Estimation of Critical Point in Branching Reactions: Further Examination of Gel Point Formula

The theory of gel point in real polymer solutions is examined with the empirical correlation between the reciprocal of the percolation threshold and the coordination number given by the percolation theory. Applying a larger value of the relative frequency of cyclization, an excellent agreement is obtained between the present theory and the percolation result. This suggest that while the ring distribution on lattices is similar to that in real systems, ring production is more frequent in the lattice model than in real systems. To confirm this conjecture, we derive the ring distribution function of the lattice model as a limiting case of d→∞, and show that the solution is in fact identical to the asymptotic formula of C→∞ in real systems except for the coefficient C, which has a maximum at d = 5, in support of the above conjecture. To examine the validity of the asymptotic solution for the lattice model, we apply it to the critical point problem of the percolation theory, showing that the solution works well in high dimensions greater than six.     

Dynamic and static light scattering study of the formation of cross-linked PMMA gels

Free radical co-polymerization of methyl methacrylate (MMA) and ethyl glycol dimethyl metacrylate (EGDMA) was investigated in solution at different molar ratios R = [EGDMA]/[MMA] between 0 and 0.05. Initially mainly linear PMMA was formed with weight average molar mass 7.5 g/mol independent of R. At larger reaction extents branched polymers were formed and the systems gelled. The scattering intensity rose initially with the reaction extent, but reached a plateau value at larger reaction extents. The plateau value increased strongly with R. Dynamic light scattering showed the appearance of a slow relaxation not observed in linear PMMA solutions. The data can be interpreted by assuming that the excess scattering originates from the branching points and relaxes through self diffusion of the branched particles. The results agree with predictions of the percolation model for gelation and Rouse dynamics. Viscosity measurements corroborate this interpretation. Measurements on a progressively diluted sample quenched close to the gel point again showed quantitative agreement with the percolation model for gelation. Received 11 May 1998 and Received in final form 22 October 1998     

Piezoelectricity of chiral nematic elastomers

A molecular model of freely jointed chains of chiral monomers is developed to describe the piezoelectric effect in chiral nematic elastomers. The model, an extension of the neo-classical theory of nematic polymer networks, takes into account a chiral biasing of molecular alignment under shear which leads to induced polarisation if the monomers contain a transverse dipole moment. The resulting theory is fully non-linear in elastic deformations, in the spirit of ordinary rubber elasticity. The expansion to the highest order in small strains gives the three linear piezoelectric coefficients predicted by phenomenological models. Received 7 September 1998 and Received in final form 19 October 1998     

Long Optical Delay Lines Enhanced by Ring Configuration in Optical Fibres

A long optically controlled delay line enhanced by ring configuration is demonstrated by using the group-velocity control of signal pulses based on stimulated Brillouin scattering. In experiment, two optical fibre ring cavities are used： one is used as the Brillouin laser, providing single-mode Stokes wave as probe wave; the other is used as the Brillouin amplifier, working as slow light medium. We achieve a maximum time delay of 215ns using the ring Brillouin amplifier, five times larger than the input probe pulse width of 40ns. In the meantime, a considerable pulse broadening is observed, which agrees well with the theoretical prediction based on linear theory.     

The segregation of poly(styrene-b-isoprene) diblock copolymers to the surface of a polystyrene melt: the effect of the ratio of block lengths

The effect of the ratio of block lengths on the interfacial partitioning of poly(styrene-block-1,4 isoprene) diblock copolymers from their mixtures with polystyrene homopolymer melt is investigated utilizing a series of copolymers with almost constant molecular weight but different compositions. The concentration profile of the copolymer is measured directly using the nuclear reaction analysis technique; a segregation of the diblock is found at both the air/polymer surface, due to the lower surface energy of polyisoprene, and at the substrate/polymer interface. No significant effect of the block length ratio on the free-surface excess was observed. The block molecular weights have apparently led to dangling chain conformations in the non-overlapping mushroom and in the overlapping mushroom regimes whereas the brush regime was not accessible; no indications of a real border between the two former regimes was found. Received: 20 July 1998 / Received in final form and Accepted: 11 September 1998     

Preparation,Characterization and Coreflood Investigation of Polyacrylamide/Clay Nanocomposite Hydrogel System for Enhanced Oil Recovery

