Geckeler K.E., Nishide H. (Eds.) Advanced Nanomaterials

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2.3 Solution Properties 75

tively. Other than a large size difference, a nanoﬁ ber bears remarkable structural

resemblance to PHIC. Thus, block copolymer nanoﬁ bers can be viewed as a mac-

roscopic counterpart of a polymer chain or a “ suprapolymer ” chain or “ giant ”

polymer chain [34] . In this subsection, preliminary results showing the similarities

and dissimilarities between the solution properties of polymer chains and diblock

nanoﬁ bers will be reviewed.

To study the dilute solution properties of nanoﬁ bers and polymer chains, the

ﬁ bers should be made sufﬁ ciently short, so that they remain dispersed in the

solvent for a long, or even an inﬁ nitely long, period of time. The use of relatively

short nanoﬁ bers also ensured their characterization by classic techniques, such as

light scattering (LS) and viscometry. While we have studied nanoﬁ bers prepared

from several block copolymer families, for clarity, the discussion will be restricted

to PS - PI nanoﬁ bers obtained by cross - linking cylindrical micelles of PS

130

- PI

370

formed in N , N - dimethyl acetamide [24] . The preparation of such ﬁ bers has been

discussed previously and the right - hand panel of Figure 2.5 shows a TEM image

of the nanoﬁ bers thus prepared in THE after aspiration onto a carbon - coated

copper grid. As the magniﬁ cation was known for such images, we were able to

measure manually the lengths of more than 500 ﬁ bers for this sample. The data

from such measurements allowed us to construct the length distribution function

of this sample denoted as fraction 1 or F1 in Figure 2.11 . From the length distribu-

tion function, we obtained the weight - and number - average lengths and L

and

. The L

and L

/ L

values are 3490 nm and 1.35 for this sample.

While ultracentrifugation [34] or density gradient centrifugation could have been

used, in principle, to separate the ﬁ bers into fractions of different lengths, we

obtained nanoﬁ ber fractions with shorter lengths by breaking up the longer

nanoﬁ bers by ultrasonication [26] . By adjusting the ultrasonication time, we pro-

duced ﬁ bers of different lengths. Also shown in Figure 2.11 are the length distri-

bution functions for samples denoted as F3 and F5, which were ultrasonicated for

4 and 20 h, respectively. As ultrasonication time increased, the distribution shifted

to shorter lengths.

These ﬁ ber fractions were sufﬁ ciently short and allowed us to determine their

weight - average molar, M

, by light scattering. Figure 2.12 shows a Zimm plot

Figure 2.10 Structural comparison between a PS - PCEMA

nanoﬁ ber (left) and a PHIC chain (right) at different

magniﬁ cations.

76 2 Block Copolymer Nanoﬁ bers and Nanotubes

Figure 2.12 Zimm plot for the light scattering

data of F3 in the scattering angle range

of 12 to 30 ° . The solid circles represent the

experimental data. The hollow circles

represent the extrapolated Kc / Δ R

→ 0

data.

(a) Linear extrapolation of data to zero

concentration at the highest and lowest

scattering angles of 30 and 12 ° is illustrated.

(b) The result of curve ﬁ tting of the Kc / Δ R

→ 0

data using Equation (2.1) .

Figure 2.11 Plot of ﬁ ber population density P (L) versus length

L for PS

130

- PI

370

nanoﬁ ber fractions 1 (

ⵧ

), 3 (

䊉

) and 5 (

䊊

)

generated from TEM image analysis.

2.3 Solution Properties 77

for the light scattering data for sample F3 in the scattering angle, θ , range of 12

to 30 ° .

The data quality appears high. Multiple runs of the same sample indicated that

the data precision was high.

For the large - sized ﬁ bers, the Kc / Δ R

data varied with sin

( θ /2) or the square of

the scattering wave vector q non - linearly, despite the low angles used. We ﬁ tted

the data using Equation (2.1) :

qR kqR Ac

()

−

[]

113 2

22 44

(2.1)

and obtained M

, the radii of gyration R

and the second Virial coefﬁ cient A

for

the different fractions. Figure 2.13 plots the resultant M

, versus L

, where the

values for L

were obtained from TEM length distribution functions P ( L ). The

linear increase in M

with L

suggests the validity of the M

values determined.

