Predicting multidimensional distributive properties of hyperbranched polymer resulting from AB2 polymerization with substitution, cyclization and shielding

A deterministic mathematical model for the polymerization of hyperbranched molecules accounting for substitution, cyclization, and shielding effect has been developed as a system of nonlinear population balances. The solution obtained by a novel approximation method shows perfect agreement with the analytical solution in limiting cases and provides, for the first time in this class of polymerization problems, full multidimensional results.Comment: 38 pages, 22 figure

Prediction of mean square radius of gyration of tree-like polymers by a general kinetic approach

This paper describes a kinetic method to predict the z-average molecular mean square radius of gyration of tree-like polymers formed by irreversible reactions, assuming Gaussian chains. It is based on the population balance equations for the two-sided molecular distributions of pendant chains associated with every chemically distinguishable kind of bonds. An automated method for the solution of those equations is valid both before as well as after gelation for complex kinetic schemes. Examples of its use are presented with polycondensation systems leading to hyperbranched polymers, the anionic polymerization of mono- and divinyl monomers and a radical polymerization with terminal branching and transfer to polymer.FCT European Communit

Analytical results on the polymerisation random graph model

The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different vertices. The sequence of degree bounds acts as the only input parameter of the model. This parameter entirely defines the timing of the phase transition. Moreover, the size distribution of connected components features a rich temporal dynamics that includes: switching between exponential and algebraic asymptotes and acquiring oscillations. The results regarding the phase transition and the expected size of a connected component are obtained in a closed form. An exact expression for the size distribution is resolved up to the convolution power and is computable in subquadratic time. The theoretical results are illustrated on a few special cases, including a comparison with Monte Carlo simulations.Comment: 19 pages, 7 figure

Simulation of polysilane and polysilyne formation and structure

We present Monte Carlo simulations of the formation and structure of polysilane, hybrid polysilane/polysilyne and polysilyne networks. The simulation technique allows for the investigation of large networks, containing up to 1000 silicon atoms. Our results show that ring formation is an important factor for all three types of materials. For polysilyne networks, a random structure is found incorporating cyclic substructures, linear chains and branching points.Comment: 8 pages, 11 figure

Molecular modelling of dendrimers for nanoscale applications

Dendrimers are well defined, highly branched macromolecules that radiate from a central core and are synthesized through a stepwise, repetitive reaction sequence that guarantees complete shells for each generation, leading to polymers that are monodisperse. The synthetic procedures developed for dendrimer preparation permit nearly complete control over the critical molecular design parameters, such as size, shape, surface/interior chemistry, flexibility, and topology. Recent results suggest that dendritic polymers may provide the key to developing a reliable and economical fabrication and manufacturing route to functional nanoscale materials that would have unique properties (electronic, optical, opto-electronic, magnetic, chemical, or biological). In turn, these could be used in designing new nanoscale devices. In this paper, we determine the 3D molecular structure of various dendrimers with continuous configurational Boltzmann biased direct Monte Carlo method and study their energetic and structural properties using molecular dynamics after annealing these molecular representations

Complex polymer architectures through free-radical polymerization of multivinyl monomers

The construction of complex polymer architectures with well-defined topology, composition and functionality has been extensively explored as the molecular basis for the development of modern polymer materials. The unique reaction kinetics of free-radical polymerization leads to the concurrent formation of crosslinks between polymer chains and rings within an individual chain and, thus, free-radical (co)polymerization of multivinyl monomers provides a facile method to manipulate chain topology and functionality. Regulating the relative contribution of these intermolecular and intramolecular chain-propagation reactions is the key to the construction of architecturally complex polymers. This can be achieved through the design of new monomers or by spatially or kinetically controlling crosslinking reactions. These mechanisms enable the synthesis of various polymer architectures, including linear, cyclized, branched and star polymer chains, as well as crosslinked networks. In this Review, we highlight some of the contemporary experimental strategies to prepare complex polymer architectures using radical polymerization of multivinyl monomers. We also examine the recent development of characterization techniques for sub-chain connections in such complex macromolecules. Finally, we discuss how these crosslinking reactions have been engineered to generate advanced polymer materials for use in a variety of biomedical applications

A simple Monte Carlo method for modeling arborescent polymer production in continuous stirred tank reactor

A dynamic mathematical model was developed to predict the molecular weight distribution (MWD) and branching distribution for arborescent polyisobutylene (arbPIB) in a continuous stirred tank reactor (CSTR). ArbPIB a promising biomaterial for human implantation [1] made by copolymerization of isobutylene and an inimer [2]. An inimer is a special molecule that contains an initiating group (initiator) and a vinyl group (monomer), which can form a T-shaped branch on a polymer chain. The model builds on a previous kinetic Monte Carlo (MC) algorithm developed for arbPIB production in a batch reactor [3]. A key innovation of our proposed MC approach is that inflow and outflow events are treated separately from reaction events, so that simulations are faster than would be obtained using existing approaches where inflow and outflow are treated as if they were reactions [4]. As such, we anticipate that the proposed methodology will be useful for other polymerization systems. To our knowledge, this is the first dynamic MC model for branched polymer production in a CSTR and the first model to predict the MWD of arbPIB in a CSTR, which tends to be much broader than the MWD of the corresponding batch copolymer. Model predictions are verified using a multi-dimensional method-of-moments model that predicts number and weight-average molecular weights, but not the MWD [5]. CSTR start-up was simulated beginning with fresh monomer and inimer in the reactor (no polymer at time zero). The model shows how the MWD continuously shifts to the high molecular weight region as time passes. For some operating conditions with relatively high inimer concentration or long residence times, the MWD does not reach steady state because larger and larger molecules that would eventually clog the reactor tend to form over time. Please click Additional Files below to see the full abstract

Dimension of heterogeneous network architecture formed in emulsion crosslinking copolymerization

The mean-square radius of gyration Rg2 and the graph diameter D of highly heterogeneous network polymers formed in emulsion vinyl/divinyl copolymerization are investigated to find a linear relationship, Rg2 = a D. The proportionality coefficient, a is dominated by the cycle (circuit) rank, kc or the number of intramolecular cross-links. The magnitude of a is slightly larger than that for the random cross-linked network polymers, but the functional form of a(kc) is simply proportional to that for the random networks proposed earlier. This relationship makes it possible to determine Rg2 based on D and kc, enabling quick estimation of Rg2 for large network polymers. It is found that the contraction factor g of the present heterogeneous network polymer is larger than that for the homogeneous networks formed through random cross-linking of polymer chains. The ratio of these two contraction factors is kept constant, irrespective of the magnitude of kc.journal articl

Functional aromatic polyamides

We describe herein the state of the art following the last 8 years of research into aromatic polyamides, wholly aromatic polyamides or aramids. These polymers belong to the family of high performance materials because of their exceptional thermal and mechanical behavior. Commercially, they have been transformed into fibers mainly for production of advanced composites, paper, and cut and fire protective garments. Huge research efforts have been carried out to take advantage of the mentioned characteristics in advanced fields related to transport applications, optically active materials, electroactive materials, smart materials, or materials with even better mechanical and thermal behavior.FEDER and both the Spanish Ministerio de Economía, Industria y Competitividad (MAT2014-54137-R) and the Consejería de Educación—Junta de Castilla y León (BU061U16