|  Impact of polyelectrolyte adsorption on the rheology of concentrated
Poly(N-Isopropylacrylamide) microgel suspensions†
---|---
|  Rajam Elancheliyan,∗a Edouard Chauveau,a and Domenico Truzzolillo∗a
|  We explore the impact of three water-soluble polyelectrolytes (PEs) on the
flow of concentrated suspensions of poly(N-isopropylacrylamide) (PNIPAm)
microgels with thermoresponsive anionic charge density. By progressively
adding the PEs to a jammed suspension of swollen microgels, we show that the
rheology of the mixtures is remarkably influenced by the sign of the PE
charge, PE concentration and hydrophobicity only when the temperature is
raised above the microgel volume phase transition temperature $T_{c}$, namely
when microgels collapse, they are partially hydrophobic and form a volume-
spanning colloidal gel. We find that the original gel is strengthened close to
the isoelectric point, attained when microgels are mixed with cationic PEs,
while PE hydrophobicity rules the gel strengthening at very high PE
concentrations. Surprisingly, we find that polyelectrolyte adsorption or
partial embedding of PE chains inside the microgel periphery occurs also when
anionic polymers of polystyrene sulfonate with high degree of sulfonation are
added. This gives rise to colloidal stabilization and to the melting of the
original gel network above $T_{c}$. Contrastingly, the presence of
polyelectrolytes in suspensions of swollen, jammed microgels results in a weak
softening of the original repulsive glass, even when an apparent isoelectric
condition is met. Our study puts forward the crucial role of electrostatics in
thermosensitive microgels, unveiling an exciting new way to tailor the flow of
these soft colloids and highlighting a largely unexplored path to engineer
soft colloidal mixtures.

##

††footnotetext: a Laboratoire Charles Coulomb, UMR 5221, CNRS–Université de
Montpellier, F-34095 Montpellier, France. Tel: +33 (0)467 143589; E-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>† Electronic Supplementary
Information (ESI) available: [Intensity autocorrelation functions, normalized
time-averaged scattered intensities $I(q)/I_{0}$ and viscosimetry for dilute
bare microgel suspensions. Rheology and rheological state determination at
T=20 ∘C and varying $\varphi$ of dense microgel suspensions. Rheological
ageing of concentrated microgels at $\varphi=1.5$ and $\xi=0$. Normalized
mobilities and comparison table of electrophoretic mobilities for pure PE
suspensions, bare microgels, and PE-microgel mixtures. See DOI:
10.1039/cXsm00000x/]

##  1 Introduction

Colloid-polymer mixtures represent an ever-present paradigm for manipulation
of the microscopic dynamics and the flow properties of soft matter. They offer
unique opportunities for addressing challenges of central interest in the
field of the glass transition and the gelation of colloids. Mixtures of
neutral sub-micrometer particles and non-adsorbing linear polymers have been
investigated in the last 20 years1, 2, 3 showing that the rheology of
colloidal suspensions can be drastically changed by depletion interactions of
purely entropic nature4. By contrast the effect of adsorbing polymers on the
flow properties of colloids is much less explored. One emblematic case is the
one of mixtures of charged colloids and polyelectrolytes, two types of
macroions that are ubiquitus in nature. Polyelectrolytes (PEs) are charged
polymers whose monomer segments bear an electrolyte group that dissociate in
polar solvents. For this reason PEs are very sensitive to any electrostatic
field and to the presence of other ionic species. They are widely employed to
modify the properties of colloidal particle suspensions, membranes and solid
surfaces5, 6, and they are used in industry for many purposes ranging from
water remediation to mineral separation and to control the rheology of
particle slurries and pastes7, 8, 9, 10. PEs are also often employed to create
protective and/or functional coatings11, 12, oppositely charged multilayers13,
14 or brushes by grafting or by adsorption of block copolymers15, 16. These
coatings are employed, for example, to regulate surface properties, including
wetting, lubrication and adhesion17, 18. The properties of colloid surfaces
can be therefore remarkably changed by PEs addition and the understanding of
the relationship between PE adsorption, particle interactions, and the
stability of the resulting mixtures is crucial for the future development of
both polyelectrolyte additives and novel, soft and tunable materials.
The latter have attracted the attention of a large part of the scientific
community working in materials science, and soft colloids have proved to be
excellent constituents for their conception and designing. Soft colloids like
star polymers, microgels, micelles and vesicles, whose structure can be
tailored at the molecular level3, are indeed model building blocks for
materials with adjustable rheology and microscopic dynamics. Among them
microgels made of poly(N-isopropylacrylamide) (PNIPAm) are particularly
interesting and intensely investigated because they undergo a volume phase
transition (VPT) at ambient temperature: below $T_{c}\approx 32^{\circ}C$
these microscopic crosslinked networks are fully hydrated and swollen, while
above $T_{c}$ they collapse due to their increased hydrophobicity. PNIPAm
microgels can be synthesized using standard emulsion polymerization in aqueous
media19, and since their first synthesis 20 they showed intriguing
electrostatic properties due to the presence of the ionic initiator used to
promote chain polymerization. A drastic increase of microgel electrophoretic
mobility has been reported for $T>T_{c}$ as a consequence of the large
increase of their charge density driven by the particle collapse. This has
raised many questions on the adsorbing power of PNIPAm microgels, especially
when they are co-suspended with other charged species. In this respect, some
of the authors21 have recently pointed out the "double-faced" electrostatic
behavior of PNIPAm microgels in aqueous media. On the one hand, when microgels
are swollen and oppositely charged polyelectrolytes or nanoparticles (Np) are
progressively added, cluster formation does not occur in a wide range of PE or
Np concentrations until when eventually salting out or other non-electrostatic
effects destabilize the suspensions. On the other hand when microgels are in
their collapsed state, they strongly interact with oppositely charged PEs or
NPs, a large and sharp mobility inversion occurs and large clusters form close
to the isoelectric point, i.e., where the mobility of PE- or NP-microgel
complexes is zero. This two-fold nature of PNIPAm microgels paves the way
towards a temperature-sensitive complexation with charged polymers that might
impact many potential applications including the controlled formation of
micro-capsules 22, 23 and membranes24, gene delivery25 and water treatment
protocols7, and that might also change drastically the rheology of fluid-fluid
interfaces26. However, while the effect of polyelectrolytes21, 27, 28, 29, 30,
31 and simple ions32, 33 on PNIAPm-based microgels has been very well detailed
in literature, and both the rheology and the microscopic dynamics of
concentrated bare microgel suspensions has been thoroughly investigated 34,
35, 36, the effect of soluble PE addition in dense microgel systems and the
role played by electrostatic and non-electrostatic adsorption still remain
unknown. Only very recently mixtures of concentrated PNIAPm microgels and non-
ionic surfactants have been investigated, unveiling a very rich phase
diagram37 and leaving open the question whether electrostatics has an
important impact on the dynamics of the mixtures, especially at high
temperatures where these colloids become densely charged. In this work we want
to elucidate this aspect by studying the effect of three types of known
polyelectrolytes on the rheology of concentrated microgel suspensions, both
below and above their critical temperature. We added separately two cationic
and one anionic PEs with comparable molecular weights to suspensions of
anionic PNIPAm microgels and study their linear rheology. The PEs have been
chosen to vary both the sign of their charge and their hydrophobicity. We show
that, while jammed suspensions of swollen microgels are weakly affected by the
presence of PEs even when an apparent charge neutralization occurs, the
rheology of collapsed and hydrophobic microgels is dramatically affected by PE
addition and that both PE charge and hydrophobicity are important for the
rheology of the mixtures. Electrophoresis and transmittance measurements
allowed us to relate a large enhancement of the gel elasticity to the presence
of concomitant charge inversion and reentrant condensation of microgels
occurring in diluted suspensions. The rest of the work is organized as
follows. In Section 2 we present the materials employed, we detail microgel
synthesis and the techniques used to investigate PE-microgel mixtures. In
Section 3 we first present the result of a preliminary characterization of the
pure polymers (microgels and PEs) via electrophoresis, light scattering,
transmittance and rheology experiments. We then discuss the rheology of the
mixtures and the complementary electrophoretic and transmittance experiments
that allowed to rationalize our results. Finally, in Section 4 we make some
concluding remarks, we summarize the key results and we put forward the
perspectives of our work.

