Indifference

If you were offered 7,130 today, or 10,000 in exactly 5 years time, you should be indifferent to the options, unless you could find an alternative investment opportunity which yielded a guaranteed interest rate better than the bank (in which case you should accept the money today and take the alternative investment opportunity). 

The use of more complex or more costly articles of equipment, such as catalytic hydrogenation apparatus, autoclaves, polari-meters, ultraviolet absorption spectrometers, etc., has not been described, because the type of such apparatus employed indifferent laboratories varies considerably, and students must be taught the use of their own laboratory equipment. 

Substances which decompose (or otherwise change) in contact with air must be recrystallised in an indifferent atmosphere, such as carbon dioxide, nitrogen or hydrogen. The apparatus of Fig. 

II, 36, 1 is almost self explanatory two ground glass joints are used, but these may be replaced by rubber stoppers, if desired. The crude substance is placed in the flask A. Stopcocks 1 and 2 are closed, and the apparatus is exhausted through tap 3 the indifferent gas is then allowed to enter the apparatus to atmospheric pressure. The evacuation and filling with inert gas are repeated several times. The solvent is added through the tap funnel B. 

Group V. Hydrocarbons and compounds containing C, H and 0 that are not in Groups I-IV and are soluble in concentrated sulphuric acid ( indifferent compoimds ). 

Group VII. This group comprises all compounds containing N or S which are insoluble in water and are indifferent (i.e., insoluble in dilute acid or alkali). 

At the beginning of this section we enumerated four ways in which actual polymer molecules deviate from the model for perfectly flexible chains. The three sources of deviation which we have discussed so far all lead to the prediction of larger coil dimensions than would be the case for perfect flexibility. The fourth source of discrepancy, solvent interaction, can have either an expansion or a contraction effect on the coil dimensions. To see how this comes about, we consider enclosing the spherical domain occupied by the polymer molecule by a hypothetical boundary as indicated by the broken line in Fig. 1.9. Only a portion of this domain is actually occupied by chain segments, and the remaining sites are occupied by solvent molecules which we have assumed to be totally indifferent as far as coil dimensions are concerned. The region enclosed by this hypothetical boundary may be viewed as a solution, an we next consider the tendency of solvent molecules to cross in or out of the domain of the polymer molecule. 

We shall refer to electrolytes which do not affect the charge of the polymer as indifferent electrolytes. In the situation illustrated by reaction (8.B), the HCl and NaOH are clearly not indifferent. We shall also assume that the indifferent electrolytes are 100% ionized in the polymer solution. 

We continue to designate the solvent (usually water) as component 1, the polymer as component 2, and the indifferent electrolyte MX as component 3. We arbitrarily designate the polymer to be a cation with a relative charge of +z, having associated with it the same anion as is present in MX. Accordingly, we designate the polymer PX and represent its dissociation by... 

It is conventional to use molality—moles of solute per kilogram of solvent (symbol m)—as the concentration unit in electrolyte thermodynamics. Accordingly, we shall represent the concentrations of both the indifferent electrolyte and the polymer in these units in this section m3 and m2, respectively. In the same dilute (with respect to polymer) approximation that we have used elsewhere in this chapter, m2 is related to the mass volume system of units C2 by... 

Donnan equilibrium arises from applying the phase equilibrium criterion to the indifferent electrolyte . From Eq. (8.13) this is /ia = +... 

The effect of the charge as well as that of the indifferent electrolyte, then, is contained in the term in brackets. A numerical calculation is probably the easiest way to examine this effect. This is illustrated in the following example. 

The bracketed term approaches the value of m2 as the concentration of indifferent electrolyte increases. 

For the other extreme in which the concentration of the indifferent electo-lyte is high. 

These results show more clearly than Fq. (8.126)-of which they are special cases-the effect of charge and indifferent electrolyte concentration on the osmotic pressure of the solution. In terms of the determination of molecular weight of a polyelectrolyte by osmometry. ... 

A correct value of the molecular weight is obtained for the charged polymer by the van t Hoff equation, provided that a large excess of indifferent electrolyte is present. These high concentrations are described as swamping electrolyte conditions. 

What makes the latter items particularly important is the fact that the charge and electrolyte content of an unknown polymer may not be known hence it is important to design an osmotic pressure experiment correctly for such a system. It is often easier to add swamping amounts of electrolyte than to totally eliminate all traces of electrolyte. Under the former conditions a true molecular weight is obtained. Trouble arises only when the experimenter is indifferent toward indifferent electrolyte this sort of carelessness can be the source of much confusion. 

Stmctural order varies from x-ray indifferent (amorphous) to some degree of crystallinity. The latter product has been named pseudoboehmite or gelatinous boehmite. Its x-ray diffraction pattern shows broad bands that coincide with the strong reflections of the weU-crystallized boehmite. 

