Search results for "Scaling theory"
showing 10 items of 13 documents
Frictional Forces between Strongly Compressed, Nonentangled Polymer Brushes: Molecular Dynamics Simulations and Scaling Theory
2010
By means of molecular dynamics simulations and scaling theory we study the response of opposing polymer brushes to constant shear motion under good solvent conditions. Model systems that contain explicit solvent molecules (Lennard-Jones dimers) are compared to solvent-free systems while varying of the distance between the grafted layers and their molecular parameters, chain length and grafting density. Our study reveals a power-law dependence of macroscopic transport properties on the Weissenberg number, W, beyond linear response. For instance, we find that the kinetic friction constant scales as μ ∼ W0.57 for large values of W. We develop a scaling theory that describes our data and previo…
Optically Enhanced Electric Field Sensing Using Nitrogen-Vacancy Ensembles
2021
Nitrogen-vacancy (NV) centers in diamond have shown promise as inherently localized electric-field sensors, capable of detecting individual charges with nanometer resolution. Working with NV ensembles, we demonstrate that a detailed understanding of the internal electric field environment enables enhanced sensitivity in the detection of external electric fields. We follow this logic along two complementary paths. First, using excitation tuned near the NV's zero-phonon line, we perform optically detected magnetic resonance (ODMR) spectroscopy at cryogenic temperatures in order to precisely measure the NV center's excited-state susceptibility to electric fields. In doing so, we demonstrate th…
Elastic constants from microscopic strain fluctuations
1999
Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general e…
Finite-size tests of hyperscaling.
1985
The possible form of hyperscaling violations in finite-size scaling theory is discussed. The implications for recent tests in Monte Carlo simulations of the d = 3 Ising model are examined, and new results for the d = 5 Ising model are presented.
Dynamical coexistence in moderately polydisperse hard-sphere glasses
2020
We perform extensive numerical simulations of a paradigmatic model glass former, the hard-sphere fluid with 10% polydispersity. We sample from the ensemble of trajectories with fixed observation time, whereby single trajectories are generated by event-driven molecular dynamics. We show that these trajectories can be characterized in terms of the local structure, and we find a dynamical-structural (active-inactive) phase transition between two dynamical phases: one dominated by liquidlike trajectories with a low degree of local order and one dominated by glassylike trajectories with a high degree of local order. We show that both phases coexist and are separated by a spatiotemporal interface…
SCALING THEORY AND THE CLASSIFICATION OF PHASE TRANSITIONS
1992
The recent classification theory for phase transitions (R. Hilfer, Physica Scripta 44, 321 (1991)) and its relation with the foundations of statistical physics is reviewed. First it is outlined how Ehrenfests classification scheme can be generalized into a general thermodynamic classification theory for phase transitions. The classification theory implies scaling and multiscaling thereby eliminating the need to postulate the scaling hypothesis as a fourth law of thermodynamics. The new classification has also led to the discovery and distinction of nonequilibrium transitions within equilibrium statistical physics. Nonequilibrium phase transitions are distinguished from equilibrium transiti…
Transient Reversible Growth and Percolation During Phase Separation
1988
Binary mixtures when quenched into the two-phase region exhibit transient percolation phenomena. These transient percolation phenomena and the underlying mechanism of transient reversible growth are investigated. In particular, one of the possible dynamical percolation lines between the dynamical spinodal and the line of macroscopic percolation is traced out. Analyzing the finite size effects with the usual scaling theory one finds exponents which seem to be inconsistent with the universality class of percolation. However, at zero temperature, where the growth is non-reversible and the transition of a sol-gel type, the exponents are consistent with those of random percolation.
Polyelectrolytes Grafted to Curved Surfaces
1996
We present a scaling theory to describe equilibrium conformations of weakly charged polyelectrolyte molecules grafted at one end onto impermeable surfaces of various morphologies (spheres, cylinders) and of arbitrary curvature. We focus on the case of sufficiently densely grafted chains, i.e., on curved polyelectrolyte brushes. Different regimes of the behavior of curved polyelectrolyte brushes can be distinguished, depending on grafting density, surface curvature, and chain length. We present phase diagrams of the system describing these regimes and discuss the crossover conditions. We also analyze the effect of charge annealing in curved polyelectrolyte brushes.
Formation of Ordered Structures in Quenching Experiments: Scaling Theory and Simulations
1987
In this note we want to address the particular problem of the formation of ordered structures resulting from “quenching experiments”. The generic experimental situation is depicted in Figure 1. Initially the system is in an unordered random state in the one-phase region. Then the temperature is lowered (for some systems like polymers the coexistence curve is inverted so that the temperature must be raised) until the system is in the two phase region. The system is now in a non-equilibrium situation and evolves toward equilibrium. It is during the evolution toward equilibrium that the system develops ordered structures /1,2/.
Controlling the Interactions between Soft Colloids via Surface Adsorption
2013
By employing monomer-resolved computer simulations and analytical considerations based on polymer scaling theory, we analyze the conformations and interactions of multiarm star polymers strongly adsorbed on a smooth, two-dimensional plane. We find a stronger stretching of the arms as well as a stronger repulsive, effective interaction than in the three dimensional case. In particular, the star size scales with the number of arms $f$ as $\sim f^{1/4}$ and the effective interaction as $\sim f^{2}$, as opposed to $\sim f^{1/5}$ and $\sim f^{3/2}$, respectively, in three dimensions. Our results demonstrate the dramatic effect that geometric confinement can have on the effective interactions and…