Chain Contour Research Articles

Nano-scaled intrachain ordering and dynamics in two-dimensional orientational polymer domains1)

Statistical and local relaxation properties of two-dimensional finite polymer systems (domains) are considered. The domains consist of a large number of semirigid chains with the finite contour length at free, half-free and fixed boundary conditions for chain ends. The intermolecular orientational order at short distances between chains in the thick domains is similar to the order in infinite two-dimensional systems. The correlations of orientation between sufficiently distant elements of different chains decay by the exponential law, but the effective constant of interchain interactions in the domain is proportional to the molecular weight of the chain. At the given intra-and interchain interactions an elongtation of the chains leads to a local ordering of chains in the domain (at free boundary conditions) or, on the contrary, to the decreasing of the parameter of short-range orientational order (at fixed and half-free boundary conditions). Independently of type of boundary conditions the parameter of large-range orientational order tends to zero with increasing of the chain contour length. Dynamical equations and relaxation spectrums for times of local motions are obtained. From time correlation functions of local relaxation the times of nano-scaled mobility of chains were calculated in depending on the bending rigidity of chains, the parameter of interchain interactions, and the contour length of chains. At the given intra-and interchain interactions an elongtation of chains forming the domain leads to to the slowing-down of local mobility of chains in the domain. The comparison with experimental date obtained by dielectric relaxation and polarized luminescence methods on investigation of nano-scaled mobility in the dilute melts of comb-shaped polymers has been carried out.

Dynamics of Flexible Polymer Chains in Elongational Flow

This paper focuses on the recent developments achieved in our group in the field of flexible polymer chain dynamics in elongational flow. Stress-induced orientation and deformation in flowing polymer solution is being surveyed in a wide variety of manifestations. Two types of flow fields have been investigated: the opposite-jet flow with a stagnation point, and the abrupt contraction flow with open flowlines. Emphasis has been placed on the latter geometry due to its widespread occurrence. Degradation experiments performed with dilute PS solutions in abrupt contraction flow demonstrate a distinct propensity for midchain scission, a feature apparently consistent with highly extended chains. On the other hand, the critical strain-rate for chain fracture (ἐf) determined under the same experimental conditions scales with M-1. The inverse relationship with polymer MW is characteristic of partly uncoiled chains but not of highly extended chains, for which a stronger MW dependence (ἐf) ∝ M-2 is expected. The 'yo-yo' model, which could rationalize these findings, is refuted by fluorescence depolarisation measurements which indicated that central orientation is more progressive than the average segmental orientation. For the first time, polarization-modulated birefringence was used to determine the state of local chain orientation in abrupt contraction flow. Axisymmetric contraction flow is complicated by the large variations in local molecular orientation along different streamlines. To account for this effect, a numerical inverse Abel transform has been devised to compute local birefringence (Δn) from experimental retardation (δ). Results show a steep decrease in birefringence with axial distance. Birefringence profiles determined in a direction perpendicular to the flow show a maximum, not at the centre, but in the vicinity of the orifice walls. This observation is in accord with flow simulation results which indicated the presence of extreme strain rates near re-entrant corners. Molecular extension ratios calculated with the Kuhn-Grün theory gives a qualitative description of polymer uncoiling up to about one third of the chain contour length at the approach of capillary entrance. A notable departure from the affine deformation model is, however, observed with multiple birefringence saturation levels changing with flow rate conditions. This behaviour could be explained by the presence of transient molecular conformations. Efforts are underway to visualize these metastable states by single chain fluorescence video microscopy using UHMW polystyrene randomly grafted with anthracene chromophores.

Surface Interaction Forces of Well-Defined, High-Density Polymer Brushes Studied by Atomic Force Microscopy. 1. Effect of Chain Length

We made direct force measurements by atomic force microscopy (AFM) at surfaces of polymer brushes comprised of low-polydispersity poly(methyl methacrylate) (PMMA) chains densely end-grafted on a silicon substrate by living radical polymerization. These brushes are characterized by an exceptionally high, nearly constant graft density (approximately 0.4 chains/nm2) and a wide range of molecular weights of the graft chains. This graft density is at least 10 times larger than those of the previously studied polymer brushes prepared by the adsorption of block copolymers. Force measurements were made in toluene with a silica particle-attached cantilever. The hysteresis behavior of a piezo actuator used in the AFM was corrected by simultaneously measuring its piezo current. The true distance D between the substrate surface and the silica probe, which usually is difficult to define in AFM experiments, was successfully determined by AFM imaging across the boundary of a scratched and an unscratched region on the sample surface. In this way, we could obtain quantitative force−distance profiles. The repulsive force was observed to rapidly increase with decreasing separation. The equilibrium thickness Le of the brushes, i.e., the critical distance at which a repulsive force was detectable, was found to be proportional to the weight-average chain contour length Lc,w, giving Le/Lc,w = 0.6. This indicates formation of a homogeneous polymer layer with highly stretched graft chains. Unlike the previously reported results for lower density polymer brushes, the force−distance profiles for different graft chain lengths were not scaled by the reduced distance D/Le. Longer brushes were more resistant to compression: for example, the longest studied brush was compressible only to D/Le = 0.8, which was about 3 times as large as the scaled dry thickness Ld/Le.

