Structure of a semidilute polymer solution under steady shear

We use Brownian dynamics computer simulations to investigate the structure of a semidilute polymer solution undergoing a steady, uniform shear flow. We find that the contributions to structure factor from intra- and interchain correlations, which cancel each other almost completely for an equilibrium semidilute solution, are modified in different ways by the shear flow. Incomplete cancellation of these contributions leads to anisotropic patterns that resemble those observed in light scattering experiments on sheared semidilute solutions [Wu et al., Phys. Rev. Lett. 66, 2408 (1991)]. For small wave vectors the structure factor change is dominated by the interchain contribution. We also monitor the distortion of the pair correlation function and show that for small distances it is dominated by the intrachain contribution. Finally, we investigate nonlinear shear viscosity and find that, like the short-distance part of the distortion of the pair correlation function, it is predominantly of intrachain origin.     

Dynamic light scattering in sols of a poly(N-vinylcaprolactam) and polyacrylamide mixture

The properties of semidilute solutions of a mixture of polyacrylamide and thermoresponsive polyvinylcaprolactam are studied via dynamic light scattering. It is found that the relaxation time (correlation length) distribution contains several modes. The obtained experimental data are interpreted in terms of the theory describing the dynamics of semidilute and concentrated solutions with allowance for viscoelastic interactions. The investigation of mode dispersion (the dependence of relaxation time on the wave vector of scattering) shows that the fastest and slowest modes are of the diffusion type. The fast mode is the mode of collective diffusion; it may be attributed to the fluctuation motion of polymer units inside blobs. The slowest mode corresponds to the diffusion motion of macromolecule clusters. The rate of relaxation of medium modes nonlinearly depends on the squared wave vector, and these modes are apparently viscoelastic.     

Dispersions of nanocrystalline cellulose in aqueous polymer solutions: structure formation of colloidal rods

The steady-state shear and linear viscoelastic deformations of semidilute suspensions of rod-shaped nanocrystalline cellulose (NCC) particles in 1.0% hydroxyethyl cellulose and carboxymethyl cellulose solutions were investigated. Addition of NCC at the onset of semidilute suspension concentration significantly altered the rheological and linear viscoelastic properties of semidilute polymer solutions. The low-shear viscosity values of polymers solutions were increased 20-490 times (depending on polymer molecular weight and functional groups) by the presence of NCC. NCC suspensions in polymer solutions exhibited yield stresses up to 7.12 Pa. Viscoelasticity measurements also showed that NCC suspended polymer solutions had higher linear elastic moduli than the loss moduli. All of those results revealed the gel formation of NCC particles and presence of internal structures. The formation of a weak gel structure was due to the nonadsorbing macromolecules which caused the depletion-induced interaction among NCC particles. A simple interaction energy model was used to show successfully the flocculation of NCC particles in the presence of nonadsorbing polymers. The model is based on the incorporation of the depletion interaction term between two parallel plates into the DLVO theory for cubic prismatic rod shaped NCC particles.     

Strain Hardening and Strain Softening of Reversibly Cross-linked Supramolecular Polymer Networks

The large amplitude oscillatory shear behavior of metallo-supramolecular polymer networks formed by adding bis-Pd(II) cross-linkers to poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO) solution is reported. The influence of scanning frequency, dissociation rate of cross-linkers, concentration of cross-linkers, and concentration of PVP solution on the large amplitude oscillatory shear behavior is explored. In semidilute unentangled PVP solutions, above a critical scanning frequency, strain hardening of both storage moduli and loss moduli is observed. In the semidilute entangled regime of PVP solution, however, strain softening is observed for samples with faster cross-linkers (k(d) ～ 1450 s(-1)), whereas strain hardening is observed for samples with slower cross-linkers (k(d) ～ 17 s(-1)). The mechanism of strain hardening is attributed primarily to a strain-induced increase in the number of elastically active chains, with possible contributions from non-Gaussian stretching of polymer chains at strains approaching network fracture. The divergent strain softening of samples with faster cross-linkers in semidilute entangled PVP solutions, relative to the strain hardening of samples with slower cross-linkers, is consistent with observed shear thinning/shear thickening behavior reported previously and is attributed to the fact that the average time that a cross-linker remains detached is too short to permit the local relaxation of polymer chain segments that is necessary for a net conversion of elastically inactive to elastically active cross-linkers. These and other observations paint a picture in which strain softening and shear thinning arise from the same set of molecular mechanisms, conceptually uniting the two nonlinear responses for this system.     

