Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO₂ in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO₂ pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2397–2408, 1997     

Simulations of the untying of molecular friction knots between individual polymer strands

The dynamics of molecular knots is implicated in a broad range of phenomena, from DNA replication to relaxation of polymer melts. Motivated by the recent experiments, in which biopolymer knots have been observed and manipulated at a single-molecule level, we have used computer simulations to study the dynamics of "friction knots" joining individual polymer strands. A friction knot splicing two ropes becomes jammed when the ropes are pulled apart. In contrast, molecular friction knots eventually become undone by thermal motion. We show that depending on the knot type and on the polymer structure, a microscopic friction knot can be strong (the time tau the knot stays tied increases with the force F applied to separate the strands) or weak (tau decreases with increasing F). The strong knot behavior is a microscopic analog of macroscopic knot jamming. We further describe a simple model explaining these behaviors.     

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.     

Single‐Molecule Detection Reveals Knot Sliding in TrmD Denaturation

An increasing number of proteins are found to contain a knot in their polypeptide chain. Although some studies have looked into the folding mechanism of knotted proteins, why and how these complex topologies form are still far from being fully answered. Moreover, no experimental information about how the knot moves during the protein‐folding process is available. Herein, by combining single‐molecule fluorescence resonance energy transfer (smFRET) experiments with molecular dynamics (MD) simulations, we performed a detailed study to characterize the knot in the denatured state of TrmD, a knotted tRNA (guanosine‐1) methyltransferase from Escherichia coli, as a model system. We found that the knot still existed in the unfolded state of TrmD, consistent with the results for two other knotted proteins, YibK and YbeA. More interestingly, both smFRET experiments and MD simulations revealed that the knot slid towards the C‐terminal during the unfolding process, which could be explained by the relatively strong interactions between the β‐sheet core at the N terminal of the native knot region. The size of the knot in the unfolded state is not larger than that in the native state. In addition, the knot slid in a “downhill” mode with simultaneous chain collapse in the denatured state.     

Mutual diffusion and thermodynamics in the blends of polystyrene and tetramethylbisphenol-A polycarbonate

A study was made of miscible polymer blends of deuterated polystyrene (d-PS) and tetramethylbisphenol-A polycarbonate (TMPC). The Flory interaction parameter χ was obtained from the relation between mutual and tracer diffusion coefficients, D? and D^*, which were measured by forward recoil spectrometry. The temperature dependence of diffusion at PS weight fractions ω of 0.25 and 0.5, and the composition dependence at temperatures 45°C above the glass transition temperature, T_g, were investigated. A stronger dependence of χ on both temperature (at ω = 0.5) and composition was observed in comparison with other miscible binary polymer blends involving PS. Analysis using the generalized lattice-fluid model of Sanchez and Balazs¹ showed that the incorporation of a significant specific interaction is needed to explain the temperature dependence of χ. The diffusion coefficients obtained in the one-phase region were extrapolated to the two-phase region, and these were compared with the effective diffusion coefficient extracted from phase separation dynamics measured by light scattering.² A significant discrepancy between the extrapolated and effective diffusion coefficients was observed. © 1995 John Wiley & Sons, Inc.     

Temperature dependence of exciton diffusion in conjugated polymers

The temperature dependence of the exciton dynamics in a conjugated polymer is studied using time-resolved spectroscopy. Photoluminescence decays were measured in heterostructured samples containing a sharp polymer-fullerene interface, which acts as an exciton quenching wall. Using a 1D diffusion model, the exciton diffusion length and diffusion coefficient were extracted in the temperature range of 4-293 K. The exciton dynamics reveal two temperature regimes: in the range of 4-150 K, the exciton diffusion length (coefficient) of approximately 3 nm (approximately 1.5 x 10 (-4) cm2/s) is nearly temperature independent. Increasing the temperature up to 293 K leads to a gradual growth up to 4.5 nm (approximately 3.2 x 10 (-4) cm2/ s). This demonstrates that exciton diffusion in conjugated polymers is governed by two processes: an initial downhill migration toward lower energy states in the inhomogenously broadened density of states, followed by temperature activated hopping. The latter process is switched off below 150 K.     

Characteristic behavior of short-term dynamics in reorientation for Gay-Berne particles near the nematic-isotropic phase transition temperature

A specific transition behavior was found in the tumbling motion near the nematic-isotropic phase boundary using molecular dynamics simulations of the Gay-Berne mesogenic model under isobaric conditions at a reduced pressure P* of 2.0. The relaxation time for the motion obtained from the second-rank orientational time correlation function and the rotational diffusion coefficient showed a clear jump at the nematic-isotropic phase transition temperature. Regardless of the temperature dependence of the relaxation time, the change in the rotational diffusion coefficient evaluated from the orientational order parameters and the relaxation time agreed qualitatively with that of real mesogens. The rotational viscosity coefficients gamma(1) and gamma(2) were obtained from the simulation data for the relaxation time for the short-term dynamics and for the rotational diffusion coefficients. gamma(1) was proportional to (2), where is the second-rank orientational parameter. Furthermore, the rotational behavior of the model was compared with that of the Debye approximation in the isotropic phase.     

