# Onset of slow dynamics in dense suspensions of active colloids

Antina Ghosh1, Sayan Maity1, Vijayakumar Chikkadi1 1 Indian Institute of
Science Education and Research Pune, Pune 411008, India

###### Abstract

Slow relaxation and heterogeneous dynamics are characteristic features of
glasses. The presence of glassy dynamics in nonequilibrium systems, such as
active matter, is of significant interest due to its implications for living
systems and material science. In this study, we use dense suspensions of self-
propelled Janus particles moving on a substrate to investigate the onset of
slow dynamics. Our findings show that dense active suspensions exhibit several
hallmark features of slow dynamics similar to systems approaching equilibrium.
The relaxation time fits well with the Vogel-Fulcher-Tamman (VFT) equation,
and the system displays heterogeneous dynamics. Furthermore, increasing the
activity leads to faster relaxation of the system, and the glass transition
density predicted by the VFT equation shifts to higher densities. The
measurement of the cage length and persistence length reveal they are of the
same order over the range of activities explored in our study. These results
are in agreement with recent particle simulations.

##  I Introduction

When molecular liquids are cooled, their timescales of structural relaxation
increases. If we avoid crystallization by employing rapid cooling rates, most
liquids fall out of equilibrium to enter a metastable phase of supercooled
liquids. Subsequently, they form glasses at temperatures lower than the glass
transition temperature $T_{g}$ [1, 2]. A similar phenomenon occurs in Brownian
colloidal suspensions, where the colloidal glass transition is controlled by
the particle density [3, 4, 5, 6]. As density increases, particle motion
becomes increasingly hindered by the cages formed by neighboring particles,
leading to a slowdown in dynamics. In recent years, the emergence of slow
dynamics in active matter has garnered considerable attention due to its
relevance to living systems [7]. For instance, the collective motion of cells
in tissues during embryo development [8], wound healing [9], and cancer
metastasis exhibits glass-like features such as slow relaxation and
heterogeneous dynamics [10, 11]. Bacterial cell cytoplasm shares several
properties with glass-forming liquids [12]. A central question in these
investigations is whether systems driven far from equilibrium display slow
glassy dynamics and how does it compare to systems close to equilibrium [13].
In this article, we shed new light on some aspects of slow dynamics in dense
active matter by performing experiments using a monolayer of active colloids.

Self-propelled particles have served as model systems for understanding
various aspects of dense active matter [14, 15]. They have been studied
extensively in simulations using two well-established models of active
Brownian particles (ABPs) [16, 17] and active Ornstein-Uhlenbeck particles
(AOUPs) [18, 19]. In these models the particles undergo overdamped motion in a
viscous fluid, and their self-propulsion is described using a force that
remains either constant or evolves over time. In the dilute limit, both models
depict a persistent random walker, with the mean-square displacement (MSD)
given by: $\left<\Delta
r^{2}(t)\right>=6Tt+6T_{a}\left[\tau_{p}(e^{-t/\tau_{p}}-1+t)\right]$, where
$T$ represents the thermodynamic temperature, $T_{a}$ is the active
temperature, and $\tau_{p}$ is the persistence time of the random walker [20].
The active temperature $T_{p}=f^{2}\tau_{p}/3$ for ABPs. In the limit of short
times when $t<<\tau_{p}$, the MSD $\left<\Delta r^{2}(t)\right>\approx
6Tt+3T_{a}t^{2}/\tau_{p}$, indicating a quadratic dependence on $t$ due to
ballistic motion. However, in the limit of long times $t>>\tau_{p}$, the MSD
$\left<\Delta r^{2}(t)\right>\approx 6(T_{a}+T)t\equiv 6T_{eff}t$, which
increases linearly with $t$, highlighting diffusive motion. These dilute-limit
predictions were first confirmed by Howse and coworkers [20] and have since
been validated by other experiments using colloidal models [21, 14, 22].

