J. Phys. Chem. B 2006, 110, 14557-14563
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Modified Chemistry of Siloxanes under Tensile Stress: Interaction with Environment Elizabeth M. Lupton,† Frank Achenbach,‡ Johann Weis,§ Christoph Bra1 uchle,† and Irmgard Frank*,† Department of Chemistry and Biochemistry, and Center for Nanoscience, Ludwig Maximilians UniVersity Munich, Butenandtstr. 5-13, Haus E, 81377 Munich, Germany,Wacker Chemie AG, Werk Burghausen, 84480 Burghausen, Germany, Consortium fu¨r elektrochemische Industrie GmbH, Zielstattstr. 20, 81379 Munich, Germany ReceiVed: February 2, 2006; In Final Form: June 13, 2006
We present first principles molecular dynamics simulations of stretched siloxane oligomers in an environment representative of that present in single molecule atomic force microscopy experiments. We determine that the solvent used (hexamethyldisiloxane) does not influence the stretching of the siloxane in the high force regime or the rupture process, but trace amounts of water can induce rupture before the maximum siloxane extension has been attained. This would result in a significantly lower rupture force. The simulations show that the rupture of a covalent bond through a reaction with a molecule from the environment, which would not normally occur between the species when the polymer is not stressed, is possible, opening a route to mechanically induced chemical reactions. The attack of the normally hydrophobic siloxane by water when it is stretched has wider implications for the material failure under tensile stress, where trace amounts of water could induce tearing of the material.
I. Introduction The unique physical and chemical stability of siloxane elastomers has found application in sealants and adhesives in industries ranging from aerospace to biomedical1. To improve their material performance, single molecule atomic force microscopy (AFM) experiments can be used in conjunction with first principles molecular dynamics simulations to characterize the microscopic basis of material failure. The high force regime where chemical bond rupture occurs is relevant to understanding the mechanism for permanent stress induced deformation in materials, where irreversible chemical modifications occur. To simulate this part of the experiment, a description of the evolution of the electronic structure is essential to properly describe possible chemical reactions. Factors such as temperature, influence of polymer length and pulling rate, solvent, and substrate attachments need to be considered in the interpretation. In this paper we concentrate on how the behavior of a single siloxane oligomer under stress could be modified by the presence of solvent. Single molecule AFM experiments are usually carried out in solvent to avoid capillary forces2, but the stretched molecule could have a modified chemistry whereby bonds are weakened and less sterically crowded, which could lead to unexpected interactions with solvent molecules. The advent of single molecule AFM2-5 has enabled the strength of individual covalent bonds to be probed.6 The stretching and rupture processes have been investigated theoretically to gain insight into the details of the molecular response, concentrating on possible experimental scenarios7-17. In particular, first principles molecular dynamics simulations have previously been used to characterize solvation principally for systems of biological interest in an aqueous environment. * Corresponding author. E-mail:
[email protected]. † Ludwig Maximilians University Munich. ‡ Wacker Chemie AG. § Consortium fu ¨ r elektrochemische Industrie GmbH.
Hydrogen bonding between species and between water molecules within the solvation shells have been investigated. Simulations have also been applied to the interaction of a strained polyethylene glycol (PEG) molecule in its aqueous environment.18 Here, attack of the elongated C-O bond by a water molecule leads to the formation of two alcohol molecules which is only observed when the PEG molecule is stretched. The use of simulations to identify possible chemical reactions in the experimental system is important in clarifying the observed molecular rupture in single molecule AFM. In single molecule AFM experiments, a polydimethylsiloxane (PDMS) elastomer is stretched between a silica substrate and silica AFM tip until one of the bonds in the PDMS chain or at the surface attachment is ruptured yielding a rupture force (Figure 1). The experiments are carried out in a hexamethyldisiloxane (HMDS) solvent as interactions between the two species are known to be negligible. However, as the PDMS chain is stretched, there is less steric crowding of the Si-OSi linkage by the methyl groups and polarization of the Si-O bond which could increase the reactivity of the chemically inert PDMS. Siloxanes are known to be hydrophobic, but could be more susceptible to attack by water when placed under tensile stress. Therefore both the HMDS solvent and trace amounts of water could react with PDMS in its stretched state and cause rupture before the maximum sustainable tensile force has been attained. In this study, we have carried out Car-Parrinello Molecular Dynamics (CPMD) simulations whereby an electronic structure calculation (DFT) is performed for each step of a molecular dynamics trajectory.19 We apply a tensile force to a siloxane oligomer (hexamer with six silicon atoms in the backbone) by fixing the position of one terminal silicon atom and moving the opposite terminal silicon atom along the molecular axis so as to cause stretching of the molecule. We simulate the presence of solvent molecules by adding hexamethyldisiloxane (HMDS)
10.1021/jp0607059 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/13/2006
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Figure 1. A schematic diagram of the experimental system. The sketch shows the PDMS molecule surrounded by HMDS solvent molecules. The arrows indicate the stretching of the PDMS molecule in an AFM experiment.
