Effect of polyacid architecture and polycation molecular weight on lateral diffusion within multilayer films Free

Ultrathin coatings constructed via the layer-by-layer (LbL) deposition technique are widely used in photonics, energy storage, biomedical engineering, and drug delivery applications.^1–5 In most cases, the application conditions for these coatings are different from the assembly conditions. Thus, it is essential to understand how environmental stimuli, such as changes in salt concentrations, temperatures, and/or pHs, affect the behavior of the LbL films. Multilayer assemblies exposed to different environments can swell/deswell,^6,7 alter their surface morphologies,^8–11 or even disassemble.^12–16 All these events require macromolecular adjustments on the polymer chain and segments via polymer chain dynamics, the adjustment of polymer conformation, and/or the number of ionic contacts between assembled polyelectrolytes, affecting the chain mobility within the polymer coatings. An important fundamental question that was addressed in only a few experimental studies involving linear polyelectrolytes is the molecular weight (MW) dependence of the mobility of assembled polymer chains.

Previously, our group explored this question using the fluorescence recovery after photobleaching (FRAP) technique with LbL systems containing fluorescently labeled chains of linear poly(methacrylic acid) (PMAA) of different MWs. These prior studies demonstrated that the lateral diffusion coefficient (D) scaled with the PMAA MW as D ∼ M_w^−1±0.05, suggesting the persistence of the unentangled polymer dynamics at a PMAA MW as high as 480 kDa.¹⁷ A significant contribution to studies of molecular mobility of polyelectrolytes within LbL films by Helm’s group explored the diffusion of a strong, fully charged polyanion, poly(styrene sulfonate) (PSS), in the direction perpendicular to the film surface using neutron reflectometry (NR). Helm’s work highlighted the interdependence of molecular conformations determined by the assembly conditions, post-annealing salt concentrations, and MW of a partner polymer, poly(diallyldimethylammonium) chloride (PDADMAC), on PSS mobility.^18,19 Importantly, the PDADMAC MW was the main factor affecting the diffusion coefficient of PSS (D_PSS), with D_PSS not following the power law dependences predicted by the reptation model for polymer melts (i.e., D ∝ M_w⁻² by theoretical predictions and D ∝ M_w^−2.3 as determined experimentally).^20,21 In particular, for largely mismatched MWs of PSS and PDADMAC (i.e., a larger number of repeat units in PDADMAC), D_PSS dramatically dropped with the power law, exceeding the reptation prediction, with the power exponent dependent on the conformation of assembled polyelectrolytes.¹⁹ These studies suggested a possible role of PDADMAC “entanglements,” or the diffusion landscape, which is determined by the spatial distribution of ionic pairs, on PSS diffusion and proposed coupling between PDADMAC and PSS diffusion. While the prior works provided insight into a MW dependence on the diffusion of polyelectrolytes within multilayer assemblies, they were limited only to linear chains, and similar dependences remained unexplored for branched polyelectrolytes.

Our previous work regarding polymer dynamics in star-containing LbL films demonstrated enhanced diffusivity of linear chains in the star-containing films^22,23 and an increased size of the polymer segments that participate in the diffusion of star polymers.²³ The aim of this work is to explore how the MW of PDADMAC affects the lateral diffusion of a star polyanion—8-PMAA—and compare it to its linear counterpart, L-PMAA. Unlike prior work that explored a similar question for a linear strong polyanion (PSS), we use a weak polyelectrolyte (PMAA) whose charge density is affected by solution pH and hypothesize that both the reduced charge density in acidic conditions and the intrinsically weaker binding of PMAA to polycations (as compared to PSS)²⁴ can decouple the mobility of the polyanion from that of PDADMAC. We employed the FRAP technique to directly track the diffusion of linear and star PMAA and establish the correlation between the mobility of polymers of varied architecture and the MW dependence of the polycation. Our findings indicate that the effect of MW of PDADMAC on polyacid diffusion was weaker than sticky Rouse or sticky reptation theoretical predictions²⁵ for associating polymers.

