Molecular Dynamics Simulations of Mutilayer Films of Polyelectrolytesand Nanoparticles

Junhwan Jeon,†,‡ Venkateswarlu Panchagnula,§,| Jessica Pan,⊥ and Andrey V. Dobrynin*,†,#

Polymer Program, Institute of Materials Science, Department of Chemistry, and Department of Physics,UniVersity of Connecticut, Storrs, Connecticut 06269, and Department of Chemical Engineering,

Columbia UniVersity, New York, New York 10027

ReceiVed December 20, 2005. In Final Form: March 6, 2006

We performed molecular dynamics simulations of multilayer assemblies of flexible polyelectrolytes and nanoparticles.The film was constructed by sequential adsorption of oppositely charged polymers and nanoparticles in layer-by-layerfashion from dilute solutions. We have studied multilayer films assembled from oppositely charged polyelectrolytes,oppositely charged nanoparticles, and mixed films containing both nanoparticles and polyelectrolytes. For all studiedsystems, the multilayer assembly proceeds through surface overcharging after completion of each deposition step.There is almost linear growth in the surface coverage and film thickness. The multilayer films assembled fromnanoparticles show better layer stratification but at the same time have higher film roughness than those assembledfrom flexible polyelectrolytes.

1. IntroductionThe layer-by-layer deposition of charged molecules, in which

a substrate is sequentially exposed to solutions of oppositelycharged macromolecules, is a new and promising technique forfabrication of layered polymeric nanocomposites.1-8 Thistechnique is now routinely used for fabrication of ultrathin filmsfrom synthetic polyelectrolytes, DNA, proteins, charged nano-particles (e.g., metallic, semiconducting, magnetic, ferroelectricmaterials), nanoplatelets, and other supramolecular species. Themultilayered thin films and coatings have potential applicationsin drug delivery, catalysis, functional responsive coatings forcontrolling release and adhesion, biosensors and bioreactors,photonic devices such as light emitting diodes, biocompatibility,and separation membranes (see, for review, refs 5, 6, 8, and 9).

The structure of multilayered films depends on the rigidity ofthe building blocks. For example, flexible polyelectrolytes intwo component multilayers are not stratified into well-definedlayers but are interdiffused over several adjoining layers showingsignificant intermixing.1,10-16The name “fuzzy multilayers” wascoined for such systems. Interpenetration between neighboring

layers can be reduced by using more rigid blocks for multilayerassembly. This was shown for multilayers containing rigidinorganic platelets17-19 and nanoparticles.20-26

Molecular simulations of multilayer formation provide usefulinformation about multilayer assembly processes and factorsgoverning the film buildup. Monte Carlo simulations of multilayerfilm assemblies from mixtures of oppositely charged polyelec-trolytes near charged spherical particles, charged cylinders, anduniformly charged surface were performed by Messina et al.27-30

These papers tested the hypothesis that multilayering is anequilibrium process, which occurs not only when one proceedsin a stepwise fashion, as done in experiments,1-8 but also whenoppositely charged polyelectrolytes are added together and the

* Corresponding author. E-mail: avd@ims.uconn.edu.† Polymer Program, Institute of Materials Science, University of Con-

necticut.‡ Present address: Department of Chemical Engineering, Vanderbilt

University.§ Department of Chemistry, University of Connecticut.| Present address: PerkinElmer Life and Analytical Sciences, 549 Albany

St., Boston, MA 02118.⊥ Department of Chemical Engineering, Columbia University.# Department of Physics, University of Connecticut.(1) Decher, G.Science1997, 277, 1232-1237.(2) Decher, G. InThe polymeric materials encyclopedia: synthesis, properties

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Sci.1998, 3, 32-39.(4) Hammond, P. T.Curr. Opin. Colloid Interface Sci.1999, 6, 430-442.(5) Sukhishvili, S. A.Curr. Opin. Colloid Interface Sci. 2005, 10, 37-44.(6) Schonhoff, M.Curr. Opin. Colloid Interface Sci.2003, 8, 86-95.(7) Schonhoff, M.J. Phys. Condens. Matter2003, 15, R1781-R1808.(8) Decher, G.; Schlenoff, J. B., Eds.Multilayer Thin Films: Sequential

Assembly of Nanocomposite Materials; Wiley-VCH: New York, 2003.(9) Sukhorukov, G. B.; Fery, A.; Mohwald, H.Prog. Polym. Sci.2005, 30,

885-897.(10) Decher, G.; Lvov, Y.; Schmitt, J.Thin Solid Films1994, 244, 772-777.(11) Kellogg, G. J.; Mayes, A. M.; Stockton, W. B.; Ferreira, M.; Rubner, M.

