# Light-controlled aggregation and gelation of viologen-based coordination
polymers

Shagor Chowdhury  Quentin Reynard-Feytis  Clément Roizard  Denis Frath  Floris
Chevallier  Christophe Bucher  Corresponding author, christophe.bucher@ens-
lyon.fr Univ Lyon, Ens de Lyon, CNRS UMR 5182, Laboratoire de Chimie, F69342
Lyon, France  Thomas Gibaud  Corresponding author<EMAIL_ADDRESS>Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique,
F69342 Lyon, France

###### Abstract

Ditopic bis-(triazole/pyridine)viologens are bidentate ligands that self-
assemble into coordination polymers. In such photo-responsive materials, light
irradiation initiates photo-induced electron transfer to generate
$\pi$‐radicals that can self-associate to form $\pi$-dimers. This leads to a
cascade of events: processes at the supramolecular scale associated with
mechanical and structural transition at the macroscopic scale. By tuning the
irradiation power and duration, we evidence the formation of aggregates and
gels. Using microscopy, we show that the aggregates are dense polydisperse
micron size spindle shaped particles which grow in time. Using microscopy and
time resolved micro-rheology, we follow the gelation kinetics which leads to a
gel characterized by a correlation length of a few microns and a weak elastic
modulus. The analysis of the aggregates and the gel states vouch for an
arrested phase separation process.

###### pacs:

xxx

##  I Introduction

Stimuli-responsive supramolecular self-assemblies have the potential to
organize in various structures depending on the duration and intensity of the
stimulus. Those materials may in particular self-assemble into a wide variety
of structures ranging from aggregates, capsules, gels or textured thin films
Stuart  _et al._ (2010). The gel state Chivers and Smith (2019); Haring and
Diaz (2016); Jones and Steed (2016); Panja and Adams (2021); Babu  _et al._
(2014); Datta  _et al._ (2017); Dhiman  _et al._ (2020); Wei  _et al._ (2017);
Xu  _et al._ (2018); Zhang  _et al._ (2013) is an interesting class of soft
materials with broad potential applications ranging from structure directing
agents for the synthesis of nanoporous materials, surface patterning, ink, 3D
printing to pollutant removal and biomedical applications Okesola and Smith
(2016); Kan  _et al._ (2017); Rodell  _et al._ (2015); Dong  _et al._ (2015);
Sangeetha and Maitra (2005).

Supramolecular gels are typically formed in solution from the self-assembly of
tailor-made low molecular weight building blocks yielding extended networks
stabilized through non-covalent and fully reversible bonds providing the
system with elastic properties at rest.Chivers and Smith (2019); Haring and
Diaz (2016); Jones and Steed (2016); Panja and Adams (2021); Babu  _et al._
(2014). In other words, a sol-gel transition translates molecular information
into macroscopic properties. Gelation pathways are not trivial in
supramolecular systems since they generally involve a large number of
interactions evolving over time Lan  _et al._ (2015). Moreover, examples where
irradiation leads to a strengthening of rheological properties are scarce
since photons absorption often results in the collapse of the gel Draper  _et
al._ (2016). In that context, reaching a deep understanding of photo-induced
gelation of supramolecular assemblies is crucial for the design of stimuli-
responsive soft materials.

Here, we take advantage of the photo-sensitivity of viologen-based
supramolecular polymers Datta  _et al._ (2017); Dhiman  _et al._ (2020); Wei
_et al._ (2017); Xu  _et al._ (2018); Zhang  _et al._ (2013); Li  _et al._
(2017); Wang  _et al._ (2020); Correia  _et al._ (2019); Chowdhury  _et al._
(2019); Kahlfuss  _et al._ (2018) to direct the self-assembly toward
aggregates or gels. Forming gels from viologen derivatives is all the more
important that such materials are of high interest for various fields such as
electrochromism, molecular machines, memory devices, gas storage and
separation or energy storage Ding  _et al._ (2019); Striepe and Baumgartner
(2017). In terms of application, reactive gels have already proved useful to
the development of electronic such as memristor Zhang  _et al._ (2017).
Moreover, viologens have also been used as key redox-responsive components in
large-area molecular junctions Han  _et al._ (2020); Nguyen  _et al._ (2018).
All these exploratory works demonstrate the interest of viologen-based
material in electronics and open enormous prospects for innovations.

We have been interested in recent years in the properties of viologen-based
supramolecular architectures and coordination polymers grown by spontaneous
assembly of organic ligands with various metal sources Kahlfuss  _et al._
(2016a, 2019, 2021, 2018); Abdul-Hassan  _et al._ (2018). In these studies,
the ability of viologen derivatives to form $\pi$-dimers Kahlfuss  _et al._
(2016b) in their reduced state has been exploited to achieve a remote control
over the organization of molecules within supramolecular assemblies Kahlfuss
_et al._ (2016a, 2019, 2021). The photo induced reduction of viologen-based
acceptors is a well documented phenomenon that has already been used to
generate $\pi$-dimers Frath  _et al._ (2013); Yamamoto  _et al._ (2018). We
have recently used this approach to achieve a sol/gel transition triggered by
light irradiation of the palladium-based coordination polymer Kahlfuss  _et
al._ (2018).

