Mobility of Spherical Probe Objects in Polymer Liquids

We use scaling theory to derive the time dependence of the mean-square displacement ?Δr(2)? of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (?Δr(2) (t)? ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (?Δr(2) (t)? ~ t(1/2)) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τ(e) of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τ(e)) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τ(rep). At longer times t > τ(rep), the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.     

Dynamics in atomistic simulations of phospholipid membranes: Nuclear magnetic resonance relaxation rates and lateral diffusion

It is shown that a long, near microsecond, atomistic simulation can shed some light upon the dynamical processes occurring in a lipid bilayer. The analysis focuses on reorientational dynamics of the chains and lateral diffusion of lipids. It is shown that the reorientational correlation functions exhibits an algebraic decay (rather than exponential) for several orders of magnitude in time. The calculated nuclear magnetic resonance relaxation rates agree with experiments for carbons at the C7 position while there are some differences for C3. Lateral diffusion can be divided into two stages. In a first stage occurring at short times, t<5 ns, the center of mass of the lipid moves due to conformational changes of the chains while the headgroup position remains relatively fixed. In this stage, the center of mass can move up to approximately 0.8 nm. The fitted short-time diffusion coefficient is D(1)=13 x 10(-7) cm(2) s(-1) On a longer time scale, the diffusion coefficient becomes D(2)=0.79 x 10(-7) cm(2) s(-1).     

Dynamics of polymers in a particle-based mesoscopic solvent

We study the dynamics of flexible polymer chains in solution by combining multiparticle-collision dynamics (MPCD), a mesoscale simulation method, and molecular-dynamics simulations. Polymers with and without excluded-volume interactions are considered. With an appropriate choice of the collision time step for the MPCD solvent, hydrodynamic interactions build up properly. For the center-of-mass diffusion coefficient, scaling with respect to polymer length is found to hold already for rather short chains. The center-of-mass velocity autocorrelation function displays a long-time tail which decays algebraically as (Dt)(-3/2) as a function of time t, where D is the diffusion coefficient. The analysis of the intramolecular dynamics in terms of Rouse modes yields excellent agreement between simulation data and results of the Zimm model for the mode-number dependence of the mode-amplitude correlation functions.     

Coarse grained model of diffusion in entangled bidisperse polymer melts

Chain diffusion is studied in mixtures of bidisperse linear polymers of same chemical identity by means of simulations. The two subpopulations are moderately to highly entangled, with the shorter chain length N(S), fulfilling N(S)N(e)> or =5. To this end, a coarse grained model calibrated to reproduce both the structure and dynamics of chains in monodisperse entangled melts is used [A. Rakshit and R. C. Picu, J. Chem. Phys. 125, 164907 (2006)]. Its performance in reproducing chain dynamics in a polydisperse melt is tested by extensively comparing the results with those obtained from an equivalent fine scale representation of the same system (a bead-spring model). The coarse grained model is used further to investigate the scaling of the diffusion coefficient with the length of the two types of chains and its dependence on the respective fractions. The model reproduces many features observed experimentally. For example, the diffusion coefficient of one of the chain types decreases with increasing the length of the other type chains. It is shown that, in this model, this effect is not linked to constraint release. When the matrix chains become sufficiently long, their length does not influence the diffusion coefficient of the short chains anymore. The diffusion coefficient of the short chains scales with their weight fraction in a manner consistent with experimental observations. In mixtures, the dynamics of the short chains is slower and that of the long chains is marginally faster than in their respective monodisperse melts.     

Evaluation of the dynamic properties of polymer latex particles interacting with quartz interface by evanescent wave dynamic light scattering

The diffusion behavior of polymer latex particles in dispersion near the quartz interface has been estimated by evanescent wave dynamic light scattering (EVDLS) technique. The diffusion coefficient of the particles was measured as a function of the distance between the particle and interface. The apparent diffusion coefficient estimated by EVDLS was small for particles near the interface and increased upon increasing the distance from the interface, and then saturated at a certain value which is close to the value expected for free-motion. The range of the distance over which diffusion was affected by interaction with the interface depended on the added salt concentration. This means that the diffusion of the particle is influenced by an electrostatic interaction between the particle and quartz interface in addition to the hydrodynamic effect near the wall. This range was found to be more than 800?nm at 0?M salt condition but about 400?nm at 10^-4 and 10^-3?M salt conditions. Hence it is appropriate to say that the hydrodynamic effect reaches up to 400?nm and the electrostatic effect is longer ranged, more than 800?nm, for the system studied here. The EVDLS technique is a very powerful tool for quantitative estimations of the dynamic behavior of the particle near the interface and for estimation of the range where the wall effect is dominant. EVDLS will give us an answer to the question of “where is the ‘interface’ and where is the ‘bulk’?”.     

