Charge generation in low-polarity solvents: Poly(ionic liquid)- functionalized particles

Article abstract of DOI:10.1021/la3049086

We present a straightforward strategy for the synthesis of highly charged poly(ionic liquid)-functionalized particles in low-polarity solvents. A series of cationic liquid monomers consisting of a tetraalkyl ammonium cation and a fluorinated tetrakis[phenyl] borate anion linked, via a C₃-alkyl chain, to a methacrylate unit were synthesized. The addition of this ionic monomer to a conventional dispersion polymerization of methyl methacrylate and methacrylic acid at 80 C in a mixed dodecane/hexane solvent yielded spherical, highly monodisperse particles with mean diameters of between ～50 and 2500 nm with high electrophoretic mobility and stability in nonpolar solvents such as dodecane. The surface potential in dodecane could be adjusted in the range from 0 to 180 ± 9 mV by altering the ratio of ionic monomer to methacrylate monomers. The particles open up new opportunities for the electrostatic assembly of nanoparticles and organized structures in nonpolar environments.

Full text of DOI:10.1021/la3049086

Article
pubs.acs.org/Langmuir
Charge Generation in Low-Polarity Solvents:
Poly(ionic liquid)-Functionalized Particles
Ghulam Hussain, Amy Robinson, and Paul Bartlett*
School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K.
S
* Supporting Information
ABSTRACT: We present a straightforward strategy for the synthesis of highly charged
poly(ionic liquid)-functionalized particles in low-polarity solvents. A series of cationic liquid
monomers consisting of a tetraalkyl ammonium cation and a fluorinated tetrakis[phenyl]
borate anion linked, via a C3-alkyl chain, to a methacrylate unit were synthesized. The
addition of this ionic monomer to a conventional dispersion polymerization of methyl
methacrylate and methacrylic acid at 80 °C in a mixed dodecane/hexane solvent yielded
spherical, highly monodisperse particles with mean diameters of between ∼50 and 2500 nm
with high electrophoretic mobility and stability in nonpolar solvents such as dodecane. The surface potential in dodecane could
be adjusted in the range from 0 to 180 9 mV by altering the ratio of ionic monomer to methacrylate monomers. The particles
open up new opportunities for the electrostatic assembly of nanoparticles and organized structures in nonpolar environments.
although not experimentally proven, that the nanometer-sized
reverse micelles produced in situ by the surfactant solubilize
counterions within their cores. The stabilization reduces the
energy barrier to charge separation and so enhances the charge on
the particle. The physical situation is, however, complex because the
surfactant often plays two distinct roles. In addition to stabilizing
ions, the surfactant frequently adsorbs onto the surface of the
particle and generates new surface groups that then ionize. The total
particle charge depends on a competition between the two
processes of surface adsorption and bulk micellization. As a result,
the particle charge is found experimentally to be sensitive to a large
number of factors, among which the chemical nature and
concentration of the surfactant, the surface functionality of the
particle, the adsorption of the surfactant, the presence of water, and
in some cases even the time of contact between surfactant and
particle seem to be the major ones.8,9,11−16,19 So far, most efforts
have been devoted to mapping out the consequences of this
competitive surface chemistry so as to prepare particles with
controlled levels of charge. Given these complexities, it would be
highly desirable to develop a new family of particles that would
charge spontaneously without surfactant. Adjusting the concen-
trations of surface groups would then allow the particle charge to be
tailored precisely to a specific application. Furthermore, the absence
of surfactant molecules should enhance chemical compatibility so
that nanoparticles with different surface charges or polarities could
be mixed together to self-assemble without the problems of charge
exchange, which is such a detrimental feature of surfactant-based
charging schemes. Although nonpolar asphaltene colloids, for
example, have been shown recently to charge spontaneously in the
absence of surfactants,17,18 no general synthesis method exists, as far
1. INTRODUCTION
Electrostatics is a major driving force for self-assembly at the
microscale and nanoscale.1 Charge interactions play a crucial role in
life and in many biological and industrial processes precisely
because, at least in aqueous systems, they can be easily tuned. Forces
can be attractive or repulsive and their magnitude and range can be
controlled by altering the charge on the surfaces of interacting
particles or the dielectric constant of the surrounding solvent or
simply through adjustment of the concentrations of ions in solution.
Anisotropic interactions may be generated by controlling surface
geometry by, for instance, using charged cubes, rods, tetrahedra, or
other 3D shapes1−3 or alternatively by chemically patterning the
surface to produce heterogeneous charges.4 Although the vast
majority of effort on nanoparticle electrostatics has focused quite
naturally on aqueous systems, in recent years a growing interest has
developed in nonaqueous “oily” solvents, those with dielectric
constants of εoil ≃ 2. In this regime, some dissociation of charged
groups does take place, although substantially less than in water,
because the energetic costs of separating neutral species into free
ions is larger by a factor of about εwater/εoil ≃ 40 in oil than in water.
The synthesis possibilities offered by charge-directed self-assembly
in nonpolar solvents have been most dramatically illustrated by the
beautiful work on superlattice formation in mixtures of charged
microparticles by the van Blaaderen group.5 This work sparked a
new interest in the means to produce charge in low-dielectric
solvents. Recent efforts have focused on either the fundamental
nature of nanoscale electrostatics in the extremely low ion
concentration environment (lower than nanomolar) found in
low-dielectric solvents6−11 or on controlling particle charging,12−16
which is important in the commercial development of thin film
electrophoretic particle displays (EPDs) and in the processing of
petroleum products.17,18
Microparticles are often charged in a low-polarity solvent by
the addition of a suitable surfactant8,9,11−16 or what is sometimes
called a charge-control additive.19 It is generally believed,
Received: December 12, 2012
Revised: February 8, 2013
Published: February 12, 2013
© 2013 American Chemical Society
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evaporated, and the white precipitate that appeared was washed with
diethyl ether and then recrystallized twice from acetone. The product
was dried under vacuum. In the case of the tetraoctadecylammonium
bromide, the solubility in methanol was low and the anion exchange was
carried out in warm propanol. The structure of the product was
confirmed by 1H NMR, 13C NMR, and microanalysis.
as we know, that permits the charge on a nanoparticle in a nonpolar
environment to be controlled systematically and by design.