To explore the effect of polycation MW on the polymer dynamics of linear and star polyacids within multilayer films, we assembled up to 10 bilayers of PDADMAC of different MWs (35, 75, and 300 kDa) with L-PMAA and 8-PMAA of matched MW (M_w ∼ 60 kDa) via LbL assembly from solutions at pH 5 (0.2 mg/ml in 0.01M phosphate buffer, 5 min per layer). Figure 1 shows that the MW of PDADMAC strongly impacts the growth of all-linear and star-containing LbL films. In particular, films containing 35 kDa PDADMAC demonstrated ∼2.2-fold larger bilayer thickness in the linear regime compared with films constructed with 300 kDa PDADMAC. This effect is likely related to the faster chain mobility of the low-MW PDADMAC during deposition. Note that while the average thickness of individual PMAA layers measured by ellipsometry during film construction remained ∼3–5 nm for all the films, the thickness of individual PDADMAC layers decreased from ∼15 to 2–3 nm when the PDADMAC MW increased from 35 to 300 kDa (Fig. S1). This behavior is likely due to the selected film assembly conditions (pH 5), which, according to the prior study of linear poly(acrylic acid)/PDADMAC films, corresponds to the regime in which film growth is dominated by the diffusivity of PDADMAC chains during film deposition.²⁶ The slightly higher bilayer thicknesses in the L-PMAA-containing (as compared to 8-PMAA-containing) films are distinct from the previously reported faster growth of star-containing films in a different LbL system in which growth was dominated by the faster diffusion of star PMAA.^22,23 The observed differences are also likely attributed to higher chain rigidity and the reduced charge density of PDADMAC (see Fig. S2), twice lower than that of earlier explored poly[2-(dimethylamino)ethyl methacrylate].

Next, we studied the stability of the coatings upon exposure to increasing NaCl concentrations. Figures 2(a)–2(c) show that an increase in PDADMAC MW led to enhanced stability of the films, in agreement with the stronger interpolymer interactions indicated by the growth curves. Temporal studies of the L-PMAA and 8-PMAA LbL systems upon exposure to 0.2M NaCl showed stability after about 50 min (Fig. S3). For all systems, star-containing films were more prone to deconstruction by salt ions compared to their linear counterparts, suggesting that the star architecture slightly hinders ionic pairing between the weak polyacid and PDADMAC. For the films containing 35 and 75 kDa PDADMAC, this is corroborated by the ionization of assembled PMAA analyzed via transmission FTIR of thick films [100–250 nm; Figs. 2(d), 2(e), and S4], which showed lower ionization of assembled 8-PMAA molecules.

Figures 2(d) and 2(e) also show that for both linear and star-containing films, PMAA ionization consistently decreased with the increase in PDADMAC MW, suggesting that longer PDADMAC chains are less successful in conforming to their shorter counterparts, probably due to their more sluggish dynamics. However, one of the most pronounced trends shown in Figs. 2(d) and 2(e) is a 10%–15% decrease in PMAA ionization upon the exposure of the film to 0.2M NaCl. The drop in ionization is due to the inclusion of salt ions within LbL films, disruption of polymer–polymer ionic pairs, and the resultant protonation of the released carboxylic groups, as shown in Fig. 2(f). The effect is enabled by the stronger impact of a polycation²⁷ as compared to a low-molecular salt^28,29 on the ionization of weak polyacids. The inclusion of salt within LbL films could be detected by in situ measurements of film swelling using spectroscopic ellipsometry, showing increased swelling of all films upon exposure to salt solution, with all 8-PMAA-containing films swelling more upon salt exposure than their linear counterparts (Fig. S5).

