Molecular Structure and Work of Adhesion of Poly(n-butyl acrylate

Article pubs.acs.org/Macromolecules

Molecular Structure and Work of Adhesion of Poly(n‑butyl acrylate) and Poly(n‑butyl acrylate-co-acrylic acid) on α‑Quartz, α‑Ferric Oxide, and α‑Ferrite from Detailed Molecular Dynamics Simulations Alexandros Anastassiou†,‡,⊥ and Vlasis G. Mavrantzas*,†,⊥,§ †

Department of Chemical Engineering, University of Patras, GR 26504, Patras, Greece FORTH-ICE/HT, GR 26504, Patras, Greece ‡ Department of Aerospace Engineering and Mechanics, The University of Minnesota, Minneapolis, Minnesota 55455, United States § Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, CH-8093 Zürich, Switzerland ⊥

ABSTRACT: Molecular dynamics simulations are performed for two model pressure-sensitive adhesive (PSA) materials, atactic poly(n-butyl acrylate) [poly(n-BA)] and atactic poly(nbutyl acrylate-co-acrylic acid) [poly(n-BA-co-AA)] at a very low concentration in acrylic acid (one acrylic acid monomer per fifty butyl acrylate monomers plus three acrylic acids at each one of the two chain ends) in the bulk and confined between three crystalline substrates, silica (SiO2) represented as α-quartz, α-ferric oxide (α-Fe2O3), and metallic α-ferrite (α-Fe), over a range of temperatures. The simulations are carried out with the accurate, all-atom Dreiding force-field and provide important information for the distribution of local mass density of the two polymers at the three crystalline substrates, and their adsorption in conformations that lead to the formation of loop, train, and tail structures. By analyzing potential energy interactions between the two polymers and each one of the three substrates through their van der Waals contact area or by computing the diagonal elements of the local stress tensor in the vicinity of the substrate, we have calculated the effect of the type of substrate on the work of adhesion of the two polymers. Our calculations reveal a considerably stronger adsorption on α-quartz and α-ferric oxide compared to α-ferrite, which we attribute to strong attractive oxygen interactions of the two polymers with the oxygen atoms of SiO2 and Fe2O3. Detailed calculations of the local number density distribution of individual atomic species above the three substrates, of the local variation of the bond order parameter for skeletal and side group bonds or chords, of the distribution of dihedral angles, and of the histograms of chain ends support that the two PSAs adsorb on the three substrates with both their skeletal and pendant C−C and C−O groups lying practically parallel to the surface and in such a way that the CO bond of the pendant butyl acrylate groups points toward the surface. The detailed MD simulations indicate that adding a small amount (7.1% wt. here) of acrylic acid to poly(n-BA) significantly improves its wetting characteristics on oxygen-containing substrates. This is in full support of the findings of Kisin et al. [Chem. Mater. 2007, 19, 903−907] that introducing oxygen atoms to a metallic surface or to polymer molecules increases considerably the work of adhesion.

1. INTRODUCTION

physicochemical properties of acrylic PSAs can be tuned and optimized by controlling a number of molecular-level parameters such as nature, composition and architecture of chains, particle−particle degree of interentanglement, latex particle size and particle size distribution, concentration, molecular weight between cross-links, and degree of cross-linking. This is typically achieved by using complex formulations based on random

High-alkyl acrylates such as poly(n-butyl acrylate) and poly(2-ethylhexyl acrylate) constitute key materials in the formulation of pressure-sensitive adhesives (PSAs) nowadays for many reasons: they can be produced with environmentally friendly processes (such as emulsion polymerization in water), they offer excellent control on the glass transition temperature, they are characterized by superior stability, greater resistance to oxidation and low plateau modulus, and they are stable over a wide range of temperatures.1−9 Despite their rather complex and not well-defined structure, the rheological and other © 2015 American Chemical Society

Received: July 4, 2015 Revised: October 18, 2015 Published: November 12, 2015 8262

DOI: 10.1021/acs.macromol.5b01469 Macromolecules 2015, 48, 8262−8284

Article

Macromolecules copolymers of a long-chain acrylic (e.g., n-butyl acrylate, n-BA) with a short side-chain acrylic (such as methyl acrylate) and acrylic acid (AA). Acrylic acid is a highly polar monomer whose incorporation in the adhesive can modify both the interfacial and bulk properties of the final material.4−7 For practical use and in order to meet the needs of the market, the final adhesive material must possess an overall balanced combination of tack, peel strength and shear resistance properties. From a thermodynamic point of view, the quantity that provides a quantitative measure of the strength of attachment at the interface is the work of adhesion, Wadh. Experimental studies with the probe tack test have shown that when the soft adhesive undergoes large nonlinear deformations, its actual detachment from the substrate occurs through a very complicated and inhomogeneous process involving the formation, elongation, and ultimate breakage of internal cavities leading to thin and highly elastic filaments bridging the adhesive and the substrate.1−4 In the characteristic force−displacement curve measured during the debonding process of a PSA from its adherent, the first peak in the stress is due to a process of cavity growth from the interface with the probe, mostly controlled by the elastic modulus of the adhesive. That is, failure is initiated by the nucleation of cavities at or near the adhesive-substrate interface. Lindner et al.4 mention that the maximum stress should not depend strongly on the experimental conditions provided that a good bonding is obtained between the substrate and the PSA; i.e., it should be relatively independent of the molecular weight and the presence of acrylic acid. Experimentally, one measures the integral (area) below the stress−strain curve multiplied by the thickness of the adhesive (as a result, for thin confined layers, Wadh should depend on film thickness as well), which corresponds to the total amount of the mechanical energy needed for adhesive film bond failure. This provides a measure of the adhesive strength (i.e., of the work of adhesion) but its value contains much more than the thermodynamic work, since deformation is accompanied by cavitation and fibrillation. It is also reported4 that adding acrylic acid increases both the glass transition temperature (the adhesive becomes stiffer and more dissipative) and the work of adhesion at room temperature. Given the importance of adhesive-substrate interactions, it would be highly desirable to have a means of predicting the work of adhesion of a PSA on a given substrate and addressing fundamental issues related with chain organization and structure at the PSA/substrate, if possible directly from the chemical composition of the material and the chemical structure of the substrate. With the help of detailed atomistic simulations, in particular, one could quantify differences in the enthalpic interactions within the polymer phase and between the polymer and the substrate, also to detect perturbations in the conformational and structural properties of polymer chains at the interface with the solid surface. The development of such a simulation tool and its application to PSA-substrate systems of practical relevance are the main objectives of this work. Our computer simulation study allows us to understand and predict both microscopic structural features at the polymer-solid surface interface (such as density distribution and conformation of adsorbed segments) and macroscopic thermodynamic properties (such as the distribution of stresses in the interfacial area and the work of adhesion). From the design point of view, and with the availability of more powerful and faster computational resources, such a study offers a way of predicting and selecting the best substrate(s) for a given adhesive, hence it provides an attractive alternative to direct experimental measurements in

assessing the role of molecular features on the tackiness of acrylic polymers. The paper is organized as follows. Section 2 discusses the molecular model used in the atomistic molecular dynamics (MD) simulations. In section 3 we outline the simulated systems and discuss the key points of our simulation methodology. Results from the atomistic MD simulations are presented and discussed in section 4; they refer to local mass density, chain organization and conformation of adsorbed segments, and work of adhesion of the two PSA samples on the three different substrates. The paper concludes with section 5 discussing the major findings of the present work and future plans.

