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

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700 Charged Particle and Photon Interactions with Matter

PH1-3 thin lms with varying number of incident particles. These images clearly reveal 1D rod-like

structures (nanowires) on the substrate, which is ascribed to the cylindrical formation of nanogel

along ion trajectories. It should be noted that the density of the nanowires on the substrate increased

clearly with an increase in the number of the incident particles, and the observed number density of

the nanowires coincided with the number density of the incident particle. This is also suggestive that

“one nanowire” is produced corresponding to one incident particle along its trajectory, which is a

clear evidence of the model described above. As shown in Figure 25.19, the length of the nanowires

is uniform in each image, and is consistent precisely with the initial thickness of the lm. This is due

to the geometrical limitation of the distribution of the cross-liking reaction: the gelation occurs from

the top surface to the bottom of the polymer lm. Thus, the length of the nanowires can be perfectly

controlled by the present technique. Based on the measurement of the cross-sectional trace of the

nanowires by AFM, the radial distribution of cross-links in the nanowires is discussed in terms of

dened as the radius of the cross section. It is clear that the value of r

depends on the molecular

weight of the target polymer, as shown in Figure 25.20, and that r

also changes with the LET of the

incident

particle, as summarized in Table 25.5.

The

authors previously reported that cross-linking reactions are mainly promoted by side-chain-

dissociated silyl radicals, and that the predominant reaction is determined by the radical concen-

tration in the ion tracks (Cotts et al., 1991; Seki et al., 1996a,b, 1999b). Thus, the distribution of

cross-links in an ion track is expected to reect the radial dose (deposited energy density) distri-

bution, where ρ

is the critical energy density for the predominance of cross-linking in PH1. The

radial dose distribution in an ion track is thus given by Chatterjee and Magee (1980) and Magee and

Chatterjee

(1980)

ρ π π

c c

LET LET

































≤

−

2 2

1 2

r r

e r

r rln

(25.25)

ρ π

c p

LET

( ) ln

r r

e r

r r r=

























< ≤

−

1 2

(25.26)

where

is the deposited energy density in the core area

and r

are the radii of the core and penumbra area

(a) (b)

200 nm 200 nm 200 nm

(c)

Figure 25.19 AFM micrographs of nanowires based on PH1s showing the variation in size with molecular

weight and number density on the substrate. The nanowires were formed by a 500 MeV

192

Au-beam irradiation

to (a,b) PH1-3 and (c) PH1-1 thin lms at (a) 3.0 × 10

, (b) 5.0 × 10

, and (c) 1.0 × 10

ions cm

−2

, respectively.

The

thicknesses of the target lms were (a,b) 350

and (c) 250

nm.

Nanoscale Charge Dynamics and Nanostructure Formation in Polymers 701

For gel formation in a polymer system, it is necessary to introduce one cross-link per polymer

molecule. Assuming a sole contribution from the cross-linking reactions in the chemical core, ρ

given by

100 A

G x mN( )

(25.27)

where

is Avogadro’s number

is the degree of polymerization

The value of mN/ρA reects the volume of a polymer molecule. Substituting ρ

(r) in Equation 25.26

with

gives the following requirement for r

(Seki et al., 2004b; Tsukuda et al., 2005a):

′

⋅

























−

G x mN

e r

1 2

400

LET ( )

πρ

(25.28)

Using the reported value of G(x) = 0.12, derived from radiation-induced changes in the molecular

weight (Seki et al., 1996a), the values of r

calculated by the nonempirical formulation of Equation

25.28 are compared with the experimental values showing a good consistency with the experimental

values for polymers with sufcient chain lengths (PH1-1 and PH1-2). However, a considerable dis-

crepancy occurs between the calculated and experimental results for polymers with shorter chains.

The global conguration of the polymer molecules depends greatly on the length of the polymer

chains, leading to a transformation from random coil (long-chain) to rod-like (short-chain) conforma-

tions. The gyration radius of a polymer molecule, which determines the size of a molecule spreading

in the media, is correlated with this transformation. The correlation between R

and N is discussed

previously in this chapter, giving Equation 25.2. Based on the persistence length of PH1 (1.1nm, see

Section 25.4), the scaling law for a helical worm-like chain model (Yamakawaetal.,1994) results

in an index, α, of 0.410, 0.419, 0.451, 0.485, and 0.492 for PH1-1–5, respectively. Thus, the effective

0 5

PH1-1

PH1-2

PH1-3

PH1-4

PH1-5

(observed) (nm)

(calculated) (nm)

10 15

Figure 25.20 Correlation between r′ values estimated experimentally and those calculated using Equation

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

2005b.

With permission.)

702 Charged Particle and Photon Interactions with Matter

volume of a polymer chain can be simply calculated as

4 3

/ πR

, and the substitution of mN/ρA in

Equation

25.28 with the effective volume leads to the expression (Seki et al., 2005b, 2006)

′

⋅

























−

G x N

e r

1 2

400

LET

( )

πβ

(25.29)

where β is the effective density parameter of the monomer unit (kg m

−3

). Based on Equation 25.29,

the calculated value of r′ is plotted against the experimental values in Figure 25.20. All polymers,

with a variety of molecular weights, follow a single trend, and the calculated values display good

correspondence when r′ > 7nm. The underestimate of r′ by Equation 25.29 for r′ < 7nm suggests

that the initial deposition of energy and the radial dose distribution estimated by Equations 25.25

and 25.26 do not account for the radial distribution of chemical intermediates, and thus, cannot

model the concentration of cross-linking in the core of the ion track. The value of G(x) increases

dramatically with an increase in the density of reactive intermediates. Based on the assumption that

G(x) is a function of the density of deposited energy, the present results indicate that the yield of the

chemical reaction is dependent on the energy density. Cross-linking reactions in ion tracks therefore

have the potential for not only single-particle fabrication with sub-nanometer-scale spatial resolu-

tion for any kind of cross-linking polymer, but also the study of nanoscale distributions of radial

dose

and chemical yield in an ion track.

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