DFT and Cluster Model Investigation on the Adhesion of Polyethylene Terephthalate on Metals

We investigate the adhesion mechanism of metal atoms (Al, Cu Ag, Au and Pt) on polyethylene terephthalate (PET) using Density Functional Theory (DFT) and cluster models. The structural geometry of the basic unit of PET is optimized then a metal atom is made to approach this structure at different orientations while calculating the total energy of the system under B3LYP functional. Results show that Al atom binds strongly when oriented linear to C=O at a distance of 1.80 Å. Orbital population analysis indicates that the good adhesion of Al at this orientation is due to the interaction of pz orbital of free oxygen in the carbonyl group and py orbital of Al atom. Binding is strongest for Al atom, followed by Pt, Cu, Ag, and Au, in decreasing order of adhesive strength. [DOI: 10.1380/ejssnt.2011.251]


I. INTRODUCTION
The significance of seamless incorporation of metals and thermoplastics in potential applications such as electronics, automotives, and packaging industries has led to considerable interest in studying adhesion strength between the surfaces of these two materials [1][2][3][4][5][6][7][8][9][10][11][12][13].Some specific functions include metal corrosion protection, adhesive bonding needs, and the production of delicate insulation components in integrated circuits.Stable adhesion of metals on thermoplastics is vital in electronic devices that require metalized plastics, and in miscellaneous applications that need mechanically strong metal-polymer joints to suit manufacturing requirements.
Thermoplastics are materials that are deformable, melt to a liquid when heated and solidify to a brittle and glass state when cooled sufficiently, and can be classified as chain-growth polymers that can be re-melted and re-molded.One of the most popular thermoplastics due of its use as beverage bottles and flexible food packaging is polyethylene terephthalate (PET).It consists of polymerized units of monomer ethylene terephthalate, with repeating units that contain the chemical elements carbon, hydrogen, and oxygen (Fig. 1).A PET monomer is formed from the condensation of terephthalic acid (HOOC-C 6 H 4 -COOH) and ethylene glycol (HOCH 2 -CH 2 OH).
PET can be metalized by evaporating a thin film of metal onto it [5] to reduce its permeability, and to make it reflective and opaque.These properties are useful in many applications, including flexible food packaging and thermal insulation.Because of its high mechanical strength, PET film is often used in tape applications, such as the carrier for magnetic tape or backing for pressure sensitive adhesive tapes.A number of studies were made on the metallization of PET but almost all of them are ex-perimental and use techniques like photoelectron spectroscopy [8], XPS (X-ray photoelectron spectroscopy) valence band spectra [14], and transmission electron microscopy [5].No theoretical study was made especially on the adhesion mechanism of PET on metals.It is in this light that we investigated the adhesion of PET on fcc metals such as aluminum, copper, platinum, silver and gold using first principles calculation within Density Functional Theory (DFT) and cluster models.
Density Functional Theory (DFT) describes the property of a system using electron density rather than wave functions [15].The ground state energy and electron density may be found using a variational minimization over the electron density.It consists of the kinetic energy, the electrostatic interaction between the electrons and the nuclei, the electrostatic energy of the electron in field generated by the total electron density n(r), and the exchangecorrelation potential, which contains the many-body effects (Eq.( 1)).
This equation is exact but the exchange-correlation (xc) energy, E xc is unknown, and, in practice, is treated approximately.The simplest approximation being used is the Local-Density Approximation (LDA), wherein the exchange-correlation energy of an electronic system is constructed by assuming that the exchange-correlation energy per electron at a point r in the electron gas, ε xc (r) is equal to the exchange-correlation energy per electron in a homogenous electron gas that has the same density as the electron gas at point r (Eq.( 2)).
(2) However, useful improvements over LDA in applications to atoms, molecules, and solids are demonstrated by Generalized Gradient Approximations (GGA) that takes into account the gradient of the density at the same coordinate: Various beyond-GGA functionals have appeared due to the quest for more accurate functionals.It can be much easier to represent a functional in terms of single-particle orbitals than directly in terms of the density.Such functionals are known as orbital functionals.An example of these is hybrid functionals.The most popular hybrid functional in chemistry is the combination of the LYP GGA for correlation [25] and Becke's three-parameter hybrid functional B3 for exchange [24] called B3LYP.An advantage of first principles calculations is that a small number of atoms that comprise a material is sufficient in determining its important properties, which can be verified by experiments.Optimum structures, mechanical, and other properties of certain materials can now be investigated and predicted even without experimental input using high-performance computing machines and supercomputers.Moreover, DFT, combined with local-or semilocal approximations of the exchange-correlation energy has become a widely used theoretical model for the computational study of atomic and electronic structure of surfaces.
In dealing with large and complicated structures such as a polymer, the most practical and appropriate way is to inspect the basic molecule (monomer) first before proceeding to a larger periodic computation.This method, called the cluster model [13], uses only a small number of the basic atoms of the molecule in the calculations.
In this study, cluster model was used to investigate the adhesion of PET on metals.In order to determine which part of the primary molecule binds with the metal, we examined the adhesion of aluminum atom on different parts of the basic repeating unit of PET and obtained the binding energy.The orientation that yielded the strongest binding energy for aluminum was used to calculate the binding energy for other metal atoms such as copper, platinum, silver and gold.It was shown in experimental studies that these oxide-forming metals form a bond with carbonyl-containing polymer which can be stronger than the polymer's inherent strength [16].
Results from this study on the binding mechanism of PET on metals will lead to a larger scope of investigating the metallization of PET.Though this research focuses on the atomic interactions of metals and PET, it can provide a wider understanding on the adhesion of thermoplastics on metals, which can be very useful in designing future materials and/or devices.

