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Calix[4]trap: A Bioinspired Host Equipped with Dual Selection Mechanisms

The paper I'll discuss in this post is this one: Calix (4) trap A Bioinspired Host Equipped with Dual Selection Mechanisms (Zhenchuang Xu, Nie Fang, and Yanchuan Zhao, Journal of the American Chemical Society 2021 143 (8), 3162-3168)

(The HTML codes here did not allow for me to write the title in the link as written in the actual title of the paper: Calix[4]trap: A Bioinspired Host Equipped with Dual Selection Mechanisms)

I am always interested in the separation of group I and group II elements in the periodic table. Group I consists of the elements lithium (Li), sodium (Na), potassium (K), rubidium (Rb) and cesium (Cs). (Let's forget about francium, a laboratory curiosity.) Group II consists of the elements beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba) and radium (Ra).

These separations, particularly for the heavier members, play an important role, among many other places, in the recovery of important valuable materials from used nuclear fuels, and in the clean up of historical sites contaminated with fission products.

A post I wrote yesterday in this space inspired some thinking about group II separations (although it was actually about the electrochemically driven "combustion in reverse," the reduction of carbon dioxide to elemental carbon). It seems to me that this particular technology is a path to addressing some problematic environmental problems connected with the production of aluminum metal, including, but not limited to carbon emissions from the "green" anodes.

Today I stumbled on the paper cited at the outset of this post, and thought I'd just point out some very wonderful scientific thinking.

From the introduction to the paper:

Molecular recognitions ubiquitously occur in life activities. Metal ions are vital to various physiological processes, ranging from heartbeat and muscle contraction to signal transduction.(1−3) Through evolution, living organisms have mastered the skill of selective binding and transporting ions by creating task-oriented functional units.(4,5) Prominent examples include valinomycin and K+ channels, both of which allow for ion trafficking across the cell membrane.(6) Valinomycin possesses a rigid scaffold and utilizes six carbonyl oxygens to form an ion binding cavity (Figure 1A).(7) The preorganized structure along with the optimal cavity size account for its much stronger affinity to K+ than Na+. In contrast, kinetic factors dominate in the selection mechanism of K+ channels, in which ions are conducted at vastly different rates. The successive binding sites within the channel’s selectivity filter constitute an ion transporting highway, where strict permeation of K+ is not only dictated by the ion’s charge and radius but also by the ease for the ion to undergo desolvation (Figure 1A).(8−11) These two examples demonstrate cases in which nature achieves guest discrimination through manipulating either binding affinities or rates. Although bionic designs are mostly directed to mimic one specific biological structure and function,(12−21) we asked what if we combine the selection strategies of valinomycin and K+ channels and realize them in a single host?...

A little while later they take on the task of answering their scientific question.

Inspired by the unique structure and properties of valinomycin and K+ channels, we sought to create a biomimetic ion host that discriminates ions through both thermodynamic and kinetic selection mechanisms. Given the fact many ion hosts display excellent thermodynamic ion selectivity,(22,23) our effort is directed to confer established ion hosts with a tunnel-like ion transport path that is essential for kinetically varied ion binding. We see the 1,3-alternate calix[4]arenecrown-5 (1) as a great candidate on which to perform the structural reengineering because it functionally resembles valinomycin and displays recording-setting K+/Na+ selectivity.(24,25) Unlike the orderly ion transport occurring within ion channels, metal ions approach 1’s central cavity from diverse directions, resulting in rapid and poorly controlled binding processes. Despite the exceptional K+/Na+ selectivity, 1 fails to effectively discriminate K+ from metal ions of comparable sizes, such as Rb+ and Ba2+. We thus wonder whether the not-yet-owned discrimination ability could be conferred by a confined binding tunnel biomimetic to K+ channel, where ions are uptaken with distinct rates. To test the feasibility of this idea, we first attempted to encapsulate 1’s ligating etheric oxygens within a confined tunnel to block the original ion binding path.

A few pictures from the paper show the experimental path and the results:

The caption:

Figure 1. Design and synthesis of calix[4]traps. (A) Valinomycin and the selectivity filter of K+ channel of streptomyces A (KcsA) (Protein Data Bank, 1K4C). (B) Image of a pitcher plant, the structure of 1,3-alternate calix[4]crown-5 (1), and X-ray single-crystal structure of calix[4]trap 3a. The picture of the pitcher plant was crafted by Ms. Suzhen Zhu. (C) The “flip” and “lock” strategy used to synthesize the designed ion hosts. Hydrogenation of double bond of 3a·K+ affords 4a·K+.

