Influence of Surface Concentration on Poly(vinyl alcohol) Behavior at

Article pubs.acs.org/JPCB

Influence of Surface Concentration on Poly(vinyl alcohol) Behavior at the Water−Vacuum Interface: A Molecular Dynamics Simulation Study Giulio Tesei, Gaio Paradossi, and Ester Chiessi* Department of Chemical Sciences and Technologies, University of Rome Tor Vergata, Via della Ricerca Scientifica I, 00133 Rome, Italy S Supporting Information *

ABSTRACT: Poly(vinyl alcohol) (PVA) is an amphiphilic macromolecule with surfactant activity. The peculiar behavior of this polymer at the water−air interface is at the basis of its use as material for hydrated microdevices, films, and nanofibers. This work aims to investigate the behavior of PVA and water within the surface domain of highly diluted aqueous solutions by means of atomistic molecular dynamics simulations. Monodisperse atactic oligomers of 30 residues were distributed within water slabs in a vacuum box and allowed to diffuse toward the surface. After equilibration, structural features and dynamical properties of polymer chains and water in the interfacial domains were analyzed as a function of PVA surface concentration at 293 K. Surface pressure values obtained from simulations are in agreement with experimental values at corresponding polymer specific surface areas. In the explored concentration range of 6−34 μmol of residues/m2, the chains display a transition between two states. At lower surface concentrations, elongated, quite rigid structures are adsorbed on the surface, whereas partially submerged globular aggregates, locally covered by thin water layers, are formed at higher surface concentrations. At PVA concentrations higher than about 20 μmol of residues/m2, the percolation of chain aggregates over the interface plane produces a surface-confined polymer network with stable pores filled by water molecules. A substantial slowing of polymer and water dynamics in the interfacial domains is highlighted by the mean squared displacement time behavior of terminal residues and the interaction time of PVA−water hydrogen bonding. The diffusion coefficient of water and lifetime of hydrogen bonds between solvent molecules are halved and doubled, respectively, at the interface with the highest polymer concentration. The attenuation of water and polymer mobility concur to stabilize PVA hydrated networks in contact with air. thickness of about 0.5 μm enclosing an air core with average diameter of about 2.5 μm.20 In this microdevice the internal interface between shell and gaseous core is responsible for the unexpected and exceptional stability of microbubbles in aqueous suspension medium, leading to a shelf life of years. Preserving the gaseous core is pivotal for the functionality of PVA microbubbles as an injectable ultrasound contrast agent.17 The interface behavior of PVA aqueous solutions is relevant for electrospinning and ultrasonic atomization technologies.21−23 This polymer is commonly used as the main component of electrospun composite nanofibers, fabricated for several applications depending on additive agents. The capability of producing suitable nanofibers by the electrospinning process is modulated by physical properties of the source polymer solution, such as viscosity, electrical conductivity, and surface tension. The latter influences the thermal performance, inner structure, and morphology21 of the resulting nanofibers. The recent paper of Rošic et al.21 reports

1. INTRODUCTION The interest in poly(vinyl alcohol) (PVA) in current research activity is focused on applications of this synthetic macromolecule in biomedicine1−4 and material technology.5−7 The rationale for PVA performances in these fields is both in its water affinity and in the versatility in forming networks, which can be stabilized by physical interactions involving hydroxyl groups8−10 or by chemical cross-links.11 In addition, being a polyol, PVA shares chemical features of polysaccharides, a similarity justifying its biocompatibility, enabling the possibility of functionalization12 and allowing the miming of the role of carbohydrate moieties in specific applications.13−15 A class of PVA-based systems designed for controlled drug delivery, medical imaging enhancement, and cell interaction includes micrometer sized objects, such as microparticles,16 microbubbles,17 microcapsules,18 and microreactors,19 where a hydrated PVA scaffold is the active matrix. In these microdevices the characteristics of the interface between the particle and the external medium play a relevant role, determining the colloidal and physicochemical stability, permeability, and affinity toward biological constructs. PVA microbubbles are formed by a highly hydrated polymer shell with average © XXXX American Chemical Society

