NANOCOMPOSITES,
LAYER-BY-LAYER
ASSEMBLY
Introduction
Advanced materials from inorganic nanoparticles (NPs) and other nanocolloids
such as single wall carbon nanotubes (SWNT) are currently one of the most dy-
namic areas of today’s science. They represent significant fundamental and com-
mercial interest with a wide range of applications including the next generation
optics, electronics, and sensors (1–6). Synthetic methods of colloidal chemistry
afford manipulation of their size, surface structure, and hence, their properties
(7). In optical, electrical, and magnetic devices, nanocolloids will be mostly used
as thin films. Currently, such films are typically made by spin coating, spraying,
or sometimes by simple painting of nanoparticle–matrix mixtures. The layer-by-
layer assembly (LBL) is one of the most promising new methods of thin film de-
position, which is often used for oppositely charged polyelectrolytes (PE) (8,9). It
has also been successfully applied to thin films of nanocolloids (10–33). One of the
major advantages of LBL is simplicity: the process requires neither sophisticated
hardware nor high purity of the components. At the same time under optimal con-
ditions, the method produces high quality of coatings with thickness controllable
at the nanometer level (26). This deposition technique is also quite universal: for
virtually any aqueous dispersion of NPs, one can find a matching polyelectrolyte
and deposition conditions yielding a steady film buildup (34). The lateral packing
of the NPs and SWNTs in individual adsorption layers can also be controlled by
different means producing densely packed coatings (15,27,34). The LBL coatings
are also highly homogeneous unlike the composite polymer/NP coatings obtained
by other means (35), where phase separation may occur (36). Last but not the
least, LBL affords combining NPs with other functional materials often used by
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this technique such as dyes, proteins, and DNAs, leading to a palette of multi-
functional nanostructured materials (37). In essence, LBL can be a convenient
method for processing NPs in thin films, which opens broad perspectives for this
technique, both in research and in industry. This article attempts to summarize
the current status of understanding of the LBL deposition of NPs, the structure
of produced films and the future applications for these materials.
Layer-By-Layer Assembly
Layer-by-layer assembly can be described as the sequential adsorption of posi-
tively and negatively charged species, say A and B, by dipping a substrate alterna-
tively into their solutions. Rinsing with water between adsorption steps removes
the excess of the previous solution and leaves a thin layer of charged species on
the surface, thereby preparing the surface for the next adsorption step. The dy-
namic development of LBL that has been seen recently was sparked mainly by
its great success with assembly of polyelectrolytes (9,30,38–40); However, simi-
lar ideas were previously used (41) for the assembly of colloids, for production of
semiconductor films (42,43), and for the assembly of NP/PE magnetic films (10).
The description of experimental details of the technique can be found in the orig-
inal publications of the respected authors (see also C
OLLOIDS
; P
OLYELECTROLYTES
;
L
ANGMUIR
-B
LODGETT
F
ILMS
).
From the analysis of the abundant literature on LBL, one can say that A
and B are preferentially chosen to be of relatively high molecular weight. The
experimental work on polymers with different chain lengths indicates that the
increase of the molecular mass of species promotes stable LBL growth (15,44–46),
which is related to the diverse nature of intermolecular interactions involved in
the process (see SWNT/Polyelectrolyte Composites). Although for relatively low
molecular weight species such as multicharged metal ions (47–51) and molecular
dyes (52–54), the LBL assembly was also reported, and their tendency to leach out
should be accentuated (55). Heavy mass and the multiple points of attachment of
A and B render the absorption sufficiently irreversible to allow for the deposition
of the next layer. Either A or B is almost always a PE, while the other LBL partner
can be a dispersion of NPs, clay sheets, proteins, dyes, vesicles, DNA, viruses or
other species. The omnipresence of PEs in LBL assemblies acquired popularity in
the 1990s is explained by their ability to cover irregularities owing to the rod-like
conformation of the charged macromolecules in aqueous solutions (9,56).
