Screening and fundamental length scales in semidilute Na-DNA aqueous solutions

The fundamental length scales in semidilute Na-DNA aqueous solutions have been investigated by dielectric spectroscopy. The low- and the high-frequency relaxation modes are studied in detail. The length scale of the high-frequency relaxation mode at high DNA concentrations can be identified with the de Gennes-Pfeuty-Dobrynin correlation length of polyelectrolytes in semidilute solution, whereas at low DNA concentrations and in the low added salt limit the length scale shows an unusual exponent reminiscent of semidilute polyelectrolyte chains with hydrophobic backbone. The length scale of the low-frequency relaxation mode corresponds to a Gaussian chain composed of correlation blobs in the low added salt limit, and to the Odijk-Skolnick-Fixman value of the single chain persistence length in the high added salt limit.     

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

The dispersion state of sodium-sulphonated polystyrene ( NaPSS) star-branched polyelectrolytes was investigated in salt-free aqueous solutions, by use of the small-angle X-ray scattering technique. With respect to polystyrene (PS) star-branched polymers of identical functionality, the ordering phenomenon occurring in the neighborhood of the overlap concentration c^* is reinforced and observed in a larger range of concentrations. Moreover, the degree of order is no longer maximum at c^* and is improved as the concentration decreases. The dispersion state is then mainly controlled by the electrostatic interaction. A crystalline order should therefore be achieved with stars of lower functionality, provided the electrostatic interaction is added to the osmotic repulsion. On the other hand, unusual scattering patterns are measured for aqueous solutions of NaPSS star polyelectrolytes. Indeed, a diffuse scattering is revealed at high angles, in addition to the regular diffraction rings related to preferred interstar distances. It is similar to the broad scattering peak produced by semidilute solutions of NaPSS linear polyelectrolytes and associated to the electrostatic correlation hole within the isotropic model. In the dilute regime (c < c ^*), it is just an intramolecular characteristic and represents the electrostatic repulsion between arms belonging to the same star. In the semidilute regime (c > c ^*), it also reflects the electrostatic repulsion between arms of distinct stars. So, as the concentration increases, it is mainly caused by the interpenetration of NaPSS stars. Such an observation is in agreement with the composite structure earlier proposed by Daoud and Cotton for star semidilute solutions. For c > c ^*, NaPSS star aqueous solutions can therefore be pictured as effective stars immersed in a matrix formed by the overlap of the arm ends. With respect to the dilute regime, the effective stars are smaller; the higher the concentration the smaller the size. Received 14 May 1999 and Received in final form 15 March 2000     

Salt-free aqueous solutions of polyelectrolytes: Small angle X-ray and neutron scattering characterization

We give an introduction to the application of small angle X-ray and neutron scattering techniques to the study of the structure of polyelectrolyte solutions. The goal is not to be exhaustive and to describe the latest progress in the field of polyelectrolytes but rather to present the potential of the technique. We aim to give an overview on the main features of the scattering curves, and discuss the structural information that can be drawn. We will first give the basics of small angle scattering and highlight the role played by neutron scattering and isotopic labeling. Thus, we will discuss the significance of the monomer and counterion partial scattering functions according to the scattering length densities of both components, and will emphasize the unique possibility to separate out the intra- and intermolecular correlations. Then, some examples will show how the dispersion state and the average conformation of macroions can be addressed. We will however focus on salt-free aqueous solutions of linear flexible hydrophilic polyelectrolytes in the semidilute regime.     

Scaling equations for a biopolymer in salt solution

The effect of the simultaneous presence of monovalent and divalent cations on the thermodynamics of polyelectrolyte solutions is an incompletely solved problem. In physiological conditions, combinations of these ions affect structure formation in biopolymer systems. Dynamic light scattering measurements of the collective diffusion coefficient D and the osmotic compressibility of semidilute hyaluronan solutions containing different ratios of sodium and calcium ions are compared with simple polyelectrolyte models. Scaling relationships are proposed in terms of polymer concentration and ionic strength J of the added salt. Differences in the effects of sodium and calcium ions are found to be expressed only through J.     