The caption:

Figure 2. Ion recognition behaviors and ions separation experiments. (A) 1H NMR titration of calix[4]trap 3a with K+ in d6-acetone. Two sets of NMR signals corresponding to 3a and 3a·K+ were observed, suggesting that the exchange between free and bound K+ is slow on the NMR time scale. (B) Measured log K (binding affinity, in d6-acetone/CDCl3 = 4:1 (v/v)) and log kin (associating rate constant, in d6-acetone/CDCl3 or acetone/CHCl3 = 4:1 (v/v)) of 3a at 25 °C. (C) Separation of K+, Rb+, and Cs+ based on the distinct complexation rates. Ion compositions were measured at different times using ICP-MS. (D) Selective cation extraction using 3a in the presence of various cations. Hyphens indicate that the concentration of the measured cation was lower than the limit of detection.

The caption:

Figure 3. Kinetic and thermodynamic data for the association between K+, Rb+, and Cs+ and various ion hosts. (A) Chemical and X-ray single-crystal structures of calix[4]traps 3b and 4c. (B) Measured logK for complexation of various metal cations with calix[4]traps 3a, 3b, 4a, and 4c in d6-acetone/CDCl3 = 4:1 (v/v) at 25 °C. (C) Measured log kin for complexation of various metal cations with calix[4]traps 3a, 3b, 4a, and 4c in d6-acetone/CDCl3 = 4:1 (v/v) at 25 °C.

The caption:

Figure 4. Investigation of the ion recognition pathway. (A) 1H NMR titration of calix[4]trap 3b with Cs+ before the inclusion of Cs+ into the buried cavity. (B) Proposed ion recognition path for the uptake of Cs+ with calix[4]trap 3b. For detailed assignments, see Figures S26.

From the conclusion to the paper:

By mimicking the preorganized binding sites of valinomycin and the consecutive ligating sites of K+ channels, we synthesized a series of novel ion hosts, which simultaneously possess a deeply buried binding cavity and a confined ion translocation tunnel. Mechanistic studies verify that the host’s portal could discriminate metal cations by their size, enabling varied ion uptake rates. The confined tunnel bearing consecutive binding sites promotes complete desolvation of ions during their inclusion into the buried cavity, mimicking the ion translocation within biological ion channels. The merging of selection strategies learned from valinomycin and K+ channels proved useful to further boost the record-setting selectivity and make possible the modulation of successive recognition events evolving in space and time...

It is very unlikely that these interesting reagents will prove to be of industrial importance, other than perhaps inspiring nanostructural templating, nor are they likely to be radiation stable, but this said, they are cool nonetheless.

People of course, find different things inspiring. Musicians and composers and musicologists will find Benjamin Britten's Requiem on a deeper level to which I could ever aspire, for example, and literary types can find deeper meanings in John Ashbery's "Self Portrait in a Convex Mirror" than I could ever dream of understanding.

But as a chemist, I find this paper beautiful, very beautiful.

Electrolysis of Lithium-Free Molten Carbonates

The paper I'll discuss in this post is this one: Electrolysis of Lithium-Free Molten Carbonates (Xiang Chen, Zhuqing Zhao, Jiakang Qu, Beilei Zhang, Xueyong Ding, Yunfeng Geng, Hongwei Xie, Dihua Wang, and Huayi Yin ACS Sustainable Chemistry & Engineering 2021 9 (11), 4167-4174)

I've argued before in this space that electricity is a thermodynamically degraded form of energy: Synthesizing Clean Transportation Fuels from CO2 Will at Least Quintuple the Demand for Electricity.

I have also argued, sometimes while addressing the stupid but oft discussed solar thermal energy fantasy, that the thermochemical splitting of carbon dioxide into carbon monoxide - from which pretty much any industrially produced carbon compound can be made (just add water) - and oxygen is the most efficient approach to carbon dioxide reduction: Cerium Requirements to Split One Billion Tons of Carbon Dioxide, the Nuclear v Solar Thermal cases.

