High Polymer Mass Densities at the Mouths of Carbon Nanotubes

Subscriber access provided by UNIV OF SOUTHERN INDIANA

B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

High Polymer Mass Densities at the Mouths of Carbon Nanotubes (CNTs) Control the Diffusion of Small Molecules Through CNT-Based Polymer Nanocomposite Membranes Panagiotis G. Mermigkis, Emmanuel N. Skountzos, and Vlasis G. Mavrantzas J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b05375 • Publication Date (Web): 15 Jul 2019 Downloaded from pubs.acs.org on July 18, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

High Polymer Mass Densities at the Mouths of Carbon Nanotubes (CNTs) Control the Diffusion of Small Molecules through CNT-Based Polymer Nanocomposite Membranes

Panagiotis G. Mermigkis,1 Emmanuel N. Skountzos1 and Vlasis G. Mavrantzas1,2,*

1

Department of Chemical Engineering, University of Patras & FORTH/ICE-HT, Patras, GR 26504, Greece

2

Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, CH-8092 Zürich, Switzerland

ABSTRACT Detailed molecular dynamics (MD) simulations of model single-walled carbon nanotube (CNT) membranes based on atactic poly(methyl methacrylate) (aPMMA) indicate that PMMA chains significantly penetrate nanotubes through their faces. They predict very high-density values of the polymer in the interfacial area around the CNT mouths that can exceed by 50 % the density of the bulk polymer at the same thermodynamic conditions. This dramatically decreases the diffusivity of relatively small penetrants (in our study, water molecules) in the nanocomposite membrane, because of the exceedingly long times needed by these small molecules to diffuse through such a dense interfacial layer before accessing the interior of the nanotubes where they can travel really fast. According to our simulations, the escape time of a confined water molecule from the blocked mouths of a CNT can exceed by several orders of magnitude the time needed by the same molecule to move through the CNT pore. Our work indicates the importance of completely avoiding (or at least minimizing) penetration of polymer chains into the CNT pores through the mouths of the tubes in enabling

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the efficient transport of small- to moderate-size molecules in model CNT-based polymer membranes, since this provides the highest resistance to their flow through the membrane.

I. INTRODUCTION In the past decade, numerous experimental and simulation studies have provided evidence for superfast water transport through nanometer-wide carbon nanotubes (CNTs) embedded in micrometer-wide membranes.1-3 Even if the actual rates reported by different authors are not consistent,3 it is well accepted that CNTs are characterized by exceptionally high transport rates, as a result of many factors such as inherently smooth molecular surfaces, extremely high aspect ratios, nanoscale inner diameters, and weak interactions with water molecules.4-6 However, utilizing these characteristics for practical applications by constructing highly permeable and selective membranes containing carbon nanotubes inside a polymer matrix that could be easily scaled-up to meet large-scale production requirements has been very challenging. Moreover, in many cases, contradictory results have been reported for the permeability properties of this new class of carbon nanotube mixed matrix membranes (MMMs).7-9 In general, several computational, theoretical and experimental studies have correlated permeability, selectivity and diffusivity of numerous gases through CNT-based MMMs with the structure (multi- versus single-walled nanotubes), aspect ratio, degree of dispersion in the matrix, concentration, functionalization and interaction of CNTs with the polymer, and the presence of interfacial areas.7-19 In one of the very first studies in the field, Kim et al.16 reported diffusion coefficients for several gas molecules (CO2, O2, CH4, N2) through nanocomposite membranes containing single-walled carbon nanotubes (SWCNTs) inside a polysulfone matrix at three different loadings (5 wt.%, 10 wt.%, 15 wt.%). The carbon nanotubes had been functionalized with long chain alkyl amines to facilitate dispersion in the

2


Page 2 of 31

Page 3 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


polymer. The diffusion coefficients were calculated by the time-lag method and at 5 wt.% loading of functionalized SWCNTs in the polymer they increased by around 80% for CO2, O2, and CH4 and by 37% for N2. At 10 wt.% loading of SWCNTs in the polymer matrix, the diffusivities of all gases increased further. However, at 15 wt.% SWCNT loading the diffusivities for some gases were lower than those observed at 10 wt.% SWCNT. The reasons for this were not explained. For comparison, kinetic diffusion coefficients were also calculated and, although their absolute values were different from those obtained by the time lag method, qualitatively the changes with increasing SWCNTs loading in the matrix were consistent. Kim et al.16 further reported that SWCNTs prepared by the electric arc method produced lower absolute sorption amounts of the gases in comparison to the isotherms obtained by high-pressure carbon monoxide (HiPco) nanotubes, which was attributed to their pores being partially closed or blocked to internal adsorption either by impurities or by carboxylic acid groups possibly created by the acid cutting procedure employed in the construction of the membranes. Khan et al.15 have also reported diffusion coefficients for several gas molecules through MMMs consisting of functionalized multi-walled carbon nanotubes (f-MWCNTs) embedded in a matrix made of a ladder-type polymer (referred to as polymer of intrinsic microporosity, PIM-1),20 fabricated via solution casting. The effect of f-MWCNT loading on gas permeation properties of the MMMs was investigated by varying their concentration in the PIM-1 matrix from 0.5 to 3.0 wt.%. At 0.5 wt.% f-MWCNT loading, the diffusion coefficients for N2, O2 and CO2 increased by around 15–20 % and by ~2 % for CH4. At 1–2 wt.% f-MWCNT loading, the diffusivities for all gases increased further (e.g., up to 145 % for CO2). The authors suggested that a continuous interface develops between CNTs and polymer chains at lower CNT loadings (0.5–2wt.%) leading to lower gas diffusion resistance. However, at 3wt.% f-MWCNT loading, the diffusivities for all gases were lower than those at

