|Severin, , Nikolai: Molecular Dynamics Simulations of Polymers and Micelles at Interfaces |
Plastic waste has become one of the main issues of environmental concerns. Major polymeric components of plastic waste are polyethylene (PE) and polypropylene (PP). Separation of the plastic waste into individual polymers is costly and complete sorting is sometimes impossible. Thus it is important to study blends of PE and PP in order to put recycled blends into effective and efficient use.
It is well known that PE and PP are immiscible polymers. The term ‘immiscible means that the Gibbs energy of mixing is positive, thus two immiscible components tend to macroseparate from their mixture. The immiscibility of PE and PP was established by directly visualising macroseparation in the blend of molten PE and PP. A thin film of blended PE and PP was placed between two heated glass slides and observed with light microscopy. It was shown that initially small domains of PE and PP tend to merge leading finally to macroseparation of both polymers. Despite of the immiscibility of many polymers it is possible to produce their blends. Because of the high viscosity of bulk polymers the process of macroseparation takes place on a long time scale. By extrusion of two immiscible molten components and following fast cooling below crystallisation or glass transition points of both components it is possible to prevent them from macroseparation. It is clear that properties of a blend of two immiscible components would strongly depend on the preparation conditions like, for example on the mixing and cooling rates. In general, immiscible polymers are also incompatible. The term ‘incompatible means that the mechanical properties such as impact strength, Youngs modulus, strain and elongation at the stretching limit of the blend are inferior to the mechanical properties of the pure components.
Despite the immiscible nature of PE and PP it was recently found that it is possible to process blends of PE and iPP (isotactic polypropylene) with an impact strength of the blend which is two times higher than the impact strengths of the pure components. It is very important for industrial applications that by blending of common and cheap polymers one can obtain blends with improved impact strength. The blend of PE and iPP with improved impact strength was processed by extrusion of both molten components, followed by fast cooling. Transmission electron microscopy (TEM) images of the blend show that these preparation conditions lead to a fine micro-separation of PE and iPP, hence to an
12increased total interfacial area between PE and iPP in their blend. It was suggested that the properties of PE - iPP interfaces help to dissipate a sufficient amount of energy in the blend, hence enhanced total interfacial area improves the impact performance of the blend. The suggestion of the important role that interfaces play in the impact performance of the blend was the starting point of this work.
In general one may subdivide the investigation of interfaces on the macroscopic and microscopic level. On the microscopic level the interface is characterised on atomistic length scales with changes of the structure of both components in the interfacial region. When one considers properties of interfaces on the macroscopic scale, the roughness of the surfaces of both components should be taken into account. It is hard to establish micro structure of the interfaces in a real blend, since one finds too many randomly oriented interfaces. In addition, because of the semi-crystalline nature of polymers one should expect four types of interfaces in the PE - iPP blend: amorphous-amorphous, crystallin-crystalline and amorphous-crystalline, crystalline-amorphous interfaces. The model experiment of epitaxial crystallisation of PE and iPP may help to resolve the structure of their interface. In epitaxial crystallisation one polymer is crystallised in the form of a thin layer on a thin layer of another polymer. The polymer sandwich is then investigated by X-ray scattering. But the structure of the interface is then difficult to discriminate from the structure of the polymers in the films, hence one expects that the material at the interface has exactly the same structure as in the film. It is obvious that this method may not reveal the fine structure of the interface. Molecular dynamics (MD) simulations may help to solve this problem since it allows to simulate the interface on the atomistic length scales, hence to investigate the fine structure of interfaces. That is why it was decided to perform MD simulations of PE and iPP interfaces in order to establish their exact microscopic structure.
Polyethylene macromolecules have the chemical formula: where n typically is in the range of 103-106. In the technical literature the term high density polyethylene is used for this linear polyethylene while the term low density polyethylene is used for branched polyethylene. I will focus in the following on the investigation of high density polyethylene and will use the abbreviation PE also for high density polypropylene instead of HDPE. The melting point of PE is at 138° C and its glass transition4 is between -128° and -30° C, depending on the history of the sample and the experimental method which is used to determine the glass transition temperature.
The all trans conformation (zigzag) (Fig. 2) of the PE macromolecule is the form with the lowest potential energy. Crystals are composed of PE macromolecules in the all trans conformation.
Figure 2 The all trans conformation (zigzag) of PE. Side and end-on view. The carbon atoms are large and hydrogen atoms are small. The ellipse is drawn to facilitate the display of PE crystalline forms shown in the figure 3. The shading is chosen in agreement with Figure 3 in order to outline the difference in height between sides 1 and 2.
Normally PE crystallises in the orthorhombic crystalline form (Fig. 3a). The orthorhombic PE crystalline unit cell has the following cell dimensions: a=7.40 Å, b=4.94 Å and c=2.534 Å. It was found that under extreme conditions, like for example crystallisation with extreme cooling rates or crystallisation under stress, PE can crystallise also in the monoclinic form (Fig. 3b). The monoclinic PE crystalline unit cell has the following cell dimensions: a=8.09 Å, b=2.53 Å, c=4.79 Å and =107,9°.
