Observation of single chain motion in a polymer melt

Molecular motion of single polymer chains has been investigated in a melt sample of polytetrahydrofuran and compared with results for the same polymer in dilute solution. Using a high resolution neutron scattering technique motion over distances up to 30 Å has been observed with an energy resolution of 0.01 μeV (～10⁷s^?1). The motion of the chains in the melt is described by the Rouse model and a friction factor per segment has been extracted from the data. This compares well with values obtained from viscosity and bulk relaxation measurements on similar polymers.     

Nonlinear Rouse-chain relaxations in obstacle media

The entropic interplay of a nonlinearly deformed chain in obstacle media provides elementary knowledge into single-chain dynamics and nonlinear viscoelasticity of polymer liquids flowing in porous or entangled media. This work scrutinized, using Brownian dynamics simulation, the relaxation dynamics of nonlinearly deformed Rouse chains suspended in 2D array of point obstacles. The simulation disclosed a highly confined, anisotropic path of chain retraction that forces a hierarchy of Rouse retraction propagating from the outer segments toward the central ones. Such a constrained Rouse retraction was generally more retarded than free Rouse retraction in dilute system. The classical Doi theory on a 1D Rouse chain captures a similar feature, yet it generally underpredicts the degree of chain retraction as observed in the simulation and seemingly predicts an incorrect dependence on the strain magnitude. For sufficiently long chains, the simulation revealed, in addition, a long-persisting tail of chain stretch well beyond the Rouse regime. This long-time anomaly has further been noted to be closely correlated with another previously unnoticed, dominantly diffusive coil-size relaxation taking place on time scales between the Rouse time and the reptation time. The last feature has been attributed to a general coupling between terminal chain retraction and early-stage chain reptation for relatively long chains. In light of the present findings for obstacle media, we discuss recent experimental trends noted for entangled polymer solutions.     

Concentration dependence of local chain motions of polymers

Summary The chain dynamics of an alternating 1,4-trans-butadiene-propene copolymer has been investigated by high resolution ¹³C NMR spectroscopy in a broad range of concentrations in solution and in the melt. While in semidilute solution all main chain carbon atoms have the same activation energy of motion it is found that, above a concentration of 20 wt%, the activation energy of the aliphatic carbon atoms increases faster with concentration than the activation energy of the olefinic carbon atoms. It is concluded that in dilute and in semidilute solution all carbon atoms are relaxed by localized transitions about methine-methylene bonds, i. e. the bonds with the lowest energy barrier, whereas in concentrated solution and in the melt the relaxation of aliphatic and olefinic carbon atoms is controlled by independent localized transitions about methylene-methylene and methine-methylene bonds, respectively.Generous financial support by the DEUTSCHE FORSCHUNGSGEMEINSCHAFT is greatfully acknowlegded.     

Molecular dynamics of poly(ethylene oxide) in concentrated solution

Incoherent quasi-elastic neutron scattering measurements on aqueous poly(ethylene oxide) solutions show that as the concentration of water is increased to 1:1 mole ratio of water to ethylene oxide monomer units, the polymer chain mobility is not enhanced. Increased mobility is only observed when the water content is increased beyond this ratio. The activation energy for viscous flow shows a similar behaviour, it is unchanged as the system is diluted from the melt to the 1:1 solution and as more water is added it falls sharply. Similar studies on the system poly(ethylene oxide)/toluene show that chain mobility is enhanced and the activation energy for viscous flow falls continuously, at all concentrations. The difference is attributed to the formation of polymer-water hydrogen bonded complexes in aqueous solution. High resolution data for the aqueous systems suggest that the molecular dynamics obey the scattering law predicted for the Zimm model. In the melt the behaviour changes towards the limit given by the Rouse model.     

