Molecular approach to the surface potential estimate of thiolate-modified gold nanoparticles

Article abstract of DOI:10.1021/jp014423e

The electrophoretic mobility is measured by a photocorrelation spectroscopic method to derive a ??-potential as a function of pH using gold nanoparticles with a well-defined surface. Since the Debye length, 1/?o, of the dispersion ranges from 0.5 to 340 n

Full text of DOI:10.1021/jp014423e

7260
J. Phys. Chem. B 2002, 106, 7260-7266
Molecular Approach to the Surface Potential Estimate of Thiolate-Modified Gold
Nanoparticles
Keisaku Kimura* and Suguru Takashima
Department of Material Science, Himeji Institute of Technology, Kamigori, Hyogo 678-1297, Japan
Hiroyuki Ohshima
Faculty of Phamaceutical Sciences and Institute of Colloid and Interface Science, Science UniVersity of Tokyo,
Shinjuku-ku, Tokyo 162-0862, Japan
ReceiVed: December 5, 2001; In Final Form: April 12, 2002
The electrophoretic mobility is measured by a photocorrelation spectroscopic method to derive a ú-potential
as a function of pH using gold nanoparticles with a well-defined surface. Since the Debye length, 1/κ, of the
dispersion ranges from 0.5 to 340 nm and the radius of a particle a is in nanometer scale, we use a recently
developed formula (Ohshima, H. J. Colloid Interface Sci. 2001, 239, 587) for the estimate of ú-potentials
which is applicable to wide κa region. The ú-potentials derived are compared with those of theoretical ones
in which we use only molecular parameters such as dissociation constants of mercaptosuccinic acid and
given parameters such as a particle size, pH, composition of electrolyte in a dispersion, that means no adjustable
parameters used. Qualitative agreement was attained between ú-potentials and surface potentials purely from
theory.
Introduction
is infinite) in electrolytic solution. That is to say, nanoparticles
should be a good test material to this goal. Since the develop-
ment of the synthesis of surface-modified nanoparticles with
thiolate, it is possible to characterize the surface state in a
molecular level.3 The surface of SAM particles is ideally
molecularly homogeneous and thus their surface state can be
described in a molecular level. If so, we can derive the surface
potential solely by molecular parameters of surface modifiers.
To address this object, the following conditions must be
satisfied.
There is current interest in synthesizing and characterizing a
gold nanoparticle with a self-assembled monolayer (SAM)
surface both from a technological importance as a key substance
in nanotechnology and from a scientific view of size-dependent
properties. One of the most important parameters used to
characterize a particle is the charge or the surface potential of
particles. And yet the determination of the surface charge of
nanoparticles and its theoretical derivation is still a challenging
goal in colloid chemistry. Recent development for the SAM
formation on gold nanoparticles has potential to address this
formidable subject.1 However, a quantitative calculation of the
surface potential of a colloidal particle is still difficult because
of the lack of the knowledge regarding the accurate surface
structure of a particle if one wants to derive the potential using
only a set of molecular parameters. What is a charging
mechanism of a particle in a solvent and what determines the
surface potential are thus still open questions. A lack of the
methodology for accurate determination of the experimentally
available surface potential is another problem. We often use an
experimentally derived ú-potential instead of a surface potential,
and yet, a method of accurate determination of ú-potential from
electrophoretic mobility is a current interest.2 Although the
electric double layer masks the true feature of surface charges
of a particle, systematic examination of the behavior of the
particle under the external electric field may enable us to solve
the question of what is the surface potential.
(1) Knowledge of an accurate surface structure. One guar-
antees the SAM structure using mercaptosuccinic acid (MSA)
molecule as a surface modifier. All the analytic methods
including elemental analysis, thermogravimetric measurement,
and FTIR showed that the particles can be regarded as
molecules.4 Briefly, the occupation area per MSA molecule on
gold for 2 nm-particles, 0.156 nm2, is an average of (100) and
(111) surfaces which is directly identified by recent STM
microscopy.5
(2) Homogeneity of particle ensemble. Homogeneity of the
particle system is proved by the crystallization of particles as
reported by a recent paper.6 If particles are not uniform in size,
shape, and surface species, crystallization of particles is impos-
sible. The success of crystallization suggests that the particles
can be regarded as if it were a molecule.7
(3) The system should be as simple as possible to bear the
analytic evaluations. Ideally, the system should consist of only
particles and their counterions. It is a standard procedure to use
a solution with supporting electrolyte to maintain the constant
ionic strength preventing pH fluctuation caused by unintended
spurious contamination such as dissolution of carbon dioxide
and so forth or avoiding disturbance in adsorption-desorption
equilibrium. Hence, the above requisite contradicts the standard
condition in which the composition of solution becomes more
The profound understanding of the surface potential of a
nanoparticle may bridge over the valley between the charge
concept of ions (the radius of curvature is very small) and the
surface potential concept of solid plates (the radius of curvature
* Corresponding author. Phone: 81-791-58-0159. Fax: 81-791-58-0161.
