Semidilute Solutions Of Polystyrene Research Articles

Slip and Friction Mechanisms at Polymer Semi-Dilute Solutions/Solid Interfaces

The role of the polymer volume fraction, $\phi$, on steady state slippage and interfacial friction is investigated for a semi-dilute polystyrene solutions in diethyl phthalate in contact with two solid surfaces. Signicant slippage is evidenced for all samples, with slip lengths b obeying a power law dependence. The Navier's interfacial friction coecient, k, is deduced from the slip length measurements and from independent measurements of the solutions viscosity $\eta$. The observed scaling of k versus $\phi$ clearly excludes a molecular mechanism of friction based on the existence of a depletion layer. Instead, we show that the data of $\eta$($\phi$) and k($\phi$) are understood when taking into account the dependence of the solvent friction on $\phi$. Two models, based on the friction of blobs or of monomers on the solid surface, well describe our data. Both points out that the Navier's interfacial friction is a semi-local phenomenon.

Shear thinning in dilute and semidilute solutions of polystyrene and DNA

The viscosity of dilute and semidilute unentangled DNA solutions, in steady simple shear flow, has been measured across a range of temperatures and concentrations. For polystyrene solutions, measurements of viscosity have been carried out in the semidilute unentangled regime, while results of prior experimental measurements in the dilute regime have been used for the purpose of data analysis, and for comparison with the behaviour of DNA solutions. Interpretation of the shear rate dependence of viscosity in terms of suitably defined non-dimensional variables, is shown to lead to master plots, independent of temperature and concentration, in each of the two concentration regimes. In the case of semidilute unentangled solutions, defining the Weissenberg number in terms of a concentration dependent large scale relaxation time is found not to lead to data collapse across different concentrations. On the other hand, the use of an alternative relaxation time, with the concentration dependence of a single correlation blob, suggests the existence of universal shear thinning behaviour at large shear rates.

Flow of dilute to semi-dilute polystyrene solutions through a benchmark 8:1 planar abrupt micro-contraction

We have studied the flow of thermodynamically ideal solutions of a high molecular weight ( M w = 6.9 MDa) atactic polystyrene in the θ solvent dioctyl phthalate (aPS in DOP) through a micro-fabricated 8:1 planar abrupt contraction geometry. The channel is much deeper than most micro-scale geometries, providing an aspect ratio of 16:1 and a good approximation to 2D flow in the narrow channel. The solutions span a range of concentration 0.03 wt.% < c < 0.6 wt.%, encompassing the dilute to semi-dilute regimes and providing a range of fluid viscosities and relaxation times such that we achieve a range of Weissenberg numbers (8.7 < Wi < 1562) and Reynolds numbers (0.07 < Re < 11.2), giving elasticity numbers between 31 < El < 295. We study the flow using a combination of micro-particle image velocimetry (μ-PIV) to characterize the flow field, pressure measurements to evaluate the non-Newtonian viscosity, and birefringence measurements to assess macromolecular strain. Flow field observations reveal three broad flow regimes characterized by Newtonian-like flow, unstable flow and vortex growth in the upstream salient corners. Transitions between the flow regimes scale with Wi, independent of El, indicating the dominance of elastic over inertial effects in all the fluids. Transitions in the flow field are also reflected by transitions in the relative viscosity (determined from the pressure drop) and the macromolecular strain (determined from birefringence measurements). The strain through the 8:1 contraction saturates at a value of ∼4–5 at high Wi. The results of these experiments broaden the limited set of literature on flow through micro-fluidic planar contractions and should be of significant value for optimizing lab-on-a-chip design and for comparison with modeling studies with elasticity dominated fluids.

Solvent effects on jet evolution during electrospinning of semi-dilute polystyrene solutions

Linear polystyrene with a weight average molecular weight of 393,400 g/mol was used with various solvents including tetrahydrofuran (THF), chloroform, carbon disulfide (CS 2), 1-methyl-2-pyrrolidinone (NMP), and N, N-dimethylformamide (DMF) to produce solutions, corresponding to a Berry number of about 9. The jet breakdown behavior of each of these solutions was studied with a high speed camera (2000 frames/s). The structure of the electrospun polymer was examined with a scanning electron microscope. The results indicate that jet breakdown with THF and chloroform entailed significant extensional flow, followed by the onset of instabilities, leading to the formation of numerous secondary jets under steady-state conditions. By comparison, the solution jets with DMF and NMP exhibit extensive whipping and splaying to produce a cloud of jets. In this case, few secondary jets were observed under steady-state conditions. A highly refined structure was observed in the electrospun polymer for NMP and DMF, in accordance with the extensive instabilities observed during jet breakdown. Limited jet instability observed with CS 2 solution suggests the significant effect of solvent evaporation. Typical primary jet velocities were measured to be on the order of 2–5 m/s.

