J. Phys. Chem. C 2008, 112, 3473-3481
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Molecular Dynamics Simulations of Monofunctionalized Polyhedral Oligomeric Silsesquioxane C6H13(H7Si8O12) Jinhua Zhou and John Kieffer* Department of Materials Science and Engineering, UniVersity of Michigan, Ann Arbor, Michigan 48109-2136 ReceiVed: July 4, 2007; In Final Form: December 10, 2007
Polyhedral oligomeric silsesquioxanes (POSS), functionalized with a single hexyl substituent, have been studied using molecular dynamics (MD) simulations based on a reactive interaction potential. This potential is designed for mixed covalent-ionic interactions and facilitates the charge transfer that is associated with the rupture and formation of covalent bonds. The potential has been optimized to reproduce the known structural characteristics and dynamic properties of POSS. The model was then employed to study the melting behavior of crystalline monohexyl-POSS as well as the structural reorganization during subsequent cooling and glass formation. Simulations predict a melting temperature of crystalline monohexyl-POSS of 430 K. The amphiphilic nature of the structural building block in this compound is evident in the crystal phase through preferred POSS-POSS and hydrocarbon-hydrocarbon groupings, which give rise to a bilayered structure. Melting seems to originate from within the organic layers. A preference for groupings of like species is also apparent in the glass.
1. Introduction Hybrid organic-inorganic nanocomposites, that is, structures in which components of disparate nature are juxtaposed at the nanoscale, are sought for their ability to merge the advantages of inorganic and organic materials.1,2 Functionalized polyhedral oligomeric silsesquioxane (POSS) molecules are an interesting class of nanocomposites because organic and inorganic compounds are covalently bonded to each other and therefore form inherently diverse material building blocks that combine contrasting characteristics at the molecular level. Control over the structures and consequently the thermal and mechanical properties of the resulting nanocomposites can be achieved through the size, geometry, and chemical nature of the functional groups that are attached to the POSS cores. POSS is composed of an inorganic cubic-shaped core Si8O12, where each silicon is bonded to three oxygen atoms and the remaining valence is available to attach different functional groups. By attaching various organic molecules to the corners of the POSS cage, a wide gamut of building blocks can be synthesized for the purpose of fabricating different types of nanocomposites, including highly cross-linked thermosets,3 porous networks,4 and a variety of branched copolymers.5,6 Because of the nanometer size of these building blocks and the chemical bonding between disparate materials, POSS-based nanocomposites exhibit distinct advantages over conventional filler materials. No macrophase separation occurs between the organic and inorganic components. Appropriately functionalized POSS therefore provides an effective mechanism for reinforcing polymers. Enormous improvements in the thermal and mechanical properties, such as increased glass transition and thermal decomposition temperatures, reduced flammability, and enhanced mechanical properties due to the incorporation of POSS into polymers have been reported.7-15 Composites derived from POSS cages functionalized on all eight corners usually form complex network structures with high * To whom correspondence should be addressed. E-mail: kieffer@ umich.edu. Phone: 734-763-2595. Fax: 734-763-4788.