We further explored the lateral diffusion (D_//) of the linear and star polyacids assembled with PDADMAC of different MWs. To enable D_// measurements with FRAP, the linear and 8-arm PMAAs were fluorescently labeled with Alexa-488 with one label per 800–1000 PMAA units as reported previously and denoted as PMAA*.²³ Fluorescent correlation spectroscopy (FCS) was used to study the attachment of Alexa-488 to the polymer chains by measuring the diffusion of polyacids and free labels in solutions. FCS measurements of fluorescently labeled L-PMAA*, 8-PMAA*, and control Alexa-488 in solution at pH 5 confirmed the covalent attachment of the fluorescent labels to the polymer chains (Fig. S6). The auto-correlation function of L-PMAA* and 8-PMAA* showed monodisperse model fitting (meaning all labels were attached to the polymer chains and no label was free in the polymer solutions), yielding diffusion coefficient values of 37.6 and 36.1 µm²/s, respectively, for L-PMAA* and 8-PMAA*. For the multilayer films used in FRAP experiments, the following design of (PDADMAC/PMAA)₃/(PDADMAC/PMAA*)₄/(PDADMAC/PMAA)₃ was used, in which labeled PMAA was deposited within the middle of the film to avoid any effects of the film/substrate and film/solution interfaces. Because our selected conditions for FRAP were in 0.2M NaCl solutions at pH 5.0, all films were exposed to the selected conditions overnight prior to FRAP measurements to complete minor salt-induced film thickness changes (3%–18% depending on the film composition, Fig. S3). Figure S3 shows that the minor loss of film thicknesses equilibrated after 50 min of exposure to salt so that no film thickness loss occurred during FRAP experiments, which were initiated after 12 h of film pre-conditioning in 0.2M NaCl. Further details of the experiments are described in the Materials and methods section of the supplementary material. Figure 3 shows the fluorescence recovery curves for linear [Fig. 3(a)] and star [Fig. 3(b)] PMAAs. For all systems, complete fluorescence recovery was not achieved, which could be a result of partial crosslinking of polymer chains during photobleaching.³⁰ The recovery data were fitted using an exponential fit, given by the equation: $I=Ieq+Ae−tτ$ where I_eq defines the equilibrium intensity, I is the intensity at time t, A is the amplitude, and τ is the recovery time. The half time was determined when 50% of the total intensity recovery was achieved and was calculated as $t1/2=τln2$⁠. The lateral diffusion coefficients were calculated from the half time using the following equation: $D//=yR24t1/2$ where y is the constant beam shape factor (value: 0.88), R is the bleaching spot diameter (0.33 µm), and t_1/2 is the half time.²³ 

Figure 3 shows that the diffusion of polyacids was dependent on the partner MW and was faster for 8-PMAA than L-PMAA in LbL films with all three PDADMACs exposed to 0.2M NaCl solutions. The difference in diffusivity between linear and star polyacids was significant [Fig. 3(c)], suggesting that the small differences in PMAA ionization shown in Fig. 2(e) cannot explain the observation. Instead, the higher diffusivity is likely attributed to the more compact structure of 8-PMAA star polymers. This result is consistent with our prior result on faster diffusion of more compact star molecules at moderate salt concentrations,²³ although the latter results were obtained using poly[2-(trimethylammonium)ethyl methacrylate chloride]—a polyelectrolyte with a twice higher linear charge density (charge per unit length) than PDADMAC. Note that in this prior work, the polycation and polyanion unit lengths were matched, and both differences in the polyacid architecture and polyacid ionization contributed to the faster mobility of star polyacids.²³ In contrast, the mismatch between the contour length of PMAA and PDADMAC units in this work [Figs. 2(f) and S2] minimized the effect of molecular architecture on ionization, enabling decoupling of the effect of molecular compactness on polymer diffusion.

Figure 3(c) shows that the diffusion coefficients (plotted using the power law dependence commonly used for polymer diffusion as a function of molecular weight) decreased with an increment in partner MWs for both linear and star architectures, but the trend of change was different for both architectures. For example, D_// differed by ∼70% for L-PMAA* and 8-PMAA* assembled with 35 kDa PDADMAC, but as the polycation MW increased to 300 kDa, the difference in D_// values was minimized for linear and star PMAA*. The data could be successfully fitted with the power law dependences, but the power exponents for both linear and star PMAA* in Fig. 3(c) were significantly below both sticky reptation and Rouse predictions.²⁵ In particular, the power exponent of D_// vs PDADMAC MW dependence increased from −0.22 ± 0.01 for linear PMAA to −0.53 ± 0.02 for star PMAA. To interpret these dependencies, one should note that the MW of PMAA was not varied in these experiments. Instead, changes in the MW of PDADMAC impact PMAA diffusion through its effect on film layering and molecular conformations, which determine the diffusion path of the polymer. In particular, due to the maximization of entropy through the formation of loops during adsorption of higher-MW polyelectrolytes,^31,32 both the bilayer thickness^33,34 and internal roughness (i.e., intermixing)¹⁸ of LbL films can increase with polyelectrolyte MW for non-linearly grown films with relatively sparse polymer–polymer ionic pairing. The two-fold difference in the slope in Fig. 3(c) for L-PMAA and 8-PMAA can be attributed to the difference in the size of the hopping sites between linear and star PMAA as determined previously.²³ The larger polymer segments involved in the diffusion of star PMAA²³ decrease the probability of finding a new ionic pairing, potentially leading to a stronger effect of PDADMAC MW on the diffusion of star PMAA within the films. Finally, the differences in the film layering between star and linear PMAA can also contribute to the differences in the dependencies of D_// on the polycation MW. Stronger molecular intermixing in star-containing films was indirectly suggested in several prior publications^{10,11,35–37} and directly demonstrated in our recent work by employing neutron reflectometry measurements.²³ The stronger spreading of PMAA stars and PDADMAC chains within the film, together with the different underlying mechanisms of diffusion of the star polyacids via the mechanism of arm retraction³⁸ and lower anisotropy of star-containing multilayers,²³ can all collectively contribute to the still weak, but stronger than for linear PMAA chains, dependence of star PMAA molecules on the MW of the polycation partner.

