**A Study of the Adsorption and Diffusion Behavior of a Single Polydimethylsiloxane Chain on a Silicon Surface by Molecular Dynamics Simulation**

Dan Mu1 and Jian-Quan Li2

*1College of Chemistry Chemical Engineering and Materials Science, Zaozhuang University, Shandong 2Photoelectric Engineering College, Zaozhuang University, Shandong China* 

#### **1. Introduction**

326 Molecular Dynamics – Theoretical Developments and Applications in Nanotechnology and Energy

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> In three dimensions, polymer dynamics exhibits a rich and complex behavior which depends on the solvent conditions and polymer concentration (1; 2). That the dynamics of polymer chains at and near solid interfaces differs profoundly from that in the bulk is intuitively expected. Polymer adsorption on the surface is of technological and scientific importance in the field of colloids and biomolecules. Examples include the two-dimensional (2-D) diffusion of DNA oligonucleotides confined to biological interfaces such as cell membranes (3; 4). The diffusion of confined polymers at surface is always a fundamental, yet problematical topic in polymer physics (1; 2; 5–8). The behavior of polymers at the liquid-solid interface is crucial to technologies involving molecular surface placement (9; 10). Polymers adsorbed onto a surface to form thin films is an emerging topic of modern materials science (11; 12). They can be applied, for example, in the fields of biosensors, light-emitting diodes, nonlinear optical devices, and permeation-selective gas membranes (13–18). The fabrication of the thin films always takes place in vacuum or dilute solutions. The adsorption of the polymer chains can be controlled by varying multiple parameters such as the polymer-surface interaction, the solvent quality, surface nano-roughness, temperature, polymer chain length and so on. The knowledge about the adsorption dynamics and the thermodynamics of the equilibrium adsorption is crucial to understand and furthermore improve the property of the final product. Experimentally it is difficult to control well the above influences separately, thus, clear information on the exact effect of a specific environmental parameter is hard to obtain. Due to the fast-growing computation power nowadays, it is possible to utilize the computer as an "experimental apparatus" to solve the problem, with the aid of various simulation techniques. It has attracted attention for decades already.

> Granick and co-workers studied poly(ethylene glycol) molecules adsorbed on solid surface by means of fluorescence microscopy (19–22). They found that the diffusion coefficient (*D*) of such chains scales with the degree of polymerization (*N*) as *N*−3/2, which is characteristic for

similar, but the diffusion coefficients vary greatly, showing strong dependence on the solvent

<sup>329</sup> A Study of the Adsorption and Diffusion Behavior of a Single

Polydimethylsiloxane Chain on a Silicon Surface by Molecular Dynamics Simulation

The MD simulation is carried out in a box with 3-D periodic boundary conditions. The PDMS chain is embedded into the simulation box with a fixed (111) silicon surface parallel to the *XY* plane. We choose *N* for the chain as 10, 20, 30, 40, 50 and 60. The thickness of the surface is around 12 Å. The length of the simulation box in the *Z* direction is 80 Å, which is large enough so that the interactions between the adsorbed PDMS chain and the periodic images of silicon in the top plane can be ignored. In this way, the 3-D periodicity inherent in the model is transformed into an actual 2-D periodicity thus simulating an infinitely extended surface. A high-quality force field COMPASS (condensed-phase optimized molecular potentials for atomistic simulation studies) (37; 38) is adopted in the simulation. In contrast to early force fields which were mostly parameterized based on gas-phase data or ab initio calculations, COMPASS combines ab initio and empirical parametrization procedures. In addition, it adds cross terms to potential in order to consider the influence of all atoms close-by and distortions of bond length or bond angle. It enables accurate and simultaneous prediction of structural, conformational, vibrational and thermophysical properties for a broad range of molecules in isolation and in condensed phases. The energy calculation with COMPASS is a combination of bonding and non-bonding terms. The bonding terms include stretching, bending and torsion energy as well as the diagonal and off-diagonal cross coupling terms. The van der Waals interactions are truncated at *rc*=12 Å by using a spline function from 11 Å. The Coulomb interactions are calculated via Ewald summation (39). Before the MD simulations, energy minimizations are performed to relax the local unfavorable structure of the chain. Subsequently, MD simulations with 5 ns are performed under NVT thermodynamics ensemble. Every simulation is performed three times to ensure the reliability of the results. The equations of motion are integrated with a time step of 1 fs. The constant temperature *T*=300 K is controlled through the Berendsen thermostat (40) with a relaxation

