Pik-Yin Lai

Structure and dynamics of grafted polymer layers: A Monte Carlo simulation

The bond fluctuation model of polymer chains on lattices is used to study layers of polymers anchored with one end at a hard wall, assuming good solvent conditions and repulsive interactions between the monomers and the wall. Chain lengths from N=10 to N=80 and grafting densities σ from 0.025 to 0.20 are considered, both for the ‘‘quenched’’ case, where the anchor points are kept fixed at randomly chosen surface sites, and the ‘‘annealed’’ case, where lateral diffusion of the anchored ends at the wall is considered. Profiles of monomer density and free end density, chain linear dimensions parallel and perpendicular to the wall, as well as corresponding mean square displacements of inner and end monomers are studied and discussed in the light of current theoretical predictions, and it is shown that most of these properties can be understood in terms of appropriate scaling concepts. Both the relaxation of the total chain configurations and the time dependence of monomer mean square displacements are studied...

Structure and dynamics of polymer brushes near the Θ point: A Monte Carlo simulation

Grafted polymer layers under variable solvent conditions are studied by Monte Carlo simulations using the bond fluctuation model. Structural information such as monomer density profiles, brush thickness, mean‐square displacement of monomers, and positions of the monomers along the chain are obtained for temperatures above, at, and below the Θ point. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. At the Θ point, more extensive simulations are performed to investigate the structural and dynamical properties. While the brush thickness at the Θ point agrees very well with the scaling and self‐consistent field predictions, the latter deviate from our results for the monomer density profile and the distribution function of the free chain ends. It is not clear whether these deviations result from our chains being too short or from a basic inadequacy of the theory. For the dynamics at the Θ point, both the relaxation of the chain configurations and the mean‐sq...

Grafted polymer layers under shear: A Monte Carlo simulation

Endgrafted polymers at surfaces exposed to a shear flow are modeled by a nonequilibrium Monte Carlo method where the jump rate of effective monomers to neighboring lattice sites against the flow direction is smaller than in the flow direction, assuming that this difference in jump rates is proportional to the local velocity of the flowing fluid. In the dilute case of isolated chains, the velocity profile is assumed linearly increasing with the distance from the surface, while for the case of polymer brushes the screening of the velocity field is calculated using a parabolic density profile for the brush whose height is determined self‐consistently. Linear dimensions of isolated chains are obtained over a wide range of shear rates γ, and the deformation of the coil structure by the shear is studied in detail. For brushes it is found that the density profile and the distribution for the perpendicular coordinate zN of the free ends differ only little from the shear‐free case, while the distribution of the f...

BINARY MIXTURE OF GRAFTED POLYMER-CHAINS - A MONTE-CARLO SIMULATION

Grafted polymer layer composed of a binary mixture of incompatible chains under good solvent condition is simulated using the bond‐fluctuation model. The equilibrium structures of the partially phase separated states are investigated as a function of the incompatibility and relative fraction by monitoring the monomer distribution functions and the chain linear dimensions. For the case of symmetric binary mixtures, we observe the chains of the same type cluster together laterally forming the ‘‘ripple state’’ while the layer state is never observed. For asymmetric mixtures, layer structures with the minority chains staying further away from the grafting plane are observed which is in contrary to previous theoretical predictions. The heights of both the minority and majority chains in the layer state are shown to be proportional to their chain lengths.

Statics and dynamics of adsorbed polymer chains: A Monte Carlo simulation

Monodispersed polymer chains under good solvent condition adsorbed on a short‐range attractive impenetrable wall (xy‐plane) is investigated by dynamic Monte Carlo simulation using the bond‐fluctuation model. Chain conformation, segment orientation, fraction of segment adsorbed, surface coverage, chain dimensions and volume fraction profiles are measured for systems with a different number of chains over a wide range of temperatures. An adsorbed layer begins to form at the same adsorption transition temperature Ta of a single chain. However, the second‐order phase transition at Ta in the single chain adsorption is suppressed in the multi‐chain system as is indicated in the disappearance of the peak at Ta in the specific heat. Volume fraction profiles near the adsorption regimes are found to be in agreement with previous theoretical results. For the dynamics, the time auto‐correlation function, relaxation time, and mean square displacements are measured. The auto‐correlation function can be described by a s...