Nanoparticle stability in semidilute and concentrated polymer solutions

The wetting of PDMS-grafted silica spheres (PDMS- g-silica) is connected to their depletion restabilization in semidilute and concentrated PDMS/cyohexane polymer solutions. Specifically, we found that a wetting diagram of chemically identical graft and free homopolymers predicts stability of hard, semisoft, and soft spheres as a function of the bulk free polymer volume fraction, graft density, and the graft and free polymer chain lengths. The transition between stable and aggregated regions is determined optically and with dynamic light scattering. The point of demarcation between the regions occurs when the graft and free polymer chains are equal in length. When graft chains are longer than free chains, the particles are stable; in contrast, the particles are unstable when the opposite is true. The regions of particle stability and instability are corroborated with theoretical self-consistent mean-field calculations, which not only show that the grafted brush is responsible for particle dispersion in the complete wetting region but also aggregation in the incomplete wetting region. Ultimately, our results indicate that depletion restabilization depends on the interfacial properties of the nanoparticles in semidilute and concentrated polymer solutions.     

Association under shear flow in aqueous solutions of pectin

Effects of oscillatory and steady shear flows on intermolecular associations in dilute and semidilute aqueous solutions of pectin in the absence and presence of the hydrogen bond breaking agent urea are reported. A weak oscillatory shear perturbation builds up, depending on polymer concentration, multichain aggregates or networks in the course of time and these association structures are mainly stabilized through hydrogen bonds. The association effect is more pronounced at higher concentrations, and the growth of intermolecular interactions is inhibited by the addition of urea. Steady shear measurements on the pectin-water solutions reveal shear thickening at low shear rates for all the concentrations, except the lowest one, and disruption of intermolecular junctions at high shear rates. In the presence of urea, no shear thickening is detected. The polymer concentration dependence of the viscosity at a low shear rate can be described by a power law η ∼ c^x, with x = 1.9 and 1.4 without and with urea, respectively. When a low constant shear rate is applied to pectin solutions and this monitoring shear rate is interrupted periodically by transitory high shear rates perturbations during a short time, prominent association structures evolve upon return to the monitoring shear rate. This effect is more evident at a lower polymer concentration, and in the presence of urea, the growth of the association complexes is damped. The shear-induced alignment and stretching of polymer chains and the formation of hydrogen-bonded structures are analyzed in the framework of a model, where cooperative zipping of stretched chains play an important role. Viscosity enhancement is found for a semidilute pectin-water solution in the presence of moderate levels of salt addition (NaCl), suggesting that partial screening of electrostatic interactions promotes growth of energetic cross-links.     

Temperature-induced association and gelation of aqueous solutions of pectin. A dynamic light scattering study

Dynamic light scattering (DLS) measurements were carried out on aqueous solutions of low-methoxyl pectin at different temperatures and polymer concentration. Low temperature and increased polymer concentration promote the formation of multichain aggregates. The time correlation data obtained from the DLS experiments revealed, for all polymer solutions, the existence of two relaxation modes, one single exponential at short times followed by a stretched exponential at longer times. In the semidilute regime, a temperature reduction induced enhanced chain associations in the solutions with high values of the slow relaxation time and a strong wave vector dependence of the slow mode. These features could be rationalized in the framework of the coupling model of Ngai. At low temperatures (10 °C), gelation occurs in the semidilute regime and a transparent gel is formed. In this state, the profile of the correlation function changes and nonergodic signs are observed. The conjecture is that the association complexes and the gel network are stabilized through intermolecular hydrogen bonds, which are broken-up at higher temperatures. The hydrogen-bonded structures are formed in a process where the polymer chains have been “zipped” together in a cooperative manner.     

