Ordering of urchin-like charged copolymer micelles: Electrostatic, packing and polyelectrolyte correlations

We report the results of small-angle neutron scattering (SANS) studies on aqueous solutions of spherical polyelectrolyte micelles formed by association of charged-neutral diblock copolymers. The neutral moieties are found to self-assemble into small dense spheres (cores of the micelles) whose sizes are independent of the polymer concentration c. In the dilute regime, c<c ^*, where c^* is the overlap concentration of the micelles, the conformation of the charged groups, which form the corona of the micelles, is found to be extended. A liquid-like order is observed over a wide concentration range spanning from the dilute regime to the concentrated regime. For c>c ^*, polyelectrolyte correlations appear at smaller spatial scales and coexist with the liquid-like order. These results suggest that for dense brushes, above c^*, the rod-like statistics of the charged chains begin to disappear due to contraction of corona arms or by interpenetration of coronae. For less dense brushes, the charged chains are found to be extended up to concentrations far above c^*, before the progressive development of polyelectrolyte correlations. Received 8 October 1999     

A Light and X‐Ray Scattering Study of Aqueous Micellar Solutions of a Diblock Copolymer of Propylene Oxide and Ethylene Oxide with Solubilized Alkylcyanobiphenyl Liquid Crystals

Abstract

The temperature and concentration dependences of the physicochemical properties of aqueous solutions of the diblock copolymer P₄₃E₃₁₂ (P = oxypropylene, E = oxyethylene) with solubilized liquid crystal (LC) have been studied using static and dynamic light scattering (SLS and DLS), small‐angle x‐ray scattering (SAXS), and ultraviolet (UV) spectroscopy. Relaxation time distributions from DLS obtained from inverse Laplace transformation of intensity correlation functions are multimodal, where the two fastest modes are attributed to diblock copolymer unimers and micelles, respectively. The remaining modes at longer decay times reflect the presence of free LC with hydrodynamic radii (R _h) of hundreds of nm. The R _h of both unimers and micelles were independent of temperature (T), while the hydrodynamic virial coefficient k _D and the second virial coefficient, A ₂, decreased with increasing T. The UV spectroscopy measurements showed that there is a reduction in the amount of solubilized LC per gram of copolymer (c _s) as the copolymer concentration (c _p) is increased. The SAXS results agree well with a model of a homogeneous system of polydisperse interacting hard spheres. In solution, both the effective micellar radius of interaction (R _eff) and the hard‐sphere micellar radius (R¯_s) increase in the presence of LC due to solubilization of the latter in the hydrophobic micellar core. Both SAXS and SLS results show that intermicellar interactions become important at c _p > 1% (w/w) at high temperatures [T > the critical micelle temperature (cmt)].     

Micelles of poly(isoprene-b-2-vinylpyridine-b-ethylene oxide) terpolymers in aqueous media and their interaction with surfactants

Well-defined poly(isoprene-b-2-vinylpyridine-b-ethylene oxide) (PI-P2VP-PEO) triblock terpolymers were synthesized by anionic polymerization high-vacuum techniques. The terpolymers formed spherical three-layer (onion-type) micelles in neutral and acidic pH aqueous media as evidenced by static and dynamic light scattering. In pure water, kinetically frozen micelles with a core composed of a soft PI inner part and a hard P2VP outer shell and protected by a neutral PEO corona were formed. In acidic media the core was formed by the soft PI hydrophobic segment, whereas the corona consisted of an inner cationic polyelectrolyte P2VPH⁺ part and an outer PEO shell. The aggregation numbers were found to be high in all cases, due to the high hydrophobicity of the core-forming blocks. In the latter case an increase in size was observed due to the electrostatic repulsions between the P2VPH⁺ chains in the inner part of the corona, which is also responsible for the lower aggregation numbers observed in the acidic solutions. The interaction of these onion-type micelles with cationic (DTMAB) and anionic (SDS) surfactants led to the formation of mixed polymer/surfactant aggregates. Their structural characteristics could be varied by combining changes in surfactant type and concentration, solution pH and type of electrostatic interaction, leading to interesting, block-copolymer-based, environmentally responsive colloidal systems.     