E-mail: kimura@sci.himeji-tech.ac.jp.
10.1021/jp014423e CCC: $22.00 © 2002 American Chemical Society
Published on Web 06/27/2002

Surface Potential of Thiolate-Modified Au Nanoparticles
J. Phys. Chem. B, Vol. 106, No. 29, 2002 7261
or less complex. However, instead, we expect a large surface
potential at very low ion concentration that is realized in the
simple system.
When we have ideal particles whose surfaces are molecularly
clarified and have a sharp size distribution, all requisites from
(1) to (3) are satisfied. To date, it is not easy to get ideal
particles. But recent developments in crystallizing nanoparticles
encourage us to attempt to this goal. In this report, we try to
derive the surface potentials of nanoparticles with MSA using
no fitting parameters and compare them with experimentally
obtained ú-potentials. The present paper is, to our knowledge,
the first attempt to test existing theories, which predict the
surface potential of particles and plates with no adjustable
parameters, using a nanoparticle whose surface is characterized
in molecular level enabling theoretical calculation of the
potential.
Figure 1. Optical absorption spectra as a function of surface modifica-
tion. The spectra are normalized to the plasmon peak at about 530 nm.
(a) before modification, (b) surface modification without dialysis, (c)
surface modification with dialysis. Note that no large absorption is
apparent in the UV region after surface modification. Surface modifica-
tion induced slight broadening in the surface plasmon band.
Experimental Section
Chemicals. All the chemicals in this research are of reagent
grade and used as received. Hydrogen tetrachloroaurate tetra-
hydrate (HAuCl4•4H2O, 99%), mercaptosuccinic acid (HOO-
CCH2CH(SH)COOH, 97%), citric acid monohydrate (HOOC-
CH2C(OH)(COOH) CH2COOH•H2O, 99.5%), methanol (99.8%),
ethanol (99.5%), and hydrochloric acid solution containing 36%
HCl were from Wako Pure Chemical Co. Sodium hydroxide
(95%) was from Kanto Chemical Co. Distilled water of high
resistivity > 18.0 MΩ cm was used just after distillation to
make a sample suspension.
Particle Synthesis and Surface Modification. Gold nano-
particles were prepared according to the established method.8
Briefly; 106 mL of 2.2 mM sodium citrate was brought to boil
for 10 min and 1 mL of 24.3 mM HAuCl4 was added under
vigorous stirring. After the color of the solution changed to red
for about 3 min, the solution was boiled for the next 15 min
and then left to cool. The formal reaction of this process is
expressed as follows:
reference to the above standard system. The reason for avoiding
the use of a normal buffer solution is as follows: (1) To
minimize the effect of ion adsorption on the particle surface,
which may disturb the surface charge; (2) to avoid inter-ion
interaction in bulk solution; ( 3) to simplify the theoretical
treatment using a simple dispersion constitution which we have
mentioned already in the Introduction. Hence the objective ion
species are limited to only four, H+, Na+, OH- and Cl-, and at
most three of them participate in each measurement. Table 1
shows the list of ionic species used and the observed pH
readings. We have derived the Debye parameter κ using the
parameters listed in Table 1. The κ is given by (∑ zi2e2ni/
ꢀrꢀ0kT)1/2, in which zi is the valence of ith ion, e is the elementary
electric charge, ni is the bulk concentration of ith ion and is
connected to the total bulk ion concentration by n ) ∑ ni. ꢀr
and ꢀ0 are, respectively, the relative and vacuum dielectric
constants. We used the same sample dispersion for pH measure-
ments and for electrophoretic measurements. Since the pH
reading was not stable especially for the neutral region, we had
to repeat pH measurements several times with fresh sample
dispersion in each case. The maximum number of measurements
was 20 for pH 6.7 and the minimum was 5 for pH 3.5. We
took arithmetic average for the values thus obtained as a pH
value.