Figure 3 Orthorhombic and monoclinic crystalline forms of polyethylene. Cut through ab - plane with macromolecular long axes perpendicular to it. The ellipses are just a guide for the eyes and show the orientation of PE zigzags. It is important to notice that in the monoclinic form all ellipses have the same orientation while in the orthorhombic cell they have different orientation. The shading is consistent with Figure 2.
Polypropylene has the chemical formula:
15It is known that iPP may crystallise in three different crystalline forms: (monoclinic), (hexagonal) and (triclinic). In the present work just the crystalline form of iPP will be investigated. Crystalline forms of iPP are composed of iPP 31 helices (Fig. 4).
Figure 4 The helical form of iPP macromolecule. On the side view two helical turns are presented. Arrows show three methyl groups along one helix.
The -form of crystalline iPP is composed of both right- and left-handed helices. Cell parameters of the crystalline form are: a=6.65 Å, b=20.78 Å, c=6.50 Å and =99.6°.
PE and iPP are known as immiscible polymers. The term ‘immiscible means that the Gibbs energy of mixing of two components is positive or by another words that they tend to macro-separate from their mixture. It is known that most blends of immiscible polymers exhibit lower mechanical properties for example stretching limit or impact strength. Materials whose blends has lower mechanical properties are called also incompatible materials. Since PE and iPP are immiscible polymers they are also expected to be incompatible. However, it was found recently that PE and iPP can be considered technically compatible materials. It was reported that it is possible to make a blend of PE and iPP with a higher Young modulus than the Young modulus of the pure components. It was also found that the impact strength of PE and iPP blend is about two times as high as the impact strength of the pure components.
The impact strength is an important factor for the commercial value of polymers or polymer blends. It is defined as the energy, which leads to the
16destruction of the sample, normalised to the area of the sample cut, perpendicular to the sample surface. The shape and the size of a sample is defined according to technical standards. The measurement of the energy, leading to sample destruction is also defined by technical standards. For example: a hammer is dropped on a sample from different heights. The minimum height, which leads to a sample destruction allows to estimate the impact strength of a sample. It is important to distinguish notched and unnotched impact strength, i.e. whether the sample was notched before impact strength measurements or not.
Two types of materials with respect to impact strength measurements can be distinguished: brittle and ductile materials. Brittle materials have usually low impact strength. The unnotched impact strength of an ideal brittle material consists of the energy for crack formation and the surface energies of surfaces formed by crack propagation. For notched impact strength it is just the second component. Ductile materials which are also called tough materials, have usually higher impact strength. The impact strength of ductile materials includes in addition to brittle materials the energy of polymer matrix plastic deformation.
The toughness of polymeric systems has been studied intensively. It was established that a substantial increase in toughness of brittle polymers can be achieved by blending them with rubber particles. The mechanisms which are responsible for the increasing impact strength are multiple crazing, shear yielding, crazing with shear yielding and rubbery particles stretching and tearing. A common accepted view on the role of rubber particles is that this particles alter the stress in the material and induce plastic deformation of the polymer matrix. In general it is accepted that the plastic deformation in the polymer matrix, such as multiple crazing and shear yielding or both, absorb a major part of the total fracture energy.
It was proposed that blends with rubber particles larger than 1 µm prefer crazing, whereas shear deformation in a ductile polymer matrix is favoured by particles3 smaller than 1 µm.
The multiple crazing mechanism
It was noticed that the fracture of rubber-toughened polystyrene is usually preceded by an opaque whitening of the stress area. It was also concluded that whitening is associated with the absorption of a large amount of energy11. Later it was established that polymer matrix crazing is responsible for stress whitening and therefore for the absorption of energy. Transmission electron microscopy shows that extensive crazing occurs in a nylon matrix within the whitening zone. Crazes are micro-cracks filled by voids and fibrils which are formed by
17yielding12. The energy dissipated by crazing consists of two components: 1. energy dissipated by yielding in fibril formation, and 2. energy stored as surface energy in the craze matter.
The mechanism for shear yielding
It was found that by blending of brittle polymer with rubber particles it is possible to obtain material with ductile characteristics thus improving its impact performance. It was further supposed that dilation which should occur in certain regions near the rubber particles aids in the lowering of Tg. The rubber particles are subjected to combined tensile stresses which prevent catastrophic crack propagation in the matrix14.
On the other hand it was established that the sharp brittle to ductile transition occurs when surface-to-surface inter-particle distances become lower than a critical value Rc, which depends on the type of polymer matrix and rubber particles15. Rc was established to be independent of particle size and rubber volume fraction. This is in agreement with the results on stress-strain behaviour of PS (polystyrene) thin films. It was found that with decreasing PS film thickness, the material undergo a brittle to ductile transition16. A lattice of holes, which can represent non-adhering rubber particles, creates thin ligaments of polymeric material, i.e. potential initiation places of deformation. Brittle fracture of this ligaments can only occur if the stored elastic energy per ligament overcomes the surface energy of this ligament. It was shown that for thin ligaments (small inter-particle distances) brittle fracture does not occur, however complete deformation of the ligament takes place, eventually ductile macroscopic fracture behaviour is observed17.