一种四臂聚苯乙烯凝胶的激光光散射研究

采用原子转移自由基方法(ATRP)合成窄分布的末端基为巯基的四臂星型聚苯乙烯(4-PS-SH).巯基容易被空气中的氧气氧化生成二硫键,会引起四臂星型聚苯乙烯分子间交联.利用激光光散射研究了四臂聚苯乙烯在亚浓溶液中氧化交联生成大的胶束进而生成宏观化学凝胶的过程.静态激光光散射测量结果表明四臂聚苯乙烯亚浓溶液以及凝胶样品的时间平均散射光强不随测量位置的变化而涨落,说明此凝胶是结构均一的化学凝胶.动态光散射结果表明在四臂聚苯乙烯亚浓溶液氧化生成凝胶的过程中,动态强度-强度时间相关函数的慢运动衰减的贡献最初随着氧化时间的增加逐渐增强,当氧化反应进行到一定程度时慢运动的贡献又逐渐减弱,最终慢运动消失.生成的化学凝胶的相关函数与最初亚浓溶液的相关函数几乎重合.静态和动态激光光散射结果表明生成的四臂聚苯乙烯凝胶是结构均匀的化学凝胶.     

Capillary electrophoresis of RNA in dilute and semidilute polymer solutions

We report separations of RNA molecules (281-6583 nucleotides) by capillary electrophoresis in dilute and semidilute solutions of aqueous hydroxyethylcellulose (HEC) ether in varying buffers. RNA mobility and peak band widths are examined under both nondenaturing and also denaturing conditions. From studies of sieving polymer concentration and chain length, it is found that good separations can be obtained in semidilute solutions as well as in dilute solutions. The dependence of RNA mobility on its chain length is consistent with separation by a similar to transient entanglement mechanism in dilute solutions. In semidilute entangled solutions the separation proceeds by segmental motion.     

Molecular dynamics simulations of supramolecular polymer rheology

Using equilibrium and nonequilibrium molecular dynamics simulations, we studied the equilibrium and rheological properties of dilute and semidilute solutions of head-to-tail associating polymers. In our simulation model, a spontaneous complementary reversible association between the donor and the acceptor groups at the ends of oligomers was achieved by introducing a combination of truncated pseudo-Coulombic attractive potential and Lennard Jones repulsive potential between donor, acceptor, and neighboring groups. We have calculated the equilibrium properties of supramolecular polymers, such as the ring/chain equilibrium, average molecular weight, and molecular weight distribution of self-assembled chains and rings, which all agree well with previous analytical and computer modeling results. We have investigated shear thinning of solutions of 8- and 20-bead associating oligomers with different association energies at different temperatures and oligomer volume fractions. All reduced viscosity data for a given oligomer length can be collapsed into one master curve, exhibiting two power-law regions of shear-thinning behavior with an exponent of -0.55 at intermediate ranges of the reduced shear rate β and -0.8 (or -0.9) at larger shear rates. The equilibrium viscosity of supramolecular solutions with different oligomer lengths and associating energies is found to obey a power-law scaling dependence on oligomer volume fraction with an exponent of 1.5, in agreement with the experimental observations for several dilute or semidilute solutions of supramolecular polymers. This implies that dilute and semidilute supramolecular polymer solutions exhibit high polydispersity but may not be sufficiently entangled to follow the reptation mechanism of relaxation.     

Quantitative comparison between dynamic structure factors obtained experimentally and those calculated with Doi-Onuki theory

This paper reports results of quantitative comparison between dynamic structure factors obtained experimentally and those calculated by using the Doi and Onuki (DO) theory for semidilute polymer solutions. The authors obtained the dynamic structure factors with dynamic light scattering (DLS) experiment while the dynamic structure factors were calculated by using DO theory with osmotic compressibility, viscoelastic relaxation function, and friction coefficient which are obtained independently of DLS experiment. Calculated dynamic structure factors agree with experimental ones well and can express the q-dependent fast modes and the q-insensitive slow mode which experimental ones show. The authors estimated the characteristic parameters, interdiffusion coefficient and cooperative diffusion coefficient, from experimental and calculated results by using the procedure proposed by Einaga and Fujita [Polymer 40, 565 (1999)]. The estimated parameters for the DLS experiment agree with those for the calculation. These agreements in dynamic structure factors and the parameters indicate that DO theory can describe well the relaxation processes of semidilute polymer solutions.     

