Influence of Polymer Molecular Weight on the Parabolic and Linear

Jul 8, 2013 - pairs a transition from a parabolic to a linear growth occurs. For molecular weights above a threshold (Mw(PSS) > 25 kDa and Mw(PDADMAC)...
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Influence of Polymer Molecular Weight on the Parabolic and Linear Growth Regime of PDADMAC/PSS Multilayers Peter Nestler, Malte Paßvogel, and Christiane A. Helm* Institut für Physik, Ernst-Moritz-Arndt Universität, Felix-Hausdorff-Straße 6, D-17489 Greifswald, Germany S Supporting Information *

ABSTRACT: The buildup of polyelectrolyte multilayers is investigated in solution with multiple angle null-ellipsometry. Polyanion poly(styrenesulfonate) (PSS) and polycation poly(diallyldimethylammonium) (PDADMAC) are adsorbed sequentially from 0.1 M NaCl solution. First the films grow parabolically. After Ntrans deposited PDADMAC/PSS layer pairs a transition from a parabolic to a linear growth occurs. For molecular weights above a threshold (Mw(PSS) > 25 kDa and Mw(PDADMAC) > 80 kDa), Ntrans is 15, the thickness per layer pair in the linear growth regime is 12.3 nm. If either the PDADMAC or the PSS molecular weight is decreased below the threshold value, Ntrans either falls (for PDADMAC, lowest value observed is 8) or rises (for PSS, highest value observed is 33), respectively. Simultaneously, in the linear growth regime, the thickness per layer pair decreases (down to 4.3 nm) or rises (up to 25 nm). Furthermore, for low molecular weight PSS, three growth regimes are observed: exponential, parabolic, and linear. The opposite effect of PDADMAC and PSS molecular weight reduction is discussed in terms of persistence lengths and linear charge density. The data suggest that molecular weight provides a way to control growth and internal structure of polyelectrolyte multilayers.

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INTRODUCTION Two decades after their discovery,1,2 polyelectrolyte multilayers (PEMs) formed by alternating layer-by-layer deposition of polyanions and polycations have become a popular tool for preparing functionalized, organized nanomaterials.3,4 Understanding the internal properties is helpful when PEMs are tailored toward specific applications. Therefore, this subject has received increased attention in the last few years.5−7 Of particular interest is the conformation of the polyelectrolytes within a PEM. From a salt-free deposition solution the polyelectrolytes adsorb flatly8 and charge reversal occurs.9 In these PEMs, the small thickness increase per deposited polycation/polyanion layer pair is consistent with flatly adsorbed polyelectrolytes.5 However, biological and biotechnical solutions contain salt (about 0.1 M). In salt-free solutions, the loss of entropy due to flat adsorption is compensated by a gain in electrostatic energy due to the formation of ion pairs.10 With increasing salt concentration, the electrostatic interaction is shielded. Then, the surface coverage of adsorbed polyelectrolytes increases. The adsorbed polymer molecules have only a part of their segments on the surface, while a fraction of segments protrudes into the solution.11 The segments on the surface are in trains of variable length, the others are in loops (with both ends in contract with the surface), and in one or two tails at the end of the adsorbed molecule. However, little is known about the vertical or lateral extension of a polyelectrolyte chain in a PEM. Neutron reflectivity indicates a vertical extension which exceeds the © 2013 American Chemical Society

average thickness per adsorbed layer by a factor two or three.2,12,13 Both stratified layers characteristic for films with linear growth mode,2,12,13 and strongly intermixed layers associated films with exponential growth mode have been reported.14,15 To control the thickness per deposited layer pair not only the salt concentration was varied,2,16 but also the pH,15 or the temperature of the deposition solution.17 While these measurements provide valuable information, pH, salt concentration or temperature are not variables which can be easily varied in a biological solution. To obtain a PEM with certain properties, one has to adjust the chemical composition.18 To keep the inter- and intramolecular interactions constant, we choose strong polyelectrolytes and vary their respective molecular weight. Theoretical calculations of polyelectrolyte multilayers provide limited guidance: the thickness per deposited polycation/polyanion pair is either not influenced by the molecular weight19 or it increases with molecular weight.20 The variation of the molecular weight of polyelectrolytes is motivated by surface forces experiments: If polyelectrolytes are adsorbed from high salt solutions, a small part of the chain forms a train, most segments are in one tail which protrudes into solution.21,22 The adsorbed layers swell and shrink in dependence of the salt concentration in solution. MathematiReceived: February 15, 2013 Revised: May 24, 2013 Published: July 8, 2013 5622

