Polyelectrolyte spin assembly: Influence of ionic strength on the growth of multilayered thin films

Polyelectrolyte Spin Assembly: Influence of Ionic Strengthon the Growth of Multilayered Thin Films

CHRISTOPHE J. LEFAUX,1 JESSICA A. ZIMBERLIN,2 ANDREY V. DOBRYNIN,1,3 PATRICK T. MATHER1,2

1Polymer Program, Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269

2Chemical Engineering Department, University of Connecticut, Storrs, Connecticut 06269

3Physics Department, University of Connecticut, Storrs, Connecticut 06269

Received 7 January 2004; revised 12 March 2004; accepted 20 March 2004DOI: 10.1002/polb.20209Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: Layer-by-layer (LbL) assembly of polymer electrolyte multilayers is now awell-established method for the fabrication of thin films by sequential adsorption of alter-nating layers of oppositely charged polyelectrolytes. Most commonly, such adsorptions havebeen from quiescent solutions of varying ionic strength and pH. Here, we report results onan alternative processing route for the achievement of polymeric multilayer assemblies ofpoly(sodium-4-styrene sulfonate) and poly(allylamine hydrochloride) that utilizes conven-tional spin coating. We investigated and describe herein the dependence of multilayer filmbuildup on solution ionic strength for comparison with similar dependence in quiescentadsorption. Using UV-Vis spectroscopy we monitored the growth of the multilayered films,while with Atomic Force Microscopy (AFM) we examined the surface features and mea-sured coating thicknesses at different salt concentrations. AFM and UV-Vis data revealtwo regimes of behavior with increasing salt: strong salt-dependence at low salt contents,and weak salt-dependence for high salt contents. To explain this observation, we introducethe relevance of the dimensionless group De � �̇�, the local Deborah Number, to theproblem. As ionic strength increases, � increases so that spin-assembly flow influencesadsorbed conformation, and thus LbL growth rate. Our results indicate the ability to designand control polyelectrolyte multilayered structures prepared via spin assembly by varyingsolution properties that influence the conformation of deposited polymer chains. Addition-ally, our studies reveal the need for study of the fundamental mechanisms of polyelectro-lyte adsorption within complex flow fields. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B:Polym Phys 42: 3654–3666, 2004Keywords: layer-by-layer assembly; polyelectrolytes; multilayers; spin coating

INTRODUCTION

The layer-by-layer (LbL) deposition of chargedobjects was first reported in 19661 for colloidalparticle assembly and later rediscovered in the

early 1990s for polyelectrolytes.2,3 This directedassembly technique is based on the long-rangeelectrostatic attraction between oppositely char-ged molecules, and has been introduced for fabri-cation of the molecularly layered multicomponentthin films with seemingly unlimited complexity.The interested reader is referred to several re-view articles on this subject.4–7 The key to a suc-cessful deposition of multilayer assemblies in alayer-by-layer fashion is the achievement of

Correspondence to: P.T. Mather (E-mail: [email protected])Journal of Polymer Science: Part B: Polymer Physics, Vol. 42, 3654–3666 (2004)© 2004 Wiley Periodicals, Inc.

3654

charge inversion and subsequent reconstructionof surface properties at each step of the process.For example, this can be achieved by first im-mersing (“dipping”) a substrate into a dilute aque-ous solution of cationic (or anionic) polyelectro-lytes for a period of time required for adsorptionof the layer of given thickness, followed by rinsingin water. The rinsing step is necessary to removethe polymers that are not tightly adsorbed to thesubstrate. During the next step, the same sub-strate that is now covered with adsorbed polyelec-trolytes is exposed to a dilute solution of comple-mentary anionic (or cationic) macromolecules,and again rinsed. The result is a more or lessirreversibly adsorbed bilayer whose interpenetra-tion and thickness are sensitive to polyelectrolytecharge, ionic strength, and adsorption time. LbLprocessing ensues by repetition of this processmany times to thus build up multilayers withthicknesses spanning 100 to 1000 Å, or 10 to 30 Åper bilayer step. Interestingly, the observedbuildup is found to depend on solution conditions,such as pH or ionic strength. For example, it hasbeen reported that multilayered films producedwith high salt concentration are thicker, and havea higher surface roughness than without saltwhen obtained using the dipping LbL method.8,9

Although a robust and well-tested processingroute, it is generally recognized that the dippingLbL approach to multilayer deposition is exces-sively time-consuming—each complete processrequiring hours to complete and robotic equip-ment for acceptable reproducibility. Additionally,it has been found that the dipping method yieldsa relatively high roughness, compared to methodsintroduced below, in the resulting multilayeredthin coating.5,10 Considering this throughput lim-itation, some effort has been directed toward de-veloping more rapid processing schemes that stillexploit electrostatic adsorption. An obvious selec-tion has been the spin-coating method, a processthat offers an alternative approach to a dippingdeposition of alternating layers. Here, a spincoater is operated in a conventional manner withexcess solution (polycation or polyanion) appliedto a substrate before spinning, during which timesolution is first rapidly (�1 s) expelled from thesurface, following which a thin film of polyelectro-lyte solution more slowly thins and dries over thecourse of 2–10 s. To build up polyelectrolyte mul-tilayers in an LbL fashion, this spin-coating stepis applied sequentially to solutions of oppositelycharged polyelectrolytes with intervening rinsingsteps also achieved using the spin coater. It was

shown recently11–13 that such a method, heretermed polyelectrolyte spin assembly (PSA), al-lows for rapid processing and for uniform coatingof the substrate. Furthermore, the process isfound to produce highly ordered coatings that aresmoother and thicker when compared with thecoatings attained by dipping technique applied toidentical solutions.3,11