Instruments. ú-Potential and dynamic light scattering mea-
surements were conducted with an Otsuka ELS 800 electro-
phoretic light-scattering spectrophotometer with a 10-mW He-
Ne laser. Applied voltages were selected in the range 50∼100
V. We washed the measurement cell at least two times with a
sample dispersion to avoid unintended contamination with
spurious species from the cell wall. This is because the
electrophoretic behaviors are very sensitive, especially in the
neutral region on account of the low ionic intensities in the
sample dispersion. We also took care of the contamination from
air and the wall of the vessel used so that all distilled water
was used just after distillation and each measurement was
finished within 2 h after commencement of the experiment to
avoid the above-mentioned contamination. Electrophoretic
measurements were also repeated several times because of the
fluctuation of the readings. The maximum number of measure-
ments was 14 for the neutral region and the minimum 5 for the
acidic region. Size histogram was obtained with a Hitachi-8100
transmission electron microscope (TEM), operated at 200 kV
with 2.1 Å point resolution. The specimen was prepared by
dropping the suspension on an amorphous carbon-coated copper
2HAuCl4 + 3C6H8O7 (citric acid) f
2Au + 3C5H6O5 (3-ketoglutaric acid) + 8HCl + 3CO2
Eighty milliliters of the cooled solution was then mixed with
80 mL of 6 mM (largely excess amount) mercaptosuccinic acid
aqueous solution for 90 min, then sealed into a Visking tube
(30/32), and dialyzed against distilled water. We needed 5-days-
dialysis with two times exchange of water per day during
dialysis until there was no smell of sulfur from free mercap-
tosuccinic acid. The byproduct, HCl, was also removed during
this process. The final pH of the solution was 5.8. After dialysis,
the UV bands in the absorption spectra which are originated
from citrate or mercaptosuccinic acid disappeared showing that
pure carboxylate-modified gold particles were formed (Figure
1, compared c to a or b). We have made many preparations,
because, as stated in the next paragraph, fresh sample dispersions
were needed for the every pH reading and mobility measure-
ments to avoid any unintended exogenous contamination. These
particles have a mean diameter in the range 15∼25 nm for the
different lots, 24 nm for the majority. The number of MSA
molecules per single particle is calculated to be 8500 for the
size of a 24-nm particle .
pH Titration. Hydrochloric acid was used in the acidic region
to change the pH of the dispersion and sodium hydroxide was
used in alkaline region. This is in contrast to the standard
electrolytic solution in which ion strength is maintained constant
with buffer solution. Hence, our system is rather unusual in

7262 J. Phys. Chem. B, Vol. 106, No. 29, 2002
Kimura et al.
TABLE 1: List of Concentration of Proton, Hydroxyl Ion, Chloride Ion, and Sodium Ion, Debye Length, and Kr
pH
[H+] (M)
[OH-] (M)
[Cl-] (M)
[Na+] (M)
1/κ (nm)
κa
2.5
3.5
4.9
5.8
6.7
3.16 × 10-3
3.16 × 10-4
1.26 × 10-5
1.58 × 10-6
2.00 × 10-7
3.98 × 10-10
2.51 × 10-12
2.00 × 10-13
2.00 × 10-14
3.16 × 10-12
3.16 × 10-11
7.94 × 10-10
6.31 × 10-9
5.01 × 10-8
2.51 × 10-5
3.98 × 10-3
5.01 × 10-2
5.01 × 10-1
5.00 × 10-3
0
0
0
0
5.00 × 10-4
15.1
54.4
342
60.7
18.8
4.54
1.36
0.795
0.221
0.035
0.198
0.638
2.643
8.824
5.00 × 10-5
0
0
0
0
0
0
5.00 × 10-5
5.00 × 10-4
5.00 × 10-3
5.00 × 10-2
5.00 × 10-1
9.4
11.6
12.7
13.7
Figure 2. TEM photograph of surface-modified particles and the size
histogram.
mesh and drying it in air. Fourier transform infrared spectra
were measured with a HORIBA FT-210 infrared spectropho-
tometer to trace the surface modification of the particles.
Ultraviolet-visible absorption spectra of the suspension were
recorded on a Hitachi U-3210 spectrophotometer. No correction
was made for the scattering effect.
Results
Characterization of Particles. FTIR, electrophoretic mobil-
ity, and high-resolution transmission electron microscopic
measurements were used for the examination of surface structure
of the particles. A brief summary is given for IR data.4 The
strong doublet at 1580 cm-1 and singlet at 1404 cm-1 confirmed
the stretching vibration of a carboxylate group. The band at
1700 cm-1 showed the carbonyl of carboxyl group. The broad
peak at around 3400 cm-1 identified the existence of bound
water. The content of water was confirmed by thermal gravi-
metric analysis in the previous paper giving MSA:water ∼ 1:1.4
The disappearance of the band at 2548 cm-1 in the RS-H region
confirmed the formation of RS-Au bonding. No change was
observed in the size histogram before and after the surface
modification, suggesting that there was no coagulation induced
by the surface modification. Figure 2 stands for the typical size
histogram after surface modification and TEM photograph. The
number of sample particles were 305 and the median diameter
was determined to be 24 nm.
