ISSN 10637834, Physics of the Solid State, 2013, Vol. 55, No. 2, pp. 443–449. © Pleiades Publishing, Ltd., 2013. Original Russian Text © D.V. Novikov, G.K. Elyashevich, V.K. Lavrentyev, I.S. Kuryndin, N.N. Saprykina, G.I. Vorobyev, A.V. Varlamov, V. Bukošek, 2013, published in Fizika Tverdogo Tela, 2013, Vol. 55, No. 2, pp. 398–404.
POLYMERS
Superlattices of Lamellae in Microporous Oriented Polyolefine Films D. V. Novikova, *, G. K. Elyashevicha, **, V. K. Lavrentyeva, I. S. Kuryndina, N. N. Saprykinaa, G. I. Vorobyevb, A. V. Varlamovb, and V. Bukošekc a
Institute of Macromolecular Compounds, Russian Academy of Science, Bolshoi pr. 31, St. Petersburg, 199004 Russia * email:
[email protected] ** email:
[email protected] b SaintPetersburg State University of Cinema and Television, ul. Pravdy 13, St. Petersburg, 191119 Russia c Faculty for Natural Sciences and Engineering, University of Ljubljana, ∨ Sne z niška cesta 5, Ljubljana, 1000 Slovenia Received June 26, 2012
Abstract—The structure and mechanism of the formation of superlattices lamellae in microporous polyole fine (polyethylene and polypropylene) films obtained by polymer melt extrusion followed by annealing, uniaxial extension, and thermal fixation stages have been studied by scanning electron and atomicforce microscopy. It has been shown that oriented anisometric particles, i.e., lamellae aggregates, are formed in films as the spin draw ratio λf increases. At the stage of uniaxial extension (pore formation) of annealed films, a particle ensemble transforms to spatial superlattices of lamellae. Numerical processing of electron micros copy images of the film surface show that the nonmonotonic dependences of the correlation length of density fluctuations and the ratios of the alternation period of particles along extension to their thickness on the parameter λf correspond to a unified mechanism of lamellae ordering. DOI: 10.1134/S1063783413020212
1. INTRODUCTION Microporous films fabricated based on polyolefine melt extrusion [1] are characterized by a multilevel (multifractal) structure. Such a structure is formed by stacks of crystalline lamellae arranged normally to the orientation (extension) direction of samples, so that molecular chains in crystallites are oriented in the extension direction. Lamellae stacks are connected by thin “bridges” (stressed ties) and form the framework of the solidphase percolation cluster [2]. Cluster cav ities are pores which can be classified into three types, i.e., surface, closed, and through flow ones [1]. Char acteristic sizes of structural elements of the lowest scale level (individual lamellae) and the highestscale level (pores) can differ by two–three orders of magni tude [2, 3]. The irreversible nature of the processes of the formation of the multilevel supramolecular struc ture makes possible its selfordering [4] at various stages of microporous film fabrication. Two structure selfordering types are implemented in microporous polyolefine films [1, 2]. The first type includes percolation over pores (the formation of through pores) or the geometrical phase transition occurring upon reaching a critical degree of film porosity [1]. The second type is associated with the periodic spatial superlattice of lamellae due to the dis order–order transition resulting in ordering of particle aggregates, i.e., stacks of lamellae [2]. Both transitions
occur with the spin draw ratio λf at the stage of poly mer melt extrusion, provided that the other parame ters of the multistage film fabrication process remain fixed. Therefore, in [2], it was assumed that the melt extrusion stage predetermines the regularities of the structure formation when fabricating microporous films by the used method. We note that the percolation transition on the film surface from isolated pores to the spatially continuous network of the porous phase on the scale λf precedes the formation of superlattices of lamellae [2]. In this study, using scanning electron microscopy (SEM), we comparatively analyzed superlattices of lamellae in microporous films of polyethylene (PE) with various molecular masses and polypropylene (PP). The surface topography of annealed PP films obtained at various parameters λf was investigated by atomicforce microscopy (AFM). The objective of this study is to validate the unified mechanism of the structure formation of microporous polyolefine films, including the system selfordering controlled by the parameter λf at the stage of polymer melt extrusion. 2. OBJECTS AND METHODS OF STUDY Porous films were fabricated using commercial samples Nos. 1 and 2 of linear PE with molecular mass
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Structural parameters of superlattices and lamellae in microporous polyolefine films Solid phase No. 1 2 3
l0||, nm 25 – 26
Ωs
ξ, μm ±5%
l||, μm
0.43 0.62 0.71
0.20 1.80 0.07
0.06 0.90 0.04
Porous phase
L||, μm L⊥, μm ±5% ±5% 0.17 2.50 0.11
0.20 2.70 0.11
D
D||
D⊥
1.7 1.83 1.87
1.47 1.8 1.83
1.8 1.9 1.9
d, μm L||, μm L⊥, μm ±5% ±5% ±5% 0.09 1.20 0.05
0.17 2.50 0.11
0.40 1.30 0.11
D 1.7 1.5 1.4
Note: The fractal dimensions were calculated at R < ξ with an error of ±0.03.