激光光散射研究二醋酸纤维素在丙酮中的聚集

采用激光光散射研究了二醋酸纤维素的溶液性质. 发现在丙酮中二醋酸纤维素除了以单链形式存在外,还形成了胶束以及胶束簇集体. 随着浓度的增加,平均流体力学半径线性增加,而均方根回旋半径与平均流体力学半径的比值线性减小,表明由于二醋酸纤维素分子间的相互作用,胶束之间发生聚集,并形成胶束簇集体.     

Stratification of foam films made from polyelectrolyte solutions

Studies of thin liquid films, made from semidilute polyelectrolyte solutions, are presented. The disjoining pressure variation with film thickness exhibits oscillations, corresponding to film stratification. The oscillations become sharper as the polymer concentration c increases, and disappear when salt is added. The period of the oscillations scales as c ^-1/2. The observed stratification is related to the polymer network and the size of the steps to the mesh size ξ. Received 25 April 2000 and Received in final form 3 October 2000     

Phase behavior of a suspension of hard spherocylinders plus ideal polymer chains

We study isotropic-isotropic and isotropic-nematic phase transitions of fluid mixtures containing hard spherocylinders (HSC) and added non-adsorbing ideal polymer chains using scaled particle theory (SPT). First, we investigate isotropic-nematic (I -N phase coexistence using SPT in the absence of polymer. We compare the results obtained using a Gaussian form of the orientational distribution function (ODF) to minimize the free energy versus minimizing numerically. We find that formal numerical minimization gives results that are much closer to computer simulation results. In order to describe mixtures of HSC plus ideal chains we studied the depletion of ideal chains around a HSC. We analyze the density profiles of ideal chains near a hard cylinder and find the depletion thickness δ is a function of the ratio of the polymer's radius of gyration R_g and the cylinder radius R_c. Our results are compared with a common approximation in which the depletion thickness is taken equal to the radius of gyration of the polymer chain. We incorporate the correct depletion thickness into SPT and find that for R _g/R _c < 1.56 using ideal chains gives phase transitions at smaller polymer concentrations, whereas for R _g/R _c > 1.56 , which is a common experimental situation, the phase transitions are found at larger polymer concentrations with respect to δ = R _g . The differences are significant, especially for R _g ≫ R _c , so we can conclude it is essential to take into account the properties of ideal polymer chains and the resulting depletion near a cylinder. Finally, we present phase diagrams for rod-polymer mixtures which could be realized under experimental conditions.     

Mixed micellization study of ibuprofen (sodium salt) and cationic surfactant (conventional as well as gemini)

Herein, we have studied the interaction between cationic surfactant (conventional [myristyltrimethylammonium bromide, MTAB] as well as gemini surfactant 1, 4‐butanediyl‐α, ω‐bis(dimethyltetradecylammonium bromide) (14‐4‐14)) and anti‐inflammatory sodium salt of ibuprofen (IBU) drug in aqueous solutions by using tensiometry method at 298.15 K. The means of the interaction of drugs by added foreign materials is of paramount importance in the drug delivery. Ibuprofen is used for the relief of pain, fever, and swelling. From this study we have evaluated different parameters, for example, critical micelle concentration (cmc), micellar mole fraction of mixed micelles/mixed interface (X₁^m/X₁^σ), micellar/surface interaction parameter (β^m/β^σ), activity coefficients (f₁^m/f₁^σ and f₂^m/f₂^σ) of the mixed micelles/mixed interface, excess Gibbs free energy of mixed monolayer/mixed micelle formation ( $\mathrm{\Delta }{G}_{\mathrm{ex}}^{\mathrm{\sigma }}$/ $\mathrm{\Delta }{G}_{\mathrm{ex}}^{\mathrm{m}}$), surface excess concentration (Γ_max) etc. and discussed in detail. The micellar interaction parameter (β^m) was determined from the critical micelle concentration values of the pure surfactant (MTAB/14‐4‐14) and IBU (cmc₁ and cmc₂) and the mixed system (cmc) using the Rubingh's model. In addition to this, various other parameters such as packing parameters of amphiphiles in the micelles (P), volume contribution of the hydrophobic chain (V₀), and its effective length (l_c), have also been calculated. The value of micellar mole fraction ( $X_1^{\mathrm{m}}$) is found to be more for IBU + 14‐4‐14 mixtures as compared to IBU + MTAB mixtures at lower mole fraction and vice versa at a higher mole fraction of surfactant. The ΔG^o_m and ΔG^o_ads values for all studied systems were found out to be negative, ie, micellization, as well as adsorption processes, are found to be energetically favorable.     