Structure and dynamics of thin polymer films: a case study with the bond-fluctuation model

This paper reports Monte Carlo simulation results of a polymer melt of short, non-entangled chains which are embedded between two impenetrable walls. The melt is simulated by the bond-fluctuation lattice model under athermal conditions, i.e. only excluded volume interactions between the monomers and between the monomers and the walls are taken into account. In the simulations, the wall separation is varied from about one to about 15 times the bulk radius of gyration R_g. The confinement influences both static and dynamic properties of the films: Chains close to the walls preferentially orient parallel to it. This parallel orientation decays with increasing distances from the wall and vanishes for distances larger than about 2R_g. Strong confinement effects are therefore observed for film thicknesses D?4R_g. The preferential alignment of the chains with respect to the walls suppresses reorientations in perpendicular direction, whereas parallel reorientations take place in an environment of high monomer density. Therefore, they have a relaxation time larger than that of the bulk. On the other hand, the influence of confinement on the translation motion of the chains parallel to the walls is very weak. It almost coincides with the bulk behavior even if D≈1.5R_g. Despite these differences between translational and reorientational dynamics, their behavior can be well reproduced by a variant of Rouse theory which only assumes orthogonality of the Rouse modes and determines the necessary input from the simulation.     

Effects of high molecular weight species on shear-induced orientation and crystallization of isotactic polypropylene

In situ rheo-SAXS (small-angle X-ray scattering) and—rheo-WAXD (wide-angle X-ray diffraction) techniques were used to investigate the role of high molecular weight species on the evolution of oriented microstructure in isotactic polypropylene (iPP) melt under shear flow. The two iPP samples, designated as PP-A and PP-B, respectively, had the same number-average (M_n) but different weight-average (M_w) and Z-average (M_z) molecular weights. Molecular weight distribution (MWD) of PP-A and PP-B was such that for MW<10⁵ the MWD curves overlapped; whereas in the high MW tail region, the amount of high molecular weight species was higher in PP-B than PP-A. Both samples were subjected to an identical shear condition (rate=60 s⁻¹, duration=5 s, T=155 °C). In situ 2D SAXS and WAXD images allowed the tracking of shear-induced oriented structures in the melt. It was found that the shish structures evolved much earlier, and the degree of crystal orientation and oriented crystal fractions were higher in PP-B than PP-A. Moreover, PP-B exhibited faster crystallization kinetics than PP-A. These results, along with the predictions of double reptation models of chain motion and experimental studies of chain conformation dynamics in dilute solutions under flow, suggest the following: When a polymer melt that consists of entangled chains of different lengths is deformed, the chain segments aligned with the flow eigenvector can undergo the abrupt coil-stretch-like transition, while other segments would remain in the coiled state. Since, flow-induced orientation decays much more slowly for long chains than for short chains, oriented high molecular weight species play a prominent role in formation of the stretched sections, where shish originates. Our experimental results are strong evidence of the hypothesis that even a small increase in the concentration of high molecular weight species causes a significant increase in the the formation, stability and concentration of the flow-induced oriented microstructure.     

Molecular size and aggregation behavior of Erwinia gum in aqueous solution

Erwinia (E) gum, a stabilizer and thickening agent of food, is composed of glucose, fucose, galactose, and glucuronic acid (1 : 0.1 : 0.05 : 0.3 by molar ratio). The apparent weight‐average molecular weight M_w and intrinsic viscosity [η] in 0.2 M NaCl aqueous solution were measured to be 7.83 × 10⁵ and 268 mL g⁻¹, respectively, by light scattering and viscometry. The aggregation behavior of E gum in aqueous solution was investigated by gel permeation chromatography (GPC) and dynamic light scattering. The results showed that 7.5% E gum exists as an aggregate, whose diameter is 12 times greater than single‐stranded chain, in aqueous solution at 25°C, and the aggregates' content decreased with increasing temperature or decreasing polymer concentration. The aggregates at higher temperature were more readily broken than in exceeding dilute solution. GPC analysis proved that a significant shoulder, corresponding to a fraction of higher molecular weight due to chain aggregation, appeared in the chromatogram of E gum in 0.05 M KH₂PO₄/5.7 × 10⁻³ M NaOH aqueous solution (pH 6.0) at 35°C, and decreased with increasing temperature, finally disappeared at 90°C. The disaggregation process of E gum in aqueous solution can be described as follows: with increasing temperature, large aggregates first were changed into the middle, then disrupted step by step into single‐stranded chains. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 1083–1088, 2000     