On the basis of this work it should be possible to explain the improved impact strength of PE/PP blends. It was clearly shown that PE is a ductile material. On the other hand PP shows semibrittle characteristics. Most of experimental work considered improving of impact performance of brittle polymers by blending them with rubber particles. Therefore let us consider improving of PP impact performance by blending it with PE. a) at low concentrations of PE in PP one can suppose large distances between PE inclusions, thus multiple crazing mechanism of impact strength improvement. b) at high concentration of PE in PP it is reasonable to suppose shear yelding mechanism of improving impact performance, moreover it was found that the better dispersion of PE in PP (thinner ligaments of PP) leads to a better impact performance of PE/PP blends. Therefore interfacial properties play an important role in the determination of the impact performance of polymer blends. The ‘strong interfaces would favour the multiple crazing mechanism while a
18polymer matrix plastification mechanism would be favoured by ‘weak interfaces. That is why it is important to investigate PE/PP interfaces in blends.
Up to now there is no experimental method which would allow to investigate polymer interfaces on a molecular scale directly in a blend. A polymer blend contains too many randomly oriented interfaces, therefore it becomes impossible to focus with experimental method on the structure of a single interface. In addition both PE and PP are semicrystalline polymers at room temperature both in the pure state and in the blend. That is why one may suppose the existence of three types of interfaces: amorphous-amorphous, crystalline-crystalline and amorphous-crystalline, crystalline-amorphous. The semicrystalline nature of PE and iPP below their crystallisation temperatures is common for all polymers.
The so called crystals formed by polymer molecules are different from those formed by small molecules as the unit cell of the crystal contains part of a molecule rather than the hole molecule. The single crystals composed of flexible polymer molecules usually have one face with a much larger area than the other two and hence one dimension of the crystal is smaller than the other two and much smaller than the molecular length of the polymer. A single polymer crystal of this type is called lamella crystal. It was found that polymer molecules are packed in the lamella crystal perpendicular to the surface with the large area. This leads to the conclusion that the chains should fold back in the crystal. The detailed picture of chain folding as well as the crystal size depends on many parameters such as chemical structure of a polymer chain, crystallisation temperature and crystallisation procedure.
When polymers are crystallised from the melt, they form aggregates composed of lamella crystals. The most common shape of such aggregates is a spherulite (Fig. 5). Voids in between lamellae are filled with chains folding back to the lamellae from which they emerged or going to the neighbouring lamella. The material in-between lamellae is not crystalline and it is not also fully amorphous because chain orientation is induced by the presence of crystalline lamellae. The chain folding is not so obvious when lamellae form superstructures like spherulites. The usual argument for the polymer chains folding in spherulites formed from melt is that amorphous material between lamellae is less dense than the crystal and that if all the chains emerge from the crystal, adopt random conformations and do not fold back into the same crystal, then the density at the surface will be significantly higher than in the crystal. The co-existence of crystalline lamellae and amourohuse material in-between lamellae is the origin of the semicrystalline nature of melt crystallised polymers.
Figure 5 Schematic structure of a spherulite. Lamella crystals grow from the centre of the spherulite. The enlarged part shows several lamellae and an amorphous regions in-between lamellae. The amorphous part is formed by chains that fold back to the same lamella where they emerged from or by chains that reach into the neighbouring lamella.
As it was discussed above that a direct investigation of PE-iPP interfaces in a blend is quite difficult. However it is possible to perform a model experiment by epitaxial crystallisation of PE and iPP. In this case PE and iPP form a single interface and it is possible to establish a relationship of PE and iPP crystals. Several examples of epitaxial crystallisation of PE and iPP are listed below.
It was supposed in the literature that the ‘cross hatched morphology of PE and iPP established by epitaxial crystallisation of PE on iPP is responsible for the improved mechanical properties of PE and iPP blends. Lamellae of PE grow epitaxially at about 50° with respect to the orientation of PP lamellae. Hence a PE lamella epitaxially crystallised on iPP bridges many lamellae of iPP and vice versa. It was supposed that the bridging leads to hardening of the PE/iPP blend (Fig. 6).
Figure 6 Bridging mechanism established by epitaxial crystallisation. It was found that lamellae of PE form an angle of about 50° with iPP lamellae. This figure shows the bridging of several iPP lamellae by PE lamellae.
Epitaxial crystallisation was carried out by two methods: 1. annealing of sandwiched films of PE/iPP; and 2. vacuum deposition or cast film crystallisation of PE or iPP onto single crystals or oriented films of iPP or PE respectively1-2.
1. A thin film of highly oriented iPP was sandwiched with a thin film of PE the following way: Solution of 0.5% PP and PE, respectively in xylene were poured on two separately heated glass slides. After evaporation of the solvent, a motor driven cylinder was brought into contact with the two glass slides, lifted up and to allowed to wind up very thin PP and PE-films simultaneously. The films were 50 nm thick and highly oriented. The film of compressed PE and iPP was annealed at a temperature above the melting point of PE but below the melting point of iPP. After cooling down the film to room temperature, PE crystallised epitxially on iPP1.
2. Polymer films are produced by melting the polymer and a solvent which can crystallise, between two with PE and iPP covered slides. On cooling, the solvent crystallises first and the polymer crystallises next in the form of a thin epitaxially oriented film if the substrate is appropriate. The crystallised solvent substrates are then dissolved. A vapour (of molecular weight 1300 for
21PE and 3000 for iPP) condenses and crystallises on the substrate surface held at room temperature2.
