Polymer Chains In Solution Research Articles

Coupling of the Polymer Threading a Membrane Transition to the Membrane Adsorption Transition

AbstractA polymer molecule threading through a pore in a plane membrane is allowed to adsorb on either or both sides of the membrane. Further, it is confined to the vicinity of the membrane by two plane barriers lying on either side of the membrane. A lattice model of this problem is exactly solvable by matrix techniques. The equilibrium translocation behavior is described as a function of the polymer MW, the membrane adsorption energies, the solution properties, the barrier separations, applied force, and the temperature. The transition is first‐order, meaning that small changes in any of these 9 quantities can in the limit of infinite MW, completely translocate the polymer. The work of Park and Sung who used Smoluchowski‐like equations to calculate translocation transit times can be generalized by use of the sea‐snake model which is relevant to isolated polymer chains in solution. The physics behind the sea‐snake model is that if one monomer is pulled into the membrane, the distance the center of mass of the untranslocated portion of the chain moves is MW−1/2 of the distance between monomer units. This reduces the effective friction coefficient by MW1/2. It is found for the sea‐snake model that the MW dependence of transit times varies as MW3/2 or MW depending on whether we use a free draining or a non‐free draining picture for the polymer.

Intermolecular adhesion in conducting polymers

We analyze the interaction of two conducting, charged polymer chains in solution using a minimal model for their electronic degrees of freedom. We show that a crossing of the two chains in which the polymers pass within angstroms of each other leads to a decrease of the electronic energy of the combined system that is significantly larger than the thermal energy and thus promotes interchain aggregation. We consider the competition of this attractive interaction with the screened electrostatic repulsion and thereby propose a phase diagram for such polymers in solution; depending on the charge density and persistence length of the chains, the polymers may be unbound, bound in loose, braidlike structures, or tightly bound in a parallel configuration.

Conformation of a polymer chain in solution: An exact density expansion approach

The conformation of a polymer chain in solution is intrinsically coupled to the thermodynamic and structural properties of the solvent. Here we study such solvent effects in a system consisting of a flexible interaction-site n-mer chain immersed in a monomeric solvent. Chain conformation is described with a set of intramolecular site-site probability functions. We derive an exact density expansion for these intramolecular probability functions and give a diagrammatic representation of the terms contributing at each order of the expansion. The expansion is tested for a short hard-sphere chain (n=3 or 4) with site diameter sigma in a hard-sphere solvent with solvent diameter D. In comparison with Monte Carlo simulation results for 0.2< or =D/sigma< or =100, the expansion (taken to second order) is found to be quantitatively accurate for low to moderate solvent volume fractions for all size ratios. Average chain dimensions are predicted accurately up to liquidlike solvent densities. The hard-sphere chains are compressed with both increasing solvent density and decreasing solvent size. For small solvent (D<sigma), depletion effects are found and the chain structure is strongly perturbed even at low solvent volume fractions.

Effect of solvent quality on kinetics of tethered layer formation

AbstractWe conducted a study of the effect of solvent quality on the kinetics of formation of a layer of polymer chains tethered to a solid substrate. In these experiments, tethering was accomplished by means of chemical bond formation between reactive sites on the surface and the end‐functional groups of the polymer chains in solution. All experimental variables were held constant except for the χ‐parameter between the polymer and solvent. Variation in the χ‐parameter was achieved by use of a series of nonpolar, organic solvents. The distinct three‐regime kinetics, typical of tethering reactions run in a good solvent and in the absence of segmental adsorption, was observed over the range of values for the χ‐parameter. As expected, an increase in the χ‐parameter (a decrease in solvent quality) did result in increased tethering density, but, contrary to expectation, no increase in tethering rate was observed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5530–5537, 2004

Kinetics of semidilute and dense polymer solution: the time dependence of single-chain dynamics

The single-chain motion of flexible bead polymer chains in solution was investigated taking into account hydrodynamic screening. The Oseen-like tensor was found within the Debye–Bueche–Brinkman effective-medium model, which describes the polymer solution. Two dynamical regimes in time scales were predicted: Zimm-like motion and Rouse-like motion. The time dependence of the hydrodynamic screening length was considered.

