Langevin Dynamics of a Polymer with Internal Distance Constraints

We present a novel and rigorous approach to the Langevin dynamics of ideal polymer chains subject to internal distance constraints. The permanent constraints are modelled by harmonic potentials in the limit when the strength of the potential approaches infinity (hard crosslinks). The crosslinks are assumed to exist between arbitrary pairs of monomers. Formally exact expressions for the resolvent and spectral density matrix of the system are derived. To illustrate the method we study the diffusional behavior of monomers in the vicinity of a single crosslink within the framework of the Rouse model. The same problem has been studied previously by Warner (J. Phys. C: Solid State Phys. {\bf 14}, 4985, (1981)) on the basis of Lagrangian multipliers. Here we derive the full, hence exact, solution to the problem.Comment: To appear in PRE, Figures on reques

Size and scaling in ideal polymer networks

The scattering function and radius of gyration of an ideal polymer network are calculated depending on the strength of the bonds that form the crosslinks. Our calculations are based on an {\it exact} theorem for the characteristic function of a polydisperse phantom network that allows for treating the crosslinks between pairs of randomly selected monomers as quenched variables without resorting to replica methods. From this new approach it is found that the scattering function of an ideal network obeys a master curve which depends on one single parameter $x= (ak)^2 N/M$, where $ak$ is the product of the persistence length times the scattering wavevector, $N$ the total number of monomers and $M$ the crosslinks in the system. By varying the crosslinking potential from infinity (hard $\delta$-constraints) to zero (free chain), we have also studied the crossover of the radius of gyration from the collapsed regime where R_{\mbox{\tiny g}}\simeq {\cal O}(1) to the extended regime R_{\mbox{\tiny g}}\simeq {\cal O}(\sqrt{N}). In the crossover regime the network size R_{\mbox{\tiny g}} is found to be proportional to $(N/M)^{1/4}$.Comment: latex, figures available on request, to be published: J. Phys I Franc

Collapse of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N. This result is inconsistent with results obtained from free energy considerations by Brygelson and Thirumalai (PRL76, 542 (1996)).Comment: 1 page, 1 postscript figure, LaTe

Dynamical signatures of the vulcanization transition

Dynamical properties of vulcanized polymer networks are addressed via a Rouse-type model that incorporates the effect of permanent random crosslinks. The incoherent intermediate scattering function is computed in the sol and gel phases, and at the vulcanization transition between them. At any nonzero crosslink density within the sol phase Kohlrausch relaxation is found. The critical point is signalled by divergence of the longest time-scale, and at this point the scattering function decays algebraically, whereas within the gel phase it acquires a time-persistent part identified with the gel fraction.Comment: 4 page

Conformations of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean squared end to end distance growing as r^2 ~ M/N. A possible collapse transition (to a region of order unity) is related to percolation in a one dimensional model with long--ranged connections. A directed version of the model is also solved exactly. Based on these results, we conjecture that the typical size of a self-avoiding polymer is reduced by the links to R > (N/M)^(nu). The number of links needed to collapse a polymer in three dimensions thus scales as N^(phi), with (phi) > 0.43.Comment: 6 pages, 3 Postscript figures, LaTe

Shear viscosity of a crosslinked polymer melt

We investigate the static shear viscosity on the sol side of the vulcanization transition within a minimal mesoscopic model for the Rouse-dynamics of a randomly crosslinked melt of phantom polymers. We derive an exact relation between the viscosity and the resistances measured in a corresponding random resistor network. This enables us to calculate the viscosity exactly for an ensemble of crosslinks without correlations. The viscosity diverges logarithmically as the critical point is approached. For a more realistic ensemble of crosslinks amenable to the scaling description of percolation, we prove the scaling relation $k=\phi-\beta$ between the critical exponent $k$ of the viscosity, the thermal exponent $\beta$ associated with the gel fraction and the crossover exponent $\phi$ of a random resistor network.Comment: 8 pages, uses Europhysics Letters style; Revisions: results extende

The symbiotic star CH Cygni. II. The broad Ly alpha emission line explained by shocks