Effect of Surface Modification on Electrophoretic Behav-
iors. Comparison of osmotic curves was made before and after
the substitution of MSA. It is not easy to determine the surface-
adsorbed species on as-prepared particles because of the
contamination with byproducts through chemical reaction. After
a surface modification, we confirmed that the entire surface is
covered basically with one species of mercaptosuccinic acid.
Figure 3 is photographs of the electro-osmotic profiles before
(b) and after (a) surface modification. The monotonic peak
profile as a function of cell position in (a) stands for the
existence of unique species in the sample dispersion and the
complex profile in (b) indicates that there are at least three
different charged states in the sample particles.
Figure 3. Electro-osmotic profile at several different positions from
the cell wall. (a) After surface modification by MSA at pH 5.8. (b)
Before modification at pH 7.0.
TABLE 2: List of Electrophoretic Mobility, µ, Scaled
Electrophoretic Mobility, Em, Surface Charge Density, σ,
ú-potential, and Surface Potential ψ0
pH µ (10-4 cm2/V s) -Em σ (C/m2) ú-pot (mV) surf. pot. (mV)
3.5
4.9
5.8
6.7
9.4
11.6
12.7
-1.05
-2.84
-6.52
-7.15
-3.06
-2.55
-1.51
0.79 -0.1335
2.11 -0.7590
4.86 -1.2045
5.34 -1.4460
2.28 -1.5000
1.91 -1.5000
1.13 -1.5000
-19.8
-55.7
-128.0
-169.7
-61.8
-49.4
-23.9
-240
-397
-516
-436
-378
-305
-243
in Table 2 with relevant experimental parameters such as surface
charge density σ, ú-potential derived from µ, and theoretical
surface potential ψ0, all of which are discussed in the Calcula-
tions section. As stated in the Experimental Section, the
measured mobility scattered in a wide range especially for the
neutral region, so we took a statistical average in order to
determine the value. The value listed in Table 2 is thus the one
after averaging process. To clarify this fluctuation, the mobility
dispersion, the difference of the reading of the electrophoretic
mobility at each measurement from the averaged value, is plotted
in Figure 4. As seen in this figure, an increase in electrolyte
Electrophoretic Mobility of Particles at Several pH. The
electrophoretic mobility µ (µm/s/(V/cm)) at several pH are listed

Surface Potential of Thiolate-Modified Au Nanoparticles
J. Phys. Chem. B, Vol. 106, No. 29, 2002 7263
hold:
RH1H2 f RH2- + H1
RH2- f R2- + H2
K1[RH1H2] ) [RH2 ][H+]
+
-
K2[RH2 ] ) [R2-][H+]
+
+
-
RH1H2 f RH1- + H2
RH1- f R2- + H1
K2[RH1H2] ) [RH1 ][H+]
-
K1[RH1 ] ) [R2-][H+] (1)
+
-
For simplicity, we abbreviate [H+] ) x, [RH1H2] ) R, and the
initial value of R as R0. Therefore the relation of mass balance
and eq 1 lead to
Figure 4. Dispersion diagram of electrophoretic mobility at several
pH. Each plot is drawn for the difference from the mathematical average
(horizontal line at position 0) at each pH. The plots are not symmetric
against acid and alkaline end, and have maximum fluctuation around
pH 7.
R0 ) [RH1H2] + [RH1 ] + [RH2 ] + [R2-]
-
-
RK2 RK1 RK1K2
) R +
+
+
x2
x
x
R
x2
)
(x + K1)(x + K2)
(2)
From the charge balance relation in the absence of electrolytes,
we have
x ) 2[R2-] + [RH1 ] + [RH2 ] + [OH-]
-
-
K1K2 K2 K1
Kw[H2O]
) R 2
+
+
+
, (3)
(
)
x2
x
x
x
in which Kw is a dissociation constant of water. From eqs 2
Figure 5. Optical absorption spectra as a function of pH. To avoid
overlapping of spectra, the data of pH 4.9 and 11.6 are omitted in this
figure. The spectra are normalized to that of the plasmon band. Three
lines for pH 5.8, 11.6, and 12.7 overlapped completely. The line for
pH 4.9 lies between pH 3.5 and 5.8. The plasmon peak value, 526 nm,
is the same for pH 5.8, 11.6, and 12.7, but is 528 nm for pH 3.5 and
4.9.
and 3,
R0x2
K1K2 K2 K1
Kw
x
x )
2
+
+
+
(4)
(
)
x2
x
x
(x + K1)(x + K2)
Equation 4 relates the initial concentration of MSA to the
observed pH of the suspension for free dissociation of MSA
bound to the particle under no addition of electrolytes. This is
discussed in a later section.