porosity,16 while for monofunctionalized POSS, better control over structural arrangements can be achieved due to simplified steric constraints in these systems.17 The principal process variables are the length of the substituent corner groups and the solvent chemistry. The present work focuses on monofunctionalized POSS copolymer, as the relative simplicity of these systems allows for a detailed investigation of the relationship between molecular design of the building blocks and the structures that result from their assembly, yielding a fundamental understanding that is needed for controlling structural developments in hybrid nanocomposite materials. One can conceive either linear or branched architectures for monofunctionalized POSS composites. In the former, POSS cages are attached to one or both ends of a linear polymer chain, such as in amphiphilic telechelics;17-20 in the latter, POSS cages are attached through the substituent corner groups to a polymer backbone and reside at the tips of branches.21,22 These pendent POSS structures have been successfully synthesized by several research groups using different organic substitutes and various compositions,5,6,19,23-25 including a noncovalently bonded pendent structure.26 In this paper, we focus on the linear molecules. We will address the pendent structures in a forthcoming publication. So far, of the large number of publications on POSS systems, relatively few describe computational investigations. Atomic scale simulations provide a unique approach for elucidating the local morphologies and their effects on mechanical reinforcement in hybrid nanocomposites, at a level that is difficult, if not impossible, to access in experiments. For example, polydispersity is inevitable in polymer synthesis, whereas in simulations, the length of the substituent organic groups is precisely known when examining their effect on the structure and properties of the composite materials. Quantum mechanical calculations have been utilized to characterize the structure of isolated POSS molecules.27,28 This work yielded information such as equilibrium bonding distances and bonding angles of POSS molecules in their ground state. Furthermore, the relative
10.1021/jp0752217 CCC: $40.75 © 2008 American Chemical Society Published on Web 02/15/2008
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TABLE 1: Parameters for the Simulation element
σi (nm)
ni
zi
q0i (ecu)
element
σi (nm)
ni
zi
q0i (ecu)
Si O
0.101 0.143
8 8
+4 -2
0 0
C H
0.095 0.065
8 2
+4 +1
0 0
pair
Aij (10-19 J)
Fij (nm-1)
ηij (nm-1)
κij (nm-1)
eλij
ij
jrij (nm)
Si-Si Si-O Si-C Si-H Si-H3 O-O O-C O-H O-H3 C-C C-H C-H3 H-H H-H3 H3-H3
0.1000 0.0550 0.1900 0.1300
34.5000 43.5000 48.5000 49.5000
0.00 3.60 1.10 2.80
14.500 46.500 43.000 41.500
0.0000 30.6760 1.0834 2.3270
3.8700 × 10-2 2.2850 × 10-2 2.5350 × 10-2 9.0000 × 10-3
0.3822 0.3513 0.3653 0.3455
0.1000 0.1800 0.1800
35.5000 17.0000 50.5000
0.00 0.00 0.00
10.500 19.000 30.500
0.0000 0.0000 0.0000
2.3650 × 10-2 1.8775 × 10-2 1.1575 × 10-2
0.2940 0.3233 0.2783
0.2000 0.2000
45.0000 37.3000
1.20 0.40
45.500 31.000
1.7435 0.5353
1.5275 × 10-2 1.0300 × 10-2
0.3500 0.3000
0.1000
14.5000
0.00
14.500
0.0000
6.9625 × 10-3
0.2500
charge transfer
δij (ecu)
a (nm)
b (nm-1)
charge transfer
δij (ecu)
a (nm)
b (nm-1)
Si-O Si-C Si-H
-0.194 -0.06 -0.023
0.200 0.225 0.190
57.00 105.0 75.00
C-C C-H
0.000 0.040
0.160 0.140
15.00 20.00
triplet
γijk (rad-2)
θ h (rad)
triplet
γijk (rad-2)
θ h (rad)
O-Si-O O-Si-C O-Si-H Si-O-Si Si-C-C Si-C-H
0.305 0.340 0.390 0.162 0.480 0.480
1.892 1.941 1.911 2.653 1.910 1.910
C-C-C C-C-H C-C-H3 H-C-H H-C-H3
0.230 0.120
2.094 2.071
0.330
1.823
torsiona C-C-C-C C-C-C-H3 H-C-C-H3 a
B1 (10-19 J) 4.9018 × 0.0000 0.0000
10-2
B2 (10-19 J) -9.4145 × 10 0.0000 0.0000
B3 (10-19 J) -3
1.0925 × 10-1 1.1791 × 10-1 9.8998 × 10-2
From ref 41.
