ISSN 10637834, Physics of the Solid State, 2015, Vol. 57, No. 5, pp. 1028–1032. © Pleiades Publishing, Ltd., 2015. Original Russian Text © D.V. Novikov, I.S. Kuryndin, G.K. Elyashevich, 2015, published in Fizika Tverdogo Tela, 2015, Vol. 57, No. 5, pp. 1012–1016.
POLYMERS
Topological Structure of Microporous Oriented Polypropylene Films D. V. Novikov*, I. S. Kuryndin, and G. K. Elyashevich** Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoi pr. 31, St. Petersburg, 199004 Russia * email:
[email protected] ** email:
[email protected] Received November 11, 2014
Abstract—According to the data of scanning electron microscopy, gravimetry, and permeability measure ments, the porous structure of membrane samples obtained in a multistage process including extension of annealed polypropylene films formed at the stage of polymer melt extrusion has been studied. It has been shown that, as the cooperativity of lamella ordering (selfassembly) increases at the stage of film extension (pore formation), the topological model of the porous phase of membranes changes from model (1), i.e., a random network of channels, to model (2), i.e., oriented through flow channels. The transition between two models is controlled by the melt spin draw ratio. DOI: 10.1134/S1063783415050248
1. INTRODUCTION In [1], the features of crystalline lamella ordering (selfassembly) in the production of porous mem branes from polypropylene (PP) in the multistage pro cess [2] including melt extrusion, annealing of extruded films, their uniaxial extension, and thermal fixation were studied. It was shown [1] that lamellae are selfassembled at the stage of uniaxial extension of films (pore formation stage) and is controlled by the annealing temperature (Tann). As a result, a regular (along the extension axis s) lamella lattice is formed on the membrane surface due to moving apart of these structural elements and the formation of discontinui ties (pores) between them. In such a lattice, lamellae are perpendicular to the s axis and are linked by tie chains (ties), while molecular chains in crystallites are aligned along the orientation direction (Fig. 1). In [1], two selfassembly mechanisms with increas ing Tann were detected: the gradual and bifurcation ones; the latter differs is characterized by a higher cooperativity of the lamella ordering process. These mechanisms correspond to different dependences of the order parameter (degree of lamella ordering) along the s axis) on Tann. The choice of this or that mecha nism by the system depends on the melt spin draw ratio λs during extrusion. It is known that both the orientational order of lamellae [1] and the degree of orientation of polymer chains [3] increase with increasing λs. This increase is nonlinear, which is indicated by both the nonmono tonic dependence of the correlation length on λs for polyolefin membranes [4] and a significant scatter of the data on birefringence in polyethylene membranes, obtained by changing the parameter λs [3]. It can be assumed that the nonlinear in λs orientation behavior
in membranes reflects different conditions of their structure formation depending on conditions of poly mer melt extrusion. In this case, the transition from one mode to another is accompanied by a change in the orientation of both molecules and supramolecular structures themselves and porous phase clusters. Of particular interest is the disorder–order orientation transition on the λs scale, associated with the forma tion of oriented through channels in membranes. As shown previously [5], the formation of the porous structure of membranes has a percolation mechanism, and the dependence of the permeability G (flow rate through the membrane) on λs exhibits a per
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Fig. 1. SEM image of the regular lamella lattice on the PP membrane surface (λs1 = 78, Tann = 443 K).