The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h (h is the distance between two plates), until a basin occurs, and a universal h/〈R _g〉₀ dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain’s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.     

Novel distance dependence of diffusion constants in hyaluronan aqueous solution resulting from its characteristic nano-microstructure.

Material transports in hyaluronan (HA) aqueous solution were investigated applying two different techniques, i.e., pulsed field gradient NMR (PFG-NMR) and photochemical quenching, to the measurement of diffusion constants to show a sharp contrast resulting from the difference of the spectroscopic observation time while the same probe molecules were commonly used in two experiments. The value from PFG-NMR reflects the relatively long transport along which the majority of the molecules are retarded by the mesh structure of HA solution. In such inhomogeneous fluids, the observable diffusion constant should generally depend on the observation time and, i.e., the averaged distance of diffusion. Quantitative discussion, which compares the obtained characteristic distance of diffusion with the pore size, clarifies the role of the nano-microstructure of HA solution forming small pores surrounded by the polymer chain networks.     

Fluorescence recovery after photobleaching measurements of polymers in a surface forces apparatus

The surface forces apparatus has been combined with fluorescence recovery after photobleaching to measure translational diffusion of polymer confined between mica sheets. This article presents findings using polydimethylsiloxane with number‐average molecular weight M_n = 2200 g mol^?1, the chains end‐labeled with soluble fluorescent dye. Melts with thickness 10 nm display a translational diffusion coefficient (D) with a bulk component and a slower component assigned to surface diffusion. Reduction of thickness to 1.8 nm causes mobility to split into two populations—an immobile fraction (immobile on the time scale of 30–60 min) and a mobile fraction who's D slow only weakly with diminishing film thickness. However, when load causes the confining mica sheets to flatten, D of the mobile fraction drops by up to an additional order of magnitude, depending on the local pressure that squeezes on the polymer. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Dynamics of poly(L-lysine) in hyaluronic acid/poly(L-lysine) multilayer films studied by fluorescence recovery after pattern photobleaching

Poly( L-lysine) (PLL)/hyaluronic acid (HA) multilayers are films whose thickness increases exponentially with the number of deposition steps. Such a growth process was attributed to the diffusion, in and out of the whole film, of at least one of the polyelectrolytes constituting the film. In the case of PLL/HA, PLL is known to be the diffusing species. In order to better understand the growth mechanism of such films, it is of primary importance to well characterize the diffusion process of the polyelectrolytes in the multilayer. This process is studied here by fluorescence recovery after pattern photobleaching. We show that the diffusion behavior is different when we consider either PLL chains that are deposited on top of the film or PLL chains embedded in the film, even below only one HA layer. For chains that are embedded, we find two populations: a mobile one with a diffusion coefficient, D, of the order of 0.1 microm(2) x s(-1) and a population that appears immobile ( D < 0.001 microm(2) x s(-1)). For chains deposited on top of the multilayer, a third population appears which is rapidly diffusing ( D congruent with 1 microm(2) x s(-1)). These results confirm the validity of the model generally accepted for the exponential growth process and in particular the existence of up to three subgroups of PLL chains from the point of view of their diffusion coefficient.     

The effect of riboflavin-photoinduced degradation of alginate matrices on the diffusion of poly(oxyethylene) probes in the polymer network

The effect of irradiation, in the wavelength range of 310-800 nm, on the tracer diffusion of poly(oxyethylene) (POE) of different molecular weights embedded in various alginate matrices with the photosensitizer riboflavin (RF) present, has been investigated with the aid of pulsed field gradient spin-echo NMR (PGSE-NMR). Both alginate solutions of different polymer concentration were studied as well as corresponding acid gels of alginate produced by introduction of different amount of glucono-δ-lactone (GDL). In 2 wt.% alginate solutions, the values of the tracer diffusion coefficient suggest a strong obstruction effect as the probe molecular weight increases. Faster probe diffusion was observed for the irradiated samples, which indicates a photochemical scission of the polymer chains and the formation of a fragmented polymer network that facilitates the migration of the tracer chains. A semidilute alginate/RF solution was transformed into a gel by adding sufficient amount of GDL. GDL lowers the pH of the solution under the pK_a of alginate, favouring intermolecular associations and the evolution of a less homogeneous network with more open structure. Therefore, the POE chains were shown to diffuse faster in the acid gel matrix than in the corresponding more homogeneous alginate solutions. The photochemically induced cleavage again promoted faster migration of the probe chains in the irradiated samples. The probe diffusion of the eight-arm star-shaped POE sample revealed an augmented obstruction effect with increasing alginate concentration and higher values of the diffusion coefficient were found in gels. The evolution of a tighter network inhibits the diffusion of the probe molecules. At lower alginate concentrations the values of the tracer diffusion coefficients are higher for the irradiated samples than for the non-exposed systems.     

