# Controlling phase separation in microgel-polymeric micelle mixtures using
variable quench rates

S L Fussell,∗123 C P Royall,1234 and J S van Duijneveldta
<EMAIL_ADDRESS>1School of Chemistry, University of Bristol,
Cantock’s Close, Bristol, BS8 1TS, UK. 2 HH Wills Physics Laboratory,
University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK. 3 Bristol Centre
for Functional Nanomaterials, University of Bristol, Tyndall Avenue, Bristol,
BS8 1TL, UK. 4 Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005
Paris, France.

(August 27, 2024)

###### Abstract

We investigate the temperature dependent phase behaviour of mixtures of
poly(N-isopropylacrylamide) (pNIPAM) microgel colloids and a triblock
copolymer (PEO-PPO-PEO) surfactant, which undergoes micellisation. Gelation in
these systems results from an _increase_ in temperature. Here we alter the
heating rate and observe that the mechanism for aggregation changes from one
of depletion of the microgels by the micelles at low temperatures to
association of the two species at high temperatures. We use this to access
multiple structures at one microgel concentration. Samples with a micelle
concentration above 7 wt% were found to demix into phases rich and poor in
microgel particles at temperatures below 33∘C, under conditions where the
microgels particles are partially swollen. Under rapid heating full demixing
is bypassed and gel networks are formed instead. The temperature history of
the sample therefore allows for kinetic selection between different final
structures, which may be metastable.

Microgels, gelation, phase behaviour

##  I Introduction

Phase separation from a one-phase fluid to a demixed system can be achieved
very differently in atomic and molecular systems on the one hand and soft
matter on the other. In an atomic or molecular system, the interactions
between the constituents themselves are largely independent of the
temperature, and a quench would entail a lowering of temperature. In soft
matter systems, on the other hand, one may often _integrate out_ the degrees
of freedom of smaller components, and consider _effective_ interactions
between larger species such as colloidal particles Likos _et al._ (2000). In
some such systems, for example colloid-polymer mixtures Poon (2002), the
concentration of one species (here the polymer) may play the role of an
(inverse) _effective temperature_. Thus here effectively “quenching” the
system pertains to increasing the polymer concentration Poon (2002).

While much research is carried out at room temperature, one may enquire as to
the response of soft materials to changes in temperature. These are often
complex. In the case of colloid polymer-mixtures for example, upon heating,
polymer molecules can expand, thus increasing the polymer volume fraction and
hence effectively quenching the system. In this, one may observe the counter
intuitive behaviour of (effectively) quenching by heating and raising the
effective temperature by cooling Taylor _et al._ (2012). Often more complex
behaviour can be observed, due for example to changes in hydrophobicity as a
function of temperature between different species in the system. The system of
interest here is a mixture of microgel particles and triblock copolymer
micelles, which exhibits a complex response to temperature, in addition to a
composition dependent phase behaviour typical of soft materials Fussell _et
al._ (2019); Gottwald _et al._ (2004); Velikov _et al._ (2002); Camerin _et
al._ (2020); Mohanty _et al._ (2017). Systems that are capable of triggered
gelation or viscosity-switchable materials are sort after for reconstructive
surgery and drug delivery applications Sierra-Martin and Fernandez-Nieves
(2012).

In the case that the interactions are controlled through the composition of
the system (rather than temperature), the attractions that drive this phase
separation can have a variety of sources, including the depletion interaction
induced by _non-absorbing_ polymers Asakura and Oosawa (1954); Poon (2002),
the attractions can come from _bridging_ between colloidal particles Zhao _et
al._ (2012); Gao _et al._ (2015) or through the critical Casimir effect Shelke
_et al._ (2013); Gnan _et al._ (2014). Under the right conditions such
attractions can lead to a network formed through spinodal decomposition, which
undergoes arrest due to the asymmetry in viscosity of the two demixing phases,
which is termed viscoelastic phase separation, or sometimes no attractions are
actually needed to form such a network of fluids with very different
viscosities Ferreiro-Córdova _et al._ (2020). Whatever the origins of the
emergence of the viscoelastic network, _understanding_ colloidal gelation due
to arrested spinodal decomposition is a long-standing challenge Poon (2002);
Lu _et al._ (2008); Zaccarelli (2007); Cipelletti and Ramos (2005); Verhaegh
_et al._ (1997); Truzzolillo _et al._ (2014), although the mechanism of
solidification has been related to the emergence of rigid clusters, leading to
a gel with viscoelastic mechanical properties Royall _et al._ (2008); Royall
and Williams (2015).

Gels are far-from-equilibrium systems and their properties exhibit complex
time-dependent behaviour, as they relax towards the equlibrium state of phase
coexistence between the colloid-rich (high-viscosity) phase and colloid-poor
(low viscosity) phase Cipelletti and Ramos (2005); Bonn _et al._ (2017);
Royall and Malins (2012); Bartlett _et al._ (2012); Aime _et al._ (2018);
Harich _et al._ (2016); Tsurusawa _et al._ (2017); Zhang _et al._ (2013);
Griffiths _et al._ (2013); Royall and Williams (2015). Studies of assembly of
so-called “sticky spheres” out of equilibrium, which is a basic model system
which undergoes gelation where the colloid-rich phase may crystallise Klotsa
and Jack (2011), have shown that assembly at different temperatures leads to a
complex response of fast yet poor-quality assembly upon deep (effective)
quenches, and slower but high-quality assembly when the (effective)
temperature is higher Whitelam and Jack (2015). This is backed up by
experimental work where the system evolved more quickly to its equilibrium
demixed state in the case of weak quenches Zhang _et al._ (2013); Razali _et
al._ (2017). Time-dependent assembly protocols have also been investigated,
and it has been found that slow quenches promote high-quality assembly Royall
and Malins (2012), and time-dependent protocols of a deep quench at short
times followed by a shallow quench at longer times optimise the process of
assembly further Klotsa and Jack (2013). Here we consider a soft matter system
that displays both liquid-liquid phase separation and formation of gel
networks, depending on the heating rate.

