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

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240 Charged Particle and Photon Interactions with Matter

n n

n n n n

-C H -C H CH

42 1 2 2

i i+

− −

→ +

(10.3c)

As a result of these reactions, the lifetime of alkane radical cations at room temperature falls in the

range of 1–20ns. Branched alkanes were found to form less stable parent ions, which is caused by

unimolecular fragmentation such as that in (10.3c). The radical cations of alkyl chlorides exhibit

lifetimes

up to 200

ns.

Certainly, this depends, in each case, also on the purity of the substances.

Alkene

radical cations formed by reaction type (10.3c) are of minor importance. They are formed

in lower yields as the parent ions and exhibit a lower reactivity (Mehnert etal., 1982) (see also

Section 10.3). Now we focus on the reactivity of the parent ions of alkanes and alkyl chlorides and

present

some recently found kinetic phenomena.

10.3 reaCtion oF parent solvent Cations with added sCavengers

The ionization of alkanes and alkyl chlorides results mainly in parent radical cations where the

σ-bond skeleton is preserved. The spin and the charge are uniformly distributed in such species (see

Figure 10.1) (Brede and Naumov, 2006). A small quantity of alkene radical cations is also formed

either as direct by-products of the ionization or as fragments of the decay of the parent ions (10.3c).

These alkene radical cations have a more localized spin and charge distribution (cf. Figure 10.3),

and therefore, a lower reactivity, because, in practical terms, they are derived from an unsatu-

rated system.

In the presence of any additives (scavengers), both types of solvent-derived radical cations

tend to undergo ion–molecule reactions, such as proton transfer (PT) (reactions 10.4a and 10.4b)

or ET (reaction 10.4c). PT mainly involves polar and protic scavengers, and hence the rate con-

stants depend on polarity parameters, such as nucleophile power, and perhaps dielectric constants

(Mahalaxmi etal., 2001). Quenching of transient signals by such reactions was often used for the

400

100 200 300

500 600 700

λ (nm)

λ = 500 nm

t (ns)

OA(×10

–3

)

n-C

•

n-C

•

n-C

•

800 900

Figure 10.2 Optical absorption spectra of parent radical cations taken in the pulse radiolysis of the pure

solvents n-decane or n-butyl chloride. The inset shows a time prole of the n-butyl chloride radical cation at

characteristic wavelength.

Reactivity of Radical Cations in Nonpolar Condensed Matter 241

identication of radical cations. Apparently, anions like chloride also act as nucleophiles and ef-

ciently quench parent radical cations.

RHX RYH RX RYH , Y O, N, RHX alkanes, alkyl chlorides

i i+ +

+ → + = =

(10.4a)

RHX Cl RX HCl, Cl from, for example, Bu N Cl

i i+ − − + −

+ → + ( ) (10.4b)

RX D RX D , 10 dm mol s , that is, diffusion control

10 3 1 1i i+ + − −

+ → + ≈k lled,

RX alkanes, alkyl chlorides=

(10.4c)

ET as the ion–molecule reaction (10.4c) plays a dominant role. Here, the additives act as electron

donors (D). The reason for this is the high IP of the RX compounds, which is often 1–3eV higher

than that of the donors. To judge the energetics of the ET reactions, the well-known gas-phase

ionization potentials (Wedenejew etal., 1971; Meot-Ner etal., 1981), IP

gas

, are used, neglecting the

polarization energy part in condensed matter (Brede etal., 1987). Hence, the ionization potential

difference, ΔIP, between the IPs of RX and D can be used as a measure of the free energy of the

(10.4c).

For

a bimolecular reaction, apart from the energetics, the mobility of the reaction partners should

also be considered. At ΔIP ≥ 0.5eV, the ET was found to be diffusion controlled (Brede etal., 1987),

that is, under normal conditions (RT, relaxed parent ions), possessing a rate constant of k ≈ 10

mol

−1

. So far as to the principle of ET (10.4c).