stability of POSS cages with different ring sizes was evaluated based on the calculated ground-state energies.27 Xiang et al. studied the structure, electron distribution, and bonding character in the POSS cages.28 Using ab initio calculations, Li et al. found that functionalization with alkyl groups, linear or cyclic, has little effect on the structure of the POSS cage.29 These findings suggest that force fields describing the interactions within the inorganic and the organic portions of these hybrid molecules can be developed independent of one another, thus supporting the approach followed in the work described here. Molecular dynamics (MD) simulations have also been used to study POSS-polymer composites. Zhang et al. determined the pore sizes of a POSS-polymer complex structure.16 Bharadwaj et al. focused on the effect that corner groups, for example, cyclohexyl and cyclopentyl, have on the thermal properties of the resulting systems.30 Other researchers investigated the properties of POSS in organic solvents31-33 and explored the phase diagrams by conducting mesoscale simulations of the nanocomposites during self-assembly.34-36 Most of the aforementioned simulations were based on force fields that are commonly available in commercial simulation packages and that have originally been developed for different types of materials. In some respects, these force fields yield unsatisfactory results for POSS systems, such as the drastic overestimation of the melting temperatures.37 MD simulations of molecules combining species that exhibit disparate bonding types are relatively scarce due to the lack of
adequate force fields. In polymer-functionalized POSS, silicon and oxygen undergo mixed covalent-ionic bonding, whereas carbon and hydrogen exhibit predominantly covalent bonding and long-range dispersive interactions. To study the selfassembly process of POSS-based hybrid materials and to determine how functionalizing inorganic cores with various types of organic groups affects the resulting structures and properties, we carried out MD simulations based on a chargetransfer multibody interaction potential that we adapted for this purpose. We originally developed this potential to model interactions in inorganic compounds. To expand the applicability of the potential to hydrocarbons, we included terms commonly used to simulate organic polymer molecules. In this paper, we describe the potential, the optimization procedure, and present the case study of crystalline and amorphous POSS functionalized with a single hexyl group. 2. Simulation Details The force field used for the simulations described here was originally developed to model the mixed covalent-ionic bonding in silica.38-40 It contains three-body terms to describe the directionality of the covalent bonds and a charge-transfer term that controls the charge polarity within a bond and modulates between the covalent and ionic character of this interaction. The charge-transfer term also allows for charge redistribution upon rupture or formation of a bond so that the potential can be used
MD Simulations of Monofunctionalized POSS
J. Phys. Chem. C, Vol. 112, No. 10, 2008 3475
to simulate reactive systems. The single particle energy is expressed as
qj
N
Ui ) qi N
∑ j*i 4π r
NC
+
Cije(σ +σ -r )‚F ∑ j)1 i
[( ) ( ) ]
4ij ∑ j*i
∑
0 ij jrij 12
rij
-
jrij rij
6
j
ij
ij
+
NC-1 NC
+
∑ ∑ (φij + φik)Λijk + j)1 k)j+1
[B1(1 + cos φljkn) + B2(1 - cos 2φljkn) +
i∈{l,j,k,n}
B3(1 + cos 3φljkn) + B4] (1) The first term of eq 1 describes the Coulomb interactions that exist between every pair of charged atoms. Instead of fixing the point charge on each atom, the charges are calculated during the simulation process according to the charge-transfer function, ζij ) (1 + eb(rij-a))-1, which controls the changes in electron distribution as a function of the interatomic spacing. The rij is the interatomic distance, and a and b are adjustable parameters. Accordingly, the charge on each atom is given by NC
qi ) q0i - 2
δijζij ∑ j)1
(2)
where q0i is the charge of species i in the reference state and δij depends on the polarizability difference between species i and j. The second term in eq 1 is the Born-Mayer-Huggins expression representing the repulsion between atoms due to the Pauli exclusion principle, with Fij defined as the hardness parameter. The third term describes covalent bonding interactions, where φij ) -Cij(κij/ηij)ζijeλije-rijηij is purely attractive and Λijk ) e-γijk(θijk-θh )2 accounts for the directionality of these bonds by constraining the angle θijk between the i-j and i-k pairs of bonds. Note that the charge-transfer function modulates between covalent attractive and ionic interactions, and the angular constraints are conditional upon the existence of a covalent bond. The next term in eq 1 is the Lennard-Jones potential, which describes dispersive interactions between nonbonded atoms. Specifically for this force field, the Lennard-Jones interaction is excluded between atom pairs that experience torsion restriction, that is, it takes effect only when the two atoms involved are more than three neighbors away, more than four away if one atom is hydrogen, and more than five neighbors away if both atoms are hydrogen. The last term in eq 1 describes a fourbody torsion interaction about the dihedral angle φljkn, most commonly used in force fields such as OPLS-AA41 and TraPPEEH.42,43 The torsion angle potential reaches local minima at the trans and gauche conformations and gives a maximum energy at the cis conformation. All other symbols in eq 1 represent empirical parameters, and their values are given in Table 1. The parameters for the charge and charge-transfer term were optimized based on comparison with the results from first-principles quantum mechanical calculations. The parameters for the repulsive and directionally attractive interactions, that is, the second and the third terms, were optimized in the course of simulating various POSS compounds so as to reproduce experimentally known bond distances and angles, crystalline structures, and vibrational properties. The parameters for the torsion terms Lennard-Jones terms were obtained from references 41-43, while the rest of the parameters were optimized based on trial-and-error process to fit the experiment results.
