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Molecular Dynamics Simulation of Thermomechanical Properties of Montmorillonite Crystal. 3. Montmorillonite Crystals with PEO Oligomer Intercalates Mikhail A. Mazo,*,† Leonid I. Manevitch,† Elena B. Gusarova,† Mikhail Yu. Shamaev,† Alexander A. Berlin,† Nikolay K. Balabaev,‡ and Gregory C. Rutledge§ SemenoV Institute of Chemical Physics Russian Academy of Science, Kosygin str. 4, Moscow, 119991, Russia, Institute of Mathematical Problems of Biology Russian Academy of Science, Pushchino, 142290 Russia, and Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 ReceiVed: July 30, 2007; In Final Form: December 24, 2007
We present the results of molecular dynamics (MD) simulation of the structure and thermomechanical behavior of Wyoming-type Na+-montmorillonite (MMT) with poly(ethylene oxide) (PEO) oligomer intercalates. Periodic boundary conditions in all three directions and simulation cells containing two MMT lamellae [Si248Al8][Al112Mg16]O640[OH]128 oriented parallel to the XY-plane were used. The interlamellar space, or gallery, between neighboring MMT lamellae was populated by 24 Na+ counterions and PEO macromolecules of different lengths, ranging from 2 up to 240 repeat units. We considered three different loadings of PEO within the gallery: 80, 160, and 240 repeat units, corresponding to 13, 23, and 31 wt % PEO based on total mass of the nanocomposite, respectively. In the cases of 13 and 23 wt %, the polymer chains formed one or two well-defined amorphous layers with interlayer distances of 1.35 and 1.8 nm, respectively. We have observed also formation of a wider monolayer gallery with interlayer distances of 1.6 nm. Three-layer PEO films formed in the case of 31 wt % loading. The thermal properties were analyzed over the range 300-400 K, and the isothermal linear compressibility, transversal moduli, and shear moduli were calculated at 300 K. These properties are compared with the results of our simulation of thermal and mechanical properties of MMT crystal with galleries filled by one or two water layers as well as with those of an isolated clay nanoplate.
1. Introduction In recent years polymer-clay nanocomposites have drawn much attention by researchers because of the significant improvement in mechanical and thermal properties, decreasing permeability that influences the biodegradation of polymers in biomedical applications, etc., in comparison to polymers without nanoclay fillers.1-4 Now they are used for barrier films in packaging, fire retardant coatings, car components, etc., and have potential applications in the automobile, aviation, biomedical, and other polymer industries. In general, two idealized polymer layered silicate structures are possible: intercalated and exfoliated. In an intercalated nanocomposite, a few (usually, one or two) molecular layers of polymer occupy the gallery region between clay lamellae, in contrast to an exfoliated nanocomposite, in which the individual, ∼1 nm thick clay lamellae are dispersed in a continuous polymer matrix and segregated from one another by average distances that depend on the clay dimensions and polymer volume fraction.2 Our understanding of intercalated polymer systems is now at an essential stage of progress. The reason is a more general theoretical and industrial interest in the behavior of polymers under confinement. The packing and mobility of polymer fluids under confinement can be very different from that in the bulk, which in turn influences essentially the physicomechanical properties of intercalated polymers. In such problems, molecular * Corresponding author. Fax: (7495)-137-8284. E-mail: mazo@ polymer.chph.ras.ru. † Semenov Institute of Chemical Physics RAS. ‡ Institute of Mathematical Problems of Biology RAS. § Massachusetts Institute of Technology.