3



2 wt.% f-MWCNT loading. For this nanocomposite, the authors hypothesized that the created nano-gaps between CNTs and polymer chains become discontinuous. In a more recent study, Bounos et al.7 examined the permeability of MMMs composed of multi-walled carbon nanotubes (MWCNTs) dispersed in isotactic polypropylene (i-PP) to water vapor and several gas molecules. The permeability of the nanocomposites to water vapor was found to increase with the filler content but only up to a critical concentration after which the composite membrane became water impermeable. The authors attributed this to the formation of filler aggregates or/and labyrinth-type networks that act as traps for the penetrant water molecules. They also reported that using functionalized PP-chain grafted MWCNTs (MWCNT-g-PP), the maximum water permeability (achieved at the critical filler concentration) increased by a factor of approximately 35 compared to the pure i-PP membranes. On the other hand, the transport rate of several light gases (N2, H2, CH4 and CO2) was not affected by filler loading and dispersion. Ge et al.12 investigated the gas permeability and selectivity in poly(ether sulfone) membranes with embedded pristine and functionalized CNTs. Compared to pristine CNTs, Ru modifications resulted in higher gas selectivity, while the behavior was reversed when carboxyl modifications were imposed. In addition, based on observations via experiments and molecular simulations, they claimed that the gas molecules prefer to diffuse through the interfacial polymer-CNT areas rather than inside the CNT channels. We should also mention the study of Mondal and Hu18 on composites of multi-walled carbon nanotubes with segmented polyurethane (MWCNT-SPU) membranes, where a decrease in water permeability was observed with increasing filler content; the phenomenon was attributed to the increased stiffness of polymer chains. It appears that the experimental studies provide convincing evidence that (even partial) blockage of CNT pores, due to the employed surface modification techniques needed to

4


Page 4 of 31

Page 5 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


improve compatibility with the polymer matrix, can dramatically influence permeability and thus separation performance. Here, we will provide evidence for yet an additional and equally important mechanism that can lead to blockage of CNT pores in a nanotube-polymer nanocomposite membrane: polymer penetration in the CNTs accompanied by the development of a dense polymer film right next to CNT mouths characterized by a density that can be up to 50 % higher than the density of the pure polymer matrix at the same thermodynamic conditions. In a recent simulation study21 on the conformational properties of adsorbed PMMA chain conformations on the surface of CNTs in terms of trains, loops and tails and their statistical properties, we also observed that PMMA chains can significantly penetrate CNTs through their faces. We also observed that polymer density can be very high not only radially as we approach the CNT surface (due to PMMA adsorption on the CNT surface) but also axially as we approach the CNT mouths (due to PMMA penetration in the empty CNT pores); this brings increasingly more polymer mass next to the CNT mouths, thus resulting in the development of a very dense polymer film right at the entrance of the CNT pores. The existence of such a dense polymer film should be expected to cause a dramatic decrease locally in the value of the diffusion coefficient of small penetrant molecules (such as gases or water vapor), strongly suppressing permeation through the membrane. In the past, water mobility inside CNT-polymer nanocomposites at large scales has been studied by Mermigkis et al.22 through a kinetic Monte Carlo (kMC) algorithm for a poly(methyl methacrylate) (PMMA) matrix containing CNTs at several loadings. The simulations (discrete in space, continuum in time) were conducted on a cubic lattice to the bonds of which different rate constants (pre-computed on the basis of independent atomistic molecular dynamics (MD) simulations)23 were assigned governing the elementary jumps of water molecules from one lattice site to another. Lattice sites belonging to PMMA domains of

5



the membrane were assigned different rates than lattice sites belonging to CNT domains; these were consistent with the pre-computed diffusivity data according to which water diffusivity in CNTs is 3 orders of magnitude faster than in PMMA. The effective water diffusivity in the nanocomposites, Deff, was found to vary linearly with the CNT volume fraction C and CNT aspect ratio L/D (L denotes the length and D the diameter of the nanotube). In the simulations, boundary effects at the CNT-polymer interface were neglected. As we will show below, these are very important and can have a dramatic effect on the overall water diffusivity through the membrane. The rest of our paper is organized as follows: in Section 2 we discuss the systems simulated and the molecular model employed in the MD simulations. In Section 3 we provide a thorough analysis of the polymer mass density in the interfacial area next to CNT mouths and discuss how it affects water diffusivity. We analyze in detail how the density varies as a function of distance from the mouths of CNTs (both outside and inside the pore) and calculate the distribution of times needed for a water molecule to escape from or enter a CNT by slowly diffusing through this adsorbed, dense polymer layer. Our paper concludes with Section 4 summarizing the most important results of this work and briefly discussing future directions.

