225 research outputs found
Depletion-induced biaxial nematic states of boardlike particles
With the aim of investigating the stability conditions of biaxial nematic
liquid crystals, we study the effect of adding a non-adsorbing ideal depletant
on the phase behavior of colloidal hard boardlike particles. We take into
account the presence of the depletant by introducing an effective depletion
attraction between a pair of boardlike particles. At fixed depletant fugacity,
the stable liquid crystal phase is determined through a mean-field theory with
restricted orientations. Interestingly, we predict that for slightly elongated
boardlike particles a critical depletant density exists, where the system
undergoes a direct transition from an isotropic liquid to a biaxial nematic
phase. As a consequence, by tuning the depletant density, an easy experimental
control parameter, one can stabilize states of high biaxial nematic order even
when these states are unstable for pure systems of boardlike particles
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
Algebraic equations of state for the liquid crystalline phase behavior of hard rods
Based on simplifications of previous numerical calculations [Graf and
L\"{o}wen, Phys. Rev. E \textbf{59}, 1932 (1999)], we propose algebraic free
energy expressions for the smectic-A liquid crystal phase and the crystal
phases of hard spherocylinders. Quantitative agreement with simulations is
found for the resulting equations of state. The free energy expressions can be
used to straightforwardly compute the full phase behavior for all aspect ratios
and to provide a suitable benchmark for exploring how attractive interrod
interactions mediate the phase stability through perturbation approaches such
as free-volume or van der Waals theory.Comment: 12 pages,accepted for publication in Phys. Rev.
Polydispersity Effects in Colloid-Polymer Mixtures
We study phase separation and transient gelation in a mixture consisting of
polydisperse colloids and non-adsorbing polymers, where the ratio of the
average size of the polymer to that of the colloid is approximately 0.063.
Unlike what has been reported previously for mixtures with somewhat lower
colloid polydispersity, the addition of polymers does not expand the
fluid-solid coexistence region. Instead, we find a region of fluid-solid
coexistence which has an approximately constant width but an unexpected
re-entrant shape. We detect the presence of a metastable gas-liquid binodal,
which gives rise to two-stepped crystallization kinetics that can be
rationalized as the effect of fractionation. Finally, we find that the
separation into multiple coexisting solid phases at high colloid volume
fractions predicted by equilibrium statistical mechanics is kinetically
suppressed before the system reaches dynamical arrest.Comment: 11 pages, 5 figure
Defying the Gibbs Phase Rule: Evidence for an Entropy-Driven Quintuple Point in Colloid-Polymer Mixtures
Using a minimal algebraic model for the thermodynamics of binary rod--polymer
mixtures, we provide evidence for a quintuple phase equilibrium; an observation
that seems to be at odds with the Gibbs phase rule for two-component systems.
Our model is based on equations of state for the relevant liquid crystal phases
that are in quantitative agreement with computer simulations. We argue that the
appearance of a quintuple equilibrium, involving an isotropic fluid, a nematic
and smectic liquid crystal, and two solid phases can be reconciled with a
generalized Gibbs phase rule in which the two intrinsic length scales of the
athermal colloid--polymer mixture act as additional field variables
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