Figure 1. Structure of the monotether hexyl-POSS crystal. (a) Snap shot at about 5 K from simulation; silicon is blue, oxygen is red, carbon is black, and hydrogen is omitted for clearer appearance. (b) Sketch from X-ray data in experiment.44
The system under investigation contained 64 monofunctionalized hexyl-POSS molecules. The initial crystal structure was constructed based on coordinates from X-ray diffraction data of the monofunctionalized hexyl-POSS crystal.44 Inside each triclinic P1h unit cell were two oppositely positioned molecules with the tails pointing to each other. The simulated configuration contained 4 × 4 × 2 unit cells. A random velocity obeying a Boltzmann distribution at the target temperature was assigned to each atom. The system was then relaxed for about 1 ns to ensure that it reached the energy minimum. All simulations were carried out using the MD code FLX developed in house. In Figure 1, we compare the experimentally determined ideal atomic positions and unit cell shape with a snapshot of simulated crystal structure cooled from 291 to 5 K. The latter retains a small degree of frozen disorder due to the relatively rapid quenching rate of 1 K/ps. In fact, some of the atoms are displaced to the opposite side of the simulation box due to
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TABLE 2: Bonding Configuration of Monohexyl-POSS at 291 K exp. sim. a
Si-O (Å)
Si-C (Å)
1.606(8)a 1.62
1.832(4)a 1.82
Si-H (Å)
C-C (Å)
C-H (Å)
O-Si-O (°)
O-Si-C (°)
Si-O-Si (°)
1.44
1.529b 1.54
1.09b 1.10
109.37(45)a 109.5
110.42(18)a 109.2
148.52(1.73)a 146.6
b
From ref 44. From ref 42.
TABLE 3: Crystal Structure Analysis a
exp. sim. a
a (Å)
b (Å)
c (Å)
U (Å3)
R (°)
β (°)
γ (°)
7.7775(9) 7.8029 ( 0.0491
7.9747(9) 7.7532 ( 0.0284
18.033(2) 18.0630 ( 0.0864
1093.5(2) 1077.8 ( 5.7
86.941(13) 89.225 ( 0.410
79.443(9) 82.305 ( 0.456
84.378(11) 84.481 ( 0.577
Experimental data from ref 44.