Ultrastrong Materials
The mass–strength ratio of materials is of exceptional importance for many dif-
ferent applications. The critical parts of different vehicles and crafts depend on
strength and toughness of the materials they are made of, while strict limitations
on the weight of the different components are placed by the modern air and space-
craft technology. SWNT presents significant potential as a basic material for space
applications. Exceptional mechanical properties of SWNT (57–62) have prompted
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
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intensive studies of SWNT composites. These qualities can also be used in a va-
riety of other technologies from automotive to military and medical. However,
the present composites have shown only a moderate strength enhancement when
compared to other hybrid materials (53–65). Although substantial advances have
been made (66), mechanical characteristics of SWNT-doped polymers are notice-
ably below their highly anticipated potential. Pristine SWNTs are well known for
poor solubilization, which leads to phase segregation of composites. Severe struc-
tural inhomogeneities result in the premature failure of the hybrid SWNT/polymer
materials. Connectivity with and uniform distribution within the matrix are es-
sential structural requirements for strong SWNT composites (67–69). A new pro-
cessing approach based on sequential layering of chemically-modified nanotubes
and polyelectrolytes can greatly diminish the phase segregation and render SWNT
composites highly homogeneous. Combined with chemical cross-linking, this pro-
cessing leads to drastically improved mechanical properties. Tensile strength of
the composites is several times higher than that of SWNT composites made via
mixing; it approaches values seen for hard ceramics. The universality of the lay-
ering approach applicable to a wide range of functional materials makes possible
successful incorporation of SWNT into a variety of composites imparting to them
required mechanical properties.
The thin film membranes that are obtained as a result of the layer-by-layer
process can be used as an intermediate or as a component of ultrastrong laminates.
At the same time, the prepared membranes can also be utilized in the as-prepared
form for space and biomedical technologies because they combine the strength and
multiple functionality of the SWNT membranes.
SWNT composites are typically prepared by blending, in situ polymerization,
and extrusion. After extensive surface modification, such as grafting or polymer
wrapping (68–70), the phase segregation from a macromolecular matrix is smaller
than for pristine SWNT, but still remains high owing to the high affinity of SWNTs
to each other. Vastly different molecular mobilities of both components also con-
tribute to widespread phase separation. Very intense research on appropriate
surface modification of SWNT is currently under way in many groups around the
world. Nevertheless, most common loadings of nanotubes in the polymer matrix
are within the 1–15 wt% range, whereas more than 50% of the SWNT content is
needed for materials with special mechanical performance without compromis-
ing the homogeneity of the composite at the nanometer level. This high loading
of the nanotubes is particularly important when both electrical and mechanical
qualities of the nanotubes are going to be utilized.
The phase segregation between dissimilar materials can be circumvented by
applying a layer-by-layer assembly (LBL) (71). The immobilization of the macro-
molecular compounds and strong interdigitation of the nanometer-thick film al-
lows for the close-to-perfect molecular blending of the components (72,73).
SWNT/Polyelectrolyte Composites.
The SWNT/polyelectrolyte com-
posites produced in this study were assembled onto a solid support via alter-
nate dipping of a solid substrate (glass slides, Si wafers) into dispersions of
SWNT and polyelectrolyte solutions (74–76). The individual assembly steps, ie
adsorption of SWNT and polyelectrolyte monolayers, were interlaced by rinsing
steps to remove the excess of assembling materials. When the LBL procedure
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
473
was complete, the multilayer films were lifted off the substrate to obtain uni-
form free-standing membranes, which can be handled as regular composites
(77). Such films make possible straightforward testing of their mechanical
properties.
SWNT were produced by laser ablation and subsequently purified via acid
treatment. Single-wall nanotubes were manufactured by laser vaporization of
carbon rods doped with Co, Ni and FeS in an atmosphere of Ar:H
2
. Standard
SWNT products made by HiPCO and other methods contain significant amount
of sooth, graphite flakes, and remnants of the catalyst, which need to be removed
prior to the assembly. The quality of the dispersion directly affects the mechanical
performance of the resulting composite.
A suspension of SWNT raw material was refluxed in 65% HNO
3
and sub-
sequently purified by centrifugation. Supplemented by sonication, this treatment
results in the partial oxidation of ca 5% of the total number of carbon atoms both
in caps and walls of SWNT (78). A similar type of dispersion can also be made
following other recipes such as polymer wrapping the nanotubes, and chemical
derivatization. Optimization of the aqueous nanotube dispersions should be con-
sidered as one of the most critical direction of the optimization of the carbon
nanotube composites and speed and quality of their processing in the compos-
ites. Dispersions made by other methods are expected to be also applicable for
the preparation of LBL films. The strength and other mechanical properties will
depend though on energy of attractive interactions between the coating agent and
the matrix as well as between SWNT and the coating agent.
