as Barrier Layer for Polyelectrolyte Diffusion in ... - ACS Publications

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Branched Poly(ethylenimine) as Barrier Layer for Polyelectrolyte Diffusion in Multilayer Films Peter Nestler,† Malte Paßvogel,† Heiko Ahrens,† Olaf Soltwedel,‡,§ Ralf Köhler,∥ and Christiane A. Helm*,† †

Institut für Physik, Ernst-Moritz-Arndt Universität Greifswald, Felix-Hausdorff-Str. 6, D-17487 Greifswald, Germany Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany § Max Planck Society Outstation at FRM-II, Garching, Germany ∥ Institut für Weiche Materie und funktionale Materialien, Helmholtz Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany ‡

S Supporting Information *

ABSTRACT: Linearly assembled polyelectrolyte multilayers (PEMs) are prepared by sequential adsorption of polyanions and polycations from 0.1 mol/L NaCl. The internal structure of PEMs is investigated with neutron reflectivity. The films are made from poly(ethylenimine) (PEI), poly(diallyldimethylammonium) (PDADMA) and poly(styrenesulfonate) (PSS or deuterated PSS-d). Each film consists of a protonated and a deuterated block, built from m protonated and n deuterated polycation/polyanion layer pairs, respectively. Annealing in salt solution (1 mol/L NaCl) allows the polyelectrolytes to gain entropy by adopting a more coiled conformation and by intermixing. During annealing the internal interface between the two blocks broadens due to interdiffusion; thus, the PSS diffusion coefficient is measured. Eventually the annealing leads to a uniform distribution of protonated and deuterated PSS throughout the film. Yet, if one polycation layer in the film center is branched PEI, then this PEI layer serves as a diffusion barrier, which is impenetrable for up to 33% of PSS macromolecules. The equilibration time of the remaining mobile PSS fraction increases which is attributed to the low permeation rate through the barrier layer. Possibly, some PSS molecules have a conformation that hinders them to cross the barrier layer, or the barrier layer gets clogged with time.

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In the linear growth mode of LbL films, the film thickness is proportional to the number of adsorbed polycation/polyanion pairs. However, the linear growth mode is an inherently nonequilibrium process, yielding a nonequilibrium structure.8 The polymer chains have a propensity to gain entropy by adopting a more coiled conformation and by intermixing. Within the film, the adsorbed chains overlap across a few layers, as was shown by neutron reflectometry.9 The degree of intermixing depends on the interpolyelectrolyte binding strength.10−12 For instance, poly(allylamine hydrochloride)/ poly(styrenesulfonate) (PAH/PSS) films consistently show a small degree of layer interpenetration due to strong ionic monomer/monomer bonds.9,13−15 If the film is immersed into a salt solution with high concentration of monovalent ions, some of the ionic monomer/monomer bonds are replaced by ion/monomer bonds. Then, the movement of the chains is similar to “sticky reptation”; the chains move in an entangled

INTRODUCTION

Polyelectrolyte multilayer films (PEMs) assemblied by the layer-by-layer (LbL) technique are used as coatings and/or as nanostructured materials in many different applications, such as biomedical, sensing, separation, and photonic applications.1−3 The broad range of applications is possible, since the LbL technique allows control over the sequence in which multiple functional elements are incorporated into the film. Actually, many applications of LbL assemblies in photonics4 and for multistage drug delivery5 rely on different compartments within the film separated by barrier layers.6 Barrier layers have been investigated in the past: chemically cross-linked layers proved to be a barrier for underlying layers,5 and the inclusion of specific layer pairs inhibited “in and out” diffusion.7 Here, we focus on linearly assembled LbL films. We report the permeation rate of polyanions through a barrier layer consisting of a branched polycation. For the determination of the permeation rate, also the diffusive mobility of the polyanions needs to be known because only those polyanions that are next to the barrier can pass through it. © 2015 American Chemical Society

Received: May 18, 2015 Revised: November 8, 2015 Published: November 19, 2015 8546

DOI: 10.1021/acs.macromol.5b01065 Macromolecules 2015, 48, 8546−8556

Article

Macromolecules

a defined number of deposited layer pairs the film grows linearly. Always, the internal interface under investigation is in the linearly growing part of the film. The block architecture is designed in the following way: first, a protonated block consisting of m PDADMA/PSS layer pairs followed by a deuterated block with n PDADMA/PSS layer pairs. The interface between the protonated and deuterated block is positioned at the center of the film. Because the thickness per layer pair next to the substrate is smaller, one has m > n. As barrier layer, the branched polycation poly(ethylenimine) (PEI) is chosen. At first, PEI as a barrier layer seems counterintuitive since PEI is known to be mobile within an LbL film.24 However, the mobility of PEI can be enhanced by adjusting the pH and by choosing weak polyanions. pH and ionic strength are critically important for the assembly of LbL films.25,26 We use PSS, a strong polyanion and a neutral pH at 7.7, when PEI is found to be immobilized on the substrate.17 Both the diffusion constant of PSS, DPSS, within the homogeneous film and the permeation rate, PPSS, need to be in an experimentally accessible time scale. The chain length is one key parameter within a polymer network. Therefore, the molecular weight of the polycation, Mw(PDADMA), is varied. Measurements of the diffusion constant DPSS of LbL films without a barrier layer are performed postassembly; the films are immersed in 1 mol/L NaCl solution for the annealing time tanneal. Simultaneously, identical films with a PEI barrier layer in their center are characterized postassembly, and the permeation rate PPSS is determined.

network of linear chains with many temporary cross-links.16 Immersion into the annealing solution reduces the “sticker density”, i.e., the ionic monomer/monomer bonds, and thus increases the chain mobility.12,17 About 15 years ago, the swelling and smoothing of PEMs in concentrated salt solutions were first described.18 Ten years ago, the first experiments about intermixing within linearly grown PEMs were published.19,20 Interesting is the observation by Sukhishvili and co-workers that in linearly assembled LbL films the lateral diffusion constant exceeds the vertical diffusion constant by several orders of magnitude.10,12 This finding is attributed to the oblate conformation of the adsorbed polymer chains. Which parameters determine the respective diffusion constants is not clear yet. Many external factors influence assembly and postassembly behavior of LbL, e.g., temperature, solvent, pH, and salt concentration, among others.3 However, internal parameters such as polymer molecular weight are also expected to play a role.11 Recent experiments show a strong dependence of the PSS diffusion constant on the molecular weight of poly(diallyldimethylammonium) (PDADMA), suggesting a cooperative motion of PSS and PDADMA.17 To shed some light on these questions, with neutron reflectometry the one-dimensional scattering length density profile perpendicular to the substrate surface is determined. The neutron reflectivity technique is based on scattering of neutrons by the core of atoms; therefore, it is isotope sensitive. This offers the ability to label and distinguish molecules and structures, although they exhibit the same chemical functionality. The LbL films have a block architecture. Each film consists of a protonated and a deuterated block (cf. Scheme 1),

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Scheme 1. Exchange of PSS Against PSS-d Due to Intermixing during Annealing