Overall, the weak dependence of the diffusion of PMAA chains on PDADMAC MW suggests that it is unlikely that PMAA diffuses together with the polycation chains being bound within a PMAA/PDADMAC complex, but instead, PMAA moves individually in the landscape of obstacles determined by the ionic pairing within the multilayer film. This result differs from the observation of PSS diffusion in PSS/PDADMAC films, where a strong power dependence of PSS on PDADMAC MW was observed,¹⁹ highlighting the important roles of polyanion type and charge density on its diffusion within the multilayers. While in the PSS/PDADMAC system, the linear charge densities in the polycation and the polyanion are mismatched (i.e., the charge-to-charge distance in the PDADMAC chain is twice as large as in PSS or fully ionized PMAA), the charge density in PMAA can be controlled by pH and reduced in acidic conditions (such as at pH 5 used in our experiments). Perhaps even more importantly, carboxylate ions are known to form weaker ionic pairings with polycations,²⁴ favoring the decoupling of PMAA mobility from the polycation partner molecules.

While FRAP experiments followed only the diffusion of L-PMAA* or 8-PMAA*, we were also able to evaluate the diffusivity of unlabeled PDADMAC. To that end, we monitored the adsorption of PDADMAC on preassembled LbL films using in situ ellipsometry, as detailed in the caption in Fig. 3, the supplementary material, and Fig. S7. Figure 3(d) shows that the diffusion coefficients of the polycation for both L-PMAA/PDADMAC and 8-PMAA/PDADMAC systems decreased with the increase in PDADMAC molecular weight, but the scaling laws differed for all-linear and star-containing films, following D ∼ M_w^{−0.98±0.22} and D ∼ M_w^{−0.69±0.01} dependences, respectively. The power exponents of these dependences were much lower than the prediction for the diffusion of unentangled chains using the sticky Rouse model²⁵ and slightly lower than the values for the PSS diffusion in a matrix of relatively low MW PDADMAC reported by Helm and co-workers.¹⁹ An interesting observation in Fig. 3(d) is a weaker effect of PMAA architecture on the polycation molecular diffusivity. Comparisons in Figs. 3(c) and 3(d) also show that the scaling dependences for diffusion of poly(carboxylic acid)s and the polycations as a function of polycation MW are drastically different. This further supports the concept of relatively independent diffusion of polycation and linear or star weak polyacids in their assemblies.

Refer to the supplementary material for detailed descriptions of the materials and methods used in this manuscript, figures for PMAA and PDADMAC component ratios within the LbL films, schematics for charge mismatch between PDADMAC and PMAA units, the kinetics of thickness loss from PMAA/PDADMAC films upon exposure to 0.2M NaCl, example deconvolutions of carboxyl peaks from the infrared spectrum of L-PMAA/PDADMAC films, swelling on PMAA/PDADMAC films in 0M and 0.2M NaCl conditions, FCS data for Alexa-488, labeled L-PMAA and labeled 8-PMAA in solution, and in situ measurements of PDADMAC adsorption for the calculation of vertical PDADMAC diffusion coefficients.

This work was supported by the National Science Foundation under Award No. DMR-1905535 (S.A.S.). J.B. acknowledges the support from the National Science Foundation Graduate Research Fellowship Program.

The authors have no conflicts to disclose.

J.B., P.P.S., and A.A. contributed equally to this work.

Conceptualization, A.A. and S.A.S.; synthesis, A.A.; investigation, P.S. and J.B.; writing—original draft preparation, J.B., P.S., A.A., and S.A.S.; writing—review and editing, J.B., P.S., A.A., and S.A.S.; funding acquisition, S.A.S. All authors have read and agreed to the published version of the manuscript.

Jordan Brito: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Parin Purvin Shah: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Aliaksei Aliakseyeu: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Svetlana A. Sukhishvili: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.