How might spin coating afford more rapid pro-cessing? Although equilibrium adsorption isachieved after 10–20 min in quiescent adsorptionthat transpires by diffusion from solution, PSAleads to apparent complete adsorption withcharge inversion after only one step (2–10 s) aspromoted by convection and hydrodynamic stress.The centrifugal force induced by the fast spinningrate and short spinning time, simultaneouslydrives out unassociated water and loosely boundpolymer chains from the substrate. The combina-tion of hydrodynamic shear stress due to flow,acting to distort adsorbing polymer chains, andelectrostatic attraction between the polyelectro-lytes and the oppositely charged substrate isthought to cause irreversible adsorption of highlyordered layers as evidenced by a high degree ofsurface planarization.3,11 The combination ofthese effects produces a “thick” and highly denselayer of the charged polymers when compared tothe dipping method. Direct comparisons of thetwo techniques by Hong’s group has shown thatthe spin-assembly process yields faster buildupwith substantial increase in polyelectrolyte ad-sorbed amount,11 although a quantitative expla-nation was not provided.

The promise offered by PSA of rapid coatingassembly has triggered research efforts directedtoward elucidation of the effect of spin rate andpolyelectrolyte concentration on multilayer depo-sition. In particular, Lee et al. have used UV-Visspectroscopy and ellipsometry to reveal that layerthickness increases in proportion to polyelectro-lyte concentration in a manner similar to quies-cent (dipping) LbL processing. However, the pro-portionality constant—or slope of thickness ver-sus cycle number—was larger for PSA than forthe dipping deposition process.13 The effect ofspinning rate on the layer thickness increment forPSA of salt-free solutions was studied by Chiarelliet al.,12 who found using ellipsometry that in-creasing the spin speed leads to thinner, perhapsmore compacted, multilayers with an asymptoticbehavior at high spin speeds. The observationwas explained by the “increased mechanicalforces” experienced by the films at higher spin-

POLYELECTROLYTE SPIN ASSEMBLY 3655

ning rates that lead to a shorter contact timebetween polyelectrolyte solution and the sub-strate.

On the basis of the prior work summarizedabove, we hypothesized that the addition of salt topolyelectrolyte solutions processed by a spin assem-bly may lead to interesting results, as increasingsalt addition for dipping LbL compared with in-creasing spin speed for a salt-free spin assemblyhave yielded opposite trends in growth rate. Thus,in this article, we report on the role of added salt inthe polyelectrolyte spin-assembly process, espe-cially regarding growth rate and ultimate surfacemorphology, using UV-Vis spectroscopy and AFM,respectively, and with consideration of the influenceof added salt on chain structure preceding and dur-ing adsorption. A scaling theory is developed andfound to be in good agreement with our experimen-tal observations.

EXPERIMENTAL

Materials

The deposition of polyelectrolytes by spin assem-bly was performed on both quartz and silicon(100) substrates. Quartz substrates were 25.4 mmin diameter, while Si wafers were roughly squarein shape with edge dimension of 10 mm. In bothcases, substrates were treated with piranha solu-tion (70:30 H2SO4/H2O2) at 80 °C for 1 h, followedby rinsing and sonication in ultrapure water for15 min. After that cleaning step, surfaces weretreated by a base treatment (1:1:5 NH3/H2O2/H2O) at 50 °C for 1 h, followed by a rinsing step inultrapure water (Milli-Q, � � 18 M� � cm) for15 min. To achieve the adsorption of the first poly-electrolyte layer and to produce a positivelycharged surface, a layer of low molecular weightpoly(ethyleneimine) (PEI) was deposited on thesubstrate by spin coating at 3000 rpm for a dura-tion of 8 s. The polyanion used in our experimentswas poly(sodium 4-styrene sulfonate) (PSS), Mw� 70 kDa, and whose pKa is approximately 7. Thepolycation was poly(allylamine hydrochloride)(PAH), Mw � 15 kDa and pKa �8.5. The struc-tures of these polymers are shown in Scheme 1.The solution conditions, including pH ionicstrength, were varied, and are detailed in thecontext of the experiments described.

Preparation of Multilayer Assemblies

The polyelectrolyte spin-assembly (PSA) processfor a single cycle or “bilayer”—to be repeated mul-

tiple times—includes: (1) deposition of severaldrops of PSS solution to wet the whole chargedsurface followed by substrate spinning at3000 rpm for 8 s (Scheme 1); (2) two washingsteps with several drops each of pure deionizedwater at 3000 rpm for 8 s; (3) repetition of step (1)for PAH polyelectrolyte solution. The polymerdeposition was performed using aqueous solu-tions with polymer concentration 10�2 M, on thebasis of repeat unit molar mass, and pH � 3.5adjusted with 0.1 M solution of HCl. At this pH,both the PSS and PAH are fully ionized.14,15 Theeffect of salt concentration on the layer absor-bance and thickness was studied for the followingconcentrations of NaCl: 0, 0.01, 0.05, 0.1, 0.5,and 2 M.