Rheology of viscoelastic solutions of cationic surfactant. Effect of added associating polymer

Rheological studies were performed with aqueous salt solutions of viscoelastic cationic surfactant erucyl bis(hydroxyethyl)methylammonium chloride (EHAC) and its mixtures with hydrophobically modified polyacrylamide. The solutions of surfactant itself above the concentration of crossover of wormlike micelles exhibit two regions of rheological response. In the first region, they behave like polymer solutions in semidilute regime characterized by viscoelastic behavior with a spectrum of relaxation times. In the second region, unlike polymer solutions their relaxation after shear is dominated by a single relaxation time. Being composed of "living" micelles, the EHAC solutions easily lose their viscosity at the variation of the external conditions. For instance, heating from 20 to 60 degrees C reduces viscosity by up to 2 orders of magnitude, while added hydrocarbons induce a sudden drop of viscosity by 3-6 orders of magnitude. Polymer profoundly affects the rheological properties of EHAC solutions. The polymer/surfactant system demonstrates a 10,000-fold increase in viscosity as compared to pure-component solutions, the effect being more pronounced for polymer with less blocky distribution of hydrophobic units. A synergistic enhancement of viscosity was attributed to the formation of common network, in which some subchains are made up of elongated surfactant micelles, while others are composed of polymer. At cross-links the hydrophobic side groups of polymer anchor EHAC micelles. In contrast to surfactant itself, the polymer/surfactant system retains high viscosity at elevated temperature; at the same time it keeps a high responsiveness to hydrocarbon medium inherent to EHAC.     

Self-diffusion of polystyrene in solution 2. Discussion of experimental results on the basis of the reptation mechanism and entanglements

The expressions for polymer self-diffusion in semidilute solutions, theoretically derived from the reptation mechanism, the blob concept and scaling considerations, are discussed and compared against experimental data from the authors' investigations and the literature. In the nonentangled (from viscoelastic data) semidilute solution, the experimentally observed concentration and molar mass exponents are in fair agreement with those derived theoretically. However, a quantitative estimation shows that the experiments cannot be explained by reptation. Experiments with polymer mixtures also give strong evidence against reptation. It is concluded, that in the nonentangled semidilute solution, the polymer self-diffusion is more complicated than simple reptation. This is also supported by recently observed long-range density fluctuations or cluster formation in this concentration region detected by scattering techniques and NMR-PFGT. In the entangled semidilute solution, the self-diffusion data are in accordance with the reptation mechanism; reptation being within a tube having approximately 20 blobs between entanglements.     

Collective dynamics of semidilute polyelectrolyte solutions with salt

We present a theory of coupled fluctuations of polymer segments, counterions, and coions in semidilute polyelectrolyte solutions containing added salt. The coupling among the three species results in three relaxation modes, instead of the previous common usage of only two relaxation modes by absorbing the role of salt as an effective solvent. Among the three modes, one is the nondiffusive plasmon mode and the other two are diffusive modes. These three modes are unrelated to any other slow mode that may arise from effects such as aggregation. Explicit expressions are derived for the decay rates in terms of concentrations of polyelectrolyte and salt, and the degree of ionization of the polymer. The specific values for the decay rates of the three modes are shown as an illustration for a chosen set of values of experimental variables. In the absence of added salt, the present theory reduces to the previous theory of fast diffusion in salt‐free polyelectrolyte solutions and to the Nernst–Hartley theory for simple electrolytes. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1263–1269     

Noncontinuum effects on the mobility of nanoparticles in unentangled polymer solutions

The results for the diffusivity of nanoparticles in unentangled semidilute polymer solutions obtained using coarse‐grained simulations are presented. The results indicate that for particle sizes smaller than the polymer radius of gyration, the nanoparticle diffusivities deviate from Stokes–Einstein predictions and depend explicitly on the polymer radius of gyration and the polymer solution correlation lengths. Scaling ideas proposed are invoked for rationalizing such noncontinuum effects and demonstrate that the simulation results could be collapsed onto a single universal function of the depletion thickness, the polymer radius of gyration, and the particle radius. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2145–2150.     

Direct measurement of depletion and hydrodynamic forces in solutions of a reversible supramolecular polymer

In this paper, the investigation of surface forces in semidilute solutions of a nonadsorbing hydrogen-bonded reversible supramolecular polymer is described. Colloidal probe atomic force microscopy was used for direct measurement of depletion forces. Hydrodynamic drag on the AFM cantilever with the colloidal probe was measured both far away from and close to the planar substrate surface. The results indicate that the presence of the depletion layer causes slip at the surfaces with a large apparent slip length. Our analysis explains how the presence of slip enables the measurement of (relatively weak) depletion forces in solutions with a high viscosity by significantly reducing the hydrodynamic forces. The range and magnitude of the measured depletion forces are qualitatively in agreement with previous experiments and theoretical predictions. Due to the relatively large experimental error, no quantitative conclusions can be drawn. Depletion-induced phase separation of suspensions of stearylated silica particles was also observed. Phase separation becomes more pronounced with increasing polymer concentration.     