molecules at a concentration equivalent to the room temperature density. First principles molecular dynamics simulations are then carried out on a prestretched siloxane molecule surrounded by water molecules to assertain the mechanism by which the species interact. This interaction is then investigated systematically by carrying out static semiempirical calculations to pinpoint at which extension water could react with the siloxane chain. We finally simulate the full system, namely the PDMS oligomer in HMDS solvent, with trace amounts of water. II. Method We perform Car-Parrinello Molecular Dynamics simulations (CPMD)19,20 where the electronic structure of the system is described using density functional theory (DFT).21,22 The BLYP functional23,24 is used for the electron exchange and correlation potential. The core electrons are described using the TroullierMartins pseudopotentials,25 and the Kohn-Sham orbitals are expanded using a plane wave basis set with a cutoff of 70 Ryd. In a previous study on isolated siloxanes31 we did not observe radical formation after rupture in any of the simulations and so the spin restricted Kohn-Sham formalism is used. The electronic structure calculations are performed on the fly during a molecular dynamics simulation with a time step of 0.1 fs and carried out over a period of up to 2 ps. We stretch the oligomer in the simulations of the hexamer in HMDS by keeping one terminal silicon atom of the hexamer fixed and moving the other by a predefined displacement for each time step to cause stretching with a constant velocity of 55 m/s. The Car-Parrinello approach has previously successfully been applied by many groups to the investigation of molecules in solvent (see, for example, refs 26-28), and also to the study of molecule rupture (see, for example, refs 11,15,17). Appropriate systems are constructed in periodically repeating supercells. To examine the stretching of a siloxane oligomer in solvent, we place a siloxane hexamer in a supercell (17.5 Å × 24.0 Å × 9.0 Å) surrounded by six hexamethyldisiloxane (HMDS) molecules at a concentration equivalent to a density of 0.77 g/cm3. To make the calculations tractable, the hexamer is already extended with an average Si-O bond length of 1.8 Å, which compares to 1.7 Å of the unstretched hexamer. The HMDS molecules are placed around the hexamer and the system equilibrated for 0.6 ps at 300 K. After an equilibration phase
Lupton et al. of 0.6 ps in which no attraction or interaction between the siloxane hexamer and the solvent HMDS molecules was observed, one of the terminal silicon atoms of the hexamer is displaced at a constant velocity of 55 m/s along the molecular axis so as to cause stretching of the molecule. The molecule was stretched for 1.5 ps until one of the central Si-O bonds of the hexamer ruptured. The simulation was run for a further 0.4 ps after rupture to see if there was any interaction between the fragments and the solvent molecules. To investigate the interaction between PDMS and water, we performed an initial study using semiempirical PM3 calculations from the Gaussian29 package. The PM3 Hamiltonian has previously been used to study the mechanically induced rupture of siloxanes.30 For the siloxane hexamer and decamer (six and 10 silicon atoms in the backbone, respectively), the geometry was initially optimized and then the separation between the terminal silicon atoms was increased in steps of 0.1 Å to obtain a series of optimized geometries. A water molecule was then placed above one of the central silicon atoms of the optimized siloxanes with an O (water)-Si (siloxane) separation of 2.0 Å and a geometry optimization was performed with only the siloxane extension fixed. Although the PM3 calculations do not give information about the dynamics of the rupture process, this allows us to determine qualitatively whether rupture could be induced by water molecules before the maximum extension had been reached. From the PM3 calculations we can determine a starting point for the corresponding CPMD simulations. These simulations with a temperature set at 300 K were then performed of the interaction between the siloxane hexamer and water to understand the mechanism of the rupture process. We are only interested in whether water can induce rupture in a stretched siloxane molecule, and not in the behavior of siloxanes in a water environment. Therefore, the siloxane molecule is not