2. MOLECULAR MODEL Two model acrylic systems were studied in this work: the homopolymer poly(n-butyl acrylate) denoted here as poly(n-BA) and a random copolymer of butyl acrylate (50 monomers) and acrylic acid (7 monomers) denoted here as poly(n-BA-co-AA). Both materials were assumed to be atactic. We chose to study their adhesion on three substrates of industrial and practical relevance, crystalline silica represented by α-quartz (SiO2), α-ferric oxide (α-Fe2O3), and α-ferrite (α-Fe), which are characterized by different interaction strengths. For example, Kisin et al.10 who studied the work of adhesion of a copper(acrylonitrile-butadiene-styrene) interface with MD simulations found that introducing oxygen atoms in the polymer poly(styrene-co-acrylonitrile) or the copper metallic surface (copper oxide) significantly increased the work of adhesion. Of course, our results for α-Fe will not be useful (since pure Fe interfaces do not exist), but we have included it in our study in order to directly check the argument by Kisin et al.10 that introducing oxygen atoms to metallic surfaces improves adhesion. To represent as closely as possible the corresponding real systems, an all-atom description was used for the materials; this made possible the quantitative prediction of the relevant interfacial thermodynamic properties and their comparison against experiment. The chemical structure and repeat units of the two acrylics are illustrated in Figure 1. In the figure, n denotes the number of butyl acrylate monomers in poly(n-BA), n1 and n2 the number of butyl acrylate monomers in poly(n-BA-co-AA), and m and p the number of acrylic acid monomers in poly(n-BA-coAA). For the systems simulated in this work, n = 50, n1 = 25, n2 = 25, m = 3, and p = 1. For the poly(n-BA-co-AA) system, in particular, these numbers imply that each chain contains three AA blocks, one in the middle of the chain and two at the two ends. Each poly(n-BA) chain had the structure shown at the top panel of Figure 1 with n = 50 butyl acrylate repeat units while each poly(n-BA-co-AA) chain had the structure shown at the bottom panel of Figure 1 with n1 = n2 = 25, m = 3, and p = 1. We further note that poly(n-BA-co-AA) chains were terminated with sulfate ions at their ends; then, to maintain electroneutrality (see Figure 1) in the simulations with this system, two sodium ions had to be added to the simulation cell. With the above choices, the composition of the copolymer in AA was 7.1% wt. The molecular model employed is based on an implementation of the Dreiding all-atom force field11 potential functions to describe bonded and nonbonded interactions between atomistic units. The potential energy expression used in Dreiding is Etotal = Estretching + E bending + Edihedral + Eimproper + E LJ + EC (1) 8263


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Figure 1. Schematic representation of the repeat chemical units of poly(n-BA) and poly(n-BA-co-AA).

polymers; these are described by a harmonic potential function of the form

i.e., it consists of six types of terms corresponding to contributions due to bond length stretching, bond angle bending, torsional angles, improper angles, Lennard-Jones, and Coulomb interactions. Parts a and b of Figure 2 show the atom types to the interaction sites of which values of the force field parameters should be assigned; the first character in each atom type refers to the corresponding element. Contributions due to bond length stretching are governed by a harmonic potential function of the form: Estretching (l) =

1 kstr(l − l0)2 2

E improper(ξ) =

1 k bend(θ − θ0)2 2

⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ E LJ(r ) = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎝r⎠ ⎦ ⎣⎝ r ⎠

(2)

(6)

We further consider a Coulomb potential of the form qiqj EC(r ) = 4πε0r

(7)

to describe electrostatic interactions associated with partial atomic charges (q); the latter were calculated using the Gasteiger method12 of partial equalization of orbital electronegativity through the MAPS simulation platform of Scienomics13 and their values (in units of e−) for the various atom types considered in this work are reported in parts c and d of Figure 2. We further note that 1−4 pairwise Lennard-Jones and Coulomb interactions in the estimation of the system’s potential energy are taken into account with a factor of 1. The use of the Dreiding force field was motivated by its success in providing accurate predictions of the structural, thermodynamic and mainly mechanical properties of another polar acrylic polymer, syndiotactic poly(methyl-methacrylate) (sPMMA), including the mechanical properties of its nanocomposites with functionalized graphene sheets at small

(3)

with kbend the corresponding force constant. Values of the parameters kbend and θ0 for all types of bond angles encountered in the simulated systems are reported in Table 1. Contributions due to rotation of nonterminal bonds along the backbone of the two polymers are described by a potential function that depends on the corresponding dihedral angle φ and has the form Edihedral = K[1 + cos(Nφ − d)]

(5)

with values of the parameters kξ and ξ0 as reported in Table 1. Nonbonded interactions (intermolecular and intramolecular for all atom pairs separated by more than three bonds along each chain of the two polymers) are described by a 12−6 LennardJones (LJ) potential of the form (see Table 1)

where kstr represents the stiffness of the harmonic spring and l0 the value of the bond length at equilibrium; their values for all types of bonds appearing in the systems modeled here are summarized in Table 1. Contributions due to bond-angle bending are described by a harmonic potential expression around the equilibrium value θ0 E bending (θ ) =

1 kξ(ξ − ξ0)2 2

(4)

with values for the set of coefficients K, N, and d as reported in Table 1. We also consider contributions due to improper dihedral interactions needed to maintain the tacticity and planarity of four atoms in each monomer group along the two 8264


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The following eight model systems of the homopolymer and copolymer PSAs were simulated: 1 a 27-chain poly(n-BA) system in the bulk 2 a 27-chain poly(n-BA-co-AA) system in the bulk 3 a 27-chain poly(n-BA) system confined between two α-quartz substrates 4 a 27-chain poly(n-BA-co-AA) system confined between two α-quartz substrates 5 a 27-chain poly(n-BA) system confined between two α-ferric oxide substrates 6 a 27-chain poly(n-BA-co-AA) system confined between two α-ferric oxide substrates 7 a 27-chain poly(n-BA) system confined between two αferrite substrates, and 8 a 27-chain poly(n-BA-co-AA) system confined between two α-ferrite substrates. For the simulation of the PSA films, α-quartz, α-ferric oxide, and α-ferrite substrates were placed at the bottom of the polymer cell (below the xy plane) and periodic boundary conditions were again applied along all three directions (x, y, z). For the α-quartz substrate, we assumed a rhombohedral crystal symmetry; the corresponding model substrate system used in the simulations consisted of 8100 atoms in a rectangular parallelepiped cell with dimensions Lx = 81.075 Å, Ly = 73.7 Å, and Lα‑quartz ∼ 13 Å. For the α-ferric oxide, we assumed a z trigonal crystal structure with the substrate structure used in the simulations consisting of 8400 atoms placed in a rectangular parallelepiped cell with dimensions Lx = 68.86 Å, Ly = 70.532 Å, oxide ∼ 16 Å. For the α-ferrite substrate, a bodyand Lα‑ferric z centered cubic crystal structure was assumed; here, the corresponding substrate structure considered in the simulations consisted of 5760 atoms placed in a rectangular parallelepiped cell with dimensions Lx = Ly = 68.79 Å and Lα‑ferrite ∼ 14 Å. z The total number of polymer chains (=27 in all cases) was chosen so as to correspond to a large enough thickness so that the middle region of the film is structurally indistinguishable from that of bulk polymer. This was checked by running independent MD simulations with the two acrylic polymers using cubic boxes subject to periodic boundary conditions in all three space directions. We call these “bulk” simulations. These were performed at a high enough temperature (T = 700 K) and pressure P = 1 atm and, then, selected (about 8) configurations from these simulations were cooled down to lower temperatures (T = 500, 400, 300 K) where they were left to relax even further until their density reached a constant value. The average density from these 8 structures at each temperature was then computed and its value is reported in Table 2. In Table 2 we also report an experimental15 value for the density of poly(n-BA) at T = 300 K, which is equal to 1.040 g cm−3. The predicted value from the MD simulations (1.021 ± 0.001 g cm−3) deviates from this by only 1.8%. Since under room conditions the two acrylic polymers under examination are in the glassy state, for the simulation of their bulk amorphous cells we followed an approach that consisted of the following steps: i Use of the “Amorphous Builder” module of the MAPs software package to create initial configurations for the two polymers characterized by low density values to avoid unrealistic packing of atoms ii Static structure optimization using a molecular mechanics (MM) algorithm16 to remove significant intra- and intermolecular overlaps

Figure 2. Atom type notation used to represent different atoms in (a) the butyl acrylate repeat unit and (b) the acrylic acid repeat unit and sulfate ion. The first character in each atom type indicates the corresponding element. The corresponding partial charges (in units of e−) on each atom in the two repeat units and the sulfate ion are reported in parts c and d.

loadings.14 We note, in particular, that structural properties of sPMMA modeled with Dreiding came out to be identical to those obtained with another popular force field for polymer simulations, OPLS.

