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Salt-induced changes in the growth of polyelectrolyte layers of poly(diallyl-dimethylammonium chloride) and poly(4-styrene sulfonate of sodium)†

Eduardo Guzm�an, Hern�an Ritacco, Jos�e E. F. Rubio, Ram�on G. Rubio* and Francisco Ortega

Received 20th January 2009, Accepted 26th February 2009

First published as an Advance Article on the web 21st April 2009

DOI: 10.1039/b901193e

Multilayers formed by the sodium salt of poly(4-styrene sulfonate), PSS, and

poly(diallyldimethylammonium) chloride, PDADMAC, have been built by electrostatic self-assembly

from polyelectrolyte aqueous solutions of different ionic strengths. The growth of the multilayers has

been followed using dissipative quartz crystal microbalance and ellipsometry. Neutron reflectometry

and XPS data indicate that the PSS and PDADMAC layers interpenetrate leading to an almost

homogeneous polymer film. The results show that on increasing [NaCl] the growing process changes

from a linear to a non-linear regime. The comparison of the thickness values obtained from QCM and

ellipsometry has allowed us to calculate the water content of the polymer film. The results agree with

those obtained by neutron reflectometry. The analysis of the QCM data has provided values of the

complex shear modulus, which are typical of a rubber-like polymer system. The analysis of the mass

adsorbed calculated by the ellipsometry measurements indicated that the charge compensation

mechanism changes from intrinsic at low ionic strengths to mainly extrinsic at high ionic strengths.

Finally, it was found that the response of a polymer film to a change in [NaCl] is rather different for

films grown at low or at high ionic strengths.

1. Introduction

Nanostructured materials are nowadays a fundamental field of

research with implications in many important present and future

applications. Self-assembled multilayers are among this type of

materials. One of the most versatile and promising techniques for

constructing functionalized thin layers is the layer-by-layer

(LbL) method. In this method charged materials are used

sequentially to build-up multilayers by self-assembly. Since the

pioneering work of Decher et al.,1–3 who used polyelectrolytes of

opposite charges as building blocks in the multilayer assembly,

the list of possible construction components has increased

enormously: biopolymers4–7 (such as peptides, proteins, nucleic

acid, etc.), colloidal particles,8–10 carbon nanotubes7,11 and

microgels.12 Furthermore, the method is not limited to materials

with charged groups like strong polyelectrolytes, making it

possible to build multilayers based on other types of interactions

such as acid–base reactions of weak polyelectrolytes13 or

hydrogen bonds.14 An advantage of the LbL method compared

to other techniques, like the Langmuir-Blodgett,15 is that LbL-

multilayers can be built-up on substrates other than flat ones,1

e.g. colloidal particles16–18 or fluid interfaces (floating multi-

layers).19

The LbL method has been successfully used in many appli-

cations and in the design of functional materials such as contact

lenses,3 conductive layers,20 permselective membranes,21,22

Departamento de Quımica-Fısica I, Facultad de Ciencias Quımicas,Universidad Complutense de Madrid, Ciudad Universitaria s/n,28040-Madrid, Spain. E-mail: rgrubio@quim.ucm.es; Fax: +34 91 3944135; Tel: +34 91 394 4123

† Electronic supplementary information (ESI) available: Ellipsometryresults and refractive index. See DOI: 10.1039/b901193e

2130 | Soft Matter, 2009, 5, 2130–2142

sensors,23 light-emitting thin films,24 electrochromic films,25,26

and non-linear optical devices.27

Several variables have a strong influence in the building

process of polyelectrolyte multilayers, among them: ionic

strength,28,29 solvent quality for the polyelectrolytes,29 pH30 and

temperature31 are the most relevant. A quantitative under-

standing of their effect on the structure of the layers is important,

in part due to the fact that multilayers are non-equilibrium

systems, and therefore their structures strongly depend on the

conditions and procedure used for their growth.

Most studies concerning the building of polyelectrolyte

multilayers have focused on dry systems. However, for applica-

tions such as nanocapsules, the drying process between two

consecutive polymer layers is not carried out, and only the

process in ‘‘wet’’ conditions is relevant. The same is true for other

applications. Therefore, it is important to study the ‘‘in situ’’

build-up of the multilayers.

In this work, experimental results on layer thicknesses as

a function of the number of layers constructed in different ionic

strength conditions are presented. The mechanism of multilayer

growth, its water content and the mechanical properties will be

discussed. The multilayer formed by the sodium salt of poly(4-

styrene sulfonate), PSS, and poly(diallyldimethylammonium)

chloride, PDADMAC, has been chosen because some studies

have been published previously, for example: the effect of solvent

quality on multilayer growth,29 and the effect of temperature on

the building process.31

A combination of several experimental techniques was used

in this study including: dissipative quartz crystal microbalance

(D-QCM), ellipsometry, X-ray photoelectron spectroscopy

(XPS), neutron reflectivity (NR) and atomic force microscopy

(AFM).

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2. Experimental

2.1. Materials

The polyanion used was the sodium salt of poly(4-styrene

sulfonate) (PSS). The PSS molecular weight was 70 kDa. The

polycation used was poly(diallyldimethylammonium) chloride

(PDADMAC); the molecular weight of this polymer being in the

range 200–350 kDa. Both polymers were purchased from Sigma-

Aldrich (Germany).

The solution ionic strengths were controlled by adding NaCl

(Sigma-Aldrich, purity >99.9%). For the experiments on neutron

reflectivity we used a sodium salt of perdeuterated sodium

poly(styrene sultonate) with a molecular weight of 55 kDa,

purchased from Polymer Source (Canada). The water was of

Milli-Q quality (Millipore RG model) with a resistivity higher

than 18 MU and Total Organic Content (TOC) lower than 10

ppb. All the experiments were done at (298.1 � 0.1) K. For some

of the ellipsometry and neutron reflectivity experiments, D2O

(99% of D) was used (Aldrich, Germany).

The solutions were prepared by weight using an analytical

balance with a precision of �0.01 mg.

