Hatano Y., Katsumura Y., Mozumder A. (Eds.) Charged Particle and Photon Interactions with Matter - Recent Advances, Applications, and Interfaces

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690 Charged Particle and Photon Interactions with Matter

at the Delft University of Technology have vigorously investigated charge dynamics in organic

liquids (van den Ende et al., 1982), in TiO

(Warman et al., 1984), and in conjugated materials

(van de Craats et al., 1996; Hoofman et al., 1998a; Warman et al., 2005). Siebbeles and Grozema

etal. at Delft extended the researches further to charge transport along conjugated molecular wires

(Prins

et al., 2006; Pieter et al., 2007; Feng et al., 2009; Kocherzhenko et al., 2009).

combining ash-photolysis time-resolved microwave conductivity (FP-TRMC) and ash-

photolysis transient absorption spectroscopy (FP-TAS), nanosecond EB PR-TAS, and DC current

integration upon photoirradiation (DC-CI), we have investigated charge carrier dynamics in various

organic/inorganic semiconductors, such as liquid crystals (Li et al., 2008; Sakurai et al., 2008;

Motoyanagi et al., 2009), self-assembled nanotubes (Yamamoto et al., 2006a,b, 2007b), conjugated

polymers (oligomers) (Acharya et al., 2005a,b; Saeki et al., 2005b, 2008a; Umemoto et al., 2008),

DNA (Yamagami et al., 2006), organic crystals (Imahori et al., 2007; Hisaki et al., 2008; Saeki etal.,

2008b; Amaya et al., 2009), inorganic nanorods (Nagashima et al., 2008), and dendrimers (Seki et al.,

2005a, 2008). PR-TRMC can directly assess the charge carrier mobility from the obtained conductiv-

ity (Δσ = e∑μN, where Δσ, change of conductivity; e, an elementary of charge; ∑μ, sum of mobilities;

N, generated charge carrier concentration). N, generated by a high-energy EB, can be, thanks to its

nonselective ionization process, estimated by an empirical formula considering the bandgap energy

of the semiconductor and its density (Alig et al., 1980; Warman et al., 2004). However, the N of

FP-TRMC, namely, ϕ, the quantum yield of charge carrier generation for one photon absorption at a

given time resolution, varies considerably among materials. The photoresponse property of organic

semiconductors is a matter of great importance, especially in organic photovoltaics (OPV). The prob-

lem in the estimation of ϕ is addressed quantitatively using FP-TAS, DC-CI, or other techniques.

There is a case where the thin lm of FP-TAS shows transient absorption maxima that are attributed

to a radical cation (hole) or a radical anion (electron). Otherwise, the incorporation of an electron

acceptor (donor) molecule into the donor (acceptor) host material is an alternative way, which leads not

only to an increase of photoconductivity utilizing enhanced electron-transfer yield between donor and

acceptor, but also to the possibility of spectroscopic detection of the acceptor radical anion (Saeki et al.,

2008a). These situations allow us to obtain ϕ on the basis of the extinction coefcient of the radical ion,

which is known or estimated by PR-TAS. On the other hand, the DC-CI technique, analogous to TOF,

characterizes the photocurrent upon exposure to pulsed laser, giving the total charge number collected

by the electrodes by integrating the transient current over the time.

In this fashion, AC mobilities of charge carriers have been measured and found to be on the

orders of 10

−3

−10

−1

, which is, in most of the cases, a few orders of magnitude higher than

those estimated by the DC technique, demonstrating the potential feasibility for use as efcient

organic semiconducting materials. The kinetics of transient conductivity is sensitive to lm mor-

phology, grain size of thin lms, bicontinuous ordering of liquid crystal, and π-stacking distance

(e.g., side-chain length of a conjugated polymer). The photoconductivity intensities are dependent

signicantly on nanometer-scale ordering, such as amorphous versus crystal; random stacking ver-

sus ordered stacking; pristine polymer lm versus lm mixed with an additive, which disturbs the

stacking; donor-type materials versus acceptor-incorporated donor materials; and random chain

versus rod-like backbone of conjugated polymers. These differences are sometimes not observed in

measurements because of unexpected factors like impurities and lm/device conditions.