3. SYSTEMS STUDIED AND SIMULATION METHODOLOGY Using the molecular model described in the previous section, detailed atomistic MD simulations were performed with model PSA and PSA/substrate samples in an xyz Cartesian coordinate system. Bulk systems were simulated using cubic simulation cells with equal edge lengths along the x, y, and z directions of the coordinate system. Interfacial systems, on the other hand, were simulated using orthorhombic simulation cells with different edge lengths Lx, Ly and Lz along the x, y and z directions. More specifically, Lx and Ly were constrained and held fixed in the course of the simulations to values that corresponded to integer multipliers of the corresponding dimensions of the α-quartz, α-ferric oxide and α-ferrite unit cells along x and y, respectively, while Lz was assigned a large enough value so that periodic boundary conditions could be applied along all three directions x, y and z of the simulation cell, implying the simulation of a polymer film that is simultaneously confined between two identical substrates. 8265


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Macromolecules iii Execution of long MD simulation runs in the NPT ensemble initially at a very high temperature (close to 700 K) where equilibration is much easier to achieve iv Selection of a few (approximately 8) independent and fully relaxed atomistic configurations from this high temperature

simulation which were gradually cooled down to the temperature of interest (300 K) using MD v Thermal equilibration of the cooled atomistic configurations using the MD technique in the isothermal−isobaric (NPT) statistical ensemble

Table 1. Dreiding Force-Field Parameters According to the Potential Energy Functions of eq 1

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P = 1 atm using a Nosé−Hoover thermostat-barostat17,18 to control temperature and pressure with corresponding relaxation times equal to 10 and 100 fs, respectively. The equations of motion were integrated using the velocity Verlet integrator with a time step equal to 1 fs. Electrostatic interactions were computed using the PPPM (particle−particle particle−mesh) method with a real space cutoff of 12 Å. For the Lennard-Jones interactions, the cutoff radius was set equal to 12 Å. All MD runs were carried out with the LAMMPS19 (large-scale atomic/ molecular massively parallel simulator) code. Representative fully equilibrated configurations from the simulations with the poly(n-BA-co-AA)/α-quartz, poly(n-BA-co-AA)/ α-ferrite, and poly(n-BA-co-AA)/α-ferric oxide interfacial systems at T = 300 K are reported in Figure 3.

vi Calculation of the desired system properties by averaging over all selected configurations in step iv. For the corresponding interfacial simulations, we also used bulk polymer structures that had been thoroughly preequilibrated at the higher temperature (700 K), and which were subsequently brought into contact with the α-quartz, α-ferric oxide, and α-ferrite crystalline phases. Again, use was made of periodic boundary conditions in all three directions of the coordinate system. Through the interaction of the polymeric film with the periodic image of the substrate at the top of the simulation cell, such a design implies the simulation of a polymeric film that is simultaneously confined between two chemically identical substrates. In total, eight interfacial simulations were performed for each of the poly(n-BA)/α-quartz, poly(n-BA)/α-ferric oxide, poly(n-BA)/α-ferrite, poly(n-BA-co-AA)/α-quartz, poly(n-BAco-AA)/α-ferric oxide and poly(n-BA-co-AA)/α-ferrite model systems. The MD simulations at all temperatures (the highest one at 700 K and all intermediate ones down to and including 300 K) were carried out in the NPT statistical ensemble at pressure

4. RESULTS AND DISCUSSION Local Density Profiles. All structural and conformational properties of the two PSA systems adjacent to the three solid substrates (α-quartz, α-ferric oxide and α-ferrite) were analyzed by dividing the space above the solid surface into bins, each of width equal to 0.1 Å, separated by planes parallel to the 8267


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Table 2. MD Predictions for the Density of the Bulk (Unconstrained) Acrylic PSA Systems Studied in This Work as a Function of Temperaturea ρ (g cm−3) poly(n-BA) temperature (K) 600 500 400 300 a b

poly(n-BA-co-AA)

current work

experimental values

± ± ± ±

− − − 1.040b

0.799 0.878 0.941 1.021

0.004 0.003 0.003 0.001

current work

experimental values

± ± ± ±

− − − −

0.863 0.938 1.005 1.076

0.004 0.003 0.002 0.001

The results have been obtained by averaging over a large number (approximately 8) of equilibrated structures at a given temperature (P = 1 atm). Reference 15

Figure 3. Typical atomistic snapshots in wrapped coordinates of the 27-chain poly(n-BA-co-AA) system confined between two α-quartz (a), two α-ferrite (b), and two α-ferric oxide (c) substrates, from the NPT MD simulations of the present work [T = 300 K, P = 1 atm].

substrate surface. Averages of the characteristic structural quantities were then computed within each bin.20−23 To further decrease statistical noise, estimates were averaged over the eight microstructures obtained according to the procedure outlined in the previous section. This number (= 8) of microstates was found to be sufficient to provide adequate predictions of almost all properties of interest here (as could be checked, e.g., by looking at the symmetry of the resulting profiles with respect to the film midplane). Figure 4 displays the MD predictions for the mass density distribution across the two PSA films (poly(n-BA) and poly(nBA-co-AA)), confined between the three different substrates (α-quartz, α-ferric oxide and α-ferrite), at T = 300 K. For both polymers, the local mass density profiles in the interfacial region exhibit several peaks, the highest one being the one right next to the substrate face; this appears at a distance roughly equal to the sum of the van der Waals radii of polymer and substrate atoms. In the middle regions of the two films, the total

density attains practically a constant value, which is found to be identical to that of the unconstrained PSA systems at the same temperature and pressure conditions, shown by the dashed line (see also Table 2). The data indicate that the copolymer material, poly(n-BA-co-AA), is denser than the corresponding homopolymer, poly(n-BA), at all temperatures studied. This is a direct manifestation of the hydrogen bonds that form between the hydroxyl groups of acrylic acid monomers in the copolymer, leading to a denser molecular packing, thus also to a higher density structure than in the pure poly(n-BA) system where no hydrogen bonds can form. We also note that the characteristic peaks in the local mass density profile above the α-quartz and α-ferric oxide substrates (see Figure 4e,f) are significantly stronger than in the case of α-ferrite. From the graphs shown in Figure 4, the following two additional conclusions can be drawn: (a) based on perturbations in the total density profile from its bulk value, the thickness of the interfacial region in the three films is approximately equal 8268


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Figure 4. Variation of the local polymer mass density in the six interfacial systems, as predicted by the present MD simulations at T = 300 K and P = 1 atm. The black dashed line indicates the bulk density at the same temperature and pressure conditions as obtained from separate MD simulations using bulk model structures of the two acrylic polymers subject to periodic boundary conditions along all three space directions.

for this is the reduced efficiency of the MD technique in equilibrating samples of such very complicated polymers as those of interest here at this relatively low temperature; overall, however, and as already mentioned above, the average density values around which the local mass density seems to fluctuate in the middle of the three films are fully consistent with those reported in Table 2 from the independent MD simulations using bulk samples of the two polymers. With an eye on the correlation of local structure with the adhesive properties of the two PSA polymers on the three substrates (it will be discussed later in the paper), Figure 5 displays the distribution of the number density of the individual C, H and O atoms across the simulated films (due to their scarcity, the corresponding distribution of S atoms was left out). This information has been accumulated in 0.5-Å-thick bins along the z axis. According to Figure 5, the most systematic differences are observed in the case of carbon atoms (see parts a and b of Figure 5) which are seen to adsorb most strongly on

to 13 Å (this is the value we get from Figure 4 if we subtract from the value of z where density fluctuations subside in each film the corresponding substrate thicknesses reported in Section 3), and (b) acrylic chains adsorb considerably stronger onto α-quartz and α-ferric oxide than onto α-ferrite, as evidenced by the higher intensities of the local mass density peaks. These sharp peaks indicate a well-ordered atomic structure next to α-quartz and α-ferric oxide due to the very attractive (electrostatic and van der Waals) interactions developing primarily between atoms of the acrylic polymer and atoms of the two oxides. There exist partial charges on α-quartz and α-ferric oxide mediating strong Coulomb interactions with all polymer atoms (carbon, hydrogen, oxygen, and sulfur atoms); in addition, the ε Lennard-Jones parameter of a silicon (Si) atom is greater than that of iron (Fe) (see Table 1). The mass density profiles shown in Figure 4 for T = 300 K are slightly noisy in the middle region of the films. The reason 8269


