10.3.1 Effect of Metals

Dupuy and Douay (2001) studied of the behavior of heavy metals in soils requires the knowledge of the complexation between soil constituents and metals and this information is not available from conventional analytical techniques such as atomic absorption. Since metals do not absorb mid infrared radiation, we wanted to characterize them using their interaction with the organic matter of soils. The use of chemometrics treatment of the spectroscopic data has demonstrated firstly that the interaction between soil constituents and metals takes place preferentially via organic matter, secondly the high difference between the complexation of lead and zinc into organic matter should be noted. The study of the infrared spectra shows that two bands at 1670–1690 and 1710 cm⁻¹ vary according to the concentration of lead, which seems to be preferentially complexed by the salicylate functionality.

Five distinct layers have been identified based on following features (NOAA, 2018)

• thermal characteristics (temperature changes);
• chemical composition;
• movement; and
• density.

Each of the layers are bounded by “pauses” where the greatest changes in thermal characteristics, chemical composition, movement, and density occur. These five basic layers of the atmosphere are Figure 10.11:

Exosphere: This is the outermost layer of the atmosphere and is external to our atmospheric system. It extends from the top of the thermosphere to 10,000 km above the earth. In this layer, all matters escape into space and satellites orbit the earth. At the bottom of the exosphere is the thermopause located around 375 miles (600 km) above the earth.

Thermosphere: This layer is between 85 km and 600 km from the surface of the earth. This layer is known as the upper atmosphere. The density of gases is very low but starts to increase drastically toward lower layers. In this layer that high energy ultraviolet and x-ray radiation from the sun begins to be absorbed by the molecules in this layer, causing temperature increases. Because of this absorption, the temperature increases with height. From as low as –120 C at the bottom of this layer, temperatures can reach as high as 2,000 C near the top. However, even at that high temperature, the actual heat retention is not large because of the low density of matter in that layer.

Mesosphere: This layer extends from around 50 km above the Earth’s surface to 85 km. In this layer, the density of gases increases drastically, accompanied with rise in ambient temperature. This is the layer that is dense enough to slow down meteors hurtling into the atmosphere, where they burn up, leaving fiery trails in the night sky. The transition boundary which separates the mesosphere from the stratosphere (next one) is called the stratopause.

Stratosphere: The Stratosphere extends around 50 km down to anywhere from 6 to 20 km above the surface of the Earth. This layer holds 19 percent of the atmosphere’s gases but very little water vapor. In this region the temperature increases with height. Heat is produced in the process of the formation of Ozone and this heat is responsible for temperature increases from an average –51 C at tropopause to a maximum of about –15 C at the top of the stratosphere. As such, warmer air is located above the cooler air, thus minimizing intra-layer convection.

Troposphere: The troposphere begins at the surface of the Earth and extends from 6 to 20 km high. The height of the troposphere varies from the equator to the poles. At the equator it is around 18–20 km high, at 50°N and 50°S, 85 km and at the poles just under 65 km high. The sun’s rays provide both light and heat to Earth, and regions that receive greater exposure warm to a greater extent. This is particularly true of the tropics, which experience less seasonal variation in incident sunlight. As the density of the gases in this layer decrease with height, the air becomes thinner. Therefore, the temperature in the troposphere also decreases with height in response. As one climbs higher, the temperature drops from an average around 17 C to –51 C at the tropopause.

Scientists have spent great amount of time and energy in explaining how greenhouse gases have created the global warming. At present, it is theorized that many molecules in the atmosphere possess pure-rotation or vibration-rotation spectra that allow them to emit and absorb thermal infrared (IR) radiation (4–100 μm), such gases include water vapor, carbon dioxide and ozone (but not the main constituents of the atmosphere, oxygen or nitrogen). It is this property that gives special status for greenhouse gases. Because this absorption of IR prevents heat from escaping the earth, the greenhouse gas effect kicks in. It is customary to consider that convection is the dominant mechanism below tropopause. As such, it is often justified that instant mixing occurs up to that interface. Overall, thermal balance is maintained through exchange of IR back and forth from the Earth’s surface. Consequently, the change in the radiative flux at the triopopause, which marks the interface between convective layer and a stable layer becomes the most crucial zone for overall climate control (Ramanathan et al., 1987). Mechanically, Earth’s spin creates three belts of circulation due to its continuous spinning motion (Stevens, 2011). Air circulates from the tropics to regions approximately 30° north and south latitude, where the air masses sink. This belt of air circulation is referred to as a Hadley cell, after George Hadley, who first described it (Holton, 2004). Two additional belts of circulating air exist in the temperate latitudes (between 30° and 60° latitude) and near the poles (between 60° and 90° latitude). A further consideration is the spectroscopic strength of the bands of molecules which dictates the strength of the infra-red absorption. Molecules such as the halocarbons have bands with intensities about an order of magnitude or greater, on a moleculeper-molecule basis, than the 15 |im band of carbon dioxide. This is further impacted by the presence of any fraction of artificial chemicals that often have heavy metals. The actual absorbance by a band is, however, a complicated function of both absorber amount and spectroscopic strength so that these factors cannot be considered entirely in isolation.

Other factors involve radiative forcing and in particular the spectral absorption of the molecule in relation to the spectral distribution of radiation emitted by a matter. The distribution of emitted radiation with wavelength is shown by the dashed curves for a range of atmospheric temperatures as shown in Figure 10.12. Unless a molecule possesses strong absorption bands in the wavelength region of significant emission, it can have little effect on the net radiation. The solid line shows the net flux at the tropopause (Wm²) in each 10 cm^-1 interval using a standard narrow band radiation scheme and a clear-sky mid-latitude summer atmosphere with a surface temperature of 294K (Shine et al., 1990). Under this scenario, the wavelength is important.

There has been a perfect balance in the concentration of naturally occurring gases in the atmosphere and all strata that are described above. These concentrations dictate the level of absorption that would take place within the tropopause. It is understood that gases, such as halocarbons that didn’t exist in nature before, the forcing is linearly proportional to the concentration. On the other hand, for gases such as methane and nitrous oxide, their forcings are considered to be proportional to the square root of their concentration (Shine et al., 1990). For CO₂, the spectrum is so opaque that additional molecules of carbon dioxide are considered to have little impact, making forcing to be logarithmic in concentration. Molecules such as the halocarbons have bands with intensities about an order of magnitude or even greater, on a molecule-per-molecule basis, than the 15 μm band of carbon dioxide The actual absorptance by a band is, however, a complicated function of both absorber amount and spectroscopic strength so that these factors cannot be considered entirely in isolation (Rey et al., 2018). Initial work of Rey et al. (2018) indicates that for these artificial chemicals (CF₄ in this particular case), “hot bands” corresponding to transitions among excited rovibrational states contribute significantly to the opacity in the infrared even at room temperature conditions. Such molecules have a particularly long atmospheric lifetime (scientifically, they never become assimilated with the ecosystem) and their very estimated global warming potentials are very large. They report a list on such data for CF₄ in the range 0–4000 cm⁻¹, containing rovibrational bands that are the most active in absorption. is partitioned into strong & medium intensity transitions and the quasi-continuum of individually indistinguishable weak lines. The latter ones are compressed using “super-lines” (SL) databases for an efficient modelling of absorption cross-sections (Figure 10.13).

This behavior is strongly affected by the presence of heavy metals (Vernooij et al., 2016). Table 10.1. gives atomic absorption data for select metals, along with their intensity and corresponding wave numbers.

10.3.2 Indirect Effects

In addition to their direct radiative effects, many of the greenhouse gases also have indirect radiative effects on climate through their interactions with atmospheric chemical processes. Note that these processes are continuous and take place under any temperature and pressure, albeit at different rates. In addition, the presence of contaminats alter the nature of these reactions, as will be shown in latter section of this chapter. Some of these interactions are listed in Table 10.2.

This table focuses on the role of Ozone. Ozone plays an important dual role in affecting the climate. Ozone concentration in the atmosphere depends on its vertical distribution throughout troposphere and stratosphere. This is in addition to concentration in the atmosphere – this concentration being dynamic as Ozone concentration is not stable like other greenhouse gases, such as CO₂. Ozone is also a primary absorber of solar radiation in the stratosphere, thus contributing to the increase with altitude. The greenhouse effect is directly proportional to the temperature contrast between the level of emission and the levels at which radiation is absorbed. This contrast is greatest near the tropopause, where temperatures are at a minimum compared to the surface. Above about 30 km, added ozone causes a decrease in surface temperature because it absorbs extra solar radiation, effectively depriving the troposphere of direct solar energy that would otherwise warm the surface (Lacis et al, 1990). Lacis et al. (1990) observed a cooling of the surface temperature at northern mid-latitudes during the 1970s equal in magnitude to about half the warming predicted for CO₂ for the same time period. However, the measurement uncertainty of the observed trends is large, with the best estimates for mid-latitude cooling being –0.05 ± 0.05 °C. The surface cooling was determined to be caused by ozone decreases in the lower stratosphere, which outweigh the warming effects of ozone increases in the troposphere. The results obtained differ from predictions based on one-dimensional photochemical model simulations of ozone trends for the 1970s, which suggest a warming of the surface temperature equal to ~20% of the warming contributed by CO₂. Also, the ozone decreases observed in the lower stratosphere during the 1970 s produce atmospheric cooling by several tenths of a degree in the 12- to 20-km altitude region over the northern mid-latitudes. This temperature decrease is larger than the cooling due to CO₂ and thus may obscure the expected stratospheric CO₂ greenhouse signature.

The presence of metals affect the IR absorption. This principle has been used for material characterization, the technique being called Surface-enhanced IR absorption (SEIRA). It is established that IR absorption of molecules adsorbed on metal nanoparticles is significantly enhanced than would be expected in the normal measurements without the metal (Miki et al., 2002). SEIRA spectroscopy (SEIRAS) has been applied to in situ study of electrochemical interfaces. A theoretical calculation predicts that SEIRA effect can be observed on most metals if the size and shape of particles and their proximity to each other are well tuned. It has been observed for Au, Ag, Cu, and Pt. From a comparison with the spectra of CO adsorbed on smooth Pt surfaces, it has been reported that the absorption is 10–20 times enhanced on Pt nanoparticles (Miki et al., 2002).

Figure 10.14 shows the fluxes of energy in and out of Earth’s surface. The Sun provides most of the incoming energy, shown in yellow. Most of this energy is absorbed at the surface with the exceptions of:

• - energy reflected by clouds or the ground; and
• - energy absorbed by the atmosphere.

Most of the outgoing energy is emitted by Earth’s surface as long wavelength radiation, shown in red in Figure 10.14. These are the radiations that mostly get absorbed by greenhouse gases the atmosphere. The atmosphere re-emits some of this energy up to space and some of it back down to Earth. The red arrow labeled “back radiation” represents the greenhouse effect, which can create imbalance if there is a perturbation in thermochemical features of the atmosphere.

Arrhenius set out to account for all the energy coming into and leaving the Earth system – a kind of energy budget (Arrhenius, 1896). That required tallying up all the sources of energy, the ways energy could be lost (known as energy sinks) and the ways energy could be transferred (known as energy fluxes). Arrhenius did not include an illustration in his 1896 paper, but essentially captured what is shown in Figure 10.14. This diagram shows the fluxes of energy in and out of Earth’s surface. The Sun provides most of the incoming energy, shown in yellow. Most of this energy is absorbed at the surface, except for a small amount that gets reflected by clouds or the ground, or that gets absorbed by the atmosphere. Most of the outgoing energy is emitted by Earth’s surface as long wavelength radiation, shown in red. However, most of this energy gets absorbed by greenhouse gases in the atmosphere. The atmosphere re-emits some of this energy up to space and some of it back down to Earth. The red arrow labeled “back radiation” represents the greenhouse effect. Thin black arrows in Figure 10.14 represent solar radiation in Arrhenius’ equation. Because long-wave infrared radiation is absorbed by greenhouse gases, they were known to have a role in global temperatre.

