Research
IRG III
Jamming, Slow Relaxation and Rigidity Onset in Materials Far from Equilibrium
Faculty (*=Coordinators): A. Dinner, E. Isaacs, H. Jaeger, K.-Y. Lee,
G. Mazenko S. Nagel, S. Rice, T. Rosenbaum, T. Witten, W. Zhang
Affiliates: M. Gardel, G. Karczmar, B. Lin, X.-M. Lin
Int'l Collaborators: D. Price, M.-L. Saboungi
This IRG studies the basic question of why some amorphous materials are
rigid and others can flow easily. In particular, it addresses the role of
control parameters and the effect of boundaries on the flow properties,
the origins of slow relaxation, and the coupling of structure and dynamics.
This IRG identifies similarities in many far from equilibrium systems and
analyzes the manifestations of jamming/freezing in systems as diverse as
liquids supercooled into a glass or grains streaming from an orifice. A
jamming phase diagram provides a common unified framework for describing
the thermodynamic and dynamic aspects of these transitions [Jamming and
Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales, A.
J. Liu and S. R. Nagel, eds. (Taylor and Francis, London, 2001).].
Near the jamming transition stress networks span the material to give rigidity
to the marginally jammed solid. It is not understood how the stress network
deforms when a jammed material is under stress and begins to flow. Nagel
and Jaeger and co-mentored graduate student, Corwin, have been studying
the stress distributions at the boundaries of a granular material using
a new pressure-induced birefringence technique that allows in situ measurements
as a function of time. These experiment uncovered a qualitative signature
of the jamming transition [Nature 435, 1075 (2005)].
In the static regime the distribution follows the non-equilibrium form given
by, e.g., the Q-model, originally proposed by MRSEC researchers Coppersmith,
Witten and Nagel [Science 269, 513-515 (1995)].
In the past year, this group has concentrated on the fluctuations that this
network undergoes as a function of time. There is an extraordinarily wide
distribution of time scales in the stresses imposed by different particles.
This suggests an analogy with the kinetic heterogeneities observed in liquids
near the glass transition. This new form of an effective temperature is
in accord with simulations of sheared glasses or foams by Nagel and collaborators.
Jaeger, Nagel and Karczmar used high-resolution, non-invasive imaging techniques
to probe 3-D shear profiles and fluctuations in flowing material in a modified
Couette cell where the shear bands are of arbitrary width. They discovered
several novel phenomena, including a torsional instability in the vertical
direction. These results were corrobrated by large scale computer simulations
of the full experimental system, in collaboration with Gary Grest and his
group at Sandia [PRL 96, 038001 (2006)].
The vibrational states near the jamming onset have unusual behavior. This
shows up prominently in the density of states D(w)
of the low-lying normal modes of a model system studied by Nagel and collaborators:
D(w) approaches a constant at low frequency with
no signature of the usual Debye w2
behavior. Witten, Nagel and Wyart, a long-term visiting student from Saclay,
showed that such features necessarily occur in solids near the isostatic
point where there are just sufficient constraints for rigidity [Phys.
Rev. E 72, 051306 (2005)]. Their analysis elucidates
the fundamentally different character of the low w
modes in a glass from those in a crystal.
Diffusion of particles in quasi one-dimensional pores occurs in ion transport
in cell membranes, molecular motion in zeolites and particle flows in microfluidic
devices. In such cases boundaries play an important role in the diffusion
and interaction of particles. As such it is an important aspect of jamming
in low dimensions. Lin, Rice and collaborators have studied the center-of-mass
and relative pair diffusion coefficients in quasi-1 and -2 dimensional binary
colloid suspensions [J. Chem. Phys, accepted, (2006)]. This extends
their similar studies of single-component quasi-1 [PRL 95,
158301 (2005)] and quasi-2 dimensional colloid suspensions [PRL,
92, 258301 (2004)]. They found that the presence of the
smaller diameter component can destroy the oscillatory structure of the
separation dependence of the quasi-2-dimensional relative pair diffusion
coefficient of the large particles even though the oscillatory character
of the large particle equilibrium pair correlation function remains prominent.
No such effect occurs with the quasi-1 dimensional suspension.
