Article pubs.acs.org/JPCC
How Thick is the Interphase in an Ultrathin Polymer Film? CoarseGrained Molecular Dynamics Simulations of Polyamide-6,6 on Graphene Hossein Eslami*,†,‡ and Florian Müller-Plathe† †
Eduard-Zintl Institut für Anorganische und Physikalische Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 20, D-64287, Germany ‡ Department of Chemistry, College of Sciences, Persian Gulf University, Boushehr 75168, Iran ABSTRACT: Coarse-grained molecular dynamics simulations have been performed to study a nanometric polyamide-6,6 film containing long chains (100 chemical repeat units), in contact with a graphene surface and with vacuum, in a huge simulation box (the distance between the interfaces ≈ 36 nm) for a long time (70 ns). Compared with atomistic simulations, with limitations in chain length, box size, and simulation time, restricting them to the study of local structural and short-time dynamic properties, this simulation covers a broad range of length scales and captures the long-time relaxation regime of long chains. This enables one to discriminate the interphase thickness for local and global structural properties and to study the interplay between the change in structural and the associated dynamic properties in the interphase compared with the bulk polymer. Our results indicate that the interphase thickness depends on the length scale of particular property of interest for the bulk polymer. At both interfaces a minimum interphase thickness, ∼3.0 nm, is associated with local structural properties such as layering of individual superatoms and the hydrogen bonding between amide groups. The interphase thickness, however, extends to an intermediated length of about one radius of gyration, Rg, of the unperturbed polymer (6 nm) and a maximum length of 2Rg in the case of such polymer structural properties as the chain conformations and reach of chains with at least one contact to the interface to the polymer phase, respectively. Accordingly, the time scales for both short- and long-time dynamic properties in the interphase vary (with respect to the corresponding property in the bulk) as a function of distance from the surfaces. The change in time scales, in a 3 nm thick slab parallel to the interfaces, is shown to cover a broad range from 10% to four orders of magnitude. The former change in time scales occurs in the case of such a short-time dynamic property like HB formation (occurring in a few picoseconds for bulk polymer) at the vacuum interface, whereas the latter one corresponds to a long-time dynamics process such as the center-of-mass translation in the perpendicular direction at the graphene interface (occurring in hundreds of nanosecond for bulk polymer).
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INTRODUCTION Controlling the surface and interfacial structure of polymers is a vital problem for tailoring novel materials.1 Among the various polymers, polyamides (PAs) have important characteristics such as high thermal stabilities, good mechanical properties, excellent abrasion, low coefficient of friction, easy processing, and solvent resistance, which makes them the most common engineering polymers applied to build machines in mechanical engineering.2 Although considerable experimental measurements have been performed to elucidate the properties of complex nanoconfined systems,3 there is still much to be learned about these systems. At present, computer simulations seem to be promising for capturing the molecular-level properties of confined fluids. However, the main difficulty to study such systems as polymers in contact with surfaces using computer simulation methods is that one is confronted with a variety of time and length scales. Therefore, it is not feasible to run computer simulations of systems of experimentally relevant © 2013 American Chemical Society
sizes with atomistically detailed models. Thus, so far, atomistic simulations of confined polymer systems are limited to short polymer chains, which may not be representative of systems studied experimentally. A solution to this problem is construction of coarse-grained (CG) models by lumping together a group of atoms into CG beads.4 Instead of hard atomistic potentials, CG models are often described by so-called potentials of mean force, which are constructed from the atomistic potentials by averaging the molecular field over the rapidly fluctuating short time scale motions.4 Although many developments of CG models for bulk polymers have been reported in the literature,4 there are few reports on the CG models of polymers in contact with surfaces. This is due to the fact that the structure of polymers in contact with surfaces depends on the polymer−surface interactions and Received: January 5, 2013 Revised: February 12, 2013 Published: February 13, 2013 5249
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Figure 1. Chemical structure of PA-6,6 and indication of mapping between atomistic and CG models of PA-6,6 and graphene surface. The centers of beads in graphene surface are indicated as filled circles. The bead types are indicated by Roman numerals.