Another

advantage over DC techniques is the implementation of nanometer-scale anisotropic

conductivity measurements with high angle resolution, performed just by rotating a sample in a

resonant cavity, where the direction of the microwave electric eld is xed (Hoofman et al., 1998b;

Grozema et al., 2001). A self-assembled hexabenzocoronene nanotube shows a 10 times higher con-

ductivity along the parallel direction of a macroscopically aligned nanotube relative to the perpen-

dicular direction (Yamamoto et al., 2006b). Anisotropies of organic semiconducting crystals, such as

rubrene (2.3 times) (Saeki et al., 2008b), dehydrobenzoannulene (12 times) (Hisaki et al., 2008), and

sumanene (9.2 times) (Amaya et al., 2009), were revealed, which were rationalized by tighter inter-

molecular packing along the crystalline axis affordable for more efcient charge carrier transport.

Nanoscale Charge Dynamics and Nanostructure Formation in Polymers 691

This chapter introduces the charge carrier transport in single-crystal rubrene through a combi-

nation of FP-TRMC and FP-TAS. We focus on intermolecular charge transport in single-crystal

rubrene, which is discussed in terms of anisotropy, ambipolarity, second-order charge recombina-

tion, and exciton–exciton annihilation. The latter provides an insight into the intramolecular charge

transport along the molecular wires in conjunction with their backbone conformations and lengths.

Single-crystal rubrene, a tetraphenyl derivative of tetracene, shown in Figure 25.11, is one of

the most appropriate benchmarks for the investigation of the intrinsic nature of organic electron-

ics, due to the elimination of grain boundary and minimization of charge-trapping sites (Podzorov

etal., 2004; Sundar et al., 2004; Takenobu et al., 2007). Single-crystal rubrene was grown by physi-

cal vapor transport in a stream of Ar gas (Takeya et al., 2004). The crystal, the size of which is

approximately 1 (a-axis) × 9 (b-axis) mm × 8 μm (thickness), was placed on a quartz plate without

any adhesives and used for both TRMC and TAS experiments. The third harmonic generation of

the nanosecond Nd:YAG laser (355nm) was used as an excitation pulse for the experiments, where

the incident photon density was varied from 0.59 to 17.8 × 10

photon

−1

−2

pulse

−1

. The TAS

experiments were performed using a wide-dynamic-range streak camera. All experiments were

performed

at room temperature.

Figure

25.12 shows the transient photoabsorption (PA) spectrum together with steady-state PA

and emission spectra of single-crystal rubrene. The transient PA spectrum indicates a broad feature

Figure 25.11 Chemical structure of rubrene. The picture shows single crystals of rubrene grown by physi-

cal

vapor transport in a stream of Ar gas. The length of each crystal is about 1

at maximum.

300 400 500 600 700

ΔO.D. (10

–3

–1

) or

ε(10

mol

–1

)

800 900

Wavelength (nm)

Abs. or intensity (arb. units)

1000

Figure 25.12 End-of-pulse transient PA spectrum of single-crystal rubrene upon exposure to a 355nm

nanosecond laser. It is depicted as closed black circles, and its unit is 10

−3

ΔO.D. The gray solid and dotted

lines are normalized steady-state PA and emission spectra, respectively. The open triangles interpolated by a

gray line represent the sum of PA spectra of the radical cation and anion (1:1) of rubrene in a unit of 10

mol

−1

, which was assessed by nanosecond EB pulse radiolysis.

692 Charged Particle and Photon Interactions with Matter

from the visible to the near-IR region with two distinct peaks (835 and 895nm). In order to assess

PA spectra of the radical cation (Ru

•+

, hole) and the radical anion (Ru

•−

, one excess electron) of the

rubrene molecule and their extinction coefcients, we performed a nanosecond EB pulse radiolysis

experiment, using pyrene and biphenyl as mediators of electrons and holes, respectively. The sum of

the spectra composed of an equivalent ratio of Ru

•−

and Ru

•+

is superimposed in Figure 25.12, since

the hole and the electron are equally produced via exciton dissociation upon exposure to a laser

pulse. The spectrum looks exactly like the transient PA spectrum in single crystals, and therefore it

is ascribable to the overlap of Ru

•−

and Ru

•+

. The contribution of triplet excited state is ruled out as

its

PA peak locates at ca. 500

(Saeki et al., 2008b).