II. COMPUTATIONAL MODEL
Calculations were done using Firefly version 7.1.G (2009).It is a freely available ab initio and DFT computational program developed to offer high performance on Intel-compatible x86, AMD64, and EM64T processors [17].Firefly is partially based on US GAMESS [18] source code of ISUQCG, while extending its functionality in many important areas.Since it is based on the laws of quantum mechanics, it can predict energies, molecular structures, and vibrational frequencies of molecular systems, along with numerous molecular properties derived from the basic computational types.It can be used to study molecules and reactions under a wide range of conditions, including both stable species and compounds which are difficult or impossible to observe experimentally such as short-lived intermediate and transition structures.
Softwares MacMolPlt [19] and Chemcraft [20] were used to generate and view molecular structures.These are modern graphics programs for plotting 3-D molecular structures and normal modes (vibrations) that are compatible with the output files from Firefly.
For small and medium sized atoms such as C, O, and Al, we used 6-311G (d,p) basis set to allow the orbitals to change size and shape.It is a commonly used splitvalence basis and so far the most effective known especially for molecules involving C, O, and H.This basis set allows changes in orbitals by adding angular momentum beyond what is required for the ground state to the description of each atom.Specifically, 6-311G (d,p) adds p functions to hydrogen atoms to account for the distortion of the s orbital of hydrogen during bonding.Likewise, d function is added to carbon atoms and other heavy atoms, especially in the p block of the periodic table, to account for the distortion of its orbital in bonding.
For larger atoms (usually from Sc to Hg), the electrons near the nucleus are treated approximately using Effective Core Potential (ECP), in order to replace the Coulomb, exchange, and core-orthogonality effects of the chemically inert core electrons.In this study, SBKJC (  for atoms Au, Ag, Cu, and Pt.It is a widely used ECP especially for Li to Rn [21].
In the Firefly program, a variety of functionals were included depending on the way they treat the exchange and correlation components.Among these functionals, the one used in this study was the B3LYP.This hybrid functional is the best known and proven to be superior to the traditional functionals especially those involving carbon and oxygen atoms [22].
In energy and optimization calculations, we considered all systems to be neutral, that is, the total charge is zero (icharge=0 in the input code).For a system with odd number of electrons, the resulting spin is not equal to zero (s ̸ = 0) so the default multiplicity (mult =1) of the system must be changed.Since the multiplicity (mult) of the system is defined as 2s+1, we used mult = 1 for M = Pt and mult = 2 for M = Al, Cu, Ag, and Au for M/PET systems.
The initial positions in Cartesian coordinates of the atoms of the basic unit of PET were inferred and underwent self-consistent field (SCF) iterations until its ground state energy with its corresponding conformation was achieved.Just like the models of David et al. [1] in their study on PBT and Chtaib on PET [8], the two ends of the repeating unit of PET polymer were terminated with hydrogen atoms.
Using the optimized structure of the basic unit of PET, aluminum atom was placed on different orientations as shown in Fig. 2.These orientations were partly based on the computational model of David et al. [1] in their study of PBT.
Total energy calculations were performed while varying the separation distance between the metal atom and PET model from 6.00 Å to 1.00 Å at an interval of 0.20 Å. Binding energies for the models were obtained from the difference between the energy values for relatively large separation distance between the metal atom and the basic unit of PET and the minimum energy of the system.This method for computing the binding energy was also based on the study of David et al. [1] in their study of PBT.The total energy graphs for the different orientations of aluminum atom on the PET basic unit were compared to present the binding mechanism.
The binding energies for different metals such as copper, platinum, silver and gold were also calculated.This was done by performing total energy calculations while varying the separation distance between the metal atom and the basic unit of PET from 8.00 Å to 1.00 Å, at the orientation of aluminum atom that gave the strongest binding energy.