Does the Principle of Equivalence Prohibit Trapped Surfaces from Forming in the General Relativistic Collapse Process?

It has recently been shown that time-like spherical collapse of a physical fluid in General Relativity does not permit formation of trapped surfaces. This result followed from the fact that the formation of a trapped surface in a physical fluid would cause the time-like world lines of the collapsing fluid to become null at the would-be trapped surface, thus violating the Principle of Equivalence in General Theory of Relativity (GTR). For the case of the spherical collapse of a physical fluid, the no trapped surface condition 2GM(r, t)/R(r, t) c ²<1 was found to be required to be satisfied in all regions of spacetime, where R(r, t) is the invariant circumference variable, r is a co-moving radial coordinate and M(r, t) is the gravitational mass confined within the radius r. The above result was obtained by treating the problem from the viewpoint of an internal co-moving observer at radius r. The boundary of the fluid at r _s=R _s(r _s, t) must also behave in a similar manner, and an external stationary observer should be able to obtain a similar no trapped surface relationship. Accordingly, we generalize this analysis by studying the problem of a time-like collapsing radiating plasma from the point of view of the exterior stationary observer. We find the Principle of Equivalence implies that the physical surface surrounding the plasma must obey 1/(1+z _s)>0, where z _s is the surface red shift seen by a zero-angular momentum observer. When this condition is applied to the first integral of the time-time component of the Einstein equation, it leads to the no trapped surface condition 2GM(r _s, t)/R(r _s, t) c ²<1 consistent with the condition obtained above for the interior co-moving metric. The Principle of Equivalence enforces the no trapped surface condition by constraining the physics of the general relativistic radiation transfer process in a manner that requires it to establish and maintain an Eddington limited secular equilibrium on the dynamics of the collapsing radiating surface so as to always keep the physical surface of the collapsing object outside of its Schwarzschild radius. The important physical implication of the no trapped surface condition is that galactic black hole candidates GBHC do not possess event horizons and hence do possess intrinsic magnetic fields. In this context the spectral characteristics of galactic black hole candidates offer strong evidence that their central nuclei are highly red-shifted Magnetospheric Eternally Collapsing Objects (MECO) within the framework of General Relativity.     

Speculations on the cluster radius below the percolation threshold

We suggest the average radius of percolation clusters withs sites to vary belowp _c ass ⁰, where ₀ is the exponent for the mean radius of self-avoiding walks. This result gives the desired asymptotic behavior of the correlation function for percolation (connectivity) and is consistent with Leath's Monte Carlo data.     

A determination of the low energy parameters of the 2-d Heisenberg antiferromagnet

We perform numerical simulations of the 2-d Heisenberg antiferromagnet using a cluster algorithm. Comparing the size and temperature effects of various quantities with results from chiral perturbation theory we determine the low energy parameters of the system very precisely. We finde ₀=–0.6693(1)J/a ² for the ground state energy density, _s = 0.3074(4)/a ² for the staggered magnetization,c=1.68(1)J a for the spin wave velocity andp _s =0.186(4)J for the spin stiffness. Our results agree with experimental data for the precursor insulators of high-T _c superconductors.Supported by the Schweizer Nationalfond     

Annihilation of nematic point defects: Pre-collision and post-collision evolution

The annihilation of the nematic hedgehog and anti-hedgehog within an infinite cylinder of radius R is studied. The semi-microscopic lattice-type model and Brownian molecular dynamics are used. We distinguish among the i) early pre-collision, ii) late pre-collision, iii) early post-collision, and iv) late post-collision stages. In the pre-collision stage our results agree qualitatively with the existing experimental observations and also continuum-type simulations. The core of each defect exhibits a ring-like structure, where the ring axis is set perpendicular to the cylinder symmetry axis. For ξ⁽⁰⁾_d/(2R) > 1 the interaction between defects is negligible, where ξ⁽⁰⁾_d describes the initial separation of defects. Consequently, the defects annihilate within the simulation time window for ξ⁽⁰⁾_d/(2R) < 1. For close enough defects their separation scales as ξ_d (t_c - t)^0.4±0.1, where t_c stands for the collision time. In elastically anisotropic medium the hedgehog is faster than the anti-hedgehog. In the early pre-collision stage the defects can be treated as point-like particles, possessing inherent core structure, that interact via the nematic director field. In the late pre-collision stage the cores reflect the interaction between defects. After the collision a charge-less ring structure is first formed. In the early post-collision stage the ring adopts an essentially untwisted circular structure of the radius ξ_r. In the late post-collision stage we observe two qualitatively different scenarios. For μ = ξ_r/R < μ_c ∼ 0.25 the ring collapses leading to the escaped radial equilibrium structure. For μ > μ_c the chargeless ring triggers the nucleation growth into the planar polar structure with line defects.     

