The W Value

If an incident particle with energy generates on the average n. ions of either sign while being completely absorbed, then the integral W value of the medium is defined by 

Dalgarno and Griffing (1958) made a detailed theoretical analysis of the ionization produced by a beam of protons penetrating a gas of H atoms. They find that the W value remains constant at around 36 eV, to within 2.5 eV, for proton energies of 10 KeV and up. However, below about 100 KeV, the near constancy of the W value is also partially due to the fact that the beam is a near equilibrium composition of protons and H atoms because of charge exchange. Therefore, at 

Platzman (1961) gave the ratio of the W value to the ionization potential (I) as 

respectively. Thus, Platzman obtained W = 42.3 eV and W/I = 1.71 for He, in agreement with the main experimental results. Although the exact relationship between W and I remains somewhat elusive, many empirical rules are known. For molecules, as an example, Christophorou (1971) obtained by the method of least squares W = 9.8 + 1.671 for a-particles and W= 5.9 + 1.821 for /1-particles and high-speed electrons. 

N is the number density of molecules, Jx is the cross section for production of any primary species x at electron energy E having an energetic threshold Ix for its production, and N/T) is the total number of such species formed by the complete absorption of an electron of kinetic energy T. In this sense, y can be thought of as a distribution function. Specifically, if x refers to ionization, Ix is simply the ionization potential I, Ox is the ionization cross section a, and N = n., the total number of ionizations. 

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The non-Newtonian index is plotted against the blend ratio in Fig. 8. We see that for both the preblends and the preheated blends, the w value increases with NBR content up to about 50% of NBR. Beyond this while the preblend shows a continued increase in n value at a slower rate, the preheated blends seem to show a saturation in n value. The low values of may be attributed to the interchain crosslinking at higher levels of NBR in the blends. 

Stored elastic energy (Fig. 12) also increases with shear rate both for preblends and preheated blends. Here again, we see that the W values increase sharply with NBR, attain a maximum at 50 50 level, and beyond 50% NBR the stored elastic energy decreases. 

In liquefied rare gases (LRG) the ejected electron has a long thermalization distance, because the subexcitation electrons can only be thermalized by elastic collisions, a very inefficient process predicated by the small mass ratio of the electron to that of the rare gas atom. Thus, even at a minimum of LET (for a -1-MeV electron), the thermalization distance exceeds the interionization distance on the track, determined by the LET and the W value, by an order of magnitude or more (Mozumder, 1995). Therefore, isolated spurs are never seen in LRG, and even at the minimum LET the track model is better described with a cylindrical symmetry. This matter is of great consequence to the theoretical understanding of free-ion yields in LRG (see Sect. 9.6). 

The minimum energy I required for ionization is called the (first) ionization potential. The W value is the average energy required to produce a pair of ions in the medium. Experimentally this value is obtained by dividing the absorbed dose by the total number of collected ions. The W value depends primarily on... 

Another method for finding the W value, called the Fowler equation approach (Inokuti, 1975), is based on three assumptions, some of which can be relaxed. These are (1) that the incident particle is an electron (2) that there is only one ionization potential and (3) that the ionization efficiency is unity— that is, any energy loss E > I results in an ionization with a primary of energy... 

Another procedure for calculating the W value has been developed by La Verne and Mozumder (1992) and applied to electron and proton irradiation of gaseous water. Considering a small section Ax of an electron track, the energy loss of the primary electron is S(E) Ax, where S(E) is the stopping power at electron energy E. The average number of primary ionizations produced over Ax is No. Ax where o. is the total ionization cross section and N is the number density of molecules. Thus, the W value for primary ionization is 0)p = S(E)/No.(E). If the differential ionization cross section for the production... 

Scavenging experiments in hydrocarbon liquids (Rzad et al, 1970 Kimura and Fueki, 1970) tend to give low observed ionization yield, although the primary yield may be greater. The situation is similar for free-ion yield measurement under a relatively large external field. Both processes require large extrapolations to obtain the W value. 

In Sect. 4.9.1, experimental rationalization was provided for the W value of ionization in gaseous and liquid water, giving respectively 30.0 and 20.8 eV. The corresponding ionization potentials are respectively 12.6 and 8.3 eV. For the purpose of diffusion and stochastic kinetics, one often requires the statistical distribution P(i,j) of the number of ionizations i and excitations j, conditioned on i ionizations, for a spur of energy . Pimblott and Mozumder (1991) write P(i, j) = r(i) 2(j i), where F(i) is the probability of having i ionizations and 2(j i) is the probability of having j excitations conditioned on i ionizations. These probabilities are separately normalized to unity. 

Ionization yield is readily measured this offers relatively simple dosimetry, as the W value for ionization is nearly independent of the quality and energy of the incident particle (see Sect. 4.8). 

Since this book is primarily concerned with condensed-phase studies, we do not go into the details of gas-phase radiation chemistry. We will briefly outline some important mechanisms of gas-phase reactions, followed by a presentation of some specific examples and certain theoretical considerations. In Chapter 4, we considered ionization and excitation in some detail. Many of these considerations apply to the gas phase these will not be repeated. We stress that the measurement of the W value is of utmost importance in the... 

These statements seem to mean that the molecule BaO is a resonance hybrid of 85% of the ionic structure Ba+0 and 15% of covalent structures which have no dipole moment and at least part of which have the double bond Ba + 64 0 +, contrary to the single bond structure Ba+C2F+. If so, one would have to conclude that the BeO molecule, which allegedly has 114% ionic character, contains a contribution of —14% of covalent structures which appear to have a double bond since the force constant of BeO is 1.30 times (based on the w values given by Herzberg) larger than that of BeF. 

Now, half of the w values will be positive, and the other half will be negative. We will use this criteria to divide them into two parts ... 

Cole [52] measured the W value in air for electron energies from 5 to 20 eV, while the electrons were completely absorbed in the ionization chamber. Later, Combecher [53] extended the measurements of W E) to several gases including water vapor. Fig. 6 shows the variation of W E) with electron energy in water vapor, as measured by Combecher,... 

As the W -values of the major component of flue gas are nearly 30 eV, the total amount of positive ions produced will be 3 in G-value. The most important reaction of positive ions is that with H2O. For example, Nj reacts with H2O to produce OH radical, decomposing H2O through charge transfer reaction. 

Many investigations have been undertaken regarding the effect of the water concentration in the microemulsion on the catalytic behaviour of enzymes. The surfactant concentration of the microemulsion defines the size of the internal interface but it often has no measurable influence on the enzyme kinetics. On the other hand, the physical properties of the water located inside the reverse micelles differ from those of bulk water, and the difference becomes progressively smaller as the water concentration, expressed in the w -value, increases. 

QLUTIQI1 Starting with the circuit of EXERCI5E 1-7, let the W value of the PMOS transistor be set by the parameter Wp val. Also, add the PARAM part ... 

A and B. DE values were calculated from the W values given in Section IV, A for the Kekul6 structures of types 131 and 132. The data for benzothiophenes (Fig. 18) make it clear that Model Al yields DE... 

At this point, we might wonder how reasonable it is to use (W) values as given in Tables 14.2 and 14.3 for assessing whether a reaction will occur spontaneously in a given natural system. The species involved will not, of course, be present at standard concentrations. To evaluate this problem, let us compare the En value of a 1CT4 M aqueous hydrogen sulfide (H2S) solution at pH 8 with the ]](W) value of reaction 10 in Table 14.2 (-0.27 V). The calculated value (see Illustrative Example 14.3) is -0.18 V, which is still in the same ballpark. Of course, if we want to evaluate the free... 

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