Article pubs.acs.org/Macromolecules
Molecular Dynamics of Crystallization in a Helical Polymer Isotactic Polypropylene from the Oriented Amorphous State Takashi Yamamoto* Department of Physics and Informatics, Yamaguchi University, Yamaguchi 753-8512, Yamaguchi, Japan ABSTRACT: Molecular simulation is attracting great interest in these days as a powerful tool to reveal the molecular mechanism of polymer crystallization. Most of the studies reported hitherto have dealt with simple model polymers like polyethylene, and the majority of polymers having more complex chemical structures remain almost untouched. In this report, we make a new challenge to the crystallization in a typical helical polymer isotactic polypropylene (iPP). We consider a relatively small system of 40 iPP oligomers each made of 50 propylene monomers by use of a realistic flexible model. The crystallization of iPP has long been considered too sluggish to be investigated by molecular simulations. We here take advantage of the accelerated crystallization from the highly stretched amorphous state. By carrying out very long simulations of about 600 ns total, we succeed in observing the onset of crystallization and subsequent crystal growth. Very unexpectedly, we come to see the growth of the smectic mesophase, which is believed to grow at temperatures much lower than the melting point. For the growth of crystals of stable forms of definite chirality, such as the α-form or the β-form, the chirality selection process will need a much longer time. The hypothesis is that the very fast crystallization observed here does not allow the slower processes of helical selection and gives rise to the formation of the smectic mesophase with somewhat random disposition of helices.
1. INTRODUCTION The emergence of crystalline order from disordered states of molecules is ubiquitous in nature. The molecular processes involved are prototypical self-organization and have long been the subjects of innumerable investigations in physical, chemical, and biological sciences. Crystallization is also of great importance in synthetic and biological macromolecules, and indeed a vast amount of work has been reported since the first recognition of crystals in linear macromolecules.1−3 Despite the astonishingly diverse molecular structures of polymers, intensive studies for more than half a century revealed the presence of simple universal laws in mesoscopic and macroscopic scales such as the temperature dependence of the crystal growth rate, the morphology of the crystals, etc. The recognition of the universality greatly stimulated researches on the molecular mechanism of polymer crystallization.4−9 A standard model was proposed as early as 1950;5 however, the model was constructed on bold assumptions about details of the molecular processes. With the accumulation of experimental data and the advent of new experimental techniques, the weakness of the standard model is coming to be realized. Greatly desired is the invention of a new standard model of polymer crystallization taking more realistic molecular pathways into account. In these days, many computer simulation studies, by molecular dynamics (MD) or the Monte Carlo (MC) method, are emerging and are making great contributions.10−31 Besides the universal aspects of crystallization described above, the polymer crystallization involves various interesting features that essentially reflect specific molecular structures of the polymers. One of the topics that we have been studying and that we © 2014 American Chemical Society
are going to discuss in this paper is the molecular recognition process in the crystallization of helical polymers.32−34 For example, the molecules of isotactic polypropylene (iPP) in the crystal adopt ordered 3/1 helical conformation of one helicalturn by three propylene monomers either of the right-handed (R-handed) or the left-handed (L-handed) helical sense. In the ordered crystalline phases, which are named α-, β-, and γ-forms, the R- and the L-handed helical molecules are known to take orderly arrangements with specific macroscopic chirality; the β-form crystal is chiral while two others are racemic. Very interesting is that the chirality of the crystal was suggested35 and also confirmed by molecular simulations36,37 to be closely related to the symmetry of the crystal lattice, which is in other words the relative positions of the helical molecules in the lattice. Despite the great interest in the molecular mechanism