Self-Avoiding Random Walks as a Model to Study Athermal Linear Polymers under Extreme Plate Confinement

Monte Carlo (MC) simulations, built around chain-connectivity-altering moves and a wall-displacement algorithm, allow us to simulate freely-jointed chains of tangent hard spheres of uniform size under extreme confinement. The latter is realized through the presence of two impenetrable, flat, and parallel plates. Extreme conditions correspond to the case where the distance between the plates approaches the monomer size. An analysis of the local structure, based on the characteristic crystallographic element (CCE) norm, detects crystal nucleation and growth at packing densities well below the ones observed in bulk analogs. In a second step, we map the confined polymer chains into self-avoiding random walks (SAWs) on restricted lattices. We study all realizations of the cubic crystal system: simple, body centered, and face centered cubic crystals. For a given chain size (SAW length), lattice type, origin of SAW, and level of confinement, we enumerate all possible SAWs (equivalently all chain conformations) and calculate the size distribution. Results for intermediate SAW lengths are used to predict the behavior of long, fully entangled chains through growth formulas. The SAW analysis will allow us to determine the corresponding configurational entropy, as it is the driving force for the observed phase transition and the determining factor for the thermodynamic stability of the corresponding crystal morphologies.

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Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

10.20944/preprints201811.0112.v2 ◽

2018 ◽

Author(s):

Javier Benito ◽

Nikos Ch. Karayiannis ◽

Manuel Laso

Keyword(s):

Random Walks ◽

Approximate Expression ◽

Polymer Chains ◽

Face Centered Cubic ◽

Single Chain ◽

Confined Geometries ◽

Confined Polymers ◽

Ordered Phases ◽

Face Centered ◽

Chain Conformations

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

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Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

Polymers ◽

10.3390/polym10121394 ◽

2018 ◽

Vol 10 (12) ◽

pp. 1394 ◽

Cited By ~ 4

Author(s):

Javier Benito ◽

Nikos Karayiannis ◽

Manuel Laso

Keyword(s):

Random Walks ◽

Approximate Expression ◽

Polymer Chains ◽

Face Centered Cubic ◽

Single Chain ◽

Confined Geometries ◽

Confined Polymers ◽

Ordered Phases ◽

Face Centered ◽

Chain Conformations

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is (a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and (b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

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Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

10.20944/preprints201811.0112.v1 ◽

2018 ◽

Author(s):

Javier Benito ◽

Nikos Ch. Karayiannis ◽

Manuel Laso

Keyword(s):

Random Walks ◽

Approximate Expression ◽

Polymer Chains ◽

Face Centered Cubic ◽

Single Chain ◽

Confined Geometries ◽

Confined Polymers ◽

Ordered Phases ◽

Face Centered ◽

Chain Conformations

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Molecular Theories of Rubberlike Elasticity and Polymer Viscoelasticity

Rubber Chemistry and Technology ◽

10.5254/1.3544728 ◽

1972 ◽

Vol 45 (3) ◽

pp. 638-666 ◽

Cited By ~ 1

Author(s):

Mitchel Shen ◽

William F. Hall ◽

Roger E. Dewames

Keyword(s):

Physical Properties ◽

Configurational Entropy ◽

Polymer Chains ◽

Elastic Response ◽

Linear Polymers ◽

Polymer Molecules ◽

Recent Developments ◽

Conformational Statistics ◽

Polymer Viscoelasticity

Abstract The foundation for nearly all the molecular theories of the physical properties of polymers was laid in 1934 when Guth and Mark and Kuhn first recognized the role of configurational entropy of polymer chains. By virtue of ability of their segments to rotate with respect to each other along the chain backbone, macromolecules are capable of assuming a myriad of conformations. It is this long, flexible chain nature of polymer molecules that provides us a link in interpreting the macroscopic physical properties in terms of microscopic molecular dynamics. In this review we shall demonstrate the utilization of conformational statistics in the formulation of molecular theories for two important aspects of the mechanical properties of polymers. The first part deals with the equilibrium elastic response of a crosslinked rubberlike network. A simplified derivation will be given on the basis of the entropic approach. Some of the underlying assumptions will then be examined, and the contribution of internal energy to rubber elasticity scrutinized. The second part describes the transient viscoelastic properties of linear polymers in solution and in bulk. Limitations of the model will be assessed and its applications to experimental data explored. It should be pointed out that a number of reviews are available in the literature both for elasticity and viscoelasticity of polymers. The present work is not an exhaustive review of these fields, but rather concentrates on the more recent developments not previously discussed. The emphasis will be placed upon polymers in the bulk state, although solution properties will be mentioned where appropriate.