By definition, the degree of electrolytic dissociation is given
as
concentration at both pH sides largely depressed the fluctuation
in mobility measurement.
Effect of pH on Absorption Spectrum. No change was
found for the peak position and line profiles for the surface
plasmon band of the sample before modification as a function
of pH, but a slight difference was observed for the surface-
modified sample in the long wavelength region (Figure 5). This
slight broadening in this region may suggests that a large change
of surface charge affects the surface plasmon oscillation or more
likely suggests the formation of a weakly coupled embryo in
the dispersion at the acid condition.
-
-
2[R2-] + [RH1 ] + [RH2 ]
R )
)
2R0
2K1K2 + (K1 + K2)x
2(K1 + x)(K2 + x)
(5)
Calculations
where we neglect the term Kw that has minor contribution.
Equation 5 is independent of the existence and the absence of
electrolyte, because the concentration of constituent species
[R2-], [RH1-], and [RH2-] are solely determined by eq 1. Figure
6 shows the degree of electrolytic dissociation as a function of
x, in which we use the values of K1 and K2 as those of succinic
acid,9 because of the lack of available data for thiol derivation.
Moreover, we assume no effect from gold particles on K1 and
K2. The curve shows monotonic trends as a function of pH,
because the values K1 and K2 are close to each other. From this
figure, the charge density of particles is easily seen as a function
of pH.
Before deriving the surface potential, we need to calculate
relevant parameters such as degree of electrolytic dissociation,
surface charge density as a function of pH, and a maximum
charge density. The external variables to take into account are
the amount of MSA on the particles, pH, as well as ionic
strength of the added electrolytes.
Degree of Electrolytic Dissociation r. First, we abbreviate
MSA bound on a particle as RH1H2 since MSA is dicarboxylic
acid. We assume that there is no interaction between the two
carboxylic groups, so that the equilibrium constant is indepen-
dent of the order of dissociation. We also assume that added
electrolytes such as HCl and NaOH dissociate completely in
whole pH region. Hence we have only two equilibrium constants
K1 for proton H1 and K2 for H2 and the following four relations
Charge Density at the Surface. It was reported that the
maximum packing density of thiol, S0, for the gold flat surface
was 0.214 nm2.10 We accept this value for large particles. Since

7264 J. Phys. Chem. B, Vol. 106, No. 29, 2002
Kimura et al.
Smoluchowski or Hu¨ckel equation. However, these equations
have severe restriction to the applicability in the range of κa,
in which κ is the Debye parameter and a is the particle radius.
Very recently, Ohshima2 derived an interpolation formula which
is applicable to κa in the wide range. Following this formula,
electrophoretic mobility µ is given by
2ꢀrꢀ0ú
3η
m+ + m- zeú
2 f3(κa) -
2 f4(κa)
zeú
kT
µ )
f1(κa) -
[
]
(
)
(
)
2
kT
(7)
in which η is the viscosity of the solution, m( are dimensionless
ionic drag coefficients for cation and anion, f1, f3, and f4 are a
function of κa and are given by
1
f1(κa) ) 1 +
2[1 + 2.5/{κa(1 + 2e-κa)}]3
Figure 6. Degree of electrolytic dissociation as a function of pH.
Assuming monolayer coverage of MSA and using eq 5 with the
literature values K1 and K2, R is plotted against pH.
κa{κa + 1.3e-0.18κa + 2.5}
f3(κa) )
2{κa + 1.2e-7.4κa + 4.8}3
9κa{κa + 5.2e-3.9κa + 5.6}
MSA is a divalent acid, the calculated charge density from the
value, 2e/0.214 nm2, becomes 1.5 C/m2, which is the largest
ever reported among SAM particles. Compare this value to that
of the fully charged metal surface in electrolytic solution,11
around 0.1∼0.3 C/m2 and to that of sodium and potassium ion,
1.3 and 0.72 C/m2, respectively, assuming that the ionic radius
the same as in a solid salt. The surface charge density as a
function of pH is given by using the maximum surface charge
density σ0 stated above and by the degree of electrolytic
dissociation
f4(κa) )
(8)
(9)
8{κa - 1.55e-0.32κa + 6.02}3
2ꢀrꢀ0kTNA
m( )
0
3ηzΛ(
in which the limiting conductance of cation and anion Λ(0 are
given by the limiting mobility of constituent ions u( as Λ(
0
)
0
Fu( in which F is the Faraday constant. From a handbook,
u( values are known for ions of H+, Na+, OH-, and Cl-, hence
we can solve eq 7 using experimental µ. Table 1 includes the
list of parameters relevant to solve the above equation and the
final result; ú-potential is given in Table 2 for the sake of
comparison with surface potential.
