Shear thinning in dilute polymer solutions

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.     

Electrical conductance of CHCl3 solutions of polyethylene oxide doped with KCI

CHCl3 solutions containing a few percent polyethylene oxide PEO (M_W = 200 000) or the low-molecular model dioxane are stirred at 50°C during more than 100 h in the presence of small amounts of KCl. The specific conductance, the viscosity and the density of the solutions are measured at 25°C as a function of time. Both PEO and dioxane act as ligands improving the solubility of KCl. The relaxation times are of the order of several hours. After 40 h or more the viscosity of the solutions increases in a spectacular way. However, the most striking observation is that the specific conductance of the polymeric solutions at 25°C is systematically 5% higher than the value measured with the same sample at 45°C, just as for metals. The effect of the dilution of the primary stirred solutions either in the pure solvent or in the initial polymer solution is investigated. These results are discussed in terms of a three-step mechanism in the polymer systems: (1) Loading of the coils to polymeric cations with a full elementary charge, as a consequence of charge transfer interactions of the crown-ether type with numerous K⁺ ions penetrating into the coils; (2) Electron tunnelling conduction of the Hamill—Ceulemans type from one positive coil to the neighbouring one; (3) Alteration of the structure of the coils and of their hydrodynamic radius by the motions of K⁺ in the coils. These ‘brachiation’ motions by a hopping mechanism result from an increased mobility of the complexed K⁺ ions, which is also the origin of the Zundel effect. They do not directly contribute to the conductance but are responsible for the delayed increase of the viscosity.     

Influence of ionic strength, sample size, and flow conditions on the retention behavior of pullulan in flow field-flow fractionation

Polymer molecular parameters such as hydrodynamic size are expected to be invariant regardless of the technique used to measure them, and to vary only, to some extent, with the solvent power and the polymer structure and properties as predicted from polymer chemistry. The hydrodynamic size of five pullulan standards derived from FlFFF in solutions of different ionic strength appears to correlate well to molecular mass as expected for neutral polymers for all fractions except that of lower mass. The correlation also holds for large amounts of injected sample even though with a slope which increases with rising polymer load. The evidence that the same result is obtained also for low sample amounts but with a higher cross-flow rate is interpreted as the manifestation of the presence of hydrodynamic interactions in concentrated polymer systems.     

Rheological measurements and light-scattering experiments of dilute solutions of high molecular polystyrene. Light-scattering of flowing polymer solutions

We describe the behavior of dilute polymer solutions by means of light-scattering under shear flow. Solution properties of polystyrene in benzene over a wide range of molecular weight has been studied to determine the coefficientsa andK of the Mark-Houwink relationship and to estimate the rheological conditions with regard to light-scattering experiments of flowing polymer solutions. The investigations were carried out to measure the shear-rate dependence of macromolecules in solution, e.g., to observe an orientation and changing of the mean-square radius of gyration.     

Hydrodynamic properties of rigid pyridine-containing poly(phenylene) dendrimers in solutions

The hydrodynamic properties of pyridine-containing polyphenylene dendrimers of the third and fourth generations in chloroform are studied by photon correlation spectroscopy and viscometry. It has been demonstrated that the hydrodynamic characteristics of these macromolecules in dilute solutions are similar to those of nondraining spheres. The hydrodynamic radius of these dendrimers is shown to be proportional to their molecular mass to a power of 1/3. It has been established that the macromolecules of the dendrimers under examination in solutions conserve the conformation and size over a wide temperature range. The detailed analysis of hydrodynamic data allowed a conclusion concerning an extremely low content of the polymer inside the equivalent sphere for the above dendrimers in solutions. The compounds of interest may be referred to as rigid dendritic systems.     

