Dilute Polystyrene Solutions Research Articles

Modeling hydrodynamic interaction in Brownian dynamics: Simulations of extensional and shear flows of dilute solutions of high molecular weight polystyrene

The nonlinear transient extensional and steady-state shear rheological properties of dilute polystyrene solutions of molecular weight 3.9 and 10.2 million in a theta solvent are predicted using Brownian dynamics (BD) simulations with the bead-spring model. Full hydrodynamic interaction is incorporated into BD simulations using the Rotne–Prager tensor. The hydrodynamic interaction parameter h* is obtained a priori by matching the drag force from a fully extended bead-spring model in extensional flow with that from Batchelor’s theory for a cylindrical rod [Hsieh et al. (2003)]. The agreement between experimental data [Gupta et al. (2000)] and simulation results for the transient Trouton ratio versus strain is good from low to medium strains. However, the plateaus at high strains predicted by the simulations are higher than measured. We also find that hydrodynamic interaction hinders the unraveling of a polymer chain in strong extensional flow (Wi≫1) due to the hydrodynamic clustering of beads. In steady she...

Exploring the universal dynamics of dilute polymer solutions in extensional flows

A systematic framework introduced recently to obtain parameter-free predictions of material properties of dilute polymer solutions in extensional flows is reviewed. The essential constraint of ensuring that the model polymer molecule has a finite length is met by using a bead–spring chain model with finitely extensible springs, and the important microscopic phenomenon of excluded volume and hydrodynamic interactions are incorporated in the model. The key aspect of the scheme is the use of Brownian dynamics simulations in the context of a successive fine-graining procedure, which enables the consistent extrapolation of finite bead–spring chain data to the limit of a bead–rod model with the correct degree of flexibility and chain length. Predictions are shown to compare favourably with experimental observations of dilute solutions of polystyrene and DNA molecules.

Pressure dependence of the second virial coefficient of dilute polystyrene solutions

AbstractThe pressure derivatives of the second virial coefficients [dA2/dP; 0.1 ≤ P (MPa) ≤ 35.0] for dilute polystyrene (PS) solutions in good, θ, and poor solvents were measured with static light scattering. The solvent quality improved (dA2/dP > 0) in the good and poor solvents that we investigated (toluene, chloroform; and methylcyclohexane) but deteriorated (dA2/dP < 0) in θ solvents (cyclohexane and 50‐50 cis,trans‐decalin). The effects of temperature [22 < T (°C) < 45] and molecular weight [25 × 103 < weight‐average molecular weight (amu mol−1) < 900 × 103] on dA2/dP for PS/cyclohexane solutions were examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3070–3076, 2003

Modeling hydrodynamic interaction in Brownian dynamics: simulations of extensional flows of dilute solutions of DNA and polystyrene

We describe a method to include full hydrodynamic interactions (HI) using the Rotne–Prager tensor into the bead–spring model without excluded-volume interactions in a way suitable for Brownian dynamics (BD) simulations of the transient nonlinear rheological properties of dilute polymer solutions. First, we develop a scheme to determine the HI parameter h ∗ and bead radius “ a” that keeps the number of beads N modest at high molecular weight and yet matches the bead–spring model to the “real” polymer both in its longest relaxation time or diffusivity near equilibrium and in the drag on the chain at full extension, the latter being estimated by a formula of Batchelor. Second, we compare three different numerical integration methods, namely an explicit Euler’s method, a semi-implicit Newton’s method and a semi-implicit predictor–corrector method, and conclude that the predictor–corrector method is the best one available now, because of its ability to use larger time-steps and the relatively low computational expense for each step. Third, we perform simulations for two different macromolecules, namely λ-phage DNA and high molecular weight polystyrene (PS). We find that we can model λ-phage DNA with full HI with only 10 beads, and find that HI has negligible effect on extensional-flow behavior because of DNA’s expanded configuration even at rest, and therefore, its small value of h ∗=0.03 . For PS in a theta solvent, however, molecular configurations are much more compact, and to avoid bead overlap we must keep h ∗<0.5 . This requires the use of more beads, at least N=20 for a molecular weight of 2 million, even if we drop the requirement that we match the longest relaxation time. Surprisingly, despite our inability to match the experimental longest relaxation time with a limited number of beads, excellent agreement with experimental filament-stretching strain–stress data is obtained except for the plateau Trouton ratio for PS of molecular weight of 2 million at various Weissenberg numbers. The inclusion of HI eliminates the “lag”, the delay in growth of the Trouton ratio relative to experimental data, seen in earlier simulations.