2.2. Techniques

2.2.1. Dissipative quartz crystal microbalance. A D-QCM

from KSV (Finland), model QCM Z-500, with AT-cut quartz

sensors (characteristic resonant frequency of 5 MHz in vacuum)

was used. The quartz crystals, were cleaned with piranha solution

(70% H2SO4 (conc)/30% H2O2(aq)) over a period of thirty minutes

and then thoroughly rinsed with pure water. Afterwards they

were mounted in a liquid-solid cell with one of the two gold

electrodes in contact with the polymer solution. Before starting

the multilayer assembly, and in order to obtain a high charge

density over the substrate, a self-assembled monolayer of the

sodium salt of 3-mercapto propanosulfonic acid (Na + HS–

(CH2)3–SO3�, purchased from Sigma-Aldrich) was built onto the

gold electrode. The average surface charge (1015 –SO3� groups

per cm2) was calculated from the frequency shift in the adsorp-

tion experiment of thiol using the quartz crystal microbalance,

this result is in accordance with the results of Love et al.32 This

value is also in agreement with that obtained by z-potential

measurements33 of a suspension of gold microparticles on which

a SAM of the thiol had been deposited using the same protocol

followed for the quartz sensors. The microbalance allowed us to

obtain the impedance spectra of the crystal for the fundamental

mode and for odd overtones up to the 11th (central frequency f11

¼ 55 MHz).

The adsorbed mass was calculated using the model of

Johannsmann et al.34 that relates the changes of the impedance

spectra of the quartz sensor to the adsorbed mass and the

complex shear modulus of the adsorbed film. The total adsorbed

mass is given by

m* ¼ m0 1þ JðfÞrqð2pfÞ2hac

2

3

" #(1)

where m0 is the sensed mass according to the the classical Sau-

erbrey equation,35

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m0 ¼ �CDf

n(2)

Df being the frequency change of the maximum of the impedance

spectra once the sensor is in contact with the polymer solution

(Df ¼ f0 � f); n is the overtone order (3, 5, 7, 9 and 11 in this

work), and C is a characteristic constant of the quartz crystal, C

¼ 17.9 ng$Hz�1$cm�2. In eqn (1) m* is the true sensed mass once

m0 is corrected for the viscoelastic character of the adsorbed

layer. J(f) is the complex shear compliance, rq the quartz density

and hac the film thickness. Because several variables have to be

determined from the impedance spectra (m*, J*¼ J0 + iJ00), it was

necessary to obtain the impedance spectra for different over-

tones, and to assume a constant value for the film density. A

typical density value used in polyelectrolyte multilayers29 is 1.2�0.1 g$cm�3, and this is the value used in this work. For the

solutions we have taken rl ¼ 1 g$cm�3 and hl ¼ 1$10�3 Pa$s�1, as

for pure water. All the experimental spectra were fitted using the

Voigt function.36

The D-QCM allows one to obtain the relationship between the

dissipated and stored energies during the oscillation of the quartz

sensor as the dissipation factor, D. D is analogous to the loss

tangent in classical experiments of rheology.

D ¼ Edissipated

2pEstored

(3)

where Estored is the energy stored in the oscillating system and

Edissipated is the energy dissipated during one period of oscilla-

tion.

2.2.2. Ellipsometry. Ellipsometry experiments were per-

formed in a Nanofilm (Germany) EP3 ellipsometer with a single

wavelength of 532 nm. All the experiments were carried out on

a solid-liquid cell at a fixed angle of 60�. Silicon wafers (Siltronix,

France) were used as the substrates. The wafers were cleaned

with the same protocol used for the QCM quartz sensors. Over

the silicon, there is a native layer of negatively charged oxide.

In order to be able to obtain the refractive index and the

thickness, the ellipsometric angles D and J were obtained. These

angles describe the changes in the state of polarization, when the

light is reflected at a surface.37 This reflection may be described as

the relation between the Fresnel reflection coefficients for the light

wave components parallel, rp, and perpendicular, rs, to the inci-

dence plane.37 This ratio is related to the ellipsometric angles by

r ¼ rp

rs

¼ eiD tanJ ¼ ðcosDþ i sinDÞ tanJ (4)

In order to better determine the thickness of a given layer,

ellipsometric angles were measured using subphases with

different refractive indeces, using mixtures of H2O and D2O.38,39

The accuracy of D and J was better than �0.1 and �0.05

degrees, respectively.

2.2.3. Refractive index increment. The refractive index

increment, (dn/dc)T was measured in a Brookhaven differential

refractometer (USA), with a precision of �0.001 (mL/g). The

refractive index increment was obtained at a wavelength of 532

nm, the same as was used for the ellipsometric measurements.

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Combining ellipsometric thickness, hop, and (dn/dc)T data, it is

possible to obtain the mass adsorbed on the substrate, G, using

Feijter’s equation,40

G ¼�nf � nl

�$hop

ðdn=dcÞT(5)

where nf and nl, are the refractive index of the film and solvent,

respectively.

2.2.4. Neutron reflectivity. The experiments on neutron

reflectivity were performed in a time of flight reflectometer,

EROS, at Leon Brillouin Laboratory in Saclay (France). In

order to compare the multilayer thickness with the optical

thickness the multilayers were built with different repetition

patterns, for this purpose some PSS layers were substituted by

deuterated PSS layers, and the measurements were made under

different contrast conditions. The reflectivity was measured in

the momentum transfer range of 0.007 < Qz < 0,12 A, in order to

obtain the reflectivity curves in this interval of Qz it was necessary

to obtain measurements in two different positions for the

detector, which implies different experimental error for the data.

The analysis of the data was made using the software package

Parrat 32 from HMI (Berlin, Germany).

2.2.5. XPS. The experiments were made in an Omicron X-

ray spectrophotometer with non-monochromatic radiation from

an anode of Mg (150 W) in ultrahigh vacuum (10�7 Pa). The

multilayers were subject to a vacuum of 10�8 Pa in order to dry

the samples before measuring them. The concentration of each

element was obtained as the intensity of the peak of interest

corrected for the sensibility factor of the corresponding transi-

tion.

2.2.6. Kelvin probe. A Kelvin probe from Trek, Inc. (U.K.),

located approximately 2 mm above the substrate, was used in

order to measure the surface potential (Dz) of the multilayer in

the dry state after each cycle of deposition. The surface potential

measurements were reproducible to �20 mV and are referenced

to the value of Dz of the bare solid-air interface.

2.2.7. AFM. AFM measurements were performed in air at

room temperature using a Nanoscope III (Digital Instruments,

USA) in the tapping mode. A silicon tip, model RTESP (Veeco

Instrument Inc, USA), was used for the measurements.

