arXiv subjects

George D. J. Phillies

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

At least 19 recordsLinked to original sources

arXiv2024

Diffusing Wave Microrheology in Polymeric Fluids

Recently, there has been interest in determining the viscoelastic properties of polymeric liquids and other complex fluids by means of Diffusing Wave Spectroscopy (DWS). In this technique, light-scattering spectroscopy is applied to highly turbid fluids containing optical probe particles. The DWS spectrum is used to infer the time-dependent mean-square displacement and time-dependent diffusion coefficient $D$ of the probes. From $D$, values for the storage modulus $G'(ω)$ and the loss modulus $G''(ω)$ are obtained. This paper is primarily concerned with the inference of the mean-square displacement from a DWS spectrum. However, in much of the literature, central to the inference that is said to yield $D$ is an invocation $g^{(1)}(t) = \exp(- 2 q^{2} \overline{X(t)^{2}})$ of the Gaussian Approximation for the field correlation function $g^{(1)}(t)$ of the scattered light in terms of the mean-square displacement $\overline{X(t)^{2}}$ of a probe particle during time $t$. Experiment and simulation both show that the Gaussian approximation is invalid for probes in polymeric liquids and other complex fluids. In this paper, we obtain corrections to the Gaussian approximation that will assist in interpreting DWS spectra of probes in polymeric liquids. The corrections reveal that these DWS spectra receive contributions from higher moments $\overline{X(t)^{2n}}$, $n >1$, of the probe displacement distribution function.

cond-mat.soft↗

arXiv2024

Quantitative Interpretation of Simulated Polymer Mean-Square Displacements

We propose a path for making quantitative analyses of mean-square displacement curves of polymer chains in the melt or in solution. The approach invokes a general functional form that accurately describes $g(t) \equiv \langle (Δx(t))^{2} \rangle$ for all times at which $g(t)$ was measured, and that gives values for the logarithmic derivative of $g(t)$ for the same times. By these means we can readily distinguish between regimes in which $g(t)$ follows a power law in time, does not follow a power law in time, or has an inflection point. In a power-law regime, the method accurately determines the exponent, without imposing any assumption as to the exponent's value.

cond-mat.soft↗

arXiv2022

Review: Simulational Tests of the Rouse Model

The file is a Chapter from my review volume "Polymer Physics: Phenomenology of Polymeric Fluid Simulations". The chapter treats literature tests of the Rouse model, which is widely invoked as a description of polymer motion in melts. In summary: The literature conclusively demonstrates that the Rouse model does not describe polymer motion in melts. Simulations find that the temporal autocorrelation function of a single Rouse amplitude is a stretched exponential in time, not the pure exponential predicted by the Rouse model. Also, the mean-square amplitude of the Rouse modes <(X_p (0) X_p (0) > deviates from the model's prediction, at least for p > 3. Furthermore, the relaxation time of <(X_p (0) X_p (t) > depends on p, but not as predicted by the Rouse model. According to the Rouse model, bead displacements are driven by independent Gaussian random processes. Accordingly, the intermediate structure factor g(q,t) is predicted to be accurately described by the Gaussian approximation. Doob's theorem then guarantees that g(q,t) decays as a single exponential in time. Simulations show that these predictions of the Rouse model are incorrect.

cond-mat.soft↗

arXiv2022

Polymer Physics: Phenomenology of Polymeric Fluid Simulations -- Chapter: Collective Coordinates and Collective Models

Polymer Physics: Phenomenology of Polymeric Fluid Simulations is a review volume that I am writing. I anticipate it will take a while to complete, so I am supplying individual chapters when each is more-or-less completed. This Chapter considers collective coordinates and collective models for isolated polymer chains. Collective coordinates can be effective tools for isolating aspects of polymer motion that are less obvious if only the Cartesian coordinates of the individual atoms or monomers are viewed. I treat Fourier, Rouse, and Haar wavelets as suppliers of collective coordinates. One of the sets of collective coordinates that i consider, the Rouse coordinates, follows naturally from the Rouse model of polymer dynamics. We therefore consider the Rouse model as well as its more important predecessor, the Kirkwood-Riseman model. Haar wavelets are noteworthy because they allow one to isolate individual regions of a polymer