Dynamics of forest fire under rotational constraint

A rotationally constrained forest fire model is studied on square and triangular lattices of size 400×400. The critical probabilityp _c for onset of fire propagation is determined. The scaling relationsMt ^d _r, R_gt^v andMR _g ^d _f are analysed at fire propagation probabilityp=p _c whereM is the number of burnt trees,R _g the radius of gyration andd _f the fractal dimension of the cluster of burnt trees at timet. Numerical estimates ofd _t, v andd _f have been obtained.     

Kinetics of phase separation in ramified polymer blends of arbitrary topology

We present here a theoretical study of kinetics of phase separation within a mixture made of two chemically incompatible ramified polymers. For simplicity, we assume that they have the same topology. We are interested in the variation of the relaxation rate, _q, versus the wave number q, in the vicinity of the spinodal temperature. The kinetics is governed by local (Rouse) and reptation motions (faster and slower modes). For qR_G 1 (R_G being the gyration radius), kinetics is entirely controlled by local motions where each chain moves inside its own tube, and we show that the corresponding characteristic frequency, ^{-1}_q, scales as ^{-1}_{q G}q⁶, where _G is a known topological factor. For qR_G 1, however, kinetics is rather dominated by long-wavelength (reptation) motions where unlike ramified polymers creep inside a long tube. For this case, we find that ^{-1}_q ( 0 )q² (_c - ), where ( 0 ) is another known topological factor that represents the total mobility of free monomers belonging to connected chains and reticulation points, and _c accounts for the critical value of the segregation parameter. Finally, the derived relaxation rate must be compared to that relative to a linear polymer mixture.     

Protonated dye-surfactant ion pair formation between neutral red and anionic surfactants in aqueous submicellar solutions

Spectral and surface tension behavior of aqueous neutral red in the presence of sodium dodecyl sulfate (SDS), sodium dodecyl benzene sulfonate (SDBS) and sodium dodecyl sulfonate (SDSN) have been studied to understand the nature of the interactions in their submicellar concentration ranges. The variations in spectra and surface tension with variation in the concentrations of the surfactants suggest the formation of a 1:1 close-packed dye-surfactant ion pair, HNR⁺S⁻ between the acid form, HNR⁺ of the dye and the surfactant anion at very low concentrations of the surfactant below critical micelle concentration (cmc) of the pure surfactant. The dye-surfactant ion pair behaves like a nonionic surfactant having higher efficiency and lower cmc than that of the corresponding pure anionic surfactant. The ion pairs are adsorbed on the air/water interface at very low concentrations of the surfactant. As the concentration of the surfactant increases and the ion pairs form micelles of their own, the dye in the ion pair is protonated to form H₂NR²⁺S⁻. As the cmc of the pure surfactant is approached, the protonation equilibrium gradually reverses and pure surfactant ions gradually replace the ion pairs at the interface. Finally, a homogeneous monolayer of pure surfactant anions exists at the air/water interface and the dye remain solubilized in pure micelles above the cmc of the pure surfactant. The equilibrium constants, K_c for the close-packed protonated dye-surfactant ion pair (PDSIP) formation have been determined at varying pH. The submicellar interaction has been found to be stronger with SDS than SDBS. The plots of logarithm of K_c vs. pH have been found to be quite linear which consolidates the assumption of formation of the species, H₂NR²⁺S⁻. The interaction is driven by enthalpy as well as entropy.     

Nature of contact resistance in high-T c YBa2Cu3O7−δ Superconductors

The contacts between various metals and the high-T_c superconductor YBa₂Cu₃O_7– are characterized by contact resistance,R _c, andI–V measurements from 300 K to 90 K. The contacts with bulk superconductor were made by vacuum deposition. Four metals, Au, Ag, Al, and Bi were investigated. The current transport across the contact is by carrier tunneling. All contacts were ohmic as theirI–V characteristics were symmetrical with respect to current direction.R _c values range between 10^–2 to 10¹ cm² and increase linearly as the temperature is lowered. The contact resistance originates from two distinct physical processes. One is the modification of the carrier concentration at the interface by the contact metal. The second is the nature of carrier injection at the free surface of the superconductor. TheR _c values depend on the contact metal-oxygen interaction parameter signifying the need for oxygen passivation for obtaining low contact resistances.     

