Properties of star-branched polymer brushes

A simple model of a polymer brush was constructed. The star polymers with three arms were terminally attached with one arm (the stem) to an impenetrable surface with the other two arms (branches) free. The excluded volume effect was included into the model as the only interaction. Therefore, the system was studied in good solvent conditions. The simulations were carried out by means of the dynamic Monte Carlo method using the local changes of chain conformations to sample efficiently the conformational space. The influence of both the number of chains (the grafting density) and the length of chains on the static properties of the polymer brush was studied. The internal and local structure of a formed polymer layer was determined. It was shown that the size of the stems increased rapidly with the increase of the grafting density, while the size of the branches diminished. The changes of the spatial orientations of the stems and the branches for different grafting densities were shown and discussed.     

Effect of bidispersity in grafted chain length on grafted chain conformations and potential of mean force between polymer grafted nanoparticles in a homopolymer matrix

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles.     

Computational methods in coupled electron-ion Monte Carlo simulations.

In the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer approximation: the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT-based ab initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.     

Ab initio stochastic optimization of conformational and many-body degrees of freedom

Moderate to large size molecules in solution have complex energy surfaces due to intramolecular (conformational) and intermolecular (many-body) interactions. The first principles Monte Carlo (FPMC) method, previously shown to effectively locate minimum-energy structures for systems with only many-body complexity, has been extended to address conformational flexibility by adding three new Monte Carlo move types. The primary advantage of the FPMC method is the ability to efficiently locate minimum energy structures of molecules with conformational flexibility in the presence of explicit solvent molecules using highly accurate quantum chemical calculations. The additions to FPMC were validated by studying conformers of glycerol, glyceraldehyde, and a large humic acid monomer unit. The structure of glyceraldehyde in the presence of one and two water molecules was also explored to demonstrate the power of FPMC to study systems with both conformational and many-body degrees of freedom.     

Dynamics of grafted star-branched polymers. A Monte Carlo study

Monte Carlo simulations of simple models of star-branched polymers were carried out. The model chains were confined to simple cubic lattice and consisted of f = 3 branches of equal length and the total number of polymer segments as well as the density of grafted chains on the surface were varied. The chains have had one arm end attached to an impenetrable plate. The simulations were performed by employing the set of local micromodifications of the chain conformations. The model chains were athermal, i.e. good solvent conditions were modeled, the excluded volume effect was present at the model. The density of grafted chains on the surface was varied from a single chain up to 0.3. The static and dynamic properties of the system were studied. The influence of polymer concentration as well as the polymer length on static and dynamic properties of the system studied was shown. The relation between the structure and short-time dynamics (relaxation times) was discussed.     

Size and pH effect on electrical and conformational behavior of poly(acrylic acid): Simulation and experiment

Monte Carlo simulations, experimental titrations and fluorescence correlation spectroscopy experiments were used to investigate the conformational and electrical properties of polyacrylic acids (PAA). On the one hand, titration curves were calculated to get an insight into the role of pH on the degree of ionization and conformation of PAA chains. On the other hand, experimental potentiometric titrations of PAA were also achieved for different PAA molecular weights and compared to the calculated titration curves obtained by Monte Carlo coarse grained simulations. It was found that for a large range at intermediate PAA ionizations, a good correlation is obtained between experimental and simulations data thanks to the prominence of electrostatic interactions in this domain. The effect of ionic concentration and PAA molecular weight on the titration curves was also investigated. In order to get a better understanding of PAA conformational behavior, we also investigated PAA diffusion properties in aqueous solutions as a function of pH and ionic strength by fluorescence correlation spectroscopy (FCS), thanks to its high sensitivity to measure diffusion coefficients of tracer solutes. Good qualitative agreements were observed between experimental diffusivities and polymer properties calculated from MC simulations. It was shown that the high molecular weight PAA chains display more significant changes in diffusivity in agreement with the ionization degrees and conformational changes observed in the simulations.     