##  2 Materials and methods

###  2.1 Microgel synthesis

Poly(N-isopropylacrylamide) microgels were synthesized via emulsion
polymerization38. 150 mL of ultra-pure water was introduced in a 250 mL three-
necked flask, and degassing was carried out using vacuum/argon cycles. Vacuum
was achieved by a vane pump and the argon/vacuum sequence was repeated 6
times. Finally, argon was bubbled for 15 min. After having completed
degassing, 3 to 4 mL of the (degassed) water was withdrawn via a syringe to
dissolve 29.8 mg of the initiator (potassium peroxodisulfate, KPS – purchased
from Sigma Aldrich and used without further purification) that was added in a
later stage. Once the bubbling was stopped and the mechanical agitation was
set up (via Teflon rotating anchor), the two side necks were plugged. At this
stage 27.08 mg of Sodium Dodecyl Sulfate (SDS – purchased from Sigma Aldrich
and used without further purification) was added in the flask right before the
solution was heated up to the desired temperature ($T_{s}=70\pm 1$
${}^{\circ}C$). Once the target temperature was attained, 1.25 g of
N-isopropylacrylamide (NIPAm) (from Sigma Aldrich, used without further
purification) and 91.96 mg of N,N-methylene-bis-acrylamide (BIS) (from Sigma
Aldrich, used without further purification) were introduced into the three-
necked flask. During the heating ramp, the initiator (KPS) was dissolved in 4
mL of deionized and degassed water, and it was injected by hand slowly once
the temperature of the batch reached $T_{s}$. The mixture was left under
stirring at $T_{s}$ for 6 hours. The polymerization terminated spontaneously.
All samples have been purified via three consecutive
centrifugation/supernatant removal cycles 39, 40 and 19.5 mg (2 mM) of Sodium
Azide have been added to prevent bacterial growth.

After the purification step, the microgel suspensions were centrifugated to
get a final microgel volume fraction $\varphi=1.57$. Where $\varphi$ is the
generalized volume fraction measured via rolling-ball viscosimetry (section
2.4). We further diluted an aliquot of this sample to study the rheological
behavior of pure PNIPAm suspensions at varying $\varphi$ and to prepare
successively PE-microgel mixtures at fixed microgel volume fraction.

###  2.2 Polyelectrolytes (PEs)

Cationic Poly-(l-lysine hydrobromide) (PLL) (Mw=50 kDa) and anionic
Polystryrene sulfonate sodium salt (PSS) (Mw=43 kDa) were purchased from
Polymer Source, Inc. (Canada). Cationic polydiallyldimethylammonium chloride
(PDADMAC) (Mw<100 kDa) was purchased from Sigma Aldrich (Merck KGaA, USA). All
PEs were used without further purification. They were dissolved in deionized
salt-free water at varying concentrations and successively mixed with the
microgel suspensions. The structure formula for the three repeating units of
the PEs are shown in Figure 1. The three polymers are characterized by
different persistence lengths $l_{p}$ (stiffness) and hydrophobicity. In
particular $l_{p}=$0.3 nm for PSS41, $l_{p}=$1 nm for PLL42 and $l_{p}=$2.7 nm
for PDADMAC43. PLL is a weak polyelectrolyte44 and it is the most hydrophobic
polymer among those employed here, since each lysine bear a hydrophobic
methylene side-chain that is responsible for chain association at high
concentrations45, 46 and a tendency to penetrate into lipid membranes47. Its
degree of protonation depends on the pH, whose variation however stays very
limited in M-PLL mixtures (see section 2.3). PSS is a strong polyelectrolyte
whose hydrophobicity depends on its degree of sulfonation that in our case is
high (90 %), but not complete. Therefore we expect possible residual
hydrophobic interactions between PSS chains and microgels, when the latter are
in their collapsed state. Finally PDADMAC is a strong polyelectrolyte and it
is the most hydrophilic polymer48 among those used in this work to investigate
the rheology of PE-microgel mixtures, since it has neither large hydrophobic
side chains as PLL nor neutral hydrophobic monomers on the backbone as PSS.

Fig. 1: The structure formula of the polyions employed in this study: (a)
$\alpha$-polylysine hydrobromide (PLL); (b) polydiallyldimethylammonium
chloride (PDADMAC); (c) polystrirene sulfonate sodium salt (PSS)

###  2.3 PE-Microgel suspensions

Mixtures of polyelectrolytes and microgels, hereafter called PE-microgel
mixtures and coded as M-PLL, M-PSS and M-PDADMAC, were prepared following the
same protocol for both anionic (PSS) and cationic (PLL, PDADMAC) PEs: $23.33$
$\mu$L of PE solution at the required concentration was added to 500 $\mu$L of
microgel suspension at T=20 ∘C with generalized volume fraction
$\varphi=1.57$. This protocol allows to get mixtures with fixed microgel
volume fraction $\varphi=1.5$ and different concentrations of PEs. The
mixtures were stirred for about 2 mins using vortex, and the resulting
suspensions were then used for rheology measurements at T=20 ∘C and T=40 ∘C.
Figure 2 sketches the protocol, including the mixing and the successive
heating of the samples in the rheometer geometry.

Fig. 2: Schematic representation of the adopted protocol, including the mixing
and the successive heating of the samples from T=20 ∘C to T=40 ∘C. Because of
microgel deswelling the generalized volume fraction (section 2.4) decreases
from $\varphi(20^{\circ}C)=$1.5 to $\varphi(40^{\circ}C)=$0.11.

We quantify the amount of PE contained in each suspension via the nominal
polyelectrolyte to KPS monomolar ratio $\xi$, where KPS is considered as fully
reacted during the synthesis. This is supported by the barely measurable
weight of the residual mass ($m_{r}<$0.1 mg) present after drying the
supernatant that has been extracted after each centrifugation. The monomolar
ratio $\xi$ reads:

$\xi=\frac{C_{PE}\cdot M_{w}^{KPS}}{2\cdot C_{KPS}\cdot M_{w}^{PE}}$ (1)

where, $C_{PE}$, $C_{KPS}$, $M_{w}^{PE}$ and $M_{w}^{KPS}$ are respectively
the concentrations (mg/ml) and the molecular weights of PE monomers and of the
initiator. One would expect to find an iso-electric point, where all the
charges due to the anchored KPS are neutralized by the cationic PEs, to be
close to $\xi=1$. However, we anticipate here that this condition will not be
fulfilled, since not all the initiator molecules participate to build up the
net charge of microgels49. The pH of the concentrated suspensions has been
monitored showing in all cases only a weak dependence on the PE concentration:
5.5<pH<6.0 for M-PLL mixtures, 5.3<pH<6.0 for M-PDADMAC mixtures and
6.5<pH<6.0 for M-PSS mixtures. In this range of pH we do not expect any
drastic change in PNIPAm microgel properties50, 51. Most of mixtures have been
further diluted 250 times and then used to measure the electrophoretic
mobility of the diluted complexes and the fraction of the incident light
transmitted through each sample at different temperatures. A small leftover
volume of the the concentrated microgel suspension ($\varphi=$1.57) has been
further mixed with PEs solutions to perform complementary mobility and light
transmission experiments in the same range of $\xi$ explored via rheology.