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colation threshold for which the overall porosity P (the sample volume fraction occupied with pores) in the case of PP membranes is 23 ± 2% [6]. In [1], by the example of PP membrane samples formed at λs1 = 44 and λs2 = 78, the dependence of G on the parameter τ = (P – P*)/P* characterizing the degree of deviation of the parameter P from the percolation threshold P* was studied. At fixed λs and the degree of film exten sion, the parameter P in the region P > P* was varied by changing Tann (P linearly increases with Tann [6]). It was shown that the function G(τ) has a powerlaw form G ~ τt and is characterized by the critical indices t = 1.5 and t = 1.9 for λs1 = 44 and λs2 = 78, respec tively. We note that the membrane thickness increases with Tann by no more than 20% (within experimental error), hence, the effect of the thickness on the depen dence G(τ) behavior can be neglected. By analogy between the membrane permeability and the conductivity of twophase systems such as conductor–dielectric [7, 8], it was assumed [1] that the change of the critical index t with increasing λs can be associated with the transition from percolation in a random inhomogeneous medium (t = 1.5) to anisotro pic percolation over oriented through channels (t = 1.9). Such a transition should be a consequence of an increase in the cooperativity of the lamella ordering process at the stage of pore formation and the forma tion of a regular spatial 3D lattice of particles. In this paper, we present the set of experimental data, which confirms the validity of the previously advanced hypothesis of two models of the topological structure of the porous phase of membranes. Calcula tions by the data of scanning electron microscopy (SEM), gravimetry, and permeability measurements are presented. Unlike [1] in which the emphasis was on the solid phase of membranes, in this work, we comprehensively study the evolution of porous phase clusters as the degree τ of deviation from the percola tion threshold P* increases in PP membranes formed at λs1 = 44 and λs2 = 78. Membranes with different porosity P, produced under different annealing condi tions were used. The objective of this study is to validate different models of percolation in the membrane samples under study and to determine the relation between the coop erative mechanism of lamella selfassembly at the stage of pore formation and the formation of the spe cial topological structure of the porous phase, i.e., ori ented through channels. 2. OBJECTS AND METHODS OF INVESTIGATION Porous films were prepared using grades of isotac tical PP with molecular mass Mw = 380000 (Mw/Mn = 4–5). The films formation at the stage of polymer melt extrusion was performed using a flat die. The melt was crystallized in air. The degree of melt orientation was PHYSICS OF THE SOLID STATE
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set by the spin draw ratio λs: λs1 = 44 and λs2 = 78. Extruded films were annealed under isothermal con ditions. The porous structure of membranes was formed at the stage of uniaxial extension of annealed films [2], performed at room temperature; the degree of extension at this stage was 200% is for studied sam ples. As in [1], P of samples was varied by changing Tann in the range of T* < Tann < Tm, where T* corre sponds to the percolation threshold P* and depends on λs, and Tm is the polymer melting temperature. At the final stage, thermal fixation of samples was per formed for relaxation of inner stresses resulting from extension [2]. The membrane permeability G was determined by measuring the liquid (ethanol) flow rate through the sample [9]; the overall porosity P was determined by the gravimetric method [6]. Computer processing of SEM images was carried out using the cluster twophase model on a square lat tice with the ratio r/ξ ≈ 0.1, where r is the distance between nodes and ξ is the correlation length [1] of phase clusters. Within this model, we calculated the average lattice density Ωp of porous phase clusters (porous phase fraction in twodimensional space), the average area S of clusters, their concentration C on the lattice, the radial distribution function gcc(R) of clus ters (cluster–cluster correlation function), and the radial distribution functions g(R) of the cluster net work density: one averaged over directions and the other calculated along the s axis. The effective size d and fractal dimension D of porous phase clusters were determined by the initial region (R < d) of the drop of curves g(R) using the powerlaw asymptotics, g(R)~ RD – 2 [1]. The topological structure of the membrane porous phase was analyzed using two approaches. The first approach is based on the general stereology principles [10] and is concerned with a comparison of similar structural characteristics (overall porosity) in the bulk (P) and in the twodimensional image of the surface (Ωp). The second approach is based on the study of the membrane permeability depending on the pore size d on the surface and a comparison of the obtained experimental dependence with that calculated by the Hagen–Poiseuille law [9] under the assumption that through channels are shaped as cylinders perpendicu lar to the membrane surface. It is known [11] that the liquid flow J through a capillaryporous body is defined in the general form by the Darcy law: J = KΔp/ηΔx, where Δp is the pressure difference on both membrane sides, η is the viscosity of filtered liquid, Δx is the membrane thickness, and K is a constant defined by the porous structure and, in theoretical treatment, depends on model selection for a real body. For the 2 2 model of through capillaries, K = P〈 R p 〉/8, where 〈 R p 〉 is the rootmeansquare pore radius. In the case of 2 cylindrical capillaries, P = Nπ R p Δx, where N and Rp
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Fig. 3. Dependences of the average lattice density Ωp of porous phase clusters on the surface of membranes on their overall porosity P. Membrane samples correspond to dif ferent film annealing temperatures Tann. The spin draw ratios are (1) λs1 = 44 and (2) λs2 = 78. The dashed line corresponds to the equality Ωp = P.
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increases, which corresponds to the pore growth under steadystate conditions at which the lamellar structure of membranes is ordered [1].