Arrhenius reasoned that if the atmosphere was absorbing infrared radiation, it too was heating up. Thus, he added another level of complexity to his model: an atmosphere that could absorb and radiate heat just like Earth’s surface. For simplicity, he treated the whole atmosphere as one layer. The atmosphere absorbed outgoing radiation emitted by the surface (thick red arrow), and then emitted its own radiation both up to space and back down to Earth (thin red arrows). This was the beginning of the so-called 2-layer model.

This was an important realization, because it showed that the atmosphere didn’t block outgoing radiation as Fourier had proposed. It absorbed it. Then, like the hotbox, it heated up and emitted infrared energy. The atmosphere emits this energy in all directions, including back toward the earth. This flux of energy from the atmosphere to the surface represents another important source of heat to Earth’s surface, and it explains the real mechanism behind the greenhouse effect.

10.4.1 Connection to Subatomic Energy

Islam (2014) presented comprehensive mass-energy balance equation that erases the artificial boundary between mass and energy. Every chemical reaction involes mass transfer and every mass transfer involves energy transfer. Starting with Newton, mass and energy have been disconnected in all analyses of New Science. Only recently, it has been recognized that energy exchange is inherent to chemical reactions¹. Problem, however, persists because currently there is no mechanism to discern between organic/natural mass and synthetic/artificial mass, which are the source of organic energy and artificial energy, respectively. The use of quantum chemistry has made the situation worse because instead of seeking scientific reasoning, it has made it easier to invoke dogmatic and often paradoxical concepts. Even then, the latest discoveries are useful in gaining insight into physic-chemical reactions. In that regard, Rahm and Hoffmann (2015) introduced new ways of understanding the origins of energy in chemical reactions Starting with the premise that all of the interactions between the molecules, atoms, and the electrons that bind atoms together can collectively be understood in terms of energy, they propose a new energy decomposition analysis in which the total changing energy of any chemical reaction can be broken down into three components:

• nuclear-nuclear repulsion (the repulsive energy between the positively charged nuclei of different atoms);
• the average electron binding energy (the average energy required to remove one electron from an atom); and
• electron-electron interactions (the repulsive energy between negatively charged electrons).

The first one (repulsion) occurs when two atoms are brought together by decreasing the distance between nuclei. This repulsion leads to accumulation of electron to fill in the space caused by repulsion. In the presence of the two nuclei, the average binding energy of the electrons changes due to differences in electron-nuclear attraction. As the electrons move closer together, they also begin to interact more strongly with each other. At this point, quantum chemistry focuses on quantifying these electron-electron interactions with the assumption that all electrons are similar, irrespective of what element it belongs to. We argued in previous chapters that not only they are different from element to element, they are also different in their spinning depending on the source of the element, meaning a natural source would have them spin in a different direction from the direction of artificial sources. Not surprisingly, Rahm and Hoffmann (2015) focused on the electron interactions and estimated their interactions from experimental data, relying on quantum analysis. Conventionally a wave function is used to estimate the solutions to the Schrödinger equation, which assumes simultaneous existence of the wave–particle duality. They used experimental data to correlate with solutions of quantum equations to justify their applicability. Similarly, electronegativity, an old term used to describe is propensity of an atom to attract a bonding pair of electrons, was redefined. When Nobel laureate Chemist, Linus Pauling first defined this term in 1932, he referred to it as “the power of an atom to attract electrons to itself.” An alternative definition was proposed by Allen (1989), who introduced electronegativity as the third dimension of the periodic table. In essence, Allen legitimizes Schrödinger equation by calling it an intimate property of the periodic table. As such, the door to experimentally validating electronegativity values, which were not explicitly called energy until Allen’s paper. Allen expressed electronegativity on a per-electron (or average one-electron energy) basis as:

(10.1)

where m and n are the number of p and s valence electrons, respectively. The corresponding one-electron energies, ϵ_p and ϵ_s, are the multiplet-averaged total energy differences between a ground-state neutral and a singly ionized atom. Rahm and Hoffmann (2015) used the same concept but used all of the electrons, not just the valence ones, in their definition of electronegativity. They showed that traditional electronegativity values (such as Allen’s) and average all electron binding energies often provide the same general trends over a reaction, while preserving lower electrons that would make the description more complete.

With this information, Rahm and Hoffman (2015) explain that all chemical reactions and physical transformations can be classified into eight types based on whether the reaction is energy-consuming or energy-releasing, and on whether it is favoured or resisted by the nuclear, multielectron, and/or binding energy components. This information in turn relates to the nature of a chemical bond. They also showed that, in four of the eight classes of reactions, knowledge of the binding energy alone is sufficient to predict whether or not the reaction is likely to take place. Although their focus was to measure absolute energy, this work led the background of characterizing energy in terms of its sustainability.

In the experiment, the baseline is created with a one-electron system (such as C⁵+, which is a carbon atom with all but one of its electrons removed). The absolute energy of this system is easy to measure because, with only one electron, there is zero electron-electron repulsion. Then the absolute energy of the carbon atom, and the electron-electron interactions within it, could be measured as electrons are added back one by one. This is possible because it is theoretically possible to experimentally measure the average electron binding energy for each step.

The following are the major consequences of Rahm and Hoffman’s work.

• connects electronegativity to total energy;
• allows quantification of electron-electron interactions in governing chemical reactions from experimental data;
• gives an avenue to track energy sources through experiment and subsequent refinement through computational models.

The average binding energy of a collection of electrons () is a defined property of any assembly of electrons in atoms molecules, or extended materials (Rahm and Hoffmann, 2015):

(10.2)

where ε_i is the energy corresponding to the vertical (Franck– Condon) emission of one electron i into vacuum, with zero kinetic energy, and n is the total number of electrons. For extended structures in one-, two-, or three-dimensions, can be obtained from the density of states (DOS) as (10.3)

(10.3)

here ε_f is the Fermi energy². A related expression for the partial DOS has been found useful for determining the average position of diverse valence states in extended solids and for estimating covalence of chemical bonds. With the definitions of 10.2 and 10.3, one can choose to estimate for any subset of electrons, such as “valence-only” (as Allen (1989) did). Comparison with Traditional Electronegativities. Do the average electron binding energies correlate with timehonored measures of electronegativity, for instance Pauling’s values? Figure 10.15 shows the relation for the first four periods. The correlation is clearly there, but with one important difference. By the definition, heavier elements will naturally attain larger absolute values of , simply because the definition includes the cores, i.e., the binding of a larger number of electrons. values correlate linearly with normal atomic electronegativity scales (we show a correlation with Pauling χ, but similar ones are obtained with other scales) only along each period, but not down the periodic table. We note that, however, the trend of increasing electronegativity down the periodic table, where each atom of necessity attracts more electrons, is from a certain perspective in accord with Pauling’s original definition, as quoted above. It is ∆χ, i.e., the change in average electron binding energy that is important in this analysis, not absolute values of χ. If one wishes to maintain a connection to more traditional electronegativity values, one can estimate Δ using a valence-only approach, i.e., using the Allen scale of electronegativity, which correlates linearly with Pauling’s values. As we saw in the CH₄ example, such valence-only values of ∆ will be similar to ∆ estimated with an all-electron approach and, in our experience, lead to the same general conclusions. Because energies of lower levels can, in fact, shift in a reaction, we nevertheless recommend the use of all-electron for a more rigorous connection to the total energy. We understand that the all-electron electronegativities are unfamiliar and seem to run counter to chemistry’s fruitful concentration on the valence electrons. We beg the reader’s patience; there is a utility to this definition that will reveal itself below.

The designation of total energy as a sum of three primary contributions, namely, the average electron binding energy, the nuclear–nuclear repulsion, and multielectron interactions can be adjusted by assigning electrons a phenomenal configuration, that is, a collection of particles that continues to include smaller particles in an yin yang pairing fashion. This can help amalgamate the galaxy model with the model proposed by and Rahm and Hoffman (2015). If the premise that natural material follows a different orientation of spinning than artificial material, each matter can carry a signature. The following sequence of events occur with artificial materials:

Characteristic time is changed → Natural frequency and orientation is changed → bond energies change → becomes a ‘cancer’ to natural materials.

New Science observed such behaviour of artificial materials and exploited these features in order to develop new line of products. Scientifically New Science also attempted to explain such behaviour with dogmatic assertions, some of which has been presented earlier. Much of previous material characterization delved in considering nuclear stability. As we have seen in previous section, there is a general understanding that subatomic features relate to both energy and mass characteristics. At the outset there is a correlation between abundance and atomic number, Z. Figure 10.16 shows elements with an even number of protons, reflected by an even atomic number Z, are more abundant in Nature than those with an uneven number. Also, most abundant elements are also most stable and more difficult to denature. While every element is useful in its natural state, a denatured element is inherently harmful (Khan and Islam, 2016).

10.4.2 Isotopes and Their Relation to Greenhouse Gases

Figure 10.17 shows binding energy per nucleon for elements with atomic number greater than 20. Using this graph, scientists conclude that fission of a heavy nucleus into lighter nuclei or fusion of two H atoms into He are exo-energetic because the process results in nuclei/a nucleus characterized by a substantially higher binding energy per nucleon. Figure 10.18 shows the average binding energy for elements of mass number lower than 20. This figure shows that nuclei with an even number of protons show a higher binding energy per nucleon and thus higher stability (compare, e.g., the binding energies for ⁴He and ³He, ¹²C and ¹³C, and ¹⁶O and ¹⁷O.

Around a mass number of 60, there is an optimum in average binding energy (Figure 10.19). Fewell (1995) indicated that the most tightly bound of the nuclei is ⁶²Ni. This is in contradiction to previous assertion that ⁵⁶Fe is the most strongly bounded nucleus. Fewell demonstrated that both ⁵⁸Fe and ⁶²Ni are more strongly bound than ⁵⁶Fe. Table 10.3 shows the tabulation of the binding energy B divided by the mass number A (somewhat equivalent of atomic density). It is interesting to note that ⁵⁶Fe has higher number than ⁵²Cr, ⁵⁴Cr, as well as ⁶⁰Ni. It is also true that ⁵⁶Fe has the highest absolute nuclear binding energy³. The optimum is explained through the fact that the more nucleons, the stronger the total strong force is in the nucleus. However, as nucleons are added, the size of the nucleus gets bigger, so the ones near the outside of the nucleus are not as tightly bound as the ones near the middle of the nucleus. Other data are shown in Tables 10.3–10.4. The binding energy per nucleon, because of the variation of the strong force with the distance, increases until the nucleus gets too big and the binding energy per nucleon starts decreasing again. This binding energy per nucleon achieves a maximum around A = 56, and the only stable isotope with that Atomic number is ⁵⁶Fe. Figure 10.19 shows the nuclear binding energy per nucleon of those seven “key” elements denoted in the graph by their abbreviations (four with more than one isotope referenced). Increasing values of binding energy can be thought as the energy released when a collection of nuclei is rearranged into another collection for which the sum of nuclear binding energies is higher. As can be seen in this figure, light elements such as hydrogen release large amounts of energy (a big increase in binding energy) when combined to form heavier nuclei. This is the process of fusion. Beyond, iron, heavy elements release energy when converted to lighter nuclei—processes of alpha decay and nuclear fission. Figure 10.19 shows that the curve increases rapidly with low A, hits a broad maximum for atomic mass numbers of 50 to 60 (corresponding to nuclei in the neighbourhood of iron in the periodic table, which are the most strongly bound nuclei) and then gradually declines for nuclei with higher values of A. In this figure, iron’s ranking as optimum carries significance in terms of sustainability. In turns out iron sticks out in between toxic elements, similar to silver and gold, which also represent optimum properties. When it comes to organic applications, these optima are paramount (Bjørklund et al., 2017).