Traditionally, steady state irradiation experiments at low temperature (77K) glasses of D

dissolved in RX were performed to observe donor radical cations. The nature of these species can

be tentatively characterized by bleaching as well as stepwise warming up (heating) experiments

(Hamill, 1968; Shida, 1988). This causes changes in the viscosity and, therefore, slightly acceler-

ates the diffusion. Hence, a qualitative identication of the donor radical cations and, sometimes, of

their decay products can be performed. Furthermore, optical properties as absorption maxima and

extinction coefcients of the donor cations can be obtained. As an example, Figure 10.4 shows the

optical absorption spectra, taken by the matrix insulation technique, of a sample containing the ste-

rically hindered 4-methyl-2,6-di-tert-butyl-phenol (Zubarev and Brede, 1997). At room temperature

(a)

(b)

–e

–

–e

–

Figure 10.3 Electron density and spin distribution of cyclohexene and n-heptene and of the parent alkene

radical

cations derived from them.

242 Charged Particle and Photon Interactions with Matter

and in polar solvents, phenol radical cations are extremely unstable (pK

around −1) (Dixon and

Murphy, 1978). In nonpolar glass at 77K, rst the spectrum of ArOH

•

is observed; on heating up

the sample, the well-known phenoxyl radical appears. Additionally, the EPR spectrum of ArOH

•

taken at 77K is shown in the inset of Figure 10.4.

The formation of donor radical cations by ET in rigid matrices at low temperatures, however,

cannot be explained by normal diffusion and, therefore, assumes something like a nonclassical

transport process. A similar conclusion has been drawn from pulse radiolysis measurements with

liquid solutions of aromatic donors in cyclohexane (Zador et al., 1973; Brede et al., 1974) and

n-alkanes (Brede etal., 1974), where an unusually rapid formation of donor species has been found.

This was interpreted as a reaction of extremely mobile positive holes (+), which are postulated to be

precursors

of the relaxed parent radical cations (see reaction 10.5):

( )+ + → + ≤

+ − −

12 3 1 1

D D RH 0 dm mol s

(10.5)

The mechanism of this rapid migration is not completely clear. It is hypothesized that something

like a resonance transfer or a special hole migration takes place (Mehnert, 1991). For most of the

alkanes and alkyl chlorides, after about 1ns, relaxed parent radical cations with normal diffusion-

conditioned

mobility exist. These species are the subject matter of our further elucidations.

donor concentrations of up to some 10

−3

mol dm

−3

, the reaction of free and homogeneously dis-

tributed ions is observed. If the concentration is increased (c > 10

−3

mol dm

−3

), then the product cation

yield increases dramatically. This is explained by scavenging the inhomogeneously distributed parent

ions (geminate ions), which normally decay by inhomogeneous neutralization in the spurs (reac-

tion 10.3a). This behavior can be described by scavenger curves (see Figure 10.5). The shape of the

400

0.00

0.05

0.10

0.15

0.20

0.25

0.30

450 500 550

λ (nm)

600

325 330 335

B (mT)

340 345

650 700

Figure 10.4 UV–vis optical absorption spectra of ArOH

•

(boldfaced curve) and ArO

•

(dotted curve) in an

irradiated s-BuCl glassy matrix. The inset shows the EPR spectrum at 77K; the central part of the spectrum

shows

the characteristic quartet due to ArOH

•

. ArOH = 4-methyl-2,6-di-tert-butyl-phenol.

Reactivity of Radical Cations in Nonpolar Condensed Matter 243

scavenger curves depends on the efciency of scavenging, that is, on the rate constant and free energy

of the reaction and on the molecule size and other donor-specic parameters (Warman etal., 1969),

and is preferably used for the description of steady state experiments. The described concentration-

dependent yield, however, does not inuence markedly the kinetics of the ET reaction of type (10.4c).

The ET (10.4c) from donors to relaxed parent solvent radical cations has been often used for

the generation of donor cations and the subsequent investigation of their properties. Insofar, it is a

valuable tool for donor cation formation and identication, also in comparison with photochemical

investigations. Among the many others, a few examples from our own research are mentioned. For

the

most part, unknown radical cations of

•

Pyrimidines (Lomoth etal., 1999), of various phenols (Mahalaxmi etal., 2000)

• HALS

compounds as cationic intermediates of photostabilization (Brede etal., 1998)

•

Styrene

type as polymerizing cationic species (Brede etal., 1982)

were

found and kinetically characterized.