Figure 1: Schematic representation of the photo-responsive supramolecular
coordination polymer used in this study.

As shown in Fig. 1, the ditopic ligand 1 involved in these polymers features
two planar nitrogen-containing binding units (triazole-pyridine) introduced on
both sides of a viologen-based mechanical hinge that can toggle under
stimulation between a folded and a stretched conformation. This ligand was
found to self-assemble in the presence of palladium ions to yield linear
coordination polymers capable of undergoing large scale reorganizations in
solution under light or electrical stimulation Kahlfuss  _et al._ (2018). The
driving force of the folding motion is the $\pi$-dimerisation of the in-situ
generated viologen cation radicals. At this stage, the exact structure of the
$\pi$-dimerized structure(s) still remains hypothetical but all available data
suggest the formation of either box-shaped discreet complexes (3 in Fig. 1) or
of accordion-shaped folded polymers (4 in Fig. 1). As mentioned in a recent
report, the formation of inter-chain dimers (5 in Fig. 1) in the gel phase can
also not be ruled out Courtois  _et al._ (2020). Following these initial
findings, we have carried out detailed microscopy and rheological
investigations to provide further insights into the gelation mechanism.

Main goals of the present paper are to map the state diagram of the assemblies
obtained after irradiation of the viologen-based coordination polymer and to
characterise the kinetics and final properties of the self assembled
structures at the microscopic scale. We first describe the preparation of the
samples and the characterization techniques that were implemented to perform
detailed analyzes on microliters-scale samples under airtight conditions.
Second, we present the state diagram of the system depending on the
characteristic of the stimulus: a light irradiation of duration $t_{i}$ and
power $P$. As $t_{i}$ and $P$ increase, we evidence that we can direct the
self-assembly toward first aggregates then gels. Third, using microscopy, we
show that the aggregates are dense polydisperse micron size spindle shaped
particles with an aspect ratio of about two. Fourth, using microscopy and
micro-rheology, we show that the gel forms within a few hundreds of seconds.
This gel displays a correlation length of about 7 microns and a weak elastic
modulus. Those characterisations leads us to formulate a scenario based on
arrested phase separation that is compatible with both the aggregates and gel
formation.

##  II Materials and methods

Sample preparation. All samples were prepared under an argon atmosphere (glove
box) from compounds obtained according to procedures reported earlier Kahlfuss
_et al._ (2018). In a typical experiment a fresh 100 $\mu$L stock solution was
prepared upon mixing equimolar amounts of 1 and [Pd(CH3CN)4](BF4)2 in DMF (20
mM) in the presence of triethanolamine (10 mM). The as-prepared solution was
introduced into a dismantled quartz absorption cuvette featuring a 0.1 mm
layer thickness. The sample was then taken out of the glovebox and submitted
to light irradiation during $t_{i}$ at a power $P$ using a led lamp (X-Cite
120Led Boost from Excelitas) in the reflection mode through the 10x objective
of the microscope (Nikon Plan fluor, N.A.=0.3).

Microscopy experiments. Microscopy experiments were carried out on a Nikon Ti-
eclipse inverted light microscope in bright field. We used a 10x and a 40x
objective to image the sample. After photo activation, images of the sample
were recorded with a camera (ORCA-Flash4 Digital CMOS camera from Hamamatsu)
during a time $t$ at 20 Hz. The total recording time was chosen long enough so
that the image display stationary statistical properties, $\sim$ 2000 s. The
images $I(r)$ are 1024x1024 pixels. The image intensity was encoded in a 16
bits/pixel grey scale. $r$ is the coordinate of a pixel in the image. With the
objectives 10x and 40x, one pixel represents respectively 0.644 and 0.161
$\mu$m.

Micro-structure analysis. Depending on the sample, the structure was analysed
either with a shape recognition or a Fourier transform algorithm. For
aggregated samples, the molecules form microscopic spindle shape particles.
This shape was quantified using an ellipsoid recognition algorithm which gives
the diameter of the particle along $r_{\parallel}$ and perpendicular
$r_{\perp}$ to its long axis Modlińska  _et al._ (2015). As set up, this
methods is sensitive to structure down to 1.8 $\mu$m. For the gel samples, the
molecules form a uniform and isotropic network with a network characteristic
length of a few microns. This characteristic length was extracted from the
radial average of the Fourier transform ($FFT$) of the image at a time $t$:
$I(q,t)=|FFT[I(r,t)-\langle I(r,t)\rangle]|^{2}$. The wave vector amplitude
$q$ is the variable in Fourier space associated to $r$ in real space. $\langle
I(r,t)\rangle$ is the spatial average intensity of the image.