Our model system is a mixture of microgels and micelle-forming triblock
copolymers which exhibits a complex response to temperature Fussell _et al._
(2019). Microgels are colloidal particles comprised of a cross linked polymer
Schneider _et al._ (2018); Wedel _et al._ (2016); Varga _et al._ (2001);
Bonham _et al._ (2014); Bergman _et al._ (2018); Pelton and Chibante (1986)
which exhibit some similar phenomena to hard colloids Yunker _et al._ (2014);
Royall _et al._ (2013); Bergman _et al._ (2018). In particular,
poly(N-isopropylacrylamide) (pNIPAM) microgels are known to form colloidal
gels in the presence of additives, such as salt, which screens the
electrostatic interactions Hu and Xia (2004); Immink _et al._ (2019);
Bischofberger and Trappe (2015). Their swelling behaviour is temperature
responsive, which is a result of the polymer-solvent interactions Nigro _et
al._ (2015). In our system, a number of phenomena occur as the temperature is
increased between $25^{\circ}$C and $40^{\circ}$C. pNIPAM microgels exhibit a
so-called volume phase transition where the particles which are swollen at
room temperature undergo a collapse McPhee _et al._ (1993). The micelles are
formed from a PEO-PPO-PEO triblock copolymer Alexandridis _et al._ (1994).

Upon heating, there are two underlying phenomena: firstly, the microgels
undergo the volume phase transition and collapse over a temperature range of
around $10^{\circ}$C, between $30$ and $40^{\circ}$C. Bandyopadhyay _et al._
(2017) The degree of swelling is controlled by the cross link density in the
particle, in our system this volume phase transition corresponds to a two-fold
change in diameter (i.e. 8-fold change in volume). It is important to note
that this does not correspond to a _complete_ collapse and expulsion of all
solvent, rather, about half of the material within the microgel is solvent in
the collapsed state Sbeih _et al._ (2019). Moreover, the distribution of the
pNIPAM and solvent is non-uniform with a higher density of pNIPAM and cross
links towards the centre and a lower density of polymer and cross links
towards the periphery of the particle Ninarello _et al._ (2019). The volume
phase transition which thus provides the ability to tune the interaction
potential between pNIPAM microgels with temperature Sierra-Martin and
Fernandez-Nieves (2012). When the microgels are swollen, they are purely
repulsive Heyes and Brańka (2009); Månsson _et al._ (2019), due to the minimal
van der Waals (vdW) interactions. With increasing temperature, the deswollen
particles are often modelled as “sticky spheres”, due to increased vdWs
interactions and hydrophobic interactions Bergman _et al._ (2018).

The second effect, which drives the gelation in our system Fussell _et al._
(2019), is that upon heating above the volume phase transition temperature,
the micelles associate with the microgels due to hydrophobic interactions,
which leads to the microgel particles aggregating and undergoing gelation
(Fig. 1). Thus, here, the system is _effectively_ quenched by _increasing
temperature_ Fussell _et al._ (2019), in a manner reminiscent of the mixtures
of colloids and non-absorbing polymers noted above Taylor _et al._ (2012).
Here, we explore the response of our system to _time-dependent temperature
protocols_. We find a complex behaviour resulting from the competition between
thermodynamic forces driving phase separation and slow dynamics. By changing
the _effective_ quench rate, we tune the system towards arrested phase
separation, when the rate of temperature change is fast with respect to the
demixing kinetics or towards phase separation when the rate is slow with
respect to demixing kinetics.

We use differential interference contrast and confocal microscopy to identify
the structure of the gel networks, and study the phase behaviour of this
system. Firstly, we observed the high temperature gelation of these species,
but also a change in the phase behaviour, as a result of altering the
conditions by which gelation occurred. Secondly, under specific conditions we
observe demixing (phase separation), where microgel rich and poor liquid
regions form. We highlight the trends in phase behaviour that results from
tuning the gelation conditions (quench rate) and the sample concentration.

Figure 1: Scheme representing the gelation mechanism between pNIPAM microgels
and triblock-copolymer micelles at temperatures above the $T_{\text{VPT}}$.
The micelles are represented by the pink circles. Fussell _et al._ (2019)

This paper is organised as follows: in section 2 we show our methods, in
section IV, we present our main findings including the phase behaviour,
control over phase using quench rates and detailed characteristics of our
system, including structure and droplet growth kinetics.

##  II Methods

###  II.1 Materials

For the microgel synthesis N,N’-methylenebis(acrylamide) (99% Sigma Aldrich),
N-isopropylacrylamide (99% Acros Organics), potassium persulfate (>99% Sigma
Aldrich), sodium dodecylbenzenesulfonate (technical grade Sigma Aldrich),
fluorescein isothiocyanate (98% Sigma Aldrich) and methacryloxyethyl
thiocarbonyl rhodamine B (Polysciences) were used as received without further
purification. The triblock-copolymer surfactant was labelled using Nile red
dye (technical grade Sigma Aldrich). Synperonic SE/P105 is the triblock-
copolymer used for all the experiments, a polyethyleneoxide-
polypropyleneoxide-polyethyleneoxide (PEO-PPO-PEO) type polymer (6500 MW).

Figure 2: Scheme representing the observed behaviour of samples of pNIPAM and
triblock-copolymer surfactant, imaged using confocal microscopy. For a sample
heated slowly, phase separation is observed (blue) at lower temperatures and
gelation (pink) at higher temperatures. If the sample is heated quickly, the
liquid-liquid phase separation is bypassed, and only gels (pink) are observed
at all concentrations. Images highlighting the difference in both the
macroscopic and microscopic phase behaviour of pNIPAM samples are included.
All samples contain 3 wt% pNIPAM, the images on the left are of samples with 4
wt% triblock-copolymer. The images on the right are of samples with 11 wt%
triblock-copolymer. Images on the bottom have been heated up slowly in a oven
set to 40∘C (b,c). Images on the top are of samples which were submerged into
a hot water bath (a,d). Both images of the macroscopic gel and the structure
of the gel observed using confocal microscopy have been included. The green
images are of the labelled microgels, the red images are of the labelled
micelles and the combined image of both dyes is also included. The scale bar
included for all the confocal images is 10 $\mu$m. The corresponding location
of each sample on the phase diagram has been highlighted. The $T_{\text{VPT}}$
of pNIPAM has been highlighted on the figure using a dashed blue line.