###  2.4 Viscosimetry

Rolling-ball viscosimetry measurements were performed to obtain the
generalized colloidal volume fraction of microgel suspensions 38. The
measurements were done at $T=$ 20 ∘C using an Anton Paar Lovis 2000 ME
microviscosimeter in the range 4.68 $\cdot$ 10-5 $<$ $c$(wt/wt) $<$ 1.5
$\cdot$ 10-3, where the viscosity $\eta$ increases linearly with the mass
fraction of microgels $c$ (See Supplementary Material). The particulate volume
fraction is defined as $\varphi$ = $n_{p}v_{p}$, where $n_{p}$ is the particle
number density and $v_{p}=4\pi r^{3}/3$ is the volume of a single particle of
radius $r$ at infinite dilution. Experimentally, only the concentration $c$
(wt/wt) of a (purified) suspension can be measured directly, by weighting a
small volume of the sample before and after removing the solvent by
evaporation. Since the generalized volume fraction $\varphi$ is proportional
to the mass concentration $c$, it can be replaced by $k\cdot c$, where $k$ is
a factor for converting the mass concentration to the generalized volume
fraction. We determined the constant $k$ matching the $c$ dependence of the
zero shear viscosity $\eta$ of the purified suspensions with the values
expected from the Einstein equation27:

$\frac{\eta}{\eta_{s}}=1+\frac{5}{2}\varphi=1+\frac{5}{2}kc,$ (2)

where $\eta_{s}$ is the viscosity of the solvent. By fitting $\eta/\eta_{s}$
to a straight line (see Supplementary Material), we thus obtained $k$, which
allows extracting the colloidal volume fraction of the suspension. We obtained
$k=28.5$ $\pm$ $0.6$. This value embeds the effect of microgel permeability
and that of the primary electroviscous effect as discussed recently 49.
Finally, we remind that for microgels with very similar synthesis 36 but lower
crosslinker content, the onset of glassy dynamics at $T=20$ ∘C occurs at
$\varphi\approx 0.8$, that in our case represents an approximate lower bound
for the liquid-to-solid transition. This threshold is compatible with our
rheology data, as shown in sections 3.1.

###  2.5 Light scattering

Dynamic and static light scattering experiments have been performed to
characterize the microgels at the single particle level. For this purpose an
Amtec goniometer and a laser source ($\lambda$ = 532 nm) were used to collect
the light at scattering angles in the range 16∘ $\leq$ $\theta$ $\leq$ 150∘,
corresponding to scattering wave vectors in the range 4.4 $\mu m^{-1}$ $\leq$
$q$ $\leq$ 30.3 $\mu m^{-1}$. All scattering experiments have been performed
in dilute samples: an aliquot of the purified mother batch was diluted in
deionized water, to get a final generalized microgel volume fraction
$\varphi=$0.006.

The hydrodynamic radius, $R_{H}$, and the polydispersity of the microgels were
measured by means of dynamic light scattering. The scattered light intensity
was collected at a fixed scattering angle ($\theta=70^{\circ}$) correspondent
to a scattering vector $q_{DLS}=18$ $\mu m^{-1}$ and analyzed using a digital
autocorrelator. The time decay of the autocorrelation function
$F_{s}(\vec{q},t)^{2}$ was then fitted by a second-order cumulant expansion
(see Supplementary Material) to extract the diffusion coefficient $D$ as shown
below 52:

$F_{s}(\vec{q}_{DLS},t)^{2}\propto
exp\left(-2q^{2}_{DLS}Dt\right)\left[1+\frac{\mu_{2}t^{2}}{2!}+o(t^{3})\right]^{2}$
(3)

where $\mu_{2}$ is related to the second moment of the distribution of the
diffusion coefficients of the suspended particles. The average diffusion
coefficient is then used to obtain the hydrodynamic radius using the Stokes-
Einstein relation: $D=K_{B}T/6\pi\eta_{s}R_{H}$, where $K_{B}$ is the
Boltzmann constant, $T$ is the bath temperature and $\eta_{s}$ is the zero
shear viscosity of the solvent. The corresponding size dispersion and
polydispersity index are respectively
$\sigma_{R_{H}}=\sqrt{\mu_{2}}R_{H}/(Dq^{2}_{DLS})$ and
$\gamma=\mu_{2}/D^{2}q_{DLS}^{4}$. The polydispersity index here never
exceeded 0.20. For commercial PEs solutions, characterized by larger
polydispersities indexes (PDI>0.2) autocorrelation functions have been
analyzed by means of the CONTIN algorithm 53 trough which we extracted the
number-weighted size distributions.

The gyration radius, $R_{g}$, was measured by collecting the intensity of the
light $I(q)$ scattered by the microgel samples at different scattering angles.
The scattered light was subsequently fitted (see Supplementary Material) to
the Guinier equation54 to extract $R_{g}$:

$I(q)=I(0)\exp\left[-\frac{(qR_{g})^{2}}{3}\right],$ (4)

where $I(0)$ is a constant depending on the number of particles in the
scattering volume and on the scattering factor of a single particle. The
Guinier regime for all samples was attained in the range $0.5\leq qR_{g}\leq
2.5$, coherently with previously reported microgel syntheses 55, 56. The
uncertainty on $R_{g}$ is given by the fit error, the latter being less than
$1.5\%$ of the best-fit value.

###  2.6 Electrophoresis and Transmittance measurements

The electrophoretic mobility and the transmittance of the suspensions were
simultaneously measured using a Litesizer 500 (Anton Paar). The apparatus uses
the new cmPASLS method, which is a recently developed PALS technology57. The
absolute transmittance $T_{A}$, is computed as the ratio between the intensity
of the light transmitted through the sample ($I$) and that of the incident
beam ($I_{0}$):

$T_{A}=I/I_{0},$ (5)

To filter out any effect due to solvent and the cell we computed the relative
transmittance

$T_{R}=T_{A}/T_{A}^{H_{2}O},$ (6)

that is the ratio between the absolute transmittance of the suspension and
that of the pure solvent (water here). This has been done for each set
temperature.

The electrophoretic mobility and transmittance were measured between 20
${}^{\circ}C$ to 50 ${}^{\circ}C$ after a proper thermalization to monitor the
effect of polyelectrolytes addition onto the mobility of swollen and collapsed
microgels. The volume fraction of all the samples was fixed at
$\varphi=0.006$.