The validity of the M

value for F3 was further conﬁ rmed recently by Professor

Chi Wu ’ s group at the Chinese University of Hong Kong, who performed a light

scattering analysis of a nanoﬁ ber sample down to θ = 7 ° . At such low angles, the

kq R

term in Equation (2.1) was not required for curve ﬁ tting and data analysis

by the Zirnm method should yield accurate M

and R

values.

After nanoﬁ ber characterization, we then proceeded to check the dilute solution

viscosity properties. Our experiments indicated that the nanoﬁ ber solutions were

analogous to polymer solutions and were shear thinning, i.e., the viscosity of a

sample decreased with increasing shear rate. This occurred for the alignment

of the nanoﬁ bers along the shearing direction above a shear rate γ of ≈ 0.1 s

− 1

[35] . While both nanoﬁ ber and polymer solutions are shear thinning, the ﬁ elds

required for shear thinning are dramatically different. Polymers of ordinary molar

mass, e.g. < 10

g mol

−

, would experience shear thinning only if γ 10

− 4

− 1

[36] .

Figure 2.13 Increase in LS M

with TEM L

for PS

130

- PI

370

nanoﬁ ber fractions.

78 2 Block Copolymer Nanoﬁ bers and Nanotubes

The huge difference should be a direct consequence of the drastically different

sizes between the two.

To minimize the shear - thinning effect, we measured the viscosities of dilute

solutions of the nanoﬁ ber fractions in THF using a laboratory - built rotating cyl-

inder viscometer at γ = 0.082 s

−

[37] . Figure 2.14 shows the ( η

− 1)/ c data plotted

against nanoﬁ ber concentrations c , where η

, the relative viscosity, is deﬁ ned as

the ratio between the viscosities of the nanoﬁ ber solution and solvent THF. The

solid lines represent the best ﬁ t to the experimental data by Equation (2.2) :

ηηη

−

()

[]

ckc

(2.2)

where [ η ] is the intrinsic viscosity and k

is the Huggins coefﬁ cient. The linear

dependence between ( η

− 1)/ c and c is in striking agreement with the behavior

of polymer solutions. Even more interesting, k

took values mostly between 0.20

and 0.60 in agreement with those found for polymers [36] .

We further treated the [ η ] data with the Yamakawa – Fujii – Yoshizaki (YFY)

theory, originally developed for wormlike chains [38, 39] . According to Bohdanecky

[40] , the YFY theory could be cast in a much simpler form, Equation (2.3) :

MABM

[]

()

(2.3)

for chains with a wide range of reduced chain lengths. In Equation (2.3) , A and B

are ﬁ tting parameters that are related to the persistence length l

and the hydro-

dynamic diameter d

of the chains, respectively. Figure 2.15 shows the data that

we obtained for the PS

130

- PI

370

nanoﬁ bers in THF plotted following Equation (2.3) .

From the intercept A and slope B of the straight line, we calculated l

and d

for

the nanoﬁ bers to be (1040 ± 150) and (69 ± 18) nm, respectively.

Figure 2.14 From top to bottom, plot of ( η

− 1)/ c versus c

for PS

130

- PI

370

nanoﬁ ber fractions 2, 3, 4 and 6 in THF. All the

data were obtained using the viscometer at a shear rate of

0.082 s

− 1

with the exception of those denoted by ( Δ ), which

were obtained at a shear rate of 0.047 s

− 1

2.3 Solution Properties 79

This procedure was repeated for the nanoﬁ bers in different solvents. Table 2.1

summarizes the l

and d

values that we determined in three different solvents for

the PS

130

- PI

370

nanoﬁ bers. The d

value in THF compares well with what we esti-

mated from the sum between the diameter of the cross - linked PI core determined

from TEM and the root - mean - square end - to - end distance of the PS coronal chains,

and thus suggests the applicability of the FYF theory to the nanoﬁ ber solutions.

What is more convincing is the decreasing trend for the determined d

values with

increasing DMF content in THF – DMF mixtures. While both THF and DMF solu-

bilize PS, d

decreased with increasing DMF content because the extent of swelling

for the cross - linked PI core decreased with increasing DMF content.