periodic boundary condition. Nevertheless, agreement between experimental and simulated structures is visually apparent; a quantitative analysis of the simulated structure is provided in the next section. This crystalline configuration, equilibrated at 291 K, served as the starting point for a simulated heating and cooling cycle under ambient pressure. Temperature was ramped at a rate of 1 K/ps, both for heating and cooling. Every 20 K, the system was further relaxed isothermally for 1 ns with the NPT ensemble to obtain the equilibrium structure. To accommodate the high frequency of the motion of hydrogen atoms, a time step of 0.5 fs was used. The data for structural and spectral analyses were collected and averaged over a period of 100 ps after equilibration. Two constant-pressure algorithms were employed; for the simulation of crystals, we used the Rahman-Parrinello algorithm,45 which allows for both the size and the shape of the simulation box to change; the Andersen algorithm,38 in which the simulation box is allowed to dilate and contract isotropically, was used to simulate the material in the liquid and supercooled liquid states since liquid systems do not withstand shear stress and become unstable under the Rahman-Parrinello scheme. 3. Results and Discussion The monohexyl-POSS configuration was relaxed at 291 K and ambient pressure for a minimum of 1 ns to ensure its stability. In Table 2, we compare the characteristics of local configurations, including bond distances and bond angles, of the simulated crystal with experimental findings.44 As can be seen from this table, the difference between the simulation and experiment is negligibly small. The largest discrepancy in bond distances occurs in the Si-O bond, with a mere 0.87% overestimate by the simulations. As for the angles, the average bending angles from simulation are very close to experimental values, with the largest difference being 2° for the Si-O-Si angle. The simulated cage diameter is 5.36 Å, compared to 5.356 Å in experiments.44 Hence, our potential model accurately reproduces molecular-level structural features. The crystal structure can be considered as composed of alternative layers of inorganic POSS cages and organic hydrocarbon chains. In Table 3, we list the lattice parameters of the crystal structure, comparing simulations and experimental results.44 The simulation box undergoes some degree of deformation as a result of the thermal motion of the atoms. The dimension along the c-axis, which is approximately perpendicular to the layers, matches perfectly well with the experiment result, accurately capturing the interlayer spacing. As for the cross-sectional area, a small deformation is observed; the a-axis is extended by 0.33%, and the b-axis is reduced by 2.78%. Overall, the volume of the unit cell is reduced by 1.44%. The axis angles R, β, and γ follow the same sequence as that in experiments, that is, R > γ > β, with R and γ slightly larger
than the experimental values by 2.63 and 3.6%, respectively. As a result, the density of the simulated crystal is 1.571 g/cm3, compared to 1.546 g/cm3 in experiments. For the crystalline configurations, no structural parameter deviates by more than 3.6% from experiment. Moreover, the optimization of potential parameters was not only based on reproducing structural characteristics but also vibrational properties, as detailed below. On the basis of MD simulations by Xia and Landman, the root-mean-squared end-to-end distance for liquid hexane averages 5.596 Å at 334 K.46 In our simulations, with one end of the carbon chain fixed onto the POSS cage, the root-meansquared end-to-end distance of the hexyl chain is 6.36 Å at 291 K, noticeably larger than that for pure hexane. Compared to pure hexane in the liquid state, the flexibility of the hexyl groups within the POSS lattice is constrained from adopting the cis configuration, which explains this difference. Aside from the structural features, we required that our interaction model also reproduce dynamical properties of this materials system. A crucial test for this is the infrared (IR) spectrum, which we calculated as the Fourier transform of the total dipole moment time correlation function. In Figure 2, we compare IR spectra from experiments44 and our simulations. All spectral features are reproduced with good agreement, both in terms of the position and relative intensity of the peaks. Furthermore, in simulations, we can easily verify which vibrational modes give rise to each of these spectral features. The most intense peak is located around 1139 cm-1 and is assigned to the Si-O-Si antisymmetrical stretching mode. Compared to the experimental spectrum where five distinct peaks appear within the range from 847 to 916 cm-1, in the simulated spectrum, the δ(Si-H) modes overlap with the ν(Si-C) stretching mode to produce a broad absorption band with slightly reduced intensity. The absorption band corresponding to the Si-H stretching mode appears around 2350 cm-1 in the simulated spectrum, compared to 2274 cm-1 in the experimental one, with a comparable width and somewhat lower intensity than that observed in the experiment. For all other major absorption bands from the experiment, including the C-H stretching modes, the Si-O-Si symmetric stretching, the O-Si-O bending modes, and the relatively weak CH2 wagging modes between 1150 and 1350 cm-1, we find excellent agreement between simulation and experiment. To our knowledge, this is the first calculation of the infrared spectrum for the hexyl-functionalized POSS crystal and serves as validation of our force field in correctly describing the structural dynamics in such systems. After ascertaining adequate performance of our force field with respect to the structure and dynamics of crystalline monofunctionalized alkyl-POSS, we explored the behavior of this system under conditions for which no experimental data exist yet, that is, melting and glass formation. To this end, we
MD Simulations of Monofunctionalized POSS
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Figure 2. Infrared spectrum of the monofunctionalized hexyl-POSS: top, simulation; bottom, experiment.44
Figure 3. Heating and cooling curves of monofunctionalized hexylPOSS: (a) volume; (b) potential energy.