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(16) Schlenoff, J. B. InMultilayer Thin Films: Sequential Assembly ofNanocomposite Materials; Decher, G., Schlenoff, J. B., Eds.; Wiley-VCH: NewYork, 2003.

(17) Kleinfeld, E. R.; Ferguson, G. S.Science1994, 265, 370-373.(18) Glinel, K.; Laschewsky, A.; Jonas, A. M.Macromolecules2001, 34,

5267-5274.(19) Lvov, Y.; Ariga, K.; Ichinose, I.; Kunitake, T.Langmuir1996, 12, 3038-

3044.(20) Schmitt, J.; Decher, G.; Dressick, W. J.; Brandow, S. L.; Geer, R. E.;

Shashidhar, R.; Calvert, J. M.AdV. Mater. 1997, 9, 61-65.(21) Joly, S.; Kane, R.; Radzilowski, L.; Wang, T.; Wu, A.; Cohen, R. E.;

Thomas, E. L.; Rubner, M. F.Langmuir2000, 16, 1354-1359.(22) Koetse, M.; Laschewsky, A.; Verbiest, T.Mater. Sci. Eng, C1999, 10,

107-113.(23) Lvov, Y.; Ariga, K.; Onda, M.; Ichinose, I.; Kunitake, T.Langmuir1997,

13, 6195-6203.(24) Ariga, K.; Lvov, Y.; Kunitake, T.J. Am. Chem. Soc.1997, 119, 2224-

2231.(25) Ariga, K.; Lvov, Y.; Onda, M.; Ichinose, I.; Kunitake, T.Chem. Lett.

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(27) Messina, R.Langmuir2003, 19, 4473-4482.(28) Messina, R.J. Chem. Phys.2003, 119, 8133-8139.(29) Messina, R.; Holm, C.; Kremer, K.J. Polym. Sci., Part B2004, 42,

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4629Langmuir2006,22, 4629-4637

10.1021/la053444n CCC: $33.50 © 2006 American Chemical SocietyPublished on Web 04/08/2006

resulting solution is exposed to a charged substrate. It was shownthat additional short-range attractive interactions between poly-electrolytes and the surface are necessary to successfully initiatechain adsorption. These simulations do not represent theexperimental situation in which polyelectrolytes are depositedfrom a solution in a sequential manner.1-8Thus, it was impossibleto test the linear increase of the layer thickness and mass withthe number of deposition steps as seen in the experiments.

The molecular dynamics simulations were also recently usedto study the sequential deposition of polyelectrolyte chains at acharged surface31,32 and at charged spherical particles.33,34 Inthese simulations the charged substrates were periodically exposedto dilute polyelectrolyte solutions. The steady-state film growthproceeds through a charge reversal of the adsorbed polymericfilm, which leads to an increase in the polymer surface coverageand in the average layer thickness after completion of the firstfew deposition steps. In the case of adsorption onto a chargedspherical particle, the polymer adsorbed amount grows fasterthan linear with number of deposition steps. This unusual behavioris due to the increase in the polymer adsorbing area aftercompletion of the each deposition step.

In the case of multilayer deposition at charged surfaces, MDsimulations have shown that the film build up follows a lineargrowth with both the thickness of the adsorbed layer and polymersurface coverage increasing linearly with the number of depositionsteps.31 This steady state linear growth regime is generallyobserved in experiments after the deposition of the first fewlayers.1-8 For partially charged chains with a fraction of chargedmonomersf ) 1/2 and 1/3, the growth rate of the polymer surfacecoverage is higher than in the case of fully charged chains. Inthe case of partially charged chains, there are an additional 1/f- 1 monomers added to the adsorbed layer for each adsorbedcharge. This is in agreement with experimental observations ofthe thicker layers for partially charged polyelectrolytes comparedto very thin layers obtained for the fully charged chains.

Unfortunately, all previous molecular simulations were dealingwith multilayers assembled from linear polyelectrolytes. In thispaper, we use MD simulations to study the effect of the molecularrigidity on the layer-by-layer assembly. We perform MDsimulations of the multilayered films formed from flexiblepolyelectrolytes, polyelectrolytes and nanoparticles, and op-positely charged nanoparticles. Our simulation results show thatincorporation of the nanoparticles into multilayered films resultsin a better layer separation in comparison with that in the filmsformed by flexible polyelectrolyte chains. However, this layeredstructure comes with the price of a higher film roughness. Therest of the manuscript is organized as follows. The model andsimulation details are described in section 2. In section 3, wepresent simulation results with a detailed discussion of theevolution of the surface coverage and film thickness, polymerdensity profile, film roughness, and surface overcharging duringthe deposition process. Finally, in section 4, we summarize ourresults.