In slightly oxidized nanotubes, the presence of carboxylic acid groups affords
the preparation of metastable SWNT dispersions after 1 min sonication in deion-
ized water without any additional surfactant. Thus prepared negatively charged
SWNT with zetapotential of
−0.08 V can be layer-by-layer assembled with posi-
tively charged polyelectrolyte, such as branched poly(ethyleneimine), M
w
= 70,000
(PEI) (Fig. 1). Since the overall negative charge of the SWNT used here was fairly
small, after every 5th deposition cycle, a layer of SWNT was replaced with a layer
of poly(acrylic acid), M
w
= 450,000 (PAA) (Fig. 1). These additional layers improve
Fig. 1.
Common polyelectrolytes, used for LBL process.
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
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the linearity of the deposition process and present a convenient chemical anchor
for subsequent chemical modification. For the same reasons, a single PEI/PAA
bilayer was deposited on a bare glass or Si substrate prior to the SWNT assembly.
The assembly conditions of the entire procedure (pH, ionic strength, concentra-
tions, etc) were optimized so that the dipping cycles can be repeated as many times
as needed with linear growth of the multilayers (Fig. 2a). This enables the prepa-
ration of films with any desirable thickness and architecture tailored to different
applications. The ionic conditions of LBL assembly were the following: 1% solution
of PEI at pH 8.5; 1% PAA at pH 6 (pH 3 for wafer coating); SWNT at pH 6.8. All
solutions were made in 18 M
deionized (DI) water without addition of any extra
salt or other low molecular weigh electrolyte. DI water was also used for rinsing at
pH 8.5 adjusted by NaOH. Wafers/glass slides were cleaned in piranha solution,
rinsed with DI water, sonicated for 15 min and again thoroughly rinsed with DI
water. After that, they were coated with a precursor layer: PEI (10 min)
+ PAA
(15 min, pH 3), followed by the deposition of (PEI/SWNT)
5
. The layer sequence
of (PEI/PAA)(PEI/SWNT)
5
was repeated until the desirable thickness is obtained.
Exposure times of 10 and 60 min was used for polylectrolytes and SWNT baths,
respectively.
Multilayer stacks with a cumulative structure of ((PEI/PAA)(PEI/SWNT)
5
)
6
and ((PEI/PAA)(PEI/SWNT)
5
)
8
containing 30 and 40 (PEI/SWNT) bilayers, re-
spectively, were typically used in this study.
Currently, other methods are being investigated for dispersing SWNT in wa-
ter to avoid excessive damage to the SWNT wall such as wrapping of the nanotubes
with copolymers, which can equally well work on the SWNT and multiwall carbon
nanotubes (MWNT). For some applications, MWNTs can be a preferred materials
due to lower cost.
Similarly to other polyelectrolyte LBL systems (71), a submonolayer of
SWNT is deposited in each deposition cycle. The final morphology of the mul-
tilayers can be described as a mixture of individual carbon nanotubes and their
4–9 nm bundles intricately interwoven together in a fine fabric (Fig. 2c) (74,75).
Two important structural characteristics should be pointed out. SWNT uniformly
cover the entire surface of the substrate without any evidence of phase separa-
tion. Also, the presence of oxidized flat graphite sheets and other forms of carbon
colloids in the experiments was very small. Both these factors contributed to the
mechanical properties of the composites. The quality of the nanotube material was
also assessed by Raman spectroscopy. (Raman measurements were performed in
a backscattering configuration with a 50 mW of 514.5 nm laser light was inci-
dent on the samples.) The characteristic Raman peaks for SWNTs, eg the radial
breathing mode at
∼182 cm
− 1
and the tangential C–C stretching modes located at
∼1560 cm
− 1
(G1 mode) and
∼1583 cm
− 1
(G2 mode), were very sharp and narrow
indicating the high uniformity of the SWNT and low level of impurities present in
the films. A barely visible peak at
∼1340 cm
− 1
(D mode) revealed the presence of
residual amounts of disordered carbon structures. Using the correlation between
the frequency of the radial breathing mode,
ν, and the SWNT diameter, d, ex-
pressed as d
= 223.75/ν (79), a value of d = 1.2 nm is obtained, which is in a good
agreement with the SWNT diameters obtained from AFM images of many indi-
vidual nanotubes. From these images, the length of the nanotubes was estimated
to be 2–7
µm.
