Monte carlo simulations of polydisperse polymers grafted on spherical surfaces

This article presents effects of polydispersity in polymers grafted on spherical surfaces on grafted polymer chain conformations, grafted layer thickness, and free‐end monomer distribution within the grafted layer. At brush‐like grafting densities, as polydispersity index (PDI) increases, the scaling exponent of radius of gyration of grafted chains approaches that of a single chain grafted on the same nanoparticle, because polydispersity alleviates monomer crowding within the brush. At high PDI, the chains shorter than the number average chain length, N_n, have more compressed conformations, and the chains longer than N_n overall stretch less than in the monodisperse case. As seen in polydisperse flat brushes at high grafting densities, the grafted layer thickness on spherical nanoparticle increases with PDI. Polydispersity eliminates the region near the surface devoid of free‐end monomers seen in monodisperse cases, and it reduces the width of free‐end monomer distribution and shifts the free‐end monomer distribution close to the surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Effect of matrix bidispersity on the morphology of polymer-grafted nanoparticle-filled polymer nanocomposites

We present a simulation study showing the effect of bidispersity in matrix homopolymer length on the wetting/dewetting of homopolymer-grafted nanoparticles and the morphology of polymer nanocomposites where the graft and matrix polymer chemistries are identical. In a bidisperse matrix with equal number of short and long chains and average matrix length greater than the monodisperse graft length, the densely grafted polymer layer is preferentially wet by the short chains and relatively dewet by the long chains. This is driven by a larger gain in entropy of mixing between graft and matrix for short matrix chains than long matrix chains. Despite the preferential wetting of the short and dewetting of long chains, matrix length bidispersity does not significantly change the overall wetting of the grafted layer. Unlike graft length bidispersity that significantly improves particle dispersion, matrix length bidispersity slightly increases particle aggregation in the polymer matrix. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1661–1668     

Influence of polymer matrix composition and architecture on polymer nanocomposite formation: Coarse-grained molecular dynamics simulation

Coarse-grained molecular dynamics simulations of stacks of two-dimensional platelets immersed in a polymer melt were performed to investigate aspects of the polymer matrix that promote the formation of intercalated or exfoliated nanocomposite structures. Such factors include temperature, copolymer architecture, and blend composition. Increasing the polymer-sheet attractive interaction led to binding of the sheets, where individual beads simultaneously attract two neighboring sheets, thus kinetically blocking intercalation by occupying the perimeter of the affected gallery. Polymers with a small polymer-sheet attraction, but having a strongly attractive chain end (end-functionalized polymers) minimized the bonding of adjacent sheets. These systems exhibited some sheet sliding because a majority of the confined polymer beads only interacted weakly with adjacent sheets; however, the number density of intercalated polymer was low. Mixtures of end-functionalized and nonfunctionalized polymers, however, yielded better intercalation efficiency. For the mixed system, the reduced number of highly attractive beads provided sufficient interaction for intercalation to occur, enabling greater intercalation rates, less sheet-bridging, and incorporation of the nonfunctionalized polymers into the galleries. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3272–3284, 2003     

Effect of homopolymer matrix on diblock copolymer grafted nanoparticle conformation and potential of mean force: A molecular simulation study

We study the effect of homopolymer A or B matrix on the conformations and effective interactions of AB diblock copolymer grafted particles using coarse‐grained molecular dynamics simulations. In an A homopolymer matrix we observe patchy conformations within the AB diblock copolymer grafted layer, where the number of B patches is controlled by the A‐A attractive interaction strength. In a B homopolymer matrix the grafted particle takes on a core‐corona conformation, where the inner A block aggregates near the particle surface and the outer B block forms a corona that interacts with the B matrix. The potential of mean force (PMF) between two particles in an A homopolymer matrix has a long‐ranged attractive well with a minima at intermediate distances corresponding to the location of the outer B block patches. The PMF between two particles in a B homopolymer matrix has an attractive well at short interparticle distances corresponding to the size of the inner A block. We isolate the contribution of the homopolymer matrix on the PMF between the two diblock copolymer grafted particles, by deducting the PMF in the absence of a matrix, assuming the contributions of the grafted particle and matrix to the PMF to be additive. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 76–88     

