Polymer Chains In Solution Research Articles

Molecular dynamics simulation of a single polymer chain in vacuum and in solution

Molecular dynamics simulations are carried out to study the structure formation of a single polymer chain in vacuum and in solution. We find that, in both cases, the folded orientationally ordered structure is formed at a low temperature by quenching from a random configuration at a higher temperature. It is also found that the stem length of the folded orientationally ordered structure formed in solution is longer than that formed in vacuum. This result is caused by the fact that the persistence length of a polymer chain in solution becomes longer than that in vacuum.

Partitioning of polymer chains in solution with a square channel: lattice Monte Carlo simulations

Cubic lattice Monte Carlo simulation studies were conducted to examine the effect of confinement on dilute and non-dilute solutions of polymer chains in a channel with a square cross section. In dilute solutions, the partition coefficient Kc with channels of different widths d followed the scaling-law prediction, and was close to the square of the partition coefficient Ks with a slit of the same d. The chain with its bulk radius of gyration greater than ∼d/2 adopted a conformation extending along the channel and, with a decreasing channel width, the chain ends were forced to face outside. The chain conformation in broader channels was a compressed random coil. The Kc increased with an increasing polymer concentration φE in the exterior solution equilibrated with the channel. In a weak confinement, Kc closely followed Ks2 of the same φE and d. The chains contracted at higher concentrations as they did in the bulk solutions. In a strong confinement, Kc was smaller than Ks2 at the same φE in the semidilute regime, and, at higher concentrations, sharply increased to the value close to Ks2.

Rapid, Unambiguous Polymer Characterization by Flow-Referenced Capillary Viscometry

Flow of a two component fluid in a capillary is studied analytically and numerically to obtain an understanding of the basic parameters and their effect on the advection-diffusion flow process. One fluid (the solvent) is Newtonian, and the other is a dilute polymer plug (the solution) introduced into the flowing solvent. The polymer plug is modeled as a Maxwell fluid. The ultimate goal is characterization of industrially manufactured polymers in real time, at-line. Experimentally, the evolution of a dilute plug introduced into a fully developed capillary solvent flow is tracked by observing the pressure drop downstream. The volumetric flow rate is held constant. While the pressure plateau has been identified with the intrinsic viscosity of the polymer, in this work, we relate the leading edge behavior of the plug/plateau to the elasticity and diffusivity of the polymer. The combination of these three parameters should unambiguously characterize the polymer chains in solution. In this paper, asymptotic exp...

Effect of Orientational Motion of Mobile Chromophores on the Dynamics of Förster Energy Transfer in Polymers

Brownian dynamics (BD) simulations have been carried out to explore the effects of the orientational motion of the donor−acceptor (D−A) chromophore pair on the Forster energy transfer between the D−A pair embedded in a polymer chain in solution. It is found that the usually employed orientational averaging (that is, replacing the orientational factor, κ, by κ2 = 2/3) may lead to an error in the estimation of the rate of the reaction by about 20%. In the limit of slow orientational relaxation, the preaveraging of the orientational factor leads to an overestimation of the rate, while in the opposite limit of very fast orientational relaxation, the usual scheme underestimates the rate. The latter results from an interesting interplay between reaction and diffusion. On the other hand, when one of the chromophores is fixed, the preaveraged rate is found to be fairly reliable if the rotational relaxation of the chromophore is sufficiently fast. The present study also reveals a power law dependence of the FRET r...