Received: March 12, 2014 Revised: May 27, 2014

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dx.doi.org/10.1021/jp502486a | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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bulk greater than the affinity for the surface domain, leaving a polymer-depleted air−solution interface. In this context, the motivation of the present study is to give a description at the molecular level of PVA behavior at the air− water interface. Our interest is increased by the need to understand the reasons for the stability of the gas core and of the shell-confined water in PVA-based microbubbles, a system which involves us on the experimental front.17,20 In addition, the analysis of available experimental data on PVA features at the air−solution interface shows that an interpretation with atomistic detail of polymer-induced interface effects would be relevant in view of several PVA applications. We address the problem by atomistic molecular dynamics (MD) simulations, a computing method already applied by us to investigate PVAbased polymer hydrogels32−34 and recently used to describe the liquid−vacuum interface of pure water,35−38 simple electrolytes and surfactants solutions,39−41 and polymer films.42 Taking into account that the solution behavior of PVA is strongly affected by inter- and intrachain association, the influence of aggregation effects can be expected at the interface, leading to surface features strictly dependent on polymer surface concentration. Therefore, we modulated this variable in the simulations by considering PVA hydrated slabs with equal size but including different numbers of polymer chains. The goal is to characterize the structure of the interface domain, both on the surface layer and across the interface, and to evaluate the effect of the interface confinement on water and segmental polymer dynamics. The satisfactory agreement between surface pressure values derived from simulations and experiments supports the results of this work. MD simulations highlight peculiar characteristics of the surface of hydrated PVA layers, with possible implications in applications based on this polymer.

an investigation on physical characteristics of PVA solutions in relation to electrospun nanofiber formation. This work shows that nanofibers change from a bead-on-string morphology to a fibrous form, using polymer solutions with PVA concentration from 8% to 12% (w/w) and surface tension from 63 to 70 mN/ m, respectively. In these conditions, the right balance between bulk and interface features of polymer in the source solution enables the jet initiation and fiber elongation.21 As compared to poly(vinyl acetate) (PVAc), which is the precursor polymer in the PVA standard synthesis and happens to be the canonical example of polymer monolayer at the air− water interface,24 the interface characteristics of PVA-based systems in an aqueous environment have been little investigated. A few articles on the adsorption behavior of PVA at the liquid−air interface were published in the early 1980s;25,26 however, current experimental techniques for characterizing the behavior of macromolecules at the air− solution interface, including X-ray reflectivity,27 neutron reflectometry,28 surface light scattering,24 and surface shear rheology,29 have not been applied to this polymer. PVA has an amphiphilic nature, with alternating hydrophobic methylene and hydrophilic hydroxymethine groups, and, in the diluted regime, behaves as a typical surface active compound. Surface tension γ of diluted PVA aqueous solutions is lower than that of water, and γ decreases at increasing polymer concentration up to a PVA concentration of about 3% (w/w).30 The surfactant effect is influenced by the molecular weight MW, being higher at larger MWs, and to a lesser extent by temperature. It is noteworthy that a certain discrepancy between γ literature data of PVA solutions has to be ascribed to the residual amount of vinyl acetate residues because of incomplete deacetylation of the precursor PVAc. The acetate residues increase the surface activity of this polymer, as reported in the work of De Feijter and Benjamins25 on vinyl alcohol and vinyl acetate copolymers. In addition, the polymer stereochemistry affects the PVA surfactant features. Matsuzawa et al.26 showed that the equilibrium γ of aqueous solutions of syndiotactic and isotactic PVA, at concentrations lower than 1% (w/w), is lower than the surface tension of atactic PVA solutions. Moreover, the rate of the decrease in γ, during equilibration, is in the order of syndiotactic > isotactic > atactic. The authors explain these results with the hypothesis that stereoregular chains can more easily adopt a uniform surface arrangement at the interface.26 In 1956, Llopsis and Rebollo31 obtained the compression isotherms of thin PVA films spread at the air−water interface in the 20−45 °C temperature range, using high molecular weight, atactic, and completely deacetilated PVA samples. At the highest PVA surface density of 1 mg/m2, the surface pressure Π of the film, corresponding to the difference between surface tension of pure water and film, was about 6 mN/m at 20 °C. Lower Π values were obtained at lower polymer surface concentrations.31 The behavior of surface tension for PVA aqueous solutions with bulk concentrations higher than about 5% (w/w) is anomalous, showing an increase of γ at increasing polymer concentrations. For a PVA concentration of 12% (w/w), γ of the polymer solution becomes practically equal to that of pure water.21 This anomaly was already noticed in 1980,26 and it can be observed in other works reporting data of γ for concentrated PVA solutions.22,23 Rošic et al.21 explain this result with the hypothesis that PVA chains in concentrated solutions are rearranged and folded into structures with a affinity toward the

2. SIMULATION PROCEDURES The first step of a MD simulation work is the model formulation and the preparation of the initial configuration. For this investigation we built three slabs with thickness of 6 nm, containing water and different numbers of atactic PVA oligomers, initially homogeneously distributed within the slab. The slabs were centered in a vacuum box of the suitable size to include top and bottom slab−vacuum interfaces and to prevent the interactions between periodic images of the slab in the direction perpendicular to the surfaces. After equilibration, the PVA chains were spontaneously adsorbed at the surfaces of the slabs, leading to six water−vacuum interfaces with different polymer surface concentration. These interfacial domains are assumed as models of the surface layer of the experimentally observed surface layers having comparable PVA surface concentrations. It is noteworthy that the length scale that can be explored by atomistic simulations does not permit accurate modeling of the bulk polymer solution between the two water− vacuum interfaces. This task can be tackled via mesoscale simulations with a coarse-grained polymer model in implicit solvent at the expense of atomistic detail and with loss of any information regarding solvent structure and dynamics. The surface adsorption of PVA was obtained by a “from bulk solution to interface” route, rather than layering the polymer chains on the surface, following the procedure described in section 1.1 of the Supporting Information. This modeling strategy was preferred with the aim to mimic the process of PVA distribution at the solution−air interface during the synthesis of PVA microbubbles.17 B