heated the crystal structure until molten, equilibrated the system at high temperature, and cooled this configuration back down to room temperature. While for the initial equilibration of the crystalline configurations we used the Rahman-Parrinello algorithm, which allows for shear deformation of the simulation box, the thermal expansion during heating and cooling was captured by the Anderson algorithm. This was indicated because the melting temperature of the system was unknown and because molten configurations, which do not sustain shear deformations, cannot be simulated stably within the Rahman-Parrinello representation. Figure 3 shows the equilibrium volume of the system as a function of temperature. The volume of the system gradually increased with the average thermal expansion rate of
5.033 × 10-4 K-1 before the crystal melted. At 430 K, the volume of the system increased sharply, indicating a melting transition. There are no experiment data for the melting point of monofunctionalized POSS. Octafunctionalized hexyl-POSS is reported to have a melting point of about 305 K,47 while for hydrogen-terminated POSS, the melting point is 523 K;48 the predicted melting temperature of monofunctionalized POSS is halfway in between. No covalent bonds broke during the melting process or while the system was in the liquid state. The structure was further heated as high as 610 K, with the liquid-phase expanding at a rate of 1.357 × 10-3 K-1. Although no experimental data exist characterizing the melts of monofunctionalized hexyl-POSS, we can compare our results to those of other simulations. Peng et al. predict a density of approximately 1.25 g/cm3 for this compound at 700 K using MD simulations based on a combined hybrid Compass and TraPPE force field,49 while our simulations extrapolate to a density of about 1 g/cm3 at that temperature. It should be noted, however, that the force field these authors used significantly underestimates thermal expansion and overestimates the melting temperatures of monofunctionalized POSS systems.37 Upon cooling, our simulated system remained liquid to as low as 355 K, and then, the supercooled liquid went through a glass transition, marked by the change in the slope of the volume versus temperature data. The glass has an average thermal expansion coefficient of 3.4699 × 10-4 K-1, slightly less than that in the crystal. Next, we examine the melting process in detail. Snapshots of the structures at the transition temperature of 430 K are shown in Figure 4. Just as the system reaches 430 K, without going through relaxation, both POSS cages and hydrocarbon chains are periodically arranged in space, only slightly displaced from their average lattice sites due to thermal motion (Figure 4a). While pure n-hexane melts at 178 K,50 the hexyl chains in this hybrid structure are prevented from leaving lattice sites by being connected to POSS cages. Then, as time goes on, the structure undergoes a sequence of transitions. According to our simulations, melting is initiated by hydrocarbon chains departing from lattice positions into random directions and becoming entangled with the hydrocarbon chains of neighboring molecules. This stage is apparent after 500 ps, as shown in Figure 4b. The entropy gain associated with the polymer entanglement gradually
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Figure 4. Snapshots of the structures at 430 K, equilibrated for (a) 0, (b) 500, (c) 800, (d) 1000, (e) 1200, and (f) 1500 ps.
overcomes the POSS-POSS interactions. After 800 ps, POSS cages have noticeably rotated about their lattice positions (Figure 4c), and after 1 ns, noticeable translational disorder has arisen within the POSS sublattice (Figure 4d). By 1.2 ns of simulation time, POSS cages originating from different bilayers begin to mix (Figure 4e) and evolve toward an entirely amorphous structure containing small domains of POSS and hydrocarbon,
such as is shown for 1.5 ns in Figure 4f. This sequence of configurational changes coincides with the sharp increase in the V-T curve in Figure 3a. We can also observe the different stages of the melting process through various quantitative measures of structural analysis. Figure 5a shows the cage-cage pair correlation function, calculated based on the coordinates of the cage centers.
MD Simulations of Monofunctionalized POSS
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Figure 6. Ratio of the diffusion coefficient of the end carbon to that of silicon and the ratio of the instantaneous mean squared displacement of the end carbon to that of silicon at 80 ps, as a function of temperature.
Figure 5. (a) Cage-center distribution; (b) torsion angle distribution; (c) distribution of spacing between one silicon atom, Si(C), which is bonded to carbon and the end of the C6 chain.