Creating porous tubes by centrifugal forces for soft tissue application

Chemically crosslinked poly(2-hydroxyethyl methacrylate) (PHEMA) tubes were synthesized by applying centrifugal forces to propagating polymer chains in solution. Initiated monomer solutions, with a composition typical for PHEMA sponges, were placed into a cylindrical mold that was rotated about its long axis. As polymerization proceeded, phase separated PHEMA formed a sediment at the periphery under centrifugal action. The solvent remained in the center of the mold while the PHEMA phase gelled, resulting in a tube. By controlling the rotational speed and the formulation chemistry (i.e., monomer, initiator and crosslinking agent concentrations), the tube dimensions and wall morphology were manipulated. Tube manufacture was limited by a critical casting concentration [M] c, above which only rods formed. All tubes had an outer diameter of 2.4 mm, reflecting the internal diameter of the mold and a wall thickness of approximately 40–400 μm. Wall morphologies varied from interconnecting polymer and water phases to a closed cell, gel-like, structure. Concentric tubes were successfully prepared by using formulations that enhanced phase separation over gelation/network formation. This was achieved by using formulations with lower concentrations of monomer and crosslinking agent and higher concentrations of initiator. This technique offers a new approach to the synthesis of polymeric tubes for use in soft tissue applications, such as nerve guidance channels.

Conformational disorder of a substituted polythiophene in solution revealed by excitation transfer

Anisotropy and isotropic transient absorption decays of a polythiophene derivative in dilute solution have been measured and compared to calculated decays on Monte Carlo simulated polymer chains to obtain knowledge about the geometrical conformation of the polymer. The polymer chain conformations are generated by a partially correlated self-avoiding random walk. Excitation migration along the isolated chain is modeled assuming a hopping mechanism. This approach can be used to determine conformational disorder and possible realizations of the polymer chains in solution as well as the trapping time and migration length of the excitation.

Novel polymers: Molecular to nanoscale order in three dimensions

The assembly of polymer chains in solution is a powerful method that is leading to the preparation of interesting and unique macromolecular-based synthetic nanostructures. Specific control over the intramolecular and intermolecular physical interactions dictates either the folding of single chains or the aggregation and ordering of multiple chains. This control is provided through the selective placement of functional groups along the polymer backbone and the relative strengths of their attractive and repulsive interactions.

Distribution of reaction times in diffusion controlled reactions in polymers

Brownian dynamics simulations of the distribution of reaction times for Forster energy migration between the two ends of a polymer chain in solution have been carried out. The distribution is non-exponential and broad in almost all cases except when the Forster radius ( R F) is close to the mean radius ( R 0) of the polymer chain. Similar results are also obtained for the Heaviside sink function.

Improved Precision in Multi-Angle Laser Light Scattering Data Processing

A general method for improving the precision in the estimation of the root-mean-square radius of linear polymer chains in solution from light scattering data has been developed. Specifically, the variance in the estimation of the Rayleigh factors has been found to depend on the concentration of the measured polymer solution. Therefore, with angle-dependent measurement of the Rayleigh factors, at only a single concentration, the root-mean-square radius can be estimated more precisely (3.7%) than if all the concentrations are employed (7.2%), without sacrificing accuracy. With the knowledge of the dependence of the second virial coefficient on molar mass, the root-mean-square radius can be iterated from the Rayleigh factors of the polymer solution with the lowest variance. This has been applied to aqueous polyacrylamide solutions as well as polystyrene in toluene and 2-butanone; the one-concentration method has been found to improve the precision twofold over classical Zimm data treatments. At the same time the measurement time is shortened significantly. It has also been found that the concentration with the lowest variance depends on molar mass of the polymer and an equation to predict this concentration in general for any polymer-solvent combination has been developed.

Critical Dynamics of Cross-Linked Polymer Chains near the Gelation Threshold

The dynamics of cross-linked polymer chains in solution near the gelation threshold has been investigated by dynamic light scattering. The time−intensity correlation function (ICF) was obtained as a function of initial monomer concentration, CNIPA, and cross-linker concentration, CBIS, where NIPA and BIS denote N-isopropylacrylamide and N,N‘-methylenebis(acrylamide), respectively. The ICF exhibited a distinct change at a unique set of (CNIPA, CBIS) for a given RBIS (≡2CBIS/(CNIPA + 2CBIS)), i.e., (1) from a stretched exponential to a clear power-law behavior and (2) depression of the initial amplitude of ICF. According to the previous work [Norisuye et al. Macromolecules 1998, 31, 5316], this point was determined to be the gelation threshold, (CNIPAth, CBISth). The locus of (CNIPAth, CBISth) was a decreasing function of CNIPAth with the lower cutoff at CNIPAth ≈ CNIPA* and was in good agreement with the prediction of the site-bond percolation theory, where CNIPA* is the so-called chain overlap concentrati...