MATERIALS AND METHODS

Sample Preparation. Polyelectrolyte multilayers are deposited on polished Si (100) wafers (Wacker Siltronic AG, Burghausen, Germany) by dip-coating. The wafers are cleaned according to the RCA standard (which is a mixture of 25% ammonia solution (VWR, Hannover, Germany), 35% hydrogen peroxide (VWR), and ultrapure water in a ratio of 1:1:5, heated for 15 min to 75 °C) and freshly used. All deposition solutions contain a polyelectrolyte concentration of 1 mmol/L (with respect to the monomer concentration) and 0.1 mol/L NaCl (Merck, Darmstadt, Germany). Always the branched polycation poly(ethylenimine) (PEI; Mw(PEI) = 75 kDa, Aldrich, Germany) serves as substrate anchoring layer and sometimes as barrier layer (cf. TOC image). Subsequently the linear polyanion poly(styrenesulfonate) sodium salt (PSS; Mw(PSS) = 75.6 kDa, contour length lc = 92 nm with PDI < 1.2) and the linear polycation poly(diallyldimethylammonium) chloride (PDADMA) of a selected molecular weight (either Mw(PDADMA) = 24 kDa, lc = 80 nm with PDI = 1.9, Mw(PDADMA) = 35 kDa, lc = 117 nm with PDI = 2.1 or Mw(PDADMA) = 45 kDa, lc = 150 nm with PDI = 1.5) are deposited alternately. For the purpose of selective deuteration of the multilayer film deuterated PSS-d (Mw(PSS-d) = 80.8 kDa, lc = 95 nm with PDI < 1.2) is used. PDADMA, PSS, and PSS-d were all purchased from Polymer Standard Service (Mainz, Germany). Ultrapure water is from a Milli-Q unit (Millipore, Eschborn, Germany). PEM preparation is performed for all polyelectrolytes in the same way via a dipping robot (Riegler & Kirstein, Berlin, Germany) with 30 min for each adsorption step followed by three washing steps with pure water for 1 min each. All solutions are kept at 20 °C, which is adjusted externally by a thermostat (Haake, Karlsruhe, Germany). The salt concentration in solution is kept constant during multilayer preparation. In a postpreparation step each sample is exposed to a 1 mol/L NaCl annealing solution for the time tanneal, washed three times in pure water for 1 min each, and dried in a weak stream of dry nitrogen for several minutes. The pH of the PEI solution with 0.1 mol/L NaCl is 7.7 (SevenCompact S22 pH meter equipped with a Pure Pro ISM electrode (Mettler Toledo, Columbus, OH)).

which is achieved by using protonated and deuterated PSS, respectively. The internal width σint is used as a measure of the layer interdiffusion.14 σint increases when intermixing occurs. If the film is homogeneous, from Fick’s second law one obtains σint2 = 2Dtanneal. Here, D is the diffusion constant and tanneal the annealing time in solution with high salt concentration (boundary conditions: σint = 0 for tanneal = 0).14,17,21 In this paper, we want to quantify the influence of a barrier in the center of the PEM on vertical polyelectrolyte movement. The challenge is to distinguish the permeation rate through the barrier from the diffusion within the homogeneous parts of the film. Therefore, we have to consider diffusion in a confined space. As a barrier layer, a branched polycation is chosen, which is placed at the interface between the protonated and the deuterated block (cf. TOC image). We use strong polyelectrolytes as polycation/polyanion pair, PDADMA/PSS; each adsorption solution contains 0.1 mol/L NaCl. The growth of the LbL films starts parabolically,22,23 after 8547


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Macromolecules Neutron Reflectivity. The samples are investigated with neutron reflectometry at instrument V6 at the neutron scattering facility of the Helmholtz Zentrum Berlin, Germany.27 Neutron reflectivity measurements are performed at nominal 0% relative humidity (rh) inside a home-built gastight enclosure. The enclosure contains a Petri dish filled with P2O5 (Merck, Darmstadt, Germany) as drying agent and is flooded with dry nitrogen for 30 min before each measurement. Additionally, the relative humidity is monitored constantly with a humidity sensor (Hygrometer TH 309, B+B ThermoTechnik GmbH, Donaueschingen, Germany) and amounts to 0.5−2% rh during a reflectivity measurement. It varies slightly during one measurement which takes 6−7 h. To ensure that no change in the scattering length density (SLD) or the thickness of the PEM during measurement occurs each measurement is repeated at low Qz (0.0028−0.033 Å−1). Prior to the neutron reflectivity measurement each sample is investigated by X-ray reflectivity (Seifert XRD 3003 TT diffractometer, Seifert, Germany) under room conditions to quantify the roughness of the air/PEM (σair) as well as the PEM/Si interface (σSi) independently. For all samples the corresponding values are σair = 14 ± 4 Å and σSi = 5 ± 1 Å, respectively. Neutron reflectivity R of the sample is measured as a function of Qz = 4π/λ sin(αinc). Here, αinc is the angle of incidence, and λ = 4.66 Å is the neutron wavelength. Qz is varied between 0.0028 and 0.0941 Å−1 (corresponding to αinc between 0.06° and 2°). The neutron beam is partly reflected from each step or gradient in the SLD profile along the surface normal. Such gradients occur at the air−PEM interface, the PEM−Si interface, and the interfaces between deuterated and protonated polymer blocks inside the multilayer film. The resulting interference pattern R(Qz) is first normalized to the Fresnel reflectivity, RF, of an ideally smooth air/Si interface and further analyzed by a least mean-squares fitting procedure to quantify the film structure. Details concerning neutron reflectivity and the fitting procedure can be found elsewhere.14,17,28 The advantage of PEMs with block deuteration architecture is the low number of parameters necessary to determine the SLD profile of the sample. Actually, there are seven fit parameters: the SLD and thickness of both blocks (SLDp and lp for the protonated block as well as SLDd and ld for the deuterated block), the width of the internal interface between both blocks σint, and the roughness of the air−PEM as well as the PEM−Si interface (σair and σSi, respectively). Since the shape of each interface in the SLD profile is described by the integral of one Gaussian distribution function, we define the corresponding standard deviation σ as the width of the interface.13 Please note that σ is a factor 2.35 = 2[2 ln(2)]1/2 smaller than interfacial widths given as the full width at half-maximum (fwhm).29 Always, σair is determined with X-ray reflectivity and σSi is set to 5 Å. The remaining parameters can be determined independently since they are each identified by different features of the neutron reflectivity R(Qz)/RF: the periodicity of R(Qz)/RF at high Qz is inversely proportional to the total film thickness lp + ld, while the shape of the beat pattern at low Qz depends on the ratio lp/ld. In case of equal-sized blocks (lp = ld) this pattern is an alternating sequence of Kiessig fringes amplified by constructive interference and attenuated by destructive interference, respectively. The transition of the beat pattern into a single harmonic oscillation with increasing Qz is a measure for σint, the width of the internal interface. The higher the Qz value at which an amplitude modulation can still be observed, the smaller is σint. Finally, SLDp and SLDd, the scattering length densities of protonated and deuterated block, can be deduced from the height of the Kiessig fringes. For instance, at high Qz (Qz > 0.05 Å−1) the dominant oscillation term is proportional to 2(SLDSi − SLDp)SLDd/(SLDSi)2.17 Here, SLDSi = 2.073 × 10−6 Å−2 is the SLD of the Si substrate. At low Qz (Qz < 0.05 Å−1) the situation is more sophisticated and requires an evaluation using the exact matrix formalism.28 Theoretical Background. One-Dimensional Diffusion under Geometrical Constraints. The one-dimensional distribution c(z,tanneal) of deuterated PSS-d diffusing into the protonated block (and vice versa) obeys Fick’s second law ∂c/∂tanneal = DPSS ∂2c/∂z2. Here, tanneal is the exposure time to high salt annealing solution, and DPSS is the PSS diffusion coefficient in the z direction, i.e., perpendicular to the