The

kinetic traces of transient PA are shown in Figure 25.13a. The inset provides the quantum

efciency, ϕ, of charge carrier generation at the pulse end, estimated by using the transient optical

density, the extinction coefcient, and the reported procedure (Saeki et al., 2006a, 2007). With an

increase in excitation photon density (I

), the ϕ decreases, which is caused by exciton–exciton annihi-

lation (mainly, singlet–singlet annihilation), leading to a decrease in the efciency of charge separation

from excitons. This is supported by the dependence of emission intensity on photon density, where

the normalized emission intensity divided by I

is identical to the dependence of ϕ on I

(Saeki et al.,

2008b). The validity of exciton–exciton annihilation is also strongly corroborated by the relatively

long radiative lifetime of the singlet (τ

= 25.9ns), estimated from the steady-state PA corresponding

to a highest occupied molecular orbital (HOMO) → lowest unoccupied molecular orbital (LUMO)

transition in solution and the relationship 1/τ

·f =

·4.32 × 10

∫ε dυ, where f and υ

are the

–0.2

(a)

0 0.2 0.4 0.6

φΣμ

φ (10

–2

)

(10

–3

–1

)

0 5 10

(10

–2

)

(10

–2

)

0 5 10 15 20

Time (μs)

ΔO.D. (10

–3

)

Δσ (10

–9

s cm

–1

)

0.8 1 –0.2

(b)

0 0.2 0.4 0.6

Time (μs)

0.8 1

1.2

0.8

0.4

0.0

–0.4 0.0 0.4 0.8

PA @ 835 nm

PA @ 895 nm

TRMC

1.2 1.6 2.0

1.2

0.8

0.4

0.0

Normalized ΔO.D. or Δσ

–4

(c)

0 4 8

Time (μs)

12 16

Figure 25.13 (a) Kinetic decays of transient PA at 835nm. The inset shows the dependence of ϕ on excita-

tion photon density (I

). The arrow indicates the increase of I

. (b) Kinetic decays of transient conductivity

(Δσ). ϕΣμ, the product of quantum efciency and charge carrier mobility, is plotted in the inset. The arrow

indicates the increase of I

. (c) Comparison of TRMC (black solid line) and transient PA kinetics at 835 (gray

closed

circles) and 895 (open circles) nm on the long timescale. The inset is the magnication.

Nanoscale Charge Dynamics and Nanostructure Formation in Polymers 693

oscillator strength and the center of emission (cm

−1

), respectively. The singlet lifetime might be short-

ened, particularly on the surface, by oxygen under the atmosphere; however, exciton migration would

be extremely enhanced by the well-dened lattice environment, resulting in the enhancement of the

exciton–exciton annihilation efciency.

An interesting fact is that the decay of transient PA is accelerated by increased I

. This ten-

dency is linked to the second-order reaction between holes and electrons. By a linear function t-

ting to an inverse of decay, we obtained a second-order bimolecular rate constant of (2.0 ± 0.3) ×

mol

−1

. It should be noted that such a clear acceleration of decay with photon density is

not

always observed for other organic semiconductors, for example, pentacene thin lms deposited

on a quartz substrate by thermal vapor deposition (Saeki et al., 2006b), and amorphous conjugated

polymer lms (Pieter et al., 2007). The single-crystal nature is anticipated to account for the clear

dependence on photon density, while many grain boundaries and chemical/physical defects in usual

organic semiconductors would hide this dependence.

Figure 25.13b demonstrates the change of conductivity (Δσ) measured by TRMC, where Δσ is

derived from charge carriers generated by irradiation of the laser pulse. The b-axis of the single

crystal is placed in the resonant cavity parallel to the direction of the microwave electric eld. The

kinetic decays are in good agreement with the PA kinetics, suggesting that TRMC and PA signals

originate from charge carriers. The triplet is assumed not to contribute to TRMC as much, because

there is no signicant dipole change between S

and T

states. The Δσ is converted into ϕ∑μ: the

product of quantum efciency of charge carrier generation, ϕ, and the sum of charge carrier mobili-

ties, ∑μ (=μ

+ μ

−

). In other words, ϕ∑μ is in proportion to Δσ divided by I

. The dependence of ϕ∑μ

on photon density (shown in the inset of Figure 25.13b) corresponds to that of ϕ (shown in the inset

Figure 25.13a), implying almost constant ∑μ over the whole photon densities examined.