stretched in bulk water, but the starting system surrounds the siloxane molecule with single water molecules to determine whether there is any attraction between the species. A stretched siloxane hexamer (average Si-O: 1.8 Å) was placed in a supercell of dimensions (25.4 Å × 6.9 Å × 5.8 Å) and surrounded by water molecules, the closest Si (siloxane)-O (water) distance was 2.3 Å at the start of the simulation. The hexamer was not stretched further in the simulation. The positions of the hexamer terminal silicon atoms were kept fixed at a constant distance apart. Four simulations at 300 K were completed with 4, 6, 8, and 10 water molecules surrounding the siloxane hexamer. All four systems were equilibrated for 200 fs before a simulation lasting 300 fs. Finally we performed a CPMD simulation of the siloxane hexamer in HMDS solvent with an additional two water molecules. We used the same supercell as for the simulation of siloxane in HMDS described above with the water molecules placed next to the siloxane chain with a distance of at least 2.7 Å between the oxygen atom of the water molecules and the siloxane backbone in the starting geometry. We equilibrated the system for 0.2 ps at 300 K then performed a simulation for 0.4 ps without further stretching the siloxane hexamer. We then performed a simulation where the water molecules were fixed next to the siloxane during the equilibration for 0.2 ps before a simulation for 0.05 ps. III. Rupture of a Siloxane Hexamer in HMDS As an isolated siloxane molecule is stretched, the Si-O bonds in the backbone become polarized until a random bond in the middle of the chain ruptures ionically and the charged fragments recede to the coiled equilibrium geometry apart from shorter
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Figure 2. Simulation of the siloxane hexamer in HMDS. The arrows indicate the stretching of the hexamer in the simulation. (i) The starting geometry. (ii) The geometry after rupture of a Si-O bond in the siloxane hexamer. (Si: turquoise, O: blue, C: red, H: gray).
Figure 3. Energy/extension curve for (i) the isolated siloxane hexamer and (ii) the siloxane hexamer surrounded by six HMDS molecules, both pulled at 55 m/s at 300 K. The oscillation of the energy curve of the siloxane in solvent is is due to the contribution from the movement of the HMDS molecules to the total energy. However, the curves have the same form and demonstrate that the hexamer is ruptured at the same extension in solvent as without solvent.
oligomers where proton transfer between fragments occurs to neutralize the products.31 To understand how the stretching and rupture of a siloxane oligomer could be restricted or promoted by the presence of solvent, we investigate the stretched siloxane hexamer surrounded by six solvent HMDS molecules as described in section II. As the hexamer is stretched, the Si-O backbone becomes exposed thus making it more susceptible to chemical attack. However, during the simulations, in the equilibration phase, and during stretching and rupture, no attractive interaction is observed between the species on the
time scale of the simulation. Figure 2 shows two snapshots from the simulation before and after rupture. At the density investigated, there is no enforced close approach of the species. Even after the rupture of the hexamer, there is no strong attraction between the siloxane hexamer and the HMDS molecules. A comparison of the energy/extension curves of the isolated siloxane hexamer and the hexamer in solvent shows that the solvent does not have any influence on the form of the curve or the rupture extension (Figure 3). The overlap of the curves indicates that the increase of bond angles and lengths in the
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Lupton et al. TABLE 1: The Total Extensions (distance between the terminal silicon atoms) and Average Bond Lengths for the Siloxane Hexamer and Decamer for Different Rupture Scenarios Obtained with Static Semi-empirical Calculations.a rupture without water
hexamer decamer
rupture extension (Å)
Si-O (Å)
18.80 (≡100%) 33.40 (≡100%)
1.89 (≡100%) 1.88 (≡100%)
rupture with water rupture extension (Å)
Si-O (Å)
17.10 (91%)
1.80 (95%)
30.4 (91%)
1.79 (95%)
a The percentages of the water-induced rupture extension and bond lengths compared to the normal rupture are shown in brackets. The calculated equilibrium bond lengths are 1.67 Å for both the hexamer and decamer.
