scholarly journals Monte Carlo Simulation of Stochastic Adsorption of Diluted Solute Molecules at an Interface

2020 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Monte Carlo ◽  
Analytical Solution ◽  
Observation Time ◽  
Patterned Surfaces ◽  
Fractal Function ◽  
Self Assembled Monolayer ◽  
Power Law Decay ◽  
Sensing Platforms ◽  
Surface Collision ◽  
Measuring Frequency

<div> <p>Here an analytical solution of Fick’s 2<sup>nd</sup> law is used to predict the diffusion and the stochastic adsorption of single diluted solute molecules on flat and patterned surfaces. The equations are then compared to the results of several numerical Monte Carlo simulations using a random walk model. The 1D diffusion simulations clarify that the dependence of the solute-surface collision rate on the observation-time (measurement time resolution) is because of the multiple collisions of the same molecules over different time regions. It also surprisingly suggests that due to the self-mimetic fractal function of diffusion, the equation should be corrected by a factor of two. The absorption rate of solute on an adsorptive surface is found to follow a power-law decay function due to an evolving concentration gradient near the surface along with the depletion of the bulk solute molecules on the surface, for example, in a self-assembled monolayer adsorption kinetics. Thus, the analytical equations developed to calculate the collision at a fixed measuring frequency can be extended to map the whole curve over time. In the last section of this work, 3D diffusion simulations suggest that the analytical solution is valid to predict the adsorption rate of the bulk solute to a small group of adsorptive target molecules/area on a bouncing surface, which is a critical process in analyzing the kinetics of many bio-sensing platforms.</p> </div>

scholarly journals Stochastic Adsorption of Diluted Solute Molecules at Interfaces

2020 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Analytical Solution ◽  
Observation Time ◽  
Patterned Surfaces ◽  
Fractal Function ◽  
Self Assembled Monolayer ◽  
Power Law Decay ◽  
Sensing Platforms ◽  
Surface Collision ◽  
Measuring Frequency ◽  
Multiple Collisions

<div> <p>Here an analytical solution of Fick’s 2<sup>nd</sup> law is used to predict the diffusion and the stochastic adsorption of single diluted solute molecules on flat and patterned surfaces. The equations are then compared to the results of several numerical Monte Carlo simulations using a random walk model. The 1D diffusion simulations clarify that the dependence of the solute-surface collision rate on the observation-time (measurement time resolution) is because of the multiple collisions of the same molecules over different time regions. It also surprisingly suggests that due to the self-mimetic fractal function of diffusion, the equation should be corrected by a factor of two. The absorption rate of solute on an adsorptive surface is found to follow a power-law decay function due to an evolving concentration gradient near the surface along with the depletion of the bulk solute molecules on the surface, for example, in a self-assembled monolayer adsorption kinetics. Thus, the analytical equations developed to calculate the collision at a fixed measuring frequency can be extended to map the whole curve over time. In the last section of this work, 3D diffusion simulations suggest that the analytical solution is valid to predict the adsorption rate of the bulk solute to a small group of adsorptive target molecules/area on a bouncing surface, which is a critical process in analyzing the kinetics of many bio-sensing platforms.</p> </div>

scholarly journals Stochastic Adsorption of Diluted Solute Molecules at Interfaces

2021 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Analytical Solution ◽  
Observation Time ◽  
Patterned Surfaces ◽  
Fractal Function ◽  
Self Assembled Monolayer ◽  
Power Law Decay ◽  
Sensing Platforms ◽  
Surface Collision ◽  
Measuring Frequency ◽  
Multiple Collisions