substrate, during annealing. The solution to Fick’s second law is c(z,tanneal) = c0Φ((z − z0)/(2DPSStanneal)1/2) in the case of an initial concentration step at z0 between two semi-infinite reservoirs with c = 0 and c = c0, respectively.30 Here, Φ is the cumulative Gaussian distribution function Φ(z) = (2π)−0.5∫ z−∞ exp(−0.5τ2) dτ (with τ as dimensionless variable for integration).31 Comparison with SLD profile parametrization leads to σint = (2DPSStanneal)1/2, i.e., an increase of the interfacial width with the square root of annealing time. However, the non-annealed concentration profile (tanneal = 0) already possesses the initial interfacial width σ0 introduced during film buildup. In this case the solution to Fick’s second law is modified

σint =

2DPSStanneal + σ0 2

(1)

Since σ0 is determined from neutron reflectivity of freshly prepared samples, the time dependence of σint is given by DPSS only. This means σint increases approximately proportionally to the square root of tanneal as long as the finite dimension of the PEM can be neglected. Yet, when the tails of the internal SLD distribution reach the outer boundaries of the PEM the assumption of two semi-infinte reservoirs is no longer appropriate, and thus eq 1 becomes invalid. In this case the geometrical constraints have to be considered when solving Fick’s second law. Accordingly, we include two new boundary conditions by setting the flux f = ∂c/∂z of diffusing polyanions to be zero at either the position of the Si/PEM interface (z = 0) or the PEM/ambient interface (z = lp + ld). The first of these conditions is obvious since the Si substrate is impenetrable to PSS or PSS-d, respectively. Additionally, the latter condition is justified since the PEM is stable against desorption of polyelectrolytes during annealing in high salt concentration (cf. section Neutron Reflectivity of Films with Block Structure). Hence, there is no flux of diffusing polyanions beyond the dimension of the PEM film. In a first approximation, both boundary conditions are taken into account by including image interfaces on the opposite side of either Si/PEM or the PEM/ambient interface. Thus, the solution to Fick’s second law fulfilling both boundary conditions reads ⎡ ⎛ z − lp ⎞ ⎛ z + lp ⎞ c(z , tanneal) = c0⎢Φ⎜ ⎟ + Φ⎜ − ⎟ ⎢⎣ ⎝ σ ̃ ⎠ σ̃ ⎠ ⎝ ⎛ z − lp − 2ld ⎞⎤ − Φ⎜ ⎟⎥ σ̃ ⎝ ⎠⎦⎥

with 0 ≤ z ≤ lp + ld

(2)

within the PEM and c(z,tanneal) = 0 outside the PEM (cf. Figure 1). The denominator of each argument is given by σ̃ = (2DPSStanneal + σ02)1/2. Again, lp + ld is the total film thickness, and lp is the distance between substrate and internal interface (i.e., the thickness of the protonated block). The first summand of eq 2 describes the distribution of deuterated PSS-d without geometrical constraints. The two latter ones account for the flux f = ∂c/∂z of polyanions being reflected from either the Si/PEM or the PEM/ambient interface, respectively. For small annealing time (tanneal ≪ 0.5lp2DPSS) these additional terms are equal to zero, and eq 1 serves as a good approximation. On the other hand, for annealing time exceeding 0.5(lp + ld)2/DPSS additional terms of even higher order have to be included to account for multiple reflections of the flux f. However, from textbooks on statistics32,33 the width σint of an arbitrary steplike distribution c(z,tanneal) is given by the square root of the variance of f = ∂c/∂z l +l

σint(tanneal) =

∫0 p d (z − μ(tanneal))2 f (z , tanneal) dz l +l

∫0 p d f (z , tanneal) dz

(3)

with the mean value μ given by l +l

μ(tanneal) =

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∫0 p d zf (z , tanneal) dz l +l

∫0 p d f (z , tanneal) dz DOI: 10.1021/acs.macromol.5b01065 Macromolecules 2015, 48, 8546−8556

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Macromolecules

Figure 2. Normalized neutron reflectivity curves (left) and corresponding SLD profiles (right). Samples without (top) and with (bottom) internal PEI barrier layer are measured as prepared and after annealing in 1 mol/L NaCl solution for the time indicated. Measurements are performed in dry air (0% rh). PDADMA molecular weight is Mw(PDADMA) = 45 kDa. Layer sequence is (PEI/PSS)1/ (PDADMA/PSS)12/(PDADMA/PSS-d)7 (top) and (PEI/PSS)1/ (PDADMA/PSS)12/(PEI/PSS-d)1/(PDADMA/PSS-d)6 (bottom). For clarity, the reflectivity curves are shifted vertically.

Figure 1. Top: position-dependent scattering length density inside a PEM containing one protonated and one deuterated block. Profiles are calculated using eq 2 and DPSS = 160 × 10−22 m2/s for the annealing times indicated. Bottom: corresponding interfacial width calculated using eq 3 vs square root of annealing time. The model parameters necessary to calculate σint(tanneal) via eqs 2 and 3 are the diffusion coefficient DPSS, the initial interfacial width σ0, the total film thickness lp + ld, and the position of the internal interface lp inside the multilayer film. Of these parameters σ0, lp, and ld can be determined independently from the neutron reflectivity data. The prefactor c0 in eq 2 is arbitrary since it is canceled out when applying eq 3. Thus, again the time dependence of σint is given by DPSS only. For large annealing time σint levels off since the interfacial width is limited by the total film thickness (cf. Figure 1). According to limit calculation of eq 3, the maximum of the interfacial width σint, as tanneal approaches infinity, is roughly 0.2(lp + ld).