Collapse‐expansion transition of elastic shell induced by grafted polymer chains

A coarse‐grained model for an elastic shell grafted with polymer chains is investigated by molecular dynamics methods. With increasing the number of grafted polymer chains (GPCs), it is found that the conformation of the shell undergoes from expansion to collapse and back to the expansion. By varying the density of the GPCs, the phase transition of the elastic shell can be successfully controlled at moderate bending energy of the shell and at moderate binding energy between the shell and GPCs. Furthermore, the self‐assembly structures of the GPCs are also affected by the elastic shell in certain conditions. In the case of a few GPCs on the shell, the chains tend to be adsorbed on the shell surface unfolded at high value of bending energy. However, when the bending energy is small, the chains can be folded several times easily. This may be an important step toward a deeper understanding of how to control the microstructure in the production of biocomposites. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Effect of particle agglomeration and interphase on the glass transition temperature of polymer nanocomposites

In this article, we utilize finite element modeling to investigate the effect of nanoparticle agglomeration on the glass transition temperature of polymer nanocomposites. The case of an attractive interaction between polymer and nanofiller is considered for which an interphase domain of gradient properties is developed. This model utilizes representative volume elements that are created and analyzed with varying degrees of nanoparticle clustering and length scale of interphase domain. The viscoelastic properties of the composites are studied using a statistical approach to account for variations due to the random nature of the microstructure. Results show that a monotonic increase in nanofiller clustering not only results in the loss of interphase volume but also obstructs the formation of a percolating interphase network in the nanocomposite. The combined impacts lead to a remarkable decrease of T_g enhancement of clustering nanofillers in comparison with a well‐dispersed configuration. Our simulation results provide qualitative support for experimental observations that clustering observed at high nanofiller concentrations negatively impacts the effects of the nanofiller on overall properties. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Heterogeneities in Polymer Structural and Dynamic Properties in Graphene and Graphene Oxide Nanocomposites: Molecular Dynamics Simulations

The effect of graphene (G) and graphene oxide (GO), used as the nanofiller in polymer nanocomposites (NC), on the structural and dynamic properties of polymer chains, has been studied by means of molecular dynamics (MD) simulations. Two polymers, i.e., poly(propylene) and poly(vinyl alcohol), are employed as matrices to cover a wider range of polymer–filler interactions. The local structural properties, e.g., density profile, average R _g, and end‐to‐end distance as well as dynamic properties, e.g., estimated translational and orientational relaxation times, of polymer chains are studied. In addition, the interaction energies are estimated between polymers and nanofillers for different hybrid systems using MD pullout simulations. Strong heterogeneities in polymer structural and dynamic properties have been observed such that chains are more oriented and exhibit slower dynamics in the vicinity of the nanofillers (G and GO) as compared to bulk. It is also found that the orientation of polymer chains at the interface is more influenced by the nanofiller in such a way that the more oriented polymer chains are observed in G‐based NC for both polymers. However, the immobilization of polymer chains at the interface proves to be very much dependent on the polymer–filler interactions.

     

Modeling the Viscoelastic Response of Suspension of Particles in Polymer Solution: The Effect of Polymer‐Particle Interactions

A conceptual model is proposed for the viscoelastic response of dilute polymer solutions containing well‐dispersed low volume fraction spherical particles. The equilibrium structure of the reversibly adsorbed polymer layer on the particle surface was characterized by a scaling theory. The dynamics of the polymer chains were studied by a Maxwell type kinetic model. At the limit of small particle size, our results show that the monomer‐filler energetic affinity, particle volume fraction and surface friction strongly affect the overall viscoelastic response of the filled solutions and lead to unusual viscoelastic properties that have been observed experimentally. These properties include a dramatic increase in shear viscosity, intense shear thinning, and solid‐like behavior at low frequency domains.