Characterization Techniques

UV-Vis Spectroscopy

UV-Vis spectra were collected with a Perkin-Elmer Lambda 6 spectrometer with a scan rate of120 nm/min. A clean quartz disk with the samethickness as the spin-assembly substrate wasused as a reference. The choice of PSS was dic-tated by its chromophoric nature that allows mon-itoring of the deposition process by UV-vis spec-troscopy.16 Thus, the amount of PSS in the spin-assembled films was monitored by UV-Vis

Scheme 1. Spin self-assembly process (3000 rpmduring 8 s with a rinse step in between) and the chem-ical structures of the polyanion and polycation, poly-(styrene sodium sulfonate) (PSS) and poly(allylaminehydrochloride) (PAH), respectively.

3656 LEFAUX ET AL.

spectroscopy through the detection of the benzene� 3 �* transition peak around 225 nm, withUV-Vis spectra being taken every two or five cy-cles of deposition, one cycle consisting of the con-secutive deposition of PSS and PAH with a wash-ing step in between (same speed). In contrast toPSS, PAH polymer shows no detectable feature inthe UV-Vis spectrum. In most cases, we reportthe absorbance at the precise center of rotationfor the disks; however, a radial dependence ofmultilayer thickness, and thus UV absorbance,was investigated by translation of the circulardisk with respect to the beam along a line thatintersected the disk center. For such measure-ments, it is pertinent that the beam diameter wasapproximately 1 mm.

Atomic Force Microscopy

The morphology, thickness, and surface rough-ness of the multilayer buildups were obtainedusing a Topometrix TMX 2000 Scanning ProbeMicroscope. The images were collected in the con-tact mode using model 1520-00 tips. Measure-ments were performed in air on dried film. Sev-eral images were recorded from different areasand representative images are being reported.The polymer film thickness was measured byscratching the multilayer assembly with a freshrazor blade and then scanning it with AFM toreveal a clear step at the scratch that is pene-trates to the quartz substrate but no further.

Scaling Model

In the Appendix section, we derive expressions forthe polymer surface coverage, �, and thickness,H, for each “bilayer” using a Flory-type theory.The starting point for the derivation is a freeenergy expression for adsorbing chains that in-cludes, in the quiescent case, electrostatic, elastic,and binding terms. For steady growth, whereeach LbL cycle contributes equally to the surfacecoverage and thickness, minimization of this freeenergy predicts that the coverage per cyclefollows:

� � m�* ��a

lBrD(1)

where �a s a dimensionless binding energy forionic pair formation, lB is the Bjerrum length, andrD (�c�1/2) is the Debye screening length. In ourderivation, we have assumed that the interpene-

tration between two neighboring layers occurs atthe length scale comparable with the Debyescreening length. Such intermixing between thelayers is driven by the electrostatic interactionsthat exists between oppositely charged chainsand that is exponentially screened for distanceslarger than the Debye screening length. Furtherintermixing between layers is precluded by theformation of ionic pairs that significantly retardchain dynamics and the short duration of eachdeposition cycle.

In the presence of shear flow, the brush ofadsorbed chains stretches and tilts from the nor-mal direction. Additional chain extension occursdue to hydrodynamic drag on each chain sectionthat forms a brush-like layer. Determination ofthe equilibrium conformation of a section of achain under external shear flow requires balanc-ing the hydrodynamic drag and electrostatic re-pulsion between charged monomers by the ten-sion within such a section. However, the externalflow is largely screened within each brush layer,the velocity field penetrating only a thin outerboundary layer whose thickness is comparable tothe size of the outermost blob. The size of this blobis determined from the condition that the blobDeborah number Dec � �̇�e � 1, where �e is theZimm relaxation time of the last blob.27,28 Thus,the extension of an adsorbed brush due to shearflow is localized to an outer region whose thick-ness is the size of the last blob. With these con-cepts (detailed in the Appendix), we arrive at theprediction,

� ��arD / lB

rD2 �b2�̇�o

2/3 (2)

where b is the Kuhn segment size, �̇ is the shearrate, and �o is a “bare” relaxation time for eachKuhn segment—generally an unknown quantity.The thickness per bilayer is predicted to follow asimilar form. To fit experimental data, we mayuse the expression,

� � �c�1/2

c�1 � �̇2/3 (3)

where � and should be considered to be fittingparameters, and c is the concentration of free ionsin solution, including both added salt and poly-electrolyte counterions. Inspection of eq 3 revealsthat in the no-flow limit � � c1/2, while in the

POLYELECTROLYTE SPIN ASSEMBLY 3657

strong-flow limit � � c�1/2 with an interveningmaximum.

Recognizing that in spin coating the shear rateclose to the surface has a radial dependence:

�̇ ��2rh/� (4)

where � is the solution mass density, � is theangular velocity, r is the radial position, h is theinstantaneous solution thickness, and � is theviscosity, eq 3 takes on a form that reveals boththe spin speed and radial dependences:

� ��o

1 � �2r2/3 (5)

where �o and are fitting parameters. Below, wewill make use of both eqs 3 and 5 in examinationof the experimental data and to assess the level ofconsistency between our experiment and thesimple theory.