Before annealing (tanneal = 0, cf. Figure 2, top left, red curve) the neutron reflectivity R(Qz)/RF shows strong amplitude modulations for Qz < 0.05 Å−1. For instance, the intermediate region between first and second Kiessig fringe (Qz ≈ 0.017 Å−1) is rather a shoulder than a distinct minimum. Additionally, the local minimum at Qz = 0.035 Å−1 possesses an intensity larger than zero which is attributed to the reflection from the internal interface. However, on further increase of Qz this beat pattern vanishes due to pronounced damping from the SLD gradient between protonated and deuterated blocks. Quantitative analysis leads to σint = 37 Å for the width of the internal interface of the pristine film. After annealing in 1 mol/L NaCl for tanneal = 0.25 h (cf. Figure 2, top left, yellow curve) the amplitude modulations are less pronounced. Again, please consider exemplary the local minimum at Qz = 0.035 Å−1 which now possesses a reflected intensity close to zero. Actually, for Qz > 0.03 Å−1 the neutron reflectivity can be described as one harmonic oscillation with decaying amplitude. Since the transition from a beat pattern to a harmonic oscillation with increasing Qz is a measure for σint, the neutron data give evidence for a broadening of the internal interface. In fact, σint amounts 72 Å after tanneal = 0.25 h and thus has nearly doubled compared to its pristine state. On further increase of tanneal (0.5 and 1 h) the broadening of the internal interface continues (σint = 91 Å and σint = 115 Å, respectively). Eventually, the tails of the internal SLD distribution reach the external boundaries of the PEM (Si/PEM boundary on one side and PEM/ambient boundary on the opposite side). In this case (tanneal ≥ 2 h) the height of the first Kiessig fringe at Qz = 0.014 Å−1 decreases with tanneal. Since the height of this first fringe is a measure for the SLD contrast between protonated and deuterated block, its decrease demonstrates equalizing of the SLD in both blocks. On the other hand, for the different annealing times, the periodicity of the Kiessig fringes is unchanged. Furthermore, the Kiessig fringes at large Qz show nearly the same amplitude. Therefore, the thickness of the film is the same after annealing; also, the PEM/air roughness is

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RESULTS AND DISCUSSION Neutron Reflectivity of Films with Block Structure. Figure 2 shows neutron reflectivity measurements of PEMs consisting of 20 polycation/polyanion layer pairs. First we investigate the diffusion behavior inside a PEM consisting of one precursor layer followed by layer pairs of linear polyelectrolytes only, i.e., in the absence of an internal barrier layer of branched PEI (Figure 2, top). As polycation we apply PEI as anchoring layer and PDADMA for all subsequent layer pairs. The polyanion of the first 13 layer pairs is protonated PSS followed by seven layer pairs with deuterated PSS-d on top (abbreviated as p13 d7). Always the last adsorbed layer is PSS-d. Thus, the total layer sequence listed beginning at the Si substrate is (PEI/PSS)1/(PDADMA/PSS)12/(PDADMA/PSSd)7. The ratio of protonated to deuterated layer pairs was adjusted to achieve a similar thickness of both blocks (lp = 375 Å for the protonated and ld = 300 Å for the deuterated block). Please note the larger number of protonated layer pairs compared to the deuterated ones due to the thin precursor layer pairs in the protonated block next to the substrate.23 Each sample is measured twice with neutron reflectivity: first as prepared and second after annealing for tanneal in 1 mol/L NaCl solution, washing in pure water, and drying. During annealing the electrostatic inter- and intramolecular forces of the adsorbed polyelectrolytes are shielded, and a significant fraction of ionic monomer/monomer bonds are temporaly exchanged by monomer/counterion bonds. 8549


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profile, resulting in a local SLD peak: The additional slab has a thickness of 38 Å thickness and is situated between the protonated and the deuterated block. This thickness corresponds to one polyanion/polycation layer pair adsorbed onto a preexisting PEM (the precursor layer pair is thinner). The increased scattering length density is due to the PEI/PSS-d layer pair. (The scattering lengths of the monomer pairs PEI/ PSS-d and PDADMA/PSS-d are almost identical, 124 × 10−5 and 122.8 × 10−5 Å, respectively. Yet, the volume per PEI/PSSd monomer is much smaller than of PDADMA/PSS-d, 260 and 406 Å3, respectively.) The electrostatic balance is maintained within resolution (one polycation and one polyanion monomer). After annealing for tanneal = 1 h and tanneal = 3 h the width of the internal interface is unchanged within experimental resolution (σint = 30 Å and σint = 36 Å, respectively). Therefore, within 3 h annealing time the internal PEI layer appears impenetrable for either PSS-d diffusing into the protonated block or PSS diffusing into the deuterated one; thus, it can be described as a barrier layer. Yet, all evidence for a local SLD peak at the internal interface is vanished; i.e., the neutron reflectivity R(Qz)/RF can be explained again conveniently using a PEM profile containing two homogeneous SLD blocks only. The excess SLD has reached equilibrium because PEI is now more broadly distributed. Mixing of PEI side chains with PDADMA occurs without detectable center of mass movement. Eventually, the width of the internal interface increases noticeably, if the annealing time is increased by 1 order of magnitude. Moreover, in the case of longest annealing time used (tanneal = 72 h, cf. Figure 2, bottom, green curve) the height of the first Kiessig fringe at Qz = 0.014 Å−1 is nearly halved compared to its original state. This reduction originates from the equalizing SLD in the protonated and deuterated block and is similar to the effect observed previously for the p13 d7 PEM for tanneal ≥ 2 h. Yet, one qualitative difference between both PEM architectures remains: in the case of p13 d7 samples the SLD levels of protonated and deuterated block begin to equalize once the broadness of the internal SLD distribution reaches the dimension of the PEM. Therefore, aside from the first Kiessig fringe the corresponding neutron reflectivity is a harmonic oscillation with slightly decaying amplitude. In contrast, after longest annealing (tanneal = 72 h) the neutron reflectivity of p13 PEI d7 samples exhibits both features: reduced amplitude of the first Kiessig fringe as well as amplitude modulations for Qz < 0.03 Å−1. The effect is weak but unambiguous. The quantitative analysis leads to σint = 61 Å, which is clearly below either the thickness of protonated or deuterated block (lp = 400 Å and ld = 270 Å, respectively). Additionally, the SLD step height between protonated and deuterated block decreases from 1.64 × 10−6 Å−2 before annealing down to 1.14 × 10−6 Å−2 after tanneal = 72 h. In short, with an internal PEI barrier layer the block profile consisting of two distinct plateaus still persists. Yet, the SLD contrast between both blocks decreases with tanneal. These findings suggest two different time scales which characterize the diffusion behavior inside a PEM containing an internal PEI barrier layer: (1) the diffusion of polyelectrolyte molecules across the barrier layer consisting of branched PEI and (2) once a PSS molecule has passed the PEI barrier layer, it diffuses with a time scale comparable to the one observed for the p13 d7 sample, i.e., within a few hours throughout the whole protonated or deuterated block, respectively.