Polymerized ionic liquids (PILs) offer a potential new approach
to the problems of nonpolar charging. PILs are a special type of
polyelectrolytes that carry an ionic liquid (IL) functionality in each
of their repeating units. In contrast to classical water-soluble
polyelectrolytes, the IL functionality renders PILs soluble in organic
solvents and insoluble in water. The family of PILs is very broad and
includes organic cations such as dialkyl imidazolium, alkyl-
pyridinium, and tetraalkyl-ammonium species and hydrophobic
anions such as tetrafluoroborates (BF4−), hexafluorophosphates
(PF6−), and fluorinated imides (such as (CF3SO2)2N−). Interest in
PILs has expanded considerably in the past few years20,21 because
they combine the unique versatility of ionic liquids with the design
and control over architecture available in macromolecular systems
and so offer opportunities for creating materials with new properties
and functions. Although PILs have been exploited in applications as
varied as ion-conductive electrolytes,22,23 stabilizing agents for
carbon nanotubes and graphene,24,25 and carbon dioxide
absorbents,26 there seems to be no previous work on their use to
generate charged particles in nonpolar environments.
In this Article, we construct ILs with polymerizable groups based
on tetraalkyl-ammonium tetrakis[phenyl]borates and tetrakis[3,5-
bis(trifluoromethyl)phenyl]borates. We utilize the hydrophobic
nature of the cationic and anionic centers and the bulky size of the
ions to reduce Coulombic interactions and enhance ion-pair
dissociation in low-dielectric environments. The molecular archi-
tecture of the IL precursors was modified to maximize the ionic
conductivity in nonpolar solvents such as dodecane and cyclohexane.
Comparison with traditional surfactant-based approaches, using
Aerosol-OT (AOT or sodium di-2-ethylhexylsulfosuccinate), for
instance, shows that the ionic conductivity of the optimized IL
precursors is 2 to 3 orders of magnitude greater than micellar
surfactants in dodecane at the same molar concentration. The
prepared IL monomers were mixed with methyl methacrylate and
methacrylic acid and used in dispersion polymerization to prepare
monodisperse poly(ionic liquid)-functionalized particles. Electro-
phoretic measurements demonstrate that the PIL-functionalized
particles are highly charged in hydrophobic solvents such as dodecane.
A preliminary report of this approach has already been published,27
but in the present contribution, we report on our further efforts to
optimize this system. In particular, we demonstrate that the surface
potential of a polymer microparticle may be tuned continuously over
a very wide range of values by altering the PIL content. Overall, our
study shows that copolymerized PILs act efficiently as ionic groups in
low-dielectric solvents, generate a high surface potential, and allow a
high degree of control to be exercised over the particle charge.
2.3. Preparation of Ionic Liquid Monomers. The synthesis of the
ionic liquid monomers (ILMs) was accomplished using a three-step
synthesis procedure illustrated for the [ILM-C12][TFPhB] monomer
(13). In the first step, a hydroxyl-terminated n-tetraalkylammonium salt
(11) was prepared by the quaternization of a tertiary amine with 3-
bromo-1-propanol. In the next step, a methacryloyl group was introduced
by reaction of the terminal hydroxyl group with methacryloyl chloride. The
bromide anion was then exchanged with highly lipophilic anion tetrakis[3,5-
bis(trifluoromethyl)phenyl]borate (TFPhB) to yield the desired product.
2.3.1. Synthesis of n-Tridodecyl-propyl-3-hydroxy Ammonium
Bromide (11). Compound 11 was prepared by the Menschutkin
reaction.29 Tridodecylamine (10 mmol) and 3-bromo-1-propanol (11 mmol)
were refluxed in DMF at 110 °C in the presence of the catalyst30 dodecyl
1
trimethyl ammonium bromide (DTAB, 1 mmol). H NMR showed that
quaternization was essentially complete after 24 h. The reaction mixture was
cooled to room temperature, and 100 mL of ice-cold diethyl ether was added.
The precipitate was washed thoroughly with further diethyl ether and
recrystallized from an equal volume mixture of ethyl acetate and methanol.
2.3.2. Synthesis of n-Tridodecyl-propyl-3-methacryloyloxy Am-
monium Bromide (12). One millimole of 11 was loaded into a 50 mL
reactor under nitrogen in the presence of 2.5 mmol of triethylamine in
dichloromethane. The mixture was cooled by an ice bath. Three
millimoles of methacryloyl chloride was added dropwise over a hour
with vigorous stirring. The resulting mixture was poured into water (100
mL) and extracted with diethyl ether twice. The organic extracts were
filtered and concentrated in vacuo to yield a white precipitate.
2.3.3. Synthesis of [ILM-C12][TFPhB] Monomer (13). A solution of
sodium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (Na-TFPhB)
(1 mmol) in 10 mL of methanol was added dropwise to a solution of 12
in methanol at 0 °C. After a hour, an excess of ice-cold distilled water was
added. The precipitate was extracted with diethyl ether and concentrated in
vacuo. The residue was purified by flash column chromatography on silica
gel and eluted with 0 to 5% methanol in a 1:1 (v/v) mixture of dichlor-
methane and hexane.
2.4. Polymerization Process. Dispersion polymerizations of
methyl methacrylate (MMA), methacrylic acid (MA), and ILM were
carried out in a mixed solvent of hexane and dodecane at 80 °C under
nitrogen following the procedure detailed by Antl et al.31 2,2′-Azobis-
(isobutyronitrile) (AIBN) and a comb copolymer, poly(12-hydroxy stearic
acid)-co-poly(methyl methacrylate) (P(HSA-co-MMA)), were used as the
initiator and stabilizer, respectively. Chain-transfer agent 1-octanethiol (OT)
was added to limit the polymer molecular weight. The weight percentage of
the ionic monomer (ILM) was varied from between 0 and 8% of the masses
of the MMA and MA monomers, as detailed in Table 1. The total mass of
Table 1. Typical Recipe for the Preparation of PIL-Containing
Particles
2. EXPERIMENTAL SECTION
ingredients
[ILM]
mass (g)
a
2.1. Materials. All reagents were purchased from Aldrich, Acros, or
Alfa Aesar Chemicals and used in the synthesis procedures described
below without significant further purification. All solvents used were of
analytical grade. Poly(ionic liquid)-containing particles after synthesis
were resuspended in hexane or dodecane, which were dried under
nitrogen and stored in contact with 4 Å molecular sieves to minimize
their water content prior to use.