In these simulations, the total and potential energies show an initial decrease, possibly with a few separate kinetic stages, and then fluctuate around a constant value, indicating the achievement of the equilibrium state. This process corresponds to the adsorption and diffusion dynamics of the PDMS chain from the initial configuration. We then change the dielectric constant to 78.0 to mimic the good solvent condition. Of course in this way the explicit solvation effects cannot be considered. Nevertheless, we can directly study the effects by simply changing the bad to the good solvent condition on the chain configurations and

In this section, we show the simulation results, such as the chain configurations, the diffusion coefficient and the adsorption energy. All simulations are run until the chain reaches its equilibrium structure, i.e., until the simulated chain lost its memory of the initial configuration, and running the program further results in no discernible changes in the

condition.

time of 0.1 ps.

dynamics.

**3. Simulation results and discussion**

structural properties and energy beyond natural fluctuations.

**2. Models and simulation details**

2-D chain models. On the other hand, Maier and Rädler found much weaker scaling, namely *N*−1, when studying adsorbed DNA in a lipid bilayer (3; 4). In the simulations, Milchev and Binder (23) showed that *D* scales with the chain length as *N*−1.1; Azuma and Takayama (24) obtained *<sup>D</sup>* <sup>∼</sup> *<sup>N</sup>*−3/2; but Falck et al. (25) found that *<sup>D</sup>* should scale as *<sup>N</sup>*0. Therefore, the dynamics behavior of a confined polymer on a surface is still an interesting research topic.

Computer simulations for the mechanism of a single polymer chain adsorbed and diffusing on a surface are important, as experimental studies on an isolated polymer chain are difficult in most cases. Many simulations had been performed for different polymeric systems with multiple chains (or a single chain) adsorbing and diffusing on the surface (24–27).

Binder and coworkers successfully studied polymer films in different conditions via computer simulations (28–31). Lu and Kim observed the surface pattern of a thin polymer film by using a three-dimensional electrostatic model. The competition between the electrostatic energy and the surface energy leads to a characteristic pillar size. Furthermore, the film thickness significantly influences the growth rate and the distance between pillars (32). Recently, Kumar and coworkers found that a non-wetting solvent aids adsorption of the polymer chain at low sticking energies compared to wetting solvent by the aid of molecular dynamics simulations (33). However, there was no literature about the adsorption and diffusion of the PDMS (polydimethylsiloxane) single chain on the silicon surface. In this research, our main objective is to study the adsorption and diffusion processes of a hydrophobic chain on a hydrophobic surface. The similar hydrophobic-hydrophobic systems usually appears in the wetting, surface adhesion and flow in confined geometries are examples of such systems. Because we have completed some research about the poly (vinyl alcohol) adsorbing on the hydroxylated *β*-cristobalite (34), polyethylene chain adsorbing on the hydroxylated *β*-cristobalite (35), and the polyethylene chain adsorbing on the silicon (111) surface (36), then the results of the polydimethylsiloxane adsorbing on the silicon (111) surface may be helpful and enriching for further understanding of the configuration change and the dynamics of the hydrophobic polymer chain adsorbed on a hydrophobic surface.

We consider a single PDMS chain adsorbed on the rigid (111) silicon surface in a vacuum and in mimetic good solvent condition. The adsorption and diffusion processes of the chain are investigated through energy minimizations and molecular dynamics simulations with all the molecular degrees of freedom being taken into account. Only one single chain is adopted in a simulation because it relates directly to 2-D polymer diffusion in very dilute solution. In addition, PDMS is a widely available polymeric material, comes in a range of molecular weights, and is easy to use. The hydrophobic silicon is chosen because of its relative simplicity and rigidity, so it can be treated as a fully rigid body for our purposes. We follow a two-step strategy: first, we carry out direct energy minimizations of the PDMS chain close to the silicon surface with different initial configurations in order to relax the model; second, we use the most stable configuration after minimization to perform MD (Molecular Dynamics) simulation. In the theory of dynamical scaling the two key quantities are the radius of gyration (*Rg*) and the center-of-mass diffusion coefficient *D* of the chain. We thus use them to describe the characteristics for the system in this paper. We also change the effective dielectric constant to 78.0 to mimic good solvent condition. The results are compared with the systems in a vacuum (which can be taken as in bad solvent condition). The chain configurations show similar, but the diffusion coefficients vary greatly, showing strong dependence on the solvent condition.
