Probability of knots in a polymer ring

We generate equilibrium configurations of a ring polymer in an infinite space, or confined to the interior of a sphere. Using a new algorithm, the a priori probability for the occurence of a knot is determined numerically. The results are compatible with power laws and scaling laws of striking simplicity.     

Dynamics of a polymer chain confined in a membrane

We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free-membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical structure factor. For large polymer size, both quantities show Zimm-like behavior in the free-membrane case, whereas they are Rouse-like for the sandwiched membrane geometry. We use the scaling argument to discuss the effect of excluded-volume interactions on the polymer relaxation time.     

Dynamics of a tethered polymer in shear flow

The dynamics of a single polymer tethered to a solid surface in a shear flow was observed using fluorescently labeled DNA chains. Dramatic shear enhanced temporal fluctuations in the chain extension were observed. The rate of these fluctuations initially decreased for increasing shear rate gamma; and increased above a critical gamma;. Simulations revealed that these anomalous dynamics arise from a continual recirculating motion of the chain or cyclic dynamics. These dynamics arise from a coupling of the chain velocity in the flow direction to thermally driven fluctuations of the chain in the shear gradient direction.     

Smoothening transition of a two-dimensional pressurized polymer ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, p_c ∼ N^-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N². The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which 〈A〉 ∼ N^3/2. For p ≫ p_c we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.     

Kinetics of water flow through a polymer gel

The water flow through the poly(acrylamide) gel under a constant water pressure is measured by newly designed apparatus. The Young modulus and Poisson’s ratio of the rod shape gels are measured by the uni-axial elongation experiments, which determine the longitudinal modulus independently from the water flow experiments. The time evolution of the water flow in the dilute gel is calculated based on the collective diffusion model of the polymer network coupled with the friction between the polymer network and the water. The calculated results are compared with the time evolution of the flow experiments, and the values of the longitudinal modulus and the friction coefficient are estimated. The estimated values are consistent with the results of our mechanical-response experiments and the light scattering experiments reported previously. We find that the time evolution of the water flow is well described by a single characteristic relaxation time predicted by our model for dilute gels.     

Dynamics of polaron in a polymer chain with impurities

In a polymer chain, an extra electron or hole distorts the chain to form a charged polaron, which is the charge carrier being responsible for conductivity. When an intermediate-strength electric field is applied, the polaron will be accelerated for a short time and then move at a constant velocity. The dynamical process of polaron in a polymer chain with impurities is simulated within a non-adiabatic evolution method, in which the electron wave function is described by the time-dependent Schrödinger equation while the polymer lattice is treated classically by a Newtonian equation of motion. We have considered two kinds of dynamical processes, one is the field-induced depinning of a charged polaron, which is initially bound by an attractive impurity; and the other is the scattering of a polaron from an impurity. In the former process, the charged polaron will depart from the attractive impurity only for the applied field with strength over a threshold, otherwise, the polaron will oscillate around the impurity. In the latter process, the charged polaron moves through the impurity in the presence of an electric field while it will be bounced back for a repulsive impurity or trapped to oscillate around an attractive impurity in the case that the applied electric field is weak and just be present for the polaron acceleration.Received: 4 June 2004, Published online: 14 December 2004PACS: 71.38.-k Polarons and electron-phonon interactions - 72.80.Le Polymers; organic compounds (including organic semiconductors)     

A semiflexible polymer ring acting as a nano-propeller

The dynamics of a rotating elastic nano-ring driven in a viscous fluid by an externally applied torque about a specific axis is studied using elasto-hydrodynamic simulations. We show that a helical deformation of the ring filament is excited, and that this leads to directed propulsion which is independent of the direction of rotation. It is found that the propulsive force and efficiency initially increase as the torque is increased, and then decrease discontinuously at a buckling transition at a critical torque. This unique propulsive behavior at the shape transition arises due to its specific geometry, i.e., circularity of an elastic filament. The implications of the behavior for artificial microscopic devices are discussed.     

Fluctuating semiflexible polymer ribbon constrained to a ring

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.     

Equilibrium ring formation in polymer solutions

This paper delivers a flexible formalism for handling equilibrium ring formation. Based on graphical models of polymerization, it includes as special cases the Flory-StockmayerRA _f model, the FloryA _f RB _g model, and Gordon's branching process formalism. When simple ring formation occurs in equireactive systems, it also includes the Jacobson-StockmayerRA ₂ and HoeveRA _f models. The formalism is built from first principles in statistical mechanics and all assumptions are clearly stated. All parameters are given in terms of thermodynamic variables. With ring weights generalizing the Jacobson-Stockmayer Gaussian random walk, the formalism yields results for branchingRA _f ,A _f RB _g , andRA _f -RB _g polymer models. Equireactivity then gives explicit solutions. The equireactiveRA _f -RB _g model compares favorably with data from gel-point vs. dilution experiments. With the exception of the Spanning Tree Approximation, graphical models of polymerization suffer from combinations of the following defects: equireactivity assumptions, restrictions to one type of monomer or bond, absence of rings, or absence of fused rings. This paper provides a promising exact approach to handling all of these problems simultaneously.     