     

Filler size effects on the conductivity of polymer nanocomposites: Semiconductive phthalocyanine nanoparticles in epoxy matrices

Three Cobalt(III) phthalocyanine (Phthalcon) powders with different particle sizes and chemical compositions, but almost equal XRD spectra and powder conductivity were synthesized and used as conductive fillers in crosslinked epoxy matrices. Two of these Phthalcons are new compounds. The relation between the conductivity of the composites and the type and amount of filler used was determined. The influence of particle size and chemical composition on this relation appeared to be minimal. These composites had a percolation threshold of 0.9 vol % and a maximum volume conductivity of 10^?7 S/cm. Detailed analysis showed that the particle networks have very similar fractal structures and that they are likely to be formed by diffusion limited cluster‐cluster aggregation during processing. Evidence is presented that these particle networks are formed at an early stage of crosslinking and that the charge transfer between particles in the networks is neither limited by the Phthalcon particle size, nor by the presence of polymer matrix between the particles. The maximum volume conductivity of these composites is likely to be limited by the amount of filler used, the crystal structure defects on the particle surface, and the fractality and the imperfection of the particle networks. The impact of these findings on the conductivity of other polymer nanocomposites is discussed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1079–1093, 2008     

Modeling of Polymer Structure and Conformations in Polymer Nanocomposites from Atomistic to Mesoscale: A Review

Over the past two decades polymer nanocomposites have received tremendous interest from industry and academia due to their advanced properties comparative to polymer blends. Many computational studies have revealed that the macroscopic properties of polymer nanocomposites depend strongly on the microscopic polymer structure and conformations. In this article we review computer simulation studies of the fundamental problem of homopolymers structure and dimensions in nanocomposites containing bare or grafted spherical or rod nanoparticles. Experimentally, there is controversy over whether the addition of nanoparticles in a polymer matrix can perturb the polymer chains.     

Flow‐induced particle orientation and rheological properties of suspensions of organoclays in thermoplastic resins

The influence of nano‐scale particles on the viscoelastic properties of polymer suspensions is investigated. We have developed a simulation technique for the particle orientation and polymer conformation tensors to study various features of the suspensions. The nano‐particles are modeled as thin rigid oblate spheroid particles and the polymers as FENE‐P type viscoelastic and Newtonian fluid. Both interparticle and polymer‐particle interactions have been taken into account in our numerical computations. The nonlinear viscoelastic properties of nanocomposites of layered silicate particles in non‐Newtonian fluids are examined at the start‐up of shear flow and are interpreted using the model to examine the effects of model parameters as well as flow conditions on particle orientation, viscosity, and first normal stress difference of the suspensions. We have studied the microstructure of polymer‐clay nanocomposites using X‐ray diffraction (XRD) scattering and transmission electron microscopy (TEM). The rheology of these nanocomposites in step‐shear is shown to be fairly well predicted by the model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2003–2011, 2010     

Revisiting the dispersion mechanism of grafted nanoparticles in polymer matrix: a detailed molecular dynamics simulation

By focusing on the grafted nanoparticles (NPs) embedded in polymer melts, a detailed coarse-grained molecular dynamics simulation is adopted to investigate the effects of the grafting density, the length of the matrix and grafted chains on the dispersion of the NPs. We have employed visualization snapshots, radial distribution functions (RDFs), the interaction energy between NPs, the number of neighbor NPs, and the conformation of the brush chains to clearly analyze the dispersion state of the grafted NPs. Our simulated results generally indicate that the dispersion of the NPs is controlled by both the excluded volume of the grafted NPs and the interface between the brushes and the matrix. It is found that increasing grafting density or grafted chain length leads to better dispersion, owing to larger excluded volume; however, increasing the length of the matrix chains leads to aggregation of NPs, attributed to both a progressive loss of the interface between the brushes and the matrix and the overlap between brushes of different NPs, intrinsically driven by entropy. Meanwhile, it is found that there exists an optimum grafting density (σ(c)) for the dispersion of the NPs, which roughly obeys the following mathematical relation: σ(c) is proportional to N(m)(K)/N(g)(L), where K, L > 0 and N(m) and N(g) represent the length of the matrix and grafted chain length, respectively. Considering the practical situation that the grafted brushes and the matrix polymer are mostly not chemically identical, we also studied the effect of the compatibility between the brushes and the matrix polymer by taking into account the attraction between the grafted chains and the matrix chains. In general, our comprehensive simulation results are believed to guide the design and preparation of high-performance polymer nanocomposites with good or even tailored dispersion of NPs.     

