Vulcanized matter is matter whose constituents move subject to a large number of permanent random constraints. These constraints are generally due to the presence of covalent bonds that permanently connect randomly selected atoms. Prime examples of vulcanized matter include crosslinked macromolecular systems (such as rubber), as well as certain chemical gels (such as silica) that are formed from atomic or low-molecular-weight fluids. When present in sufficiently large numbers, permanent random constraints cause vulcanized matter to undergo an equilibrium phase transition from a fluid state, in which all constituents are delocalized, to a new state---the amorphous solid state---, in which at least a fraction of the constituents are localized near randomly located mean positions and to a random extent. In this talk I shall review theoretical approaches aimed at describing the amorphous solid state of vulcanized macromolecular matter, especially in the regime of constraint-densities near to the liquid-to-amorphous solid transition.(R.\ T.\ Deam, S.\ F.\ Edwards, Phil.\ Trans.\ R.\ Soc.\ 280A, 317 (1976).)^,(P.\ M.\ Goldbart, N.\ Goldenfeld, Phys.\ Rev.\ Lett.\ 58, 2676 (1987); Phys.\ Rev.\ A 39 1402 (1989); ibid.~1412.) In this regime, a surprisingly rich and universal picture of the equilibrium structure(P.\ M.\ Goldbart, H.\ E.\ Castillo, A.\ Zippelius, Adv.\ Phys.\ 45, 393 (1996).) and elastic response(H.\ E.\ Castillo, P.\ M.\ Goldbart, Phys.\ Rev.\ E 58, R24 (1998); cond-mat/9712050.) of the amorphous solid state has been obtained via rather general arguments based on symmetry and length-scales.(W.\ Peng, H.\ E.\ Castillo, P.\ M.\ Goldbart, A.\ Zippelius, Phys.\ Rev.\ B 57, 839 (1998); cond-mat/9709250.) Support for this picture is provided by results from detailed analyses of semi-microscopic models of an array of vulcanized systems, as well as from extensive computer simulations.(S.\ Barsky, M.\ Plischke, Phys.\ Rev.\ E 53, 871 (1996); unpublished (1997); S.\ Barsky, Ph.D.~thesis, Simon Fraser U.\ (1996).) I shall also review extensions of these theoretical approaches aimed at describing the amorphous solid state of chemical gels and other non-macromolecular random-network-forming media,(P.\ M.\ Goldbart, A.\ Zippelius, Europhys.\ Lett.\ 27 599 (1994); K.\ A.\ Shakhnovich, P.\ M.\ Goldbart (1998, in preparation).) as well as theoretical approaches to the dynamics of vulcanized matter.
[ZC17.02] Stability of the amorphous solid state of randomly constrained systems near the solidification transition
Horacio E. Castillo (Laboratoire de Physique Théorique de l'Ecole Normale Supérieure), Paul M. Goldbart (University of Illinois at Urbana-Champaign), Annette Zippelius (Institut für Theoretische Physik, Universität Göttingen)
The amorphous solid state is analyzed for a class of systems undergoing liquid--to--amorphous-solid phase transitions driven by random constraints. This class of systems includes vulcanized macromolecular matter, both crosslinked and endlinked, as well as others. A proposed description of the amorphous solid state,(P. M. Goldbart, H. E. Castillo, A. Zippelius, Adv. Phys. 45, 393 (1996)) in which the state is characterized by the fraction of localized particles and the distribution of localization lengths, is shown to be stable with respect to all small fluctuations (except for the expected zero-mode associated with spontaneously broken translational symmetry).
[ZC17.03] Hydration of glucose in the rubbery and glassy states studied by molecular dynamics simulation
J.Raul Grigera, Ernesto R. Caffarena (IFLYSIB, La Plata, Argentina)
We have studied by Molecular Dynamics the hydration properties of an 85% (w/w) aqueous solution of glucose. The experimental values of the relative populations of \alpha and \beta anomers were introduced into the description of the system. We computed the radial distribution function, hydrogen bond residence times, hydration number and mean lifetimes, as well the mean glucose and water cluster sizes. The simulated glass transition temperature (Tg) of the solution was computed to evaluate the quality of the model; the computed value of 241K was in fair agreement with the experimental value of 232 K. It was concluded that most of the water molecules are connected to more than one glucose molecule by hydrogen bonds. The residence time of the water molecules in hydration sites changes from one site to another, but for the anomeric and chain-oxygen atoms, the residence time is greater than for the rest. The average residence time goes from 2.00 ps for the rubbery state at 280K to 5.75 ps for the glassy state at 200K. The mean value of the cluster size of glucose is very close to the corresponding to full connectivity and does not vary much from the rubbery to the glassy state.