###  II.2 pNIPAM microgel synthesis

The microgels were synthesised using precipitation polymerisation.McPhee _et
al._ (1993) Each synthesis was conducted in a 1000 mL three necked round
bottom flask, fitted with a condenser, an argon inlet and an overhead stirrer.
The NIPAM (12.5 g), N,N’-methylenebis(acrylamide) (1.0 g) and sodium dodecyl
benzenesulfonate (0.5 g) were added to the flask along with 475 mL of
deionised water and heated to 70∘C with stirring under an inert atmosphere.
Once heated potassium persulfate (0.5 g dissolved in 25 mL of DI water) was
slowly added to the reaction and the solution left stirring at temperature for
4 hours. The microgels produced were then purified using dialysis against
deionised water for 2 weeks. Fluorescein labelled particles were synthesised
using 9 mg of fluorescein isothiocyanate and 15 $\mu$L 3-amino-propene, added
to 38 mL of a solution of 10-4 M sodium hydroxide. This solution was then
added at the start of the pNIPAM reaction discussed above, in place of 38 mL
of water.Meijer (2015) All particles were then characterised using a Malvern
Autosizer 4800 with a 532 nm laser at a 90∘ scattering angle. This was used to
determine the diameter of the particles and to study the deswelling behaviour.
All samples were diluted using deionised water and left to equilibrate at each
temperature for 15 minutes.

###  II.3 Microscopy

An Olympus BX-51 DIC microscope was used to obtain the differential
interference contrast (DIC) images. All images were captured using a Pixelink
5MP colour CCD PL-B625CU camera and a 20$\times$ objective. A Linkam PE120
heating stage was used to control the slide temperature. The samples were
prepared by adding a drop of solution to the centre of a doughnut shaped
sticker (Office Depot) attached to a microscope slide, and a cover slip was
then placed onto the sample. This gave a sample environment for imaging with a
of diameter 5 mm and a depth of 200 $\mu$m. For the fast heating experiments,
the samples were heated at a rate of 10∘Cmin-1 from room temperature to 35∘C.
For the slow heating experiments, the samples were heated at a rate of
0.1∘Cmin-1 to a specified temperature above the gelation temperature. For all
experiments this was 35∘C unless otherwise stated. The temperature quoted as
the gelation temperature is the temperature the microscope stage read when
gelation occurred. There may be some discrepancies between the temperature of
the slide and the read out temperature, these are assumed to be equivalent
across all samples therefore the general trends should remain the same.

Confocal images were taken using a Leica SP8 confocal microscope. The sample
preparation was as described for DIC microscopy along with the heating
protocol. The micelles were labelled with Nile red, a 543 nm HeNe laser was
used to excite the dye. The microgels were labelled with fluorescein, an Argon
laser (488 nm) was used to excite the dye. All samples were heated using a
TC-1-100s temperature controller, along with a Bioscience Tools objective
heater, set to 35∘C.

The DIC images have been edited using ImageJ software. The images have been
converted to grey scale, then to the ‘glow’ colour table, then the image
inverted. This was done to highlight the polymer rich phase using this imaging
technique. An example of the process to edit the DIC images is included in the
ESI (Fig. S1 ESI).

###  II.4 Macroscopic characterisation of phase behaviour

To replicate the fast heating experiments for macroscopic gels, the samples
were made up in sealed vials and submerged into hot water (approximately
70∘C). The phase behaviour was then recorded after 10 minutes. To replicate
the slow heating experiments, samples were placed into a oven set to 40∘C and
allowed to slowly heat up from room temperature, and the phase behaviour was
recorded after 24 hours.

###  II.5 Image analysis

To determine the size of the droplets formed, the images were fitted manually
using Fiji image analysis software. The diameter of 100 droplets was measured
and averaged to obtain an estimate of diameter and the polydispersity in the
sample. To investigate the droplet growth over time, the data obtained from
image analysis was plotted. The droplet size as a function of time was plotted
on a log-log plot and the linear fit was used to obtain the power law
exponent. The data was fitted up to the point where the droplet growth
plateaus, which varied depending on the sample.

##  III Results and discussion

In this section, we present the temperature induced gelation of pNIPAM
microgels and triblock-copolymer micelles. We present the temperature response
of these systems characterised at both the macroscopic (cm) and microscopic
($\mu$m) length scale. We characterise the structure formed in these mixtures
using DIC and confocal microscopy. We also use DIC imaging to characterise the
temperature where the microgel particles aggregate (Fig. 2), and highlight how
the temperature response at the particle level can be related to the
structures observed. We alter the heating rate in order to determine the
relationship between heating rate and the structures observed. We also use
image analysis to characterise the droplet phase formed under appropriate
conditions. We use confocal microscopy to identify the position of species in
the structures. We note that the critical micelle concentration for the
triblock-copolymer surfactant is 0.3 wt% at 25∘C and 0.005 wt% at 35∘C,
therefore it is assumed in this work that the majority added is present in the
form of micelles, rather than as free surfactant Alexandridis _et al._ (1994).

###  III.1 Heating rate

Figure 3: Summary of the aggregation temperatures observed using DIC
microscopy. The samples were heated at a rate of 0.1∘Cmin-1, and the
temperature was recorded as the point where aggregation was first observed.
The colours represent the phase observed on the microscope. Pink points
represent concentrations where gels were observed, blue points indicate
concentrations where phase separation was observed. The black solid curve has
been added to highlight the general trend of decreasing gelation temperature
with increased triblock-copolymer concentration. If gelation occurs at
temperatures above about 33∘C, then gels are always observed. The deswelling
curve for pNIPAM microgels has also been included (c), to highlight how at
33∘C the particles are still somewhat swollen, this temperature is again
indicated by a dashed line. The shading added is to represent whether gel
phases preferentially form (pink) or phase separation (blue) at each
temperature/ swelling. The data has been plotted as a function of triblock-
copolymer concentration (a), pNIPAM concentration (b) and total polymer
concentration (c). The dark pink circles indicate samples that are uniform
gels, the light pink circles samples that form gels with voids, light blue
circles samples that from droplets and dark blue circles samples that phase
separate.