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Crystal, Fivefold and Glass Formation in Clusters of Polymers Interacting with the Square Well Potential

Polymers ◽

10.3390/polym12051111 ◽

2020 ◽

Vol 12 (5) ◽

pp. 1111

Author(s):

Miguel Herranz ◽

Manuel Santiago ◽

Katerina Foteinopoulou ◽

Nikos Ch. Karayiannis ◽

Manuel Laso

Keyword(s):

Local Density ◽

Hard Spheres ◽

Local Environment ◽

Crystal Nucleation ◽

Average Chain Length ◽

Model Parameters ◽

Face Centered Cubic ◽

Polymer Systems ◽

Hexagonal Close Packed ◽

Square Well

We present results, from Monte Carlo (MC) simulations, on polymer systems of freely jointed chains with spherical monomers interacting through the square well potential. Starting from athermal packings of chains of tangent hard spheres, we activate the square well potential under constant volume and temperature corresponding effectively to instantaneous quenching. We investigate how the intensity and range of pair-wise interactions affected the final morphologies by fixing polymer characteristics such as average chain length and tolerance in bond gaps. Due to attraction chains are brought closer together and they form clusters with distinct morphologies. A wide variety of structures is obtained as the model parameters are systematically varied: weak interactions lead to purely amorphous clusters followed by well-ordered ones. The latter include the whole spectrum of crystal morphologies: from virtually perfect hexagonal close packed (HCP) and face centered cubic (FCC) crystals, to random hexagonal close packed layers of single stacking direction of alternating HCP and FCC layers, to structures of mixed HCP/FCC character with multiple stacking directions and defects in the form of twins. Once critical values of interaction are met, fivefold-rich glassy clusters are formed. We discuss the similarities and differences between energy-driven crystal nucleation in thermal polymer systems as opposed to entropy-driven phase transition in athermal polymer packings. We further calculate the local density of each site, its dependence on the distance from the center of the cluster and its correlation with the crystallographic characteristics of the local environment. The short- and long-range conformations of chains are analyzed as a function of the established cluster morphologies.

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Entropy-Driven Heterogeneous Crystallization of Hard-Sphere Chains under Unidimensional Confinement

Polymers ◽

10.3390/polym13091352 ◽

2021 ◽

Vol 13 (9) ◽

pp. 1352

Author(s):

Pablo Miguel Ramos ◽

Miguel Herranz ◽

Katerina Foteinopoulou ◽

Nikos Ch. Karayiannis ◽

Manuel Laso

Keyword(s):

Phase Transition ◽

Volume Fraction ◽

Hard Spheres ◽

Local Symmetry ◽

Crystal Nucleation ◽

Surface Crystallization ◽

Face Centered Cubic ◽

Bulk Crystallization ◽

Wide Range ◽

Heterogeneous Crystallization

We investigate, through Monte Carlo simulations, the heterogeneous crystallization of linear chains of tangent hard spheres under confinement in one dimension. Confinement is realized through flat, impenetrable, and parallel walls. A wide range of systems is studied with respect to their average chain lengths (N = 12 to 100) and packing densities (ϕ = 0.50 to 0.61). The local structure is quantified through the Characteristic Crystallographic Element (CCE) norm descriptor. Here, we split the phenomenon into the bulk crystallization, far from the walls, and the projected surface crystallization in layers adjacent to the confining surfaces. Once a critical volume fraction is met, the chains show a phase transition, starting from regions near the hard walls. The established crystal morphologies consist of alternating hexagonal close-packed or face-centered cubic layers with a stacking direction perpendicular to the confining walls. Crystal layer perfection is observed with an increasing concentration. As in the case of the unconstrained phase transition of athermal polymers at high densities, crystal nucleation and growth compete with the formation of sites of a fivefold local symmetry. While surface crystallites show perfection with a predominantly triangular character, the morphologies of square crystals or of a mixed type are also formed. The simulation results show that the rate of perfection of the surface crystallization is not significantly faster than that of the bulk crystallization.

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Fabrication of Spherical Titania Inverse Opal Structures Using Electro-Hydrodynamic Atomization

Molecules ◽

10.3390/molecules24213905 ◽

2019 ◽

Vol 24 (21) ◽

pp. 3905 ◽

Cited By ~ 1

Author(s):

Jong-Min Lim ◽

Sehee Jeong

Keyword(s):

Composite Structure ◽

Self Assembly ◽

Interstitial Site ◽

Titania Nanoparticles ◽

Face Centered Cubic ◽

Inverse Opal ◽

Uniform Size ◽

Anatase Titania ◽

Inverse Opal Structure ◽

Fcc Structure

Spherical PS/HEMA opal structure and spherical titania inverse opal structure were fabricated by self-assembly of colloidal nanoparticles in uniform aerosol droplets generated with electro-hydrodynamic atomization method. When a solution of PS/HEMA nanoparticles with uniform size distribution was used, PS/HEMA nanoparticles self-assembled into a face-centered cubic (FCC) structure by capillary force with the evaporation of the solvent in aerosol droplet, resulting in a spherical opal structure. When PS/HEMA nanoparticles and anatase titania nanoparticles were dispersed simultaneously into the solution, titania nanoparticles with relatively smaller size were assembled at the interstitial site of PS/HEMA nanoparticles packed in the FCC structure, resulting in a spherical opal composite structure. Spherical titania inverse opal structure was fabricated after removing PS/HEMA nanoparticles from the spherical opal composite structure by calcination.

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