σ ) σ0R
(6)
Several σ values are listed in Table 2. It should be noted that
the surface of a particle is almost fully charged even at a neutral
region.
Surface Potential. Surface potential is very sensitive to the
adsorption of ion species to the dissociative site.12 Since we
have carefully selected ion species, there are only symmetric
electrolyte ions as listed in Table 1. A surface potential is
connected to the surface charge density as shown in the
following formula for a spherical particle.13
MSA Coverage on a Particle. We have already reported
the average MSA coverage as being 1/2 of all surface Au atoms
from the elemental analysis.4 This value is also confirmed by
the recent STM direct observation on Au(100) and (111)
surfaces.5 Comparing the above data with the result of the
current experiment is interesting. Assuming that there is no ionic
contamination, we can estimate the average MSA coverage on
the gold surface using the degree of electrolytic dissociation.
The basic idea is that the number of free protons, thus pH of
the solution, can be correlated to the dissociation constant of
succinic acid as well as to the number of MSA molecules
adsorbed on the particle, which can be calculated from the
diameter of particles. The result is, hence, compared with the
observed pH, 5.8, of the suspension. To calculate pH from eq
4, we need to evaluate R0. The weight of gold in a unit volume
of suspension is given by w ) 4π(D/2)3FN/3, in which D is a
diameter of particle, F is the density of gold, and N is the number
of particles in a unit volume of suspension. The number of MSA
molecules is N(4π(D/2)2/S0). Finally, the number of MSA
molecules in a unit volume is given by 6w/FDS0, leading to
8.71 × 1014/cm3 ) 1.45 × 10-6 M using experimental values
w ) 1.39 × 10-5 g/cm3, F ) 19.3 g/cm3, D ) 24 nm, S0 )
0.214 nm2. Setting pK1 ) 4.19, pK2 ) 5.64, and R0 ) 1.45 ×
10-6 M, pH is calculated to 5.7. The above estimate is an ideal
case. If half of the surface is occupied, that is, the occupied
area per single MSA molecule is twice that of S0, we have
pH ) 5.9.
2ꢀrꢀ0κkT
y
1
κa
2
σ )
sinh
1 +
+
2
( )
(
)
[
e
2
cosh (y/4)
1/2
8 ln[cosh(y/4)]
sinh2(y/2)
1
(10)
2
(
)
]
(κa)
in which y ) eψ0/kT and other parameters already appeared.
Since all parameters in eq 10 are known, we can determine
surface potential ψ0 from σ and it is listed in Table 2.
Discussion
Evidence of Self-Assembled Monolayer. In the absence of
electrolyte, the pH of the dispersion became 5.8. Assuming
complete coverage, it is calculated to be 5.7 and 5.9 for half
coverage. Considering the size distribution of this particle and
the limited accuracy of pH-measurement at neutral region, the
calculated surface density 1-0.5 layer implies that almost of
all particles are fully covered by a MSA monolayer. In other
words, about half of the surface gold atoms are directly bound
to MSA molecules.5 Recall that two gold atoms occupied 0.17
nm2 on the (100) surface using a bulk lattice constant of 0.408
nm. This is consistent with other observations such as elemental
Derivation of ú-Potential. It is a most common process to
derive ú-potential from electrophoretic mobility using the

Surface Potential of Thiolate-Modified Au Nanoparticles
J. Phys. Chem. B, Vol. 106, No. 29, 2002 7265
Figure 9. Comparison of ú-potential with surface potential ψ0 as a
function of pH.
Each domain named, say, Henry, is the Em-κa region in which
the Henry equation is good.18 It should be noted that the present
data points scatter into a wide range and that it is impossible to
apply one of these well-known equations for the whole region.
All particles deposited to sediment at the two points corre-
sponding to pH ) 2.5 and 13.7, indicating that the ú-potential
were almost zero.
Figure 7. Debye length 1/κ as a function of pH.