simulation plays an important role, as evidenced by the number of computer simulation studies on the morphology, thermodynamic and electrical properties, ions, and polymer mobility in thin polymer layers.5-9 It was demonstrated that the computer simulation of the models of real systems could be used to gain an understanding about the local arrangement and dynamics of intercalated organic molecules in clay-organic systems. Hydrophilic polymers, such as poly(ethylene oxide), PEO, can intercalate within hydrophilic silicates such as sodium or lithium montmorillonite (MMT). These materials, in which a polymer electrolyte/cation system is confined between inorganic layers, show interesting electromechanical responses, rendering them potential candidates for applications as electrolytes in solidstate batteries.6 Investigation of PEO intercalated within MMT by solid-state 2H NMR11,12 and thermally stimulated depolarization current13 revealed rich dynamics over a broad temperature range, with fast relaxing segments existing even at such low temperatures where the bulk PEO shows a completely solidlike response. A detailed study of the bonding between the surfactants and smectite and the molecular conformations of the surfactants in the interlayer of smectite has been reported.14 As it turned out, PEO chains form a monolayer structure inside the gallery of an intercalated clay with a periodic d spacing of 1.32-1.37 nm, when a polymer concentration is e13 wt % monomer (based on total).7,10,12 As the PEO concentration increases, chains form a bilayer structure with d spacing of 1.71.8 nm.7,10,12,14-16 These results were obtained for short7,10 as well as long7,10,12,14-16 molecules having molecular weights 200 and 400 or 2000, 3400, and 10 000 g‚mol-1 correspondingly. These results have also been obtained in computer simulation.7,15,17,18
10.1021/jp076028f CCC: $40.75 © 2008 American Chemical Society Published on Web 03/01/2008
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Figure 1. Time dependence of Lz during relaxation at stage e for each system with different initial configurations, with PEO oligomers having degree of polymerization n ) 20. S80, four oligomers per gallery (A); S160, eight oligomers per gallery (B); S240, 12 oligomers per gallery (C).
Figure 2. Equilibrium dimension of the cell in the Z-direction Lz vs degree of polymerization of PEO oligomers.
“sandwich”-like tactoid has not been reported. It was convincingly shown26,27 that knowledge of the tactoid’s mechanical properties is a critical component for the prediction of the mechanical properties for polymer-clay nanocomposites using micromechanical composite modeling. In summary, one can conclude that thermomechanical properties of tactoids, being very important for estimation of those for nanocomposites, remain less well understood than those of other physical properties. This circumstance has motivated us to undertake a detailed treatment of this problem. Earlier we calculated elastic and thermal properties of the pyrophyllite lamella28 and the Na+-montmorillonite crystal with one and two water layers within the gallery between lamellae at different temperatures.29 This paper extends those results to the case of intercalated polymer. The paper is organized as follows: section 2 is devoted to selection of the force field and to details of the molecular dynamics (MD) simulations, including the procedures followed to derive initial configurations. The results of the simulations are presented and discussed in section 3. A final discussion is provided in the Conclusion. 2. Model and Simulation Details
Figure 3. Equilibrium values of the gallery thickness h vs degree of polymerization: curve 1, S240; curve 2, S160; curves 3 and 4, S80w; curves 5 and 6, S80n. Because the series S80n and S80w formed the galleries of different thicknesses, we use filled symbols for the thinner gallery and open symbols for the thicker one.