2. Model and Simulation Details

The molecular dynamics simulations of multilayer assemblieswere performed from dilute solutions of linear polyelectrolytesand charged nanoparticles. The flexible polyelectrolytes were

modeled by chains of charged Lennard-Jones (LJ) particles(beads) with a diameter ofσ and a degree of polymerization ofN) 32. The charged nanoparticles consisted of 32 charged beadsand have a diameter equal to 4σ. To model charged nanoparticles,we utilized the fullerene C32 structure by rescaling the coordinatesof the C atoms in such a way to set the bond length between themto σ (see Figure 1). The simulation box had the followingdimensionsLx × Ly × Lz ) 40σ × 41.6σ × 81σ. The adsorbingpositively charged surface located atz ) 0 was modeled by ahexagonally packed lattice ofNsurface) 1920 particles with adiameter ofσ. Every second bead on the surface had a univalentcharge. A similar but uncharged nonselective surface is locatedin the opposite side of the simulation box,z ) 81σ, to preventmacromolecules from escaping and hence maintaining 2-Dperiodicity in the lateral (x andy) directions. All particles in thesystem interacted through the truncated-shifted Lennard-Jones(LJ) potential

whererij is the distance betweenith andjth beads andσ is thebead diameter chosen to be the same regardless of the bead type.The cutoff distance,rcut ) 2.5σ, was chosen for surface-nanoparticle/polymer and nanoparticle/polymer pairs, andrcut)x62σ was chosen for other pairwise interactions. The interactionparameterεLJ is equal tokBT for all pairs, wherekB is theBoltzmann constant, andT is the absolute temperature. The choiceof parameters for surface-nanoparticle/polymer and nanoparticle/polymer LJ-potential corresponds to effective short-range at-traction while interaction potential withrcut ) x62σ correspondsto pure repulsive interactions.

The connectivity of beads in both nanoparticles and poly-electrolyte chains was maintained by the finite extension nonlinearelastic (FENE) potential

with the spring constantkspring ) 30kBT/σ2, whereRmax ) 1.5σis the maximum bond length. The combination of FENE and LJpotentials prevents the bonds from crossing each other duringthe simulation run.

(31) Patel, P. A.; Jeon, J.; Mather, P. T.; Dobrynin, A. V.Langmuir2005, 21,6113-6122.

(32) Abu-Sharkh, B.J. Chem. Phys.2005, 123, 114907.(33) Panchagnula, V.; Jeon, J.; Dobrynin, A. V.Phys. ReV. Lett. 2004, 93,

037801.(34) Panchagnula, V.; Jeon, J.; Rusling, J. F.; Dobrynin, A. V.Langmuir2005,

21, 1118-1125.

Figure 1. C32 fullerene-like structure of nanoparticle with bondlength equal toσ.

ULJ(rij) )

{4εLJ[(σrij

)12- (σ

rij)6

- ( σrcut

)12+ ( σ

rcut)6] r e rcut

0 r > rcut

(1)

UFENE(r) ) - 12kspringRmax

2 ln(1 - r2

Rmax2) (2)

4630 Langmuir, Vol. 22, No. 10, 2006 Jeon et al.

The rigidity of the nanoparticles was kept by the harmonicbending potential

whereθ is an angle between two consecutive bonds and thebending constant beingkbend ) 100kBT/rad2. The value of thevalence angleθ0 was equal to 108° for pentagons and to 120°for hexagons (see Figure 1).

Interaction between any two charged beads with chargevalencesqi andqj, and separated by a distancerij, is given bythe Coulomb potential

wherelB ) e2/εkBT is the Bjerrum length, defined as the lengthscale at which the Coulomb interaction between two elementarychargese, in a dielectric medium with the dielectric constantε,is equal to the thermal energykBT. In our simulations, the valueof the Bjerrum lengthlB is equal toσ. Counterions from chargedsurface, polyelectrolyte chains or nanoparticles are explicitlyincluded in our simulations.

The particle-particle particle-mesh (PPPM) method35,36forthe slab-geometry, with the correction term37 implemented inLAMMPS38 with the sixth order charge interpolation schemeand estimated accuracy 10-5, was used for calculations of theelectrostatic interactions. In this method, the 2-D periodic imagesof the system are periodically replicated along thez directionwith distanceL ) 3Lz between their boundaries.