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The structure of the sample perpendicular to the surface is represented by a stack of four slabs, each with a constant refractive index (Si substrate, SiO2 layer, PEM, and surrounding solution). The roughnesses between different slabs are set to zero. In this model the refractive indices of the Si wafer and the SiO2 layer are fixed to 3.882 − 0.02i and 1.457, respectively.26 Before the preparation of a PEM, the thickness of the native oxide layer is determined for each Si waver. The refractive index of each surrounding solution is determined independently with a refractometer (J357 Automatic Refractometer, Rudolph, Hackettstown, NJ) at λ = 632.8 nm. Thus, the only remaining unknown sample parameters are the PEM film thickness and refractive index (d, nPEM). The angle of incidence traverses during the measurement, the range from 66° to 72° (with respect to the surface normal) in 1° steps. In each position the corresponding ellipsometric angles of the sample are measured. This range was chosen, because it contains the Brewster angle of a water−silica interface (71.1°) and the resulting angles Ψ and Δ are particularly sensitive to changes caused by the PEM film. d and nPEM are determined by a least mean square algorithm.25 Each measurement is carried out in both accessible ellipsometric zones.27 PEM films are prepared by sequential adsorption of oppositely charged polyelectrolytes1,2 at room temperature. The cleaned substrate is horizontally aligned and fixed in the sample cell which is filled with the respective polyelectrolyte solution (30 min for each adsorption step). During adsorption the PE solution is kept stagnant to achieve the same deposition conditions as with dipping assisted film growth. After each adsorption step the deposition solution is pumped out and replaced by a washing solution of pure water (1 min for each washing step; three replacements of the washing solution). The sample always stays wet. In the last washing solution, the ellipsometric multiangle measurements are carried out. All measurements are performed on PEMs with PSS as top layer. X-ray Reflectivity. X-ray reflectometry experiments are performed with a Seifert XRD 3003 TT diffractometer (Seifert, Germany) with Cu Kα radiation (wavelength λ = 1.54 Å) at nominal 0% rh (relative humidity). The film is placed into a gastight enclosure (THC, temperature−humidity chamber, Anton Paar GmbH, Graz, Austria) containing a Petri dish filled with P2O5 (Merck, Darmstadt, Germany). X-ray reflection curves provide information about the electron density variation perpendicular to the surface.28 However, during conventional reflectivity measurements the phase information is lost, and hence, the analysis of the reflectivity data is based on finding a suitable electron density profile of the PEM film. Therefore, the PEM film is modeled by a homogeneous slab (the slab is parametrized by the total PEM film thickness d, a film−air roughness σ, and an electron density ρPEM), which is situated onto a silicon substrate with a certain roughness σSub and electron density ρSub. Using the Paratt algorithm,29 it is possible to calculate the exact X-ray reflection curve for each PEM model. Hence, the model parameters for each sample can be obtained by performing a root-mean-square (rms) fit of the calculated reflection curves to the measured data.30 For X-ray reflectivity, films are prepared using a programmable dipping robot purchased from Riegler & Kirstein (Berlin, Germany). Solutions, temperature, and layer sequence are identical to the films characterized by ellipsometry.