2.2. Preparation of Ionic Liquid Precursors. Fluorinated
tetraalkyl-ammonium tetrakis[3,5-bis(trifluoromethyl) phenyl]borates
(compounds 1−5) and the analogous unfluorinated tetra-alkyl-
ammonium tetrakis[phenyl] borates (compounds 6−10) were prepared
by anion exchange.28 In a typical synthesis procedure, the quaternary
ammonium bromide salt was dissolved in the minimum amount of
methanol and then added to a methanolic solution of sodium
tetrakis[3,5-bis(trifluoromethyl)phenyl]borate. The excess solvent was
0.4
[MMA]
4.9
[MA]
0.1
b
[P(HSA-co-MMA)]
[AIBN]
0.83
0.04
0.03
0.98
[OT]
[dodecane]
[hexane]
3.12
b
a
Varied between 0.0 g (0% ILM) and 0.4 g (8% ILM). 30% by weight
solution in dodecane.
MMA and MA monomers was fixed at 50% of the total weight of the
preparation. After 2 h, the comb stabilizer was chemically bound to the
surfaces of the particles by raising the temperature to 120 °C in the presence
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of catalyst diethanol amine (0.025 g). After being refluxed for 8 h, the cooled
suspension was then passed through tightly packed glass wool to remove
coagulant and cleaned by five repeated cycles of centrifugation and
redispersal in fresh hexane before use.
At low salt concentrations, eq 3 shows that, for Kρs ≪ 1, all ion pairs
are almost completely dissociated (α ≈ 1) as a result of the favorable
gain in entropy on dissociation. By contrast, at high salt
concentrations, where Kρs ≪ 1, the entropy of mixing is less
important in comparison to the ion-pair binding energy, and the
majority of ions remain bound as ion pairs with α ≈ 1/(Kρs)1/2. The
dividing boundary between the dissociated and associated regimes
may be identified with the line Kρs = 2, where α = 1/2.
The equilibrium constant K may be extracted from
experimental measurements of the conductivity S. If the mixture
of cations, anions, and cation−anion pairs is sufficiently dilute to
be ideal, then the conductivity is
2.5. Characterization Methods. NMR spectra were recorded at
room temperature using a Varian 400-MR spectrometer operating at
400 MHz for 1H spectra and 101 MHz for 13C spectra. The average radius
⟨a⟩ of the poly(ionic liquid) particles and their coefficient of variation Cv =
(⟨a⟩ − ⟨a⟩2)1/2/⟨a⟩ were determined from scanning electron microscopy
(SEM, JEOL JSM-5600LV, Jeol Ltd., U.K.). A drop of each dispersion was
diluted in a few milliliters of pure hexane and then deposited on a glass
coverslip attached to an aluminum stub with conductive glue. The sample
was dried at room temperature in an enclosed cabinet before sputter coating
with gold. Five images, containing about 250 particles each, were collected
and measured using image analysis software (Vision Assistant, National
Instruments). The hydrodynamic radius ah was determined by dynamic
light scattering (DLS) from dilute suspensions (0.006 to 0.01 wt %) in
dodecane using a Malvern Instruments system (Zetasizer Nano Series S,
Malvern Instruments, U.K.). Electrophoretic mobilities μ were determined
using a combined laser Doppler velocimetry and phase analysis light
scattering (M3-PALS) technique (Zetasizer Nano Series Z, Malvern Instru-
ments, U.K.). Particles were driven with an ac electric field of 2 × 104 V m−1,
and the particle velocity was determined from the phase shift of the scattered
laser light. Measurements were made at 25 °C on dilute dispersions (0.006
wt %, colloid volume fraction ηc = 3.8 × 10−5) in dry filtered dodecane. No
appreciable variation of μ with field strength was detected for field strengths
from between 2 × 104 V m−1 and 6 × 104 V m−1; however, systematic
measurements to investigate a wider range of electric fields are currently
planned. For each particle sample, at least 20 runs, each consisting of 100
individual measurements, were recorded to ensure the accuracy of the
results. The conductivity of electrolyte solutions in cyclohexane was
measured at an ac frequency of 18 Hz and 25 °C using a Scientifica (U.K.)
model 627 conductivity meter.
⎛
⎞
⎛
⎞
ρ
ρ
A
+
−
N
S =
Λ +
Λ + S
−
⎜
⎝
⎟
⎠
⎜
⎝
⎟
⎠
+
o
N
(4)
A
where Λ+ (Λ−) is the molar conductivity of the cation (anion) at
infinite dilution and So is the background conductivity of the
solvent. For a 1:1 electrolyte, the total molar conductivity Λ0 is
just the sum of the contributions from each ion, so Λ0 = Λ+ + Λ−.
By replacing the equilibrium constant K by the dimensionless
molar ion-pairing constant KM = KNAc°, where the standard
concentration is c° = 1 mol m−3, and using the expression for α
from eq 3, the conductivity may be re-expressed in a form
convenient for data analysis,
⎛
⎝
⎞
⎠
Λ0c◦
2KM
⎛ cs ⎞
⎜
⎝
⎟
⎠
⎜
⎜
⎟
S =
1 + 4KM
− 1 + S
⎟
o
c◦
(5)
The association of ions in low-dielectric solvents is dominated
by the long-range Coulombic interactions between ions. The
details of the short-range repulsive interactions and the attractive
van der Waals interactions between ions, which are a function of
their precise chemistry, are believed to be much less important
than an accurate modeling of the electrostatic forces.34 To
interpret the measured ion association constants, we use a
restricted primitive model (RPM) of the ionic fluid. This model
assumes spherical hard ions of unit positive and negative charge
and equal diameter d in a solvent, which is regarded as a dielectric
continuum of dielectic permittivity εrε0. The hard-sphere ions
interact only via pairwise additive Coulombic interactions. The
electrostatic binding energy Uc/kBT at contact between
oppositely charged ions is defined conveniently as λB/d (in units
of kBT), where the Bjerrum length λB is
3. THEORY
3.1. Ion Pairing. To detail the interactions between ions in a
low-polarity solvent, we use the quasi-chemical ion pairing approach
pioneered by Bjerrum,32 which gives excellent agreement with
Monte Carlo simulations33 of associating ionic fluids at the very low
concentrations relevant here. For completeness, we summarize the
key features below for a dilute 1:1 electrolyte and refer the interested
reader to the recent presentation of Valeriani et al.33 for a more
detailed analysis.