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Figure 5. Variation of the number density of carbon, hydrogen and oxygen atoms with distance from the three substrates. To emphasize differences among the various systems close to the three surfaces, the graphs are shown up to distances only 15 Å from each substrate.

strongly on α-quartz than on the other two surfaces but they differ in that they show a higher preference for the α-ferrite surface than for the α-ferric oxide one. Conformational Characteristics. Since local orientational tendencies of bonds are also of interest in interfacial systems, we have calculated the average second-rank bond order parameter P2 = (3/2)⟨cos2 θ⟩ − (1/2) where θ is the angle formed between a skeletal or pendant bond and the z coordinate axis (i.e., the axis normal to the surface), and its variation with distance above the three substrates. As discussed in refs 20−23, this bond order parameter assumes values in the interval [-0.5, 1.0] with the limiting values of −0.5, 0.00, and 1.0 corresponding to bonds characterized by perfectly parallel, completely random, and perfectly normal orientation, respectively, relative to the surface. Given the anticipated highly anisotropic nature of the two PSAs at the three substrates, we have examined the variation of P2 separately for skeletal and pendant bonds or chords, as a function of distance from each substrate by dividing the space above it in 0.5-Å-thick bins and assigning bonds to the bins according to the distance of their midpoint from the substrate. In Figure 6 we show our notation for the different atoms that were considered in this work for the calculation of the P2 order parameter. To study the relative

α-quartz than on α-ferric oxide, and more strongly on α-ferric oxide than on α-ferrite. Judging then from the closest distance that carbon atoms approach the three substrates, the relative order of adsorption is α-quartz > α-ferric oxide > α-ferrite. The same conclusion is reached if we compare the maximum local number density of carbon atoms in the vicinity of the three crystalline surfaces. This is much higher in the case of α-quartz and α-ferric oxide than in the case of α-ferrite. It is also seen that these differences prevail up to only about 10 Å from each substrate; beyond this distance, the profiles become practically homogeneous and identical, i.e., representative of the unperturbed polymer under the same T and P conditions. A similar situation is observed for oxygen atoms (see parts c and d of Figure 5): these adsorb strongly on α-quartz, less strongly on α-ferric oxide, and even less strongly on α-ferrite, i.e., the relative order of adsorption is again α-quartz > α-ferric oxide > α-ferrite. Overall, however, the profiles of the local number density of oxygen atoms are smoother and show fewer differences above the three different substrates than the corresponding profiles of carbon atoms. The situation is somewhat different in the case of hydrogen atoms. Here the relative order for adsorption is α-quartz > α-ferrite > α-ferric oxide. Indeed, and similar to carbons and oxygens, hydrogens are observed to adsorb more 8270


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chains indicate a rather strong adsorption not only of chain skeletons but also of side groups, especially on α-quartz and α-ferric oxide. To confirm this, we calculated the spatial variation of the average end-to-end distance of the butyl acrylate side groups, ⟨R2b⟩, above the three substrates and in the bulk (at T = 300 K), and the results are shown in Figure 10. In all cases, side chains attain longer end-to-end distances right above the three substrates, a situation which is more pronounced in the case of the copolymer above α-ferric oxide. It is also seen that the average size of a BA side chain is 42.5 Å (T = 300 K). Our results suggest that poly(n-BA-co-AA) chains adopt somewhat elongated conformations above the three crystalline surfaces (especially above α-ferric oxide) compared to their bulk conformation. This is consistent with the picture that PSA chains develop preferentially parallel on the surface of the three substrates with their side groups also lying parallel to the surface and in such a way so as to maximize oxygen interactions with surface atoms. On the basis of the examination of the local mass density distribution, of the bond orientational profiles discussed in Figures 4, 5, and 7−9, and of the average size of side chains discussed in Figure 10, it appears that anisotropic effects above all three substrates are confined to approximately 13 Å. Motivated by this, we compared next the distribution of the C−C−C−C bond torsion angle in the interfacial zone (the one that extends up to 13 Å inside the film from the surface of each substrate) to that in the bulk region of the film where surface effects presumably have subsided, based on the position of the bond midpoints. Representative results from these computations are shown in Figure 11. In the bulk, the corresponding distributions were found to be identical to those obtained separately from the independent bulk simulations with the two polymers. We see that in the interfacial zones, there is a slight enhancement of trans states accompanied by a small (but non-negligible) depletion of gauche states as chains prefer to lie parallel to the solid surfaces. This result is opposite to the findings of Mansfield−Theodorou21 for the structure of glassy atactic polypropylene on the basal plane of crystalline graphite, according to which adsorption decreases the population of dihedral angles in trans states. Of course, Mansfield−Theodorou21 dealt with a polymer with a relatively short pendant group, while in our study we deal with polymers bearing rather long side groups (especially in the case of poly(n-BA-co-AA)), implying a more delicate balance between energetic and entropic interactions and polymer conformations. But clearly the most important difference is in the degree of adsorption energy which is significantly higher in the case of the surfaces studied here (graphite is rather hydrophobic while the oxides are rather hydrophilic), and this seems to promote the formation of alltrans arrangements. In Figures 12 and 13, we show histograms for the distribution of free ends of the two PSAs at the three interfaces where we further distinguish between main chain ends and side group ends. For poly(n-BA), these have been computed according to the distance (from the substrate) of the head and tail carbon atoms of the skeletal backbone and of the carbon atom at the end of each pendant group, respectively. For poly(n-BA-co-AA), the corresponding histograms have been based on the distance of the two sulfur atoms at the two ends of the main chain backbone and of the carbon atom at the end of each side chain, respectively. The plots are symmetric with respect to the mid plane of the films, which indicates sufficient averaging over the eight independent microstructures discussed in section 3. Our results seem to be in support of an enhancement in the

Figure 6. Atom notation used in the calculations of the bond order parameter P2.

orientation of polymer backbones we computed the P2 bond order parameter for chords CB1···CB1 and CB2···CB2 connecting successive skeletal atoms CB1 and CB2 along the chain. For the corresponding analysis of side groups, we calculated the P2 order parameter for all successive bonds along a butyl acrylate chain, namely C1OD, C1−OS, OS−C2, C2−C3, C3−C4, and C4−C5 in Figure 6. Typical bond orientation profiles obtained from these calculations are shown in Figures 7−9. Figure 7 shows that P2 attains slightly positive values for chords CB1···CB1 and CB2···CB2 exactly at the three surfaces but moving a little further inside the films, its values become strongly negative. Even further (i.e., in the middle region of the films) P2 becomes zero, exactly as we would have anticipated for a completely random distribution of orientations. Closer examination showed that the slightly positive values right at the surface of the three substrates are due to chords located at the ends of the chains, which tend to adsorb on the three substrates by slightly bending toward the corresponding surface. The deep negative values, on the other hand, of P2 slightly further inside the films are due to the majority of CB1···CB1 and CB2···CB2 chords along the main backbone of chains in the films that tend to develop considerable orientation parallel to the solid surface. This tendency is stronger at the α-quartz and α-ferric oxide surfaces than at the α-ferrite surface. That skeletal bonds orient parallel to the surface has been reported in the past by Mansfield−Theodorou21 and Daoulas et al.22 in their studies of adsorbed atactic polypropylene and linear polyethylene, respectively, on the basal graphite plane. The situation is different for ODC1 bonds (see blue curves in Figure 8) for which we observe very high positive values in the vicinity of all three substrates, indicative of a strong preference for an orientation that is almost normal to the corresponding solid phase. As we will see below, this is due to the strong interaction of oxygen atoms with the three substrates, especially with the oxygen-containing ones (α-quartz and α-ferric oxide). The rest of the bonds of the side butyl acrylate groups, however, tend to orient parallel to the surface above all substrates. Overall, and as confirmed by the large negative values of the P2 bond order parameter referring to the vector OD···C5 connecting the first and last atom in the side chains (see Figure 9), butyl acrylate side groups tend to orient parallel to the surface above all three solid substrates. The strong positive values of the P2 bond order parameter for ODC1 bonds right at the surface of the three solid phases and the overall parallel arrangement of the side (butyl acrylate) 8271