Morphological reversible contour representation

In this paper, a novel morphological reversible contour representation of discrete binary images is proposed. A binary image is represented by a set of nonoverlapping multilevel contours and a residual image. In this proposed representation, the total number of pixels representing an image is far less than the total number of pixels obtained by the seed-based morphological contour-skeleton lossless representation. The proposed contour representation is simple, unique, and general without restrictions on the binary image to be represented. The resulting multicontour image component is robust to noise. An efficient differential chain contour coding scheme is employed to further compress the represented image. The proposed method yields very low bit rates compared to the existing morphological techniques. An automatic filling procedure, which properly fills a proper multicontour image according to its topological structure without need of seed points, is proposed.

Stress overshoot of polymer solutions at high rates of shear: semidilute polystyrene solutions with and without chain entanglement

The overshoot of the shear stress (σ) and the first normal stress difference (N1) in the shear flow was investigated for polystyrene solutions in tricresyl phosphate. The magnitudes of the shear (γσm and γNm) corresponding to the maxima of σ and N1 were compared with the theory of Pearson et al. (J Polym Sci Part B: Polym Phys 1991, 29, 1589), a modification of the tube model theory of entanglement including the possible elongation of polymer chains in a fast flow. The results for the entangled systems were in excellent agreement with the theory if the equilibration time of the chain contour length (τe) was equated with 2τR, in accord with the dynamics of the tube model chain. Here, τR was the longest Rouse relaxation time evaluated from the dynamic viscoelasticity at high frequencies. The results for the nonentangled systems were fitted with the same theoretical function, with τe = 1.2τR. This result may indicate that at the same concentration, nonentangled chains contract faster than entangled chains. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3271–3276, 2000

Molecular dynamics simulations of dielectric relaxation of concentrated polymer solutions

Molecular dynamics simulations are conducted for concentrated solutions of flexible polymers. The results are contrasted with literature dielectric spectroscopy data, in an attempt to elucidate the observed phenomena from a molecular level perspective. A bead-spring model is used and systems with chain sizes up to N=150 beads at reduced densities 0.5⩽ρ⩽0.8 are studied. The dimensions of the chains follow a universal behavior with ρ/ρ*, where ρ* is the crossover density demarcating the onset of chain overlapping. All the chains are found to follow random-walk behavior. The global motion of the chains is investigated in terms of the dielectric loss E″. As in dielectric spectroscopy experiments, the motion of the chains induces prominent dielectric relaxation at low frequencies. The shape of E″ broadens with increasing density, and a normal-mode analysis indicates that overlapping of the chains with increasing density progressively renders the distribution of relaxation times more heterogeneous. For denser systems a second, smaller peak appears at the high frequency end of the spectrum. This secondary peak is not identified with segmental motion, since the simulated chains lack components of the segmental dipoles perpendicular to the chain contour. Entanglement effects are investigated calculating the mean squared displacement g1(t), and the results suggest that the topological constraints of entanglements render at least two different relaxation mechanisms with disparate time scales important. An attempt to explain the shape of the spectra in terms of a phenomenological separation of the motion of chains into a rotational and a stretching mode showed that stretching plays no important role in the relaxation function and the shape of E″.

Nonlinear viscoelasticity of entangled polymeric liquids

The Doi–Edwards (D–E) theory for entangled polymer dynamics is extended to account for polymer chain stretching in fast flows. Our analysis is based on a new estimate for the non-equilibrium size of the tube under a macroscopic deformation and yields an optimum primitive chain contour length E · u 1/2 times greater than the equilibrium (no-flow) value. This finding implies that polymer chains subjected to nonlinear step strain will only retract partially and should therefore maintain significant chain stretch up to the time the primitive chain escapes the deformed tube. Primitive chain retraction is also shown to reduce the number of entanglements between a deformed polymer chain and its neighbors, yielding significant enhancement of molecular relaxation at high deformations. Various steady-state and transient stress predictions based on this partial strand extension concept are compared with existing experimental data.

