Heterodyne coincidence spectroscopy

A new type of light-scattering experiment, which should measure directly the triple static structure factor S ⁽³⁾ (k, q) of a fluid, is proposed. S ⁽³⁾(k, q) is the full spatial Fourier transform of the equilibrium triplet distribution function g ⁽³⁾(r ₁, r ₂, r ₃). The experiment may also be used to study dynamic correlation functions of the form <a_k (t)a_q (t′)a_k_q(t″)> (where a_k () is the kth spatial Fourier component of the density), thereby giving new information on mode-mode coupling. The method obtains its information from triple correlations in the arrival of scattered photons at three detectors. The detectors must be operated in the heterodyne mode (i.e. with a local oscillator); the scattering volume must be much larger than the volume over which molecular positions are correlated. Comparison is made with previous analyses of other multi-detector experiments.     

Higher order hydrodynamic interactions in the calculation of polymer transport properties

Higher order hydrodynamics interactions are short-range modifications to the Oseen tensor T _ij and its self-interaction counterpart T _ii. They differ from the Oseen tensor in having terms of higher order than the first in a/R, a being a bead radius and R being a bead-bead distance. Effects of higher order hydrodynamic interactions on whole chain–whole chain hydrodynamic interactions are here computed. Higher order hydrodynamic interactions are shown to lead to a concentration dependence of the diffusion and friction coefficients of a free monomer. However, while higher order interactions make contributions of the same nature to the drag coefficients of a monomer and of a whole chain, the contributions are not simply multiplicative, removing a justification for the common practice of correcting polymer solution transport data for “monomer friction effects” via a normalization with data on friction coefficients of free monomers. © 1993 John Wiley & Sons, Inc.     

Neutral polymer slow mode and its rheological correlate

Quasi‐elastic light scattering spectroscopy intensity–intensity autocorrelation functions [S(k,t)] and static light scattering intensities of 1 MDa hydroxypropylcellulose in aqueous solutions were measured. With increasing polymer concentration, over a narrow concentration range, S(k,t) gained a slow relaxation. The transition concentration for the appearance of the slow mode (c^t) was also the transition concentration for the solution‐like/melt‐like rheological transition (c⁺) at which the solution shear viscosity [η_p(c)] passed over from a stretched exponential to a power‐law concentration dependence. To a good approximation, we found c^t[η] ≈ c⁺[η] ≈ 4, [η] being the intrinsic viscosity. The appearance of the slow mode did not change the light scattering intensity (I): from a concentration lower than c^t to a concentration greater than c^t, I/c fell uniformly with increasing concentration. The slow mode thus did not arise from the formation of compact aggregates of polymer chains. If the polymer slow mode arose from long‐lived structures that were not concentration fluctuations, the structures involved much of the dissolved polymer. At 25 °C, the mean relaxation rate of the slow mode approximately matched the relaxation rate for the diffusion of 0.2‐μm‐diameter optical probes observed with the same scattering vector. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 323–333, 2005     

Extended-range order, diverging static length scales, and local structure formation in cold Lennard-Jones fluids