basically unchanged. This indicates that annealing in 1 mol/L NaCl leads to intermixing of the adsorbed polyelectrolytes, while the PEM itself remains stable against desorption of polyelectrolytes. To prove this hypothesis, we calculate NPEM = ∫ l0p+ldSLD(z) dz, the integral of SLD across the PEM, i.e., the area under the SLD profile from Si/PEM interface to PEM/air interface (NPEM = ∫ l0p+ldSLD(z) dz = lp SLDp + ld SLDd when the film consists of one protonated and one deuterated block only). NPEM is a measure for the amount of deposited polyelectrolytes per unit area. For instance, adsorption of 1 mol PSS monomers per m2 increases NPEM by 2.9 Å−1. This value is obtained assuming the absence of salt ions inside the PEM and using the stoichiometric composition of one PSS monomer and the specific scattering lengths of its isotopes. The corresponding values for 1 mol monomers of PSS-d and PDADMA are 7.2 and 0.2 Å−1, respectively. However, NPEM amounts to 1.2 × 10−3 Å−1 and varies by 5% from sample to sample. Yet, within experimental error NPEM is independent of the annealing time. Thus, there is no indication of polyelectrolytes desorbing into 1 mol/L NaCl solution. Finally, after long annealing (tanneal = 10 h) in 1 mol/L NaCl solution one additional feature becomes apparent: In the range from Qz = 0.02 Å−1 to Qz = 0.06 Å−1 one observes under close inspection a slight increase of the oscillation amplitude with Qz (cf. Figure 2, top left, green curve). This observation is unexpected since in general the interference fringes are damped with increasing Qz and thus lead to fringes with decreasing amplitude. But now the interference pattern of neutron reflectivity can be understood as a superposition of two oscillations with similar frequencies leading to a low-frequency envelope. The corresponding SLD profile shows a pronounced decrease of SLD next to the Si substrate. In contrast to the intermixed PEM the region next to the substrate (21 Å) is nearly free of deuterated PSS-d. The thickness of this protonated zone corresponds to the precursor PEI/PSS layer pair. We conclude that the PEI anchoring layer at the substrate is immobile in 1 mol/L NaCl solution. Hence, also the protonated PSS which was adsorbed onto PEI remains partly immobile. We conclude that the ionic monomer/monomer bonds between PSS and PEI are stronger than between PSS and PDADMA. These findings raise the question whether introducing a single PEI layer can modify the diffusivity and possibly serve as barrier layer inside a multilayer film. Accordingly, we modify the layer architecture by introducing a single PEI layer at the internal interface between protonated and deuterated block. Hence, the new layer sequence reads (PEI/PSS)1/(PDADMA/ PSS)12/(PEI/PSS-d)1/(PDADMA/PSS-d)6. Its abbreviation is p13 PEI d7 (Figure 2, bottom). As for the previous PEM architecture, before annealing both blocks show two distinct SLDs (tanneal = 0, cf. Figure 2, red curves). The width of the internal interface amounts σint = 34 Å, which is nearly the same compared to the PEM without a PEI layer (σint = 38 Å). Still, both reflectivity curves with tanneal = 0 are clearly not identical: Especially the two adjacent Kiessig fringes at Qz = 0.045 Å−1 and Qz = 0.055 Å−1 are influenced by the presence of a PEI layer at the internal interface. The first of these fringes shows attenuation due to destructive interference from the internal interface, while the next is amplified due to constructive interference. In fact, it is not possible to fit the height of both fringes using a SLD profile with two homogeneous blocks only. In consequence, one additional slab was introduced to the SLD 8550


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is exchanged by deuterated PSS-d, and thus ΔSLD(z) is positive. On the other hand, within the deuterated block the same exchange leads to a decrease in SLD, equivalent to a negative ΔSLD(z). Subsequently integrating ΔSLD(z) across either the protonated or the deuterated block, i.e., calculating ∫ l0pΔSLD(z) dz and ∫ llpp+ldΔSLD(z) dz, delivers two quantities which are both a measure for the exchange of PSS against PSSd during the time interval tanneal. The first of these integrals is the area enclosed by the SLD profiles before and after annealing in the protonated block, and the latter one is the corresponding area in the deuterated block (cf. Scheme 1). Moreover, these areas can be converted directly into the total number of PSS/PSS-d monomer pairs which have moved across the internal interface during annealing. The exchange of 1 mol of PSS monomers originally located in the protonated block with 1 mol of PSS-d monomers originally located in the deuterated block through 1 m2 surface of the internal interface is equivalent to ∫ l0pΔSLD(z) dz = 4.4 Å−1 and ∫ llpp+ldΔSLD(z) dz = −4.4 Å−1, respectively. These proportionality factors are obtained assuming the absence of salt ions inside the PEM (which are removed by washing in pure water after annealing)22 and using the difference in scattering length between PSS and PSS-d per mole of monomers. Of course, during annealing also the polycations diffuse across the internal interface. Yet there is no SLD contrast attributed to PDADMA molecules from either side of the internal interface. Moreover, it is known that even after drying in 0% rh there is still some residual water inside the PEM.34 Again assuming the absence of salt ions inside the PEM, this residual water content can be determined from the SLD of either protonated or deuterated block and amounts to 9% volume fraction H2O in both blocks (equivalent to 1.4 H2O molecules per PSS/PDADMA monomer pair). Interestingly, the water content and the adsorbed PDADMA sum up to a SLD which is 2 orders of magnitude smaller compared to adsorbed PSS (or PSS-d), since H2O possesses a slightly negative SLD and PDADMA a slightly positive one. Hence, all changes in the SLD profile due to annealing are attributed to the diffusion of PSS and PSS-d only. Accordingly, the number of moles N of exchanged PSS/PSS-d monomer pairs is quantified by

Figure 3 (left) shows the interfacial width σint as a function of the annealing time for the neutron reflectivity data presented in

Figure 3. Left: width of the internal interface σint deduced from reflectivity measurements shown in Figure 2 vs square root of annealing time. The solid lines are fits to eqs 2 and 3 using the diffusion coefficient as indicated. PDADMA molecular weight is Mw(PDADMA) = 45 kDa. Right: number of PSS monomers exchanged by PSS-d monomers (and vice versa) per area of sample surface vs annealing time. The black line is obtained from numerical integration of eq 2 using DPSS deduced from σint. The green line is a linear fit to the data obtained from films containing an internal PEI barrier layer. The permeation rate PPSS is given by the slope of the linear fit. For clarity, top x-axes of both figures contain the annealing time of selected samples.

Figure 2. As expected from eq 1 for a homogeneous film σint increases linearly with the square root of tanneal as long as the finite dimension of the PEM can be neglected. Yet, after 2 h of annealing the tails of the internal SLD distribution reach the outer boundaries of the PEM. As predicted by eqs 2 and 3 in this case σint starts to level off since the broadness of the internal SLD distribution is limited by the total film thickness. However, the corresponding diffusion coefficient DPSS is quantified by adjusting DPSS to fit the interfacial width measured via neutron reflectivity with values obtained from eqs 2 and 3. The resultant value of the p13 d7 sample amounts DPSS = 160 × 10−22 m2/s. In the presence of the PEI barrier layer DPSS decreases by 2 orders of magnitude to 0.6 × 10−22 m2/s. Without a barrier layer (cf. film p13 d7) the diffusion behavior due to annealing is completely described by DPSS alone. In contrast, the SLD profiles of the p13 PEI d7 sample suggest two different diffusion processes: first the diffusion of polyanions across the PEI barrier which results in broadening of the internal interface and afterward the establishment of a uniform distribution within the distinct blocks, whose SLD values approach each other. Hence, in the presence of the internal PEI barrier layer DPSS quantifies the local diffusion coefficient at the position of the barrier layer. int For clarity, it is denoted Dint PSS. Unfortunately DPSS does not account for the equalizing SLD between protonated and int deuterated block since Dint PSS depends on σint alone. Thus, DPSS alone is insufficient to describe the overall diffusion properties of the p13 PEI d7 sample. Therefore, to understand the overall diffusion properties of the p13 PEI d7 film, an alternative approach of quantifying the diffusion behavior is necessary. Figure 3 (right) shows the total number of PSS (or PSS-d) monomers normalized to 1 m2 sample surface which have crossed the internal interface versus tanneal. The numbers are derived from the SLD profiles shown in Figure 2 by calculating the change ΔSLD(z) = SLD(z,tanneal) − SLD(z,0) of a sample before and after annealing. Within the protonated block annealing leads to an increase in SLD since protonated PSS