cally, the swelling/shrinking can be described by the equations developed for a polyelectrolyte brush.22,23 If a polyelectrolyte adsorbs mainly as a tail, we expect a pronounced increase of the thickness per deposited polycation/polyanion pair with increasing molecular polymer weight. However, if a polyelectrolyte adsorbs flatly or with a well-defined layer thickness due to a well-defined segment density profile, there should be no dependence on the polyelectrolyte weight. A better understanding of the polyelectrolyte conformation needs quantitative data on the influence of the molecular polymer weight. We use the strong polyelectrolytes poly(styrenesulfonate) (PSS) as polyanion and poly(diallyldimethylammonium) (PDADMAC) as polycation, deposited from 0.1 M NaCl solution. The charge spacing between monomer units is larger for PDADMAC (0.62 nm) than for PSS (0.25 nm).24 Therefore, PSS has the larger linear charge density. Furthermore, PDADMAC has the larger persistence length LP = 2.5 nm (in 0.5 M NaCl24) than PSS, LP = 1.2 nm.13 The PEM growth is monitored by in situ multiple angle nullellipsometry, because it can determine the thickness of a layer pair in solution with sub-nm resolution.25 However, in most applications, the PEM is formed by a dip and rinse approach. Therefore, some films are prepared by the standard approach and their thickness is determined with X-ray reflectivity.

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MATERIALS

Poly(styrenesulfonate) sodium salt (PSS) with different polymer weights (Mw(PSS) = 8.6 kDa with PDI < 1.2; 13.2 kDa with PDI < 1.2; 16.8 kDa with PDI < 1.1; 33.8 kDa with PDI < 1.1; 48.6 kDa with PDI < 1.2; 75.6 kDa with PDI < 1.2; 130 kDa with PDI < 1.2; 168 kDa with PDI < 1.1) and poly(diallyldimethylammonium) chloride (PDADMAC) with different polymer weights (Mw(PDADMAC) = 23.6 kDa with PDI = 1.88; 34.8 kDa with PDI = 2.08; 44.8 kDa with PDI = 1.47; 72.1 kDa with PDI = 1.83; 159 kDa with PDI = 1.91; 210 kDa with PDI = 1.87; 322 kDa with PDI = 2.19) were obtained from Polymer Standard Service (Mainz, Germany). Branched poly(ethylenime) (PEI; Mw = 75 kDa) was purchased from Sigma-Aldrich (Steinheim, Germany). Sodium chloride (NaCl; pro analysis grade) was obtained from Merck (Darmstadt, Germany). All solutions were prepared with ultrapure water using a Milli-Q device (Millipore, Billerica, MA). Polished silica (100) wafers (Wacker Siltronic AG, Burghausen, Germany) are used as substrates. The wafers are cleaned according to the RCA standard and freshly used. Each polyelectrolyte (PE) deposition solution contains a concentration of 1 mM of the respective PE (with respect to the monomer concentration). The substrate is functionalized by the adsorption of one PEI layer dissolved in pure water (21 °C). The salt concentration of the PSS and PDADMAC deposition solutions is set to 0.1 M NaCl. Ellipsometry. PEM film thicknesses and indices of refraction are measured with ellipsometry.25 The measurements are performed with a null-ellipsometer (Multiskop; Optrel GbR, Kleinmachnow, Germany) in PCSA configuration (polarizer−compensator−sample− analyzer). A He−Ne laser (intensity = 4 mW; wavelength λ = 632.8 nm) is used as light source. The measured quantities are the ellispometric angles Ψ and Δ, which correspond to the changes in amplitude and phase of the light due to reflection at the sample. The ellipsometric angles are related to the ratio of the Fresnel reflection coefficients by rp rs

= tan(Ψ) exp(iΔ)

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RESULTS Figure 1a shows null-ellipsometry in situ measurements of the film growth with 0.1 M NaCl in the deposition solution. Three different polyelectrolyte (PE) weight combinations for Mw(PDADMAC)/Mw(PSS) are shown: 159/76, 159/13.2, 44.8/76 (all molecular weights in kDa). The first PDADMAC/PSS pair consists of two large molecular weight polyelectrolytes. The molecular weight of PSS is reduced for the second film, and the molecular weight of the PDADMAC is reduced for the third film. Always, one observes for the first polycation/polyanion layer pairs a moderate and nonlinear film growth as has been often

(1)

where rp and rs are the reflection coefficients of the parallel and normal components of the electric vector E (with respect to the plane of incidence). 5623