A new direction for this IRG is to extend this approach to other forms of
rigidity onset. In particular, to self-organization induced by the stress
itself. This includes self-strengthening, structures such as the crumpling
of thin films and surfactant monolayers and the feedback in the moduli of
the cytoskeleton in biological cells.
Lee and Witten study a striking form of rigidity onset in lipid monolayers
where abrupt buckling events in the form of folds appear to arrest themselves
(or one another) suddenly during buckling [J. Phys. Chem. B, 110,
10220 (2006)]. They seek to understand the self-strengthening implicit in
such self-arresting mechanical failure. Recently they identified a minor
additive, glycerol, that can block the self-strengthening, so that the buckling
proceeds until the stress is relaxed. By measuring the monolayer dynamic
modulus as a function of the amount of additive, they will use this control
parameter to leverage their understanding of the self-strengthening phenomenon.
We also aim to use automatic video analysis to provide a quantitative characterization
of the effect of the additive on the buckling.
Zhang and her student have been motivated by Gardel’s work showing
that actin networks cross-linked with filamin show rigidity onset in the
form of strain-hardening. These results suggest that the rheology of cells
under physiological conditions can be described as a soft glassy material.
The effect of this unusual rheology on cell shape changes has not received
much analysis. Currently Zhang is incorporating these results into a simple
model for cell division to see if taking strain hardening into account can
qualitatively account for how the strain and elastic modulus at which rupture
occurs depends on the crosslinker concentration. This offers a natural explanation
for several puzzling features of the dynamics in the shape change dynamics
measured by Robinson's group at Johns Hopkins University. They have found
furrow-thinning trajectories that can have a linear, exponential or power-law
decay. Motivated by models for glasses, Dinner introduced a model for molecular
self-assembly built on a lattice of discrete interacting variables. The
dynamics are encoded through a set of Monte Carlo rules based on empirical
data and reproduces observed cytoskeletal morphologies as protein concentrations
are varied. This model shows the de novo formation of cytoskeletal structures
consistent with earlier speculations based on static microscopy images.
By enabling simulation of the growth of competing morphologies, the approach
complements earlier models of cytoskeletal assembly that have largely been
limited to analytic mean-field and numerical rigid-rod studies of force-velocity
relationships. A paper has been submitted to Phys. Rev. E.
Delineating the relationship between the structure and the dynamics is a
critical element in establishing the essential nature of the glassy state,
but this correspondence remains difficult to access in most systems. The
proton glass, a structural analogue to magnetic spin glasses with competing
ferroelectric and antiferroelectric order, is different. By analogy to the
approach taken to relate statics and dynamics in granular systems -- a hallmark
of this IRG -- Nagel, Price and Rosenbaum have combined dielectric spectroscopy
over seven decades in frequency with a direct mapping of the real space
energy potential via neutron Compton scattering to probe the unjamming of
the frozen state in mixed ferroelectric RDP and antiferroelectric ADP crystals
[PRL 97, 145501 (2006)]. They are able to describe
quantitatively the highly choreographed proton dynamics within a hydrogen
bond network. Proton tunneling builds correlations between neighboring hydrogen
bonds and dominates the long-time relaxation over a surprisingly large temperature
range. Being piezoelectric and electrostrictive these crystals now afford
the opportunity to tune the hydrogen bond potential, and hence the dynamics.
We will map the potentials and modulate the descent through the free-energy
surface via the application of a polarizing, dc electric field, with emphasis
on the low temperature behavior where quantum relaxation dominates.
Magnetic Ising dipoles in a transverse magnetic field represent the simplest
quantum spin system. The transverse field tunes quantum-mechanical tunneling
to speed relaxation and "unjam" the system when the anisotropy
of the dipole interaction and the disorder combine to produce a glassy ground
state. Levin and Rosenbaum combine experiment and simulations to study the
non-equilibrium states in disordered magnetic systems. The presence of a
nearby quantum phase transition provides the opportunity to quantify the
onset of magnetic order and the development of the magnetic excitation spectrum
[Phys. Rev. B 75, 054426 (2007)]. Nagel and Rosenbaum
will now focus on the decoherence of the relaxing dipoles, attempting to
separate out the effects of coupling to the nuclear spin bath and to the
lattice through temperature and transverse field excursions.
From annual report to the NSF, March 2007