Simulations are carried out in a constant number of particles,volume, and temperature ensemble (NVT) with periodic boundaryconditions in thex andy directions. The constant temperatureis achieved by coupling the system to a Langevin thermostat.35

In this case, the equation of motion ofith particle is

whereVbi is the bead velocity, andFBi is the net deterministic forceacting onith bead of massm. FBi

R is the stochastic force withzero average value⟨FBi

R(t)⟩ ) 0 andδ-functional correlations⟨FBi

R(t)FBiR(t′)⟩ ) 6êkBTδ(t - t′). The friction coefficientê is set

to ê ) m/τLJ, whereτLJ is the standard LJ timeτLJ ) σ(m/εLJ)1/2.The velocity-Verlet algorithm with a time step∆t ) 0.01τLJ isused for integration of the equations of motion (eq 5).

Simulations of the multilayer assembly are performed byalternating a substrate exposure to dilute solutions of nanoparticlesor polyelectrolytes in four different ways as explained in Table1. The simulation procedure of the multilayer assembly bysequential deposition of charged macromolecules is similar to

that previously implemented in refs 31, 33, and 34. At thebeginning of the first deposition step, counterions from the chargedsurface are uniformly distributed over the simulation box.Negatively charged polyelectrolytes or nanoparticles (M1 ) 160)consisting of 32 monomers each, corresponding to monomerconcentrationc) 0.038σ-3, together with their counterions werethen added to the simulation box, and the simulation continuesuntil the completion of 106 MD steps. After completion of thefirst simulation run (“dipping” step), unadsorbed polyelectrolytechains were removed (“rinsing” step). The unadsorbed poly-electrolytes or nanoparticles were separated from the adsorbedones by using a cluster algorithm with a cutoff radius equal to2.5σ.31,33,34(The large cutoff distance was selected to ensure thecorrect identification of the adsorbed nanoparticles.) The clusteranalysis was performed by analyzing the matrix of distancesbetween all beads in the system. After completion of the simulationrun (deposition step), only the counterions needed for compensa-tion of the excess charge of the growing film were kept in thesimulation box to maintain electroneutrality of the system.

At the beginning of the second deposition step, the simulationbox is refilled with M2 ) M1 ) 160 oppositely chargedpolyelectrolytes or nanoparticles together with their counterionsresulting in the concentration of newly added polyelectrolytes/nanoparticles being the same as before,c ) 0.038σ-3. This isfollowed by the simulation run (“dipping step”) lasting another106 MD steps. The duration of each simulation run was sufficientfor the system to reach steady state. (The optimization of theduration of the simulation run was discussed in our previouspublication.31) We repeated the dipping and rinsing steps to model10 deposition steps. During each deposition step, the data werecollected during the final 5× 105 MD steps.

In the case of the nanoparticles-nanoparticles system, wehave increased the simulation box size alongz direction by theaverage increment of the layer thickness∆zafter each depositionstep, starting with the third deposition step. This allowed us tomaintain approximately the same volume accessible to nano-particles on top of the growing film during the whole depositionprocess. Such increase in the simulation box size is not necessaryfor other systems since the growing film occupies the smallerfraction of the simulation box in comparison with NN system.

3. Results and Discussion

The evolution of the film structure during deposition stepsfrom 1 to 5 is shown in Figure 2. Nanoparticles and polyelec-trolytes deposited during different deposition steps are displayedin different colors. The counterions are not shown in the snapshots.Oppositely charged nanoparticles/flexible polyelectrolytes werealternately adsorbed on the charged substrate in a series ofconsecutive deposition steps. The construction of the multilayeredfilm can start either with deposition of nanoparticles (NN andNP systems) or with deposition of flexible polyelectrolytes (PPand PN systems). The structure of the adsorbed layer appearingafter completion of the first deposition step is qualitativelydifferent for nanoparticle and flexible polyelectrolyte systems.The nanoparticles, forming the primer layer at the substrate (NPand NN systems), are arranged into an almost perfect hexagonallattice. Such a high degree of ordering in the distribution of

(35) Frenkel, D.; Smit, B.Understanding Molecular Simulations; AcademicPress: San Diego, CA, 2001.

(36) Dobrynin, A. V. InSimulation methods for polymers; Kotelyanskii, M.,Theodorou, D. N., Eds.; Marcel Dekker: New York, 2004.