The l

values reported in Table 2.1 are comparable to those reported by Discher

and coworkers [41, 42] and by Bates and coworkers [43, 44] for PEO - PI cylindrical

micelles with a core diameter of ≈ 20 nm prepared in water, where PEO denotes

poly(ethylene oxide). While Bates and coworkers deduced the l

values from small -

angle neutron scattering, Discher and coworkers determined the l

values from

ﬂ uorescence microscopy. In the latter case, they compared the dynamic behavior

of single cylindrical micelles before and after PI core cross - linking. After micelle

cross - linking, the micelles became much more rigid dynamically, which means

that the contour or conformation of the ﬁ bers, in contrast to the micelles, changed

or ﬂ exed very little with time, despite their rotation in space as approximate rigid

rotors. By performing a dynamic analysis of the ﬂ exion motion by subtracting off

the spontaneously curved average shape of the ﬁ bers, they concluded that the

Figure 2.15 Nanoﬁ ber viscosity data plotted following the Bohdanecky method.

Table 2.1 Persistence length l

, and hydrodynamic diameter d

of the nanoﬁ bers calculated from the viscosity data for

130

- PI

370

nanoﬁ ber fractions in various solvents.

Solvent d

/ nm l

/nm

THF

69 ± 18 1040 ± 150

THF − DMF = 50/50 61 ± 850 ± 90

THF − DMF = 30/70 51 ± 12 830 ± 60

80 2 Block Copolymer Nanoﬁ bers and Nanotubes

dynamic l

values of the ﬁ bers were about 50 times higher than those of the cylin-

drical micelles. From viscometry, one deduces the static l

values of the nanoﬁ bers,

which measure on average how much an ensemble of ﬁ bers bends. Therefore,

one should not compare the viscometry l

values determined by us with those

determined by Discher and coworkers, who totally ignored the locked - in curva-

tures of the ﬁ bers in their analysis.

To get a clue to the static l

values of the PEO - PI ﬁ bers studied by Discher and

coworkers, from their ﬂ uorescence microscopy images we noticed that the kinks

in the original cylindrical micelles were locked in after micelle cross - linking and

the ﬁ bers assumed conformations similar to those before micelle cross - linking.

Thus, the static l

values of the nanoﬁ bers should be similar to those of the cylin-

drical micelles. The fact that the l

values that we determined from viscometry are

comparable to those of the PEO - PI cylindrical micelles with similar core diameters

again suggests the validity of the YFY theory in treating the nanoﬁ ber viscosity

data.

The above study demonstrates that block copolymer nanoﬁ bers have dilute solu-

tion properties similar to those of polymer chains. In an earlier report [45] , we also

demonstrated that block copolymer nanoﬁ bers have concentrated solution proper-

ties similar to those of polymer chains. According to the theories of Onsager [46]

and Flory [47] , polymer chains with l

/ d

> 6 would form a liquid crystalline phase

above a critical concentration. We did show the presence of such a liquid crystal-

line phase by polarized optical microscopy for PS - PCEMA nanoﬁ bers dissolved in

bromoform at concentrations above ≈ 25 wt - % [45] . Furthermore, we observed that

such liquid crystalline phases disappeared as the temperature was raised and the

liquid crystalline to disorder transition was fairly sharp.

While block copolymer nanoﬁ bers behave similarly to polymer chains in many

aspects, the drastic size difference between the two dictates that they have sub-

stantial property differences. Because of the large size of the nanoﬁ bers, they

obviously move more sluggishly. Hence, we observed that a liquid crystalline

phase was formed only after the PS - PCEMA nanoﬁ ber solution was sheared

mechanically. Also, because of their sluggishness, the liquid crystalline phase

could not reform spontaneously after cooling a system if it had been heated above

the liquid crystalline to disorder transition temperature. Thus, we can predict,

without performing any sophisticated experiments, that the analogy between

nanoﬁ bers and polymer chains will fail after the molar mass or the size of the

nanoﬁ bers exceeds a critical value. As the size of the nanoﬁ ber increases, the

gravitational force driving the settling of the nanoﬁ ber increases and the dispers-

ibility of the nanoﬁ ber decreases. Furthermore, the van der Waals forces between

different nanoﬁ bers increase [48] , which can cause different nanoﬁ bers to cluster

and settle.