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The system setup for the final simulations in the NVT ensemble consisted of a slab parallel to the xy plane with thickness of about 6 nm, centered in a tetragonal box with size 4 × 4 × 18 nm3. In this configuration, two vacuum regions with height of about 6 nm are located below and above the slab (see Scheme 1), with two interfaces perpendicular to the z-axis.

The graphic visualization was done using the molecular viewer software package VMD.44

3. RESULTS AND DISCUSSION 3.1. Interface Features. An immediate description of the distribution of the components in the systems is provided by the density profiles across the slab. Figure 1, displaying the

Scheme 1. Simulation Box and Domains of the Slaba

Figure 1. Number density profiles of PVA carbon and oxygen atoms (green and red lines, respectively) and of water oxygen atoms (blue line) for I4 (a), I12 (b), and I16 (c) systems. Averages over production run. Dotted lines indicate the position of the Gibbs plane.

number density profiles of carbon, PVA and water oxygen atoms calculated along the z axis, normal to the surface, and averaged over the last 55 ns trajectory, highlights that polymer chains are accumulated in the surroundings of the surfaces and included in the interface domains A and B, at lower and higher z values, respectively (see Scheme 1). In the central domain C, the PVA concentration is scarce in I12 and I16 systems, and equal to zero in I4 system. The polymer depletion of the internal region of the slab is in agreement with the surface activity of PVA. Matsuzawa et al. obtained the value of the polymer surface excess in aqueous solutions of atactic PVA by applying the Gibbs equation to surface tension data as a function of PVA concentration.26 For solutions in the polymer concentration range of 0.01−10 g/dm3, the surface excess of PVA is 74 × 10−5 mol of repeating units/m2. This value shows a strong asymmetry in PVA distribution between interface and bulk solution phase, especially if compared with the surface excess of single-chain surfactant molecules at the critical micelle concentration, which is typically in the range of 2−4 × 10−6 mol/m2. It is noteworthy that the position of each maximum of the PVA oxygen atoms profiles is always more internal than the position of a corresponding maximum of the carbon atoms profiles (Figure 1). This behavior confirms the surfactant character of PVA, showing the preference of the hydrophobic backbone for the vacuum interface and the tendency of the hydroxyl groups to point toward the aqueous domain. The profiles are pseudosymmetric with respect to the xy plane bisecting the simulation box only for the system with the lowest PVA concentration (Figure 1a), where two PVA chains with a planar conformation are adsorbed at each surface. Density profiles of polymer atoms in I4A and I4B interfaces show a single peak, with the maximum of the oxygen atom curve situated on the Gibbs dividing plane and the maximum of the carbon atom curve placed more externally toward the vacuum region. In I12 and I16 systems, the domains A are richer in PVA than domains B and density profiles are characterized by local fluctuations. The sharp and indented profiles of Figure 1c indicate that the aggregates of PVA chains

a

Carbon, oxygen, and hydrogen atoms of PVA are drawn in green, red, and white, respectively. Oxygen atoms of water are drawn in blue.

Simulations of systems containing 4, 12, or 16 PVA oligomers of 30 repeating units with 2953, 2396, and 2144 water molecules, respectively, were carried out at 293 K. The nomenclature of the systems is I4, I12 and I16, the number indicating the total number of oligomers in the slab. A capital letter, A or B, is added as subscript to specify the interface. Final MD simulations in the NVT ensemble were carried out using periodic boundary conditions in three dimensions, for a total trajectory time of 110 ns; the last 55 ns were considered for the analysis. Equilibration criteria and trajectory sampling modality are reported in section 1.2 of the Supporting Information. A corresponding MD simulation of a system containing only water molecules, referred to as IA, was carried out to obtain the properties of liquid water−vacuum interface for the sake of comparison. The protocol applied to prepare the interfaces in the IA system is described in section 1.1 of the Supporting Information. The final simulation of the water slab, with thickness of about 6 nm in a 4 × 4 × 18 nm3 box, was carried out in the NVT ensemble for 13 ns. The last 3 ns trajectory was considered for analysis, with a sampling of 10 frames per picosecond. Tables S1 and S2, reported in the Supporting Information, summarize the system composition and the characteristics of simulations of this work, respectively. The computing activity was carried out within the GROMACS software environment,43 using the GROMOS force field G45A4, with the CHn united atom convention and the SPC water model. Technical details on simulations and trajectory analysis procedures are described in sections 1.3 and 1.4 of the Supporting Information, respectively. C