Viscometric investigations on the intrinsic viscosity of poly(methyl methacrylate) (PMMA) affected by polymer–polymer interactions in binary system

The viscosity behavior of poly(methyl methacrylate) (PMMA) (referred to as guest polymer) in pure solvent and in a solvent containing a constant concentration of PMMA (referred to as host polymer) was thoroughly investigated. It has been found that the solvent in which the PMMA was dissolved played a key role in the determination of polymer–polymer interactions in solution, and thus the viscosity behavior of PMMA in a solvent. In good solvent, the intrinsic viscosity of PMMA in (PMMA + solvent), η PMMA , is less than the intrinsic viscosity of PMMA in pure solvent, η 0 , due to the repulsive intermolecular interaction between polymer chains in solution. On the contrary, in poor solvent, η PMMA is larger than η 0 , due to the attractive intermolecular interaction between polymer chains in solution. According to the equation presented in this article, the correlation between η PMMA and the concentration of PMMA in (PMMA + solvent), C PMMA, can be obtained by transforming the plot of the reduced viscosity( η sp/ C) versus concentration of PMMA in pure solvent. It is noted that, in good solvent, η PMMA decreased with the increase of C PMMA in solution, indicating that the polymer chains shrank in size in concentrated solutions. However, in poor solvent, the correlation between η PMMA and C PMMA became much complicated, and η PMMA increased in lower concentration of C PMMA and decreased in higher concentration of C PMMA, which can be attributed to both the attractive intermolecular interaction and the concentration-dependent excluded volume effect in solution.

Conjugation Length Control in Soluble Poly[2-methoxy-5-((2‘-ethylhexyl)oxy)-1,4-phenylenevinylene] (MEHPPV): Synthesis, Optical Properties, and Energy Transfer

Poly[2-methoxy-5-(($2^{\prime}$-ethylhexyl)oxy)-1,4-henylenevinylene] (MEHPPV) of varying conjugation length was prepared by the selective thermal elimination of one of the substituents in a suitable precursor polymer. The precursor, a dialkoxy poly(1,4-xylylene) derivative with varying amounts of acetoxy and methoxy groups, was prepared by a competitive nucleophilic substitution of the Wessling polyelectrolyte, using methanol and sodium acetate in acetic acid as nucleophiles. Selective thermal elimination(in solution) of the acetate groups alone yielded MEHPPV of varying conjugation lengths. The selective nature of the acetate elimination was confirmed by $^1H$ NMR spectroscopy. As expected, both the absorption and emission maxima of the eliminated samples shifted to the red with increasing conjugation length. While there was very little difference between the absorption spectra of thin film and solutions of MEHPPV-x, there was a significant bathochromic shift in the emission spectra of the thin films when compared to their dilute solution spectra. Additionally, separate emission from the various oligomers, which are occasionally visible in solution, is absent in thin films. Energy transfer from short to longer conjugated segments, within a single polymer chain in solution, was inferred by comparison of the fluorescence spectra of the partially conjugated polymers with those expected from a system where simultaneous independent emission occurs from a similar collection of noninteracting oligophenylenevinylene (OPV)molecules. The latter was calculated assuming a statistically random substitution/elimination process of the precursor in conjunction with the fluorescence spectral data of OPV's reported by previous workers. The extent of energy transfer increases as the average conjugation length increases. Furthermore, unlike in the model oligomers, in the case of polymers the fluorescence quantum yield in solution rapidly decreases with increase in the average conjugation length.

Theory on inclusion behavior between cyclodextrin molecules and linear polymer chains in solutions

The inclusion–dissociation behavior in the complex formation between cyclodextrin molecules and linear polymer chains in solution is theoretically investigated by using a lattice model. The cyclodextrins cooperatively include or dissociate the linear polymer chain when the interaction energy between the adjacent cyclodextrins is strong. Copyright © 2000 John Wiley & Sons, Ltd.