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
475
Fig. 2.
Structural characterization of SWNT multilayers. (a) Sequential UV–vis spectra of
a glass substrate in the course of the LBL deposition of SWNT. The spectra were taken for a
total number of (PEI/SWNT) bilayers indicated in the graph. (b) Raman scattering spectra
of SWNT dispersion (1), LBL film on a glass substrate (2) and free-standing film (3). (c) Tap-
ping mode AFM image (DI, multimode IIIA) of a Si wafer bearing (PEI/PAA)(PEI/SWNT)
5
.
See Refs. 74,75.
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
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PEI was utilized as the LBL partner of SWNT because of terminal
NH
2
and backbone
NH
groups in the main chain and branches suitable for the
subsequent chemical modification of the composite (80). The PEI chains can be
cross-linked (1) with each other and (2) with carboxyl groups on SWNT and PAA.
Chemical stitching increases the connectivity of the polyelectrolyte matrix with
SWNT, and therefore, load transfer in the composite (80). The combination of
both modification pathways was used. SWNT/PEI/PAA composite was heated to
130
◦
C after the deposition of each layer. According to the study by Sullivan and
co-workers (81), this treatment should result in amide bonds between a variety
of protonated and nonprotonated functional groups of PEI, PAA, and SWNT com-
plementing the intrinsic ionic cross-linking of the LBL films (81). Subsequently,
the film was exposed to glutaraldehyde at room temperature. This treatment is
well known to produce covalent bonds with primary amine groups present in the
polyelectrolyte. Samples were cross-linked in 0.5% glutardialdehyde solution in
phosphonate buffer (0.054 M Na
2
HPO
4
, 0.013 M NaH
2
PO
4
, pH 7.4) for 1 h at room
temperature. To remove unreacted glutaraldidehyde, the film was rinsed with tap
water for 3
× 10 min and then with DI water the same number of times. This
reaction produces a tight network of polymeric chains and nanotubes connected
by dialdehyde linkages. It was found that if only 1% of all carbon atoms of SWNT
are chemically bonded to the polymer matrix, such as cross-linking drastically
increases the shear between them by an order of magnitude (80). Therefore, a 5%
density of
COOH groups on the SWNT surface cited above should be sufficient
to obtain good connectivity with the polyelectrolyte matrix. Note these groups are
not completely utilized at the moment, because of the relatively low temperature
of amide bond cross-linking step.
Mechanical Properties and Testing
The mechanical properties of the LBL-assembled SWNT thin films were studied
in their free-standing form prepared by the chemical delamination from the sub-
strate (77). SWNT multilayers were separated from the silicon wafers by immer-
sion into 0.5% aqueous HF for 3 min. The Raman scattering spectrum of the sepa-
rated film is almost identical to that of the supported film and original nanotubes
(Fig. 2b), demonstrating that the structure of SWNT remains mostly unaltered
during the cross-linking and delamination. The breathing mode frequency shifts
from 185 cm
− 1
in the assembled film to 182 cm
− 1
in the cross-linked self-standing
films indicating a small expansion of the tube diameters.
The delaminated thin films (Fig. 3a), can be easily handled in a variety of
ways. They can be made of any desirable size or shape determined only by the
dimensions of the substrate. The films that we routinely prepare in this study
were ca 1
× 3 cm. Assemblies with a structure of ((PEI/PAA)(PEI/SWNT)
5
)
6
and
((PEI/PAA)(PEI/SWNT)
5
)
8
displayed an SWNT content of 50
± 5 wt% as calculated
from carbon and nitrogen EDAX peak integrals. Previously reported composites
made with modified SWNT revealed strong inhomogeneities even at SWNT load-
ings as low as 6–8% (64,65). The cross-sectional image of the free-standing film
(Figs. 4a and 4b) clearly demonstrates the absence of micrometer-scale inhomo-
geneities although the occasional inclusion of a round 30–60 nm particles can be
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
477
Fig. 3.