This lab scale and thus hardly optimized result raises the cerium requirements by a huge amount. It means that for the nuclear case, the requirement for exactly one billion tons of carbon dioxide to be split would be 7,566,562 metric tons of cerium (as the metal) and that for the solar thermal case, it would be 45,399,372 metric tons also as the metal.

Although for certain reasons I am very fond of the cerium based thermochemical splitting of carbon dioxide, many other such catalytic systems are known for this highly endothermic reaction.

The international symbol for dangerous fossil fuel free energy has become a wind turbine or solar cell graphic object, which is frankly as silly as waving a graphic of a Roman executioner's cross as a symbol for the way to address immorality; both are faith based. It has been experimentally verified, at a cost of trillions of dollars, that wind turbines and solar cells are not even remotely capable of addressing climate change. In fact, the worship of them - and let's be clear that it's nothing more than faith based worship - has led to the acceleration of climate change. The average concentration of the dangerous fossil fuel waste carbon dioxide in the atmosphere measured at the Mauna Loa Carbon Dioxide Observatory during the week beginning on March 19, 2000 was 370.98 ppm. This morning, the latest figure was 417.67 ppm. The current 12 month running average of weekly measured increases over carbon dioxide increases over the last ten years is 24.24 ppm, 2.42 ppm/year. The same 12 moth running average for the week beginning March 19, 2000 was 15.14 ppm, 1.51 ppm/year.

These are facts. Facts matter.

Heckuva job humanity at addressing climate change with all those wind turbines, solar cells and electric cars, heckuva job.

The graphic attached to the introduction of this paper is nonetheless the equivalent of the Roman execution's cross as applied to so called "green" energy. Here it is:

What I like about this paper is that it is cognizant of the fact that matter, specifically the individual elements in the periodic table, is not "renewable." The claim that we can save the world with batteries is no different than the claim that supplies of dangerous petroleum, dangerous natural gas, and dangerous coal are infinite, as well as the claim that places to put the waste, chiefly, but hardly limited to, carbon dioxide is unlimited.

They start out talking about lithium and then consider elements that are far more available, one of which, strontium, catches my eye. Overall this discussion of batteries clearly has some relevance to the "batteries will save us" fantasy.

From the introduction to the paper:

Molten carbonate electrolysis offers an efficient route to convert CO2 or carbonate to C/CO at a rapid rate and high product selectivity(1−11) without using rationally designed catalysts to overcome the kinetic barrier.(12−17) Currently, most molten carbonate eletrolyzers employ lithium-containing salts due to the thermodynamic favorability of Li2CO3, relatively low eutectic temperature, and adequate solubility of Li2O.(18−24) However, lithium resource is limited in the Earth’s crust (e.g., lithium’s reserve is only less than one-thousandth of that of calcium in the Earth’s crust, Figure 1a) and will become scanter with increasing demand for lithium-based energy-storage devices.(25−27) Thus, exploiting lithium-free molten carbonate electrolyzers is of great importance to expand the novel systems and achieve the practical viability of molten carbonate electrolysis.

They have a nice graphic on the point:

The caption:

Figure 1. (a) Profiles of the abundance of alkali/earth alkali metal in the crust; data are derived from ref (43). (b) Schematic illustration of the electrolysis of molten carbonates and CO2 electrochemical conversion in molten carbonates. (c) Potential profiles as a function of temperature in molten MCO3–Na2CO3–K2CO3 (M = Mg, Ca, Sr, and Ba); all thermodynamic data are obtained from HSC Chemistry 6.0.

They continue:

Thermodynamically, alkaline-earth metal carbonates (AEMCs) can be electrochemically reduced to C/CO at a potential more positive than that of metal deposition. Thus, AEMCs are alternatives to replace Li2CO3, thereby preventing the use of strategic lithium salts. The use of CaCO3 or BaCO3 in Li2CO3-containing(28−30) or chloride melts(31−33) has been studied, which proves that AEMCs are suitable candidates to be reduced in molten salt systems. However, it is difficult to find a low-cost inert oxygen-evolution anode in the molten halides dissolved with AEMCs.(34−38) To date, a lithium-free molten carbonate system has not been systematically studied. Therefore, it is necessary to study the underlying mechanisms of the lithium-free molten carbonate electrolysis employing more abundant and inexpensive electrolytes.