TABLE 1: Equilibrium Cell Size in Z-Direction Lz and Widths of the Galleries h1 and h2 series of run
Lz, nm
h1, nm
h2, nm
S80n S80w S160 n > 2 S160, n ) 2 S240 n > 2 S240, n ) 2
2.92 ( 0.01 3.38 ( 0.02 3.62 ( 0.01 3.64 ( 0.005 4.32 ( 0.02 4.55 ( 0.005
0.73 ( 0.02 1.167 ( 0.004 1.165 ( 0.005 1.169 ( 0.007 1.53 ( 0.03 1.63 ( 0.01
0.93 ( 0.02 0.92 ( 0.01 1.165 ( 0.05 1.169 ( 0.07 1.52 ( 0.03 1.63 ( 0.01
In the past few years, the combination of both experimental study and computer simulation has been effective for study of the PEO molecules between MMT lamellae. Selected papers7,10,12,14-25 containing, in particular, detailed analysis of PEO including the structure and mobility of the polymer in different layers between the MMT silicate lamellae are worth mentioning. However, to date the role of the molecular weight of the polymer intercalate in the structure of the interlayer space as well as in the mechanical properties of the resulting
The system under consideration is a fully atomistic model of PEO oligomers intercalated in Na+MMT. We used an oblique parallelepiped computational cell with periodic boundary conditions in all three directions. The cell contained two MMT lamellae [Si248Al8][Al112Mg16]O640[OH]128 parallel to the XYplane. Each space between the MMT lamellae (the galleries) was populated with 24 counterions of Na+ and PEO macromolecules C-(CH2-CH2-O)n-H of different degrees of polymerization n from 2 up to 240. We carried out three series of calculations with different numbers of PEO repeat units in each gallery: 80, 160, and 240, which corresponded to 13, 23, and 31 wt % PEO (based on total), respectively. We denote these series as S80, S160, and S240. The empirical CLAYFF force field30 for MMT and AMBER31 for PEO were used to compute the energy of the system. The cutoff radius for van der Waals interaction was set to 1.05 nm, and the cutoff radius for screened Coulombic interactions was set to 1.25 nm. The system evolved according to the Newtonian equations of motion with additional terms providing the Berendsen barostat32 and the collisional thermostat.33 We also applied a correction to velocities at each time step to prevent translation of the system as a whole. The equations of motion were integrated using the velocity Verlet algorithm,34 and the integration step was 0.5 fs. Preparation of the relaxed samples consisted of the following five successive stages: (a) Creation of Wyoming-type montmorillonite lamella with periodic boundary conditions in the XY-plane, with the dimensions 3.58 × 4.16 nm and adsorbed Na+ counterions. The positions of the sites in the unit cell of the clay were as given by Cha´vez-Pa´ez et al.35 Each lamella consisted of 32 unit cells
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Figure 4. Snapshot of projection on the YZ-plane of the PEO molecules in MMT for the three loadings simulated, S80, S160, and S240, for lowest (n ) 2) and highest (n ) 80) degrees of polymerization n for each case. Na+ ions are shown in blue.
Figure 5. Number density profiles of PEO molecules with degree of polymerization n ) 20 and Na+ cations in galleries. The narrower gallery of S80n (A); the wider gallery of S80n (B); the galleries of S160 (C) and S240 (D). Black, MMT (1); magenta, C of PEO (2); red, O of PEO (3); blue, H of PEO (4); green, Na+ (5).
of MMT (1280 atoms), eight cells in the Y-direction (a-axis of the unit cell) and four in the X-direction (b-axis of the unit cell). (b) Creation of a thin, condensed amorphous film of PEO molecules, independently for each gallery. (c) Construction of a computational cell (parallelepiped) which comprised two Wyoming-type MMT lamellae separated on each side by a thin amorphous PEO film. Periodic boundary conditions were imposed in all directions. The cell size in the Z-direction Lz for S80 was 4.0 nm, for S160 was 5.0 nm, and for S240 was 6.0 nm. (d) Molecular dynamics simulation of the systems in the canonical (NVT) ensemble at 500 K for 200 ps. After this, we gradually decreased the temperature of the samples to 300 K over the course of 100 ps and simultaneously compressed them