II. METHODS For all systems studied, the host polymer matrix consists of strictly monodisperse atactic PMMA chains with molecular weight (MW) equal to 4511.25 g mol-1 (corresponding to 45 MMA monomers per chain) whereas the length (L) and diameter (D) of the CNTs are chosen to be equal to 10 nm and 1.085 nm, respectively, implying an aspect ratio L/D ~ 10. All technical aspects regarding the simulated systems are listed in Table I. Our goal is to: a) study the mobility of water molecules in the PMMA matrix in the absence (System 1) and presence (System 2) of CNTs, and b) calculate the distribution of residence times of water

6


Page 6 of 31

Page 7 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26System 27 28 29 30 1 31 2 32 3 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


molecules in the CNT-PMMA nanocomposite as well as its mean value, and how these compare to the corresponding results for the water molecule travelling times in a CNT (from one face to the other) of given length and diameter (System 3). Overall, interactions between PMMA and carbon-based nanomaterials are highly attractive as described in previous simulation works,21,24-28 while interactions between water and CNTs are repulsive23 due to the hydrophobic nature of the latter. This unique combination of interactions renders CNTPMMA nanocomposites excellent structures for designing MMMs for applications in several industries, especially for wastewater treatment.

Table 1.21 Technical details of the model systems studied in the present work. Number of PMMA chains 280 280 28

Number of CNTs 12 1

CNT diameter (Å) 10 10

CNT loading (w/w %) 13.03 11.1

Number of water molecules 104 104 0 (1)

CNT length (nm) 10 10

Total number of atomistic units 189,872 206,000 20,300 (3)

System 1 was built by randomly inserting in the simulation cell 280 atactic PMMA chains followed by the random addition of a small but non-negligible number of water molecules (= 104) in order to have a good population necessary to observe their diffusive behavior without affecting the density of the matrix. System 2 was built by first inserting in the simulation cell 12 CNTs and then randomly adding 280 PMMA chains and 104 water molecules. It was found that most (about 90) of these water molecules were placed in the polymer phase of the host nanocomposite as this occupies the majority of space in the simulation box; the rest were placed inside CNTs. System 3 was built by placing one CNT of the same size (L and D) as in the case of System 2 at the center of the simulation box with its axis pointing practically along the z axis of the coordinate system, followed by the addition of 28 atactic PMMA chains around it.

7



Page 8 of 31

The MD simulations were carried out in the isothermal-isobaric (NPT) statistical ensemble at pressure P = 1 atm and temperature T = 550 K, conditions at which PMMA exists in the molten state21 implying that system equilibration is easier to achieve. System 3, in particular, was thoroughly equilibrated through a microsecond-long MD simulation at the conditions of the simulation (T = 550 K and P = 1 atm) and, from the accumulated long NPT MD trajectory, 150 relaxed configurations were selected in each one of which one water molecule was inserted at the center-of-mass of the CNT in order to compute the time it takes it to exit the CNT. The resulting 150 configurations were subjected to MD simulation under the same simulation conditions as above with initial velocities for all atoms in the simulation cell assigned according to a Maxwell-Boltzmann distribution at the temperature of interest (T = 550 K). The simulations were executed with rectangular parallelepiped simulation cells subject to periodic boundary conditions along all three space dimensions. Following a recent study of the

structural,

conformational

and

dynamical

properties

of

CNT-based

PMMA

nanocomposites,21 and of the mechanical properties of PMMA enhanced with functionalized and non-functionalized graphene sheets,24 bonded and non-bonded interactions between CNT and PMMA atoms were described with the help of the all-atom DREIDING forcefield.29 Water molecules, on the other hand, were modeled using the SPC/E forcefield.23,30 More details concerning the applied forcefield can be found in our previous studies.21,23,24,31-33 The Amorphous Builder module34 of the MAPS 3.4 software35 was used to build initial configurations and the MD simulations were performed using GROMACS.36

III. RESULTS AND DISCUSSION Polymer density next to CNT mouths. An important finding of our simulations was that PMMA chains close to CNT entrances tend to enter the nanotube.21,37 For example, after

8


Page 9 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


about 800 ns of simulation time (time period I), the penetration length was ~ 5 Å but for longer times (time period II) the penetration length was even higher, close to ~ 10 Å. This was quantified by examining the local PMMA density along the axial direction of CNTs and monitoring the change in the computed polymer density profile between time periods I and II. The curves computed are shown in Figure 1. Positive values in the horizontal axis of the figure correspond to the area inside CNTs. When short times are studied, the axial density distribution fades out at about 5 Å; for longer times, however, PMMA segments penetrate even deeper in the CNTs, up to approximately 1 nm. Negative values of the horizontal axis refer to the external CNT-area where high mass densities are observed locally, indicative of the strong tendency of chains to adsorb on the mouths of the CNTs or slightly inside them. Several PMMA chains are found next to CNT mouths as shown in Figure 2; but when it comes to penetration inside the CNTs, end-monomers are clearly preferred as (e.g.) shown in Figure 3 where an atomistic snapshot of a CNT penetrated by two chains is depicted. Clearly, deep PMMA chain penetrations are accompanied by adsorption of entire monomers (including their side ester branches) on CNTs as schematically shown by the yellow dots in Figure 3. It is this adsorption of PMMA segments on the lateral and internal areas of a CNT next to its faces (see Figure 2) that leads to the very high density values observed locally in Figure 1.