10.4 Free eleCtron transFer

Using substituted aromatics as donors in the ET (10.4c), a surprising anomaly was observed, which

discussed in the following text.

10.4.1 the phenoMenon

In pulse radiolysis experiments, it has been found that in the ET from substituted aromatic donors to

parent solvent radical cations, two products are simultaneously formed, for example, the expected

donor radical cations as well as (unexpected) radicals derived from them (for phenol, cf. Equation

10.6). Also for diverse additionally substituted phenols, the product ratio was found to be 50:50,

which

means that it is not simply a deprotonation effect (Mahalaxmi etal., 2000):

C H Cl ArOH C H Cl ArOH 50% , ArO 50% H

4 9 4 9

i i i+ + +

+ → + +( ) ( )

solv.

(10.6)

From an experimental point of view, it should be mentioned that to avoid any disturbing radical

anion formation, an internal electron scavenger is used (here, n-butyl chloride, BuCl) or an efcient

–5 –4 –3 –2 –1

Log C

Figure 10.5 Common shape of a scavenger curve describing the yield of donor radical cations dependent

on the scavenger concentration: a—range of competition between reactions (10.4c) and (10.3a), b—range of

reaction

(10.4c) with free ions, c—range of additionally scavenging geminate ions.

244 Charged Particle and Photon Interactions with Matter

electron scavenger is added (e.g., CCl

), (cf. reaction 10.7). All the reported effects appear in alkanes

as well as alkyl chlorides (Mahalaxmi etal., 2000; Brede etal., 2001a). For practical reasons, in

most

of the subsequently reported ET experiments, BuCl was preferred as the solvent.

RCl e R Cl

solv.

+ → +

− −i

(10.7)

Giving an example from pulse radiolysis at room temperature, Figure 10.6 shows optical absorp-

tion spectra representing the products of ET (10.6) (Brede etal., 1996 2002a), using the same

sterically hindered phenol as described above for matrix insulation experiments (see Figure 10.4).

The spectrum taken immediately after the ET (

•

) consists of a superposition of both the product

species ArOH

•

and ArO

•

. As for the identication, a polar additive (ethanol) quenches ArOH

•+

and ArO

•

remains. So the phenol transients can be well distinguished. We repeat that both tran-

sients appeared from the very beginning.

Using a variety of phenols (Brede etal., 1996, 2001a, 2002a; Mahalaxmi etal., 2000), biphenols

(Brede etal., 2002b), naphthols (Mohan etal., 1998; Baidak etal., 2008a), and other chalcogenols

(Hermann etal., 2000; Brede etal., 2001b) an analogous behavior has been observed. This was also

the case for primary and secondary aromatic amines (Brede etal., 2005; Maroz etal., 2005). As

already mentioned, the radical cations of chalcogenols are relatively unstable (very low pK

values,

Dixon and Murphy, 1978) in polar media and, therefore, tend to deprotonate, whereas the radical

cations

of aromatic amines are persistent (Alkaitis etal., 1975). Nevertheless, the two-product situ-

ation

exists also in the amine case. This is concluded in Table 10.2 for donors of the type Ar-Y-H,

where

Y = O, S, Se, N.

Considering

the yields of the two kinds of ionization products, it is obvious that the products

are synchronously formed in a constant ratio for each class of compounds. This does not depend

on steric and electronic effects. But the intramolecular mobility of the substituent seems to be an

important factor. In the case of restricted mobility, because of hydrogen bonding (ortho-salicylate)

and a rigid molecule structure (carbazol), only one product of the ET (10.4c) was found, that is, only

donor radical cations were generated.

