Segmental dynamics of polymers in nanoscopic confinements,as probed by simulations of polymer/layered-silicate nanocomposites

In this paper we review molecular modeling investigations of polymer/layered-silicate intercalates, as model systems to explore polymers in nanoscopically confined spaces. The atomic-scale picture, as revealed by computer simulations, is presented in the context of salient results from a wide range of experimental techniques. This approach provides insights into how polymeric segmental dynamics are affected by severe geometric constraints. Focusing on intercalated systems, i.e. polystyrene (PS) in 2 nm wide slit-pores and polyethylene-oxide (PEO) in 1 nm wide slit-pores, a very rich picture for the segmental dynamics is unveiled, despite the topological constraints imposed by the confining solid surfaces. On a local scale, intercalated polymers exhibit a very wide distribution of segmental relaxation times (ranging from ultra-fast to ultra-slow, over a wide range of temperatures). In both cases (PS and PEO), the segmental relaxations originate from the confinement-induced local density variations. Additionally, where there exist special interactions between the polymer and the confining surfaces (e.g., PEO) more molecular mechanisms are identified.Received: 1 January 2003, Published online: 14 October 2003PACS: 83.10.Rs Computer simulation of molecular and particle dynamics - 81.07.Nb Molecular nanostructures - 81.07.Pr Organic-inorganic hybrid nanostructures     

Structure of a tethered polymer under flow using molecular dynamics and hybrid molecular-continuum simulations

We analyse the structure of a single polymer tethered to a solid surface undergoing a Couette flow. We study the problem using molecular dynamics (MD) and hybrid MD-continuum simulations, wherein the polymer and the surrounding solvent are treated via standard MD, and the solvent flow farther away from the polymer is solved by continuum fluid dynamics (CFD). The polymer represents a freely jointed chain (FJC) and is modelled by Lennard-Jones (LJ) beads interacting through the FENE potential. The solvent (modelled as a LJ fluid) and a weakly attractive wall are treated at the molecular level. At large shear rates the polymer becomes more elongated than predicted by existing theoretical scaling laws. Also, along the normal-to-wall direction the structure observed for the FJC is, surprisingly, very similar to that predicted for a semiflexible chain. Comparison with previous Brownian dynamics simulations (which exclude both solvent and wall potential) indicates that these effects are due to the polymer–solvent and polymer–wall interactions. The hybrid simulations are in perfect agreement with the MD simulations, showing no trace of finite size effects. Importantly, the extra cost required to couple the MD and CFD domains is negligible.     

Muon spin relaxation as a probe of molecular dynamics of organometallic compounds

LF‐Muon Spin Relaxation data are reported for the organometallic compounds Pb(C₆H₅)₄, (C₆H₆)Cr(CO)₃ and (C₅H₅)₂Ru. In each case the change in relaxation rate with temperature shows a peak analogous to the T_1 minimum in NMR. The activation parameters were calculated, and the mechanism of muon spin relaxation in the case of (C₆H₆)Cr(CO)₃ is shown to be the reorientation motion of the benzene ring. This revised version was published online in August 2006 with corrections to the Cover Date.     

Giant permittivity of three phase polymer nanocomposites obtained by modifying hybrid nanofillers with polyvinylpyrrolidone

In this work, the combination of graphene decorated with graphene quantum dots (G-D-GQDs) and barium titanate (BaTiO₃) nanoparticles filled poly (vinyledene fluoride) (PVDF) nanocomposites are prepared using solvent casting method. The modification of G-D-GQDs and BaTiO₃ nanoparticles with polyvinyl pyrrolidone (PVP) show finer dispersion in PVDF matrix as compared to unmodified G-D-GQDs and BaTiO₃ nanoparticles in PVDF matrix. XRD of PVDF nanocomposites shows the formation of α and β form of PVDF crystals. The incorporation of the combination of PVP modified BaTiO₃ nanoparticles and G-D-GQDs in PVDF matrix show a decrease in crystallization temperature (T_c), percent crystallinity (X_c) and increase in thermal stability as compared to unmodified PVDF/BaTiO₃/G-D-GQDs nanocomposites, due to interaction of PVP modified nanoparticles with PVDF. Further, the incorporation of the combination of 20 wt.% BaTiO₃ nanoparticles and 3 wt.% G-D-GQDs in PVDF matrix show a giant dielectric constant. The giant dielectric constant is achieved due to accumulation of more charges across conductor-insulator interface, more numbers of microcapacitor formed and enhanced interfacial compatibility between BaTiO₃/G-D-GQDs with PVDF through PVP. The loss tangent (tan δ) of PVP modified G-D-GQDs and BaTiO₃ nanoparticles and its PVDF nanocomposites is low due to lower leakage current, which make the material suitable for various applications.     

The twice-renormalized Rouse formalism of polymer dynamics: Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice-renormalized Rouse formalism, a refined version of Schweizer’s renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended to include the terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts (such as the reptation (tube) model or the polymer mode-mode coupling formalism), the predictions perfectly coincide with all the results of recent spin-lattice relaxation dispersion and diffusion experiments as well as with computer simulations. On the other hand, the twice-renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity is largely a manifestation of collective multichain modes. In the rigorous sense, no such multichain treatment has yet been established to our knowledge. The necessity to consider interchain cooperativity in any real comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions.     