The addition product, C QHgNa, called naphthalenesodium or sodium naphthalene complex, may be regarded as a resonance hybrid. The ether is more than just a solvent that promotes the reaction. StabiUty of the complex depends on the presence of the ether, and sodium can be Hberated by evaporating the ether or by dilution using an indifferent solvent, such as ethyl ether. A number of ether-type solvents are effective in complex preparation, such as methyl ethyl ether, ethylene glycol dimethyl ether, dioxane, and THF. Trimethyl amine also promotes complex formation. This reaction proceeds with all alkah metals. Other aromatic compounds, eg, diphenyl, anthracene, and phenanthrene, also form sodium complexes (16,20). 

The closer one is to the failure, the more its direct effects are apparent. The cumulative effects of failure are often overlooked in the rush to fix the immediate problem. Too often, the cause of failure is ignored or forgotten because of time constraints or indifference. The failure or corrosion is considered just a cost of doing business. Inevitably, such problems become chronic associated costs, tribulations, and delays become ingrained. Problems persist until cost or concern overwhelm corporate inertia. A temporary solution is no longer acceptable the correct solution is to identify and eliminate the failure. Preventative costs are almost always a small fraction of those associated with neglect. 

The human element, seen in errors, ignorance, lack of training, lethargy, illiteracy or indiscipline, or indifference, must be monitored carefully. This may require either an adequately qualified and experienced person or proper job training. Indifference, for reasons other than the above, would be a matter for human resource development, where a worker s skills and habits may have to be adapted to fit into the system. 

Several generalizations of the inelastic theory to large deformations are developed in Section 5.4. In one the stretching (velocity strain) tensor is substituted for the strain rate. In order to make the resulting constitutive equations objective, i.e., invariant to relative rotation between the material and the coordinate frame, the stress rate must be replaced by one of a class of indifferent (objective) stress rates, and the moduli and elastic limit functions must be isotropic. In the elastic case, the constitutive equations reduce to the equation of hypoelastidty. The corresponding inelastic equations are therefore termed hypoinelastic. 

In the language of Section A.4, s and d are indifferent but s is not, involving extra terms in Q. In order to render the stress rate indifferent, the extra terms must be cancelled out. This may be done using the spin tensor w defined in (A.l Ij), following the steps leading to (A.68). The result is... 

In order to consider the inelastic stress rate relation (5.111), some assumptions must be made about the properties of the set of internal state variables k. With the back stress discussed in Section 5.3 in mind, it will be assumed that k represents a single second-order tensor which is indifferent, i.e., it transforms under (A.50) like the Cauchy stress or the Almansi strain. Like the stress, k is not indifferent, but the Jaumann rate of k, defined in a manner analogous to (A.69), is. With these assumptions, precisely the same arguments... 

Of course, k may be taken to be comprised of a number of such tensors, and it is not difficult to extend the theory to include a number of indifferent scalars and vectors, if desired. 

Jaumann s stress rate is not the only indifferent rate which could be used to render (5.117) objective. Truesdell s rate defined by (A.42) is indifferent, as shown in (A.70), and can serve just as well. Inserting Truesdell s rate instead of Jaumann s rate, (5.117) reduces to the three ordinary differential equations... 

In this case, the shear stress is linear in the shear strain. While more physically reasonable, this is not likely to provide a satisfactory representation for the large deformation shear response of many materials either, since most materials may be expected to stiffen with deformation. Note that the hypoelastic equation of grade zero (5.117) is not invariant to the choice of indifferent stress rate, the predicted response for simple shear depending on the choice which is made. 

A number of other indifferent stress rates have been used to obtain solutions to the simple shear problem, each of which provides a different shear stress-shear strain response which has no latitude, apart from the constant Lame coefficient /r, for representing nonlinearities in the response of various materials. These different solutions have prompted a discussion in the literature regarding which indifferent stress rate is the correct one to use for large deformations. 

It is possible to assume other transformation properties for k. For example, for some purposes it may be more desirable to attribute strainlike properties obeying a transformation law like (A. 19), in which case the equations of this section will take a somewhat different form. Of course, k may be taken to be comprised of a number of such tensors, and it is not difficult to extend the theory to include a number of indifferent scalars and vectors, if desired. 

The objectivity of the spatial stress rate relation (5.154) may be investigated by applying the coordinate transformation (A.50) representing a rotation and translation of the coordinate frame. The spatial strain and its convected rate are indifferent by (A.58) and (A.62). So are the stress and its Truesdell rate. It is readily verified from (5.151), (5.152), and the fact that K has been assumed to be invariant, that k and its Truesdell rate are also indifferent. Using these facts together with (A.53) in (5.154) with c and b given by (5.155)... 

A vector is said to be indifferent if it does not change magnitude or direction under (A.50). For example, the vector a = x — y where x and y are positions in space, under the transformation (A.50), becomes... 

An indifferent second-order tensor is one which maps indifferent vectors into indifferent vectors. Consider the mapping A such that b = Aa where a and b are arbitrary indifferent vectors. Then under the transformation (A.50) b = Qb and fl = Qa, so that... 

Since a is an arbitrary vector, from the second relation it follows that an indifferent second-order tensor transforms as... 

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