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the linear growth regime is found when low weight PDADMAC is used (Mw(PDADMAC)/Mw(PSS) = 44.8/76). When both PEs have a large molecular weight, the film growth is between these two extreme cases. The decrease of the molecular weight has opposite effects for polyanion and polycation, either the film growth is much steeper (low molecular weight PSS) or much flatter (low molecular weight PDADMAC). To better understand the influence of the respective polymer weights on the film growth, the film formation is investigated in detail. Figure 1b shows the thickness of the top layer pair, Δd(N), calculated according to Δd(N ) = d(N ) − d(N − 1),

with N ≥ 1

(2)

d(N) symbolizes the thickness of a film consisting of N layer pairs. Two different growth regimes can be distinguished. For the first layers, Δd(N) increases linearly with N. After Ntrans polycation/polyanion layer pairs are deposited, Δd(N) is constant. The transition at Ntrans is well-defined with respect to the total number of deposited layer pairs. The following equations quantify the two growth regimes observed: Δd(N ) = αN

for N < Ntrans

Δd(N ) = αNtrans for N ≥ Ntrans

Figure 1. Top: Thickness of PDADMAC/PSS films vs number of deposited layer pairs N as measured with multiple angle ellipsometry in salt-free water for different molecular weights as indicated. Bottom: thickness of the top layer pair as a function of the number of supporting layer pairs. The lines are fits to eq 4 and 3 using the same parameters Ntrans and α for each combination of molecular weights. The PEMs are prepared in 0.1 M NaCl solution.

(3)

with α as a constant which depends on the respective molecular weights of the polycation/polyanion pair. The PEM thickness is calculated by summing over the thickness increases, according to d(N) = ∑nN= 1Δd(n). One obtains α d(N ) = N (N + 1) for N < Ntrans 2 α d(N ) = αNNtrans − Ntrans(Ntrans − 1) for N ≥ Ntrans 2 (4)

These equations describe for N < Ntrans a parabolic PEM growth, which turns linear at N ≥ Ntrans. Ntrans marks the transition from a parabolic to a linear growth. Note that in the linear growth regime the thickness per layer pair dBL only depends on the parameters α and Ntrans: dBL = αNtrans

or

α = dBL/Ntrans

(5)

for film growth according to eq 3. Therefore, the slope in the parabolic growth regime together with Ntrans determines the thickness per layer pair, dBL, in the linear growth regime. For each PDADMAC/PSS pair with their respective molecular weights, Ntrans and α are determined by least mean square fits; both to the film thickness (cf. Figure 1a) and the thickness increase (cf. Figure 1b), using eqs 4 and 3, respectively. This works well for all molecular weights investigated. Yet, two exceptions have to be considered: (i) the transition from parabolic to linear growth is sometimes not sudden, it takes at most three layer pairs to complete it (cf. Figure 1b). (ii) The films made from low molecular weight PSS show exponential growth for the first few layers (cf. Figure 1, N < 11; note that dBL(N) and Δd(N) have a similar curvature). In the exponentially growing part, the thickness increase is very small. To account for the three growth regimes, eqs 3 and 4 have to be adapted. Both for the parabolic and the linear growth regime, a constant is added to d(N) and Δd(N) to account for the additional thickness caused by the exponential growth.

Figure 2. Top: Thickness of a PEM vs number of deposited layer pairs N as measured with multiple angle ellipsometry in salt-free water (blue) and in air at 3% r.h. with X-ray reflectometry (black). The PEM investigated in water is always in solution while the film in air is prepared by the dip and rinse method. Bottom: thickness of the top layer pair as a function of the number of supporting layer pairs (cf. eq 1). The lines are fits to eq 4 and 3 using the same parameters Ntrans and α for each preparation method. Polycation is PDADMAC, polyanion PSS, salt concentration 0.1 M, and the polymer weights are indicated.

described in the literature.31 If N, the number of layer pairs, is large, then the layer thickness increases linearly. One observes the steepest film growth with the low molecular weight PSS (Mw(PDADMAC)/Mw(PSS) = 159/13.2). Accordingly, in the linear growth regime, the thickness per deposited polycation/ polyanion layer, dBL, is largest. In contrast, the smallest dBL in 5624

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Table 1. Ntrans for Different Combinations of Polycation and Polyanion Molecular Weightsa

a

Green background indicates large PDADMAC and PSS molecular weight, where the exact polymer weight has little influence. Blue indicates lowered PDADMAC molecular weight and weak film growth, whereas red stands for lowered PSS molecular weight and strong film growth. An asterisk (∗) marks films which exhibit three growth regimes (exponential, parabolic, and linear).