The synthesis and characterization of polyacrylamide/clay nanocomposites for the development of hydrogel system used in enhanced oil recovery is described. The synthesized nanocomposite copolymer was crosslinked with Chromium (III) acetate to form the hydrogel which exhibited an acceptable gel strength, gelation time and gel stability. The nanocomposite gels prepared with low crosslinker concentration (2000 ppm chromium acetate) showed higher gel strength and required longer gelation time than the conventional polyacrylamide (PAAm) gel; these are desirable properties for the effective placement of gel during enhanced oil recovery operations. The effects of various parameters, such as polymer and crosslinker concentration, on the gelation time and gel strength were evaluated using the bottle testing method. X-ray diffraction (XRD) and field-emission scanning electron microscopy (FESEM) revealed the formation of intercalated and exfoliated clay morphologies. The effects of the clay content on the thermal stability and gel strength of the gel network were also investigated by thermogravimetric analysis (TGA) and rheological measurements (oscillatory time sweep profiles), respectively. Also, in-situ gelation and core flooding experiments revealed that a significant permeability reduction of the sand pack cores could be achieved at reservoir conditions when they were treated with the developed nanocomposite gel formulation. Hence, this nanocomposite gel system with low crosslinker concentration (10,000 ppm of nanocomposite polymer concentration containing 2000 ppm of clay with 2000 ppm chromium acetate crosslinker) may be suitable in water shut-off treatments required for enhanced oil recovery from the oil fields.     

Gauge model of a crack

The paper proposes a model of a crack system as local symmetry breaking for a group of 3D rotations compensated by fictitious fields that make Lagrangian equations of elastic energy density covariant in the effective Riemannian space. Equilibrium equations are solved using the perturbation theory with the number of notches being a small parameter, and exact expressions are derived for stress and gauge fields in a 2D problem by applying Hilbert transform to orthogonal Chebyshev polynomials. The model is generalized to nonlinear elasticity (deformation theory of plasticity) and statistical mesomechanics models. Also presented is a solution for stress concentration in a system of arbitrarily oriented cracks which takes into account their mutual influence at any order of the perturbation theory and reduces to a system of linear equations with explicit exact solutions.     

Phase time in Kane type barrier tunneling

The behavior of Wigner phase delay time in the reflection mode is studied taking into account the real band structure of Kane type semiconductor quantum ring. It's calculated the analytical expression for the saturated delay time. It's shown that the saturated delay time is independent of the width of the opaque barrier.     

Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations

The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with f=4 arms in a Θ -solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with N=300 , 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries.     

Chirp-Z analysis for sol-gel transition monitoring

Gelation is a complex reaction that transforms a liquid medium into a solid one: the gel. In gel state, some gel materials (DMAP) have the singular property to ring in an audible frequency range when a pulse is applied. Before the gelation point, there is no transmission of slow waves observed; after the gelation point, the speed of sound in the gel rapidly increases from 0.1 to 10 m/s. The time evolution of the speed of sound can be measured, in frequency domain, by following the frequency spacing of the resonance peaks from the Synchronous Detection (SD) measurement method. Unfortunately, due to a constant frequency sampling rate, the relative error for low speeds (0.1 m/s) is 100%. In order to maintain a low constant relative error, in the whole speed time evolution range, Chirp-Z Transform (CZT) is used. This operation transforms a time variant signal to a time invariant one using only a time dependant stretching factor (S). In the frequency domain, the CZT enables us to stretch each collected spectrum from time signals. The blind identification of the S factor gives us the complete time evolution law of the speed of sound. Moreover, this method proves that the frequency bandwidth follows the same time law. These results point out that the minimum wavelength stays constant and that it only depends on the gel.     

“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

Molecular photodynamics involved in multi-photon excitation fluorescence microscopy

We present a simple model for calculating the fluorescence generated by the multi-photon excitation (MPE) of molecules in solution. The model takes into account internal molecular dynamics such as ground-state depletion due to inter-system crossing (ISC), as well as external molecular dynamics associated with diffusion into and out of an excitation volume confined in 3-dimensions. Internal and external molecular dynamics are combined by using a technique of linearization of a modified diffusion equation which takes into account the possibility of concentration depletion due to photobleaching. In addition, we discuss the phenomenon of pulse saturation which effectively limits the molecular excitation rate constant in the case of short pulsed excitation. Our results are specifically applied in the context of fluorescence autocorrelation functions and single-molecule detection. In the latter case, we discuss some consequences of high-order multi-photon photobleaching. Finally, we include three appendices to rigorously define the temporal and spatial profiles of an arbitrary excitation beam, and also to discuss some properties of an exact evaluation of concentration depletion due to photobleaching. Received: 9 March 1998 / Accepted: 20 April 1998     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Analysis of car-following model considering driver’s physical delay in sensing headway

An extended car-following model is proposed by taking into account the delay of the driver’s response in sensing headway. The stability condition of this model is obtained by using the linear stability theory. The results show that the stability region decreases when the driver’s physical delay in sensing headway increases. The KdV equation and mKdV equation near the neutral stability line and the critical point are respectively derived by applying the reductive perturbation method. The traffic jams could be thus described by soliton solution and kink-antikink soliton solution for the KdV equation and mKdV equation respectively. The numerical results in the form of the space-time evolution of headway show that the stabilization effect is weakened when the driver’s physical delay increases. It confirms the fact that the delay of driver’s response in sensing headway plays an important role in jamming transition, and the numerical results are in good agreement with the theoretical analysis.     