III. RESULTS AND DISCUSSIONS
Figure 3 shows the ground state structure of the basic unit of PET and Table I shows the optimized bond lengths and angles.The optimized geometric structure shows that all the carbon and oxygen atoms lie on a plane.The phenyl ring is planar since the orbitals of carbon atoms are sp 2 hybridized.The carbon atoms in the phenyl ring are approximately separated by a distance of 1.40 Å.The shortest distance between atoms was found in the double bonds in the carbonyl group (C7-O11 and C8-O9).
Since it was shown in previous experimental studies [5,8]  that was probed.Aluminum atom was made to approach the free oxygen of the carbonyl group from a distance of 6.00 Å to 1.00 Å. Figure 4 shows the total energy of the Al/PET system with respect to the total energy for large distance of separation.It shows that the lowest energy was achieved when the Al atom was oriented at 180 • with C=O.This was followed by 150 • , then by 120 • , and finally, by 90 • with the C=O.This result is in good agreement with the study of David et al. [1] on PBT and almost similar to one of the most stable structures of PET/Al with C-O-Al angle≈173 • , shown by Chtaib's experimental study [8] on PET, in which two atoms are connected separately on the free oxygen.Total Mulliken population [26] was also computed for oxygen and aluminum at the most stable distance of Al on PET and large distance from PET.It can be seen from Table II that there is a considerable change in the electron distribution of the free oxygen for 180 • and 150 • orientations.Detailed analysis of atomic population shows that the greatest change in electron distribution occurred in the p z orbital of the free oxygen.The greatest difference was observed for 180 • orientation, followed by 150 • , then by 120 • , and finally, by 90 • .
For Al atom, it can be seen from Table III that there is a considerable increase in the total Mulliken population for Al when oriented near the carbonyl group.Greatest charge transfer occurs for 120 • orientation with C=O.Detailed analysis has shown that the greatest change in orbital population occurred at p y orbital of Al atom.From these, it can be said that the strong adhesion of Al for this orientation is due to the π bond on the p orbital of free oxygen in the carbonyl group and Al atom and that the double bond of C-O in the ester group is broken.
The other orientations probed were 90 • and 60 • with the phenyl ring, and 120 • and 90 • with the linking C-O.As shown in Fig. 4, Al atom has negligible adhesion on the linking oxygen oriented at 120 • and 90 • .From the total Mulliken population analysis shown in Table IV, it can be seen that there is almost no charge transferred to Al atom for these two orientations.For the two orientations with the phenyl ring, the adhesion strength is small which can be explained by the stability of the phenyl ring due to the delocalization of π electrons.Thus, it can undergo substitution but not addition reactions.
The binding energy for the Al/PET system was computed by getting the difference between the total energies for large distance of separation between the Al atom and PET basis unit, and the minimum energy.Table V shows the computed binding energies and equilibrium distances for the different orientations.It can be seen from the table that the binding energies are generally larger for orientations in the C=O, followed by the orientations in the phenyl ring.There are almost negligible binding energies for the orientations in the linking oxygen.
The adhesion of different metal atoms such as copper, platinum, silver, and gold on PET was also investigated.Since it was shown earlier that the greatest binding energy was achieved when the Al atom was oriented linear to C=O, different metal atoms were made to approach the PET basic unit from 8.00 Å to 1.00 Å at this orientation.
As shown in Fig. 5, the lowest energy was achieved by Al, followed by Pt, Cu, Ag, and finally Au.Binding energies were computed and shown in Table VI.Al bonds strongly with binding energy of 0.9924 eV at 1.80 Å, followed by Pt with 0.6702 eV at 2.00 Å, then by Cu with 0.1285 eV at 2.20 Å, then by Ag with 0.0536 eV at 3.00 Å, and finally by Au with 0.0494 eV at 3.00 Å.It is surprising to note the small difference between the binding energies of Ag and Au.For the case of PBT, it was shown in the literature [1,9,10] that 1.96 eV of difference in binding energies was noted for these two metals with Ag higher in binding energy [23].From this result, it can be said that Ag adheres stronger to PBT than in PET.It may also be noted that for elements from the same family in the http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology  Based on the total Mulliken population analysis, the greatest change in the electron distribution for free oxygen in the carbonyl group occurred for Al (Table VII).This shows that there is a better interaction between this oxygen and Al compared to other metals considered.Also, as shown in Table VIII, Al has greater charge transfer than other metal atoms.These observations confirm the strong adhesion of Al to PET compared to other metals.This result is in good agreement with the experimental study of Silvain et al. [3] using TEM, which says that Al bonds strongly compared to Cu.
The difference in the binding energies for these metals may also be related to the electronic structure of these metals.For the case of Al, the outermost electron occupies the p orbital so the noted π binding with the oxygen in the carbonyl group is strong.Binding is stronger for Pt compared to Cu, Ag and Au because the d orbital of the bulk Pt has a large density of states at the Fermi level whereas the d orbitals of the other metals are fully occupied.Also, the stronger binding energy for Cu compared to Ag and Au may be explained by the difference in radial distribution of the valence (n+1)s atomic orbitals.Since the radial distribution of the Cu 4s orbital is smaller than that of the Ag 5s and Au 6s orbitals, the Cu 4s orbital can overlap more effectively than can the Ag 5s and Au 6s orbitals.