Polymer turbulent drag reduction near the theta point

Turbulent drag reduction efficiencies (%DR) of aqueous poly (ethylene oxide) solutions at various distances τ≡(Tθ−T)/Tθ away from the theta temperature (Tθ) are studied. It is found that only the long-time behavior of %DR of the system is sensitive to τ in that %DR decays faster for systems closer to the theta-point. Usually, this faster decay is attributed to the faster mechanical molecular degradation (MMD) of polymers in bad solvents produced by turbulence. However, temperature quenches experiments close to Tθ show that the apparent faster decrease in %DR for polymers closer to Tθ is not due to MMD but rather because of the shrinking of the polymer after they have been injected into the turbulent flow. The relative insensitivity of the initial maximum %DR can be understood if Tθ is considered as a function of the flow.

Grafted polymer layers with chain exchange: A Monte Carlo simulation

By introducing a head‐group energy of adsorption with the grafting surface, we simulate the grafted polymer layer including chain exchange with the bulk solution using the bond‐fluctuation model. The kinetics of adsorption is relatively rapid in short times and becomes much slower in later time as the layer is formed. The self‐adjusted surface coverage is measured for different values of chain lengths and head‐group energies. We also found that the polymer chains in a grafted layer are replaced by introducing shorter chains of identical head groups, which is also observed in recent experiments.

Monte Carlo simulations of chain dynamics in polymer brushes

The bond-fluctuation model of polymer chains has been used to study layers of end-grafted polymers anchoring at repulsive walls for a broad range of chain length, grafting densities and solvent quality. The dynamics of monomers and associated relaxation times are investigated and interpreted by phenomenological theories and scaling arguments. The case is also considered where a chain is cut off from its anchor point and the chain is subsequently expelled from the brush. Both the velocity with which the chain leaves the brush and the associated conformational changes (chain contraction etc.) are analysed and interpreted in terms of recent theoretical concepts.

KINETICS AND STRUCTURE OF IRREVERSIBLY ADSORBED POLYMER LAYERS

The kinetics of formation and the structure of an adsorbed layer formed by homopolymer chains irreversibly adsorbed onto a flat wall are studied by Monto Carlo simulation using the bond fluctuation model. The rapid initial adsorption is followed by slow kinetics at later times. The surface coverage can be described by an empirical law of stretched exponential approach to the final value. The formation time constant τ can be interpreted by scaling theories of diffusion inside a dense pseudo‐brush. The detailed structure of the layer in a good solvent saturated by the adsorbed chains is also measured. The extension of the layer and the distributions of the loops and tails are also analyzed in light of recent scaling theories.

Nonlinear Dynamic Compensation of Sensors Using Inverse-Model-Based Neural Network

Many sensors (such as low-cost sensors), in essence, display strongly nonlinear dynamic behavior that cannot be calibrated by well-developed linear dynamic compensation methods. So far, no general nonlinear dynamic compensation (NLDC) method exists, although there are some approaches based on nonlinear models (including Volterra series expansion, Wiener kernels, the Hammerstein model, and finite impulse response) that were developed to compensate some special kinds of nonlinear sensors. In this paper, we suggest a general framework for NLDC, in which removal of the influence of disturbance by using an auxiliary sensor is significantly studied and presented. The inverse model and differential-estimation-filter arrays are embedded in this general framework, where a neural network is applied to approximate the inverse mapping, and differential-filter arrays are used to estimate signal differentials up to a certain order. We also discuss the existence conditions of the general framework. The detailed design procedure of this general method is given as well. Simulation and experiments are presented to illustrate the proposed general NLDC method.