###  2.7 Rheology

Rheological tests were performed on freshly prepared PE-microgel mixtures
using a stress-controlled MCR501 rheometer (Anton Paar, Germany). Standard
stainless-steel sandblasted cone-plate geometry (25 mm diameter, 0.998∘ cone
angle) has been used for all the tests. Temperature control has been ensured
by means of a Peltier element (PTD- 200). The measuring temperatures were
fixed at T=20 ∘C and T=40 ∘C. To ensure thermal equilibrium the sample has
been kept at the desired temperature for 10 mins prior to each measurement.
The outer rim of the samples has been covered with a low viscosity silicon oil
(0.1 Pa s) to minimize evaporation. Dynamic strain sweep (DSS) tests were
carried out before each dynamic frequency sweep (DFS) test to evaluate the
extent of the linear regime, namely where the first-harmonic viscoelastic
moduli $G^{\prime}(\gamma_{0})$ and $G"(\gamma_{0})$ do not appreciably change
upon varying the strain amplitude. The lack of important ageing and the
absence of evaporation were further tested for about the same duration of one
experiment ($\sim$ 2500 s) at 20 ∘C and 40 ∘C via a time sweep experiment on
one PE-free microgel suspension (Supplementary Material). This excluded that
the variation of the moduli observed for the mixtures results from different
ages of the pure microgel system. All frequency sweeps were done at strain
amplitudes within the linear viscoelastic regime were the two moduli do not
appreciably change for increasing $\gamma_{0}$. DSS and DFS tests at 20 ∘C
started on freshly loaded samples after 10 mins of thermalization. The samples
have been successively heated up to 40 ∘C and, after other 10 mins of
thermalization, a DFS test has been carried out. Our rheological measurements
therefore probe only the rapid formation, strengthening or melting of the
original glassy or gel phases and they do not take into consideration possible
coarsening processes that might occur over time scales much longer (several
hours) than our experiment duration ($\sim$ 2500 s). For liquid-like samples
responding with torques well below the lower limits imposed by rheometer under
oscillatory shear we performed steady rate experiments in the range 42
$s^{-1}$ $\leq\dot{\gamma}\leq$ 1000 $s^{-1}$ to measure their flow curves
$\sigma(\dot{\gamma})$, to probe their Newtonian behavior and to extract
possibly their zero-shear viscosity.

##  3 Results and discussion

###  3.1 Bare microgels and PEs

Prior to mixture preparation we characterized the bare microgels and the PEs
to confirm the sign of their charge in water, to measure their size and to
identify rheologically the PE-free sample ($\xi=$0). The bare microgels were
characterized using DLS and SLS in the dilute regime to measure their
hydrodynamic radius ($R_{H}$), gyration radius ($R_{g}$) and mobility $\mu$ as
a function of temperature. As shown in fig 3 (left panel) the microgels
undergo a volume phase transition (VPT) when the temperature is raised above
the LCST temperature of pNIPAM20. The critical temperature ($T_{c}$) at which
the microgels undergo the volume transition are estimated by fitting both
$R_{g}$ and $R_{H}$ to an auxiliary function 40:

$R_{H,g}(T)=[R_{0}-\Delta R_{H,g}\tanh(s(T-T_{c}^{H,g}))]+A(T-T_{c}^{H,g})$
(7)

where, $R_{0}$ is the radius of the microgel at the VPT, $\Delta R_{H,g}$ is
the amplitude of the VPT and the parameter $s$ quantifies its sharpness. We
obtained $T_{c}^{H}$ = 32.9 $\pm$ 0.2 ${}^{\circ}C$ and $T_{c}^{g}$ = 31.8
$\pm$ 0.3 ${}^{\circ}C$ for for $R_{H}$ and $R_{g}$ respectively. The lower
$T_{c}$ for $R_{g}$ compared to $R_{H}$ can be attributed to uneven
distribution of the charges between the core and periphery49, 29, 27. Despite
of that, given the dispersion of the data, we do not detect a clear onset of a
minimum of $R_{g}/R_{H}$ that is strictly related to the two-step deswelling
of PNIAPm microgels40, 49, with the core collapsing at temperatures always
lower than those marking the transition of the peripheral corona. In this
respect we have already reported49 for a synthesis of microgels with the same
crosslinker-to-monomer molar ratio (5.3 %) as the present one, the existence
of a barely detectable minimum in $R_{g}/R_{H}$ crossing the VPT. Such a
feature has to be ascribed to the higher crosslinker density of the microgels
employed here with respect to other syntheses where the minimum was more
evident40. As a matter of fact, increasing crosslinker density reduces the
extent of the minimum of $R_{g}/R_{H}$ since it homogenizes the local
deswelling within the microgel volume: the core and the corona deswell to the
same extent for high crosslinker-to-monomer molar ratios and increasing
temperatures, suppressing the decoupling between the transitions in $R_{g}$
and $R_{H}$ of the microgels. This has been carefully investigated and
established via simulations40. The ratio $R_{g}/R_{H}$ stays within the range
0.61-0.63 for $T\leq T_{c}^{H}$ and increases sharply at $T\simeq T_{c}^{H}$
consistently with the microgel shrinking above the VPT40.

Fig. 3: Gyration and hydrodynamic radius (left) and mobility (right) of bare
PniPam microgels as a function of temperature. Here $\varphi=0.006$. The inset
(left panel) shows the ratio $R_{g}/R_{H}(T)$. The relative error on $R_{H}$
and $R_{g}$ obtained from the fit of the intensity correlation function and
the q-dependent scattered intensity (Equations 3 and 4) (See Supplementary
Material) never exceeded the 1.5% of the best fit values. Error bars for
$R_{H}$, $R_{g}$ and $R_{H}/R_{g}$ are smaller than or equal to the symbol
size. The error on the mobilities obtained from the full width at the half
maximum of the mobility distribution never exceeded the 7% of each mean value.
Fig. 4: Panel a): Electrophoretic Mobility of the three PEs as a function of
temperature at $C_{PE}$=1.25 mg/ml (for PLL), $C_{PE}$=1.75 mg/ml (for PSS)
and $C_{PE}$=1.38 mg/ml (for PDADMAC). These concentrations are the highest
ones (highest $\xi$) characterizing PE-microgel mixtures discussed in section
3.2. Electrophoretic Mobility at $C_{PE}$=28.0 mg/ml (for PLL), $C_{PE}$=5.1
mg/ml (for PSS) and $C_{PE}$=35.0 mg/ml (for PDADMAC). Error bars are the full
widths at half maximum of mobility distributions. The inset (Panel b)) shows
the normalized relative transmittance measured for the three concentrated PE
samples as a function of temperature.

The electrophoretic mobility of the same microgels are shown in Figure 3
(right panel). The negative mobility is due to the anionic initiator used for
the microgels synthesis. Microgel mobility is remarkably affected by the
VPT20: it drastically decreases (algebraically) above about $T_{c}^{H}$ due to
the increase of the microgel charge density. We extracted the electrokinetic
transition (EKT) temperature ($T_{c\mu}$) using the same auxiliary function as
in equation 7, namely

$\mu(T)=[\mu_{0}-\Delta\mu\tanh(s_{\mu}(T-T_{c\mu}))]+A_{\mu}(T-T_{c\mu})$ (8)

where, $\mu_{0}$ is the mobility of the microgel at the EKT, $\Delta\mu$ is
the amplitude of the EKT and the parameter $s_{\mu}$ quantifies its sharpness.
We obtain $T_{c\mu}$=35.8 $\pm$ 0.1 ${}^{\circ}C$. The discrepancy between the
critical temperatures marking the VPT and EKT is
$\Delta$=$T_{c\mu}$-$T_{c}^{H}\simeq$ 2.9 ${}^{\circ}C$. Such a significant
difference between the transition temperature has been reported by Pelton et
al.20, Daly et al.58 and more recently by Truzzolillo et al.27, and it is
attributed to a further charge restructuring (densification) well above
$T_{c}^{H}$58.