A general simulation method for computing conformational properties of single polymer chains

Rotational isomeric state (RIS) theory is the standard method for computing the conformational statistics of polymer chains. It applies to chains under theta conditions, either in the melt or in theta solution. RIS statistical weights can also be used in a Monte Carlo scheme for generating independent chain conformations with the correct statistics. One practical drawback of RIS methods is that statistical weights must be derived before any chain properties can be calculated. This can be tedious for all but relatively simple chains. Here, an efficient method is presented for computing the properties of theta chains without the intermediate step of deriving statistical weights. The method—‘RIS’ Metropolis Monte Carlo (RMMC) simulation-allows computation of the same type of properties as does RIS theory. It shares certain approximations with RIS theory but is not, strictly speaking, a rotational isomeric state method, as it allows bond torsion angles to vary continuously.     

Dual cross-linked networks hydrogels with unique swelling behavior and high mechanical strength: based on silica nanoparticle and hydrophobic association

A series of physically cross-linked hydrogels composed poly(acrylic acid) and octylphenol polyoxyethylene acrylate with high mechanical strength are reported here with dual cross-linked networks that formed by silica nanoparticles (SNs) and hydrophobic association micro-domains (HAMDs). Acrylic acid (AA) and octylphenol polyoxyethylene acrylate with 10 ethoxyl units (OP-10-AC) as basic monomers in situ graft from the SNs surface to build poly(acrylic acid) hydrophilic backbone chains with randomly distributed OP-10-AC hydrophobic side chains. The entanglements among grafted backbone polymer chains and hydrophobic branch architecture lead to the SNs and HAMDs play the role of physical cross-links for the hydrogels network structure. The rheological behavior and polymer concentration for gelation process are measured to examine the critical gelation conditions. The correlation of the polymer dual cross-linked networks with hydrogels swelling behavior, gel-to-sol phase transition, and mechanical strength are addressed, and the results imply that the unique dual cross-linking networks contribute the hydrogels distinctive swelling behavior and excellent tensile strength. The effects of SNs content, molecular weight of polymer backbone, and temperature on hydrogels properties are studied, and the results indicate that the physical hydrogel network integrity is depended on the SNs and HAMDs concentration.     

Collapse transitions of a supersized neutral chain due to irreversibly adsorbed small colloidal particles

 We performed Monte Carlo simulations to study the destabilization processes of large neutral and flexible polymer chains due to irreversibly adsorbed colloidal particles attached to the chains like beads on a necklace. The particles are modeled as charged spherical units which interact with each other via repulsive electrostatic and attractive van der Waals (vdW) potentials. The usual Monte Carlo search procedure is extended and carefully checked to completely sample the chain conformational space and achieve dense conformations in the limit of both strong attractive and repulsive interaction potentials. Configurational properties, such as the radius of gyration, the end-to-end length, and the Kuhn length, are calculated as a function of the intensity of the vdW interactions and ionic strength values. It is observed that chains exhibit a new range of possible conformations compared to the classical random walk and self avoiding walk chains or polyelectrolytes. In the limit of low salt concentration, by gradually increasing vdW interactions, chains undergo a cascade of transitions from extended structures to dumbbells, from dumbbells to pearl necklaces, and from pearl necklaces to collapsed coils. Because of strong competition between the vdW and electrostatic forces, the distance along the chain between the interacting particles, and the sampling limitations, these transitions are found to sample metastable domains and to depend on the initial conformations. To gain insight into the spatial organization of the collapsed conformations, the pair correlation functions of both monomers and particles are calculated. It is shown that collapsed conformations which are the result of strong particle–particle interactions exhibit two distinct parts: a hard core mainly composed of particles and a surrounding polymeric shell composed of loops and tails. Possible effects of such a collapsed transition on the kinetics of flocculation of a mixture containing large flexible chains and small adsorbing colloidal particles are discussed. Received: 26 July 1999 Accepted in revised form: 9 November 1999     

Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

The structure of a polystyrene matrix filled with tightly cross-linked polystyrene nanoparticles, forming an athermal nanocomposite system, is investigated by means of a Monte Carlo sampling formalism. The polymer chains are represented as random walks and the system is described through a coarse grained Hamiltonian. This approach is related to self-consistent-field theory but does not invoke a saddle point approximation and is suitable for treating large three-dimensional systems. The local structure of the polymer matrix in the vicinity of the nanoparticles is found to be different in many ways from that of the corresponding bulk, both at the segment and the chain level. The local polymer density profile near to the particle displays a maximum and the bonds develop considerable orientation parallel to the nanoparticle surface. The depletion layer thickness is also analyzed. The chains orient with their longest dimension parallel to the surface of the particles. Their intrinsic shape, as characterized by spans and principal moments of inertia, is found to be a strong function of position relative to the interface. The dispersion of many nanoparticles in the polymeric matrix leads to extension of the chains when their size is similar to the radius of the dispersed particles.     

Force field development for poly(dimethylsilylenemethylene) with the aid of ab initio calculations

The molecular geometries, conformational energies, and zero-point energies of di(trimethylsilylene)methylene have been determined from high-level quantum chemistry calculations. The results are further used in the parametrization of a classical potential energy function suitable for performing simulations of the corresponding polymer, namely, poly(dimethylsilylenemethylene). Di(trimethylsilylene)methylene geometrical parameter optimizations for a proper location of the global minimum and other local minima, constrained at certain dihedral and bond angles, were performed at both the B3LYP/6-311G and MP2(full)/6-311G levels of theory. The global minimum configuration is slightly displaced from a perfectly staggered geometry, approximately by 16.0 degrees, at both levels of theory. Molecular mechanics and Monte Carlo calculations for isolated polymer chains together with molecular dynamics runs for the modeled dimer provide very good results in terms of conformational and thermodynamic properties.     

Monomer density profiles for polymer chains in confined geometries: massive field theory approach

Taking into account the well known correspondence between the field theoretical ?(4) O(n)-vector model in the limit n → 0 and the behavior of long flexible polymer chains in a good solvent, the universal density-force relation is analyzed and the corresponding universal amplitude ratio B(real) is obtained using the massive field theory approach in fixed space dimensions d < 4. The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order. Besides, the monomer density profiles for the dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

Conformational Entropy as a Means to Control the Behavior of Poly(diketoenamine) Vitrimers In and Out of Equilibrium

Control of equilibrium and non‐equilibrium thermomechanical behavior of poly(diketoenamine) vitrimers is shown by incorporating linear polymer segments varying in molecular weight (MW) and conformational degrees of freedom into the dynamic covalent network. While increasing MW of linear segments yields a lower storage modulus at the rubbery plateau after softening above the glass transition (T_g), both T_g and the characteristic time of stress relaxation are independently governed by the conformational entropy of the embodied linear segments. Activation energies for bond exchange in the solid state are lower for networks incorporating flexible chains; the network topology freezing temperature decreases with increasing MW of flexible linear segments but increases with increasing MW of stiff segments. Vitrimer reconfigurability is therefore influenced not only by the energetics of bond exchange for a given network density, but also the entropy of polymer chains within the network.     

Conformational behavior of polymers adsorbed on nanotubes

The importance of hydrophobic interactions in determining polymer adsorption and wrapping of carbon nanotubes is still under debate. In this work, we concentrate on the effect of short-ranged weakly attractive hydrophobic interactions between polymers and nanotubes (modeled as an infinitely long and smooth cylindrical surface), neglecting all other interactions apart for chain flexibility. Using coarse-grained Monte Carlo simulation of such simplified systems, we find that uniform adsorption and wrapping of the nanotube occur for all degrees of chain flexibility for tubes with sufficiently large outer radii. However, the adsorbed conformations depend on chain stiffness, ranging from randomly adsorbed conformations of the flexible chain to perfect helical or multihelical conformations (in the case of more concentrated solutions) of the rigid chains. Adsorption appears to occur in a sequential manner, wrapping the nanotube nearly one monomer at a time from the point of contact. Once adsorbed, the chains travel on the surface of the cylinder, retaining their helical conformations for the semiflexible and rigid chains. Our findings may provide additional insight to experimentally observed ordered polymer wrapping of carbon nanotubes.     