Figure 7 The two (010) faces of iPP (-modification). The face with the higher density of methyl groups (surface of type A) results in rows of methyl groups parallel to and with inter-row distances of 5.05 Å and 4.25 Å respectively. Faces with the lower density of methyl groups (surface of type B) have less pronounced rows of methyl groups but exhibit the same symmetry as the faces with the higher density of methyl groups.
PE crystallises in the orthorhombic crystalline form on the -modification of iPP, such that molecules of PE are inclined at an angle of about 50° with respect to the substrate chain axes. The contacting planes are (100) for PE and (010) iPP respectively. It was postulated, that epitaxially grown PE chains interact with rows of methyl groups that populate the (010) plane of the iPP -modification. The distance between PE chains in the (100) crystallographic plane is 4.95 Å, while the distance between neighbouring rows of methyl groups in the (010) plane of iPP is 5.05 Å. There are two (010) crystallographic planes of iPP, which differ just by the density of methyl groups. It is not possible to find experimentally, whether PE crystallise on the (010) plane of iPP with the high density of methyl groups or with the low density of methyl groups (Fig. 7 adopted from the work of Lotz and Witmann2).
It is important to notice that methyl groups on the (010) crystallographic plane of iPP form patterns of the ‘four or ‘five faces of a dice3, for the low or high density of methyl groups, respectively. Diagonals of the dice elements form rows with inter-row distance 5.05 A and 4.25 A.
The advantage of the epitaxial crystallisation method is that it allows to investigate the relationship between PE and iPP lamellae. However it does not allow to investigate the detailed structure of the interface. In particular, it does not allow to look into structural changes that may occur in a layer of several angstroms thickness. MD simulations may help to resolve this problem, as it can yield a detailed picture of the interface structure. But MD simulations have other disadvantages: while they allow to simulate an interface of very thin layers of two components, the properties of an interface between two very thin layers could be different from the properties of an experimentally investigated of microscopically thick interfaces. That is why it is important to combine results of MD simulations with experimental results.
As explained above it was decided to model three types of interfaces: amorphous/amorphous, crystalline/crystalline and amorphous/crystalline interfaces of PE and iPP. In order to model these interfaces first amorphous and crystalline PE and iPP were simulated separately.
Amorphous bulk systems were created by packing 18 molecules in the case of PE and 16 molecules in the case of iPP into a box with periodic boundary conditions. The densities of amorphous iPP and PE were set to fulfil the experimental value of the density 0.85 g/cm3 for both iPP and PE. During the packing procedure the neighbourhood of each atom is checked by the distance criteria such that the distance between two nonbonded atoms are longer than the sum of the corresponding Van der Waals radii.
The structures of amorphous PE and iPP were then prerelaxed by energy minimisation. In order to optimise the sample further the system was subjected to annealing cycles of 20 ps duration where the temperature was increased linearly from 300 K to 800 K with a 100 K temperature step. After annealing the system was cooled down to 300 K with 100 K temperature steps in 20 ps time intervals. After another 200 ps at constant temperature of 300 K no further decrease of the potential energy could be observed.
23The crystalline cells were constructed by adopting the orthorhombic unit cell of PE and the crystalline form unit cell of iPP. The orthorhombic unit cell of PE has cell dimensions a=7.26 Å, b=4.8 Å, c=2.57 Å, ===90°, and consists of two methylene units ( ) (fig.3 and fig.4). The -modification of iPP has cell dimensions: a=6.43 Å, b=20.86 Å, c=6.1 Å, ==90° =83.2°. All crystalline iPP modifications are formed by helixes. Each helix consist of three repeat units ( )5 of iPP (fig.4). The unit cell of crystalline form of iPP consists of four helices having the following sequence: 1. Left Up, 2. Right Up, 3. Left Down, 4. Right Down, where Left = left handed helix, right = right handed helix, Up = helix points upwards, Down = helix points downwards.
The structures of crystalline PE and iPP were prerelaxed by energy minimisation, and then subjected to MD simulation with constant pressure. Two pressure control methods were tested to keep constant pressure: 1. isotropic Berendsen and 2. Parinello-Rahman methods. 1. We had to rise the pressure to 1.4 GPa in order to keep the crystalline systems stable and with correct density. 2. Systems showed good agreement with experimental parameters under a pressure 1 Bar. That is why Parinello-Rahman method of pressure control was used for the simulation of systems containing crystalline PE or iPP. The systems with crystalline PE or iPP were annealed for 50 ps at the temperatures 400 K, 350 K. Heating over 500 K caused gauche defects in PE and a higher potential energy of the crystalline system, respectively.
amorphous PE - amorphous iPP
Amorphous iPP and PE systems were created with exact matching of a and b cell sizes and with molecules of iPP and PE not crossing ab cell faces. The interface of amorphous iPP and PE was created by layering of ab cell faces of these systems of amorphous iPP and PE. The combined system was subjected to energy minimisation and then treated by MD simulation at 300 K for 500 ps.
crystalline PE - amorphous iPP, amorphous PE - crystalline iPP. Crystalline iPP was constructed with matching of its (010) crystallographic plane, (low density of methyl groups on the surface), with ab cell face. The amorphous cell of PE was constructed with matching of a and b cell sizes with a and b cell sizes of the iPP crystalline cell. The interface of crystalline iPP and amorphous PE was created by layering of this ensembles by ab faces.
