Universal dynamics of dilute and semidilute solutions of flexible linear polymers

Experimental observations and computer simulations have recently revealed universal aspects of polymer solution behaviour that were previously unknown. This progress has been made possible because of developments in experimental methodologies and simulation techniques and the formulation of scaling arguments that have identified the proper scaling variables with which to achieve data collapse, both for equilibrium and nonequilibrium properties. In this review, these advances in our understanding of universal polymer solution behaviour are discussed, along with a brief overview of prior experimental observations and theoretical predictions to provide a context for the discussion. Properties for which the existence of universality is still unclear, and those for which it has not yet been verified theoretically are highlighted, and theoretical predictions of universal behaviour that require experimental validation are pointed out.     

Scattering functions of semidilute solutions of polymers in a good solvent

Expressions for analyzing small-angle scattering data from semidilute solutions of polymers in a good solvent over a broad range of scattering vectors are examined. Three different scattering function expressions are derived from Monte Carlo simulations. The expressions are similar to those of polymer reference interaction site models, with a scattering-vector-dependent direct correlation function. In the most advanced model, the screening of excluded-volume interactions beyond the overlap concentration is taken into account. Two simpler expressions, in which the screening of excluded-volume interactions is not included, are also applied. The three models are tested against small-angle neutron scattering (SANS) experiments on polystyrene in deuterated toluene for a broad range of molar masses and concentrations over a wide range of scattering vectors. For each model, simultaneous fits to all the measured scattering data are performed. The most advanced model excellently reproduces the SANS data over the full range of the parameters. The two simpler models fit the data almost equally well. On the basis of an extensive study, an optimal fitting strategy can be recommended for experimentalists, who want to analyze small-angle scattering data from polymers at any concentration. For data sets that do not contain data on the single-chain scattering function, the simpler model is recommended; it uses a direct correlation function equal to the form factor of an infinitely thin rod, which is independent of the concentration and molar mass. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3081–3094, 2004     

Relaxation processes in semidilute solutions of polymers in liquid crystal solvents

We investigate the relaxation phenomena in a polymer (polystyrene)/liquid crystal (4-cyano-4'-n-octyl-biphenyl) system, in its homogeneous isotropic phase near the isotropic-isotropic, isotropic-nematic, and isotropic-smectic coexistence curve, using both polarized and depolarized photon correlation spectroscopy (PCS). We study this system for different polystyrene molecular weights (4750, 12 500, and 65 000 g/mol), different compositions (50, 40, 30, and 10% polystyrene (PS) by weight), and different temperatures close to phase boundaries. First of all, we determine the phase diagrams of this system for the different molecular weights. The shape of the phase diagrams strongly depends on the molecular weight. However, in all cases, at low temperatures, these systems separate into an almost pure liquid crystalline (LC) phase and polystyrene-rich phase. PCS measurements show that the relaxation processes in the homogeneous phase are not affected by the proximity of the nematic, or smectic, boundaries (even at a temperature of 0.1 degrees C above the phase separation in two phases). In polarized PCS experiments, we always see three relaxation processes well separated in time: one, very fast, with a relaxation time of the order of 10(-5) s; a second one with a relaxation time within the range 10(-2)-10(-3) s; and a last one, very slow, with a relaxation time of the order of 1 s. Both the fast and slow modes are independent of the wave vector magnitude, while the intermediate relaxation process is diffusive. In depolarized PCS experiments, the intermediate mode disappears and only the fast and slow relaxation processes remain, and they are independent of the magnitude of the wave vector. The diffusive mode is the classical diffusive mode, which is associated with the diffusion of polymer chains in all polymer solutions. The fast mode is due to the rotational diffusion of 4-cyano-4'-n-octyl-biphenyl (8CB) molecules close to polystyrene chains (transient network). Finally, we assign the slowest mode to reorientational processes of small aggregates of PS chains that are not dissolved in 8CB.     

On the universality of sedimentation of flexible polymers in dilute and semidilute solutions

In the present investigation, the sedimentation behavior, over an extended concentration range, in solutions of polystyrenes under good, marginal, and theta solvent conditions, is analyzed in the framework of a recent theoretical model, which takes into account the gradual screening of both hydrodynamic and excluded-volume interactions in the semidilute regime. The model inspires the construction of universal plots of the form S/S₀ versus k_sc, where S is the sedimentation coefficient at polymer concentration c, S₀ is that at infinite dilution, and k_s is the concentration dependence coefficient. The resulting analytical expressions, without adjustable parameters, are consistent with experimental sedimentation data over the whole concentration range studied.     