In the low-dielectric-constant solvents studied here, the ion
concentrations are very small, typically less than 10−9 M, so triple
ions and other highly charged clusters may be safely ignored.
Bjerrum’s theory assumes that a dynamic equilibrium exists
between free ions and the bound ion pairs in solution.
e2
λB =
K
4πε0εrkBT
(6)
cation + anion ⇌ cation−anion pair
(1)
Experimental data may be converted into equivalent RPM units by
determining an effective hard-sphere diameter dRPM that reproduces
the measured association constant KM. An approximate closed-form
expression for K = KM/(NAc°), valid at the large ion-pair binding
energies Uc/kBT ≫ 25 appropriate to this study, has been given for
the restricted primitive model by Valeriani et al.33
In terms of α, the fraction of salt molecules that are dissociated
into free ions, and ρs, the total number density of salt molecules,
the number densities of cations ρ+ = αρs, anions ρ− = αρs, and ion
pairs are ρIP = (1 − α)ρs . The molar salt concentration is
accordingly cs = ρs/NA, where NA is Avogadro’s constant and ρs =
1/2(ρ+ + ρ−) + ρIP . (Note that the maximum ion concentration is
actually 2cs when all ion pairs are completely dissociated.)
Applying the law of mass action to eq 1 yields
2
3
⎡
⎢
⎤
⎥
⎛
⎞
⎛
⎞
d
λB
d
d
K = 4πd3eλ /d
+ 2
+ 2
B
⎜
⎟
⎠
⎜
⎟
⎠
⎢
⎣
⎥
⎦
λ
λ
⎝
⎝
B
B
(7)
1 − α
Kρ =
s
α2
The effective hard-sphere diameter dRPM is obtained by equating the
experimentally determined values of the ion-pair association
constant K with the expression in eq 7. The ion diameter dRPM is
obtained by a numerical solution of eq 7 using the known λB.
3.2. Electrokinetics in Counterion-Free Systems. When
a colloidal particle of radius a containing a large number of ionizable
(2)
Here, K is the ion-pair association constant. Solving eq 2 for α gives
1
2Kρ
α =
( 1 + 4Kρ − 1)
s
(3)
s
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poly(ionic liquid) groups at its surface is immersed in a low-dielectric
solvent, some of the ionizable groups dissociate, releasing counterions
into the solution and leaving opposite charges on the surface. Because
of the dissociation of surface groups, the colloidal surface acquires a
net surface charge density of eσ that is assumed to be distributed
homogeneously over the surface. Poisson−Boltzmann (PB) theory,
which ignores ion−ion correlations, provides an extremely
convenient description of the ion distribution outside such a charged
colloidal particle. For monovalent ions, the mean-field picture that
underlies the PB theory is accurate provided that the dimensionless
Debye screening parameter κ in the case with added electrolyte,
although in the absence of a salt reservoir κ is strictly undefined.44
The counterion density in the WS cell is ρ−(r) = ρ0eΦ, where ρ0 is
the average number density of counterions38 chosen so that the
neutrality condition Z = 3/4π(R3 − a3)ρ0 is satisfied. In terms of ρ0,
the prefactor γ satisfies the equality γ2 = 4πλBρ0 that can be
rearranged to give
⎛
⎝
⎞
⎠
η
ZλB
a
c
(γa)2 = 3
⎜
⎜
⎟
⎟
1 − η
(9)
(10)
(11)
c
2
coupling constant Ξ = 2πσλB < 1. This weak coupling condition
equates to a surface charge density of approximately 1 elementary
charge per 10 square Bjerrum lengths.35 As we will see later, this
condition is satisfied in the nonpolar suspensions relevant here, where
maximum charge densities are on the order of 1e per 100 square
Bjerrum lengths, so PB theory should provide an accurate description
of the ion distribution in a low-polarity solvent.
The boundary conditions are, at the colloid surface,
ZλB
a
dΦ
dr
r
= −
r=a
and through electroneutrality, at the cell boundary,
The electrophoretic mobility μ = v/E, defined by the ratio of the
colloid drift velocity v to the applied electric field E, of a spherical
charged colloidal particle immersed in an electrolyte solution has
been extensively studied within the framework of a PB approach. In
the common salt-dominated regime, the large reservoir of salt ions
results in a strong screening of the equilibrium electrostatic potential
ϕ(r) (where r is the distance from the center of the particle) so that
the space charge density is essentially zero throughout the solution,
except for within a narrow ionic atmosphere (the “Debye cloud”)
surrounding each colloid. Because the bulk solution phase is
electroneutral, an applied electric field exerts forces only on the
particle and its Debye layer. The hydrodynamic interactions between
particles subject to electrophoresis are therefore strongly screened
and the mobility μ is essentially constant, being only weakly
dependent on the particle concentration.36 The situation becomes
very different in the much less frequently studied counterion-
dominated regime. Here the intervening solution between charged
particles contains only counterions, which are ions of one charge sign
generated by the dissociation of colloid surface groups. There is no
bulk ion reservoir, so the space charge density in the solution cannot
become zero, even far from the particle surface. Screening is reduced,
and the dependence of μ on the particle concentration is now found
to be significant. The different electrokinetic phenomena in the
counterion- and salt-dominated regimes have been explored
theoretically by Ohshima37−39 and others.40−42 Here we briefly
review the counterion-only model of electrophoresis that we use to
interpret our experimental data.
dΦ
dr
= 0
r=R
The system of differential and algebraic equations (eq 8−11) is solved
numerically by the elegant algorithm proposed in ref 44. The potential
drops rapidly in the vicinity of the particle surface from Φs = Φ(a)
before going negative and reaching a finite negative value of Φo =
Φ(R) at the edge of the WS cell. The total potential difference from the
surface of the particle to the boundary of the WS cell is Φd = Φs − Φo.