The effect of stiffness in wormlike micelles

The effect of stiffness in a 2D living polymer system is investigated by Monte-Carlo simulation in a canonical ensemble. As the flexibility decreases, the mean chain contour length \(\) decreases and goes through a local maximum. The mean end to end square distance shows a non-monotonic behaviour due to the coil-to-rod transition and the decrease in chain contour length. Near the maximum of chain ordering in the bulk, the chain length distribution adapts itself to increase the configurational entropy. With the parameters used in this simulation, it seems that the effect of the stiffness for high stiffness is to decrease \(\) as in the isotropic case, since the ordering decreases again.

Birefringence of dilute PS solutions in transient elongational flow

Transient elongational flow, created by forcing a polymer solution across a narrow contraction, is characterized by a high strain rate of limited duration. Due to an inherent short residence time, this type of flow generally is considered as being less efficient in extending isolated flexible molecular coils than “stagnation” point elongational flow. Rheo-optical measurements revealed, nevertheless, a readily detectable birefringence zone above a critical strain rate in the immediate orifice entrance. Birefringence was studied for dilute PS solutions (100–400 ppm) in decalin as a function of fluid strain rate (\documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon $\end{document} = 1000–38,000 s−1) and polymer molecular weight (M = 1.93–10.2·106). Transient elongational flow is complicated by the presence of local orientation distribution along the different streamlines. To account for this effect, a numerical technique has been devised to compute local birefringence (Δn) from experimental retardation (δ). Results show a uniform birefringence distribution across the capillary entrance and a steep decrease with the axial distance. Molecular extension ratio calculated with the Kuhn-Grün theory suggests that polymers may uncoil up to one third of the chain contour length at the approach of capillary entrance. Although extension ratio determined at the inlet could be fitted with an affine deformation model, notable departure from this simple representation is observed when molecular strain is calculated along the streamline. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1483–1500, 1998

Birefringence of dilute PS solutions in transient elongational flow

Transient elongational flow, created by forcing a polymer solution across a narrow contraction, is characterized by a high strain rate of limited duration. Due to an inherent short residence time, this type of flow generally is considered as being less efficient in extending isolated flexible molecular coils than “stagnation” point elongational flow. Rheo-optical measurements revealed, nevertheless, a readily detectable birefringence zone above a critical strain rate in the immediate orifice entrance. Birefringence was studied for dilute PS solutions (100–400 ppm) in decalin as a function of fluid strain rate (\documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon $\end{document} = 1000–38,000 s−1) and polymer molecular weight (M = 1.93–10.2·106). Transient elongational flow is complicated by the presence of local orientation distribution along the different streamlines. To account for this effect, a numerical technique has been devised to compute local birefringence (Δn) from experimental retardation (δ). Results show a uniform birefringence distribution across the capillary entrance and a steep decrease with the axial distance. Molecular extension ratio calculated with the Kuhn-Grün theory suggests that polymers may uncoil up to one third of the chain contour length at the approach of capillary entrance. Although extension ratio determined at the inlet could be fitted with an affine deformation model, notable departure from this simple representation is observed when molecular strain is calculated along the streamline. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1483–1500, 1998

Anomalous adhesion in adsorbed polymer layers

Anomalous adhesion behaviour observed in the polydimethylsiloxane/heptane/silica system is reported. This behaviour is characterised by the infrequent appearance of one or more elastic minima which occur in addition to the ever-present primary adhesion. The resulting elastic force is attributed to loops connecting the tip to the substrate and can be described by two models; a worm-like chain, and a freely jointed chain. Both models give similar values for the characteristic segment length of around 0.24 nm and indicate that the chains have been extended by between 90 to 95% of their chain contour length before desorption. In some cases multiple adhesions were observed between tip and substrate and have been used to suggest a method for determining the distribution of adsorbed polymer loops.

Modeling Chain Folding in Protein-Constrained Circular DNA

An efficient method for sampling equilibrium configurations of DNA chains binding one or more DNA-bending proteins is presented. The technique is applied to obtain the tertiary structures of minimal bending energy for a selection of dinucleosomal minichromosomes that differ in degree of protein-DNA interaction, protein spacing along the DNA chain contour, and ring size. The protein-bound portions of the DNA chains are represented by tight, left-handed supercoils of fixed geometry. The protein-free regions are modeled individually as elastic rods. For each random spatial arrangement of the two nucleosomes assumed during a stochastic search for the global minimum, the paths of the flexible connecting DNA segments are determined through a numerical solution of the equations of equilibrium for torsionally relaxed elastic rods. The minimal energy forms reveal how protein binding and spacing and plasmid size differentially affect folding and offer new insights into experimental minichromosome systems.