Figure 4. Semiempirical PM3 calculations of the interaction between water and PDMS oligomers under stress. (a) The PDMS hexamer. (b) The PDMS decamer. (i) Ground-state geometry. (ii) Just before rupture next to water molecule. (iii) After rupture by the water molecule. (Si: turquoise, O: blue, C: red, H: gray).
high force regime is in no way restricted by the presence of solvent. At this density the solvent molecules can easily rotate and translate and do not crowd the hexamer. There was no indication that solvent mediated rupture would occur in the system. Although the crowding of the Si-O backbone by the methyl groups is reduced as the hexamer is stretched, the methyl groups of HMDS inhibit the close approach of the solvent molecules. Rupture occurs when the distance between the terminal silicon atoms is 17.5 Å for both the isolated hexamer and hexamer in solvent which would result in the same rupture force of 4.4 nN. It should be noted that this value corresponds to an upper bound of the rupture force as the pulling velocity is greater than that applied in the experiments (∼ 10-6 m/s).31 The weak interactions between species in the system allow stretching and recoil of the short chain PDMS hexamer to occur without being inhibited by the solvent molecules. The rupture process itself is, therefore, not influenced by the presence of solvent. IV. Interaction of the Siloxane Hexamer with Water We performed static semiempirical PM3 calculations as described in section II. No attractive interaction was observed between the water molecule and the siloxane hexamer and decamer in their ground-state relaxed geometries. On increasing the siloxane extension, a reaction was observed whereby the siloxane chain is broken, the water -OH group going to the siloxane Si+, and the water H+ going to the siloxane O- (Figure 4). Table 1 shows the siloxane extensions at which rupture occurs for different chain lengths indicating essentially barrierless rupture. Water does not induce rupture at the equilibrium
Figure 5. Snapshots from a CPMD simulation of eight water molecules surrounding a stretched siloxane molecule. (i) The system after equilibration. (ii) The circle indicates the alignment of the water molecule with a Si-O bond in the siloxane backbone. (iii) The water molecule attacks and ruptures the siloxane backbone after 250 fs of simulation.
geometries but does react causing rupture before the maximum extension has been obtained (9% less than the maximum extension for the hexamer and decamer). This would indicate a lower rupture force as rupture occurs before the maximum gradient (corresponding to the force) has been obtained on the energy/extension curve. A threshold average Si-O bond length can also be estimated for attack by water (Table 1). For the siloxane hexamer this bond length is shown to be 5% less than the average bond length of 1.9 Å for rupture of a siloxane in the absence of water. The same value applies to the siloxane decamer but the average bond length both for the water induced rupture and the normal rupture are 0.01 Å less than that of the siloxane hexamer. This trend corresponds with the expectation that longer chain oligomers rupture more readily.17,31 Using the information obtained from the PM3 calculations, CPMD simulations were then carried out to examine the dynamics of water-induced bond rupture. As described in section II, different numbers of water molecules were spaced around the pre-stretched siloxane molecule. For the systems containing six and eight water molecules, no interaction was observed in the 300 fs of simulation after equilibration. The water molecules do not closely approach the siloxane and no interactions between species is observed. However, in the systems containing four and 10 water molecules rupture of the siloxane hexamer occurred after 80 and 250 fs, respectively. In both cases the water oxygen first approaches a silicon atom in the siloxane
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Figure 6. The changing bond lengths over the period of the simulation showing the rupture process for the simulation of a siloxane hexamer surrounded by four water molecules. (i) Siloxane Si-O water. (ii) Siloxane Si-O siloxane. (iii) H water-OH water. (iv) H water-O siloxane.
backbone, then the water O-H bond aligns with a siloxane Si-O bond, the water -OH group bonds to the hexamer Si+ and the water H+ saturates the siloxane O- in a concerted reaction in which the siloxane oligomer is ruptured. Snapshots from the simulation with eight molecules are shown in Figure 5 where the interaction between the stretched Si-O bond and the water molecule can be seen, resulting in rupture of the siloxane backbone. As can be seen in the snapshots, the approach of the water molecule to the backbone is not hindered by the methyl groups when the siloxane hexamer is stretched. For the reaction to occur, it is important that the alignment of the two participating bonds in the siloxane and the water molecule takes place. In cases where this alignment is hindered by hydrogen bonding between water molecules preventing an attractive interaction between a water molecule and the siloxane backbone, no reaction takes place in our simulations and the water molecule retreats from the siloxane chain. The relevant bond lengths for the simulation of a siloxane hexamer surrounded by four water molecules are shown in Figure 6. Here it can be seen that the siloxane Si-O water distance and siloxane O-H water distance decrease after 60 fs and the siloxane Si O siloxane distance and water H-OH water distance increase after 80 fs indicating the completion of the reaction. The distance between the terminal silicon atoms of the hexamer in all four simulations is 16.2 Å, which is 8% less than the distance at which the isolated siloxane molecule ruptures (17.6 Å) when stretched. This extension would correspond to a rupture force of 3.6 nN if calculated from the gradient of the energy/extension curve of the isolated siloxane hexamer. This is 18% less that the rupture force of 4.4 nN reported for the rupture of the isolated hexamer.31 Again, the estimated value (3.6 nN) represents an upper bound for the rupture force, as at longer time scales more reactive conformations can be tested by the system because entropy plays a major role in this type of reaction. The CPMD simulations, therefore, demonstrate that a lower measured rupture force would be obtained if water is present to enable an alternative rupture mechanism, indicating the importance of keeping the solvent dry to experimentally characterize siloxane rupture.
