DOI:10.9734/bpi/tac/v2
ABSTRACT
This article presents a critical analysis of the frequent practice of using the Arrhenius equation for mathematical modeling of very many physical and chemical rate processes. This approach may also be used to characterize the controls and mechanisms of the rate processes investigated. We also discuss the specific form of the Arrhenius-type equation as a relationship meriting detailed investigations. In our opinion, the use of the Arrhenius relationship often can only approximate to the behavior of such systems, exemplified by the systems discussed below, including the work of N N Semenov, A K Galwey, A G Mershanov, etc. We draw attention to "erroneous" experimental designs, including the so-called "global kinetic mechanism" and other widespread uses of theoretical models which do not necessarily represent the real situation. Such limitations in rate data analyses impact negatively throughout this branch of science. Here we attempt to question these accepted practices realistically and find answers to the types of studies under consideration that do not include the misconceptions often contained (concealed) therein. Unfortunately, besides the scientific component, various political and social applications often interfere in the process by introducing errors. This symbiosis of delusions is considered for the example of “solid flame”, a Russian theme that may not be familiar to English-speaking readers. The consequences of repression for scientists in connection with their position on scientific issues are described.
1. INTRODUCTION
The original article “On the anniversary of the phenomenon of "solid flame" about some features of modern practice of the theoretical description of combustion processes” [1], the author contacted several like-minded scientists and confirmed that the problem analyzed here relates not only to Russian (Soviet) science, but is universal.
These problems include both the difficulties for a practical scientist, without philosophical training to acquire knowledge capable of addressing fundamental scientific problems. Much and varied damage has been inflicted on science by scientists themselves, some of whom are sincerely mistaken, others parasitize the current situation for the sake of financial flows and/or their own careers, still others work under imposed pressures of various kinds. Students are attracted to careers in academic science because of their interest in the subject rather than financial reward. But then they hear messages that make them think twice about this career choice. A big attraction and important component of a job as an academic scientist is to launch a research program. Unlike the case of jobs in hierarchal companies or organizations, projects are not dictated or handed down by a senior authority [2].
In this article, we use a concrete example to discuss clearly the difficulties of changing scientific "paradigms" which have been shown to be erroneous. The word "paradigm" came into general use following the success of the book by the American thinker, the historian of science, Thomas Kuhn "The Structure of Scientific Revolutions" (1962) and long ago gave rise to the term parasite "paradigm". According to T. Kuhn, an incorrect paradigms can "endure indefinitely", and he describes the mechanisms by which the successors of an “old and wrong theory” can continue in use.
Kuhn writes that even if the scientific community as a whole is permeated by a spirit of tolerance, it has double standards of reasoning, and the judgment in support of a “paradigmatic” ontology is perceived in the context of “yes”. While any attempt to substantiate data that contradicts a “main”, but erroneous, theory, includes the “no” context perception barrier, which is almost impossible to overcome. Kuhn's numerous arguments can be found in his book, and the author has already accumulated his own experience of examples of opposition to this information from scientific colleagues.
This article attempts to breach the wall of "no-strategy" and, therefore it is polemical. At first glance, the questions raised by this author are even trivial so obvious is the fallacy of the dominant paradigms. However, the author's many years of attempts to break through the wall described by Kuhn have been in vain.
As mentioned, thanks to publications by like-minded scientists, including, English-speaking scientist Galwey (Hirsch index 33), and, through him, Professor Steve Strauss of the University of Colorado, USA, and others. Now a joint publication is being prepared with Galwey A K, Khatchoyan A V, a mathematician and author of books on the Arrhenius equation. Its coverage is intended to be generally similar to the present text, though with greater detail and more citations.