The use of molten calcium salts is the essence of the FFC Cambridge process for the electrochemical reduction of metals, which I personally believe should be world changing, even if it is true that electricity is a thermodynamically degraded form of energy.

In saying this, they do raise some issues to be addressed:

In essence, the active species in molten carbonate electrolyzers is CO32– derived from the dissociation of carbonates or/and the captured CO2 by O2– rather than CO2 because the solubility of CO2 in molten carbonates is low.(39,40) The reduction of CO32– at the cathode releases O2– to capture CO2 and replenish CO32– or combine with alkaline-earth cation to generate the corresponding alkaline-earth metal oxides (MO).(41) Meanwhile, CO32– and O2– could directly diffuse to the anode and then be oxidized to O2 if the anode is inert (Figure 1b). However, there are two different reaction processes of molten carbonate electrolysis, which depends on the solubility of alkaline-earth metal oxides (MO) in the molten carbonates. If MO is insoluble in the molten AEMCs, MCO3 will be converted to MO and C at the cathode and O2 at the anode. In this case, the molten carbonate electrolyzer consumes MCO3. If the MO is soluble in the molten AEMCs, the dissolved MO will absorb CO2 to replenish carbonate. In this scenario, the molten carbonate electrolyzer consumes CO2, while the composition of the electrolyte remains unchanged. However, fundamental data of the solubility of MO in molten AEMCs and electrochemical properties of molten AEMCs urgently need exploring in lithium-free molten carbonates. In addition to atmospheric CO2, AEMCs (e.g., CaCO3) are one of the major CO2 hosts with a huge reserve in the forms of limestone and magma,(42) promising another way to valorize CO2 in terms of carbonates.

These factors are what they examine in the paper, and then propose an electrode to reduce carbon dioxide to carbon, in effect reversing the combustion of the dangerous fossil fuel coal.

This process, which requires the input of a thermodynamically degraded form of energy, electricity, as well as heat suggests an important point that is often over looked, which is this: In order to capture carbon dioxide in air one needs to put more energy into the system than all of the original energy ever released by the original combustion of the dangerous fossil fuel produced. This reality should sober up all the drunken handwaving and wishful thinking that goes on when energy and the environment is discussed, but I confidently predict, on the basis of being a tired old man, that it won't.

Their important concern is thermodynamics:

During the electrolysis of the ternary molten MCO3–Na2CO3–K2CO3 (M = Mg, Ca, Sr, and Ba) mixture, several reactions may take place as follows:



If the MO in eq 2 is soluble, then the carbonization reaction between MO and CO2 spontaneously occurs and forms fresh carbonate to maintain the concentration of CO32– of the electrolyte:


The overall reaction of eqs 2 and 3 is


Thermodynamically, alkaline-earth metal carbonates (MCO3, M = Mg, Ca, Sr, and Ba) can be electrochemically converted to carbon at the potential prior to the deposition of the alkaline-earth metal (Figure 1c). Therefore, the deposition of carbon is thermodynamically easier than that of metal. Moreover, the thermodynamic favorability of generating carbon is different depending on the different alkaline-earth metal cations. For example, the thermodynamic deposition potential sequence follows CaCO3 < SrCO3 < BaCO3. In other words, CaCO3 can be reduced to carbon at the potential more positive than that of SrCO3 and BaCO3. Note that the potentials of carbon generation in Na2CO3 and K2CO3 are more negative than that of the deposition of the corresponding alkali metals. Thus, Na2CO3 and K2CO3 are usually employed as the supporting electrolyte.(39,44) Therefore, alkaline-earth carbonates are the solute to be reduced for the carbon generation in MCO3–Na2CO3–K2CO3 (M = Mg, Ca, Sr, and Ba).

The reduction behaviors at a Mo electrode in a variety of carbonates containing different alkaline-earth metals are studied. As shown in Figure 2a, no reduction peaks were observed before the cathodic limit in the pure molten Na2CO3–K2CO3, demonstrating that Mo is an inert material that does not involve in any electrochemical reactions in the selective potential range.