Fig. 2. Average (a) concentrations C and (b) areas S of porous phase clusters as functions of degree of deviation τ from the percolation threshold P*. Membrane samples correspond to different temperatures Tann of film anneal ing. The spin draw ratios are (1) λs1 = 44 and (2) λs2 = 78.
are their volume concentration and average radius, respectively; for the permeability G = J/Δp at N = 4 const, the relation G ~ R p or G ~ d4 following from the Hagen–Poiseuille law is valid. 3. RESULTS AND DISCUSSION An analysis of the twodimensional SEM images of the membrane surface makes it possible to clear up the features of pore formation with increasing porosity P or the degree of deviation τ from the percolation threshold P*. The average concentrations C of porous phase clusters and their areas S = Ωp/C in the region τ > 0 (P > P*, T* < Tann < Tm) change nonmonotoni cally (Fig. 2) and similarly for two samples (λs1 and λs2). When passing through the percolation threshold P* (τ = 0), the value of C increases more than twice with increasing τ in the range τ = 0–0.2 (Fig. 2a) due to new pore formation; then in the range τ = 0.2–0.4, it decreases to the initial value due to pore coalescence [6] (aggregation of porous phase clusters). In this case, the average cluster area S changes antibatically to C (Fig. 2b): the decrease in S is caused by the formation of new smallersize pores, and the further increase in S is caused by pore coalescence. In the region τ > 0.4, C remains almost unchanged, while S slightly
The investigation of correlations between the two dimensional network density Ωp of porous phase clus ters and the volume porosity P of membranes shows (Fig. 3) that Ωp is independent of P in the case of λs1 = 44 (curve 1); at λs2 = 78 (curve 2), the linear correla tion between these parameters is observed. The equal ity Ωp = P (dashed line in Fig. 3) is valid for homoge neous systems [10]. Porous phase clusters in the mem branes under study are topologically inhomogeneous due to the presence of three pore types: through, closed, and open cell [6]. The establishment of the lin ear dependence Ωp(P) in going from λs1 to λs2 suggests that, among three pore types, through channels begin to dominate. In going from λs1 to λs2, the shape anisotropy of porous phase clusters decreases. Figure 4 shows the function g(R) (curve 1) averaged over the sdirection and the function g||(R) (curve 2) plotted in the sdirec tion for membrane samples corresponding to λs1 (Fig. 4a) and λs2 (Fig. 4b). In this case, membranes were obtained by extension of the films annealed under identical conditions (near Tm). On the scale R < d, the slope of the functions g(R) and g||(R) is different for λs1 and insignificantly differs for λs2. The calculated fractal dimensions of clusters are D = 1.3, D|| = 0.85 (λs1) and D = D|| = 1.4 (λs2). The convergence of D and D|| in going from λs1 to λs2 is associated with a decrease in the cluster shape anisotropy and is explained by establishing the preferred orientation of through chan nels perpendicular to the surface plane. It is important
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Fig. 4. (1) Radial density distribution function g(R) aver aged over directions and (2) the function g || (R) calculated in the sdirection for porous phase clusters on the mem brane surface. Samples: (a) λs1 = 44, Tann = 444 K and (b) λs2 = 78, Tann = 443 K.
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that Figs. 4a and 4b correspond to membranes whose surfaces contain regular spatial lamella lattices identi cal to each other in such parameters as the lamella alternation period Ls|| along the s axis, equal to 110 nm, and the ratio of Ls|| to the lamella thickness, equal to 2.7–2.8 [1]. The curves f(S) of the distributions of porous phase clusters over the area (Fig. 5) are also almost identical. Thus, the decrease in the cluster shape anisotropy on the sample surface results from relative ordering of individual lamella layers (quasitwodimen sional lattices) over the membrane thickness. Figure 6 shows the dependences of the membrane permeability G on the effective pore size d on the sam ple surface for the films formed at λs1 and λs2. The experimental points correspond to the stationary dis tribution of porous phase clusters on the membrane surface, at which the cluster concentration C remains changed with increasing porosity (Fig. 2a). The dependences G(d) are approximated by the power function. In the case of λs2 = 78, it can be described as G ~ d4.4, which is well consistent with the Hagen–Poi seuille law (G ~ d4 [9]) for the model of oriented cylin drical through channels. For λs1 = 44, approximant (G ~ d2.7) significantly deviates from this behavior law, which, taking into account the validity of the classical relation G ~ τ1.5, allows reasoning about percolation over a random network of channels [1, 12]. The through channel orientation in the membrane bulk leads to an increase in the shortrange order of porous phase clusters in the twodimensional surface G, 1/(m2 h atm) 300 G ~ d 4.4 2
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Fig. 6. Dependences of the membrane permeability G on the effective cluster size d in the porous phase on the sur face. Membrane samples correspond to different film annealing temperatures Tann. The melt spin draw ratios are (1) λs1 = 44 and (2) λs2 = 78.