Polymer-mediated interactions of fluid membranes in a lyotropic lamellar phase: a small angle X-ray and neutron scattering study

Small angle X-ray and neutron scattering data on an effective three-component lamellar phase composed of water, a non adsorbing water-soluble polymer (polyvynilpyrolidone), fluid membranes, made from a mixture of a cationic surfactant (cetylpiridiumchloride) and a cosurfactant (hexanol), are presented for various membrane as well as polymer concentrations. The data are fitted with a recently proposed model which takes into account the geometry and the fluctuations of these periodic structures. This allows a quantitative study of the polymer contribution to the smectic compression modulus of the lamellar phase. Four different regimes of polymer confinement are expected. The associated variations in are compared to a recent theoretical model, which predicts the polymer-mediated contribution to the smectic compression modulus. Received 20 January 1998     

Formation of ordered micro-porous membranes

Regular micro-porous polymeric membranes have recently been discovered by rapidly evaporating a solution of CS₂ containing poly(p-phenylene)-block-polystyrene [#!ref1!#]. 1,2-dichloroethane (a chlorated solvent in which polystyrene gel phase has never been observed) is also found to produce ordered structures, which definitively excludes eventual effect of the gelation process during the membrane formation. The observation of the solution surface during the solvent evaporation reveals the growing of micron-sized water droplets trapped at the surface and forming compact aggregates. The study of the solution/water interface shows that the water droplets profile is in agreement with the pore shape observed in the membranes. Moreover, the copolymer was found to precipitate at the interface, forming a layer encapsulating the droplets and preventing their coalescence. In that way, the final structure results from the droplets stacking under the action of large surface currents. Finally, we argue that the decisive element in the formation of ordered structures is the ability of the polymer to precipitate at the solution/water interface, which seems to be related the star-polymer microstructure. Received: 18 August 1998     

Holographic behavior of a photopolymer at high thicknesses and high monomer concentrations: mechanism of photopolymerization

One of the main problems involved in the development of holography is that of the recording material used. In this study the behavior of a photopolymer is analyzed when thicknesses greater than 100 μm are used. The photopolymer is made up of acrylamide as monomer, triethanolamine as radical generator, yellowish eosin as sensitizer and polyvinyl alcohol as binder. The main problem is that an increase in thickness produces more scattering and consequently a decrease in the diffraction efficiency. In this study we analyzed the influence of the concentration of monomer on scattering and found that an increase in the concentration reduces scattering. The behavior of the material varies as the concentration of acrylamide is increased. Two polymerization mechanisms compete and so the behavior of the photopolymer is not linear, the reaction is slower and the expected maximum efficiency is not reached. It has been demonstrated experimentally that when the recording intensity is reduced the photopolymer behaves in a linear way. Received: 28 January 2000 / Revised version: 25 July 2000 / Published online: 13 December 2000     

Polarisation effect of laser field in inelastic electron - hydrogen collisions

We study the influence of the laser polarization on the electron impact excitation of atomic hydrogen. Our method takes into account the “dressing” of the target states by including the laser-atom interaction to first order time-dependent perturbation theory, while the interaction of the laser field with the incident electron is treated to all orders by using the non relativist Volkov function. The interaction of the fast projectile with the target atom is treated in the first Born approximation. The calculations are performed via two distinct computations. The first one is based on a direct calculation, the second based on a Sturmian approach. Important differences appear between the angular distributions depending on the polarization chosen. Received : 17 february 1998 / Revised : 20 july 1998 / Accepted : 2 september 1998     

Radiative lifetimes of excited W II levels

Radiative lifetimes of 19 selected W II levels with energies between 36 000 cm^-1 and 55 000 cm^-1 have been measured with the time-resolved laser-induced fluorescence technique. The ions are generated in a hollow cathode discharge and stored in a linear Paul trap. Selected states are populated with tunable dye laser pulses and the subsequent fluorescence is measured by means of a 5 Gigasample transient digitizer and a fast photodetector with a risetime of 700 ps. By taking into account both the temporal profile of the laser pulses and the separately measured response function of the system, the lifetime can be determined from the full decay curve. A refined evaluation procedure, taking into account saturation effects in the signals, reduces the uncertainty in our data to around 1%. Received: 30 July 1998 / Revised: 18 August 1998     

Langevin dynamics of the glass forming polymer melt: Fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all “water-melon” diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation. Received: 9 January 1998 / Revised: 24 April 1998 / Accepted: 2 July 1998