9



Figure 1. Axial variation of PMMA mass density around the CNT faces. Positive values on the x-axis of the graph refer to the area inside the CNT and negative ones to the area outside the CNT.

Figure 2. Characteristic atomistic snapshot from the MD simulations focusing around a CNT. The snapshot provides a good picture of the crowdness of the area around the CNT in PMMA chains, with several of these chains penetrating the CNT.

10


Page 10 of 31

Page 11 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

Figure 3. Characteristic atomistic snapshot of a CNT, the entrances of which have been blocked by two PMMA chains: (a) radial view, (b) axial view. For clarity, only the CNT and the penetrating PMMA chains are shown. Red and grey colors show carbon and oxygen atoms, atoms of PMMA segments that have penetrated the CNT are shown in yellow, and PMMA hydrogens have been omitted for clarity.

We also examined the distribution of local mass densities (in dimensionless units) in the simulated systems by decomposing the simulation cell into smaller cubic sub-cells each of volume approximately equal to 250 Å3, and the results are presented in Figure 4. The dimensionless densities are obtained by dividing local mass densities with the average density of (the pure or bulk) System 1 at the same conditions (T = 550 K and P = 1 atm). In the pure PMMA matrix, the distribution is normal with a mean equal to the average density of the pure

11



PMMA phase. For the PMMA-CNT nanocomposite, on the other hand, the distribution is shifted to higher densities due to polymer adsorption on CNTs. To identify the regions in the nanocomposite (System 2) where the highest PMMA densities are observed, in Figure 5 we have highlighted the areas in the simulation cell of System 2 where the computed densities are at least 50 % higher than the corresponding bulk PMMA density at the same temperature and pressure conditions. As a guide for the eye, in the same graph we also indicate with black dots the positions of CNT atoms in the simulation cell. The graph confirms that the highest PMMA-density regions in the nanocomposite are those located near CNTs, i.e. in the interfacial zones. Clearly, CNTs are surrounded (both radially and axially) by highly dense polymer regions that are never found in the bulk.

12


Page 12 of 31

Page 13 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

Figure 4. Histograms of dimensionless local density distributions in: (a) System 1, and (b) System 2. With ρpure,bulk we denote the average mass density of (the pure or bulk) System 1 at T = 550 K and P = 1 atm.

13



Figure 5. “Heat” map of local mass density in System 2. Black dots depict CNT atoms while red dots show grid points in the PMMA regions of the nanocomposite characterized by density values that are at least 50 % higher than the corresponding bulk PMMA density.

Water dynamics in the pure aPMMA and the CNT-based nanocomposite. How fast water molecules travel in the pure PMMA matrix (System 1) and in the CNT-based PMMA nanocomposite (System 2) was quantified by examining their mean-squared displacements (msdw). Results for the msdw averaged over all water molecules present in the simulation cell from the long NPT MD simulations with Systems 1 and 2 at T = 550 K and P = 1 atm are shown in Figure 6. Unexpectedly, it is seen that the mobility of water is significantly slower in the PMMA matrix containing CNTs than in the pure PMMA melt. Extensive analysis of the obtained MD trajectories revealed that this is caused by PMMA chains that enter the mouths of the CNTs and block their entrances. As a result, water molecules that perform diffusive motion in the host polymer matrix (corresponding to the blue curve in Fig. 6) cannot enter the fast channels of CNTs. In particular, it is observed that these water molecules

14


Page 14 of 31

Page 15 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


outside CNTs are moving slower compared to water molecules in the pure PMMA matrix (System 1), mostly because of the presence of the dense interfacial areas around CNTs characterized by more compact chain packing compared to the situation in bulk PMMA far away from CNTs. Similar, water molecules placed initially inside CNTs are found not to exit the nanotubes; instead, they remain trapped within the CNTs practically for the entire simulation time (see inset in Fig. 6). As already discussed, this is caused by the high-density regions in the areas next to CNT mouths due to strong PMMA adsorption both on the lateral surfaces and on the faces of CNTs. Due to confinement, the maximum value of the msdw of these permanently trapped water molecules within CNTs should be less than L2/4 (= 25 Å2) where L denotes the axial length of the CNT, which is indeed confirmed to be the case in the inset of Fig. 6.

Figure 6. Mean-squared displacement of water molecules in the pure PMMA matrix (black color) and in the CNT-based nanocomposite (System 2, red color). Also shown in the figure (blue curve) is the mean-squared displacement of water molecules moving outside CNTs for the entire duration of the simulation. In the inset, we show the mean-squared displacement of

15



those water molecules that were permanently confined within CNTs (they never came out) during the corresponding MD run.