Micelles of SDS Surfactants in Concentrated NaCl Solutions

We investigated the aggregation behavior of rod-like micelles of sodium dodecyl sulfate (SDS) in concentrated NaCl solution by quasi-elastic light scattering (QLS) and viscosity measurement over a range of temperature (25 °C to 50 °C) and NaCl concentration. The reduced viscosity of aqueous SDS in the presence of NaCl has been measured by an Ubbelohde-type capillary viscometer. We show mean hydrodynamic radius of micelles can be determined from viscosity data. We also determined mean hydrodynamic radius using quasi-elastic light scattering. Micellar size decreases with increasing temperature, whereas it increases with increasing ionic strength. The results of viscosity and dynamic light-scattering measurements are interpreted as the extension of length of rod-like micelles. We compare viscosity and light scattering experimental results.     

Effect of Chemical Structure and Charge Distribution on Behavior of Polyzwitterions in Solution

Summary: The hydrodynamic and conformational properties of polyelectrolyte poly(N,N-diallyl-N,N-dimethylammonium chloride) and its corresponding polybetaine poly(2-diallyl(methyl)ammonio)acetate) molecules in aqueous solutions with various ionic strength and pH, were studied by viscometry, static and dynamic light scattering methods. It was established that a 1 M NaCl solution is a thermodynamically good solvent for poly(N,N-diallyl-N,N-dimethylammonium chloride). In water solutions conformation of poly(2-diallyl(methyl)ammonio)acetate) molecules corresponds to polymer coil under θ–conditions. An increase in the concentration of NaCl in water and 0.1M NaOH solutions from 0 to 1 mol/l brings about a sharp gain in the intrinsic viscosity of the polymer and in the hydrodynamic radius of molecules. This effect results from the decomposition of zwitterion pairs responsible for the compact conformation of polymer molecules in water and 0.1 M NaOH. The Kuhn segment length for poly(2-diallyl(methyl)ammonio)acetate) molecules A = 6.3 nm determined in water and in 0.1 M NaOH solutions practically coincided with A value 6.6 nm, received in 1 M NaCl and in 0.1 M NaOH/1M NaCl. For poly(N,N-diallyl-N,N-dimethylammonium chloride) molecules in 1 M NaCl solutions A = 3.9 nm.     

New polymer systems exhibiting microphase separation transition with the formation of nano-microstructures

The concept of microphase separation was up to now widely applied mainly to the conformational transitions in block-copolymer solutions and melts. However, recently it became obvious that this concept has a much more general meaning. It was shown that microphase separation transition can be observed in random copolymers, interpenetrating polymer networks, polyelectrolyte mixtures, poor solvent polyelectrolyte solutions, ionomer solutions and melts, polymer blends and solutions with nonlocal entropy of mixing. In all these examples the emerging microdomain structures correspond to the nanometer scale, therefore the study of these effects can lead to the new ways of obtaining polymer materials with controlled nano-microstructure. In this presentation the review of our recent findings on microphase separation in some of the above-mentioned systems will be presented. 1. The problem of microphase separation in the systems containing weakly charged polyelectrolytes (polyelectrolyte mixtures and poor solvent polyelectrolyte solutions) will be considered. From the methodic point of view, it will be shown that this problem can be solved by direct minimization of the free energy, without the use of “weak segregation” or “strong segregation” assumptions which are common in the theory of block-copolymers. The final phase diagrams exhibit wide macroscopic phase separation regions, which is their main difference from the corresponding phase diagrams for block-copolymer systems. The formation of microdomains is thus coupled with macroscopic phase separation: in most of the cases microdomain structure is formed in one of the coexisting phases after macroscopic phase separation takes place [1] - [2]. 2. The formation of the multiplet structure in ionomer melts and solutions can be also considered as the microphase separation in the random copolymer system with the formation of the “micelles” (or clusters) of ionic links. The parallels with micelle formation in block-copolymer systems can be established if one considers a new “superstrong segregation regime” for block-copolymer microstructures. This regime can be indeed observed for diblock copolymers with one ionomeric and one neutral block [3]. 3. The microphase separation transition in ordinary polymer blends and solutions is also possible. The conditions for this effect are: (i) significant entropic contribution to polymer/polymer or polymer/solvent miscibility, (ii) the nonlocal character of this contribution with a high value of the nonlocality radius. It is argued that one can expect that the entropy nonlocality radius increases in the vicinity of the glass transition for the blend or polymer solutions (in the latter case solvent molecules act like “poor solvent plasticisers”). Computer simulation data supporting the theoretical prediction of microphase separation transition in these systems will be presented [4] - [5].     