Mw = 170000 (Mw/Mn = 4–5) and Mw = 250000 (Mw/Mn = 9–10), respectively, and sample No. 3 of isotactical PP (Mw = 380000, Mw/Mn = 4–5). At the stage of extrusion, the films were formed using a flat slit spinneret. The melt was crystallized in air. The degree of melt orientation was controlled by the spin draw ratio. The extruded films were annealed at a tem perature close to the polymer melting point. Uniaxial extension of annealed films at the pore formation stage was performed at room temperature to a degree of extension of 200% with a rate of 400% min–1. The final stage, i.e., thermal fixation, provided relaxation of internal stresses caused by extension and film size sta bilization [1]. Electron microscopy images of the porous film sur face were obtained using a LEO 1550 FE SEM (ZIESS, Germany) scanning electron microscope. Numerical processing of SEM images of the porous film surface was performed using the cluster twophase model on a square lattice [2, 3]. The lattice densities of clusters of solid (Ωs) and porous (Ωp = 1 – Ωs) phases in a twodimensional representation corre sponded to the relative fraction of marked lattice sites. The spatial distribution of phase clusters was stud ied using the radial function g(R) of the distributions of the lattice density with the powerlaw asymptotic behavior g(R) ~ RD – 2 in the initial region, where D is the fractal dimension of particles [2]. The periods of phase cluster alternation along (L||) and across (L⊥) the film orientation (extension) direction were deter mined using the functions g(R) calculated for corre sponding directions [2]. An analysis of the lattice models of oriented lamel lar structures showed that the particle thickness l|| sat isfies the relation l|| = 0.87Rmin, where Rmin is the posi tion of the first minimum of the function g(R), calcu lated normally to the particle orientation. The effective pore size d is correlated with Rmin for the directionaveraged function g(R) for the porous phase [2]. The correlation length ξ of density fluctuations was determined using the dependence of the “fractal” [5] lattice density ρ of the solid phase cluster on the scale, constructed in log–log coordinates [3].
To analyze the orientational order, we studied the parameter f = |ρ|| – ρ⊥|/(ρ|| + ρ⊥), where ρ|| and ρ⊥ are the densities ρ of the marked lattice sites, calculated in the film extension direction and in the transverse direction, respectively. The densities ρ|| and ρ⊥ are determined by averaging over oriented rectangles (after subtracting the background contribution of the lattice) [3]. In this case, the rectangle width was set equal to the doubled distance r between lattice sites, and the length l was varied. The surface topography of annealed PP films was studied by the AFM method (Solver Pro EC, Zeleno grad, Russia). The long period d0 in annealed films was deter mined by smallangle Xray scattering using a KRATKI camera. Using the values of the parameter d0 and the Xray degree of sample crystallinity κ, the thickness l0|| of individual lamellae in the orientation direction was calculated as l0|| = κd0. 3. RESULTS AND DISCUSSION In [1], it was found that at a fixed degree of uniaxial extension of annealed PE and PP films, their volume degree of porosity Ωp increases with λf in the region of λf lower than the threshold one at which through channels appear in the sample. As λf further increases, the parameter Ωp growth becomes slower, the depen dence of Ωp on λf flattens out, and Ωp reaches a certain constant value. The latter circumstance can be corre lated with the formation of a specific periodic struc ture of the solid phase cluster on the microporous film surface [2, 3]. Such a structure is characterized by identical periods L|| of alternating solidphase particles and pores in the film extension direction and can be considered as a superlattice of oriented lamellae [2]. We note that the value of the parameter λf at which the superlattice is formed depends on the sample fabrica tion conditions and polymer nature. Figure 1 shows the SEM images of superlattices in samples Nos. 1–3; Figs. 2 and 3 show the functions g(R) for clusters of two phases, averaged over direc tions and calculated along and across the film exten sion directions.
