124 research outputs found
Self-assembling multiblock amphiphiles: Molecular design, supramolecular structure, and mechanical properties
We perform off-lattice, canonical ensemble molecular dynamics simulations of
the self-assembly of long segmented copolymers consisting of alternating,
tunably attractive and hydrophobic {\em binder} domains, connected by
hydrophilic {\em linker} chains whose length may be separately controlled. In
such systems, the molecular design of the molecule directly determines the
balance between energetic and entropic tendencies. We determine the structural
phase diagram of this system, which shows collapsed states (dominated by the
attractive linkers' energies), swollen states (dominated by the random coil
linkers' entropies) as well as intermediate network hydrogel phases, where the
long molecules exhibit partial collapse to a {\em single molecule network}
state. We present an analysis of the connectivity and spatial structure of this
network phase, and relate its basic topology to mechanical properties, using a
modified rubber elasticity model. The mechanical properties are further
characterized in a direct computational implementation of oscillatory rheology
measurements. We find that it is possible to optimize the mechanical
performance by an appropriate choice of molecular design, which may point the
way to novel synthetics that make optimal mechanical use of constituent
polymers
Curvature-induced cross-hatched order in two-dimensional semiflexible polymer networks
A recurring motif in the organization of biological tissues are networks of
long, fibrillar protein strands effectively confined to cylindrical surfaces.
Often, the fibers in such curved, quasi-2D geometries adopt a characteristic
order: the fibers wrap around the central axis at an angle which varies with
radius and, in several cases, is strongly bimodally distributed. In this
Letter, we investigate the general problem of a 2D crosslinked network of
semiflexible fibers confined to a cylindrical substrate, and demonstrate that
in such systems the trade-off between bending and stretching energies, very
generically, gives rise to cross-hatched order. We discuss its general
dependency on the radius of the confining cylinder, and present an intuitive
model that illustrates the basic physical principle of curvature-induced order.
Our findings shed new light on the potential origin of some curiously universal
fiber orientational distributions in tissue biology, and suggests novel ways in
which synthetic polymeric soft materials may be instructed or programmed to
exhibit preselected macromolecular ordering
Catch Bonding in the Forced Dissociation of a Polymer Endpoint
Applying a force to certain supramolecular bonds may initially stabilize
them, manifested by a lower dissociation rate. We show that this behavior,
known as catch bonding and by now broadly reported in numerous biophysics
bonds, is generically expected when either or both the trapping potential and
the force applied to the bond possess some degree of nonlinearity. We enumerate
possible scenarios, and for each identify the possibility and, if applicable,
the criterion for catch bonding to occur. The effect is robustly predicted by
Kramers theory, Mean First Passage Time theory, and finally confirmed in direct
MD simulation. Among the catch scenarios, one plays out essentially any time
the force on the bond originates in a polymeric object, implying that some
degree of catch bond behavior is to be expected in {\em any} protein-protein
bond, as well as in more general settings relevant to polymer network mechanics
or optical tweezer experiments
Confinement without boundaries: Anisotropic diffusion on the surface of a cylinder
Densely packed systems of thermal particles in curved geometries are
frequently encountered in biological and microfluidic systems. In 2D systems,
at sufficiently high surface coverage, diffusive motion is widely known to be
strongly affected by physical confinement, e.g., by the walls. In this Letter,
we explore the effects of confinement by shape, not rigid boundaries, on the
diffusion of particles by confining them to the surface of a cylinder. We find
that both the magnitude and the directionality of lateral diffusion is strongly
influenced by the radius of the cylinder. An anisotropy between diffusion in
the longitudinal and circumferential direction of the cylinder develops. We
demonstrate that the origin of this effect lies in the fact that screw-like
packings of mono- and oligodisperse discs on the surface of a cylinder induce
preferential collective motions in the circumferential direction, but also show
that even in polydisperse systems lacking such order an intrinsic finite size
confinement effect increases diffusivity in the circumferential direction
Disorder, pre-stress and non-affinity in polymer 8-chain models
To assess the role of single-chain elasticity, non-affine strain fields and
pre-stressed reference states we present and discuss the results of numerical
and analytical analyses of modified 8-chain Arruda-Boyce model for cross-linked
polymer networks. This class of models has proved highly successful in modeling
the finite-strain response of flexible rubbers. We extend it to include the
effects of spatial disorder and the associated non-affinity, and use it to
assess the validity of replacing the constituent chain's nonlinear elastic
response with equivalent linear, Hookean springs. Surprisingly, we find that
even in the regime of linear response, the full polymer model gives very
different results from its linearized counterpart, even though none of the
chains are stretched beyond their linear regime. We demonstrate that this
effect is due to the fact that the polymer models are under considerable
pre-stress in their ground state. We show that pre-stress strongly suppresses
non-affinity in these unit cell models, resulting in a marked stiffening of the
bulk response. The effects of pre-stress we discuss may explain why fully
affine mechanical models, in many cases, predict the bulk mechanical response
of disordered stiff polymer networks so well.Comment: 29 pages, 7 figures. Submitted to J. Mech. Phys. Solid
Fluctuation-stabilized marginal networks and anomalous entropic elasticity
We study the elastic properties of thermal networks of Hookean springs. In
the purely mechanical limit, such systems are known to have vanishing rigidity
when their connectivity falls below a critical, isostatic value. In this work
we show that thermal networks exhibit a non-zero shear modulus well below
the isostatic point, and that this modulus exhibits an anomalous, sublinear
dependence on temperature . At the isostatic point, increases as the
square-root of , while we find below the isostatic
point, where . We show that this anomalous dependence
is entropic in origin.Comment: 9 pages, 7 figure
Harnessing entropy to enhance toughness in reversibly crosslinked polymer networks
Reversible crosslinking is a design paradigm for polymeric materials, wherein
they are microscopically reinforced with chemical species that form transient
crosslinks between the polymer chains. Besides the potential for self-healing,
recent experimental work suggests that freely diffusing reversible crosslinks
in polymer networks, such as gels, can enhance the toughness of the material
without substantial change in elasticity. This presents the opportunity for
making highly elastic materials that can be strained to a large extent before
rupturing. Here, we employ Gaussian chain theory, molecular simulation, and
polymer self-consistent field theory for networks to construct an equilibrium
picture for how reversible crosslinks can toughen a polymer network without
affecting its linear elasticity. Maximisation of polymer entropy drives the
reversible crosslinks to bind preferentially near the permanent crosslinks in
the network, leading to local molecular reinforcement without significant
alteration of the network topology. In equilibrium conditions, permanent
crosslinks share effectively the load with neighbouring reversible crosslinks,
forming multi-functional crosslink points. The network is thereby globally
toughened, while the linear elasticity is left largely unaltered. Practical
guidelines are proposed to optimise this design in experiment, along with a
discussion of key kinetic and timescale considerations
Persistence-driven durotaxis: Generic, directed motility in rigidity gradients
Cells move differently on substrates with different elasticities. In
particular, the persistence time of their motion is higher on stiffer
substrates. We show that this behavior will result in a net transport of cells
directed up a soft-to-stiff gradient. Using simple random walk models with
controlled persistence and stochastic simulations, we characterize this
propensity to move in terms of the durotactic index measured in experiments. A
one-dimensional model captures the essential features of this motion and
highlights the competition between diffusive spreading and linear, wavelike
propagation. Since the directed motion is rooted in a non-directional change in
the behavior of individual cells, the motility is a kinesis rather than a
taxis. Persistence-driven durokinesis is generic and may be of use in the
design of instructive environments for cells and other motile, mechanosensitive
objects.Comment: 5 pages, 4 figure
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