scholarly journals Forward Flux Sampling of Polymer Desorption Paths from a Solid Surface into Dilute Solution

Polymers ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2275
Author(s):  
Kyle J. Huston ◽  
Christina E. Rice ◽  
Ronald G. Larson
Keyword(s):  
Interaction Energy ◽  
Solid Wall ◽  
Scaling Law ◽  
Rare Event ◽  
Degree Of Polymerization ◽  
Radius Of Gyration ◽  
Exponential Dependence ◽  
Excluded Volume Effects ◽  
Desorption Time ◽  
Wall Interaction

We compute desorption rates for isolated polymers adsorbed to a solid wall with a rare event sampling technique called multilevel splitting, also known as forward flux sampling. We interpret computed rates with theories based on the conjecture that the product tdesDRg2 of the desorption time tdes and diffusivity D divided by squared radius of gyration Rg scales with exp(h/Rg) where h is the equilibrium ratio of adsorbed surface concentration of polymer Γ to bulk concentration of polymer c. As the polymer–wall interaction energy is increased, the slope of lntdesDRg2 vs. NVMFkBT nearly approaches unity, as expected for strongly-adsorbing chains, where N is the degree of polymerization and VMF is the height-averaged monomer–wall interaction energy for a strongly adsorbed chain. However, we also find that this scaling law is only accurate when adsorption strength per monomer exceeds a threshold value on the order of 0.3–0.5 kBT for a freely jointed chain without or with excluded volume effects. Below the critical value, we observe that tdesDRg2 becomes nearly constant with N, so that tdes∝Nα, with α≈2. This suggests a crossover from “strong” detachment-controlled to a “weak” diffusion-controlled desorption rate as VMF/kBT drops below some threshold. These results may partially explain experimental data, that in some cases show “strong” exponential dependence of desorption time on chain length, while in others a “weak” power-law dependence is found. However, in the “strong” adsorption case, our results suggest much longer desorption times than those measured, while the reverse is true in the weak adsorption limit. We discuss possible reasons for these discrepancies.

Effect of finite sampling time on estimation of Brownian fluctuation

2015 ◽  
Vol 767 ◽  
pp. 65-84 ◽  
Author(s):  
Shahram Pouya ◽  
Di Liu ◽  
Manoochehr M. Koochesfahani
Keyword(s):  
Diffusion Coefficient ◽  
Scaling Laws ◽  
Solid Wall ◽  
Exact Analytical Solution ◽  
Scaling Law ◽  
Time Interval ◽  
Free Diffusion ◽  
Mean Velocity ◽  
Hindered Diffusion ◽  
Near Wall

AbstractWe present a study of the effect of finite detector integration/exposure time $E$, in relation to interrogation time interval ${\rm\Delta}t$, on analysis of Brownian motion of small particles using numerical simulation of the Langevin equation for both free diffusion and hindered diffusion near a solid wall. The simulation result for free diffusion recovers the known scaling law for the dependence of estimated diffusion coefficient on $E/{\rm\Delta}t$, i.e. for $0\leqslant E/{\rm\Delta}t\leqslant 1$ the estimated diffusion coefficient scales linearly as $1-(E/{\rm\Delta}t)/3$. Extending the analysis to the parameter range $E/{\rm\Delta}t\geqslant 1$, we find a new nonlinear scaling behaviour given by $(E/{\rm\Delta}t)^{-1}[1-((E/{\rm\Delta}t)^{-1})/3]$, for which we also provide an exact analytical solution. The simulation of near-wall diffusion shows that hindered diffusion of particles parallel to a solid wall, when normalized appropriately, follows with a high degree of accuracy the same form of scaling laws given above for free diffusion. Specifically, the scaling laws in this case are well represented by $1-((1+{\it\epsilon})(E/{\rm\Delta}t))/3$, for $E/{\rm\Delta}t\leqslant 1$, and $(E/{\rm\Delta}t)^{-1}[1-((1+{\it\epsilon})(E/{\rm\Delta}t)^{-1})/3]$, for $E/{\rm\Delta}t\geqslant 1$, where the small parameter ${\it\epsilon}$ depends on the size of the near-wall domain used in the estimation of the diffusion coefficient and value of $E$. For the range of parameters reported in the literature, we estimate ${\it\epsilon}<0.03$. The near-wall simulations also show a bias in the estimated diffusion coefficient parallel to the wall even in the limit $E=0$, indicating an overestimation which increases with increasing time delay ${\rm\Delta}t$. This diffusion-induced overestimation is caused by the same underlying mechanism responsible for the previously reported overestimation of mean velocity in near-wall velocimetry.