An expression for the electrophoretic mobility μ of a spherical
colloidal particle in a salt-free suspension has been derived under
the condition of a weak applied electric field by Ohshima.37,39,45
The analytical result was obtained by approximating the exact
electrokinetic equations of motion for dilute particle concen-
trations (ηc ≪ 1). More sophisticated numerical calculations on
cell models41,42 confirm the validity of these approximations
whereas recent mesoscopic46 and lattice Boltzmann simula-
tions40 show that the electrophoretic response of salt-free
systems is indeed captured reasonably well by the analytical
predictions of Ohshima. The mobility was obtained by balancing
the Stokes drag force on the uncharged particle with the pressure
from the excess counterion charges on the boundary of the WS
cell. In the dilute limit ηc ≪ 1, the result is37
Ze
6πηa
μ =
Ω exp(Φ)
o
(12)
We assume that the colloids are positively charged and that the
only ions present in the bulk of the solution are the negative
counterions. To allow a straightforward numerical solution of the
nonlinear Poisson−Boltzmann equation, a cell model first proposed
by Alexander et al. is used.43 A suspension of N charged spheres is
approximated by N identical spherical Wigner−Seitz (WS) cells of
radius R, each containing a single colloid of charge +Ze at the center
and surrounded by Z negative monovalent counterions such that
the cell is overall electrically neutral. The cell radius R is chosen such
that ηc = (a/R)3 equals the volume fraction occupied by the colloidal
particles. Let Φ(r) = eϕ(r)/kBT be the reduced electrostatic
potential a distance r from the center of the colloid. Then in a mean-
field approximation the potential Φ(r) inside the cell (a ≤ r ≤ R) is
the solution of the nonlinear PB equation,
with
9η 1/3
5
η 2
5
c
c
Ω = 1 −
+ η −
c
(13)
In the low-charge (or low surface potential) limit, where the
potential at the outer boundary of the cell approaches zero, eq 12
reduces to the conventional Huckel equation. Increasing the particle
charge Z (or surface potential Φs) increases the retardation due to
the enhanced counterion density at the boundary of the cell, which
in turn reduces the magnitude of the electrophoretic mobility. By
introducing the dimensionless mobility μ*,
̈
6πηλ
μ* =
B μ
(14)
e
d2Φ
2 dΦ
r dr
+
= γ2eΦ
eq 12 may be rewritten as
dr2
(8)
Zλ
μ* =
B Ω exp(Φ)
where γ is a prefactor whose value is fixed by the electroneutrality
constraint. The prefactor γ plays a role analogous to that of the
o
(15)
a
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Accurate values of μ* were obtained from a numerical solution of
the Poisson−Boltzmann equation (eq 8).
4. RESULTS AND DISCUSSION
4.1. Selection of IL Precursors. Since the late 1990s, the
group of Ohno23 has devoted considerable efforts to the
synthesis of PILs via free radical polymerization of suitable
monomers with the goal of preparing a solid ionic electrolyte for
batteries. The IL monomers used typically contain a cation fixed
into the main chain of the unit, polymerizable methacryloyl or N-
vinylimidazolium groups, and a suitable anion. Methacryloyl-
based IL monomers, in particular, offer versatility because they
may be readily copolymerized with other monomers to tune ion-
conductive properties. Ohno et al. has systematically studied the
relationship between molecular structure and the resulting solid-
state ionic conductivities.23 Key structural parameters were
identified to be the nature of the anion, the length of the spacer
group between the polymerizable group and the cation (for
methacryloyl-based monomers), and the length of alkyl chains
attached to the cation center. Although in the current work we
are aiming for solution rather than solid-state properties, the
approach of Ohno et al. provides a natural starting point for
optimization. Our synthesis strategy was therefore to prepare
methacryloyl-based monomers with a long-chain tetraalkyl
ammonium cation separated from the polymerizable group by a
short flexible C3-alkyl chain, chosen to improve ionic conductiv-
ity.23,47 The nature of the counteranion is known to have a strong
influence on the solubility behavior of cationic PILs.20 Abbott et al.
have reported28,48 that quaternary ammonium salts with carbon
chains greater than C8 show surprisingly high solubilities in
cyclohexane and supercritical carbon dioxide, particularly when
combined with tetraphenylborate anions. For instance, the
hydrophobic species tetrakis(decyl) ammonium tetraphenylborate
has a solubility of approximately 0.045 mol dm−3 in cyclohexane at
room temperature, and the solubility may be increased still further
by using fluorinated hydrophobic anion tetrakis[3,5-bis-
(trifluoromethyl) phenyl]borate [TFPhB].
We chose to investigate the family of ionic liquid precursors,
compounds 1−10, that are characterized by two structural features:
(1) a tetraalkyl ammonium unit containing a Cn chain and (2)
counterions of either tetrakis[phenyl]borate [TPhB]− or the more
hydrophobic species tetrakis[3,5-bis(trifluoromethyl)phenyl]borate
[TFPhB]−. To optimize the ionization of the IL precursors in low-
polarity solvents, we altered both the length n of the carbon chain in
the cation and the nature of the counterion. The degree of ionization
was determined from the measured conductivity of dilute solutions
(cs = 0.1−100 μM) of the ILs in cyclohexane (ε = 2.02) using the
expressions outlined in section 3.1.
The strong influence of the counteranion is clearly seen in the
solubility behavior in low-polarity solvents such as cyclohexane.
When a tetrakis[phenyl]borate anion and a tetraalkylammonium
[H(CH2)n]4N+ cation of the materials synthesized (n = 4, 6, 8,
12, and 18) were used, only the C12 version of the compound was
soluble in cyclohexane. However, when the [TPhB]− anion was
replaced with the fluorinated species [TFPhB]−, all of the
different chain length compounds readily dissolved in cyclo-
hexane. The dramatic effect of fluorination is evident in the ionic
conductivity, plotted in Figure 1. Although both the fluorinated
and nonfluorinated ionic liquids offer higher conductivities than
conventional surfactant systems,14 the fluorinated anion
produces a substantial increase in the number of ions, with an
ionic conductivity that is about 10 times higher at a salt
concentration of cs = 1 μM. The performance increase, however,
Figure 1. Conductivity (in cyclohexane) as a function of molar
concentration for the fluorinated IL [Dod4N][TFPhB] and the
unfluorinated IL [Dod4N][TPhB]. For comparison, the conductitivity
of Na-AOT in dodecane14 at 25 °C is also shown. The solid curve
(black) through the [Dod4N][TFPhB] data is the prediction of eq 5,
while the line (red) through the AOT data is calculated for a critical
micellar concentrations of 3 μM. The [Dod4N][TPhB] data, which
shows an approximate linear dependence on electrolyte concentration
(dashed line), cannot be fitted with eq 5.
decreases with increasing cs because the conductivity of
[Dod4N][TPhB] increases more markedly than that of the
[Dod4N][TFPhB] solution with increasing concentration.