of chirality control during crystallization, the molecular origin is quite far from being well-understood. Since the experimental hurdles are very high, molecular simulations of the helical polymers have long been yearned for. The random coils of iPP are mixtures of the short R- and L-handed helical segments and the nonhelical ones. In order to build up ordered crystalline stems from the random coils, the helical segments must be elongated by frequent helix-reversals traveling along the chains to sweep out the conformational defects. Such molecular processes must be very slow since both of the helical hands are of equal energy level and there are high Received: February 10, 2014 Revised: April 18, 2014 Published: April 25, 2014 3192
dx.doi.org/10.1021/ma500307h | Macromolecules 2014, 47, 3192−3202
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In spite of the difficulties we can find recent efforts, though still very scarce, toward better understanding of the molecular mechanisms of crystallization36−43 and melting44 in helical polymer iPP. By adopting the rigid 3/1 helix model, the crystal polymorphs and the molecular processes of their growth were reproduced successfully by MC simulations,36,37 while the flexible model38 and the coarse-grained model42 of iPP were successfully used in studying the appearance of initial order in the isotropic melt. The molecular process of crystallization in iPP were also studied by MD method with a special focus on the mechanism of chirality selection, where a single chain of iPP confined within a slit or tube and placed on an ordered iPP substrate of definite chirality was found to rapidly adsorb and crystallize to form the ordered 3/1 helix with distinct chirality selection.40,41 Crystallization and melting in much larger systems of iPP oligomers were recently challenged by Theodorou’s group.43 They carried out intensive work using an elaborate model of iPP, but they could not directly observe crystallization without imposing constraints on the chains to take the 3/1 helical conformation. The conformational freedom in the helical polymers was thus shown to be a formidable obstacle to the direct observation of crystallization. However, the constraints on the conformational freedom rule out the study of detailed molecular mechanisms of crystallization. Toward the direct observation of crystallization in a realistic
Figure 1. Rapid elongation of the isotropic amorphous iPP in the Z-direction by the lateral compression along the X- and the Y-axis at T = 321 K. During the elongation the MD cell was assumed to be a rectangular parallelepiped. The nine time elongation from C = 5.0σ (the left figure) to C = 45.3σ(the right figure) was accomplished in about 350 ps. In the snapshots, the backbone carbons are only drawn with right-handed and the left-handed helical segments colored in red and blue, while the nonhelical segments are in white.
energy barriers for the motions of the helix reversal defects in the crystal. Indeed, the extremely slow crystallization of iPP has long constituted great obstacles to the computer simulations.
Figure 2. Changes in the chain conformation during the elongation of Figure 1. (a) The MD cell size (a, b, c) and the orientatonal order parameter P2 (open circles) of the vector connecting the atoms six bonds apart as functions of time, (b) weight-averaged lengths of the helical sequences (black) and the nonhelical sequences (red), and (c) weight-fractions of helical sequences vs their lengths, where each weight-fraction is the number of the helical sequence multiplied by its length; the helical and the nonhelical sequences are plotted in black bars and red bars, respectively. The red bars are shifted along the abscissa by half the division 0.5 in order to avoid complete overlap of the black and the red bars for the same helical sequence length. The lengths of all the helical sequences are seen to be within the threshold length of lĥ = 13 monomers. 3193
dx.doi.org/10.1021/ma500307h | Macromolecules 2014, 47, 3192−3202
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Figure 3. The onset of ordering or nucleation at T = 344 K in terms of (a) the weight-averaged lengths of the helical (black) and the nonhelical (red) sequences, (b) the crystallinity, and (c) the snapshots of the molecules at four representative stages; the colors for the backbone atoms are the same as those of Figure 1. The oblique parallelepiped drawn in thin white lines represents the MD cell.