We recently examined the stability of nanoﬁ bers dispersed in THF prepared

from PS

130

- PI

370

. This particular nanoﬁ ber sample had L

= 1650 nm, L

/ L

= 1.21

and M

= 4.3 × 1 0

g mol

− l

, respectively. At a concentration of ≈ 8 × 1 0

− 3

g mL

− l

and

under gentle stirring, no nanoﬁ ber settling was observed during 4 days of observa-

tion by light scattering. Without stirring, we noticed a 10% decrease in the light

2.4 Chemical Reactions 81

scattering intensity of the solution, which corresponded to ≈ 10 wt - % settling of

the nanoﬁ bers in the ﬁ rst 4 days. No noticeable further settling was observed in

another 8 days [24] . This could indicate that the longer ﬁ bers in this sample

exceeded the critical size for settling. Our light scattering and centrifugation

experiments suggested that the longer ﬁ bers ﬁ rst clustered and then settled. The

fact that the clustering could be prevented by gentle stirring suggests that only a

very shallow attraction potential existed between the ﬁ bers.

Although the critical length for settling was short for this sample, several rni-

crometers, the critical length depends on many factors including the relative

length between the core and soluble block and the absolute diameter of the cores.

Methods of increasing the nanoﬁ ber dispersity may include increasing the length

of the soluble block relative to the core block and decreasing the core diameter.

Because of the differences between the polymer chains and the nanoﬁ bers, we

expect differences in the performances of these two classes of bulk materials.

Unfortunately, the mechanical properties of block copolymer nanoﬁ bers or

nanoﬁ ber composites have not been studied so far. We have not performed any

detailed studies of solution properties of block copolymer nanotubes. As a result

of the structural similarities between the two, we expect the nanoﬁ bers and nano-

tubes to have many similar solution properties.

2.4

Chemical Reactions

The similarities between the structure and the properties of the solutions between

nanoﬁ bers and polymer chains prompted us to ask the question as to whether

nanoﬁ bers and nanotubes would have chemical reaction patterns similar to those

of polymer chains. A PI chain can be hydrogenated via “ backbone modiﬁ cation ”

to yield a polyoleﬁ n chain. Through techniques such as anionic polymerization,

etc., one can readily prepare “ end - functionalized ” polymers. The end - groups can

be further derivatized or used for additional end - ﬁ inctionalization. This section

will show that block copolymer nanotubes can also undergo backbone modiﬁ ca-

tion and end - functionalization.

2.4.1

Backbone Modiﬁ cation

Backbone modiﬁ cation has already been involved to convert triblock nanoﬁ bers

into nanotubes. Apart from the performance of organic reactions to the nanoﬁ bers

and nanotubes, this sub - section discusses the performance of inorganic reactions

in the cores of the nanotubes to convert them into polymer – inorganic hybrid

nanoﬁ bers. Block copolymer nanoﬁ bers and nanotubes are soft materials. They

will most probably ﬁ nd applications in bio - related disciplines, such as in the

medical, pharmaceutical and cosmetic industries. For applications in nanoelec-

tronic devices, polymer – inorganic hybrid nanoﬁ bers would be more desirable [49,

82 2 Block Copolymer Nanoﬁ bers and Nanotubes

50] . The ﬁ rst report on the preparation of block copolymer – inorganic hybrid

nanoﬁ bers appeared in 2001, which dealt with ﬁ lling of the core of the PS - PCEMA -

PAA nanotubes by γ - Fe

[10] .

The preparation ﬁ rst involved the equilibration between the nanotubes and

FeCl

in THF. Fe(II) entered the nanotube core to bind with the core carboxyl

groups. The extraneous FeCl

was then removed by precipitating the Fe(II) -

containing nanotubes into methanol. Adding NaOH dissolved in THF containing

2 vol - % of water precipitated Fe(II) trapped in the nanotube core as ferrous oxide.

The ferrous oxide was subsequently oxidized to γ - Fe

via the addition of hydro-

gen peroxide [51] . The top panel in Figure 2.16 shows a TEM image of the hybrid

nanoﬁ bers. The γ - Fe

particles can be seen to be produced exclusively inside the

nanotube cores.

The production of γ - Fe

in the conﬁ ned space of the “ nanotest - tubes ” resulted

in particles that were nanometer - sized. Hence the particles were superparamag-

Figure 2.16 Top: TEM image of PS - PCEMA - PAA/Fe

hybrid

nanoﬁ bers. Bottom: Bundling and alignment of the nanoﬁ bers

in a magnetic ﬁ eld. The arrow indicates the magnetic ﬁ eld

direction.

