Exact effective force between star-polymers in a $\Theta$-solvent

We re-examine here the computation of the effective force between two star-polymers of respective numbers of branches f₁ and f₂, immersed in a common -solvent. Such a force originates essentially from the repulsive three-body interactions. To achieve this, we take advantage of some established results using renormalization theory for three-dimensional star-polymers, or conformal invariance for two-dimensional ones. We first show that, in dimension d = 3, the force, , decreases with the center-to-center distance r as , with the exact universal amplitude . Second, in dimension d = 2, we find that the force decays more slowly as , with the exact universal amplitude . For high distances compared to the gyration radius, , of a single polymer chain at the -point, an exponential decay of the force is expected.Received: 3 February 2004, Published online: 24 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.20.-y Classical statistical mechanics     

Dynamics of propylene glycol and its oligomers confined in clay

The dynamics of propylene glycol (PG) and its oligomers 7-PG and PPG, with (about 70 monomers), confined in a Na-vermiculite clay have been investigated by quasi-elastic neutron scattering and dielectric spectroscopy. The liquids are confined to a single molecular layer between the clay platelets, thus giving a true 2D liquid. The results show that the average relaxation time , deduced from neutron scattering at a momentum transfer Q of about , is in perfect agreement with the dielectric -relaxation time, although neutron scattering does not only probe the main ( -) relaxation, but all motions of hydrogens on the experimental time scale. At room temperature is proportional to Q ², indicating that the relaxations are mainly due to ordinary translational diffusion. The most unexpected finding is that (or the dielectric -relaxation time) is almost unaffected by the 2D confinement, in contrast to the dielectrically active normal mode of PPG which is substantially slower in the confinement. Only the 7-mer has a significantly slower segmental translational diffusion in the clay. The results suggest that the interactions to the clay surfaces are weak and that the present 2D confinement has a very small influence on the time scale of all our observed relaxation processes, except the normal-mode relaxation.Received: 1 January 2003, Published online: 8 October 2003PACS: 61.25.Em Molecular liquids - 68.35.Ja Surface and interface dynamics and vibrations - 61.12.-q Neutron diffraction and scattering     

Frequency dispersion of sound propagation in Rouse polymer melts via generalized dynamic random phase approximation

An extended generalization of the dynamic random phase approximation (DRPA) for L-component polymer systems is presented. Unlike the original version of the DRPA, which relates the matrices of the collective density-density time correlation functions and the corresponding susceptibilities of concentrated polymer systems to those of the tracer macromolecules and so-called broken-links system (BLS), our generalized DRPA solves this problem for the matrices of the coupled susceptibilities and time correlation functions of the component number, kinetic energy and flux densities. The presented technique is used to study propagation of sound and dynamic form-factor in disentangled (Rouse) monodisperse homopolymer melt. The calculated ultrasonic velocity and absorption coefficient reveal substantial frequency dispersion. The relaxation time is proportional to the degree of polymerization N, which is N times less than the Rouse time and evidences strong dynamic screening because of interchain interaction. We discuss also some peculiarities of the Brillouin scattering in polymer melts. Besides, a new convenient expression for the dynamic structure function of the single Rouse chain in representation is found.Received: 30 April 2003, Published online: 3 September 2003PACS: 43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions - 47.10. + g Fluid dynamics: General theory - 83.80.Sg Polymer melts     

Enhancement of the orientational order parameter of nematic liquid crystals in thin cells

We report measurements of birefringence of several nematic liquid crystals having transverse as well as longitudinal dipole moments in thin (1.4 to ) and thick (7 to cells. Rubbed polyimide-coated glass plates are used to get planar alignment of the nematic director in these cells. We find significant enhancement (6 to ) of ( , where S is the orientational order parameter) in thin cells in all compounds with aromatic cores even at temperatures far ( C) below the nematic-isotropic transition point. The enhancement is larger in compounds having several phenyl rings and lower if the number of phenyl rings is reduced. In a compound that does not have an aromatic core no significant enhancement is observed, implying that the strength of the surface potential depends on the aromaticity of the cores. Assuming a perfect orientational order at the surface, calculations based on the Landau-de Gennes theory show that the thickness averaged enhancement of S is sharply reduced as the temperature is lowered in the nematic phase. The measured order parameter S is further enhanced in thin cells because of the stiffening of the elastic constant which reduces the thermal fluctuations of the nematic director. The combined effect is however too small at low temperatures to account for the experimental data.Received: 22 February 2004, Published online: 24 May 2004PACS: 61.30.-v Liquid crystals - 61.30.Pq Microconfined liquid crystals: droplets, cylinders, randomly confined liquid crystals, polymer dispersed liquid crystals, and porous systems - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitionsSurajit Dhara: Present address: Department of Physics, Birla Institute of Technology and Science, Pilani 333 031, India.     