Although the [Dod4N][TFPhB] system shows the square-root
dependence expected for a weak electrolyte, the nearly linear
dependence on cs seen for [Dod4N][TPhB] clearly points to a
different mechanism of charging in the nonfluorinated system.
Symmetric tetra-alkyl ammonium cations are known to be
surface-active,49 so we postulate that the [Dod4N][TPhB]
solution contain micelles in addition to associated molecular
ions. A micellar disproportionation mechanism, analogous to
that identified in Na-AOT,50 would account for the linear
dependence of conductivity on cs observed. However, because
the unfluorinated system was only sparingly soluble in nonpolar
solvent we did no further work to prove these speculations and
focused solely on the fluorinated system.
The length (n) of the alkyl chain substituent on the quaternary
ammonium cation [H(CH2)n]4N+ has a dramatic effect on the
conductivity and solubility of the fluorinated salts. Increasing the
carbon chain length from C4 to C12 led to a nearly 40-fold
increase in the conductivity in cyclohexane (Figure 2). The C12
species, however, had the maximum conductivity of all of the Cn
compounds studied (n = 4, 6, 8, 12, and 18), with the C18
compound being only sparingly soluble in cyclohexane. To relate
these changes to the change in the Coulombic interactions, the
conductivity data for the fluorinated salts was analyzed
quantitatively using the ion-pairing theory detailed in section 3.1.
The conductivity S was fitted to eq 5, with the dimensionless ion-
pairing association constant KM as a fitting parameter. The
predicted conductivities, shown as the solid lines in Figure 2, well
reproduce the experimental dependence of S on the salt
concentration. The limiting molar conductivity at infinite dilution
Λ0 = Λ++Λ− was calculated from r , the radii of the ions, using the
expression51 Λ = NAe2/(6πηr ), where η is the viscosity of the
solvent. The radius of the cation r+ was estimated from the van der
1/3
Waals volume Vvdw of the isolated ion, r+ = [(3/4 πNA)Vvdw
] ,
using the group contributions tabulated by Marcus.34 The anion
radius was taken from the literature.48 The resulting values are
summarized in Table 2. The fitted values of KM are reported in
Table 3, with, as expected, the highest association constant being
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Figure 2. Conductivity as a function of salt concentration for
[Bu4N][TFPhB], [Hex4N][TFPhB], and [Dod4N][TFPhB] in cyclo-
hexane at 25 °C. The solid curves are the theoretical predictions of eq 5
using the ion-pairing association constants KM listed in Table 3.
Figure 3. Difference between the van der Waals diameter and the restricted
primitive diameter for [H(CH2)n]4N+[TFPhB]− as a function of n.
Waals attractions between ions, the values of Δ are unlikely to be
exactly zero. Nonetheless, the data in Figure 3 reveals that Δ is first a
relatively small fraction (between 12 and 18%) of the ion diameter
and second rather unexpectedly almost constant at Δ ≈ 1.3 Å,
independent of the alkyl chain length. The central conclusion is that
the restricted primitive model gives a surprisingly accurate
description of the ion-pairing association of tetra-alkyl ammonium
salts in a low-polarity solvent. Within the RPM, the Coulombic
interaction between ions at contact is Uc/kBT = λB/dRPM. The
derived values are reported in Table 3. Although the binding
energies are substantial, the fraction of dissociated ions is still larger
than for surfactant systems typically used in nonpolar solvents. For
instance, at a solute concentration of cs = 0.1 μM more than 1 in 103
molecules in the [Dod4N][TFPhB] system are ionized compared to
less than approximately 1 in 106 micelles in a surfactant system.9
4.2. Synthesis of Ionic Liquid Monomers (ILMs). Having
identified [Hex4N][TFPhB] and [Dod4N][TFPhB] as the two
most conductive combinations, we introduced these moieties into
two methacrylic monomers, [ILM-C6][TFPhB] and [ILM-C12]-
[TFPhB]. The cations were incorporated into the backbone of the
monomer, and the anion was left free to dissociate. The full details of
the synthesis procedure used to prepare the cationic monomers are
contained in section 2.3, but essentially a methacryloyl functional
group was introduced, separated from the cationic C6- and C12-alkyl
substituted ammonium cation by a short three-carbon spacer chain.
Ohno et al. has shown23,47,52 that the length of this spacer group has
an important influence on the solid-state ionic conductivity in the
case of the analogous polyelectrolyte, poly[2-alkyl imidazolium
bis(trifluoromethanesulfonyl)imide]. With too short a spacer, the
ionic conductivity drops precipitously, whereas for spacer groups of
C3 or larger the conductivity increases. The dependence on the alkyl
chain length was relatively weak for n ≥ 3, so in the present work we
used a fixed C3 spacer.
Table 2. Physical Parameters of Long-Chain Tetra-n-
alkylammonium Salts in Cyclohexane
r
r−
(Å)
Λ+ (S cm2
Λ
− (S cm2
+ a
(Å)
b
salt
n
mol−1
)
mol−1
)
[Bu4N][TFPhB]
[Hex4N][TFPhB]
[Oct4N][TFPhB]
[Dod4N][TFPhB]
[OD4N][TFPhB]
4
4.13 4.40
4.68 4.40
5.13 4.40
22.2
19.6
17.9
15.7
13.7
20.8
20.8
20.8
20.8
6
8
12 5.85 4.40
18 6.67 4.40
20.8
b
a
Cation radius estimated from van der Waals volumes.34 Anion
radius from Abbott et al.48
Table 3. Conductivity of Long-Chain Tetra-n-
alkylammonium Salts in Cyclohexane at 25°C
dRPM
b
Uc/
c
a
d
salt
n
KM
(Å)
kBT
cion (nM)
[Bu4N][TFPhB]
[Hex4N][TFPhB]
[Oct4N][TFPhB]
[Dod4N][TFPhB]
4
6
8.8 × 1012
6 2.9 × 1011
8 6.1 × 1010
5.1 × 109
7.0
7.8
8.2
8.9
39.4
35.5
33.8
30.9
0.003−0.11
0.019−0.59
0.041−1.28
0.140−4.41
8
12
18
e
[OD4N][TFPhB]
a
Dimensionless ion-pair association constant determined from
b
conductivity data. Equivalent RPM hard-sphere diameter determined
from eq 7 with λB = 27.7 nm. Ion-pair binding energy. Ion
c
d
concentration cion = (ρ+ + ρ−)/NA determined for salt concentrations
e
of cs = 0.1 and 100 μM. The octyldecyl salt was insoluble in
cyclohexane.
found for the soluble tetraalkyl ammonium salt with the smallest
cation where the Coulombic interactions are maximized.