A comparison of the stress and birefringence growth of dilute, semi-dilute and concentrated polymer solutions in uniaxial extensional flows

Filament stretching experiments are used to follow the evolution in the flow-induced birefringence (FIB) and the tensile force in polymeric fluid threads undergoing uniaxial elongation. The tests are performed with several monodisperse polystyrene solutions spanning concentrations from 0.025 to 12 wt.%, and the measurements are used to investigate the extent of hysteresis in the polymeric stress and molecular conformation during imposed stretching and subsequent stress relaxation. For Deborah numbers above De>0.5 (based on the longest or Zimm relaxation time), a pronounced stress-conformation hysteresis is observed in the dilute polystyrene solution at large Hencky strains, and the magnitude of the deviation from the quasi-static FENE connector force increases with imposed deformation rate. However, tests with a semi-dilute entangled polystyrene solution and a concentrated entangled polystyrene solution show that although the stress-optical rule is violated at large deformation rates and large strains, there is no evidence of any hysteresis during extension and relaxation. These observations are interpreted in terms of the relative magnitude of the stretching rate as compared to the reptation time, and also as compared to the Rouse time scales for stretching of the entire chain or for a single entangled segment. These distinct time scales depend on the number of entanglements in the fluid and govern the different relaxation mechanisms that exist in entangled polymer solutions for the polymeric stress and the molecular conformation.

Polymer Depletion-Induced Instability of Silica Suspensions in the Presence of Flexible and Semiflexible Polymers

Polymer depletion-induced instability of silica suspensions in dilute toluene solutions of flexible polystyrene (PS) or semiflexible poly(hexyl isocyanate) (PHIC) was investigated by direct observation and oscillatory moduli measurements as functions of silica volume fraction and polymer molecular weight. Addition of the respective polymers to the gelled silica suspensions induces a gel settling. Below the silica volume fraction φ=4 vol%, PS chains compress the volume of the sediment silica phase, whereas PHIC chains expand it and play a role in swelling agents. Thus, PHIC chains lead to the formation of aggregates in the silica suspensions that are larger and less compact than those formed by the PS chains. On the other hand, above φ=4 vol% where the silica suspension occurs gelation, the effect of nonadsorbing polymers on changes in the volume of the silica phase is opposite. Moreover, polymer depletion interaction results in a mechanically stronger gelled phase, leading to the storage modulus G′ values larger than those without polymer, but the effects of polymer concentration and polymer molecular weight on the G′ values are not clear.

THE FORMATION OF 31 HELIX AND CRYSTALLIZATION BEHAVIOR OF NANOPOLYMERIC PARTICLES CONTAINING SINGLE OR PAUCI CHAINS

Collections of single-and pauci-chain particles were prepared by freezedrying dilute solutions of isotactic polystyrene (i-PS) in benzene. Fourier transform infrared (FTIR) spectroscopy of the particle samples showed that the i-PS chains in very dilute solutions had a highly ordered 31 helical conformation while adopting a random coil conformation in concentrated and semidilute solutions. The transformation from the random coil to the helix takes place as the solution concentration decreases. Differential scanning calorimetry (DSC) analysis revealed that the collected particles from very dilute solution crystallized much faster than bulk polymer. This can be attributed to the retention of the 31 helices in the i-PS chains in the particles. It is presumed that the 31 helix exerted a large influence on the crystallization behavior and ultimate crystallinity of i-PS.

