42 research outputs found
Star polymers: From conformations to interactions to phase diagrams
We review recent progress achieved in the theoretical description of the
interactions, correlations, and phase behavior of concentrated solutions of
star polymers, sterically stabilized colloids, and micelles. We show that the
theoretical prediction of an ultrasoft, logarithmically diverging effective interaction
between the star centers, which has been confirmed by SANSexperiments
and computer simulations, lies in the core of a host of unusual
phenomena encountered in such systems. These include anomalous structure
factors, reentrant melting behavior, as well as a variety of exotic crystal
phases. Extensions to polydisperse stars and the role of many-body forces
are also discussed. A particular ‘mean-field’ character of star polymer fluids
is presented and it is shown that it manifests itself in the shape and
structure of sedimentation profiles of these systems.Здійснено огляд недавніх досягнень у теоретичному описі взаємодій, кореляцій і фазової поведінки концентрованих розчинів зіркових полімерів, просторово стійких колоїдів і міцел. Ми покажемо,
що теоретично передбачена надм’яка логарифмічно розбіжна ефективна взаємодія між центрами зірок, що була підтверджена SANS-експериментами і комп’ютерними симуляціями, потрапляє в множину незвичних явищ, які спостерігаються в таких системах. Сюди
відносяться аномальні структурні фактори, поведінка зворотнього
плавлення, множини екзотичних кристалічних фаз. Також обговорено узагальнення на випадок полідисперсних зірок і роль сил багатьох
тіл. Представлено особливу поведінку типу “cереднього поля” плинів
зіркових полімерів і показано, що вона проявляється у формі і структурі профілів осаджування цих систем
Structure, phase behavior, and inhomogeneous fluid properties of binary dendrimer mixtures
The effective pair potentials between different kinds of dendrimers in solution can be well approximated by appropriate Gaussian functions. We find that in binary dendrimer mixtures the range and strength of the effective interactions depend strongly upon the specific dendrimer architecture. We consider two different types of dendrimer mixtures, employing the Gaussian effective pair potentials, to determine the bulk fluid structure and phase behavior. Using a simple mean field density functional theory (DFT) we find good agreement between theory and simulation results for the bulk fluid structure. Depending on the mixture, we find bulk fluid-fluid phase separation (macrophase separation) or microphase separation, i.e., a transition to a state characterized by undamped periodic concentration fluctuations. We also determine the inhomogeneous fluid structure for confinement in spherical cavities. Again, we find good agreement between the DFT and simulation results. For the dendrimer mixture exhibiting microphase separation, we observe a rather striking pattern formation under confinement. © 2006 American Institute of Physics
Generation of defects and disorder from deeply quenching a liquid to form a solid
We show how deeply quenching a liquid to temperatures where it is linearly
unstable and the crystal is the equilibrium phase often produces crystalline
structures with defects and disorder. As the solid phase advances into the
liquid phase, the modulations in the density distribution created behind the
advancing solidification front do not necessarily have a wavelength that is the
same as the equilibrium crystal lattice spacing. This is because in a deep
enough quench the front propagation is governed by linear processes, but the
crystal lattice spacing is determined by nonlinear terms. The wavelength
mismatch can result in significant disorder behind the front that may or may
not persist in the latter stage dynamics. We support these observations by
presenting results from dynamical density functional theory calculations for
simple one- and two-component two-dimensional systems of soft core particles.Comment: 25 pages, 11 figure
Ground state at high density
Weak limits as the density tends to infinity of classical ground states of
integrable pair potentials are shown to minimize the mean-field energy
functional. By studying the latter we derive global properties of high-density
ground state configurations in bounded domains and in infinite space. Our main
result is a theorem stating that for interactions having a strictly positive
Fourier transform the distribution of particles tends to be uniform as the
density increases, while high-density ground states show some pattern if the
Fourier transform is partially negative. The latter confirms the conclusion of
earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and
Likos et al. (2007). Other results include the proof that there is no Bravais
lattice among high-density ground states of interactions whose Fourier
transform has a negative part and the potential diverges or has a cusp at zero.
We also show that in the ground state configurations of the penetrable sphere
model particles are superposed on the sites of a close-packed lattice.Comment: Note adde
Counterion Penetration and Effective Electrostatic Interactions in Solutions of Polyelectrolyte Stars and Microgels
Counterion distributions and effective electrostatic interactions between
spherical macroions in polyelectrolyte solutions are calculated via
second-order perturbation (linear response) theory. By modelling the macroions
as continuous charge distributions that are permeable to counterions,
analytical expressions are obtained for counterion profiles and effective pair
interactions in solutions of star-branched and microgel macroions. The
counterions are found to penetrate stars more easily than microgels, with
important implications for screening of bare macroion interactions. The
effective pair interactions are Yukawa in form for separated macroions, but are
softly repulsive and bounded for overlapping macroions. A one-body volume
energy, which depends on the average macroion concentration, emerges naturally
in the theory and contributes to the total free energy.Comment: 15 pages, 5 figure
Dynamic density functional study of a driven colloidal particle in polymer solutions
The Dynamic Density Functional (DDF) theory and standard Brownian dynamics
simulations (BDS) are used to study the drifting effects of a colloidal
particle in a polymer solution, both for ideal and interacting polymers. The
structure of the stationary density distributions and the total induced current
are analyzed for different drifting rates. We find good agreement with the BDS,
which gives support to the assumptions of the DDF theory. The qualitative
aspect of the density distribution are discussed and compared to recent results
for driven colloids in one-dimensional channels and to analytical expansions
for the ideal solution limit
Phase separation in star polymer-colloid mixtures
We examine the demixing transition in star polymer-colloid mixtures for star
arm numbers f=2,6,16,32 and different star-colloid size ratios. Theoretically,
we solve the thermodynamically self-consistent Rogers-Young integral equations
for binary mixtures using three effective pair potentials obtained from direct
molecular computer simulations. The numerical results show a spinodal
instability. The demixing binodals are approximately calculated, and found to
be consistent with experimental observations.Comment: 4 pages, 4 figures, submitted to PR
Vapour-liquid coexistence in many-body dissipative particle dynamics
Many-body dissipative particle dynamics is constructed to exhibit
vapour-liquid coexistence, with a sharp interface, and a vapour phase of
vanishingly small density. In this form, the model is an unusual example of a
soft-sphere liquid with a potential energy built out of local-density dependent
one-particle self energies. The application to fluid mechanics problems
involving free surfaces is illustrated by simulation of a pendant drop.Comment: 8 pages, 6 figures, revtex
Structure factor of polymers interacting via a short range repulsive potential: application to hairy wormlike micelles
We use the Random Phase Approximation (RPA) to compute the structure factor,
S(q), of a solution of chains interacting through a soft and short range
repulsive potential V. Above a threshold polymer concentration, whose magnitude
is essentially controlled by the range of the potential, S(q) exhibits a peak
whose position depends on the concentration. We take advantage of the close
analogy between polymers and wormlike micelles and apply our model, using a
Gaussian function for V, to quantitatively analyze experimental small angle
neutron scattering profiles of semi-dilute solutions of hairy wormlike
micelles. These samples, which consist in surfactant self-assembled flexible
cylinders decorated by amphiphilic copolymer, provide indeed an appropriate
experimental model system to study the structure of sterically interacting
polymer solutions