Table 2. dBL [nm] for Different Combinations of PDADMAC and PSS Molecular Weightsa

a

The color code corresponds to Table 1, as does the assignment of the asterisk (∗).

Figure 3. Left: Three-dimensional contour plot of Ntrans (top) and two cross sections through this contour plot which show Ntrans as a function of PDADMAC and PSS molecular weight, as indicated. (bottom) Right: Three-dimensional contour plot of dBL (top) and two cross sections of this plot (bottom). Ntrans is the number of layer pairs which marks the onset of the linear growth regime and dBL is the thickness of a layer pair in the linear growth regime. In the contour plots the same symbols are used as in the cross sections.

films from PSS and PDADMAC. Until now, we presented only data obtained from films which are always in solution. Standard is the preparation by dipping and subsequent rinsing.2

Before the influence of polymer weight on the parabolic and linear growth is investigated further, we want to make sure that the two growth regimes (parabolic and linear) are typical for 5625

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Therefore, PDADMAC/PSS (322/75.6) films are prepared by both techniques (cf. Figure 2). With ellipsometry, in the linear growth region we obtain dBL = 12.8 nm (in salt-free water), the transition between the two growth regimes occurs at Ntrans = 14 ± 2 (cf. Tables 1 and 2). The X-ray data are measured at nominal 0% r.h., therefore the films are about 30% thinner. Nevertheless, the dependence of the film thickness on N can be fitted with the same two regime model. If the film thickness increase is considered (cf. Figure 2b), a considerable scatter is observed. Yet, Ntrans = 14 ± 2 is the same. Because of the large error, the X-ray data do not allow distinguishing parabolic film growth from another sort of nonlinear film growth, yet they are consistent with parabolic growth. The values of Ntrans and dBL depend on the molecular weight of the polyelectrolytes used as shown in Figure 3, and Tables 1 and 2 (The thickness increase as a function of the number of deposited layers for all molecular weights not depicted in Figure 1 or the TOC image is shown in the Supporting Information). Three different regions can be distinguished: for large molecular weight (Mw(PDADMAC) ≥ 80 kDa and Mw(PSS) ≥ 25 kDa), Ntrans and dBL are constant (Ntrans = 15 ± 1; dBL = 12.3 ± 1.3 nm, cf. green area in Figure 3 and Tables 1 and 2). If the molecular weight of PDADMAC is decreased, while the one of PSS remains large, then both Ntrans and dBL decrease (cf. blue area in Figure 3 and Tables 1 and 2). The more the molecular weight of the polycation is reduced, the smaller are Ntrans and dBL. The smallest Mw(PDADMAC) used is 23.6 kDa. For this special PDADMAC, Ntrans and dBL amount to 9 ± 1 and 4.3 ± 0.2 nm, respectively. Note that dBL is reduced by a factor of 3 compared to PEMs made from large molecular weight PDADMAC/PSS. However, if the molecular weight of PSS is decreased, while the one of PDADMAC remains large, the opposite is observed (cf. red area in Figure 3 and Tables 1 and 2). Both Ntrans and dBL increase monotonically. For the three PSS used (Mw(PSS): 8.6, 13.2, and 16.8 kDa) dBL increases up to 28 nm, that is by a factor of 2 compared to PEMs made from large molecular weight PDADMAC/PSS. Ntrans is increased, too. For Mw(PSS) = 16.8 kDa, we obtain Ntrans = 21 ± 3 (cf. TOC image). If Mw(PSS) is decreased even further, we obtain the largest Ntrans observed so far (Ntrans = 33, cf. Figure 3, Table 2 and Supporting Information). Finally, in the hope to reconcile the two opposing trends, films consisting of low molecular weight polycation and polyanion are considered (Mw(PDADMAC) = 44.8 kDa, Mw(PSS) = 16.8 kDa). The transition from the parabolic to the linear growth regime occurs only after more layer pairs are deposited than in the regime of large molecular weight (Ntrans = 18 ± 2 instead of 15 ± 1). However, the thickness of layer pairs is a factor of 2 smaller (dBL = 6.3 nm instead of 12.3 ± 1.3 nm). If the PDADMAC polymer weight is lowered further (Mw(PDADMAC) = 34.8 kDa), both Ntrans and dBL are decreased (Ntrans = 11 ± 3, dBL = 4.4 nm). Apparently, the effect of PDADMAC is stronger. Thus, for low molecular weight PEs we get first an increase of Ntrans and a decrease of dBL, and on further reduction of Mw(PDADMAC) a decrease of both parameters. To investigate the growth mechanism further, we plot dBL as function of Ntrans, cf. Figure 4. If both PEs have a large molecular weight, or if the molecular weight of only one constituent is lowered below the respective threshold, we find that dBL depends linearly on Ntrans, according to dBL [nm] =