Monitoring Diffusion of Reptating Polymer Chains by a Direct Energy Transfer Method: A Monte Carlo Simulation

A kinetic Monte Carlo method was used to simulate the diffusion of reptating polymer chains across an interface. A time‐resolved fluorescence technique in conjunction with a direct energy transfer method was used to measure the extent of diffusion of dye‐labeled reptating polymer chains. The diffusion of donor‐ and acceptor‐labeled polymer chains between adjacent compartments was randomly generated. The fluorescence decay profiles of donor molecules were simulated at several diffusion steps to produce mixing of the polymer chains. Mixing ratios of donor‐ and acceptor‐labeled polymer chains in compartments were measured at various stages (snapshots) of diffusion. It was observed that for a given molecular weight, the average interpenetration contour length was found to be proportional to the mixing ratio. Monte Carlo analysis showed that the curvilinear diffusion coefficient is inversely proportional to the weight of polymer chains during diffusion.     

Monte Carlo study of defect fluctuations and reptation in polymer melts

Defect fluctuations in highly distorted polymer chains were simulated by Monte Carlo calculation. The NMR autocorrelation function was derived and described by the superposition of three exponential functions with time constants spread over two orders of magnitude. As a consequence of defect diffusion, longitudinal chain diffusion (reptation) can be expected in polymer melts. By simulating the mean-square displacement of a segment, it was found that after sufficiently long times, compared with defect density correlation times, a linear relationship holds fairly well. As a rule of thumb, it can be stated that the linear Einstein equation is valid for times much greater than 10³ mean step times in practical cases (chain length: several thousand segments, defect concentration: 10–20%), or, in other words, for mean-square displacements greater than a few diffusion step lengths. A long-time chain-diffusion coefficient depending on the molecular weight and on the defect concentration could be derived. Effects on the low-field NMR relaxation behavior are derived and discussed.     

Diffusive solvent dynamics in a polymer gel electrolyte studied by quasielastic neutron scattering

A quasielastic neutron scattering study has been performed on a polymer gel electrolyte consisting of lithium perchlorate dissolved in ethylene carbonate/propylene carbonate and stabilized with poly(methyl methacrylate). The dynamics of the solvent, which is crucial for the ion conduction in this system, was probed using the hydrogen/deuterium contrast variation method with nondeuterated solvent and a deuterated polymer matrix. Two relaxation processes of the solvent were studied in the 10-400 microeV range at different temperatures. From analysis of the momentum transfer dependence of the processes we conclude that the faster process ( approximately 100 microeV) is related to rotational diffusion of the solvent and the slower process ( approximately 10 microeV) to translational diffusion of the solvent. The translational diffusion is found to be similar to the diffusion in the corresponding liquid electrolyte at short distances, but geometrically constrained by the polymer matrix at distances beyond approximately 5 A. The study indicates that the hindered diffusion of the solvent on a length scale of the polymer network interchain distance ( approximately 5-20 A) is sufficient to explain the reduced macroscopic diffusivity and ion conductivity of the gel electrolyte compared to the liquid electrolyte.     

Pair diffusion, hydrodynamic interactions, and available volume in dense fluids

We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard sphere particles in a dense monodisperse fluid. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from molecular dynamics simulations. At distances exceeding ~3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with predictions from exact macroscopic hydrodynamic theory for large Brownian particles suspended in a solvent bath, as well as the Oseen approximation. However, the asymptotic 1/r distance dependence of D(r) associated with hydrodynamic effects emerges only after the pair distance dynamics has been followed for relatively long times, indicating non-negligible memory effects in the pair diffusion at short times. Deviations of the calculated D(r) from the hydrodynamic models at short distances r reflect the underlying many-body fluid structure, and are found to be correlated to differences in the local available volume. The procedure used here to determine the pair diffusion coefficients can also be used for single-particle diffusion in confinement with spherical symmetry.     