length σ = 0.395 [nm], time τ = ((mσ2)/(ε))1/2 = 2.4 [ps], and pressure P = ε/σ3 = 10[MPa]. All the MD simulations are conducted by the program COGNAC in OCTA,52 using the constant temperature-stress (N,T,{σ}) ensemble with variable MD-cell lengths and MD-cell angles and the Brown−Clarke method.53 The control parameters for the temperature and the pressure in the loose coupling method are τT = 1.0 [τ] and τP = 10 [(Pτ)/(σ)]. The system is rather small being made of 40 chains of short iPP consisting of 50 propylene monomers. The experimental melting point Tm of the iPP oligomer was estimated to be about 411 K.54 However, as to the melting temperature of our present model, we made no quantitative estimation. The initial isotropic melt prepared around 500 K is elongated along the Z-axis at T = 321 K, which is much lower than Tm, by the lateral compression under anisotropic stress condition of σx = σy = −10,σz = 0, where (σx,σy,σz) are the diagonal components of the stress tensor. Since the molecules were rather short, the subsequent removal of the anisotropic stress did not cause serious shrink along the Z-axis, which was in contrast to our previous simulation of much longer polyethylene.49 Therefore, all the simulations of crystallization are conducted under weak isotropic compression, σx = σy = σz = −1. Our present use of slight compression of 10 MPa is only for the sake of easy preparation of the initial dense melt and possible stability of the simulation. The pressure of 10 MPa was found very small and was considered to give negligible effects to the present discussions; for example the experimental melting temperature of iPP is known to increase only 3 K by the application of pressure at 10 MPa.55 Data Analyses. The development of crystalline order are monitored using various quantities. The basic energy terms for
flexible model of iPP, we have attempted many simulations, and we here present some of the results of our recent studies. It is well acknowledged that polymer crystallization is greatly accelerated by uniaxial drawing; the extremely fast development of crystalline fibers is a typical example. This feature of polymer crystallization confers a great advantage in simulating polymer crystallization. Indeed, we can find recent reports on simulations from oriented melt of simple polymers or oligomers.45−50 However, previous simulations were exclusively on polyethylene analogues. We here challenge the simulation of helical polymer iPP.
2. MOLECULAR MODEL AND SIMULATION METHOD The molecule of iPP is composed of alternating CH2 and CH groups, where a pendent CH3 group is added to each CH residue in the isotactic fashion. As in our previous work,40 we here adopt a flexible model of iPP by using the force field (TraPPE-UA) obtained by Martin and Siepmann,51 which was confirmed to work successfully in our former studies of iPP.37,40 The LennardJones potentials among CH, CH2, and CH3 separate by more than four bonds and those of different chains are considered (Table 1 of ref 51). The bond angle bending potentials and the torsion potentials are also taken from Table 2 of ref51. As to the C−C bonds which were treated as rigid in the original work,51 we here consider the conventional harmonic spring, the force constant kb of which is chosen somewhat arbitrary close to the conventional values for polyethylene kb = 15000ε/σ2, where the unit of energy ε and length σ are the Lennard-Jones parameters between the methylene groups CH2−CH2. For the sake of convenience, we here write the unit values of the important parameters; the units of mass m = 14 [g/mol], energy ε = 383 [J/mol], 3194
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Figure 4. Fraction by weight (number of helices multiplied by their lengths) of the helical (black bar) and the nonhelical (red bar) sequences at four stages during the onset of ordering at T = 344 K. Here again the red bars are shifted along the abscissa by half the division 0.5 in order to avoid complete overlap of the black and the red bars for the same helical sequence length. The arrows show the threshold length lĥ given in Figure 2.
describing the crystallization process are the intramolecular torsion energy, and the nonbonded interaction energy between atoms more than three bonds apart within the chain and those between different chains. In addition, we define the following intra- and intermolecular order parameters. As the intramolecular order parameter, we consider the helical sequence length and its distribution. Each dihedral angle ϕ is calculated from the angle between the vectors normal to the planes spanned by the neighboring bond vectors, and the sign of the internal rotation (the helical sense) is given by the sign of the determinant of the three relevant bond vectors (Appendix 1). Then, we here consider that the bonds are in the trans-state (t) when the dihedral angles ϕ are within 30° around the strict trans ϕ = 0°: |ϕ|