Investigations into active matter systems at high densities and the onset of
slow dynamics have primarily focused on theoretical models and numerical
simulations. The earliest studies [23, 13, 24] revealed that slow dynamics in
active systems exhibit all the essential features of supercooled liquids
approaching an equilibrium glass transition. These features include caging,
dynamical slowing down, non-exponential time correlation functions, and
dynamic heterogeneity. Particle simulations of active systems based on hard-
sphere models have demonstrated a monotonic effect of activity, showing that
an increase in activity pushes the glass transition to higher densities [23,
24]. However, subsequent simulations using Lennard-Jones potentials, which
include an attractive component, revealed a non-monotonic effect of activity.
In these simulations, activity could either enhance or suppress the
fluidization of the system [25, 26, 27]. Further simulations conducted by
Berthier and coworkers [28], using a model that allowed continuous
interpolation from hard-sphere-like repulsive interactions to Lennard-Jones-
type models with an attractive component, clarified the contradictory effects
of activity. In the hard-sphere limit at low temperatures and moderate
densities, activity had a monotonic impact on the relaxation time of the
system, leading to faster relaxation with increased activity. However, at
moderate temperatures and high densities (resembling Lennard-Jones models),
activity exhibited a non-monotonic impact on relaxation. This study showed
that interparticle interactions and the structure changes induced by activity
have a significant influence on the onset of slow glassy dynamics. A recent
study[29] identified that the long-time diffusion constant increases with
increasing persistence time when it is small compared to the cage length. An
opposite effect is observed when the cage length is smaller than the
persistence length. Active glasses are reported to display other interesting
features, including multiple aging regimes for highly persistent forces [30,
31], and tunable fragility due to doping of active particles in passive
glasses [26].

Experimental investigations of this topic are scarce. The earliest
experimental reports of glassy dynamics in active matter involved living
systems consisting of tissues [8, 9, 10, 11]. As far as synthetic systems are
concerned, a recent study [32] reported the role of topological defects and
the re-entrant effect of activity in dense active matter consisting of
granular ellipsoidal particles. The only experimental study with colloidal
spheres was conducted by Klongvessa and co-workers [33, 34], where they
reported a non-monotonic influence of activity on the dynamics of the system.
Their primary findings were that increasing activity leads to faster
relaxation in an ergodic state at lower densities. However, in a non-ergodic
state at higher densities, activity shows a non-monotonic effect on relaxation
time. Initially, relaxation time increases with higher activity levels, but
decreases again at higher activity intensities. The platinum-coated gold
colloids used in their study exhibit characteristics similar to soft
particles, such as poly(N-isopropyl acrylamide) (PNiPAM) microgel particles
[35]. It is important to clarify whether these conclusions apply generically
to quasi-hard particle systems. Recent simulations [29, 36] suggest that the
relative sizes of the cage and the persistence length of active particles
critically influence the activity’s impact. However, these numerical results
lack experimental validation. Furthermore, the nature of slow dynamics in
quasi-hard particle systems remains to be explored.

In this article, we present an experimental investigation of the onset of slow
relaxation in a dense layer of photoactive colloids. The strength of activity
is varied by tuning the intensity of UV light. In the absence of activity, the
relaxation time of the system increases monotonically, suggesting quasi-hard
particle nature of our system. Our experiments reveal a monotonic effect of
activity on the relaxation time over the range of densities and activities
studied in our experiments. Increasing the activity leads to faster
relaxation. The relaxation time over a range of densities and at various
magnitudes of activity is well described by a Vogel-Fulcher-Tamann (VFT)
relation. The glass transition densities obtained from the VFT fits reveal
that increasing the activity shifts the glass transition density to higher
values. The examination of structural changes and length-scale of cooperative
motion due to activity point to faster relaxation due to activity. The
investigation of the ratio of cage size and persistence length due to activity
reveals that our results are in agreement with simulation results [23, 29,
28].