cond-mat.soft↗

arXiv2021

An $[η]$ Linear in $M$ Does Not Imply Rouse Dynamics

Contrary to some expectations, an experimental finding for a polymer that the solution intrinsic viscosity $[η]$ or the melt viscosity is linear in the polymer molecular weight $M$ does not indicate that polymer dynamics are Rouselike. Why? The other major polymer dynamic model, due to Kirkwood and Riseman [\emph{J. Chem.\ Phys.\ } \textbf{16}, 565-573 (1948)], leads in its free-draining form to a prediction $[η] \sim M$, even though the polymer motions in this model are totally unlike the polymer motions in the Rouse model. In the Rouse model, the chain motions are linear translation and internal ('Rouse') modes. In the Kirkwood-Riseman model (and its free-draining form, derived here), the chain motions are translation and whole-body rotation. The difference arises because Rouse's calculation implicitly refers only to chains subject to zero external shear force (And, as an aside, Rouse's construction of $[η]$ is invalid, because it concludes that there is viscous dissipation in a system that Rouse implicitly assumed to have no applied shear).

cond-mat.soft↗

arXiv2021

The Kirkwood-Riseman Polymer Model of Polymer Dynamics is Qualitatively Correct

We use Brownian dynamics to show: For an isolated polymer coil in a shear field, the Kirkwood-Riseman model for chain motion is qualitatively correct. Under the same circumstances the Rouse model for chain motion is qualitatively incorrect. The models are qualitatively different. Kirkwood and Riseman say polymer coils in a shear field perform whole-body rotation; in the Rouse model rotation does not occur. Our simulations demonstrate that \emph{in shear flow}: Polymer coils rotate. Rouse modes are cross-correlated. The amplitudes and relaxation rates of Rouse modes depend on the shear rate. Rouse's calculation only refers to a polymer coil in a quiescent fluid, where there is no viscous dissipation. Application of the Rouse model to a polymer coil undergoing shear is invalid.

cond-mat.soft↗

arXiv2018

Hydrodynamics of Interacting Rods

This note considers how hydrodynamic interactions between a pair of rods slow the motion of each rod. Rods are approximated as being nearly straight lines of pointlike beads. Hydrodynamic interactions between the beads are treated with generalizations, developed by Kynch (J. Fluid Mech. 5, 193-208 (1959)) and by Mazur and van Saarloos (Physica A 115, 21-57 (1982)) of the Oseen and Rotne-Prager hydrodynamic interaction tensors. We find that the hydrodynamic interactions between two rods, as they affect the mobility of a given rod, are with a minor exception not very different from the interactions between two beads, especially when the two rods are even modestly separated. At the level of approximation of bead-spring models of polymer coils, it therefore does not appear to be advantageous to replace sphere-sphere hydrodynamic interaction tensors with more elaborate rod-rod hydrodynamic interaction tensors.

cond-mat.soft↗

arXiv2017

Readings and Misreadings of J. Willard Gibbs Elementary Principles in Statistical Mechanics

J. Willard Gibbs' Elementary Principles in Statistical Mechanics was the definitive work of one of America's greatest physicists. Gibbs' book on statistical mechanics establishes the basic principles and fundamental results that have flowered into the modern field of statistical mechanics. However, at a number of points, Gibbs' teachings on statistical mechanics diverge from positions on the canonical ensemble found in more recent works, at points where seemingly there should be agreement. The objective of this paper is to note some of these points, so that Gibbs' actual positions are not misrepresented to future generations of students.

physics.hist-ph↗

arXiv2017

FCS and RICS Spectra of Probes in Complex Fluids

The Fluorescence Correlation Spectroscopy (FCS) spectrum G(t) and Raster Image Correlation Spectroscopy (RICS) spectrum R(t) of dilute diffusing particles are determined by the displacement distribution function P(x,t) of the particles and by the experimental parameters of the associated optical trains. This letter obtains the general relationships between P(x,t) and these spectra. For dilute diffusing molecules in simple liquids, P(x,t) is a Gaussian in the displacement x; the corresponding G(t) is a Lorentzian in (<(x(t))^2>)^(1/2). In complex fluids such as polymer solutions, colloid and protein solutions, and the interior of living cells, P(x,t) may have a non-Gaussian dependence on x, for example an exponential in |x|. We compare theoretical forms for FCS and for RICS spectra of two systems in which P(x,t) is a Gaussian or an exponential in x, but in which the mean-square displacements are precisely equal at all times. If the G(t) and R(t) arising from an exponential P(x,t) are interpreted by using the forms for G(t) and R(t) that are appropriate for a Gaussian P(x,t), the inferred diffusion coefficient may be substantially in error.