Termination mechanism of polymethyl methacrylate and polystyrene studied by ultrasonic degradation technique

A new method for determining the dominant termination mechanism in radical polymerization based on ultrasonic scission of long chains is used to study the termination of polystyrene and polymethyl methacrylate. The method is extended to obtain the disproportionation/combination ratio. Long dead polymer chains in solution were broken by ultrasound. The chain radicals thus formed were then allowed to terminate in the presence and absence of a chain terminating agent (radical trap). The resulting molecular weights are compared to find the dominant termination mechanism. It is found that the dominant mechanism in polystyrene is combination and that in polymethyl methacrylate is disproportionation. These results are in accordance with those quoted in the literature and obtained by other methods.The effectiveness of the radical trap used (2-chloroethyl benzene) was tested by NMR and it was found that when the trapping agent is present it terminates 100% of the polymethyl methacrylate chains. The time evolution of the degree of polymerization was compared to simulations based on Schmid's model. The disproportionation/combination ratios were found for polymethyl methacrylate as 2 and for polystyrene as 1/7 respectively through simulation studies.

Entanglement Effects in Semiflexible Polymer Solutions. 3. Zero-Shear Viscosity and Mutual Diffusion Coefficient of Poly(n-hexyl isocyanate) Solutions

To critically compare with the fuzzy-cylinder-model theory for the dynamics of stiff-chain polymers in solution, zero-shear viscosities and mutual diffusion coefficients have been measured for dilute through concentrated isotropic solutions of poly(n-hexyl isocyanate) (PHIC) samples with the number N of Kuhn's statistical segments between 0.21 and 55. The theory describes quantitatively both viscosity data for PHIC samples with N smaller than 20 and diffusion coefficient data for PHIC samples with N up to 26, with a single set of hydrodynamic parameters characteristic of PHIC. This confirms the validity of the theory to explain the global-motion dynamics of semiflexible polymer chains in solution. On the other hand, such a quantitative description is not achieved with zero-shear viscosities for PHIC samples with N larger than 20, where a power-law concentration dependence appears at higher concentrations in a form different from a scaling law seen for flexible polymer solutions. This indicates the limitation of the validity of the fuzzy-cylinder-model theory.

Simulation of a single polymer chain in solution by combining lattice Boltzmann and molecular dynamics

In this paper we establish a new efficient method for simulating polymer–solvent systems which combines a lattice Boltzmann approach for the fluid with a continuum molecular-dynamics (MD) model for the polymer chain. The two parts are coupled by a simple dissipative force while the system is driven by stochastic forces added to both the fluid and the polymer. Extensive tests of the new method for the case of a single polymer chain in a solvent are performed. The dynamic and static scaling properties predicted by analytical theory are validated. In this context, the influence of the finite size of the simulation box is discussed. While usually the finite size corrections scale as L−1 (L denoting the linear dimension of the box), the decay rate of the Rouse modes is only subject to an L−3 finite size effect. Furthermore, the mapping to an existing MD simulation of the same system is done so that all physical input values for the new method can be derived from pure MD simulation. Both methods can thus be compared quantitatively, showing that the new method allows for much larger time steps. Comparison of the results for both methods indicates systematic deviations due to nonperfect match of the static chain conformations.

Shear induced fluctuations and fluctuation-length transition in the quasiflexible polymer in a solution of a hydrogen-bond enhancing solvent