##  II Experimental systems

The active colloids in our experiments are light-driven, self-propelled Janus
particles composed of SiO_2 and anatase TiO_2 halves [37]. The details of the
experimental methods followed is given in the supplementary information. To
obtain amorphous configurations, we have used a binary mixture of particles
with diameters of $\sigma_{s}=2.64~{}\mu m$ and $\sigma_{l}=3.12~{}\mu m$. The
ratio of small to large particles in our system is in the range 2:1, and all
the analysis was performed using small particles. The Fig.1a shows an image of
the dense monolayer of the particles that was obtained by sedimenting
particles in a circular cavity of $30\mu m$ thickness, fabricated using
photolithography techniques. The diameter of the circular cavity is $150\mu
m$. An array of such cavities was created to study the systems over a range of
densities. The particles only in the central region or in the unshaded region
were considered for analysis to prevent the influence of walls. When the Janus
particles are dispersed in an aqueous hydrogen peroxide solution (H_2 O_2
$3\%$, pH$\sim 7$), they display passive Brownian diffusion in the absence of
UV light. However, upon illumination of UV light of wavelength $365~{}nm$ the
Janus colloids show self-propulsion giving rise to ballistic motion on short
time scales and a diffusive motion on long time scales. The propulsion arises
from the photocatalytic decomposition of H_2O_2 at the TiO_2 surface by UV-
promoted electron–hole pairs [38, 37]. Since the rate of photocatalytic
decomposition near the TiO_2 surface depends on the intensity of light, the
velocity of Janus particles increases with UV power. The details about these
aspects are provided in the supplementary information. The rotational
diffusion time of the particles is $\tau_{R}\sim 3s$, which was measured from
the MSD of particles (see supplementary information). The UV power is varied
in our experiments to obtain velocities in the range of $0.05\mu m/s$ to
$0.2\mu m/s$. The strength of activity in our study is expressed using an
effective temperature, $T_{eff}$, see supplementary information for details.
The density of particles is represented by the area fraction $\phi\sim
N\pi\sigma^{2}/4A$, where A is the area of the field of view.

Figure 1: Relaxation of passive Brownian system in the absence of activity,
corresponding to $\frac{T_{eff}}{T_{0}}=1$. (a) A bright-field image of
circular cavity with binary colloids. The diameter of the cavity is $\sim
150\mu m$ and it’s depth is $\sim 30\mu m$. The particles in the unshaded
region of diameter $90\mu m$ are considered for analysis. (b) Self part of the
intermediate scattering function $F_{s}(k,t)$, where $k=2\pi/\sigma_{s}$, over
a range of area fractions of the colloidal particles from $\phi\sim
0.55-0.72$. The x-axis is scaled by the rotational diffusion time scale
$\tau_{R}$. (c) The relaxation time $\tau_{\alpha}$ is plotted as a function
of the area fraction of colloidal particles. The thick line is a fit to the
data of the form .

##  III Onset of slow dynamics in the absence of activity

When the density of system is small, the particles diffuse freely and the
relaxation is fast. With increasing density, the particles motion is hindered
due to the cage formed by nearest neighbors, leading to the onset of slow
dynamics in the system. The dynamics of particles within the cage and the
their escape from it is well captured by the self part of the intermediate
scattering function, $F_{s}(k,t)$, given by

$F_{s}(k,t)=\left<\frac{1}{N}\sum_{i=1}^{N}\textnormal{exp}\left[j\textbf{k}\cdot\Delta\mathbf{r}_{i}(\tau)\right]\right>,$
(1)

where the $k=2\pi/\sigma_{l}$ and $\Delta\mathbf{r}(\tau)$ is the cage-
relative displacement [39] defined with respect to $N_{i}$ nearest neighbors
in the following way:

$\Delta\mathbf{r}_{i}(\tau)=\mathbf{r}_{i}(t+\tau)-\mathbf{r}_{i}(t)-\frac{1}{N_{i}}\sum_{i}^{N_{i}}[\mathbf{r}_{j}(t+\tau)-\mathbf{r}_{j}(t)].$
(2)