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1.5 (a)
2
1.0 1
0.1
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(b)
g(R)
1.5 1 1.0
200 nm
(а)
0.4
2 1
1.5
2
3 (c)
2 1.0
0.5 0
200 nm
(c)
Fig. 1. SEM images of superlattices of lamellae in polyole fine microporous films. Samples (a) No. 1 (λf = 69), (b) no. 2 (λf = 78), and (c) No. 3 (λf = 78).
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R, μm
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Fig. 2. Directionaveraged radial functions g(R) of phase cluster density distributions in superlattices ((1) solid phase and (2) porous phase). Samples (a) No. 1, (b) No. 2, and (c) No. 3.
200 nm
(b)
1
The data of the table and Fig. 3 show that the superlattices have structural features general for all the studied porous samples. First, the necessary equality of the alternation periods L|| for solid and porous phases is exactly satisfied (Fig. 3a). Second, the peri odicity of the alternation of the lattice density of two phases across the orientation direction is observed; therewith, the corresponding periods L⊥ are multiple of each other (Fig. 3b). Third, the ratio of the period L|| of alternation of particles (lamellae stacks) to their thickness l|| is 2.7–2.8. As the solidphase cluster density Ωs increases, reg ular changes occur in the superlattices (see the table). The fractal dimension of porousphase clusters sharply decreases from D = 1.7 to D = 1.4–1.5, which is caused by the loss of percolation in pores in the two dimensional representation of the film surface. The lattice symmetry transforms, and the film surface tex ture changes [3]. In this case, the fractal dimensions of 2013
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(a) 1.5
1.5 1
No. 1
No. 1 1
1.0 2
0.1
0.2
0.3
0.4
0.1
0.2
0.3
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0.5
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No. 2 g(R)
1.5 g(R)
2
1.0
0.5
1.5 1 2
1.0
1
2
3
1
2
3
1.5 1.5 No. 3 No. 3
2 1
1.0
1.0
2
0
0.05
0.10 R, μm
0.15
0
1 0.05
0.10 R, μm
0.15
Fig. 3. Radial functions g(R) of phase cluster density distributions in superlattices ((1) solid phase and (2) porous phase) in the directions (a) along and (b) across film extension. Samples Nos. 1–3.
the solidphase cluster (on the scale R < ξ), calculated along (D⊥) the orientation direction and normally (D⊥) to it come close to each other and to the average D. The directionaveraged functions g(R) for clusters of two phases do not reveal periodicity of the structure of porous films with increasing Ωs (Fig. 2, curves c). We can see in Fig. 4 that the orientational parame ter f for sample No. 3 is almost unchanged with increasing rectangle length and is close to zero (Fig. 4, curve 3), which, along with the equality L|| = L⊥ for clusters of two phases indicates the homogeneous biaxial [3] surface texture. On the contrary, for sample No. 1, the parameter f sharply increases at l < ξ, whereas it remains almost unchanged at l > ξ (Fig. 4, curve 1). Such behavior of the function f(l) results from the axial [3] textures on the scale of the correla tion length ξ. In the case of sample No. 2, the f increase is followed by flattening at l > 2ξ (Fig. 4, curve 2), which reflects the surface texture inhomoge neity, whose type depends on the scale of the study.
The texture transformation is caused by a change in the relative contribution of lamellae stacks and con necting stressed ties to the spatial distribution of the solidphase cluster density [3]. To reveal the genesis of superlattices of lamellae, let us consider the general features of structural changes in microporous films with increasing parameter λf. First, among such features is the nonmonotonic behavior of the correlation length ξ of the solidphase cluster (Fig. 5). The ξ maximum on the scale λf pre cedes the superlattice formation and is associated with the appearance of percolation over pores in the two dimensional (E = 2) surface representation [2, 3]. Sec ond, as shown previously [3], the formation of the per colation cluster of the porous phase results in surface fractalization on the scale R > ξ. As a result, the surface becomes multifractal. On the scale R < ξ, the fractal properties of the surface are controlled by the selfsim ilar structure of particles, i.e., lamellae stacks; on the scale R > ξ, the surface fractal dimension is close to
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D ≈ 1.9 (E = 2) for the internal percolation cluster [3, 6]. It is important that the fractal dimension of the solidphase cluster at R > ξ during the superlattice for mation is identical to the Euclidean space dimension; in the twodimensional representation, D = 2 [3].