Computer simulation of solutions of telechelic polymers with associating end-groups

We present the results of numerical Monte Carlo simulations of solutions of telechelic chains with strongly attracting end-groups. Formation of micelles (aggregates), their structure and structural characteristics of the system as a whole are studied in detail. The features revealed in computer experiments are qualitatively similar to the recent theoretical predictions. In particular, we show that micelles formed by telechelic chains attract each other even if the solvent is good for the soluble blocks forming micellar shells. As a result, A “micellar gel” structure with a number of chain “bridges” connecting micelles is formed. The bridging chains turn out to be significantly stretched. Furthermore, we observe a pronounced maximum in the wave-vector dependence of the static structure factor for the associating end-units which is a manifestation of a quasiperiodic pattern of alternating microdomains consisting of dense micellar cores and the swollen soluble chain blocks.     

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.     

Lattice cluster theory of associating polymers. IV. Phase behavior of telechelic polymer solutions

The newly developed lattice cluster theory (in Paper I) for the thermodynamics of solutions of telechelic polymers is used to examine the phase behavior of these complex fluids when effective polymer-solvent interactions are unfavorable. The telechelics are modeled as linear, fully flexible, polymer chains with mono-functional stickers at the two chain ends, and these chains are assumed to self-assemble upon cooling. Phase separation is generated through the interplay of self-assembly and polymer/solvent interactions that leads to an upper critical solution temperature phase separation. The variations of the boundaries for phase stability and the critical temperature and composition are analyzed in detail as functions of the number M of united atom groups in a telechelic chain and the microscopic nearest neighbor interaction energy ε(s) driving the self-assembly. The coupling between self-assembly and unfavorable polymer/solvent interactions produces a wide variety of nontrivial patterns of phase behavior, including an enhancement of miscibility accompanying the increase of the molar mass of the telechelics under certain circumstances. Special attention is devoted to understanding this unusual trend in miscibility.     

Shear banding in semidilute entangled polymer solutions

Shear banding in semidilute polymer solutions and other soft materials is one of the most intensely debated topics in current rheology. By means of rheo-optical experiments, physical modeling, and numerical simulations, researchers have started to develop a more thorough understanding of this flow instability within the past few years. Nevertheless, much effort is still required to identify the exact microscopic mechanisms leading to shear band formation and to clarify whether the phenomenon is universal for polymers. For this purpose, basic rheological characteristics, such as the appearance of a stress overshoot during start-up of a simple shear flow, have to be revisited and better related to the dynamics of the polymeric network.     

Electrophoretic migration of proteins in semidilute polymer solutions

We present a systematic study of the electrophoretic migration of 10-200 kDa protein fragments in dilute-polymer solutions using microfluidic chips. The electrophoretic mobility and dispersion of protein samples were measured in a series of monodisperse polydimethylacrylamide (PDMA) polymers of different molecular masses (243, 443, and 764 kDa, polydispersivity index <2) of varying concentration. The polymer solutions were characterized using rheometry. Prior to loading onto the microchip, the polymer solution was mixed with known concentrations of SDS (SDS) surfactant and a staining dye. SDS-denatured protein samples were electrokinetically injected, separated, and detected in the microchip using electric fields ranging from 100 to 300 V/cm. Our results show that the electrophoretic mobility of protein fragments decreases exponentially with the concentration c of the polymer solution. The mobility was found to decrease logarithmically with the molecular weight of the protein fragment. In addition, the mobility was found to be independent of the electric field in the separation channel. The dispersion is relatively independent of polymer concentration and it first increases with protein size and then decreases with a maximum at about 45 kDa. The resolution power of the device decreases with concentration of the PDMA solution but it is always better than 10% of the protein size. The protein migration does not seem to correspond to the Ogston or the reptation models. A semiempirical expression for mobility given by van Winkle fits the data very well.     

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     

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.     

Elastic modulus and relaxation times in telechelic associating polymers

Dynamic mechanical measurements have been performed on solutions of HEUR-associating polymers with different molar mass, end-cap length, and extent of modification. These systems appear as Maxwellian fluids although at high frequencies a short-time relaxation process is evidenced for the systems with a strong hydrophobicity. This relaxation process could be attributed to the Rouse dynamics of active links in the temporary network. The high-frequency elastic modulus G_X decreases with increasing temperature according to an Arrhenius law. The associated activation energy decreases with increasing concentration. This is interpreted in terms of two contributions to the elastic modulus (osmostic and entropic elasticity).     