Computer simulation of dilute polymer solutions in transient elongational flows

The growing interest in the behaviour of polymer solutions in porous media is stimulated by a practical application of polymers for drug reduction, oil recovery etc. Different models of porous media were used to study such a behavior. Particularly, a model device which represents two arrays of glass cylinders was recently suggested by Dyakonova et al [1]. In this flow cell the behaviour of dilute polystyrene solutions in trycresylphosphate flowing through a succession of contractions and expansions was investigated. When the flow rate, Q, exceeded some critical value the accumulation of strain by polymer molecules was observed. It manifested in a slight increase of maximum birefringence value on the symmetry axis of the cell from one pair of cylinders to another along the cell.

Extensional viscosity of dilute polystyrene solutions: Effect of concentration and molecular weight

This paper reports a detailed investigation of the steady shear and extensional properties of mono-disperse polystyrene solutions for a range of molecular weights from 1.95 to 20 million and a range of concentrations from 69 ppm to 777 ppm. The steady shear and dynamic properties are reasonably well described by the Zimm model. The relaxation time and polymer viscosity evaluated using the Zimm model exhibit the expected scaling with concentration and molecular weight for theta solutions. In an extensional flow, these solutions show strain hardening and need about 5.5 to 6 strain units to reach steady state. The stress growth depends both on strain rate and strain. However, at moderate values of strain and when the Weissenberg number exceeds 6, the extensional stress growth depends only on total strain. The steady state extensional viscosity for each fluid was observed to depend on the magnitude of Weissenberg number (Wi). For Wi&amp;lt;6, the steady state extensional viscosity was observed to be an increasing function of the strain rate. At a Wi∼10, the steady state extensional viscosity exhibits a maximum and surprisingly, for Wi&amp;gt;10, the steady state extensional viscosity is a decreasing function of the strain rate. The results indicate that even dilute solutions, with concentrations as low as 0.21 times the critical concentration, do show extension thinning under certain conditions. The transient and steady state extensional viscosities are found to be proportional to molecular weight (Mw) and concentration (c). This result is rather unexpected as the Zimm model would predict a scaling with c and Mw0.5 for the transient viscosity and scaling with c and Mw1.5 for the steady state viscosity. On the other hand, the Rouse model predicts a scaling with c and Mw (for transient extensional viscosity) and with c and Mw2 (for steady state extensional viscosity). Hence the data appear to follow a Rouse-like behavior for the transient viscosity. This implies that the advent of the stretching reduces the hydrodynamic interaction and a free draining behavior is obtained. As a result, predictions using the Zimm model parameters, estimated from shear data, are unable to predict the transient extensional viscosity. The data are analyzed using a constitutive equation that incorporates an anisotropic drag coefficient along with a Rouse spectrum of relaxation time. Such a model captures the extensional behavior of the solutions.

Light scattering from nonequilibrium concentration fluctuations in a polymer solution

We have performed light-scattering measurements in dilute and semidilute polymer solutions of polystyrene in toluene when subjected to stationary temperature gradients. Five solutions with concentrations below and one solution with a concentration above the overlap concentration were investigated. The experiments confirm the presence of long-range nonequilibrium concentration fluctuations which are proportional to (∇T)2/k4, where ∇T is the applied temperature gradient and k is the wave number of the fluctuations. In addition, we demonstrate that the strength of the nonequilibrium concentration fluctuations, observed in the dilute and semidilute solution regime, agrees with theoretical values calculated from fluctuating hydrodynamics. Further theoretical and experimental work will be needed to understand nonequilibrium fluctuations in polymer solutions at higher concentrations.

FTIR Analysis of Nanoparticles of Syndiotactic Polystyrene Containing Single and/or Multiple Chains

Samples of nanoparticles containing single and/or multiple chains were prepared by precipitation from dilute solutions of syndiotactic polystyrene (s-PS). Vibrational spectra of the nanoparticles were determined at room temperature and were compared with bulk s-PS. Significant changes in line shape and line width were observed in the spectra of the nanoparticles. Infrared (IR) analysis of the nanoparticles also indicated a faster crystallization rate and higher crystallinity than for the bulk sample.