Previous studies [39, 40] have demonstrated long-wavelength fluctuations in
two-dimensional disordered colloidal systems leading to large particle
displacements without neighbor changes. Investigating the relative
displacement of particles relative to their first neighbors provided a
consistent understanding of the relaxation dynamics and the glass transition
in both two and three dimensions. Therefore, the displacements in our study
are computed relative to their first nearest neighbors, which we refer to as
relative displacements in the rest of the article. The main panel of Fig.1b
presents the $F_{s}(k,t)$ computed using relative displacements over a range
of area-fractions from $\phi\sim 0.55-0.72$ in the absence of activity, which
is due to Brownian motion. The slowing down of the dynamics is apparent from
the slower decay of $F_{s}(k,t)$ with increasing density. The relaxation time
scale $\tau_{\alpha}$ is estimated from the time taken for $F_{s}(k,t)$ to
decay by a factor of $1/e$. It is shown as a function of the area fraction of
colloids in Fig.1c. The thick line in the figure shows a Vogel-Fulcher-Tamann
fit of the form
$\tau_{\alpha}=\tau_{R}~{}\textnormal{exp}\left[\frac{A}{(\phi_{c}-\phi)}\right]$,
$\phi_{c}$ is the critical area-fraction where $\tau_{\alpha}$ diverges. The
best-fit procedure yields a critical density of $\phi_{c}=0.79\pm 0.012$,
which reasonably agrees with earlier simulation studies [41]. The non-
exponential relaxation of density correlation is apparent from the form of
$F_{s}(k,t)$, and it arises from the multiple relaxation time scales of the
system. To confirm the onset of slow glassy dynamics in our system, we have
tested for the signatures of aging at $\phi\sim 0.72$ and $0.55$, the two
extreme densities in our study. The mean square displacement (MSD) of
particles was plotted for different waiting times. The dynamics were found to
be dependent on the waiting time at $\phi\sim 0.72$, while at $\phi\sim 0.55$,
the MSD curves overlapped on each other. See supplementary information for
details. These results establish the onset of glassy dynamics at higher
densities in our system.

Figure 2: Relaxation of active systems. (a)The self part of the intermediate
scattering function $F_{s}(k,t)$ at various effective temperatures ranging
from $\sim 1-4.44$, and at two different area fractions $\phi\sim 0.72$ and
$\phi\sim 0.55$. Different marker symbols are used to distinguish the
effective temperatures, and the colors distinguish area fractions. (b) The
relaxation time $\tau_{\alpha}$ of the system is presented as a function of
area fraction of colloids at various effective temperatures. The marker
symbols indicate experimental data and the thick lines are the VFT fit to the
curves. (c) The critical area fraction $\phi_{c}$ obtained from the fits in
(b) is shown as a function of the effective temperature $T_{eff}$.

##  IV Influence of activity on the dynamics

We present the influence of activity on the dynamics of the system in this
section. As discussed earlier, the activity of our systems is quantified using
an effective temperature and it is controlled by the intensity of UV light.
The effective temperature is varied from $T_{eff}\sim 1-4.4$, and the
intermediate scattering function $F_{s}(k,t)$ show in Fig.2a at $\phi\sim
0.72$ and $0.55$ reveals a monotonic decrease of the relaxation time
$\tau_{\alpha}$ with increasing activity. What is also apparent is that the
activity has a stronger effect at $\phi\sim 0.72$ compared to $\phi\sim 0.53$.
The relaxation time $\tau_{\alpha}$ decresases by a factor of $3$ at $\phi\sim
0.72$. We next present the effect of activity over a range of area fractions
for various effective temperatures in Fig. 2b. The lines show a VFT fit to the
curves. The fit provides an estimate of the critical density $\phi_{c}$ where
$\tau_{\alpha}$ diverges. We plot $\phi_{c}$ as a function of the effective
temperature $T_{eff}$ in Fig.2c. Clearly, the critical area-fraction
$\phi_{c}$ is pushed to higher densities with increasing activity over the
entire range of the area fractions and activities investigated in our
experiments. These results are in agreement with simulations of active
particles performed using hard-sphere like interactions [23]. Unlike earlier
experiments [33, 34] using Janus colloids as active particles, which showed a
non-monotonic variation of relaxation times $\tau_{\alpha}$ due to activity in
the nonergodic states, our experiments reveal a monotonic variations over the
range of effective temperatures explored in our experiments. These results
highlight the fact that interparticle interactions play a significant role
when the effect of activity is considered on the onset of slow dynamics.