Equivalence between polymer nanocomposites and thin polymer films: Effect of processing conditions and molecular origins of observed behavior

Recently we established a quantitative equivalence in thermomechanical properties between polystyrene-silica nanocomposites and planar freestanding polystyrene thin films. This equivalence was quantified by drawing a direct analogy between film thickness and an appropriate experimental particle spacing. Using these findings, here we unequivocally show that the glass transition process in confined geometries is controlled by the mean volume fraction of polymer that is affected by the presence of surfaces. Since separate signatures of the bulk and the surface layers are never found, we can clearly rule out any simple “two layer” model which postulates the existence of surfaces which are dynamically decoupled from the bulk. Rather, we argue that the modification of properties at the surfaces propagates into the bulk through a spatial gradient: macroscopic experimental techniques average over these gradients and yield a broadened signature relative to the bulk polymer. In a second aspect of this paper we focus on the role of processing conditions on the results obtained. We have developed a new method of processing the nanocomposites which results in a better dispersion of the nanoparticles in the matrix. However, these samples did not show the unique glass transition behavior seen in the first set of nanocomposites discussed above. This indicates that processing conditions can profoundly affect the nature of the particle-polymer interface which controls the macroscopic behavior of these important systems.     

Gradient of molecular dynamics at the glass transition of PETg-Montmorillonite nanocomposites

Temperature Modulated Differential Scanning Calorimetry (TMDSC) is used to estimate Cooperative Rearranging Region (CRR) average sizes for polymer/clay nanocomposites, obtained by mixing polyethylene 1,4-cyclohexylenedimethylene terephthalate glycol (PETg) filled and organically modified nanoclay (C15A) following a master-batch process. Two different basal distances are obtained. It is shown that the greater the basal distance and the nanofiller content, the lower the heat capacity step at the glass transition temperature ΔCp(T_g), and the lower the CRR volume. It is also shown that the evolution of the CRR volume is consistent with the evolution of the fragility index obtained by DSC and Broadband Dielectric Spectroscopy (BDS) when the nanofiller content changes. The fragility index and the CRR size decreases can be correlated to nanofiller presence, hindering the molecular movements. From the Vollenberg and Heikens [34] approach, this behaviour can also be interpreted through the existence of an interfacial bilayer. This interfacial bilayer is composed by a zone, which is next to the nanofiller, with a density higher than the matrix one, followed by a more expanded zone with a density lower than the matrix one.     

A perturbation-variational theory for molecular fluid interphases in the presence of an electric field

The perturbation-variational theory of Tarazona and Navascués is extended to analyse the effect of the presence of an electric field in the interphase. Molecular orientation in the interphase of polar fluids is found at first order. Different electrostatic surface properties have been analysed, including the surface polarizability and surface susceptibility. Numerical results for carbon monoxide are presented.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

Role of surface ligands in nanoparticle permeation through a model membrane: a coarse-grained molecular dynamics simulations study

How nanoparticles interact with biological membranes is of significant importance in determining the toxicity of nanoparticles as well as their potential applications in phototherapy, imaging and gene/drug delivery. It has been shown that such interactions are often determined by nanoparticle physicochemical factors such as size, shape, hydrophobicity and surface charge density. Surface modification of the nanoparticle offers the possibility of creating site-specific carriers for both drug delivery and diagnostic purposes. In this work, we use coarse-grained molecular dynamic simulations to explore the permeation characteristics of ligand-coated nanoparticles through a model membrane. We compare permeation behaviors of ligand-coated nanoparticles with bare nanoparticles to provide insights into how the ligands affect the permeation process. A series of simulations is carried out to validate a coarse-grained model for nanoparticles and a lipid membrane system. The minimum driving force for nanoparticles to penetrate the membrane and the mechanism of nanoparticle–membrane interaction were investigated. The potential of the mean force profile, nanoparticle velocity profile, force profile and density profiles (planar and radial) were obtained to explore the nanoparticle permeation process. The structural properties of both nanoparticles and lipid membrane during the permeation, which are of considerable fundamental interest, are also studied in our work. The findings described in our work will lead to a better understanding of nanoparticle–lipid membrane interactions and cell cytotoxicity and help develop more efficient nanocarrier systems for intracellular delivery of therapeutics.     

Influence of line defects on relaxation properties of graphene: A molecular dynamics study

The relaxation properties of single layer graphene sheets containing line defects were investigated using molecular dynamics simulation with AIROBE bond-order interatomic potential. The dynamic evolution of graphene sheets during relaxation condition was analyzed. The simulation results show that the single layer graphene sheets are not perfectly flat in an ideal state, and the graphene sheet shows a significant corrugations at the verge of sheet. The graphene sheet is bent with the line defects at the end of the sheet, and the extent of this bend also increases with the increase of the defect number. Furthemore, the graphene sheet transforms into a paraboloid with the line defects at the middle of the sheet.     