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at increasing PVA surface concentration can be noted. However, data in Table 1 show that the thickness of the interfacial region is affected not only by the quantity of polymer adsorbed but also by the homogeneity of the polymer layer at the surface, this feature being dictated by the chains’ conformation. Indeed, domain I12A, characterized by a PVA coverage that is more uniform than that of domain I16B, has a thickness similar to that of domain I16B, although the polymer surface concentration in the last interface is sensibly lower. The distribution of PVA on the interface surface is illustrated in Figure 2, showing maps of PVA mass fraction wPVA calculated in the whole interface thickness as reported in section 1.4 of the Supporting Information. These maps were used to estimate the degree of coverage of the interface surface by PVA, Θ. Inspection of wPVA maps and of their time behavior highlights a not homogeneous arrangement of the polymer within the interface domain. Regions with very high local polymer concentration can be observed, and regions containing only water are present even in the interfaces with the greatest number of polymer chains. A direct inspection of the trajectories shows that in the most crowded interfaces the oligomers are aggregated and segments of the chains protrude toward the aqueous phase because of the hydrophilic character of PVA, determining a polymer depletion in the surface layer. The surface hydration degree (SHD) described in section 1.4 of the Supporting Information, was estimated by mapping the interface surface within the depth of 0.69 nm, namely, in the surface layer whose thickness corresponds to the diameter of a water molecule including its first hydration shell. This analysis was carried out to reveal the presence of water directly in contact with the vacuum region and covering PVA in the interfacial domain. The behavior of average surface degree of coverage by polymer ⟨Θ⟩ and average surface hydration degree ⟨SHD⟩ as a

at the interfaces I16A and I16B have a very stable structure in the time window used for averaging. The analysis of the density profiles of the individual chains (Figure S1 of the Supporting Information) shows that in the interface domains with lower PVA concentrations, oligomers are arranged in parallel to the surface, whereas in interfaces I12A and I16A, they form clusters where a few chains span almost the whole thickness of the interface. The lack of symmetry in profiles of systems I12 and I16 is a consequence of the PVA aggregation in bulk phase,45observed as the formation of clusters with different sizes during the equilibration step. Such clusters are stably adsorbed at the interface because of the surface activity of PVA. The specific surface area of PVA a0 and the thickness of each polymer surface domain, calculated by analyzing the density profiles as described in section 1.4 of the Supporting Information, are reported in Table 1. An increase of thickness Table 1. Properties of PVA at the Water−Vacuum Interfacesa

interface I4A I4B I12A I12B I16A I16B

average surface concentration of PVA (μmol of residues/m2) 6.28 6.28 23.0 13.1 33.62 14.6

± ± ± ± ± ±

0.01 0.04 0.2 0.2 0.05 0.6

average specific surface area of PVA, a0 (m2/mg) 3.619 3.62 0.986 1.73 0.676 1.56

± ± ± ± ± ±

0.007 0.02 0.007 0.03 0.001 0.06

thickness (nm) 1.04 1.28 2.1 1.6 3.1 2.0

± ± ± ± ± ±

0.07 0.03 0.2 0.1 0.1 0.2

surface pressure (mN/m) 0±1 4±2 8±3

a

Time averages over the production run. Errors estimated using the blocking method.

Figure 2. PVA mass fraction maps within the whole interface thickness and van der Waals radii representation of the corresponding configurations at 102 ns. D



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aggregates in both x and y directions, and in this case the surface regions occupied by only water, shown as black zones in the maps of Figure 2, can be considered as pores of the 2dimensional polymer network at the vacuum−water interface. These pores correspond to water channels crossing the whole thickness of the polymer layers. Interfaces I16A and I12B display a single pore in almost the whole trajectory, whereas I12A interface shows few pores of similar size. The time evolution of the area AP of the largest pore of I12A, I12B, and I16A interface domains is shown in Figure 4 (left

function of PVA specific surface area is reported in Figure 3. The value of ⟨Θ⟩ is affected by polymer surface concentration

Figure 3. PVA surface degree of coverage (⟨Θ⟩, blue circles), surface hydration degree (⟨SHD⟩, green squares), and ⟨Δ⟩/⟨Θ⟩ ratio (red triangles) as a function of PVA specific surface area.