RESULTS AND DISCUSSION

To elucidate the effect of salt concentration on themultilayer build up by the spin-assembly techniquewe have conducted a set of experiments at differentionic strengths. Figure 1 shows the dependence ofabsorbance on the number of deposition cycles for

PSS/PAH system at pH � 3.5 and salt concentra-tion 0.1 M. The amplitude of the absorbance peak at225 nm shows a linear increase with the number ofdeposition cycles, indicating regular (linear) growthduring spin-coating process (Fig. 1). We note thatthe lower wavelength absorption peak near �� 195 nm has been reported before for a similarsystem,17 and identified by one group to be an ad-ditional absorption from PSS.18 Nevertheless, thelinear relation between absorbance (at 225 nm) andpolymer adsorbed amount allows us to evaluatehow much polyelectrolyte was adsorbed on the sub-strate during each deposition cycle. Figure 2 showsgrowth curves for PSS/PAH spin-assembly for arange of salt concentrations. In all cases we haveobserved a linear increase in polymer’s adsorbedamount with number of deposition cycles; however,the growth rates (slopes of the lines of Fig. 2) showsaturation behavior described in more detail below.

The data shown in Figure 2 were obtained usingUV-Vis transmission spectra where the transmittedbeam was passed through the disk center. However,we have found a significant radial dependence ofthe absorbance, and thus coating mass. This depen-dence, shown in Figure 3, features a monotonicallydecreasing absorbance that follows an analyticalform given in eq 5 (vide supra) using the absorbanceat 225 nm for the surface coverage, �, and where ris the radial position in mm. The best fit to the datais obtained for parameters �0 � 0.298 and � 1.0 �10�4, but these parameters are sensitive to the poly-

Figure 1. Plot of the absorbance versus wavelengthof PSS/PAH (10�2 M, pH � 3.5) for a salt concentrationof 0.1 M preparing by spin assembly at different num-ber of bilayers: (i) 5 (i); (ii) 10; (iii) 15; and (iv) 20. Spinconditions: 3000 rpm, 8 s. Inset is peak absorbance(225 nm) versus cycle number of PSS/PAH (10�2 M, pH� 3.5) for 0.1 M NaCl concentration in both solutions.The solid line is a linear regression of the data.

Figure 2. Plot of the absorbance at 225 nm versus thenumber of deposition cycles of PSS/PAH (C � 10�2 M,pH � 3.5) for varying NaCl concentration: No salt (F);0.1 M (E); 2.0 M (�) in both polyelectrolyte solutionspreparing by spin assembly (3000 rpm, 8 s). Solid linesrepresent linear regressions.

3658 LEFAUX ET AL.

mer composition (absorbance) and solution details.It is noted that the multiple observations for posi-tions 5 and 10 mm in Figure 3 were made at differ-ent azimuthal positions on the same disk. The basisof eq 5 is in the crossover from electrostatic to hy-drodynamic dominance with increasing radius andis derived in the appendix. Although conventionalspin coating of uncharged polymers leads to highlyplanarized coatings,19,20 Chirelli et al.12 found asimilar radial dependence for spin-assembled poly-electrolytes, although a different functional formwas selected to fit their data. Thus, it appears thatsuch a radial gradient is unique to the PSA process,and should be an important clue in understandingthe underlying mechanisms of coating growth. Forsimplicity, however, the rest of our study focuses oncoatings examined at the axis of rotation, but withan aperture large enough (1 mm) to reveal floweffects.

Figure 4 show the dependence of PSA growthon salt as examined via absorbance from PSS atdifference stages of multilayer growth. For lowsalt concentrations, the rate of LbL growth in-creases with increasing salt concentration, butthen saturates (or reaches a broad maximum) forsalt concentrations beyond 0.5 M. For higher saltconcentrations, the growth rate becomes nearlyconstant, suggesting a dominant effect of hydro-dynamic drag on the chain conformations. Toshow that the observed saturation behavior isindependent of the number of deposition cycles,we plot in Figure 4 the absorbance at 10 and 20cycles versus the salt concentration. Both sets ofdata reveal saturation beginning for concentra-tions greater than 0.5 M. We did not expect to

observe such a plateau as shown in Figure 4.Indeed, eq 3 suggests that this plateau reallyrepresents a transition from electrostatic-domi-nated to hydrodynamic-dominated regimes, al-though for the parameters chosen we were unableto observe a regime for which � � c�1/2. Higherrotation speeds should allow such observations.

The observed trends shown in Figure 4 aredistinct from similar results reported in the liter-ature for quiescent LbL processing. For the latter,is has been conjectured that ionic strength has astrong effect on the layering process through itseffect on the structure of the polyelectrolytes insolution, with layers deposited at higher ionicstrength being thicker, less interpenetrating, andless stable.21 Dubas and Schlenoff have found analmost linear dependence of layer thickness onsalt concentration22 while Lvov and Decher re-ported that the layer thickness scales as thesquare root of ionic strength.23 In the case ofpolyelectrolyte spin assembly, as discussed previ-ously, the addition of shear forces caused by ra-dial flow and a no-slip boundary condition shouldhave a significant effect on chain conformationbefore and after adsorption and thus may explainthe observed unique behavior.

To gain an understanding of the surface mor-phology, roughness, and thickness of the multi-layered coatings, contact-mode AFM was con-ducted. To show typical results, we have selectedAFM images of multilayered coatings obtainedafter 20 cycles of spin-coating PSS/PAH solutionson quartz substrates and with varying added

Figure 4. Absorbance values at 225 nm for 10 (ƒ) and20 (F) spin assembly cycles of PSS/PAH (10�2 M, pH� 3.5) versus NaCl concentration. The reported absor-bance was measured at the rotation axis center.

Figure 3. Radial dependence of the absorbance at 225nm after 20 cycles of deposition of PSS/PAH (C � 10�2 M,pH � 3.5) and NaCl concentration of 0.5 M. The solid linerepresents the best fit of eq 5 to the experimental data.