To determine preliminarily the viscoelastic properties of the PE-free microgel
suspensions, the rheology of bare microgels dispersions was also investigated
as a function of $\varphi$ at T=20 ∘C. This allowed us to determine precisely
the rheological state of the suspension in which PEs are progressively added:
At the microgel concentration ($\varphi=1.5$) that will characterize all the
PE-microgel mixtures, microgels are in a jammed glassy state at T=20 ∘C. (see
Supplementary Material for more details).

Prior to mixture preparation we have further investigated the temperature
dependence of PE mobility and, since PLL and PSS bear also hydrophobic
segments, we also inspected the PE stability via light transmission
experiments at high concentration. Figure 4-a shows the electrophoretic
mobility of the three PEs at the highest concentrations of the range explored
in rheology experiments. As expected the 2 cationic PEs (PLL and PDADMAC) show
positive mobility while PSS chains are characterized by negative mobilities at
all temperatures. For the three PEs we observe a smooth increase of the
mobility modulus with increasing temperature. Such an increase is mainly due
to the decrease of the solvent viscosity (see Supplementary Material). Figure
4-b shows the mobility and the normalized transmittance of solutions that are
more concentrated in PE chains. We used these samples to test the stability of
all the PEs in water, reduce the uncertainties on the mobility measurements
and test the effect of PE concentration on the mobility itself. By increasing
PE concentration we observe a clear decrease in mobility for all the polymers,
that is consistent with an increased fraction of condensed counterions59 and
possibly an augmented friction due to more frequent collisions among different
chains, while the observed temperature dependence can be still filtered out by
taking into account the viscosity variation of the solvent (see Supplementary
Material). Most importantly, the normalized transmittance of the same samples,
namely the transmittance measured at temperature $T$ divided by its value at
20∘C (inset of Figure 4), does not vary remarkably when temperature increases
and the non-normalized relative transmittance was $T_{R}$(20∘C)= 1.00$\pm$0.01
for the three PE solutions. The polyions employed here stay therefore well
dissolved in water and any possible conformational change, local chain
association, or variation of the fraction of free counterions 60, 61, 62 do
not cause any massive condensation or chain swelling. This is an important
starting point since transmittance will allow us to discern whether colloidal
condensation occurs or not in the mixtures. To establish whether polyions can
penetrate microgels we have finally measured or estimated the size of the PEs
and the average mesh size of the microgels, the latter being equal to the
average distance between two crosslinker molecules thought as uniformly
distributed within the microgel volume. The hydrodynamic size distribution of
PSS and PDADMAC chains has been obtained via the CONTIN analysis of the
intensity autocorrelation functions 53. DLS experiments have been performed
using dilute PE suspensions, namely for $C_{PE}\ll
C_{PE}^{*}=\frac{M_{w}}{4/3\pi NaR_{H}}$, where $C_{PE}^{*}$ is the overlap
concentration and $N_{A}$ is the Avogadro number. We obtained number-weighted
size distributions with a main peak at hydrodynamic diameters
$D_{H}^{peak}=4.5$ nm for PSS and $D_{H}^{peak}=184$ nm for PDADMAC. We
attribute this large difference in size between these two PEs to both a
different average molecular weight and a known large difference in backbone
stiffness (see section 2.2). PLL chains did not give enough scattering signal
for their hydrodynamic size to be measured reliably in the dilute regime. We
have however estimated their average end-to-end distance by considering a
worm-like chain model for semiflexible chains63, 64 and the known persistence
length of PLL, $l_{p}=1.0$ nm 42. We obtained an end-to-end distance
$R_{ee}=28$ nm. The overlap concentration for PLL chains has been then
estimated by replacing the hydrodynamic radius with half of the end-to-end
distance. The average mesh size $d_{m}$ of PNIPAm microgels has been computed
by knowing the amount BIS molecules and the number of microgels contained in
the mother batch. The former is known from the synthesis, while the latter can
be computed knowing the value of the generalized volume fraction obtained by
viscosimetry at T=20 ∘C, the hydrodynamic size of microgels at the same
temperature and the total volume $V$ of the suspension. We obtained
$d_{m}=R_{H}[4\pi/(3N_{c})]^{1/3}=$ 4.9 nm, where $N_{c}$ is the number of
crosslinkers per microgel. Since $d_{m}$ is always comparable to or lower than
the measured or estimated size of the PEs the penetration of PE chains is
limited to the outer shell of the microgels where a lower than average
crosslinker density characterizes PNIPAm microgels synthesized via free
radical polymerization65, 66. We further expect therefore that the PE
penetration is maximum for the small PSS chains and nearly absent for the
large PDADMAC polymers. Finally, PE diffusion within the microgel volume is
supposed to be additionally reduced at $40$ ∘C, where microgels collapse and
their mesh size consequently decreases.

###  3.2 Rheology of PE-microgel mixtures

Fig 5 shows selected dynamic frequency sweeps for the three sets of mixtures
and different charge ratio $\xi$ at 20 ∘C (a,c,e) and 40 ∘C (b,d,f), namely
below and above the microgel VPT. The limited range of frequency at 40 ∘C is
due to inertia problems, that are routinely encountered at high frequencies
($\gtrsim$ 10 rad/s) and standard shear geometries like the one given by the
cone-and-plate fixture used in this work, producing a non-physical drop of the
moduli for ultra soft solids ($Gp\lesssim$ 10 Pa). At 20 ∘C the addition of
PEs has only a weak effect on the rheology of the suspensions: we observe a
weakining of the original jammed glass for M-PLL (a) and M-PSS (b) mixtures
for increasing $\xi$, while the linear viscoelastic spectra of the mixtures
stay basically unaltered when PDADMAC is added (c). We attribute this to 3
synergistic effects: i) microgel deswelling due to an increased ionic strength
67 and osmotic pressure exerted possibly by unadsorbed chains 68; ii)
depletion interactions that may act in presence of free chains, especially in
the case of anionic PSS polymers 69; iii) a reduction of the net repulsions
between microgels due to a partial adsorption of the cationic polymers that
lowers the electrostatic repulsion between microgel coronas bearing most of
the microgel charge 40. As said, however, the effect PDADMAC chains on swollen
microgel glasses does not emerge. In this respect it is worth recalling that
PDADMAC chains showed a lower mobility at all temperatures (Figure 4-a,b)
compared to PLL pointing to a lower charge density on the polymer backbone. We
thus expect a lower adsorption energy and a weaker impact on the swollen
microgels with low charge density. Finally, further effects might be produced
by the PE polydispersity that we expect to be larger for PDADMAC as indicated
by the supplier and by the different microgel-to-PE size ratio, since they
both affect residual depletion effects. In particular, since at T=20 ∘C the
hydrodynamic PDADMAC/microgel size ratio is $\simeq$ 1.08, while the
(estimated) hydrodynamic PLL/microgel size ratio is $\simeq$ 0.082 and the
adsorption is limited by the low charge density and high hydrophilicity of the
microgels, a more prominent depletion (short-ranged) attraction might
characterize their mutual interaction in presence of PLL rather than of
PDADMAC chains, the latter being almost equally sized with respect to the
PNIPAm microgels. In addition to that, depletion effects in M-PDADMAC mixtures
are further reduced due to the presumable higher polydispersity of the
depletants (the PEs here), whose impact on entropy driven interactions have
been discussed in detail70.  This said, despite these effects are difficult to
quantify or decouple, they all point towards a softening of the colloidal
glasses due to a reduction of the repulsive forces between the microgels.