Crystallization of condensation droplets on a liquid surface

Highly ordered microporous two-dimensional membranes have been obtained from polymer solutions (Widawski et al. (1994) Nature 369: 397–399). Recently, a mechanism for the formation of such membranes was proposed, involving water vapour condensation (induced by the rapid evaporation of the volatile solvent) onto the surface of solutions and the formation of floating water droplets. Unfortunately, the droplets growth process was not observed, and consequently only qualitative information was reported. In the present paper, results of light-scattering experiments with this system are reported. The formation of water droplets growing at the surface of the solution has been observed and the evolution with time of the mean droplet radius has been found to be described by a power law with an exponent of 1/3, proving that no coalescence processes occur. This particular behaviour is attributed to the precipitation of the polymer at the water/solution interface and to the formation of a mechanically resistant polymer layer encapsulating each droplet. In this way, water droplets behave like solid particles, allowing compact sheets to be formed. The presence of important surface currents is believed to promote the formation of “polycrystal” and “monocrystal” patterns. Received: 4 January 1999 Accepted in revised form: 15 February 1999     

Light scattering and size exclusion chromatography of semi-flexible polyimide precursors

Measurement of the molecular weight, radius, and molecular weight distribution of polyimide precursors (amic acids and easters) is quite difficult due to strong polymer–solvent interactions, electrostatic interactions, and the possibility of partial imidization in solution. The large quantities of solvent and high dilutions necessary in liquid chromatography make this technique the most sensitive to these effects. The distortions in the chromatogram from these effects can make assessment of the molecular weight distribution from a polystyrene calibration very tenuous. Use of a light-scattering detector permits direct measurement of the scattering intensity (and thus the molecular weight), as the sample elutes from the column. For the esters, anomalous peaks and unexpectedly large apparent values for both the molecular weight and molecular weight distribution are shown to be due primarily to partial imidization in solution catalyzed by basic solvent impurities. Chromatographic results obtained in neutralized solvent are in agreement with light-scattering results obtained at higher concentrations.     

Diffusion, sedimentation, and rheology of concentrated suspensions of core-shell particles

Short-time dynamic properties of concentrated suspensions of colloidal core-shell particles are studied using a precise force multipole method which accounts for many-particle hydrodynamic interactions. A core-shell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ(-1). The solvent flow inside the permeable shell is described by the Brinkman-Debye-Bueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact non-hydrodynamically by a hard-sphere no-overlap potential of radius b. Numerical results are presented for the high-frequency shear viscosity, η(∞), sedimentation coefficient, K, and the short-time translational and rotational self-diffusion coefficients, D(t) and D(r). The simulation results cover the full three-parametric fluid-phase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Many-particle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the core-shell systems can be approximated neither by no-shell nor by no-core models. However, one of our findings is that for κ(b - a) ? 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration.     

Synthesis,hydrodynamic, and conformational properties of poly(<Emphasis Type="Italic">N</Emphasis>-acryloyl-11-aminoundecanoic acid) in solutions

Poly(N-acryloyl-11-aminoundecanoic acid) samples are synthesized in monomer solutions occurring in both micellar and nonmicellar states. It is shown that polymeric ionogenic surfactants of various molecular masses can be prepared through variation in the concentration of a polymerizable surfactant or in the ionic strength of a solution. The polymer of interest is investigated in detail via the methods of molecular hydrodynamics (viscometry, isothermal diffusion, and velocity sedimentation), dynamic light scattering, GPC, and scanning probe microscopy. The solubility of the polymer in various solvents is examined in detail, and the tendency of this polymer toward association in DMF solutions is discovered. The equilibrium rigidity of macromolecules, which is characterized by the Kuhn segment length A = 100 × 10⁻⁸ cm, and the effective hydrodynamic radius are determined in a dioxane-cyclohexanol mixed solvent.     