In the Electronic Supporting Information (ESI), we have uploaded a video from the MD simulation with System 2 showing a trapped water molecule inside a CNT that could not exit the nanontube even after 100 ns of simulation time. We have copied four atomistic snapshots from that video at times equal to 25 ns, 50 ns, 75 ns, and 100 ns and we show them in Figure 7. Moreover, in Figure 8 we show the trajectories followed by four water molecules in the nanocomposite of System 2. Two of these water molecules (the red and the blue) are confined inside CNTs while the other two (the black and the green) execute a diffusive motion outside the CNTs, in the PMMA domain of the nanocomposite. The four different trajectories are shown for the first one nanosecond of the simulation. The confined water molecules execute an oscillatory motion, moving back and forth within the CNT they have been trapped. The free water molecules, on the other hand, execute a motion which looks very much like normal diffusion as they seem to explore rather efficiently and uniformly the free or accessible volume available to them within the PMMA domains of the nanocomposite. Clearly, the transition of a water molecule from the slowly-moving PMMA areas to the fastmoving CNT domains of the nanocomposite and vice versa is a rare event, whose characteristic time scale is beyond the typical time scales that can be captured in our MD simulations. As suggested by Greenfield and Theodorou, one way to address this problem is to resort to a geometric analysis38,39 of free volume followed by multidimensional Transition State Theory (TST),40,41 which is currently underway in our group. For the time being, we calculated (see next Section) the distribution of residence times of water molecules inside CNTs surrounded by the host polymer matrix at the conditions of the simulations.

16


Page 16 of 31

Page 17 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

(c)

(d)

17



Page 18 of 31

Figure 7. Characteristic atomistic snapshots of a water molecule confined inside a CNT, the entrances of which have been blocked by one PMMA chain per mouth. The snapshots have been taken at time: (a) t = 25 ns, (b), t = 50 ns, (c) t = 75 ns, and (d) t = 100 ns. For clarity, only the water molecule, the CNT and the two penetrating PMMA chains are shown. Grey colors refer to the carbon atoms of PMMA and CNT, red colors to the oxygen atoms of PMMA, yellow and blue colors to the oxygen and hydrogen atoms of the water molecule, and PMMA hydrogen atoms have been omitted for clarity.

(a)

18


Page 19 of 31


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(b)

(c)

19



Figure 8. Three-dimensional trajectories of four water molecules from the MD simulations with System 2, for the first: (a) 100 ps, (b) 500 ps, and (c) 1000 ps of simulation time. Two of these water molecules (the red and blue ones) are confined within CNTs whose mouths are blocked by PMMA mass while the other two (the black and green ones) execute diffusive motion in the PMMA domains of the nanocomposite.

Residence time of water inside CNT surrounded by polymer: A long NPT MD simulation with System 3 without any water molecules present in the matrix was carried out at T = 550 K and P = 1 atm to provide us with a good number (approximately 150) of well-equilibrated configurations for the subsequent calculation of the distribution of water residence times inside CNTs. The water residence time is defined as the time needed for the water molecule to exit the CNT. According to our analysis, if a water molecule comes out from a CNT and stays outside it for at least 100 ps, it will not return back to the CNT. In each of these 150 relaxed configurations, a water molecule was placed at the center-of-mass of the corresponding CNT with a random orientation and the NPT MD simulation was continued (again at T = 550 K and P = 1 atm) for several nanoseconds. In all cases, the water molecule was observed to travel very fast along the axial direction of the tube for several times, exploiting practically all available space for motion, before eventually escaping from to pore to continue moving in the outer PMMA domains of the nanocomposite. By running the MD simulation with all 150 configurations sufficiently enough (i.e., for the corresponding water molecule to escape the CNT) we were able to estimate the distribution of water residence times τr inside CNTs at the given conditions (T = 550 K, P = 1 atm). The results obtained for the case corresponding to a relatively mild penetration of PMMA chains into CNTs (on the order of 5 Å, see Figure 1) are shown in Figure 9a. The computed distribution is very broad spanning almost three orders of magnitude, with the shortest residence time being ~ 1 ns and the longest ~ 450 ns. Overall, it

20


Page 20 of 31

Page 21 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


has the shape of a Poisson distribution with a peak at ~ 20 ns and a mean of ~ 92 ns. In Figure 9b, we also show the corresponding distribution of water travelling times τt inside a CNT. The travelling time τt is defined as the time it takes a water molecule to travel from the middle point of the CNT where it was initially placed to one of its ends. Similar to Figure 9a, the distribution of τt is also very broad but corresponds to picosecond time scales, as compares to nanoseconds characterizing the distribution of residence times. This indicates the extremely fast mobility of water inside CNTs (which is also evident in the graphs of Figure 8). From Figure 9b, the value of mean travelling time is computed to be ~ 30 ps. Our calculations support the hypothesis that PMMA mass blocking the CNT mouths presents a strong resistance to water mobility inside the nanocomposite significantly delaying its escape from the CNT channels to the PMMA domains and vice versa. The MD simulations indicate that the characteristic times of the two processes are separated by three orders of magnitude, which is a huge difference: a water molecule needs only a few picoseconds to reach the CNT mouth but must wait for approximately one hundred nanoseconds before escaping from the CNT due to the strong resistance to transport presented by the intervening polymer mass.

(a)

21



(b)

Figure 9. Distribution of: (a) residence and (b) travelling times of water molecules inside CNTs surrounded by PMMA. Results averaged over 150 individual NPT MD simulations with System 3 at T = 550 K and P = 1 atm.