Computer Simulation of Polymer Diffusion Under External Electric Field

Molecular dynamics simulations were carried out to investigate the diffusion of polymer chains in solvent under an external electric field. Polyethylene‐like polymer and methyl chloride molecule were chosen as solute and solvent. The external DC electric field strength was varied from 10 to 50 (4.3×10⁸ V/m). Both polar and non‐polar polymer chains in polar and non‐polar solvents were investigated. The simulation shows that the center of mass diffusion coefficient of polymer is sensitive to the polarities of polymer and solvent, field strength, polymer concentration and the density of the system. Various factors that affect the diffusion constant of the polymer are discussed. The present simulation is consistent with the results from light scattering experiments.     

Diverse spreading behavior of binary polymer nanodroplets

Molecular dynamics simulations are used to study the spreading of binary polymer nanodroplets in a cylindrical geometry. The polymers, described by the bead-spring model, spread on a flat surface with a surface-coupled Langevin thermostat to mimic the effects of a corrugated surface. Each droplet consists of chains of length 10 or 100 monomers with approximately 350,000 monomers total. The qualitative features of the spreading dynamics are presented for differences in chain length, surface interaction strength, and composition. When the components of the droplet differ only in the surface interaction strength, the more strongly wetting component forms a monolayer film on the surface even when both materials are above or below the wetting transition. In the case where the only difference is the polymer chain length, the monolayer film beneath the droplet is composed of an equal amount of short chain and long chain monomers even when one component (the shorter chain length) is above the wetting transition and the other is not. The fraction of short and long chains in the precursor foot depends on whether both the short and the long chains are in the wetting regime. Diluting the concentration of the strongly wetting component in a mixture with a weakly wetting component decreases the rate of diffusion of the wetting material from the bulk to the surface and limits the spreading rate of the precursor foot, but the bulk spreading rate actually increases when both components are present. This may be due to the strongly wetting material pushing out the weakly wetting material as it moves toward the precursor foot.     

Dynamics of poly(p‐phenylene) ladder polymers in solution

Photon correlation spectroscopy in both polarized and depolarized geometry was employed to investigate the dynamics of a ribbon‐type polymer exhibiting good solubility. In dilute solution, the translational diffusion for all examined molecular weights has confirmed the picture of wormlike chains with rather short (∼ 7 nm) persistence length (Macromolecules 1997, 30, 273). In the semidilute regime, the total concentration fluctuations display, besides the fast dominant cooperative diffusion, a second slower diffusive process that exhibits weak concentration dependence and is not related to the self‐diffusion measured by pulse‐field‐gradient NMR. The concentration dependence of the cooperative and the self‐diffusion coefficient as well as of the zero‐shear viscosity cannot be consistently described by neither flexible nor stiff chain models. Presence of aggregates was revealed at high concentrations. Owing to the short persistence length, the rotational diffusion is too fast to be adequately investigated. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2211–2220, 1999     

Bifunctional acoustooptical cell of the sensor type for studying gas chemosorption by polymer films

Potentialities of the bifunctional cell of the sensor type, in which acoustoelectric (based on surface-acoustic waves) and optical (in the visible spectral region) measurements of ammonia chemosorption by thin films of a PDMS-based functional polymer may be simultaneously performed, have been demonstrated. It has been found that the gas diffusion coefficient associated with chemosorption and calculated from optical measurements (2.65 × 10^?11 cm²/s) differs from that obtained from acoustoelectric studies (4.16 × 10^?12 cm²/s). The diffusion coefficient determined from the acoustoelectric data presumably characterizes the propagation of structural relaxation of polymer chains from chemosorption sites into the polymer bulk.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Estimation of the kinetic characteristics of sorption of an organic ion on a heterogeneous crosslinked polymer sorbent within the framework of a bidisperse model

For the sorption of rubomycin, an antitumor athracycline-type antibiotic, on BDM-12 carboxyl-containing heterogeneous crosslinked polymer sorbent, it was shown that the measured time dependences of the extent of process are determined by two characteristic times: τ₁ (in the range of short times) and τ₂ (at long times). A phenomenological theory of the kinetics of sorption on the heterogeneous sorbent was developed on the basis of a biporous sorbent model. The dependences of the characteristic times τ₁ and τ₂ on the sorbent grain radius were obtained. It was concluded that the theory makes predictions in good agreement with experimental data and allows calculating the most important kinetic parameters of sorption of organic ions on polymer sorbents: the time of diffusion of the sorbate into microgranules, the diffusion coefficient of the sorbate in transport pores, the effective coefficient of the sorbate diffusion into the heterogeneous sorbent, etc.