Molecular properties of poly(carboxybetaine) in solutions with different ionic strengths and pH values

Viscometry and dynamic and static light scattering are employed to study the molecular properties of water-soluble poly(carboxybetaine), that is, poly(2-(diallyl(methyl)ammonium) acetate). It is shown that, in solutions with pH 1, the polymer behaves as a polyelectrolyte. In media with pH 6 and 13, an increase in the concentration of sodium chloride increases the intrinsic viscosity of the polymer and the hydrodynamic radius of its macromolecules, thereby indicating the antipolyelectrolyte effect typical of polymer zwitterions. In water and 0.1 M NaOH, the second virial coefficient of the polymer is close to zero, while exponent ν, which relates the sizes of macromolecules to their molecular masses, is 0.5. In 1 M NaCl, the second virial coefficient becomes positive, while exponent increases to 0.58. The Kuhn segment lengths of poly(carboxybetaine) molecules are 6.3 and 6.6 nm in water and 1 M NaCl, respectively. An increase in the hydrodynamic radius of macromolecules with the ionic strength of the solution is due to the shielding of attraction between zwitterions belonging to polybetaine monomer units located far apart along a macromolecular chain.     

Polymer chain dynamics at interfaces: role of boundary conditions at solid interface

Using classical molecular dynamics simulations, we study the dynamical properties of a single polymer chain dissolved in an explicit solvent and strongly adsorbed at solid-liquid interface. To circumvent a serious challenge posed by finite size effects due to long-range hydrodynamic effects, we developed a correction procedure that substantially limits the finite size effects. Concurrently, we provide an analysis of distinctly different size effects in the directions transverse and normal to the interface. We find that on analytically smooth interfaces, corresponding to the slip boundary condition, the motions of the polymer chain and the surrounding solvent are hydrodynamically coupled. This leads to the chain diffusion coefficient D scaling with the chain degree of polymerization N as D approximately N(-3/4), consistent with the Zimm dynamics for strongly adsorbed chains. Introduction of transverse forces at the interface results in loss of correlation between the motion of the polymer chain and the solvent. Consequently, D approximately N(-1), which is a characteristic of the Rouse dynamics.     

Capillary zone electrophoresis of proteins in semidilute polymer solutions: inter- and intra-polymer predictability of size-dependent retardation.

The retardation of three "spherical" proteins with Stokes' radii of 2.0, 2.4, and 3.0 nm (35-104 kDa) was studied in capillary zone electrophoresis (CZE), using semidilute solutions of polyethylene glycol (PEG), linear polyacrylamide (PA), and polyvinyl alcohol (PVA). The purpose was to test the models predicting that the ratio of particle radius, R, to the mesh size of polymer network (the correlation or screening length of a semidilute polymer solution), xi, directly governs the size-dependent retardation in the form: mu/muo = exp (-R/xi). Here xi = kc-0.75, where c is polymer concentration and the numerical factor kcan be calculated based on polymer molecular weight. In application to polymers in a "good solvent" (PA and PEG in the aqueous buffer) and to proteins of 2.4 and 3.0 nm radius, that relation between relative mobility and R/xi was found to be obeyed for PA, while for PEG the value of k derived from retardation experiments significantly exceeded that which was theoretically calculated. Thus, the retardation appears to be polymer-specific, rather than universal, even for polymers in a "good solvent". It is suggested that, in that case, retardation of proteins of R > 2 nm be quantitatively described in the form mu/muo = exp[-p(R/xi], where p is a parameter depending on monomer type and/or polymer polydispersity. For PVA, the logarithm of mu/muo was found to be linearly related to c (in line with the prediction that the aqueous buffer is a "poor solvent" for this polymer) and to be near-independent of R.     

Length-scale dependent relaxation shear modulus and viscoelastic hydrodynamic interactions in polymer liquids

A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τ(R), the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τ(i) ∝ r(4∕3) and viscoelastic time τ(?) ∝ r(4). It is shown that for t > τ(i) the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τ(R) and/or for r < R(coil), turns out to be much lower than the macroscopic "polymer" viscosity η(m). The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well.     