Figure 3: Structural changes due to activity. The pair correlation function
$g(r)$ of the system at different effective temperatures is presented at
$\phi\sim 0.72$ (a) and $\phi\sim 0.55$ (b). The insets show a magnified view
of the first peak.

##  V Structural changes due to activity

###  V.1 Pair correlation function

In this section, we investigate the effect of activity on the structure. We
elucidate the effect of activity by computing the pair correlation function of
small particles in the system,

$g_{\alpha\beta}(r)=\frac{A}{N_{\alpha}N_{\beta}}\left<\sum_{i}^{N_{\alpha}}\sum_{j\neq
i}^{N_{\beta}}\delta(r-|\mathbf{r}_{i}-\mathbf{r}_{j}|)\right>\\\ $ (3)

where the $N_{\alpha}$ and $N_{\beta}$ is the number of particles of different
species. Only small particles were considered for all the calculations, so we
denote $g_{ss}(r)$ simply as $g(r)$. The Fig.3a presents $g(r)$ for different
effective temperatures at $\phi\sim 0.72$. The effect is apparent from the
variations in the height and position of the peaks. A magnified view of the
first peak in the inset shows a decrease in the height of the peak with
increasing activity. Even though the changes are small, there is a systematic
variation due to activity. Similar changes are observed in the second peak
too. All these observations point to restructuring of particles to achieve
higher diffusivity in the system. The main panel in Fig.3b presents the
changes in $g(r)$ due to activity at a lower area fraction of $\phi\sim 0.55$.
The corresponding inset presents a magnified view of the first peak. The
variations in peak height appear to be smaller. A comparison of the changes in
the Figs.3a and 3b suggests that the effect of activity on the structure is
pronounced at higher densities.

Figure 4: Effect of activity on the local hexagonal ordering. (a) & (b)
Snapshots of the local hexagonal order of particles at an area fraction of
$\phi\sim 0.72$ and varying effective temperatures. The particles are color
coded based on their value of $\psi_{6}$, and the panels in (a) and (b) are at
effective temperatures $T_{eff}=1.0,\textnormal{ and }4.44$, respectively. (c)
The main panel shows the average $\psi_{6}$ as a function of $T_{eff}$ at area
fractions $\phi\sim 0.72$ and $0.55$. Different symbols are used to
distinguish the area fractions. The inset is the histogram of $\psi_{6}$ at
$\phi\sim 0.72$ and $T_{eff}=1$.

###  V.2 Local ordering of particles

We continue our investigation of the effect of activity on the structure by
studying the local ordering of particles. In particular, we quantify the
hexagonal order using local bond-orientational order parameter [42] defined
as,

$\psi_{6}^{i}=\frac{1}{6}\sum_{j=1}^{N_{f}}\textnormal{exp}(i6\theta_{ij}),$
(4)

where $N_{f}$ is number of first nearest neighbors and $\theta_{ij}$ is the
angle made by the bond between particles $i$ and $j$ with the $x-$axis. The
local $\psi_{6}$ calculation were done using all kinds of particles. A color
coded representation of local ordering is shown in Fig.4a and Fig.4b, where
the particles are colored based on their $\psi_{6}$ values at $\phi\sim 0.72$
and $T_{eff}=1.0$ and $4.44$, respectively. Red color indicates crystal-like
hexagonal order and blue color indicates its absence. The presence of ordered
patches are apparent and it appears to diminish with increasing activity in
Fig.4a and Fig.4b. For a better understanding, a distribution of $\psi_{6}$ is
shown in Fig.4c at $\phi$ and $T_{eff}$. Note that symbols are used to
distinguish the activity and colors identify the area-fraction $\phi_{s}$. The
peak of distribution $P(\psi_{6})$ shifts to smaller values of $\psi_{6}$ with
increasing activity. This effect is also clear from the inset of Fig.4c, which
shows the mean of the distributions as a function of activity ($T_{eff}$).