All of the above results have been obtained for CNTs that are mildly blocked by PMMA (corresponding to a penetration length of about 5 Å). As we said, however, after approximately 800 ns of MD simulation, the mass penetration length increased to ~ 10 Å. We thus repeated the previous analysis also for the case where PMMA had penetrated CNTs for about 10 Å. Surprisingly enough, and even after approximately 1 μs of MD simulation, none of the water molecules had exited the CNTs. That is, for the case of deep penetration, a water molecule needs more than 1 microsecond to escape from the CNT to the outside (polymer) phase. Given that MD simulations for times longer than 1 microsecond are computationally too demanding, we did not pursue the issue further, leaving the estimation of the corresponding rates to a future study by means of transition state theory (TST) calculations. However, our results are indicative of the big effect of adsorbed polymer mass on the CNT

22


Page 22 of 31

Page 23 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


mouths to the mobility and transport of small molecules such as water through CNT-based polymer membranes.

IV. CONCLUSIONS Atomistic-scale MD simulations have been performed to study the mobility of water molecules inside a CNT-based PMMA nanocomposite, under equilibrium conditions. Our simulations revealed the tendency of PMMA chains to penetrate CNTs and block their entrances, a phenomenon that can have a dramatic effect on water mobility and transport through the nanocomposite. Our simulations indicated that residence times of water molecules trapped inside CNTs blocked by PMMA mass depend strongly on the degree of polymer penetration in the CNT. For mild penetration lengths (on the order of 5 Å), the residence times at T = 550 K were computed to be on the order of a few hundreds of nanoseconds (exceeding by 3 orders of magnitude the corresponding water travelling times inside the CNTs) whereas for larger penetrations (on the order of 10 Å), the corresponding residence times were well above 1 microsecond at T = 550K and too long to be computed by atomistic MD simulations. Clearly, more efficient methods (such as those based on transition state theory) are needed to access these time scales. Our studies indicate the key role of the structural (density and local packing) properties of the interfacial zones around CNT mouths in CNT-polymer nanocomposites in controlling the permeability properties of the corresponding materials to small penetrants such as water. For example, one can carry out nonequilibrium (e.g., pressure-driven) simulations of water molecules inside CNT-based polymer nanocomposites with blocked CNT mouths in order to predict the effect of water confinement on its transport diffusivity, the property typically measured by experimetal methods involving uptake or permeation rate measurements,42 and how it can be described by theoretical models. Overall, our simulation findings suggest that fabricating CNT-based

23



polymeric membranes with improved permeability properties calls for new designs or modification methods targeting selectively the nanotube faces, the aim being to prevent polymer chains from penetrating the tubes and blocking their pores.

AUTHOR INFORMATION Corresponding Author *

Email: [email protected] and [email protected] (V.G. Mavrantzas). Phone:

(+30) 6944 6025 80, (+41) 44 632 85 03. ORCID Vlasis G. Mavrantzas: 0000-0003-3599-0676 Panagiotis G. Mermigkis: 0000-0001-7848-8235 Emmanuel N. Skountzos: 0000-0002-2401-7865 Notes The authors declare no competing financial interest.

Supporting Information The video in the Electronic Supporting Information (ESI) presents a sequence of frames extracted from the MD simulation with nanocomposite System 2 at T = 550 K. It emphasizes water confinement in a CNT whose pores are blocked by PMMA chains that have penetrated the tube though its faces. The total duration of the movie is 100 ns. The water molecule is moving fast from one end of the CNT to the other and back, indicative of its high mobility due to the smoothness of CNT walls and their hydrophobicity. With black we have colored CNT and PMMA carbon atoms, with red PMMA oxygen atoms, with white CNT terminal hydrogen atoms, and with blue and yellow the oxygen and hydrogen atoms of the trapped water molecule.

24


Page 24 of 31

Page 25 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ACKNOWLEDGEMENTS We gratefully acknowledge financial support by the Limmat Foundation, Zürich, Switzerland, through the project “Multiscale Simulations of Complex Polymer Systems” (MuSiComPS). The work was supported by computational time granted from the Greek Research & Technology Network (GRNET) in the National HPC facility - ARIS - under the project CoaBrush_I (pr006011).

25



REFERENCES 1.

Holt, J. K.; Park, H. G.; Wang, Y. M.; Stadermann, M.; Artyukhin, A. B.;

Grigoropoulos, C. P.; Noy, A.; Bakajin, O. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 2006, 312, 1034-1037. 2.

Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. J. Nanoscale hydrodynamics -

Enhanced flow in carbon nanotubes. Nature 2005, 438, 44-44. 3.

Qin, X. C.; Yuan, Q. Z.; Zhao, Y. P.; Xie, S. B.; Liu, Z. F. Measurement of the rate of

water translocation through carbon nanotubes. Nano Lett. 2011, 11, 2173-2177. 4.

Walther, J. H.; Ritos, K.; Cruz-Chu, E. R.; Megaridis, C. M.; Koumoutsakos, P.

Barriers to superfast water transport in carbon nanotube membranes. Nano Lett. 2013, 13, 1910-1914. 5.