Electron microscopy of the rupture region in SWNT multilayers. (a) SEM image
of the surface and broken edges of ((PEI/PAA)(PEI/SWNT)
5
)
8
. (b) and (c) TEM images of
ruptured areas of the freestanding films. The arrows indicate the likely stubs of the broken
nanotubes bundles. They were identified as such because (1) the diameter of both of them is
equal to theat of the actual SWNT bundle bridging the gap and (2) their mutual positioning
presents a virtually perfect match with the expected location of the ends of a bundle broken
during gap opening.
seen (possibly dust). The slight variations in the gray scale contrast between dif-
ferent strata show the actual variations in SWNT distribution within the sample.
They originate from small deviations in SWNT adsorption conditions, such as dis-
persion concentration and pH, during the buildup procedure. In SEM microscopy
(Fig. 3a), the surface of the sample also appears smooth and continuous. Typically,
the separation of single/multiwall carbon nanotubes and their bundles in mixed
polymer composites can be observed as whiskers clearly visible in TEM and SEM
images (60,82). The TEM examination of the initial stages of rupturing showed
that virtually no fiber pullout occurs in the LBL multilayers (Fig. 3b). This can
be contrasted by extensive nanotube pullout reported before by several groups
(60,82). For many TEM images obtained in different areas of the self-standing
films, we were able to observe only one SWNT bundle bridging the break region
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
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Fig. 4.
TEM examination of the homogeneity of the SWNT LBL film. Survey (a) and
closeup (b) TEM images of SWNT film cross sections. The top and botom sides of the
film are slightly different in roughness: the one that was adjacent to the flat substrate is
smoother than the “growth” surface of the film. See Refs. 74,75.
(Fig. 3c). The same image also shows two broken carbon fiber stubs imbedded in
the walls of the crack (marked by arrows in Fig. 3c). In total, the microscopy results
indicate efficient load transfer in the LBL composite. Currently, similar films are
prepared from multiwall carbon nanotubes utilizing polymer wrapping (Fig. 5).
The mechanical properties of the layered composites were tested on a
custom-made thin film tensile strength tester (McAllister Inc.) recording the dis-
placement and applied force by using pieces cut from ((PEI/PAA)(PEI/SWNT)
5
)
6
and ((PEI/PAA)(PEI/SWNT)
5
)
8
free-standing films. The tester was calibrated
on similar pieces made from cellulose acetate membranes and Nylon threads.
((PEI/PAA)(PEI/SWNT)
5
)
6
and ((PEI/PAA)(PEI/SWNT)
5
)
8
samples had an aver-
age TEM thickness of 0.75 and 1.0
µm, respectively. Their typical stress (σ) vs
strain (
ε) curves differed quite markedly from stretching curves seen previously
Fig. 5.
Optical photograph of the freestanding LBL films made from multiwall carbon
nanotubes.
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
479
Fig. 6.
Typical tensile strength curves of the SWNT LBL films. Stress–strain dependence
for (a) ((PEI/PAA)(PEI/SWNT)
5
)
8
and (b) a similar free-standing multilayer film made
solely from polyelectrolytes. The dependence of the mechanical properties of the cross-
linked LBL composites on humidity was tested in the range of relative humidity of 30–
100%, T
= 298
◦
C, and was found to be negligible See Refs. 74,75.
for SWNT composites (66) and for LBL films made solely from polyelectrolytes,
(PEI/PAA)
40
, obtained by the same assembly procedure (Fig. 6b). They displayed
a characteristic wave-like pattern, gradual increase of d
σ/d ε derivative, and the
complete absence of the plateau region for high strains corresponding to plastic
deformations (Fig. 6a). The latter correlates well with the enhanced connectivity of
SWNT with the polymer matrix (Fig. 3). Other mentioned stretching features in-
dicate the reorganization of the layered composite under stress. A process similar
to the sequential breakage of cross-linked parts of coiled molecules (see AFM im-
age in Figure 2) observed in natural nanocomposites, such as seashells and bones
(83,84), is likely to be responsible for the wave-like pattern and the increase of the
stretching curve slope.