Excluded-volume effects on the mean-square radius of gyration of oligo- and polystyrenes in dilute solutions

1993 ◽  
Vol 26 (8) ◽  
pp. 1884-1890 ◽  
Author(s):  
Fumiaki Abe ◽  
Yoshiyuki Einaga ◽  
Takenao Yoshizaki ◽  
Hiromi Yamakawa
Keyword(s):  
Excluded Volume ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Dilute Solutions ◽  
Excluded Volume Effects ◽  
The Mean ◽  
Volume Effects

Scaling law for the radius of gyration of poly[bis(2-naphthoxyphosphazene)] (PBNP)

1992 ◽  
Vol 29 (3-4) ◽  
pp. 469-475 ◽  
Author(s):  
Maria P. Tarazona ◽  
Julio Bravo ◽  
Enrique Saiz
Keyword(s):  
Scaling Law ◽  
Radius Of Gyration

Miscibility Studies on Heterogeneous Polymer Blends by Radioluminescence Spectroscopy and Particle Coarsening Measurements

1977 ◽  
Vol 50 (4) ◽  
pp. 714-722 ◽  
Author(s):  
G. G. A. Böhm ◽  
K. R. Lucas ◽  
W. G. Mayes
Keyword(s):  
Rare Event ◽  
Polymeric Composite ◽  
State Theory ◽  
Degree Of Polymerization ◽  
Solution Temperature ◽  
Subtle Difference ◽  
Polymer Systems ◽  
Physical Strength ◽  
Heterogeneous Polymer ◽  
Polymer Miscibility

Abstract Interest in the subject of polymer miscibility has been stimulated by the investigation and common use by industry of heterogeneous polymer systems. Particularly, in recent years we have seen the development of materials, such as ABS, high-impact polystyrene, block copolymers, thermoplastic elastomer blends (TPR, etc.), and many more, which owe their unique properties to a certain critical degree of immiscibility of the polymeric constituents. This subtle difference in miscibility contributes to the formation of morphological features in the above-mentioned materials. More importantly, it governs the adhesion between the domains of the phase-separated polymeric composite. The latter property provides for stress transfer across the interface and thus is needed for the attainment of physical strength. Thus the questions posed by researchers are not so much concerned with whether two polymers are fully miscible on a molecular scale, a rare event indeed, but rather in the degree of miscibility of the two materials. In spite of recent advances made, the bulk miscibility of polymers cannot be predicted by theory. The lattice theory of Flory leads to unsatisfactory conclusions. It can, however, be used for an after-the-fact representation of experimental findings by use of an empirically determined concentration- and temperature-dependent polymer interaction coefficient. More insight and qualitative postulates on polymer miscibility are provided by the equation-of-state theory. It correctly predicts the marked influence of the degree of polymerization and of the thermal expansion and pressure coefficients and, more importantly, it anticipates the lower critical solution temperature observed in a number of polymer systems. However, the equations are complicated and contain many generally unknown, but experimentally accessible, parameters, and thus this theory too is of little help to the investigator seeking miscibility data for a specific pair of polymers.