Dynamics of cellulose diacetate (a typical polysaccharide) in N,N-dimethylacetamide (a hydrogen-bond enhancing solvent) at 27 °C was investigated in a shear field of velocity gradient γ=0–5.3 s−1 through dynamic light scattering under circular Couette flow. The polymer mass concentration was set around the crossover of dilute and semidilute regimes. Growth of extra-large length-scale fluctuations and their transitions with shear were detected, which were originated by the long-ranged interaction, or the hydrogen bond, operating on the OH and CO groups in the glucose residues of cellulose acetates via high electronegative solvent. Two modes of fluctuations with fast and slow decay rates Γf and Γs were induced and each Γ value changed stepwise and linearly with γ, respectively. The decay rate distribution, which was estimated from the electric-field time correlation function expressed in the KWW-type of stretched exponential decay form g(1)(t)=A exp[−(t/τ)β] with β the index of decay rate distributions, was changed from 1/2 (one-sided stable distribution) to 3/2 (Holtzmark distribution) around γ=0.8–1 s−1 for the fast mode, while β=2 (Gaussian, or the sharpest distribution) over the full range of 0.40<γ<5.3 s−1 for the slow mode. The usual Cauchy distribution (β=1) at γ=0 (the quiescent state) was destroyed above a threshold γ*=0.033 s−1. At γ*<γ<0.2 s−1, fluctuations of various length-scale modes (0<β<1/2) were created but finally converged to two modes of fixed β(=1/2, 3/2, 2) at γ>0.4 s−1. In addition, oscillatory feature was conspicuous in g(1)(t) at every γ of 0.40<γ<5.3 s−1 and periodic fluctuations became remarkable in the scattered intensity IVv at γ>3.7 s−1, which may come from the competition between shear flow distortion and the Brownian diffusion of polymer chain in solution and can be grasped qualitatively by the initial stage of spinodal decomposition under the control of long-ranged attractive interactions.

Determination of the adsorbed layer thickness of polystyrene on glass surface by viscosity measurements to the extremely dilute concentration region

A newly developed theory regarding solute adsorption effect in viscometry of a polymer solution is reviewed and extended for determining the adsorbed layer thickness of polystyrene on a glass surface in viscosity measurements. This theory can adequately describe the concentration dependence of the viscosity of a polymer solution measured by glass capillary viscometer to the extremely dilute concentration region. Using this theory, both the free polymer chains in solution and the adsorbed polymer chain on the viscometer inner wall surface can be characterized. Examples are given for the characterization of six polystyrene samples with different molar masses by measuring their solution viscosity in benzene.

Polymer solution viscoelasticity from two-parameter temporal scaling

A novel approach for computing aspects of the loss modulus G″(ω) of a polymer solution is proposed. The path predicts the functional dependence of G″ on ω over a wide range of ω, independent of assumptions as to the nature of the dominant forces acting between polymer chains in solution. Comparison with representative results from the published literature finds excellent agreement with the predicted functional form for G″(ω). The approach is based on extension of the renormalization-group derivation [G. Phillies, Macromolecules 31, 2317 (1998)] of the hydrodynamic scaling model of polymer solution dynamics [G. Phillies, J. Phys. Chem. 93, 5029 (1989)] to the zero-shear viscosity, considering the fixed-point structure of η(c) as inferred from experiment, and analytic extrapolation of the fixed-point structure to a two-variable η(c,ω).

Steady-state behavior of dilute polymers in elongational flow. Dependence of the critical elongational rate on chain length, hydrodynamic interaction, and excluded volume

The steady-state properties of flexible polymer chains in solutions undergoing elongational flow have been studied using Brownian dynamics simulation. The coil–stretch transition is observed when the elongational rate, ε̇ exceeds a certain critical value ε̇c. In this work, we describe in detail the simulation procedure and how to extract polymer dimensions, solution viscosity, and birefringence from the trajectories. Preliminary simulations involving no hydrodynamic interaction (HI) are used to check the simulation procedures by comparing their results with theoretical predictions for such an (unphysical) case. Afterwards, simulations with fluctuating nonaveraged HI are carried out to provide results comparable with experiments. After simulations with and without intramolecular potential, we arrive at a most important conclusion: the chain length dependence of ε̇c is the same in theta conditions as in good solvent conditions. Combining ε̇c with other solution properties such as the longest relaxation time, the intrinsic viscosity, and the radius of gyration, dimensionless compound quantities can be formulated. From our simulation results, we obtain numerical values for such quantities, which include the HI effect, and which are therefore useful for analyzing experimental data.