Time resolved micro-rheology. Micro-rheology measurements involved acquiring
movies under the microscope of the sample seeded with colloidal tracers. We
used 5 $\mu$m diameter polystyrene colloidal particles (Fluka) as tracers. The
amount of colloids was adjusted to reach a diluted colloid regime – the
distance between colloids is at least 5 colloid diameters – to avoid colloid-
colloid interactions. Micro-rheology consists in taking advantage of the
dynamics of the embedded colloids. The colloids act as local probes whose
dynamics, activated by the thermal motion, depend on the mechanical properties
of the sample: the loss modulus $G^{\prime\prime}$, which accounts for the
viscous dissipation of the sample and the elastic modulus $G^{\prime}$, which
accounts for the elastic properties of the sample. To retrieve the
viscoelastic properties $G^{\prime}$ and $G^{\prime\prime}$ of the sample,
micro-rheology experiments requires image analysis and calculations. In brief,
image analysis consists in tracking the trajectories $r(t)$ of each embedded
colloids in the sample as a function of the time $t$ Maurer  _et al._ (2014);
Parthasarathy (2012). We obtain about 50 trajectories per movies. The tracking
algorithm precision on $r(t)$ is about 1/10th of a pixel: $\simeq 16$ nm, with
the 40x objective. From those trajectories, the mean square displacement of
the colloids $\langle\Delta r^{2}\rangle$ is calculated as a function of the
lag time $\Delta t$. Micro-rheology principles Mason  _et al._ (1997); Gao and
Kilfoil (2007) then rely on computing the complex viscoelastic modulus $G$ or
the creep compliance $J$. $G$ is obtained from the unilateral Laplace
transform $\mathcal{L}[.]$ of $\langle\Delta r^{2}\rangle$ using the
generalized Stokes-Einstein equation:
$G(s)=\frac{k_{B}T}{isa\mathcal{L}[\langle\Delta r^{2}\rangle]}$. $i$ is the
imaginary number such that $i^{2}=-1$, $s$ is the Laplace frequency, $k_{B}$
is Boltzmann’s constant, $T=20^{\circ}$C is the temperature of the sample (in
Kelvin for the formula) and $a$ is the radius of the colloids. This equation
is based on a generalized Langevin equation which describes the sphere’s
motion in the continuum (neglecting the sphere’s inertia), and it is
consistent with energy equipartition and the fluctuation dissipation theorem.
$G=G^{\prime}+iG^{\prime\prime}$ is the shear modulus. Its real part yields
the elastic modulus $G^{\prime}(f)$ and its imaginary part gives the loss
modulus $G^{\prime\prime}(f)$ where $f$ is the frequency in Hz, with $s=2\pi
f$. The calculation method is based on Mason  _et al._ (1997); Gao and Kilfoil
(2007). An alternative consists in working directly on the mean square
displacement which is proportional to the creep compliance $J(t)=k_{B}T/[\pi
a\langle\Delta r^{2}\rangle]$ Gittes  _et al._ (1997); Palmer  _et al._
(1998). $J(t)$ relates the material strain deformation $\gamma(t)$ to the rate
of applied stress $\dot{\sigma}(t)$ via
$\gamma(t)=\int_{0}^{t}J(t-t^{\prime})\dot{\sigma}(t)dt^{\prime}$ Ferry
(1980). The direct proportionality of the mean square displacement and creep
compliance avoids artifacts from converting the data to the complex
viscoelastic modulus $G$ Palmer  _et al._ (1998). Those artefacts can be seen
in Fig. 6c where $G^{\prime}$ may drop drastically at the edges of frequency
domain.

As our samples evolve in time, we decomposed the movies in a succession of
sequences of duration 50 s. 50 s therefore represents the time during which a
micro-rheology experiment is performed and the kinetics resolution. Doing so,
we assumed that the sample properties are stationary or evolve very little
during this 50 s time scale.

##  III Results

###  III.1 Directing the microscopic state of self-assemblies with light
irradiation

Figure 2: State diagram as a function of the initial photo-activation time
$t_{i}$ and power $P$. (a) State diagram of the dispersion inferred from
microscopy images and micro-rheology as $P$ and $t_{i}$ increase. (b)
Microscopy images of the sample after reaching its final state at $t=2000$ s
after irradiation as function of the photo activation time $t_{i}$ and the
power $P$. Upper arrow: $P=100$% while $t_{i}$ varies from 0 to 180 s. Lower
arrow: $t_{i}=180$ s while $P$ varies from 0 to 100%. Circular spot on the
images are the 5 $\mu$m diameter tracer colloids used for micro-rheology.