Black holes associated with galaxies

A small and a large black hole are naturally associated with a galaxy of total massM and spherical halo radiusR. Also of massM, the large black hole is a spatial contraction of the galaxy down to its Schwarzschild radius,r r, with=2GM/c ²R, whereG/c ²=4.78×10^–17 kpc/M is Newton's gravitational constant divided by the speed of light squared. The small black hole is ther r contraction of the large hole, i.e., the iterated double contraction of the galaxy itself, with the resulting massm=M=2GM ²/c²R. In the case of the Milky Way (M=7.0×10¹¹ M andR=15 kpc) the latter equation for the small black hole mass yieldsm=3.1×10⁶ M , which is close to the observed value for the mass of the black hole at the center of the Milky Way. Black holes of the small type may evolve to the large by mass accretion, perhaps during a quasar phase. Vast regions of the universe may in fact be populated by large black holes—missing mass—which validates the cosmological principle and effects the closure of the universe.     

Multistage radiation-stimulated changes in the microhardness of silicon single crystals exposed to low-intensity β irradiation

Radiation-stimulated and postradiation changes in the microhardness of silicon single crystals exposed to irradiation with a low-intensity flux of β particles (I = 9 × 10⁵ cm^?2 s^?1, W = 0.20 + 0.93 MeV) are studied. It is established that the inversion of the radiation-induced plastic effect occurs at a characteristic irradiation time τ_c = 75 min; i.e., irradiation of silicon single crystals for a time τ < τ_c leads to nonmonotonic reversible hardening, whereas nonmonotonic reversible softening is observed under irradiation for a time τ > τ_c. It is demonstrated that there exists a correlation between the nonmonotonic dependences of the microhardness and the concentration of electrically active defects at acceptor levels with energies E _c ? 0.11 eV, E _c ? 0.13 eV, and E _c ? 0.18 eV on the irradiation time.     

Percolation cluster numbers by real-space renormalization

The average numbern _s (p) of percolation clusters withs sites is calculated for the triangular lattice using real-space renormalization. Fors up to 2,000 the whole range of concentrationsp was analyzed;n _s varied over sixty decades. We found logn _s –s forp belowp _c =0.5, andn _s s ^–, =2.35 atp=p _c . For smallp one hasn _s (p · ) ^s . Nearp _c we found the scaling fromn _s s ^– f((p _c –p) ·s ) with=0.53. Presumably for the first time renormalization methods were used to calculate percolation properties not only nearp _c but also far away from the critical point.Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Scaling functions for critical surface scattering

Scattering of x-rays at grazing angles is studied for semi-infinite systems which exhibit a second order phase transition. We calculate the scaling functions for the diffuse scattering intensity aboveT _c and for the Bragg-intensity belowT _c, using -expansion techniques. Corrections to the leading critical surface behaviour and the size of the asymptotic scaling region are discussed. In addition, we obtain the crossover function for the excess susceptibility _s.This work was supported by Bundesministerium für Forschung und Technologie     

Instability of layered quantum liquids: 4. Intraplane and interplane correlations

We calculate the local-field correctionsG(q, q _z) f electron superlattices with interlayer distanced in order to describe many-body effects. A generalized Hubbard expression for the local-field correction is derived. The sum-rule version of the self-consistent approach for the local-field correction is developed and used to discuss the effects of exchange and correlation. The RPA-parameterr _s and the ratiod/a ^* determine the many-body effects.a ^* is the effective Bohr radius. The stability region for the Fermi liquid behavior of the layered electron gas is discussed: (i) forda ^* the critical RPA-parameterr _sc1 is determined by exchange andintraplane correlation effects, (ii) forda ^* withr _sc1 correlation effects are small and the instability point is mainly determined by exchange effects, (iii) forda ^* withr _sc<1 exchange andinterplane correlation effects are both important for the instability point. Our results are important for high-T _c superconductors, organic superconductors and semiconductor superlattices.