Spectral Change. We have noticed a slight broadening at
the plasmon band by virtue of the surface modifications (Figure
1) and pH change (Figure 5). We have already pointed out two
possibilities such as a surface charge directly affecting the
electronic state of metallic particles or the surface charge
inducing particle coagulation, although there is no direct
evidence in the TEM photograph. Since we have already
observed the formation of a particle crystal in the presence of
hydrochloric acid added to the suspension,6 the pH-dependent
broadening in Figure 5 may be ascribed to the formation of
flocculent in the suspension. This can be easily explained by
the DLVO (Derjaguin-Landau-Verway-Overbeek) theory. On
the other hand, the broadening associated with the surface
modification is not yet clear.
Comparison of Surface Potential with ú-Potential. First
we will discuss the accuracy of mobility measurement. Indeed,
a large fluctuation was observed around pH 7 as shown in Figure
4. There is less quantity of additional electrolyte in this region
and a small amount of contaminating ions may induce a large
effect. This is the reason the fluctuation was depressed in both
extreme pH regions where we added HCl or NaOH.
Figure 8. Diagram for κa and scaled electrophoretic mobility Em.
Each domain named person’s abbreviation is the applicable region of
the equations proposed by those authors. Concerning details, see
ref 18.
analysis and STM. The uniformity of the surface is also
confirmed by electro-osmosis curves after the surface modifica-
tion by MSA contrast to the untreated samples, which show
the existence of at least three different charged states. Observed
packing density is almost the limit of coverage when taking
into account the molecular size of MSA and its molecular
motion.14 Thus the largest surface charge density up to -1.5
C/m2 is substantiated in a nanoparticle as has been mentioned
in the Calculations section..
Figure 9 compares the observed ú-potential with the calcu-
lated surface potential as a function of pH. The agreement
between calculated surface potential and the observed ú-potential
is not successful, especially at both strong acid and alkaline
regions. This may be due to removal of ligands from the surface
of particles at such extreme conditions, which induces the
overestimate of the surface charge leading to a large surface
potential in the calculation. This preposition was consistent with
the finding that some parts of aggregates of colloids did not
disperse again when returned to neutral pH. The incompleteness
of surface coverage induces strong coagulation. If the adsorp-
tion-desorption equilibrium constant of MSA as a function of
pH is available, we can correct the deviation. Although there is
a significant difference in quantity between theory and calcula-
tion, we have qualitative agreement between them. The differ-
ence between ú-potential and surface potential will be ascribed
to the following reasons.
Adequacy of Equation. The well-known Smoluchowski
equation correlates the electrophoretic mobility µ with ú-po-
tential at the limit of κa .1, while the Hu¨ckel formula is
applicable to the limit of κa , 1. In the present system, the
ionic concentration ranges from µM to 10mM, implying that
the Debye length has largely changed. We show this result
clearly in Figure 7 by plotting the 1/κ value as a function of
pH where 1/κ ) 1.36 nm at pH 12.7 and 342 nm at pH 5.8 at
which nothing was added to the dispersion. Hence we cannot
apply both equations to estimate ú-potential. For arbitrary values
of κa and ú, eq 7 predicts the mobility accurately. In all cases,
Smoluchowski and Hu¨ckel equations gave smaller absolute
values for ú-potential. The applicability of Smoluchowski,
Hu¨ckel, Henry15 as well as Ohshima-Healy-White16 or O’Brien-
White’s numerical program17 for the parameter range of κa and
scaled electrophoretic mobility Em is shown in Figure 8. The
scaled electrophoretic mobility is a dimensionless mobility and
is defined by
1. ú-Potential is defined at the slipping layer, hence its
absolute value is always smaller than that of the surface
potential.
2. The glass wall may contaminate the system though we
washed several times with the same sample dispersions.
3ηze
Em )
µ.
(11)
2ꢀrꢀ0kT

7266 J. Phys. Chem. B, Vol. 106, No. 29, 2002
Kimura et al.
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3. Dissolution of carbon dioxide from air though we did all
experiments within a short time interval.
4. Incomplete coverage of MSA against our estimate of full
coverage.
5. We used distilled water instead of ultra clean water.
Among these, 2 and 3 are an exogenous impurity effect and
can be treated by “the effect of background ion”. This effect
largely depresses the absolute value of the surface potential.19
An unknown contaminant may largely decrease the surface
potential of the particles because of the low ionic intensity in
the present study. The effect of the variation of ionic strength
on the adsorption-desorption equilibrium has already been
discussed. Reason 1 is consistent with the results shown in
Figure 9 in the point that all measured potentials are less than
those of theory.