Considering the complexity of the deformation process, the assessment
of elastic and inelastic behavior in each part of the curve will be done upon
detailed microscopy investigation. Meanwhile, the values of d
σ/d ε exceeding
50 GPa should be noted.
The comparison with stretching curves for polyelectrolytes (Fig. 6b) shows
that the incorporation of nanotubes in the LBL structure resulted in the trans-
fer of the SWNT strength to the entire assembly. The stretching curves of the
SWNT multilayers display a clear break point. The ultimate tensile strength, T,
was found to be 220
± 40 MPa with some readings being as high as 325 MPa.
This is several times to an order of magnitude greater than the tensile strength of
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NANOCOMPOSITES LAYER-BY-LAYER ASSEMBLY
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strong industrial plastics with T
= 20–66 MPa (85). It is also substantially higher
than the tensile strength of carbon fiber composites made by mixing: polypropy-
lene filled with 50 vol% Carbon Fibers (qv) has T
= 53 MPa (86). A recent study
on SWNT/poly(vinyl alcohol) ribbons with axially aligned nanotubes reported a
tensile strength of 150 MPa (66). The T values obtained for SWNT LBL films
are, in fact, close to those of ultrahard ceramics and cermets such as tungsten
monocarbide, T
= 340 MPa, silicon monocarbide, T = 300 MPa, and tantalum
monocarbide, T
= 290 MPa (85). Such strength and failure strain greater than in
cermets (ca
>1% in SWNT LBL vs. 0.2–0.6% in carbides) displayed by an organic
composite is quite remarkable.
The tensile strength of single carbon nanotubes was experimentally deter-
mined to be between 13 and 50 GPa (82,87). The lower values obtained for the
SWNT multilayers should be mainly attributed to the contribution of polyelec-
trolytes and some uncertainty in the actual cross-sectional area at the break point
and a degree of cross-linking. The mixing law predicts that a polyelectrolyte ma-
trix with T
= 9 MPa makes a negligible contribution to the strength of the com-
posite while taking about 50% of its volume fraction (SWNT is d
= 1.14 g/cm
3
).
Since the density of the polyelectrolytes used for the preparation of the multi-
laters, ie PDDA d
= 1.04 g/cm
3
, PAA d
= 1.14 g/cm
3
is almost the same, the
volume fraction of SWNT in the composite can be considered to be equal to the
mass fraction). Additionally, the decrease of the mechanical strength of the nan-
otubes in the process of ionic functionalization (estimate 15%) (88) should also
be considered as a factor affecting the strength of these composites. These issues
are pointed out as means of further optimization of the multilayers. Tuning of
their molecular structure and composition should lead to vast improvement of
their mechanical properties that could possibly approach those of pristine carbon
nanotubes.
It is also interesting to compare the T values for SWNT composite films
to those obtained for other LBL films made with other inorganic compo-
nents such as montmorillonite platelets, M, and nanoparticles, NP, for instance
8–10 nm magnetite nanoparticles. The free-standing films (PDDA/NP)
40
and
(PDDA/NP/PDDA/M)
40
made according to Reference (77) revealed T equal to 40
and 72 MPa, respectively. In conjunction with the tensile strength data (see above),
it can be concluded that inorganic or SWNT components act as a molecular armor
in the layered composites significantly reinforcing them. The molecular organiza-
tion of the material made possible the transfer of a part of their strength to the
entire assembly.
The high structural homogeneity and interconnectivity of the structural com-
ponents of the LBL films combined with high SWNT loading leads to significant
increase of the strength of SWNT composites, being somewhat weaker than some
other organic and carbon fiber materials but at the same time being far beyond
their potential as ultrastrong composites. The described technique minimizes the
structural defects originating from phase segregation and opens a possibility for
the molecular design of layered hybrid structural materials from different poly-
mers and other nanoscale building blocks. The prepared free-standing membranes
can serve as a unique component for a variety of technologies. One of the great
advantages of it in respect to other technologies is the ability to prepare ultrathin,
ultrastrong membranes with minimal heterogeneity.
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N
ICHOLAS
A. K
OTOV
A
RIF
A. M
AMEDOV
University of Michigan
D
IRK
M. G
ULDI
University of Notre Dame
M
AURIZIO
P
RATO
Universit `a di Trieste
J
AMES
W
ICKSTED
Oklahoma State University
A
NDREAS
H
IRSCH
Universit ¨at Erlangen-N ¨
urnberg