(37) Yeh, I.; Berkowitz, M. L.J. Chem. Phys.1999, 111, 3155-3161.(38) Plimpton, S. LAMMPS User’s Manual, Sandia National Lab.: Albu-

querque, NM, 2005

Table 1. Procedure of the Layer-by-Layer Deposition and System Notations

system procedure of the layer-by-layer deposition

NN nanoparticles(-) f nanoparticles(+) f nanoparticles(-) f fNP nanoparticles(-) f polyelectrolytes(+) f nanoparticles(-) f fPP polyelectrolytes(-) f polyelectrolytes(+) f polyelectrolytes(-) f fPN polyelectrolytes(-) f nanoparticles(+) f polyelectrolytes(-) f f

Ubend(θ) ) 12kbend(θ - θ0)

2 (3)

UCoul(rij) ) kBTlBqiqj

rij(4)

mdVbi

dt(t) ) FBi - êVbi + FBi

R(t) (5)

Mutilayer Films of Polyelectrolytes and Nanoparticles Langmuir, Vol. 22, No. 10, 20064631

nanoparticles is due to strong electrostatic repulsion betweenthem. On the contrary, the flexible polyelectrolytes (PP and PNsystems) cover the surface uniformly forming a thin polymericlayer. Deposition of the positively charged species during thesecond deposition step (in our simulations, the surface is positivelycharged) alters the well-organized structure of the surface layer.For all systems, positively charged chains or nanoparticles forma complex with previously adsorbed ones exposing the originalsubstrate. The amount of the uncovered space is the largest forthe NN and PN systems. Thus, the screening of the strongelectrostatic interactions between negatively charged nanopar-ticles can be effectively achieved either by covering nanoparticleswith polyelectrolytes (one polyelectrolyte chain can form acomplex with several nanoparticles) or by forming strings ofnegatively and positively charged nanoparticles with positivelycharged nanoparticles filling the gaps between negatively chargedones. The deposition of positively charged nanoparticles on topof the negatively charged polyelectrolytes (PN system) leads toa lesser amount of the uncovered original substrate. In this case,the positively charged particles are positioned on top of the regionswith the higher polymer surface coverage. One can envision thisprocess as nanoparticles pulling polyelectrolyte chains to protectthemselves from unfavorable electrostatic repulsion with apositively charged substrate. Deposition of the positively chargedpolyelectrolytes on top of the negatively charged chains leadsto nucleation of several small holes protruding toward the baresubstrate. As the simulation run continues, these small holescoagulate forming one huge hole shown in Figure 2. Thecoalescence of the smaller holes is a result of minimization ofthe line tension energy, which favors the appearance of the singlehole. As the film buildup proceeds further, the newly adsorbing

macromolecules first cover the substrate and then start buildingup the new layer on top of the previously assembled ones. ForNP and NN systems, the gaps and empty spots on the substratepersist as the number of deposition steps increases. This ultimatelyleads to a hollow thicker film in comparison with the film startedwith the deposition of flexible polyelectrolytes.

Figure 2. Evolution of the multilayer assembly at charged surface. Snapshots are taken after completion of the deposition steps 1-5. Thepositively charged particles on the substrate are shown in green and neutral particles are colored in black. The molecules deposited duringdifferent deposition steps are colored as follows: blue (1), red (2), cyan (3), magenta (4), and orange (5).

Figure 3. Number of molecules in contact with the substrate as afunction of the number of deposition steps. Filled circles, open circles,filled triangles, open triangles correspond to nanoparticles-nanoparticles, nanoparticles-polymers, polymers-polymers, andpolymers-nanoparticles systems, respectively.

4632 Langmuir, Vol. 22, No. 10, 2006 Jeon et al.

The reorganization of the film structure can be followed bymonitoring the number of molecules in contact with the originalsubstrateNcontact (see Figure 3). In every odd deposition step,negatively charged molecules adsorb onto the surface resultingin an increase of the number of contacts,Ncontact. At the samedeposition step, nanoparticles (NN and NP systems) are in contactwith the surface to a lesser extent than the flexible polyelectrolytes(PP and PN systems). For flexible polyelectrolytes, it is sufficientto displace a chain segment to free a space for newly incomingchains to contact a substrate and still keep a chain in contact withthe substrate. The number of nanoparticles in contact with thesurface is limited by their large excluded volume and electrostaticrepulsion between them. After completion of the seconddeposition step in the NP system, nanoparticles are pulled together(neutralized) by polyelectrolytes (see Figure 2) leaving an emptyspace available for the additional adsorption of new nanoparticlesdirectly on the substrate. This available space is filled by newlyadsorbed nanoparticles during the third deposition step (see Figure3). Consequently, the number of nanoparticles in contact withthe substrate in NP system is larger than in NN system. Similarlythe number of polyelectrolytes in contact with the surface in thePP system is larger than in the PN system. Therefore, the observedjump in the number of molecules in contact with the substrateat every other deposition step, as seen in Figure 3, is a result ofthe reorganization process within growing film. Another factthat has to be pointed out here is the rigidity of the moleculesadsorbed at the “even” deposition steps. Nanoparticles adsorbedat the even deposition steps have a larger excluded volume, as

