Neutron-mapping polymer flow: Scattering, flow visualization, and molecular theory

Flows of complex fluids need to be understood at both macroscopic and molecular scales, because it is the macroscopic response that controls the fluid behavior, but the molecular scale that ultimately gives rise to rheological and solid-state properties. Here the flow field of an entangled polymer melt through an extended contraction, typical of many polymer processes, is imaged optically and by small-angle neutron scattering. The dual-probe technique samples both the macroscopic stress field in the flow and the microscopic configuration of the polymer molecules at selected points. The results are compared with a recent tube model molecular theory of entangled melt flow that is able to calculate both the stress and the single-chain structure factor from first principles. The combined action of the three fundamental entangled processes of reptation, contour length fluctuation, and convective constraint release is essential to account quantitatively for the rich rheological behavior. The multiscale approach unearths a new feature: Orientation at the length scale of the entire chain decays considerably more slowly than at the smaller entanglement length.

Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

Effects of molecular size in solvation dynamics

The effects of molecular size on the dynamics of polar solvation are studied by using a microscopic theory which includes the translational relaxation modes of the solvent consistently. It is shown that while in the absence of the translational contribution the solvation rate increases with the size of the solute (in agreement with the conclusions of the nonequilibrium MSA theory),a complete reversal of the solute size dependence occurs when translational modes make a significant contribution to the solvent polarization relaxation.

Solvation dynamics of a charge bubble in water

A microscopic theory is used to calculate the solvation-time correlation function, (S(t)), of a light, non-stationary charge bubble in water. The calculated correlation function is found to be similar to the energy-time correlation function of a solvated electron. The ionic mobility of a charge bubble of the size of the hydrated electron is also calculated. It is found that the mobility of the charge plays a very important role in its own solvation.

Design of antenna-coupled lumped-element titanium nitride KIDs for long-wavelength multi-band continuum imaging

Many applications in cosmology and astrophysics at millimeter wavelengths including CMB polarization, studies of galaxy clusters using the Sunyaev-Zeldovich effect (SZE), and studies of star formation at high redshift and in our local universe and our galaxy, require large-format arrays of millimeter-wave detectors. Feedhorn and phased-array antenna architectures for receiving mm-wave light present numerous advantages for control of systematics, for simultaneous coverage of both polarizations and/or multiple spectral bands, and for preserving the coherent nature of the incoming light. This enables the application of many traditional "RF" structures such as hybrids, switches, and lumped-element or microstrip band-defining filters.

Simultaneously, kinetic inductance detectors (KIDs) using high-resistivity materials like titanium nitride are an attractive sensor option for large-format arrays because they are highly multiplexable and because they can have sensitivities reaching the condition of background-limited detection. A KID is a LC resonator. Its inductance includes the geometric inductance and kinetic inductance of the inductor in the superconducting phase. A photon absorbed by the superconductor breaks a Cooper pair into normal-state electrons and perturbs its kinetic inductance, rendering it a detector of light. The responsivity of KID is given by the fractional frequency shift of the LC resonator per unit optical power.

However, coupling these types of optical reception elements to KIDs is a challenge because of the impedance mismatch between the microstrip transmission line exiting these architectures and the high resistivity of titanium nitride. Mitigating direct absorption of light through free space coupling to the inductor of KID is another challenge. We present a detailed titanium nitride KID design that addresses these challenges. The KID inductor is capacitively coupled to the microstrip in such a way as to form a lossy termination without creating an impedance mismatch. A parallel plate capacitor design mitigates direct absorption, uses hydrogenated amorphous silicon, and yields acceptable noise. We show that the optimized design can yield expected sensitivities very close to the fundamental limit for a long wavelength imager (LWCam) that covers six spectral bands from 90 to 400 GHz for SZE studies.

Excess phase (frequency) noise has been observed in KID and is very likely caused by two-level systems (TLS) in dielectric materials. The TLS hypothesis is supported by the measured dependence of the noise on resonator internal power and temperature. However, there is still a lack of a unified microscopic theory which can quantitatively model the properties of the TLS noise. In this thesis we derive the noise power spectral density due to the coupling of TLS with phonon bath based on an existing model and compare the theoretical predictions about power and temperature dependences with experimental data. We discuss the limitation of such a model and propose the direction for future study.

Ultrafast collinear scattering and carrier multiplication in graphene.