Fast heating. —  We begin our presentation of our results by considering the
case of fast heating ($10\ ^{\circ}$C min-1 from room temperature to $40\
^{\circ}$C). Samples of pNIPAM microgels and triblock-copolymer surfactant
micelles were heated and imaged using DIC microscopy. Upon heating at a rate
of 10$\ {}^{\circ}$C min-1, there is very little observable difference in the
gel structures, regardless of concentration of _either_ of the two species,
microgel colloids or micelles. All samples were heated to 35∘C, a temperature
above the volume phase transition temperature ($T_{\text{VPT}}$) for pNIPAM,
meaning the microgels used in this study are close to fully deswollen (Fig. S2
Electronic Supplementary (ESI)). The structure observed for all samples is a
uniform gel network with fine features below the resolution of the DIC
microscope. The gel branches are of order 1 $\mu$m width with very few
observable pores. An example of the structure observed is included in Fig. 6.
There is an increase in the density of the network with an increase in
concentration of either microgel colloids or micelles. The mechanism for
gelation upon fast heating is one of association, where the microgels and
micelles associate due to hydrophobic interactions and hydrogen bonding. This
association was characterised in our previous work, using small angle neutron
scattering, confocal microscopy and DLS Fussell _et al._ (2019).

At low microgel concentrations, on experimental timescales, we find that the
system remains fluid at elevated temperature, microscopic observation reveals
finite sized aggregates. We expect that for sufficient waiting times and
system size, gelation would occur Griffiths _et al._ (2013). The
concentrations investigated here were 1-5 wt% pNIPAM microgel and 1-10 wt%
triblock-copolymer micelles. The lower concentrations of microgels and
micelles show evidence of aggregates forming with heating, as the samples
become increasingly opaque compared to microgels alone. At high enough
concentrations of the micelles and microgels, the mixtures from macroscopic
gels (>3 wt% microgel), which are originally space spanning and subsequently
collapse over time, leaving a liquid supernatant around the dynamically
arrested gel Fussell _et al._ (2019). These gels form reversibly. The mixtures
form gels upon heating but redisperse at low temperatures to reform a
colloidal suspension. This behaviour has been investigated in our previous
work Fussell _et al._ (2019).

Confocal microscopy indicates that both the microgels and micelles are present
in the gel network, where the green fluorescent signal (microgels) and red
fluorescent signal (micelles) can be seen in the same location of the gel.
This indicates that association has occurred (Fig. 2 a,d). At the highest
concentrations of micelles, there is an excess where there is evidence that
the micelles are still present in the supernatant. This indicates that the
mechanism for gelation is likely through the micelles/surfactants adsorbing
into the microgel, preventing the particles from deswelling, resulting in
gelation due to the increased vdW interactions between the larger, more hard
sphere like microgels.

Figure 4: Sketch of the interaction potentials between microgel particles at
different temperatures in the presence of triblock-copolymer micelles. At low
temperatures (a), the interaction between microgels is purely repulsive
(fluid). At intermediate temperatures (b), weak vdW forces now dominate and a
depletion force is also present due to the non adsorbing micelles, which
results in liquid phases rich in the two polymer species (phase separation).
At high temperatures (c), pNIPAM microgels now associate with the micelles,
resulting in the microgels not fully collapsing, there are now strong vdW
forces between them and the particles stick together as a result of
association (leading to gelation). The blue circles represent the pNIPAM
microgels at different extents of deswelling.

Slow heating. —  Figure 2 summarises the general behaviour observed for
mixtures of microgels and micelles when samples are heated slowly (0.1$\
{}^{\circ}$C min-1). The structures observed are totally different compared to
those found using fast heating. At high concentrations of micelles and
microgels and temperatures below $T_{\text{VPT}}$, demixing occurred at a
micelle concentration of around 7 wt% micelle. Droplets rich in microgels are
seen. These droplets contain just the microgel species, with the micelles
remaining free in solution. This was evidenced using confocal microscopy, as
the fluorescent signal of the micelles and microgels appear in different
regions of the image (Fig. 2 d). This implies the mechanism for microgel
aggregation in this system is one of depletion, where non-adsorbing polymer
causes colloidal aggregation. With increasing time or concentration of
microgels and micelles, these droplets coalesce leading to phase separation.
These demixed phases were observed at temperatures _lower_ than the
$T_{\text{VPT}}$ for pNIPAM, the temperature where aggregation was originally
assumed to occur in these samples. In comparison to structures formed by our
system as a result of the fast heating, we see more striking differences at
higher microgel and micelle concentrations. At lower concentrations and higher
temperatures, gel networks form (a, 4 wt% micelle), which are similar to those
formed at the same composition with the faster heating rate.

When mixtures of microgels and micelles are heated quickly (10$\ {}^{\circ}$C
min-1), the phase separation is bypassed and colloidal gels are observed at
all concentrations (b, d). Whether phase separation or gelation occurs can be
related to the quench rate in other colloidal systems. Slow quenching often
results in phase separation rather than gelation Royall and Malins (2012);
Royall and Williams (2011). Gels are non-equilibrium structures, and therefore
the effects of kinetic trapping can be important. Poon (2002); Lu _et al._
(2008); Zaccarelli (2007); Cipelletti and Ramos (2005); Verhaegh _et al._
(1997). Hence in our system, gel networks are always observed on fast heating
(10∘Cmin-1) as the equilibrium structure cannot be accessed. For the lower
concentration samples, heating rate has little effect on the structure and gel
phases are observed at both heating rates (a,b 4 wt% micelle). However, for
the higher concentration samples, large differences in the structure were
observed (c,d 11 wt% micelle). This is where the aggregation of the micelles
and microgels occurs at lower temperatures.