In practical terms, it means it is the hardest to denature iron than any other element.

This variation in binding energy per nucleon also exerts a pronounced effect on the isotopic composition of the elements, especially for the light elements. “Even– even isotopes” for elements such as C and O (¹²C and ¹⁶O) are much more abundant than their counterparts with an uneven number of neutrons (¹³C and ¹⁷O). Despite the overall limited variation in binding energy per nucleon as a function of the mass number for the heavier elements, its variation among isotopes of an element may vary substantially, leading to a preferred occurrence of even–even isotopes, as illustrated by the corresponding relative isotopic abundances for elements such as Cd and Sn, as shown in Table 10.5. In both the lower (¹⁰⁶Cd through ¹¹⁰Cd) and the higher (¹¹⁴Cd through ¹¹⁶Cd) mass ranges, only Cd isotopes with an even mass number occur. In addition, the natural relative isotopic abundances for ¹¹³Cd and, to a lesser extent, ¹¹¹Cd are low in comparison with those of the neighboring Cd isotopes with an even mass number. Similarly, Sn, for which 7 out of its 10 isotopes are characterized by an even mass number, the isotopes with an odd mass number have a lower natural relative abundance than their neighbors. This trend continues with silicon, nitrogen, oxygen, sulphur. The only exception is hydrogen, for which uneven isotope is the stable form. Hydrogen has no neutron, deuterium has one, and tritium has two neutrons. The isotopes of hydrogen have, respectively, mass numbers of one, two, and three. Their nuclear symbols are therefore ¹H, ²H, and ³H. The atoms of these isotopes have one electron to balance the charge of the one proton.

Electrons Are Fermions of Half-Integer Spin. Particles with Integer Spin Are Bosons. Fermions and Bosons Avoid Each Other

Figure 10.20 asserts the existence of number of stable isotopes of an element (upper right corner), the mass of the isotope commonly used in the delta value or alternatively the most abundant isotope (upper left corner), and the potential influence of radiogenic (RAD) and cosmogenic processes (COS) as well as mass-independent fractionation (MIF) on the stable isotope system (below the element symbol). In most cases, MIF due to nuclear volume or magnetic isotope effects has only been observed in laboratory-scale studies and has not yet been detected in natural samples (except for O, S, and Hg, marked in bold). The “traditional” stable isotope systems are marked with a red border. Elements for which high-precision stable isotope methods have been developed are marked with a bold symbol. In order to gain insight into isotopic fractionation, Hg offers an excellent case, because it has seven stable isotopes. Table 10.6 shows atomic mass and natural relative abundance of various Hg isotopes.

Figure 10.21 illustrates the influence of different fractionation mechanisms on Hg isotopes. In this figure, the arrows indicate qualitatively the influence of the mass difference effect (MDE), the nuclear volume effect (NVE), and the magnetic isotope effect (MIE) on the seven stable Hg isotopes. Mass-independent fractionation (MIF), which is defined as a measured anomaly compared with the trend of the MDE, is observed mainly for the two odd-mass isotopes ¹⁹⁹Hg and ²⁰¹Hg and can be caused either by the NVE due to their nonlinear increase in nuclear charge radii or the MIE due to their nuclear spin and magnetic moment. As can be seen from Table 10.7, natural abudance of these two isotopes are markedly lower than their corresponding ‘even-even’ counterparts, ²⁰⁰Hg and ²⁰²Hg, respectively. Here, MIF by the NVE and the MIE can be differentiated by the relative extent of MIF on ¹⁹⁹Hg and ²⁰¹Hg. Elements for which MIF has been detected in natural samples (only O, S, Hg) or observed in laboratory studies are marked in Figure 10.20. The relative extent of the nuclear charge radius anomalies (x/y = 1.6) causes the characteristic slope in a Δ¹⁹⁹Hg/Δ²⁰¹Hg plot for the NVE in comparison to slopes observed for Hg(II) photoreduction (1.0) and methyl-Hg photodemethylation (~1.36) due to the MIE. The magnitude of MIF due to the NVE is generally much smaller than MIF by the MIE. The MIE occurs only during kinetically controlled processes (in natural systems probably always related to photochemical reactions) whereas the NVE and the MDE occur during both kinetic and equilibrium processes. The relative importance of MDE and NVE on the overall fractionation can vary depending on the reacting species.

In assessing greenhouse gas pollution, metal concentrations are paramount. Modern refining and material processing rely heavily on the use of catalysts that use metals, including heavy metals. For tracking these contaminants, isotope signatures can be used in different ways to deduce information about composition and history of environmental samples. The most important applications are source and process tracing. If the isotopic compositions of the involved end members are known and sufficiently distinct, contributions of different source materials in a sample can be quantified by mixing calculations. Figure 10.22 shows how to conduct material balance with two metal pools of opposite isotope signatures. depicts the mass balance between two metal pools of opposite isotope signatures and equal size. shows the effect of different pool sizes (pool A = 4 × pool B), whereas shows the combined effect of different pool sizes and isotope signatures. illustrates a schematic example of a natural river system for which the relative fractions of natural and anthropogenic metal sources can be quantified by metal isotope signatures. The delta (δ) value of a sample can be explained by the sum of the δ values of the mixing final products multiplied by their relative fractions of the total amount present (Equation 10.3), where where f describes the relative fraction of the involved pools A and B (f_{pool_A} + f_{pool_B} = 1, as per the material balance requirement).

(10.4)

Rearranging the equation allows determining the fraction of one end product (Equation 10.4):

(10.5)

For example, if the geogenic (naturally occurring) background in a soil has an isotopic composition of +0.5‰ relative to the reference standard and the soil has been polluted by an anthropogenic source with a δ value of –1.5‰, a delta value of –1.0‰ would indicate an anthropogenic contribution of 75%. Here, of course, it is assumed that linear mixing rule is applied. As we’ll see in latter sections, real life contamination bears far greater consequence of anthropogenic materials. Chen et al. (2008) presented a case study involving Zn isotopes in the Seine River, France. This is depicted in. Chen et al. (2008) used of Zn isotope ratios as a tracer of anthropogenic contamination using an extensive collection of river water samples from the Seine River basin, collected between 2004 and 2007. The ⁶⁶Zn/⁶⁴Zn ratios (expressed as δ⁶⁶Zn) of dissolved Zn have been measured by MC-ICP-MS after chemical separation of Zn. Significant isotopic variations (0.07–0.58 ‰) occurred along a transect from pristine areas of the Seine basin to the estuary and with time in Paris, and were found to be coherent with the Zn enrichment factor. Dissolved Zn in the Seine River displays conservative behavior, making Zn isotopes a good tracer of the different sources of contamination. Dissolved Zn in the Seine River is essentially of anthropogenic origin (>90%) compared to natural sources (<7%). Roof leaching from Paris conurbation was a major source of Zn, characterized by low δ⁶⁶Zn values that are distinct from other natural and anthropogenic sources of Zn. Their study highlights the absence of distinctive δ⁶⁶Zn signatures of fertilizer, compost or rain in river waters of rural areas, and therefore suggests the strong retention of Zn in the soils of the Basin. They demonstrate that Zn isotope ratios can be a powerful tool to trace pathways of anthropogenic Zn in the environment.

Estrade et al. (2010) also used source tracing for several stable isotopes of Hg. They investigated in lichens over a territory of 900 km² in the northeast of France over a period of nine years (2001–2009). The studied area was divided into four geographical areas: a rural area, a suburban area, an urban area, and an industrial area. In addition, lichens were sampled directly at the bottom of chimneys, within the industrial area. While mercury concentrations in lichens did not correlate with the sampling area, mercury isotope compositions revealed both mass dependent and mass independent fractionation (MIF) characteristic of each geographical area. Odd isotope deficits measured in lichens were smallest in samples close to industries, with Δ¹⁹⁹Hg of –0.15 ± 0.03 ‰, where Hg is thought to originate mainly from direct anthropogenic inputs. Samples from the rural area displayed the largest anomalies with Δ¹⁹⁹Hg of –0.50 ± 0.03‰. Samples from the two other areas had intermediate Δ¹⁹⁹Hg values. Mercury isotopic anomalies in lichens were interpreted to result from mixing between the atmospheric reservoir and direct anthropogenic sources. Furthermore, the combination of mass-dependent and mass independent fractionation was used to characterize the different geographical areas and discriminate the end products (industrial, urban, and local/regional atmospheric pool) involved in the mixing of mercury sources. Figure 10.23 shows how Rural Area (RA), Suburban Area (SA), Urban Area (UA), Industrial Valley (IV), Industrial sites (I). For these cases, the total Hg concentrations varied little between zones. However, the average δ²⁰²Hg value of lichens from the IV zone was significantly lighter (–2.07 ‰) than those measured for the three nonindustrial areas. Furthermore, lichens sampled at the two industrial sites (I) within IV displayed similar δ²⁰²Hg (–1.90‰) trends. This suggests that the Hg taken up by the lichens in the industrial area had different emission sources from that found in the urban, suburban, and rural areas. Furthermore, average Δ¹⁹⁹Hg measured in IV, UA, SA, and RA were found to be significantly different from one area to another, suggesting the contribution of different mercury sources. Odd isotope deficits in lichens are believed to be representative of atmospheric Hg, which is the complementary reservoir of aquatic Hg in terms of isotope fractionation (Carignan et al., 2009). It is known that redox reactions govern mercury (Hg) concentrations in the atmosphere because fluxes (emissions and deposition), and residence times, are largely controlled by Hg speciation. Recent work on aquatic Hg photoreduction suggested that this reaction produces MIF or non-mass dependent fractionation (NMF) and that residual aquatic Hg(II)is characterized by positive δ¹⁹⁹Hg and delta δ²⁰¹Hg anomalies. Carignan et al. (2009) showed that atmospheric Hg accumulated in lichens is characterized by NMF with negative δ¹⁹⁹Hg and δ²⁰¹Hg values (–0.3 to –1 ‰), making the atmosphere and the aquatic environment complementary reservoirs regarding photoreduction and NMF of Hg isotopes. Because few other reactions than aquatic Hg photoreduction induce NMF, photochemical reduction appears to be a key pathway in the global Hg cycle. Carignan et al. (2009) also observed isotopic anomalies in several polluted soils and sediments, suggesting that an important part of Hg in these samples was affected by photoreactions and has cycled through the atmosphere before being stored in the geological environment. Thus, mercury isotopic anomalies measured in environmental samples may be used to trace and quantify the contribution of source emissions.

They argued that this is because Hg(II) photoreduction of the aquatic reservoir yields positive ∆¹⁹⁹Hg and ∆²⁰¹Hg for residual Hg(II) with a ∆¹⁹⁹Hg/∆²⁰¹Hg close to unity, whereas Hg in lichens have negative ∆¹⁹⁹Hg and ∆²⁰¹Hg, also with a ∆¹⁹⁹Hg/∆²⁰¹Hg close to unity. The magnetic isotope effect (MIE)⁴ is believed to be responsible for these anomalies. Whereas lichens sampled in I, IV, RA yielded ∆¹⁹⁹Hg/∆²⁰¹Hg ratios falling on the 1:1 line (see), significant deviations were observed for all the lichens sampled in UA (average ∆¹⁹⁹Hg/∆²⁰¹Hg) 0.74 and some lichens in SA. The ratio of anomalies suggests a higher ²⁰¹Hg deficit that is not in agreement with theoretical as well as experimental works which both suggest ratios between 1 and 1.3 for the MIE. This is a significant discovery because it unlocks many mysteries of quality of photosynthesis in the presence of polluted CO₂.