We used microscopy to image the sample and map the state diagram of the
dispersion under different irradiation conditions. We varied the irradiation
time $t_{i}$ from 0 to 180 s and the lamp power $P$ from 0 to 100%. Fig. 2
shows bright field microscopy images of the same sample under different
irradiation conditions. Images were taken when the structure of the sample no
longer varied, $t=2000$ s after switching off the lamp. At low $t_{i}$ and
$P$, the sample was found to form aggregates. The aggregated sample is
spatially heterogeneous and composed of individual elongated aggregates
randomly oriented of size a few tens of microns. At higher $t_{i}$ and $P$,
the sample forms a gel. All the gels display the same structural and
mechanical properties: a spatially homogeneous and weakly contrasted network
with a correlation length $\xi\simeq 7$ $\mu$m and a weak elastic modulus
$G^{\prime}\simeq 0.3$ Pa. The measurements of those properties are presented
later in the article. We define $t^{*}$ the time when the first structures
appear under the microscope, Fig. 3. For aggregates, $t^{*}$ is of about 1000
s. For gels $t^{*}$ is lower and decreases with $t_{i}$ and $P$.

Figure 3: Aggregation and gelation time $t^{*}$ as a function of the initial
photo-activation time $t_{i}$ and power $P$. $t^{*}$ is define as the first
time structures appear on the microscopy images after the irradiation in turn
off. Evolution of $t^{*}+t_{i}$ as function of $P$ while $t_{i}$ is kept
constant and equal to 180 s (black). Evolution of $t^{*}+t_{i}$ as function of
$t_{i}$ while $P$ is kept constant and equal to 100% (blue). Full symbols
correspond to the aggregate state while open symbols correspond to the gel
state.

###  III.2 Micro-structure characterization of the aggregation and the
gelation

It is remarkable that a simple change in the time and power of irradiation
lead to such different states: aggregate or gel. Irradiation conditions to
form aggregates were best achieved using a combination of low power or short
irradiation time as indicated in Fig. 2. As shown in Fig. 4a, molecular
dispersion irradiated with $P=100$ % for $t_{i}=30$ s,gave isolated elongated
micro-particles. Although those micro-particles coalesce, within our
experimental time window, we never observed the formation of homogeneous
phases. The first particle observed under the microscope appears around
$t\simeq 850$ s after irradiation. Such particles display two important
characteristics. ($i$) A spindle like morphology with a long axis of length
$r_{\parallel}$ and a short axis of length $r_{\perp}$. As shown in Fig. 4b,
on average, $\langle r_{\parallel}\rangle$ and $\langle r_{\parallel}\rangle$
grow with time up to roughly 10 $\mu$m. The average aggregated particles
aspect ratio, defined by $r_{\parallel}/r_{\perp}$, is about 1.8, Fig. 4c. The
particle polydispersity, defined by the ratio between the standard deviation
of the particle size divided by the particle size, is always large and
increases from $\simeq 0.8$ to 1.1. ($ii$) High molecular densities, as
revealed by the dark coloration of the microscopy images, Fig. 4a. The density
difference between the particle and the background can be estimated through
$\sigma_{I}$ the standard deviation of the image $I(r,t)$, Fig. 4b. Particles
are much denser that the gel backbone as shown in Fig. 2.

Figure 4: Aggregation kinetics using time resolved microscopy for an
irradiation of $P=100$ % during $t_{i}=30$ s (a) Bright field images of the
aggregate $I(r,t)$ at $t=370$, 420 and 700 s. (b) Evolution of the average
value of $r_{\parallel}$ (blue) and $r_{\perp}$ (green) as a function of $t$.
Light blue and green curves shown the evolution of a typical single particle.
Inset: superposition of the image of a particle and its contour. (c) From top
to bottom, time evolution of $\sigma_{I}$ the standard deviation of $I(r,t)$,
the particle aspect ratio $r_{\parallel}$/$r_{\perp}$, and the polydispersity.
The vertical dash line indicate $t^{*}=850$ s.

The best gelation conditions were obtained using high power and long duration
irradiations (Fig. 2). As shown in Fig. 5, with pictures recorded for a
molecule dispersion subjected to irradiation of $P=100$ % for $t_{i}=120$ s,
the first structures appear under the microscope at about $t=690$ s. The gel
kinetics and micro-structure are very different from the aggregation state.
First, the gel structure does not shown any evidence of local anisotropy. The
images display a well defined length scale. This is evidenced in Fig. 5b
through the Fourier spectrum $I(q,t)$ of the gelling molecular dispersion.
$I(q,t)$ shows in particular a peak at $q_{p}$ of intensity $I_{p}$. $q_{p}$
is related to the correlation the length of the gel $\xi$, i.e., the
characteristic length of the gel network defined by $\xi=2\pi/q_{p}$. $I_{p}$
is an indicator of the structure contrast and therefore the molecular density
of the network structure with respect to the background. Above $t=690$ s,
$\xi$ is constant, $\xi=6.9\pm 0.2$ $\mu$m, and $I_{p}$ increases by almost
two orders of magnitude. Contrary to the aggregate state, the gel length scale
is set a the early beginning of the kinetics and remains afterward unchanged.
However, the contrast and therefore the gel backbone becomes denser during the
kinetics. To sum up, the gel forms an homogeneous porous network structure of
typical size $\xi\simeq 7$ $\mu$m.

