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Studying the Role of Surface Chemistry on

Polyelectrolyte Adsorption Using Gold-thiol Self-

assembled Monolayer with Optical Reflectivity

Plinio Maroni, Francisco Javier Montes Ruiz-Cabello and Alberto Tiraferri*

Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II,

Quai Ernest-Ansermet 30, 1205 Geneva, Switzerland

*Corresponding author e-mail address: alberto.tiraferri@unige.ch, phone: +41 22 379 6421

Supporting Information

Electronic Supplementary Material (ESI) for Soft Matter.This journal is © The Royal Society of Chemistry 2014

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Electrokinetic and sizing measurements of polymers. Electrokinetic and sizing

measurements were performed by light scattering with a ZetaNano ZS (Malvern Instruments,

Worcestershire, UK). A final polyelectrolyte concentration of 1 g/L was employed. The samples

were equilibrated for 90 s in the cell prior to the measurements. All experiments were conducted

in 10 mM NaCl. The electrophoretic mobility and the size of sodium poly(styrene sulfonate)

(PSS) were determined at pH 4.3, while those of poly(diallyldimethyl ammonium chloride)

(PDADMAC) were measured at pH 9.6. The measured values are reported in Table S1.

Table S1

polymer pH electrophoretic mobility

(×10−8, m2 V−1s−1)

hydrodynamic radius

(nm)

PSS 4.3 −3.51 ± 0.02 17.0 ± 3.5

PDADMAC 9.6 2.26 ± 0.54 3.3 ± 0.2

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Surface potential measurements and calculations. Measurements were conducted with

a closed-loop atomic force microscope (AFM, MFP-3D, Asylum Research) mounted on an

inverted optical microscope (Olympus IX70), adapting the procedure described in detail

elsewhere.1,2

All force measurements were conducted in a fluid cell, which was separated with a

Teflon spacer into two compartments. The substrate carrying the SAM film was located on one

side of the spacer and this side was filled with pure electrolyte solution of the desired chemistry.

On the other side of the spacer, a suspension of sulfate latex particles with diameter of 3 μm

(Invitrogen) was injected and left to deposit on the substrate. The fluid cell was then flushed with

the same salt solution as the one used to prepare the latex suspension in order to exchange the

liquid and to remove the remaining particles that did not attach to the substrate. Prior to use, the

particles had been dialyzed for about one week against Milli-Q water, until the conductivity

reached the value of the pure water.

The surface potential of the particle was initially measured by conducting force

measurements between two individual sulfate latex particles. One particle was picked up with

the cantilever, and the particle was centered above another particle deposited on the substrate.

The forces were obtained from the cantilever deflection recorded in the approach part of the force

curves and the spring constant of the cantilever. The spring constant was measured with the

thermal noise method. The surface potential of the particle probe was thus calculated. Forces

between latex particles and the SAM film were subsequently measured by recording the

interaction forces between the surface and the cantilever modified with the latex particle of

known surface potential. In particular, a measurement sequence consisted in measuring the

symmetric system, then the asymmetric system, and finally the symmetric system again. All

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experiments were conducted in 10 mM NaCl and the surface potential of the various SAM films

was measured at pH 4 and 10.

Forces between electric double layers were modeled with the Poisson-Boltzmann (PB)

theory.2,3

In particular, the Poisson-Boltzmann equation was solved for the case of two charged

plates and the Derjaguin approximation was applied to model the sphere-sphere and sphere-plate

geometries of our experiments. We consider two charged plates with an electrolyte solution in

between containing different types of ions i of number concentration ci and charge zi expressed in

units of the elementary charge q. The electric potential ψ(x) depends on the position x, whose

origin is fixed at the midplane and the two surfaces are located at x =± h/2, where h is the

separation distance between the plates. This potential profile can be obtained from the PB

equation:4,5

2

2

0

iz q

i ii

d qz c e

dx

, (S1)

where ε0 is the dielectric permittivity of vacuum, ε the dielectric constant with a value of 80 for

water at room temperature, β = 1/(kBT) is the inverse thermal energy, T is the absolute

temperature, and kB is the Boltzmann constant. The PB equation can be solved numerically

subject to the constant regulation (CR) boundary conditions:

0

/2

/ 2I D

x h

dC h

dx

, (S2)

where the subscript ± refers to the right (+) or left (−) surface, D

and

denote the diffuse-

layer potentials and surface charge density of the isolated surfaces, and

IC

their inner layer

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capacitances. The diffuse-layer potential of an isolated surface is related to the surface charge

density by

1/2

02 1i Dz q

B iik T c e

, (S3)

where the ± signs on the right-hand side of the equality sign refer to positive and negative

potentials. Instead of the inner layer capacitance, we report the regulation parameter defined

as:4,6

D

D I

Cp

C C

, (S4)

where for either surface the diffuse-layer capacitance is given by

1/22

0

1/2

1

21

i D

i D

z q

i ii

Dz qBD

ii

z c eqC

k Tc e

. (S5)

The regulation parameter provides a more intuitive interpretation of the boundary

conditions, since 1p

refers to constant charge (CC) conditions, and

0p to constant

potential (CP) conditions. One should recall that the parameters D

,

,

C

, and p

refer

to the surfaces at infinite separation, and are thus properties of the single, isolated surface. When

two surfaces approach, the actual diffuse-layer potentials and the surface charge densities will

vary with the separation distance.2,5,6

Forces between particles are calculated from the disjoining pressure, using the following

equations:3,4

2

012

iz q

B ii

dk T c e

dx

. (S6)

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Once the pressure is known as a function of the separation distance, free energy per unit

area can be calculated by its integration:

' 'h

W h h dh

. (S7)

Once this quantity is obtained, the forces between two particles can be found by invoking

the Derjaguin approximation:3

2 effF R W , (S8)

where the effective radius is given by:

1 2

1 2

eff

R RR

R R

, (S9)

where R1 and R2 are the radii of the two particles involved (sphere-sphere geometry). In the

symmetric sphere-sphere case R1 = R2 = R, and 2effR R , while in the particle-surface system,

effR R . This PB calculation of the forces was implemented in a least-squares fitting procedure,

and the modeled parameters were extracted from the experimental force curves. In the symmetric

situation, the diffuse-layer force depends on three parameters, namely, the salt concentration, c,

the diffuse-layer potential, ψD, and the regulation parameter, p. In the asymmetric situation, the

force depends on five parameters, namely the salt concentration, c, the diffuse-layer potentials

D

and D

for the right and left surfaces, and the corresponding regulation parameters p

and

p

. In our case, we shall omit the superscripts ±, since it will be clear from the context to

which surface one refers. More details about this theory and the respective calculations can be

found elsewhere.2 The charging parameters from this study are summarized in Table S1 below.

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Table S2

surface

surface potential

(mV)

regulation parameter

pH 4 pH 10 pH 4 pH 10

sulfate latex probe

-83 ± 2 -111 ± 3 0.66 ± 0.05 0.66 ± 0.05

OH -11.4 ± 0.4 -40 ± 2 0.39 ± 0.02 0.45 ± 0.02

NH2 +30.5 ± 1.0 +0.8 ± 0.5 0.56 ± 0.02 0.30 ± 0.02

CH3 -13.5 ± 0.3 -45 ± 2 0.31 ± 0.02 0.49 ± 0.02

COOH -13 ± 0.5 -39 ± 2 0.47 ± 0.02 0.31 ± 0.02

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Calculation of the sticking coefficient. The sticking coefficient is defined as the ratio

between the experimental adsorption rate coefficient and the theoretical value of the adsorption

rate, calculated by assuming perfect sink conditions:

ads

1 320.776

Rec

k

Dr

(10)

In this equation, r is the radius of the bore hole in the prism, 78.94 10 m2/s is the kinematic

viscosity of water, Dc is the diffusion coefficient of a polymer molecule, Re ur is the

Reynolds number, and is the dimensionless flow intensity parameter calculated for the

impinging jet geometry. The flow rate, u, was set at 1.3 mL/min. The theoretical rate is related

to the hydrodynamic radius of the polymer molecules, Rh, via the diffusion coefficient, Dc, in the

Stokes-Einstein equation: 6c B hD k T R , where kB is the Boltzmann constant, T is the

absolute temperature, and 48.9 10 Pas is the dynamic viscosity of water. The average value

of hydrodynamic radius presented in Table S1 of the Supporting Information was used to

describe the polymer molecules.

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Adsorbed mass at saturation as a function of pH on each individual surface type.

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Adsorption rate coefficient as a function of pH on each individual surface type.

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Adsorbed mass at saturation as a function of salt concentration on each individual surface

type.

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Adsorption rate coefficient as a function of salt concentration on each individual surface

type.

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References

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