Differential constitutive equation for entangled polymers with partial strand extension

Beginning with a formal statement of the conservation of probability, we derive a new differential constitutive equation for entangled polymers under flow. The constitutive equation is termed the Partial Strand Extension (PSE) equation because it accounts for partial extension of polymer strands in flow. Partial extensibility is included in the equation by considering the effect of a step strain with amplitude E on the primitive chain contour length. Specifically, by a simple scaling argument we show that the mean primitive chain contour length after retraction is L=L 0 E 1/2, not the equilibrium length L 0 as previously thought. The equilibrium contour length is infact recovered only after a characteristic stretch relaxation time λ s that is bounded by the reptation time and longest Rouse relaxation time for the primitive chain. The PSE model predictions of polymer rheology in various shear and extensional flows are found to be in good to excellent agreement with experimental results from several groups.

Molecular Dynamics Simulations of Polar Polymer Brushes

Brushes of end-grafted, polar polymer chains in a good, nonpolar solvent are studied via molecular dynamics simulations of a bead-spring model. The monomers are connected by finitely extensible nonlinear springs. The springs connecting consecutive monomers in a chain are labeled with dipoles parallel to the chain contour. We consider the dipoles as limits of charge pairs, replacing each dipole by a pair of charges positioned at the centers of mass of two consecutive beads. Equilibrium simulations are performed, and the static and dynamic properties of the chains are related to the dipole magnitude. It was found that the electrostatic interactions lead to a shorter brush and the collapse becomes more pronounced with increasing segmental dipole moment. The dielectric relaxation of the tethered chains is studied, and the dielectric permittivity is obtained from equilibrium dipole moment correlation functions. Results on the dielectric relaxation of tethered chains from experiments conducted by Yao et al. exhibited a broader dielectric dispersion spectrum than that of free macromolecules in homogeneous solutions. These authors attributed the results to the thermodynamic confinement (to keep uniform segment density) and the spatial confinement that prohibits a chain to cross the tethering domain boundary. The simulations indicate that neither the spatial confinement nor the thermodynamic confinement lead to a broader dielectric dispersion spectrum for the tethered chains, and we attribute the discrepancies to the morphology differences between the experimental system and the simulated one. Weak electric fields parallel and perpendicular to the grafting surface are applied, and the system response is related to the equilibrium fluctuations. We also examine the structural properties of the brushes at steady state under the influence of external electric fields.

Polyisoprene local dynamics in solution: Comparison between molecular dynamics simulations and optimized Rouse–Zimm local dynamics

The optimized Rouse–Zimm local dynamics (ORZLD) approximation to the Smoluchowski generalized diffusion approach has been used to predict the local dynamics of cis-1,4-polyisoprene in dilute solution. The equilibrium averages needed in the theory are calculated from a time average along a molecular dynamics trajectory. The first and second order orientation autocorrelation functions for C–H, C–C, and virtual bonds in the repeat unit are calculated from the theory and compared to the same quantities calculated directly from the molecular dynamics trajectory. The correlation functions from the simulation and the theory decay on similar time scales (within a factor of two) and have somewhat similar shapes. The theory predicts a universal relationship between P1 and P2 correlation functions which is obeyed to a good approximation by the correlation functions from the simulation. Variations in the local dynamics along the chain contour are qualitatively well described by the theory.

Correlated fluctuations in polymer networks

Polymer micronetworks with Cayley tree and random topologies are compared. The fluctuations of junctions in random networks exhibit significant departures from the mean value corresponding to those in Cayley tree topology. Correlations among the fluctuations are examined for the two types of networks. Correlations are stronger, and cover longer distances along the chain contours in random networks, compared to those observed in Cayley trees. This is a consequence of the non-uniform spatial distribution of connected vertices in a random network, as opposed to Cayley trees in which chains extend between junctions located in successive tiers only. The relaxation spectra of the two types of networks are compared. The cumulative distribution of frequencies obeys a power law dependence on frequency, with exponents of 1.4 and 1.1 for trifunctional Cayley tree and random networks, respectively. These exponents are significantly smaller than the Debye value of 3 for regular three dimensional crystals.