Crystalline PE was constructed with matching of its (100) crystallographic plane with ab cell face. The amorphous cell of iPP was constructed with matching of a and b cell sizes with a and b sizes of the PE crystalline cell. The interface of crystalline PE and iPP was created by layering of these ensembles by ab cell faces. Crystalline - amorphouse interfaces were subjected to energy minimisation and then treated by MD simulation at 300 K for 500 ps.
crystalline PE - crystalline iPP
Direct layering of the iPP crystalline ensemble with the PE crystalline ensemble is not a good strategy: due to the periodic boundary conditions, chains of PE would not be able to rotate during MD simulation with respect to the orientation of iPP chains, and therefore MD simulation of one PE/PP crystalline-crystalline interface would not allow to investigate all possible PE/PP crystalline-crystalline interfaces. On the other hand the direct simulation of epitaxial crystallisation of PE on the PP substrate is also not possible, since the characteristic times of epitaxial crystallisation are much longer than times accessible in the MD simulation. Therefore we decided to create ensembles of crystalline PE with different orientations of PE chains inside the cell. This method allows to investigate properties of crystalline-crystalline PE/PP interface with a particular orientation of PE molecules with respect to the orientations of PP chains. The experiments predict several possible orientations of PE molecules with respect to the orientation of PP molecules, as has been described above.
It was decided to restrict the investigation of crystalline-crystalline interfaces to those established in epitaxial crystallisation and to several reference interfaces. Crystalline iPP was constructed with matching of the (010) crystallographic plane, both low and high density of methyl groups, with the ab cell face. Crystalline PE was constructed with matching of the (100) crystallographic plane with the ab cell face, and matching of a and b cell sizes as close as possible to a and b cell sizes of crystalline iPP. The exact matching was of course impossible and the cell sizes mismatched by 6%-8% of their cell sizes. Initial orientations of crystalline PE chains inside the cell were set to 0°, 90°, 47°, -47°, where the angle 47° denotes an interface where PE molecules are parallel to rows formed by methyl groups on the iPP surface with an 5.05 Å inter-row distance.
Ensembles of pure crystalline PE with polyethylene chains initially rotated in the cells were treated by MD simulation in order to check whether they have the same structural and energy properties as an unrotated PE
25crystalline ensemble. The potential energy terms like bond stretching, changing of angle and e.i. of rotated PE ensembles fitted to energetically parameters of unrotated PE within 5%. The rotated ensembles of crystalline PE preserved the orthorhombic crystalline structure. Since the cell sizes of crystalline PE and crystalline iPP did not match exactly, the cells sizes were adjusted. The a and b cell sizes of PE and iPP were scaled in order to fit to each other and the c cell sizes were scaled in order to keep the volume constant. For example, for the layering of the iPP (010) plane with the low density of methyl groups on the surface and the (100) plane of PE, iPP had a=28.12 Å, b=26.41 Å and a=25.7 Å, b=24.64 Å, which gives 9% and 7% mismatch of the cell sizes, respectively.
Crystalline PE - crystalline iPP interfaces were subjected to energy minimisation and then treated by MD simulation at 300 K. In total they were treated by 200-500 ps of MD simulation, but since molecules at crystalline-crystalline interfaces do not have much freedom, no further decrease of the potential energy could be observed after the first 50 ps of MD run.
In order to compare crystalline - crystalline interfaces with different initial orientation of PE molecules with respect to the orientation of iPP chains, adhesion energies were calculated. Adhesion energies were calculated as the sum of the energy of mixing and surface energies.
The energy of mixing was calculated for each particular orientation of PE molecules with respect to the orientation of iPP chains, as a difference in energy of the combined system and the energies of bulk crystalline PE and iPP.
Surface energies of crystalline PE and PP were calculated in the environment of benzene. The calculation of surface energies with vacuum as environment caused melting of crystalline surfaces of iPP and PE. Therefore we had to apply pressure on the surfaces of iPP and PE. We considered benzene as a better environment. Benzene is a non-polar solvent and should cause less perturbation of PE and PP surfaces.
Energies of PE and iPP ensembles as well as combined systems were extracted from MD trajectories of this systems. Adhesion energies and surface energies were normalised to the interfacial (or surface) area.
Energies of bulk PE and iPP or combined systems were determined from the MD trajectories of these systems. Potential energies of the systems were stored every 0.5 ps and then averaged over least 50 ps. It is important to notice that the potential energy determined for two last runs of 50 ps duration differ less than the error bar of the potential energy determination. It is also important that the difference between the potential energy of the combined system and the sum of the potential energies of bulk PE and PP was much higher than the error bar of the potential energy determination.
Computation of crystalline PE and iPP surface energies in benzene environment were carried out for the (100) and (010) crystallographic planes respectively: 29
Here ‘high means high density of methyl groups on the (010) crystallographic surface of iPP at the interface with PE, and ‘low means low density of methyl groups on the (010) crystallographic surface of iPP at the interface with PE. Both energy of mixing and adhesion energies are presented since it is important to notify that the energy of mixing is always positive, while the adhesion energies vary from positive to negative values.