Figure 4. Thickness of a layer pair in the linear growth regime, dBL, vs the number of layer pairs which characterize the onset of the linear growth regime, Ntrans. The straight line is calculated according to dBL[nm] = Ntrans − 4. The color code is the same as in Figure 3, and in the tables. A deviation occurs when the molecular weight of PDADMAC is slightly lowered, and the one of PSS drastically (open square, Mw(PDADMAC) = 44.8 kDa, Mw(PSS) = 16.8 kDa).

Ntrans − 4. If the films grow at first exponentially, then the first layers are very thin (cf. Figure 1). However, in the parabolic growth regime, the thickness increase is larger than for films which have only two growth regimes (parabolic and linear). In summary, the first layers of PDADMAC/PSS films will always follow a parabolic growth regime, independent of the exact molecular weight. Before the onset of the linear growth regime, at least 4 layer pairs have to be deposited. A drastic deviation from dBL [nm] = Ntrans − 4 is observed when the weight of both PEs is reduced (Mw(PADMAC)/ Mw(PSS) = 44.8/16.8). dBL is lower than expected. This observation suggests a different conformation of both PDADMAC and PSS, which needs to be explored further. Finally, we want to make sure that the observed growth regimes provide an appropriate description for all polycation/ polyanion pairs investigated. For that end, a parameter is needed which characterizes each growth regime unambiguously, and which is also independent of N, the number of deposited layer pairs. Therefore, we define f (N ) =

d (N ) Δd(N )

and

f ′(N ) ≡ f ′

(6a)

f ′ is the slope of f(N) = d(N)/Δd(N). If the film growth can be described by an exponential function or by a power law, then one obtains for f ′ f (N ) =

1 eCN and f ′ = 0 for exponential growth = C C eCN

f (N ) =

1 C·N β N and f ′ = for power law growth = β β C·β ·N β− 1 (6b)

In case of linear growth, β = 1. Then, the slope of f(N) = d(N)/Δd(N) is f ′ = 1. Similarly, for parabolic growth one obtains β = 2 and f ′ = 0.5. Note that f ′ is independent of N, both for exponential and power law growth. Yet, f ′ is a meaningful parameter: it does depend on the exact power in the case of power law growth, and is zero in case of exponential growth. Therefore, with the help of f ′ the different growth regimes can be distinguished unambiguously. Figure 5 gives an example for the application of eq 6. A film with three growth regimes is analyzed (Mw(PDADMAC)/ 5626