Effects of Concentration on Steady-State Viscometric Properties of Short Chain Polymer Solutions Over the Entire Concentration Range

Relationships between viscometric behavior and concentration are observed and evaluated through a series of nonequilibrium molecular dynamics simulations of the behavior of 20-site polymers in solution with explicit solvent across the full concentration range. The zero-shear viscosities, first normal stress coefficients and steady-state shear compliance of the solutions are examined alongside conformational properties including the excluded volume effect. The variation of viscosity with concentration in these solutions is described by the Huggins equation up to relatively high concentrations. At these high concentrations, the effects on conformation of excluded volume interactions decline, while no clear semi-dilute region is identifiable. Although the steady-state shear compliance of the system appears concentration-independent, the dilute and melt behaviors of this system are accurately described by the theories of Zimm and Rouse, respectively.

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods.

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.

Concentration dependence of viscometric properties of model short chain polymer solutions

We study the concentration dependence of the conformational and viscometric behaviour of short-chain polymer solutions in shear flow by conducting a series of non-equilibrium molecular dynamics simulations, covering the entire concentration range. Our model explicitly incorporates all of the important generic features of real polymer solutions—excluded volume, hydrodynamic interactions and finite chain extensibility. Hydrodynamic interactions are included exactly by treating the solvent explicitly as an atomic fluid. The polymer molecules studied consist of 20-site bead-rod model molecules, which correspond approximately to 12 Kuhn steps in the melt. For polyethylene, this represents a molar mass of 1800 g mol21. In some respects, our results are consistent with experimental and theoretical results obtained for long-chain polymer solutions. We calculate the Flory–Fox constant and find a value that agrees reasonably well with results for long chain polymer solutions. Due to the short chain length of the molecules investigated, no semidilute region exists for these solutions. However, the radius of gyration and viscosity still exhibit strong concentration dependence, which is well described by power series, rather than power law expressions, in contrast to the behaviour usually observed in long-chain polymer solutions.

Concentration dependence of viscometric properties of model short chain polymer solutions

We study the concentration dependence of the conformational and viscometric behaviour of short-chain polymer solutions in shear flow by conducting a series of non-equilibrium molecular dynamics simulations, covering the entire concentration range. Our model explicitly incorporates all of the important generic features of real polymer solutions—excluded volume, hydrodynamic interactions and finite chain extensibility. Hydrodynamic interactions are included exactly by treating the solvent explicitly as an atomic fluid. The polymer molecules studied consist of 20-site bead-rod model molecules, which correspond approximately to 12 Kuhn steps in the melt. For polyethylene, this represents a molar mass of 1800 g mol −1. In some respects, our results are consistent with experimental and theoretical results obtained for long-chain polymer solutions. We calculate the Flory–Fox constant and find a value that agrees reasonably well with results for long chain polymer solutions. Due to the short chain length of the molecules investigated, no semidilute region exists for these solutions. However, the radius of gyration and viscosity still exhibit strong concentration dependence, which is well described by power series, rather than power law expressions, in contrast to the behaviour usually observed in long-chain polymer solutions.

Ultrasonically induced birefringence in polymer solutions

Abstract For ultrasonically induced birefringence in polymer solutions, both the linear sinusoidal birefringence and the nonlinear stationary birefringence were observed. The sign and value of the stationary ultrasonically induced birefringence depended on the molecular structure of segment and its anisotropy in polarizability. Furthermore, no molecular weight dependence could be observed above the molecular weight 104. The theory based on the viscoelastic ones using the Rouse-Zimm model could not explain our experimental results as a whole. These results strongly suggest that the stationary ultrasonically induced birefringence should be caused by the local segmental motion of polymer chain in solution. For all polymer solutions investigated here, the stationary birefringence per ultrasonic intensity decreased with increasing frequency. This frequency dependence is not consistent with the present treatment for the ultrasonically induced birefringence.