Brownian dynamics simulations of dilute polystyrene solutions

Brownian dynamics simulations of a bead-spring chain are used to predict the shear and extensional flow properties of dilute polystyrene “Boger fluids” in the filament-stretching device. Using an accurate representation of the inverse Langevin function for the elastic “spring” force of a freely jointed chain, and parameter values extracted from Zimm molecular theory combined with the molecular properties of the polystyrene solutions, quantitatively accurate predictions of the steady-state shear viscosity and first normal stress difference are obtained. The growth of the uniaxial extensional viscosity after startup of steady extension is also reasonably accurately predicted for solutions of 1.95 and 3.9 million molecular weight polystyrene, but for higher polystyrene molecular weights there is a growing overprediction of the high-strain plateau viscosity and a growing lag in the predicted stress growth relative to the measured one. Introduction of “deformation-dependent drag” into the simulations only wors...

Hindered diffusion of flexible polymers through polyimide ultrafiltration membranes

The hindered diffusion of polystyrene in dilute solutions of ethyl acetate through polyimide ultrafiltration membranes has been investigated. The present system did not show specific membrane-solute interactions; furthermore, polystyrene can be considered as a flexible polymer coil. It is shown that the hindered diffusive permeability for monodisperse dilute solutions for a series of molecular weights can be compared well with the diffusive permeability curve of one polydisperse dilute polystyrene solution. In the case of very dilute solutions, the polymer coils have no interaction with each other, and the whole range of molecular-weight-dependent permeabilities can be determined from only one measurement. The diffusion behavior of polydisperse solutions through various polyimide membranes has been investigated as well. It was found that the diffusive permeability curve is strongly dependent on the type of membrane, that is, on the pore size distribution. It was not possible to calculate a pore size distribution from diffusion experiments due to mathematical limitations. Nevertheless, it was shown that hindered diffusion measurements are useful to estimate a maximum pore size for each membrane.

Comparison of Brownian Dynamics Simulations with Microscopic and Light-Scattering Measurements of Polymer Deformation under Flow

Using Brownian dynamics simulations, we predict the deformation of a polymer coil in dilute solution and compare the results to direct measurements for DNA molecules and for polystyrene. For DNA, optical microscopy measurements of Smith and Chu yield measurements of 〈x〉, the average projected length of the molecule onto the flow direction as a function of shear rate, while for dilute polystyrene solutions, light scattering experiments yield 〈Rg2〉1/2, the root-mean-square radius of gyration. Both measurements of deformation, 〈x〉 and 〈 〉1/2, are obtained from the simulations using input parameters required to match the molecular characteristics of both the DNA and the polystyrene solutions used in the experiments. We find that while the agreement between the simulations and the measurements of coil deformation for DNA is excellent, for polystyrene the measured deformation is much less than predicted.

Crystallization and Melting Behavior of Nanopolymeric Particles Containing Single or a Few Chains

Samples of nanopolymeric particles, each containing a single chain or a few chains, were prepared by a freeze-drying method from dilute solutions of isotactic polystyrene (iPS) in benzene. Thermal analysis of the particle samples revealed that the cold crystallization temperature greatly decreases and the crystallization rate remarkably increases as the solution concentration decreases. The increase in crystallization rate can be attributed to fewer interchain entanglements within and between particles, thus proving experimentally for the first time that entanglements can be a large barrier to the crystallization of polymers. Annealing of the particle samples at 373.2 K slightly changed the crystallization behavior, indicating that the interdiffusion of chains between these particles is rather sluggish in the vicinity of T g of bulk iPS. Crystallization is assumed to be accomplished before the chain interdiffusion, and nanocrystals form in situ within compact single- and few-chain globules. The average size of crystals is larger than that of single-chain crystals because the single-chain crystals may initiate other chains to crystallize on the growing crystal surface. Meanwhile, we also found that the nanocrystals have a lower melting temperature than the bulk polymer as a result of their small size.