[ZC17.04] Experimental Observation of a Violation of the Fluctuation-Dissipation Theorem in a Structural Glass
Tomas S. Grigera, Nathan E. Israeloff (Department of Physics, Northeastern University)
It has been theoreticaly known for some years that at least some mean-field
models of spin glasses fail to obey the fluctuation-dissipation theorem (FDT)
below the transition temperature, due to their slow dynamics. This violation
can be characterized by defining an effective temperature(
L.F. Cugliandolo, J.\ Kurchan and L.\ Peliti, Phys.\ Rev.\ E55, 3898 (1997))
T_eff, different from the bath temperature T.
Recent computer simulations have shown that other, more realistic, models of
spin and structural glasses also violate the FDT. However, no experimental
observation of such sublte violations has been reported to date.
We have measured FDT violations in glycerlol slightly below its glass transition,
by simultaneously recording dielectric response and fluctuations. This was done
by measuring thermal noise at the resonance of an LC circuit, where glycerol
forms the dielectric of the capacitor. The sample is quenched to T
The glass transition, i.e. the process of formation of
glasses from supercooled liquids, is believed to be of
dynamic nature. More than a decade ago inelastic neutron
scattering studies revealed a characteristic feature in the
dynamic structure factor near the glass transition. This
so-called "fast" process appears on the time scale of 1 ps
and its spectral line shape can be described by a power law.
The nature of this process remained an open question ever
since. Extending neutron scattering exploration of the
dynamic behavior to the length scale of the intermediate
range order in an archetypal fragile glass CKN, we found for
the first time direct experimental evidence showing that
this process is a first, fast step of the structural
relaxation, and cannot be attributed to local or propagating
vibrations. This finding is in agreement with a most
fundamental prediction by mode coupling theories of the
glass transition.
In an effort to understand the glass transition, the kinetics of a spin model
with frustration
but no quenched randomness, has been analyzed. The phenomenology of the spin
model is remarkably similar to that of structural glasses. In the supercooled
phase, an ergodicity breaking transition is observed where the system falls out
of equilibrium. The approach to this transition is characterized by anomalously
slow dynamics. Mapping the model onto a tiling model, we find that the slow
dynamics, observed in spin-flip Monte Carlo simulations, is due to the
appearance
of large-scale structures. The high-temperature phase can be viewed as a rough
(1,1,1) surface and the ground-state of the model is a three-fold degenerate,
smooth (1,0,0) surface. The dynamics is controlled by vortex-like defects in
the tiling. Our studies show that near the glass transition, similarly oriented
defects attract and form clumps on short-time scales. On a much longer
time-scale, clumps of oppositely oriented defects come together creating large
regions of the smooth (1,0,0) surface. We analyze
these observations in terms of an effective defect-defect interaction.
The elastic constants of diluted central-force networks are
known to vanish at a concentration p_r that issubstantially higher
than the corresponding connectivity percolation
concentration p_c. However, this is only true for zero
temperature, where the only contribution to the elastic moduli is
energetic. We have used molecular dynamics simulations to
determine these moduli at finite temperature, where there is also an
entropic contribution. Continuing earlier work, we
show that the elastic moduli of bond-diluted triangular and square
networks vanish at p_c rather than at p_r, with a power law
\mu\sim (p-p_c)^f. f appears to be equal to the
exponent for conductivity percolation, and we present renormalization
group arguments which indicate why this should be true.
We consider a soluble model of rigidity percolation on a random bond network
(RBN), in which sites have prescribed coordination numbers, but any two sites
can be connected regardless of the distance between them. There are constraints
on both bond lengths and angles between bonds. We show how to map the RBN
with the angular constraints onto that with the length constraints only, replacing pointlike sites
with 3-dimensional bodies. For the network with two types of sites having
different coordinations we allow for different chemical bonding schemes ranging
from a phase-separated case, when the sites of different types are not
connected, to a more usual chemical bonding, when there is always a site of the
different type between any two same-type sites. We show that the conventional
Maxwell counting fails for the networks close to phase separation and propose a
modification of constraint counting which gives remarkably good results in the
whole range of bonding parameters. We also consider the influence
of dangling bonds in the network. This work was partially supported by NSF.
We extend the analysis of rigidity percolation to a random bond model with
tunable coordination. Beyond showing that simple changing of the initial
coordination does not effect the percolation threshold, this work investigates
the influence of rings on the model -- specifically how the size and
concentration of rings intentionally placed into the random bond model affect
the percolation coordination and the order of transition. We show how rigid
rings act as nucleation centers in an otherwise randomly conneced network.
This work was partially supported by NSF.
The concept of bond constraints has been used to describe
the development of rigidity in network glasses at zero
temperature. Recently, Gupta and Patton have proposed a
finite temperature constraint model which successfully
accounts for macroscopic properties of systems like Ge-Se
chalcogenide glasses and alkali-silicate glasses as well as
the origin of the difference between strong and fragile
glass-forming liquids. Using a new microscopic model of
covalently-bonded glasses which incorporates the electronic
states involved in the formation of bonds, we investigate
the properties of the supercooled liquid state. Monte Carlo
and molecular dynamic simulations are used to calculate the
entropy, specific heat and viscosity through the glass
transition. Results are compared with simulations of viscous
liquids using conventional approaches such as Lennard-Jones
and bond-angle dependent potentials.