cond-mat.soft↗

arXiv2016

The Hydrodynamic Scaling Model for the Dynamics of Non-Dilute Polymer Solutions: A Comprehensive Review

This article presents a comprehensive review of the Hydrodynamic Scaling Model for the dynamics of polymers in dilute and nondilute solutions. The Hydrodynamic Scaling Model differs from some other treatments of non-dilute polymer solutions in that it takes polymer dynamics up to high concentrations to be dominated by solvent-mediated hydrodynamic interactions, with chain crossing constraints presumed to create at most secondary corrections. Many other models take the contrary stand, namely that chain crossing constraints dominate the dynamics of nondilute polymer solutions, while hydrodynamic interactions only create secondary corrections. This article begins with a historical review. We then consider single-chain behavior, in particular the Kirkwood-Riseman model; contradictions between the Kirkwood-Riseman and more familiar Rouse-Zimm models are emphasized. An extended Kirkwood-Riseman model that gives interchain hydrodynamic interactions is developed and applied to generate pseudovirial series for the self-diffusion coefficient and the low-shear viscosity. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger-Dahler Positive-Function Renormalization Group are developed and applied to the pseudovirial series for $D_{s}$ and $η$. Based on the renormalization group method, a two-parameter temporal scaling ansatz is invoked as a path to determining the frequency dependences of the storage and loss moduli. A short description is given for each of the individual papers that developed the Hydrodynamic Scaling Model. Phenomenological evidence supporting aspects of the model is noted. Finally, directions for future development of the Hydrodynamic Scaling Model are presented.

cond-mat.soft↗

arXiv2015

Review: Dynamics of Crowded Macromolecules/Interacting Brownian Particles

I review theoretical treatments of diffusion in crowded (i.~e., non-dilute) solutions of globular macromolecules. The focus is on the classical statistico-mechanical literature, much of which dates to before 1990. Classes of theoretical models include continuum treatments, correlation function descriptions, generalized Langevin equation descriptions, Smoluchowski and Mori-Zwanzig descriptions, and a brief but encouraging comparison with experimental results. The primary emphasis is on measurements made with quasi-elastic light scattering spectroscopy; I also discuss outcomes from fluorescence photobleaching recovery, fluorescence correlation spectroscopy, pulsed-gradient spin-echo nuclear magnetic resonance, and raster image correlation spectroscopy. I close with a list of theoretical papers on the general topic.

cond-mat.soft↗

arXiv2014

The Gaussian Diffusion Approximation for Complex Fluids is Generally Invalid

Simulations are made of a probe particle diffusing through a complex fluid. Probe particle motions are described by the Mori-Zwanzig equation and Mori's orthogonal hierarchy of random forces scheme, subject to the approximation that the fluid creates a rapidly-fluctuating random force corresponding to solvent motions and a slowly fluctuating random force corresponding to solute (e.~g., matrix polymer) motions. The Gaussian diffusion approximation is seriously incorrect in this physically-plausible model system. $P(x,t)$ has exponential wings. $g^{(1s)}(q,t)$ can differ from $\exp(-q^{2} \langle x^{2}\rangle/2)$ by up to orders of magnitude. Experimental interpretations that rely on the Gaussian approximation, such as the Stejskal-Tanner equation for pulsed-field-gradient NMR or particle tracking, can not be assumed to be reliable in complex fluids.

cond-mat.soft↗

arXiv2013

Interpretation of Quasielastic Scattering Spectra of Probe Species in Complex Fluids