Wiederhold (2015) pointed out that source tracing in natural systems is complicated because:

1. isotopic compositions of mixing end members are not known with sufficient precision or not distinct enough;
2. multiple sources contribute to a sample; and
3. the isotope signature of the sample has been additionally affected by fractionating processes.

As a consequence, source tracing works best in systems with well-defined, distinct sources which are not overprinted by fractionating processes. Process tracing is based on the concept that a sample has been affected by a transformation process, causing a shift in the isotope signature. An example is the partial transformation of soluble to insoluble elemental species involving a separation of aqueous and solid phases (e.g., reduction of soluble Cr(VI) in groundwater to Cr(III) which precipitates). If the isotopic enrichment factor (ε) for the transformation process is known, the extent of reaction can be quantified from the heavy isotope enrichment in the remaining reactant using a Rayleigh model. The Rayleigh model assumes an exponential relationship that describes the partitioning of isotopes between two reservoirs as one reservoir decreases in size. This is reasonable if the material is continuously removed from a mixed system containing molecules of two or more isotopic species, the fractionation accompanying the removal process at any instance is described by a constant fractionation factor. However, in a natural setting, such conditions rarely prevail.

In understanding atmospheric pollution, the notion of Redox processes is helpful.

These processes, involving stable isotope fractionation between different oxidation states of metals represent one of the most important sources of isotopic variability in natural samples. Because nature is continuous, such oxidation is ubiquitous. However, an in-depth study is rare. Interestingly, the equilibrium isotope effect between aqueous Fe(II) and Fe(III) is one of the best studied systems (Wiederhold, 2015). Theoretical studies provide a fundamental basis for equilibrium isotope fractionation between oxidation states of metals, such as Cr,⁹⁷ Cu,^98,55 Zn,⁹⁹ Se,¹⁰⁰ Hg,⁴¹ generally predicting an enrichment of heavy isotopes in the oxidized species, except for U,⁴² where an inverse redox effect is observed due to the dominance of the NVE. Note, here, that the use of NVE to explain such behaviour is not satisfactory. Such description is not necessary with our galaxy model discussed in previous chapters.

Of relevance is the fact that anthropogenic processing can induce redox changes for metals. For example, ore smelting and roasting, the production of elemental metals or engineered nanoparticles for industrial purposes, and combustion processes can cause isotope fractionation due to redox effects (e.g., Zn,^101–104 Cd,^105,106 Hg^107,108,78), which may be preserved if the process is incomplete and isotopically fractionated metal pools with different oxidation states are released into the environment. Practically all industrial processes have such oxidation in place. Also, the most popular catalysts as well as pesticides contain these metallic products. Furthermore, electroplating can cause large isotope effects due to redox processes. More importantly, electroplated materials may constitute isotopically distinct metal sources released to the environment as metal wastes and mobilized via corrosion processes.

Significant pollution through metal isotope fractionation can take place with the formation of aqueous solution complexes and the binding of metals to functional groups of organic matter. This can take place under thermodynamic imbalances. Even without redox changes, the coordination of ligand complexes can be distinct enough to cause significant metal isotope fractionation. This is an extremely important phenomenon during photosynthesis. Numerous experimental observations indicate that heavy isotope enrichments are observed in organically complexed species compared with free aqueous species in the presence of stronger bonding environments (e.g., Fe,^112,116 Zn,¹¹³ Cu^114,115). In contrast, organic thiol complexes have been shown to be enriched in light Hg isotopes, consistent with theoretical calculations predicting light Hg isotope enrichments in coordination with reduced sulfur, compared with hydroxyl or chloride ligands in solution (Wiederhold, 2015). Similarly, organic complexes enriched in light Mg isotopes were explained by a longer bond length compared with corresponding inorganic complexes. None of these studies, however, identifies long-term impact on the organic matter and how the resulting oxidation products are contaminated.

The environmental fate of metals is often strongly controlled by sorption. In most cases, the magnitude of fractionation is smaller than for redox effects of the same element. For most metals, isotopic enrichment factors of <1 o/oo were determined for sorption, but larger values were found in some cases (e.g., Mo¹³²). Fractionation during sorption is mostly governed by differences in bonding environment between dissolved and sorbed phases or solution species sorbing to a different extent. It is often difficult to verify that equilibrium conditions have been established, and desorption rates are often much slower than adsorption rates, delaying the attainment of isotopic equilibrium. Many studies were conducted with metal oxides (mainly Fe and Mn (oxyhydr)oxides), but other sorbents (e.g., clay minerals, bacteria) were also used. A first summary of metal isotopic enrichment factors during sorption to metal oxides 134 suggested that sorption of cationic species (e.g., Fe, Cu, Zn) causes heavy isotope enrichments in the sorbed phases and sorption of anionic metal species (e.g., Ge,¹³⁵ Se,¹³⁶ Mo,¹³² U¹³⁷) results in light isotope enrichments in the sorbed phases. However, newer studies also reported light isotope enrichments in the sorbed phase for cationic metal species (e.g., Ca,¹³⁸ Cu,¹³⁹ Cd,¹⁴⁰ Hg⁵¹). Data are limited on the topic of kinetic isotope effects during adsorption and desorption of metals. For instance, Miskra et al. (2014), using enriched Hg isotope tracers, revealed slow kinetics and incomplete exchange of Hg(II) with organic complexes and mineral surfaces, suggesting that kinetic isotope effects during the initial sorption step may be partially preserved in the presence of non-exchangeable pools. They discovered that mobility and bioavailability of toxic Hg(II) in the environment strongly depends on its interactions with natural organic matter (NOM) and mineral surfaces. They investigated the exchange of Hg(II) between dissolved species (inorganically complexed or cysteine-, EDTA-, or NOM-bound) and solid-bound Hg(II) (carboxyl-/thiol-resin or goethite) over 30 days under constant conditions (pH, Hg and ligand concentrations). The Hg(II)-exchange was initially fast, followed by a slower phase, and depended on the properties of the dissolved ligands and sorbents. The time scales required to reach equilibrium with the carboxyl-resin varied greatly from 1.2 days for Hg(OH)₂ to 16 days for Hg(II)–cysteine complexes and approximately 250 days for EDTA-bound Hg(II). Other experiments could not be described by an equilibrium model, suggesting that a significant fraction of total-bound Hg was present in a non-exchangeable form (thiol-resin and NOM: 53–58%; goethite: 22–29%). Based on the slow and incomplete exchange of Hg(II) described in that study, Miskra et al. (2014) suggested that kinetic effects must be considered to a greater extent in the assessment of the fate of Hg in the environment and the design of experimental studies, for example, for stability constant determination or metal isotope fractionation during sorption.

The arctic represents an interesting test ground for observing atmospheric pollution with heavy metals. Studies show that atmospheric Hg deposition has increased about 3-fold from pre-industrialized background levels (Fitzgerald et al., 2014). Representing about 26% of the global land surface area, polar regions are unique environments with specific physical, chemical, and biological processes affecting pollutant cycles including that of Hg (Douglas et al., 2012). Trace gas exchanges between the atmosphere and the tundra are modulated by sinks and sources below and within snowpack, by snow diffusivity, snow height, and snow porosity (Agnan et al., 2018). Agnan et al. (2018) investigated Hg dynamics in an interior Arctic tundra snowpack in northern Alaska during two winter seasons. Using a snow tower system to monitor Hg trace gas exchange, they observed consistent concentration declines of gaseous elemental Hg (Hg⁰ gas) from the atmosphere to the snowpack to soils. They found no evidence of photochemical reduction of HgII to Hg⁰ gas in the tundra snowpack, with the exception of short periods during late winter in the uppermost snow layer. Chemical tracers showed that Hg was mainly associated with local mineral dust and regional marine sea spray inputs. Mass balance calculations showed that the snowpack represents a small reservoir of Hg, resulting in low inputs during snowmelt. Taken together, the results from this study suggest that interior Arctic snowpacks are negligible sources of Hg to the Arctic.

Precipitations can help with isotope enrichments. Isotope fractionation during precipitation can be described by a Rayleigh model, the shortcomings of which are discussed earlier. For precipitates, it means the process unidirectional and no significant re-equilibration of the formed precipitate with the solution phase occurs. It is generally understood that kinetic and equilibrium isotope fractionation is a complex process that has can play a pivotal role in view of the fact that aqueous phase is connected to organic matters. The formation of aqueous solution complexes and the binding of metals to functional groups of organic matter sets up possibilities for metal isotope fractionation. Even without redox changes, the coordination of ligand complexes can be distinct enough to cause significant metal isotope fractionation. In general, it has been observed that heavy isotope enrichments take place within organically complexed species compared with free aqueous species and explained by their stronger bonding environments (e.g., Fe,^112,116 Zn,¹¹³ Cu^114,115).

Metals are involved in biological cycling. However, biological processes behave different in presence of artificial chemicals from how they behave in presence of natural chemicals. In either cases, significant metal isotope fractionation will occur through redox change, complexation, sorption, diffusion, etc. Many biological processes are kinetically controlled (e.g., bond-breaking in enzymatic reactions) and may thus induce kinetic isotope effects. Although New Science rarely acknowledges the fact that these effects are preserved in signatures of natural samples, the use of the galaxy model, it becomes evident, each of these effects will carry a signature that is detectable by the natural system.

What is missing in today’s literature is answer to the question what role does artificial chemicals play in creating atmospheric pollution. What we know is natural materials are available in certain proportion and each material has a function for overall welfare of humans. From the above discussion, we know that it is easier to denature elements that are heavier than iron and by denaturing them they become agents of pollution and start to act as a ‘cancer’ to the environment. In producing denatured metals, we create these ‘agents’ that pollute much bigger fraction of the atmosphere. Figure 10.24 shows the amount of emissions caused by the production of various metals. This figure shows the global production and consumption of selected toxic metals during 1850–1990.

The most commonly found heavy metals in waste water include arsenic, cadmium, chromium, copper, lead, nickel, and zinc, all of which cause risks for human health and the environment. Heavy metals enter the surroundings by natural means and through human activities. Various sources of heavy metals include soil erosion, natural weathering of the earth’s crust, mining, industrial effluents, urban runoff, sewage discharge, insect or disease control agents applied to crops, and many others (Morais et al., 2012).

Each of these metals have crucial biological functions in plants and animals, yet the artificial (e.g., processed with artificial energy source or chemicals) version of them become inherently toxic to the organism. Previous research has found that oxidative deterioration of biological macromolecules is primarily due to binding of heavy metals to the DNA and nuclear proteins (Flora et al., 2008).

Consequence of such effects on organic matter must be reflected on the overall greenhouse gas emission. Take for instance, the case of N₂O emissions. Majority of that emission is derived from nitrogen fertilization and indirect emissions. These are entirely toxic to the environment. Most of it would be rejected by the ecosystem and some of them get assimilated in organic matter, it will only create amplified pollution by passing through increased amount of biomass in an organic body (Galloway et al. 2008). Generally, for every 1000 kg of applied nitrogen fertilizers, it is estimated that around 10–50 kg of nitrogen will be lost as N₂O from soil, and the amounts of N₂O emissions increase exponentially relative to the increasing nitrogen inputs (Shcherbak et al., 2014). Given that farmlands and fertilizer application are predicted to increase by 35–60% before 2030, global N₂O concentrations are likely to continuously rise in the coming decades and it is expected that agricultural soils will contribute up to 59% of total N₂O emissions in 2030 (Hu et al., 2015). This is shown in Figure 10.25.