Fig. 1 Kinetics of the adsorption and washing-out processes for the first

six layers of the (PDADMAC + PSS)n film built with [NaCl] ¼ 100 mM

followed as the time dependence of the frequency shift for the third

overtone of the quartz sensor (a), and of the ellipsometric angles (b). The

vertical continuous lines (—) mark the polyelectrolyte injection and the

dashed lines (----) mark the washing with solvent.

3. Results and discussion

3.1. Multilayer growth process

The (PDADMAC + PSS)n multilayer was built from poly-

electrolyte solutions of concentration c ¼ 1 mg/mL, and with

different ionic strengths (NaCl concentration in the range 50 mM

to 1 M). Between each layer adsorption, the multilayers were

washed with a NaCl solution of the same ionic strength as the

one used during the building process. In this rinsing process, the

polymer chains that are not strongly adsorbed in the multilayer

are removed.

A typical sequence of the experiments using both QCM and

ellipsometry are represented in Fig. 1. To a first approximation

2132 | Soft Matter, 2009, 5, 2130–2142

the behavior observed in both techniques is similar, although the

parameters obtained from the detailed analysis indicate that the

information obtained is different and complementary (see

below). Both techniques clearly show the polymer adsorption as

reflected in the changes observed in the frequency in the micro-

balance experiments and the changes in ellipsometric angles after

injecting the polymer solution. Both D-QCM and ellipsometric

experiments of the adsorption process were performed under

static conditions. The measurement chambers were first cleaned

with a salt water solution to avoid bulk complex precipitation

and then filled with the appropriate polyelectrolyte solution. The

filling process takes a few seconds and leads to a fast shift in the

signal in both techniques, these fast variations were not used in

the analysis of the adsorption kinetics.41

In addition to the expected decrease of f as mass is adsorbed

onto the quartz resonator, Fig. 1a also shows that the washing-

out process leads to a very small increase in f. In general this is

related to the loss of polymer chains that are weakly adsorbed.

However, the reorganization of polymer chains in the film might

also lead to an increase in f. In any case, the change of frequency

during the washing-out is much smaller than the decrease found

during the adsorption process for all the layers studied. The

changes in the ellipsometric angles during the process of

adsorption (Fig. 1b), lead to the same conclusions.

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The absence of desorption after the rinsing process is an indi-

cation of the quasi-irreversibility of the adsorption process.42 This

irreversibility may be related to the thermodynamics of the

polymer adsorption process which are accompanied by the release

of counterions from the polymer and the surface into the solution.

This greatly increases the entropy of the system, thus reducing the

free energy and making adsorption to the surface very favourable.

For the desorption it is neccesary that all polymer segments detach

simultaneously from the surface, however during this process it is

possible that some non-attached segments adsorb onto the surface

and this implies that the desorption process has a very slow

dynamics, thus the adsorption may be considered as an irrevers-

ible process during the time scale of our experiments.

The analysis of the results in Fig. 2 indicates that the

adsorption kinetics is a bimodal process,43–45 with a first fast

adsorption step related to the transport of chains to the surface

and fast mass deposition, and a second slower process that may

be related to the internal reorganization of the polymer chains in

the multilayer. In order to describe the adsorption kinetics we

have used the model proposed by Raposo et al.46

Fig. 2 Two exponential fits to eqn (7) of the adsorption kinetics (inset of

part a). (a) Plot of the logarithm of (GN -G) vs. time, where GN represents

the surface concentration at the equilibrium, after long adsorption times

where the fastest exponential becomes negligible, it can be fitted to

a straight line (solid line). (b) Short time behavior of the absorption

kinetics, a plot of ln(GN-G- A2e�t/t2) vs. time gives a straight line (solid

line). The parameters obtained from the data shown are: A1 ¼ 4.6 � 0.1,

A2 ¼ 5.0 � 0.1, t1 ¼ 164 � 6s and t2 ¼ 1450 � 25s.

This journal is ª The Royal Society of Chemistry 2009

G ¼ A1(1 � e�t/t1) + A2(1 � e�t/t2)n (6)

where A1 and A2 are the amplitudes and t1 and t2 the charac-

teristic times of the fast and slow adsorption steps, respectively.

The second term accounted for any reorganization process of the

polymer chain after its adsorption at the interface, and it was

modeled according to Avrami’s model for polymer crystalliza-

tion.44,45 All the data obtained in this work are compatible with n

¼ 1. This allows one to rewrite eqn (6) in terms of the maximum

surface concentration, GN, as

GN ¼ A1 þA2

G ¼ GN �A1e�t=t1 �A2e�t=t2(7)

Fig. 2a and 2b illustrate the validity of eqn (7) to describe the

long and short time behavior of a typical adsorption kinetic. We

found that for all of our adsorption kinetics eqn (7) holds,

independently of the polyelectrolyte type, the number of layers

and the ionic strength.

3.2. Optical vs. acoustic thickness

Fig. 3 shows the shifts of reduced frequency and dissipation for

the D-QCM experiments. These changes are related to the

quantity of material adsorbed in the layers and to the mechanical

properties of the system.

In the case of the frequency shifts (Fig. 3a) we see two different

growing regimes; the first regime appears at low ionic strength

where a linear dependence of the frequency shifts with the layer

number was observed. This dependence becomes non-linear

(second regime) when the ionic strength increases. It is customary

to call this second type of behavior an exponential growth of the

polyelectrolyte multilayer.47 In the present multilayer this

so-called exponential growth starts at N z 6 for [NaCl] ¼ 500

mM, and at N z 4 for [NaCl] ¼ 1000 mM. This change can be

related to the mechanism of the multilayer build-up,47 and to the

internal structure of the layers (see below). Also the shift of the

frequency for a given number of layers increases dramatically

with the NaCl concentration. At low salt concentrations the data

corresponding to different overtones collapses on a master curve

�Df/n vs. N, which indicates that the film is quite rigid (Sauer-

brey limit).34,38,48 Such frequency independent behavior was not

observed at high salt concentrations. This is in accordance with

the high values of the dissipation factor (Fig. 3b) at high ionic

strengths, which suggest that the multilayers are viscoelastic.49 A

first consequence is that Sauerbrey’s equation is not valid for

calculating the adsorbed mass, and therefore a fit of the full

experimental impedance spectra to the theoretical predictions

has to be carried out. Because the spectra corresponding to n¼ 3,

5, 7, 9 and 11 have been measured, it has been possible to

calculate the adsorbed mass, and the real and imaginary

components of the complex shear modulus (G h 1/J¼G0 + iG00)

of the polymer layer (it will be assumed that G0 and G00 are

frequency independent in the 15 to 55 MHz range).50

The dissipation factor, D, shows an oscillatory behavior as

a function of N for all values of [NaCl] (see inset of Fig. 3b). This

kind of behavior seems to agree with the results of Liu et al.51 for

multilayers of PDADMAC and PSS, although they studied only

multilayers with N # 8. The explanation of the oscillations is

Soft Matter, 2009, 5, 2130–2142 | 2133

Fig. 4 Ellipsometric trajectory for the polyelectrolyte multilayer built at

the solid-air interface, and for an ionic strength of NaCl with a concen-

tration of 300 mM. The multilayer was started by adsorbing a layer of

PDADMAC. N is the number of layers deposited.

