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SUPPORTING INFORMATION
The general fabrication process is illustrated in Figure 1
.
Si wire growth.
Si wires were
grown from
Si(111)
substrate
that had a
low miscut angle
of
0.1°. The Si was covered with
100 nm of
thermal oxide. 3
μ
m-diameter
Cu particles
were deposited at a
7
μ
m pitch using photolithography. Vapor
-liquid
-solid (VLS)
catalyzed
growth of Si micro
wires was performed
in a
chemical vapor deposition (CVD)
reactor
with H
2
and SiCl
4
as
the
vapor
-phase reactant
s [12].
For this work, t
he Si
micro
wires were grown to a height of
25 μm
-
35
μm.
Surface chemical functionalization process.
Chemicals were used as received, and
H
2
O was obtained from a Barnstead nanopure
system (18.2 M
cm resistivity).
A. Cu removal
Following
growth, the wire arrays were etched in buffered HF (Transene company) for
20-
30 s
, and then repeatedly submerged in fresh H
2
O. Arrays were then heated to 65 °C
in a 5:1:1 solution of H
2
O:HCl:H
2
O
2
(RCA
-II) for 25 min. The arrays were then rinsed
with copious amounts of water, and
were dried under a
stream of
N
2
.
B. H
-termination
For hydrogen functionalization, w
ire arrays were submerged in buffered HF for 30 s to
remove silicon di
oxide. The b
uffered HF solution was rinsed from the arrays by repeated
submersion in f
resh H
2
O, followed by
drying
under a stream of N
2
.
C.
Cl
-termination
Freshly etched Si wire arrays were immediately introduced to a N
2
purged glovebox
that
contained < 10 ppm O
2
. Wire arrays were submerged in a saturated phosphorous(V)
chloride (PCl
5
, Al
fa Aesar, 99.998% metal basis) in solution chlorobenzene (anhydrous,
Sigma Aldrich, 98%) at 90 °C for 45 min. The solution was allowed to cool to near room
temperature. The wire array
s were then
removed from solution followed by a rinse
with
tetrahydrofu
ran
THF (Anhydrous, Sigma Aldrich).
D. Methyl
- and butenyl
- surface functionalization
Cl-terminated Si micro
wire arrays were alkylated at 60 °C for > 3 h in a 0.5 M solution in
THF of either CH
3
MgCl (Sigma Aldrich, diluted from 3.0 M in THF) or 3
-butenylMgCl
(Sigma Aldrich, 0.5 M in THF). Mixed CH
3
/butenyl
-terminated wire arrays were
prepared by submersion of Cl
-terminated wires for 10 min in 0.5 M 3-
butenylMgCl in
THF at 60 °C. The mixed Cl/butenyl
-terminated wire arrays were rinsed with copi
ous
amounts of THF,
and were then submerged in 0.5 M of CH
3
MgCl for > 3 h at 60 °C.
After completion of both reactions, the Si samples were rinsed thoroughly with THF and
removed from the N
2
(g)-
purged glovebox. Samples were cleaned of residual Mg salts b
y
repeated submersion sequentially in
THF, methanol, and water. Finally, the arrays were
dried under a stream of N
2
(g).
Si-PDMS matrix composite sample preparation.
A 10:1 ratio mix of PDMS base and
curing agent (Sylgard 184, Dow Corning) was spin-
cast i
nto
a Si wire array
that had been
grown on Si wafer. The PDMS was then
cured at 120 °C for 2 hours. The w
ire array was
then peeled off from the substrate using a razor blade and bonded onto
a clean Si wafer
using a cyanoacrylate adhesive.
Carving of dog-
bone shapes for tensile gripping
.
A
Focused Ion Beam (FIB) with a
Ga+ ion source was used to mill out the T
-shaped top of the wire (see Figure 1 step 6)
.
The pull
-out test was then performed by
using
a diamond grip.
Uniaxial Tensile
Pullout Experiment
s.
T
he pullout tests were performed using an
in-
situ nanomechanical tester, SEMentor, at a constant displacement rate of 50 nm/s. The
resulting load vs. displacement data were used to calculate the
interfacial shear stress by
dividing by the surface area of th
e wires.
Calculating Interfacial Strength.
The s
hear lag model
30
was used to calculate the shear force along the sliding interface
between the fiber and the matrix.
Figure S1 presents a schematic that illustrates
the
parameter
s that were utilized in
this derivation.
First, the
shear force in the matrix was equated with the shear force at the interface using
the relationships
and
,
where
τ
e
is the shear stress at the
interface.
Figure S1.