Influence of the adjustable parameters of the DPD on the global and local dynamics of a polymer melt

We present DPD simulations of linear polyethylene melts with force fields derived from microscopic simulations using the concept of potential of mean force. We aim at simulating realistic short polymers from a qualitative and quantitative point of view. An interesting issue is then to know the influence of the adjustable parameters of the DPD: γ, the friction coefficient, and r_C, the cut-off radius, on the global and local dynamics of the polymer, i.e., the diffusion coefficient, D_CM, the end-to-end decorrelation time, τ_R and the Rouse times. By varying these two parameters, we investigate structural and dynamical properties for different polymeric systems at a given chain length. Although scaling laws typical of the Rouse model have been reproduced using this DPD method, we observe deviation from the Rouse theory for the local dynamics of certain systems. The dynamical properties of the polymer melt are defined simultaneously by γ and r_C. Therefore we combine these two parameters, introducing a new parameter, the effective friction coefficient, γ^eff.     

Studies of cyclic and linear poly(dimethyl siloxanes): 12. Observation of diffusion behaviour by quasielastic neutron scattering

High resolution neutron scattering experiments have been used to observe the diffusive motion of low molecular weight linear and cyclic poly(dimethyl siloxane) molecules in dilute solution in deuterated benzene. Diffusion coefficients (D) and hydrodynamic radii (R_H) have been compared with values obtained by light scattering for higher molecular weight samples and with radii of gyration (R_g) obtained by small-angle neutron scattering. While the ratio $\text{D}{}_{\mathrm{<mtext>ring</mtext>}}\text{D}{}_{\mathrm{<mtext>chain</mtext>}}$ is close to the predicted value of 0.85, the ratio $\text{R}{}_{\mathrm{g}}\text{R}{}_{\mathrm{<mtext>H</mtext>}}$ falls below the theoretical value for both ring and chain molecules. The scattering curves show effects arising from both centre of mass diffusion and internal molecular motion, and the observed inverse correlation times are compared with calculated behaviour as a function of scattering vector, Q.     

Study of solution properties of poly(deamino‐tyr‐tyr carbonate hexyl ester) by light scattering and viscometry in dilute and semidilute regime

The structure and properties of poly(deamino‐tyr‐tyr carbonate hexyl ester), in dilute and semidilute solutions, were studied using static, dynamic light scattering, and viscometry. The overlap concentration, c^* is determined by viscosity. The angular dependence of Zimm plots shows no downturn at low angles. In addition, bimodal distribution curves were computed from the quasielastic measurements. The radius of gyration and the second virial coefficient A₂ are found to be respectively 45.8 nm and 9.4 mol cm³ g^?2. The correlation and persistence lengths are discussed. The poly (deamino‐tyr‐tyr carbonate hexyl ester) or poly(DTH‐carbonate) chain in THF, at T = 20°C, behaves as a wormlike chain with persistence length. The persistence length obtained using light scattering is compared with that obtained using viscosity with good agreement. These values obtained from these measurements reflect a high degree of local chain persistence. The reduced viscosity in dilute regime provides a value of apparent viscosity hydrodynamic radius three times lower than obtained by static light scattering. POLYM. ENG. SCI., 50:1605–1612, 2010. © 2010 Society of Plastics Engineers     

Cyclization dynamics of polymers: 7. Applications of the pyrene excimer technique to the internal dynamics of poly(dimethylsiloxane) chains

Poly(dimethylsiloxane) (PDMS) polymers end-capped on both ends with pyrene chromophores have been synthesized. Rate constants for end-to-end cyclization 〈 k₁ 〉 have been determined for dilute solutions of these polymers in toluene solution using a combination of fluorescence decay and steady-state fluorescence measurements. While precise values of the critical exponent for the chain length (N¯) dependence of 〈 k₁ 〉 are not yet available, these results are consistent with the N¯^{? 3/2} dependence predicted by Wilemski-Fixman theory. PDMS chains cyclize somewhat more than two times faster than polystyrene chains of the same length in solvents of similar solvating power and viscosity. These results provide strong support for similar predictions made several years ago by Perico and Cuniberti, who used intrinsic viscosity data to parametrize the Rouse-Zimm model for analysis of polymer cyclization dynamics.     