Raman scattering and T-modulated DSC measurements have been performed on the
Ge_25S_75-yBr_y ternary glass in the 0 < y < 0.30 composition range.
Raman frequency variation, \nu (y), of corner-sharing Ge(S_1/2)_4
units reveal a step-like red shift of 1 cm^-1 centered around y = 0.16
superposed over an approximately linear blue-shifted background. T-modulated
DSC measurements reveal glass transitions T_g(y) to decrease with y and
the
non-reversing-heat-flow \Delta H_nr to display a local minimum near y =
0.15. Counting algorithms have recently shown(P. Boolchand and M.F.
Thorpe, Phys. Rev. B50, 10366 (1994)) that a ternary Ge_25S_75-yBr_y
glass, in which Ge, S and Br bond with coordination number of 4, 2 and 1, will
display a rigid to floppy transition when the Br content y increases to 0.166.
Thus the step-like red-shift feature in \nu (y) near y = 0.16 constitutes
direct evidence for the stiffness transition. The blue-shifted background
variation of \nu (y) is ascribed to internal stress build-up as the
oversized halogen (Br-1.95Åreplaces the chalcogen (S-1.04Åin the
network backbone.
Te-125 Lamb-Mössbauer factors in the titled glasses and thin films have
been measured as a function of temperature in the 10K < T < 150K range
and at several compositions 0.07 < x < 0.33. The first inverse and
second inverse moments of the vibrational density of states both reveal
an anomaly near x \sim 0.20 or mean coordination of 2.4.
These results suggest that the floppy mode frequency in
these glasses is low ( < 3 meV). The existence of
a solitary transition near
Although the structure of the titled glasses has been examined in neutron
scattering and P^31 solid state NMR experiments earlier(H.
Eckert, Angew. Chem. Int. Engl. Adv. Mater. 28, 1723 (1989).), the nature
of the structural transition from a random network at low x ( x < 0.30
) to a network of P_4Se_3 monomeric units at high x ( x >0.5 ) has
remained largely unexplored. The transition may be related to the onset of
rigidity. We have synthesized bulk glasses over a wide composition range
(0.10 < x < 0.66) and have now examined them in Raman scattering,
temperature Modulated DSC, and Molar volumes measurements systematically
with x. In Raman scattering, a multitude of narrow vibrational features
are observed at x > 0.40 , with scattering strength of these narrow
modes increasing with x. These represent normal modes of P_4Se_3
monomers that have decoupled from the network backbone. At low x, several
modes of larger width are observed and are ascribed to the backbone
consisting of Se_n -chains that are cross-linked by pyramidal and
quasi-tetrahedral P atoms. Results of Raman, MDSC and V_M measurements
will be correlated to elucidate the rigidity transition.
[ZC17.05] Direct Evidence for a Fast Step in Structural Relaxation Near the Glass Transition.
Ferenc Mezei, Margarita Russina (Los Alamos National Laboratory, Los Alamos, NM 87545)
[ZC17.06] Slow Dynamics in Frustrated Spin System: Defects and Tilings
Mark Sobkowicz, Bulbul Chakraborty (Martin Fisher School of Physics, Brandeis University)
[ZC17.07] Entropic Contribution to Rigidity Percolation
Daniel Vernon, Michael Plischke (Department of Physics, Simon Fraser University, Burnaby, B.C., Canada V5A 1S6), Béla Joós (University of Ottawa, Ottawa, Ontario, Canada K1N 6N5)
[ZC17.08] Random Bond Model of Rigidity Percolation and Modified Constraint Counting in Covalent Glasses
Mykyta V. Chubynsky, Donald J. Jacobs, Michael F. Thorpe (Michigan State University)
[ZC17.09] Computational Analysis for Random Bond Model Rigidity Percolation
A.J. Rader, D.J. Jacobs, M.F. Thorpe (Michigan State University)
[ZC17.10] Microscopic Bond-Constraint Model for Glass-Forming Liquids
Saeid Davatolhagh, Bruce Patton (The Ohio State University)
[ZC17.11] Evidence for the Stiffness Transition in Chalcogenide Glasses
Y. Wang, J. Wells, W.J. Bresser, P. Boolchand (Department of Electrical Engineering, University of Cincinnati)
[ZC17.12] Stiffness Transition in Ge_x Te_1-x Glasses
R.N. Enzweiller (Department of Physics and Geology, Northern Kentucky University), D. Selvanathan, W.J. Bresser, P. Boolchand (Department of Electrical Engineering, University of Cincinnati)
[ZC17.13] Molecular Structure of P_xSe_1-x Glasses
D.G. Georgiev, M.I. Mitkova, P. Boolchand (Department of Electrical Engineering, University of Cincinnati)