much more than the surface hydration degree; the last property changes only 10% in the explored concentration range. The scarce decrease of ⟨SHD⟩ at decreasing PVA specific surface areas suggests a concomitant decrease of affinity of PVA for the surface interface. The difference between ⟨SHD⟩ and ⟨1 − Θ⟩ values, referred to as ⟨Δ⟩, represents the fraction of surface where a layer of water, with a thickness equal or greater than 0.69 nm, covers PVA segments in the interface domain. Dividing ⟨Δ⟩ by the fraction of interfacial surface occupied by PVA, given by ⟨Θ⟩, we can estimate the depletion of PVA concentration in the most external surface layer. The value of the ⟨Δ⟩/⟨Θ⟩ ratio, reported in Figure 3, increases by about 0.3 moving from the interfaces of I4 system, containing 2 PVA chains, to domain I16A, where 10 oligomers are segregated. This result is a further evidence of the PVA tendency to occupy the subregion of the interface at increasing surface concentrations. These simulation findings can be compared with the recent hypothesis of Rošic et al.21 on the behavior of PVA chains at the air−water interface of concentrated solutions. The authors find that for PVA concentrations exceeding about 5% (w/w), the surface tension of the polymer solution has an increasing trend and it reaches the value of pure water at a polymer concentration of about 12% (w/w).21 A similar anomaly of the surface tension of concentrated PVA aqueous solutions was previously described.26 According to Rošic et al.,21 the interpretation of this behavior is that at a bulk solution concentration of about 5% (w/w), the surface is saturated by polymer and that at increasing concentrations, polymer aggregates, formed within the solution, subtract PVA from the interface. 21 As a result, the higher the polymer concentration, the less occupied the solution surface by dissolved PVA molecules. The trend to a rehydration of the surface at increasing polymer surface concentration is observed also in these simulations, at very low bulk PVA concentrations. The results show that the formation of polymer aggregates within the interfacial domain is related to a decrease in the affinity of PVA for the interface surface. We analyzed the distribution of the polymer over the interface surface. Figure 2 shows a snapshot of the wPVA maps and of the corresponding system configurations. Maps of domains I12A, I12B, and I16A display the percolation of polymer

Figure 4. Time evolution of the area of the largest pore of I12A, I16A, and I12B interfaces (bottom, center, top curve, respectively) and snapshot of corresponding maps including nine periodic replicas.

panel). AP values provide an estimate of the maximum size of a molecule able to permeate the interface polymer layer. Pores are stable in the explored time interval, and AP values range approximately from 0.5 to 6 nm2, depending on the interface domain considered. It is noteworthy that the average pore area varies nonmonotonically with the specific surface area of PVA and that the smallest pores are formed not in the interface with the lowest PVA specific surface area, corresponding to I16A, but in the interface with the most homogeneous distribution of the polymer on the surface. This feature is visible in Figure 4 (right panels) where images of wPVA maps, including the eight adjacent periodic replicas, are reported. The PVA mass fraction maps of domains I4A, I4B, and I16B did not show the formation of a stable polymer 2-dimensional network, and the AP value could not be estimated. In these interfaces the large PVA specific surface area and the intermolecular aggregation of chains hinder the percolation of the polymer moiety in both directions of the interfacial plane. The presence of residual porosity in PVA layers adsorbed at the air interface can explain the ability of PVA microbubbles to be reconditioned after freeze-drying treatment by suspending them in water.46 Indeed, during rehydration the solvent can penetrate the polymer network up to the internal interface of the microbubble and the air gases dissolved in liquid water can restore equilibrium with the vapor phase, according to their Henry constant values, by reforming a stable gaseous core. Permeability to O2 and N2 of PVA membranes swollen with pure water is practically not selective for degrees of hydration E



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Π ∼ a 0 −y

higher than 50%.47 Simulation results are consistent with this evidence because the porosity of I12 and I16 interfaces, with average degree of hydration above 50% (w/w), is compatible with the size of both O2 and N2 molecules. Surface pressure values of I4, I12, and I16 systems, calculated as described in section 1.4 of the Supporting Information, are reported in Table 1 and in Figure 5, where the horizontal error

(1)