Nanostructure of polymer layers formed upon the adsorption from binary and ternary solutions

Thicknesses of nanolayers formed upon the adsorption from dilute and semidilute solutions of polystyrene, poly(butyl methacrylate), and their mixtures on the surface of solid SiO2 are estimated on the basis of adsorption isotherms and atomic force microscopy measurements. It is established that the thickness of an adsorption layer is determined by the sizes of individual macromolecular coils and clusters arising in a solution. In the case of polymer blends, adsorption leads to the formation of mosaic structures with the alternation of polymeric components in the substrate plane; the characteristic size of a domain is ≈200 nm for each component. It is shown that adsorption layers formed on the surface of a silicon single crystal (covered with intact oxide) are fractal objects whose dimension depends on the nature of polymer and conditions of its adsorption.

Relaxation processes in mixtures of liquid crystals and polymers near phase boundaries and during phase separation.

We present experimental studies of the relaxation of concentration fluctuations in a semidilute solution of polystyrene (PS) (30% by weight) in 4-cyano-4'-n-octyl-biphenyl (8CB) (70% by weight) using the photon correlation spectroscopy (PCS). In the homogeneous phase there are two modes of relaxation. The slow one (typical time scale is taus = 0.001 s) is due to the diffusion of polymer chains (of molecular mass 65,000) in the LC matrix (of molecular mass 290), while the fast one has the time scale of the order of tauf approximately 0.00001 s. The amplitude of the fast mode is much weaker than the one for the slow mode. Moreover it does not depend on the scattering wave vector, q. The value of the diffusion coefficient, Dc = 1/(tausq2) for the slow mode decreases with temperature according to the Arhenius law until we reach the coexistence curve. Its value close to the coexistence is Dc = 4 x 10(5) nm2/s and the activation energy in the homogeneous mixture is Ec=127 kJ/mol. If we gradually undercool the mixture below the coexistence into the metastable two-phase region without inducing the phase separation we find unexpectedly that Dc does not change with temperature even 4 degrees below the coexistence curve. The characteristic time of the fast mode does not depend on the scattering wave vector indicating that it is related to the transient gel structure. We have shown that it is possible to measure the short time relaxation of concentration fluctuations during the phase separation in the mixture. At low temperature close to the isotropic-nematic phase transition we have observed that the relaxation is well separated in time from the typical time of the domain growth. This relaxation mode is characterized by the large diffusion coefficient D = 2 x 10(8) nm2/s. The mode probably comes from the coupling between the orientational dynamics of liquid crystals and the transient gel structure of polymers.

Rheology of Polystyrene Solutions with Scarcely Entangled Chains; Role of Slow Relaxation Mode in Nonlinear Behavior

Linear viscoelasticity behavior was described with sum of two terms for semi-dilute polystyrene solutions in tricresyl phosphate with molecular weights (M) close to 2Me, where Me is the entanglement molecular weight in the solution. One was a Rouse-Zimm (RZ) term represented by the Rouse-Zimm theory with arbitrarily chosen value of the longest relaxation time (τRZ). The other (L term) consisted of a relaxation mode with single relaxation time, τL (>τRZ), and high-frequency limiting modulus (GL) proportional to square of concentration, c. The shear stress, σ, and the first normal stress difference, N1, in steady shear were described with simple formulas proposed previously for more dilute solutions. The stress due to L term was assumed to be given by a K-BKZ equation with damping function h(γ)= (1+0.2γ2)−1/2, where γ is magnitude of shear. Contributions to σ and N1 from RZ term were derived from the Rouse-Zimm model theory, in which the relaxation time in steady flow decreased with rate of shear, γ, as τst=τRZ0+(τRZ−τRZ0)/(1+0.35τRZ γ). Here τRZ0 is the longest relaxation time of the polymer at the infinite dilution limit. The result together with previous result for more dilute solutions implies that η and Ψ1 for any non-entangled solutions are well described with use of parameters derived from dynamic viscoelasticity.