Fig. 5: Storage modulus G’ (solid symbols) and loss modulus G" (open symbols)
as a function of the oscillatory frequency $\omega$ at T=20∘C (a,c,e) and
T=40∘C (b,d,f) for M-PLL mixtures (a,b), M-PSS mixtures (c,d) and M-PDADMAC
mixtures (e,f). The inset in panel (d) shows the flow curves
$\sigma(\dot{\gamma})$ of liquid samples for which LVE moduli were not
measurable. The straight line is a linear fit of the data at $\xi=$0.309. Fig.
6: Storage (full points) and loss modulus (empty/shaded points) of PE-microgel
mixtures for the three PEs as a function of monomolar ratio $\xi$ (eq. 1) at
$\omega=$0.07 rad/s, T=20∘C (a) and T=40∘C (b,c). For M-PSS mixtures the zero
shear viscosity is also shown (c). The moduli of PE-free suspensions (grey
squares) are also shown as reference. Solid lines in panel b) are a guide to
the eye.

At 40 ∘C by contrast, the emerging scenario is very different and the rheology
of microgel suspensions become very sensitive to both PE concentration and
sign of the PE charge (Figure 5-b,d,f). First of all, we point out that at
this temperature PE-free microgel suspensions ($\xi=0$) are still viscoelastic
solids characterized by a nearly frequency-independent storage modulus
$G_{p}=0.47\pm 0.05$ Pa. The generalized microgel volume fraction in this case
is much lower than its value at 20 ∘C, since microgels are in their collapsed
state. By rescaling $\varphi$ using the the hydrodynamic radii measured at the
two temperatures we obtain
$\left.\varphi\right|_{40{{}^{\circ}}C}=\left.\varphi\right|_{20{{}^{\circ}}C}\frac{R_{H}(40{{}^{\circ}}C)^{3}}{R_{H}(20{{}^{\circ}}C)^{3}}=0.11$.
At this volume fraction the suspensions cannot be considered any more as
jammed glasses but they are rather in a gel phase, consistently with other
rheological studies on concentrated PNIPAm suspensions 34. Microgels aggregate
and form percolating networks due to hydrophobic forces acting between the
particles for $T>T_{c}^{H}$. It’s worth remarking that this occurs despite of
the temperature-induced increase of the charge density of the microgels, that
stabilizes the suspensions at lower volume fractions, and it is caused by both
the high number density of counterions, that screen microgel charges, and the
large number density of microgels, that enhances the collision probability
between two of these colloids, increasing the rate of cluster formation. The
impact of the microgel charge and the counterion concentration on microgel
gelation has been investigated only very recently71, confirming that the
suppression of electrostatic repulsions gives rise to a net increase of gel
elasticity. As PE concentration is progressively increased we observe three
interesting phenomena: i) the presence of a large gel strenghtening followed
by a sharp softening for both the sets of mixtures containing cationic PEs
(M-PLL, M-PDADMAC); ii) a complete melting of the gel in wide range of PE
concentrations as the anionic PSS chains are progressively added; iii) a clear
gel strengthening or re-gelification at the largest PE concentrations in M-PLL
and M-PSS mixtures. For liquid-like M-PSS mixtures, since the linear
viscoelastic moduli were not measurable, we performed continuous steady-rate
tests and we extracted their flow curves (Inset Figure 5-d). They all showed a
Newtonian behavior $\sigma(\dot{\gamma})=\eta_{0}\dot{\gamma}$, from which we
obtained the zero shear viscosity $\eta_{0}$.

Figure 6 summarizes our results for all the samples investigated via rheology
and serves to detail more clearly the effect of PEs. We report both the
storage and the loss modulus of the solid-like suspensions at $\omega=0.07$
rad/s and the zero shear viscosity for the liquid-like samples. Panel (a)
shows the moduli of all the mixtures as a function of $\xi$ at T=20 ∘C:
Increasing $\xi$ does not affect remarkably the rheology of the mixtures and
produces only a weak decrease of both the moduli in M-PLL and M-PSS mixtures,
while the effect of PDADMAC addition is not even detectable. Panels (b) and
(c) by contrast show the relevant impact that PEs have on microgel networks.
On the one hand both M-PLL and M-PDADMAc mixtures (b) are characterized by
moduli that increase by almost two order of magnitudes with respect to the
original gel ($\xi=0$) at $\xi\simeq 0.04-0.05$. The same moduli decrease
again sharply at $\xi\simeq 0.1$. At higher PE concentration ($\xi>0.1$) the
two cationic PEs act differently on the network dynamics: the gel moduli
increase again in M-PLL mixtures while this does not occur in M-PDADMAC
suspensions. On the other hand, in stark contrast with the phenomenology
encountered by adding oppositely charged PEs, the gel network is melted by PSS
chains even at the lowest $\xi$, with the mixtures becoming Newtonian liquids
with low viscosities ($\eta_{0}\simeq$3 mPa s). Also in this case, however, a
large PE content destabilize the suspensions and a gel-phase is observed
again. The rheology of the binary PE-microgel mixtures therefore point to the
existence of an emergent reentrant behavior of the gel at high temperature
when cationic PEs are added, suggesting that PEs may first screen completely
the entire microgel charge and then overcompesate for it, producing globally
an overcharge of the PE-microgel complexes so formed. This is in line with the
findings that some of the authors 21 obtained in dilute suspensions of similar
M-PLL mixtures and it will be confirmed by mobility and light transmittance
experiments discussed later (section 3.3). The further gel strengthening
occurring at high PLL content ($\xi>$0.1) and its absence for PDADMAC points
to a key role played by PE hydrophobicity. PLL chains are more hydrophobic
than PDADMAC, they tend to aggregate at high concentrations as mentioned in
section 2.2 and they can thus participate actively to the enhanced elasticity
of the gel. In this respect we point out that for M-PLL mixtures the PE
concentration reaches values above the overlap concentration $C_{PLL}^{*}$,
spanning the range $0\leq C_{PLL}\leq 4.1C_{PLL}^{*}$. Our results thus
suggest that, for high PE content, gels are at least partially PE-mediated:
the gelation is driven also by the PE-PE interaction rather than only the PE-
microgel one. We recall also that both the cationic polymers progressively
adsorb on the microgels at 40 ∘C (see also section 3.3) and depletion effects
should be considered of secondary importance.
The completely different behavior observed in M-PSS mixtures points quite
surprisingly to a strong influence of polystyrene sulfonate on the state of
the microgel suspensions, since PSS has been considered as a non adsorbing
polymer for anionic PNIPAm microgels67. We stress once again the PSS chains
used in this work consist of 90 % sulfonated polystyrene monomers, that is to
say, polymer backbones having 1 hydrophobic styrene monomer over 10. This puts
forward that PE adsorption might occur also in this case. In addition to this,
since the mixtures have been prepared at T=20 ∘C, i.e. at $\varphi=1.5$, PSS
chains might partially penetrate microgels for entropic reasons, and after
microgel collapse part of them can be still confined within the microgel
volume. PSS adsorption or inclusion would explain the gel melting, since
sulfonated chains are globally hydrophilic and their layer on microgels
increase the negative charge of the M-PSS complexes hampering gelation. As for
partially hydrophobic PLL chains, PSS causes a re-condensation of microgels at
high concentrations ($\xi>$0.31). Enhanced clustering in this case is only
driven by hydrophobic interactions since there cannot be charge patch
attraction72 characterizing M-PLL and M-PDADMAC systems. In more detail, we
attribute this microgel aggregation to i) concomitant energetic bridging due
to the residual hydrophobic interactions between non-sulfonated styrene
monomers and those between hydrophobic PNIPAm segments, ii) a simple salting
out effect and iii) possibly depletion attractions due to non-adsorbed chains
at high concentrations. Although our mobility measurements, that we discuss
hereafter, confirm the (at least partial) inclusion of PSS chains within the
microgel volume, a more systematic study involving other complementary
techniques and simulations, that goes beyond the scope of this work, is in
order to decouple all these effects. In what follows, we report on detailed
electrophoretic and light transmission experiments in diluted mixtures,
through which we have unravelled the role of the sign of the PE charge, and
investigated the presence of an isoelectric point and colloidal overcharging
causing a reentrant condensation of PE-microgel complexes in the same range of
charge ratios probed by rheology experiments.