Figure 5: Displacement fields and correlations that characterize spatially
heterogeneous dynamics in dense systems of active colloids. The displacement
vectors of particles are computed over a time scale $\tau_{\alpha}$ for
$\phi\sim 0.72$ at $T_{eff}=1$ (a) and $T_{eff}=4.44$ (b). (c) The
displacement correlations for $\phi\sim 0.72$ are shown at various effective
temperatures $T_{eff}$ in the main panel. The inset shows the correlation
lengths $\xi$ extracted from the correlation functions in the main panel.

##  VI Spatially heterogeneous dynamics

One of the hallmark features of passive super-cooled liquids and passive
glasses is the spatially heterogeneous dynamics [43]. This means the mobility
of particles differs significantly from one region to another region of the
system, leading to clusters of slow and fast moving particles. The increase in
the relaxation time of system with increasing density is related is attributed
to the growth of length-scales of cooperative motion in the system . We
analyze the effect of activity on the cooperative motion in our system by
computing equal time displacement correlations,

$C(r)=\frac{\left<u_{i}u_{j}\right>-\left<u_{i}\right>\left<u_{j}\right>}{\left<u^{2}\right>},$
(5)

where $u$ is the displacement of the particle, i and j denote particle
indices, and the angular brackets denote averaging over all particles and
several instances. The correlations $C(r)$ are dynamic, they depend on the
time scale of observation used for determining the displacements [44, 45].
Simulation and experiments have shown that the dynamic correlations are
optimal when the time scale of observation equals the relaxation time
$\tau_{\alpha}$. So, the relaxation time $\tau_{\alpha}$ obtained from the
intermediate scattering function $F_{s}(k,t)$ (Eq.1) is used to determine the
displacements $u_{i}$. We first discuss the effect of activity on the
displacement correlations in the denser system, which is at $\phi\sim 0.72$.
The Figs. 5(a) and 5(b) are snapshots of the displacement vectors at
$T_{eff}=1.0\textnormal{ and }4.44$, respectively. The displacements vectors
suggest that the motion of particles is correlated over longer distances at
$T_{eff}=1$ when compared to the displacements at $T_{eff}=4.4$. To quantify
these observations, we compute their correlations $C(r)$ and extract a length
scale $\xi$ that characterizes the distance over which the motion is
correlated. These results are presented in Fig. 5(c) for $\phi\sim 0.72$ and
various effective temperatures ranging from $T_{eff}=1-4.44$. The correlations
$C(r)$ are long-ranged at $T_{eff}=1$ as the correlations reveal a power-law
decay extending to $20-30\sigma$. This also confirms that the onset of slow
dynamics in the system at higher densities. As the activity increases, the
correlations decay faster and they display an exponential decay at
$T_{eff}=4.4$. We extract a length scale of the correlated motion by fitting
the correlations using a function of the form
$C(r)\sim(1/r)~{}\textnormal{exp}(-r/\xi)$, where $\xi$ is the correlation
length. The best fit method yields length scales $\xi$ that diminishes with
increasing activity, which is shown in the inset of Fig. 5c. Clearly, the
activity has a strong effect on the length scales of cooperative motion. These
observations are similar to the effect of activity on the relaxation time of
the system presented in Fig.2a.

Figure 6: Displacement of particles and their spatial correlations at
$\phi\sim 0.57$. (a) The displacements are computed over a time scale
$\tau_{\alpha}$ at $T_{eff}=1$. (c) The displacement correlations C(r) are
shown at various effective temperatures $T_{eff}$ in the main panel. The inset
shows the correlation lengths $\xi$ extracted from the correlation functions
in the main panel.

We next focus on the system at a lower area fraction of $\phi\sim 0.57$. A
snapshot of the displacement vectors of the particles are shown in Fig.6a.
Note that the displacements are computed over a time window corresponding to
$\tau_{\alpha}$ at $T_{eff}=1$. The motion of the particles appear to be
correlated over shorter distances when compared to displacement vectors in
Fig.5a. The correlations $C(r)$ in the main panel of Fig.6b indeed display an
exponential decay of the form $C(r)\sim\textnormal{exp}(-x/\xi)$. We also
observe that increasing the activity does not lead to significant changes in
the correlation length. This is consistent with the observation made in
Fig.2a, where the activity had a small effect on the relaxation time of the
system at $\phi\sim 0.57$. The correlation lengths extracted from the best fit
method is shown in the inset of Fig.6b. The length scales are considerably
small compared to high density systems.