Ritos, K.; Mattia, D.; Calabro, F.; Reese, J. M. Flow enhancement in nanotubes of

different materials and lengths. J. Chem. Phys. 2014, 140, 014702. 6.

Wang, L. Y.; Dumont, R. S.; Dickson, J. M. Nonequilibrium molecular dynamics

simulation of pressure-driven water transport through modified CNT membranes. J. Chem. Phys. 2013, 138, 124701. 7.

Bounos, G.; Andrikopoulos, K. S.; Moschopoulou, H.; Lainioti, G. C.; Roilo, D.;

Checchetto, R.; Ioannides, T.; Kallitsis, J. K.; Voyiatzis, G. A. Enhancing water vapor permeability in mixed matrix polypropylene membranes through carbon nanotubes dispersion. J. Memb. Sci. 2017, 524, 576-584. 8.

Dong, G. X.; Li, H. Y.; Chen, V. K. Challenges and opportunities for mixed-matrix

membranes for gas separation. J. Mater. Chem. A 2013, 1, 4610-4630. 9.

Ismail, A. F.; Goh, P. S.; Sanip, S. M.; Aziz, M. Transport and separation properties of

carbon nanotube-mixed matrix membrane. Sep. Purif. Technol. 2009, 70, 12-26.

26


Page 26 of 31

Page 27 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10.

Chehrazi, E.; Sharif, A.; Omidkhah, M.; Karimi, M. Modeling the effects of interfacial

characteristics on gas permeation behavior of nanotube-mixed matrix membranes. ACS Appl. Mater. Interfaces 2017, 9, 37321-37331. 11.

Cong, H. L.; Zhang, J. M.; Radosz, M.; Shen, Y. Q. Carbon nanotube composite

membranes of brominated poly(2,6-diphenyl-1,4-phenylene oxide) for gas separation. J. Memb. Sci. 2007, 294, 178-185. 12.

Ge, L.; Zhu, Z. H.; Li, F.; Liu, S. M.; Wang, L.; Tang, X. G.; Rudolph, V.

Investigation of gas permeability in carbon nanotube (CNT)-polymer matrix membranes via modifying CNTs with functional groups/metals and controlling modification location. J. Phys. Chem. C 2011, 115, 6661-6670. 13.

Hamid, M. R. A.; Jeong, H. K. Recent advances on mixed-matrix membranes for gas

separation: Opportunities and engineering challenges. Korean J. Chem. Eng. 2018, 35, 15771600. 14.

Khan, M. M.; Filiz, V.; Bengtson, G.; Shishatskiy, S.; Rahman, M.; Abetz, V.

Functionalized carbon nanotubes mixed matrix membranes of polymers of intrinsic microporosity for gas separation. Nanoscale Res. Lett. 2012, 7, 1-12. 15.

Khan, M. M.; Filiz, V.; Bengtson, G.; Shishatskiy, S.; Rahman, M. M.; Lillepaerg, J.;

Abetz, V. Enhanced gas permeability by fabricating mixed matrix membranes of functionalized multiwalled carbon nanotubes and polymers of intrinsic microporosity (PIM). J. Memb. Sci. 2013, 436, 109-120. 16.

Kim, S.; Chen, L.; Johnson, J. K.; Marand, E. Polysulfone and functionalized carbon

nanotube mixed matrix membranes for gas separation: Theory and experiment. J. Memb. Sci. 2007, 294, 147-158. 17.

Kim, S.; Pechar, T. W.; Marand, E. Poly(imide siloxane) and carbon nanotube mixed

matrix membranes for gas separation. Desalination 2006, 192, 330-339.

27



18.

Page 28 of 31

Mondal, S.; Hu, J. L. Microstructure and water vapor transport properties of

functionalized

carbon

nanotube-reinforced

dense-segmented

polyurethane

composite

membranes. Polym. Eng. Sci. 2008, 48, 1718-1724. 19.

Weng, T. H.; Tseng, H. H.; Wey, M. Y. Preparation and characterization of multi-

walled carbon nanotube/PBNPI nanocomposite membrane for H-2/CH4 separation. Int. J. Hydrogen Energy 2009, 34, 8707-8715. 20.

McKeown, N. B.; Budd, P. M. Polymers of intrinsic microporosity (PIMs): organic

materials for membrane separations, heterogeneous catalysis and hydrogen storage. Chem. Soc. Rev. 2006, 35, 675-683. 21.

Skountzos, E. N.; Mermigkis, P. G.; Mavrantzas, V. G. Molecular dynamics study of

an atactic poly(methyl methacrylate)-carbon nanotube nanocomposite. J. Phys. Chem. B 2018, 122, 9007-9021. 22.

Mermigkis, P. G.; Tsalikis, D. G.; Mavrantzas, V. G. Determination of the effective

diffusivity of water in a poly (methyl methacrylate) membrane containing carbon nanotubes using kinetic Monte Carlo simulations. J. Chem. Phys. 2015, 143, 164903. 23.

Anastassiou, A.; Karahaliou, E. K.; Alexiadis, O.; Mavrantzas, V. G. Detailed

atomistic simulation of the nano-sorption and nano-diffusivity of water, tyrosol, vanillic acid, and p-coumaric acid in single wall carbon nanotubes. J. Chem. Phys. 2013, 139, 164711. 24.

