In this work, we
have synthesized polystyrene particles that carry
short end-grafted polyethylene glycol (PEG) chains. We then added
dissolved 100 kDa PEG polymers and monitored potential flocculation
by confocal microscopy. Qualitative predictions, based on previous
theoretical developments in this field (Xie, F.; et al. Soft
Matter
2016, 12, 658), suggest
a non-monotonic temperature response. These theories propose that
the “free” (dissolved) polymers will mediate attractive
depletion interactions at room temperature, with a concomitant clustering/flocculation
at a sufficiently high polymer concentration. At high temperatures,
where the solvent is poorer, this is predicted to be replaced by attractive
bridging interactions, again resulting in particle condensation. Interestingly
enough, our theoretical framework, based on classical density functional
theory, predicts an intermediate temperature regime where the polymer-mediated
interactions are repulsive! This obviously implies
a homogeneous dispersion in this regime. These qualitative predictions
have been experimentally tested and confirmed in this work, where
flocs of particles start to form at room temperature for a high enough
polymer dosage. At temperatures near 45 °C, the flocs redisperse,
and we obtain a homogeneous sample. However, samples at about 75 °C
will again display clusters and eventually phase separation. Using
results from these studies, we have been able to fine-tune parameters
of our coarse-grained theoretical model, resulting in predictions
of temperature-dependent stability that display semiquantitative accuracy.
A crucial aspect is that under “intermediate” conditions,
where the polymers neither adsorb nor desorb at the particle surfaces,
the polymer-mediated equilibrium interaction is repulsive.
We conduct Metropolis
Monte Carlo simulations on models of dilute
colloidal dispersions, where the particles interact via isotropic
potentials of mean force (PMFs) that display a long-ranged repulsion,
combined with a short-ranged and narrow attraction. Such systems are
known to form anisotropic clusters. There are two main conclusions
from this work. First, we demonstrate that the width of the attractive
region has a significant impact on the type of structures that are
formed. A narrow attractive well tends to produce clusters in which
particles possess fewer neighbors than in systems where the attraction
is wider. Second, metastable clusters appear to persist in the absence
of specific simulation moves designed to overcome large energy barriers
to particle accumulation. The so-called “Aggregation-Volume
Bias Monte Carlo” moves were previously developed by Chen and
Siepmann, and they facilitate particle exchanges between clusters
via unphysical moves that bypass high energy intermediate states.
These facilitate the progression of metastable clusters to equilibrium
clusters. Metastable clusters are generally large with significant
branching of thin filaments of aggregated particles, while stable
clusters have thicker backbones and tend to be more compact with significantly
fewer particles. This general behavior is observed in both two- and
three-dimensional systems. In two dimensions, less anisotropic clusters
with backbones possessing lattice structures will occur, particularly
for systems where the particles interact with a PMF that has a relatively
wide attractive region. We compare our results with PMF calculations
established from a more specific model, namely weakly charged polystyrene
particles, which carry a thin surface layer of grafted polyethylene
oxide polymers in aqueous solution. We hope that our investigations
can serve as crude guidelines for experimental research, aiming to
construct linear or branched polymers in aqueous solution built up
by colloidal monomers that are large enough to be studied by confocal
microscopy. We suggest that metastable clusters are more relevant
to experimental scenarios where the energetic barriers are too large
to be surmounted over typical timescales.
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