<div> <p>Here an analytical solution of Fick’s 2<sup>nd</sup> law is used to predict the diffusion and the stochastic adsorption of single diluted solute molecules on flat and patterned surfaces. The equations are then compared to the results of several numerical Monte Carlo simulations using a random walk model. The 1D diffusion simulations clarify that the dependence of the solute-surface collision rate on the observation-time (measurement time resolution) is because of the multiple collisions of the same molecules over different time regions. It also surprisingly suggests that due to the self-mimetic fractal function of diffusion, the equation should be corrected by a factor of two. The absorption rate of solute on an adsorptive surface is found to follow a power-law decay function due to an evolving concentration gradient near the surface along with the depletion of the bulk solute molecules on the surface, for example, in a self-assembled monolayer adsorption kinetics. Thus, the analytical equations developed to calculate the collision at a fixed measuring frequency can be extended to map the whole curve over time. In the last section of this work, 3D diffusion simulations suggest that the analytical solution is valid to predict the adsorption rate of the bulk solute to a small group of adsorptive target molecules/area on a bouncing surface, which is a critical process in analyzing the kinetics of many bio-sensing platforms.</p> </div>

scholarly journals Stochastic Adsorption of Diluted Solute Molecules at Interfaces

2020 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Analytical Solution ◽  
Observation Time ◽  
Patterned Surfaces ◽  
Fractal Function ◽  
Self Assembled Monolayer ◽  
Power Law Decay ◽  
Sensing Platforms ◽  
Surface Collision ◽  
Measuring Frequency ◽  
Multiple Collisions

<div> <p>Here an analytical solution of Fick’s 2<sup>nd</sup> law is used to predict the diffusion and the stochastic adsorption of single diluted solute molecules on flat and patterned surfaces. The equations are then compared to the results of several numerical Monte Carlo simulations using a random walk model. The 1D diffusion simulations clarify that the dependence of the solute-surface collision rate on the observation-time (measurement time resolution) is because of the multiple collisions of the same molecules over different time regions. It also surprisingly suggests that due to the self-mimetic fractal function of diffusion, the equation should be corrected by a factor of two. The absorption rate of solute on an adsorptive surface is found to follow a power-law decay function due to an evolving concentration gradient near the surface along with the depletion of the bulk solute molecules on the surface, for example, in a self-assembled monolayer adsorption kinetics. Thus, the analytical equations developed to calculate the collision at a fixed measuring frequency can be extended to map the whole curve over time. In the last section of this work, 3D diffusion simulations suggest that the analytical solution is valid to predict the adsorption rate of the bulk solute to a small group of adsorptive target molecules/area on a bouncing surface, which is a critical process in analyzing the kinetics of many bio-sensing platforms.</p> </div>

Combining Molecular Dynamics and Monte Carlo Simulations to Model Chemical Vapor Deposition: Application to Diamond

1992 ◽  
Vol 278 ◽  
Author(s):  
D.W. Brenner ◽  
D.H. Robertson ◽  
R.J. Carty ◽  
D. Srivastava ◽  
B.J. Garrison
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Chemical Vapor Deposition ◽  
Vapor Deposition ◽  
Surface Reactions ◽  
Chemical Vapor ◽  
Md Simulations ◽  
Monte Carlo Algorithm ◽  
Surface Collision ◽  
Classical Trajectories

AbstractGas-surface reactions of the type that contribute to growth during the chemical vapor deposition (CVD) of diamond films are generally completed in picoseconds, well within timescales accessible by molecular dynamics (MD) simulations. For low-pressure deposition, however, the time between collisions for a surface site can be microseconds, which makes direct modeling of CVD crystal growth impossible using standard MD methods. To effectively bridge this discrepancy in timescales, the gas-surface reactions can be modeled using MD trajectories, and then this data can be used to define probabilities in a Monte Carlo algorithm where each step represents a gas-surface collision. We illustrate this approach using the reaction of atomic hydrogen with a diamond (111) surface as an example, where we use abstraction and sticking probabilities generated using classical trajectories in a simple Monte Carlo algorithm to determine the number of open sites as a function of temperature. We also include models for the thermal desorption of hydrogen that predict that growth temperatures are not restricted by the thermal loss of chemisorbed hydrogen.

scholarly journals Interfacial energetics of globular–blood protein adsorption to a hydrophobic interface from aqueous-buffer solution

2005 ◽  
Vol 3 (7) ◽  
pp. 283-301 ◽  
Author(s):  
Anandi Krishnan ◽  
Yi-Hsiu Liu ◽  
Paul Cha ◽  
David Allara ◽  
Erwin A Vogler
Keyword(s):  
Protein Adsorption ◽  
Adsorption Isotherms ◽  
Contact Angles ◽  
Observation Time ◽  
Blood Protein ◽  
Buffer Solution ◽  
Self Assembled Monolayer ◽  
Spreading Pressure ◽  
Aqueous Buffer ◽  
Interfacial Energetics