Preparation and properties of novel hydrogels from oxidized konjac glucomannan cross-linked chitosan for in vitro drug delivery

In this paper, a novel composite hydrogel was prepared by the use of dialdehyde konjac glucomannan (DAK) as macromolecular cross-linking agent for chitosan (CS). This biocompatible material cross-links and gels in minutes. The structure and morphology were characterized by various analyses. The results indicate that the hydrogels formed through the Schiff-base reaction between the amino groups of CS chains and the aldehyde groups of DAK. The cross-link density (rho(x)) increases with the enhancement of DAK content in hydrogels, while equilibrium swelling ratio (SR) and the average molecular weight between cross-links (Mc) value decrease. Drug release was evaluated by varying the pH of the release medium, reversed dependence of release rate on the equilibrium SR of hydrogel indicated that drug release may be impeded by the association of drug with the polymer. Importantly, this process offers an entirely new window of materials preparation when compared with the traditional preparation of CS-based hydrogels with small molecules cross-linking agent.     

Microphase separation in two-dimensional athermal polymer solutions on a triangular lattice

The results of Monte Carlo simulations of 2D polymer solutions are presented. The simulations were performed under athermal conditions for long chains (up to 1024 beads) over a full range of polymer concentration phi, explicitly taking into account the solvent molecules. The results obtained for short chains (N < or = 256) are in good agreement with previous simulations whereas for long chains microphase separation is observed below phi = 0.6. This phenomenon is attributed to strong excluded volume interactions in 2D systems. A sort of interpenetration of the coils is also observed.     

Conformation of Chains in Cores of Block Copolymer Micelles with Solubilized Homopolymer: a Monte Carlo Study

A system of compatible self‐avoiding polymer chains solubilized in spherical cores of block copolymer micelles was studied by lattice Monte Carlo simulations. The core is modeled as a spherical cavity on a simple cubic lattice, filled in partially by tethered (core‐forming) chains and partially by free (solubilized) chains. Molecular parameters (e.g., the ratio of the contour length of the model chains to the core radius) correspond to those in real micellar systems. The density (the fraction of lattice sites occupied) is 0.6 which corresponds to swollen micellar cores in real micellar systems. Simulations yield a constant segment density profile in the core. Both the tethered and solubilized chains acquire an ellipsoidal shape. The ellipsoids equivalent to both types of chains are more spherical than those in a melt and strongly oriented. The chains in the core show a Gaussian‐like behavior. Minor deviations from Gaussian behavior for tethered chains are due to surface effects.     

Properties of branched confined polymers

A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain's local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out.     

Synthesis and characterization of mechanically flexible and tough cellulose nanocrystals–polyacrylamide nanocomposite hydrogels

The unique combinations of hard and soft components with core/shell structures were proposed to synthesize high strength nanocomposite hydrogels. The elastomeric hydrogels containing rod-like cellulose nanocrystals (CNCs) core and polyacrylamide shell were made from aqueous solutions via free radical polymerization in the absence of chemical cross-links. The obtained hydrogels possessed greater tensile strength and elongation ratio when compared with chemically cross-linked counterparts. Oscillatory shear experiments indicated that CNCs interacted with polymer matrix via both chemical and physical interactions and contributed to the rubbery elasticity of the hydrogels. The nanocomposite hydrogels were more viscous than the chemical hydrogels, suggesting the addition of CNC led to the increase of energy dissipating and viscoelastic properties. The network structure model was proposed and it suggested that the high extensibilities and fracture stresses were related to the well-defined network structures with low cross-linking density and lack of noncovalent interactions among polymer chains, which may promote the rearrangements of network structure at high deformations.