On the Emergence of the Payne Effect in Polymer Melts Reinforced with Nanoparticles

This study presents a molecular model for the amplitude‐dependent dynamic moduli of polymer melts reinforced with nanoparticles. This study shows that intense strain‐thinning reported in experimental studies of polymer nanocomposites can be attributed to disentanglement of bulk polymer chains from those strongly adsorbed to the surface of nanoparticles. This flow‐induced relaxation is what is frequently termed as convective constraint release and is similar to the cohesive slip of polymer melt at solid interfaces.

     

“Click” synthesis of thermally stable au nanoparticles with highly grafted polymer shell and control of their behavior in polymer matrix

Thermally stable core–shell gold nanoparticles (Au NPs) with highly grafted polymer shells were synthesized by combining reversible addition‐fragmentation transfer (RAFT) polymerization and click chemistry of copper‐catalyzed azide‐alkyne cycloaddition (CuAAC). First, alkyne‐terminated poly(4‐benzylchloride‐b‐styrene) (alkyne‐PSCl‐b‐PS) was prepared from the alkyne‐terminated RAFT agent. Then, an alkyne‐PSCl‐b‐PS chain was coupled to azide‐functionalized Au NPs via the CuAAC reaction. Careful characterization using FT‐IR, UV–Vis, and TGA showed that PSCl‐b‐PS chains were successfully grafted onto the Au NP surface with high grafting density. Finally, azide groups were introduced to PSCl‐b‐PS chains on the Au NP surface to produce thermally stable Au NPs with crosslinkable polymer shell ( Au‐PSN₃‐b‐PS 1 ). As the control sample, PS‐b‐PSN₃‐coated Au NPs ( Au‐PSN₃‐b‐PS 2 ) were made by the conventional “grafting to” approach. The grafting density of polymer chains on Au‐PSN₃‐b‐PS 1 was found to be much higher than that on Au‐PSN₃‐b‐PS 2 . To demonstrate the importance of having the highly packed polymer shell on the nanoparticles, Au‐PSN₃‐b‐PS 1 particles were added into the PS and PS‐b‐poly(2‐vinylpyridine) matrix, respectively. Consequently, it was found that Au‐PSN₃‐b‐PS 1 nanoparticles were well dispersed in the PS matrix and PS‐b‐P2VP matrix without any aggregation even after annealing at 220 °C for 2 days. Our simple and powerful approach could be easily extended to design other core–shell inorganic nanoparticles. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Diblock copolymers as emulsifying agents in polymer blends: Influence of molecular weight,architecture, and chemical composition

Interfacial agents used in the compatibilization of immiscible polymer blends often consist of block copolymers containing at least one segment compatible with each of the two phases of the blend. This work examines the influence of the molecular weight, architecture, and chemical composition of the interfacial agent on its ability to emulsify a polymer blend. The system chosen is a blend containing 80% polystyrene and 20% ethylene-propylene rubber, compatibilized by diblock copolymers of poly(styrene-hydrogenated butadiene). The emulsification curve, which relates the dispersed phase particle size to the concentration of interfacial agent added to the system, was used as a tool to characterize the efficacy of the different interfacial agents. The observed behavior is similar to that of classical emulsions: a rapid drop in phase size at low concentrations of interfacial modifier, followed by a levelling off to an equilibrium diameter value once a “critical” concentration has been reached. For systems compatibilized by symmetrical diblocks (i.e., containing approximately 50% styrene by weight), the volume average particle diameter decreased from 2.7 μm for the unmodified system to about 0.4 μm once interfacial saturation is reached. The critical concentration for emulsification decreased with increasing interfacial agent molecular weight, due to the higher interfacial area occupied by longer molecules; however, this parameter did not affect the equilibrium particle diameter. The asymmetrical diblock copolymer (30% styrene) was found to be less effective than the symmetrical ones over the entire range of concentrations studied (5 to 35% modifier, based on the volume of the minor phase). Asymmetrical diblock copolymers would tend to form micelles, whereas symmetrical copolymers are less constrained at the interface. No significant difference was observed between the emulsifying capability of tapered and pure diblocks of similar composition and molecular weight. © 1996 John Wiley & Sons, Inc.     

