arXiv subjects

George D. J. Phillies

Publications and source records attributed to George D. J. Phillies.

26 records · Page 2Linked to original sources

arXiv2007

Optical Probe Diffusion in Polymer Solutions

The experimental literature on the motion of mesoscopic probe particles through polymer solutions is systematically reviewed. The primary focus is the study of diffusive motion of small probe particles. Comparison is made with measurements of solution viscosities. A coherent description was obtained, namely that the probe diffusion coefficient generally depends on polymer concentration as D_p = D_0 exp(-alpha c^nu). One finds that alpha depends on polymer molecular weights as alpha ~ M^0.8, and νappears to have large-M and small-M values with a crossover linking them. The probe diffusion coefficient does not simply track the solution viscosity; instead, D_p eta typically increases markedly with increasing polymer concentration and molecular weight. In some systems, e.g., hydroxypropylcellulose:water, the observed probe spectra are bi- or tri-modal. Extended analysis of the full probe phenomenology implies that hydroxypropylcellulose solutions are characterized by a single, concentration-independent, length scale that is approximately the size of a polymer coil. In a very few systems, one sees re-entrant or low-concentration-plateau behaviors of uncertain interpretation; from their rarity, these behaviors are reasonably interpreted as corresponding to specific chemical effects. True microrheological studies examining the motion of mesoscopic particles under the influence of a known external force are also examined. Viscosity from true microrheological measurements is in many cases substantially smaller than the viscosity measured with a macroscopic instrument.

cond-mat.soft↗

arXiv2005

Interpretation of Diffusing Wave Spectra in Nontrivial Systems

Mathematical methods previously used (Phillies, J. Chem. Phys., 122 224905 (2005)) to interpret quasielastic light scattering spectroscopy (QELSS) spectra are here applied to relate diffusing wave spectroscopy (DWS) spectra to the moments \bar{X^{2n}} of particle displacements in the solution under study. DWS spectra of optical probes are like QELSS spectra in that in general they are not determined solely by the second moment \bar{X^{2}}. In each case, the relationship between the spectrum and the particle motions arises from the field correlation function g^{(1)}_{s}(t) for a single quasi-elastic scattering event. In most physically interesting cases, g^{(1)}_{s}(t) receives except at the shortest times large contributions from higher moments \bar{X(t)^{2n}}, n >1. As has long been known, the idealized form g^{(1)}_{s}(t) =\exp(-2 q^{2} \bar{X(t)^{2}}), sometimes invoked to interpret DWS and QELSS spectra, only refers to (adequately) monodisperse, noninteracting, probes in purely Newtonian liquids and is erroneous for polydisperse particles, interacting particles, or particles in viscoelastic complex fluids. Furthermore, in DWS experiments fluctuations (for multiple scattering paths of fixed length) in the number of scattering events and the total-square scattering vector significantly modify the spectrum.

cond-mat.soft↗

arXiv2005

Non-invertibility of Multiple-Scattered QELSS Spectra

We consider the spectrum S(q,t) and field correlation function f(q,t) of light quasielastically scattered from diffusing optical probes in complex viscoelastic fluids. Relationships between the single-scattering f_1(q,t) and the multiple-scattering f_m(t) are examined. We show that it is fundamentally impossibly to invert f_m(t) to obtain f_1(q,t) or particle displacement moments , except with assumptions that are certainly not correct in complex, viscoelastic fluids. For diffusing dilute probes in viscoelastic fluids, f_1(q,t) is determined by all even moments , n > 0$, of the particle displacement X; this information is lost in f_m(t). In the special case of monodisperse probes in a true simple fluid, f_1(q,t) can be obtained from f_m(t), but only because the functional form of f_1(q,t) is already known.