Figure 5: Gelation kinetics using time resolved microscopy for an irradiation
of $P=100$ % during $t_{i}=120$ s. (a) Bright field images $I(r,t)$ of the
gelation process at different time $t$. (b) Evolution the Fourier spectrum
$I(q,t)$ of the microscope images $I(r,t)$ as function of the wave number $q$
for different time $t$. Colors code for the time $t$ after irradiation. (c)
From top to bottom, time evolution of the correlation length $\xi$ and peak
intensity $I_{M}$. The vertical dash line indicate $t^{*}=690$ s.

###  III.3 Viscoelastic characterization of the sol-gel transition

Figure 6: Gelation – from the embedded colloids dynamics to time resolved
micro-rheology. This sample is photo-activated during $t_{i}=120$ s at
$P=100\%$. (a) Representative trajectories $r(t)$ of a colloid embedded in the
sample at different time $t$ after photo activation. The color from blue to
yellow codes for the time $t$ after photo activation. The grey scale codes for
the time from 0 s (dark grey) to 50 s (light grey). The scale bar always
represent 0.2$\mu$m. Note that the scale bar increases size as $t$ increases,
meaning the trajectory is zoom in as $t$ increases. The doted red circle in
the trajectory at $t=1100$ s indicate the localization of the colloid before
diffusing to other location. (b) Mean square displacement of the colloids
$\langle\Delta r^{2}\rangle$ as a function of the lag time $\Delta t$. Each
$\langle\Delta r^{2}\rangle$ is extracted from movies sequences of duration 50
s. (c) Viscoelastic proprieties of the sample deduced from $\langle\Delta
r^{2}\rangle$: loss $G^{\prime}$ (line) and elastic modulus $G^{\prime\prime}$
(dot line) as a function of the frequency $f$.

We have next focused on the mechanical properties of the molecular dispersions
leading to the gel state. We found that irradiation, in the limit where $P$ or
$t_{i}$ is high, induces full gelation of the sample on times scales of the
order of $t^{*}$. In Fig. 6, for the gelation conditions, $P=100$ % during
$t_{i}=120$ s, conditions identical to the sample whose structure is analysed
in Fig. 5, we extract, thanks to the dynamics of colloids dispersed in the
sample, the mechanical properties of the sample after photo-activation using
time resolved micro-rheology. This analysis is decomposed in tree main steps:
tracking the trajectory of the colloids $r(t)$ (Fig. 6a), computing mean
square displacement of the colloids $\langle\Delta r^{2}\rangle(\Delta t)$
(Fig. 6b), and extracting the variation of the loss $G^{\prime\prime}$ and
elastic $G^{\prime}$ modulus as a function the frequency $f$ (Fig. 6c). We
choose to focus on four characteristic times of the gelation kinetics to
describe its evolution: $t=100$, 700, 1100 and 1300 s.

At $t=100$ s, the sample is translucent and homogeneous (Fig. 5a). As shown in
Fig. 6a, the colloid trajectory is open and the colloid diffuses micrometric
distances during this acquisition of 50 s. As shown in Fig. 6b, this
corresponds to a linear variation of the mean square displacement
$\langle\Delta r^{2}\rangle$ with the lag time $\Delta t$: $\langle\Delta
r^{2}\rangle=4D\Delta t$. The colloid diffuses with a diffusion constant
$D=0.018\mu$m2/s. At this stage, the sample is a newtonian fluid. In, Fig. 6c
$G^{\prime}$ is negligible and $G^{\prime\prime}$ varies linearly with $f$:
$G^{\prime\prime}=\eta 2\pi f$ with $\eta\simeq 5$ mPa.s the viscosity of the
sample.

At $t=700$ s, the sample display for the first time a structure at the micro
scale: a network of correlation length $\xi\simeq 7$ $\mu$m (Fig. 5a). The
colloid trajectory $r(t)$ is more compact (Fig. 6a). The mean square
displacement behave as a power law of time $\langle\Delta
r^{2}\rangle\sim\Delta t^{0.6}$. $G^{\prime}$ and $G^{\prime\prime}$ are power
law of the frequency, parallel and equal to one another. This behavior is very
close to the behavior of a dispersion at the gel point as defined by Chambon
and Winter Chambon and Winter (1987). We note that the time at which the
dispersion structure at the microscale $t^{*}$ coincides with the gelation
time $t_{g}$ defined by Chambon and Winter, $t_{g}=t^{*}$. Given that $t_{g}$
is measured with a precision of 50 s and $t^{*}$ of one second, we selected
the structure measurements rather that the microrheology measurement to define
$t_{g}$.