The concentration dependence of the diffusion and permeability in a homogeneous membrane

For the sorption and diffusion coefficient dependence on the concentration of the penetrant the transport properties of a homogeneous medium are calculated. The diffusion current is assumed to be proportional to the negative gradient of the chemical potential. This is in contrast with the first Fick's law that assumes this current to be proportional to the negative gradient of the concentration of the penetrant. The difference between the two cases depends on the concentration dependence of the sorption coefficient. In a homogeneous membrane the chemical potential formulation leads to an equation which is very similar to the Fickian expression. The apparent diffusion coefficient, however, depends not onlly on the transport resistance but also on the deviation of the sorption coefficient from constancy.     

Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献   

Counterion associative behavior with flexible polyelectrolytes

At low ionic strength, organic counterions dress a flexible charged polymer as measured directly by small-angle neutron scattering and neutron spin-echo spectroscopy. This dressed state, quantified by the concentration dependence of the static correlation length, illustrates the polymer-counterion coupled nature on the nanometer length scale. The counterions, made visible by selective hydrogen and deuterium labeling, undress from the polymeric template by addition of sodium chloride. The addition of this electrolyte leads to two effects: increased Debye electrostatic screening and decoupled organic counterion-polymer correlations. Neutron spin-echo spectroscopy measures a slowing down of the effective diffusion coefficient of the labeled counterions at the length scale of 8 nm, the static correlation length, indicating the nanosecond counterion dynamics mimics the polymer. These experiments, performed with semidilute solutions of tetramethylammonium poly(styrene sulfonate) [(h-TMA(+)) d-PSS], apply to relevant biopolymers including single and double stranded DNA and unfolded proteins, which undergo orchestrated dynamics of counterions and chain segments to fold, unfold, and assemble.     

Comparison of kinetic Monte Carlo and molecular dynamics simulations of diffusion in a model glass former

We present results from kinetic Monte Carlo (KMC) simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the "inherent structure entropy." The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.     

Influence of the Electrolyte Film Thickness on Charge Dynamics of Ionic Liquids in Ionic Electroactive Devices

Developing advanced ionic electroactive devices such as ionic actuators and supercapacitors requires the understanding of ionic diffusion and drifting processes, which depend on the distances over which the ions travel, in these systems. The charge dynamics of [C(4)mim][PF(6)] ionic liquid films and Aquivion membranes with 40 wt% [C(2)mim][TfO] were investigated over a broad film thickness (d) range. It was found that the double layer charging time τ(DL) follows the classic model τ(DL) = λ(D)d/(2D) very well, where D is the diffusion coefficient and λ(D) the Debye length. In the longer time regimes (t ? τ(DL)) where diffusion dominates, the charge dynamics become voltage dependent. For low applied voltage, the later stage charge process seems to follow the d(2) dependence. However, at high voltages (> 0.5 V) in which significant device responses occur, the charging process does not show d(2) dependence so that τ(diff) = d(2)/(4D), corresponding to the ion diffusion from the bulk region, was not observed.     

Studies of translational diffusion in the smectic A phase of a Gay-Berne mesogen using molecular dynamics computer simulation

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.     

Atomistic molecular modeling of the effect of chromophore concentration on the electro-optic coefficient in nonlinear optical polymers

We employ fully atomistic molecular modeling to investigate the concentration dependence of the electro-optic coefficient of two guest-host polymer composites. Using classical molecular dynamics, we record the time-evolution of the guest-host system under the application of an external electric field. Through analysis of the orientation of the nonlinear optical chromophores in the guest-host composite with respect to the direction of the external electric field, we calculate the orientational parameter N < cos(3)theta >, with N being the number density of chromophores in the composite. This parameter is directly proportional to the electro-optic coefficient. We find agreement between the concentration dependence of the electro-optic coefficient calculated through our simulation and that from experimental data and also from Monte Carlo models.     