Fig. 5 Model of the four layers used for the analysis of the ellipsometric

results.

Fig. 3 (a) Ionic strength and number of layers dependence of the

reduced frequency of the quartz crystal for the different overtones

measured (overtones n ¼ 3, 5, 7, 9 and 11 are shown for each NaCl

concentration, in the figure the different overtones are represented with

different symbols). Notice that for low salt concentrations the data of the

different overtones collapse into a single curve (rigid film) while at high

salt concentrations the data of the different overtones lie on different

curves (viscoelastic film). (b) Ionic strength and number of layers

dependence of the dissipation factor for the third overtone of the quartz

crystal. Notice that the increase in dissipation factor is stronger when the

ionic strength increases, this is in accordance with the behavior observed

in the frequency shift of the different overtones. The inset shows the detail

of the dissipation changes of the multilayer for a [NaCl] ¼ 0.1M.

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related to the interpenetration and complexation of the poly-

electrolytes. In the case of the adsorption of the PDADMAC

layer there is an increase in the dissipation factor, related to the

existence of loops and tails protruding into the solution further

than in the case in which PSS is the top layer.51 The extension of

the loops and tails may be related to the lower value of the ratio

between the end-to-end distance and size of the electrostatic

blob, R/L, for the PDADMAC than for PSS (for further infor-

mation see Appendix A), this makes the flexibility of the chains

of PDADMAC greater than for PSS, and that the formation of

loops and tails takes place at greater extensions. After subse-

quent adsorption of PSS a complexation between the chains of

PSS and of PDADMAC takes places and the film becomes more

compact, thus leading to a decrease in the dissipation due to the

water release from the interior of the multilayer.51 The oscillatory

behavior of D is lost for large values of N (especially for high

ionic strengths).

2134 | Soft Matter, 2009, 5, 2130–2142

The ellipsometry results are summarized in Fig. 4 in the form

of an ellipsometric trajectory. Normally, when a homogeneous

film (with real refractive index) is built the behavior of the

ellipsometric angles must describe a single elliptic trajectory.52

However in the case of the (PDADMAC + PSS)n multilayers it is

possible to distinguish two well differentiated trajectories that are

related to the alternate adsorption of two different poly-

electrolytes. This even-odd effect is related to the different

refractive index of both polymers.

The increase in the ionic strength leads to different evolution

of the shifts of ellipsometric angles, D and J. However, the

ellipsometric trajectories are similar for all the ionic strengths

considered, the N dependence of D and J is greater for high

values of the ionic strength (see ESI†), this implies that the same

pair of D–J values corresponds to a lower number of layers as

the ionic strength increases. This is again related to the enhanced

thickness, for a given value of N, as [NaCl] increases, which is in

qualitative agreement with the D-QCM results shown in Fig. 3.

In order to obtain the ellipsometric thickness, hop, the system

was modeled as four layers (see Fig. 5): the first layer was the Si

substrate where its refractive index was taken as n ¼ 4.1653 �0.049i,53 the second layer was the native oxide layer which was

assumed to have a refractive index n ¼ 1.4653,53 with a thickness

that was obtained from the ellipsometric results on the clean Si

wafer. The external layer (fourth layer) was the solution which

was assumed to have a constant refractive index equal to that of

the polymer solution.

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Finally the multilayer (third layer of the model) thickness and

refractive index has to be obtained from the fitting of D and J to

the Fresnel equation.37 In order to do so, it is necessary to assume

a model for the multilayers (single slab, multiple slabs, etc). The

neutron reflectivity and XPS results have been used to get insight

into this fact.

Neutron reflectivity provides information about the internal

structure of the multilayer. Contrary to the results obtained for

multilayers of poly(allylamine) + PSS,54 the reflectivity curves for

(PDADMAC + PSS)n show no pattern, reflecting a non layered

structure of the multilayers. Fig. 6a shows the reflectivity profiles

for the different samples summarized in Table 1. This means that

the multilayer can be modeled as a highly interpenetrated almost

homogeneous layer. This implies that our system is not really

Fig. 6 (a) Neutron reflectivity results represented as R$QZ4 vs. QZ for

several multilayers with 24 layers (see Table 1 for the characteristics of the

multilayers), the reflectivity of multilayer B is rescaled for a factor of 10,

and for multilayer C for a factor of 100 in order to show the different

results in the same graph. (b) Neutron scattering length density profile,

rn, for one of the multilayers shown in part a. The inset shows similar

data for the other two multilayers. A small oxide layer was considered in

the analysis.

This journal is ª The Royal Society of Chemistry 2009

a layered structure; it is a blend layer that grows in each step of

deposition. Fig. 6b shows the corresponding scattering length

density, rn, of the multilayers obtained from the fit. This highly

interpenetrated structure cannot be fully homogeneous as indi-

cated by the odd-even effects mentioned above. Table 2 includes

the thickness obtained from ellipsometry and the reflectivity

model curves for two multilayers, showing that the agreement is

satisfactory. The results of Fig. 6 show that the absence of

internal structure in the multilayer is not a consequence of the

combination of hydrogenated and deuterated layers used as

shown in the results for the different samples.54 The neutron

reflectivity results also allowed us to obtain a value of the water

content of the multilayer as discussed below.

The S and N atomic concentrations provided by angle-

dependent XPS measurements confirm the existence of a fuzzy

structure in the (PDAMAC + PSS)n multilayers as summarized

in Table 3. Although a very small odd-even effect may be

observed, it is essentially related to the composition of the

outermost layer. The XPS results confirm that the multilayers are

not stratified structures. In the case of a multilayer with a real

stratification, the atomic content should be different at different

angles because of the different depths explored. This is not the

case of the present results, thus confirming the fuzzy structure of

our films.