Self‐diffusion coefficient of ring polymers in semidilute solution

In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self‐diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008     

Electrophoretic mobility of linear and star-branched DNA in semidilute polymer solutions

Electrophoresis of large linear T2 (162 kbp) and 3-arm star-branched (N(Arm) = 48.5 kbp) DNA in linear polyacrylamide (LPA) solutions above the overlap concentration c* has been investigated using a fluorescence visualization technique that allows both the conformation and mobility mu of the DNA to be determined. LPA solutions of moderate polydispersity index (PI approximately 1.7-2.1) and variable polymer molecular weight Mw (0.59-2.05 MDa) are used as the sieving media. In unentangled semidilute solutions (c* < c < c(e)), we find that the conformational dynamics of linear and star-branched DNA in electric fields are strikingly different; the former migrating in predominantly U- or I-shaped conformations, depending on electric field strength E, and the latter migrating in a squid-like profile with the star-arms outstretched in the direction opposite to E and dragging the branch point through the sieving medium. Despite these visual differences, mu for linear and star-branched DNA of comparable size are found to be nearly identical in semidilute, unentangled LPA solutions. For LPA concentrations above the entanglement threshold (c > c(e)), the conformation of migrating linear and star-shaped DNA manifest only subtle changes from their unentangled solution features, but mu for the stars decreases strongly with increasing LPA concentration and molecular weight, while mu for linear DNA becomes nearly independent of c and Mw. These findings are discussed in the context of current theories for electrophoresis of large polyelectrolytes.     

Viscosity behavior of silica suspensions flocculated by associating polymers

Associating polymers are hydrophilic long-chain molecules containing a small number of hydrophobic groups, and act as flocculants in aqueous suspensions. The effects of associating and nonassociating polymers on viscosity behavior are studied for silica suspensions. Since flocculation is induced by polymer bridging, the viscosity behavior is converted from Newtonian to shear-thinning profiles. The additions of surfactant cause an increase in viscosity for suspensions prepared with associating polymer, whereas the flow behavior of suspensions with nonassociating polymer is not significantly influenced. In adsorption of associating polymers onto silica particles, the chain may adopt a conformation with a water-soluble backbone attached to the particle surfaces. The hydrophobic groups extending from the chains adsorbed onto different particles can form a micelle by association with surfactant. Therefore, the bridging flocculation is enhanced by surfactant. The cooperative micellar formation between associating polymer and surfactant is responsible for viscosity increase in suspensions.     

Rheological properties of multisticker associative polyelectrolytes in semidilute aqueous solutions

Multisticker associative polyelectrolytes of acrylamide (≈86 mol %) and sodium 2‐acrylamido‐2‐methylpropanesulfonate (≈12 mol %), hydrophobically modified with N,N‐dihexylacrylamide groups (≈2 mol %), were prepared with a micellar radical polymerization technique. This process led to multiblock polymers in which the length of the hydrophobic blocks could be controlled through variations in the surfactant‐to‐hydrophobe molar ratio, that is, the number of hydrophobes per micelle (N_H). The rheological behavior of aqueous solutions of polymers with the same molecular weight and the same composition but with two different hydrophobic block lengths (N_H = 7 or 3 monomer units per block) was investigated as a function of the polymer concentration with steady‐flow, creep, and oscillatory experiments. The critical concentration at the onset of the viscosity enhancement decreased as the length of the hydrophobic segments in the polymers increased. Also, an increase in the N_H value significantly enhanced the thickening ability of the polymers and affected the structure of the transient network. In the semidilute unentangled regime, the behavior of the polymer with long hydrophobic segments (N_H = 7) was studied in detail. The results were well explained by the sticky Rouse theory of associative polymer dynamics. Finally, the viscosity decreased with an increase in the temperature, mainly because of a lowering of the sample relaxation time. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1640–1655, 2004     

Phase separation in semidilute aqueous poly(N-isopropylacrylamide) solutions

The phase separation mechanism in semidilute aqueous poly(N-isopropylacrylamide) (PNIPAM) solutions is investigated with small-angle neutron scattering (SANS). The nature of the phase transition is probed in static SANS measurements and with time-dependent SANS measurements after a temperature jump. The observed critical exponents of the phase transition describing the temperature dependence of the Ornstein-Zernike amplitude and correlation length are smaller than values from mean-field theory. Time-dependent SANS measurements show that the specific surface decreases with increasing time after a temperature jump above the phase transition. Thus, the formation of additional hydrogen bonds in the collapsed state is a kinetic effect: A certain fraction of water remains as bound water in the system. Moreover, H-D exchange reactions observed in PNIPAM have to be taken into account.