Irreversible adsorption from dilute polymer solutions

We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two broad cases are considered, distinguished by the magnitude of the local monomer-surface sticking rate Q: chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single-chain adsorption. While single-chain physisorption times are typically micro- to milli-seconds, for chemisorbing chains of N units we find experimentally accessible times , ranging from seconds to hours. We establish 3 chemisorption universality classes, determined by a critical contact exponent: zipping, accelerated zipping and homogeneous collapse. For dilute solutions, the mechanism is accelerated zipping: zipping propagates outwards from the first attachment, accelerated by occasional formation of large loops which nucleate further zipping. This leads to a transient distribution of loop lengths s up to a maximum size after time t. By times of order the entire chain is adsorbed. The outcome of the single-chain adsorption episode is a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb onto, late-arriving chains form a diffuse outer layer. In a simple picture we find for both chemisorption and physisorption a final loop distribution and density profile whose forms are the same as for equilibrium layers. In contrast to equilibrium layers, however, the statistical properties of a given chain depend on its adsorption time; the outer layer contains many classes of chain, each characterized by a different fraction of adsorbed monomers f. Consistent with strong physisorption experiments, we find the f values follow a distribution .Received: 13 January 2003, Published online: 8 July 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 68.08.-p Liquid-solid interfaces     

The $\eta_{c}(2980)$ formation in two-photon collisions at LEP energies

production in interactions has been detected via its decays into ,K ⁺ K ^- K ⁺ K ^- and in the data taken with the DELPHI detector at LEP1 and LEP2 energies. The two-photon radiative width averaged over all observed decay channels is = 13.9 2.0 (stat.) 1.4(syst.) 2.7 (BR) keV. No direct decay channel has been observed. An upper limit < 5.5 keV at 95% confidence level has been evaluated for this decay mode.Received: 3 July 2003, Published online: 7 November 2003     

Can the glass transition in bulk polymers be modeled by percolation picture?

Recent observations (Eur. Phys. J. E 9, 135 (2002)) showed that the vitrification process, which sets in during the linear bulk methyl methacrylate (MMA) polymerization carried out below glass transition temperatures, can be modelled by static percolation picture. To generalize this observation for different kind of bulk linear or crosslinked polymers not enough data are present in the literature. To cover partly this deficit we studied the glass transition of MMA and styrene (Sty) crosslinking copolymerization in varying ratios of MMA and Sty. Both the fluorescence intensity I and the lifetime of pyrene (Py) used as a nanosecond in situ fluoroprobe were monitored during the gelation time. Both I and increase dramatically as a result of the reduced mobility of the probes trapped in the glassy regions, appearing near the glass transition point. The average size of the glassy regions just below, and the strength of the infinite network formed upon the connection of the glassy regions above the glass transition point obey power law relations. The data around were interpreted on the basis of the percolation theory and we observed that the corresponding exponents and give static percolation values independent of the polymer composition.Received: 9 July 2004, Published online: 1 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 64.70.Pf Glass transitions - 82.35.Jk Copolymers, phase transitions, structure     

Monte Carlo simulation of particle aggregation and gelation: II. Pair correlation function and structure factor

Diffusion-limited cluster aggregation and gelation are studied using lattice and off-lattice Monte Carlo simulations. The pair correlation function g(r) and the structure factor S(q) of the particle gels were investigated as a function of the volume fraction ( ) and time. At volume fractions below , the gel structure is fractal on small length scales with . g(r) shows a weak minimum at the correlation length ( ), before reaching the average concentration at large length scales. The cut-off function of g(r) varies during the aggregation process, but at a given , where is the gel time, it is a universal function of . At high volume fractions, the structure is dominated by excluded-volume interactions, while at low volume fractions, it is determined by the connectivity.Received: 27 April 2004, Published online: 26 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 02.70.Uu Applications of Monte Carlo methods     

Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions

We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective-diffusion coefficients and , respectively, where D₀ is the single-particle diffusion coefficient, as a function of the density of the colloids . At low Schmidt numbers , we find that hydrodynamics has essentially no effect on the behaviour of . At larger Sc, seems to be enhanced at all densities, although the differences compared to the case without hydrodynamics are rather minor. The collective-diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case without hydrodynamic interactions.Received: 20 October 2003, Published online: 23 March 2004PACS: 68.35.Fx Diffusion; interface formation - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 82.20.Wt Physical chemistry and chemical physics: Computational modeling; simulation     

Power law polydispersity and fractal structure of hyperbranched polymers

Using the complementary approaches of Flory theory and the overlap function, we study the molecular weight distribution and conformation of hyperbranched polymers formed by the melt polycondensation of A-R_N0-B_{f - 1} monomers in their reaction bath close to the mean field gel point p_A = 1, where p_A is the fraction of reacted A groups. Here , N₀ is the degree of polymerisation of the linear spacer linking the A group and the f-1 B groups and condensation occurs exclusively between the A and B groups. For , we assume that the number density of hyperbranched polymers with degree of polymerisation N generally obeys the scaling form and we explicitly show that this scaling assumption is correct in the mean field regime (here N_l is the largest characteristic degree of polymerisation and the function cuts off the power law sharply for ). We find the upper critical dimension for this system is d_c = 4, so that for the mean field values for the polydispersity exponent and fractal dimension apply: , d_f = 4. For d = 3, mean field theory is still correct for where is the Ginzburg point; for , mean field theory applies on small mass scales N<N_c but breaks down on larger mass scales N>N_c where is a cross-over mass. Within the Ginzburg zone (i.e., d<d_c, ), we show that the hyperbranched chains on mass scales N>N_c are non-Gaussian with fractal dimension given by d_f = d (for d = 2,3,4). Our results are qualitatively different from those of the percolation model and indicate that the polycondensation of AB_f-1, unlike polymer gelation, is not described by percolation theory. Instead many of our results are similar to those for a monodisperse melt of randomly branched polymers, a consequence of the fact that so that polydispersity is irrelevant for excluded volume screening in hyperbranched polymer melts.Received: 15 December 2003, Published online: 2 March 2004PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.70.Jk Critical point phenomena     

The $ B\to\pi K$ puzzle and its relation to rare B and K decays

The standard-model interpretation of the ratios of charged and neutral rates, R _c and R _n, respectively, points towards a puzzling picture. Since these observables are affected significantly by colour-allowed electroweak (EW) penguins, this puzzle could be a manifestation of new physics in the EW penguin sector. Performing the analysis in the R _n- R _c plane, which is very suitable for monitoring various effects, we demonstrate that we may, in fact, move straightforwardly to the experimental region in this plane through an enhancement of the relevant EW penguin parameter q. We derive analytical bounds for q in terms of a quantity L, which measures the violation of the Lipkin sum rule, and point out that strong phases around are favoured by the data, in contrast to QCD factorisation. The modes imply a correlation between q and the angle that, in the limit of negligible rescattering effects and colour-suppressed EW penguins, depends only on the value of L. Concentrating on a minimal flavour-violating new-physics scenario with enhanced Z ⁰ penguins, we find that the current experimental values on require roughly . As the data give , L has either to move to smaller values once the data improve or new sources of flavour and CP violation are needed. In turn, the enhanced values of L seen in the data could be accompanied by enhanced branching ratios for the rare decays , , and . Most interesting turns out to be the correlation between the modes and , with the latter depending approximately on a single scaling variable .Received: 8 September 2003, Published online: 12 November 2003     