compared to the flexible polyelectrolytes, which prevents chainsfrom approaching the surface at the odd deposition steps. For theNN system, the number of nanoparticles in the contact with thesurface saturates after completion of the fifth deposition step.The number of chains in contact with the substrate for the PPsystem also shows saturation, but this happens at the later stage(after completion of the 8th deposition step) indicating highmobility and flexibility in the local chain rearrangements incomparison with that for the nanoparticles. However, for PN andNP systems, the number of molecules in contact with the substratecontinues to increase during the entire simulation run, 10deposition steps. This is due to high porosity and heterogeneityinside growing films. There is the following order in the numberof molecules in contact with the substrate PP> PN> NP> NN.

The surface roughness shows a strong correlation with thetype of molecules covering the substrate (primer layer) as wellas with the rigidity of macromolecules used for the film assembly.To obtain the film topography, we utilize the bead height sortingalgorithm which selects a bead located at the furthest distancefrom the substrate for each bin in the 20× 20 array that coversthe surface. The 3-D plot of this 20× 20 matrix gives a localfilm height distribution that provides information similar to theatomic force microscopy (AFM) measurements. All of thetopographic images shown in Figure 4 are obtain using the lastconfigurations of the fifth deposition step simulations. Thesnapshots of these configurations are shown in the last columnin Figure 2. Several steps can be clearly identified based on thecolor assigned to the local film thickness. The NN system has

Figure 4. Surface topography as obtained from the bead height distribution after completion of the fifth deposition step for the nanoparticles-nanoparticles (a), nanoparticles-polymers (b), polymers-polymers (c), and polymers-nanoparticles (d) systems.

Mutilayer Films of Polyelectrolytes and Nanoparticles Langmuir, Vol. 22, No. 10, 20064633

four steps, NP and PN systems have three steps, and the PPsystem has a smooth surface coverage if an insignificant bumpis ignored. Based on this observation, one can see that the surfacebecomes rougher when nanoparticles are used in the film assembly(NN > NP g PN > PP). The average thickness of the layer⟨h⟩is calculated as the average value of the height distribution andthe surface roughness is obtained from the second moment ofthis distributionRrh ) ⟨Nbin

-1∑i[(hi - ⟨h⟩)2]1/2⟩ whereNbin is thenumber of bins. These quantities were averaged during the last5 × 105 MD steps during each deposition step. Figure 5 showsthe evolution of the average film thickness⟨h⟩ and film roughnesswith the number of deposition steps. The film thickness increasesalmost linearly with the number of deposition steps for the systemscontaining flexible chains. The incorporation of the nanoparticlesresults in a faster increase in the average film thickness. Thisshould not be surprising since nanoparticles have a larger excludedvolume and leave less space available for the newly adsorbedmolecules. The fastest growing film thickness is observed forthe NN system. However, this fast increase in the film thicknessleads to higher film roughness (see Figure 5b). Although thesurface roughness for the systems containing nanoparticlessteadily increases with the number of deposition steps, it saturatesfor the film consisting of flexible polyelectrolytes (PP system)after completion of four deposition steps.

The increase in the surface coverageΓ, the number of adsorbedbeads per unit area, during the film build up process is shownin Figure 6. The number of macromolecules adsorbed duringeach deposition step is given in Table 2. The steady state regimeis achieved after completion of the first couple of depositionsteps, after which the surface coverage increases linearly withnumber of deposition steps for the systems containing poly-electrolyte chains. The surface coverage shows slightly fasterthan linear increase for the NN system. Such nonlinear increasein the surface coverage is an indication that the growth in thefilm mass not only occurs from the surface but also has a bulk

Figure 5. Dependence of the average film thickness (a) and thesurface roughness (b) on the number of deposition steps. Notationsare the same as in Figure 3.

Figure 6. Surface coverageΓ, the number of adsorbed beads perunit area, as function of the number of deposition steps. Notationsare the same as in Figure 3.