l

2

NPSS [mol/m ] =

∫0 p ΔSLD(z) dz 4.4 Å−1

as well as NPSS ‐ d [mol/m 2] =

∫l

l p+ ld

ΔSLD(z) dz

p

−4.4 Å−1

Both definitions are applied independently on all SLD profiles and deliver pairs of quantities which are each identical within a range of at most 6 × 10−6 mol/m2 (cf. Figure 3, right). Moreover the diffusing objects are not single monomers but instead PSS and PSS-d polymers consisting of 370 monomers per molecule (for Mw(PSS) = 75.6 kDa and Mw(PSS-d) = 80.8 kDa, respectively). Therefore, the exchange of protonated against deuterated macromolecules is a factor 370 smaller than the exchange of monomers depicted in Figure 3 (right). However, without the internal PEI barrier layer (sample p13 d7) the amount of exchanged PSS/PSS-d monomer pairs increases nonlinearly with tanneal. The observed time dependence is in good agreement with the theoretically predicted 8551


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Macromolecules trajectory calculated using DPSS = 160 × 10−22 m2/s and integrating eq 2 numerically from 0 to lp as well as from lp to lp + ld. The black line depicted in Figure 3 (right) is the result of this integration. In other words, the black line is not a fit to the data points but instead the theoretical expectation using the film geometry as well as DPSS deduced from σint. The trajectory reaches an upper limit once complete intermixing of PSS and PSS-d is achieved. However, in the presence of the internal PEI barrier layer the amount of exchanged PSS/PSS-d monomer pairs increases linearly with tanneal for the first 72 h (cf. Figure 3, right, green symbols). Explaining this time dependence with Dint PSS deduced from σint alone leads to unsatisfying results, since the broadening of σint by polyelectrolytes crossing the internal PEI barrier layer is small compared to the contribution of polyanions establishing an uniform distribution within their respective block. Instead, the diffusion in the presence of the internal barrier layer can be described with a constant rate of polyanions permeating the barrier. The permeation rate PPSS is quantified by the slope of the exchanged PSS/PSS-d monomer pairs vs tanneal; i.e., the permeation rate PPSS satisfies the relation N = PPSStanneal and amounts PPSS = 5.3 × 10−6 mol/m2/d. Influence of Polycation Molecular Weight on PSS Diffusion. Figure 4 shows diffusion parameters of PEMs

prepared film decreases with Mw(PDADMA).17 σ0 originates from local intermixing during the multilayer buildup. This intermixing is driven by the relaxation of entropic stress of freshly adsorbed polyelectrolytes. However, the PSS diffusion constant corresponding to this relaxation during film buildup increases with the polycation molecular weight Mw(PDADMA). In other words, the PSS molecules do not diffuse independently, but some parts of the moving PSS molecules are strongly coupled to neighboring PDADMA molecules, suggesting cooperative motion.17 However, during annealing the situation is different. The fraction of ionic monomer/ monomer bonds is reduced in 1 mol/L NaCl annealing solution compared to 0.1 mol/L NaCl solution during multilayer buildup. Still the PSS diffusion coefficient DPSS observed for PEMs prepared from 24 kDa PDADMA (sample p12 d10) is halved (DPSS = 81 × 10−22 m2/s) relative to PEMs prepared from 45 kDa PDADMA. In short, the PSS diffusion coefficient in 1 mol/L NaCl solution depends on PDADMA molecular weight. If the diffusing objects are single PSS molecules, DPSS should be independent of Mw(PDADMA). Thus, in fact the diffusing objects are not single PSS molecules, but cooperative motion plays an important role, also sticky reptation. The neutron reflectivity data suggest that for PEMs the relation between molecular weight and diffusion coefficient is more complex, and further investigations using dedicated experiments are required to explain the unexpected result. However, adsorbing one layer of branched PEI at the position of the internal interface (sample p12 PEI d10) again results in a delayed broadening of the internal interface. −22 m2/s in the Quantitative analysis leads to Dint PSS = 21 × 10 presence of the internal PEI barrier layer. Interestingly, the influence of the internal PEI barrier layer depends strongly on Mw(PDADMA): for PEMs prepared from 45 kDa PDADMA the time scale of the broadening is slowed down by 2 orders of magnitude due to the presence of the internal PEI barrier layer, while for a lower Mw(PDADMA) the diffusion coefficients in both layer architectures (p12 d10 as well as p12 PEI d10) are within the same order of magnitude (cf. Table 1). As a consequence, both molecular processes diffusion across the PEI barrier layer and equilibrating within one particular blocktake place on the same time scale. This means that a single PEI layer is a more efficient barrier for PSS, when high molecular weight PDADMA is used. This observation is supported by PPSS, the rate of PSS/PSS-d monomer pairs permeating the internal PEI barrier layer, which increases by 1 order of magnitude when Mw(PDADMA) is halved. A possible explanation is a decrease in cooperative motion of PSS when the polycation molecular weight Mw(PDADMA) decreases. When less PSS monomers are attached to one short PDADMA molecule, cooperative motion is reduced and PSS can move more easily; thus, the diffusion constant DPSS increases. PEI, on the other hand, forms a flatly

Figure 4. Left: width of the internal interface σint vs square root of annealing time. PDADMA molecular weight is Mw(PDADMA) = 24 kDa. Corresponding neutron reflectivity data are shown in Figure S2 (cf. Supporting Information). The solid lines are fits to eqs 2 and 3 using the diffusion coefficient as indicated. Right: number of PSS monomers exchanged by PSS-d monomers (and vice versa) per area of sample surface vs annealing time. The black line is obtained from numerical integration of eq 2 using DPSS deduced from σint. The green line is a linear fit to the data obtained from films containing an internal PEI barrier layer. The permeation rate PPSS is given by the slope of the linear fit. For clarity, top x-axes of both figures contain the annealing time of selected samples.

prepared from 24 kDa PDADMA; i.e., the polycation molecular weight Mw(PDADMA) is decreased by nearly a factor of 2 compared to the data shown in Figure 3. It is known that in the PEM center the initial interfacial width σ0 of the freshly

Table 1. PSS Diffusion Coefficient DPSS and Permeation Rate PPSS through the PEI Barrier Layer for Different Polycation Molecular Weights; Effective Diffusion Coefficient Dint PSS at the Position of the Barrier Layer; lc(PDADMA)/lc(PSS): Ratio of the Contour Lengths absence of PEI barrier

presence of PEI barrier

Mw(PDADMA) [kDa]

ratio lc(PDADMA)/lc(PSS)

DPSS [10−22 m2/s]

−22 Dint m2/s] PSS at internal interface [10

PPSS [10−6 mol/m2/d]