Curves at different temperatures are shifted along the y-axis for clarity. Upon heating, the structural correlations between 10 and 16 Å gradually attenuate and then abruptly vanish upon melting. In the melt, only the first nearest-neighbor peak, which decreases in intensity to about 60% of its room-temperature value and shifts from 7.75 to 8 Å by 450 K, as well as a feature just below 16 Å prevails. This reveals strongly preferred spacing in the arrangement of POSS cages. During heating, the flexibility of the hydrocarbon chain increases, as is evident from the torsion angle distribution. At 291 K, a small portion of the hexyl chain segments visit the cis configuration, as reflected by the small peak at 60°. This peak grows continuously as temperature increases below the melting point but jumps up abruptly when the structure melts. The end-to-end distance of the hexyl chain is defined as the distance between the silicon atom to which the hexyl chain is attached and which we will refer to as the “neck” and the carbon at the other end of the chain, which we
will refer to as the “tail.” The distribution of the neck-to-tail distances shows a sharp peak around 7.72 Å at 291 K; this peak moves to a shorter distance and broadens upon heating. Accordingly, the chain becomes increasingly more flexible, even while still constrained within the POSS lattice. Mean squared displacements of different elements were calculated to assess their mobility at different temperatures. To quantify the difference in mobility between the organic and inorganic segments of the structure, we compare the displacement of silicon atoms to that of the carbon atom located at the free end of the hydrocarbon chain. In Figure 6, we plot the ratio of the instantaneous mean squared displacement at 80 ps, 〈r2C(6)〉/〈r2Si〉80ps, versus temperature. Below the melting temperature of 430 K, this quantity represents the ratio of squared vibrational displacements from equilibrium positions, as does the Debye-Waller factor, and is consistently larger than 2. At 291 K, 〈r2C(6)〉/〈r2Si〉80ps is about 2.4 in the crystal, and as the temperature rises, this ratio increases to above 3.2, indicating that thermal activation accelerates the displacement of hydrocarbons more than that of the POSS cages. This behavior can be explained as a remnant tendency of the hydrocarbons to melt before crystalline order is abandoned within the sublattice formed by the POSS cages. After the melting temperature of 430 K is surpassed, 〈r2C(6)〉/〈r2Si〉80ps abruptly drops below 2 and appears to be converging toward 1 with increasing temperature. The melting of the crystal allows for the POSS cages to catch up with the motion of hydrocarbon chains, that is, at high temperatures, both components of the hybrid molecule migrate as a coupled entity. Above the melting temperature, the ratio of diffusion coefficients DC(6)/DSi, derived from the slope of the mean squared displacement function, closely tracks 〈r2C(6)〉/ 〈r2Si〉80ps. Hence, Figure 6 illustrates how the hydrocarbons tend to escape from the crystalline order at temperatures below the melting point of the hybrid material but are prevented from doing so by being bonded to POSS cages that prevail in the crystalline state. To better identify the local structural rearrangements and certain inherent packing preferences of hexyl-functionalized POSS upon melting and subsequent cooling to the glassy state, we present a series of refined spatial correlation functions in Figure 7. In addition to the “neck” and “tail” atoms, defined
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Figure 7. Marker atom distribution: (a) head-head correlation distribution; (b) tail-tail correlation distribution; (c) head-tail correlation distribution; (d) neck-tail correlation distribution.
