Hole volume

The greatly reduced hole volume of slim hole wells can lead to problems if an influx is experienced (see section 3.7). The maximum depth drillable with slim hole configurations is another current limitation of this technology. 

Rifle bullet sensitivity. About 60% of trials affected by 0.30 cal bullet fired at 90 ft, vs 92% affected for Pentolite Shaped charge effectiveness. Steel cone, hole volume 130% TNT... 

It follows from what has been said above that free-volume is a value that is determined by both hole volume and empty volume, the latter being connected with the packing mode. In this case an empty volume ve = vr — vw, where vr is the real (observed) volume at temperature T and vw the volume of the substances as calculated from the Van der Waals dimensions obtained by an X-ray diffraction method or from the gas-kinetic collision cross-section3. Then the expansion volume vex = v - v0, where v0 is the volume occupied by the molecules at 0 K in a close-packed crystalline state. 

Indeed, these values appear to be more constant for various polymers than those commonly calculated. Fractions y>fi and corresponding state at glass temperature. From Eqs. (59) it follows that at Tt the ratio of hole volume to expansion volume must be constant, the latter being determined by translational movements of molecules. In particular, these values are present in the equation describing T as a function of degree of polymerization. 

Later Kanig took into account the temperature dependence of the fractional free-volume, calculated according to his equations. Below Tg, as temperature decreases, sPfl increases as a result of a decrease in expansion volume at frozen hole volume. Above Tg, pn increases due to the sharp rise in hole volume. At Te the value ip i is at its minimum. From the condition d [Pg.75]

It is apparent that only the average value corresponds to the universal value in WLF theory, and that the deviations from this value can be very considerable. In spite of this, we may believe that free-volume is determined mainly by the hole volume. At the same time it follows from Eq. (63) that the SB constant is a very complex value and a function of p and a. Plotting the experimental data in coordinates... 

Here oth is the fraction of thermal expansion connected with changes in hole concentration (free-volume expansion), ), is the energy of hole formation, r=M/p0 Vn Na, where NA is the Avogadro number,M molecular weight, p0 the density of a liquid without holes at absolute zero, and Vn the hole volume. For polymeric systems r is very small, and then ahTis the function of E IRTalone. The value Of, is identified with experimentally observed changes in the thermal expansion coefficients A a at Tg, i.e. 

Polymer ApTg ACT P g J.g-1 Nh number of holes per gram at T°° ( x 1021) Eh hole energy (kj/mole) F g hole fraction Vg hole volume (A3)... 

Crack propagation velocity Volume of the hole Volume of the border-wall... 

Hole Volume and Propagation of Explosion", Kogyo Kayaku (J. Ind. Explosives Soc. 

Alternative ways of determining the free volume fraction without using I3 have also been proposed by Dlubek et al [28], as well as, Brandzuch et al [29], Dlubek et al used the coefficient of thermal expansion of the amorphous regions and hole volume determined from positron data to determine the number density of the free volume holes. Brandzuch et. al. used the coefficient of thermal expansion just above and just below the Tg to estimate the fractional free volumes. This model is based on the assumption that the expansion of the holes of the free volume, as seen by positrons, reflects the expansion of the total volume of the material. 

Bockris and Richards experimental value of the free volume for KCI (V = 0.68 cm mol" ) agrees well with that of Woodcock and Singer. The volume change on melting obtained experimentally, however, is 8.2 cm mor )which is only 3% less than the entirely acceptable calculated value obtained by Woodcock and Singer s Monte Carlo simulation. Their actual model for liquid KCI is shown in Fig. 5.14 and appears to contain hole volume corresponding to modelistic concepts which feature this property (Section 5.5.1). 

This is the distribution function which was said to be the goal at the beginning of Eq. (5.17). From it, the average hole volume and radius will shortly be seen to be obtainable (see Fig. 5.22). 

Surface Tension, Mean Hole Volume Mean Hole Radius... 

What of rij at Ts other than the melting point, at which temperature has been assumed to be unity From Eq. (5.44), the hoie voiume—and hence its surface area—should increase as T increases (and y decreases, as it does with an increase in 7). Of course, ions surround the hole and it seems reasonable to assume that as the hole volume increases, the number of ions that surround it will increase, and thus the number that is needed to fill it (thus causing the work An yj) will also increase. 

Fig. 5.47. Plot of the free volume per ion against the average hole volume ( ) LiCI, (a) NaCI, ( ) KCI, (a) CsCI, (+) NaBr, (v) KBr, ( ) CsBr, ( ) Nal, (o) Kl.

In a molten salt (as shown by a diagram in the text), the free volume increases with the hole volume in a roughly proportional way. Consider this correlation and make deductions as to what kind of structure in a molten salt would be eonsistent with the observation quoted. 

There is a linear relation between the free volume from sound velocity measurements and the hole volume (from volume of fusion data). 

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