Some physics highlights from the EUROBALL spectrometer

Exotic, neutron-rich proton-induced spallation products of ²³²Th and ²³⁸U obtained from the PS Booster ISOLDE facility have been investigated by - , - coincidence and spectrum-multiscaling measurements. A new method for the reduction of isobaric contamination enabled to study the unknown region beyond ²⁰⁸Pb for the decay chain A = 217. A new isotope ²¹⁷Bi with a half-life of s was discovered and its -decay studied. For the first time, a half-life value of s for the -decay of ²¹⁷Po was measured.Received: 3 March 2003, Revised: 13 May 2003, Published online: 30 September 2003PACS: 23.20.Lv transitions and level energies - 23.60.+e decay - 27.80.+w 190 A 219 - 29.30.Kv X- and -ray spectroscopyV. Fedoseyev: Present address: ISOLDE, CERN-PPE, CH-1211, Geneva 23, Switzerland.M. Górska: Present address: GSI, Darmstadt, D-64220, Germany.M. Huhta: Present address: Nokia, Tampere, Finland.     

Miscible displacement of non-Newtonian fluids in a vertical tube

The influence of rheology on the miscible displacement of a viscous fluid by a less viscous, Newtonian one in a vertical tube is studied experimentally as a function of the flow velocity. For Newtonian displaced fluids the transient residual film thickness is nearly of the tube radius at large viscosity ratios between the two fluids in agreement with experimental and numerical results from the literature. For shear-thinning fluids with a zero yield stress (mostly xanthan-water solutions), decreases down to of the radius for the most concentrated solutions. For fluids with a non-zero yield stess, further decreases down to 24-25% of the radius. The orders of magnitude of these values can be obtained through numerical simulations (commercial code) for the various types of fluids. Instabilities of the film at its boundary develop downstream and lead to a reduction of the final thickness of the film at longer times: this reduction is larger for lower viscosity ratios and larger velocities.Received: 15 February 2003, Published online: 8 July 2003PACS: 47.20.Gv Hydrodynamic stability: Viscous instability - 83.60.Wc Rheology: Flow instabilities     

Energy dependence of the Λ/Σproduction cross-section ratio in p-p interactions

The production of the - and -hyperons has been measured via the reaction at the internal COSY-11 facility in the excess energy range between 14 and 60 MeV. The transition of the cross-section ratio from about 28 at MeV to the high-energy level of about 2.5 is covered by the data showing a strong decrease of the ratio between 10 and 20 MeV excess energy. Effects from the final-state interactions in the p- channel seem to be much smaller than in the p- channel. Estimates of the effective range parameters are given for the and the systems.PACS: 13.75.-n Hadron-induced low- and intermediate-energy reactions and scattering (energy GeV) - 13.75.Ev Hyperon-nucleon interactions - 13.85.Lg Total cross-sections - 25.40.Ep Inelastic proton scattering     

Isomeric and ground-state decay of 215 Bi

A new high-spin isomer in ²¹⁵Bi, with a half-life of 36.9(6) s, has been identified at the PSB-ISOLDE on-line mass separator using the pulsed-release technique combined with the element selective RILIS source. A decay scheme of Bi was constructed and complemented with the low-spinstructure observed in Bi decay. The population of a cascade on top of the level in ²¹⁵Poprovides evidence for Gamow-Teller -decay of the high-spin ²¹⁵Bi isomer.Received: 3 March 2003, Revised: 10 June 2003, Published online: 9 October 2003PACS: 23.20.Lv transitions and level energies - 27.80.+w - 29.30.Kv X- and -ray spectroscopyV. Fedoseyev: Present address: ISOLDE, CERN-PPE, CH-1211, Geneva 23, Switzerland.M. Górska: Present address: GSI, Darmstadt, D-64220, Germany.M. Huhta: Present address: Nokia, Tampere, Finland.     