One further generalization: though this article specifically concerns the Arrhenius Equation (AE), authors are convinced that similar 'corrosion' of science (i.e., the use of incorrect paradigms) often arises in other fields of science and in many countries. The author is a specialist in chemical physics and suggests that colleagues should study their field's history in search of similar “corrosive” examples. Such examples of fake science should be identified as the aimed or non-intended falsifications of scientific investigations over long periods of time. The “corrosion” arises when a wrong interpretation is successfully established, developing and even become a mainstream concept in the given scientific field, as described below. Moreover, the “corrosion” of science can't exist without some social surrounding, implying the public, economic or even the cultural influence. Kuhn has shown that there are scientists and groups who accept the wrong approaches (and their applications and uses) thereby rejecting all alternative opinions. In addition, there are interested political or cultural authorities, social leaders, politicians and even foreign agents or spies interfering in some concrete scientific activities (such as economic and other interests). Maybe some of these types of example will be useful for consideration b specialists in philosophy and sociology, who have hitherto taken little interest in problems of scientific truth or its deviations in the social content.
Topics considered in the present article include: the story of how incorrect paradigms, based on the surprisingly capacious and useful Arrhenius equation, manage to survive within different historical contexts, e.g., USSR and Russia.
Initially, the historical story of the appearance of the Arrhenius equation, and how it became so widely applicable, was justified within different disciplines by attempts to explain its amazing ability to adapt to quite diverse situations.
The next section presents the case of a like-minded scientist, Galwey from Ireland, who, throughout his scientific career, agreed that the AE can replace true processes and support incorrect scientific paradigms.
But the particular accuracy of these applications, and the corresponding danger, lurks when the AE encounters the equations of physics and 'infiltrates' them into the science called macrokinetics. Macrokinetics most successfully solved a huge number of tasks. This article presents a successful example, the problem of thermal explosion, with the reservation that. If perfect agreements are obtained with experimental data and good prognostic criteria, but the so-called activation energy has no physical meaning, then these results should be regarded with caution.
This situation becomes quite dangerous when the AE with macrokinetics encounter with certain political and
social circumstances. Then, Kuhn's mechanisms for defending the wrong paradigms become important.
Political devices and methods of influencing scientists who resist scientific iniquity are changing dramatically, but the wrong paradigms have been surviving, unquestioned for many decades.
This article focuses on the paradigm of "solid flame" (SHS), perhaps less-well known to Englishspeaking readers. This story is still in the “hot” stage and the author still hopes that the wrong paradigms will be defeated in the near future, and the affected scientists rehabilitated.
Furthermore, the author has already accumulated a huge archive of court cases, including all sorts of correspondence with various government structures on the scientific issue of combating false science. All this material can be published in the now-fashionable "nonfiction" genre and this can serve as an interesting historical source about modern Russia.
1. ARRHENIUS EQUATION IN ITSELF
1.1 The Arrhenius Equation: History, Properties, Applications, Limitations
2019 is the 130th anniversary of publication of Svante August Arrhenius' seminal paper: "On the rate of inversion of cane sugar under the action of acids". This arose through the introduction, to physics and chemistry, of the famous equation (1). This equation was not inferred, but selected empirically from several variants used to describe the rate variation with temperature of a specific chemical reaction: cane sugar breakdown in acid. In Arrhenius' article seven empirical equations from the works of different authors were cited, number 5 being from the work of Van't Hoff and Schwab (1884), which is closely similar to the modern form of the equation now (so widely) associated with Arrhenius' name:
k = A exp(-E / RT) (1)
(k -reaction constant/t, A - pre-exponential factor, Е - activation energy, T - temperature/K)
Very often, especially the rate constant tables [3] and under the chemical processes numerical modeling the rate constant is presented in the form:
к = A expTn (-E / RT) (2)
(with n as an empirical factor).
In the transition state theory it is supposed that factor n reflects a role of the reacting particle inner freedom degrees into the activation process. Sometimes this formula (2) with the three empiric constants is called kinetic triad, and below we describe a history of problems, including Galwey's attempts to define these constants.