All the above has led us to model the multilayer as a single slab

for the analysis of the ellipsometry results. The fuzzy structure

found for the (PDADMAC + PSS)n multilayer contrasts with the

layered structure reported for other multilayers.54 The absence of

stratification might be due to the use of PDADMAC or to the

protocol used for building the layers: first no drying between

layer deposition has been carried out; second long adsorption

times (until the equilibrium was reached) have been allowed in

each layer. The adsorption times were much larger than the

15–20 minutes frequently used by others in the building-up

process.55 The longer times might facilitate a mixing-up process

(caterpillar-like dynamics56) of the polymer chains similar to the

process described in ref. 47.

The analysis of the D-QCM data in terms of eqn (1), and of the

ellipsometry data in terms of the four layer model, led to the

acoustical, hac, and to the optical, hop, thickness plotted in Fig. 7.

Both sets of results led to qualitatively similar conclusions. The

increase in the ionic strength leads to an increase in the film

thickness, as is described in the literature for other multi-

layers.29,51 Increasing the ionic strength makes the PDADMAC

change from an extended conformation for low ionic strength to

a coil conformation for high ionic strength (see Appendix A).

Experimental evidence of this is shown in Fig. 7b where the

growth of PSS layers is almost constant for all the ionic strengths

studied and it is always smaller than the growth of PDADMAC

layers. This is in agreement with the fact that the change of

[NaCl] has a rather small effect on the conformation of PSS (see

Appendix A). The change in the polymer conformation is due to

the screening in the electrostatic interactions between the charged

groups of the polymer. In principle, the deposition of chains with

a more coiled conformation leads to thicker layers and higher

polymer surface concentrations.

Changing ionic strength has a clear effect, accentuating the

non-linear character of multilayer growth.57,58 The non-linear

behavior is evident for [NaCl] higher than 0.3 M, in accordance

Soft Matter, 2009, 5, 2130–2142 | 2135

Table 1 Summary of the multilayers with 24 layers represented in Fig. 6:number of repeat units (r.u.), layer sequence, and measurement condi-tions (m.c.)

Sample Layer sequence

Multilayer A cNaCl ¼ 100 mM [(PDADMAC + PSS-d7])] r.u. ¼ 12m.c.: H2O

Multilayer B cNaCl ¼ 500 mM [(PDADMAC + PSS-h7)3 +(PDADMAC + PSS-d7])] r.u. ¼3 m.c.: mixture 75% H2O + 25%D2O

Multilayer C cNaCl ¼ 500 mM [(PDADMAC + PSS-h7)3 +(PDADMAC + PSS-d7])] r.u. ¼3 m.c.: dry film

Table 2 Comparison of optical and neutron thicknesses in multilayerscomposed of 12 bilayers

[NaCl]/mM Optical thickness/nm Neutron reflectivity thickness/nm

100 84 � 5 85 � 6500 316 � 5 318 � 13

Table 3 Angle-dependent XPS atomic content (atomic percent) formultilayers of 15 bilayers. (Note that the experimental error is approxi-mately �0.5.) The atomic content predicted by a model multilayer(column model) with segregated polyelectrolyte layers is included forcomparison

[NaCl]/mM Atom

XPS measurement angle

Model�40 �30 �20 �10 0 10

100 N 2.2 2.7 2.4 2.3 2.2 2.1 7.9S 1.7 1.9 2.1 1.8 2.0 1.5 1.6

300 N 1.6 1.8 1.8 1.8 0.9 1.9 8.4S 2.2 2.4 2.3 2.7 2.3 2.5 1.3

Fig. 7 Evolution of thickness with the layer number for multilayers of

PDADMAC and PSS built with different NaCl concentrations. (a)

Acoustic thickness (QCM). (b) Optical thickness (ellipsometry).

Table 4 AFM average roughness of multilayers in the dry state withdifferent numbers of layers, N, and ionic strengths

[NaCl]/M N Roughness/nm

0.1 7 60.1 30 81.0 9 20

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with the results of McAloney et al.59 This supra-linear growth is

linked to two main factors. On one side at high ionic strengths

the polymer chains are in a coiled shape (see Appendix A), and

on the other side the roughness of the multilayer is higher, as is

evident from the AFM results shown in Table 4. The increase of

roughness leads to an increase of adsorbed mass, associated with

the corresponding increase in area. On the other hand a mixing-

up process of the chains in the multilayer is favoured,47 thus

leading to a fuzzy structure, with a lack of layering order.

3.3. Charge overcompensation

The fundamental principle of multilayer construction is the

charge overcompensation.60 Fig. 8 shows the charge inversion

found in the (PDADMAC + PSS)n multilayers as monitored by

the surface potential measured with a Kelvin probe. The

formation of the multilayers is driven by the overcompensation

of charge at the surface of the multilayer. However, the multi-

layer must be electrically neutral from a macroscopic point of

view (at a length scale beyond the Debye length). The electrical

2136 | Soft Matter, 2009, 5, 2130–2142

neutrality can be achieved by two different mechanisms.28,61 In

the so-called intrinsic compensation mechanism, the charges

carried by an adsorbed polyion are compensated by charges of

the polyion adsorbed in the next layer. While in the so-called

extrinsic mechanism, some of the charges are compensated by

counterions (Fig. 9).

The existence of intrinsic compensation implies a stoichio-

metric 1:1 ratio (polyanion:polycation) in the multilayer, whereas

for extrinsic compensation other stoichiometries can be found.

Since the ellipsometric experiments allow one to measure the

amount of polymer adsorbed in each layer, it is possible to

discuss the compensation mechanism in the (PDADMAC +

PSS)n multilayers. In order to obtain the monomer surface

density (rmonomer) for each adsorption cycle, we have used eqn (8)

rmonomer ¼NAvG

Mw

(8)

This journal is ª The Royal Society of Chemistry 2009

Fig. 8 Change of the surface potential with the number of layers for

a multilayer of (PDADMAC + PSS)n build with a concentration of NaCl

of 50 mM.

Fig. 9 Intrinsic vs. extrinsic charge compensation.28

Fig. 10 Surface density of monomer with respect to the layer number for

both polyelectrolytes in multilayers with a NaCl concentration of 50 mM

(filled symbols) and 300 mM (open symbols). In the extrinsic zone there is

a ratio PDADMAC/PSS of 3:1 for 50 mM and 7:1 for 300 mM (note the

similar values found for the density of monomer for the PSS at different

ionic strengths).