Features of the Rheological Behavior of Polymer-Colloidal Dispersions Based on a Sodium Salt of Carboxymethyl Cellulose and Silver Iodide Sols

The rheological properties of aqueous solutions of a sodium salt of carboxymethyl cellulose are studied. The occurrence of a region of unstructured semidilute solutions in which the entanglement network is absent is found. The introduction of both opposite and like-charged micelles of the lyophobic sol into a semidilute polymer solution leads to its structuring due to the appearance of an additional network because of polymer adsorption on the surface of the sol. As a result of the network formation a decrease in the interval between the crossover and the formation concentration of the entanglement network and also an increase in the viscosity of the semidilute solution are observed.     

Monte Carlo simulation of polymers in solution and bulk

The behavior of polymers in solution depends on both temperature and concentration. At least four different regions of the concentration-temperature plane exist in which the physical properties are fundamentally different. These regions are known as the dilute good solvent, theta solvent, semidilute, and concentrated regions. In this investigation, Monte Carlo simulations were performed in order to examine how properties change in going from one region to another. Two series of simulations were performed. In the first series, properties were studied as a function of concentration so that crossover from dilute, to semidilute, and then to concentrated was obtained. In the concentrated or bulk region, it was found that the second and fourth moments of the end-to-end distance were characteristic of ideal chains (without excluded volume), consistent with neutron scattering results. In the semidilute region, the concentration dependence of the mean square end-to-end distance was not in agreement with scaling theory. In the second series of simulations, the temperature was changed for an isolated chain (zero concentration limit), so that crossover from good solvent to theta solvent behavior was obtained. Over the chain length range studies (10–300), no evidence was seen for the existence of “thermal blobs.” In addition, expansion of the average internal conformation over the expected result was observed and found to be increasingly important as the temperature increases from the theta temperature.     

Multiple scattering of polarized light in a turbid medium

It is shown that multiple scattering of polarized light in a turbid medium can be represented as independent propagation of three basic modes: intensity and linearly and circularly polarized modes. Weak interaction between the basic modes can be described by perturbation theory and gives rise to “overtones” (additional polarization modes). Transport equations for the basic and additional modes are derived from a vector radiative transfer equation. Analytical solutions to these equations are found in the practically important cases of diffusive light propagation and small-angle multiple scattering. The results obtained are in good agreement with experimental and numerical results and provide an explanation for the experimentally observed difference in depolarization between linearly and circularly polarized waves.     

Viscoelastic Nanocomposites of Wormlike Micelles of Surfactant and Aluminosilicate Clay Nanoplates

Bulletin of the Lebedev Physics Institute - Viscoelastic nanocomposites based on a matrix of semidilute aqueous solutions of entangled wormlike (polymer-like) micelles of a cationic surfactant and...     

Structure and dynamics of concentrated micellar phase in nonionic surfactant-water systems

Dynamic light scattering has been measured on aqueous solutions of a nonionic surfactant C₁₄E₆ (C_nE_m represents a chemical formula C_nE_2n+1(OC₂H₄)_mOH). In the time correlation function of the scattered field for semidilute solutions were wormlike micelles are entangled, we have found the so-called slow mode in addition to the diffusion mode. Concentration and temperature dependences of the relaxation time of the slow mode (τ_s) are strongly correlated with those of the surfactant self-diffusion coefficient (D), suggesting that self-diffusion and structural relaxation are dominated by the same kinetic process. These results are consistent with our previous study on the C₁₆E₇ system. In order to refine the kinetic model, we have compared τ_s and D quantitatively based on our diffusion model reported before where intramicellar diffusion and intermicellar migration are taken into account. Static light scattering measurements have been performed to estimate one of parameters included in this model. It has been suggested that entangled micelles form a transient connection whose lifetime is of the order of 10⁻³ s, depending on concentration and temperature, and that surfactant molecules migrate to another micelle through such a transient connection.     