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Figure 7. Variation of the P2 bond order parameter referring to CB1···CB1 and CB2···CB2 chords along the main chain backbone with distance from the substrate for all six interfacial systems studied here.

concentration of chain ends next to the three surfaces but this should be taken with caution since the histograms are not conclusive. The preference of chain ends for the solid surface had also been observed in the computational studies of Mansfield−Theodorou21 who argued that chain heads and tails should be expected to concentrate preferentially near a solid surface since they experience a less entropic cost than middle segments. The physical picture that emerges from all the above studies (the analysis of the bond order parameter, of the mass density distributions of atomic species, of the distribution of dihedral angles and of the histograms of chain ends) is that the two PSAs adsorb strongly on the three substrates, especially on α-quartz and α-ferric oxide, with both their skeletal and pendant C−C and C−O groups lying practically parallel to the surface and in such a way that the CO bond of the pendant butyl acrylate groups points toward the surface. Such a picture is explicitly supported by the graphs shown in parts a−f of

Figure 14 displaying atomistic configurations of selected chains from the simulations with the two PSAs adsorbed on the three substrates (both side and normal-to-the substrate views are shown). The graphs show that poly(n-BA) and poly(n-BA-coAA) chains arrange themselves above the three surfaces so that their OD atoms come as closer as possible to the three substrates in order to maximize oxygen interactions with surface atoms. This is more pronounced in the case of the two oxygencontaining substrates (α-SiO2 and α-Fe2O3) where in addition to O−Si and O−Fe interactions, strong O−O attractions develop which can explain the preferential adsorption of the two PSAs on these two surfaces compared to α-ferrite. Additional confirmation for this comes from the plots of Figure 15 showing the variation of the number density of carbon atoms belonging to chain skeletons (noted as CB1 and CB2 in Figure 6) and of carbon and oxygen atoms belonging to butyl acrylate side groups (noted as OD, C1 and OS in Figure 6) above the three substrates. In all cases, it is the OD atoms that are observed 8272


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Figure 8. Variation of the P2 bond order parameter referring to ODC1, C1−OS, OS−C2, C2−C3, C3−C4, and C4−C5 bonds along the butyl acrylate side groups with distance from the substrate for all six interfacial systems studied here.

sequences that are in direct contact with the surface along their entire path; they are defined as successive C−C bonds whose centers lie inside the adsorbed layer, i.e., at a distance less than 6 Å from the solid surface plane. Tails are segments at the ends of a polymer chain with only one side adsorbed on the substrate plane; they are defined as sequences of C−C bonds terminated at one side by a nonadsorbed chain end and at the other side by an atom connected to a train. Loops are segments along the polymer chain with both of their ends adsorbed on the surface; they are defined as sequences of C−C bonds connecting two trains, with all of their intermediate centers, however, outside the adsorbed layer. The length of a train, tail or loop conformation is defined as the number of successive skeletal bonds forming a train, a tail or a loop. We monitored the instantaneous values of all train, tail, and loop conformations in the course of the MD simulations with the six interfacial systems and we calculated the average value of their square length l2. We also computed the

to come closest to the substrate, supporting the tendency of ODC1 bonds to point toward the corresponding surface. Adsorbed Chain Segment Analysis. Our interest in this section is in the way adsorbed polymer chain segments are organized in the vicinity of the three substrates (α-quartz, α-ferric oxide, and α-ferrite). Motivated by similar studies in the literature on the adsorption of polymers from solution,24−26 we looked for adsorbed polymer configurations on the substrates that can be categorized in terms of trains, loops and tails (see Figure 16). First, we note that a polymer chain is defined as adsorbed if it has at least one adsorbed skeletal atom that lies at a distance less than approximately 6 Å from the adsorbing surface plane; 6 Å is the distance separating the first two stronger peaks in the local mass density profiles in Figure 4, and is considered to define the boundaries of the first adsorption layer. Next, we consider that an adsorbed polymer molecule can exist (in general) in three different conformations: trains, tails, and loops.23−26 Trains are 8273


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Figure 9. Variation of the P2 bond order parameter referring to the vector OD···C5 connecting atoms OD and C5 in the butyl acrylate side groups with distance from the substrate for all six interfacial systems studied here.

obtained from the present MD simulations can be used in combination with a recently proposed wall-slip law28 to formulate suitable boundary conditions for the shear deformation of adsorbed polymers melts. Representative results for the surface number density ρ, square size l2 and characteristic correlation or relaxation time trelax for trains, loops, and tails are listed in Table 3. According to the data in Table 3, the size of train and loop conformations (counted together) is larger on α-quartz and α-ferric oxide than on α-ferrite, indicating that longer (overall) chain segments in the two polymer films are in actual contact with α-quartz and α-ferric oxide than with α-ferrite. Tails in all six systems, on the other hand, have practically the same average length. Another observation is that the correlation time trelax of adsorbed chain segments on α-quartz and α-ferric oxide is considerably higher than on α-ferrite, which provides further indication that the adhesive interactions developing between the two polymers and α-quartz or α-ferric oxide are stronger than with α-ferrite.

time autocorrelation function for the unit vector u directed along the end-to-end vector R of an adsorbed train, loop or tail segment, according to Φ(t ) = ⟨u(t ) ·u(0)⟩ =

⟨R(t ) ·R(0)⟩ ⟨R2⟩

(8)

and we fitted the resulting curves with the stretched exponential (KWW) function introduced by Kohlrausch−Williams and Watts:27 β⎞ ⎛ ⎛ t ⎞ ⎟ Φ(t ) = exp⎜⎜ −⎜ ⎟ ⎟ ⎝ ⎝ t KWW ⎠ ⎠

(9)

with tKWW and β being the characteristic relaxation time and stretching exponent parameters, respectively. From the fitted values of tKWW and β, we calculated then the characteristic correlation time trelax by computing the integral below each curve according to trelax = tKWW((Γ(1/β))/β). From a mesoscopic modeling point of view, the set of parameters (ρ, l2, trelax) 8274


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Figure 10. Variation of the average end-to-end distance of a butyl acrylate side group with distance from the substrate for all six different interfacial systems studied in this work.