Nanoscale

charge carrier mobility, ∑μ, obtained by a fully experimental protocol, is calculated by

dividing ϕ∑μ with ϕ at the pulse end. We found the TRMC mobility to be (5.2 ± 0.7) × 10

−2

−1

by averaging over the examined photon densities. Normalized TRMC and PA kinetics are shown

in Figure 25.13c to facilitate the comparison in the long time range. Although the kinetic traces at 835

(mainly attributed to Ru

•−

) and 895 (mainly attributed to Ru

•+

) are identical at less than 1μs of delay

time, the former disappeared at the later than 10μs of delay. This suggests that electrons are more likely

to be trapped by oxygen and other chemical impurities than holes even in a single crystal. The TRMC

mobility of holes obtained at 10μs of delay was found to be (3.6 ±0.8) × 10

−2

−1

, which is about

70% of that at the pulse end. This result leads to the separation of the sum of the charge carrier mobility

at the pulse end, ∑μ, into μ

= 3.6 × 10

−2

and μ

−

= 1.6×10

−2

−1

, demonstrating the ambipolar

nature of single-crystal rubrene. These values are, however, approximately three orders of magnitude

smaller than the highest reported FET mobility in single-crystal rubrene. The reasons for the low TRMC

mobility are speculated as follows: (1) underestimation of the extinction coefcient of the hole in a crys-

tal, (2) increase of the trapping site for the larger single crystal used in the TRMC measurement, (3) AC

characteristics for highly mobile charge carriers (Prins et al., 2006), (4) insufciency of time resolution

and microwave frequency, (5) small carrier density enough not to ll most of the carrier traps, and (6)

the difference of charge transport efciency between the surface and the inside of the single crystal.

Presently, we cannot settle this issue, and thus, further investigations are required, such as those on

changes of microwave frequency, sample thickness, and excitation wavelength.

The mean concentration of the pair of positive and negative charge carriers was estimated to be

on the order of 10

16–17

−3

, which implies one pair of charge carriers per 10

3–4

rubrene molecules.

This carrier density is, however, a few orders of magnitude smaller than those usually accumulated

in FET devices. It has been reported that the trap density in rubrene crystals ranges from 10

−3

−1

on the surface to 10

15–17

−3

−1

in the bulk (Goldmann et al., 2006). Therefore, the low carrier den-

sity in the present study did not reach the situation of fully occupied traps, and thus, the estimated

TRMC mobility might be lower even though the trapping effect is reduced by the nanosecond time

resolution of TRMC (reasons (4) and (5)). The bimolecular rate constant leads to the sum of charge

carrier mobility as ca. 10

−3

−1

. This mobility is about one order of magnitude lower than

694 Charged Particle and Photon Interactions with Matter

TRMC mobility, because the former is reected from the diffusive motion of charge carrier during

the recombination process, which is more affected by traps than the latter. Due to the exponential

prole of photo charge carrier generation in the direction of the depth, the transport property on

the surface would contribute more to the TRMC results than that inside the bulk; therefore, TRMC

mobility is thought to be lowered (reason (6)), which may be inferred from the report that transport

efciency inside a crystal is superior to that on the surface (Takeya et al., 2007).

The anisotropic conductivity of single-crystal rubrene was investigated by rotating the sample

stage relative to the direction of the microwave electric eld in the resonant cavity, as demonstrated

in Figure 25.14. The highest Δσ was observed when the b-axis of a crystal was parallel to the elec-

tric eld. The Δσ in the b-axis direction was found to be about 2.3 times larger than that in the

a-axis. This anisotropy is almost equal to the reported values assessed by FET (Podzorov et al.,

2004), suggesting that the anisotropy of charge carrier motion on the nanometer scale is achieved

also on the micrometer scale. Since the microwave power is small enough in order not to deviate

the charge carrier generation efciency, the observed anisotropy of Δσ is readily translated into the

anisotropy of charge carrier mobility. The appearance of anisotropic conductivity predicts the band-

like motion of charge carrier transport in single crystals.