cond-mat.soft↗

arXiv2005

Interpretation of Light Scattering Spectra in Terms of Particle Displacements

Quasi-elastic light scattering spectroscopy of dilute solutions of diffusing mesoscopic probe particles is regularly used to examine the dynamics of the fluid through which the probe particles are moving. For probes in a simple liquid, the light scattering spectrum is a simple exponential; the field correlation function $g^{(1)}_{P}(q,τ)$ of the scattering particles is related to their mean-square displacements $\bar{X^{2}} \equiv < (Δx(τ))^{2}>$ during $τ$ via $g^{(1)}(q,τ) = \exp(- {1/2} q^{2} \bar{X^{2}})$. However, historical demonstrations of this expression refer only to ideal Brownian particles in simple liquids, and show that if the form is correct then it is also true that $g^{(1)}(q,τ) = \exp(- Γτ)$, a pure exponential in $τ$. In general, $g^{(1)}_{P}(q,τ)$ is not a single exponential in time. $g^{(1)}_{P}(q,τ)$ reflects not only the mean-square particle displacements but also all higher-order mean displacement moments $\bar{X^{2n}}$. A correct general form for $g^{(1)}(q,τ)$, replacing the generally-incorrect $\exp(- {1/2} q^{2} \bar{X^{2}})$, is obtained. A simple experimental diagnostic determining when the field correlation function gives the mean-square displacements is identified, namely $g^{(1)}(q,τ)$ reveals $\bar{X^{2}}$ if $g^{(1)}(q,τ)$ is exponential in $τ$.

cond-mat.soft↗

arXiv2005

Enhanced Septahedral Ordering in Cold Lennard-Jones Fluids

We report molecular dynamics calculations on two-component, cold (1.2 > T > 0.56 in natural units), three-dimensional Lennard-Jones fluids. Our system was small (7813 A, 7812 B particles), dense (N/V = 1.30), and distinctly finite (L \times L \times L cube, periodic boundary conditions, with L=22.96 σ_AA), σ_AA being the range of the $AA$ interaction in the Lennard-Jones potential U_{ij} = 4 ε[(σ_ij/r)^12 -(σ_ij/r)^6]. We calculated spherical harmonic components Q_LM for the density of particles in the first coordination shell of each particle, as well as their spherical invariants <(Q_L)^2>, time-correlation functions and wavelet density decompositions. The spherical invariants show that non-crystalline septahedral <(Q_{7)^2> ordering is important, especially at low temperature. While <(Q_10)^2> could arise from icosahedral ordering, its behavior so closely tracks that of the nonicosahedral <(Q_11)^2> that alternative origins for <(Q_10)^2> need to be considered. Time correlation functions of spherical harmonic components are bimodal, with a faster temperature-independent mode and a slow, strongly temperature-dependent mode. Microviscosities inferred from mean-square particle displacements are exponential in static amplitude <(Q_7)^2>, and track closely in temperature dependence the orientation density slow mode lifetime. Volume wavelet decompositions show that when T is reduced, the correlation length of <(Q_7)^2> increases, especially below T=0.7, but the correlation length of <(Q_5)^2> is independent of T.

cond-mat.soft↗

arXiv2004

Viscosity of Suspensions of Hard and Soft Spheres

From a reanalysis of the published literature, the low-shear viscosity of suspensions of hard spheres is shown to have a dynamic crossover in its concentration dependence, from a stretched exponential at lower concentrations to a power law at elevated concentrations. The crossover is sharp, with no transition region in which neither form applies, and occurs at a volume fraction (ca. 0.41) and relative viscosity (ca. 11) well below the sphere volume fraction and relative viscosity (0.494, 49, respectively) of the lower phase boundary of the hard sphere melting transition. For soft spheres -- taking many-arm star polymers as a model -- with increasing sphere hardness $η(ϕ)$ shows a crossover from random-coil polymer behavior toward the behavior shown by true hard spheres.

cond-mat.soft↗

arXiv2004

Self and Tracer Diffusion of Polymers in Solution

The literature on self- and tracer- diffusion of polymers in solution, and on tracer diffusion of probe polymers through solutions of matrix polymers, is reviewed. I show via systematic reanalysis that the entirety of the published literature has its concentration c and matrix M and probe P molecular weight dependences described by a single functional form, namely the stretched exponential in c, P, and M. Correlations of the scaling prefactor and exponents with polymer molecular weight, concentration, and size are examined. Scaling parameters for the diffusion of star polymers do not differ substantially from scaling parameters for the diffusion of linear chains of equal size.

cond-mat.soft↗

arXiv2004

Diverging Static Length Scales and Clustering in Cold Lennard-Jones Fluids

We report molecular-dynamics simulations on a three-dimensional two-component Lennard-Jones fluid. We identify two distinct static length scales. The longer length scale, which diverges at low temperatures, is continuous with the high-temperature static correlation length. The shorter length scale reflects static clusters that form below a T_mc of approximately 2 well above an apparent melting point T_m of approximately 1.08. We partially visualize the clusters; their maximum radius is temperature-independent. Cluster static and dynamic properties match Kivelson's model (S. A. Kivelson, et al., J. Chem. Phys. 101, 2391 (1994)) for frustration-limited cluster-forming glasses.

cond-mat.soft↗