Some General Experimental Problems

Superficially one might expect that the determination of critical exponents for binary mixtures should entail only the selection of an appropriate property, its measurement as a function of temperature (or composition) with sufficient care and precision, and a log-log plot of the results according to equation (7) - aided perhaps by a least-squares analysis. Unfortunately, the situation in reality is much more complicated. Several problems must be recognized and resolved before one can reliably infer exponents from experimental results in the critical solution region. 

---

Some experimental problems involve mixtures of ingredients and the independent variables are the proportions of the various materials present in the mixtures. In general, the factorial and centra composite designs are not applicable except in certain specific cases. The reason is that the design must be set up in such a way that the sum of the proportions of the ingredients present must always be equal to one (or to some constant percentage of a larger mixture). 

The problem of how to stabilize nitrostarch has been solved by different means, but the majority of stabilization processes remain obscure as patent secrets. None the less, from certain observation some general conclusions can be made. It was early observed by Bechamp [13] that nitrostarch obtained by nitration in nitric acid alone is more stable than one obtained by means of nitric acid mixed with sulphuric acid. This has been confirmed experimentally by Hackel and T. Urbanski [18], and seems likely to be explained by the formation of starch sulphates or mixed nitric and sulphuric esters of starch. 

There are as many potential scaleup parameters as there are individual process mixing results. However, we can make some generalizations which are very helpful in dealing with actual mixing problems, but for reliable scaleup, some experimental verification of the scaleup method to be used is desirable. 

When attempting to use these polymer interface theories (1-22) in planning and interpreting experiments, we encounter two problems associated with the interaction parameter in polymer-polymer systems. First we have to find a way of determining the values of the interaction parameters for the polymer pairs of interest. There is as yet no general experimental procedure which allows us evaluation of the x parameter. Without reliable values of the x parameter, comparative tests of the competing theories can only be made qualitatively. Secondly, to be able to use these theories with more confidence we have to have some idea about the dependence of the x parameter on concentration, temperature, etc. 

I believe that empirical observations only attain the status of laws when they are accompanied by theories that support their generality or, sometimes, show their limitations. The second law of thermodynamics, with which I began this chapter, is surely a case in point. The claim that spontaneous processes will always increase the entropy of the universe is something that one can accept as a law primarily because of the statistical argument that there are more ways for things to be disordered than ordered. Certainly, one wants experimental studies to bolster the claim, but such studies by themselves would not be convincing because of the general inductive problem of empirical science—one could never rule out the possibility that some particular set(s) of conditions not studied in the experimental tests would lead to an exception to the... 

The intermediacy of metal carbonyl complexes in some catalytic processes is well established. Specific examples are presented in 14.6. Here, only some general aspects of the problem are discussed. Often the species having a key role in the catalytic cycle is not recognized as a chemically defined substance. Its structural characterization is based on indirect evidence only. Kinetic studies are of paramount importance in addition, very sensitive experimental methods, such as ESR spectroscopy, can detect catalytically relevant species at low concentrations. However, since an efficient catalyst should be present in a reaction mixture at steady-state and small concentrations, its physical detection can be difficult. 

Following the previous steps, a good problem definition should now be available. In some cases (e.g., the debutanizer), the cause may be identified. If not, there will be sufficient information to narrow down the possible causes and to form a theory. In general, when problems emerge, everyone will have a theory. In the next phase of the investigation, these theories are tested by experimentation or by trial and error. The following guidelines apply to this phase ... 

After the brief introduction to the modem methods of ab initio quantum chemistry, we will discuss specific applications. First of all, we will discuss some general aspects of the adsorption of atoms and molecules on electrochemical surfaces, including a discussion of the two different types of geometrical models that may be used to study surfaces, i. e. clusters and slabs, and how to model the effect of the electrode potential in an ab initio calculation. As a first application, the adsorption of halogens and halides on metal surfaces, a problem very central to interfacial electrochemistry, will be dealt with, followed by a section on the ab initio quantum chemical description of the adsorption of a paradigmatic probe molecule in both interfacial electrochemistry and surface science, namely carbon monoxide. Next we will discuss in detail an issue uniquely specific to electrochemistry, namely the effect of the electric field, i. e. the variable electrode potential, on the adsorption energy and vibrational properties of chemisorbed atoms and molecules. The potential-dependent adsorption of carbon monoxide will be discussed in a separate section, as this is a much studied system both in experimental electrochemistry and ab initio quantum electrochemistry. The interaction of water and water dissociation products with metal surfaces will be the next topic of interest. Finally, as a last... 

---