POLYELECTROLYTE SPIN ASSEMBLY 3659

NaCl concentration. The results are shown inFigure 5 where we observe that the coatings pre-pared using low salt concentration solutions arecomparatively smooth, with only a slight granu-lar texture as illustrated in Figure 5(a). Qualita-tively, the surface roughness increases as saltconcentration increases to 0.5 M, as shown inFigure 5(b), leading to significant roughness forthe highest salt concentration of 2.0 M, with largefeatures shown in Figure 5(c).

To quantify the AFM observations, we haveemployed height histogram analysis. Figure 6shows histograms for the same AFM scans de-picted in Figure 5; thus, for three different addedsalt concentrations of 0, 0.5, and 2 M. One canquickly see from the width of the distributionsthat the roughness of the coatings increases withionic strength. In salt-free solutions the rough-

ness (narrow width of the Gaussian peak) re-mained very low and indistinguishable from theunderlying silicon substrate. But as salt concen-tration is increased, the height distribution be-comes increasingly broadened, indicating roughercoatings. We quantified these observations bycomputing the root-mean-square roughness:

Ra � 1N��hi � h��2

(6)

where N is the total number of height measure-ments, hi is each height value, and h� is the meanheight. These data are plotted as inset to Figure 6revealing a nearly linear increase in roughnesswith salt concentration. This is in contrast to thesurface coverage measurements (Fig. 4), whichshowed clear saturation behavior with increasingsalt. Presently, we have no theoretical model forroughness, but this key distinction should be cap-tured in such a prediction.

Direct thickness measurements for the multilay-ered structures were obtained by scratching thesurface with a fresh razor blade and then scanningthe surface with contact mode AFM in a directionorthogonal to the scratch. An example result fromthis procedure is shown in Figure 7, with the darkerregion in the image being the substrate (where thefilm was removed by the razor plowing) and thebright regions are the multilayer stacks. The thick-ness of the film is obtained from the height differ-ence between the substrate side and the multilayerstacks. Figure 8 shows the dependence of the layerthickness on the number of deposition cycles at dif-ferent salt concentrations. There is a linear rela-tionship between the layer thickness and the num-

Figure 5. AFM images of the morphology of 20 bilayer films of PSS/PAH (10�2 M, pH� 3.5) deposited by the spin assembly process from: (a) 0 M, (b) 0.5 M, and (c) 2 M NaClsolutions.

Figure 6. Peak-valley height distributions for differ-ent NaCl concentrations: (i) 0 M; (ii) 0.5 M; and (iii)2 M. Inset is RMS roughness versus salt concentration.

3660 LEFAUX ET AL.

ber of deposition cycles for each salt concentration,as was observed for the surface coverage using UVabsorption. For deposition from salt free solution,the slope is approximately 1.65 nm/bilayer, but theslope increases drastically with the addition of saltto be 4.73 nm/bilayer for 0.1 M salt, and saturatesnear 5.43 nm/ bilayer for 2 M solutions in a mannersimilar to the surface coverage measured with UVabsorbance.

Both trends are clearly shown in Figure 9,where we plot the thickness and the absorbancegrowth rates versus the salt concentration. Thedependence of thickness on salt concentrationshows the same saturation behavior as one ob-served for UV-Vis measurement: the growth ratefirst increases as salt concentration increasesthen saturates beyond salt concentrations of ap-proximately 0.5 M. For higher salt concentrationthe growth rate is independent of salt, indicatingthe dominant effect of hydrodynamic drag on thechain conformations.

CONCLUSIONS

In this study, we have examined a process termedpolyelectrolyte spin assembly (PSA) by sequential

spin coating of polyelectrolyte solutions using UVspectrometry and atomic force microscopy tostudy the growth, morphology, and roughness ofthe resulting coatings at different salt concentra-tions. Additionally a scaling theory was developed

Figure 8. Thickness from AFM versus cycle numberfor spin assembly of PSS/PAH films using different saltconcentrations: No salt (F); 0.01 M (E); and 2.0 M (�).The solid lines represent linear regressions.

Figure 7. Thickness measurements are obtained by scratching with a razor blade toremove all the polyelectrolytes multilayer film. Dark side in the AFM image representsthe scratch. Thickness measurements are made at several points (15 points). Forinstance, AFM from a 20 bilayers film of PSS/PAH (C � 10�2 M, pH � 3.5) with a0.05 M salt concentration: Thickness 0.8831 1.98 nm.

POLYELECTROLYTE SPIN ASSEMBLY 3661

that considers the compaction of adsorbing chainspossible at the high shear rates involved in spincoating. Experimentally, PSA allowed rapid for-mation of polymeric multilayer structures to re-veal trends in growth rate, which grew to satura-tion with increasing salt concentration and addi-tionally showed drastic morphological alterationwith salt addition. Additionally, a peculiar radialdependence of surface coverage was observed,showing a strong peak at the axis of rotationwhere the influence of flow is the least. Reason-able fitting quality for our scaling theory suggeststhat our underlying assumptions are correct, spe-cifically that adsorption of polyelectrolyte chainsequilibrates to locally achieve De �1 and that thecondition is achieved with chains of increasingcompactness as salt content increases. Future in-vestigations will more rigorously test our theoret-ical picture by independent variation of both thespinning rate and salt concentration.

We thank the Office of Naval Research (ContractN00014-01-1-06412) and the Connnecticut Global FuelCell Center (Batelle Agreement #DAAB07-03-3-K-415)for financial support. A.V.D. acknowledges support ofthe donors of the Petroleum Research Fund, adminis-tered by the American Chemical Society under thegrant PRF#39637-AC7.