To understand quantitatively the strength of the association
between IL ions in a low-polarity solvent, we map the fitted
values of KM onto an equivalent restricted primitive model
(RPM) of the ionic fluid using the approach of Valeriani et al.33
An effective ion diameter dRPM was determined by equating the
experimental values for K with the asymptotic RPM expression
given in eq 7. The results are summarized in Table 3. To gauge
the validity of an RPM description, the diameter difference Δ =
(r+ + r−) − dRPM between the van der Waals diameter and the
RPM ion diameter is plotted in Figure 3 as a function of the alkyl
chain length n. Because the restricted primitive model considers
only Coulombic interactions and ignores both the precise details of
the short-range repulsive interactions and any long-range van der
4.3. Preparation of PIL-Containing Particles by Dis-
persion Polymerization. The ILMs were used as a comonomer
in a conventional dispersion polymerization of poly(methyl
methacrylate) particles at 80 °C in a mixed solvent of dodecane
and hexane with 2.5 wt % poly(12-hydroxy stearic acid-co-
poly(methyl methacrylate) (P(HSA-co-MMA)) as a stabilizer. Thermal
initiator 2,2′-azobis(isobutyronitrile) (AIBN) was used. The
ILM was mixed with a fixed weight of methyl methacylate (MMA)
and methacrylic acid (MA) chosen so that before any addition of
ILM the reaction mixture contained 50 wt % monomer. To control
the particle charge, the proportion of ILM was varied from between
0 to 8 wt % (based on the mass of the non-ILMs). The system was
homogeneous before polymerization. The copolymer formed is
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insoluble in the hydrocarbon medium and precipitates out after
about 10 min of polymerization with the reaction mixture becoming
noticeably turbid, indicating the formation of colloidally stable
particles. Figure 4 shows SEM images of particles prepared by
4.4. Surface Potentials of PIL Particles in Low-Polarity
Solvents. Poly(ionic liquid)-functionalized particles, when dis-
persed in a low-polarity solvent such as dodecane where the
concentration of ionic impurities can be robustly controlled, provide
a very close experimental approximation to what is probably the
simplest theoretical model of a charged colloid, namely, a
counterion-only or salt-free system. Free ions are generated only
by the dissociation of surface groups and so must have the opposite
sign of charge to that of the particles. Furthermore, in the absence of
impurities, the concentration of co-ions in solution is negligible. The
relatively high ionic dissociation efficiency, which is evident in
Figure 2, suggests that our particles will be highly charged and
develop large surface potentials. To quantify the magnitude of the
surface potential, the motion of PIL-containing microparticles was
measured in an electric field. This motion is quantified by the
electrophoretic mobility μ = v/E, the ratio of the particle velocity v to
the electric field E. The electrophoretic mobility depends on both
the potential at the surface of the particle and the concentration of
ions in solution through the polarization of the screening cloud that
surrounds a charged particle in solution and generates a drag effect
as it moves in the opposite direction to the particle as a field is
applied. Theoretical studies38,39,54−56 have shown that the ion
distribution around a spherical charged particle of radius a in a salt-
free medium containing only counterions is very different from that
present in an electrolyte solution. If the salt concentration cs is low
enough to satisfy the condition ξ ≫ a, where ξ = (8πλBcs)−1/2 is the
Debye length, then a highly charged spherical particle at a finite
concentration exerts such a powerful attraction on its counterions
that a certain fraction condenses onto the particle. Counterion
condensation is much more marked in a low-salt environment and
occurs only where ξ ≫ a. The resulting nonlinear ion distribution
around a charged particle has a dramatic effect on the electro-
phoretic mobility.39 A plot of the mobility as a function of the charge
ZλB/a (or the surface potential Φs) grows initially linearly before
exhibiting a plateau, at a threshold value of the charge, beyond which
μ should become independent of the charge level as counterion
collapse onto the surface of the particle is initiated. Consequently, to
determine the zeta (or surface) potential properly from the
measured electrophoretic mobility, we must solve simultaneously
the full coupled nonlinear Poisson−Boltzmann and Navier−Stokes
Figure 4. SEM images of poly([ILM-C12][TFPhB]) copolymer
particles prepared with (a) 2.0, (b) 4.0, (c) 6.0, and (d) 8.0 wt %
ionic monomer as a fraction of the total monomer weight.
dispersion polymerization containing different concentrations of
monomer [ILM-C12][TFPhB]. The particles obtained were
spherical and micrometer-sized and had a high degree of
monodispersity as evidenced by the ∼3% value measured for the
coefficient of the radius of variation Cv. The size and polydispersity
of the particles prepared are listed in Table 4. Increasing the
Table 4. Characterization of Poly(ionic liquid)-Containing
Latices
W
a
ah
C
vd
ILM a
(wt %) (nm) (nm) (%) dye (10−2 wt %)
b
c
e
latex
IL-monomer
L1
L2
L3
L4
L5
L6
L7
L8
L9
0.0
2.0
4.0
6.0
8.0
0.0
2.0
4.0
6.0
8.0
270
790
345
775
7
5
0.00
0.00
0.00
0.00
0.13
0.13
0.13
0.13
0.13
0.13
[ILM-C6][TFPhB]
[ILM-C6][TFPhB]
[ILM-C6][TFPhB]
[ILM-C6][TFPhB]
1070 855
8
1250 1265
9
575
430
365
600
900
935
620
475
440
655
925
985
8
equations. The conventional Huckel result, which assumes linear
̈
6
electrostatics, is increasingly inaccurate at high surface potentials37 as
the nonlinear interactions that result in condensation become
increasingly significant. To calculate the surface potential from the
measured μ, we use the method proposed by Ohshima and outlined
in section 3.2. A numerical solution of the Poisson−Boltzmann
equation in a salt-free medium is employed together with a single-
particle solution of the full electrokinetic equations, valid if the
particle volume fraction ηc is sufficiently small,37,41,42 to calculate the
dependence of μ as a function of Φs − Φo. A numerical interpolation
routine is then used to evaluate the surface potential from the
measured mobility data. In a counterion-only system, the surface
potential and ion concentration are no longer independent of each
other. Because the ions in solution arise from the dissociation of
surface groups, an increase in either the surface charge or the
concentration of particles results in an increase in the ion
concentration and a subsequent change in μ. Consequently, the
mobility μ in a salt-free system will depend strongly on the particle
concentration.