with y = 2ν/(2ν − 1) and ν being the critical exponent of the excluded volume.49 A y value of 3 is predicted by theory for flexible chains in good solvent conditions, however y ∼ 3 was found for water-insoluble vinyl polymers, such as poly(terbutyl-acrylate) and poly(vinyl acetate), spread at the air−water interface.29,50 In the concentrated regime, the polymer distribution is complicated by multilayer arrangements, extensive chain overlay, and entanglements with a not predictable dependence of both Π and layer thickness on the specific surface area. A test of the scaling law in eq 1 for partially acetylated PVA adsorbed at the air−water interface was indirectly carried out by measuring the high-frequency limit of the surface modulus as a function of the surface pressure.49 The exponent ν was found to be equal to 0.81 ± 0.3 and y equal to 2.6 ± 0.2, irrespective of the degree of polymerization, in agreement with the scaling theory for the good solvent condition. The validity of eq 1 was verified in the 0.3−1.8 mN/m range of surface pressure. Therefore, assuming that fully hydrolyzed and partially acetylated PVA have similar Π threshold values, we could locate the I12 and I16 interface models with Π values higher than 2 mN/m, outside the semidiluted regime of surface concentration. The structural features of polymer chains in I12 and I16 interfaces are coherent with this statement. According to ellipsometric data, equilibrium thicknesses of adsorbed layers of partially acetylated PVA at a specific surface area of about 0.3 m2/mg are larger than 10 nm51 for polymer aqueous solutions with Π values of about 20 mN/m.25 To the best of our knowledge, an extensive experimental characterization of fully hydrolyzed PVA at the air−water interface as a function of polymer specific surface area is still lacking, as well as a correlation between surface tension of polymer solution and thickness of interfacial layer. In this respect, data of Π and thickness reported in Table 1 suggest that PVA aqueous solutions with surface tension much lower than that of water are characterized by several nanometer thick polymer layers at the surface in contact with air. 3.2. Structural and Dynamic Features of PVA. To analyze the structural characteristics of PVA oligomers in the interface domains, we calculated the persistence length p, an indicator of the rigidity of polymer chains, the relative shape anisotropy k2, and the asphericity parameter b described in section 1.4 of the Supporting Information. The value of k2, ranging from 0 to 1, provides information on symmetry and dimensionality of the polymer conformation. For symmetrical planar conformations, k2 is equal to 1/4. Three-dimensional symmetric and ideal linear conformations have k2 equal to zero and 1, respectively. Spherical chain conformations are characterized by near-zero b values. Figure 6 reports the behavior of these structural parameters, averaged over the interface chain ensemble, as a function of PVA specific surface area. In spite of the heterogeneity of values within domains, shown by the error bars of Figure 6, an evolution of the chain conformation at increasing PVA surface concentration can be noted. In I4A and I4B interfaces, the oligomers, adsorbed with the center of mass over the Gibbs dividing surface, mainly adopt a linear conformation, with nearunity values of k2. The persistence length is about 1/3 of the contour length L, equal to 9.3 nm, and direct trajectory inspection displays the chains’ preference for hairpin conformations and dimeric aggregation, visible in Figure 2.

Figure 5. Comparison between surface pressure values from simulations (circles) and from ref 31 (squares). PVA specific surface area in the abscissa.

bar is due to the different PVA surface concentration in the A and B interfaces. Figure 5 displays the comparison between Π values from simulations and the compression isotherm experimentally obtained by Llopsis and Rebollo at 20 °C for atactic PVA films spread at the air−water interface.31 The satisfactory agreement between the two data sets validates the G45A4 force field, previously tested for modeling PVA in aqueous solution,48 also for the simulation of PVA features in interface domains. Π values of I12 and I16 systems show that a considerable decrease in surface tension is produced by a few nanometer thick polymer layer. For the I4 system, where PVA chains cover less than half of the interface surface and the layer thickness is similar to the monomer size, surface tension value is indistinguishable from that of pure water within the precision of the simulation. A surface pressure of about 10 × 10−3 N/m, similar to the value obtained for the I16 system, was measured for PVA solutions with bulk concentration of about 0.01% (w/v) at 20 °C.30 Solutions of not completely deacetylated PVA with bulk concentrations of about 10−4 % (w/w) displayed surface pressure values lower than 6 × 10−3 N/m at 25 °C.49 From these data we can conclude that our models describe the interface of highly diluted PVA bulk solutions. The Π dependency on polymer specific surface area defines different regimes of surface concentration for flexible polymers in good solvent conditions.29 In the diluted regime, the surface pressure scales with the specific surface area as Π ∼ a0−1 according to the prediction of the ideal gas law. In this regime, all monomers of the chains are adsorbed at the surface without segments overlapping and the thickness of the polymer layer is approximately constant and similar to the size of the repeating unit. In the semidiluted regime, at surface concentrations above the overlapping concentration, chains partially interpenetrate each other and chain loops and entanglements are formed. A significant increase of thickness at increasing concentration is observed, coupled to a sharp increase of surface pressure. The scaling law usually applied in the semidiluted regime is F