APPENDIX: THEORETICAL MODEL FORPOLYELECTROLYTE ADSORPTION INSHEAR FLOW

In this Appendix we present a Flory-like theory todescribe the basic elements of layer-by-layer poly-

electrolyte assembly generally in shear flow, andpolyelectrolyte spin assembly (PSA) in particular.Consider adsorption of fully charged polyelectro-lyte chain containing N Khun monomers of lengthb (for polystyrene sulfonate b � 18 Å) at a chargedsurface with surface charge number density� (mol/m2) from a salt solution characterized byDebye radius rD,24

rD 9.61

z2c1/2 nm (A.1)

for aqueous salt solutions at T � 25 °C withvalency z and concentration c in mol/m3. Here, wewill assume that charged sites (monomers) oneach polyelectrolyte chain form ionic pairs withsurface charges during the adsorption process.25

The energy of the ionic pair is equal to �kBT�a,where kB is the Boltzmann constant, T is theabsolute temperature, and �a is a dimensionlesssticking energy strength. The adsorbed layer hasa brush-like structure of loops [see Fig. 10(a)]with 2m monomers in each loop as determined bythe fine interplay between the electrostatic repul-sion between adsorbed chains, the elastic energy

Figure 10. Schematic representation of the adsorbedlayer (a) without shear; (b) without shear and withindication of Pincus blobs; and (c) under applied shear.

Figure 9. Thickness (E) and absorbance at 225 nm(F) at (PSS/PAH)20 versus salt concentration, films pre-pared with Polyelectrolyte Spin Assembly method(3000 rpm, 8 s, C �10�2 M, pH � 3.5).

3662 LEFAUX ET AL.

of each loop, and the strength of the stickingenergy of ionic pair that holds the two ends ofeach loop attached to the surface. (1) The electro-static repulsion energy per polymeric strand withm monomers (a half-loop) within an adsorbedlayer of thickness H in the limit of high ionicstrength (H/rD �� 1) is estimated to be25:

FelH

kBT �m2lBrD

2 �

H (A.2)

where lB � e2/�kBT is the Bjerrum length thatdefines the length scale at which the energy ofelectrostatic interaction between two elementarycharges e in the medium with dielectric constant� is equal to the thermal energy kBT. The totalelectrostatic energy per chain is N/m times thisquantity. (2)The elastic energy per half-loop of mmonomers stretched to thickness H is,

Felast

kBT �H2

mb2 (A.3)

Again, the total elastic energy for each adsorbedchain is (N/m) times this expression. (3) Finally, apolyelectrolyte chain with N monomers will haveN/2m contact points with a surface each of whichcontributes a favorable sticking energy �kBT�a tothe total chain-free energy. Combining electro-static, elastic, and sticking energy terms togetherone obtains the following expression for the freeenergy of an adsorbed chain.

Fch

kBT �Nm�m2lBrD

2 �

H �H2

mb2 ��a

2� (A.4)

Minimization of the chain free energy with re-spect to the thickness of the adsorbed layer H gives

H � mbu�rD2 1/3 (A.5)

where u � lB/b is the ratio of the Bjerrum lengthto the Kuhn length, approximately 5 for aqueousPSS. Substituting this expression into eq A.4 andsimplifying we obtain the chain-free energy asfunction of the number of monomers m in a loop:

Fch

kBT � N�u�rD2 2/3 �

�a

2m�. (A.6)

In equilibrium the chemical potential of chainsin free solution is equal to that of chains in an

adsorbed layer. Thus, we can set the chain freeenergy given by eq A.6 equal to zero. This leads tothe number of monomers in each loop being:

m ��a

�u�rD2 �2/3 (A.7)

noting that we have dropped the factor of 2 forsimplicity. The polymer surface coverage, relatedto the experimentally observed UV-Vis absor-bance, can then be calculated using the surfacecharge density:

� � m� ��1/3�a

u2/3rD4/3 (A.8)

In the case of the multilayer LbL assembly, theprocess reaches steady state growth with the sur-face charge density of the previous layer deter-mining the thickness of the next one. The electro-static interaction between charges in salt solu-tions is exponentially screened for length scaleslarger than rD. We will assume that newly ad-sorbed chains are capable of forming ionic pairsonly with the charged monomers (m for fully ion-ized chains) of the previous layer within thicknessrD from the top of the adsorbing layer. Thus, theeffective surface charge density of each new layer,�i�1, includes only the fraction of charges pre-sented by the adsorbed chains:

�i�1 � �imrD

H ��i

2/3rD1/3

u1/3b (A.9)

For steady-state (linear) growth, each newlyadsorbed layer completely reconstructs the sur-face properties so that �i�1 � �i, leading to asurface charge density of the form:

�* �rD

b2lB(A.10)

Along with eqs A.5 and A.7, this allows estima-tion of the adsorbed layer thickness and the num-ber of monomers m per half-loop:

H � �a

b2

rDm � �a

b2

rD2 (A.11)

Both quantities increase with added salt, asrD�c�1/2; for example, the thickness of each ad-

POLYELECTROLYTE SPIN ASSEMBLY 3663

sorbed layer increases as a square root of saltconcentration, as reported experimentally byLvov and Decher,23 among others. For compari-son with experiments, we consider the polymersurface coverage in the steady state regime,which increases with salt concentration as:

� � m�* ��a

lBrD. (A.12)

This surface coverage, measurable by UV-Vis ab-sorption spectroscopy as the absorbance per bi-layer increases as square root of salt concentra-tion, as does the thickness, H, measurable withAFM profilometry.