Electrophoretic dynamics of large DNA stars in polymer solutions and gels

We have developed a procedure for synthesizing large stable branched DNA structures that enables visualization via fluorescence microscopy. Using this procedure we have synthesized large DNA stars and observed their electrophoretic behavior in polymer solutions and gels. In dilute polyacrylamide solutions, the DNA stars move as random coils and appear to experience only brief collisions with the polymer chains in solution. The effect of polymer solution concentration on the electrophoretic mobility of stars in the dilute regime is found to be in good accord with predictions of the transient entanglement coupling (TEC) model. In semidilute polymer solutions, the star arms extend in the field direction and drag the core through the matrix. The star arms form several U-shaped conformations as they collide and engage with polyacrylamide chains. The U-shaped conformations occasionally evolve into J-shaped conformations as the star arms slide off the matrix chains they engage during electrophoretic migration. In concentrated polymer solutions, the arms of the star extend and form V-shaped structures with the core as the apex. The arms then pull the core through the matrix. These V-shaped conformations are much longer-lived than U-shaped ones and, unlike the latter, do not transform to J-shaped conformations. In polyacrylamide and agarose gels, where matrix entanglements are fixed, DNA stars become trapped when entanglements with matrix molecules prevent the core from being pulled through the matrix by the extended arms. This trapping was observed at all gel concentrations and electric fields studied.

The Formation and Recombination Kinetics of Positively Charged Poly(phenylene vinylene) Chains in Pulse-Irradiated Dilute Solutions

In this paper, we describe how we derive the mobility of positive charges (holes) along isolated conjugated polymer chains from the results of pulse-radiolysis time-resolved microwave conductivity (PR-TRMC) experiments on dilute polymer solutions. The method is illustrated with results for oxygen-saturated, benzene solutions of the well-known poly(phenylene vinylene) derivative, MEH-PPV with an average chain length of 800 monomer units. Nanosecond pulsed irradiation results initially in ionization of the solvent with the formation of excess electrons and benzene radical cations, Bz + . The former rapidly (<1 ns) undergo attachment to O 2 to form O 2 - with a rate constant of 1.5 x 10 M - 1 s - 1 . The Bz + ions diffuse through the solvent and react with the (lower ionization potential) polymer chains via electron abstraction forming holes on the polymer backbone. This is accompanied by a large increase in the conductivity of the solution after the pulse, demonstrating that the mobility of holes on the polymer chains is very much larger than the mobility, via molecular diffusion, of Bz + ions in the solvent. To describe the after-pulse growth in conductivity, a large effective reaction radius, R e f f , of ca. 400 A is required for the diffusion-controlled reaction of Bz + with MEH-PPV chains. This requires taking into account the time-dependent term in the rate coefficient. The value of R e f f is compared with theoretical predictions for the reaction of a small entity with a 1-D linear or a 3-D cubic array of 800 reactive moieties. The conclusion that individual polymer chains in solution must have a very open structure with a large persistence length is in agreement with the results of previous static and dynamic light-scattering studies. The conductivity eventually decays because of the recombination of the positively charged polymer chains with negative counterions (O 2 -) with a rate coefficient of 1.2 x 10 M - 1 s - 1 , which is somewhat slower than predicted by the Debije equation. No evidence could be found for first-order trapping of the mobile positive charge on the polymer chains prior to recombination. The pseudo-one-dimensional mobility of holes along the polymer backbone derived from the absolute magnitude of the conductivity transients is 0.46 cm 2 V - 1 s - 1 .

Polyimide asymmetric membranes: Elaboration, morphology, and gas permeation performance

AbstractAsymmetric 2,2‐bis‐(3,4‐dicarboxyphenyl) hexafluoropropane dianhydride (6FDA)‐2‐methyl‐1,3‐phenylenediamine (mPDA) polyimide membranes were prepared according to a phase‐inversion mechanism by using different solvent/nonsolvent blends. The membrane formation mechanism and the final performances of the asymmetric membranes have been found both nonsolvent and solvent nature dependent. From the visualization of cross sections of asymmetric membranes by scanning electron microscopy and the study of the permeation of two gases (N2, CO2) through asymmetric membranes, a relationship between elaboration conditions and asymmetric membranes characteristics could be drawn. The organization of polymer chains in solution strongly affects the final polymer arrangement and thus the final performances of the membrane. The influence of preliminary solvent evaporation before immersion has been shown to be dependent on the structure of the asymmetric membrane: finger‐like or sponge‐like structures. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 1838–1848, 2003

Effective force between confined colloids clothed by end-grafted polymer chains in solution