[ILM-C12][TFPhB]
[ILM-C12][TFPhB]
[ILM-C12][TFPhB]
8
12
6
L10 [ILM-C12][TFPhB]
7
a
Percentage of ionic liquid monomer as a fraction of the weight of
b
c
MMA and MAA monomers. Average radius from SEM. Average
hydrodynamic radius from DLS. Coefficient of radius variation from
SEM. Fluorescent DiIC18 dye added as a percentage of the total
d
e
preparation weight.
concentration of either the [ILM-C6][TFPhB] or [ILM-C12]-
[TFPhB] monomer in the synthesis resulted in an increase in the
mean particle radius. This dependence probably reflected the greater
solubility of the ILM-containing copolymer in the medium and the
consequent delay in precipitation until later in the reaction, at which
point the precursor polymer particles have grown significantly larger.
However the microstructure and, in particular, the location of the
ionic groups within the particles have not been determined. A
hydrophobic fluorescent dye (DiIC18, 1,1′-dioctadecyl-3,3,3′,3′-
tetramethylindocarbocyanine perchlorate) was incorporated53 into
preparations L5−L10 to confirm that model fluorescent particles,
suitable for confocal microscopy, could be prepared by this route.
The dimensionless electrophoretic mobility μ* is plotted in
Figure 5a as a function of WILM, the percentage by weight of ionic
monomer, for both the C6 and C12 systems. To ensure that the
mobility data reflects the concentration of surface groups and is
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an already-existing dispersion polymerization, resulting in
spherical, highly monodisperse particles with diameters ranging
from ∼50 nm to a few micrometers. A polymerizable ionic liquid
monomer was synthesized in which a tetra-alkyl ammonium
cation and a tetrakis[3,5-bis(trifluoromethyl) phenyl]borate
anion were bridged by a short C3 alkyl chain to a methacrylate
group. A homologous series of monomers were prepared with
different alkyl chain lengths (C4−C18). The charge on the
particle can be varied almost at will by changing the proportion of
the ionic liquid monomer copolymerized with methyl meth-
acrylate and methacrylic acid. In contrast to conventional
surfactant-based approaches, this new class of colloids represents
a nearly perfect approximation to a classical counterion-only
charged system. The ability to tune the charge and so control the
electrostatic interactions between nonpolar particles offers the
opportunity to explore systematically the complex phase diagram
of binary superlattice formation5,9 and establish the conditions
necessary for the self-assembly of new photonic materials.60 In
addition the ability to define a specific charge state in a mixture of
different particles may offer benefits for a new generation of high-
resolution electrophoretic displays.
Figure 5. (a) Reduced mobility μ* and (b) potential difference Φd = Φs
− Φo between the surface of the particle and the boundary of the WS cell
as a function of the weight percent of poly(ionic monomer), WILM
,
expressed as a fraction of the total weight of monomer used in the
particle synthesis. The solid lines are guides to the eye.
not affected by the particle concentration, all measurements were
recorded at a fixed colloid volume fraction of ηc = 3.8 × 10−5. The
full dependence of the mobility on the concentration of particles
will be the subject of a forthcoming paper. Without any
poly(ionic liquid) groups, the particles exhibit no response to the
applied electric field. Particles with ionic monomer move in the
same direction as the applied field, so the particles are positively
charged. The mobility increases as the concentration of PIL
groups increases although the dependence of μ* on WILM is less
than linear. As might be expected from the ionic dissociation data,
the particles functionalized with C12 cations display higher mobilities
than those containing C6 cations. We use this data to calculate the
dimensionless potential difference Φs − Φo between the surface of
the particle and the cell boundary, which in an interacting system
defines the electrophoretic mobility. The results are plotted in Figure
5b. Remarkably, we note that the corresponding potential differences,
derived from the solution of the full nonlinear PB equation, are now
very close to linear in the fraction of ionic monomer, suggesting that
the concentration of charged surface groups is directly proportional to
their bulk concentration. The potential differences are surprisingly
large with a maximum value for the 8 wt % C12 cation of Φs − Φo =
+7.0 0.4 or equivalently a potential of 180 9 mV. The high
particle charge results in a substantial pair repulsion that is apparent in
the strong, long-range ordering that is clearly visible in dilute
suspensions with optical microscopy. Preliminary holographic optical
tweezers experiments demonstrate the existence of strong electro-
static forces, and more detailed measurements are underway to check
the estimates of Φs found by electrophoresis. Surface potentials in
nonpolar solvents reported in the literature8,9,12,14,15 seldom exceed
100 mV and often are appreciably smaller.57,58 Indeed, the surface
potential of our PIL-functionalized particles is remarkably large even
by comparison to that of a highly charged aqueous system.59 Taken
together, these observations demonstrate that PIL-functionalized
particles form a unique model system with strong and adjustable
electrostatic interactions in a nonpolar environment.
ASSOCIATED CONTENT
■
S
* Supporting Information
NMR and elemental analysis data for all compounds. This
material is available free of charge via the Internet at http://pubs.
acs.org/.
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: p.bartlett@bristol.ac.uk.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
G.H. thanks the Punjab Educational Endowment Fund for
financial support. We thank Dr. N. Greinert of Merck Chemicals
Ltd. U.K., an affiliate of Merck KGaA, Darmstadt, Germany, for
providing the Na[TFPhB] precursor and for many helpful
discussions.
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