350

ArO

•

ArOH

•

0.025

0.050

0.015

0.010

0.020

400 500 600

λ (nm)

Cl-(CH

)

-Cl

•

400 450 500

λ (nm)

ΔOD

Figure 10.6 Transient optical absorption spectra of ArOH

•

and ArO

•

taken 50ns after the electron pulse

on a solution of 4-methyl-2,6-di-tert-butylphenol in 1,2-dichlorethane (

•

). After adding 0.1 mol dm

−3

ethanol

only ArO

•

(▪) remains. The inset shows the spectrum of the 1,2-dichlorethane radical cation taken in the pure

solvent.

Reactivity of Radical Cations in Nonpolar Condensed Matter 245

table 10.2

product

atio

of the electron t

ransfer

(10.6), Calculated t

imes

ofonem

otion

of b

ending

(wagging)

and v

alence

ibration

(

stretching)Calculated

with (

b3lyp/6-31g(d))

electron donor

bending

[10

−15

round

valence

[10

−15

tate

kJ mol

−1

inglet (Cation)

product ratio

(

•

+)/(

•

) remarks

97 9.3 12.6 (62) 50:50 Also deuterated:

Ar-OD

HO Cl

98 9.3 13.0 (55) 50:50

OMe

110 9.3 10.0 (57) 50:50

35 9.1 9.8 (46) 50:50 Sterically

hindered

phenols

HO OH

100 9.3 9.7 (60) 40:60 All biphenols

OMe

89 9.3 17 50:50 Para-salicylate

294 12.8 34 (50) 62:38 Curcumin, weak

hydrogen

bond

OMe

294 12.8 61 100:0 Ortho-

salicylate,

strong

hydrogen

bond

294 12.8 1.7 (89) 35:65 Various

thiophenols

HSe

347 14.8 2.9 (82) 10:90 Selenophenol

ArHN

608 9.2 13 50:50 Also primary

and

secondary

aromatic

amines

— 9.1 — 100:0 Carbazol, rigid

skeleton

Note: E

denotes the energy barrier of rotation along the Ar–X axis for the singlet ground state, as well as for the radical

cation

(in brackets).

246 Charged Particle and Photon Interactions with Matter

10.4.2 Molecule dynaMicS

With the above experimental behavior in mind, a reasonable explanation for the two-product phe-

nomenon should be found. In the used nonpolar liquids, solvation (solvent molecule shells) of ions

and polarized molecules plays only a minor role. Under normal conditions, the donor molecules are

mobile and can move without the inuence of a solvent shell. This also holds for the intramolecular

mobility. Molecule dynamics takes place in the femtosecond time range and involves different kinds

of oscillations: stretching of bonds, bending motions (torsion, wagging, etc.) are simply taken here

rotations.

The

rotation of a polarizing group in a molecule of Ar-↺-Y-H (Y = hetero atom) is accompa-

nied with shifts of the electron density within the highly occupied π- and n-orbitals (Brede and

Naumov, 2006). For the donor molecules, this effect can be visualized by quantum chemical cal-

culation and results of the electron density dependent on the angle of deformation. So the critical

bond (marked with a rotating arrow) is twisted out of the plane of the stable state (here, 0°) in a

stepwise manner. For the phenol molecule, the results of the calculations are given in Figure 10.7.

It can be seen that the electron distribution changes in a stepwise manner from an even one (0°) to

localization (90°) on the oxygen hetero atom. Under molecule dynamics conditions, it is implied

that with the rotational motion in the femtosecond time range, a continuous change in the electron

density in the ground-state molecules takes place. In chemical terms, it means that a dynamic mix-

ture of rotational conformers exists (see feature article Brede and Naumov, 2006).

Focusing the interest on the ET, the elementary reaction (10.4c) can be put into the following

steps

(reaction sequence 10.8):

RX D RX D RX D

diffusion e-jump diffusi

i i i

 

+ + +

 →

← 

 →

← 

oon

RX D

 →

← 

(10.8)

Diffusion brings the reactants together. During the encounter of the reactants, the electron jumps to

the parent solvent ion, and diffusion separates the products. According to the Born–Oppenheimer

approximation, the molecular geometry remains stiff during the electron jump, which is assumed to

be an instantaneous and, therefore, extremely rapid process. If the ET is not hindered by a solvent

shell and if the jump occurs in the rst encounter of the reactants, then the dynamic mixture of

donor conformers is chemically noticed. The molecule is ionized in the momentum of a distinct

deformation state, and therefore, initially, donor radical cations of different spin distributions are

formed (see Born–Oppenheimer approximation). A differing spin (and charge) distribution means

that

donor cations of different stabilities exist.

