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

The adsorption and diffusion of polydimethylsiloxane (PDMS) with different chain lengths on a silicon (111) surface were studied by molecular dynamics simulations. The relative dielectric constant was selected to be 1 to mimic a vacuum. The chains were all present as two dimensional (2D) adsorption conformation on the surface but different conformations and dynamic properties were found in the two absolutely different environments. The relationship between the adsorption energy of the different chain lengths and the degree of polymerization follows a linear function and the average adsorption energy per segment is -0.42 kcal/mol. In addition, the diffusion coefficient (D) of these chains scales with the degree of polymerization (N) as N-3/2.


Introduction
In three dimensions, 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 [1][2]. The diffusion of confined polymers at surface is always a fundamental, yet problematical topic in polymer physics [3][4]. Polymers adsorbed onto a surface to form thin films is an emerging topic of modern materials science [5]. They can be applied, for example, in the fields of biosensors, light-emitting diodes, nonlinear optical devices, and permeation-selective gas membranes [6]. Granick and co-workers studied poly(ethylene glycol) molecules adsorbed on solid surface by means of fluorescence microscopy [7]. 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 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 [8]. In the simulations, Milchev and Binder [9] showed that D scales with the chain length as N -1.1 ; Azuma and Takayama [10] obtained D～N -3/2 ; but Falck et al. [11] found that D should scale as N 0 . However, there was no literature about the adsorption and diffusion of the PDMS single chain on the silicon surface. Fig.2 The mean radius of gyration R g vs the chain length N. The symbols are MD simulation results.
The error bars are the standard deviation measured in three parallel simulations.

Models and Simulations
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) [12] 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

Advanced Materials Research Vols. 391-392
consider the influence of all atoms close-by 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 [13]. 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 [14] with a relaxation time of 0.1 ps.
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.

Simulation Results and Discussion
Configuration of PDMS at Adsorption Equilibration State. Fig. 1 shows the simulation snapshots of the PDMS chains with N=10, 40, 50 and 60 in equilibrium, but the configurations of N=50 and 60 present partial arched part. Furthermore, it shows good adsorption of no matter short or long PDMS single chain on this silicon surface. Interestingly, these configurations present curved, especially the long chains. Furthermore, they all present 2-D adsorption configuration from the side view.
With time evolution, the chain configuration changes from initially isolated "random-coil" in a vacuum to a compact form adsorbed on the surface. In the first several hundred picoseconds, chain adsorption occurs accompanied by diffusion. When the energy dynamically reaches constant, the chain dynamics is mainly dominated by the diffusion process. To show the chain configuration change during the adsorption, we calculate the mean radius of gyration (Rg) which is defined as where r i and rcm denote the position vector of each atom in a chain and the center-of-mass for the whole chain, respectively. Figure 2 shows the change of calculated R g with increasing N. We fit this curve with the first order exponential decay function as R g =A 1 exp(-N/t 1 )+y 0 ，therein y 0 =6.82±0.35, A 1 = -9.62±0.55，t 1 = 18.76±2.90. By seeing the simulation snapshots, we can find that all the PDMS chain are ultimately well-adsorbed on the silicon surface with 2-D configurations. For the sake of characterizing the anisotropic configuration of the polymer and interpreting the configuration change during adsorption, we calculate two ratios such as (R x 2 +R y 2 )/R z 2 and R max /R min . R x , R y and R z are the components in three principal directions of R g . Rmax and Rmin correspond to the large and small magnitude between R x and R y , respectively. The results are shown in Figure 3, panels a and b. Both ratios have the same tendency that the values first increase then keep in slight change with increasing N. One turning point corresponds to N=50. This is consistent with the result of the first appearance of the partial arched part as shown in Figure 1. The component of R g along the Z axis that is perpendicular to the surface is strongly reduced during the adsorption. The components of R g along the X and Y axes display significant increase due to the chain spreading on the surface. All the chains are well adsorbed on the surface and therefore present 2-D configurations. Thus R x and R y are larger and R z is very small.
Diffusion of PDMS Chain on the Surface. After the adsorption process, which is monitored by the interaction energy between the chain and the surface starting to fluctuate only around a constant value, the dynamics of PDMS is mainly dominated by the chain diffusion on the surface. We calculate the diffusion coefficients of the chains via the Einstein relation. Figure 4 shows the change of D with varying degree of polymerization. There is apparent scaling between D and N, that is, D～N -3/2 . The dependence of D on N can be explained by the change of interaction energy between the chain and surface with increasing N. This adsorption energy can be calculated via int ( ) tot frozen plane where E tot is the potential energy of the chain plus the surface system in equilibrium, E frozen is the potential energy of the adsorbed chain isolated in a vacuum with the geometry unchanged, and E plane is the potential energy of the surface. Larger molecular configuration deformation allows for better adsorption of the chain onto the surface; however, this will break the intramolecular interaction which causes a free energy penalty. Therefore such an interaction competition results in all the adsorption energy with increasing N, which can be seen in Figure 5. We fit this curve with the linear function, and the average adsorption energy per segment (E/N) is -0.42 kcal/mol.

Summary
In this paper, MD simulations are used to investigate the adsorption and diffusion behavior of a single flexible PDMS chain on a silicon surface. Because of their similar characteristics between them, the PDMS chain are all adsorbed well onto the surface and possess 2-D configurations. In a vacuum, the PDMS chains are well adsorbed onto the hydrophobic surface and displays 2-D configuration. The calculated results of mean radius of gyration and two ratios such as (R x 2 +R y 2 )/R z 2 and R max /R min manifest the chain length dependence of the adsorption configuration. The adsorption energies are linear scaled with N, therein the average E/N value is -0.42 kcal/mol. In addition, the data of their diffusion coefficient obey scaling law with N -3/2 for the considered chain lengths.