At $t=$1100 s, the structure is very similar to the one observed at 700 s.
However, the tracers dynamics become different. Indeed, the colloid’s
trajectories $r(t)$ display dynamical heterogeneities: a colloid spends some
time at a specific location before jumping to another location. In other
words, a colloid is mildly trap by the network and explore a small region for
a characteristic time before the sample rearrange and let the colloid escape
to another location where it is again trapped, and so on. The associated
$\langle\Delta r^{2}\rangle$ shows at small $\Delta t$ a diffusive behavior,
Fig. 6b. At intermediate $\Delta t\simeq 1$ s, $\langle\Delta r^{2}\rangle$
reaches a plateau around $2.10^{-3}$ $\mu$m2: the colloid is confined to
region of average size of $0.045~{}\mu$m. At long $\Delta t$, the colloid
diffuse again. This scenario is typical of viscoelastic fluids Stokes and
Frith (2008) as corroborated by Fig. 6c. At high frequencies (short $\Delta
t$), $G^{\prime\prime}>G^{\prime}$ and $G^{\prime\prime}\sim f$ the sample is
fluid and the energy is dissipated in the thermal vibration of the sample. At
intermediate frequencies (intermediate $\Delta t$) $G^{\prime}\sim
G^{\prime\prime}$ the sample is mildly elastic. At small frequencies (large
$\Delta t$), $G^{\prime}<G^{\prime\prime}$, the sample can rearrange itself
and is therefore fluid.

At $t=1300$ s, the sample kept its micro structure, with a correlation length
$\xi\simeq 7$ $\mu$m but the network is more contrasted, Fig. 5b. The colloid
trajectory is now very compact: the colloid is trapped to a single location by
the network, Fig. 6a. The associated $\langle\Delta r^{2}\rangle$ shows a
diffusion process at short time scales and then a plateau at long time scales,
Fig. 6b. This behavior is typical of viscoelastic solids Stokes and Frith
(2008); Gibaud  _et al._ (2020), Fig. 6d. At high frequencies $f$, just like
the viscoelastic fluid, $G^{\prime\prime}>G^{\prime}$, the sample dissipate
energy due to the thermal vibrations of the network against the background
solvent, but at intermediate and small frequencies $f$, $G^{\prime}$ dominates
$G^{\prime\prime}$ and $G^{\prime}$ plateaus to $G^{\prime}\simeq 0.3$ Pa: The
sample cannot rearrange on long time scales and is as such an elastic solid.
$G^{\prime}\simeq 0.3$ Pa is a very low value of elasticity. For such a value,
the gel would probably flow due to its own weight if put in an incline vial.

Figure 7: Gelation – scaling behavior of the mean square displacement
$\langle\Delta r^{2}\rangle$ for $t<t_{g}$. (a) $\langle\Delta r^{2}\rangle$
as a function of $\Delta t$ rescaled by $b$ and $a$ respectively. The colored
rescaled series correspond to the data presented in Fig.6b with the same color
code. The black lines correspond to rescaled data for other photo-activation
conditions ($P,t_{i}$), namely: (6%, 180 s), (12%, 180 s) and (25%, 180 s).
Inset – Evolution of the scaling parameters $a$ (circle) and $b$ (square) as a
function of the normalized time $(t-t_{g})/t_{g}$. $t_{g}$ is defined by
$t_{g}=t^{*}$. Large symbols correspond to the photo-activation conditions
$t_{i}=120$ s and $P=100\%$ and the smaller symbols correspond to the other
photo-activation conditions. Lines are power law fits to the data:
$a\sim[(t-t_{g})/t_{g}]^{y}$ with $y=3.0\pm 0.3$ and
$b\sim[(t-t_{g})/t_{g}]^{z}$ with $z=1.8\pm 0.2$.

The time-resolved microrheology data displayed in Fig. 6b are reminiscent of
Larsen and Furst work on gelation Larsen and Furst (2008). These authors have
indeed studied the viscoelastic properties of physical and chemical polymer
gels and focused on the sol-gel transition using time resolve microrheology.
They showed that the mean square displacements of their colloidal tracers
embedded in the dispersion could be scaled on a master curve. This is also the
case for our data provided that $t<t_{g}$. As shown in Fig.7, the master
curves is constructed by shifting individual $\langle\Delta r^{2}\rangle$
curves along the ordinate and abscissa. Starting from the initial diffusive
dynamics, subsequent $\langle\Delta r^{2}\rangle$ curves are divided by a
time-shift factor $a$ and a mean square displacement shift factor $b$. The
resulting master curve has a logarithmic slope $\alpha=d\ln(\langle\Delta
r^{2}\rangle)/d\ln(\Delta t)=$1 for $\Delta t/a>1$, which decreases
monotonically to a value $\alpha\simeq 0.6$ with decreasing $\Delta t/a$. At
this point, subsequent curves can no longer be scaled onto this initial master
curve.