We consider colloidal particles clothed each by f end-grafted polymer chains, and immersed in a good solvent. The clothed particles are small enough to be regarded as star polymers. The purpose is a quantitative study of the influence of the confinement on the expression of the effective force between a pair of particles. Such a force originates from the swelling of grafted chains due to the presence of solvent. To simplify, we chose as confining geometry a thin space of thickness D delimited by two parallel plates. The problem depends on two natural lengths, which are the gyration radius, R3∼af1/5N3/5, of an isolated star polymer and the thickness D. Thus, there exist two regimes depending on whether R3 is smaller or greater than D. The system is confined only when D is below R3. We first present a detailed study of conformations of a confined star polymer (R3≫D). The confinement imposes to the star polymer to adopt a configuration parallel to the plates, which is characterized by a parallel radius, denoted by R∥. We show that the latter increases when D is decreased according to R∥∼af1/4D−1/4N3/4. The main result is that the star polymer becomes two dimensional, and where the grafted chains have blobs of size D as new units. The second purpose is a quantitative investigation of the effective force between two confined star polymers. For the unconfined regime (R3≪D), it is found that the force, F3(r), decays with interparticle distance r as F3(r)/kBT≃θ3(f )/r, with the amplitude θ3(f )≃(5/18)f3/2. Hence, for this regime, the force is similar to that relative to a three-dimensional colloidal solution of infinite extent. For the confined regime (R3≫D), however, a drastic change of the force expression occurs. For this regime, we show that the force is similar to the one governing the interaction between two-dimensional star polymers, and is given by F2(r)/kBT≃θ2(f )/r, with the exact amplitude θ2(f )=(2+9f2)/24. The two forces then decrease with distance according to the same decay, but with different amplitudes. As a conclusion, the effective force between two confined star polymers is θ2(f )/θ3(f )≃(3/20)(2+9f2)/f3/2 times more intense than that between unconfined ones. Finally, we say that the confinement may be a mechanism that reinforces the colloidal stabilization.

Structure Formation of a Single Polymer Chain in Solution: A Molecular Dynamics Study

Molecular dynamics simulations are carried out to study the structure formation of a single polymer chain in solution. A random conformation of a polymer chain in solution at high temperature (550K) is quenched to several lower temperatures (300, 350, and 400K). Our simulations show the following characteristics: 1) At lower quenching temperature (300K), local orientationally ordered domains are formed first, and they grow to be a folded orientationally ordered structure. 2) At a higher quenching temperature (400K), a toroidal structure can be formed. 3) At an intermediate quenching temperature (350K), a toroidal structure can be formed before a folded orientationally ordered structure is formed. The last characteristic indicates that an intermediate toroidal structure at 350K is in a metastable state. We also find that it depends on the initial conformation of a polymer chain, whether a toroidal structure is formed or not.

Interaction force between colloidal particles clothed by end-grafted polydisperse polymer chains in solution

We consider colloidal particles clothed each by f end-grafted flexible polymer chains, and immersed in a good solvent. We assume that these are small enough to be viewed as star-polymers. We suppose that the lengths of the f grafted chains is distributed at random, with a distribution P (n) (the probability to find a grafted chain having n monomers). The presence of a good solvent induces an effective force between particles. The aim is a quantitative study of the polydispersity effects on the interaction force. To make explicit calculations of the force, F (h), which depends on the interparticle-distance h, we choose a fractal distribution, i.e., P (n) ∼ n - α , if n N. Here, 1 N c . For N N c , the size of the clothed particle is dominated by that of the longest grafted chain, i.e., aN 3 / 5 . To obtain the force expression, we use some method developed by Witten and Pincus for monodisperse star-polymers. For N N c , however, we show the existence of two distance-ranges. For small distances, that is for h < 2R' c ≃ 2af 3 / 5 ( α - 1 ) , the force expression is similar to that relative to the case with N < N c . For high distances, that is for 2R' c < h < 2R' ≃ aN 3 / 5 , the force decays as h - 1 , independently on the polydispersity nature.

Interaction of the europium chloride and polyaniline: formation of a novel conductive complex

A novel polyaniline (PANI):EuCl 3 complex has been prepared and its conductivity, electronic absorption and luminescent spectra were studied. Changes in electronic absorption spectra showed that the europium ions possess both oxidative and pseudoprotonation activity with respect to the polymer chains in solution and solid films, respectively. Photoluminescence (PL) spectra showed that the charge transfer from the polymer to Eu 3+ ions occurs and that there are two types of europium luminescent centers in the disordered polymer matrix. Electrical conductivity of the composite films with a stoichiometric ratio of PANI to the europium salt was found to be unexpectedly high and comparable with that of the protonic acid doped PANI. Mechanisms of the PANI:EuCl 3 complex formation are discussed.