Figure 5: Scheme highlighting the behaviour of pNIPAM microgels in the
presence of triblock-copolymer surfactant, comparing the difference when
samples are heated slowly and quickly. The interactions are shown as a
function of both temperature and time. The top layer shows samples that are
heated quickly. At low temperatures the microgel particles are repulsive, then
when heated quickly, they associate strongly, likely through the
micelles/surfactant adsorbing inside the microgels preventing them from
deswelling. This results in a particle network without the ability to
rearrange, resulting in the formation of collapsing gels. The bottom layer
highlights the behaviour when samples are heated slowly. At low temperatures
the samples are again repulsive, then depletion occurs at intermediate
temperatures when the pNIPAM is still swollen. This results initially in the
formation of liquid droplets, which are rich in microgel, and eventually in
phase separation. Figure 6: Phase behaviour of mixtures of pNIPAM microgels
and triblock-copolymer surfactant, imaged using DIC microscopy. All samples
were heated to 35 ∘C at a heating rate of 0.1 ∘Cmin-1 before the final phase
was recorded. Pink circles indicate where gel networks were observed. Light
pink circles indicate where gels with larger voids were observed, and dark
pink circles where uniform gels are observed. Blue circles indicate where
phase separation is observed. The light blue circles indicate where isolated
droplets were observed, and the dark blue circles indicate where phase
separation occurred. The coloured squares indicate the concentrations of the
samples in the example DIC images included. The shading has been added to
guide the eye. The scale bar on all the images is 40 $\mu$m. Figure 7: DIC
images of a sample of pNIPAM (4 wt%) and triblock-copolymer (8 wt%) on
cooling. The sample was initially heated at a rate of 10 ∘Cmin-1 to 35∘C,
forming a uniform gel structure. The sample was then cooled at a rate of
0.1∘Cmin-1. This was to highlight that the droplet liquid phase can be
accessed both on heating and cooling. Scale bar 40 $\mu$m.

In the case of slow heating, macroscopic observation of the phase behaviour
were consistent with the microscopic observations discussed above. When
samples at the same composition were heated quickly, by immersion in hot
water, all samples formed collapsing gels (Fig. 2 a,d). The temperature of the
hot water was approximately 70∘C. Here the pNIPAM microgels all aggregate
leaving a liquid supernatant consisting of water and excess triblock-copolymer
micelles Fussell _et al._ (2019). When the samples were left in an oven to
heat slowly from room temperature to 40∘C, higher concentration samples
instead showed evidence of phase separation. A layer rich in pNIPAM formed
along with a layer of clear liquid (Fig. 2 c). These samples flowed upon
inversion of the vial, highlighting that the sample forms a weaker structure
than the collapsing gel networks. This difference in structure with heating
rate was only observed in samples where demixing was also observed under the
DIC microscope. Samples that formed gel networks microscopically on slow
heating also formed collapsing gels macroscopically (Fig. 2 b).

Figure 8: An example of the droplet size evolution over time for two
concentrations where droplets were indicated to form in Fig. 3. (a) Droplet
size evolution over time when the samples are heated at a rate of 0.1∘Cmin-1,
to a final temperature of 33∘C (circles) or 35∘C (triangles). The time is
started from the first indication of aggregates forming. Samples had 4 wt%
pNIPAM, 9 wt% triblock (purple) and 4 wt% pNIPAM, 8 wt% triblock (blue). (b)
Shows data for a wider range of concentrations, on a log-log scale. The fitted
power law for each droplet series measured is also included. Each data set has
been scaled by a pre-factor to highlight the similar trend observed at each
concentration. The data at 33∘C has been shifted to separate the data sets on
the graph. The black lines are the average fitted power laws for the droplet
growth series at both temperatures for all concentrations that formed
droplets. The data at 35∘C has been fitted up until the plateau in droplet
size. For the concentration, the first number indicates the wt% of pNIPAM
microgels in the sample, and the second number the wt% of triblock-copolymer
micelles.

###  III.2 Aggregation behaviour under slow heating

In the case of the slow heating rate, we now consider the phase boundary
between fluid (low temperature) and gel or demixed phases at higher
temperature as a function of concentration of microgels and triblock-copolymer
micelles. This is shown in Fig. 3. We find changes in the nature of the
demixing can be obtained as a function of composition as well as heating rate,
as discussed above. At temperatures below approximately 33∘C droplet formation
and phase separation occurred (Fig. 3 a, blue data points), whereas at higher
temperatures gels are formed (Fig. 3, pink data points).

For samples undergoing demixing, the aggregation occurs below the
$T_{\text{VPT}}$ for several concentrations of polymer (Fig. 3). This shows
that aggregation in these systems occurs when the particles are still swollen.
When gels result (Fig. 3 pink), aggregation occurs when the pNIPAM is close to
fully deswollen. However, for the concentrations where the aggregation
temperature is lower than the $T_{\text{VPT}}$, a different phase behaviour is
observed and phase separation occurs. The confocal images indicate a change of
interaction mechanism with temperature. At lower temperatures the mechanism
for aggregation is depletion, where the micelles behave like non-adsorbing
polymer resulting in aggregation, evidenced by the micelle signal remaining in
the supernatant around the droplets. At higher temperatures than the
$T_{\text{VPT}}$, gels result and the confocal signal of the micelles and
microgels overlap.

At room temperature, the microgels are swollen with water, their periphery is
poorly defined and the particles are purely repulsive. vdW attractions between
the particles are very weak, hence no depletion is observed at these
temperatures. At intermediate temperatures, the microgels deswell, becoming
more attractive due to increased vdW interactions and more defined due to the
periphery collapsing. The micelles cause depletion interactions between these
partially swollen particles. The concentrations of micelles needs to be high
in order to see depletion interactions as microgels are more stable to
depletion than hard spheres Bergman _et al._ (2018). Droplets form at these
intermediate temperatures and high concentrations. To form droplets through
depletion, the interactions need to be moderately strong and of sufficiently
long range. Our micelle / microgel size ratio at these concentrations is
approximately 0.25 so is of the order where a colloidal liquid is
thermodynamically stable in colloid polymer mixtures Ilett _et al._ (1994). At
longer times, the droplets coalesce and fully phase separate.

At high temperatures the microgels can be modelled as attractive spheres, and
depletion interactions no longer occur in these systems as the micelles now
associate with the microgels. In the systems where the samples are heated
slowly, aggregation due to depletion has already taken place, hence the
droplet structures and phase separation remain once heated to the temperature
where association occurs.

The temperature of the phase boundary decreases with increasing micelle
concentration, as shown in Fig. 3(a). The phase boundaries are shown for
various microgel concentrations from 1–6 wt%. At low concentration of
microgels (1 wt%), we encounter only gelation. Increasing the concentration of
microgels to 6 wt%, we find phase separation at a progressively lower micelle
concentration. Also at low concentration of microgels, the phase boundary is
almost flat as a function of micelle concentration, but slopes down
progressively upon increasing the microgel concentration.