To describe chain conformations inside the ad-sorbed layer it is useful to introduce a concept ofthe Pincus blob26 of size D, which separates twodifferent length scales. For length scales smallerthan the Pincus blob size, a chain section adoptsan unperturbed Gaussian conformation (at theselength scales the electrostatic repulsion betweenneighboring chains is not strong enough to per-turb chain conformations), while for length scaleslarger than the blob size the chains are stronglystretched by electrostatic repulsion betweenneighboring chains. To minimize these interac-tions chain sections adopt an elongated conforma-tion of array of Pincus blobs, as shown schemati-cally in Figure 10(b), where we have sketched ablob picture of the adsorbed layer. Each section ofa chain with m monomers in this brush-like layeris stretched by the electrostatic repulsion be-tween adsorbed chains with a force:

f � kBTH

mb2 � kBTrD

b2 �kBTD (A.13)

Inspection of this expression reveals that the Pin-cus blob size, D � b2/rD, increases as more salt isadded to the solution, while the force within theloop decreases.

The development until now considered onlyelectrostatic, elastic, and sticking energetics, withno consideration of hydrodynamic drag that mayinfluence the adsorbed layer thickness in thepresent PSA process or other adsorption/flow pro-cesses. To proceed, we consider the magnitude ofthe shear rate that will force deformation of thePincus blobs of size D. The shear force exerted bythe external shear flow with shear rate �̇ in asolvent with viscosity � on a Pincus blob can beestimated as Fshear � ��̇D2, where D�̇ is typical

variance of solvent velocity on the length scale ofthe order of the blob size D and �D is the blobfriction coefficient within an unknown numericalprefactor. The shear flow will start deforming thePincus blobs when the shear force, ��̇D2, becomescomparable to the tension inside polymer chain,kBT/D. This leads to the following condition forthe crossover shear rate �̇c.

��̇cD2 � kBT/D (A.14)

We can rewrite this relation by introducing therelaxation time of the Pincus blob (Zimm relax-ation time):26

� ��D3

kBT (A.15a)

Substituting into eq A.15a an expression forthe blob size D � b2/rD we obtain the Zimm re-laxation time

�e ��b3

kBT � brD�3

(A.15.b)

of the blob whose dimensions are controlled byelectrostatic repulsion between neighboringbrush strands. An external shear flow will influ-ence the brush structure when the dimensionlessgroup Dee � �̇c�e is of order unity.27,28 For highershear rates, �̇ � �e

�1, following the results of refs.27 and 28, we assume that adsorbing chains willcontinue to adjust their configuration until thecriterion �̇� � 1 is satisfied. For example, chainswith large blob size D may feature �̇� �� 1 andadjust their configuration accordingly, whilechains with small D will expand until �̇� � 1.

Continuing more quantitatively, we considerdeformation of the adsorbed polyelectrolyte layerby shear flow with the shear rate �̇. Shear tilts the“brush” [see Fig. 10(c)] in such a way that thevector sum of (1) the shear force Fshear � ��̇D2,acting at the top of the brush layer, (2) the elasticforce, and (3) the electrostatic repulsive force be-tween charged monomers Fel � ��Uel (H)/�H iszero, indicating mechanical equilibrium.27,28 Thetilting of the brush results in the total brush

length becoming �H2�R2, where R is the lateraldisplacement of the end point of the loops fromthe grafting point [see Fig. 10(b)]. The balance ofprojections of the forces onto normal and parallel

3664 LEFAUX ET AL.

to the surface direction leads to two equations,respectively, dictating H, R, and m:

kBTH

mb2 � kBTm2lB�*rD

2

H2 (A.16)

kBTR

mb2 � ��̇D2 � ��̇1/3kBT2/3 (A.17)

In the second equation (A.17) we use the ex-pression for the blob size D obtained from thecondition �̇� � �̇�D3/kBT � 1.27,28 Equation A.16yields the same relation between the height of thebrush and the number of monomers in a strand mas eq A.5. Substituting the relation between H, R,and m we can write the expression of the chainfree energy (single chain chemical potential) asfunctions of the Debye radius, shear rate, andsticking energy.

Fch

kBT �Nm � H2

mb2 �R2

mb2 ��a

2�� N�rD

2

b2 � ���̇b3

kBT �2/3

��a

2m� (A.18)

Setting eq A.18 to zero yields a prediction forthe number of monomers per half-loop of chainsadsorbing in a shear flow:

m �b2�a

rD2 � b2�̇�0

2/33�a

�̇�02/3 (A.19)

where factoring leaves �0 � �b3/(kBT), the relax-ation time of a Kuhn monomer, and the arrowindicates the limit of high shear. The crossoverbetween electrostatic-dominated and shear-dom-inated regimes occurs when the Debye length rDbecomes smaller than b(�̇�0)1/3. Beyond this tran-sition, the number of monomers in a brush stranddecreases as the shear rate increases. Using thisnew expression for the number of monomers in astrand m and shear rate we can obtain the depen-dence of the brush thickness H and polymer sur-face coverage �:

H � bm�*urD2 1/3 �

rD�ab2

rD2 � b2�̇�0

2/3 (A.20)

� � �*m ��arD / lB

rD2 � b2�̇�0

2/3 (A.21)

observing that in the low-shear regime � � c1/2

while in the high shear regime, � � c�1/2. Due touncertainty in absolute values for the bare relax-ation time, �0, as well as other parameters, a moregeneral form of eq A.21 for the purpose of datafitting is given as:

� � �c�1/2

c�1 � �̇2/3 (A.22)

where � and �� are fitting parameters, c is theconcentration of free ions, and �̇ is the shear rate.