Colloidal dynamics in polymer solutions: optical two-point microrheology measurements.

We present an extension of the two-point optical microrheology technique introduced by Crocker et al. [J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh and D. A.Weitz, Phys. Rev. Lett., 2000, 85, 888] to high frequencies. The correlated fluctuations of two probe spheres held by a pair of optical tweezers within a viscoelastic medium are determined using optical interferometry. A theoretical model is developed to yield the frequency-dependent one- and two-particle response functions from the correlated motion. We demonstrate the validity of this method by determining the one- and two-particle correlations in a semi-dilute solution of polystyrene in decalin. We find that the ratio of the one- and two-particle response functions is anomalous which we interpret as evidence for a slip boundary condition caused by depletion of polymer from the surface of the particle.

Shear-Induced Structures in Semidilute Polystyrene Solution: Effect of Solvent Quality

The effect of solvent quality on shear-induced structures in semidilute polystyrene solutions are investigated by using light-scattering and rheological methods. We found that the shear-induced structures are universally formed in various solvents employed in this experiment. We especially focus on a critical shear rate γ̇cx, at which the light scattering intensity starts to increase in our experimental geometry, and on a critical shear stress, σxy,cx, at γ̇ = γ̇cx. We found that γ̇cx is not well correlated with χ but rather that σxy,cx is better correlated with χ, where χ is the Flory−Huggins interaction parameter between polystyrene and solvents. σxy,cx increases with decreasing χ. This indicates that the structure formation is strongly affected by solvent quality, mainly through the thermodynamic state of the solution. We also analyzed the solvent quality dependence of γ̇cx in the context of Onuki's linear theory, and found that γ̇cx can be scaled by Kos/η0, where Kos is the osmotic modulus and η0 the zero-shear viscosity.

Critical conditions for structure formation in semidilute polymer solutions induced under continuous shear flow

Critical conditions for shear-induced structure formation in semidilute polystyrene solutions with dioctyl phthalate as a solvent are studied by light scattering and rheological measurement. The critical shear rate γ̇cx for the onset of the nonlinear enhancement (defined in the text) of the concentration fluctuations are investigated as functions of temperature and concentration. γ̇cx increases with increasing temperature or decreasing concentration, reflecting the temperature and concentration dependence of the thermodynamic and viscoelastic properties. This temperature and concentration dependence of γ̇cx was found to be in parallel to that of the critical shear rate for the onset of the linear enhancement (also defined in the text) of the concentration fluctuations, which can be explained in terms of a linear theory proposed by Onuki. The critical shear stress and the critical first normal stress difference corresponding to γ̇cx are also explored, the physical interpretation of which will be discussed in detail in conjunction with the stress components arising from anisotropic concentration fluctuations, based on the calculation by van Egmond.

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

Dynamic Light Scattering of Polymer/Solvent Solutions Under Pressure. Near-Critical Demixing (0.1 &lt; P/MPa &lt; 200) for Polystyrene/Cyclohexane and Polystyrene/Methylcyclohexane

A conveniently sized high-pressure scattering cell used for 90° DLS (dynamic light scattering) measurements on polymer solutions is described (0 < P/MPa < 200; 283 < T/K < 373). DLS parameters are reported for semidilute solutions of polystyrene (PS) of various molecular weight in ϑ-solvents (cyclohexane (CH) and methylcyclohexane (MCH)), above and below Tϑ, and at high enough concentration to ensure that precipitation, when it occurs, follows spinodal decomposition/percolation. In the homogeneous region, close to and above Tϑ, the correlograms, initially monomodal and diffusive, split at high pressure. The intensity and the correlation radius of the diffusive mode diverge as critical demixing is approached during pressure or temperature quenches. That process is described in the (T,P)ψcr plane using a multidimensional reduced scaling formalism developed for the purpose. The analysis of the scattering and the phase equilibrium data for PS/CH is complicated by the pressure dependence of the CH freezing curve, but that for PS/MCH nicely exemplifies behavior across a good part of the (T,P)ψcr reentrant miscibility island showing multiple hypercritical points. It has been discussed in that context.

