Morphology and Transport Properties of Two-Dimensional Sheet Polymers

Abstract

Whereas there has been extensive theoretical and experimental investigation of the properties of linear polymer chains in solution, there has been far less work on sheet-like polymers having 2D connectivity and 3D crumpled or collapsed shapes caused by thermal fluctuations, attractive self-interactions, or both. Sheet-like polymers arise in a variety of contexts ranging from self-assembled biological membranes (e.g., the spectrin network of red blood cells, microtubules, etc.) to nanocomposite additives to polymers (carbon nanotubes, graphene, and clay sheets) and polymerized monolayers. We investigate the equilibrium properties of this broad class of polymers using a simple model of a sheet polymer with a locally square symmetry of the connecting beads. We quantify the sheet morphology and the dilute-limit hydrodynamic solution properties as a function of molecular mass and sheet stiffness. First, we reproduce the qualitative findings of previous work indicating that variable sheet stiffness results in a wide variety of morphologies, including flat, crumpled or collapsed spherical, cylindrical or tubular, and folded sheets that serve to characterize our particular 2D polymer model. Transport properties are of significant interest in characterizing polymeric materials, and we provide the first numerical computations of these properties for sheet polymers. Specifically, we calculate the intrinsic viscosity and hydrodynamic radius of these sheet morphologies using a novel path-integration technique and find good agreement of our numerical results with previous theoretical scaling predictions.

Intrinsic conductivity of carbon nanotubes and graphene sheets having a realistic geometry

“…A similar model has been studied extensively in reference. [54]. Here, we choose σ ≈ 1 nm as the average experimental value reported for graphene thickness [13–15] ( z –direction).…”

“…We model the GSs as two–dimensional polymers [54] having different flexibilities and a finite thickness, where the lateral dimensions are larger than the thickness. A continuum approach is used to calculate the polarizability tensors of model CNTs and GSs whose structures are generated by MD.…”

Methods for calculating the physical properties of polymers

“…In order to express the glass transition temperature T g as a function of the mole fraction of polymer 2, it is possible for totally miscible polymers to use complete equation (19), which is valid for copolymers [4][5][6][7]: (99) Equation (99) more precisely relates T g to the mole fraction of polymer 2. If we take into account the calculated values of T g,1 and T g,2 and substitute all parameters into formula (99), we will obtain (100)…”

“…The dependence of the glass transition temperature on the mole fraction of polymer 2, α m,2 for miscible blends is described by relationship (99). If the physical parameters listed in Table 16 are used, for the poly mer 1b + polymer 2 blend we will obtain (107)…”

Biofunctionalization and immobilization of a membrane via peptide binding (CR3-1, S2) by a Monte Carlo simulation

“…[9][10][11][12] The dynamics of a tethered membrane has been extensively studied by computer simulation. [13][14][15] A tethered membrane exhibits multiple dynamics 13,14 over a range of time scales, e.g., short time ͑R ϰ t 1/8 ͒ to long time asymptotic diffusion ͑R ϰ t 1/2 ͒ where R is the root mean square displacement of a local node and t is the time step. What happens when the membrane is placed in a host matrix consisting of peptides?…”