2.4 Chemical Reactions 83

netic, as demonstrated by the results of our magnetic property measurement [10] .

This meant that they were magnetized only in the presence of an external magnetic

ﬁ eld and were demagnetized when the ﬁ eld was removed. To see how such ﬁ bers

behaved in a solvent in a magnetic ﬁ eld, we dispersed the ﬁ bers in a solvent

mixture consisting of THF, styrene, divinylbenzene, and a free radical initiator

AIBN. The ﬁ ber dispersion was then dispensed into an NMR tube and mounted

in the sample holder of an NMR instrument. In the 4.7 - T magnetic ﬁ eld of the

NMR, the solvent phase was gelled by raising the temperature to 70 ° C to polymer-

ize styrene and divinylbenzene. Thin sections were obtained from the gelled

sample by ultramicrotoming. Shown in the bottom panel of Figure 2.16 is a TEM

image of nanoﬁ bers in a gelled sample. One consequence of the induced magneti-

zation of the ﬁ bers is that they attracted one another and bundled in a magnetic

ﬁ eld. Also clear from this image is that the ﬁ bers aligned along the magnetic ﬁ eld

direction.

The bundling and alignment of the hybrid nanoﬁ bers in a magnetic ﬁ eld have

important practical implications. For example, the controlled bundling of several

nanoﬁ bers may form the basis of magnetic nanomechnical devices. For the

construction of water - dispersible magnetic nanomechanical devices, the super-

paramagnetic nanoﬁ bers need to be water dispersible. We recently prepared water -

dispersible polymer – Pd hybrid catalytic nanoﬁ bers from a tetrablock copolymer

[52] and more recently polymer – Pd – Ni superparamagnetic nanoﬁ bers from a

triblocic copolymer [53] . The tetrablock that we used was PI - P t BA - P(CEMA -

HEMA) - PGMA, where PGMA, being water soluble, denotes poly(glyceryl

methacrylate) and P(CEMA - HEMA) denotes a random copolymer of CEMA and

2 - hydroxyethyl methacrylate. The hydroxyl groups of the precursory PHEMA block

was not fully cinnamated because P(CEMA - HEMA) facilitated the transportation

of Pd

and Ni

We prepared the polymer – Pd hybrid nanoﬁ bers following the scheme depicted

in Figure 2.17 [52] . This involved ﬁ rst dispersing freshly - prepared PI - P t BA -

P(CEMA - HEMA) - PGMA in water to yield cylindrical aggregates (A → B in Figure

2.17 ). Such aggregates consisted of a PGMA corona and a PI core. Sandwiched

between these two layers are a thin P t BA layer and a P(CEMA - HEMA) layer. Such

cylindrical aggregates were then irradiated to cross - link the (CEMA - HEMA) layer

(B → C). The PI core was degraded by ozonolysis (C → D). By controlling the

ozonolysis time, we could control the degree of PI degradation. When not fully

degraded, the residual double bonds of the PI fragments trapped inside the nano-

tubular core were able to sorb Pd(II), most probably via π - allyl complex formation,

Scheme 2.3 .

The complexed Pd(II) was then reduced by NaBH

to Pd (D → E). The left panel

of Figure 2.18 is a TEM image for such nanotubes containing 4.0 wt - % reduced

Pd nanoparticles. The Pd - loaded nanoﬁ bers were dispersible in water where

many water - based electroless plating reactions occur. Thus, Pd could serve as a

catalyst for the further electroless deposition of other metals. We, for example,

loaded more Pd into the tubular core via electroless Pd plating onto the initially

formed Pd nanoparticles to yield essentially continuous Pd nanowires (E → F ,

84 2 Block Copolymer Nanoﬁ bers and Nanotubes

Figure 2.18 TEM image of nanoﬁ bers containing 4 wt - % Pd

(left); TEM image of nanoﬁ bers containing 18.4 wt - % Pd

(right). The scale bars in the form of white boxes are 730 and

1000 nm long, respectively.

Figure 2.17 Schematic illustration of the processes involved

to produce water - dispersible polymer – Pd hybrid nanoﬁ bers.

Scheme 2.3