Graphene is emerging as a viable alternative to conventional optoelectronic, plasmonic and nanophotonic materials. The interaction of light with charge carriers creates an out-of-equilibrium distribution, which relaxes on an ultrafast timescale to a hot Fermi-Dirac distribution, that subsequently cools emitting phonons. Although the slower relaxation mechanisms have been extensively investigated, the initial stages still pose a challenge. Experimentally, they defy the resolution of most pump-probe setups, due to the extremely fast sub-100 fs carrier dynamics. Theoretically, massless Dirac fermions represent a novel many-body problem, fundamentally different from Schrödinger fermions. Here we combine pump-probe spectroscopy with a microscopic theory to investigate electron-electron interactions during the early stages of relaxation. We identify the mechanisms controlling the ultrafast dynamics, in particular the role of collinear scattering. This gives rise to Auger processes, including charge multiplication, which is key in photovoltage generation and photodetectors.

NEAR-RESONANCE RAMAN-SCATTERING OF LONGITUDINAL OPTICAL PHONON MODES AND INTERFACE MODES IN GAAS/ALAS SUPERLATTICES

The near-resonance Raman scattering of GaAs/AlAs superlattices is investigated at room temperature. Owing to the resonance enhancement of Frohlich interaction, the scattering intensity of even LO confined modes with A1 symmetry becomes much stronger than that of odd modes with B2 symmetry. The even modes were observed in the polarized spectra, while the odd modes appear in the depolarized spectra as in the off-resonance case. The second-order Raman spectra show that the polarized spectra are composed of the overtone and combinations of even modes, while the depolarized spectra are composed of the combinations of one odd mode and one even mode. The results agree well with the selection rules predicted by the microscopic theory of Raman scattering in superlattices, developed recently by Huang and co-workers. In addition, the interface modes and the combinations of interface modes and confined modes are also observed in the two configurations.

Calculation of the electronic properties of neutral and ionized divalent-metal clusters

The electronic properties of neutral and ionized divalent-metal clusters have been studied using a microscopic theory, which takes into account the interplay between van der Waals (vdW) and covalent bonding in the neutral clusters, and the competition between hole delocalization and polarization energy in the ionized clusters. By calculating the ground-state energies of neutral and ionized. Hg_n clusters, we determine the size dependence of the bond character and the ionization potential I_p(n). For neutral Hg_n clusters we obtain a transition from van del Waals to covalent behaviour at the critical size n_c ~ 10-20 atoms. Results for I_p(Hg_n) with n \le 20 are in good agreement with experiments, and suggest that small Hg_n^+ clusters can be viewed as consisting of a positive trimer core Hg_3^+ surrounded by n - 3 polarized neutral atoms.

On the localization of electrons and holes in Hg_n and rare-gas clusters

We have used a microscopic theory to study the size dependence of the degree of localization of the valence electrons and holes in neutral an ionized rare-gas and Hg_n clusters. We discuss under which circumstances localization of the electrons and holes is favoured. We have calculated the ionization potential of Xe_n, Kr_n and small Hg_n clusters. Good agreement with experiments is obtained. We have also determined the dependence of the ionization potential on cluster structure.

Slave-boson approach to the size-dependent transition from van der Waals to covalent bonding in Hg_n clusters

We use a microscopic theory to describe the dynamics of the valence electrons in divalent-metal clusters. The theory is based on a many-body model Harniltonian H which takes into account, on the same electronic level, the van der Waals and the covalent bonding. In order to study the ground-state properties of H we have developed an extended slave-boson method. We have studied the bonding character and the degree of electronic delocalization in Hg_n clusters as a function of cluster size. Results show that, for increasing cluster size, an abrupt change occurs in the bond character from van der Waals to covalent bonding at a critical cluster size n_c ~ 10-20. This change also involves a transition from localized to delocalized valence electrons, as a consequence of the competition between both bonding mechanisms.

Universal trend for heavy-ion total reaction cross-sections at energies above the Coulomb barrier

Heavy-ion total reaction cross-section measurements for more than 1100 reaction cases covering 61 target nuclei in the range (6)Li-(238)U and 158 projectile nuclei from (2)H to (84)Kr (mostly exotic ones) have been analyzed in a systematic way by using an empirical, three-parameter formula that is applicable to the cases of projectile kinetic energies above the Coulomb barrier. The analysis has shown that the average total nuclear binding energy per nucleon of the interacting nuclei and their radii are the chief quantities that describe the cross-section patterns. A great amount of cross-section data (87%) has been quite satisfactorily reproduced by the proposed formula; therefore, the total reaction cross-section predictions for new, not yet experimentally investigated reaction cases can be obtained within 25% (or much less) uncertainty.