In conclusion, we have elucidated the dynamics of charge carriers in rubrene single crystals

through the combination of FP-TRMC and FP-TAS without using an attached electrode. By

comparing the kinetics and estimating independently the extinction coefcients of charged species,

the 9.1GHz AC mobility of the charge carrier was found to be (5.2 ± 0.7) × 10

−2

−1

, which

consists of approximately 70% holes and 30% electrons. This mobility is, however, expected to be the

minimum value because of several reasons, such as much smaller carrier density than those in FET

devices, effect of surface traps, and underestimation of extinction coefcients of charged species in

the crystal phase. We also demonstrated an anisotropy ratio of 2.3 of charge carrier mobility along

the b-axis relative to the a-axis. The optoelectronic property of single-crystal rubrene claried here

of great importance for further investigation on the intrinsic nature of charge carriers.

25.4 nanostruCture Formation

In this section, the radiation sensitivity of σ-conjugated polymers is discussed, especially upon irra-

diation to high-energy charged particles. The radiation-induced reactions in σ-conjugated polymers

have been revealed to depend strongly on the nature of radiation sources exhibited, for example, by

the linear energy transfer (LET) that represents the concentration of energy deposited by radiations

along their paths (trajectories) in the media (Chatterjee and Magee, 1980; Magee and Chatterjee,

1980; Seki et al., 2004b). Polysilanes were cross-linked by high-LET radiations including high-

energy charged particles, despite predominant main-chain scission reactions observed for low-LET

90°(//a)

180°

(//b)

270° (//a)

0°

(//b)

b-axis

a-axis

Figure 25.14 Anisotropic conductivity of single-crystal rubrene. The 0° corresponds to the case when the

electric eld is parallel to the b-axis. The gure to the right illustrates the crystal structure, where rubrenes in

the

b-axis are more preferable π–π stackings than in the a-axis.

Nanoscale Charge Dynamics and Nanostructure Formation in Polymers 695

radiations or photons (Seki et al., 1996a, 1999b). It should be noted that the cross-linking reactions

depended strongly on the density of neutral reactive intermediates, that is, silyl radicals (Maeda

etal., 2001), and the reactions seemed to occur within a nanometer-scaled cylindrical space along an

incident particle trajectory where the intermediates are distributed densely and nonhomogeneously

(Chatterjee and Magee, 1980; Magee and Chatterjee, 1980; Seki et al., 2004b). This process will

potentially give an insoluble “nanogel” along each corresponding particle, and produce wire-like

1D nanostructures via the isolation of the “nanogel” on a substrate by removing soluble non-cross-

linked

parts (Seki et al., 2001c, 2003, 2005b, 2006; Tsukuda et al., 2004a,b, 2005a,b, 2006).

Simple

procedures were employed to cause cross-linking reactions: coating of the polymers onto

Si substrates at 0.2–1.0μm thickness, irradiation to a variety of MeV-order high-energy charged

particles from several accelerators in vacuum chambers, and washing the lm in solvents to remove

non-cross-linked parts of the lm (Seki et al., 2006). After the washing and drying procedures,

the

surface structure of the substrate was observed directly by an atomic force microscope (AFM).

High-energy

charged particle irradiation of PH1 lms was found to cause gelation of the poly-

mers for all particles, all energies, and all molecular weights of PH1. Figure 25.15 shows the evolu-

tion curves of the gel volume for irradiation of PH1 lms with 2MeV He

particles. In the gure,

the gel fraction corresponds to the normalized thickness, and the evolution curve was calibrated

by the absorbed dose (D). According to the statistical theory of cross-linking and scission of poly-

mers induced by radiation, the G-values of cross-linking (efciency of the cross-linking reaction,

G(x)) and main-chain scission (G(s)) are expressed by the Charlesby–Pinner relationship as follows

(Charlesby, 1954; Charlesby and Pinner, 1959):

s s

M D

+ = +

1 2/

(25.17)

0.01 0.1 1 10 100

Dose (MGy)

Fluence (cm

–2

)

0.8

0.6

PH1-1

PH1-2

PH1-3

PH1-5

PH1-4

0.4

0.2

1000

Figure 25.15 Sensitivity curves (gel evolution curves) for PH1s with various molecular weights under

irradiation with a 2MeV

beam. (Reprinted from Seki, S. et al., Chem. Lett., 34, 1690, 2005a; Seki, S.

etal.,

Macromolecules, 38, 10164, 2005b. With permission.)