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ratio Mw(PSS)/Mw(PDADMAC) was varied between 0.1 and 1, however we did not notice any effect (cf. green region in Figure 3 and Tables 1 and 2). On comparing the threshold values for PSS and PDADMAC, we observe that the contour length of PSS (30 nm) is much lower than the corresponding value for PDADMAC (250 nm). Presumably, the different threshold values are due to the higher linear charge density and the shorter persistence length of PSS. For polyelectrolytes with large molecular weight (Mw(PDADMAC) ≥ 80 kDa; Mw(PSS) ≥ 25 kDa) each adsorbing chain has an equilibrium thickness, which is characterized by many anchoring points per chain. During adsorption, the chain conformation is characterized by trains, loops and tails.32 When the polymer weight of PDADMAC is reduced below 80 kDa, one gains more insight into its conformation. Specifically, Ntrans and dBL decrease monotonically with the molecular weight of PDADMAC. The PSS molecular weight was varied by a factor of 2 (75.6, 130, and 168 kDa), but had no influence. These facts suggest a reduced polycation layer thickness, when the molecular weight is lowered below a threshold of 80 kDa. This molecular weight corresponds to a contour length of 250 nm. With a persistence length of about LP = 2.5 nm, a radius of gyration of 25 nm is obtained (according to (L C L P /3) 1/2 with the contour length L C determined from the molecular weight33), or a diameter of gyration of 50 nm. That number exceeds dBL for large molecular weight PDADMAC (12.3 nm). However, after deposition the layers interdiffuse and mix with adjacent PSS and PDADMAC layers; we do not know how far one PDADMAC layer within a PEM extends. Apparently, a PDADMAC coil with the diameter of gyration exceeding 50 nm is flattened during adsorption on the oppositely charged PEM surface. If the diameter of gyration is reduced further, the thickness of the adsorbed PDADMAC layer is smaller, even in the linear growth regime. In a simple picture, a different conformation of the adsorbing low molecular weight PDADMAC is suggested: only one train and one or two tails. According to theory, loops would ensure an equilibrium thickness independently of the contour length,19 therefore we suggest that loops are missing. Adsorbed chains consisting of a tail and a train only were observed for a polyelectrolyte adsorbed from high salt conditions onto a flat surface.21,23 A very different effect occurs when the PSS molecular weight is decreased below its threshold value, 25 kDa. Both Ntrans and dBL increase. The PDADMAC molecular weight is varied by a factor of 2 (159, 322 kDa), but no effect is found. The low molecular weight of PSS corresponds to a contour length of 30 nm and a radius of gyration of 4 nm. Even the diameter of gyration, 8 nm, is smaller than the thickness of a PDADMAC/ PSS pair in the linear growth regime, 12.3 nm. At first view, this observation is not in agreement with the flattened conformation associated with polyelectrolytes adsorption in a saltfree solution.10,11,19 A possible explanation for the thickness of a layer pair which exceeds the diameter of gyration of the PSS would be that the top PDADMAC layer is a corrugated surface. The anchoring points of the PSS are vertically distributed. During film formation the PSS interdiffuses and forms a fuzzy layer with the thickness of two or three layer pairs.12,13 Intriguingly, a decrease of the molecular weight of PSS below the threshold value has the opposite effect as the decrease of the molecular weight of PDADMAC: Ntrans and dBL increase. Furthermore, the first layers grow exponentially. Exponential

Figure 5. Left, from top to bottom: thickness of a PEM d, thickness of the top layer pair Δd, and ratio f(N) = d/Δd vs number of deposited layer pairs N for Mw(PDADMAC) = 159 kDa and Mw(PSS) = 16.8 kDa. The three different growth regimes can be distinguished by their slope, f ′. Right: histogram of f ′, the slope of f(N) = d/Δd as determined from all PEMs investigated.

Mw(PSS) = 159/16.8). The plot of f(N) = d(N)/Δd(N) allows to distinguish exponential, parabolic and linear growth by the different slopes of f(N). Thus, f ′ is determined for each growth regime. To quantify the growth of all PEMs prepared, f ′, the slope of d(N)/Δd(N) is determined for each growth regime of each PEM. A histogram of f ′ visualizes the results (cf. Figure 5). Three different maxima can be distinguished: (i) f ′ = 0 characterizes exponential growth and is observed for the first layers of all PEMs built from low molecular weight PSS (cf. Tables 1 and 2, and Supporting Information); (ii) f ′ = 0.51 ± 0.15 corresponds to the parabolic growth regime which all films show; (iii) f = 1.04 ± 0.16 is obtained from the linear growth regime, which occurs at large N, again for all films. The width of the peaks indicates the sample to sample variation, and the neglected offsets of d(N) and Δd(N) when f(N) was defined. The three growth regimes can be distinguished unambiguously.