From quantum to classical dynamics: The relativistic O ( N ) model in the framework of the real-time functional renormalization group

We investigate the transition from unitary to dissipative dynamics in the relativistic O(N) vector model with the λ(φ2)2 interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent z in the limit of large temperatures and in 2≤d≤4 spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.

Constriction flows of monodisperse linear entangled polymers: Multiscale modeling and flow visualization

We explore both the rheology and complex flow behavior of monodisperse polymer melts. Adequate quantities of monodisperse polymer were synthesized in order that both the materials rheology and microprocessing behavior could be established. In parallel, we employ a molecular theory for the polymer rheology that is suitable for comparison with experimental rheometric data and numerical simulation for microprocessing flows. The model is capable of matching both shear and extensional data with minimal parameter fitting. Experimental data for the processing behavior of monodisperse polymers are presented for the first time as flow birefringence and pressure difference data obtained using a Multipass Rheometer with an 11:1 constriction entry and exit flow. Matching of experimental processing data was obtained using the constitutive equation with the Lagrangian numerical solver, FLOWSOLVE. The results show the direct coupling between molecular constitutive response and macroscopic processing behavior, and differentiate flow effects that arise separately from orientation and stretch. (c) 2005 The Society of Rheology.

Measuring and predicting the dynamics of linear monodisperse entangled polymers in rapid flow through an abrupt contraction. A small angle neutron scattering study

Small-angle neutron scattering measurements on a series of monodisperse linear entangled polystyrene melts in nonlinear flow through an abrupt 4:1 contraction have been made. Clear signatures of melt deformation and subsequent relaxation can be observed in the scattering patterns, which were taken along the centerline. These data are compared with the predictions of a recently derived molecular theory. Two levels of molecular theory are used: a detailed equation describing the evolution of molecular structure over all length scales relevant to the scattering data and a simplified version of the model, which is suitable for finite element computations. The velocity field for the complex melt flow is computed using the simplified model and scattering predictions are made by feeding these flow histories into the detailed model. The modeling quantitatively captures the full scattering intensity patterns over a broad range of data with independent variation of position within the contraction geometry, bulk flow rate and melt molecular weight. The study provides a strong, quantitative validation of current theoretical ideas concerning the microscopic dynamics of entangled polymers which builds upon existing comparisons with nonlinear mechanical stress data. Furthermore, we are able to confirm the appreciable length scale dependence of relaxation in polymer melts and highlight some wider implications of this phenomenon.

Mode-coupling theory: generalizations, high dimensions and microscopic dynamics

This work contains several applications of the mode-coupling theory (MCT) and is separated into three parts. In the first part we investigate the liquid-glass transition of hard spheres for dimensions d→∞ analytically and numerically up to d=800 in the framework of MCT. We find that the critical packing fraction ϕc(d) scales as d²2^(-d), which is larger than the Kauzmann packing fraction ϕK(d) found by a small-cage expansion by Parisi and Zamponi [J. Stat. Mech.: Theory Exp. 2006, P03017 (2006)]. The scaling of the critical packing fraction is different from the relation ϕc(d)∼d2^(-d) found earlier by Kirkpatrick and Wolynes [Phys. Rev. A 35, 3072 (1987)]. This is due to the fact that the k dependence of the critical collective and self nonergodicity parameters fc(k;d) and fcs(k;d) was assumed to be Gaussian in the previous theories. We show that in MCT this is not the case. Instead fc(k;d) and fcs(k;d), which become identical in the limit d→∞, converge to a non-Gaussian master function on the scale k∼d^(3/2). We find that the numerically determined value for the exponent parameter λ and therefore also the critical exponents a and b depend on the dimension d, even at the largest evaluated dimension d=800. In the second part we compare the results of a molecular-dynamics simulation of liquid Lennard-Jones argon far away from the glass transition [D. Levesque, L. Verlet, and J. Kurkijärvi, Phys. Rev. A 7, 1690 (1973)] with MCT. We show that the agreement between theory and computer simulation can be improved by taking binary collisions into account [L. Sjögren, Phys. Rev. A 22, 2866 (1980)]. We find that an empiric prefactor of the memory function of the original MCT equations leads to similar results. In the third part we derive the equations for a mode-coupling theory for the spherical components of the stress tensor. Unfortunately it turns out that they are too complex to be solved numerically.