The calculated surface energies for amorphous PE and iPP in benzene environment are 0.26 and 0.13 respectively. The adhesion energy for crystalline iPP and amorphous PE interface is -0.18 , while for the interface of crystalline PE and amorphous iPP it is 0.17 .
Structural changing at the interface
The structure of crystalline PE and iPP did not change when PE and iPP were layered with amorphous PE and iPP.
Rotation 47° of PE molecules with respect to the orientation of PP chains, low density of methyl groups on the PP contacting surface
The ensemble consisting of two layers of PE and PP has two PE/PP interfaces due to the periodic boundary conditions. In order to avoid possible interference of two interfaces we constructed model systems, consisting of three layers - PE layer, PP layer and layer of benzene. It should be mentioned that no significant structural difference of PE and iPP between the three layer and the two layer systems were observed after MD simulation.
The structure of PE changed from orthorhombic to monoclinic for the entire layer of PE. We could not detect the interfacial depth of PE: increasing the thickness of PE layer from 20 Å to 40 Å did not help to resolve an interfacial depth of PE. The (
The structure of iPP did not change drastically in the entire layer of iPP, only one layer of PP helices closest to the PE has changed: every second methyl group along the PP helix has a bit rotated, these methyl groups are indicated on the figure 8 with arrows.
PE:(monoclinic) a=8.7 Å, b=2.54 Å and c=4.5 Å, =89°; =95.5° and =91°
PP: a=6.7 Å, b=21 A and c=6.6 Å, =90°; =94° and =91°
Figure 8 A) Interface of crystalline iPP and crystalline PE with low density of methyl groups on the PP contacting surface. End on view on PE molecules, iPP molecules are rotated about 47° to the point of view. Arrows point out the methyl groups on the surface of iPP which were initially oriented upwards. B) Top view on orthorhombic crystalline polyethylene.
Rotation 47° of PE molecules with respect to the orientation of PP chains, high density of methyl groups on the PP contacting surface
The structure of PE and iPP crystalline unit cells did not change significantly.
PE:(orthorhombic) a=7.85 Å, b=4.8 Å and c=2.55, ===90°
iPP: a=6.7 Å, b=20 Å and c=6.6 Å, =89°, =93° and =92°
Figure 9 shows the snapshot of the MD equilibrated structure of the PE/iPP interface.
Figure 9 Interface of crystalline iPP and crystalline PE with high density of methyl groups on the crystalline iPP contacting surface. End on view on PE molecules, iPP molecules are rotated about 47° with respect to the point of view.
Amorphous - amorphous and amorphous - crystalline interfaces
One of the present limitations of the MD simulation method is that we can simulate just several nanoseconds, while all processes which we are interested in this work e.g. (crystallisation and epitaxial crystallisation) take place on much longer time scales than several nanoseconds. If we choose a starting structure far from its equilibrium, we cannot expect that during MD simulation it would converge to its equilibrium state. This disadvantage should be taken into account during simulation of amorphous polymers at temperatures below the temperature of their crystallisation. If we perform MD simulations long enough we should see partial crystallisation of amorphous polymers.
30The fact, that PE and PP are semicrystalline polymers both as neat materials and in the blend suggest amorphous - amorphous and crystalline - amorphous interfaces. It should be pointed out that amorphous parts, which give an amorphous halo in X-ray scattering experiments, are not purely amorphous, but are just parts of polymer chains in-between crystalline lamellae, which are forced to stay in a non crystalline state. This state can even not be called amorphous because the chain orientation is induced by the presence of the crystalline lamellae as it was mentioned in the introduction. In computer simulation nothing prevents polymers from crystallisation at temperatures below temperature of crystallisation.
From the statements made above one can conclude that even when we do not see any further decrease of potential energy with time, this does not mean that amorphous ensembles are already equilibrated. This is true for the bulk amorphous systems and as well as for the interfaces of two amorphous polymers or for the interfaces of semi-crystalline polymers. If we simulate amorphous systems for a very long time, we should see crystallisation of bulk amorphous PE and PP and epitaxial crystallisation of layered system.
On the other hand crystalline-crystalline interfaces do not have much freedom - e.g. PE macromolecules can not rotate laterally on top of iPP chains. If we assume that the crystalline structures of both PE and iPP do not differ very much from bulk crystalline PE and iPP (orthorhombic and -modification respectively), then the system of combined PE and iPP should not undergo large conformational changes during MD. Therefore, MD trajectories should not be very long to minimise the energy of crystalline-crystalline ensembles. Experimental investigations of structures, formed by PE during epitaxial crystallisation show that PE crystallises epitaxially either in the orthorhombic structure or in the monoclinic depending on substrate and environmental conditions. iPP can crystallise in three different crystalline forms: -, -, and -modifications. On the other hand it was established that just the crystalline modification of iPP induces epitaxial crystallisation of PE, and iPP crystallises epitaxially in the -modification on the PE substrate. Based on the assumptions made above one can conclude that it could be possible to investigate by means of computer simulations crystalline-crystalline interfaces of PE and iPP.