Simplifying

this complex situation, we distinguish product radical cations into two kinds,

namely, metastable and dissociative. The dissociation should occur during the rst vibration motion

90600 30

Figure 10.7 Transformation of the n-orbital of the Ar-OH singlet ground state (isocontour = 0.1) dependent

on the angle of the OH-group rotation.

Reactivity of Radical Cations in Nonpolar Condensed Matter 247

of the critical bond. Otherwise, relaxation immediately forms stable donor cations. Concluding

this deduction, as products of the ET (10.4c, 10.8) we distinguish metastable as well as dissocia-

tive product radical cations. They are derived from different types of dynamic conformers of the

ground-state molecules, distinguished as being near to the plane or twisted. Now, we generalize and

rewrite

reaction (10.6) and explain it in terms of molecule dynamics (10.9):

[Ar-Y-H] RX +

- -Y-H

plane

(metastable)

→

Ar Y H

- -



(10.9a)

[Ar-Y-H] [Ar-Y-H ] RX + +H

twisted

(dissociative) solv.

→ →

i i

ArY

(10.9b)

where

= H, Cl

Ar = aromatic ring

= O, S, Se, N

species in boldface can be directly observed

Because

of the elucidated special properties—immediate electron jump and dynamic control—

we call this reaction type “free electron transfer.” So, FET stands for an electron transfer process

where the molecule oscillations of the donor are reected in a bimolecular reaction. Thus, “free”

means

unhindered and refers to the transfer and not to the electron.

10.4.3 energeticS

A critical point of the FET hypotheses is the interpretation of the rapid dissociation of the twisted

donor radical cation (reaction 10.9b). For a clear understanding of this point, we made an energetic

analysis

of the reaction path.

The

ET from the neutral ground-state substrate (ArOH) to the solvent cation radical (BuCl

•

)

isenergetically favored by about 2.05eV. For an energetic analysis, the following primary reaction

steps

should be considered (Brede and Naumov, 2006):

ArOH BuCl ArOH BuCl

1.32 eV

e-transfer

unrela

+  → +

{ }

=−

+i i

∆H

xxed

0.73 eV

relaxation

ArOH BuCl

∆H =−

 → +

(10.10)

FET occurs between two electronically relaxed reaction partners. After the electron jump, both

products, namely, ArOH

•+

and the solvent molecule (BuCl), are primarily in an unrelaxed state, due

to the change in the electronic conguration within the same molecular structure. This rst step is

exergonic by 1.32eV. It follows a rapid relaxation via the adjustment of the molecular geometry to

the new electron distribution. The relaxation (reorganization) energy of about 0.73eV is distributed

between

ArOH

•+

(0.19eV) and BuCl (0.53eV).

Primarily, before reaching the thermal equilibrium, the excess energy of the ET (ΔH = −1.32eV)

is partitioned off the reactants. Considering the proton dissociation energy of about 8.7eV in the gas

phase and 2.6eV in the liquid state (BuCl as the proton acceptor), the excess energy is far from being

enough for achieving deprotonation in the planar state of the phenol radical cation. Because of the

strong electron–vibration coupling, the excess electron energy is accepted by its nearest vibrations,

rst of all by the C-H valence vibrations (∼3200 cm

−1

= 0.39eV), and then is dissipated by interaction

↺

248 Charged Particle and Photon Interactions with Matter

with the surroundings (Brede etal., 1987). However, the additional destabilization of the deformed

(twisted) donor radical cations (see reactions 10.9a and 10.9b) helps to overcome easily the dissocia-

tion

barrier (cf. also Figure 10.8).

Any

deprotonation in the sense of self-dissociation is energetically unfavorable. Therefore, for a

mechanistic explanation of the prompt deprotonation within FET, we have to take into account the

solvent as the proton acceptor and stabilizer (reaction 10.11):

Ar-O -H ArO H BuCl

perpend.

