A u f oca talysis A n a Iyzed Sir:
I have read the article “Autocatalysis Analyzed by Analog Computer and by Experimentation” by Dr. W. E. Walles and Dr. A. E. Platt (7). I found this treatment of autocatalysis unclear. The authors also appear to have serious misconceptions about the relation of mathematics and model building to reality. I will comment on these topics in sequence. Walles and Platt postulate a model for autocatalysis. They define the range of parameters they wish to study and then calculate, with a n analog computer, the appropriate results. They then describe these results in excruciating detail. For example, the authors state, “Figure 4 shows d(c)/dt for a varying from 100 to 1000 in steps of 200, again on a time scale and rate scale different from Figure 2.” While it is certainly important for the authors to comment on the significance of their graphical results, it is surely not in the reader’s best interest to merely list the variables presented and their ranges. The authors provide what appears to be an example of the application of their model; however, the reader soon discovers that the authors modify their original model to such a great degree, in order to accommodate the physical requirements of the system, that it is difficult for the reader to see a clear relationship between the model originally proposed and the one which was finally selected. The reader finds further that the range of parameters discussed initially does not include a discussion of those parameters which the authors discuss in the example. Throughout the example the reader is asked to struggle numbly through such units as, “lines/sec.” and vague conversion factors carelessly inserted in a confusing numerical example. The tragedy of the article is that the authors have selected what is, in all probability, a good example of a n autocatalytic system; however, any virtue that the original selection had has been lost in the confused treatment. I a m also concerned about the attitude the authors adopt for the interpretations of the results obtained by the analog computer. Such statements as: (a) “An empirical relationship has been derived between u and a from our analog computer runs. . .” and (b) “The maximum rate (from the analog plots) for a = 800 was determined
as 0.945 hour-l, which is 257 times as fast as the starting rate (as observed on the analog). This supports the contentions that, in cases with a equal to 100 to 1000 the background reactions would tend to go unnoticed.” The authors must realize that (a) a n empirical relation is derived from experimental observation, and not reading the graphs plotted by an analog computer programmed to execute the solution of a set of differential equations, and (b) to say that the solution of a set of differential equations for the description of a physical system “supports” an original mathematical model is trivial. The only thing that the solution “supports” is the authors’ intuition that the model would have enough built-in features to fit the data. If the data can be matched by the simulation, the authors could say that their mechanism is a possible explanation of the observed phenomena. T h e conclusions the authors have drawn from the analog computer have no meaning unless supported by experimental data. No mechanism can be proved by a computer alone. There are other disturbing features of this report such as Equation 13 (if kS is zero then there are two simultaneous chemical equations and the observed rate equation will follow the simple exponential relationship of Equation 13 only in special cases) and the lack of rigor in the derivation of Equation 19. However, these are minor in comparison with the objections above. T h e authors have treated an interesting topic, established a reasonable model, developed clever experimental techniques to evaluate applicable rate constants, and chosen a suitable experimental example, but they have failed to transform their ideas into meaningful or useful results. By failing this task, they have failed to serve science and engineering. RICHARD N. FOSTER
307 E. 78th St. New York, N . Y . REFERENCE (1)
walh w. E., Platt, A. E., I N D . ENC. CHEM. 59 (6),41
(1967).