Adsorption isotherms of nine globular proteins with molecular weight (MW) spanning 10–1000 kDa confirm that interfacial energetics of protein adsorption to a hydrophobic solid/aqueous-buffer (solid–liquid, SL) interface are not fundamentally different than adsorption to the water–air (liquid–vapour, LV) interface. Adsorption dynamics dampen to a steady-state (equilibrium) within a 1 h observation time and protein adsorption appears to be reversible, following expectations of Gibbs' adsorption isotherm. Adsorption isotherms constructed from concentration-dependent advancing contact angles θ a of buffered-protein solutions on methyl-terminated, self-assembled monolayer surfaces show that maximum advancing spreading pressure, , falls within a relatively narrow band characteristic of all proteins studied, mirroring results obtained at the LV surface. Furthermore, Π a isotherms exhibited a ‘Traube-rule-like’ progression in MW similar to the ordering observed at the LV surface wherein molar concentrations required to reach a specified spreading pressure Π a decreased with increasing MW. Finally, neither Gibbs' surface excess quantities [ Γ sl − Γ sv ] nor Γ lv varied significantly with protein MW. The ratio {[ Γ sl − Γ sv ]/ Γ lv }∼1, implying both that Γ sv ∼0 and chemical activity of protein at SL and LV surfaces was identical. These results are collectively interpreted to mean that water controls protein adsorption to hydrophobic surfaces and that the mechanism of protein adsorption can be understood from this perspective for a diverse set of proteins with very different composition.

A Solar Trough Concentrator for Pill-Box Flux Distribution Over a CPV Panel

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
R. Bader ◽  
A. Steinfeld
Keyword(s):  
Monte Carlo ◽  
Analytical Solution ◽  
Ray Tracing ◽  
Focal Plane ◽  
Flux Distribution ◽  
Solar Flux ◽  
Target Area ◽  
Mirror Surface ◽  
Surface Imperfections ◽  
Flux Concentration

An integral methodology is formulated to analytically derive the exact profile of a solar trough concentrator that delivers a uniform radiative flux distribution over a flat rectangular target area at the focal plane. The Monte Carlo ray-tracing technique is applied to verify the analytical solution and investigate the effect of sun shape and mirror surface imperfections on the radiation uniformity and spillage. This design is pertinent to concentrating photovoltaics at moderate mean solar flux concentration ratios of up to 50 suns.

scholarly journals Simulation model for dynamics of three types of annual plants

2016 ◽  
Author(s):  
Andrzej Pękalski
Keyword(s):  
Monte Carlo ◽  
Mean Field ◽  
Observation Time ◽  
Type Model ◽  
Limited Time ◽  
Annual Plants ◽  
Trade Off ◽  
A Site ◽  
The Impact ◽  
Adult Plants

AbstractA Monte Carlo type model describing dynamics of three pairs of annual plants living in a homogeneous habitat is presented and discussed. Each plant follows its own history with growing, fecundity and survival chances determined individually as functions of the plant’s condition and environment. The three plants - Valerianella locusta, Mysotis ramosissima and Cerastium semidecandrum differ by the weight of their seeds, which in the model determines the competition preference. Heavier seeds have a better chance for germination from a site containing seeds of different plants. Better colonisers produce more seeds and disperse them over a larger distance. I show that without absolute asymmetry in the impact effects between better competitors and better colonisers and in a spatially and temporarily homogeneous habitat, coexistence of species is possible, however only in a limited time. This is different from statements coming from models using mean-field type methods. I demonstrate also that in a system of two species clustering of plants of the same type are more frequent. From the calculated survival chances of seedlings and adult plants it follows that elimination of plants occur mostly at the early stages of the plants life cycle, which agrees with the field data.I show that this competition/colonisation trade-off model is sufficient to maintain coexistence and I determine the conditions for dominance of one type of plants. I show that the time of extinction of the weaker species goes down with increasing observation time as a power function with the exponent independent of the type of plants.

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