Critical behaviour of the Rouse model for gelling polymers

It is shown that the traditionally accepted "Rouse values" for the critical exponents at the gelation transition do not arise from the Rouse model for gelling polymers. The true critical behaviour of the Rouse model for gelling polymers is obtained from spectral properties of the connectivity matrix of the fractal clusters that are formed by the molecules. The required spectral properties are related to the return probability of a "blind ant"-random walk on the critical percolating cluster. The resulting scaling relations express the critical exponents of the shear-stress-relaxation function, and hence those of the shear viscosity and of the first normal stress coefficient, in terms of the spectral dimension $d_{s}$ of the critical percolating cluster and the exponents $\sigma$ and $\tau$ of the cluster-size distribution.Comment: 9 pages, slightly extended version, to appear in J. Phys.

HOPS 361-C's Jet Decelerating and Precessing Through NGC 2071 IR

We present a two-epoch Hubble Space Telescope (HST) near-infrared (NIR) study of NGC 2071 IR highlighting HOPS 361-C, a protostar producing an arced 0.2 parsec-scale jet. Proper motions for the brightest knots decrease from 350 to 100 km/s with increasing distance from the source. The [Fe II] and Pa$\beta$ emission line intensity ratio gives a velocity jump through each knot of 40-50 km/s. We show a new [O I] 63 $\rm \mu$m spectrum taken with the German REciever for Astronomy at Terahertz frequencies (GREAT) instrument aboard Stratospheric Observatory for Infrared Astronomy (SOFIA), which give a low jet inclination. Proper motions and jump velocities then estimate total flow speed throughout the jet. We model knot positions and speeds with a precessing jet that decelerates within the host molecular cloud. The measurements are matched with a precession period of a few thousand years and half opening angle of 15$\rm\deg$. The [Fe II] 1.26 $\rm \mu$m to 1.64 $\rm \mu$m line intensity ratio gives the extinction to each knot ranging from 5-30 mag. Relative to $\sim$14 mag of extinction through the cloud from C$^{18}$O emission maps, the jet is well embedded at a fractional depth from 1/5 to 4/5, and can interact with the cloud. Our model suggests the jet is locally dissipated over 0.2 pc. This may be because knots sweep through a wide angle, giving the cloud time to fill in cavities opened by the jet. This contrasts with nearly unidirectional protostellar jets that puncture host clouds and can propagate significantly further than a quarter pc.Comment: 24 pages, 9 figures, submitted to Ap

RAFT polymerization of temperature- and salt-responsive block copolymers as reversible hydrogels

Reversible-addition fragmentation chain transfer (RAFT) polymerization enabled the synthesis of novel, stimuli-responsive, AB and ABA block copolymers. The B block contained oligo(ethylene glycol) methyl ether methacrylate (OEG) and was permanently hydrophilic in the conditions examined. The A block consisted of diethylene glycol methyl ether methacrylate (DEG) and [2-(methacryloyloxy)ethyl]trimethylammonium chloride (TMA). The A block displayed both salt- and temperature-response with lower critical solution temperatures (LCSTs) dependent on the molar content of TMA and the presence of salt. Higher TMA content in the AB diblock copolymers increased the critical micelle temperatures (CMT) in HPLC-grade water due to an increased hydrophilicity of the A block. Upon addition of 0.9 wt% NaCl, the CMTs of poly(OEG-b-DEG95TMA5) decreased from 50 °C to 36 °C due to screening of electrostatic repulsion between the TMA units. ABA triblock copolymers displayed excellent hydrogel properties with salt- and temperature-dependent gel points. TMA incorporation in the A block increased the gel points for all triblock copolymers, and salt-response increased with higher TMA composition in the A block. For example, poly(DEG98TMA2-b-OEG-b-DEG98TMA2) formed a hydrogel at 40 °C in HPLC-grade water and 26 °C in 0.9 wt% NaCl aqueous solution. These salt- and temperature-responsive AB diblock and ABA triblock copolymers find applications as drug delivery vehicles, adhesives, and hydrogels

Variational bounds for the shear viscosity of gelling melts

We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\eta$, which implies that it diverges algebraically with a critical exponent $k\ge 2\nu-\beta$. Here, $\nu$ and $\beta$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size.Comment: 5 pages; CHANGES: typos corrected, some references added; version as publishe

Probing the Inner Disk Emission of the Herbig Ae Stars HD 163296 and HD 190073

The physical processes occurring within the inner few astronomical units of proto-planetary disks surrounding Herbig Ae stars are crucial to setting the environment in which the outer planet-forming disk evolves and put critical constraints on the processes of accretion and planet migration. We present the most complete published sample of high angular resolution H- and K-band observations of the stars HD 163296 and HD 190073, including 30 previously unpublished nights of observations of the former and 45 nights of the latter with the CHARA long-baseline interferometer, in addition to archival VLTI data. We confirm previous observations suggesting significant near-infrared emission originates within the putative dust evaporation front of HD 163296 and show this is the case for HD 190073 as well. The H- and K-band sizes are the same within $(3 \pm 3)\%$ for HD 163296 and within $(6 \pm 10)\%$ for HD 190073. The radial surface brightness profiles for both disks are remarkably Gaussian-like with little or no sign of the sharp edge expected for a dust evaporation front. Coupled with spectral energy distribution analysis, our direct measurements of the stellar flux component at H and K bands suggest that HD 190073 is much younger (<400 kyr) and more massive (~5.6 M$_\odot$) than previously thought, mainly as a consequence of the new Gaia distance (891 pc).Comment: 19 pages, 6 figure

Dynamics of gelling liquids: a short survey

The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium, its critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies.Comment: 21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday; Changes: added comments on the gel phase and some reference

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

Critical Dynamics of Gelation

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation $k=\phi-\beta$ for the critical exponent of the shear viscosity. Here $\beta$ is the thermal exponent for the gel fraction and $\phi$ is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results.Comment: 34 pages, 2 figures (revtex, amssymb); revised version (minor changes