Amy Bug, Tim Cronin and Zach Wolfson

1
Simulation of Ps Toward more realistic models
of void spaces in materials

• Amy Bug, Tim Cronin and Zach Wolfson
• Dept. of Physics and Astronomy, Swarthmore
  College, U.S.A.
• Philip Sterne
• Lawrence Livermore National Laboratory, U.S.A.

2
In insulating materialsPs forms, thermalizes in
defects, cages, bubbles , and annihilates
either by pickoff or self-annihilation
PALS and ACAR indicate size distribution,
contents, and chemical nature of voids
t -1 p re2 c ? dr- dr r(r) r-(r-) gr-(
r-) d3(r- - r)
N(p) ?n ? dr e -ip .r f(r) yn(r) vgr-(
r) 2
3
This talk Application of a two-particle model of
Psto three situations of interest
1 Pore within a polarizable, dielectric
medium
2 Cylindrical geometries
3 Fluid-filled, cylindrical pores
4
Ground state Single particle hard sphere
Tao-Eldrup (TE) model
??-1 t?-1 D / Rc (1/2p) sin(2p (Rc -D? /
Rc)
Brandt et al, 1960 Tao, 1972 Eldrup et al, 1981.
Data typically fit with D 1.66 Å, t????0.5ns
Data from molecular solids (Jean, 1995)
Mixture of states Single
particle hard parallelpiped
Extended Tao-Eldrup (RTE) model
Itoh et al, 1999 Gidley et al, 1999 Gorowek et
al, 2002
Data from silicas and zeolites (Dull, 2001)
These are single particle-in-a-box (SPIB) models
5
We simulate Ps in materials with two-chain Path
Integral Monte Carlo (PIMC)
Beyond SPIB models
(cf. single-chain model Miller, Reese et al,
1996, 2002)
Ps wave packet
Ps chains
The Quantum density matrix r(b) exp( - b H) is
represented in the position basis ltr r(b) rgt
? ltr r(e) r1gt lt r1 r(e) r2gt ... ltrP-1
r(e) rgt d r1 rP-1 (e b/P) The solution
of the Bloch equation for Ps is instantiated by
two chains of beads which have become analogous
to two interacting, harmonic, ring polymers.
The location of each e bead is determined by
the likelihood of measuring e at this location
in the solid.
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
Application of a two-particle model of Ps to
1 Pore within a polarizable, dielectric medium
Polarizability?????? 36
?
Even a non-polar medium interacts electrically
with e Ps is polarized and attracted to surface
of dielectric
E
ko gt 1
Wave function and lifetime are a function of
dielectric constant, ko
15
Annihilation / Polarization model
16
Dielectric material polarizes Ps and alters
distribution of e within spherical void
ground state, Rc 10 au
ko 1
ko 15
17
In absence of polarizationLifetimes predicted
by two-particle model of Ps aredramatically
increased over SPIB predictions
18
Radial distribution function for e ground
state, Rc 20 au
19
Pickoff lifetime varies with Rc in a way which
is sensitive to ko
(ns)
20
Pickoff lifetime varies with ko in a way which
is sensitive to Rc
(ns)
21
Application of a two-particle model of Ps to
2 Cylindrical geometries
Many interesting materials contain void spaces
which are well-modelled as cylindrical pores
Bamford et al, 2001
SPIB and two-chain Ps lifetimes are functions of
pore radius and temperature
22
SPIB For ground state behavior, a scaling
relationship maps the Tao-Eldrup lifetime in a
sphere directly to lifetime in a cylinder
cylinder radius R
Sphere radius R
Sphere radius ?R
See poster by T. Cronin et al. for details
23
Ps Orbital in cylindrical pore Probablility
densityfor relative coordinate in terms of r, z,
and ?Rc 25 au
24
Ps Probablility densityfor e coordinate shows
that lifetime decreases with temperature
25
Orbital becomes anisotropic but is compressed
in axial and radial directions
R Q
26
Application of a two-particle model of Ps to
3 Fluid-filled, cylindrical pores
Cylindrical pores are good models for connected
void spaces which can adsorb fluid
Iannacchione et al, 1996
Fluid atoms and pore walls compete to annihilate
Ps
27
MMC simulation is performed at constant fluid
density and temperature
Argon-lepton potential
28
Snapshots from MMC simulation at constant
fluid density and temperature
before equilibration
in equilibrium
29
Radial distribution function for e Rc 16 au
, T 632K
At intermediate densities, Ar excludes volume and
Ps expands outward in pore compressed at higher
densities into bubble
30
Snapshots from MMC simulation at two densities
? 0.35
? 0.25
31
Pickoff rate with wall and with fluid atoms
as a function of fluid density Rc16 au , T
632 K
32
Ps orients preferentially in pore which is
cylindrical or spherical
33
Ps orients preferentially in a spherical geometry
ko does not strongly effect orientation
34
In conclusion
Two particle, PIMC calculations of Ps in pores
taking into account temperature dielectric
polarizability of the bulk solid elongated
(cylindrical) geometry of pores the presence of
fluid atoms yield lifetimes and information on
the structure of Ps. It is hoped that
encorporating these realistic features of
materials will allow these (fairly simple)
calculations to further refine our understanding
of results of PALS experiments.
35
Many thanks to ...
Colleagues Roy Pollock (LLNL), Terrence Reese
(Southern U) Students at Swarthmore Lisa
Larrimore, Robert McFarland, Peter Hastings,
Jillian Waldman Funding agencies Provosts
office of Swarthmore College Petrolium Research
fund of the ACS U.S. DOE The Organizing
Committee (Adriano de Lima,Chair) and
Participants of PPC-8