until the desired Lz,0 for each series was obtained. We chose two values for Lz,0 to test the influence of the procedure for obtaining initial configurations on the equilibrium structure of the system: we used Lz,0 ) 3.0 and 3.5 nm for S80, 3.5 and 4.0 nm for S160, and 4.5 and 5.0 nm for S240. (e) Molecular dynamics simulation of the systems in the isobaric-isothermal ensemble (NPT) at atmospheric pressure, zero shear tension, and 300 K, for no less than 1 ns. The plots showing equilibration of Lz during this stage are presented in Figure 1. The equilibrium dimensions of the simulation cell in the Xand Y-directions are determined primarily by the clay lamellae and fluctuate little, due to the stiffness of the MMT plates; these were 3.6 and 4.15 nm, respectively. The equilibrium dimension
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TABLE 2: Calculated Value of CTEs in Transversal Direction KT,z × 10-5 K-1 pyrophyllite27 MMT + 1 water layer28 MMT + 2 water layers28 S80n S80w S160, n > 5 S160, n ) 5 S160, n ) 2 S240, n > 5 S240, n ) 5 S240, n ) 2
1.01 ( 0.03a 1.47 ( 0.03 3.01 ( 0.03 1.6 ( 0.3 1.8 ( 0.1 4.9 ( 0.2 6.4 ( 0.2 11.6 ( 0.9 7.9 ( 0.2 14 ( 1 21.4 ( 0.6
a Taking into account the van der Waals atomic radii, which increased the effective width of the clay plate from 0.6425 to 0.98 nm.35
TABLE 3: Calculated Estimates of KT,z for PEO and H2O Thin Films in the Galleries of Na+MMT at 300 K KT,z × 10-5 K-1
βz, TPa-1
1 water layer 2 water layers
Only H2O in MMT Galleries 2.5 ( 0.1 6.0 ( 0.1
28 ( 5 27 ( 15
S80n S80w S160, n > 5 S160, n ) 5 S160, n ) 2 S240, n > 20 S240, n ) 5 S240, n ) 2
Only PEO in MMT Galleries 2.3 ( 0.7 2.6 ( 0.3 9.4 ( 0.4 12.8 ( 0.2 24 ( 1; 11.9 ( 0.4 24.8 ( 2 35.9 ( 0.8
55 ( 6 59 ( 11 64 ( 8 64 ( 8 64 ( 8 134 ( 17 134 ( 17 134 ( 17
Experimental Data for PEO in Bulk36 70.4 ( 0.5
130 ( 1
n)5
in the Z-direction depends on the loading of polymer in the gallery. The equilibrium dimensions and the potential energy of the systems for S160 and S240 were found not to depend on the magnitude of Lz,0; this confirms that the resulting tactoids are fully equilibrated with respect to interlayer distance. On the contrary, for the case S80, Lz relaxed from 3.0 to 2.9 nm and from 3.5 to 3.4 nm for all degrees of polymerization n. The equilibrium values of Lz are shown in Figure 2 for all of the calculations performed. One can see that, in the case of the galleries with the lowest loading of polymer (S80), the composite can be in one of two stable states depending on the procedure for preparation of the initial configuration. Hereafter, we refer to the more dense samples as S80n (“narrow”) and the less dense ones as S80w (“wide”). Below (section 3.1) we discuss this point in more detail. All of the systems obtained were stable with respect to heating up to 400 K and compression up to 1000 atm. 3. Results and Discussion 3.1. Interlayer Structure. In our model, the magnitude of the cell dimension Lz is determined by the thicknesses of the two MMT lamellae and the two galleries. Similar to our previous paper,36 we calculated the gallery thickness h as the distance between the two planes of oxygen atoms at the surface of the two lamellae bounding the gallery. The results of calculations for h are presented in Figure 3. The results for h are relatively insensitive to the degree of polymerization n for n > 2. Thus, the average magnitude for h, including or excluding n ) 2, is shown in Table 1. As one can see, for series S160 and S240, the two galleries in each simulation have similar thicknesses, and the equilibrium thickness of the galleries depends on the loading of intercalated
Figure 6. Equilibrium values of potential energy (“Upot”) vs degree of polymerization: curve 1, S80n; curve 2, S80w; curve 3, S160; curve 4, S240.