###  3.3 Mobility and light transmission experiments for diluted mixtures

Fig. 7: Electrophoretic mobility of a) M-PLL, b) and M-PSS and c) M-PDADMAC
complexes at varying PE concentrations as a function of temperature. The
arrows are a guide for the eye and point to the mobility variation at
$T>T_{c}^{H}$ from $\xi=$0 to the maximum PE concentrations. Panels d), e) and
f) show the mobility values for the larges PE concentrations in the mixtures
compared to the values measured in pure polyelectrolyte solutions at the same
concentrations as indicated in the panels.

Most of the suspensions studied via rheology have been diluted in deionized
water so to obtain PE-microgels mixtures with generalized microgel volume
fraction $\varphi=0.006$ at T= 20 ∘C. Figure 7 shows the elctrophoretic
mobility for the three systems as a function of temperature. The behavior of
$\mu(T)$ changes drastically depending on whether the cationic PLL and PDADMAC
polymers (Panels a,c) or anionic PSS (Panel b) are progressively added,
staying qualitatively unaltered when the effect of the temperature dependence
of the viscosity and the permittivity of the solvent is filtered out
(Supplementary Material). For both the cationic PEs we observe a pronounced
overcharging starting at $\xi\simeq 0.1$ that increase radically at
$T>T_{c\mu}$. Such overcharging has been already observed 27, 21 and it is
driven by the microgel EKT, with the largest increase of mobility occurring
close to the native electrokinetic transition of PNIPAm microgels. This will
be briefly discussed below. The mobility behavior for the M-PSS reveals by
contrast an unexpected behavior: after a first algebraic increase, presumably
due to an increase of the ionic strength and a scarce PE adsorption, the
mobility increases in modulus at all temperatures almost doubling its
magnitude at T=50 ∘C. This strongly indicates that PSS chains adsorb onto
microgels or stay confined within their peripheral volume. We must conclude
that part of the PSS chains adsorb, potentially penetrating inside the
microgel periphery, and that the hydrophobic interactions between PSS chains
and microgels, due to the not fully sulfonation of polystyrene chains, might
favor PE coating despite of the anoinic nature of the PE.

Such mobility change does explain why microgels are stabilized by PSS chains
in concentrated suspensions and hamper the formation of gels (Figure 6-c):
when this like-charged polymers coat the collapsed microgels, they both
enhance electrostatic repulsion between the so-formed decorated objects and
screen out the hydrophobic interactions originally driving the gel formation
of bare microgels.

With this in mind, we can also speculate, now more pertinently, that the
(reentrant) gelation observed at $\xi=0.645$, can be ascribed to PE-mediated
hydrophobic interactions, to the screening of the residual charge due to the
increased counterion concentration and, since the mobility of the complexes
does not varies remarkably for $\xi>$0.21, to depletion interactions due to
unadsorbed chains.

The encountered phenomenology is therefore at odds with the assumption that
highly sulfonated PSS is strictly a non-adsorbing polymer in the presence of
PNIPAm microgels. Such an assumption has been adopted in the past 67, 69 to
justify the observed flocculation of PNIPAm microgels induced by PSS for
$T\lesssim T_{c}$. If this was the case, the presence of PSS chains could only
give rise to an enhanced depletion mechanism between the microgels driven by
the unbalanced osmotic pressure exerted by the free chains. In concentrated
suspensions such scenario would consequently result in a progressive gel
strenghtening that is not observed, while by contrast the gel melting and the
increase of the mobility modulus in dilute suspensions represent a robust
indication that small PSS polymers adsorb on and partially interpenetrate
hydrophobic microgels. In this respect, the presence of hydrophobic
interaction between PNIPAm chains and non-sulfonated polystyrene is well
documented in literature73.

We obtain a further insight on the charge restructuring process occurring in
PE-microgel mixtures when we compare the mobility of the complexes to those of
the pure PEs at the same concentration $C_{PE}$, namely the highest $\xi$ in
the mixtures, below and above $T_{c}^{H}$ (Figure 7-d,e,f). Remarkably, at
T=20 ∘C the average mobility modulus is always lower than the one measured in
pure PE suspensions, signaling the absence of a large charge accumulation with
respect to pure PEs. By contrast at 40 ∘C, the mobility is always
algebraically higher with respect to the pure PE solutions for the M-PLL and
M-PDADMAC mxtures and it is comparable to that of the free PSS chains for
M-PSS systems. The contrasting behavior observed below and above $T_{c}^{H}$
for cationic PEs confirms the occurrence of a net increase of the positive
charge density in the presence of microgels for $T>T_{c}^{H}$. The latter can
be due to both a compaction of the polyions and/or to an increase of the
fraction of free counterions promoted by PE adsorption 74. We remind also,
that a simple local increase of the polyion concentration would give rise to a
decrease in mobility due essentially to an increased amount of condensed
counterions in line with the data shown in figure 4-a,b and other results
discussed in literature 59. In the case of PSS chains this is less evident
despite the mobility of the complexes is much larger in modulus compared to
that measured for the pure PNIPAm microgels (Figure 7-b). A summary of the
mobility values is also reported for comparison in Supplementary Material
(Table 1).

Fig. 8: Mobility (a,c) and transmittance (b,d) of microgel suspensions
($\varphi=0.006$) at varying concentrations of PEs at $20^{\circ}C$ (a,b) and
$40^{\circ}C$ (c,d). Error bars in a) and c) are the full widths at half
maximum of mobility distributions. The blue circles in the panels (a,c) mark
the isoelectric condition $\mu=0$.

The charging and neutralization process of the complexes, and their stability
at the two selected temperatures, can be finally rationalized if mobility and
transmittance data are combined. This is shown in Figure 8. For both M-PLL and
M-PDADMAC mixtures a mobility reversal occurs at both 20 ∘C and 40 ∘C, while
M-PSS mixtures show a progressive average mobility that becomes more and more
negative as the PE concentration is increased (Figure 8-a,c). Interestingly
for both cationic PEs the mixtures undergo a reentrant condensation signalled
by the large decrease of the relative transmittance (Figure 8-d) in
conjunction with the charge reversal observed at 40 ∘C, while the suspensions
stays stable at 20 ∘C (Figure 8-b). The simultaneous occurrence of an
isoelectric condition and a large collodal condensation further confirm that
the measured mobility has to be assigned to the PE-microgel complexes, as also
pointed out by the sistematic unimodal mobility distribution measured for all
the mixtures at any $T$ and by the sigmoidal temperature dependence of the
mobility in the presence of PEs.