BuCli i+ + +









→ → +

( )

(10.11)

The fact that the proton afnity of many solvents (Wedenejew etal., 1971), such as butyl chloride,

lies just between those of the metastable planar radical cation structure and of the twisted unstable

one

(see Figure 10.8) fully corroborates our view.

potential energy diagram concerning the energetics of the solvent-driven deprotonation

(10.9b, 10.11) of dissociative cations is displayed in Figure 10.8. The ground-state (singlet)

potential is rather at and shows the energy changes during the rotation of the Ar-↺-OH group,

which amounts to <15 kJ mol

−1

. After ionization, the potential of the radical cation [Ar-↺-OH]

•+

becomes considerably deeper and the rotational motion is hindered by an activation barrier of

≈60 kJ mol

−1

The planar radical cation is metastable and is placed at the bottom of the vibration potential

(Figure 10.8, right-hand side). The perpendicular radical cation state, however, has a much higher

(Singlet)

diss( )

–e

–

(ionization)

–90 –60 –30 0 30 60 90 0.8 1.0 1.2

L(OH) (Å)OH rotation (degree)

1.4 1.6 1.8

Relative energy

Stable (planar)

radical cation

ArO

•

+ H

solvent

Destabilized (perpendicular)

radical cation

Radical cation

Singlet

diss(||)

•+

Figure 10.8 Potential diagrams describing the energetic situation of phenol as a donor in the ground state

and for the different conformer radical cations. The left part shows the potentials dependent on the rotation

angle,

and the right part illustrates energy changes dependent on the bond length (L) of Ar-OH.

Reactivity of Radical Cations in Nonpolar Condensed Matter 249

energy. At distances L > 1.3 Å, the potential of the latter crosses the level of the proton afnity of the

solvent. This critical length is easily reached during the rst vibration motion and, as a consequence,

dissociation

(deprotonation) takes place.

The

energetic data used in the discussion originated from quantum chemical calculations (DFT)

using the program B3LYP/6-31G(d) (Becke, 1993, 1996). Although the results of quantum chemical

calculations have already been used for rationalizing the experimentally observed unusual product

distribution in the FET (of phenols), the calculated parameters should be listed here: The informa-

tion of interest included, in particular, (a) the dynamic behavior of the donor molecules (frequencies

of vibration and bending motions), (b) the electron distribution in the affected orbitals and the con-

sequences of its ionization, and (c) the detailed mechanism of the dissociation of the unstable donor

radical cations as far as this is a reection of the energetics of the reaction and of some structural

details

(changes in bond lengths, etc.).

10.4.4 generalization of the fet phenoMenon

The experimental characteristics of FET consist in the appearance of two different products, which

are formed synchronously in the bimolecular ion–molecule reaction (cf. reactions 10.4 and 10.9).

These products are derived from two kinds of donor radical cations, one stable and another dissocia-

tive. The background is the electron distribution changing in connection with the bending motion of

the

hetero substituents at the aromatic moiety.

Aromatic

molecules with hetero substituents other than those capable of deprotonation should

exhibit a comparable dynamic behavior. Hence, FET involving donors with other leaving groups

was

studied (cf. Table 10.3). The experiments are discussed in the following text.

10.4.4.1

benzylsilanes

In benzyltrimethylsilane-type compounds (Ar-↺-CH

SiMe

), the substituent is freely mobile ver-

sus the aromatic ring, which causes dynamic changes in the electron distribution similar to those

explained above. In this case, however, an inverse electron shift exists insofar that π-electrons from

the aromatic ring are shifted toward the substituents. This is different from the phenol situation

(Brede etal., 2004; Karakostas etal., 2005) (see Figure 10.9). In particular, changes in the ArCH

–

SiMe

bond have to be taken into account.

For benzylsilanes, FET (10.12) results in the formation of metastable donor radical cations

as well as unstable radical cations, which immediately dissociate into benzyl radicals and silyl

cations.

BuCl

•+

–BuCl

SiMe

•+

40%

60%

•

SiMe

Planar

Metastable

(10.12)