Effect of Bidispersity on Structure and Entanglement of Confined

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Effect of Bidispersity on Structure and Entanglement of Confined Polymer Films Sijia Li, Mingming Ding, and Tongfei Shi J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b04468 • Publication Date (Web): 13 Jul 2017 Downloaded from http://pubs.acs.org on July 15, 2017

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The Journal of Physical Chemistry

Effect of Bidispersity on Structure and Entanglement of Confined Polymer Films Sijia Li,1 Mingming Ding,*2 and Tongfei Shi*2 1

Department of Fire Command, Chinese People’s Armed Police Force Academy, Langfang 065000, P. R. China

2

State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Science, Changchun 130022, P. R. China E-mail: [email protected]; [email protected]

Abstract Using Monte Carlo simulations combined with a geometric primitive path analysis method (Z1 algorithm), we investigate the effect of bidispersity on the structure and entanglement of polymer films which consist of short (the molecular length is below the characteristic entanglement molecular length) and long (the molecular length is above the characteristic entanglement molecular length) chains between two neutral walls. Our results demonstrate the length-based migrations of chains in bidisperse films (the longer chains reside away from the walls and the shorter chains are close to the walls), which becomes more obvious with the decrease in the weight fraction of long chains. With decreasing the weight fraction of long chains, the number of short-long entanglements exhibits a dramatic increase, whereas the number of long-long entanglements exhibits a slight decrease, which indicates that short chains can significantly affect the local situations of entanglements of bidisperse polymer films. On the basis of constraint release mechanism, our simulations imply that for the lower weight fraction of long chains, the local degree of confinement instead of the long-long entanglements has a marked effect on the relaxation of long chains, due to the fast relaxation of short chains dilating the tube diameter of long chains. However, for the higher weight fraction of long chains, after the relaxation of short chains, the long-long entanglements are in sufficient quantities to restrict long chains within a tube, which implies that the relaxation of long chains is hardly affected by the number of short-long entanglements. Our work can be helpful for understanding the microscopic structure and entanglement of bidisperse polymer films, which can provide computational supports for their various technological applications.

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Introduction The properties of polymer films under different types of confinement has been a subject of intense interest, where much of this attention has focused on elucidating changes in monodisperse polymer films.1-16 It is known, however, that the existence of polydispersity in polymer films is inevitable, which plays a fundamental role in their behaviors. Polydispersity is known to affect the processing,17 and the

structural and

thermodynamic properties of polymer melts.18-19 The tube model has successfully described the effect of polydispersity in bulk systems: for the monodisperse polymer melts, the lifetime of an entanglement that confines a chain inside a tube is as long as the relaxation time of the surrounding chains; whereas for the polydisperse polymer melts, the lifetime of an entanglement also depends on the length of the involved chains.20 In the description of reptation, the chains crawls out of the tube along the contour line like a slithering snake.21 However, the entanglements between short and long chains quickly dissolve due to the fast relaxation of short chains.20 As a consequence, a long chain may also leave its confining tube in a direction perpendicular to its contour line.21 This constraint release allows the long chains to relax more quickly than that of a pure reptation process.20 However, a unified understanding of how polydispersity affects the structure and entanglement of polymer films has not been achieved. Experimentally, Sabzevari et al. have investigated the effects of bidispersity and tridispersity on the wall slip of polymer films, which can be accounted for the entanglement degree of chains.22-23 Simulations provide an excellent tool to obtain a molecular scale understanding of polydispersity effects. In a previous dynamic Monte Carlo study on the polydispersity effects in the polymer melts capped between two hard walls, Rorrer and Dorgan have observed the length-based migrations, which corresponds to that the longer chains reside away from the walls and the shorter chains get close to the walls.24 They also found that the polydispersity can reduce the confinement effects on the orientation and relaxation time of polymer chains, and attributed it to the greater degrees of freedom that the polydispersity provides to the configurations of chains.24 In fact, the entanglement evidently represents an important characteristic feature of polymers. However, a link between the changes of structure and the changes of entanglement 2


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of polymer films induced by polydispersity has been addressed in a limited way in previous studies. A deep understanding of the effect of polydispersity on the structure and entanglement of confined polymer films is crucial for their various technological applications. In this work, we investigate the effect of polydispersity on the structure and entanglement of confined polymer films by considering the simplest case of polydispersity, a bidisperse mixture, using Monte Carlo simulations combined with a geometric analysis method (Z1),25-28 which has been proved to be suitable for extracting the entanglement length in an anisotropic sample.12, 29 The polymer films consist of short chains of which the molecular length is below the characteristic entanglement molecular length, and long chains of which the molecular length is above the characteristic entanglement molecular length. The remainder of this article is organized as follows: In Simulation Methods, we describe the simulation method and the corresponding simulation details. In Results and Discussion, we systematically investigate the effect of bidispersity on the structure and entanglement of the short and long polymers capped between two walls. Our simulations confirm the existence of the length-based migrations of polymer chains and indicate that short chains can significantly affect the local situations of entanglements of bidisperse polymer films. In Conclusions, we briefly summarize our results and provide some concluding remarks.