Gas diffusion in partially crystalline polymers part I: Concentration dependence

In this work, a phenomenological model for the gas diffusion in partially crystalline polymers using differential effective medium theory is presented. By making an analogy with the power law known as Archie's law which relates the d.c. conductivity of a brine saturated porous rock to its porosity; we show that gas diffusion through semicrystalline polymers can be described in a similar way. It is assumed that the diffusion coefficient in the crystalline region is zero, while in the amorphous region it is given by a free volume model, and an effective diffusion coefficient D^eff, is obtained using the mentioned analogy. The variation of D^eff upon concentration is analyzed through its free volume dependence. The crystallinity dependence is considered through an average chain immobilization factor 〈β〉 which is explicitely derived. Finally, the results of this model are compared with experimental data given by Kreituss and Frisch, obtaining a good agreement. © 1996 John Wiley & Sons, Inc.     

Enhancement of Na+ diffusion in a bicontinuous cubic phase by the ionophore monensin

Pulsed field gradient spin-echo NMR diffusion and relaxation measurements were used to investigate how the Na+ ionophore monensin affected the dynamics of sodium ions in a Myverol 18-99/saline bicontinuous Ia3d cubic phase (BCP). The monensin Na+ binding number was estimated from 23Na line widths to be between 3 and 6. The dependence of the apparent Na+ diffusion coefficient on the concentration of monensin revealed monensin-induced Na+ transport. At high monensin concentrations, the enhancement of D(Na+) was offset by Na+-monensin binding. The greatest enhancement was measured at short diffusion times (delta < or = 5 ms), which we explain in terms of the bicontinuous topology of the cubic phase and a combination of tortuosity and bilayer permeability effects. We also propose numerical simulations which would enable the separation of the two effects. To our knowledge, this is the first study of ionophore-mediated cation diffusion in a bicontinuous cubic phase. The approach could be used to study the dynamics of hydrophilic species in the aqueous channels of BCPs and similar structures, as well as to measure the ion-transporting efficiency of ionophores.     

Atomistic simulation of lipid and DiI dynamics in membrane bilayers under tension

Membrane tension modulates cellular processes by initiating changes in the dynamics of its molecular constituents. To quantify the precise relationship between tension, structural properties of the membrane, and the dynamics of lipids and a lipophilic reporter dye, we performed atomistic molecular dynamics (MD) simulations of DiI-labeled dipalmitoylphosphatidylcholine (DPPC) lipid bilayers under physiological lateral tensions ranging from -2.6 mN m(-1) to 15.9 mN m(-1). Simulations showed that the bilayer thickness decreased linearly with tension consistent with volume-incompressibility, and this thinning was facilitated by a significant increase in acyl chain interdigitation at the bilayer midplane and spreading of the acyl chains. Tension caused a significant drop in the bilayer's peak electrostatic potential, which correlated with the strong reordering of water and lipid dipoles. For the low tension regime, the DPPC lateral diffusion coefficient increased with increasing tension in accordance with free-area theory. For larger tensions, free area theory broke down due to tension-induced changes in molecular shape and friction. Simulated DiI rotational and lateral diffusion coefficients were lower than those of DPPC but increased with tension in a manner similar to DPPC. Direct correlation of membrane order and viscosity near the DiI chromophore, which was just under the DPPC headgroup, indicated that measured DiI fluorescence lifetime, which is reported to decrease with decreasing lipid order, is likely to be a good reporter of tension-induced decreases in lipid headgroup viscosity. Together, these results offer new molecular-level insights into membrane tension-related mechanotransduction and into the utility of DiI in characterizing tension-induced changes in lipid packing.     

Three-dimensional Brownian diffusion of rod-like macromolecules in the presence of randomly distributed spherical obstacles: molecular dynamics simulation

Brownian diffusion of rod-like polymers in the presence of randomly distributed spherical obstacles is studied using molecular dynamics simulations. It is observed that dependence of the reduced diffusion coefficient of these macromolecules on the available volume fraction can be described reasonably by a power law function. Despite the case of obstructed diffusion of flexible polymers in which reduced diffusion coefficient has a weak dependence on the polymer length, this dependence is noticeably strong in the case of rod-like polymers. Diffusion of these macromolecules in the presence of obstacles is observed that is anomalous at short time scales and normal at long times. Duration time of the anomalous diffusion regime is found that increases very rapidly with increasing both the polymer length and the obstructed volume fraction. Dynamics of diffusion of these polymers is observed that crosses over from Rouse to reptation type with increasing the density of obstacles.     

Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed.     

The temperature dependence of the surface tension of monatomic liquids and the boiling transition

We have reviewed recent model theories of the surface tension and examined the data on the temperature dependence of the surface tension of elemental liquids. From this, we have been able to show that the surface tension of these liquids vary linearly with temperature with the linear coefficient being related to both the transition temperatures at melting and at boiling. We use this to show that the boiling transition temperature may be expressed in a form which was previously proposed by us in a general phenomenological theory of phase transitions involving quasi-particles.