Some considerations about the structure of polystyrene model-networks

Model-networks designed for neutron scattering experiments were synthesised anionically. Each of the crosslinkages is surrounded by deuterated segments. The well defined correlation distance d between neighbouring crosslinkages is shown by the unique peak in the scattering diagrams. The product d Q^?1/3 - Q being the swelling ratio of the network - is a constant, which demonstrates the affine character of the deformation introduced by swelling. Taking into account the modulus G* of uniaxial deformation, the swelling into Q and the distance d between crosslinkages it was possible to estimate the memory-term h more accurately.     

On the correlation between the viscosity of partially hydrolyzed polyacrylamide solution and the diffusion coefficient in the semidilute concentration regime

The solution viscosity of neutral polyacrylamide (PAM), the partially hydrolyzed polyacrylamide (70% HPAM), and polyacrylic acid (PAA) were measured concurrently with the apparent diffusion coefficient in the dilute and semidilute concentration regimes. We identified the scaling relation η − η_s = A/D in the semidilute regime, where η is the solution viscosity, η_s is the solvent viscosity, D is the coefficient of the slow diffusion mode obtained from dynamic light scattering, and A is a prefactor found to have a unique value of ∼1.0 × 10⁻⁸ cP cm²/s. The scaling relation as well as the prefactor are independent of the the ionic strength, the solvent quality, the molecular weight, the charge density, the polyelectrolyte, and salt concentrations. For the neutral PAM, the product [η – η_s]D is proportional to the polyelectrolyte concentration C_p, consistent with Rouse theory and previous experimental findings.     

Interpretation of quasi-elastic light scattering data for flexible chains: model dependence

The autocorrelation functions and corresponding relaxation times obtained from the forward depolarized quasi-elastic light scattering experiment are exhibited for two quite similar models of flexible polymer chains in solution. A very small change in the chain dynamics is found to be sufficient to change the relaxation time from a relatively short time independent of chain length, with an autocorrelation function suggestive of an unweighted sum of contributions from all the relaxation times in the spectrum of chain motion, to a long time with an autocorrelation function identical with that for the end-to-end vector, strongly dependent upon chain length and dominated by the longest relaxation time in the spectrum. These results raise the question whether widely-used models in which information about short-range chain structure and motion is deliberately omitted can be expected to be appropriate for the interpretation of depolarized scattering experiments.     

Molecular Configuration in Bulk Polymers

Abstract

Experimental results on the following topics are examined and discussed from the point of view of their bearing on the molecular configurations and intermolecular correlations in amorphous polymers: (i) the effect of dilution on the force of retraction f in stretched elastomers; (ii) the effect of dilution on the force-temperature coefficient, and the correspondence of -[?ln(f/T)/?T]_V,_L, to dln < r² >_o/dT found for the linear polymer in dilute solution; (iii) comparison of experimental cyclization constants K_x , for siloxanes, both in absence and in presence of an inert diluent, with values calculated from dimensions (< r² > 0) for the Iinear polymer; (iv) thermodynamic activities of solutions in the Henry's law range; (v) meager results currently available from direct determination of dimensions of polymer chains in the bulk polymer; (vi) depolarized light scattering and the effect thereon of dilution with an isotropic diluent; and (vii) strain birefringence and the effects of dilution on the stress-optical coefficient. Optical anisotropies from (vi) and (vii) and their dependence on concentration indicate local intermolecular correlations, which, however, appear to be not much greater than for simple liquids. None of the experiments (i) to (iv) gives any intimation of an effect of dilution that could be ascribed to dispersal of an ordered arrangement of chains. Results from (ii) and (iii) demonstrate that the same chain configurational parameters found in dilute solutions hold quantitatively in the bulk polymer. Evidence is thus compelling that chain configurations in the bulk amorphous polymer differ inappreciably from the configurations in a dilute solution, apart from effects of excluded volume in the latter environment.     