Figure 10.26. shows how intricately all materials, natural and artificial, form a close cycle. It shows everytime there is anartificial molecule in the system, its effects continue to multiply.

10.5.1 Removable Discontinuities: Phases and Renewability of Materials

By introducing time spans of examination unrelated to anything characteristic of the phenomenon itself being observed in nature, discontinuities appear. These are entirely removable, but they appear to the observer as finite limits of the phenomenon itself, and as a result, the possibility that these discontinuities are removable is not even considered. This is particularly problematic when it comes to the matter of phase transitions of matter and the renewability or non-renewability of energy.

The transition between the states of solid, liquid and gas in reality is continuous, but the analytical tools formulated in classical physics are anything but; each P-V-T model applies to only one phase and one composition, and there is no single P-V-T model applicable to all phases (Cismondi and Mollerup, 2005). Is this an accident? Microscopic and intangible features of phase-transitions have not been taken into account. As a result, this limits the field of analysis to macroscopic, entirely tangible features and modeling therefore becomes limited to one phase and one composition at a time.

When it comes to energy, everyone has learned that it comes in two forms—renewable and nonrenewable. If a natural process is being employed, however, everything must be “renewable” by definition in the sense that, according to the Law of Conservation of Energy, energy can be neither created nor destroyed. Only the selection of the time frame misleads the observer into confounding what is accessible in that finite span with the idea that energy is therefore running out. The dead plant material that becomes petroleum and gas trapped underground in a reservoir is being added to continually, but the rate at which it is being extracted has become set according to an intention that has nothing to do with what the optimal timeframe in which the organic source material could be renewed. Thus, “non-renewability” is not any kind of absolute fact of nature. On the contrary, it amounts to a declaration that the pathway on which the natural source has been harnessed is anti-Nature.

10.5.2 Rebalancing Mass and Energy

Mass and energy balances inspected in depth disclose intention as the most important parameter, as the sole feature that renders the individual accountable to, and within, nature. This is rife with serious consequences for the black-box approach of conventional engineering, because a key assumption of the black-box approach stands in stark and howling contradiction to one of the key corollaries of that most fundamental principle of all: the Law of Conservation of Matter.

In fact, this is only possible if there is no leak anywhere and no mass can flow into the system from any other point. However,

mass can flow into the system from any other point – thereby rendering the entire analysis a function of tangible measurable quantities; i.e., a “science” of tangibles-only Figure 10.27.

The mass conservation theory indicates that the total mass is constant. It can be expressed as follows:

(10.8)

where m = mass and i is the number from 0 to ∞.

In the true sense, this mass balance encompasses mass from macroscopic to microscopic and detectable to undetectable; i.e., from tangible to intangible. Therefore, the true statement should be as illustrated in Figure 10.28:

(10.9)

The unknown masses and accumulations are neglected, which means they are considered to be equal to zero.

Every object has two masses:

1. Tangible mass.
2. Intangible mass, usually neglected.

Then, equation [3.5] becomes:

(10.10)

The unknowns can be considered intangible, yet essential to include in the analysis as they incorporate long-term and other elements of the current timeframe.

In nature, the deepening and broadening of order is continually observed, with many pathways, circuits and parts of networks being partly or even completely repeated and the overall balance being further enhanced. Does this actually happen as arbitrarily as conventionally assumed? A little thought suggests this must take place principly as a result and/or as a response to human activities and the response of the environment to these activities and their consequences. Nature itself has long established its immediate and unbreachable dominion over every activity and process of everything in its environment, and there is no other species that can drive nature into such modes of response. In the absence of the human presence, nature would not be provoked into having to increase its order and balance, and everything would function in the “zero net waste” mode.

An important corollary of the Law of Conservation of Mass, that mass can be neither created nor destroyed, is that there is no mass that can be considered in isolation from the rest of the universe. Yet, the black-box model clearly requires just such an impossibility. Since, however, human ingenuity can select the time frame in which such a falsified “reality” will be exactly what the observer perceives, the model of the black box can be substituted for reality and the messy business of having to take intangibles into account is foreclosed once and for all.

10.5.3 Energy: Toward Scientific Modeling

There have been a number of theories developed in the past centuries to define energy and its characteristics. However, none of the theories is enough to describe energy properly. All of the theories are based on much idealized assumptions which have never existed practically. Consequently, the existing model of energy and its relation to others cannot be accepted confidently. For instance, the second law of thermodynamics depends on Carnot cycle in the classical thermodynamics where none of the assumptions of Carnot’s cycle exists in reality. Definitions of ideal gases, reversible processes and adiabatic processes used in describing the Carnot’s cycle are imaginary. In 1905, Einstein came up with his famous equation, E=mc² which states an equivalence between energy (E) and relativistic mass (m), in direct proportion to the square of the speed of light in a vacuum (c²). However, the assumptions of constant mass and the concept of vacuum do not exist in reality. Moreover, this theory was developed on the basis of Planck’s constant which was derived from black body radiation. Perfectly black bodies don’t even exist in reality. So it is found that the development of every theory is dependent on a series of assumptions which do not exist in reality.

The scientific approach must include restating the mass balance.

For whatever else remains unaccounted for, the mass balance equation, which in its conventional form necessarily falls short of explaining the functionality of nature coherently as a closed system, is supplemented by the energy balance equation.

For any time, the energy balance equation can be written as:

(10.11)

Where a is the activity equivalent to potential energy.

In the above equation, only potential energy is taken into account. Total potential energy, however, must include all forms of activity, and here once again, a large number of intangible forms of activity, e.g., the activity of molecular and smaller forms of matter, cannot be “seen” and accounted for in this energy balance. The presence of human activity introduces the possibility of other potentials that continually upset the energy balance in nature. There is overall balance but some energy forms, e.g., electricity (either from combustion or nuclear sources), would not exist as a source of useful work except for human intervention which continually threaten to push this into a state of imbalance.

In the definition of activity, both time and space are included. The long term is defined by time being taken to infinity. The “zero waste” condition is represented by space going to infinity. There is an intention behind each action and each action is playing an important role in creating overall mass and energy balance.

The role of intention is not to create a basis for prosecution or enforcement of certain regulations. It is rather to provide the individual with a guideline. If the product or the process is not making things better with time, it is fighting nature – a fight that cannot be won and is not sustainable. Intention is a quick test that will eliminate the rigorous process of testing feasibility, long-term impact, etc. Only with “good” intention can things improve with time. After that, other calculations can be made to see how fast the improvements will take place.

In clarifying the intangibility of an action or a process, the equation has some constant which is actually an infinite series:

(10.12)

If each term of Equation (3.8) converges, it will have a positive sign, indicating intangibility; hence the effect of each term thus becomes important for measuring the intangibility overall. On this path, it should also become possible to analyze the effect of any one action and its implications for sustainability overall as well.

It can be inferred that man-made activities are not enough to change the overall course of nature. Failure up until now, however, to include an accounting for the intangible sources of mass and energy, has brought about a state of affairs in which, depending on the intention attached to such interventions, the mass-energy balance can either be restored and maintained over the long-term, or increasingly threatened and compromised in the short- term. In the authors’ view, it would be far better to develop the habit of investigating Nature and the prospects and possibilities it offers Humanity’s present and future, by considering time t at all scales, going to infinity, and giving up once and for all the habit of resorting to time scales that appear to serve some immediate ulterior interest in the short-term but which in fact have nothing to do with natural phenomena, must therefore lead to something that will be anti-Nature in the long-term and the short-term.,

The main obstacle to discussing and positioning the matter of human intentions within the overall approach to the Laws of Conservation of Mass, Energy and Momentum stems from notions of the so-called “heat death” of the universe, predicted in the 19^th century by Lord Kelvin and enshrined in his Second Law of Thermodynamics. In fact, however, this idea that the natural order must “run down” due to entropy, eliminating all sources of “useful work,” naively attempts to assign what amounts to a permanent and decisive role for negative intentions in particular without formally fixing or defining any role whatsoever for human intentions in general. Whether they arise out of the black-box approach of the mass-balance equation or the unaccounted missing potential energy sources in the energy balance equation, failures in the short-term become especially highly consequential when they are used by those defending the status quo to justify anti-Nature “responses” of the kind well-described elsewhere as typical examples of “the roller coaster of the Information Age” (Islam et al., 2003).

10.5.4 The Law of Conservation of Mass and Energy

Lavoisier’s first premise was “mass cannot be created or destroyed”. This assumption does not violate any of the features of Nature. However, his famous experiment had some assumptions embedded in it. When he conducted his experiments, he assumed that the container was sealed perfectly — something that would violate the fundamental tenet of Nature that an isolated chamber can be created. Rather than recognizing the aphenomenality of the assumption that a perfect seal can be created, he “verified” his first premise (law of conservation of mass) “within experimental error”.

Einstein’s famous theory is more directly involved with mass conservation. He derived E = mc² using the first premise of Planck (1901). However, in addition to the aphenomenal premises of Planck, this famous equation has its own premises that are aphenomenal. However, this equation remains popular and is considered to be useful (in the pragmatic sense) for a range of applications, including nuclear energy. For instance, it is quickly deduced from this equation that 100 kJ is equal to approximately 10^-9 gram. Because no attention is given to the source of the matter nor of the pathway, the information regarding these two important intangibles is wiped out from the conventional scientific analysis. The fact that a great amount of energy is released from a nuclear bomb is then taken as evidence that the theory is correct. By accepting this at face value (heat as a one-dimensional criterion), heat from nuclear energy, electrical energy, electromagnetic irradiation, fossil fuel burning, wood burning or solar energy, becomes identical.

In terms of the well-known laws of conservation of mass (m), energy (E) and momentum (p), the overall balance, B, within Nature may be defined as some function of all of them:

(10.13)

The perfection without stasis that is Nature means that everything that remains in balance within it is constantly improving with time. That is:

(10.14)

If the proposed process has all concerned elements so that each element is following this pathway, none of the remaining elements of the mass balance discussed later will present any difficulties. Because the final product is being considered as time extends to infinity, the positive (“<0”) direction is assured.

10.5.5 Avalanche Theory

A problem posed by Newton’s Laws of Motion, however, is the challenge they represent of relying upon and using the principle of energy-mass-momentum conservation. This principle is the sole necessity and the sufficient condition for analyzing and modeling natural phenomena in situ, so to speak — as opposed to analyzing and generalizing from fragments captured or reproduced under controlled laboratory conditions.

The underlying problem is embedded in Newton’s very notion of motion as the absence of rest, coupled with his conception of time as the duration of motion between periods of rest. The historical background and other contradictions of the Newtonian system arising from this viewpoint are examined at greater length in Abou-Kassem et al. (2008), an article that was generated as part of an extended discussion of, and research into, the requisites of a mathematics that can handle natural phenomena unadorned by linearizing or simplifying assumptions. Here the aim is to bring forward those aspects that are particularly consequential for approaching the problems of modeling phenomena of Nature, where “rest” is impossible and inconceivable.

Broadly speaking, it is widely accepted that Newton’s system, based on his three laws of motion accounting for the proximate physical reality in which humans live on this Earth coupled with the elaboration of the principle of universal gravitation to account for motion in the heavens of space beyond this Earth, makes no special axiomatic assumptions about physical reality outside the scale on which any human being can observe and verify for himself / herself (i.e., the terrestrial scale on which we go about living daily life). For example, Newton posits velocity, v, as a change in the rate at which some mass displaces its position in space; s, relative to the time duration; t, of the motion of the said mass. That is:

(10.15)

This is no longer a formula for the average velocity, measured by dividing the net displacement in the same direction as the motion impelling the mass by the total amount of time that the mass was in motion on that path. This formula posits something quite new (for its time, viz., Europe in the 1670s), actually enabling us to determine the instantaneous velocity at any point along the mass’s path while it is still in motion.