Simulation Methods We construct a coarse-grained computational model for the polymer melts capped between two hard walls on the basis of our earlier work.16 We perform the simulations using the lattice-based Monte Carlo model introduced by Shaffer (S-BFM),30-32 which can simply switch “on” and “off” the chain crossing and obtain equilibrium conformations for noncrossing chains ( real chains) within a relatively short period by starting from equilibrated crossing chains.30 In our model, each monomer on chains occupies a single site on a primary cubic lattice with a lattice constant ap=1, and the excluded volume interactions are taken into account by forbidding double occupancy of the primary lattice sites. By following the bond lengths to fluctuate with the values of 1, 21/2, 31/2, the polymer configurations can evolve through local displacements of the single monomer and still maintain chain connectivity.

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In this work, lengths are given in the units of primary lattice spacing (ap), and times are given in the units of attempted Monte Carlo steps (MCs) per monomer in the simulation box. We have demonstrated that the average length of entanglements is Ne≈33 by Z1 algorithm in our previous work.16 Therefore, we fix the length of short chains as Ns=20 and that of long chains as Nl=150. The weight fraction of long chains in the system is defined as φl=Nlnl/(Nsns+Nlnl), where ns and nl are the numbers of short and long chains, respectively. We set φl as 16.7%, 33.3%, 50.0%, 66.7% and 83.3% (see Table 1 for details). Table 1. Compositions of bidisperse polymer meltsa

a

System(φl)

ns×Ns

nl×Nl

16.7%

4500×20

120×150

33.3%

3600×20

240×150

50.0%

2700×20

360×150

66.7%

1800×20

480×150

83.3%

900×20

600×150

ns and nl are the numbers of short and long chains with the lengths Ns and Nl, respectively, and φl

represents the weight fraction of long chains.

Both the short and long chains are put into a rectangular simulation box with dimensions of (Lx, Ly, Lz). Periodic boundary conditions are applied in the x and y directions, and two flat and impenetrable walls are fixed at z= 0 and Lz+ 1 in the z direction. The walls are constructed of stationary particles, where each particle occupies a single lattice site. Only the excluded volume interaction is considered between the monomers and the wall particles. Lz layers of lattice sites are occupied by monomers in the z direction, and therefore, the film thickness is denoted as H = Lz. In all cases, the fraction of occupied lattice sites is one-half, which has been shown to correspond to polymer melts in this model.33 We adjust the film thickness from 2 to 38 in our simulations (see Table 2 for details), where Rgs,b≈ 2.81 and Rgl,b≈ 8.06 are the mean-square radii of gyration of short and long chains in the absence of walls, respectively. Table 2. Simulation details for bidisperse polymer meltsb Lx=Ly

H=Lz

H/Rgs,b

H/Rgl,b

330 190 146 124 110

2 6 10 14 18

0.71 2.14 3.57 4.99 6.42

0.25 0.74 1.24 1.74 2.23

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100 90 84 80 76 b

22 26 30 34 38

7.85 9.27 10.68 12.10 13.52

2.73 3.23 3.72 4.22 4.72

Lx=Ly is the lateral length of the simulation box, H=Lz denotes the film thickness, H/Rgs,b and H/Rgl,b

represent the film thicknesses normalized by the mean-square radii of gyration of short and long chains, respectively.

We first put both the short and long chains on the lattice and run 106-107MCs to equilibrate the system. The chain crossing is allowed in this process. Then, 106-107MCs are run to gradually remove those chain crossings. Finally, we obtain the equilibrium configurations by running 107-108MCs (see Figure 1a for the schematic illustration). We employ the

Z1 algorithm

to analyze

chain entanglements

in the equilibrium

configurations,25-28 which uses geometrical moves to monotonically reduce the chain contour lengths to the limit of infinitely thin primitive path (PP) thickness (see Figure 1b for the schematic illustration). Our work is based on the original implementation of the Z1 code, which was kindly provided by the developers.25,27 According to the coordinates of the shortest multiple disconnected path returned by the Z1 code and the resulted local situations of two different types of kinks,25 we can precisely locate the entanglements along the long chains. In this work, an entanglement which solely involves the long chains is considered as a long-long entanglement, otherwise, it is marked as a short-long entanglement. Therefore, our model can effectively describe the structure and entanglement of polymer films. We perform 10 parallel simulations with different random seeds to provide the final average results.

Figure 1. (a) Representative configuration of the polymer film and (b) the corresponding PP network with the short (red) and long (blue) chains, where the film thickness is H=10 and the weight fraction of long chains is φl=50.0%.

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Results and Discussion We define the center-of-mass density as ρcom,i(z)=ni(z)/(ni/H), where i=s or l, representing the short or long chains, respectively. ni(z) denotes the number of center-of-mass of chains on the zth layer of the lattice (between z-0.5 and z+0.5) and ni is the total number of chains. Obviously, the center-of-mass density should be equal to 1 in the absence of walls. Because of the symmetry of the system, we only show the density profiles of center-of-mass of chains with z

Effect of Bidispersity on Structure and Entanglement of Confined

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