Dielectric normal mode relaxation of tethered polyisoprene chains in styrene-isoprene block copolymers

Abstract

Crossover behavior in the viscosity of semiflexible polymers: Intermolecular interactions as a function of concentration and molecular weight

A simple relation is presented for the viscosity of isotropic solutions of flexible, semiflexible and rodlike chains over a range of concentration from dilute solutions to undiluted polymer, chain contour length L and persistence length â. The expression is designed to account for the separate effects of screening of thermodynamic and hydrodynamic interactions, and the onset of intermolecular chain entanglements under Flory theta solvent conditions, or in ‘‘good’’ solvents, for which intramolecular excluded volume is important in dilute solutions. The relation includes a revised (dimensionless) Fox parameter Xc that determines the onset of intermolecular entanglements, where Xc=πNAρLcâ/3ML for semiflexible polymers with â≪L, with ρ the polymer density, ML the mass per unit length of the chain, and Lc the value of L for the onset of entanglement effects in undiluted polymer; Xc≊100 for a number of systems, including rodlike chains.

A quantitative theory of linear chain polymer dynamics in the melt. III. Dependence of quantities on bead location along the chain contour

The dependence of the bead mean squared displacement on the position of the bead along the chain backbone is considered within the lateral motion model for the dynamics of linear chain polymer melts. The bead position dependence has been ignored in the previous development of this theory. In the lateral motion model, the effective bead friction coefficient increases as the bead mean squared displacement increases, due to the greater interchain correlations that result because of the noncrossability of the chain backbones. In this work, a position dependent model is considered for this bead friction coefficient. The resulting equations of motion for the chain have the form of a generalized Rouse model with a position and time dependent bead friction coefficient. These equations are solved numerically. It is found that the time dependence of the center bead mean squared displacement has the same form as predicted by the simpler theory, in which the dependence of quantities on the position of the bead along the chain backbone is ignored. The scaling of the terminal time and the center of mass diffusion constant on chain length are also found to be unchanged by the inclusions of the bead position dependence of the friction coefficient. The mean squared displacement, averaged over all beads in the chain, shows a stronger time dependence than the same quantity for the center bead. The predictions are in excellent agreement with the results from previous numerical simulations.

Rheological and Dielectric Behavior of a Styrene−Isoprene−Styrene Triblock Copolymer in n-Tetradecane. 1. Rubbery−Plastic−Viscous Transition

Rheological and dielectric behavior was examined for a 50 wt % solution of a symmetric styrene−isoprene−styrene (SIS) triblock copolymer (M = 60.2K, S content = 28%) dissolved in an I-selective solvent, n-tetradecane (C14). Dynamic mechanical tests with various strain amplitudes, γ0 = 0.03−0.8, were performed at various temperatures (T). At T ≤ 30 °C, the system exhibited elastic, rubberlike responses characterized with frequency (ω)-insensitive G‘ being much larger than G‘‘ for small γ0 and slippage at the measuring assembly wall for large γ0. At 40 ≤ T/°C ≤ 80, the system showed elastic responses (similar to those at T ≤ 30 °C) for small γ0 and highly nonlinear, elastoplastic responses characterized with lozenge-shaped stress−strain patterns for large γ0. At T ≥ 90 °C, viscous behavior was observed. These rheological changes were compared with changes in the dielectric behavior of the SIS/C14 system; the I block had dipoles parallel along the chain contour and the motion of its ends was dielectrically detected. In the rubbery regime (T ≤ 30 °C), no detectable dielectric dispersion was observed, meaning that the I block ends were anchored on rigid S domains. In the viscous regime (T ≥ 90 °C), prominent dispersion was observed. This dispersion suggested that the I block motion was essentially free from the constraint due to the S domains and the S and I blocks were more or less homogeneously mixed with each other. In the plastic regime (40 ≤ T/°C ≤ 80), the system exhibited onset of dielectric dispersion (upturn of dielectric loss at low ω). This fact suggested some freedom in motion of the I block ends (in the S/I interface) at those T. In the plastic regime, the dielectric response of the SIS/C14 system remained the same at the quiescent state and under oscillatory/steady shear. A previous argument (Watanabe et al. J. Rheol. 1984, 28, 393) attributed the plasticity to strain-induced motion of the I blocks pulling out the S blocks from softened S domains. However, the shear-insensitive dielectric behavior suggests that the pullout of the S blocks was not the only mechanism providing the plasticity. From this point of view, the mechanism for the plasticity of the SIS/C14 system was discussed in relation to the possible conformations of the I blocks, a bridge connecting different S domains and a loop having two ends anchored on the same domain.