PEO but not on the length of oligomers. A small increase in the gallery thickness is observed for the shortest chains. This fact may be explained by their higher mobility and the larger free volume usually associated with a high concentration of chain ends. The interlayer spacing for S160 corresponds well with experimental data7,10,12,14-16 and numerical results.7,15,17,18,24 In this case, the oligomeric molecules form a clear bilayer within the gallery (Figures 4 and 5). In the S240 systems, the PEO molecules formed a trilayer structure within the gallery. The molecules show a preference to locate near the clay lamella surface, forming relatively extended domains, with short transitional regions being located in the middle layer (Figures 4 and 6). To our knowledge, there is no experimental counterpart for the wider galleries or the trilayer structure observed for S240 (d spacing is equal to 2.17 and 2.23 nm). The situation turned out to be more complicated in the case of S80 when the gallery size in each set of simulations was different. One of the galleries had a thickness h of 0.92-0.93 nm in all cases, which corresponds to d spacing of 1.56 nm. The other gallery had h ) 0.73 nm (d spacing is 1.36 nm) for S80n, and h ) 1.17 nm (d ) 1.82 nm) for S80w. One can see from Figures 4 and 5 that a monolayer polymer structure is formed in the thinnest gallery, and a bilayer is formed in the gallery that has thickness 1.17 nm. The PEO structure in an “atypical gallery” with h ) 0.92-0.93 nm is a monolayer, but in contrast to other cases the molecules in the gallery are preferentially not in planar conformation. The potential energy of every system in the S80n series was lower (approximately at 1.3 kcal/mol per PEO monomer) than for the S80w system with similar polymer content (Figure 6). Therefore, it may be expected that these structures will be more stable. No indications of any crystallinity in the PEO were observed in any of the PEO-MMT systems studied. The Na+ cations are found mostly close to the faces of the clay sheets, although a very small number of Na+ cations were observed farther from the clay lamellae (Figure 4). This is in agreement with the experimental data14 and results of computer simulation.19,21,24 3.2. Linear Coefficients of Thermal Expansion (CTEs). The thermal properties were analyzed over the range 300-400 K. For this purpose, we performed four to five cycles of heating and cooling for every sample at a constant rate of 0.5 K/ps, keeping the pressure constant at 1 atm. The sizes of the calculation cell in these runs were reproducible with good accuracy, which allowed us to calculate the linear and volume thermal expansion coefficients KT,a, KT,b, KT,z and
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Figure 7. Snapshot of the segments of one PEO molecule with degree of polymerization n ) 240 located within each of the three layers of a trilayer gallery. (A) and (C) are the layers closest to the surface of the MMT plates; (B) is the central layer of the trilayer.
Figure 8. Linear CTE (KT,z) of the intercalated MMT (A) and only PEO in galleries (B); curve 1, S80w; curve 2, S160; curve 3, S240.
TABLE 4: Linear (βa, βb, βz) and Volume (βV) Isothermal Compressibility of Intercalated H2O or PEO in Na+MMT at 300 K system water27
1 layer of 2 layers of water27 S80n S80w S160 S240
Lz, nm
βa, TPa-1
βb, TPa-1
βz, TPa-1
βV, TPa-1
2.46 ( 0.01 2.95 ( 0.01 2.92 ( 0.01 3.38 ( 0.02 3.62 ( 0.01 4.40 ( 0.02
1.95 ( 0.01 2.7 ( 0.2 2.9 ( 0.2 3.6 ( 0.2 3.8 ( 0.6 3.7 ( 0.6
3.14 ( 0.01 3.85 ( 0.03 3.6 ( 0.4 4.2 ( 0.2 4.1 ( 0.8 4.2 ( 0.3
11.9 ( 0.01 14.4 ( 0.1 21 ( 2 31 ( 3 35 ( 4 80 ( 10
17.0 ( 0.02 21.0 ( 0.3 27 ( 3 38 ( 3 43 ( 4 90 ( 10
KT,V for all of the types of intercalated systems studied. As was expected, the temperature behavior of the composite in the XYplane, determined primarily by the linear CTEs of the clay lamella, did not depend on polymer loading and was in accordance to our previous data for pyrophyllite27 (Table 2). We observed only a small increase of KT,b for MMT and for the shortest oligomers in the cases S160 and S240. This fact is in agreement with our conclusion about the higher mobility of short chains. As seen from Table 2, the polymer loading influences essentially only the linear CTE in the Z-direction. While KT,z was similar to that for pyrophyllite in the case of the narrowest galleries, S80n, it turned out to be larger for S80w and grew quickly with increasing d spacing and with decreasing degree of polymerization (Figure 8A). Assuming that KT,z for the MMT lamella coincides with that for a pyrophyllite lamella with a thickness of 0.98 nm,35 one can estimate the linear CTE for PEO inside the gallery (Table 3 and Figure 8B). Although the dependences shown in Figure 8 are qualitatively similar, the scale ordinates differ about 2 times. We see that the CTE of the thinnest (monolayer) gallery is independent of a polymer length and is 2.3 times greater than the CTE of pyrophyllite plate. The CTE of broader galleries is sensitive to chain length and increases as the chains become shorter. However, even for
TABLE 5: Size of Calculated Cell Lz and Calculated Elastic Moduli in the Transversal Direction MMT + 1 water layer MMT + 2 water layers S80n S80w S160 S240
Lz, nm
Cz, GPa
2.46 2.95 2.93 3.38 3.63 4.40
78.0 ( 0.4 62.3 ( 0.7 46 ( 3 28 ( 3 26 ( 2 9(3
the shortest molecules in the trilayer PEO gallery, the CTE is half that of the bulk polymer. 3.3. Calculation of Isothermal Compressibility. For calculation of isothermal compressibility we increased the isotropic pressure in the calculated cell at a constant rate of 1 MPa/ps from 0.1 to 100 MPa, and then decreased the pressure at the same rate. As a rule, we performed two to five cycles of pressurization and depressurization for every sample, keeping the temperature constant at 300 K. The MMT plates make the main contribution to the isothermal compressibility of the composite in the X- and Y-directions. Due to the distinctly linear dependence of the calculated cell size in these directions on external pressure, it was possible to find elastic moduli in compression with good accuracy (Table 4). The corresponding values of these moduli in the X- and Y-directions did not
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Figure 9. Isothermal compressibility in the transversal direction βz of PEO-Na+MMT composite (filled circles) and hydrated H2O-MMT28 (filled triangles) systems vs cell size in the Z-direction.