In the next section, we will check if the conclusions drawn above for the stronger adsorption of the two PSAs on the two oxide surfaces are supported by the computed values of the work of adhesion of the six films. Surface Energies and Work of Adhesion. From a thermodynamic point of view, the concept that is used to quantify the degree or strength of adsorption of a compound on a solid surface is the work of adhesion, Wadh.21,29 This is conventionally defined as the energy required for reversible separation of the two materials at the interface. Wadh is related to the surface free energies by the Dupré equation: Wadh = γs + γl − γsl

γs =

film bulk ⟨Esubstrate − Esubstrate ⟩ 2A

(11)

where Ebulk substrate is the energy of a bulk amorphous cell of the substrate under study, Efilm substrate the energy of this amorphous cell when it is converted to a model of a thin film with both of its faces presented to vacuum, A the area of each of the two surfaces of the thin film, and the angle brackets denote a statistical average over many independent cells. Wadh, on the other hand, can be estimated from the ratio of the interaction energy Einteraction and the contact area A of polymer molecules with the solid surface:

(10)

Wadh =

where γs is the surface free energy of the solid, γl the surface free energy of the liquid, and γsl the interfacial free energy. As explained by Natarajan et al.,29 the surface energy γs of the three substrates can be computed as

E interaction 2A

(12)

with the factor 2 in the denominator accounting for the fact that the polymeric material is simultaneously confined between two substrates. As we will explain below, however, eq 12 is not 8275


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Figure 11. Distribution of the C−C−C−C torsional angle along the main chain backbone in the bulk and in the interfacial area for all six different systems studied here.

exact but approximate, since it is based on the interaction (i.e., on the internal) energy and not on the Gibbs or Helmholtz free energy as it should, thus it must be used with caution. The interaction energy is computed according to film film E interaction = (Esubstrate + Epolymer ) − E interfacial

corresponding to different sizes Lx, Ly, and Lz in the x, y and z directions, respectively (thus also to different initial structures). Next, and in order to compute Efilm substrate, we converted the corresponding bulk amorphous cells into thin films and we carried out additional MD simulations. In these NPT MD simulations with the thin films, we kept the dimensions Lx and Ly of the simulation cell constant, equal to the corresponding average values ⟨Lx⟩ and ⟨Ly⟩, respectively, in the corresponding bulk system, and let only the third dimension, Lz, to vary in the course of the MD run. On the basis of the simulation results for the various potential film film energies (Ebulk substrate, Esubstrate, Epolymer, Einterfacial), the computed γs values came out to be equal to

(13)

where Einterfacial denotes the total potential energy of the interfacial system (polymer and substrate in contact) at equilibrium. film In the above, Efilm substrate and Epolymer are the total potential energies of the two components in contact (substrate and polymer) separately, in vacuum. To carry out the energy calculations needed for the estimation of the surface energy of the three substrates and the work of adhesion Wadh, we performed some extra simulations beyond those described in section 3 (which allowed us to compute the interfacial energy Einterfacial for each of the six PSA/substrate systems at T = 300 K). First, and in order to compute Ebulk substrate for the three surfaces (α-quartz, α-ferric oxide, α-ferrite), we performed NPT MD simulations with several different bulk substrate cells

γs = (2508 ± 62) mJ m−2 for α ‐quartz γs = (2457 ± 74) mJ m−2 for α ‐ferric oxide

and γs = (1452 ± 128) mJ m−2 for α ‐ferrite 8276


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Figure 12. Histograms showing the spatial distribution above the three crystalline substrates of the very last carbon atoms (in the case of poly(n-BA)) and of the very last sulfur atoms (in the case of poly(n-BA-co-AA)) along the main chain backbone of the two PSAs.

agreement with the predicted value. Overall, our MD simulations indicate that by adding 7.1% wt. acrylic acid in poly(n-BA) increases its surface tension from ∼35.3 mJ m−2 to ∼46.2 mJ m−2. The corresponding results for the work of adhesion (see Table 4) are • (1.120 ± 0.075) J m−2 and (1.334 ± 0.052) J m−2 for the poly(n-BA)/α-quartz and poly(n-BA-co-AA)/α-quartz interfaces, respectively, • (1.078 ± 0.087) J m−2 and (1.281 ± 0.039) J m−2 for the respective poly(n-BA)/α-ferric oxide and poly(n-BA-coAA)/α-ferric oxide interfaces, and • (0.759 ± 0.037) J m−2 and (0.794 ± 0.021) J m−2 for the poly(n-BA)/α-ferrite and poly(n-BA-co-AA)/α-ferrite interfaces, respectively. They show that the energy required to separate a PSA/ α-quartz or a PSA/α-ferric oxide interface is significantly higher than that needed to separate a PSA/α-ferrite interface. Clearly, α-quartz and α-ferric oxide are more energetic surfaces than

which compare quite well with literature values. For example, Shchipalov30 mentions that the values of surface tension for crystalline and vitreous silica are on the order of 1500 mJ m−2 while Song et al.,31 Hong,32 Hung et al.,33 and Skriver and Rosengaard34 report surface energies for the bcc (100) surface of α-Fe that are equal to 2482, 2400, 2345, and 2480 mJ m−2, respectively. As far as the surface energy of α-ferric oxide is concerned, this is typically reported35 to be in the range 2250− 2360 mJ m−2. Concerning the surface tension of the two polymers, our MD predictions based on the internal energy contribution are γl = (35.3 ± 4.9) mJ m−2 for poly (n‐BA)

and γl = (46.2 ± 4.4) mJ m−2 for poly(n‐BA‐co‐AA)

In the literature, experimental data for γs are reported only for poly(n-BA). Peykova et al.,7 for example, reports that γl = 30.7 mJ m−2 for poly(n-BA) at room temperature, which is in close 8277


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Figure 13. Same as with Figure 12 but for the last carbon atoms (marked as atoms C5 in Figure 6) of the butyl acrylate side groups in the two PSAs.

α-ferrite. The oxygen content (0.904 atoms Å−2 for α-quartz and 1.037 atoms Å−2 for α-ferric oxide) and the corresponding highly attractive interactions of adsorbed polymer chain segments (especially of oxygen atoms) with the α-quartz and α-ferric oxide phases lead to a significantly higher binding affinity and to an increase in the adhesion strength, and this is clearly reflected in the data for Wadh shown in Table 4 (left part). Furthermore, our MD simulations demonstrate that by adding 7.1% wt. acrylic acid to poly(n-BA) increases its adhesion to α-quartz and α-ferric oxide by approximately 18% (this should be contrasted with the corresponding increase of its adhesion on α-ferrite which is only 4%). We conclude that adding acrylic acid to poly(n-BA) can significantly improve its wetting characteristics on oxygen-containing surfaces. The calculation of the work of adhesion through eq 12 is approximate because it neglects entropic contributions. The presence of a solid phase boundary implies entropic constraints for chain conformations (chains cannot penetrate the substrate), an effect which is taken into account only indirectly in the

previous analysis. A more accurate way of calculating Wadh is through the polymer atomic stresses that develop near the substrate according to the following expression:21 Wadh = γl +

∫0

δz

Δσ(z) dz

(14)

where Δσ = σzz −

1 (σxx + σyy) 2

(15)

denotes the anisotropy in the stress tensor developing in the interfacial system. To compute Δσ we resorted to the virial theorem of statistical mechanics, according to which: σαβ = 8278

⎞ pi , α pi , β 1⎛ − ⎜⎜∑ + ri , αFi , β ⎟⎟ V⎝ i mi ⎠

(16)


Article

Macromolecules In eq 16, V denotes the volume of the sample in the corresponding space containing the atoms contributing to the stress tensor, pi is the momentum vector of the i-th particle, mi its mass, ri its position vector, Fi the total force acting on it, and the indices α and β run over x, y, and z. In parts a−c of Figure 17,

we show typical plots of the time evolution of the three diagonal components (σxx, σyy, σzz) of the stress tensor for polymer atoms in the poly(n-BA-co-AA) material located within ∼4 Å above the α-quartz phase. Black curves denote the instantaneous values and red curves the corresponding mean instantaneous

Figure 14. continued 8279


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Figure 14. Normal-to-the-substrate and side views of typical atomistic snapshots from the simulations with the six interfacial systems clearly showing the preference of poly(n-BA) and poly(n-BA-co-AA) chains to adsorb on the three substrates with their side groups lying parallel to them and in such a way so as to enhance O−O interactions in the cases of α-SiO2 and α-Fe2O3.