696 Charged Particle and Photon Interactions with Matter

s g= −1

(25.18)

G x q( ) .= ×4 8 10

(25.19)

G s p( ) .= ×9 6 10

(25.20)

where

is the probability of scission

is the probability of cross-linking

is the sol fraction

g is the gel fraction

is the molecular weight of a unit monomer

is the number average molecular weight before irradiation

The cross-linking G-values calculated using these equations for irradiation of PH1 with 2MeV He

, C

, and N

particles are compared in Table 25.4. The values of G(x) for high-molecular-weight

PH1 are much lower than those for low-molecular-weight PH1. Besides chain length, there are no

differences in the chemical structures of the polymers, indicating that the efciency of cross-linking

should be identical for all series of polymers to a rst approximation. The effects of the molecular

weight distribution on the radiation-induced gelation of a real polymer system were considered

by Saito (1958) and Inokuti (1960), who traced the changes in distribution due to simultaneous

reactions of main-chain scission and cross-linking. However, in the present case, the molecular

weight distributions of the target polymers are reasonably well controlled to be less than 1.2, and

the initial distributions are predicted not to play a major role in gelation. The simultaneous change

in the molecular weight distribution due to radiation-induced reactions also results in a nonlinear-

ity of Equation 25.17. Therefore, the following equations are proposed to extend the validity of the

relationship by introducing a deductive distribution function of molecular weight on the basis of an

arbitrary

distribution (Olejniczak et al., 1991):

s s

p q D D

D D

+ = +

− −

−

1 2

( / )( )

V g

(25.21)

table 25.4

values

of G(x) d

etermined

for v

arious

igh-energy

articles

and

olymer-Chain

engths

entry

2 mev h 2 mev he 0.5 mev C 2 mev C 2 mev n

v nm

−1

220 ev nm

−1

410 ev nm

−1

720 ev nm

−1

790 ev nm

−1

PH1-1 0.0018 0.0049 0.021 0.072 0.082

(0.0021)

(0.0052)

(0.022)

(0.0079)

(0.0095)

PH1-2 0.0021 0.0095 0.052 0.081 0.15

PH1-3 0.0030 0.019 0.07 0.18 0.21

PH1-4 0.0075 0.021 0.075 0.20 0.26

PH1-5 0.019 0.061 0.18 0.27 0.34

(0.021)

(0.089)

(0.19)

(0.33)

(0.42)

Sources: Data from Seki, S. et al., Radiat. Phys. Chem., 48, 539, 1996a; Seki, S. et al., Adv.

Mater., 13, 1663, 2001c; Seki, S. et al., Chem. Lett., 34, 1690, 2005a; Seki, S.

etal.,

Macromolecules, 38, 10164, 2005b.

Values in parentheses estimated by Equations 25.21 and 25.22.

Nanoscale Charge Dynamics and Nanostructure Formation in Polymers 697

uu u

−

( )

4 1 1

( / ) ( / )

(25.22)

where

is the gelation dose

is the degree of polymerization

Equation

25.21 provides a better t to the observed values of s at high doses than Equation 25.17, as

shown in Figure 25.16. However, the G(x) derived from this t are almost identical to those in Table

25.4, depending on the molecular weight, because the values are estimated in the low-dose region

where

Equation 25.17 is sufciently linear.

The

effects of the polymer structure (Seki et al., 1998) and the cross-linking precursor species

(Seki et al., 1996b) have been considered in previous studies, where it was revealed that there was

less of a dependence of G(x) on the molecular weight in the case of γ-rays or EB irradiation. The

cross-linking points in polymer materials are distributed nonhomogeneously on an ion track along

an ion trajectory. A schematic of this type of nonhomogeneous distribution is shown in Figure 25.17.

Intramolecular cross-linking, which constitutes a greater contribution to G(x) in the inner region

of ion tracks associated with higher densities of deposited energy, is not taken into account by the

statistical treatment in Equations 25.17 through 25.22, and it is this case that gives rise to an under-

estimate of the number of cross-links. As the polymer lm used in the present study is sufciently

thin to allow the change in the kinetic energy of the incident particle to be neglected, a model of

cylindrical energy deposition is sufcient, without needing to refer to the dependence of the radial

energy distribution on the direction of the ion trajectory. The total yield of gels generated by charged

particle irradiation can thus be treated using a simplied expression (Seki et al., 1997, 1999b, 2004b,

2005b), as follows:

1.5

0.5

0 0.3 0.6 0.9

1/dose (MGy

–1

)

s +s

1/2

1.2 1.5

Figure 25.16 Charlesby–Pinner plot of s + s

1/2

versus 1/D for 2MeV

irradiation of PH1-1. The solid

line denotes the t by Equation 25.17 in the high-dose region for the estimation of G(x) in Table 25.4. The

dashed line is given by Equation 25.23 for the entire dose region. (Reprinted from Seki, S. et al., Chem. Lett.,

34,

1690, 2005a; Seki, S. et al., Macromolecules, 38, 10164, 2005b. With permission.)