Fig. 11 Surface density of monomer for polyanion and polycation in the

region of extrinsic compensation for a multilayer of PDADMAC and

PSS built with different ionic strengths.

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where G is the adsorbed mass obtained using eqn (5), Mw is the

molecular weigth of the monomer, and NAv is Avogadro’s

number.

In Fig. 10, we present the number of monomers of PDAD-

MAC and of PSS versus the number of layers for [NaCl] ¼ 50

mM and [NaCl] ¼ 300 mM as typical examples. Two different

zones are clearly visible (similar results were found for all the

ionic strengths studied). Counterions do not seem to be involved

in the compensation mechanism at low N values, where coun-

terions releasing strongly contribute to stabilize the multilayer.

However, for large N values, the ratio of PDADMAC mono-

mers/PSS monomers increases up to 7 (for [NaCl] ¼ 300 mM),

indicating that there must be a strong extrinsic compensation

with an average ratio of counterions [Cl�]/[Na + ] z 7 in the

external layers. This ratio is lower in the case of [NaCl]¼ 50 mM,

indicating less importance of the extrinsic mechanism of

compensation. The differences between the values of the poly-

cation and the polyanion in the zone of extrinsic compensation

are summarized in Fig. 11 for different ionic strengths. As can be

observed, the number density of adsorbed PSS monomers is

independent of the ionic strength while that of PDADMAC is

linearly dependent on the salt concentration as observed before

by Schlenoff and Dubas28 using different experimental tech-

niques. The existence of extrinsic compensation in the external

layer has been corroborated by XPS measurements that show the

presence of counterions in the dry multilayers.

The QCM results plotted as DD vs. (Df/n), Fig. 12, for the third

overtone (n ¼ 3) allow us to get insight into the driving forces

involved in the adsorption process.62,63 The increase in the

dissipation factor as the thickness increases (for higher ionic

strengths), indicates that the importance of the entropy

This journal is ª The Royal Society of Chemistry 2009

mechanism is reduced as a consequence of being extrinsic the

main compensation mechanism, this result is in accordance with

those previously presented. This fact can be explained by the

decrease in the entropy gain with the increase in ionic strength.

Hence it is more favourable to have counterions in close vicinity

to the polyelectrolyte rather than the opposite polyelectrolyte.

This implies an increase of the extrinsical character of the

compensation mechanism.

3.4. Water content

Polymer chains and counterions adsorb in a hydrated form, thus

the total mass measured by the D-QCM technique includes the

solvent. The amount of water associated with the multilayers can

be obtained by comparing the mass obtained by QCM and

ellipsometry.64

Soft Matter, 2009, 5, 2130–2142 | 2137

Fig. 12 Plot DD vs. (Df/n) for multilayers of (PDADMAC + PSS)n with

different ionic strengths, the inset is the detail of multilayers with [NaCl]

# 300 mM.

Fig. 13 Comparison between the acoustical and optical thicknesses of

a (PDADMAC + PSS)n multilayer built with [NaCl] ¼ 100 mM. The

inset corresponds to the thicknesses of a ten bilayer multilayer as

a function of the salt concentration (the lines are only guides for the eyes).

Fig. 14 Water content for multilayers built using different NaCl

concentrations, the points are the calculated data and the lines are only

guides for the eyes.

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In all the studied cases the acoustical thickness is larger than

the optical one. This is due to the fact that ellipsometry is almost

insensitive to the adsorbed solvent because its refractive index is

too close to that of the solvent layer above the multilayer. The

similarity of the thickness obtained by ellipsometry and neutron

reflectivity supports this view (see Table 1). Fig. 13 shows

a typical example of the difference between the thickness

obtained by ellipsometry and D-QCM for a multilayer built at

100 mM NaCl. This allows us to estimate the water content

following the procedure of Halthur et al. for multilayers of

polypeptides.64 The water fraction, Xw, in the multilayer can be

calculated as

Xw ¼hac � hop

hac

(9)

where hac and hop are, respectively, the acoustical and optical

thicknesses.

Fig. 14 shows the N dependence of the water content in the

multilayer, for two different ionic strengths, Xw strongly

decreases as the film becomes thicker, independently of the

2138 | Soft Matter, 2009, 5, 2130–2142

charge compensation mechanism. The quasi-plateau value

obtained for N > 20 increases with the ionic strength. The water

content of the first few layers is very high suggesting that polymer

chains adsorb rather inhomogeneously,65 forming isolated

adsorbed coil-like pancakes. The adsorbed chains in the first

layer would not fill the whole surface due to the Coulombic

repulsion between them. The next polymer layer (PSS in our

case) might adsorb onto the first PDADMAC chain, and would

make it easy for the next PDADMAC layer to fill the empty

substrate surface, as well as to adsorb onto the PSS chains of the

second layer. A schematic representation of this adsorption

model is shown in Fig. 15. This would explain qualitatively the

fast decrease of Xw for N < 10, and the change in growing regime

already discussed (see Fig. 7). The increase in water content with

ionic strength is a consequence of the internal structure of the

polymeric layer and it is connected to the change from linear to

exponential growth. The globular chains adsorbed at higher

[NaCl] (see Appendix A) are more hydrated after adsorption.

The even-odd variation that is evidenced in Fig. 14 for the higher

salt content can be explained in terms of the interpenetration and

complexation processes discussed above.

Neutron reflectivity allows one to obtain a value for the water

content of the multilayer. For this purpose it is necessary to use

the scattering length density (SLD, r) of the multilayer, solvent

and individual polymer (this parameter was obtained for the

different materials from NIST, using a SLD calculator).66 The

water content can be calculated from

rPEM ¼ rs$Xw + rpol$(1 � Xw) (10)

where r is the scattering length density, and the subindex PEM

represents the multilayer, s is the solution and pol corresponds to

the scattering length density of the average value of the param-

eter for the polymer that build the multilayer. The values

obtained for the water content for neutrons are in good agree-

ment with the values obtained for the combination of QCM and

ellipsometry as shown in Table 5.