Multiphoton radiation in leptonic <Emphasis Type="Italic">W</Emphasis>-boson decays

We explore CP violation in decay processes in the presence of the anomalous right-handed and couplings. The complex anomalous top coupling can be a source of new CP violation and may lead to a deviation of the observed weak phase in decays, which accounts for the present disagreement of the observed between and decays. Direct CP violation is also predicted. Received: 27 November 2002, Revised: 28 March 2003, Published online: 2 June 2003     

Boltzmann-Uehling-Uhlenbech calculation of total reaction cross-section and fragmentation cross-section

, and have been calculated via the BUU model with soft EOS and 0.8 times of . The density distribution without any adjustable parameters which comes from the RMF model has been introduced into the BUU calculation to replace the normally used one-parameter square-type distribution. The calculated results can reproduce the experimental data well for both halo- and stable-nuclei-induced reactions. Here or is calculated as the difference between of halo nucleus and core nucleus, by assuming . It indicates that this assumption works very well at high energy in the BUU calculation. More experimental measurements are necessary to test the validity of this assumption at intermediate energy.Received: 12 June 2003, Revised: 29 September 2003, Published online: 27 April 2004PACS: 24.10.-i Nuclear reaction models and methods - 25.60.Dz Interaction and reaction cross-sections - 25.60.Gc Breakup and momentum distributions - 27.20. + n      

The optimal velocity traffic flow models with open boundaries

The effects of the open boundaries on the dynamical behavior of the optimal velocity traffic flow models with a delay time allowing the car to reach its optimal velocity is studied using numerical simulations. The particles could enter the chain with a given injecting rate probability , and could leave the system with a given extracting rate probability . In the absence of the variation of the delay time , it is found that the transition from unstable to metastable and from metastable to stable state occur under the effect of the probabilities rates and . However, for a fixed value of , there exist a critical value of the extraction rate above which the wave density disappears and the metastable state appears and a critical value above which the metastable state disappears while the stable state appears. and depend on the values of and the variation of the delay time . Indeed and increase when increasing and/or decreasing . The flow of vehicles is calculated as a function of , and for a fixed value of . Phase diagrams in the ( ) plane exhibits four different phases namely, unstable, metastable, stable. The transition line between stable phase and the unstable one is curved and it is of first order type. While the transition between stable (unstable) phase and the metastable phase are of second order type. The region of the metastable phase shrinks with increasing the variation of the delay time and disappears completely above a critical value .Received: 23 July 2003, Published online: 8 December 2003PACS: 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 82.20.Wt Computational modeling; simulation     

Diffusion of gelation clusters in the Zimm model

Starting from a Zimm model, we study self-diffusion in a solution of crosslinked monomers. We focus on the effects of the hydrodynamic interaction on the dynamics and the critical behaviour at the sol-gel point. Hydrodynamic interactions cause the clusters diffusion constant to depend not only on the clusters size but also on the clusters shape --in contrast to the Rouse model. This gives rise to a non-trivial scaling of the Kirkwood diffusion constant averaged over all clusters of fixed size n, with given in terms of the spectral dimension of critical percolation clusters. The long-time decay of the incoherent scattering function is determined by the diffusive motion of the largest clusters. This implies the critical vanishing of the cluster-averaged effective diffusion constant at the gel point with exponent .Received: 24 July 2003, Published online: 21 November 2003PACS: 64.60.Ht Dynamic critical phenomena - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling     

Dynamics of living polymers

We study theoretically the dynamics of living polymers which can add and subtract monomer units at their live chain ends. The classic example is ionic living polymerization. In equilibrium, a delicate balance is maintained in which each initiated chain has a very small negative average growth rate (velocity) just sufficient to negate the effect of growth rate fluctuations. This leads to an exponential molecular weight distribution (MWD) with mean . After a small perturbation of relative amplitude , e.g. a small temperature jump, this balance is destroyed: the velocity acquires a boost greatly exceeding its tiny equilibrium value. For the response has 3 stages: (1) Coherent chain growth or shrinkage, leaving a highly non-linear hole or peak in the MWD at small chain lengths. During this episode, lasting time , the MWDs first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after . The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after . By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables ( ) are enslaved to the slowly varying number of free initiators (chains of zero length). Thus fast variables are quasi-statically fine-tuned to equilibrium. The outstanding feature of these dynamics is their ultrasensitivity: despite the perturbations linearity, the response is non-linear until the late episode (3). For very small perturbations, , response remains non-linear but with a less dramatic peak or hole during episode (1). Our predictions are in agreement with viscosity measurements on the most widely studied system, -methylstyrene.Received: 23 September 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian Motion - 87.15.Rn Biomolecules: structure and physical properties; Reactions and kinetics; polymerization