Macromolecular crowding effects in flexible polymer solutions

2018 ◽  
Vol 17 (03) ◽  
pp. 1840006 ◽  
Author(s):  
Bibhab Bandhu Majumdar ◽  
Simon Ebbinghaus ◽  
Matthias Heyden
Keyword(s):  
Monte Carlo ◽  
Intermolecular Interactions ◽  
Finite Size ◽  
Macromolecular Crowding ◽  
Conformational Space ◽  
Intermolecular Potential ◽  
Radius Of Gyration ◽  
Excluded Volume Effects ◽  
Flexible Polymer ◽  
Mcmc Approach

Biological environments are often “crowded” due to high concentrations (300–400[Formula: see text]g/L) of macromolecules. Computational modeling approaches like Molecular Dynamics (MD), rigid-body Brownian Dynamics and Monte Carlo simulations have recently emerged, which allow to study the effects macromolecular crowding at a microscopic level and to provide complementary information to experiments. Here, we use a recently introduced multiple-conformation Monte Carlo (mcMC) approach in order to study the influence of intermolecular interactions on the structural equilibrium of flexible polyethylene glycol (PEG) polymers under self-crowding conditions. The large conformational space accessible to PEG polymers allows us to evaluate the general applicability of the mcMC approach, which describes the intramolecular degrees of freedom by a finite-size ensemble of discrete conformations. Despite the simplicity of the approach, we show that influences of intermolecular interactions on the intramolecular free energy surface can be described qualitatively using mcMC. By varying the magnitude of distinct terms in the intermolecular potential, we can further study the compensating effects of repulsive and nonspecific attractive intermolecular interactions, which favor compact and extended polymer states, respectively. We use our simulation results to derive an analytical model that describes the effects of intermolecular interactions on the stability of PEG polymer conformations as a function of the radius of gyration and the corresponding solvent accessible surface. We use this model to confirm the role of molecular surfaces for attractive interactions that can counteract excluded volume effects. Extrapolation of the model further allows for the analysis of scenarios that are not easily accessible to direct simulations as described here.

scholarly journals R13 moment equations applied to supersonic flow with solid wall interaction

2019 ◽  
Author(s):  
Maksim Timokhin ◽  
Henning Struchtrup ◽  
Alexey Kokhanchik ◽  
Yevgeniy Bondar
Keyword(s):  
Supersonic Flow ◽  
Solid Wall ◽  
Moment Equations ◽  
Wall Interaction

Monte Carlo Simulation of Adsorption of Di-Block Copolymers

1988 ◽  
Vol 140 ◽  
Author(s):  
Wan Y. Shih ◽  
Wei-Heng Shill ◽  
Ilhan A. Aksay
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Block Copolymer ◽  
Block Copolymers ◽  
Monte Carlo Simulations ◽  
Degree Of Polymerization ◽  
Radius Of Gyration ◽  
Adsorbed Layers ◽  
Experimental Findings ◽  
Repulsive Forces

AbstractIn this paper we are concerned with the morphology of the polymers adsorbedon surfaces, in particular di-block copolymers. Our work is motivated by the experimental findings of Fladziioannou et al. [1] on the steric forces between two adsorbed layers of di-block poly(vinyl-2-pyridine)\ polystyrene (PV2P\ PS) copolymer on mica surfaces. The PV2P block binds strongly on the mica surfaces and the PS block extends into thesolvent toluene (good solvent for PS). Hadziiouannou et al. found that the repulsive forces between the two surfaces start at a distance 1) larger than 10 times the radius of gyration RG of a free P' in toluene. Furthermore, the starting distance D increases with increasing degree of polymerization N of PS in a fashion I) ~ Na with a close to I. We,tudy the adsorption of di-block copolymer with Monte Carlo simulations. The Monte Carlo simulations are especially powerful in dealing with kinetics which is important in systems where hysteresis is observed II1 and cannot be appropriately taken into account by analytical (or numerical) calculations based onequilibrium assumptions.

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