Schematic illustrating components of shear lag model
Ratio of shear stress
τ to shear strain
γ
is the shear modulus, G=E/2(1+ν),
giving
the
expression for the shear stress at the interface
Solving for the displacement at the inter
face, w:
and
resulting in the following expression for the equivalent shear stress:
The
tensile force in the fiber was then equated to
the shear force at the interface
Differentiating and
substituting
for
and
yields
This differential equation can be expressed using
a dimensionless parameter
,
n:
The s
olution, with A and B determined by the boundary conditions
, results in:
For a single fibe
r pullout test, the following boundary conditions
are applicable: at x=0,
σ
f
max
,
and at x=L, σ
f
=0
The
tensile strain in the ma
trix away from the interface is assumed to be
negligible, ε
m
=0
This assumption gives the expression for the fiber tensile stress
and shear stress at the
interface
The s
hear stress at the interface is max
imized at x=0.
De
-bonding
occurs when this
interfacial stress exceeds a given interfacial shear stress for the system
:
The resulting
expression for
the strain energy stored in the fiber and the matrix
is:
Calculating the Work of Fracture.
Follow
ing the approach utilized by Piggott in “Load Bearing Fiber Composites,”
debonding
begins when the rate of elastic energy released by the Si
-PDMS composite
(dU
c
/dL) is equal to the rate of surface energy increase due to de
-bonding (dU
s
/dL) plus
the rate of elastic energy stored in the debonded wire (dU
db
/dL)
The rate of surface energ
y increased (dU
s
/dL) is
The elastic energy stored in the de-
bonded wire
s is (dU
db
/dL)
Simplifying and performing the integration yields the following expression:
The elastic energy of the Si
-PDMS composite (U
c
) is the sum of elastic energy stored in
the fiber (U
f
) and in the matrix (U
m
)
with the corresponding rate of
Substituting the above exercised into the first equation and rearranging gives the
expression for σ
f
at de-
bonding
, and the
corresponding interfacial shear stress at
debonding τ
i
and
The
work of fracture from interfacial shear stress at de
-bonding
is then given by:
XPS acquisition and analysis
X-ray photoelectron spectroscopy (XPS) data were collected using a Kratos
AXIS
Ultra DLD with a magnetic immersion lens with a spherical mirror and concentric
hemispherical analyzers with a delay
-line detector (DLD). An Al ka (1.486 KeV)
monochromatic X
-ray excitation source was used. Ejected electrons were collected at an
angle of 90° from horizontal. The sample chamber was maintained at < 5 ×
10
-9
Torr.
High
-resolution XPS data were analyzed using CasaXPS v2..3.15.
Survey scans from 0 to 1200 eV were performed to identify the elements that
were present on the surface. M
g was not detected on any sample after workup. Si2p
(104.5-
97.5 eV) and C1s (292-
282 eV) high
-resolution XPS data were taken.
A simple substrate overlayer model was used here to calculate the
thickness of the overlayer,
d
ov
I
ov
and
I
si
are the signal i
ntensity of the C
si
(284 eV) and Si
bulk
2p(3/2) XPS signals
respectively.
SF
ov
and
SF
Si
are the modified sensitivity factors for the Si 2p(3/2) and C
1s signals.
ρ
ov
(0.
033 mol cm
-3
based on hydrocarbon) and
ρ
Si
(0.083 mol cm
-3
based on
Si crystal structure) are the atomic density of C in the overlayer and in the Si crystal.
λ
is
the mean free path of electrons, determined empirically as 3.5 nm for Si 2p
electrons,
{haber; laibinis 1991; tufts 1992} and
θ
is the angle
from the h
orizontal to the
detector (
90°).
Modified sensitivity factors for the specific instrument were used as determined by
Kratos.
In this case,
SF
Si
= 0.
174 for the 2p
(3/2)
electrons
and
SF
C
= 0.278.
d
ov
=
0.45 for the CH
3
-Si(111) surface.
d
o
for a methyl
group is 0.468 nm, and thus gives
θ
CH3
-Si
= 0.96 ± 0.05 (based on
Γ
Si(111)
= 7.83× 10
14
cm
-2
).
Similarly, the coverage of CH
3
-, mixed butenyl/CH
3
-, butenyl
-, and octadecyl
-Si(011)
were determined.
The fractional coverage of butenyl groups on the mixed butenyl/CH
3
-Si(011)
were estimated based on the kinetics of the 3
-butenylMgCl reaction with Cl-
Si(011).
Figure X1.
Figure S2
.
Coverage of butenyl groups on a Si(011) surface vs time of reaction,
t
rxn
.
Coverage was based on the density of surface atoms
, where
θ
C-Si(111)
=
Γ
C-Si
/
Γ
Si(111)
, black
dots, and
θ
C-Si(011)
=
Γ
C-Si
/
Γ
Si(011)
surface, blue diamonds.
Table X2.
Summary of surface coverage.
Sample
θ
C-Si(011)
θ
C-Si(111)
CH
3
-
Si(111)
-
0.94 ± 0.05
CH
3
-
Si(011)
0.69 ± 0.05
0.85 ± 0.05
Mix butenyl/CH
3
0.51 ± 0.05
0.62 ± 0.05
octadecyl
0.28 ± 0.05
0.34 ± 0.07