3.5. Mechanical properties

Fig. 16 shows the values of G0 and G00 obtained from the analysis

of the D-QCM experiments, see eqn (1). For low ionic strengths

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the multilayers behave as elastic bodies (G00 ¼ 0), but for higher

ionic strengths a viscous contribution appears. This is in agree-

ment with the discussion made for the experimental results of the

D-QCM (see above). In all the cases studied the values of G0 and

Table 5 Comparison of water content (mass fraction) as a fraction ofwater in the multilayer obtained for a combination of ellipsometry andD-QCM and for neutron reflectivity (where N is the number of layers)

[NaCl]/mM N Ellipsometry + D-QCM Neutron reflectivity

100 24 0.3 0.3500 21 0.5 —500 24 — 0.6

Fig. 16 Mechanical properties (a) G0 vs hac. (b) G0 vs hac for multilayers

with different NaCl concentrations.

Fig. 15 Sketch of growth model during the initial step for a multilayer of

(PDADMAC + PSS)n.

This journal is ª The Royal Society of Chemistry 2009

G00 are in the MPa range, which corresponds to the rubbery

region of typical polymers. This is reasonable considering that

the multilayer is highly plasticised by water. The elastic compo-

nent does not depend on ionic strength until a thickness of

approximately 100 nm, and then G0 increases with [NaCl].

The increase in G00 for the high values of [NaCl] can be

understood by considering that in these conditions the multi-

layers grow exponentially, and thus the polymer chains adsorb as

globular coils. This increases the number of loops and chains

dangling into the solution, thus leading to a higher loss compo-

nent for the shear modulus. It must be noted that values of G00 so

close to the G0 as observed for [NaCl]¼ 500 mM suggest that the

multilayer behaves as a gel.67

3.6. Response of the multilayer to ionic strength stimuli

A change in the ionic strength at the external solution, once the

multilayer has built-up, may produce effects over the internal

structure of the film. We analyze the changes that take place

when the solution, with the same ionic strength as was used

during the building process, is replaced by pure water and then

during the inverse process (replace pure water with the solution

with the same ionic strength that was used to build the multi-

layer). In both exchanges, we waited enough time for equilibrium

to be reached.

For low ionic strengths, these changes did not produce any

effects on the multilayer structure, but for higher ionic strengths

changes in the structure are clearly observed. These changes in

the multilayer structure are reversible for all the systems studied

here by returning to the original ionic strength conditions.

Examples of the changes observed for the two ionic strengths are

shown in Fig. 17.

The changes in the multilayers’ total thickness due to changes

in ionic strength are shown in Table 6. As has been shown before,

when a multilayer is built from solutions at high salt concen-

trations the resulting total thickness is several times larger than

the one obtained at low ionic strengths. Then, when one

Fig. 17 Evolution of the variation of optical thicknesses during the

solvent exchange process for two multilayers with different [NaCl]. -

and C represent the changes in the thickness when the salt solution is

replaced with pure water and the inverse process respectively for multi-

layers built with a [NaCl] ¼ 100mM. P and > represent the changes in

the thickness when the salt solution is replaced with pure water and the

inverse process respectively for multilayers built with [NaCl] ¼ 300mM.

Soft Matter, 2009, 5, 2130–2142 | 2139

Table 6 Thickness evolution in the multilayer after post-buildingtreatment

[NaCl]/mM hop/nm D hop/nm %hop Condition

50 38 layers 111 � 8 — — Initial110 �1 �0.9 H2O109 �2 �1.8 End

100 32 layers 129 � 10 — — Initial130 +1 +0.8 H2O129 +0 +0 End

300 38 layers 315 � 8 — — Initial330 +15 +4.8 H2O316 +1 +0.3 End

500 26 layers 360 � 5 — — Initial480 +120 +33.3 H2O360 +0 +0 End

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decreases the ionic strength of the solution in contact with the

multilayer previously built at high ionic strength, one might

expect a structural change that approaches the system of the

multilayer built at low ionic strength. However the effect

observed is exactly the opposite.

The best explanation for this behavior is that the osmotic

pressure acts as the driving force for the multilayer swelling (or

contraction). In effect, the sudden change in ionic strength leads

to a difference in the chemical potential of the ions inside and

outside the multilayer. This fact leads to the swelling of the

multilayer as a result of the existence of the exchange process of

ionic pairs and solvent between the multilayer and the solution,

this process takes place until the chemical potentials are equili-

brated again. This interpretation is supported by the fact that

multilayers constructed at low salt concentrations do not change

their thickness upon increasing or decreasing the ionic strength

of the surrounding solution. This is because at those salt

concentrations the polyelectrolyte charges are intrinsically

compensated, which means that there is a small quantity of

counterions, and this small concentration of counterions in the

interior of the multilayer is not enough to produce a difference in

chemical potential that produces a swelling process on the

multilayer. On the contrary, when the multilayers were con-

structed from a high ionic strength solution, the difference in

chemical potentials was bigger and this led to a swelling-

shrinking process of the multilayer. The movement of the

counterions in the multilayers as a consequence of shifts in the

chemical potentials is favoured by the multilayer porosity which

is characteristic of multilayers built-up at high ionic strength.

One thing that must be emphasized is that this swelling-shrinking

process is completely reversible by simply returning to the orig-

inal ionic strength condition in spite of a noticeable hystheresis

cycle being observable (see Fig. 17). Similar swelling-shrinking

phenomena were found for the system PAH-PSS.68

4. Conclusions

The electrostatic self-assembling of PSS and PDADMAC has

been studied by QCM and ellipsometry. The effect of the ionic

strength on the growth of the multilayer has been discussed. Both

techniques indicated that the adsorption process was essentially

irreversible. This characteristic may be due mainly to the entropy

increase associated with the release of counterions during the

2140 | Soft Matter, 2009, 5, 2130–2142

adsorption process. In all the cases studied it was found that the

polyelectrolyte adsorption followed bimodal kinetics with a fast

process associated with the polymer diffusion to the surface, and

a slow process associated with the reorganization of the adsorbed

polymer chains. Contrary to what has been found for the (PSS +

PAH)n multilayers,48 the neutron reflectivity and XPS experi-

ments showed that the adsorbed layers strongly interpenetrate,

thus leading to almost homogenous films. This difference may be

due to the chemical structures of PAH and PDADMAC, or to

the fact that we allowed the polymers to adsorb until the equi-

librium was reached (typically 1 hour) whereas in ref. 54 only 20

min were allowed for each adsorption process. This might

prevent the reorganization kinetics and further interpenetration

of the chains of different layers.