The preliminary experiments investigated the cyclic voltammograms of molten carbonate systems using molybdenum electrodes:

The caption:

Figure 2. Cyclic voltammograms recorded from Mo electrode in the electrolytes of Na2CO3–K2CO3 with/without (a) 5 wt % MgCO3, (b) 5 wt % CaCO3, (c) 5 wt % SrCO3, and (d) 5 wt % BaCO3 at 750 °C under argon atmosphere. Scan rate is 100 mV/s.

Carbon was indeed deposited under these conditions, at a temperature of 750°C in sodium/potassium carbonate melts containing 10% (by weight, surprisingly) of three alkali metal carbonates, those of calcium (as in the FFC Cambridge Process), strontium and barium.

Micrographs of the carbons formed are shown:

The caption:

Figure 3. (a) XRD patterns of the electrolytic carbon obtained from molten Na2CO3–K2CO3–MCO3 (M = Ca, Sr, and Ba). SEM images of carbon obtained in the electrolytes of (b) Na2CO3–K2CO3–CaCO3, (c) Na2CO3–K2CO3–SrCO3, and (d) Na2CO3–K2CO3–BaCO3 at 3.0 V under 750 °C.

The question next turned to finding a stable electrode for the oxidation side of the reaction:

The caption:

Figure 4. (a) Digital photos of Ni10Cu11Fe electrode before and after electrolysis at various carbonate electrolytes. (b) Gas chromatograms of the outlet gas before and during electrolysis at 3.0 V under 750 °C in BaCO3–Na2CO3–K2CO3 using the Ni10Cu11Fe anode.

Next the solubility of the various oxides, calcium, strontium, and barium were determined by the simple expedient of putting pellets of these oxides in the melts and observing the amount dissolved:

The caption:

Figure 5. Digital photos of (a) CaO, (b) MgO, (c) BaO, and (d) SrO before and after being soaked in their corresponding molten 10 wt % MCO3–Na2CO3–K2CO3 (M = Mg, Ca, Sr, and Ba) at 750 °C.

Quantitative tables of the solubility of these oxides are not given in the paper, but the general conclusion was that barium oxide was the most soluble and the solubility of its oxide and carbonate were evaluated in more detail along with the rate of dissolution, as shown in the following graphic:

The caption:

Figure 6. Profiles of solubility of (a) BaCO3 in Na2CO3–K2CO3 and (b) BaO in Na2CO3–K2CO3 at 750 °C. Dissolution equilibrium cures of (c) BaCO3 in Na2CO3–K2CO3 and (d) BaO in Na2CO3–K2CO3 with different concentrations BaCO3.

It would be nice, from my perspective, if a more complex carbonate system allowing for the use of strontium in this system were considered in subsequent optimization, since strontium is available from used nuclear fuel with a heat generating isotope, Sr-90, which might defray the environmental and economic cost of maintaining a melt, although there are many heat network setting which might address this problem at an acceptable environmental and economic cost.

In any case, the barium oxide can absorb gaseous oxygen, even at these high temperatures - the decomposition temperate of barium carbonate is around 1300°C.

If the goal is, however, to produce the oxides themselves of strontium and/or calcium - the latter oxide is a key constituent of concrete, concrete production being a major contributor to climate change, the insolubility of the oxides is actually a desirable outcome.

The authors write:

Molten carbonates can be directly split by electrolysis, producing metal oxide (MO) and carbon at the cathode and oxygen at the anode. Two reduction mechanisms are shown in Figure 7. The solubility of MO determines the real reduced species in the molten carbonate: if MO is soluble (e.g., BaO), the carbonates electrolysis converts CO2 to C and O2; if MO is insoluble (e.g., CaO, SrO), the electrolysis converts MCO3 to MO, C, and O2.

This figure obviates that point:

The caption:

Figure 7. Two different reaction processes of molten carbonate electrolysis depending on the solubility of alkaline-earth metal oxides (MO) in the molten carbonates. Electrolysis of CO2 capture (left) and electrolysis of MCO3 (right).

They then write about capturing carbon dioxide from flue gas; if this gas is formed to generate electricity, they are then talking about a perpetual motion machine, but that doesn't totally negate the value of the paper itself.

I began this commentary by noting that electricity is a thermally degraded form of energy, but did not state the caveat that electricity captured by use of waste heat that would otherwise be rejected to the atmosphere is merely an improvement in overall energy efficiency. In the case where electricity is generated as a side product, using waste heat from a very high temperature process, the second law of thermodynamics is still operative - there is no physical way to make it inoperative - and increased exergy is obtained.