Impact of solvent quality on nanoparticle dispersion in semidilute and concentrated polymer solutions

We investigated how solvent quality affects the stability of polymer-grafted nanoparticles in semidilute and concentrated polymer solutions, which extends our previous studies on these types of dispersions in good solvents [Langmuir 2008, 24, 5260-5269]. As discussed in the current article, dynamic light scattering (DLS) was used to quantify the diffusion of polydimethylsiloxane-grafted silica nanoparticles, or PDMS-g-silica, in bromocyclohexane as well as in PDMS/bromocyclohexane solutions. We established that bromocyclohexane is a theta solvent for PDMS by varying the temperature of the solutions with PDMS-g-silica nanoparticles and detecting their aggregation at a theta temperature of T(Θ) = 19.6 °C. Using this temperature as a benchmark for the transition between good and bad solvent conditions, further stability tests were carried out in semidilute and concentrated polymer solutions of PDMS in bromocyclohexane at T = 10-60 °C. Irrespective of temperature, i.e., solvent quality, we found that the nanoparticles dispersed uniformly when molecular weight of the graft polymer was greater than that of the free polymer. However, when the free polymer molecular weight was greater than that of the graft polymer, the nanoparticles aggregated. Visual studies were also used to confirm the correspondence between nanoparticle stability and graft and free polymer molecular weights in a wide range of marginally poor solvents with PDMS. Further, the correspondence between nanoparticle stability and instability with graft and free polymer molecular weight and solvent quality was also supported with self-consistent mean-field calculations. Thus, by relating experiment and theory, our results indicate that nanoparticle stability in semidilute and concentrated polymer solutions is governed by interactions between the graft and free polymers under conditions of variable solvency.     

Chitosan and its derivatives in extensional and shear flows

Allylchitosan and propylchitosan with different degrees of substitution were prepared on the basis of chitosan from shrimp chitin. The dynamics of semidilute electrolytic polymer solutions of chitosan derivatives in acetic acid was studied by measuring birefringence in extensional and shear flows and by means of viscometry. The optical shear coefficient and critical velocity gradients corresponding to the loss of stability of the macromolecular coil in extensional flow were found. The chain relaxation times depending on the polyelectrolyte concentration and ionic strength of solution were determined.     

Divergent Shear Thinning and Shear Thickening Behavior of Supramolecular Polymer Networks in Semidilute Entangled Polymer Solutions

The steady shear behavior of metallo-supramolecular polymer networks formed by bis-Pd(II) cross-linkers and semidilute entangled solutions of poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO) or N,N-dimethyl formamide (DMF) is reported. The steady shear behavior of the networks depends on the dissociation rate and association rate of the cross-linkers, the concentration of cross-linkers, and the concentration of the polymer solution. The divergent steady shear behavior-shear thinning versus shear thickening-of samples with identical structure but different cross-linker dynamics (J. Phys. Chem. Lett. 2010, 1, 1683-1686) is further explored in this paper. The divergent steady shear behavior for networks with different cross-linkers is connected to a competition between different time scales: the average time that a cross-linker remains open (τ(1)) and the local relaxation time of a segment of polymer chain (τ(segment)). When τ(1) is larger than τ(segment), shear thickening is observed. When τ(1) is smaller than τ(segment), only shear thinning is observed.     

Rotational diffusivity of rodlike molecules in amorphous polymeric matrices

In this note, scaling laws for rotational diffusivity of dilute monodisperse rigid-rod molecules (guest rods) in semidilute amorphous polymer solutions (host molecules) are derived. The coillike matrix molecules are modeled as a collection of flexibly connected rigid subunits. This allows an analogy with the Doi-Edwards theory for monodisperse rigid rods in semidilute solutions to be used in the analysis. Very strong dependencies are predicted for the rotational diffusivity of the rods on host polymer volume fraction and rod length. In semidilute polymer solutions the coils dramatically hinder the rotational freedom of the rods for r² ? ψ_p^?1, r being the rod aspect ratio and ψ_p the polymer volume fraction.