In Fig. 3(b) we perform the complementary analysis of holding the micelle
concentration fixed, and plot the temperature of the phase boundary as a
function of microgel concentration. We find a very similar behaviour, in that
we find phase separation at a progressively lower micelle concentration.
Furthermore, the phase boundary is again almost flat at low micelle
concentration but slopes down more and more steeply upon increasing the
micelle concentration. This suggests that the phase behaviour may depend on
the _combined_ concentration of micelles and microgels. To test this, in Fig.
3(c) we plot the phase boundary as a function of the combined concentration of
micelles and microgels. Remarkably, we find a collapse of all data to a small
spread around a single curve. This is a _highly surprising_ result, because it
suggests that we can treat the micelle and microgel concentrations
interchangeably, even though these are wildly different species.

###  III.3 Mechanistic description of phase behaviour

The interaction potential between pure pNIPAM microgels changes as the
particles collapse. At low temperatures, microgels are soft colloidal
particles, with a layer of extended linear polymer chains. These swollen
particles are purely repulsive, vdW interactions are very small, due to the
highly diffuse nature of the outer regions of the particles Bergman _et al._
(2018). When the microgels are heated, they collapse and are often modelled as
attractive spheres, due to the increased vdW interactions and the microgels
becoming increasingly hydrophobic Bergman _et al._ (2018). The collapsed
particles are more likely to aggregate due to these attractions. These
colloids are stabilised solely by the charge on the particles left from the
initiator during synthesis.

We now consider mixtures of microgel particles and the triblock-copolymer
micelles, as summarised in Fig. 4. At low temperature, the interaction
potential between microgels is soft and purely repulsive, as inferred from DLS
measurements which showed no sign of aggregation Fussell _et al._ (2019), as
indicated in Fig. 4(a), therefore fluid phases are observed. Due to the weak
interactions between microgels and their soft nature they remain repulsive
even in the presence of the depletant. The micelles are also temperature
responsive, and at low temperatures contain high volume fractions of water,
therefore act as weak depletants at room temperature. When the micelles are
heated, it was found that the hard sphere volume fraction at equivalent
concentrations increased Sharp (2007).

At intermediate temperatures, the interaction potential becomes increasingly
attractive as the microgels collapse, where vdW attractions between the
microgels start to appear close to the $T_{\text{VPT}}$. Due to the microgels
still being partially swollen at these temperatures, the vdW potential well is
relatively shallow and the interaction is relatively soft (Fig. 4 (b)). The
phase separation at these temperatures is driven by depletion, where the non-
adsorbing micelles cause aggregation. At these concentrations and
temperatures, the depletion interaction results in droplet formation and with
increased temperature and time, phase separation. Due to microgels being more
stable to depletion compared to hard spheres at low temperatures Bergman _et
al._ (2018), this droplet phase is only observed at the highest concentration
of micelles (depletant). At these intermediate temperatures, there was no
evidence of association using DLS, evidenced by the hydrodynamic diameter of
the microgels at these temperatures being similar to the pure microgel even in
the presence of triblock-copolymer Fussell _et al._ (2019). At these
intermediate temperatures, it has been observed using small angle neutron
scattering that the aggregation number, volume fraction of polymer in the
micelle and hard sphere volume fraction all increase with temperature, while
to core radius of the micelles remains constant Sharp (2007). As the volume
fraction of micelles increases, so does the volume fraction of depletants,
hence the depletion interaction is stronger at intermediate temperatures.

When the temperature is increased further, the microgels fully collapse. If
droplets have already formed they remain with increased temperature, however
they appear to coarsen. If no depletion induced phase separation has taken
place yet, at low micelle concentrations, the microgels and the micelles
associate. These microgel particles are likely prevented from deswelling by
the micelles, increasing the vdW interactions between the particles inducing
gelation. The microgels are harder, and the vdW forces are stronger,
corresponding to a deeper attractive potential well (Fig. 4 c). This results
in the particles being unable to rearrange once association occurs, resulting
in collapsing gels. Figure S4 (lower scheme) captures how the interaction
potentials relate to the structures observed.

The difference in behaviour with heating rate indicates that the equilibrium
phase is not accessed when the samples are heated quickly (10∘Cmin-1),
resulting in gelation. In this regime, the microgels and the micelles
associate very quickly as the temperature increases rapidly above that at
which the system is dominated by microgel–micelle attractions, and the
collapse of the microgels also occurs over a fast timescale. This results in
the depletion effects at intermediate temperatures being bypassed, resulting
in gel network formation (Fig. S4 top scheme). Due to the strong vdW forces
between the particles, once the network has formed, there is little ability
for particles to rearrange. Therefore the kinetically favoured phase forms:
collapsing gel networks that undergo syneresis.

###  III.4 Detailed phase behaviour

So far, we have discussed the overall behaviour of the system at fast and slow
heating rates and have identified a mechanism. We now proceed to examine in
more detail certain phenomena and characteristics of our system. In
particular, we consider the detailed structure of the gel, the droplet phase
evolution and reversibility.

_Detailed structure of gels. —_ Figure 6 details the phase behaviour observed,
when the samples were heated slowly (0.1∘C min-1). For low concentrations of
micelle and microgel, the system gels. Two types of networks were observed.
The first was uniform gels, where little structural detail was observed at the
resolution of the microscope used (Fig. 6 dark pink). These were formed at
high concentration of microgels, more than 3 wt$\%$. The second morphology we
term gels with voids, where, when imaged under the DIC microscope the arms of
the gel network were resolvable (Fig. 6 light pink). At the lower
concentrations of microgel $(\lesssim 3$wt$\%)$, gels with voids
preferentially form, as the low volume fraction of microgel in these samples
results in sparse networks. These low concentration samples macroscopically do
not form gels, but only show evidence of aggregates which sediment Fussell _et
al._ (2019).