Fig. 5. Normalized distribution functions f(S) of porous phase clusters over the area in the twodimensional image of the membrane surface. Samples: (1) λs1 = 44, Tann = 444 K and (2) λs2 = 78, Tann = 443 K. PHYSICS OF THE SOLID STATE
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samples. A specific scaling of the permeability G as τ recedes from the percolation threshold P* corre sponded to either model. The choice of this or that model by the system is performed at the stage of uniax ial extension of films (pore formation) and depends on the degree of cooperativity of lamella ordering or on the parameter λs. As the latter increases, the cooperat ivity of lamella selfassembly increases and the first model is replaced by the second model. The problem of the mechanism of the transition on the scale λs requires additional study. The transition from model 1 to model 2 in the two dimensional image is expressed as the disorder–order transition and leads to an increase in the shortrange order of clusters of the membrane porous phase. There fore, the transformation of the topological structure of membranes can be called the porous phase selfassem bly resulting from the formation of the regular spatial 3D lattice of lamellae at the pore formation stage.
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ACKNOWLEDGMENTS This study was supported by the Russian Founda tion for Basic Research (project nos. 130300219 and 130312071ofim).
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REFERENCES 1. D. V. Novikov, G. K. Elyashevich, V. K. Lavrentyev, I. S. Kuryndin, A. Anzlovar, and V. Bukos ek, Phys. Solid State 56 (2), 396 (2014). 2. G. K. Elyashevich, E. Yu. Rozova, and E. A. Karpov, RF Patent 2140936 (April 15, 1997). 3. G. K. Elyashevich, A. G. Kozlov, and I. T. Moneva, Polym. Sci., Ser. B 40 (3–4), 71 (1998). 4. D. V. Novikov, G. K. Elyashevich, V. K. Lavrentyev, I. S. Kuryndin, N. N. Saprykina, G. I. Vorobyev, A. V. Varlamov, and V. Bukošek, Phys. Solid State 55 (2), 443 (2013). 5. G. K. Elyashevich, A. G. Kozlov, and E. Yu. Rozova, Polym. Sci., Ser. A 40 (6), 567 (1998). 6. G. K. Elyashevich, I. S. Kuryndin, V. K. Lavrentyev, A. Yu. Bobrovsky, and V. Bukos ek, Phys. Solid State. 54 (9), 1907 (2012). 7. B. I. Shklovskii and A. L. Efros, Sov. Phys.—Usp. 18 (11), 845 (1975). 8. V. G. Shevchenko and A. T. Ponomarenko, Usp. Khim. LII, 1336 (1983). 9. R. E. Kesting, Synthetic Polymeric Membranes (Wiley, New York, 1985, p. 44; Khimiya, Moscow, 1991, p. 54). 10. E. R. Weibel, Stereological Methods, Vol. 2: Theoretical Foundations (Academic, London, 1980). 11. M. Mulder, Basic Principles of Membrane Technology (Kluwer, Boston, 1991; Mir, Moscow, 1999). 12. J. M. Ziman, Models of Disorder (Cambridge University Press, London, 1979; Mir, Moscow, 1982), p. 443.
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Fig. 7. Radial distribution functions gcc(R) of porous phase clusters on the membrane surface. Samples: (a) λs1 = 44, Tann = 444 K and (b) λs2 = 78, Tann = 443 K.
4. CONCLUSIONS Thus, two topological models of the random net work of channels (model 1) and oriented through channels (model 2) can be associated with the struc ture of the porous phase of the studied PP membrane
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image. Figure 7 shows the radial distribution functions gcc(R) of porous phase clusters (cluster–cluster corre lation functions) in regular spatial lamella lattices on the surface of two membrane samples. In going from λs1 to λs2, the first peak of the function gcc(R) (short range order) sharply increases, whereas the second peak (longrange order) remains almost unchanged. We note that at given Tann, the first peak position is close to the effective size d of porous phase clusters; the second peak position is close to the lamella alter nation period Ls||. Thus, the orientational 3D transi tion associated with a change in the topological struc ture of the membrane porous phase, is a disorder– order transition in the 2D image. The case in point is the shortrange order, since the longrange order is predetermined by the degree of lamella order depend ing on both λs and Tann [1]. By the set of the presented data, such a transition should be caused by the forma tion of the regular spatial 3D lattice of lamellae.
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