Controlled Nanoparticle Formation by Diffusion Limited Coalescence

Polymeric nanoparticles (NPs) have a great application potential in science and technology. Their functionality strongly depends on their size. We present a theory for the size of NPs formed by precipitation of polymers into a bad solvent in the presence of a stabilizing surfactant. The analytical theory is based upon diffusion-limited coalescence kinetics of the polymers. Two relevant time scales, a mixing and a coalescence time, are identified and their ratio is shown to determine the final NP diameter. The size is found to scale in a universal manner and is predominantly sensitive to the mixing time and the polymer concentration if the surfactant concentration is sufficiently high. The model predictions are in good agreement with experimental data. Hence the theory provides a solid framework for tailoring nanoparticles with a priori determined size.Comment: 4 pages, 3 figure

Phase Behaviour of Binary Hard-Sphere Mixtures: Free Volume Theory Including Reservoir Hard-Core Interactions

Comprehensive calculations were performed to predict the phase behaviour of large spherical colloids mixed with small spherical colloids that act as depletant. To this end, the free volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20 (1992) 559] is used as a basis and is extended to explicitly include the hard-sphere character of colloidal depletants into the expression for the free volume fraction. Taking the excluded volume of the depletants into account in both the system and the reservoir provides a relation between the depletant concentration in the reservoir and in the system that accurately matches with computer simulation results of Dijkstra et al. [Phys. Rev. E 59 (1999) 5744]. Moreover, the phase diagrams for highly asymmetric mixtures with size ratios q . 0:2 obtained by using this new approach corroborates simulation results significantly better than earlier FVT applications to binary hard-sphere mixtures. The phase diagram of a binary hard-sphere mixture with a size ratio of q = 0:4, where a binary interstitial solid solution is formed at high densities, is investigated using a numerical free volume approach. At this size ratio, the obtained phase diagram is qualitatively different from previous FVT approaches for hard-sphere and penetrable depletants, but again compares well with simulation predictions.Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at https://doi.org/10.1063/5.003796

Self-consistent field predictions for quenched spherical biocompatible triblock copolymer micelles

We have used the Scheutjens-Fleer self-consistent field (SF-SCF) method to predict the self-assembly of triblock copolymers with a solvophilic middle block and sufficiently long solvophobic outer blocks. We model copolymers consisting of polyethylene oxide (PEO) as solvophilic block and poly(lactic-co-glycolic) acid (PLGA) or poly({\ko}-caprolactone) (PCL) as solvophobic block. These copolymers form structurally quenched spherical micelles provided the solvophilic block is long enough. Predictions are calibrated on experimental data for micelles composed of PCL-PEO-PCL and PLGA-PEO-PLGA triblock copolymers prepared via the nanoprecipitation method. We establish effective interaction parameters that enable us to predict various micelle properties such as the hydrodynamic size, the aggregation number and the loading capacity of the micelles for hydrophobic species that are consistent with experimental finding.Comment: accepted for publication in Soft Matte

Stochastic Interactions of Two Brownian Hard Spheres in the Presence of Depletants

A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and pure polymer solution (no depletion) cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shifts due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.Comment: 30 pages, 9 figures, 1 appendix, 40 formulas inside the text, 5 formulas in appendi

Macromolecular theory of solvation and structure in mixtures of colloids and polymers

The structural and thermodynamic properties of mixtures of colloidal spheres and non-adsorbing polymer chains are studied within a novel general two-component macromolecular liquid state approach applicable for all size asymmetry ratios. The dilute limits, when one of the components is at infinite dilution but the other concentrated, are presented and compared to field theory and models which replace polymer coils with spheres. Whereas the derived analytical results compare well, qualitatively and quantitatively, with mean-field scaling laws where available, important differences from ``effective sphere'' approaches are found for large polymer sizes or semi-dilute concentrations.Comment: 23 pages, 10 figure

Isotropic-nematic phase transition in suspensions of filamentous virus and the neutral polymer Dextran