Our data therefore confirm that the hydrophilic character of PNIPAm microgels
below their VPT ($T<T_{c}^{H}$) hampers microgel condensation though an
apparent isolectric condition is attained and chains partially adsorb onto
microgels. By contrast above VPT ($T>T_{c}^{H}$) both hydrophobic interaction
and a stronger charge-patch attraction between decorated microgels drive
cluster formation localized at the isoelectric point, where the average
mobility vanishes. We recall that charge patch attraction between decorated
colloids is enhanced when large surface charge density fluctuations
characterize the colloidal surfaces72, 75. This is indeed the case for
collapsed microgels, where bare portion of the microgel surfaces are
supposedly densely charged and with an enhanced hydrophobicity. Therefore,
when the destabilization due to polyelectrolyte adsorption is considered,
PNIPAm microgels behave as charged colloids at high temperatures
($T>T_{c}^{H}$) and as nearly neutral colloids below their volume phase
transition temperature ($T<T_{c}^{H}$), confirming previous results obtained
in dilute suspensions of M-PLL mixtures21. We have now shown that this has
important repercussions on the rheology of concentrated dispersions whose
viscoelasticity at high temperatures is largely affected by the presence of an
isoelectric point. The emerging general scenario for $T>T_{c}^{H}$ is sketched
in Figure 9.

Fig. 9: Schematic representation of the different states encountered when PEs
are progressively added in suspensions of PNIAPm microgels and temperature is
raised up to $T>T^{H}_{c}$.

Three final comments are in order.
i) The peak of the gel modulus (Figure 6-b) observed for mixtures of microgels
and cationic PEs occurs at $\xi\simeq 0.04-0.05$ and it is slightly shifted to
lower $\xi$ with respect to $\xi\simeq 0.1$, where the isoelectric condition
and the reentrant condensation is observed in diluted samples (Figure 8-c,d).
This can be ascribed to the smaller volume accessible to PEs in concentrated
microgel suspensions and therefore to a more effective neutralizing effect of
the chains, that presumably spend much less time in their desorbed state. In
addition to that, the counterion concentration is also larger in concentrated
samples and this could also reduce the amount of oppositely charged polymers
needed to neutralize the microgels, since the fraction of counterions
condensed on the microgel is higher.
ii) We note that at highest $\xi$ in dilute suspensions (Figure 8) there is
not evidence for large cluster formation, that would result in a decrease of
the relative transmittance, while gel strengthening is reported for
concentrated M-PSS and M-PLL mixtures. This again corroborates the hypothesis
that these gels are networks stabilized by non-electrostatic interactions
between the concentrated PE chains surrounding the microgels at high
$\varphi$. PE concentration is much lower in the diluted suspensions used to
measure the mobility and the transmittance of the PE-microgel complexes
(Figure 8). Here, the free volume accessible to PEs is much larger and their
mutual contact is very much reduced.
iii) The charge inversion and re-entrant condensation occur far ($\xi\simeq
0.1$) from the nominal isoelectric condition ($\xi=1$). One possible
explanation would be that most of the initiator ($\approx 90\%$) does not
participate to the polymerization, that then would result in a large residual
mass present in the supernatant after the first post-synthesis centrifugation
cycle. This is ruled out: after drying and removing the solvent from the
supernatant we obtain a solid content equal to only $\approx 1\%$ of the total
NIPAm monomers dissolved in water during the synthesis and that comprises also
the removed SDS. A much larger solid content, containing both unreacted NIPAm
monomers and initiator, would be present if the $\approx 90\%$ of the
initiator had not participated to the microgel formation. A second possibility
is represented by the partial involvement of the ionic initiator in the
adsorption process: within this scenario the very peripheral sulfonic groups
anchored to the microgels are mostly free from condensed counterions and
obviously more available for steric reasons to accomodate PE chains, while
groups located further inside the microgel volume are on average more screened
by confined counterions and they do not participate to the charge balance.
This hypothesis is corroborated by recent experiments and simulations 49 where
the addition of randomly distributed charges barely affects the $R_{g}$
transition of PNIPAm-based microgels. Such a scenario, although it gives a
plausible qualitative explanation for the discrepancy between the nominal and
the observed isolectric condition, is certainly not a conclusive one, and the
mechanisms of charge neutralization of microgels through polyion adsorption
remain to be understood in the future.

##  4 Conclusions

We have shown that adding polyelectrolytes bearing different charge has an
important impact on the rheology of concentrated suspensions of anionic PNIPAm
microgels, and that electrostatics influences crucially gel formation at high
temperatures. We have studied the effect of the PEs on both a jammed glassy
system, where PEs are confined in the interstitial spaces between faceted
microgels or slightly penetrate into their peripheral corona, and when the
concentrated suspension is brought beyond the microgel volume phase transition
($T>T_{c}^{H}$). We have shown that while jammed glasses are only weakly
softened by PE addition, the impact of the PE chains is important at higher
temperature, where PNIAPm microgels are charged hydrophobic colloids with high
charge density. We find that a large and reentrant gel strengthening occurs in
the presence of cationic PEs around the isoelectric point, where the average
measured mobility is zero and large clustering takes place in diluted
suspensions. Strikingly, for PE chains with residual hydrophobicity and
bearing charges with the same sign as that of the microgels, we observe a
melting of the original gel phase at $T>T_{c}^{H}$. Mobility measurements
suggested that also in this case there is at least a partial adsorption and/or
penetration of the PEs into the microgels, increasing their net charge,
screening the hydrophobic attraction between collapsed microgels and hence
hampering the gelation of the system within the probed experimental time
scale. Non-electrostatic interactions are thus also very important, especially
when microgels are in their collapsed state, and at high PE concentrations,
far from the isoelectric point, we also find that the rheology of the mixtures
is highly influenced by these specific effects: for mixtures containing
partially hydrophobic PLL or PSS chains, gelation is favoured by the presence
of a high PE content, while for the more hydrophilic PDADMAC polymers this is
not observed. Our work shows that the rheology of thermosensitive ionic
microgels can be tuned by adsorbing polyelectrolytes, and confirms that PNIAPm
microgels must be considered as highly charged hydrophobic colloids at high
temperatures. Our study paves the way for more systematic investigations
including PEs sharing the same chemistry but with different molecular weights
and degree of hydrophobicity (e.g PSS chains with different $M_{w}$ and
sulfonation degrees) that are required to discern more in depth the role
played by the chain size and the non-electrostatic effects in these composite
soft materials. In this respect, the use of fluorescent PEs and molecular
dynamic simulations, would surely help to unravel the role played by residual
unadsorbed chains on the overall microgel stability. Finally, whether PE
adsorption causes glass melting at $T<T_{c}^{H}$ or reentrant gelation at
$T>T_{c}^{H}$ and lower generalized volume fractions is still unknown and
deserves a thorough investigation.

## Conflicts of interest

There are no conflicts to declare.

## Acknowledgements

We acknowledge financial support from the Agence Nationale de la Recherche
(Grant ANR-20-CE06-0030-01; THELECTRA). D.T. thanks Dr. S. Sennato for
fruitful discussions.

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