Static and dynamic light scattering experiments on semidilute solutions of polystyrene in cyclohexane between the Θ-temperature and the binodal curve

Static and dynamic light scattering experiments are carried out with solutions of a high molar mass polystyrene (Mw=0.96×106 g mol-1) in cyclohexane at different concentrations of the polymer. At the Θ-temperature TΘ the critical concentration of the system is located in the semidilute regime. The temperature is varied between TΘ and the temperature of phase separation TP of the solutions. At TΘ the distribution of the amplitudes of the relaxation rates of the autocorrelation function of the electric field is bimodal (slow and fast relaxation rates) in the semidilute regime. It becomes monomodal approaching TP. The contribution of the fast relaxation rates disappears and the weak q-dependence of the slow mode changes over to a q-dependence similar to that of the critical relaxation rate in binary liquid mixtures of low molar mass components close to the critical temperature Tc. On approaching the temperature of phase separation by decreasing the temperature, concentration fluctuations with long range correlations develop. The change of the q-dependence of the slow relaxation rate is rationalised using the transient gel model of Brochard and de Gennes. Here it is assumed that approaching TP transient gels formed by interpenetrating polymer coils become part of the concentration fluctuations with long range correlations. The dynamics of the solutions in the vicinity of the binodal curve monitored by dynamic light scattering experiments is dominated by the dynamics of the concentration fluctuations with long range correlation.

Micellar Ordering in Concentrated Solutions of Di- and Triblock Copolymers in a Slightly Selective Solvent

Micellar ordering in semidilute solutions of polystyrene−polyisoprene diblock and triblock copolymers in the slightly selective solvent di-n-butyl phthalate has been studied using rheology and small-angle X-ray scattering (SAXS). Ordering as a function of temperature has been investigated for a range of polymer concentrations 0.1 ≤ φ ≤ 0.4. For φ < 0.2, the rheological response is liquidlike and SAXS shows that there is no intermicellar order in the liquid; however, the solution viscosity shows a strong maximum near 50 °C. Above a crossover concentration φ ≈ 0.2, ordering of micelles is indicated by the presence of a sharp structure factor peak. The ordered micellar structure, identified as hexagonal for 0.2 ≤ φ ≤ 0.3 and lamellar for φ ≥ 0.3, persists up to an order−disorder transition at T ≈ 40 °C for the diblock and T ≈ 50 °C for the triblock solutions studied. The rheological characteristics of the ordered solutions are reminiscent of those found in ordered block copolymer melts. At higher temperature...

Sharp Crossover of the Susceptibility in Polymer Solutions near the Critical Demixing Point

We have observed a sharp and nonmonotonic crossover of the susceptibility (osmotic compressibility) from mean-field to Ising critical behavior in semidilute solutions of polystyrene in deuterocyclohexane as the temperature decreases from the $\ensuremath{\Theta}$ region down to the critical temperature of the phase separation. We describe this crossover in terms of a competition between the long-range but finite intramolecular correlations of monomers in the polymer chain and the diverging correlation length of concentration fluctuations.

Rheo-Optical Studies of Shear-Induced Structures in Semidilute Polystyrene Solutions

Shear-induced structure formation in semidilute solutions of high molecular weight polystyrene (PS) was investigated by rheology, shear-dichroism, shear-birefringence, shear-small-angle light-scattering (SALS) and shear-optical-microscopy methods. At the shear rate γc < γ < γa, where γc and γa are the critical shear rates for the onset of the shear-enhanced concentration fluctuations and the onset of the anomalies in the rheological and scattering behaviors respectively, we observed negative dichroism, almost zero birefringence, and butterfly type LS patterns. All these results are consistent with the optical images captured by shear-microscopy and show the shear-induced concentration fluctuations with the following characteristics: the amplitude of the fluctuations is enhanced along the flow direction, and the domain structure (regions rich in polymer concentration) formed is extended normal to flow. However, at the shear rate γ > γa, the dichroism became positive and the absolute values of both the dichroism and the birefringence increased drastically. The changes in the dichroism and the birefringence are believed to be related to formation of the stringlike structures and molecular orientation both parallel to flow.