Let us apply the presented above analysis tothe case of polyelectrolyte spin assembly (PSA).The radial velocity profile of the liquid at point rfrom the center of the spinning disk rotating withangular velocity � is:19

�z ��2r��1�hz �z2

2 � (A.23)

where h is film thickness, and � is the density of aliquid. Close to the surface of a disk this velocityprofile can be approximated by the first term. Inthis case, the shear rate is equal to

�̇ ��2rh/� (A.24)

The shear rate increases linearly with distancer from the center of a disk. In this case, close tothe center of a disk the shear rate is not strongenough to perturb adsorbed layer, and the thick-ness of the adsorbed layer and polymer surfacecoverage are given by eqs. A.11 and A.12. Substi-tuting A.24 into A.21 reveals that the flow maysignificantly influence the layer structure for dis-tances r larger than

rflow ��

�0��2h �rD

b �3

(A.25)

beyond which the flow term of eq A.21 becomesdominant. For distances r �� rflow the polymersurface coverage decays with distance r as �� r�2/3, while for radii in the transition region(the case in our experiments) a more completeexpression is required to described the observeddata, namely:

� ��0

1 � � �2r2/3 (A.26)

where �0 and are fitting parameters.

POLYELECTROLYTE SPIN ASSEMBLY 3665

The above development allows fitting of exper-imental data and subsequent estimation of be-havior beyond that observed, with the quality offitting allows us to gauge the applicability of con-cepts incorporated into the theory and acceptabil-ity of mathematical simplifications.

REFERENCES AND NOTES

1. Iler, R. K. J Colloid Interface Sci 1966, 21, 569.2. Decher, G.; Hong, J. D. Ber Bunsen-Ges Phys

Chem 1991, 95, 1430.3. Decher, G.; Hong, J. D. Makromol Chem, Macromol

Symp 1991, 46, 321.4. Decher, G. In The Polymeric Materials Encyclope-

dia: Synthesis, Properties and Applications; CRCPress, Boca Raton, FL, 1996.

5. Decher, G. Science 1997, 277, 1232.6. Hammond, P. T. Curr Opin Colloid Interface Sci

1999, 6, 430.7. Decher, G.; Eckle, M.; Schmitt, J.; Struth, B. Curr

Opin Colloid Interface Sci 1998, 3, 32.8. Schoeler, B.; Kumaraswamy, G.; Caruso, F. Macro-

molecules 2002, 35, 889.9. Kim, D. K.; Han, S. W.; Kim, C. H.; Hong, J. D.;

Kim, K. Thin Solid Films 1999, 350, 153.10. Schmitt, J.; Grunewald, T.; Decher, G.; Pershan,

P. S.; Kjaer, K.; Losche, M. Macromolecules 1993,26, 7058.

11. Cho, J.; Char, K.; Hong, J.-D. Adv Mater 2001, 13,1076.

12. Chiarelli, P. A.; Johal, M. S.; Casson, J. L.; Roberts,J. B.; Robinson, J. M.; Wang, H.-L. Adv Mater2001, 13, 1167.

13. Lee, S.-S.; Hong, J.-D.; Kim, C. H.; Kim, K.; Koo,J. P.; Lee, K.-B. Macromolecules 2001, 34, 5358.

14. Joly, S.; Kane, R.; Radzilowski, L.; Wang, T.; Wu,A.; Cohen, R. E.; Thomas, E. L.; Rubner, M. F.Langmuir 2000, 16, 1354.

15. Shiratori, S. S.; Rubner, M. F. Macromolecules2000, 33, 4213.

16. Ferreira, M.; Rubner, M. F. Macromolecules 1995,28, 7107.

17. McAloney, R. A.; Sinyor, M.; Dudnik, V.; Goh, M. C.Langmuir 2001, 17, 6655.

18. Johal, M. S.; Casson, J. L.; Chiarelli, P. A.; Liu,D.-G.; Shaw, J. A.; Robinson, J. M.; Wang, H.-L.Langmuir 2003, 19, 8876.

19. Emslie, A. G.; Bonner, F. T.; Peck, L. G. J ApplPhys 1958, 29, 858.

20. Meyerhofer, D. J Appl Phys 1978, 49, 3993.21. Schlenoff, J. B.; Ly, H.; Li, M. J Am Chem Soc 1998,

120, 7626.22. Dubas, S. T.; Schlenoff, J. B. Macromolecules 1999,

32, 8153.23. Lvov, Y. M.; Decher, G. Crystallogr Rep 1994, 39, 628.24. Probstein, R. F. Physicochemical Hydrodynamics,

An Introduction; John Wiley &Sons, Inc.: NewYork, 1994.

25. Park, S. Y.; Rubner, M. F.; Mayes, A. M. Langmuir2002, 18, 9600.

26. Rubinstein, M.; Colby, R. H. Polymer Physics;Oxford University Press, New York, 2003.

27. Harden, J. L.; Cates, M. E. Phys Rev E 1996, 53, 3782.28. Rabin, Y.; Alexander, S. Europhys Lett 1990, 13, 49.

3666 LEFAUX ET AL.