(Continued on the following page) VOL. 5 9
NO. 1 1 NOVEMBER 1 9 6 7
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Reply by A. E. PLATTand W . E. WALLES Sir: We have received the letter concerning our article entitled “Autocatalysis Analyzed by Analog Computer and by Experimentation” which appeared in I&EC ( I ) . We regret that Dr. Foster considered our article so lacking in clarity that he brought the matter to your attention. Nonetheless, we welcome his feedback. I t seems to us that he raises two points; one relating to an alleged lack of continuity in our presentation, and the second to misconceptions he believes we hold, regarding theoretical us. experimental interpretations. Like Dr. Foster, we wish to remark on these points sequentially, Concerning his comments in the third paragraph of his letter, we simply wish to direct attention to the third and fourth paragraphs (page 41) of our article. Here, at the beginning of the paper, we pointed out quite clearly that, while our theoretical analysis was derived from the simplest possible stoichiometry and mechanism (i-e.,A 4 B C), it was our intention to demonstrate how the basic model may be extended to more complex, real systems. Dr. Foster himself points out why we were obliged to enlarge our original model, viz: “. . , .in order to accommodate the physical requirements of the system. . . ..” O n pages 47 and 48 we explained that this modification was required by the different stoichiometry, not because of any new- concept in autocatalysis. Furthermore, Dr. Foster seems to miss the point of our theoretical analysis. Our reference to the article by R. M. Noyes (Ref. 3) was made partly to justify our use of an analog computer; the differential rate equations describing our model cannot be solved analytically. Rather than carry out an exhaustive series of runs on the computer, we defined two new parameters (a and a ) , and then analyzed the model in terms of these parameters by treating the computer results as if they were experimental results. (Our use of the word “empirical,” to w-hich Dr. Foster refers in his fourth paragraph, was meant in this way, admittedly somewhat loosely.) Our reasoning was that a given change in, say, a will always affect the kinetics in the same manner, no matter what the absolute magnitudes of either a or a. Hence, the criticism that the rate constants we considered in our analysis did not encompass those we calculated, using the identical method outlined on page 47 for the decomposition of 5-methyl-2-oxazolidinone, seems to us to be unfounded. His criticism of our “excruciating detail” (paragraph 2) is rather incompatible with his later comments. I n general, where graphs are used, surely tw-o lines of description are not excessive. Our use of strange units (viz., lines/4 min. in Figure 10 of our article) is debatable, but we felt that the text accompanying Figure 10 was sufficient to convey the meaning. Dr. Foster’s comments on our interpretive skills are, perhaps, the more interesting ones. Explicitly, his quotation labeled (b) from our article, that our observation tends to support a contention, was deliberately written in
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INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
that manner in order to avoid the criticism leveled at US by Dr. Foster ! I n writing that sentence, we were referring back to a semi-intuitive guess on our part (page 42 of our article, final paragraph) that the background reaction may pass unnoticed for high a values. But our proposed scheme demands kl # 0. Surely Dr. Foster does not begrudge US a highly subdued suggestion that this simplest model also predicts what we feel intuitively, while fully acknowledging the fact that we have, as yet, no experimental evidence to support this. Dr. Foster’s comments in paragraph 5, labeled (b), are indeed trivial, Careful study of the relevant passages of our report (page 44 penultimate paragraph, left column which refers to page 42, last paragraph, and to Ref. 4 ) shows again that his criticism is not well based. SVe disagree with him that experimental results are needed before meaningful information can be obtained from an analog computer: the transformation of a series of proposed chemical reactions into a set of concentration us. time curves is always meaningful and useful, regardless of experimental data, particularly from an educational viewpoint. The remaining parts of Dr. Foster’s paragraph 5 are truisms. Our primary intention in publishing this article was to suggest the possible importance of autocatalysis to propose a simple model to account for the kinetics of the reaction, to point out a method for analyzing the kinetics by making “empirical” use of curves from an analog computer, and finally, to demonstrate, by example, how the simple reaction scheme can be modified and then used in an actual case. Even after close re-examination, we see no reason to share Dr. Foster’s general denunciation of our efforts. One further point is worth mentioning. At tu70 places in the article we make reference to future papers. O n page 47, just above the chemical equation, we mention one on oxazolidinone decomposition, and to another on page 48, third line. At present, we are unable to make available full details of our experimental techniques, although we expect this situation to be resolved shortly. We did not consider that this would, in any way, hinder understanding our present article. The seemingly strange units (linesj4 min.) are raw rate data straight from our instruments, as there are no generally accepted rate units. \$’hen we are able to publish a full description of the rate apparatus, the method of calculating rate of gas evolution will be clear.
Chemicals Department Research Laboratory 335 Building Dow Chemical Co. Midland, Mz’ch.
W.E. WALLES
Polymer @ Chemicals Research Laboratory 335 Building Dow Chemical Co. Midland, Mich.
A. E. PLATT
REF E R ENCES (1) Walles, W. E., Platt,A. E., IND.END.CHEM.5 9 (6), 41 (1967).