The algorithm of layering of crystalline-crystalline interfaces could cause artificial structural changes. As it was mentioned above ensembles of crystalline PE and PP had a mismatch in cell sizes in the a and b axes. During layering this
31mismatch was corrected by scaling of the PE and PP cell sizes, which means that bond lengths and angles were scaled as well. For example in the case of layering of a PE ensemble with PP, when PE molecules were oriented at 47° with respect to the orientation of PP chains, bonds and angles were scaled as follows:
This artificial scaling of bond length and angles could cause several shortcomings:
Changing bond lengths without a correlated scaling of the force field leads to storing of a considerable amount of energy in the system. There could be several ways leading to structural changes in the system due to the stored energy. a) If we assume that energy minimisation does not relax the molecular system to the global minimum but stops at a local minimum, then the difference of energy between global and local minima should be stored in all degrees of freedom. This means that for example the energy stored in bond lengths could be distributed to torsion potentials, and this could lead to the appearance of gauge defects in the PE structure and the changing the helical structure of PP. b) Releasing of a large amount of energy during MD simulation could be also dangerous: for example it may lead to local heating provoking local structural changing.
Analysing crystalline - crystalline interfaces shows that bond lengths and angles relax to their normal values. For example in the case of a crystalline - crystalline interface while, PE molecules are oriented at 47° with respect to the orientation of PP chains, low density of methyl groups on the PP surface, bonds and angles have converged to the following values (after energy minimisation and 50 ps of MD simulation):
Analysing of the crystalline - crystalline interface after minimisation and 50 ps of MD simulation does not reveal the appearance of gauge defects or destroying of the helical structure of PP.
Adjusting of cell sizes causes that one part of the combined system wants to increase the cell size while the second part of these molecular system wants to decrease the cell size. In the case of layering of PE and PP this could be relieved by small rotations of PE molecules with respect to PP molecules or by structural changes of PP and PE layers. I do not know how to argue that either structural
32changes of PE and PP in the combined systems were caused by cell size mismatches or induced by the interaction of PE and PP at the interface. The answer could probably be found by comparing of results of computer simulation with experimental results.
Comparing of experimental results with results of computer simulation
Computer simulated structures of pure crystalline PE and iPP -modification slightly differ from experimentally measured structures of PE and iPP -modification.
MD simulated: a=7.66 Å, b=5.06 Å and c=2.58 Å, ===90°
experiment: a=7.4 Å, b=4.94 Å and c=2.534 Å, ===90°
MD simulated: a=6.57 Å, b=21.5 Å and c=6.01 Å, ==90°, = 97°
experiment: a=6.65 Å, b= 20.78 Å and c=6.50 Å, ==90°, = 97°
It is also important to compare distances between rows of methyl groups: 5.05 A, 4.25 Å from experiment and 4.9 A, 4.28 Å from computer simulation. The model of epitaxial crystallisation was based on lattice matching of 5.05 A of iPP with 4.94 A of PE. Structures of computer simulated crystalline PE and iPP do not match exactly with experimentally established structures. On the other hand computer simulated crystalline PE and iPP exhibit a lattice matching within the same error bar.
The calculation of adhesion energies by means of computer simulation allows to establish the structure with the lowest adhesion energy, hence to predict epitaxial crystallisation of PE on PP substrate and vice versa epitaxial crystallisation of PP on a PE substrate. Adhesion energies for PE - PP interfaces are summarised in the table 1. It is hard to compare the computer calculated adhesion energy with the experimentally measured energy needed to split an interface into parts. The computer calculated adhesion energy corresponds to the energy of an ideal interface - a flat surface of PE interacting with a flat surface of PP. In a real experiment the surfaces of both samples are not flat any more, with some interpenetration of one polymer material into another. Depending on the preparation conditions mixing on the molecular level in the interfacial region should be also taken into account. In the particular case of the PE - iPP interface it is known that PE forms tongues which penetrate into iPP. The experimentally
33measured adhesion energy includes the energy of yielding of these tongues and consist mostly of this tongue yielding energy.
The calculated adhesion energies and energies of mixing could be compared effectively with experiments. The calculated energy of mixing is always positive, which means that the computer simulation predicts immisciblity of PP and PE. It was clearly proven experimentally that PE and PP are immiscible in the melt. Most of the experimental works indicate also immisciblity of PE and PP in the solid form - ‘weak PE/iPP interfaces, but it was supposed as well that improved mechanical properties of PE/iPP blends could be explained by ‘strong PE/iPP interfaces.
The lowest calculated adhesion energy (table 1) corresponds to the case of 47° orientation of PE molecules with respect to iPP chains and the low density of methyl groups on the iPP surface. PE molecules have the same orientation with rows formed by methyl groups on the iPP surface with an inter-row distance of 5.05 Å. The adhesion energy is higher when the PE molecules are oriented 47° with respect to the orientation of iPP chains, and the PE molecules have the same orientation with rows formed by methyl groups on the iPP surface with an inter-row distance of 4.25 Å. We did not consider by the computer simulation all orientations of PE molecules with respect to the orientation of iPP chains. In addition we did not investigate the interaction of different crystallographic planes of both PE and iPP. Within the range of simulated ensembles, from calculated adhesion energies we may conclude that PE molecules should crystallise epitaxially on iPP at 47° with respect to the orientation of PP chains, and with low density of methyl groups at the surface.