Early in the 20th century profound progress was made in understanding the properties of atoms and structures of molecules. Appreciation of the modest article by Arrhenius' rather narrow study resulted in the "fitting" of rate measurements to an equation and this became a revolutionary milestone in the development of chemistry and other sciences. It was now possible to describe quantitatively the most complicated physicochemical processes. The Arrhenius equation could be derived through molecular- kinetic theory and also by more complex mathematical constructions. These included, for example, inverse Laplace transformations, using various theoretical approaches: thermodynamic, collision theory, transition state theory, stochastic approaches. The modern bibliography on the Arrhenius equation is extensive. It transpires that the "rate constant", used in chemical kinetics, is called a constant only by tradition and only formally. In fact, it is a very complex parameter, which includes many specific physicochemical features characteristic of each particular system under study. During the 1960-70s, special attention was directed towards studies of plasma-chemical and radiation- chemical processes.
I regard the AE as a 20th century analogue of the "phlogiston theory". This reference arises through recognition within the current situation of specific analogies identified in the modeling of physical and chemical processes. We can recall that the phlogiston theory was one of the earliest concepts (from 1667) that can be considered scientific, in the modern sense, and was concerned with burning. This theory from the Greek (combustible) is associated with the names of German chemists Johann Joachim Becher and Georg Ernst Stahl. These authors identified Phlogiston as a hypothetical fluid, possessing a negative mass, and present in all combustible materials. According to this hypothesis, combustion is represented as an expansion with the release of phlogiston, which is scattered into the air, appearing as visible fire. Despite the absurdity of such views, from the perspective of modern science, the phlogiston theory simply and adequately described the experimental facts, was internally consistent, creative, etc. With its help many correct predictions were made and positive practical results obtained.
The theory was widely accepted by scientists for more than a century. As an illustration, we can cite the famous chemist Antoine Lavoisier, whose name is associated with the "oxygen" theory of combustion. Although Lavoisier himself mainly continued to use the phlogiston theory, he explained the successful method of bleaching sugar with activated charcoal by identifying the yellowish shade of sugar crystals as due to the presence of phlogiston, which can be removed by making it switch to charcoal (which we now know adsorbs colored impurities from solution). This successful process brought the scientist a lot of money. Later Lavoisier participated in the redemption of taxes and this led him to the guillotine of the French Revolution. Now, unlike the times of Lavoisier, our insights into understanding the steps involved in chemical reactions is very much greater.
However, the "phlogistonic" essence of the Arrhenius equation is much simpler: this equation, paraphrasing the name of a famous article by J. Wiener ("The Incomprehensible Efficiency of Mathematics in the Natural Sciences") "Inconceivably effective mathematical" object: it makes it possible to close apply to almost any system.
It is strange that this mathematical expression, very simple in form and essence, in applications becomes most interesting and fruitful. With time, the AE was found to have increasing meaning and content, not only in chemistry, but in many other fields of sciences (from physics to population statistics and dislocations theory). At the end of 19 century the equation arose within the great surge of progress and development of theoretical physics, including the formulation of the main principles of thermodynamics and physicochemical kinetics in general. The main purpose of chemical kinetics theory is to establish the chemical reaction rate dependences on reagent concentrations, temperature and other physical parameters that can influence the reacting system itself. Some of these parameters are may be inadequately defined or strictly formulated (e.g., the dependences on the electrode potential in electrochemistry, light intensity during photochemical processes, etc.). Moreover, it supposed that complex reactions can be divided into the elementary stages, each one of which can be formally independent or separated. The strength of the concept arises because the reaction rate depends on a single parameter, temperature, though this appears as one of the thermodynamic postulates. The formula proposed was very simple, convenient and effective across a very large number of chemical reactions. Therefore, this equation has become an important part of 20th century science and remains a necessary element of kinetics throughout several fields of modern science and technology.
In this sense, the Arrhenius equation resembles that other great, and very important, Schrodinger equation in quantum mechanics (though this comparison can appear spanned), because it also was derived without any physical and chemical foundation, but similarly has a great creative potential.
Attempts to justify or substantiate the AE in text-books of kinetics (e.g., by the Boltzmann's gas kinetics equation) or the activated complex theories etc. usually seem to be unconvincing.