The conceit surrounding the so called "renewable energy" fantasy is that the intermittent nature of electricity can be addressed by net metering. On the left, we like to mock the statements of the assholes running ERCOT and the racist governor of Texas that the recent events in that State that led Senator Cancun Cruz to run away, the collapse of its power system was an outgrown of the so called "Green New Deal." To be perfectly clear and unambiguous, even as a lifelong Democrat, I don't think that the "Green New Deal" is going to be green or much of a deal. I have zero respect for the tired and old, and frankly experimentally failed energy ideas of Ed Markey, whether I otherwise agree with his other politics, as I often do. So called "renewable energy" is failing us now, and worse, is failing the future. It didn't work to address climate change. It isn't working to address climate change. It won't work to address climate change. Period. A key concept in the ideology of Green New Dealism is so called "net metering" which is the idea that the use of electricity follows its availability, its availability determining its price. If we are honest with ourselves, not that it is easy for anyone to be honest with themselves when honest confronts faith, including quasi religious faith, even absurd faiths, the extreme utility bills seen by some citizens of Texas are "net metering" run wild.

A heat network run by a high temperature nuclear plant, one producing temperatures high enough thermochemically split carbon dioxide - the cerium cycle running at maximum temperatures of 1400°C - will achieve the highest efficiency - the yield of exergy - as a constituent of a heat network, possibly producing a number of Brayton, Rankine and even Sterling cycles in sequence. If this is the case, electricity may be inevitably a side product. If this electricity is used to run combustion in reverse, which is what this paper is all about, the electricity can be switched to the grid whenever electricity prices rise high enough to justify the switching. In effect, a chemical plant is run as spinning reserve. This is not a new idea. Kaiser aluminum - aluminum production is an chemoelectric process - did this historically with hydro power in the Pacific Northwest.

Power demand on the grid fluctuates regularly, with the highest demand in the late afternoon and early evening, precisely when the sun goes down ironically enough, since so many people actually believe that solar electricity will save the world. It won't. It hasn't. Exploiting these fluctuations can be utilized to produce molecular carbon from CO2 gas or provide electricity to the grid, depending entirely on the value to the operator of the plant.

From the paper's conclusion:

Lithium-free molten carbonates (Na2CO3–K2CO3–MCO3, M = Ca, Sr, and Ba) are a family of promising electrolytes to replace Li-containing molten carbonate for the electrochemical conversion of CO2 and/or carbonate. The thermodynamic calculation shows that molten carbonate containing alkaline-earth metal cations can be used for producing carbon, and the low-cost Ni10Cu11Fe oxygen-evolution inert anode is stable in the molten carbonate containing various cations. More importantly, two reaction mechanisms are demonstrated based on the solubilities of alkaline-earth oxides (CaO, SrO, and BaO) in molten carbonates. The first mechanism is the conversion of MCO3 to MO, C, and O2 if the MO is insoluble in molten carbonates (M = Ca and Sr), and the second mechanism is the conversion of CO2 to C and O2 if the MO is soluble (the solubility of BaO ranges from 3 to 16 wt %) in molten carbonates. In addition, the electrolytic carbons exhibit superior energy-storage performances. Overall, this paper shed light on screening sustainable molten carbonates for the electrochemical conversion of inexpensive carbonate or CO2 to value-added carbon with a high product selectivity.

It's a very nice paper. I like it a lot.

I trust you are enjoying your weekend.

Use of a Modified SIRD Model to Analyze COVID-19 Data

All of the scientific publishers have made all Covid-19 related papers open sourced, so there is no need to discuss this paper in any detail as interested parties can read it themselves, but here it is: Use of a Modified SIRD Model to Analyze COVID-19 Data (Devosmita Sen and Debasis Sen Industrial & Engineering Chemistry Research 2021 60 (11), 4251-4260.)

