of adsorption is dominated by the local properties of the adsorbing guest particle. This allows us to use the local similarity between a cylindrical bottlebrush and a spherical star polymer to predict the region of the parameter space in which the adsorption takes place. By employing simple scaling arguments, we thus extend the analytical results on the adsorption obtained for binary mixtures of star polymers/colloid nanoparticles. We then validate our predictions with molecular dynamics simulations. Moreover, by means of SCFC, we assess the adsorption-to-depletion transition of nanoparticles in polymeric bottlebrushes. Our results pave the road towards a smart rational design and coarse-graining of adsorbing/releasing systems, where an elongated shape might play an important role.

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.

(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.

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.

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.

Co-assembly of precision polyurethane ionomers reveals role of and interplay between individual components.

Industrial and household products, such as paints, inks and cosmetics usually consist of mixtures of macromolecules that are disperse in composition, in size and in monomer sequence. Identifying structure-function relationships for these systems is complicated, as particular macromolecular components cannot be investigated individually. For this study, we have addressed this issue, and have synthesized a series of five sequence-defined polyurethanes (PUs): one neutral-hydrophobic, one single-charged hydrophilic, one single-charged hydrophobic and two double-charged amphiphilic PUs (one symmetric and one asymmetric). These novel precision PUs - that were prepared by using stepwise coupling-deprotection synthetic protocols - have a defined composition, size and monomer sequence, where the chosen sequences were inspired by those that are abundantly formed in the production of industrial waterborne PU dispersions. By performing dynamic light scattering experiments (DLS), self-consistent field (SCF) computations and cryogenic transmission electron microscopy (cryo-TEM), we have elucidated the behavior in aqueous solution of the individual precision PUs, as well as of binary and ternary mixtures of the PU sequences. The double-charged PU sequences ('hosts') were sufficiently amphiphilic to yield single-component micellar solutions, whereas the two more hydrophobic sequences did not micellize on their own, and gave precipitates or ill-defined larger aggregates. Both the neutral-hydrophobic PU and the hydrophilic single-charged PU were successfully incorporated in the host micelles as guests, respectively increasing and reducing the micelle radius upon incorporation. SCF computations indicated that double-charged symmetric PUs stretch whilst double-charged asymmetric PUs are expelled from the core to accommodate hydrophobic PU guests within the micelles. For the ternary mixture of the double-charged symmetric and asymmetric hosts and the neutral-hydrophobic guest we have found an improved colloidal stability, as compared to those for binary mixtures of either host and hydrophobic guest. In another ternary mixture of precision PUs, with all three components not capable of forming micelles on their own, we see that the ensemble of molecules produces stable micellar solutions. Taken together, we find that the interplay between PU-molecules in aqueous dispersions promotes the formation of stable micellar hydrocolloids.

Polymer-mediated colloidal stability: on the transition between adsorption and depletion.

Addition of polymers to a colloidal dispersion modulates the interactions between the colloids. We briefly review the effects of positive and negative adsorption (also termed depletion). The effective colloid-polymer interactions sensitively affect the colloidal phase behavior. We present a theoretical framework to predict the phase behavior of colloid-polymer mixtures for varying affinities between colloid and polymer, leading to either positive or negative adsorption of polymer segments. For certain conditions, polymers are neither depleted nor adsorbed: the polymer concentration is essentially constant up to the colloidal surface, a condition which we term neutral adsorption. Near this condition, the calculated phase diagrams reveal a stable-unstable-restabilisation transition with increasing polymer concentration. Similar effects have been reported experimentally, for instance as a function of temperature [Feng et al., Nat. Mat., 2015, 14, 61-65], which may modulate the effective polymer-colloid affinity. Understanding how to achieve neutral adsorption opens up the possibility of preparing highly dense, yet stable, colloid-polymer mixtures.

Quantification of the Structure of Colloidal Gas-Liquid Interfaces.

We have quantified the structure of the colloidal gas-liquid interface using synchrotron X-ray reflectivity measurements on a model colloid-polymer mixture. The interfacial width shows mean-field scaling with the colloid density difference, and the density profiles appear to be monotonic. Furthermore, our measurements allow us to distinguish between different theoretical polymer descriptions commonly used to model colloid-polymer mixtures. Our results highlight the importance of capturing the correct polymer physics in obtaining a quantitative theoretical description of the colloidal gas-liquid interface.

Tuning the phase diagram of colloid-polymer mixtures via Yukawa interactions.

Theory that predicts the phase behavior of interacting Yukawa spheres in a solution containing nonadsorbing polymer is presented. Our approach accounts for multiple overlap of depletion zones. It is found that additional Yukawa interactions beyond hard core interactions strongly affect the location and presence of coexistence regions and phase states. The theoretical phase diagrams are compared with Monte Carlo simulations. The agreement between the two approaches supports the validity of the theoretical approximations made and confirms that, by choosing the parameters of the interaction potentials, tuning of the binodals is possible. The critical end point characterizes the phase diagram topology. It is demonstrated how an additional Yukawa interaction shifts this point with respect to the hard sphere case. Provided a certain depletant-to-colloid size ratio for which a stable colloidal gas-liquid phase coexistence takes place for hard spheres, added direct interactions turn this into a metastable gas-liquid equilibrium. The opposite case, the induction of a stable gas-liquid coexistence where only fluid-solid was present for hard spheres, is also reported.