As stated above, the AE contains only two parameters (absolute temperature T and activation energy Еа). A principal scientific problem is that the concept of absolute temperature itself, for any system, requires the postulation of the special law (principle) of thermodynamics which, in turn, requires many and complex preliminary conditions describing the system, etc. These include theories for the chemical processes involved with calculations for all the many components, ingredients, inhibitors, catalysts and other parameters (system parameters, forms, surfaces, etc.). There have been attempts to substantiate the AE, deriving it directly from the Boltzmann's equation to find solutions for various evolutionary plasmochemical and aerodynamic systems. Such an approach can be regarded as in double jeopardy, because here one tries to derive the chemical kinetics equation from the Boltzmann gas kinetics equation, having wider generality and meaning (Boltzmann's H-theorem, a general notion of entropy, direction of time or so called time's arrow, etc.). The general idea often was simply to compare theoretical and measured values of the constant E, in the AE, because in plasmochemistry many systems cannot be directly connected or described by the concept of temperature.
In this connection, it is interesting to note that the Chancellor of Germany, Angelina Merkel, was engaged in radiation chemistry, and her doctoral dissertation was devoted precisely to the "comparison" of the so-called statistical and kinetic reaction rate constants. Many works connected with this equation concern the non-equilibrium of real processes together with the concepts of Arrhenius and non-Arrhenius kinetics. Thus the positive role of this equation can hardly be overestimated: it enables many complex problems of macrokinetic to be solved. Funny enough that practically the same was titled the one of this paper authors DP thesis (in Moscow). As an illustration of kinetic in general a politics role in science let's mark that A. Merkel later becomes a Secretary of GDR Academy Young Communist Committee Secretary and have a brilliant new politician carrier.
The idea of one or several equations describing the complex process naturally lead to an idea of some equations total set writing, characterizing the history and behavior of big and complex systems. Such equations firstly were introduced by a famous W. Pauli and were called Master Equations. Later and until now they remain an object of great interest. In 1977 Ilia Prigogine wins Nobel Prize for studies of some complex physical and chemical systems (which are comparable by complexity with living organisms or some social structures). We will a little discussing the investigations in this direction that are successfully prolonging and expanding, especially in medicine etc. It can be said in general, that AE meaning (and many connected with it scientific problems) until no remain are not exhausted and the equation (and his history too) are demanding the more detailed and precise studies and analysis.
It must be also said, that there were other attempts to create an equation for the chemical reaction rate, a power law or a polynomial, can be used as closing functions that describe the chemical interaction in combustion, the main thing is the presence of coefficients that can be varied to "fit" to the experimental data. But the Arrhenius exponent unlike these functions seems to have a physical and chemical meaning and the "fit" turns into "modeling", as if based on the laws of nature.
Below we describe some examples of the Arrhenius equation being applied incorrectly.
2.2 The Case of A K Galwey
Galwey is the author or co-author of tens publications concerning the global kinetics (macrokinetic) equations used incorrectly for different, mainly complex systems involving the thermal reactions of solids and described by the AE equation incorrect or wrong usage for different and mainly complex systems described by Ae equations. His reviews [4,5] describe the strange history of degradation of the science related to the study and modeling of the changes that occur on heating a variety of diverse, initially solid, reactants. Again, we can identify the collision of two distinctive and different approaches. One is based on the careful study of complex processes by calorimetric measurements, generally complemented by kinetic investigations, supported with appropriate chemical and physical observations, e.g., the effects of changes in reaction conditions, the use microscopy, etc. From the earliest kinetic study of a solid-state decomposition, of silver oxide, Ag2O, in 1905, and up to the 1980s, this approach was actively developed and gave many interesting and important results. However, around the 1970s, those active in the field began to apply the more primitive approach, so called thermal analysis (TA): without complementary, confirmatory observations but with an increasingly sophisticated automated experimental techniques, exploiting the versatile computers becoming available at that time. The approach could be used for to analyze the many and precise experimental yield-time-temperature observations measured, collected and stored in their memories. Thus, the experiments required to obtain and to 'analyze' high quality rate measurements for thermal reactions of solids progressively became highly automated, with considerable reduction in the time and effort required by the researcher. These successes enabled 'completion' of each TA thermal reaction investigation much more rapidly and efficiently than was possible in earlier chemical-type studies within this branch of chemical kinetics.