The ionic strength has an important influence on the film

growing mechanism, which switches from a linear regime at low

salt concentrations to an exponential regime at high ionic

strengths. As a consequence, for a given number of polymer

layers, the film thickness and its surface roughness are much

larger for high values of [NaCl]. The change of growing regime is

accompanied by a change in the mechanism of charge compen-

sation. This mechanism is intrinsic at low [NaCl], and essentially

extrinsic at high ionic strengths.

The comparison of the thickness values obtained from QCM

and from ellipsometry has allowed us to estimate the water

content of the multilayer. In general, for a given [NaCl] the overall

water content decreases as the number of layers increases, being

quite large (ca. 80%) for films with less than five layers. For films

with a large number of layers (N > 20), the water content remains

almost constant with N, and increases with the ionic stength. The

dissipative QCM allows us to calculate the complex shear

modulus of the film thickness. G0 increases with the film thickness,

with values in the region of a few MPa, which is characteristic of

polymer gels. The uncertainty in the G00 values prevents any

detailed discussion of the effect of the ionic strength. Similar

conclusions can be drawn for the loss modulus G00.

Finally, several experiments have been performed in order to

study the reponse of the polymer film to an ionic strength stimuli.

It was found that the thickness shows a reversible swelling-

shrinking process when the ionic strength is changed after

building, although the system showed a hysteresis cycle that was

strongly dependent on the ionic strength at which the multilayer

was grown.

Appendix A

Current models for polyelectrolyte solutions are generally based

on counter-ion condensation ideas first introduced by Imai and

Onishini, and Oosawa69 and developed later by Manning.70 The

basic idea of this model is that when the charge density on

a linear polyelectrolyte chain exceeds a critical value, the excess

charge must be neutralized by counter-ions. Some of the free

counter-ions will condense onto the polymer chain, close to the

charged groups, to such an extent that the energy of charge

repulsion between neighbouring charged groups becomes smaller

than the thermal energy, kT. According to this, polyelectrolyte

solutions are characterized by a charge density parameter, c,

which is the ratio of the Bjerrum length, lb, and the distance

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between adjacent charges, n$b, n being the number of monomers

separating charged groups and b the monomer size,

c ¼ lb

nb¼ e2

3wkTnb(A1)

where e is the electronic charge, 3w the water dielectric constant

and we have considered monovalent counter-ions.

When c > 1 counter-ion condensation takes place reducing the

effective charge density to the maximum allowed which corre-

sponds to a minimum charge distance permitted: the Bjerrum

length. In the frame of this model we can estimate the fraction of

free counter-ions as f ¼ 1/c (for c > 1).

For PSS we have n ¼ 1 and b ¼ 2.6 A; for PDADMAC, n ¼ 1

and b ¼ 5.2 A,59 the Bjerrum length is 7 A at 298 K, and then the

estimated fractions of free counter-ions are 0.37 and 0.74

respectively. That means that the effective charge on the PSS

macromolecules is only 37% of the nominal one (63% of counter-

ions are condensed onto the polymer chain) whereas for

PDADMAC the effective charge is about 74% of the nominal.

This has an important consequence on the different behavior

observed for these polyelectrolytes when salt is added.

First, in the absence of salt, the conformation of the chains can

be represented as a chain of electrostatic blobs71,72 of length,

L ¼ Nb

�m

A2

�ð2=7Þ

in good solvent (A2)

where m ¼ lb/b and N is the polymerization degree and A is the

number of monomers separating effective adjacent charges on

the macromolecule chain including any effect of counter-ion

condensation. Because the distance between adjacent charges on

both polyelectrolytes is smaller than the Bjerrum length, the

effective distance between charges is equal to lb due to counter-

ion condensation, and A ¼ lb/b given A z 2.7 and A z 1.35 for

PSS and PDADMAC respectively. For PSS N ¼ 340 and eqn

(A2) gives L ¼ 67 nm; for PDADMAC N z 1700 and L ¼ 800

nm.

The overlap concentration of the free-salt solution can be

estimated as,72

c* ¼ N

L3(A3)

Using eqn (A3) we estimate c* z 0.39 gL�1 and c* z 9 � 10�4

gL�1 for PSS and PDADMAC respectively. Both PSS and

PDADMAC solutions used to construct the multilayers were at c

¼ 1g$L�1 then PDADMAC is far over the overlap concentration

and well inside the semi-dilute region; PSS is also in the semi-

dilute regime but very close to c* and then a small amount of salt

makes the PSS solutions enter the dilute zone. Now, if salt is

added at a concentration cs, and if c� cs, then we can estimate

the overlap concentration as,72

c* z (B/b)6/5 (2Acs)3/5 N�4/5 (A.4)

where B is the quotient between the actual extended size (L) and

the contour length (N.b), B ¼ (m/A2)2/7. For cs ¼ 300 mM, which

is the salt concentration where the exponential growth regime of

the multilayer is found, we obtain for PDADMAC c* z 1.1 gL�1

which is just above the concentration of the solution used to

This journal is ª The Royal Society of Chemistry 2009

build the multilayer. At 300 mM in salt this polymer solution

changes from the semi-dilute to the dilute regime. We can now

estimate the end-to-end distance, R (dilute, good solvent) as,72

R z bN3/5 (cb3)�1/5 B�2/5(1 + 2Acs/c)�1/5 (A.5)

For PDADMAC at a salt concentration of 300 mM, R z 74

nm and, if we remember that L for this polyelectrolyte is about

800 nm, we can see clearly that when it adsorbs onto the multi-

layer this polyelectrolyte is not in a flat conformation but in

a coiled one producing a sharp increase in the multilayer thickness

and roughness. For PSS R z 17 nm and L z 67 nm. If we

calculate now the relation R/L as a measure of the previous result,

we find for PDADMAC R/L z 0.09 and for PSS R/L z 0.25.

Acknowledgements

This work was supported in part by MICINN under grants

FIS2006-12281-C02-01 and CTQ2006-6208/BQU. E.G. was

supported by a FPU fellowship from MICINN and H.R. was

supported by a Juan de la Cierva contract from MICINN. The

authors are grateful to the UIRC of the CAI of Spectroscopy for

the use of the ellipsometric technique and with the CAI of

Electronic Microscopy for the possibility to use the AFM, both

centers from the Complutense University. The authors want to

thank to the Leon Brillouin Laboratory for the beamtime for the

reflectivity experiments, in particular to Fabrice Cousin for

helping us with the neutron experiments and in the discussion of

results, and the authors are grateful too to A. Guerrero, A.

Maroto and J. Alv�arez of the Inorganic Department of UNED

for the measurements of XPS.

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