24 35 45

0.88 1.28 1.64

81 71 160

21 30 0.6

71 30 5.5

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This conclusion is supported by the time dependence of the interfacial width σint (cf. Figure 6). Instead of increasing

adsorbed layer of branched polymers consisting of 1700 monomers per molecule (in the case of Mw(PEI) = 75 kDa). So the PEI barrier layer can be understood as a flat web of neighboring and partly overlapping PEI molecules. The stronger monomer/monomer bond between the PEI/PSS than between the PDADMA/PSS monomers slows the PSS movement further down. It is interesting to note that the PSS permeation rate increases when the PDADMA molecular weight is decreased. Since the strength. of the involved monomer/monomer bonds is independent of PDADMA molecular weight, this effect has to be attributed to the reduction of cooperative motion of the PSS in the PDADMA network. Next, the final equilibrium state of the diffusion process is studied. For that purpose PEMs prepared from a PDADMA molecular weight below 45 kDa are investigated to achieve a larger PSS mobility across the internal PEI barrier layer. Figure 5 shows neutron reflectivity data of PEMs prepared from 35

Figure 6. Width of the internal interface σint deduced from reflectivity measurements shown in Figure 5 and Figure S1 (cf. Supporting Information) vs square root of annealing time. The green line is the time dependence for 32% immobile polyanions and diffusion int as indicated. PDADMA molecular weight is coefficient DPSS Mw(PDADMA) = 35 kDa. For clarity, top x-axis contains the annealing time of selected samples.

monotonically with tanneal the interfacial width reaches a maximum (σint = 95 Å after tanneal = 12 h) and then returns to its original value (σint = 22 Å after tanneal = 146 h). This unexpected behavior can be understood by the presence of both a mobile and an immobile fraction of polyanions. First, the mobile polyanions cause the broadening of the internal interface. When all mobile macromolecules have equilibrated within their respective blocks, the shape of the remaining internal interface is dominated by the fraction of immobile polyanions. These are still separated in one protonated and one deuterated block with the original interfacial width. Indeed, the time dependence of σint can be explained by applying eq 3 on a superposition of eq 2 and the time independent initial distribution c(z,0), i.e., on (1 − α)c(z,tanneal) + αc(z,0) with an immobile fraction α = 0.32 (cf. Figure 6, solid line). In terms of diffusion properties both blocks can be understood as two adjacent PEMs consisting of only linear polyelectrolytes separated by the PEI barrier. In the absence of the internal PEI barrier all polyanions adsorbed contribute to the intermixing. Hence, the immobility of PSS and PSS-d observed for the film p12 PEI d10 is due to transversing the PEI barrier, while PSS and PSS-d are still able to diffuse freely within their respective blocks. The immobile fraction is trapped at the PEI barrier. Possible reasons for the existence of an immobile PSS fraction are (1) the PSS chains need to orient with one tail toward the PEI barrier layer in order to pass it via reptation. Yet during film preparation they adsorb flatly and have an oblate shape, oriented parallel to the sample surface. Therefore, they have to reorient. (2) PSS chains will form many monomer/ monomer PEI/PSS bonds to one PEI molecule and to different branches of it. Thus, some PSS molecules will be immobilized in their position and prevent consecutive PSS molecules from diffusing through the barrier. Although the data give evidence for an immobile fraction α in the case of 35 kDa PDADMA, still the question remains if this effect is a general feature for each PDADMA molecular weight investigated. Yet evidence of immobile polyanions and the quantification of α are only possible, when the equilibrium state of the diffusion process is observed. In the case of 45 kDa PDADMA the PSS permeation rate across the PEI barrier is very low. Even after longest annealing time used (tanneal = 72 h;

Figure 5. Normalized neutron reflectivity curves (left) and corresponding SLD profiles (right). Samples without (top) and with (bottom) internal PEI barrier layer are measured as prepared and after annealing in 1 mol/L NaCl solution for the time indicated. Measurements are performed in dry air (0% rh). PDADMA molecular weight is Mw(PDADMA) = 35 kDa. Layer sequence is (PEI/PSS)1/ (PDADMA/PSS)8/(PDADMA/PSS-d)5 (top) and (PEI/PSS)1/ (PDADMA/PSS)11/(PEI/PSS-d)1/(PDADMA/PSS-d)9 (bottom), respectively. For clarity, the reflectivity curves are shifted vertically. Additional reflectivity data of other annealing times are available in the Supporting Information (Figure S1).

kDa PDADMA. Intuitively, one would expect a uniform SLD distribution after longest annealing, since protonated PSS and deuterated PSS-d have established complete intermixing. In fact, in the absence of the internal PEI barrier layer (film p9 d5, cf. Figure 5, top) annealing for 72 h in 1 mol/L NaCl results in a uniform SLD distribution throughout the PEM with an average ⟨SLD⟩ = 2 × 10−6 Å−2. Only the first adsorbed PSS layer which is partly immobilized by the anchoring PEI layer leads to a SLD dip of 30 Å thickness at the Si substrate. In contrast, one PEI barrier layer at the internal interface between the protonated and the deuterated block (film p12 PEI d10, cf. Figure 5, bottom) preserves the original block architecture even after 6 days in annealing solution. Additionally, from the remaining SLD step height between protonated and deuterated block one can conclude that the internal PEI barrier layer is impenetrable for up to 32% of the polyanions. 8553


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The PEMs are made from linear polyelectrolytes poly(styrenesulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA), which are both adsorbed from 0.1 mol/L NaCl solution. Each film consists of a protonated and a deuterated block, built from m protonated and n deuterated polycation/polyanion layer pairs. For contrast, selective protonated PSS and deuterated PSS-d is used. Thus, the corresponding neutron scattering length density (SLD) profile is composed of two homogeneous blocks, with a distinct interface between both. This internal interface is located roughly in the film center; the interfacial width is 27 ± 6 Å (for freshly prepared films). Any changes in the SLD profile are attributed to a rearrangement of PSS and PSS-d distribution, respectively. Diffusion of polyelectrolytes within the multilayer films is induced externally by exposing the PEMs to 1 mol/L NaCl annealing solution. Some ionic monomer/monomer bonds are exchanged by monomer/ion bonds; thus, the “stickers” of the moving PSS chains within the network are reduced and the diffusion constant increases.12 During annealing the width of the internal interface broadens due to intermixing of deuterated PSS-d into the protonated block (and vice versa). NPEM, a measure of deposited polyelectrolytes per unit area, is calculated during the intermixing process. We find that NPEM is constant and conclude that the constituent polyelectrolytes are stable against desorption into the annealing solution. The diffusion occurs within the LbL film only. Indeed, the equations for diffusion in a confined space do describe the time dependence of the width of the internal interface. For films consisting only of linear polyelectrolytes the dynamic of the PSS diffusion is described completely using one constant diffusion coefficient DPSS. DPSS amounts to 160 × 10−22 m2/s in the case of Mw(PDADMA) = 45 kDa and decreases by a factor of 2 if PDADMA molecular weight is halved. Eventually the diffusion leads to a uniform distribution of protonated and deuterated PSS throughout the PEM. Interesting is the observation that the PSS next to the PEI anchoring layer is immobile (within resolution), which suggests that at neutral pH the ionic monomer bonds of PEI/PSS are stronger than of PDADMA/PSS. Branched PEI, on the other hand, adsorbs as a flat network of adjacent and partly overlapping PEI monomers. PSS is immobilized within multiple PEI layers, and PSS-d cannot penetrate the (PEI/PSS)9 block. Adsorbing a single PEI barrier layer in the center of the film between the protonated and the deuterated block changes the PSS diffusion behavior both quantitatively and qualitatively: The PEI barrier layer itself is immobile within resolution. We assume that a polyanion macromolecule diffuses within each block with the same diffusion coefficient as in a homogeneous PDADMA/PSS multilayer film. One can define an effective PSS diffusion coefficient Dint PSS assuming a homogeneous diffusion through the barrier and the two adjacent blocks. On increase of Mw(PDADMA), Dint PSS decreases substantially. (Actually, it is reduced by almost 2 orders of magnitude if Mw(PDADMA) is increased from 24 to 45 kDa.) This pronounced decrease of the effective diffusion constant Dint PSS is partly attributed to the dependence of the permeation rate PPSS on PDADMA molecular weight. If Mw(PDADMA) = 45 kDa, the permeation rate of PSS/PSS-d monomer pairs across the PEI barrier layer is PPSS = 5.3 × 10−6 mol/m2/d. In this case the time necessary for a PSS molecule to pass the PEI barrier is large compared to the time necessary to diffuse through the remaining block. For a lower polycation molecular