Time Evolution of Shear-Induced Structures in Semidilute Polystyrene Solutions

We investigated time evolution of structures induced by imposing shear flow on semidilute solutions of high molecular weight polystyrene (PS) by means of both flow light scattering and rheology. PS with weight-average molecular weights of 5.48 × 106 and 2.89 × 106 were dissolved in dioctyl phthalate (DOP). After imposing shear flow with a shear rate γ̇ > γ̇c (the critical shear rate for shear-induced concentration fluctuations), the unique butterfly-type scattering pattern appeared. The pattern had a scattering maximum along the flow direction. The wave number qm and the intensity Im at the scattering maximum decreased and increased, respectively, with time and eventually reached steady state values. The rheological experiments that were carried out on the same solution under the same shear flow revealed two stress overshoots. The second overshoot was found to be related to the development of butterfly pattern and its time change, i.e., to the formation and growth of shear-induced structures.

Shear-flow effects on self-assembly of semidilute solutions of off-critical polymer mixtures: Shear-hysteresis effects

We use flow light scattering to study the phase transitions in semidilute solutions of polystyrene and polybutadiene in dioctylphthalate under simple shear flow. The phase-separated solution was brought into a single-phase state by increasing the shear rate, γ̇, above a critical shear rate, γ̇c,i. The solution was then brought back into a two-phase state by lowering γ̇ below a critical shear rate, γ̇c,d. We previously reported a large hysteresis effect in solutions with off-critical compositions; γ̇c,i is always higher than γ̇c,d. Shear-drop experiments were conducted to illuminate the origin of this hysteresis effect. The experimental results showed that at temperatures close to the cloud point temperature the formation of phase separated structures did not occur until up to 22 h after lowering the shear rate below γ̇c,i. Thus the hysteresis effect was found to be due to a surprisingly slow ordering process at γ̇ close to γ̇c,i. The ordering induced by the shear drop needs a much longer time than the homogenization induced by increasing shear. If the time scale of observation is sufficiently long, the hysteresis effect disappears, yielding the drop of cloud point temperature with shear, ΔTc(γ̇), given by ΔTc(γ̇)∝γ̇1.0±0.1 for the off-critical mixtures, rather than ΔTc(γ̇)∝γ̇0.5±0.1 found previously for the near critical mixtures. Finally, the incubation time was found to initially increase with γ̇ and then decrease with a further increase of γ̇, suggesting that the ordering mechanisms are different in the low and high shear-rate regimes.

Self Knotting of Polystyrene Chains in a Θ Solvent

For many reasons, it is instructive to examine situations in which topological restrictions have conspicuous effects on polymer dynamics. A polymer solution, in a poor solvent at the Flory or Θ temperature, is one of them. Here, as in the case of polymer melts, the chain adopts random walk configurations which favour self entanglements. However, because of differences in space filling, effects of topological constraints are noticeably different in poor solvents and in the melt state. We present the results of a neutron quasielastic scattering experiment by a semi-dilute solution of polystyrene in cyclohexane at the Flory temperature. Both solvent and solute contain labeled molecules in proportions satisfying the zero average contrast condition. The outcome of the experiment is the dynamical, time dependent autocorrelation function of the polystyrene chain in a semi-dilute solution. Comparing the results obtained on the same sample at and above the Θ temperature, we display the observed differences and interpret them as the result of self entanglements.

A rheo‐optical study of near‐critical polymer solutions under oscillatory shear flow

The flow‐induced structure and dynamics of concentration fluctuations in a near‐critical polymer solution have been investigated using the technique of polarimetry. Specifically, this article presents scattering dichroism of a single‐phased, semidilute solution of polystyrene in dioctyl phthalate (PS/DOP) subjected to small amplitude oscillatory shear flow. The measured frequency response is compared to results obtained using the Onuki–Doi theory, which relates dichroism to structure factor, and the Helfand–Fredrickson model, from which the structure factor is calculated. The predictions are in good qualitative agreement with the experimental data when stress relaxation is taken into account in the constitutive equation relating stress to strain in the system. Our results demonstrate that the strength of the coupling between viscoelastic stress and flow governs the behavior of concentration fluctuations in semidilute polymer solutions under oscillatory shear flow.