The analysis presented in this section shows that activity has similar effects
on the relaxation timescale and cooperative length scale, both decrease with
increase in activity over the range considered in our study.

##  VII Cage size and persistence length of active particles

Recent simulations [29, 36] have pointed out the critical role of cage length
and the persistence length of active particles. The authors report an
enhancement of diffusivity due to activity when the persistence length,
$l_{p}$, is smaller then the cage size, $l_{c}$, while it is suppressed when
$l_{p}>l_{c}$. The central notion is that a particle is efficient in scanning
and escaping the cage formed by the neighbors when $l_{p}<l_{c}$. In the other
limit, ($l_{p}>>l_{c}$), it sticks to the edge of the cage, taking longer time
to escape. We test these ideas in our experiments by determining $l_{p}$ and
$l_{c}$. Following the procedure outlined in simulations [29, 36], the $l_{c}$
is the average distance of a particle from its nearest neighbors, which is
weighted by the pair correlation function $g(r)$. The other lengthscale
$l_{p}$, which is the persistence length of activity, is obtained in the
dilute limit. It is obtained from the mean square displacement data, see
supplementary information for more details. The Fig. 7 shows the ratio
$l_{p}/l_{c}$ as the activity of the systems is varied at an area fraction
$\phi\sim 0.72$. We clearly see that this ratio is of order unity, thus
underlining the importance of cage size and persistence length of active
particles.

Figure 7: The normalised persistence length ($l_{p}/l_{c}$) over a range of
activities represented by the effective temperature at $\phi\sim 0.72$. The
dotted line is a guide to the eye.

Increasing the effective temperature beyond $T_{eff}=4.44$ leads to
destabilisation of the monolayer, the particles do not sediment, especially
the small species in our binary mixture. This prevents us from studying
interesting features of active solids that manifest at large activities [46,
47]. This can be overcome using larger sized colloidal particles and the
measurements are under progress.

##  VIII Conclusions

In summary, we present a novel experimental set-up to study the onset of slow
dynamics in dense active suspensions containing photoactive Janus colloids.
The variation of relaxation timescale with increasing density in Fig.1c and
Fig.2b points to a quasi-hard particle nature of active colloids in our
system. Besides, these results reveal a monotonic effect of activity on the
relaxation of the system across the range of effective temperatures explored
in our experiments. Increasing activity leads to faster relaxation at both
high and low particle densities. This feature contrasts with the results
reported in reference [33], where the ergodic and non-ergodic states of the
system displayed different relaxation features. The variation of the
relaxation timescale ($\tau_{\alpha}$) with the density of our system is well
described by the VFT relation, and the fits indicate that the critical density
($\phi_{c}$) for the glass transition point is pushed to higher densities with
increasing activity. These results agree with those found in simulations [23].
The active system exhibits several features of passive thermal systems, such
as non-exponential relaxation, cooperative motion, and dynamic arrest.

The effect of activity on the structural ordering of the system is analyzed
using two-point density correlations $g(r)$ and local hexagonal ordering
$\psi_{6}$. The peaks of $g(r)$ move to the right with increasing activity,
while the local hexagonal ordering $\psi_{6}$ decreases. Although these
changes are small, they point to diminishing structural order due to activity.
Furthermore, the displacement correlations reveal a correlation length that
decreases with increasing activity. All these observations suggest an
enhancement of relaxation due to activity.

Recent reports based on simulations and theory [46, 48] suggest a similar
effect of activity-driven enhancement of relaxation; however, the dynamic
heterogeneity characterized using four-point correlations revealed surprising
effects of activity, the relaxation was found to be decoupled from dynamic
heterogeneity. Furthermore, simulations [47] also reveal non-linear dispersion
relation in active systems. Our experimental system motivates further
investigations along these directions.

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