cf. Figure 3) the diffusion process is far away from equilibrium. On the other hand, the PSS mobility of samples prepared from 24 and 35 kDa PDADMA is comparable. But again the maximum annealing time used for samples consisting of 24 kDa PDADMA (tanneal = 3.6 h, cf. Figure 4) is too short to deduce conclusions on the equilibrium state. Presence of Multiple PEI Barrier Layers. Until now we investigated the barrier capabilities of a single PEI layer. Yet it is possible to utilize the control over the layer sequence during PEM buildup to create a diffusion barrier consisting of multiple PEI layers. Figure 7 shows reflectivity curves and corresponding

Figure 7. Normalized neutron reflectivity curves (left) and corresponding SLD profiles (right) of (PEI/PSS)9/(PDADMA/PSSd)10 films. Samples are measured as prepared and after annealing in 1 mol/L NaCl solution for the annealing time indicated. Measurements are performed in dry air (0% rh). PDADMA molecular weight is Mw(PDADMA) = 45 kDa. For clarity, the reflectivity curves are shifted relative to each other.

SLD profiles of PEMs consisting of 9 successive layer pairs of PEI and protonated PSS followed by the deuterated block containing 10 layer pairs of PSS-d and PDADMA with Mw(PDADMA) = 45 kDa. Now on one side of the internal interface the polycation is PEI only, while on the opposite side the polycation is PDADMA. Before annealing the interfacial width amounts σint = 25 Å, which is slightly below the value of an interface between two stacks of PDADMA based multilayers (σint = 37 Å in the case of p13 d7), suggesting less interdigitation of adjacent layers during polyelectrolyte adsorption. Actually, during annealing the protonated blocks thins while the SLD of the deuterated block decreases, indicating that the PSS next to the PEI intermixes with the whole deuterated block. Because of annealing in 1 mol/L NaCl solution for 72 h, σint increases up to 38 Å, which is clearly less than observed for both the p13 d7 and the p13 PEI d7 sample (61 Å in the case of p13 PEI d7). In fact, even after annealing for 82 days (tanneal = 1982 h) σint increases barely noticeable to σint = 41 Å, suggesting a stagnation in the diffusion process. Moreover, this value is still below the PSS radius of gyration (Rg = 61 Å for Mw(PSS) = 75.6 kDa),17 which is the extent of a molecular coil in its entropically most favorable conformation. Thus, there is no proof for a center of mass movement of PSS-d diffusing into a multilayer containing branched PEI during annealing in 1 mol/L NaCl. These findings suggest that the diffusion is limited to a local exchange of the last adsorbed PSS layer in the protonated block with the first adsorbed PSS-d layer in the deuterated block. Once intermixing of both adjacent polyanion layers is finished, the diffusion at the internal interface comes to a complete standstill. Therefore, (PEI/PSS)n multilayers are impenetrable barriers for PSS.

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CONCLUSION The internal structure of linearly assembled polyelectrolyte multilayers (PEMs) is investigated using neutron reflectivity. 8554


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ACKNOWLEDGMENTS We thank BENSC at HZB, Berlin, Germany, for beamtime and for excellent support and assistance. Financial support by the DFG (He 1616/14-1) and the state of MecklenburgVorpommern is gratefully acknowledged.

weight (Mw(PDADMA) = 35 and 24 kDa, respectively) the permeation rate through a single PEI barrier layer increases by more than an order of magnitude. For low Mw(PDADMA) diffusion across the PEI barrier layer and the accompanying equilibrating within one particular block take place in the same time scale. The results suggest that the branched PEI molecules form a rather flat network which serves as a barrier layer. In fact, the neutron data give evidence for the presence of two fractions of polyanions inside the LbL film with a barrier layer between the protonated and the deuterated block: (1) a fraction intermixing across the PEI barrier as well as (2) a trapped fraction remaining in the original protonated or deuterated block, respectively. In the case of Mw(PDADMA) = 35 kDa the PEI barrier layer is impenetrable for one-third of the adsorbed PSS and PSS-d. After PSS and PSS-d are in the equilibrium stage achieved by diffusion through the barrier layer and intermixing within each block, the internal width between the two blocks is as low as for the freshly prepared film. The barrier layer does separate the trapped PSS fraction. We suggest two reasons why a fraction of PSS molecules does not pass: (a) some PSS molecules have a conformation that hinders crossing the barrier, possibly next to voids,35 or (b) with time, more and more PSS molecules bind to PEI monomers, decrease the permeation rate, and effectively turn the barrier impenetrable. To summarize, we start to describe the mobility of polyelectrolytes within PEMs. Quantified is the diffusion constant DPSS of linear PSS with constant molecular weight within a confined geometry. Varied is the molecular weight of the linear polycation. In the next step, an immobile barrier layer (branched polycation PEI) is introduced in the center of the PEM. The barrier effect is caused by stronger ionic monomer/ monomer bonds between PEI/PSS than between PDADMA/ PSS at neutral pH and by the flat web formed by the branched PEI molecules. DPSS does depend on the molecular weight of PDADMA; it seems to decrease with increase of Mw(PDADMA), and this needs to be further investigated. Decrease of Mw(PDADMA) by a factor of 2 causes an increase of the permeation rate PPSS through the immobile barrier layer by a factor of more than 10. This suggests that PSS can more easily escape a network consisting of low molecular weight PDADMA to cross a barrier layer and highlights the importance of cooperative motion.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01065. Figures S1−S2 show additional neutron data; in Tables S1−S6 the parameters obtained by least-squares fits to all experimental data are specified; Tables S7 and S8 give the specific values of the internal roughness for the original films, as well as for films after salt annealing (PDF).

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (C.A.H.). Notes

The authors declare no competing financial interest. 8555


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