The objective of this paper is to correct an error in analyses of quasielastic scattering spectra. The error invokes a valid calculation under conditions in which its primary assumptions are incorrect, resulting in misleading interpretations of spectra. Quasielastic scattering from dilute probes yields the incoherent structure factor g^(1s)(q,t) = , with q being the magnitude of the scattering vector q and Dx(t) being the probe displacement parallel to q during a time interval t. The error is a claim that g^(1s)(q,t) ~ exp(- q^2 <(Dx(t))^2> /2) for probes in an arbitrary solution, leading to the incorrect belief that <(Dx(t))^2 > of probes in complex fluids can be inferred from quasielastic scattering. The actual theoretical result refers only to monodisperse probes in simple Newtonian liquids. In general, g^(1s)(q,t) is determined by all even moments <(Dx(t))^(2n) >, n = 1, 2, 3,... of the displacement distribution function P(Dx,t). Correspondingly, <(Dx(t))^2 > cannot in general be inferred from g^(1s)(q,t). The theoretical model that ties g^(1s)(q,t) to <(Dx(t))^2 > also quantitatively determines exactly how <(Dx(t))^2> /2 must behave, namely <(Dx(t))^2 > must increase linearly with t. If the spectrum is not a single exponential in time, g^(1s)(q,t) does not determine <(Dx(t))^2>.

cond-mat.soft↗

arXiv2013

The VW transformation -- A Simple Alternative to the Wilson GF Method

An alternative, the VW transformation, is proposed to replace the Wilson GF method for calculating molecular vibration frequencies and normal modes. The VW transformation yields precisely the same eigenmodes and and eigenfrequencies that are found with the GF method. The transformation proceeds entirely in the mass-normalized Cartesian coordinates of the individual atoms, with no transformations to internal coordinates. The VW transformation thus offers an enormous computational simplification over the GF method, namely the mathematical apparatus needed to transform to internal coordinates is eliminated. All need for new researchers to understand the complex matrix transformations underlying the GF method is thus also removed. The VW transformation is not a projection method; the internal vibrations remain dispersed over all 3N atomic coordinates. In the VW method, the 3N x 3N force constant matrix V is replaced with a new 3N x 3N matrix W. The replacement is physically transparent. The matrix W has the same internal normal modes and vibration frequencies that V does. However, unlike V, W is not singular, so the normal modes and normal mode frequencies can be obtained using conventional matrix techniques.

cond-mat.other↗

arXiv2011

Capillary Electrophoresis as a Fundamental Probe of Polymer Dynamics

Capillary electrophoresis has long been been recognized as a powerful analytic tool. Here it is demonstrated that the same capillary electrophoretic experiments also reveal dynamic properties of the polymer solutions being used as the support medium. The dependence of the electrophoretic mobility on the size of the probe and the properties of the matrix polymers shows a unity of behavior between electrophoresis and other methods of studying polymer properties.

cond-mat.soft↗

arXiv2011

Interpretation of Pulsed-Field-Gradient NMR in Terms of Molecular Displacements

The relationship for Pulsed-Field-Gradient NMR between the amplitude $I(t)$ of the spin echo and the molecular displacement ${\bf X}(t)$ is examined. $I(t)$ of a single species in a simple solution is determined by the mean-square displacement $\bar{X(t)^{2}}$. With polydisperse species, or molecular probes in complex fluids showing memory effects, $I(t)$ in general includes large contributions from all higher even moments $\bar{X(t)^{2n}}$. Conditions under which the NMR signal is indeed determined by the molecular mean-square displacement are noted. A diagnostic that sometimes identifies when these conditions are not met is presented.

cond-mat.soft↗

arXiv2011

Polymer Segmental Cross-Correlations from Dielectric Relaxation Spectra of Block Copolymers

Dielectric relaxation spectra of block polymers containing sequential type-A dipoles are considered. Spectra of a specific set of block copolymers can be combined to isolate the dynamic cross-correlation between the motions of two distinct parts of the same polymer chain. Unlike past treatments of this problem, no model is assumed for the underlying polymer dynamics.

cond-mat.soft↗

arXiv2009

Falsity of the Rouse Mode Solution of the Rouse and Zimm Models

The Rouse (J. Chem. Phys. 21, 1272 (1953)) and Zimm (J. Chem. Phys. 24}, 269 (1956)) treatments of the dynamics of a polymer chain are shown to contain a fundamental mathematical error, which causes them to lose the zero-relaxation-rate, whole-body rotation motions dominant in viscosity and dielectric relaxation. As a result, the oft-cited mode solutions for these models are qualitatively incorrect. Comparison with the Wilson-Decius-Cross treatment of vibrational modes of polyatomic molecules reveals qualitatively the correct form for the solutions to the Rouse model.

cond-mat.soft↗