V. Simulation of Siloxane Hexamer in HMDS Solvent with Water Molecules Finally we have performed CPMD simulations of the complete system in order to determine what could happen in the system of the siloxane hexamer surrounded by HMDS solvent if trace amounts of water are added. We simulated the system as described in section II for the siloxane hexamer in HMDS solvent with the addition of two water molecules for 0.4 ps, in which time no close approach, attractive interaction between species, or water induced rupture of the backbone was observed (Figure 7). In a second simulation, with the oxygen atoms of the water molecules kept fixed during the equilibration phase, we observed water induced rupture of the siloxane backbone after 0.02 ps (Figure 8). This demonstrates that, although during the timespan of the simulations the water molecules are unlikely to diffuse through the solvent to closely approach the siloxane backbone and become aligned before inducing rupture, if they are positioned in the vicinity of the stretched Si-O bonds, rupture could occur. If, however, experimental pulling rates are considered, many more conformations of the system can be tested, rendering the rupture of the PDMS backbone by hydrolysis more likely. VI. Conclusions We have simulated possible interactions between stretched siloxanes and their environment in single molecule AFM experiments to determine whether the solvent or trace amounts of water can influence the rupture process, and we measured rupture force. Using CPMD simulations, we have determined that an interaction between the siloxane polymer and the HMDS solvent molecules is highly unlikely, because there is no attraction between the species, and the methyl groups on both species hinder their close approach. The solvent, therefore, has no influence on the magnitude of the rupture force. However, water molecules can induce rupture of the chain before the polymer has reached its maximum extension resulting in a lower measured rupture force. From the static semiempirical calculations it can be estimated that water can react essentially
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Figure 7. Snapshots from a simulation of the complete system. (i) The initial configuration with the water molecules circled. (ii) The system after 0.4 ps of simulation during which time no reaction between the species was observed.
Figure 8. Snapshots from a simulation of the complete system with the oxygen atoms of the water molecules placed closer to the PDMS backbone. (i) The initial configuration. (ii) The system after 0.02 ps of simulation where hydrolysis has occurred, causing rupture of the siloxane backbone.
barrierless with a stretched siloxane oligomer with an average Si-O bond length at least 7% greater than the equilibrium value (within the PM3 approximation) and 5% less than the maximum possible bond length. The CPMD simulations demonstrate the prerequisites for a concerted reaction and show that the water induced rupture would result in a lower measured rupture force in an AFM experiment. This emphasizes the importance of considering the experimental environment when using computer simulations to interpret the experimentally observed molecule rupture forces. It should be noted that at experimental velocities the rupture forces will be lower, but of the same order of magnitude. A strong influence of the pulling velocity is to be expected for the reaction with water where structural rearrangements play a major role (approach and alignment of water molecule with PDMS backbone). Therefore, we do not determine the absolute value of the experimental rupture force but our simulations demonstrate that the presence of water will significantly lower the rupture force by providing a different rupture path. Also the results show that a chemical reaction has
been induced between two normally unreactive species by the application of tensile force to one of the reactants, demonstrating a mechanically induced chemical reaction.18,32 The reactive characteristics of siloxanes can be mechanically modified through controlling the polarization of the Si-O backbone bonds and their steric protection. The possible attack by water has wider implications for the bulk siloxane elastomer. Although siloxanes are normally hydrophobic in their unstretched state, when the material is under tensile stress, trace amounts of water could induce rupture of the chains resulting in permanent material deformations and ultimately in material failure. The modified chemistry of the stretched polymer, therefore, plays an important role in the behavior of materials under stress and in developing ways to enhance material performance. Acknowledgment. This work was financially supported by Wacker-Chemie AG and Deutsche Forschungsgemeinschaft (SFB 486). Computing time was provided by the Leibniz-
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