Theory of correlations in partly labelled homopolymer melts

Small-angle neutron scattering by a polymer melt with partly tagged chains is considered. When several types of chain (differently labelled) are present in the system a new long-range correlation effect which modifies the scattering spectrum is predicted. This effect will arise because of the chemical polydispersity of the sample. A general formalism is developed to calculate the scattering intensity and is applied to special cases: diblock and triblock chains. It is shown that even a small chemical polydispersity leads to important long-range fluctuations and modifies the scattering spectrum substantially.     

Melt viscosity of poly(diethylene glycol-co-succinic acid): Molar mass dependence in the nonentangled regime

Experimental and theoretical results are reported on the dependence of melt viscosity on the molar mass of poly(diethylene glycol-co-succinic acid) (DEG-SA) in the nonentangled regime. A power law described the behavior with an exponent of 2.09 ± 0.10 at 30°C and of 2.59 ± 0.09 at 90°C. The modified Rouse theory was used to describe the relationship between melt viscosity and molar mass. The parameters related to the modified Rouse theory were determined by the WLF equation and the free-volume theory. The WLF parameters of various samples were checked at their T_g, which is the reference temperature. Results confirmed that the free volume and the monomeric friction coefficient (ξ₀) dominate the behavior of the melt. The agreement between the calculated and experimental melt viscosity is satisfactory. © 1994 John Wiley & Sons, Inc.     

Monte Carlo simulation of linear polymer melts in shear flow. Effect of shear stress and confined space on chain dynamics

Linear homopolymer melts under shear stress were studied using a Monte Carlo method in a dense system, using the cooperative motion algorithm. The simulations were performed in a plane-parallel geometry, between reflective walls, for chains up to 640 beads (entangled). Behavior of the melts under shear stress was simulated by appropriate biasing of the bead move probability. Chain dynamics was monitored during reaching the equilibrium flow in the step-shear experiment (creep) simulation, in the equilibrium flow and during melt relaxation. The results were compared with those obtained for non-flowing melt. Significant differences between step-shear and steady-state simulations were observed, while chain dynamics during recovery is almost identical with that in non-flowing melt. Dynamics of the melt depended strongly on the chain length and shear stress, showing nonlinear effects for long chains. Chain orientation, coil deformation and relaxation were analyzed. Relaxation time of long chain decreased by orders of magnitude under shear following the power law. Diffusion of beads and chains was analyzed and an anomalous diffusion was observed, also in the directions perpendicular to the flow direction. In the flowing melt the effect of confined space was important, even if the wall spacing was much bigger than R_g.     

Behaviour of mesogenic side group polyacrylates in dilute and semidilute regime

The solution behaviour of a new mesogenic side group polyacrylate in tetrahydrofuran and toluene has been investigated by static and dynamic light scattering. In the dilute regime the polymer behaves as typical polydisperse linear chains in good solvent and the dynamics is dominated by a single fast mode. Cluster formation was detected starting at a concentration around 50 g l⁻¹. It seems to be independent of the solvent as well as of polymer molecular weight. In the semidilute regime, the behaviour of the reduced osmotic modulus leads to the conclusion that repulsion between the chains is stronger than in linear macromolecules. The appearance of larger clusters was revealed above a characteristic concentration and is slightly dependent on the polyacrylate molecular weight. The dynamics was generally characterised by a fast mode related to the cooperative diffusion and by a slow mode associated with large clusters. The existence of a network of multiconnected clusters is envisaged with increasing solution concentration.     

Phase dissolution in polymer blends Estimation of diffusion coefficients and the associated activation energy

Summary Isothermal phase dissolution of regularly phase-separated structures at deep quench depths below the lower critical solution temperature was studied by light scattering technique for the blend of poly(styrene-co-acrylonitrile) and poly(methylmethacrylate). The phase dissolution studied in this work was that in the diffusion-controlled regime. During the process of phase dissolution the light scattering intensity decays exponentially with time at a rate depending on an effective diffusion coefficient for the center-of-mass motion of the chain molecules in the melt. The diffusion coefficient and the associated activation energy were estimated to be in the order of 10^–14 cm²/s and 50 kJ/mol, respectively.