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DISCUSSION PEMs from PDADMAC and PSS with well-defined molecular weight are built. The film growth is observed in situ with ellipsometry. By considering the thickness increase of the outer PDADMAC/PSS pair as function of the number of supporting layer pairs, information about the different growth regimes is obtained. Always, we find at least two regimes of film growth: first a parabolic film growth, then a linear film growth. The transition between the two regimes is well-defined, it occurs when Ntrans layer pairs are deposited. For large molecular weight of both constituent PEs above specific threshold values (Mw(PDADMAC) ≥ 80 kDa; Mw(PSS) ≥ 25 kDa), both Ntrans and the thickness per deposited layer pair in the linear growth regime, dBL, are fairly constant and independent of the actual molecular weight. The 5627

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growth is caused by adsorbing PEs which diffuse into the PEM.14,34 Note that according to polymer theory the diffusion constant increases with decreasing polymer weight.35 During film formation, we kept the adsorption time constant. On decrease of the PSS molecular weight dBL increases. The molecules diffuse further, suggesting an increased diffusion constant, well in accordance with polymer theory. To summarize the above paragraphs: we tried to find physical parameters, which explain why the molecular weight becomes important below a specific threshold value, which is different for PDADMAC and PSS. At the threshold of PDADMAC, we found that the diameter of gyration of PDADMAC in solution exceeds dBL by about a factor of 4. In contrast, at the threshold of PSS, the diameter of gyration of PSS in solution is only 65% of dBL. A possible explanation would be that PDADMAC below the threshold adsorbs as train and one or two tails, while PSS below the thresholds adsorbs onto the corrugated surface provided by the PDADMAC, and may diffuse into the film. Also, molecular rearrangements after deposition contribute to the internal structure of the PEM.

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ASSOCIATED CONTENT

S Supporting Information *

All ellipsometric measurements, with details of the thickness increase of a PEM as a function of the number of deposited layer pairs N for the used combinations of molecular weight, and the corresponding plots of the thickness of the top layer pair as a function of the number of supporting layer pairs. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Deutsche Forschungsgemeinschaft (He 1616/14−1). M.P. was supported by a fellowship of the Alfried Krupp Wissenschaftskolleg Greifswald.

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CONCLUSION

REFERENCES

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The buildup of polyelectrolyte multilayers is investigated in solution with multiple angle null-ellipsometry. Polyanion poly(styrenesulfonate) (PSS) and polycation poly(diallyldimethylammonium) (PDADMAC) are adsorbed from 0.1 M NaCl solution. At least two different growth regimes are observed, parabolic and linear. After Ntrans layer pairs are deposited, a transition from parabolic to a linear growth occurs. Ntrans is 15 and constant for molecular weight exceeding threshold values which are specific for each polymer (25 kDa for PSS and 80 kDa for PDADMAC). If either the PDADMAC or the PSS molecular weight is decreased beyond theses values, Ntrans either falls (for PDADMAC) or rises (for PSS). Simultaneously, in the linear growth regime the thickness per layer pair either falls or rises. Nevertheless, for all molecular weights the same linear relationship between Ntrans and dBL is found. For molecular weights above the respective threshold values, both polymers exhibit an equilibrium adsorption thickness which is independent of the exact polymer weight, in accordance with theoretical predictions.32 The ratio between the molecular weights of PSS and PDADMAC was varied within a factor of 10, without noticeable effects. The different threshold values of PDADMAC (80 kDa, contour length 250 nm) or PSS (25 kDa, contour length 30 nm) are attributed to the different chemical structures, which cause different persistence lengths and linear charge densities. The decrease of the molecular weight does affect not only the conformation of the adsorbing polyelectrolytes, but in case of PSS also the diffusion constant. The discussions above are qualitative; they concern mainly results obtained from the top layers. However, the thickness per layer pair is the result of the polyelectrolyte conformation during adsorption, i.e. the conformation of the top layer. The conformation may change when the next layer adsorbs. Nevertheless, below the respective threshold value, the polyelectrolyte molecular weight influences the conformation of the top layer pair, and thus the growth mode and the internal structure of a PEM. 5628

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