Effect of Chain‐Length Dependence of Interaction Parameter on Spinodals for Polydisperse Polymer Blends

Summary: The chain‐length dependence of the Flory‐Huggins (FH) interaction parameter is introduced into the FH lattice theory for polydisperse polymer‐blend systems. The spinodals are calculated for the model polymer blends with different chain lengths and distributions. It is found that all the related variables, r_n, r_w, r_z, and chain‐length distribution, have effects on the spinodals for polydisperse polymer blends.

The spinodals at different chain lengths.     

Polymer complexes. LXXVIII. Synthesis and characterization of supramolecular uranyl polymer complexes: Determination of the bond lengths of uranyl ion in polymer complexes

The UO₂(II) polymer complexes (1–5) of azo dye ligands 5(4`‐derivatives phenylazo)‐8‐hydroxy‐7‐quinolinecarboxaldehyde (HL_x) were prepared and characterized by elemental analysis, ¹H NMR, IR spectra, thermal analysis and X‐ray diffraction analysis (XRD). The molecular geometrical structures and quantum chemical of the ligands (HL_x) and their tautomeric forms (D and G) were calculated. Molecular docking between the HL_x ligands and their tautomeric form with two receptors of the breast cancer (1JNX) and the prostate cancer (2Q7K) was discussed. From the histogram of the HOMO–LUMO energy gap (ΔE) and the estimated free energy of binding of the receptors of prostate cancer (2Q7K) and breast cancer (1JNX) for the ligands (HL_x), it is observed that the ΔE values of the ligands (HL_x) increases in the order HL₂ < HL₃ < HL₄ < HL₁ < HL₅. The electronic structures and coordination were determined from a framework for the modeling of the formed polymer complexes. From the IR spectra of the polymer complexes, the symmetric stretching frequency υ₃ values of UO₂²⁺ were used for the determination of the force constant (F_U‐O (in 10^?8 N/?)) and the bond length (R_U‐O (?)) of the U–O bond by using Wilson, G. F. matrix method, McGlynn & Badger's formula and El‐Sonbati equations. The plot of the bond distance r_U‐O (r₁, r₂, r₃, and r_t) vs. υ₃ was showed straight lines with increase in the value of υ₃ and decrease in r_U‐O.     

Polymer–nanoparticle interfacial interactions in polymer nanocomposites: Confinement effects on glass transition temperature and suppression of physical aging

The effects of confinement on glass transition temperature (T_g) and physical aging are measured in polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(2-vinyl pyridine) (P2VP) nanocomposites containing 10- to 15-nm-diameter silica nanospheres or 47-nm-diameter alumina nanospheres. Nanocomposites are made by spin coating films from sonicated solutions of polymer, nanofiller, and dye. The T_gs and physical aging rates are measured by fluorescence of trace levels of dye in the films. At 0.1–10 vol % nanofiller, T_g values can be enhanced or depressed relative to neat, bulk T_g (T_g,bulk) or invariant with nanofiller content. For alumina nanocomposites, T_g increases relative to T_g,bulk by as much as 16 K in P2VP, decreases by as much as 5 K in PMMA, and is invariant in PS. By analogy with thin polymer films, these results are explained by wetted P2VP–nanofiller interfaces with attractive interactions, nonwetted PMMA–nanofiller interfaces (free space at the interface), and wetted PS–nanofiller interfaces lacking attractive interactions, respectively. The presence of wetted or nonwetted interfaces is controlled by choice of solvent. For example, 0.1–0.6 vol % silica/PMMA nanocomposites exhibit T_g enhancements as large as 5 K or T_g reductions as large as 17 K relative to T_g,bulk when films are made from methyl ethyl ketone or acetic acid solutions, respectively. A factor of 17 reduction of physical aging rate relative to that of neat, bulk P2VP is demonstrated in a 4 vol % alumina/P2VP nanocomposite. This suggests that a strategy for achieving nonequilibrium, glassy polymeric systems that are stable or nearly stable to physical aging is to incorporate well-dispersed nanoparticles possessing attractive interfacial interactions with the polymer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2935–2943, 2006