Ultrasonic absorption in polymer gel dosimeters

Ultrasonic absorption in polymer gel dosimeters was investigated. An ultrasonic interferometer was used to study the frequency (f) dependence of the absorption coefficient (alpha) in a polyacrylamide gel dosimeter (PAG) in the frequency range 5-20 MHz. The frequency dependence of ultrasonic absorption deviated from that of an ideal viscous fluid. The presence of relaxation mechanisms was evidenced by the frequency dependence of alpha/f(2) and the dispersion in ultrasonic velocity. It was concluded that absorption in polymer gel dosimeters is due to a number of relaxation processes which may include polymer-solvent interactions as well as relaxation due to motion of polymer side groups.The dependence of ultrasonic absorption on absorbed dose and formulation was also investigated in polymer gel dosimeters as a function of pH and chemical composition. Changes in dosimeter pH and chemical composition resulted in a variation in ultrasonic dose response curves. The observed dependence on pH was considered to be due to pH induced modifications in the radiation yield while changes in chemical composition resulted in differences in polymerisation kinetics.     

Dynamics of a polymer chain in an array of obstacles

On the basis of the model “polymer chain in an array of obstacles” the influence of the topology effects on the dynamics of concentrated polymer systems is investigated theoretically. The 1/z-expansion (where z is the coordinational number of the lattice of obstacles) is proposed for this problem. By means of this expansion the diffusion coefficient of a linear unclosed polymer chain is calculated. The equilibrium properties of linear closed chain (i.e. ring) unentangled with either of the edges of the lattice are investigated in detail. In particular, it is shown that the diffusion coefficient D of the center of mass of closed chain consisting of N links is proportional to N^−5/2.     

Bacto agar-based gel polymer electrolyte

The biopolymer of a Bacto agar-based gel polymer electrolyte (GPE) was prepared by addition of NaI and I₂ as redox couple. The prepared GPE was characterized using impedance spectroscopy and X-ray diffraction (XRD) in order to determine its electrical and structural properties, respectively. An optimized ionic conductivity of 12.41 × 10⁻⁴ S cm⁻¹ was achieved for the samples containing 1.6 M NaI and 50 μL I₂. Meanwhile, XRD revealed that the addition of NaI and I₂ altered agar properties and formed an amorphous structure. Linear sweep voltammetry showed that the electrochemical stability window of the sample had a working voltage of 2.0 V.     

On the scattering properties of a weakly charged polymer gel

A phenomenological model is presented to describe weakly charged polymer gels based on the classical elasticity theory. The structure factor of the gel is calculated considering both thermal and frozen concentration fluctuations as well as the screened Coulomb interaction. In agreement with the recent experimental finding the result shows anomalous crosslink-density dependence of the scattering profiles. Received: 28 March 1997 / Revised: 4 September 1997 / Accepted: 23 October 1997     

Electrical and structural studies of a LiBOB-based gel polymer electrolyte

A series of gel polymer electrolytes (GPEs) containing lithium bis(oxalato)borate (LiBOB), propylene carbonate (PC), and ethylene carbonate (EC) have been investigated. Poly(ethylene oxide) (PEO) was used as the polymer. First, a series of liquid electrolytes was prepared by varying the Li:O ratio and obtained the best composition giving the highest conductivity of 7.1?×?10^?3 S cm^?1 at room temperature. Then, the PEO-based GPEs were prepared by adding different amounts of LiBOB and PEO into a mixture of equal weights of EC and PC (40 % of each from the total weight). The gel electrolyte comprises of 12.5 % of LiBOB, 7.5 % of PEO, 40 % of EC, and 40 % of PC gave the highest ionic conductivity of 5.8?×?10^?3 S cm^?1 at room temperature. From the DC polarization measurements, ionic nature of the gel electrolyte was confirmed. Fourier transform infrared (FTIR) spectra of electrolytes showed the Li⁺ ion coordination with EC and PC molecules. These interactions were exhibited in the peaks corresponding to ring breathing of EC at 893 cm^?1 and ring bending of EC and symmetric ring deformation of PC at 712 and 716 cm^?1 respectively. The presence of free Li⁺ ions and ion aggregates is evident in the peaks due to the symmetric stretching of O–B–O at 985 cm^?1.     