698 Charged Particle and Photon Interactions with Matter

g n r= − −









exp π

(25.23)

where

is the radius of the cross section of the cylindrical region (chemical core)

represents the uence of incident ions

The

effect of diffusion of reactive intermediates, determined using a low-energy charged particle,

has

been formulated as the term δr (Seki et al., 2004b):

r r r

′

δ . (25.24)

The value of δr′ in PH1 was determined to be 0.5–0.7nm (Seki et al., 2004b). Based on traces of

the gel fraction by Equation 25.23, the estimated values of r

are summarized for a variety of high-

energy charged particles in Table 25.5. The value of r

increases substantially with the molecular

weight in all cases except for irradiation with 2MeV H

, suggesting that the cylindrical scheme may

not be applicable for the 2MeV H

because the deposited energy density is too low to promote the

cylindrical

distribution of cross-links in an ion track.

AFM

images of the cylindrical gel area are shown in Figure 25.18 for comparison with traces

of the gel fraction. Equation 25.23 provides a good t for the trace of the gel fraction, and the

estimated values of r

for both particles correspond to the values observed from the AFM micro-

graphs. Figure 25.19 shows a series of AFM micrographs observed for the irradiation of PH1-1 and

High-energy particle

Non-cross-linked

polymers

Removed by

dissolution

Polymer

molecules

Cross-links

Polymer thin film

Figure 25.17 Schematic of the nonhomogeneous distribution of cross-links in an ion track. Dissolution of

non-cross-linked

molecules results in the formation of isolated nanowires.

Nanoscale Charge Dynamics and Nanostructure Formation in Polymers 699

table 25.5

values

of r

for various high-energy particles and polymer-Chain lengths

ions

energy

(mev)

let

(evnm

−1

)

for

1-1 (nm)

for

1-2 (nm)

for

1-3 (nm)

for

1-4 (nm)

for

1-5 (nm)

2.0 15 0.15 0.15 0.14 0.14 0.15

2.0 220 1.2 0.95 0.76 0.60 0.52

0.50 410 2.2 2.1 1.6 1.1 0.94

2.0 720 5.0 4.3 4.0 3.4 2.7

2.0 790 5.1 4.8 4.2 3.8 3.0

2.0 790 4.8 4.8 4.3 3.6 2.8

5.1 1,550 5.5

5.1 1,620 5.9

10.2 2,150 6.1

175 2,200 8.2 7.3 6.1 4.0

8.5 2,250 5.8

10.2 2,600 7.7

520 4,100 10.7 9.6 8.6 7.9 6.4

520 4,100 10.2 9.2 8.3 6.1

129

450 8,500 12.1 10.5 9.3 6.9

192

500 11,600 19.4 16.2 12.5 10.7

Sources: Data from Seki, S. et al., Adv. Mater., 13, 1663, 2001c; Seki, S. et al., Chem. Lett., 34, 1690, 2005a; Seki,S.

al., Macromolecules, 38, 10164, 2005b.

Values estimated from gel traces by Equation 25.23.

Values estimated by direct AFM observation.

0.8

0.6

520 MeV Kr

2 MeV N

=6.4 nm

=3.8 nm

0.4

0.2

Fluence (ions cm

–2

)

Cross section

6.1 nm

3.6 nm

200 nm

500 nm

Figure 25.18 Gel evolution curves recorded for 520MeV

Kr irradiation of PH1-5 and 2MeV

N irradia-

tion of PH1-4. Solid lines denote the t for the respective gel fraction based on Equation 25.23. The estimated

values of r

are 6.4 and 3.8nm for the Kr and N particles. AFM micrographs were observed for the same set

of polymers and particles. The uence of Kr and N ions was set at 1.4 × 10

and 6.4 × 10

−2

, respectively.

(Reprinted from Seki, S. et al., Chem. Lett., 34, 1690, 2005a; Seki, S. et al., Macromolecules, 38, 10164,

2005b.

With permission.)