A three-dimensional polymer growth model

Vogt, Marc; Hernandez, Rigoberto

doi:10.1063/1.1477455

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…While a large number of models have been offered to describe single-step (or one-pot) growth processes such as crystallization, polymerization, and self-assembly, ,− we are unaware of any simple model that generally describes irreversible stepwise growth of discrete structures. The model we propose does not purport to accurately describe the molecular behavior of a specific system but rather aims to capture the general features of irreversible stepwise growth and synthesis processes, similar to the way in which some of the self-assembly, crystallization, and polymerization models capture the basic features of such growth processes. ,− The model focuses on the growth of a single structure in each simulation, where growth is performed by binding monomers to specific sites on the face of a structure (Figure , panel C). In each growth step a different type of monomers is added and bound to the structure.…”

Section: Model Descriptionmentioning

confidence: 99%

Errors and Error Tolerance in Irreversible Multistep Growth of Nanostructures

Eppel

Rabani

2011

J. Phys. Chem. C

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Error correction is one of the main features allowing self-assembly and other reversible growth processes to create giant, ordered molecular structures at the nanometer scale and above. On the other hand, in irreversible growth processes, such as chemical synthesis, errors (defects) are usually not removable and, as a result, growth is limited to a small number of synthetic steps and formation of relatively small structures. In this work, we develop a general model and theory to describe the behavior of errors in multistep, irreversible growth processes. Simulations of the model show that despite the large number of ways in which errors may occur in the growth, the average effect of errors seems to obey a universal pattern controlled by only a few parameters, regardless of the exact type of errors that occur. Furthermore, we show that errors that disturb growth cause damage that increases exponentially with the number of growth steps, thus leading to randomly disordered structures after a relatively small number of growth steps. If, however, growth is cooperative, the exponential increase of defects can be suppressed, suggesting that it is possible to create irreversible growth processes with error tolerance similar to that of reversible self-assembly (although without error correction). This may allow growth of ordered superstructures that exceed the limits of current systems.

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Section: Model Descriptionmentioning

confidence: 99%

Errors and Error Tolerance in Irreversible Multistep Growth of Nanostructures

Eppel

Rabani

2011

J. Phys. Chem. C

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“…Due to their transient nature, they exhibit novel static and dynamic properties on time scales both long and short compared to their finite lifetime. Theoretical treatments of wormlike micelles include grand canonical Monte Carlo simulations on 2D and 3D lattices in which the breaking and reformation of micelles is implemented via individual monomer states [23] or by polymer growth Hamiltonian [24,25] or by defining probabilities of bond breaking and forming and slithering snake dynamics with or without inclusions of chain stiffness in the models [23,[26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Wormlike Micelles as Templates for Rod-Shaped Nanoparticles: Experiments and Simulations

Gupta

Duttagupta

Chhatre

et al. 2015

Springer Tracts in Mechanical Engineering

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We report here a novel and generic method for the synthesis of rodshaped nanoparticles of AgBr, AgCl, and Fe 2 O 3 using wormlike micelles (WLMs) in aqueous solution. It is observed that the presence of a wormlike micellar phase is critical to the formation of such anisotropic nanoparticles. Spherical nanoparticles are otherwise obtained when wormlike micelles are absent. Nanoparticle precursors first form spherical primary particles at short times, which then coagulate and consolidate on a surfactant backbone to form nanorods. Interestingly, when preformed spherical nanoparticles are added to a wormlike micellar system, nanorods similar to the in situ method are observed. This technique has been explored for the synthesis of anisotropic iron oxide particles as well. Further a mechanism for the formation of these nanorods is proposed and is simulated using a framework of slithering snake dynamics for WLM. In this study, the wormlike micelles are represented by flexible polymers of fixed contour length. A rule-based intermicellar particle exchange protocol is formulated and simulated on a periodic lattice. Simulations reveal that the particles start accumulating slowly on few of the micellar backbones; toward the end, the fraction of micelles carrying no particles increases drastically which is a typical behavior observed in coagulation processes. The particulate masses accumulated on the WLMs are then converted to their respective lengths and diameters.

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“…In the last few decades, considerable researches have been devoted to the nonequilibrium cluster growth phenomenon [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], which is of fundamental interest to the understanding of diverse natural processes, such as aerosol formation, crystal growth, star formation, droplet growth, and so on. Most of these works have been focused on the kinetic behaviour of cluster growth through the binary coalescence mechanism, A i + A j → A i+ j , where A i denotes a cluster consisting of i monomers [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Solvable single-species aggregation–annihilation model for chain-shaped cluster growth

Ke¹,

Zhang²,

Zheng³

et al. 2007

J. Phys.: Condens. Matter

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We propose a single-species aggregation–annihilation model, in which an aggregation reaction between two clusters produces an active cluster and an annihilation reaction produces an inert one. By means of the mean-field rate equation, we respectively investigate the kinetic scaling behaviours of three distinct systems. The results exhibit that: (i) for the general aggregation–annihilation system, the size distribution of active clusters consistently approaches the conventional scaling form; (ii) for the system with the self-degeneration of the cluster’s activities, it takes the modified scaling form; and (iii) for the system with the self-closing of active clusters, it does not scale. Moreover, the size distribution of inert clusters with small size takes a power-law form, while that of large inert clusters obeys the scaling law. The results also show that all active clusters will eventually transform into inert ones and the inert clusters of any size can be produced by such an aggregation–annihilation process. This model can be used to mimic the chain-shaped cluster growth and can provide some useful predictions for the kinetic behaviour of the system.

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A three-dimensional polymer growth model

Cited by 6 publications

References 25 publications

Errors and Error Tolerance in Irreversible Multistep Growth of Nanostructures

Errors and Error Tolerance in Irreversible Multistep Growth of Nanostructures

Wormlike Micelles as Templates for Rod-Shaped Nanoparticles: Experiments and Simulations

Solvable single-species aggregation–annihilation model for chain-shaped cluster growth

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