Table 2. Number of Adsorbed Molecules after Each DepositionStep

system systemdepositionstep NN NP PP PN

depositionstep NN NP PP PN

1 33 33 42 42 6 48 35 25 302 29 31 26 25 7 45 37 25 303 43 36 28 30 8 47 36 26 324 42 34 26 30 9 55 39 26 335 49 35 25 33 10 60 41 26 33

Figure 7. Overcharging fraction (|∆Q|/Qads) as a function of thenumber of deposition steps. Notations are the same as in Figure 3.

4634 Langmuir, Vol. 22, No. 10, 2006 Jeon et al.

component. This can happen for a highly heterogeneous filmwith a lot of hollow space. A rough surface provides nanoparticles/polyelectrolytes with more surface area to contact with than asmooth surface does. This effect is already observed for thesecond deposition step simulations where a larger amount ofmacromolecules could adsorb on the substrate covered bynanoparticles in comparison with that for surface covered bypolyelectrolytes. This initial roughness difference determinesthe order of the adsorption amount beyond the fourth depositionstep leading to the following sequence of the growth in the filmmass NN> NP > PN > PP.

The overcharging process during the steady-state film growthis shown in Figure 7, where the ratio of the absolute value ofthe layer overcharging,|∆Q|, excess of the positively or negativelycharged monomer including those belonging to the substratewithin growing polymer film to the net charge carried by adsorbedchains at a given deposition step,Qads ) (N(s) - N(s - 1))(whereN(s) is the total number of adsorbed beads after completionof thesth step), is plotted versus the number of deposition steps.This quantity appears to fluctuate around 0.5 for all studiedsystems. This observation can be explained as follows. For asteady state growth, half of the adsorbed molecules are used forneutralization of the film excess charge, whereas the other halfrecreates the film charge necessary for the adsorption of the nextlayer. If this ratio is smaller than 0.5, the film eventually stopsgrowing. However, if it exceeds 0.5, the surface coverage willshow exponential growth. In both cases, the growth process isunstable. Thus, the surface overcharging plays a dual role: it

rebuilds the surface properties for the next deposition layer andprevents the unrestricted growth of the adsorbed amount, whichis stabilized by the electrostatic repulsions between the excesscharges. The fluctuations in the overcharging fraction|∆Q|/Qads

around a value of 0.5 are due to the fluctuations in the numberof adsorbed molecules and the substrate effect. Increasing thesystem size could diminish the first contribution. This is indeedthe case if one compares the results shown in Figure 7 for thePP system with our previous simulations results. The systemsize used in this simulation is twice the size of the systems studiedin ref 31. The substrate effect is more pronounced for the NPand PN systems, which show gradual decrease in fluctuationsof overcharging fraction|∆Q|/Qadswith the number of depositionsteps. For these systems, the substrate still influences the filmgrowth pattern up to the tenth deposition step. It is interestingto point out that the overcharging fraction|∆Q|/Qads is alwayslarger than 0.5 after completion of the deposition of polyelectrolytechains and it is below 0.5 after deposition of nanoparticles. Thistrend in evolution of the overcharging fraction is a reflection ofthe higher flexibility of the polyelectrolyte chains that are capableof wrapping around nanoparticles and at the same time better fitinto the available empty space. In the PN system, the numberof polyelectrolytes adsorbed at each deposition step is alwayslarger than or equal to that of nanoparticles adsorbed at theimmediately preceding deposition step.

The intermixing between molecules adsorbed during differentdeposition steps is shown in Figure 8, which displays the densitydistributionFn(z) of beads belonging to the molecules adsorbed

Figure 8. Density profiles of beads belonging to fully charged polyelectrolyte chains and nanoparticles after completion of 10 depositionsteps obtained for multilayer films consisting of nanoparticles-nanoparticles (a), nanoparticles-polymers (b), polymers-polymers (c), andpolymers-nanoparticles (d).

Mutilayer Films of Polyelectrolytes and Nanoparticles Langmuir, Vol. 22, No. 10, 20064635