The “v” that can be determined by the formula given in equation [4.3] above is highly peculiar. It presupposes two things. First, it presupposes that the displacement of an object can be derived relative to the duration of its motion in space. Newton appears to cover that base already by defining this situation as one of what he calls “uniform motion”. Secondly, however, what exactly is the time duration of the sort of motion Newton is setting out to explain and account for? It is the period in which the object’s state of rest is disturbed, or some portion thereof. This means the uniformity of the motion is not the central or key feature. Rather, the key is the assumption in the first place that motion is the opposite of rest.

In his First Law, Newton posits motion as the disturbance of a state of rest. The definition of velocity as a rate of change in spatial displacement relative to some time duration means that the end of any given motion is either the resumption of a new state of rest or the starting-point of another motion that continues the disturbance of the initial state of rest. Furthermore, only to an observer external to the mass under observation can motion appear as the disturbance of a state of rest and can a state of rest appear as the absence or termination of motion. Within nature, meanwhile, is anything ever at rest? The struggle to answer this question exposes the conundrum implicit in the Newtonian system: everything “works” — all systems of forces are “conservative” — if and only if the observer stands outside the reference frame in which a phenomenon is observed.

In Newton’s mechanics, motion is associated not with matter-as-such, but only with force externally applied. Inertia, on the other hand, is definitely ascribed to mass. Friction is considered only as a force equal and opposite to that which has impelled some mass into motion. Friction, in fact, exists at the molecular level, however, as well as at all other scales — and it is not a force externally applied. It is a property of matter itself. It follows that motion must be associated fundamentally not with force(s) applied to matter, but rather with matter itself. Although Newton nowhere denies this possibility, his First Law clearly suggests that going into motion and ceasing to be in motion are equal functions of some application of force external to the matter in motion; i.e., motion is important relative to some rest or equilibrium condition.

Following Newton’s presentation of physical reality in his Laws of Motion, if time is considered mainly as the duration of motion arising from force(s) externally applied to matter, then it must cease when an object is “at rest”. Newton’s claim in his First Law of Motion that an object in motion remains in (uniform) motion until acted on by some external force appears at first to suggest that, theoretically, time is taken as being physically continual. It is mathematically continuous, but only as the independent variable, and indeed, according to equation (4.3) above, velocity v becomes undefined if time-duration t becomes 0. On the other hand, if motion itself ceases— in the sense of ∂s, the rate of spatial displacement, going to 0 — then velocity must be 0. What has then happened, however, to time? Where in nature can time be said either to stop or to come to an end? If Newton’s mechanism is accepted as the central story, then many natural phenomena have been operating as special exceptions to Newtonian principles. While this seems highly unlikely, its very unlikelihood does not point to any way out of the conundrum.

This is where momentum p, and — more importantly — its “conservation”, comes into play. In classically Newtonian terms:

(10.16)

Hence

(10.17)

If the time it takes for a mass to move through a certain distance is shortening significantly as it moves, then the mass must be accelerating. An extreme shortening of this time corresponds therefore to a proportionately large increase in acceleration. However, if the principle of conservation of momentum is not to be violated, either:

1. the rate of its increase for this rapidly accelerating mass is comparable to the increase in acceleration — in which case the mass itself will appear relatively constant and unaffected; or
2. mass itself will be increasing, which suggests that the increase in momentum will be greater than even that of the mass’s acceleration; or
3. mass must diminish with the passage of time, which implies that any tendency for the momentum to increase also decays with the passage of time.

The rate of change of momentum (∂p/∂t) is proportional to acceleration (the rate of change in velocity, as expressed in the ∂²s/∂t² term) experienced by the matter in motion. It is proportional as well to the rate of change in mass with respect to time (the ∂m/∂t term). If the rate of change in momentum approaches the acceleration undergone by the mass in question, i.e., if ∂p/∂t → ∂² s/∂t², then the change in mass is small enough to be neglected. On the other hand, a substantial rate of increase in the momentum of some moving mass — on any scale much larger than its acceleration — involves a correspondingly substantial increase in mass.

The analytical standpoint expressed in equation (4.4) and equation (4.5) above work satisfactorily for matter in general, as well as for Newton’s highly specific and indeed peculiar notion of matter in the form of discrete object-masses. Of course, here it is easy to miss the “catch”. The “catch” is the very assumption in the first place that matter is an aggregation of individual object-masses. While this may well be true at some empirical level at a terrestrial scale — 10 balls of lead shot, say, or a cubic liter of wood sub-divided into exactly 1,000 one-cm by one-cm by one-cm cubes of wood — it turns out in fact to be a definition that addresses only some finite number of properties of specific forms of matter that also happen to be tangible and hence accessible to us at a terrestrial scale. Once again, the generalizing of what may only be a special case — before it has been established whether the phenomenon is a unique case, a special but broad case, or a characteristic case — begets all manner of mischief.

To appreciate the implications of this point, consider what happens when an attempt is made to apply these principles to object-masses of different orders and/or vastly different scales, but within the same reference-frame. Consider the snowflake — a highly typical piece of atmospheric mass. Compared to the mass of some avalanche of which it may come to form a part of, the mass of any individual component snowflake is negligible. Negligible as it may seem, however, it is not zero. Furthermore, the accumulation of snowflakes in the avalanching mass of snow means that the cumulative mass of snowflakes is heading towards something very substantial, infinitely larger than that of any single snowflake. To grasp what happens for momentum to be conserved between two discrete states, consider the starting-point: p=mv. Clearly in this case, that would mean in order for momentum to be conserved:

(10.18)

which Means

(10.19)

At a terrestrial scale, avalanching is a readily-observed physical phenomenon. At its moment of maximum (destructive) impact, an avalanche indeed looks like a train-wreck unfolding in very slow motion. However, what about the energy released in the avalanche? Of this we can only directly see the effect, or footprint — and another aphenomenal absurdity pops out: an infinitude of snowflakes, each of negligible mass, have somehow imparted a massive release of energy. This is a serious accounting problem—not not only momentum, but mass and energy as well, are to be conserved throughout the universe.

The same principle of conservation of momentum enables us to “see” what must happen when an electron or electrons bombard a nucleus at a very high speed. Now we are no longer observing or operating at the terrestrial scale. Once again, however, the explanation conventionally given is that since electrons have no mass, the energy released by the nuclear bombardment must have been latent and entirely potential, stored within the nucleus.

Clearly, then, as an accounting of what happens in nature (as distinct from a highly useful toolset for designing and engineering certain phenomena involving the special subclass of matter represented by Newton’s object-masses), Newton’s central model of the object-mass is insufficient. Is it even necessary? Tellingly, on this score, the instant it is recognized that there is no transmission of energy without matter, all the paradoxes we have just elaborated on are removable. Hence, we may conclude that for properly understanding and becoming enabled to emulate nature at all scales, the mass-energy balance and the conservation of momentum are necessary and sufficient. On the other hand, neither the constancy of mass, nor the speed of light, nor even uniformity in the passage and measure of time are necessary or sufficient. This realization holds considerable importance for how problems of modeling Nature are addressed. An infinitude of energy and mass transfers take place in Nature, above and to some extent in relation to the surface of the earth, comprising altogether a large part of the earth’s “life cycle”. In order to achieve any non-trivial model of Nature, time itself becomes a highly active factor of prepossessing — and even overwhelming —importance. Its importance is perhaps comparable only to the overwhelming role that time plays in sorting out the geology transformations under way inside the earth.

10.5.6 Simultaneous Characterization of Matter and Energy

The key to the sustainability of a system lies within its energy balance. In this context, equation (4.11) is of utmost importance. This equation can be used to define any process, for which the following equation applies:

(10.20)

In the above equation, Q_in in expresses for the inflow of matter, Q_acc represents the same for accumulating matter, and Q_out represents the same for the outflowing of matter. Q_acc will have all terms related to dispersion/diffusion, adsorption/desorption, and chemical reactions. This equation must include all available information regarding inflow matters, e.g., their sources and pathways, the vessel materials, catalysts, and others. In this equation, there must be a distinction made among various matter, based on their sources and pathways. Three categories are proposed:

1. Biomass (BM);
2. Convertible non-biomass (CNB); and
3. Non-convertible non-biomass (NCNB).

Biomass is any living object. Even though, conventionally dead matter is also called biomass, we avoid that denomination as it is difficult to scientifically discern when a matter becomes non-biomass after death. The convertible non-biomass (CNB) is the one that due to natural processes will be converted to biomass. For example, a dead tree is converted into methane after microbial actions; the methane is naturally broken down into carbon dioxide, and plants utilize this carbon dioxide in the presence of sunlight to produce biomass. Finally, non-convertible non-biomass (NCNB) is a matter that emerges from human intervention. These matters do not exist in nature and their existence can only be considered artificial. For instance, synthetic plastic matters (e.g., polyurethane) may have a similar composition as natural polymers (e.g., human hair, leather), but they are brought into existence through a very different process than that of natural matters. Similar examples can be cited for all synthetic chemicals, ranging from pharmaceutical products to household cook wares. This denomination makes it possible to keep track of the source and pathway of a matter. The principle hypothesis of this denomination is: All matters naturally present on Earth are either BM or CNB, with the following balance:

(10.21)

The quality of CNB₂ is different from or superior to that of CNB₁ in the sense that CNB₂ has undergone one extra step of natural processing. If nature is continuously moving to better the environment (as represented by the transition from a barren Earth to a green Earth), CNB₂ quality has to be superior to CNB₁ quality. Similarly, when matter from natural energy sources comes in contact with BMs, the following equation can be written:

(10.22)

Applications of this equation can be cited from biological sciences. When sunlight comes in contact with retinal cells, vital chemical reactions take place that results in the nourishment of the nervous system, among others (Chhetri and Islam, 2008). In these mass transfers, chemical reactions take place entirely differently depending on the light source, the evidence of which has been reported in numerous publications (e.g., Lim and Land, 2007). Similarly, sunlight is also essential for the formation of vitamin D, which is in itself essential for numerous physiological activities. In the above equation, vitamin D would fall under BM₂. This vitamin D is not to be confused with the synthetic vitamin D, the latter one being the product of artificial processes. It is important to note that all products on the right hand side are of greater value than the ones on the left hand side. This is the inherent nature of natural processing – a scheme that continuously improves the quality of the environment, and is the essence of sustainable technology development.

The following equation shows how energy from NCNB will react with various types of matter.

(10.23)

An example of the above equation can be cited from biochemical applications. For instance, if artificially generated UV comes in contact with bacteria, the resulting bacteria mass would fall under the category of NCNB, stopping further value addition by nature. Similarly, if bacteria are destroyed with synthetic antibiotic (pharmaceutical product, pesticide, etc.), the resulting product will not be conducive to value addition through natural processes, instead becoming a trigger for further deterioration and insult to the environment.

(10.24)

An example of the above equation can be cited from biochemical applications. The NCNB₁ which is created artificially reacts with CNB₁ (such as N₂, O₂) and forms NCNB₃. The transformation will be in a negative direction, meaning the product is more harmful than it was earlier. Similarly, the following equation can be written:

(10.25)

An example of this equation is that sunlight leads to photosynthesis in plants, converting NCBM to MB, whereas fluorescent lighting, which would freeze that process, can never convert natural non-biomass into biomass.