Skountzos, E. N.; Anastassiou, A.; Mavrantzas, V. G.; Theodorou, D. N.

Determination of the mechanical properties of a poly(methyl methacrylate) nanocomposite with functionalized graphene sheets through detailed atomistic simulations. Macromolecules 2014, 47, 8072-8088. 25.

Rissanou, A. N.; Harmandaris, V. A. Dynamics of various polymer-graphene

interfacial systems through atomistic molecular dynamics simulations. Soft Matter 2014, 10, 2876−2888.

28


Page 29 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


26.

Rissanou, A. N.; Harmandaris, V. A. Structure and dynamics of poly(methyl

methacrylate)/graphene systems through atomistic molecular dynamics simulations. J. Nanopart. Res. 2013, 15, 1589. 27.

Behbahani, A. F.; Allaei, S. M. V.; Motlagh, G. H.; Eslami, H.; Harmandaris, V. A.

Structure,

dynamics,

and

apparent

glass

transition

of

stereoregular

poly(methyl

methacrylate)/graphene interfaces through atomistic simulations. Macromolecules 2018, 51, 7518-7532. 28.

Behbahani, A. F.; Motlagh, G. H.; Allaei, S. M. V.; Harmandaris, V. A. Structure and

conformation of stereoregular poly(methyl methacrylate) chains adsorbed on graphene oxide and reduced graphene oxide via atomistic simulations. Macromolecules 2019, 52, 3825-3838. 29.

Mayo, S. L.; Olafson, B. D.; Goddard, W. A. DREIDING: a generic force field for

molecular simulations. J. Phys. Chem. 1990, 94, 8897-8909. 30.

Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The missing term in effective pair

potentials. J. Phys. Chem. 1987, 91, 6269-6271. 31.

Papadimitriou, K. D.; Skountzos, E. N.; Gkermpoura, S. S.; Polyzos, I.; Mavrantzas,

V. G.; Galiotis, C.; Tsitsilianis, C. Molecular modeling combined with advanced chemistry for the rational design of efficient graphene dispersing agents. ACS Macro Lett. 2016, 5, 2429. 32.

Gkermpoura, S. S.; Papadimitriou, K. D.; Skountzos, E. N.; Polyzos, I.; Carbone, M.

G. P.; Kotrotsos, A.; Mavrantzas, V. G.; Galiotis, C.; Tsitsilianis, C. 3-Arm star pyrenefunctional PMMAs for efficient exfoliation of graphite in chloroform: fabrication of graphene-reinforced fibrous veils. Nanoscale 2019, 11, 915-931. 33.

Vasileiadis, T.; Skountzos, E. N.; Foster, D.; Coleman, S. P.; Zahn, D.; Krečinića, F.;

Mavrantzas, V. G.; Palmer, R. E.; Ernstorfer, R. Ultrafast rotational motions of supported

29



nanoclusters

probed

by

electron

diffraction.

Nanoscale

Page 30 of 31

Horizons

2019,

DOI:

10.1039/c9nh00031c. 34.

Ramos, J.; Peristeras, L. D.; Theodorou, D. N. Monte Carlo simulation of short chain

branched polyolefins in the molten state. Macromolecules 2007, 40, 9640-9650. 35.

Scienomics, MAPS Platform, Version 3.4.2, France. 2015. Available online:

http://www.scienomics.com/ (accessed on 30 September 2016). 36.

Van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J.

C. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005, 26, 1701-1718. 37.

Dahal, U. R.; Dormidontova, E. E. Spontaneous insertion, helix formation, and

hydration of polyethylene oxide in carbon nanotubes. Phys. Rev. Lett. 2016, 117, 027801. 38.

Greenfield, M. L.; Theodorou, D. N. Geometric analysis of diffusion pathways in

glassy and melt atactic polypropylene. Macromolecules 1993, 26, 5461-5472. 39.

Voyiatzis, E.; Böhm, M.C., Müller-Plathe, F. A geometric approach to identify

cavities in particle systems. Comp. Phys. Commun. 2015, 196, 247–254. 40.

GrayWeale, A. A.; Henchman, R. H.; Gilbert, R. G.; Greenfield, M.; Theodorou, D.

N. Transition-state theory model for the diffusion coefficients of small penetrants in glassy polymers. Macromolecules 1997, 30, 7296-7306. 41.

Greenfield, M. L.; Theodorou, D. N. Molecular modeling of methane diffusion in

glassy atactic polypropylene via multidimensional transition state theory. Macromolecules 1998, 31, 7068-7090. 42.

Maginn, E. J.; Bell A. T.; Theodorou, D. N. Transport diffusivity of methane in

silicalite from equilibrium and nonequilibrium simulations. J. Phys. Chem. 1993, 97, 41734181.

30


Page 31 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic High Polymer Mass Densities at the Mouths of Carbon Nanotubes (CNTs) Control the Diffusion of Small Molecules through CNT-Based Polymer Nanocomposite Membranes

Panagiotis G. Mermigkis, Emmanuel N. Skountzos and Vlasis G. Mavrantzas

31


High Polymer Mass Densities at the Mouths of Carbon Nanotubes

Recommend Documents