Stress overshoot of polymer solutions at high rates of shear; Polystyrene with bimodal molecular weight distribution

Overshoot of shear stress, σ, and the first normal stress difference, N1, in shear flow was investigated for dilute solutions of polystyrene with very high molecular weight in concentrated solution of low M PS. In the case that the matrix was a nonentangled system, behavior of overshoot was similar to that of dilute solution of high M PS in pure solvent. The magnitudes of shear, γσm and γNm, corresponding to the peaks of σ and N1 lay on the universal functions of γ˙τR, respectively, proposed for dilute solutions in pure solvent. Here τR is the Rouse relaxation time for high M PS in the blend evaluated from dynamic modulus at high frequencies. In the case that the matrix was an entangled system, an additional σ peak was observed at high rates of shear at times corresponding to γσm = 2–3. This peak can be assigned to the motion of low M chains in entanglement network. When the matrix was entangled, stress overshoot was observed even at relatively low rates of shear, say γ˙τR < 10−2. This is probably due to the motion of high M chains in entanglement of all the chains. In this case the γσm and γNm values were higher than those expected for entangled chains of monodisperse polymer in pure solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2043–2050, 2000

Elastic constants in dilute poly(styrene)/nematic liquid crystal solutions – effects of concentration and molecular weight

We utilized the light scattering from the anisotropy of turbidity (LSAT) method and evaluated, for the first time, the three elastic constants of dilute solutions of polystyrene (PS) in 4-pentyl-4′-cyanobiphenyl (5CB) nematic solvent. Within the solubility range of this system (less than 5%), the elastic constants of splay ( K 1), twist ( K 2), and bend ( K 3) of PS/5CB solution were determined as a function of concentration and molecular weight of PS solute. The experimental results showed a systematic diversion of the elastic constants and, in particular, a large increase in K 1 with increasing concentration and molecular weight of PS. The results are in agreement with the predicted theoretical models and other experimental data. Determination of K i in polymer/nematic solutions with LSAT is a promising experimental approach to study the macromolecular chain structure of flexible, semi-flexible and rigid-rod polymers in anisotropic regimes.

Multimolecule glasses and crystals of isotactic polystyrene

When spreading dilute solutions of isotactic polystyrene (iPS) on water, it was observed that different concentrations produce different morphologies in the resulting amorphous films. From 10−1 to 10−2 wt% solutions, ribbonlike films and circular platelets of multimolecule aggregates were obtained. After isothermal crystallization of these amorphous films, lamellae, incipient spherulites, and single-molecule crystals were observed. The formation of lamellar crystals lying flat on the substrate is an indication of the absence of epitaxy by the substrate, which would require the molecular chains to be in the surface plane and thus yield lamellae normal to the substrate. The dense packing in the center of sheaflike spherulites is caused by screw-dislocation growth, and it produces structures similar to shish kebabs. It was also observed that the lamellae grown from the center develop secondary growth spirals, causing the branching and splaying of the structure typical for spherulitic growth.

Comparison of dumbell-based theory and experiment for a dilute polymer solution in a corotating two-roll mill

The Chilcott–Rallison FENE dumbbell model is used to solve for the polymer and flowfield response in transient startup flow of a dilute solution in a corotating two-roll mill. These predictions are then compared to experimental results obtained in an identical geometry using a high molecular weight dilute (c/c*∼0.1) polystyrene solution. As predicted by the dumbbell model, the experiments indicate a substantial coupling between the polymer deformation and changes to the Newtonian flowfield. As the polymer stretches, the experimentally measured shear rate decreases, as does the flow-type parameter. However, dumbbell model parameters based upon an isolated chain do not result in FENE model predictions quantitatively similar to the experimental results. Based upon steady-state birefringence values for the same dilute solution in an extension dominated flow at large strain rates, it appears that chain–chain interactions restrict the maximum attainable polymer deformation. Further calculations incorporating th...

GPC Data Interpretation in Mechanochemical Polymer Degradation

Molecular weight distribution obtained by gel permeation chromatography (GPC) conceals a wealth of mechanistic information which can be disclosed only after adequate data treatment. This paper discusses how GPC chromatograms may be used for the elucidation of polymer degradation kinetics. The case of ultrasonic degradation of dilute polystyrene solutions was investigated in detail. The extent of bond scission was determined as a function of sonication time and initial polymer molecular weight. Different bond scission mechanisms were evaluated by comparing calculated molecular weight distributions with experimental data. Best agreement was obtained when multiple fragmentation was included in the degradation scheme, a result experimentally supported by spectroscopic chain ends titration. The results are rationalized by establishing a parallelism between transient elongational flow and ultrasonic degradation.