We believe that the present system is a good model for
charged particles in a suspension. However, it is still an open
question whether the surface potential concept can be applied
to nanometer-sized small particles up to 1 nm or so. Therefore
the measurement of ú-potential for much smaller particles
ranging over 2 or 3 nm in size is crucial for understanding the
potential of solid surfaces in solution. We have tried to measure
the ú-potential of the particles whose sizes are in the range from
2 to 4 nm; however, an unknown unstable scattering effect
prevents the accurate determination of the mobility. It remains
to us for a future task to measure the ú-potential of this
ultimately small particle, which lies between ions with formal
charge density of the order of 1 C/m2 and particles with typical
surface charge density of the order of 0.1 C/m2.
(4) Chen, S.; Kimura, K. Langmuir 1999, 15, 1075.
(5) Liang, S.; Matsubara, H.; Sato, S.; Yao, H.; Kimura, K. To be
submitted. It was directly proved by STM microscopy on the nanoparticles
that the gold surface was completely covered by MSA molecules with no
void and the surface of two Au atoms was occupied by a single MSA
molecule irrespective of the facet (100) or (111). The details of STM analysis
will be published elsewhere.
(6) Kimura, K.; Sato, S.; Yao, H. Chem. Lett. 2001, 372.
(7) (a) van Staveren, M. P.; Brom, H. B. J.; De Jongh, L. J.; Schmid,
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Cleveland, C. L.; Luedtke, W. D.; Landman, U. AdV. Mater. 1996, 8, 428.
(c) Sandhyaranik, N.; Resmi, M. R.; Unnikrishnan, R.; Vidyasaggar, K.;
Ma, S.; Antony, M. P.; Selvam, G. P.; Visalakshi, V.; Chandrakumar, N.;
Pandian, K.; Tao, Yu-Tai; Pradeep, T. Chem. Mater. 2000, 12, 104.
(8) Handley, D. A. Colloidal Gold: Principles, Methods, and Applica-
tion; Hayat, M. A., Ed.; Academic Press: San Diego, CA, 1989; Vol. 1,
pp 13-32.
(9) The equilibrium constants, pK1 ) 4.19, pK2 ) 5.64 are from Wade,
L. G., Jr. Organic Chemistry; Prentice Hall: New York, 1987; p 978.
(10) Sellers, H.; Ulman, A.; Schnidman, Y.; Eilers, J. E. J. Am. Chem.
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(11) Typical value of surface charge density 0.1-0.3 C/m2. Israelachvili,
J. N. Intermolecular & Surface Forces, 2nd ed.; Academic Press: San
Diego, CA, 1992; Chapter 12, p 217.
In conclusion, we cannot achieve completely the original
objective that the measurement of ú-potential of a nanometer-
sized particle will check the applicability of surface potential
calculation from existing theory. We will get quantitative
agreement between the two potentials in future when one solves
above points from 1 to 5.
(12) Israelachvili, J. N. Intermolecular & Surface Forces, 2nd ed.;
Academic Press: San Diego, CA, 1992; p 234.
(13) (a) Ohshima, H. Electrical Double Layer. In Electrical Phenomena
at Interfaces; Fundamentals, Measurements, and Applications; Ohshima,
H., Furusawa, K., Eds.; 1998, Marcel Dekker: New York, 1998; p 10. (b)
Ohshima, H.; Healy, T. W.; White, L. R. J. Colloid Interface Sci. 1982,
90, 17. (c) Ohshima, H. J. Colloid Interface Sci. 1995, 171, 525.
(14) The chirality of the combined MSA molecules on the Au surface
was found by the STM images. Detailed analysis will be published soon.
(15) Henry, D. C. Proc. R. Soc. London, Ser. A 1931, 133, 106.
(16) Ohshima, H.; Healy, T. W.; White, L. R. J. Chem. Soc., Faraday
Trans. 2 1983, 79, 1613.
Acknowledgment. We thankDr. K. Takamura of BASF
Corp. for his invaluable comments on the electrophoretic
mobility in the low ionic strength region and its relation to
ú-potential. This study was supported in part by grant-in-aid
for Scientific Research on Basic Research (A: 09304068) from
Ministry of Education, Science, Sports and Culture, Japan.
(17) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2
1978, 74, 1607.
(18) Ohshima, H. Electrokinetic Behavior of Particles. Encyclopedia of
Surface and Colloid Science; Hubbard, A., Ed.; Marcel Dekker: New York,
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References and Notes
(1) (a) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman,
R. J. Chem. Soc., Chem. Commun. 1994, 801. (b) Motte, L.; Billoudet, F.;
(19) Israelachvili, J. N. Intermolecular & Surface Forces, 2nd ed.;
Academic Press: San Diego, CA, 1992; pp 235-237.