Spinodal decomposition of polymer solutions: molecular dynamics simulations of the two-dimensional case

As a generic model system for phase separation in polymer solutions, a coarse-grained model for hexadecane/carbon dioxide mixtures has been studied in two-dimensional geometry. Both the phase diagram in equilibrium (obtained from a finite size scaling analysis of Monte Carlo data) and the kinetics of state changes caused by pressure jumps (studied by large scale molecular dynamics simulations) are presented. The results are compared to previous work where the same model was studied in three-dimensional geometry and under confinement in slit geometry. For deep quenches the characteristic length scale ?(t) of the formed domains grows with time t according to a power law close to [Formula: see text]. Since in this problem both the polymer density ρ(p) and the solvent density ρ(s) matter, the time evolution of the density distribution P(L)(ρ(p),ρ(s),t) in L × L subboxes of the system is also analyzed. It is found that in the first stage of phase separation the system separates locally into low density carbon dioxide regions that contain no polymers and regions of high density polymer melt that are supersaturated with this solvent. The further coarsening proceeds via the growth of domains of rather irregular shapes. A brief comparison of our findings with results of other models is given.     

Hot electron relaxation in one-dimensional models: exact polaron dynamics versus relaxation in the presence of a Fermi sea

We present the exact solution for the time evolution of the electron and phonon momentum distribution for a one-dimensional polaron model with alinear electronic energy dispersion. The electron momentum distribution is shown to obey aMarkovian quantum kinetic equation. Numerical results for the polaron model are compared to the corresponding exact results, when the negative momentum states are filled in the initial state. The presence of this Fermi sea modifies the dynamics except in the short time regime. The different, long time dynamics might show up in comparison of hot electron relaxation of undoped and doped semiconductors.     

Hot electron relaxation in one-dimensional models: exact polaron dynamics versus relaxation in the presence of a Fermi sea

We present the exact solution for the time evolution of the electron and phonon momentum distribution for a one-dimensional polaron model with alinear electronic energy dispersion. The electron momentum distribution is shown to obey aMarkovian quantum kinetic equation. Numerical results for the polaron model are compared to the corresponding exact results, when the negative momentum states are filled in the initial state. The presence of this Fermi sea modifies the dynamics except in the short time regime. The different, long time dynamics might show up in comparison of hot electron relaxation of undoped and doped semiconductors.     

Glass transitions and dynamics in thin polymer films: dielectric relaxation of thin films of polystyrene

The glass transition temperature T(g) and the temperature T(alpha) corresponding to the peak in the dielectric loss due to the alpha process have been simultaneously determined as functions of film thickness d through dielectric measurements for polystyrene thin films supported on glass substrate. The dielectric loss peaks have also been investigated as functions of frequency for a given temperature. A decrease in T(g) was observed with decreasing film thickness, while T(alpha) was found to remain almost constant for d>d(c) and to decrease drastically with decreasing d for d相似文献   

Molecular origin of shear thickening in transient polymer networks: A molecular dynamics study

This paper proposes a simple model of transient networks of telechelic associating polymers for molecular simulations and reports the main results obtained by molecular dynamics on the rheological properties of the transient networks. The steady shear viscosity obtained by the non-equilibrium molecular dynamics simulation exhibits shear thickening at moderate shear rates and shear thinning at larger shear rates. The behavior is similar to that observed in experiments of telechelic associating polymers. By analyzing the distribution function of the end-to-end vector of bridge chains as a function of the shear rate, we find that shear thickening is mainly caused by the stress from the bridge chains highly stretched by shear flow. We also find that fracture of the transient network occurs in the shear-thinning regime at high shear rates.     

Predicting absorption and dispersion in acoustics by direct simulation Monte Carlo: Quantum and classical models for molecular relaxation

In the current study, real gas effects in the propagation of sound waves are simulated using the direct simulation Monte Carlo method for a wide range of frequencies. This particle method allows for treatment of acoustic phenomena at high Knudsen numbers, corresponding to low densities and a high ratio of the molecular mean free path to wavelength. Different methods to model the internal degrees of freedom of diatomic molecules and the exchange of translational, rotational and vibrational energies in collisions are employed in the current simulations of a diatomic gas. One of these methods is the fully classical rigid-rotor/harmonic-oscillator model for rotation and vibration. A second method takes into account the discrete quantum energy levels for vibration with the closely spaced rotational levels classically treated. This method gives a more realistic representation of the internal structure of diatomic and polyatomic molecules. Applications of these methods are investigated in diatomic nitrogen gas in order to study the propagation of sound and its attenuation and dispersion along with their dependence on temperature. With the direct simulation method, significant deviations from continuum predictions are also observed for high Knudsen number flows.     

Stochasticity from deterministic dynamics: an explicit example of generation of Markovian strings

Markov chains are used to characterize a Dynamical system after it has reached the chaotic regime when certain external parameters have passed specific critical values. For a quantitative treatment of this stochastic behavior one needs an invariant measure. This measure then depends on the external parameters. We propose an emperical method to construct from first principles an invariant measure for the particular case of the triangular map.