IV. CONCLUSION
In this paper, the adhesion mechanism of fcc metals on polyethylene terephthalate (PET) was investigated using Density Functional Theory (DFT) and cluster models.The optimized structure of the basic unit of PET has shown that all the carbon and oxygen atoms lie on a plane and carbon atoms in the phenyl ring are approximately separated by a distance of 1.40 Å.Also, the shortest distance between atoms was found in the double bond between the oxygen and carbon in the carbonyl group.
The results of the calculations have shown that Al atom binds strongly when oriented linear to C=O at a distance of 1.80 Å. Orbital population analysis have shown that the good adhesion of Al at this orientation is due to the interaction of p z orbital of free oxygen in the carbonyl group and p y orbital of Al atom.Among the metals used, Al bonds strongly with binding energy of 0.9924 eV at 1.80 Å, followed by Pt with 0.6702 eV at 2.00 Å, then by Cu with 0.1285 eV at 2.20 Å, Ag with 0.0536 eV at 3.00 Å, and finally by Au with 0.0494 eV at 3.00 Å.
The model used in this study is an initial step in a complete investigation on the adhesion mechanism of PET on metals.The scope of this research may be extended by considering the interaction of PET on metal surfaces and its oxide layers.

FIG. 4 :
FIG.4: Graph of energy differences for Al/PET system as a function of distance of separation.

TABLE I :
Bond lengths and angles.
FIG.3:The optimized structure of the basic unit of PET.

TABLE II :
that metals have preferential adhesion to the carbonyl group of PET, this was the first part of the PET unit Total Mulliken population analysis for free oxygen in the carbonyl group when Al is at equilibrium position ro and large distance r∞.

TABLE III :
Total Mulliken population analysis for aluminum atom when oriented on the free oxygen of the carbonyl group is at equilibrium position ro and large distance r∞.

TABLE IV :
Total Mulliken population analysis for aluminum atom in different orientations for equilibrium position ro and large distance r∞.

TABLE VI :
Binding energies for Metal/PET systems with equilibrium distance ro.

TABLE VII :
Total Mulliken population analysis for free oxygen in the carbonyl group with different metals oriented at 180 • at equilibrium position ro and large distance r∞.

TABLE VIII :
Total Mulliken population analysis for different metals at equilibrium position ro and large distance r∞.