For $t>t_{g}$, our data cannot be mapped on a master curve due to the
dynamical heterogeneities displayed by the colloidal tracers.

Such dynamics, involving hopping processes, is reminiscent of behaviours
monitored with more complex soft solids like food gels mainly composed of
proteins, polysaccharides and lipids Moschakis (2013) or laponite gel/glasses
Oppong  _et al._ (2008). Those dynamical heterogeneities have been inputted to
micro structural features in the gel on length scales comparable to the probe
particle sizes Gardel  _et al._ (2005); Rich  _et al._ (2011). Here, this is
exactly the case: the colloid of diameter 5 $\mu$m and the gel correlation
length $\xi\simeq 7$ $\mu$m are about the same size. These sponge-like network
structure creates a gel backbone of relatively high supra-molecular density
and regions where the supra-molecules have been depleted, resulting in a
porous network.

Based on our observations and those of previous authors, we propose the
following scenario for the evolution of the microstructure and the micro-
rheology data for the gelation conditions, $P=100$ % during $t_{i}=120$ s. In
the early stage of the kinetics, the dispersion is homogeneous at the
microscopic scale: the macro molecules are randomly distributed throughout the
medium and diffusing freely. However, as the macro molecules diffuse, they
move closer and get bound to one another through non covalent attractive
interactions. These macro molecules chains grow extensively over time and
eventually some span the container: this percolation characterizes the bulk
gelation time. The hallmark of the gel point in rheology is defined by Chambon
and Winter as the time when both moduli $G^{\prime}$ and $G^{\prime\prime}$
exhibit approximately the same power-law frequency dependence $G^{\prime}\sim
G^{\prime\prime}\sim f^{n}$ where $n=0.5$ Chambon and Winter (1987). Moreover,
near the gel point, the longest relaxation time and creep compliance are
expected to exhibit power-law behavior so that $a\sim[(t-t_{g})/t_{g}]^{y}$
and $b\sim[(t-t_{g})/t_{g}]^{z}$ with $n=y/z$ Adolf and Martin (1990). For our
sample, the gel point is at $t=t_{g}\simeq 700$ s with $n=0.6$, a slightly
higher value than the one proposed proposed by the model in Chambon and Winter
(1987). The measured critical exponents $y$ and $z$ are respectively equal to
$y=3.0\pm 0.3$ and $z=1.8\pm 0.2$ and lead to $n=0.60\pm 0.12$. Those values
are self-consistent and informs us about the gelation mechanism. Indeed, our
critical exponents are compatible with de Gennes Stauffer percolation model
for gelation De Gennes (1976); Stauffer (1976) which leads to $y=2.69$ and
$z=1.94$ but incompatible with Rousse or Zimm theory Martin  _et al._ (1988)
which leads respectively to ($y=4,z=2.67$) and ($y=2.67,z=2.67$).

For $t>700~{}s$, the structure is set and forms a sponge-like network with a
correlation length, $\xi\simeq 7$ $\mu$m. This is not the case for the
mechanical properties. Indeed the sample is still mostly viscous and the
colloidal probes diffuse with only slight hindrance. As the microstructure
densify and becomes more elastic for $t=700-1100$ s, the sample is a
viscoelastic fluid: the colloidal probe show dynamical heterogeneities and the
colloid is trapped within the structure at intermediate time scale but diffuse
on long time scales. At the end of the kinetics, for $t>1200$ s the gel
backbone is sufficiently elastic to hinder dynamical heterogeneity and the
colloid probe the gel elasticity namely $G^{\prime}\simeq 0.3$ Pa at
relatively low frequencies, $f\simeq 0.1$ Hz.

##  IV Discussion and conclusion

In summary, we have shown that depending on photo-activation conditions,
starting from a well dispersed suspension in fluid state, we can tune the
self-assembly of viologen based molecular building blocks into aggregates or
gels. Those results are compatible with a physical pathway that involves an
interplay between phase separation and dynamical arrest. We hypothesize that
the irradiation conditions allows to tune the attraction intensity between the
building blocks as shown in Fig. 8. In other words, long and high power
irradiation of the sample leads to the formation of interchain dimers causing
a reinforcement of the interactions.

Figure 8: Schematic state diagram illustrating the physical pathway leading to
aggregation and gelation. State diagram as a function of the attraction
between the building blocks and the concentration of the building blocks. The
red line corresponds to the binodale line, the orange line to the spinodal
line, the dash green line to the glass line, the horizontal green line to the
separation between the phase separation and the arrested phase separation. The
black arrows correspond to the physical pathway taken by the system and
leading from a fluid state to the aggregates or the gel state.