Transport properties in concentrated polymer solutions

Transport properties of polymer solutions at finite concentration are derived in the partial draining case by formulating a static version of the theory given by Freed and Edwards (FE) for unentangled concentrated polymer solution. The method follows the Kirkwood—Riseman theory for infinitely dilute solutions: the dynamics of the polymer are ignored apart from the overall rotation or translation of the chain and the solvent velocity is given by the Navier—Stokes equations perturbed by point friction forces. The concentration dependence of viscosity and translational friction coefficient of finite chains obtained by numerical calculations are compared with the results of the FE closed-form solution. It is shown that the screening of the hydrodynamic interaction approximately follows Debye-like behavior in the entire range of concentration. The progressive balancing of the increasing intramolecular hydrodynamic interaction with its reduction due to the screening effects, as the molecular weight increases, is well evidenced by comparing results obtained at constant number concentration for different chain lengths.     

Conformational changes of a polyelectrolyte in mixtures of water and acetone

Samples of a polyelectrolyte poly(methacryloylethyl trimethylammonium methylsulfate), PMETMMS, with molar masses M_w = 22−25 × 10⁶ were examined with viscosity, static light scattering, and conductivity measurements in a water–acetone solvent. Because acetone is a nonsolvent for this polymer the measurements were performed to determine the influence of the solvent composition, the polymer concentration, and the presence of added ions on the conformation of the polyelectrolyte in mixed solvents. The possible influence of a hydrodynamic field on the polymer conformation was also studied. The viscosity of the polymer solutions as a function of polymer concentration, as well as of the solvent composition, was studied using a broad range of shear rates. When the mass fraction of acetone in the solvent, γ, is below 0.5, the solutions show a usual polyelectrolyte behavior. When γ ≥ 0.80, the polymer adopts a compact conformation. This is observed as a decrease of the radius of gyration, R_g, second virial coefficient, A₂, the viscosity, and also as a change in the conductivity of the solution. The change in the polymer conformation may be induced also by dilution. When 0.60 ≤ γ < 0.80, a gradual decrease in the polymer concentration leads to a sudden decrease of the reduced viscosity, which indicates a decrease in the particle size. The values of M_w measured by static light scattering were constant in all experiments. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1107–1114, 1998     

低苯乙烯含量的丁二烯-苯乙烯共聚物的激基缔合物荧光研究

本文报导一种低苯乙烯含量(5％,Wt.)的丁二烯-苯乙烯共聚物,经~1H NMR证明其分子链上不存在相邻苯乙烯单元。荧光光谱结果表明,它在良溶剂(二氯乙烷)的稀溶液状态下只呈现单分子荧光。从良溶剂-θ溶剂(二氯乙烷-甲醇体系)及稀溶液-浓溶液-固体之荧光光谱的变化,证明形成了链内非近邻生色团之间和链间生色团之间的激基缔合物(Excimer)。从固体与θ溶剂的激基缔合物荧光的比较,还可区分链内非近邻和链间苯环形成激基缔合物对荧光强度的贡献。这一结果对阐明高分子链内非近邻和链间激基缔合作用提供了新的证据,并有助于了解高聚物本体中相互穿透、相互缠结的无规线团的形态。     

Synthesis and light scattering study of microgels with interpenetrating polymer networks

Monodispersed microgels composed of poly(acrylic acid) (PAAc) and poly(N-isopropylacrylamide) (PNIPAM) interpenetrating polymer networks (IPN) were synthesized by a two-step method, first preparing PNIPAM microgel and then polymerizing acrylic acid that interpenetrates into the PNIPAM network. The growth kinetics of the IPN particle formation was obtained by measuring the turbidity and particle hydrodynamic radius (Rh) as a function of reaction time. IPN and PNIPAM microgels were characterized and compared by dynamic and static light scattering techniques. The concentrated aqueous solutions of the PNIPAM-PAAc IPN microgels exhibit an inverse thermoreversible gelation. In contrast to polymer solutions of poly(NIPAM-co-AAc) that have the inverse thermoreversible gelation, our system can self-assemble into an ordered structure, displaying bright colors. Furthermore, IPN microgels undergo the reversible volume phase transitions in response to both pH and temperature changes associated with PAAc and PNIPAM networks, respectively.