The principles of the Nature model proposed here are restricted to those of mass (or material) balance, energy balance and momentum balance. For instance, in a non-isothermal model, the first step is to resolve the energy balance based on temperature as the driver for some given time period, the duration of which has to do with characteristic time of a process or phenomenon. This is a system that manifests phenomena of thermal diffusion, thermal convection and thermal conduction, without spatial boundaries but nonetheless giving rise to the “mass” component.

The key to the system’s sustainability lies within its energy balance. Here is where natural sources of biomass and non-biomass must be distinguished from non-natural, non-characteristic, industrially synthesized sources of non-biomass.

Figure 10.29 envisions the environment of a natural process as a bioreactor that does not and will not enable conversion of synthetic non-biomass into biomass. The key problem of mass balance in this process, as in the entire natural environment of the earth as a whole, is set out in Figure 10.30: the accumulation rate of synthetic non-biomass continually threatens to overwhelm the natural capacities of the environment to use or absorb such material.

In evaluating equation (4.12), it is desirable to know all of the contents of the inflow matter. However, it is highly unlikely to know all the contents, even at a macroscopic level. In absence of a technology that would find the detailed content, it is important to know the pathway of the process to have an idea of the source of impurities. For instance, if de-ionized water is used in a system, one would know that its composition would be affected by the process of de-ionization. Similar rules apply to products of organic sources, etc. If we consider the combustion reaction (coal, for instance) in a burner, the bulk output will likely to be CO₂. However, this CO₂ will be associated with a number of trace chemicals (impurities) depending upon the process it passes through. Because, equation (4.12) includes all known chemicals (e.g., from source, adsorption/desorption products, catalytic reaction products), it would be able to track matters in terms of CNB and NCNB products. Automatically, this analysis will lead to differentiation of CO₂ in terms of the pathway and the composition of the environment which is the basic requirement of equation (4.11). According to equation (4.12), charcoal combustion in a burner made up of clay will release CO₂ and natural impurities of charcoal and the materials from the burner itself. Similar phenomenon can be expected from a burner made up of nickel plated with an exhaust pipe made up of copper.

Anytime, CO₂ is accompanied with CNB matter, it will be characterized as beneficial to the environment. This is shown in the positive slope of Figure 10.31. On the other hand, when CO₂ is accompanied with NCNB matter, it will be considered to be harmful to the environment, as this is not readily acceptable by the eco-system. For instance, the exhaust of the Cu or Ni-plated burner (with catalysts) will include chemicals, e.g., nickel, copper from pipe, trace chemicals from catalysts, beside bulk CO₂ because of adsorption/desorption, catalyst chemistry, etc. These trace chemicals fall under the category of NCNB and cannot be utilized by plants (negative slope from). This figure clearly shows that the upward slope case is sustainable as it makes an integral component of the eco-system. With the conventional mass balance approach, the bifurcation graph of would be incorrectly represented by a single graph that is incapable of discerning between the different qualities of CO₂ because the information regarding the quality (trace chemicals) are lost in the balance equation.

10.6.1 Isotopic Characterization

At present, there is consensus regarding the rate of fossil fuel combustion, which should account for an annual increase in CO₂ by four ppm. However, the observed increase is only about two ppm. This discrepancy is explained in various ways. It is said that some CO₂ dissolves in seawater. In pre-industrial times, the CO₂ concentration of air was in equilibrium with the CO₂ concentration of surface seawater. As atmospheric CO₂ has risen, the equilibrium has been perturbed, such that the “excess” of CO₂ in air now drives a flux of CO₂ into the sea in an effort to re-establish equilibrium. It is also stated that the removal of CO₂ from the atmosphere is related to the growth of forests and grasslands worldwide. This latter conclusion leads to the paradox that there has been severe deforestation, also attributed to industrial activities. This is countered by asserting that the rate of growth of large masses of vegetation (mostly forests) is higher than that of deforestation. Of course, that poses the question, if forestation and vegetation is increasing, why is the CO₂ concentration rising?

To a first approximation, about half the CO₂ emitted by combustion remains in the atmosphere, about 35% dissolves in the oceans, and 15% is taken up by the increase in the biomass of forests. It is recognized that CO₂ absorption has declined in the ocean and at the same time general vegetation has not been using CO₂ from combustion activities, rejecting a bulk amount to the atmosphere, thus causing overall rise. In this section, carbon dioxide has also been classified based on the source from where it is emitted, the pathway it traveled, and age of the source from which it came. It has been reported that plants favor a lighter form of carbon dioxide for photosynthesis and discriminate against heavier isotopes of carbon decades ago (Farquhar et al. 1989). They introduced a formulation, in which carbon isotopic composition is reported in the delta notation relative to the V-PDB (Vienna Pee Dee Belemnite, see Libes, 1992 for details) standard. δ¹³C (pronounced “delta c thirteen”) is an isotopic signature, a measure of the ratio of stable isotopes ¹³C : ¹²C, reported in parts per thousand (per mil, ‰).

(10.26)

In Eq. 10.1, the standard is an established reference material. The value of δ¹³C varies in time as a function of productivity, the signature of the inorganic source, organic carbon burial and vegetation type. In essence, this term is a signature of the path traveled by a material or the time function. Biological processes preferentially take up the lower mass isotope through kinetic fractionation. Therefore, the fractionation itself becomes a measure of the quality of CO₂. The following formulation is based on Farquhar et al. (1989) and was used by several researchers, who studied the kinetic fractionation process.

(10.27)

in which, Δ¹³ is the C isotope discrimination, δ¹³C_air is the carbon isotope ratio of atmospheric CO₂ (–7.8 2030) and δ¹³C_plant is the measured δ¹³C value of leaf material.

Ever since the recognition that the past concentrations of atmospheric CO₂ level (pCO₂) is critical to plant metabolism and extent of photosynthesis, many research projects have been undertaken. These studies attempt to determine correlation between pCO₂ with changes in carbon isotope fractionation (Δ¹³C) in C₃ land plants⁶.

Figure 10.32 shows the amount of carbon isotope fractionation per change in pCO₂ (S, ‰/ppmv) as a function of pCO₂. Note the similarity among the three S-curves. Circles are plotted as the midpoint of the range of pCO₂ tested for each study. This sensitivity can vary under varying thermal conditions. Previous studies have reported that photosynthesis and plant enzyme activity can be strongly inhibited when grown at temperatures below 5C (Graham and Patterson, 1982; Ramalho et al., 2003). Some woody plants cannot withstand much below –6 C for any length of time and cease growth if the maximum daily temperature is below 9 C (Parker, 1963). For these low temperature conditions, thermal effects become the dominant limiting factors. Xu et al. (2015) reported variation in Δ¹³ with changing temperature. They observed a strong impact of mean annual temperature (MAT) on Δ¹³ in two mountain regions. MAT together with soil water content (SWC) in total accounted for a large proportion of the variation in Δ¹³ of the two mountainous regions. They observed that the impact of soil water availability on carbon isotope discrimination was limited for lower temperature values.

In (Equation 10.2), the fractionation process is controlled by the diffusion of CO₂ through the stomata (Craig 1953) as well as CO₂ fixation by ribulose bisphosphate carboxylase/oxygenase (RuBisCO; Farquhar and Richards 1984). These processes are highly sensitive to particulates of heavy metals as well as synthetic chemicals.

Hartman and Danin (2010) reported strong correlation between dry season green plants and rainfall – attributed to the combined product of ground water availability, evaporative demand, and improved water use efficiency (unique to desert shrubs and trees). Escudero et al. (2008) demonstrated that long-lived leaves from lignified species have higher δ¹³C values than short-lived leaves, due to reduced transpiration. They argued that this adaptation was designed to combat seasonal and annual shortages of water by minimizing the risk of leaf desiccation. Few studies have been available on how this process is altered in presence of anthropogenic CO₂.

Fardusi et al. (2016) conducted meta-analysis with large amount of data. They con-cuded that the relationship between ¹³C and growth is better characterized at juvenile stages, under near-optimal and controlled conditions, and by analyzing ¹³C in leaves rather than in wood. Carbon isotope composition (¹³C) in plant tissues offers an integrated measure of the ratio between chloroplastic and atmospheric CO₂ concentrations (Cc/Ca), and hence can be used to estimate the ratio between net CO₂ assimilation rate (A) and stomatal conductance for water vapour, i.e., intrinsic water-use efficiency (WUEi) after making certain assumptions about mesophyll conductance and post-photosynthetic fractionations (Farquhar et al., 1984). Note that during an adaptation cycle – a term widely used by the scientific community since 1990s – plants and vegetations are likely to develop special water use efficiency skills in response to the surge of “toxic”⁷ CO₂.

In this process, photosynthesis activities are enhanced in presence of higher WUEi. However, if higher WUEi implies a tighter stomatal control, it tends to be inversely correlated with growth (Brendel et al., 2002).

Intuitively, natural CO₂ and anthropogenic CO₂ should not behave the same way, mainly because anthropogenic CO₂ is contaminated with various chemicals that are not found naturally. However, it is a topic that has eluded mainstream researchers. Few studies have been carried out to see how these two source affect long-term behaviour of CO₂. Warwick and Ruppert (2016) attempted to document the relationships between the carbon and oxygen isotope signatures of coal and signatures of the CO₂ produced from laboratory coal combustion in atmospheric conditions. This study unravelled some of the important justifications behind the intuitive assertion that natural materials cannot be the source of global warming. In their study, they took six coal samples from various geologic ages (Carboniferous to Tertiary) and coal ranks (lignite to bituminous). Duplicate splits of the six coal samples were ignited and partially combusted in the laboratory at atmospheric conditions. The resulting coal-combustion gases were collected and the molecular composition of the collected gases and isotopic analyses of δ¹³C of CO₂, δ¹³C of CH₄, and δ¹⁸O of CO₂ were analysed by a commercial laboratory. Splits (~1 g) of the un-combusted dried ground coal samples were analyzed for δ¹³C and δ¹⁸O by the U.S. Geological Survey Reston Stable Isotope Laboratory. They reported that The the isotopic signatures of δ¹³C_V-PDB (relative to the V-PDB standard) of CO₂ resulting from coal combustion are similar to the δ¹³C_V-PDB signature of the bulk coal (– 28.46 to – 23.86 ‰) and are not similar to atmospheric δ¹³C_VPDB of CO₂ (~ — 8 ‰). The δ¹⁸O values of bulk coal are strongly correlated to the coal dry ash yields and appear to have little or no influence on the δ¹⁸O values of CO₂ resulting from coal combustion in open atmospheric conditions. There is a wide range of δ¹³C values of coal reported in the literature and the δ¹³C values from this study generally follow reported ranges for higher plants over geologic time. The values of δ¹⁸O relative to Vienna.

Standard Mean Ocean Water, VSMOW⁸) of CO₂ derived from atmospheric combustion of coal and other high-carbon fuels (peat and coal) range from + 19.03 to+27.03‰ and are similar to atmospheric oxygen δ¹⁸O_VSMOW values which average + 23.8‰. For reference, note that the isotopic ratios of VSMOW water are defined as follows:

• ²H/¹H = 155.76 ± 0.1 ppm (a ratio of 1 part per approximately 6420 parts)
• ³H/¹ hr = 1.85 ± 0.36×10⁻¹¹ ppm (a ratio of 1 part per approximately 5.41 × 10¹⁶ parts)
• ¹⁸O/¹⁶O = 2005.20 ± 0.43 ppm (a ratio of 1 part per approximately 498.7 parts)
• ¹⁷O/¹⁶O = 379.9 ± 1.6 ppm (a ratio of 1 part per approximately 2632 parts)

Figure 10.33 shows results from Warwick and Ruppert (2016). As can be seen from this figure, the δ¹³C_VPDB of the coal combustion CO₂ ranged from – 26.94 to – 24.16‰. Figure 10.34 shows results as reported by Warwick and Ruppert (2016). In this figure, the value of oxygen isotopic signature of atmospheric CO₂ (δ¹⁸O_VSMOW =+23.88) is from Brand et al. (2014). Run 1 (R1) and Run 2 (R2) are from Warwick and Ruppert (2016). shows those for δ¹⁸O_VSMOW of CO₂ ranged from + 19.03 to+27.03‰. In this experiment, two runs were conducted (Runs 1 and 2). The CO₂ gases collected during the second combustion run had slightly heavier values of δ¹³C_VPDB and lighter values of δ¹⁸O_VSMOW. Eight coal combustion gases (three from Run 1, and five from Run 2) produced sufficient quantities of CH₄ for the measurement of δ¹³C_VPDB of CH₄, and these values ranged from – 33.62‰ to – 16.95‰. Two of the collected gas samples from Run two yielded δ²H_VSMOW-CH4 values of – 243‰ and – 239.8‰.