during different deposition steps. These distribution functionswere averaged separately for each set of molecules adsorbed atdifferent deposition steps during the final simulation runrepresenting the 10th deposition step. This procedure enables usto see how well adsorbed molecules intermix within layeredfilms. For example, nanoparticles adsorbed during the firstdeposition step never move and stay in contact with the surfaceduring the entire simulation run (see Figure 8, parts a and b).This happens due to the strong electrostatic attraction betweenthe substrate and oppositely charged nanoparticles. Nevertheless,there is continuous rearrangement of nanoparticles within thegrowing film. For example, nanoparticles adsorbed during thethird deposition step could come in contact with the substrate.The bead density profile for these nanoparticles has two peaks.The first peak corresponds to nanoparticles in contact with thesubstrate, whereas another one is due to nanoparticles formingthe third layer. Similar distribution exists for nanoparticlesadsorbed during the fourth deposition step. A fraction of theseparticles completes formation of the second layer, and theremaining part initiate formation of the fourth layer (see Figure8a). As the film thickness grows, the peaks in the bead densitydistribution functions become less pronounced indicating theweakening of the effect of the substrate rigidity on the filmstructure. The more pronounced molecule rearrangements areseen for the systems containing flexible polyelectrolytes. In thesesystems, polyelectrolytes adsorbed during the first deposition

step (see Figure 8, parts c and d) could span through the entirefilm thickness showing significant intermixing (interdiffusion)between polyelectrolyte chains deposited during differentdeposition steps.

The film composition, characterized by the difference in localdensity of beads belonging to negatively and positively chargedmolecules,∆F(z) ) F-(z) - F+(z), is shown in Figure 9. Thisfunction, ∆F(z), clearly indicates a multilayer structure of theassembled films. Comparing the most probable location of thecenter of mass of nanoparticles shown by arrows, we can see analmost perfect layered distribution of nanoparticles withinmultilayers (see Figure 9, parts a, b, and d). It is worthwhile tonote that because nanoparticles are rigid they are impenetrableand typical layer thickness is comparable with the nanoparticlesdiameter. This also means that a better stratification of moleculeswithin the multilayer film can be achieved by using more rigidbuilding blocks. On the contrary, the flexible polyelectrolytes intwo component films intermix over several adjacent layers.Despite strong intermixing in the systems containing flexiblepolyelectrolytes, a multilayered nature of the film still persists.This can be clearly seen in Figure 9b-d which shows the existenceof alternating layers with excesses of positively or negativelycharged molecules.

The film composition, shown in Figure 9, supports the three-zone structure of the multilayer film. Zone I contains the layerin the vicinity from the adsorbing surface with an excess of

Figure 9. Film composition,∆F(z) ) F-(z) - F+(z), of multilayer films consisting of nanoparticles-nanoparticles (a), nanoparticles-polymers (b), polymers-polymers (c), and polymers-nanoparticles (d).

4636 Langmuir, Vol. 22, No. 10, 2006 Jeon et al.

molecules carrying a charge opposite to that on the substrate.The thickness of this layer depends on the molecular rigidity.For example, for the films consisting of the flexible polyelec-trolytes or for the film with nanoparticles in which the primerlayer is formed by flexible polyelectrolytes, the thickness of thiszone is on the order of the couple bead sizes. However, for filmsassembled from nanoparticles or for mixed films with nano-particles forming the primer layer, the thickness of this zone isof the order of the nanoparticle size. Zone II contains complexesof oppositely charged molecules. In the case of flexiblepolyelectrolytes and mixed films containing both flexible chainsand nanoparticles, the molecules are well intermixed and exhibit1:1 charge stoichiometry. Zone III includes the outmost layeralong with counterions, which neutralizes the excess charge inzone III. The growth of the film occurs by increasing the thicknessof the zone II with newly adsorbed molecules, displacingcounterions and overcharging the external molecular layer.

4. Conclusions

In conclusion, we have performed molecular dynamicssimulations of layer-by-layer assemblies of polyelectrolytes andnanoparticles from dilute solutions. In the case of the multilayersformed by flexible polyelectrolytes, the polyelectrolytes are not

perfectly stratified within the multilayer film. There is strongintermixing between chains deposited during different depositionsteps. However, despite the high degree of intermixing betweenchains, there are almost perfect oscillations in film composition.For multilayer films consisting of nanoparticles, there is betterstratification of the layers with almost constant thickness of thelayer composed of nanoparticles. For all studied systems, theprocess of multilayer formation occurs over several successivedeposition steps. Usually, four deposition steps are required tocomplete formation of the two layers. The initial deposition stepscover the surface partially and in the subsequent steps, any unfilledportions are occupied eventually leading to a more uniformcoverage, regardless of the initial layer. The film thickness andsurface coverage increase almost linearly with the number ofdeposition steps, indicating the steady-state film growth. Themultilayer films formed by nanoparticles have a higher roughnessthan films consisting of flexible polymers.

Acknowledgment. The authors are grateful to the NationalScience Foundation for the financial support under grants DMR-0305203 and DMR-0353894.

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Mutilayer Films of Polyelectrolytes and Nanoparticles Langmuir, Vol. 22, No. 10, 20064637