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square contour length L2 of the PVA 30-mer and the values of the square persistence length p2 are indicated in Figure 7 for comparison. The dynamic behavior is strongly affected by the surface concentration. For PVA oligomers of the I4 system, the mean squared displacement exceeds L2 in about 30 ns and the unity slope in the MSD(t) double-log plot shows the free diffusion of chains. The same value of the lateral diffusion coefficient, equal to 1.1 ± 0.2 nm2/ns, is obtained for both the terminal residues and the center of mass of these oligomers. Segmental diffusion coefficient values of PVA in highly hydrated hydrogels and microgels typically range between 0.1 and 0.6 nm2/ns,32,52 and the tracer diffusion coefficient of the 15 residues oligomer in dilute solution at 300 K is 0.26 ± 0.09 nm2/ns.53 The comparison of these values with the lateral diffusion coefficient of I4 oligomers highlights an enhancement of PVA diffusivity at the interfaces with the lowest polymer surface concentration. For the oligomers of the other interface domains, the mean squared displacement is limited to values lower than p2 in the explored time interval, and it displays an irregular behavior. The dynamics of terminal segments can be ascribed to subdiffusive motions, described by the Rouse model with the power law MSD ∼ t1/2.54 The influence of the surface concentration on the polymer mobility is shown also by torsional dynamics. Table 2 reports the fraction of mobile dihedral angles and the average lifetime of the rotational state for oligomers of the different interface domains, calculated as reported in section 1.4 of the Supporting Information. Both parameters display the attenuation of mobility at increasing polymer concentrations. However, even at the lowest PVA surface concentration, the chain internal motions are slower at the interface as compared to the bulk solution. This feature can be inferred by the comparison between the lowest ⟨τDIHE⟩ value, obtained for the oligomers of the I4 system and equal to 2.1 ± 0.6 ns, and the average lifetime of the rotational state of the PVA 30-mer in highly dilute aqueous solution, approximately 0.6 ± 0.4 ns.48 The slowing of the torsional dynamics of the chains in the I4 system is consistent with the rigidity of hairpin conformations and elongated dimeric aggregates formed at the water−vacuum interface. It is noteworthy that the enhanced lateral diffusivity of I4 oligomers is not in contradiction with the attenuation of torsional dynamics. These results suggest that the two kinds of motions are uncoupled at very low PVA surface concentrations. 3.3. Water Dynamics. The mean squared displacement and diffusion coefficient were calculated for water molecules in the different domains of the I4, I12, and I16 systems. Water MSD(t) is shown in Figure S2 of the Supporting Information, and the water diffusion coefficients, normalized by the value obtained for the slab of pure water in the interface domain, are reported in Table 2. For all systems, water diffusivity in the interface is slower than in the internal domain (see Figure S2 of the Supporting Information) and the diffusion coefficient values follow the order D(I16) < D(I12) < D(I4) for each domain. A further parameter monitoring the solvent dynamics is the lifetime of the hydrogen bond (HB) between water molecules τw−w, obtained from the HB intermittent autocorrelation function. The increase of τw−w values at increasing number of oligomers enclosed in the domain, approximately from 7 to 16 ps (Table 2), can be ascribed to the more effective confinement of water molecules within polymer clusters. Figure 8 highlights the polymer-induced modification of water dynamical proper-

Figure 6. Average persistence length (red squares, left ordinate values), relative shape anisotropy (blue circles, left ordinate values), and asphericity (green triangles, right ordinate values) of oligomers as a function of PVA specific surface area.

These structural arrangements satisfy both the surfactant character of PVA and the polymer capability to form intraand interchain hydrogen bonds. Therefore, at the lowest surface concentration the water−vacuum interface promotes the formation of elongated, structurally ordered polymer aggregates, with a strongly inhomogeneous coverage of the available surface. Similar conformational features can be observed for the oligomers of the I12B domain, where the four chains form a stable 2-dimensional network on the interface surface (see Figure 2). In the interfaces with higher PVA concentrations, the oligomers adopt more folded conformations because of the formation of 3-dimensional clusters partially submerged in the aqueous phase. Some chains are characterized by near-zero values k2 and b and by a lower rigidity, apparent from the smaller p values that for certain oligomers correspond to only 2 or 3 repeating units. The presence of two conformational regimes can be observed by the behavior of the parameters in Figure 6, with a threshold value of specific surface area of about 1.6 m2/mg. Segmental mobility of chains was monitored by the mean squared displacement (MSD) of the terminal residues. Curves in Figure 7 are obtained from the average of MSD(t) over the ensemble of oligomers in each interface. The value of the

Figure 7. Time behavior of the mean squared displacement of the terminal PVA residues. (a) Interfaces I12B (green triangles), I16B (yellow circles), and system I4 (violet squares). (b) Interfaces I12A (red triangles) and I16A (blue circles). Horizontal dotted lines indicate the value of the square persistence length with the corresponding color. Horizontal gray full line in (a) indicates the value of the square contour length of the PVA 30-mer. G



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Table 2. Dynamical Properties of PVA and Water in the Interface Domainsa interface

percentage of mobile dihedral angles

I4A I4B I12A I12B I16A I16B

100 97 91 88 84 88

⟨τDIHE⟩ (ns) 2.1 2.8 3.6 3.6 4.5 3.5

± ± ± ± ± ±

0.6 0.4 0.5 0.4 0.8 0.8

D/Dslabb 0.78 0.81 0.56 0.67 0.49 0.52

± ± ± ± ± ±

0.04 0.06 0.03 0.04 0.02 0.06

τw−wc (ps) 7.2 7.7 13.1 10.3 15.7 9.6

± ± ± ± ± ±

0.4 0.4 0.8 0.9 0.6 0.5

τp−wd (ps) 19 20 82 38 200 38

± ± ± ± ± ±

3 2 3 7 30 7

a Time averages over the production run. Errors estimated using the blocking method. bRatio between water diffusion coefficient in the interface domain in the presence (D) and without (Dslab) PVA. cAverage lifetime of water−water hydrogen bonds. dAverage lifetime of PVA−water hydrogen bonds.

