Steven Raymond Lustig

Thermodynamic constitutive equations for materials with memory on a material time scale

We present a complete, self‐consistent set of thermodynamic constitutive equations for viscoelastic solid and fluid materials which can be applied during arbitrary, three‐dimensional deformations and thermal processes. Deformational and thermal histories are measured using a fading memory norm in a material time which provides a quantitative indication of the constitutive models’ ability to represent the dynamic response. The free energy constitutive equation is a Frechet expansion about the deformation and temperature histories of arbitrarily large but sufficiently slow departures from equilibrium in material time. The kinetic relationship between the laboratory and material time scales does not depend on equilibrium considerations. This approach greatly extends the applicability of low‐order memory expansions to nonequilibrium polymer states. Constitutive equations for stress, internal energy, entropy, enthalpy, and heat capacity are derived. All the required material properties can be evaluated unambig...

Rheology, self‐diffusion, and microstructure of charged colloids under simple shear by massively parallel nonequilibrium Brownian dynamics

The simple shearing of a suspension of charge‐stabilized, colloidal particles close to the melting line is investigated by massively parallel, nonequilibrium Brownian dynamics (NEBD) simulation. The suspension undergoes a discontinuous transition from a distorted fluid structure to an ordered ‘‘string’’ phase. Comparisons between simulations of 43 000, 4725 particles, and previous NEBD work on ≤500 particles proves that shear‐induced ordering is not an artifact of the small system sizes. We also show that the shear‐rate dependence of the rheological properties obtained from NEBD is different than those obtained from nonequilibrium molecular dynamics (NEMD), a consequence of the solvent damping not being present in NEMD. The validity of the Ree–Eyring model for viscosity and the stress‐optic law for colloids are tested. Further, a type of generalized Stokes–Einstein relationship is discovered for systems under shear.

Microstructure and rheology of polydisperse, charged suspensions

Nonequilibrium Brownian dynamics simulations are used to study the effect of polydispersity on the thermodynamics, rheology, microstructure, and shear‐induced disorder–order transition in suspensions of charged colloids. Approximately 43 000 particles with 2000 different components of a discretized Schulz distribution at polydispersities from 0% to 30% are simulated on a massively parallel computer. Recent advances in the integral equation theory for polydisperse suspensions are tested and verified with respect to both structure and equilibrium mechanical properties. The low shear rate rheology for both monodisperse and polydisperse suspensions is found to be well represented by the Ree–Eyring model. At higher shear rates an ordered ‘‘string’’ phase is shear induced for low polydispersities (<10%). Increasing the polydispersity further (≳20%) inhibits the ordering, suggesting the existence of a critical polydispersity beyond which a colloidal suspension cannot be induced into an ordered state by shearing....

Peak-referenced integral method for size exclusion chromatography and its application to aromatic polyesters

Abstract A new peak-referenced integral method, PRIM, greatly improves the accuracy of single detector size exclusion chromatography, SEC, calibration and analysis using broad standards. PRIM combines advantages from the narrow standard peak position calibration method, which offers high precision, and the broad standard integral calibration method, which makes no assumption regarding the column’s chromatographic behavior. PRIM calibration uses the calibrant’s elution peak as a boundary condition to build the elution calibration. Separate cumulative integral matchings are made between the integrated signal area and the integrated molecular weight distribution on each side of the elution peak. SEC–PRIM is illustrated using well-characterized poly(trimethylene terephthalate) samples which follow the Flory most-probable molecular weight distribution. Calibrations are demonstrated which are independent of the sample molecular weight distribution. Valid calibrations can be made which are insensitive to the cyclic oligomer elution not being fully resolved from the linear polymer elution. A self-consistent comparison between the original integral method, Hamielec method and PRIM illustrates greatest accuracy from PRIM. The SEC–PRIM results for all molecular weight averages are accurate to within 5% of absolute, noncalibrated measurements considering all samples. The high accuracy is attributed to ensuring the calibrant peak molecular weight is assigned as accurately as possible.

The Fast Multipole Method in Canonical Ensemble Dynamics on Massively Parallel Computers

The fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale as O (N 2 ). The FMM execution times scale as O (N) on sequential workstations and vector processors and asymptotically 0 (logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.

Selectivity of Polypeptide Binding to Nanoscale Substrates

Abstract : We present new computational methodology for designing polymers, such as polypeptides and polyelectrolytes, which can selectively recognize nanostructured substrates. The methodology applies to polymers which might be used to: control placement and assembly for electronic devices, template structure during materials synthesis, as well as add new biological and chemical functionality to surfaces. Optimization of the polymer configurational sequence permits enhancement of both binding energy on and binding selectivity between one or more atomistic surfaces. A novel Continuous Rotational Isomeric State (CRIS) method permits continuous backbone torsion sampling and is seen to be critical in binding optimization problems where chain flexibility is important. We illustrate selective polypeptide binding between either analytic, uniformly charged surfaces or atomistic GaAs(100), GaAs(110) and GaAs(111) surfaces. Computational results compare very favorably with prior experimental phage display observations S.R. Whaley et al., Nature, 405, 665 (2000) for GaAs substrates. Further investigation indicates that chain flexibility is important to exhibit selective binding between surfaces of similar charge density. Such chains begin with sequences which repel the surfaces, continue with sequences that attract the surface and end with sequences that neither attract nor repel strongly.