1 0.6 f 0.4 0.2 3 0
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Fig. 4. Dependences of the orientational parameter f on the scale factor in superlattices. Samples (1) No. 1, (2) No. 2, and (3) No. 3.
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䉱
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Fig. 5. Dependences of the ratio of the correlation length ξ to the lamellae thickness l0|| on the parameter λf in microporous films. Samples (1) No. 1 and (2) No. 3.
3 1 (L/l)||
The AFM study of the surface topography of annealed PP films shows that supramolecular struc tures are selfordered already at the stages of polymer melt extrusion and subsequent annealing; as λf increases, this leads to the formation of the orienta tional order and the quasiperiodic distribution of par ticles in the orientation direction. As λf increases, the particle anisotropy increases (Figs. 7a and 7b), which results in the appearance of rather extensive structures layered on each other and extended in the direction perpendicular to the molecular orientation direction (Fig. 7c). Such regularities were previously noted in the study of crystallization of flowing melts of flexible chain polymers [11]. During the formation of an ensemble of oriented particles, the surface roughness increases more than twice, and relief height oscilla tions appear in the melt orientation direction with an average period of 0.1 μm (Fig. 7c). This value is almost identical to the period L|| of particle alternation on the microporous PP film surface (see the table, sample No. 3). Thus, pore formation at the stage of uniaxial extension of annealed PP films results in splitting of oriented supramolecular structures into smaller aggre gates, i.e., lamellae stacks; in this case, the periodicity of particle alternation is retained unchanged. The entropy production [7] within the system due to an increase in the number of particles is minimized by the PHYSICS OF THE SOLID STATE
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0.8
Thus, lamellae ordering in microporous polyole fine films, controlled by the parameter λf occurs according to the universal selfordering mechanism in the dissipative system. Such a mechanism is consistent with both the increase in fluctuations [7] and the appearance of spatial selfsimilarity [8], which pre cede the formation of superlattices of lamellae on the scale λf. The dependences of the ratio L||/l|| on the parameter λf for solidphase particles in microporous polyolefine films are also universal (Fig. 6). For two PE samples, experimental points fall on the same curve (curve 1) shifted on the scale λf with respect to the curve for the PP sample (curve 2). The valley in these dependences corresponds to increasing fluctuations in the particle distribution density and surface fractalization. It is important that the condition L||/l|| ≈ e (e is the natural logarithm base) is satisfied during the formation of superlattices of lamellae or ensembles of oriented lamellae stacks with increasing λf. Such a value of the parameter L||/l|| corresponds to the thermodynamically optimized structure of ensembles of particles [9, 10], whose size distribution is set by the maximum entropy of “mixing” of elements belonging to two structural levels, i.e., oriented lamellae and their stacks.
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2 20
40
λf
60
80
Fig. 6. Dependences of the ratio of the period L|| of alter nation of particles to their thickness l|| on the parameter λf in microporous films: (1) samples Nos. 1 and 2, (2) sample No. 3.
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(a)
μm
0.05
0 0.5 μm
1.5
μm
(b)
μm
0.05
0 0.5 μm
1.5
μm
(c)
μm
0.13
0 0.5 μm
1.5
μm
Fig. 7. Twodimensional AFM images (the melt orientation direction s is vertical) and profilograms (in the direction s) of the sur faces of annealed PP films. The spin draw ratios are 39 (a), 51 (b), and 78 (c).
entropy decrease during the formation of the ordered superlattices of lamellae. 4. CONCLUSIONS The formation of superlattices of lamellae in microporous polyolefine films occurs via the universal
mechanism of particle selfordering, controlled by the spin draw ratio λf of the melt. At the stages of extrusion and subsequent annealing, an ensemble of oriented supramolecular structures is formed in films as the parameter λf increases. At the stage of uniaxial exten sion of films, such an ensemble transforms to a spatial network of smaller particles, i.e., lamellae stacks
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(superlattices of lamellae), due to irreversible splitting of structons. The fundamental structure of the super lattice is controlled by the maximum entropy of mix ing of two structural elements of microporous films, i.e., oriented lamellae and their aggregates (lamellae stacks).
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Translated by A. Kazantsev
ACKNOWLEDGMENTS This study was supported by the Russian Founda tion for Basic Research (project no. 100300421a) and the project of collaborative research of the Russian Academy of Sciences and the University of Ljubljana (Slovenia) (BIRU/1213032). REFERENCES
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