Gelation is a commonly observed phenomena in polymers and in supramoculer
assemblies Brinker and Scherer (2013). It occurs for example when the
molecular building blocks aggregate to form a space spanning network. In our
system gelation occurs for large irradiation power or irradiation, namely when
the attraction between the building block becomes strong. The gel formed is
very peculiar as it displays a very large correlation length $\xi$, a few
order of magnitude larger than the size of the individual building blocks.
Such a very large correlation length $\xi$ vouch for a very specific gelation
mechanism: an arrested phase separation. In this scenario, the very large
correlation length $\xi$ arises from density fluctuations in the vicinity of a
critical point. At sufficiently high attraction and concentration in
$\pi$-dimers, the dispersion undergo spinodal decomposition leading to
bicountinuous network composed of a dilute and a concentrated fluid phase.
Usually the spinodal decomposition proceeds and leads to the coexistence of
two homogeneous fluid phases separated by an interface. There is however a
sweet spot where the glass transition mingle with the spinodal decomposition
and leads to gelation, Fig. 8. In this scenario, the concentrated phase
becomes denser and meets the glass line, it becomes kinetically arrested and
freezes the phase separation process leading to a gel with a large correlation
length $\xi$ Gibaud and Schurtenberger (2009); Gibaud  _et al._ (2012).

In our system, aggregation occurs for low irradiation power or time, namely
when the attraction between the building blocks is mild. At the molecular
level it might be explained by the lower concentration of $\pi$-dimers leading
to supramolecular structures 3 or 4 having less inter-molecular interactions
(Fig. 1). As shown in Fig. 8, this quench lead us in a region of the state
diagram embedded between the binodal line and the spinodal line. In this
region, phase separation proceed through the formation of isolated droplets
composed of a dense fluid in background compose of a dilute fluid phase.
Usually the phase separation proceeds and leads to the coexistence of two
homogeneous phase fluid separated by an interface. Here, as for the arrested
spinodal decompositon, as the concentration of the droplet increases and reach
the glass line, the phase separation is stopped leading to isolate aggregate
as observed experimentally.

We also observe that the aggregates display a spindle-like structures. This
structure is typical of liquid-crystal dispersion and corresponds to the
hallmark of the Isotropic-Nematic transition Modlińska  _et al._ (2015);
Gibaud (2017). The Isotropic-Nematic transition is a phase separation and
therefore is compatible with the arrested phase separation scenario. It
however deals with liquid-crystal molecular systems; i.e. rod-shaped
molecules. The spindle-like structures are called tactoids and correspond to
Nematic droplets composed of elongated molecules that tend to point in the
same direction but do not have any positional order. The spindle-like shape
results from the molecules orientation and the interplay between the
interfacial tension and the splay and bend elastic constants of the nematic
domain Tortora and Lavrentovich (2011). In viologen-based molecules, liquid-
crystal phase have recently been observed Casella  _et al._ (2014, 2016);
Pibiri  _et al._ (2019). However tactoids have not been reported maybe due to
their transient nature. We tried to check for a birefringent signature of our
spindle-like structure under cross-polarisation microscopy but fail due to the
opacity of the structure. At this point, our best guess is that the molecules
self-assemble into liquid-crystal due to the photo-induced formation of 3
presenting an appropriate rod-shaped structure. Following this hypothesis,
these more rigid structures could then form tactoids due to inter-molecular
interactions with adjacent boxes by orbital overlap involving more than two
viologen radical-cations as already reported Wang  _et al._ (2016); Qi  _et
al._ (2016). Metal-metal interaction between palladium complexes might also be
at stake.

To conclude, thanks to time resolved experiments such as the microstructure
analysis via microscopy and the mechanical properties analysis via
microrheology, we were able to propose a unique physical pathway leading to
both aggregation and gelation. This pathway is driven by an arrested phase
separation. Such a scenario is new to supramolecular systems but has already
been observed in colloidal dispersions Lu  _et al._ (2008), polymers Glassman
and Olsen (2015) and proteins solutions Cardinaux  _et al._ (2007). It opens
up new perspectives in the field of viologen-based responsive supramolecular
gels Datta  _et al._ (2017); Dhiman  _et al._ (2020); Wei  _et al._ (2017); Xu
_et al._ (2018); Zhang  _et al._ (2013). This work provides a physical
analysis of a highly complex chemical system. The chemical evolution in terms
of interactions and reactions pathway remains to be elucidated and compared to
the physical pathway proposed in this article. Indeed the influence of many
parameters remains to be addressed and will be the subject of a subsequent
article: exact structures of supramolecular self-assemblies (box, folded
chain, inter-chain $\pi$-dimers), nature of the supramolecular interactions
involved (orbital overlap of viologen radical-cations, metal-metal bonds),
solubility and electrostatic effects of the charged building blocks.

## Acknowledgements

The authors thank the Ecole Normale Supérieure de Lyon (ENSL) and the Centre
National de la Recherche Scientifique (CNRS) for financial, logistical and
administrative supports. C. Roizard thanks ILM and IDEXLYON for the COLUMN
internship grant. This work was supported by the LABEX iMUST
(ANR-10-LABX-0064) of Université de Lyon, within the program ”Investissements
d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency
(ANR).

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