Turning to the behaviour of the system as a function of micelle concentration,
we find that gels with voids also form preferentially with increasing micelle
concentration. This is most prevalent at concentrations close to the boundary
where phase separation is observed. To explain this trend we looked in detail
at the aggregation temperature as a function of both micelle and microgel
concentration. This is summarised in Fig. 3 (b and c). It can be seen that the
aggregation temperature decreases with increasing micelle concentration. This
decrease in aggregation temperature means that aggregation occurs when the
particles are partially swollen. Now, at these lower temperatures, the
interaction between the micelles and microgels is one of depletion (see
Section III.3 and Fig. 4). This results in phase separation occurring before
gelation, as the microgels are free to rearrange to some extent over short
time scales before full gelation occurs, resulting in these voids.

At the higher concentrations of microgels and micelles, demixed phases were
observed. At these concentrations samples form microgel-rich phases (Fig. 6).
At lower microgel and micelle concentrations these droplets remain stable over
the time frame of the experiment (light blue), but over long time scales
(hours) they eventually coalesce leading to macroscopic phase separation (ESI
Fig. S3). With increasing polymer concentration the rate of droplet
coalescence increases, and phase separation proceeds (Fig. 6 dark blue) over
the time frame of the experiment.

At higher microgel concentrations, lower micelle concentrations are needed to
induce phase separation. At micelle concentrations above $\sim 7$ wt%, the
aggregation temperature becomes strongly dependent on microgel concentration
and drops rapidly (Fig. 3 b, c). Phase separation (droplets coalescing) was
found to occur when the aggregation temperature was lowest (below 31∘C), as
aggregation in these samples occurs over the largest time / temperature range.

###  III.5 Reversible phase behaviour

The formation of the droplet phase appears to be reversible, highlighting that
the phase is stable. However it is found over a small temperature range only,
between the temperature at which aggregation occurs and where the microgels
are fully deswollen. We took a mixture of microgels and micelles known to form
droplets when heated slowly (4 wt% pNIPAM and 8 wt% triblock-copolymer). We
heated this sample rapidly to 35∘C so the sample gelled. The sample was then
cooled at at rate of 0.1∘C min-1. On cooling the droplet phase was again
observed, eventually phase separating into polymer rich and poor liquid
phases. This shows that the droplet phase is stable as it can be accessed both
on heating and cooling the system.

###  III.6 Droplets of Colloidal Liquid

We have characterised the droplets of colloidal liquid (microgels) that result
from the slow heating of our system. Droplets only form at high micelle
concentrations and temperatures below the $T_{\text{VPT}}$. The size of the
droplets increases with time, tending to a plateau value as shown in Fig.
8(b). We believe that the suppression of full phase separation and the trend
towards a plateau is due to the stronger interactions found between the
microgels at temperatures of 35∘C or more.

The size of the droplets formed can be controlled by changing the temperature
the droplets are held at. Two different experimental regimes were studied as
shown in Fig. 8. The first of these being where samples were heated at
0.1∘Cmin-1 from room temperature to 33∘C, which is just above the temperature
where aggregation was observed for these samples. The second was where samples
were heated from room temperature to 35∘C also at a rate of 0.1∘Cmin-1, a
temperature where pNIPAM is nearly fully deswollen (Fig. S2 ESI). Two example
data sets have been included in Fig. 8, the data for all phases where droplets
occur is included in the SI (Fig. S4 ESI). For all samples, time zero was the
time after the temperature at which aggregates were first observed. An example
set of images of the droplets increasing in size over time is included in the
SI (Fig. S5 ESI). The average difference in the diameter of the droplets is
48%$\pm$2% between 33∘C and 35∘C. The microgels themselves deswell
approximately 39% of their overall diameter over this temperature range. It is
likely that at the lower temperature of 33∘C, the droplets can continue to
grow as the interaction between the microgels are relatively weak at this
temperature, due to the particles being partially swollen, so the polymers are
free to rearrange resulting in droplet growth for longer times. However when
the samples are heated to 35∘C, the association between the microgels becomes
relatively strong, meaning the microgels are no longer free to rearrange
because of the stronger attractions between them.

The evolution of the droplet diameter with time was fitted to a power law
$y=Ax^{\nu}$ for both temperature regimes (33∘C and 35∘C). The data sets were
scaled by a prefactor A to highlight the constant power law for each
temperature. The data at 33∘C has been shifted to higher values to separate
the data sets (Fig. 8b). Each data set was fitted up to the point where the
droplet growth plateaus. Both final temperatures showed a power law regime for
droplet size growth as a function of time, where a faster evolution was
revealed for 33∘C than for 35∘C. This is to be expected as the droplets grew
to a larger size at the lower temperature over the same time frame. At 33∘C
$\nu$=0.46 and at 35∘C $\nu$=0.36. There are two important factors to consider
for droplet evolution, diffusion and coalescence. At low droplet
concentrations, there is a negligible interaction between the droplets, this
is the diffusion limited case, $\nu$ = 1/3. When the concentration of droplets
increases, droplet coalescence becomes an important factor, $\nu$ increases
towards 1 Steyer _et al._ (1991). From the values of the exponents that we
determine, it seems that with increasing temperature, droplet coalescence
becomes less important, and the droplet evolution is driven by diffusion
(35∘C). At lower temperatures, droplet coalescence becomes more important
(33∘C) hence the increased $\nu$. This again will be due to the limited
ability of the microgels to reorganise at higher temperatures due to the
stronger attraction between them. At lower temperatures the microgels are
still swollen, resulting in a weaker interaction compared to the collapsed
particles resulting in droplet growth occurring over longer time scales.

The size of the droplets observed correlates with the concentration of both
microgels and micelles in the samples. With increasing microgel concentration,
there is a linear increase in the size of the droplets observed (Fig. S6 ESI).
A similar trend is observed for the micelle concentration (Fig. S7 ESI). Both
of these trends are observed when the samples are heated to 33∘C and 35∘C.

##  IV Discussion and conclusions

We have identified a colloidal model system displaying tunable, controllable
gelation, building on the current understanding of the phase behaviour the
PEO-PPO-PEO triblock copolymer pNIPAM microgel system, in which the former
form micelles, leading to a micelle-microgel mixture. Our study reveals a
previously unreported phase separation to a phase rich in microgels coexisting
with a rich in micelles and poor in microgels. While previous work Fussell _et
al._ (2019) looked at rapid temperature changes, here we have explored the
effect of heating rate, which, along with the composition, has revealed a
range of structures formed in this non-equilibrium system. Demixing in our
system at low temperatures is driven by depletion interactions, which are
negligible at room temperature, but become apparent with increased temperature
due to the increased ability of the micelles to be depleted at higher
temperatures. At high temperatures, an associative mechanism of gelation
dominates, as hydrophobic interactions and hydrogen bonding cause the
microgels and micelles to associate.