We present an experimental study of the isotropic-nematic phase transition in an aqueous mixture of charged semi-flexible rods (fd virus) and neutral polymer (Dextran). A complete phase diagram is measured as a function of ionic strength and polymer molecular weight. At high ionic strength we find that adding polymer widens the isotropic-nematic coexistence region with polymers preferentially partitioning into the isotropic phase, while at low ionic strength the added polymer has no effect on the phase transition. The nematic order parameter is determined from birefringence measurements and is found to be independent of polymer concentration (or equivalently the strength of attraction). The experimental results are compared with the existing theoretical predictions for the isotropic-nematic transition in rods with attractive interactions.Comment: 8 Figures. To be published in Phys. Rev. E. For more information see http://www.elsie.brandeis.ed

Interfacial tension and nucleation in mixtures of colloids and long ideal polymer coils

Mixtures of ideal polymers with hard spheres whose diameters are smaller than the radius of gyration of the polymer, exhibit extensive immiscibility. The interfacial tension between demixed phases of these mixtures is estimated, as is the barrier to nucleation. The barrier is found to scale linearly with the radius of the polymer, causing it to become large for large polymers. Thus for large polymers nucleation is suppressed and phase separation proceeds via spinodal decomposition, as it does in polymer blends.Comment: 4 pages (v2 includes discussion of the scaling of the interfacial tension along the coexistence curve and its relation to the Ginzburg criterion

The Asakura-Oosawa model in the protein limit: the role of many-body interactions

We study the Asakura-Oosawa model in the "protein limit", where the penetrable sphere radius $R_{AO}$ is much greater than the hard sphere radius $R_c$. The phase behaviour and structure calculated with a full many-body treatment show important qualitative differences when compared to a description based on pair potentials alone. The overall effect of the many-body interactions is repulsive.Comment: 9 pages and 11 figures, submitted to J. Phys.: Condensed Matter, special issue "Effective many-body interactions and correlations in soft matter

In-situ liquid phase imaging of block copolymer vesicle assembly

Amphiphilic block copolymers in aqueous solution can assemble into various ordered molecular architectures, which have a wide range of applications in, for example, drug delivery and catalytic nanoreactors.1 While sustained efforts, both experimentally and theoretically, have been made to better understand the mechanism of self- assembly in order to gain more control over this process,2, 3 there has never been a real-time, real space investigation of the assembly process on the nanoscale. Here we show the first observation of block copolymer vesicle assembly via the solvent switch protocol4 using liquid phase transmission electron microscopy (LP-TEM). We also discuss the different mechanisms of self-assembly with the ex-situ cryo-TEM observation and compare them with self-consistent field (SCF) lattice calculations. Our findings illustrate the ability of LP-TEM to implement quantitative visualization of local formation process of the block copolymer vesicles to reveal the formation mechanism on an individual particle level Please click Additional Files below to see the full abstract

Phase behaviour of charged colloidal sphere dispersions with added polymer chains

We study the stability of mixtures of highly screened repulsive charged spheres and non-adsorbing ideal polymer chains in a common solvent using free volume theory. The effective interaction between charged colloids in an aqueous salt solution is described by a screened-Coulomb pair potential, which supplements the pure hard-sphere interaction. The ideal polymer chains are treated as spheres that are excluded from the colloids by a hard-core interaction, whereas the interaction between two ideal chains is set to zero. In addition, we investigate the phase behaviour of charged colloid-polymer mixtures in computer simulations, using the two-body (Asakura-Oosawa pair potential) approximation to the effective one-component Hamiltonian of the charged colloids. Both our results obtained from simulations and from free volume theory show similar trends. We find that the screened-Coulomb repulsion counteracts the effect of the effective polymer-mediated attraction. For mixtures of small polymers and relatively large charged colloidal spheres, the fluid-crystal transition shifts to significantly larger polymer concentrations with increasing range of the screened-Coulomb repulsion. For relatively large polymers, the effect of the screened-Coulomb repulsion is weaker. The resulting fluid-fluid binodal is only slightly shifted towards larger polymer concentrations upon increasing the range of the screened-Coulomb repulsion. In conclusion, our results show that the miscibility of dispersions containing charged colloids and neutral non-adsorbing polymers increases, upon increasing the range of the screened-Coulomb repulsion, or upon lowering the salt concentration, especially when the polymers are small compared to the colloids.Comment: 25 pages,13 figures, accepted for publication on J.Phys.:Condens. Matte