above, we refer to the silicon atom diagonally opposed to the neck atom as the “head” atom. The pair correlation functions in Figure 7 are shifted for clarity; the position of the baseline on the vertical axis is commensurate to the temperature of the system. As can be seen from Figure 7a, the head-head distribution exhibits sharp peaks before melting. Once the structure is melted, the peaks are broadened, their intensity is reduced, but the onset of the first peak remains unchanged. The persistence of this well-defined distance between heads into the molten state indicates a strong affinity between POSS cages. The long-range features completely disappear in the melt. Both short- and longrange features reemerge in the glassy state with smaller magnitudes, implying a partial recovery of the preferred arrangement in the glass. As for tail-tail distributions, instead of showing a definite transition between the crystal and melt, the peaks shift and decrease in intensity continuously. The main reason of this continuity is that the hexyl chain attains liquid-
like disorder before the melting point. The first peak is around 6 Å in the crystal at 291 K and moves to a shorter distance as the temperature rises. It reaches 4 Å in the melt. The close spacing between the ends of the hexyl chains is preserved in the glass and is rather well-defined, as indicated by the strong peak. In the crystal, the antiparallel alignment of hydrocarbon chains imposes the large tail-tail spacing. Once melting destroys this order and the hydrocarbon chains can coil up, closer tailtail spacings can be achieved. With the onset of the first peak located around 6.5 Å, the head-tail spacing is much larger than the head-head or tail-tail spacings in the crystal, as can be seen from Figure 7c. This reflects the preferred interactions between like species. Upon heating, a shoulder arises at about 430 K and increases in intensity with the increasing temperature as the favored POSS-POSS and hydrocarbon-hydrocarbon pairings are disrupted by thermal fluctuations. The layered structure of alternating POSS cages and hydrocarbons yields a more homogeneous distribution of these species. The neck-
MD Simulations of Monofunctionalized POSS tail correlations in the crystal gradually disappear as the temperature rises and POSS cages begin to rotate. The corresponding peaks in the pair correlation functions disappear upon melting. No particular ordering between necks and tails is evident in the glass. Figure 5a also shows the cage-cage and torsion angle distributions in the glassy state. The unfavorable cis configuration and disordered cage arrangements characteristic of the melts are largely preserved in the glass, and long-range features are partially recovered upon eliminating thermal disorder. 4. Conclusion A force field is tailored to simulate hydrocarbon/POSS systems. The force field is applied to a monofunctionalized hexyl-POSS crystal and yields good agreement with experiment results in terms of structure and vibrational properties. The melting and glass transition processes of the system have been investigated. The system shows a well-defined melting point according to T-V curve. However, qualitative and quantitative structural analysis reveals partial melting of the hydrocarbon domain prior to the disintegration of the lattice formed by POSS cages upon heating. Electrostatic POSS-POSS interactions are markedly attractive and are responsible for sustained close association and clustering of POSS cages in the molten state. This clustering is accentuated when the system goes through the glass transition upon cooling. Acknowledgment. This research was supported by a grant from the National Science Foundation NIRT-0103399. We would like to thank Drs. Siepmann and To¨rnroos for very helpful communications. We would also like to thank Feng Qi for his assistance with the force field parametrization. References and Notes (1) Lichtenhan, J. D.; Schwab, J. J.; Reinerth, W. A. Chem. InnoVation 2001, 31, 3. (2) Sanchez, C.; Soler-Illia, G.; Ribot, F.; Lalot, T.; Mayer, C. R.; Cabuil, V. Chem. Mater. 2001, 13, 3061. (3) Sellinger, A.; Laine, R. M. Macromolecules 1996, 29, 2327. (4) Morrison, J. J.; Love, C. J.; Manson, B. W.; Shannon, I. J.; Morris, R. E. J. Mater. Chem. 2002, 12, 3208. (5) Lichtenhan, J. D.; Otonari, Y. A.; Carr, M. J. Macromolecules 1995, 28, 8435. (6) Haddad, T. S.; Lichtenhan, J. D. Macromolecules 1996, 29, 7302. (7) Lichtenhan, J. D. Comments Inorg. Chem. 1995, 17, 115. (8) Schwab, J. J.; Lichtenhan, J. D. Appl. Organomet. Chem. 1998, 12, 707. (9) Laine, R. M.; Zhang, C. X.; Sellinger, A.; Viculis, L. Appl. Organomet. Chem. 1998, 12, 715. (10) Li, G. Z.; Wang, L. C.; Ni, H. L.; Pittman, C. U. J. Inorg. Organomet. Polym. 2001, 11, 123. (11) Xu, H. Y.; Kuo, S. W.; Lee, J. S.; Chang, F. C. Macromolecules 2002, 35, 8788. (12) Fu, B. X.; Namani, M.; Lee, A. Polymer 2003, 44, 7739.
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