Film Growth and Surface Roughness with Effective Fluctuating Covalent Bonds in Evaporating Aqueous Solution of Reactive Hydrophobic and Polar Groups: A Computer Simulation Model

Abstract

Summary:A computer simulation model is proposed to study film growth and surface roughness in aqueous (A) solution of hydrophobic (H) and hydrophilic (P) groups on a simple three dimensional lattice of size L x × L y × L z with an adsorbing substrate. Each group is represented by a particle with appropriate characteristics occupying a unit cube (i.e., eight sites). The Metropolis algorithm is used to move each particle stochastically. The aqueous constituents are allowed to evaporate while the concentration of H and P is constant. Reactions proceed from the substrate and bonded particles can hop within a fluctuating bond length. The film thickness (h) and its interface width (W) are examined for hardcore and interacting particles for a range of temperature (T ). Simulation data show a rapid increase in h and W followed by its non-monotonic growth and decay before reaching steady-state and near equilibrium (h s , W s ) in asymptotic time step limit. The growth can be described by power laws, e.g., h ∝ t γ , W ∝ t β with a typical value of γ ≈ 2, β ≈ 1 in initial time regime followed by γ ≈ 1.5, β ≈ 0.8 at T = 0.5. For hardcore system, the equilibrium film thickness (h s ) and surface roughness (w s ) seem to scale linearly with the temperature, i.e., h s = 6.206 + 0.302T, W s = 1 255 + 0.425T at low T and h s = 6.54 + 0.198T, W s = 1.808 + 0.202T at higher T . For interacting functional groups in contrast, the long time (unsaturated) film thickness and surface roughness, h s and W s decay rapidly followed by a slow increase on raising the temperature.Growth of the average film thickness at a temperature T = 5.

Monte Carlo simulation of a film growth with reactive hydrophobic, polar, and aqueous components by a covalent bond fluctuating model

“…Third, the restriction in bond formation and fluctuation affects the rates of water reaction and water evaporation during the film formation resulting in different patterns of the interface growth in the intermediate time region, which is more pronounced at higher temperatures. 3 The large amount of water retention via the side reaction in this study appears to smooth ͑smear͒ out the interface width just after its first overshoot and leads to a more stable relaxation afterwards. 4 shows that about the same amount of water participates in the steady-state kinetic reaction ͑65%, P A = 0.0273͒ in both EBFM and BFM despite of different bond length constraints.…”

“…The mixture consists of reactive hydrophobic and polar groups in a reactive aqueous solvent which is also allowed to evaporate. In contrast to a nonmonotonic growth for film thickness and interface width ͑with oscillatory response͒ in nonreactive aqueous solvent systems, 3 the interface width has a relatively stable relaxation without oscillation now due to water reaction. Constituents move stochastically via the Metropolis algorithm to explore thermodynamic equilibration while the kinetic reactions are incorporated through flexible covalent bonding from an adsorbing substrate which may arrest the growth before reaching equilibrium.…”

“…We would like to point out that there is an enormous amount of theoretical ͑analytical and scaling͒ work 16,17 on the growth of the interface width and scaling of the roughness on relatively simpler systems ͓e.g., one component ͑monodispersed͒ particle deposition models͔; we are not aware of any such theoretical work that involves such a complex system with multicomponent constituents participating in specific reaction kinetics without conserving the solvent concentration. Lastly, we would like to point out that the nonmonotonic growth of the interface width in this study distinguishes from the oscillatory response of the interface width in a nonreactive aqueous solvent system, 3 where the interface width has two overshoots before it finally relaxes to a saturated value. For example, at the temperature T = 5, Fig.…”

“…Computer simulation studies [1][2][3] have been recently carried out on a discrete lattice to understand the film growth in waterborne two component polyurethane ͑WB 2K-PUR͒ system consisting of a hydrophobic ͑H͒ polyisocyanate crosslinker and a hydrophilic ͑P͒ polyester polyol in aqueous ͑A͒ solution. [4][5][6][7][8][9] Simultaneous progression of such physicochemical processes as water evaporation, cross-linking reaction, phase separation, etc., in WB 2K-PUR film formation [10][11][12][13] makes these studies very complex.…”

“…3 In this paper, we improve EBFM by constraining bonds to form only between nearest neighbor monomers involved in kinetic reaction with bond fluctuations and mobility obeying the excluded volume effects strictly in this bond fluctuation model ͑BFM͒. However, the range for a covalent bond formation and its length fluctuation are too large to fully enforce the excluded volume constraints.…”