To be able to keep the details of the atomistic structure in the CG model, we separated the total potential energy into contributions due to bonded and nonbonded terms. The different contributions to the potential energy are then calculated by sampling the corresponding distribution functions at the underlying atomistic model and matching the CG distributions with atomistic ones in the so-called iterative Boltzmann inversion cycle.4 This procedure, described in detail in our previous report, is shown to generate transferable CG potentials for simulation of PA-6,6 in contact with graphene surfaces.6 Here the transferability refers to both different temperatures and different film thicknesses. In this work, the CG potentials, generated in our previous work,6 are employed to simulate films of long-chain PA-6,6 between graphene and vacuum.
on the geometry of the surface and is very sensitive to the detailed chemical structure of the confined molecules and the confining surfaces. To our knowledge, there are only three reports in the literature on the coarse graining of polymers in contact with surfaces.5 Very recently, we have developed a CG model of PA-6,6 in contact with graphene surfaces.6 The model is shown to reproduce well the atomistically obtained structures. The model is distinguished from the generic bead spring models as it retains the structural properties of the underlying all-atom model and preserves the relevant information about the chemical specificity of polymer and surface. It is the purpose of this work to simulate long chains (100 chemical repeat units) of PA-6,6, in contact with, on the one side, graphene as a model for graphitic materials and vacuum on the other, for a long time (70 ns). The molecular weight of this sample is 22.6 kg mol−1, which is in the range typically used in engineering applications. The simulations of such long time and length scales, not achievable in atomistic models, provide the possibility of reaching full equilibration and long-time dynamics of polymer. This is particularly important in the case of polymers in contact with surfaces as surface effects substantially alter the dynamics of confined polymer molecules.7 Simulating polymer molecules in a big box, six times bigger than the radius of gyration of the bulk polymer, enables us to study local properties of the system in a highly anisotropic state (the interfaces), in equilibrium with the isotropic bulk polymer (the central region of the box) and to quantify the length scales over which the surfaces affect the structure and dynamics of polymer.
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SIMULATIONS CG simulations have been performed on 100-mer PA-6,6 chains in contact with a graphene surface on one side and with vacuum on the other. Initially, a number of repeat unit conformations were sampled and randomly joined together to prepare the long chains. A total of 185 chains of PA-6,6 was randomly put in a big simulation box, containing a graphene surface, and the overlaps were removed using a soft-core potential. The system contained 93 642 beads, 92 685 beads for the polymer plus 957 in the graphene surface. A snapshot of the simulation box, in which the graphene surface (location of the centers of the graphene superatoms) is put at z = 0 is shown in Figure 2. All CG simulations were carried out using the IBISCO code.8 The temperature was kept constant at 400 K using a Berendsen thermostat9 with a temperature coupling of 0.5 ps. The nonbonded interactions were truncated at 0.95 nm with a neighbor list cutoff of 1.05 nm, and the neighbor list was updated every 10 time steps. The time step for the leapfrog integration scheme10 was 7 fs. The CG polymer beads underwent molecular dynamics, but the graphene surface was kept rigid. Periodic boundary conditions were applied in the x and y directions. The finally relaxed box has xyz dimensions of 14.27 × 14.06 × 45.0 nm3, in which the z coordinates of the polymer vary from zero, the position of the graphene beads, to about 36.50 nm, and the rest is vacuum. The middle region of the box has the same density as the bulk sample (990 kg m−3).