These mixtures from temperature responsive gels upon heating, and we have
shown that the structure and phase of these systems can be controlled by
altering the concentration of the components and by altering the heating rate
used for gelation. We highlight the broad range of states accessible for
mixtures of pNIPAM microgels and triblock-copolymer micelles. In particular,
upon high rates of heating, phase separation is suppressed, and gelation is
encountered. At lower rates of heating, the system spends sufficient time at
temperatures where depletion dominates and the attractions between the
microgels are milder, and a more complete demixing occurs, with the formation
of liquid–like droplets of microgels. This is reminiscent of the coupling
between the rate of change of attraction in “sticky spheres” and the degree of
self-assembly Royall and Malins (2012).

In addition to its response to the heating rate, our system can be tuned by
changing the composition. High concentrations of microgel particles lead to
uniform gels, while lower concentrations result in gels with voids. Increasing
the concentration of micelles promotes demixing to droplets of microgels and
micelles (which then solidify). At higher micelle concentration still, we
encounter full phase separation to a phase rich in microgels in coexistence
with a microgel poor phase. The temperature at which the microgels demix is
dependent on the concentration of both the microgels and the micelles, and at
high concentrations demixing occurs when microgels are still in the swollen
state.

This system highlights how studying the phase behaviour of a microgel-micelle
system can ultimately improve our understanding of the behaviour of colloidal
assemblies and for example can allow us to access both the equilibrium phase
behaviour and non-equilibrium gel and droplet structures. Furthermore these
systems may find use as novel temperature-responsive materials.

## Acknowledgements

SF is supported by a studentship provided by the Bristol Centre for Functional
Nanomaterials (EPSRC grant EP/L016648/1). CPR acknowledges support from EPSRC
(grants GR/M32320/01 and ERC consolidator grant NANOPRS, project number
617266). We would also like to thank Craig Davies, Croda, for supplying the
Synperonic PE/P105.

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##  V Appendix

Figure S1 highlights how differential interference contrast (DIC) images were
edited in this work. The images were converted to grey scale, then converted
to the glow colour palette, then the image inverted. The brightness of the
image was then adjusted. This results in the polymer rich regions appearing
bright and the polymer poor regions appearing dark.

Figure S1: Figure highlighting the editing process used to highlight the
regions rich in polymer in images taken using the DIC microscope. DIC images
are converted to grey scale, then converted to glow, then the images inverted
so that the polymer rich regions appear bright and the polymer poor regions
appear dark. Figure S2: Hydrodynamic diameter of the pNIPAM microgels as a
function of temperature. Figure S3: Images of droplets coalescing over time.
The concentration of the sample is 4 wt% pNIPAM and 8 wt% triblock-copolymer.
The scale bar is 40 $\mu$m.  Figure S4: Summary of the droplet size evolution
over time, for the concentrations where droplets were indicated to form in
figure 1. Droplet size evolution over time when the samples are heated at a
rate of 0.1 ∘C/min to 33∘C (a) or 35∘C (b). The same data has been plotted on
a log time scale in (c) and (d). The time is started from the first indication
of aggregates forming. 4 wt% pNIPAM, 9 wt% triblock (maroon), 4 wt% pNIPAM, 8
wt% triblock (pink), 3 wt% pNIPAM, 10 wt% triblock (grey), 3 wt% pNIPAM, 9 wt%
triblock (green), 2 wt% pNIPAM, 10 wt% triblock (purple), 2 wt% pNIPAM, 9 wt%
triblock (blue) The black lines are the average calculated fitted power laws
for the droplet growth series at both temperatures for all droplet sizes in
the series.

Figure S2 contains the deswelling data for the pNIPAM microgels used in this
study, determined using dynamic light scattering.

Figure S3 highlights the evolution of the droplet phase over time. Droplets
begin to form upon heating, then when held at 33∘C, the droplets continue to
grow and eventually merge. This results in phase separation at prolonged
times.

Figure S5: a-d) Optical micrographs of 3 wt% pNIPAM, 9 wt% triblock-copolymer
heated to 33∘C at a rate of 0.1 ∘C/min and held at that temperature. The time
was started from the first indication of gelation. The scale bar is 10 $\mu$m

.

Figure S6: Summary of how droplet size increases with increasing pNIPAM
concentration, for samples with 9 wt% triblock-copolymer. a) 2 wt% pNIPAM, b)
3 wt% pNIPAM, c) 4 wt% pNIPAM. Scale bar 40 $\mu$m. d) Summary of the final
droplet sizes recorded when samples were heated to 33∘C at a rate of 0.1
∘C/minute and held at that temperature.

Figure S4 shows the evolution of droplet size for the series of samples that
form droplets. There is a general increase of droplet size with time, tending
to a plateau value at late time. It can be seen that droplets grow to larger
sizes when held at 33∘C (a), rather than heated to 35∘C and held at that
temperature. It was also observed that a power law can be used to describe the
data set, where samples heated to 33∘C scale with gradient $\mu$ = 0.46,
whereas samples heated to 35∘C scale with $\mu$ = 0.36.

Figure S7: Summary of the final droplet sizes observed from heating mixtures
of pNIPAM and triblock-copolymer. Left are the final droplet sizes observed
for samples being heated at a rate of 0.1 ∘C/min to 35∘C. Right are for
samples heated to 33∘C at a rate of 0.1 ∘C/min. The numbers on the graph
indicate the concentration of pNIPAM in wt%. Coloured lines have been added to
guide the eye.

Figure S5 illustrates how the size of the droplets increases with time.

Figure S6 and S7 shows how the size of droplets, formed through slowly heating
mixtures of pNIPAM and triblock-copolymer, changes as a function of pNIPAM and
triblock-copolymer concentration respectively. With increasing polymer
concentration there is a general increase to the size of the droplets
observed. This effect was seen for various pNIPAM concentrations and for
different final temperatures where the drops were held.