Shear-induced concentration fluctuations and form factor changes in polymer solution in the good-solvent regime

Small-Angle Scattering from sheared semidilute polymer solution is reported in the good-solvent regime, at variance with former light and neutron measurements in the regime. First, concentration fluctuations are observed: the scattering increases noticeably along the flow at low q, but at variance with former results for the theta-solvent regime, no demixing is observed at higher shear. Here, instead, the effects follow a time-temperature superposition and saturate above a Weissenberg number around 5, like the stress which is known to present a plateau for these systems. Using the Zero Average Contrast technique, we have also measured the form factor, which displays the same saturation effect reaching a deformation ratio of the order of 2. These results agree with the Convective Constraint Release models (CCR) elaborated in order to predict the stress effects in the non-Newtonian regime (Marrucci-Ianniruberto) and their extension predicting also the scattering (Likhtman-Milner-McLeish).Received: 5 July 2004, Published online: 1 October 2004PACS: 61.12.Ex Neutron scattering (including small-angle scattering) - 47.15.-x Laminar flow - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling     

Collective dynamics of an end-grafted polymer brush in solvents of varying quality

The dynamic structure of a chemically end-grafted polystyrene brush bathed in solvents of varying interactions was studied by evanescent wave dynamic light scattering. It reveals distinct behavior under good and poor solvent conditions. The cooperative diffusion is a generic feature of a good solvent environment, whereas a second slow relaxation mode appears in the theta solvent regime. Its characteristics resemble self-diffusion of clusters in a gel while weak concentration fluctuations in the polymer brush decay similarly to a semidilute polymer solution.     

The state space of short-range Ising spin glasses: the density of states

The correlations between the segments of a semidilute polymer solution are found to induce correlations in the positions of small particles added to the solution. Small means a diameter much less than the polymer's correlation length. In the presence of polymer the particles behave as if they attracted each other. It is shown how the polymer's correlation length may be determined from a scattering experiment performed on the spheres. Received: 7 July 1997 / Received in final form: 12 November 1997 / Accepted: 19 November 1997     

Non-equilibrium relaxation and tumbling times of polymers in semidilute solution

The end-over-end tumbling dynamics of individual polymers in dilute and semidilute solutions is studied under shear flow by large-scale mesoscale hydrodynamic simulations. End-to-end vector relaxation times are determined along the flow, gradient, and vorticity directions. Along the flow and gradient directions, the correlation functions decay exponentially with sinusoidal modulations at short times. In dilute solution, the decay times of the various directions are very similar. However, in semidilute solutions, the relaxation behaviors are rather different along the various directions, with the longest relaxation time in the vorticity direction and the shortest time in the flow direction. The various relaxation times exhibit a power-law shear-rate dependence with the exponent -?2/3 at high shear rates. Quantitatively, the relaxation times are equal to the tumbling times extracted from cross-correlation functions of fluctuations of radius-of-gyration components along the flow and gradient direction.     

Can polymer coils Be modeled as "Soft colloids"?

We map dilute or semidilute solutions of nonintersecting polymer chains onto a fluid of "soft" particles interacting via a concentration dependent effective pair potential, by inverting the pair distribution function of the centers of mass of the initial polymer chains. A similar inversion is used to derive an effective wall-polymer potential; these potentials are combined to successfully reproduce the calculated exact depletion interaction induced by nonintersecting polymers between two walls. The mapping opens up the possibility of large-scale simulations of polymer solutions in complex geometries.     

KDP晶体拉曼散射角度特性

利用群理论详细分析了磷酸二氢钾(KDP)晶体的拉曼振动模式,得出了其拉曼振动模的归类。并采用拉曼光谱仪测量了Z切退火KDP晶体X(ZZ)珡X,Z(XY)珚Z和Y(XY)X三种散射配置和未退火KDP晶体Z(XY)珚Z配置下的拉曼光谱。根据拉曼选择定则得出X(ZZ)珡X,Z(XY)珚Z和Y(XY)X散射配置下的拉曼峰分别对应A1,B2(LO),B2(TO)对称类振动模,但在Z(XY)珚Z配置下的拉曼光谱中除了B2模,还观察到了A1模,而在Y(XY)X配置下的拉曼光谱中只有B2模,且退火和未退火晶体Z(XY)珚Z配置下的拉曼光谱无明显差别,此结果表明KDP晶体的对称性降低,在背向散射时A1模也具有角度特性,但与晶体的内应力无关,这是由KDP晶体内部结构决定的。     