Figure 10.35 compares δ¹³C_V-PDP values from effluents of a combustion in presence of atmospheric gases with combustion effluents in presence of high-purity combustion (brown squares in, as reported by Schumacher et al., 2011). The gases collected from the duplicate combustion runs indicate that the analytical results are generally reproducible. Schumacher et al. (2011) combusted samples of various organic materials (leaves, wood, peat, and coal) using controlled combustion temperatures (range 450 to 750 C) in the laboratory to study the effects of fuel type, fuel particle size, combustion temperature, oxygen availability, and fuel water content on the δ¹⁸O values of the produced CO₂. The samples were combusted in high-purity oxygen with an isotopic signature of δ¹⁸O =+27.2‰; however, to compare the results to those from atmospheric combustion, two samples (a charcoal and a peat) were combusted using laboratory atmosphere (brown squares on right side of). Schumacher et al. (2011) described the influences on carbon and oxygen isotopic fractionation during the combustion process and reported the major influences on the isotopic composition of combustion gases include the temperature of combustion, the carbon isotopic signature of the combusted fuel material, fuel particle size, and water content of the fuel material. Schumacher et al. (2011) also suggested the δ¹⁸O signature of the combusted organic material may influence the δ¹⁸O signature of the resulting combustion-derived CO₂. While this is intuitively correct, they did not measure δ¹⁸O of the coal samples used in their study. Schumacher et al. (2011) chose to use high-purity oxygen for their combustion experiments because of the dampening effect of nitrogen and water vapor on the combustion process in natural atmosphere. Atmospheric components may also react with the combustion gases. The role of atmospheric gases in shaping the isotopic character of CO₂ is confirmed in, which compares the two cases. It reveals that components otherwise not considered in conventional analysis (the ones we call ‘intangibles’) are the one made a difference in isotopic behavior of the two cases. Although preliminary, the results of our study may help to better characterize the oxygen and carbon isotopic character of CO₂ derived from atmospheric coal combustion.

Carbon has two isotopes, namely, ¹²C and ¹³C. Each has six protons in the nucleus of the atom, hence both are carbon. However, ¹³C has an extra neutron and thus a greater mass.

Adjacent atoms in molecules vibrate like balls attached to springs. In plain language, it means, in presence of an isotope, neighbouring atoms are more susceptible to interactions with the isotope. Lighter atoms vibrate more rapidly, and atoms vibrating more rapidly are easier to separate. Hence light atoms react more rapidly than heavy atoms in chemical and biochemical processes. In general, it is known that plant materials have less of the heavy isotope, ¹³C, than CO₂ from which it is produced, in essence plants fractionate and accumulate ¹³C, which then get transferred to animals that eat them. Fossil fuels of biogenic origin would have the same feature. The addition of organic carbon to air causes the resulting CO₂ mixture to have less ¹³C. So, for example, at night, the ¹³C/¹²C ratio of CO₂ in air decreases as plant material decays, and as fossil fuel CO₂ is added in populated areas. Similarly, in winter, the ¹³C/¹²C ratio of CO₂ in air again decreases as vegetation slowly rots. The ¹³C/¹²C ratio of CO₂ is presented as δ¹³C, which is the difference, in parts per thousand (tenths of a percent) between the ¹³C/¹²C ratio of a sample and a reference gas.

The δ¹³C signature of bulk coal has been well studied and reported in the literature (Singh et al., 2012). Gröcke (2002) has compared the carbon isotope composition of ancient atmospheric CO₂ to that of organic matter derived from higher-plants and suggested that both vary over geologic time. This observation confirms that CO₂ is part of the organic cycle and as such should not create imbalance in the ecosystem. Carbon isotope ratios in higher-plant organic matter (δ¹³C_plant) have been shown in several studies to be closely related to the carbon isotope composition of the ocean– atmosphere carbon reservoir, the isotopic composition of CO₂ being a reliable tracer. These studies have primarily been focused on geological intervals in which major perturbations occur in the oceanic carbon reservoir, as documented in organic carbon and carbonates phases (e.g., Permian–Triassic and Triassic–Jurassic boundary, Early Toarcian, Early Aptian, Cenomanian–Turonian boundary, Palaeocene–Eocene Thermal Maximum (PETM)). All of these events, excluding the Cenomanian–Turonian boundary, record negative carbon isotope excursions, and many authors have postulated that the cause of such excursions is the massive release of continental margin marine gas-hydrate reservoirs. That itself brings in Methane into the picture. In general a very negative carbon isotope composition (δ¹³C, around –60%%) is reported in comparison with higher-plant and marine organic matter, and carbonate. The residence time of methane in the ocean– atmosphere reservoir is short (around 10 years) and is rapidly oxidized to CO₂, causing the isotopic composition of CO₂ to become more negative from its assumed background value (δ¹³C of about –7‰). Such rapid negative δ¹³C excursions can be explained with geological events. Notwithstanding this, the isotopic analysis of higher-plant organic matter (e.g., charcoal, wood, leaves, pollen) has the ability to (i) record the isotopic composition of palaeoatmospheric CO₂ in the geological record, (ii) correlate marine and non-marine stratigraphic successions, and (iii) confirm that oceanic carbon perturbations are not purely oceanographic in their extent and affect the entire ocean–atmosphere system (Grocke, 2002). The problem is, there are case studies that show that the carbon isotope composition of palaeoatmospheric CO₂ during the Mid-Cretaceous had a background value of –3‰, but fluctuated rapidly to more positive (around + 0.5‰) and negative values (around –10‰) during carbon cycle perturbations (e.g., carbon burial events, carbonate platform drowning, large igneous province formation). As such, fluctuations in the carbon isotope composition of palaeoatmospheric CO₂ would compromise our use of palaeo-CO₂ proxies that are dependent on constant carbon isotope ratios of CO₂ (Grocke, 2002). Terrestrial plants can be divided into three groups on the basis of distinctions in photosynthesis and anatomy, namely:

1. C3 (Calvin–Bensen cycle, temperate shrubs, trees and some grasses, see Figure 10.36);
2. C4 (Hatch–Slack cycle, herbaceous tropical, arid-adapted grasses); and
3. Crassulacean acid metabolism (CAM, succulents).

Figure 10.36 Is a depiction of the Calvin cycle. Note that the Calvin cycle (also known as the Benson-Calvin cycle) is the set of chemical reactions that take place in chloroplasts during photosynthesis. The cycle is light-independent in the sense that it takes place after light energy has been captured during photosynthesis. represents six turns of the cycle, each turn of the cycle representing the use of one molecule of CO₂. Adenosine triphosphate (ATP) and nicotinamide adenine dinucleotide phosphate (NADPH, which is a reduced form of NADP+) are the products of the light-dependent reactions, which drive the Calvin cycle (ADP denotes adenosine diphosphate). The brackets after each element represent the number of molecules produced.

It has been suggested that C4 plants were present in the geological record prior to the Miocene (Ehleringer et al. 1991). Evans et al. (1986) conducted experiments on the isotopic composition of CO₂ before and after it passed through the leaves of a C3 plant and it was found that ¹²CO₂ was preferentially incorporated into the leaf, although if ¹²CO₂ concentrations were low, then relatively more ¹³CO₂ was incorporated into the leaf. Subsequently, it was shown that C3 and C4 plant groups have isotopically distinct δ¹³C_plant ranges: C3 plants range between –23 and –34%% with an average of –27%%, whereas C4 plants range between –8 and –16%% with an average of –13%% (Vogel 1993). Hence, the carbon isotope composition of ancient higher-plant organic matter, excluding environmental effects should provide researchers with a proxy for discriminating between these two main plant groups in the geological record. Similarly, such distinction can be made between CO₂ from fossil fuel and CO₂ from refined oil (e.g., gasoline). The fact that refining process adds many artificial chemicals, the Calvin cycle is affected. Figure 10.37 shows how the Calvin cycle can act as a fractionation column. In this figure, the term Σ_contaminants is the collection of all contaminant molecules that come from artificial components (the ones termed ‘intangible’ by Khan and Islam, 2016). It includes the entire history of a particle/molecule. For instance, if CO₂ came from plants that itself used pesticide and chemical fertilizer, this term will contain intangible amounts of the chemicals used in those processes. In the first phase, there will be components that will be rejected (Reject₀) even before entering the Calvin cycle. It is similar to rejection or fractionation of ¹³CO₂ molecules. This process of elimination continues at various stages, each corresponding to Reject_i, where i is the number of the cycle.

Table 10.8 Shows δ¹⁸O of coal results represent the average of two analyses as reported by Warwick and Ruppert (2016). The isotopic results of the δ¹³C_V-PDE of the coal combustion CO₂ ranged from –26.94 to –24.16‰ and those for δ¹⁸O_V-SMOW of CO₂ ranged from +19.03 to + 27.03‰. The CO₂ gases collected during the second combustion run had slightly heavier values of δ¹³C_V-PDB and lighter values of δ¹⁸O_V-SMOW. Eight coal combustion gases produced sufficient quantities of CH₄ for the measurement of δ¹³C_VPDB of CH₄, and these values ranged from –33.62‰ to –16.95‰. The coal combustion-derived δ¹³C_VPDB-CO₂ signatures were found to be similar to that of the δ¹³C_VPDB of the bulk coal (–28.46 to –23.86‰) and are not similar to modern atmospheric δ¹³C_VPDB of CO₂ (–8.2 to –6.7‰; as reported by Coplen et al., 2002). The values of δ¹⁸O_VSMOW of CO₂ (+19.03 to + 27.03‰) from the coal combustion gases from this study are similar to atmospheric oxygen δ¹⁸O values which average + 23.8‰ (Coplen et al., 2002). There is a wide range of δ¹³C_V-PDB values of coal reported in the literature and the values obtained by Warwick and Rupert (2016) generally follow previously reported ranges for higher plants over geologic time. The isotopic signatures of δ¹³C_VPDB of CO₂ resulting from laboratory coal partial combustion are similar to and probably derived from the original δ¹³C signatures of the coal. The δ¹⁸O_VSMOW values of coal show a strong correlation to the coal dry ash yields and appeared to have little or no influence on the δ¹⁸O_VSMOW values of CO₂ resulting from coal combustion. Coal burning is similar to crude oil burning. However, the same conclusion would not apply to refined oil burning and irrespective of the isotopic composition of the combustion products, the effect on the ecosystem will be long-lasting and irreversible. Warwick and Ruppert (2016) emphasized the need to develop better techniques for characterizing CO₂ which results from the combustion of coal.

Coplen et al. (2002) compiled a report on isotopic composition of a number of naturally occurring materials. The principal elements studied are reported in Table 10.9. Their report is a useful listing of major players of global warming.