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MODEL The CG model of PA-6,6 in contact with graphene surfaces, is explained in detail elsewhere.6 Here we restrict ourselves to a brief explanation of the method. In this model, a number of atoms are grouped together to form superatoms or beads. This is done in such a way to substantially reduce the number of degrees of freedom and at the same time maintain the structure of the original atomistic model. In Figure 1, we have shown the mapping scheme6 to group together polymer and surface atoms. 5250
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Figure 3. Number density profiles for all polymer beads (solid curve) and end beads (dotted curve). The density profiles are normalized by the bulk number density, ρ0. The dashed curve represents the density profile in the vacuum interphase, calculated with respect to the distance from surface corrugations.
tendency for the end groups to occupy the polymer−graphene interface. In contrary, they are depleted from the vacuum interface. Moreover the end-bead density profile peaks are wider than those for all-beads. This is due to the penetration of pendant end beads into the surface voids, resulting from mapping carbon atoms into bigger CG beads. We also tried to separate the effects of vacuum surface corrugations on the density profiles from surface-induced density fluctuations. Therefore, we have calculated the density profiles on the vacuum side not only with respect to an absolute value of z but also with respect to a distance from the corrugated surface. To this end, an x−y grid was applied, and the density profile in any quadratic prism volume situated at a given x and y was calculated as a function of the z distance from the outermost atom of this prism; that is, every prism has a different surface position, which is used as a reference for the calculation of the density profile. Figure 3 shows that the vacuum interface density profile calculated in this way is quite different from the profile obtained by simply averaging over x and y. With the proper reference position for the surface, there is a structure layering visible also on the vacuum side, albeit less pronounced than on the graphene side. The results in this section show that the length scales over which surfaces influence the structure of individual polymer beads to form layered structures (∼3.0 nm) are a few bead diameters (σb ≈ 0.40 nm). Similar length scales for fluid layering beside surfaces have been observed in surface force apparatus experiments with a variety of fluids of very different molecular shapes and architectures11 and in previous atomistic,7,12 bead−spring,13 and CG models6 of polymers in contact with surfaces. Hydrogen Bonding. The hydrogen bonding in PA-6,6 is responsible for the formation of a 3-D network, giving rise to the special mechanical properties of this polymer. The hydrogen bonding in nanoconfined PA-6,6 oligomers has been studied in detail in our recent atomistic simulations.7,14 In the present CG model, the atoms involved in the hydrogen bonds (HBs), namely, the NH hydrogen and the carbonyl O atoms, are both lumped into bead II. A recent study15 in our group indicated that adopting a geometric criterion in which
Figure 2. Snapshot of the simulation box, in which the graphene surface is located at z = 0. Colors represent: dark red (bead II), yellow (bead III), blue (bead IV), and green (bead V).
We have also simulated a sample of bulk polymer, containing 100 chains, to compare the results with. Simulations were performed for 30 ns to reach equilibrium, as monitored by the relaxation of the end-to-end vector. (See the later section on overall dynamics.) After equilibration, simulations were done for another 70 ns for data collection.
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RESULTS AND DISCUSSION Density Profile. Fluids in contact with surfaces form organized layered structures beside the surfaces. We have observed such layering behavior for short oligomers of PA-6,6 in our previous atomistic simulations.7 To calculate the polymer density profiles, the box length in the z direction (Figure 2) is divided into 0.02 nm slabs, and the number of polymer beads (regardless of their types) inside the slabs is time averaged. To compare with the bulk polymer, the number density is normalized by the bulk value (Figure 3). The results are indicative of three distinct regions: the polymer−graphene interface, the bulk region in the center, and the polymer− vacuum interface. In the graphene−polymer interface, PA-6,6 beads in contact with the surface form layered structures with sharp density peaks, up to distances of a few nanometers away from the surface. PA-6,6 beads, which are located beyond ∼3.0 nm away from the graphene surface, show a bulk-like behavior. For PA-6,6 beads in contact with vacuum, the density profile varies monotonically and without distinct peaks from zero, in vacuum, to the bulk value, at distances ∼3.0 nm away from the free surface (vacuum). For comparison, we have also shown in Figure 3 the density profiles for polymer end groups (bead type I in Figure 1). The results indicate that there is a higher 5251