Altogether, these results highlight a polymer-induced slowing of water dynamics, as observed in hydrated hydrophilic polymer networks. However, the comparison with water diffusion coefficients and HB lifetimes obtained in PVA aqueous solution and hydrogels32−34,48 shows that the restraining effect on water mobility in the interfacial region is more marked than that in the bulk phase, contributing to an increase in the stability of the interface.

4. CONCLUSIONS The picture of water−vacuum interface in the presence of PVA, provided in this investigation, denotes how the balance between surface activity and aggregation tendency of PVA is crucial for the structural features of interfacial polymer layers. This balance is governed by the polymer surface concentration with a threshold value of about 14 μmol of residues/m2, which separates a regime of practically monolayer adsorption of elongated polymer assemblies and a regime of multilayer adsorption of highly hydrated polymer clusters partially submerged in the water phase. The structural consequence of this behavior is the presence of pores in the polymer layer, explaining the gas permeability of these interfaces and the reversibility of the dehydration−rehydration process of PVA microbubbles, with the restoring of a stable gas core.46 The PVA torsional mobility at the interface is significantly frustrated as compared to mobility in bulk aqueous solution. At the same time, the dynamics of interfacial water is strongly attenuated. These dynamical features concur to the stability of PVA interfacial layers, with an effect further increased in chemically cross-linked PVA surfaces, such as at the interface between gaseous core and hydrated shell of PVA microbubbles.17 A remarkable behavior is displayed by interfaces with very low PVA surface concentration, where oligomer chains can freely diffuse on the surface. Concurrently, the exchange of water molecules in the polymer hydration shell is slowed, as compared to the solvation dynamics in the PVA bulk solution. The information from this study offers elements to drive the formulation of PVA-based systems in which the air−water interface plays a role. Moreover, we hope that these results can inspire experimental activities for the characterization of the surface behavior of this polymer. The degree of polymerization of PVA in this work is the result of a compromise between the size limit of fully atomistic MD simulations and the choice to include more polymer chains per interface, with the aim of investigating intermolecular interactions. Simulations of polymer films containing PVA at a higher degree of polymerization are under study, using coarsegrained modeling approaches.

Figure 8. Dynamical properties of water in the interface domain as a function of PVA specific surface area. Diffusion coefficient (green circles) and water−water HB lifetime (red squares) are relative to values for slab of pure water. PVA−water HB lifetime (blue triangles) are relative to the value in bulk diluted PVA solution.

ties at the interface, by using as a reference the dynamic parameters of the slab of pure water. The ratios D/Dslab and τw−w,slab/τw−w, Dslab and τw−w,slab being the diffusion coefficient and hydrogen bond lifetime of water in the interfacial domain of the slab of pure water, respectively, are reported in Figure 8 as a function of the PVA specific surface area. The behavior of these ratios with the polymer concentration is very similar, and at the highest PVA specific surface areas, the D/Dslab and τw−w,slab/τw−w values are equal, within errors. These findings show that in the explored range of PVA specific surface area, the slowing of the solvent diffusive motion proportionally affects the time needed for the definitive departure of two HBforming water molecules. Hydration dynamics was explored by analyzing the average lifetime of PVA−water hydrogen bond τp−w in the different domains of the system (data in the last column of Table 2). τp−w values range from 20 to 200 ps, with a remarkable increase at increasing number of oligomers segregated at the interface. This behavior is attributable to the combined effect of the decreased PVA segmental dynamics and water confinement. The value of the ratio τp−w,∞/τp−w, where τp−w,∞ is the average lifetime of the polymer−water hydrogen bond for the PVA 30mer in highly dilute aqueous solution,48 is shown in Figure 8 as a function of the polymer specific surface area. It is noteworthy that the lifetime of this interaction increases by a factor of approximately two by going from infinite dilution to the interfaces hosting only two oligomers. This effect is probably due to the 2-dimensional constraint which limits polymer mobility and reduces the availability of water molecules to take part in the interaction. H



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ASSOCIATED CONTENT

S Supporting Information *

Interface preparation (section 1.1); systems composition (Table S1); total trajectory time of simulations and percent drift of RMSD in the production runs (Table S2); equilibration criteria and trajectory sampling (section 1.2); technical details on simulations (section 1.3); trajectory analysis procedures (section 1.4); references for Supporting Information (section 1.5); density profiles of single PVA oligomers (Figure S1); mean square displacement of water molecules in the different domains of the slabs (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +39 06 7259 4462. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the CINECA award under the ISCRA initiative for the availability of high-performance computing resources and support.

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Influence of Surface Concentration on Poly(vinyl alcohol) Behavior at

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