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.     

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.     

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.     

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     

Thermogravitational effect in macromolecular solutions

We have investigated in a thermogravitational apparatus the behavior of solutions containing macromolecular solutes and of suspensions of ultramicroscopic particles such as viruses and ribosomes. We have obtained very high separation ratios with all the solutes studied, the value of the separation being characteristic of each solution. The reproducibility of the results is good, and the dependence on the geometrical and physical parameters involved fits the predictions of the phenomenological theory. Our results prove that fractionation of very high molecular weight particles is feasible by this method, and also that the characterization of the macromolecular species and the determination of the mass and shape of the particles of the solute seem to be within the possibilities of the thermogravitational method when this is applied to very high molecular weight materials.     

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.     

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     

Characteristics of rodlike micelles of cetyltrimethylammonium chloride in aqueous NaCl solutions: Their flexibility and the scaling laws in dilute and semidilute regimes

Static light scattering has been measured for aqueous NaCl solutions of cetyltrimethylammonium chloride (CTAC) at 25 °C. While spherical micelles are formed above the critical micelle concentration for 0–1.5 M NaCl solutions, rodlike micelles are formed at NaCl concentrations higher than 1.18 M.The aggregation number of rodlike micelles increases markedly with increasing NaCl concentration, and it is as large as 11400 in 4.0 M NaCl. Long rodlike micelles are semiflexible and behave like wormlike chains. Their contour length and persistence length have been calculated as 630 and 46.4 nm, respectively, in 4.0 M NaCl.Rodlike micelles overlap and entangle together to form a network in semidilute solutions above a threshold micelle concentration. The radius of gyration of the blob can be scaled for its molecular weight with the exponent, 0.55, coinciding with that for isolated rodlike micelles in dilute solutions. The scaling laws for the reciprocal envelope of light scattered in the semidilute regime and for the molecular weight and the radius of gyration of the blob are also discussed with reference to the micelle concentration.     

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.     

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.     

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     

Phenomenological analysis of elongational flow birefringence in semidilute solutions of hydroxypropylcellulose

The relaxation time of a polymer chain in an elongational flow field was investigated for hydroxypropylcellulose (HPC) semidilute solution systems by two methods: phenomenological analysis of elongational flow-induced birefringence, and dynamic light scattering (DLS) and rheological measurements. To understand the relaxation time of an entangled semiflexible polymer solution in an elongational flow field, scaling analysis of the elongational flow-induced birefringence curve was performed. The results of both temperature and concentration scaling analyses showed that birefringence curves at different temperatures and at several HPC concentrations were described well by a universal birefringence–strain rate curve. This scaling behavior was compared with the "fuzzy cylinder" model. The critical strain rate corresponded to the correlation time of the slow relaxation mode determined by DLS measurement and the relaxation spectrum obtained by dynamic viscoelasticity measurement. The elongational flow-induced birefringence observed in an HPC semidilute solution was concluded to be attributed to the orientation of the HPC segment in the entangled molecular system, because the dominant relaxation mode is found to be the concentration fluctuation of an entangled molecular cluster in a quiescent state.     

Network development during shear-thickening in semidilute solutions of gently solubilized starches

The shear-thickening behavior of semidilute waxy maize (WM) starch solutions (90/10 DMSO/water) exhibit much of the behavior of classical nonlinear viscoelasticity. Small-amplitude oscillatory shear experiments were used to investigate the network structure formed during the shear-thickening regime. The solution viscoelastic properties of WM starch prior to the shear-thickening region could be described by the GLV model. The macromolecules behave as random coils with a longest relaxation time of 0.58 ± 0.03 s. For WM starch the observed shear-thickening region creates a stable, highly entangled network which resembles the behavior found in solutions in the concentrated regime. The longest relaxation time for the entangled solution is estimated to be 1.4 s. Semidilute solutions of normal maize (NM) starch in 90/10 DMSO/water do not exhibit a shear-thickening regime. The oscillatory shear data obtained before and after a thixotropic loop experiment were identical. The semidilute solution conformational dynamics of NM starch indicate some degree of rigidity in one of the components that constitute NM starch which might be associated with the helical structure obtained by amylose in DMSO. © 1998 John Wiley & Sons, Inc.

1 This article is a US Government work, and, as such, is in the public domain in the United States of America.

J Polym Sci B: Polym Phys 36: 2085–2093, 1998     

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.     

Linear scaling approaches to quantum macromolecular similarity: evaluating the similarity function

The evaluation of the electron density based similarity function scales quadratically with respect to the size of the molecules for simplified, atomic shell densities. Due to the exponential decay of the function's atom-atom terms most interatomic contributions are numerically negligible on large systems. An improved algorithm for the evaluation of the Quantum Molecular Similarity function is presented. This procedure identifies all non-negligible terms without computing unnecessary interatomic squared distances, thus effectively turning to linear scaling the similarity evaluation. Presented also is a minimalist dynamic electron density model. Approximate, single shell densities together with the proposed algorithm facilitate fast electron density based alignments on macromolecules.