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squared radius of gyration. The normalized parallel and perpendicular components of mean-squared radius of gyration are defined as:
the distance between the centers of beads II is 30 nm), the polymer coils are also flattened against the interface, albeit to a lesser extent, with reaching a maximum of 0.9. It is worth mentioning that the radius of gyration of the bulk polymer, with a molecular weight of 22.6 kg mol−1, is 6.1 nm. This value is quite in agreement with the experimental value of 6.4 nm for a sample of PA-6,6 with a molecular weight of 25.4 kg mol−1 at 313 K.16 Configurational Properties. A different structural length scale is defined by the reach of chains with at least one contact to the interface into the polymer phase. A surface contact at the graphene interface is assumed when a bead is within 0.6 nm of the graphene surface (first bead density peak, cf. Figure 3). The polymer segments between contacts are then classified in terms of simple configurations, originally introduced by Scheutjens and Fleer in the framework of a mean-field theory.17 Consecutive monomers adsorbed on the surface (0 nm ≤ d ≤ 0.6 nm) are designated as trains. Sequences of monomers away from the surface, but delimited by two surface contacts, are denoted as loops. Similar sequences between one surface contact and a chain end are called tails. In Figure 6, we have shown the density profiles for beads belonging to trains and loops as a function of distance from the graphene surface. The 5252
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C(t ) =
⟨h(t )h(0)⟩ ⟨h⟩
(2)
The function C(t) is the probability that a randomly chosen pair of amide beads is bonded at time t provided that it was bonded at t = 0 (independent of possible breakings in the interim time). Because the HB lifetime to first breakage is short and independent of position, the results are not shown here. We show in Figure 7 the correlation function C(t) in slabs at different distances from the graphene surface. It shows an initial
Figure 6. Number density profiles for monomers belonging to tails (solid curves) and loops (dashed curves) at both interfaces, normalized by the bulk monomer density.
density of train beads is not shown as it is by construction identical to the first monomer density peak in Figure 3. Here the number density profiles for tails and loops are also normalized by the bulk number density to be able to compare the results in Figure 6 with the density profiles in Figure 3. Expectedly, loop and tail densities exhibit the same layered structure near the graphene surface (d < 3 nm) as the overall density. Then, they gradually fall to zero. As it is seen, a fraction of loops and tails extends to distances as long as Rg and 2Rg, respectively. Because of the fact that the definition of volume in our system is ambiguous, to be able to do a similar analysis in the vacuum interface, we have considered a hypothetical plane (parallel to the graphene surface) at a position at which the density profiles of Figure 3 fall off to 0.01 (d = 36.25 nm). The loop and tail profiles at the vacuum interface are calculated based on a distance criterion, in which a bead is within 0.6 nm of this surface (35.66 nm ≤ d ≤ 36.25 nm). The results, shown in Figure 6, indicate that similarly at the vacuum interface a fraction of loops and tails extends to distances as long as Rg and 2Rg, respectively, away from the interface. Because of their attachment to the interface, the behavior of such chains is possibly different from bulk polymer. By their nature, such chains are stretched in the direction of the surface normal, which may have consequences for their dynamics. In the following section, we address to the change in dynamics of such highly extended tails as well. Our results in this section indicate that the direct range of polymers attached to both surfaces extends to ∼2Rg. This is probably the longest interphase thickness found in this study. In this respect, just a limited region in the center of the box with a thickness about 2Rg (12 nm < d < 24 nm) can be regarded as bulk polymer, hence, the need for simulating a big box in the present CG model, which is not practically feasible in atomistic simulations. Hydrogen Bond Dynamics. The average number of HBs for a sample of PA-6,6 containing N amide beads is N(N − 1) /2, where denotes the time average of h(t), a binary function for each possible pair; h(t) = 1 if the pair is bonded at time t and h(t) = 0 if it is not. In equilibrium, the function h(t) fluctuates in time. The dynamic behavior of HBs can be evaluated by calculating the intermittent HB correlation functions, C(t), defined as18
Figure 7. Local intermittent correlation function C(t) for hydrogen bond formation and rupture in different slabs. The HB length is considered to be