We report molecular-dynamics simulations on a three-dimensional, two-component Lennard-Jones fluid. We used 125 000 particles (equal numbers of A and B) at density N/V=1.29 and 34 temperatures T covering 5 x 10(4) > or =T > or =0.56. The pair potential was 4epsilon[(sigma(ij)/r)(12)-(sigma(ij)/r)(6)] with sigma(AA)=1, sigma(AB)=11/12, and sigma(BB)=5/6. We computed specific and generic radial distribution functions g(ij)(r), and several density-momentum dynamic correlation functions whose static (t=0) parts vanish by symmetry. Evidence is presented that our systems were adequately annealed to eliminate remnant initial order and were adequately equilibrated at each temperature. Static spatial correlations in cold Lennard-Jones liquids have longer ranges than are often reported: g(r)-1 unequal to 0 is found out to r > or =7 at T=2 and out to r > or =10 at T=0.56. |g(r)-1| has an envelope function that simultaneously fits both crests and troughs of g(r). The envelope function implies a temperature-dependent static length scale l(1); over (0.56 < or =T< or =100), l(1) approximately T(-0.3), contrary to suggestions that g(r) is temperature independent as the glass is approached. The highest-melting-point crystal that we identified melts at T(m) approximately 1.08. In the fluid phase, we observe short-range noncrystalline local structure formation in g(r) as the glass is approached. Local structure is only found below a local structure melting temperature T(mc)=2.0. Local structure vanishes above T=2. Local structure becomes more pronounced as temperature is reduced. However, at all temperatures at which there is local structure in g(r), the local structure is confined to r < or =4. Within the region r < or =4, the amplitude of the local structure diminishes with distance r from the central atom approximately as exp(-r/l(2)), thereby defining a second distance scale in the fluid. l(2), while more difficult to measure, appears to scale with temperature as l(2) approximately T(-0.6); l(2) is not the same as l(1). The static and dynamic properties of the local structure match properties assigned by Kivelson's glass model [S. A. Kivelson et al., J. Chem. Phys. 101, 2391 (1994)] to that model's frustration-limited local clusters.     

Fourth‐order hydrodynamic contribution to the polymer self‐diffusion coefficient

A hydrodynamic scattering treatment of interacting polymer chains is extended to obtain the five‐point chain–chain–chain–chain–chain hydrodynamic interaction tensor. The tensor is used to calculate the second‐order concentration correction to the self‐diffusion coefficient of a polymer in solution. The self‐similarity assumption of the hydrodynamic scaling model of polymer dynamics is tested against these calculations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1663–1670, 2004     

Upon the utility of spherical harmonic expansions in the evaluation of cluster integrals

A novel procedure for the analytic evaluation of cluster integrals is given. By means of a result of Silverstone and Moats which transforms the spherical harmonic expansion of a function around a given point into a new spherical harmonic expansion around a displaced point, a 3N-dimensional cluster integral forN point particles (N > 2) may be reduced to 2N+1 trivial integrals andN– 1 interesting integrals, an improvement over the usual reduction to six trivial integrals and3N–6 nontrivial integrals. For hard spheres, theN–1 integrals involve only a series of simple polynomials taken between linear algebraic bounds.This work was supported in part by the National Science Foundation under Grant No. CHE79-20389.     

Viscosity of hard sphere suspensions

A simple functional representation of the concentration dependence of the low-shear viscosity eta of hard sphere suspensions is proposed. The representation, which agrees with published literature at all volume fractions phi, has a hitherto-unremarked transition in its functional form at phi approximately 0.42 identical with phi(t). phi(t) is definitely less than the volume fraction 0.49 of the hard sphere melting transition.     

Capillary zone electrophoresis and polymer dynamics

Capillary electrophoresis with a polymer solution support medium is a well-established powerful analytical tool. This paper discusses a possible alternative application of capillary electrophoresis, namely a path for studying the dynamics of polymer solutions. The key to the approach is an inversion of perspective. Instead of treating the migrating species as the object of experimental importance and the support medium as being of importance only because it facilitates separations, one treats the polymer solution as being of experimental importance, and the choice of migrating species as being of interest only because different species may probe different aspects of polymer dynamics.     

Convergence of spherical harmonic expansions for the evaluation of hard-sphere cluster integrals

ForN particles (N>2), by means of a spherical harmonic expansion of Silverstone and Moats, a 3N-dimensional cluster may be reduced to 2N+1 trivial integrals andN–1 interesting integrals. For hard spheres, theN–1 interesting integrals are products of polynomials integrated between binomial bounds. With simple clusters, closed forms are obtained; for more complex clusters, infinite series inl (ofY _lm ) appear. It is here shown for representative cases that these series converge exponentially rapidly, the leading pair of terms accounting for all but a few tenths of a percent of the total cluster integral.