Evidence of ion pair breaking by dispersed polymer in polymer gel electrolytes

Non-aqueous polymer gel electrolytes containing trifluoromethanesulfonic acid (HCF₃SO₃) and polyethylene oxide (PEO) as the gelling polymer has been studied. The increase in conductivity observed with the addition of PEO to liquid electrolytes has been explained to be due to the breaking of ion aggregates present in electrolytes at higher acid concentrations. The increase in free H⁺ ion concentration upon breaking of ion aggregates has also been observed in pH measurements and viscosity of gel electrolytes has been found to increase with PEO addition. Polymer gel electrolytes containing dimethylacetamide (DMA) have σ ∼ 10⁻² S/cm at room temperature and are stable over −50 to 125 °C range of temperature. Gels based on propylene carbonate (PC) and ethylene carbonate (EC) are stable in the −50 to 40 °C temperature range and loose their gelling nature above 40 °C.     

Evidence of ion pair breaking by dispersed polymer in polymer gel electrolytes

Non-aqueous polymer gel electrolytes containing trifluoromethanesulfonic acid (HCF₃SO₃) and polyethylene oxide (PEO) as the gelling polymer has been studied. The increase in conductivity observed with the addition of PEO to liquid electrolytes has been explained to be due to the breaking of ion aggregates present in electrolytes at higher acid concentrations. The increase in free H⁺ ion concentration upon breaking of ion aggregates has also been observed in pH measurements and viscosity of gel electrolytes has been found to increase with PEO addition. Polymer gel electrolytes containing dimethylacetamide (DMA) have σ ∼ 10⁻² S/cm at room temperature and are stable over −50 to 125 °C range of temperature. Gels based on propylene carbonate (PC) and ethylene carbonate (EC) are stable in the −50 to 40 °C temperature range and loose their gelling nature above 40 °C.     

Nonlinear effects of electrolyte diodes and transistors in a polymer gel medium

The polarization curve of an acid-base interface in a hydrogel medium has a diode characteristic. Two of each such electrolyte diodes can be combined to give an electrolyte transistor. When a salt is added to the alkaline or to the acidic part of a reverse biased electrolyte diode, the current response is highly nonlinear. If the salt is added to the acidic side, even bistability can be observed. This bistability can generate complex oscillations in a base-acid-base electrolyte transistor. These nonlinear effects are studied experimentally and theoretically. While the nonlinear salt effect can be explained with the Nernst-Planck equations, to understand the bistable behavior further investigations are necessary. (c) 1999 American Institute of Physics.     

Theory of gel point in real polymer solutions

We develop a new theory of gelation which takes into account (i) delay of the gel point and (ii) change of functionality due to ring formation. We show that the problem of finding the gel point in real polymer solutions reduces to the problem of calculating the total ring concentration and the extent of reaction of intermolecular reaction at the gel point. In this paper, we solve a special case of this problem, on the basis of the independence assumption between intermolecular reaction and cyclization which takes into account only (i) the delay of the gel point: making use of the asymptotic equality of the total ring concentration, we acquire an approximate solution for the gel point D_c as a function of the inverse concentration , the relative frequency of cyclization and dimension d. Applying the observed values of in linear polyesters, the theoretical result reproduces well the Wile and the Gordon-Scantlebury observations, showing the existence of a critical dilution beyond which gelation can not occur, and an asymptote . As the classical gel point is approached, the present theory reduces to the linear equation, which makes one-to-one correspondence with the real slope , suggesting the inequality which is just what polymer chemists have quested for so far, with the physical meaning having remained unknown. Receveid: 30 December 1997 / Revised: 28 May 1998 / Accepted: 12 June 1998     

Dynamics of twist point defects with stretching in a polymer crystal

A molecular-dynamics simulation of the behavior of a twist point defect with stretching in a chain of an equilibrium polymer crystal (“united” atoms approximation for polyethylene) is performed for immobile and mobile neighboring chains. It is shown that such a defect in a cold polymer crystal possesses soliton-type mobility. The upper limit of the spectrum of soliton velocities is found, and it is the same for both cases. The maximum possible velocity of defects is three times lower than the theoretical limit of the spectrum (which is equal to the velocity of “ torsional” sound in an isolated chain). An explanation of the reason for this discrepancy is proposed: because of the interaction of two “degrees of freedom” of the defect (twisting and stretching) the energy of a nonlinear wave is dissipated in the linear modes of the system, which results in effective friction whose magnitude depends strongly on the velocity of the defect. The “boundary of the spectrum of soliton velocities” determines the transition between regimes of strong and weak braking of defects.