局域模(实的及虚的)的一种新表述

本文给出了一种新的表述局域模(实的及虚的)的方法。我们引入了变形豫解式的迹P(z).它仅在z平面的实轴上有奇异性,孤立极点对应于实局域模。将P(E+iη)向下解析延拓至第二黎曼面,则其复极点对应于虚的(或不稳定的)局域模。复极点的实部是不稳定局域模的能量,虚部是它寿命的倒数,自然地得到了寿命为正的限制。此能量与寿命符合于相应共振散射的能量与宽度。本文还讨论了实局域模与虚局域模之间的关系。最后,比较了P(z)的奇异性与态密度的变化,并进一步阐明了寿命为正的及负的解之间的差别。指出,一般说来,只有寿命为正的解当作用强度增加时会变成实的局域模,负寿命的解是不会的。     

KDP晶体拉曼散射角度特性

利用群理论详细分析了磷酸二氢钾(KDP)晶体的拉曼振动模式,得出了其拉曼振动模的归类?并采用拉曼光谱仪测量了Z切退火KDP晶体X(ZZ)X,Z(XY)Z和Y(XY)X三种散射配置和未退火KDP晶体Z(XY)Z配置下的拉曼光谱?根据拉曼选择定则得出X(ZZ)X,Z(XY)Z和Y(XY)X散射配置下的拉曼峰分别对应A1,B2(LO)?B2(TO)对称类振动模,但在Z(XY)Z配置下的拉曼光谱中除了B2模,还观察到了A1模,而在Y(XY)X配置下的拉曼光谱中只有B2模,且退火和未退火晶体Z(XY)Z配置下的拉曼光谱无明显差别,此结果表明KDP晶体的对称性降低,在背向散射时A1模也具有角度特性,但与晶体的内应力无关,这是由KDP晶体内部结构决定的?     

On the origin of the heterogeneous orientation dynamics of semiflexible polymers in solutions

Collective rotational motion in nondilute isotropic solutions of semirigid chains is sensitively probed by depolarized light scattering over a broad time range. The bimodal shape and the peculiar dependence of the orientational relaxation function on the scattering angle might arise from the coupling between orientational and shear modes of molecular motion (P.G. de Gennes, Mol. Cryst. Liq. Cryst. 12, 193 (1971)). The dynamic heterogeneity, i.e. the separation of the time scales and the shape of the relaxation functions appears to be system specific.     

Optimal cell approach to osmotic properties of finite stiff-chain polyelectrolytes

We propose a self-consistent geometry optimized cell model approach to study osmotic properties of stiff-chain polyelectrolyte solutions. In contrast with the usual monotonic Poisson-Boltzmann prediction, the cell model predicts the correct nonmonotonic dependence of the osmotic coefficient on concentration. A lower degree of polymerization is found to reduce significantly the counterion condensation in a typical dilute strong polyelectrolyte. The results agree quantitatively with simulations of a corresponding many-body bulk system up to a dense semidilute regime.     

The pH effects on the growth rate of KDP (KH2PO4) crystal by investigating Raman active lattice modes

We report on the dependence of the pH value on the growth rates of KDP single crystals. Extensive experimental work has been carried out in order to find the optimum pH ranges for growing KDP single crystals with suitable sizes and high optical quality. Different techniques including micro‐Raman back‐scattering spectroscopy, UV/vis/IR transmission spectroscopy and X‐ray diffraction have been employed for this investigation. Deuterated substituted single crystals of KDP and DKDP also have been grown for the investigation of growth rates and Raman active mode identification purposes. The molecular vibration modes of the grown crystals, including internal modes of PO₄ tetrahedrons molecular vibrations, external modes of optical phonons and hydrogen bonding modes have been determined exactly by micro‐Raman back‐scattering spectroscopy. The best pH values of the solution for the KDP crystal growth with reasonably higher growth rates from aqueous solutions that have been supersaturated ata temperature range of 30–50 °C have been found to be in the pH range of 3.2–5.4. Copyright © 2007 John Wiley & Sons, Ltd.