The model of epitaxial crystallisation of PE on the iPP substrate is still in debate in the literature. It was supposed that the ‘cross-hatched morphology of epitaxially crystallised PE on the iPP substrate, is driven by the ‘cross hatched morphology of the iPP substrate. Due to the lattice matching of crystalline PE and iPP, PE molecules crystallise at about 50° with respect to the orientation of iPP chains. iPP substrates crystallised under normal conditions, have two chain orientations at 100° to each other. This ‘cross hatched nature of iPP substrates induces the ‘cross hatched morphology of epitaxially crystallised PE. This model does not fit to the experimental work1 of epitaxially crystallised PE on the highly oriented iPP substrate. By drawing, highly oriented films of iPP were obtained, where molecules of iPP were oriented just in one direction in this film. Epitaxially crystallised PE on this substrate also shows a ‘cross hatched morphology. In this experiment ‘cross hatched morphology of epitaxially
34crystallised PE can not be explained by the ‘cross hatched morphology of the substrate.
In order to explain the ‘cross hatched morphology one should take into account that the probability to find left and right handed helices on the surface of iPP is equal. This leads to the conclusion that the surfaces of different domains of iPP could be composed of left handed or right handed helices. If the rows of methyl groups with an interrow distance of 5.05 Å formed by right handed helices have the angle 47° with the helical axes then rows of methyl groups with 5.05 Å interrow distance formed by left handed helixes have the angle -47° with the helical axes. The ‘cross hatched morphology of epitaxially crystallised PE on iPP could be explained by the presence of both left and right handed helices on the surface of iPP.
It is not possible to distinguish by X-ray scattering whether PE crystallises on the (010) crystallographic surface of iPP with high a density of methyl groups or with a low density of methyl groups. On the other hand it was established3 that the (010) surface of iPP, produced for epitaxial crystallisation of PE, contains low density of methyl groups. To produce a (010) crystallographic surface of iPP for epitaxial crystallisation, iPP is crystallised on a crystalline low molecular weight substrate, which induces the (010) crystallographic plane of iPP. After removing of the low molecular weight substrate, the (010) crystallographic plane of iPP is ready. This result shows that the (010) crystallographic surface of iPP with the low density of methyl groups is energetically more favourable in contact with a low molecular weight solvent. It also indicates that the (010) crystallographic plane of iPP with low density of methyl groups could be energetically more favourable in contact with epitaxially crystallised PE.
The energetically most favourable combined ensemble is the ensemble with PE chains oriented at 47° with respect to the orientation of iPP molecules with the low density of methyl groups on the iPP contacting plane (table 1.). The analysis of the structural changes shows that the PE structure has changed entirely from orthorhombic to monoclinic. Energetically the orthorhombic structure is more favourable, but the energy difference between orthorhombic and monoclinic crystalline form is very low, as shown by computer simulation7,8. As it was described above structural changes in the combined system could be induced by additional energy introduced into the system or by tension induced through adjusting cell sizes, especially when the energy of orthorhombic and monoclinic structures does not differ very much. On the other
35hand it was found that some substrates do induce epitaxial growth of PE with the monoclinic structure. The observed monoclinic phase is spatially transient: it does not go beyond 3 or 5 nm from the substrate surface6. The computer simulation does not allow to go beyond 5 nm thickness of PE layer, so we just cannot see the transition from the monoclinic to the orthorhombic crystalline phase.
MD simulation of PE - iPP interfaces was performed. Amorphous - amorphous, crystalline - amorphous and crystalline - crystalline interfaces were simulated. Due to the drawback of the periodic boundary conditions which does not allow lateral rotation of one crystalline phase on top of the second one, the simulations of crystalline-crystalline interfaces were restricted to that adopted from the experiments on epitaxial crystallisation of PE and iPP and to several reference interfaces.
Adhesion energies in the benzene environment were calculated in order to compare different types of interfaces. It was found that the strongest adhesion for crystalline-crystalline interfaces corresponds to the rotation of PE macromolecules of about 47° with respect to the orientation of iPP helixes with low density of methyl groups on the iPP surface. At this particular orientation PE molecules fit exactly in the rows formed by methyl groups on the surface of iPP. Hence the structure model for epitaxial crystallisation of PE and iPP has been proven. Experimental methods do not provide information whether PE crystallises epitaxially on the surface of iPP with high or low density of methyl groups. Strong adhesion for the case PE-iPP interface with low concentration of methyl groups allow to predict epitaxial crystallisation of PE molecules on the surface of iPP with low surface concentration of methyl groups.
The unexpected transition of crystalline PE from orthorhombic to monoclinic crystalline form is observed for the interface with the strongest adhesion energy. It is possible that this phenomena is caused by the artefacts of the building of a super-cell with an interface of PE and iPP. On the other hand it is also possible that the transition from orthorhombic to monoclinic crystalline form happens just in a very thin layer of PE at the interface, while bulk PE is still in the orthorhombic crystalline form. Therefore the monoclinic crystalline form can be space transient and was not observed in the experiment on the epitaxial crystallisation because the layer of PE in the monoclinic form was too thin to be detected without special preparation conditions of the experiment.
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