Context. In 1985, at the end of the active phase 1977-1986, a broad (4000 km/s) Ly alpha line appeared in the symbiotic system CH Cygni that had never been observed previously. Aims. In this work we investigate the origin of this anomalous broad Ly alpha line. Methods. We suggest a new interpretation of the broad Ly alpha based on the theory of charge transfer reactions between ambient hydrogen atoms and post-shock protons at a strong shock front. Results. We have found that the broad Ly alpha line originated from the blast wave created by the outburst, while the contemporary optical and UV lines arose from the nebula downstream of the expanding shock in the colliding wind scenario.Comment: 5 pages, 2 figures, accepted for publication in A&A on 7th April 200

Evolution of dust and ice features around FU Orionis objects

(abridged) We present spectroscopy data for a sample of 14 FUors and 2 TTauri stars observed with the Spitzer Space Telescope or with the Infrared Space Observatory (ISO). Based on the appearance of the 10 micron silicate feature we define 2 categories of FUors. Objects showing the silicate feature in absorption (Category 1) are still embedded in a dusty and icy envelope. The shape of the 10 micron silicate absorption bands is compared to typical dust compositions of the interstellar medium and found to be in general agreement. Only one object (RNO 1B) appears to be too rich in amorphous pyroxene dust, but a superposed emission feature can explain the observed shape. We derive optical depths and extinction values from the silicate band and additional ice bands at 6.0, 6.8 and 15.2 micron. In particular the analysis of the CO_2 ice band at 15.2 micron allows us to search for evidence for ice processing and constrains whether the absorbing material is physically linked to the central object or in the foreground. For objects showing the silicate feature in emission (Category 2), we argue that the emission comes from the surface layer of accretion disks. Analyzing the dust composition reveals that significant grain growth has already taken place within the accretion disks, but no clear indications for crystallization are present. We discuss how these observational results can be explained in the picture of a young, and highly active accretion disk. Finally, a framework is proposed as to how the two categories of FUors can be understood in a general paradigm of the evolution of young, low-mass stars. Only one object (Parsamian 21) shows PAH emission features. Their shapes, however, are often seen toward evolved stars and we question the object's status as a FUor and discuss other possible classifications.Comment: accepted for publication in ApJ; 63 pages preprint style including 8 tables and 24 figure

Low Mass Stars and Substellar Objects in the NGC 1333 Molecular Cloud

We present the results of near-infrared imaging and low-resolution near- infrared spectroscopy of low mass objects in the NGC 1333 molecular cloud. A JHK survey of an 11.4' x 11.7' area of the northern cluster was conducted to a sensitivity of K < 16 mag. Using near-infrared magnitudes and colors from this and previously published surveys, twenty-five brown dwarf candidates were selected toward the high extinction cloud core. Spectra in the K band were obtained and comparisons of the depths of water vapor absorption bands in our candidate objects with a grid of dwarf,subgiant, and giant standards were made to derive spectral types. These data were then used to derive effective temperatures and stellar luminosities which, when combined with theoretical tracks and isochrones for pre-main sequence objects, resulted in estimates for their masses and ages. The models suggest a median age for the sample of < 1 Myr with substellar masses for at least 9 of the candidates including the x-ray flare source ASR 24. Surface gravities have been estimated for the brown dwarf candidates and, for a given spectral type,found to resemble more closely dwarfs than giants. Using the near-infrared imaging data and age estimates from the spectroscopic sample, an extinction-limited sample in the northern cluster was defined. Consistent with recent studies of other young clusters, this sample exhibits an accretion disk frequency of 0.75 +-0.20 and a mass spectrum slope across the hydrogen-burning limit of alpha < 1.6 where dN/dM ~ M^-(alpha).Comment: 22 postscript pages, 12 postscript figures, and 3 postscript tables. Accepted for publication in the Astronomical Journal (February, 2004

Magnetic field effect on the dielectric constant of glasses: Evidence of disorder within tunneling barriers

The magnetic field dependence of the low frequency dielectric constant $e_r$(H) of a structural glass a - SiO2 + xCyHz was studied from 400 mK to 50 mK and for H up to 3T. Measurement of both the real and the imaginary parts of $e_r$ is used to eliminate the difficult question of keeping constant the temperature of the sample while increasing H: a non-zero $e_r$(H) dependence is reported in the same range as that one very recently reported on multicomponent glasses. In addition to the recently proposed explanation based on interactions, the reported $e_r$(H) is interpreted quantitatively as a consequence of the disorder lying within the nanometric barriers of the elementary tunneling systems of the glass.Comment: latex Bcorrige1.tex, 5 files, 4 figures, 7 pages [SPEC-S02/009