Figure 10. Uniaxial compression Cz (1) and reciprocal compression βz-1 (2) vs the size of calculated cell Lz.
practically depend on the extent of polymer loading, except in the series S80n, where larger stiffness was observed. The compressibility in the Z-direction βz is 1 order magnitude larger than those in the XY-plane, and some hysteresis was observed in this case that made the calculations more difficult. However, the systems invariably recovered their starting sizes upon decompression, which allowed us to calculate compressibility with acceptable reliability. It is seen from Table 4 and Figure 9 that compressibility increases noticeably with increasing interlayer spacing. Let us note that, unlike the CTE, the linear isothermal compressibility βz for MMT with both one and two intercalated water layers turned out to be noticeably less than in the case of PEO fillers and for monolayer and bilayer PEO molecules were sufficiently similar (Table 4). One can estimate the linear compressibilities for water and for PEO inside the galleries by a method similar to that for CTE (Table 3). Contrary to the CTE, the compressibility of H2O was significantly lower than that for PEO, while the stiffnesses of monoand bilayer PEO galleries were similar. At the same time the linear compressibility of oligomers in trilayer PEO galleries was twice that of the bilayer and equal to the bulk compressibility of water and PEO.
Mazo et al. 3.4. Uniaxial Deformation in Transversal Direction. To calculate elastic modulus in the Z-direction (Cz ) dPz/dz, where z is relative cell deformation), we decreased the cell size up to z ) 10-15% at a constant rate of 0.5 m‚s-1. During these deformations, the pressure in the X- and Y-directions was held constant at 105 MPa, and the temperature held constant at 300 K. The calculated value of Cz appeared not to depend on degree of polymerization of PEO, but it did depend on the thickness of the galleries, similar to what was observed for compressibility βz (Table 5). At the same time, we observed similar dependencies of Cz and βz on the cell size in the transversal direction (Figure 10). The most interesting results have been found for the case of compression of the samples of the S80w series. Contrary to the other cases, such compression led to two transitions, resulting in the formation of new metastable states. Figure 11 shows a typical change of Lz with time and the corresponding change of the pressure for S80w and degree of polymerization n ) 10. Three stable states are apparent in the dependence Pz on Lz (Figure 11B). We present the characteristics of the first and third stable states in Tables 1 and 6. For the change of the gallery thickness under compression, one can see a continuous decrease of the thickest slit and transition to a new stable state (state 2 in Figure 11B) in which both galleries are of equal thickness. Upon further decrease of Lz, the system transitions abruptly into another new state with distinctly different sizes of galleries whose thicknesses coincide with that in series S80n. Calculated elastic moduli in points 1 and 3 coincided with those for S80w and S80n, respectively. 3.5. Shear Moduli. We used the oblique parallelepiped computational cell for simulation of shear deformation. For this purpose, we changed the angle R between the Y- and Z-axes at a constant rate of dR/dt ) 0.5 rad‚ns-1, while maintaining atmospheric pressure and zero shear tension in the other planes. Shear modulus was calculated as the ratio of the shear stress to the change of the angle in the low-strain, linear regime. The calculation of shear modulus in the XZ-plane was carried out similarly. Characteristic examples of stress-strain relationships in shear are shown in Figure 12. The shear moduli for a given polymer loading were observed not to depend on the shear direction. Therefore we have presented in Figure 13 the simulated values averaged over two “experiments” in the cases of S80n and S80w, or four in the cases of S160 and S240. One can observe a distinct increase in shear modulus with increasing degree of polymerization. The series S80n, corresponding to thinner monolayer slits, exhibits a significant increase of shear rigidity in comparison with other cases (more pronounced than similar reinforcing in the cases of longitudinal loading and thermal expansion). It is interesting to note that, besides elastic shear stiffness, analysis of the plots of stress vs strain as shown in Figure 12
Figure 11. (A) Size of calculated cell Lz and transversal stress Pz vs time for S80w and n ) 10. (B) Pz vs Lz. (C) Pz and thicknesses of galleries h1 and h2 vs time.