Photophysics of pristine andC60-doped disubstituted polyacetylene

Using a variety of steady-state spectroscopies we studied the long-lived photoexcitations and electronic excited states of poly disubstituted acetylene $(\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}),$ the backbone structure of which is a disubstituted trans-polyacetylene, as well as $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}/{\mathrm{C}}_{60}$ blends. The cw spectroscopies include absorption, photoluminescence (PL), photoinduced absorption (PA), and PA-detected magnetic resonance (PADMR). Although $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}$ is a degenerate ground-state polymer, nevertheless, and in contrast to trans-polyacetylene, we found that it has a strong PL band with quantum efficiency larger than 60%. From polarized PL studies on stretched oriented films we conclude that the PL emission originates from intrachain excitons rather than the polymer side groups. This shows that the lowest-lying exciton in $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}$ is a ${B}_{u}$ state rather than an ${A}_{g}$ state, in contrast to the order of the lowest-lying excitonic states in trans-polyacetylene. The polarized absorption in $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}$ contains three distinctly different bands with different polarization properties, which are interpreted according to the model of Shukla and Mazumdar. The PA spectra of pristine and photo-oxidized $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}$ films show neutral and charged solitons as well as polaron excitations, whereas the long-lived photoexcitations in $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}$ in solution are mainly polarons. This may be due to destabilization of the soliton-antisoliton pairs in the polymer chains in solution caused by short conjugation length. From the PA and PADMR spectroscopies of $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}/{\mathrm{C}}_{60}$ blends we conclude that a photoinduced charge-transfer reaction takes place, again in contrast to blends of other nonluminescent polymers. Interestingly the PA spectrum of $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}/{\mathrm{C}}_{60}$ blends shows both charged polarons and charged solitons that are correlated with the PA band of ${\mathrm{C}}_{60}^{\ensuremath{-}}.$ We found that the ratio between charged solitons and polaron excitations depends on the ${\mathrm{C}}_{60}$ concentration in the blend, the film morphology, and temperature. It is shown that the mechanism by which two polarons on the same $\mathrm{PDPA}\ensuremath{-}n\mathrm{Bu}$ chain recombine into two charged solitons is the dominant process that determines the soliton/polaron ratio in the blends.

Scaling Laws for Geometry and Macromolecules in Solution: An Interdisciplinary Approach to Statistical and Thermal Physics

An interdisciplinary program, dealing with statistics within basic geometry, is presented and discussed across some modern physics. Its fundamentals are of general interest in physical chemistry, but specially suit investigating conformational statistics and universal scaling of polymer chains in solution. We pointed out an equivalence principle for shape and statistics that can straightforwardly link probability distributions to geometrical quantities at smaller length scales. The average polymer size is thus expected following analytically from the energy surface of its dimeric unit. This would finally suggest extending molecular mechanics to a geometrical setting that reaches the limit of vanishing scales.

EFFECTS OF DILUTION DURING CROSSLINKING ON STRAIN-INDUCED CRYSTALLIZATION IN CIS -1,4-POLYISOPRENE NETWORKS. I. EXPERIMENTAL RESULTS

Preparing an elastomer by crosslinking polymer chains in solution and then drying the resulting network should have at least two major effects. Specifically, there should be fewer entanglements, and the drying part of the process should compress the chains into a “supercontracted” state. The former effect would be expected to increase crystallization and the latter to reduce it. The present study was conducted to investigate these opposing effects on strain-induced crystallization in cis-1,4-polyisoprene chains that had been crosslinked by peroxide thermolysis in decalin solutions, and subsequently dried. The initiation of crystallization was taken to be the elongation at which an upturn in the modulus became discernible. Higher elongations were required for the networks prepared at higher dilutions, suggesting that with regard to strain-induced crystallization, the compressed states of the chains is more important then their reduced entangling. It is likely that quantitative comparisons are complicated by non-Gaussian effects. In addition to the qualitative insights obtained, the results should be useful for evaluations of the theories of rubberlike elasticity and strain-induced crystallization, as is illustrated in the following paper of this two-part series.