From about 1980 onward, 'Main-stream' chemical Journals published progressively fewer studies in the field of solid-state thermal reactions, interest in such reactions apparently declined to almost zero. In contrast, at the same time, the number of reports of studies using TA, DSC, etc. methods proliferated considerably, appearing, almost exclusively, in Journals specializing in these, as well as some other types of investigations. These publications include: The Journal of Thermal Analysis and Calorimetry (Springer), Thermochimica Acta (Elsevier), Journal of Analytical and Applied Pyrolysis (Elsevier) and a few others. Thus, the surprising change that occurred was the virtual complete abandonment of chemical-type studies which became 'replaced' by automated studies by TA, DSC, etc. methods, published mainly, even exclusively, in the specialist Journals mentioned. We also note that remarkably few of these latter studies complement kinetic data measurements and analyses with other chemical or physical observations, not even determining whether an, initially solid reactant, melts before reaction, etc. Most have been minimalistic, including meaningless data manipulation.
The aspect of particular relevance here is that the kinetic behavior of the reactions studied are almost invariably well-represented ("fitted") and described by the Arrhenius equation (though the precision of such 'fits' is rarely considered or tested). These types of largely automated studies include a wide range of diverse (initially) solid reactants but rarely mention any confirmatory tests for conclusions reached: dehydrations of hydrated salts, often for well-characterized crystals, dissociations of metal oxides, hydroxides, carbonates and some binary compounds, decompositions of metal asides and salts of oxyacids, e.g., perhalates etc., dissociations/decompositions of ammonium salts, decompositions of metal salts of organic acids, e.g., oxalates, formates, etc., dissociations and/or decompositions of coordination compounds, etc.
One inconsistency appearing in the relevant literature is that, for the identical reaction, different researchers often report significantly different kinetic parameters. Moreover, within wide ranges of reactants considered and compared, no systematic trends in A or E magnitudes, relating kinetic triads to any reactant property (composition, structure, etc.) have yet been reported or found in literature searches. This inability to identify systematic order within the large amount of data available demonstrates that such work lacks a scientific base. The reason is not difficult to find. The Arrhenius model arises from the distribution of energies in collisions between free-flying gaseous species. The distribution of energies within a crystalline reactant is fundamentally different, a scientific fact apparently forgotten, or willfully disregarded, by workers in this field. Thus, the Arrhenius model, and therefore E and A values are empirical having no chemical significance in the reactions being studied. The above history well illustrates the ability to describe complex physicochemical processes, using the AE, while ignoring the chemistry of the reaction(s) occurring.
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COMPETING INTERESTS
Author has declared that no competing interests exist.
REFERENCES
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Biography of author(s)
He obtained his PhD in Physico-mathematical sciences, was born in 1961 in Melitopol, Ukraine. In 1985 graduated from the Moscow Institute of Physics and Technology (MIPT, Russia), joined the branch of the Institute of Chemical Physics of the Academy of Sciences of the Soviet Union (Chernogolovka, Moscow region). The first topic of scientific research was the study of the detonation of explosives using electromagnetic sensors. The first scientific work on this topic was published in 1985. Subsequently, research topics have expanded significantly: a wide range of scientific research related to the combustion and detonation of various substances in all aggregative states: experimental and theoretical study of combustion and detonation, the transition of combustion into detonation of a wide range of substances: explosives, powders, various mixtures based on metal powders and non-metals, as well as various gas mixtures. Author of more than 30 works in various scientific journals. Unfortunately, most of the works are indexed only in Russian scientific citation systems. Among the latest works, indexed in international citation systems can be distinguished article «Selective determination of rate constants of reactions of atomic hydrogen with various functional groups of a complex molecule» published in Russian Journal of Physical Chemistry A on May 18, 2016. The work presented in this collection is devoted the problems of errors that have arisen and are arising due to the inaccurate application of the Arrhenius equation in solving various physicochemical problems. Thanks to an article in the Asian Journal of Physical and Chemical Sciences, he managed to find like-minded people on this issue. For example, an outstanding English scientist (Galwey, Andrew Knox, h-index - 33), with whom more detailed work on these issues will be released soon.