The predictions of eq 14 for the work of adhesion of the six interfacial systems investigated here are reported in Table 4 (right part). The relatively large error bars accompanying these predictions are due to the large fluctuations in the stress tensor components as calculated through the virial theorem; as a result, the computed values of Wadh are subjected to a higher statistical uncertainty than those through eq 12 based on the interaction energy, Einteraction. Overall, however, the two sets of predictions for Wadh are not very different. Moreover, they are consistent with each other in the sense that both indicate a higher affinity of the two polymers on α-quartz and α-ferric oxide. In addition, they both indicate that the work of adhesion of poly(n-BA-co-AA) on the three substrates is higher than that of poly(n-BA). Given that the simulated poly(n-BA-co-AA) contains only 7.1% wt. acrylic acid, our results fully corroborate experimental assertions that adding small amounts of AA on an acrylic PSA increases its adhesion to a solid surface. In the literature, there exist experimental data only for the work of adhesion of poly(n-BA) on several substrates. For example, Peykova et al.7 have investigated the adhesion

values. Also shown in Figure 17 are the instantaneous and running-average values of the stress anisotropy Δσ. How the average value of Δσ varies with distance from the surface for the case of poly(n-BA-co-AA)/α-SiO2 interface is shown in Figure 18. The results were obtained by dividing the space above the solid substrate into sections exactly as explained by Mansfield−Theodorou21 by drawing planes parallel to the solid surface and assigning stresses to each section according to the bin the contributing polymer atom (or pairs of atoms) resided in. Stresses in our calculations here were accumulated in 4-Å-thick bins along the z-axis and we also averaged over the 8 model microstructures generated according to the procedure described in section 3. Figure 18 shows quite clearly that the intrinsically anisotropic nature of the local stress tensor extends over distances up to approximately 17 Å from the surface of α-quartz but beyond this distance the stress tensor becomes isotropic indicating that the presence of the substrate is not felt there. This is another indication that the structural and conformational properties in the middle of our model polymer films are representative of the corresponding properties of the unperturbed bulk polymer. 8280


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Figure 15. Variation of the number density of carbon atoms belonging to chain backbone (noted as CB1 and CB2 in Figure 6) and of carbon and oxygen atoms belonging to the butyl acrylate side groups (noted as OD, C1 and OS in Figure 6) with distance from the three substrates. To emphasize differences among the various systems close to the three surfaces, the graphs are shown up to distances only 15 Å from each substrate.

From a thermodynamic point of view, the internal energy part of the work of adhesion Wadh can be related to the derivative of Wadh with respect to temperature T. Thus, ideally, one could check the consistency of the two predictions (from eq 12 and form eq 14) for Wadh by computing Wadh through eq 14 at a slightly higher temperature than 300 K (e.g., at 400 K) and then use this value to compute the derivative of Wadh with respect to T, thus also its internal energy component. This should coincide then with the prediction of Wadh through eq 12. For this test to be realized, we need to compute Wadh through eq 14 with a higher accuracy than it is done here, e.g., by averaging over many more independent configurations than we did in the present work (averaging over 8 different configurations only). This will also be the subject of future work. Overall, our MD simulations suggest that incorporating small amounts of AA in the acrylic chain increases its adhesive properties, which is in perfect agreement with experimental observations and measurements. They also provide a direct confirmation of the

behavior of several statistical, un-cross-linked butyl acrylate− methyl acrylate copolymers on different surfaces (stainless steel, polyethylene, glass, hydrophobic glass, Si-wafer) using a combination of probe tack test and simultaneous videooptical imaging. Reported surface energy values calculated via contact angle measurement ranged from 26 to 68 mJ m−2 which are significantly lower than our MD-based predictions. This can be attributed to several factors such as (a) the very smooth, atomic nature of the substrates considered here, (b) their perfect crystalline nature, and (c) the absence of any impurities. In contrast, in the corresponding measurements, the substrates are quite rough (and this can have a big impact on surface energy), the surfaces are not crystalline but semicrystalline or even purely amorphous, and they can be contaminated by dirt or several organic (oily) compounds. Simulating the adhesion of the two polymers considered here on amorphous substrates (such as glass) will be the subject of future work. 8281


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5. CONCLUSIONS AND FUTURE PLANS We have presented results from detailed (explicit-atom) MD simulations with two model acrylic pressure sensitive adhesives, poly(n-BA) and poly(n-BA-co-AA), confined between two α-quartz, two α-ferric oxide, and two α-ferrite substrates. Analysis of local structural and conformational features at the two interfaces (local mass density, local number density of carbon, oxygen and sulfur atoms belonging to chain backbones and to side groups, local P2 bond order parameter for several skeletal and side group bonds and chords, distribution of backbone dihedral angles in the bulk and in the interfacial zones, local mean-square end-to-end distance of side groups, histograms of the distribution of end group atoms) showed that the two PSAs adsorb stronger on α-quartz and α-ferric oxide than on α-ferrite, with their skeletal and pendant C−C and C−O groups both lying practically parallel to the surface and in such a way that the CO bond of the pendant butyl acrylate groups points toward the surface. We also examined the structure of adsorbed layers of the two polymers on the three solid phases by calculating the surface number density (ρ), square average length (l2), and relaxation time (trelax) of segments belonging to trains, tails, and loops. Finally, we estimated the work of adhesion of the two PSAs on the three substrates through two different methods, and we found it to be significantly higher on α-quartz and α-ferric oxide than on α-ferrite. Our results support the arguments of Kisin et al.10 that introducing oxygen atoms to a metallic surface or to polymer molecules significantly increases the work of adhesion, and confirm experimental claims that adding acrylic acid to acrylic PSAs increases the work of adhesion at room temperature. The type of computer simulations presented here allows one to quantitatively assess the role of adsorptive segment/ solid interactions on the compatibility between a PSA and a substrate. In this framework, our work holds the promise to aid or even guide experimentalists in their search for approaches to improve the adhesion of acrylic waterborne PSAs to low

Figure 16. Definitions of train, tail, and loop conformations of adsorbed chains. Backbone carbon atoms along the main chain are highlighted in green.

arguments of Kisin et al.10 that introducing oxygen atoms to a metallic surface results in a significant increase in the work of adhesion.

Table 3. Estimated Values of the Average Surface Number Density ρ, Average Square Length l2, and Relaxation Time trelax for Adsorbed Chain Segments in Trains, Tails, and Loops in the Simulated PSA/Substrate Interfaces (T = 300 K, P = 1 atm) poly(n-BA) trains

tails

T (K)

substrate

ρ (segments Å−2)

l2 (Å2)

trelax (ms)


300

α-quartz α-Fe2O3 α-Fe

(2.1 ± 0.2) × 10−3 (2.8 ± 0.2) × 10−3 (3.1 ± 0.1) × 10−3

999 ± 83 134 ± 11 112 ± 18

∼10 ∼9 ∼2

T (K)

substrate


l2 (Å2)

trelax (ms)


300

α-quartz α-Fe2O3 α-Fe

(3.2 ± 0.2) × 10−3 (3.7 ± 0.3) × 10−3 (4.0 ± 0.3) × 10−3

224 ± 13 137 ± 14 70 ± 11

∼1000 ∼360 ∼70

(1.0 ± 0.1) × 10−3 (2.6 ± 0.1) × 10−3 (3.2 ± 0.3) × 10−3

loops trelax (ms)


l2 (Å2)

trelax (ms)

∼3 ∼5 ∼1

(1.3 ± 0.1) × 10−3 (2.1 ± 0.1) × 10−3 (2.6 ± 0.2) × 10−3

47 ± 10 428 ± 41 230 ± 17

∼20 ∼17 ∼3

l2 (Å2)

trelax (ms)


l2 (Å2)

trelax (ms)

201 ± 32 689 ± 49 380 ± 13

∼340 ∼890 ∼130

(2.0 ± 0.2) × 10−3 (2.1 ± 0.2) × 10−3 (2.1 ± 0.2) × 10−3

203 ± 16 141 ± 18 154 ± 18

∼410 ∼550 ∼150

l2 (Å2)