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Figure 12. Typical dependency of stress versus strain for shear deformation. Top row corresponds to shear deformation in YZ-plane; bottom row corresponds to shear deformation in XZ-plane.
Figure 13. Average shear moduli Cav in XZ- and YZ-planes. Curve 1, S80n, curve 2, S80w, curve 3, S160, and curve 4, S240.
TABLE 6: Average Values of d Spacing and Gallery Widths h1 and h2 at the Equilibrium Points 1, 2, and 3 (Figure 10B) 1 2 3
d spacing, nm
h1 nm
h2, nm
1.687 ( 0.003 1.582 ( 0.003 1.47 ( 0.005
1.17 ( 0.01 0.95 ( 0.01 0.94 ( 0.01
0.93 ( 0.02 0.92 ( 0.01 0.72 ( 0.01
allows one to draw some conclusions about structural transformations of the system under large shear. For the series S80n, such transformations are in shear deformation of approximately 0.05 rad; for the other series, approximately 0.1 rad, or twice as much shear, is required to realize such transformations. At the same time, in the case of the shortest chains, from very beginning of the loading process one can observe the absence of elastic deformation and, respectively, essential structural transformations at an earlier stage of the process. This means that such an arrangement of oligomers does not form a solid state of the system.
the tactoid. Despite the use of different force fields and initial data in comparison with refs 7 and 10, the main structural characteristics turned out to be similar in all comparable cases and are in good agreement with experimental data. The polymer chains inside the galleries formed one, two, or three amorphous layers, depending on the amount of intercalated polymer. At that, there are two possible interlayer distances (1.35 and 1.8 nm) in accordance with experimental data.7,10,12 We have revealed also the formation of monolayer loadings that are thicker (d ) 0.22 nm) but stable up to T ) 400 K and pressure ) 100 MPa, for both series S80n and series S80w. A trilayer PEO gallery is predicted in the case of 30 wt % filling. (2) Thermal expansion coefficients of the tactoid in a wide temperature range (300-400 K) correspond to those for the clay nanoplate in the X- and Y-directions. However, the polymer loading increases essentially the CTE in the transversal Zdirection in all cases except that of the thinnest gallery. The largest CTEs observed were for the trilayer gallery, with values that are one-third that of bulk PEO. (3) The mechanical behavior of the tactoid under uniaxial loading demonstrates strong dependence of the transversal modulus on the thickness of the gallery, but no dependence on the degree of polymerization. It is shown that an increase in loading can lead to two transitions into new stable states with different gallery thicknesses. (4) The shear moduli for a given gallery filling do not depend on the shear direction. However, this is not the case for its dependence on the degree of polymerization, which is rather significant and similar to uniaxial loading. There is a threshold shear deformation that determines a structure transformation of the tactoid. Acknowledgment. The study was sponsored by the CRDF (Project No. RUC2-2626-MO-04).
4. Conclusion
References and Notes
(1) Loading of PEO oligomers in the galleries between MMT lamellae, which is strongly dependent on the procedure of system formation in both MD modeling and real experiment, has a strong influence on the thermomechanical properties of
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