621 ± 54 (2.4 ± 0.2) × 10−3 518 ± 16 (1.2 ± 0.1) × 10−3 782 ± 43 (2.2 ± 0.1) × 10−3 poly(n-BA-co-AA)

trains

tails

loops

Table 4. Estimated Values of the Work of Adhesion As Obtained from Eqs 12 and 14 for the Simulated PSA/Substrate Interfaces at T = 300 K and P = 1 atma Wadh (J m‑2) (from eq 12) poly(n-BA) poly(n-BA-co-AA)

Wadh (J m‑2) (from eq 14)

α-quartz

α-Fe2O3

α-Fe

α-quartz

α-Fe2O3

α-Fe

1.120 ± 0.075 1.334 ± 0.052

1.078 ± 0.087 1.281 ± 0.039

0.759 ± 0.037 0.794 ± 0.021

1.681 ± 0.411 2.054 ± 0.453

1.654 ± 0.463 1.948 ± 0.374

1.194 ± 0.474 1.238 ± 0.461

a

The predictions of eq 12 are approximate, since they account only for energetic interactions. The predictions of eq 14 are accurate, since they account both for energetic and entropic contributions. 8282


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Figure 17. Instantaneous (black color) and running average (red color) profiles of the diagonal components of the stress tensor σxx (a), σyy (b), and σzz (c) and of the stress difference Δσ (d) within a section of 4 Å above α-quartz for the simulated poly(n-BA-co-AA)/α-quartz interfacial system [T = 300 K, P = 1 atm].

cohesive properties of the final copolymer and its degree of adhesion on test surfaces.

■

AUTHOR INFORMATION

Corresponding Author

*Telephone: +30-6944-602580. E-mail: [email protected] (V.G.M.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the European Union through the FP7-NMP-2008-SMALL-2 project titled: “Multi-scale modeling of interfacial phenomena in acrylic adhesives undergoing deformation (MODIFY)”, under Grant Number 228320. It has further been cofinanced by the European Union (European Social FundESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)−Research Funding Program: “Heraclitus II. Investing in knowledge society through the European Social Fund”. The presented simulation work was supported by the LinkSCEEM-2 project, funded by the European Commission under the seventh Framework Program through Capacities Research Infrastructure, INFRA-2010-1.2.3 Virtual Research Communities, Combination of Collaborative Project and Coordination and Support Actions (CP-CSA), under Grant Agreement No. RI261600. The authors acknowledge that the developments outlined in this paper have been achieved with the assistance of high performance computing resources provided by Cy-Tera/ LinkSCEEM on NARSS, based in Egypt. The assistance of

Figure 18. Variation of the stress difference Δσ above α-quartz for the simulated poly(n-BA-co-AA)/α-quartz interfacial system [T = 300 K, P = 1 atm].

surface energy materials such as those made by polyolefins (due to the absence of polar groups). For example, Agirre et al.36,37 have studied the effect of incorporating stearyl acrylate (SA) in the polymer backbone on its elasticity and adhesion on a low energy substrate such as Teflon and on nontreated polypropylene, and found out that the combination of the two properties defines an optimal SA content. In contrast, it was observed that the use of SA worsens the peel strength of the adhesive on a more energetic surface such as treated polypropylene. In this case, atomistic simulations of the type proposed here could be of tremendous help, since they could help screen out candidate monomers to be incorporated in the backbone of acrylic polymers on the basis of the predicted 8283


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Macromolecules Mohammed Gaafar and Mohammed Adel from Bibliotheca Alexandria, Egypt, in achieving the technical requirements is gratefully acknowledged.

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REFERENCES

(1) Lakrout, H.; Creton, C.; Ahn, D.; Shull, R. K. Macromolecules 2001, 34, 7448. (2) Gower, M. D.; Shanks, R. A. J. Appl. Polym. Sci. 2004, 93, 2909. (3) do Amaral, M.; Roos, A.; Asua, J. M.; Creton, C. J. Colloid Interface Sci. 2005, 281, 325. (4) Lindner, A.; Lestriez, B.; Mariot, S.; Creton, C.; Maevis, T.; Luhmann, B.; Brummer, R. J. Adhes. 2006, 82, 267. (5) Gower, M. D.; Shanks, R. A. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 1237. (6) Shen, H.; Zhang, J.; Liu, S.; Liu, G.; Zhang, L.; Qu, X. J. Appl. Polym. Sci. 2008, 107, 1793. (7) Peykova, Y.; Lebedeva, O. V.; Diethert, A.; Müller-Buschbaum, P.; Willenbacher, N. Int. J. Adhes. Adhes. 2012, 34, 107. (8) Benedek, I.; Feldstein, M. M. Technology of Pressure-Sensitive Adhesives and Products; CRC Press: Boca Raton, FL, 2009, Vol. 2. (9) Benedek, I.; Feldstein, M. M. Fundamentals of Pressure Sensitivity; CRC Press: Boca Raton, FL, 2008. (10) Kisin, S.; Bozovic Vukic, J.; van der Varst, P. G. T.; de With, G.; Koning, C. E. Chem. Mater. 2007, 19, 903. (11) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. J. Phys. Chem. 1990, 94, 8897. (12) Gasteiger, J.; Marsili, M. Tetrahedron 1980, 36, 3219. (13) MAPs: http://www.scienomics.com/. (14) Skountzos, E.; Anastassiou, A.; Mavrantzas, V. G.; Theodorou, D. N. Macromolecules 2014, 47, 8072. (15) Barudio, I.; Fevotte, G.; McKenna, T. F. Eur. Polym. J. 1999, 35, 775. (16) Theodorou, D. N.; Suter, U. W. Macromolecules 1985, 18, 1467. (17) Nosé, S. Prog. Theor. Phys. Suppl. 1991, 103, 1. (18) Hoover, W. G. Phys. Rev. A: At., Mol., Opt. Phys. 1986, 34, 2499. (19) LAMMPs: http://lammps.sandia.gov/. (20) Theodorou, D. N. Macromolecules 1989, 22, 4589. (21) Mansfield, K. F.; Theodorou, D. N. Macromolecules 1991, 24, 4295. (22) Daoulas, K. C.; Harmandaris, V. A.; Mavrantzas, V. G. Macromolecules 2005, 38, 5780. (23) Harmandaris, V. A.; Daoulas, K. C.; Mavrantzas, V. G. Macromolecules 2005, 38, 5796. (24) Scheutjens, J.M.H. M.; Fleer, G. J. J. Phys. Chem. 1979, 83, 1619. (25) Scheutjens, J.M.H. M.; Fleer, G. J. J. Phys. Chem. 1980, 84, 178. (26) Mavrantzas, V. G.; Beris, A. N.; Leermakers, F.; Fleer, G. J. Chem. Phys. 2005, 123, 174901. (27) Cook, M.; Watts, D. C.; Williams, G. Trans. Faraday Soc. 1970, 66, 2503. (28) Ö ttinger, H. C. J. Non-Newtonian Fluid Mech. 2008, 152, 66. (29) Natarajan, U.; Misra, S.; Mattice, W. L. Comput. Theor. Polym. Sci. 1998, 8, 323. (30) Shchipalov, Yu. K. Glass Ceram. 2000, 57, 374. (31) Song, E. J.; Bhadeshia, H. K. D. A.; Suh, D.-W. Corros. Sci. 2013, 77, 379. (32) Hong, S. Curr. Appl. Phys. 2003, 3, 457. (33) Hung, A.; Yarovsky, I.; Muscat, J.; Russo, S.; Snook, I.; Watts, R. O. Surf. Sci. 2002, 501, 261. (34) Skriver, H. L.; Rosengaard, N. M. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46, 7157. (35) Cornell, R. M.; Schwertmann, U. The Iron Oxides: Structure, Properties, Reactions, Occurrences and Uses; Wiley: New York, 2006; Chapter 4. (36) Agirre, A.; Nase, J.; Creton, C.; Asua, J. M. Macromol. Symp. 2009, 281, 181. (37) Agirre, A.; Nase, J.; Degrandi, E.; Creton, C.; Asua, J. M. J. Polym. Sci., Part A: Polym. Chem. 2010, 48, 5030.

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