Here, anyway, is an excerpt including the definition of "SIRD:"

1. Introduction
Since the beginning of 2020, the whole world has been experiencing a major and unprecedented global crisis, owing to the outbreak of the COVID-19 pandemic.(1−3) The infection is resulting in severe, and sometimes even fatal, respiratory diseases such as acute respiratory distress syndrome.(4) Such an infectious disease, with a humongous social and economic impact was never seen before, at least in the recent past.(5) COVID-19 arose due to a strain of a novel coronavirus that has rapidly spread throughout the globe,(1,6) originating from and infecting a large number of people in Wuhan, China.(7−9) The spread of this disease has a complex time dependence, which is governed not by the number of infected people alone, but is strongly correlated with aspects such as total population of the country, various norms and measures taken by the nation at a particular time, and many more.(10−14) Because of a lack of previous experience in controlling a similar pandemic with such a high impact in the recent past, it is difficult to anticipate the size of the population that may get affected by this pandemic and the typical time required for its control.

The abovementioned crisis immediately calls for a quantitative understanding of the time evolution of this complex and non-linear process through computer modeling. Statistical and mathematical analysis of reported data can provide valuable insights into the trend of the spread and thus can assist in planning various social measures to contain the spread of the virus as quickly as possible. Further, analysis of reported epidemic data plays a vital role in analyzing the underlying phenomena involved in spreading of the disease and to make predictions about future trends. This enables various organizations to efficiently plan their steps toward containing this spread.

In literature, a few models have been proposed to explain such data. These can primarily be classified into two categories, collective models(12,13,15−18) and networked models.(19−23) Some examples of the former class of models are growth and logistic models,(12) the susceptible–infected–recovered–dead (SIRD) model, and their modifications,(9,16) collectively termed as compartmental models. At this juncture, it is worthy to mention that such a phenomenon has a close resemblance to kinetics of chemical reactions in general,(24) where transition from one state to another is associated with a specific rate. In epidemic modeling, the corresponding rates may be expressed in terms of the instantaneous number of infected, recovered people, and so forth. Owing to the complex interdependence of several processes governing the spread of infections and recovery, a proper mathematical model should be able to simultaneously predict the temporal behavior of infected, recovered, and dead people. As the protection procedures demand quarantine, confinement, social distancing lockdown measures, and so forth,(26) a simple SIRD model only gives a preliminary understanding of the process and is not sufficient to describe such complex processes in general. Here, we model the spread of the present pandemic using a generalized SIRD model, taking into account the fraction of population which is exposed, under quarantine, confined, active-infected, recovered, and expired at time instant t. It is noteworthy that proper modeling calls for a simultaneous corroboration of the time evolution of all the three independent reported data sets, namely, active number of infections and cumulative number of recovered and expired people due to the infection.

In this manuscript, we report the analysis of COVID-19 time series data for five countries—China, Italy, France, the United States, and India (and two of its highly affected states)—using the modified SIRD model. We have shown that this model is capable of explaining the current data significantly well for all these five countries. It should be noted that the present approach is unique because it is capable of explaining simultaneously all the three reported data sets: active, recovered, and dead population. The data have been obtained from https://data.humdata.org/dataset/novel-coronavirus-2019-ncov-cases which is compiled by the Johns Hopkins University Center for Systems Science and Engineering (JHU CCSE) from various sources including the World Health Organization (WHO) and from reported data on Indian state websites https://arogya.maharashtra.gov.in/1175/Novel--Corona-Virus, https://gujcovid19.gujarat.gov.in/.

A picture:

The caption:

Figure 2. Schematic representation of the present model.

Enjoy if interested.

An obscure fact I never knew: All of the lanthanides except promethium exhibit a divalent state.

I was wandering around the scientific literature today and came across this very cool fact:

For many years, only six of the lanthanide metals were thought to be able to form complexes with the metal in the +2 oxidation state: Eu, Yb, Sm, Tm, Dy, and Nd.(1−3) This belief was supported by extensive solid state and solution studies,(1−5) as well as calculations of the reduction potentials.(6−10) However, recent studies of rare earth reduction chemistry have shown that the divalent oxidation state is accessible for all the lanthanides (except radioactive promethium) by reduction of tris(cyclopentadienyl) metal complexes with potassium or potassium graphite in the presence of a chelate.(11−15) This was originally shown with La and Ce by reduction of Cp′′3Ln precursors [Cp′′ = C5H3(SiMe3)2],(11) and subsequently for all the lanthanides, using Cp′3Ln precursors, (Cp′ = C5H4SiMe3).(4,5,12−14) These reactions, as well as results with Th,(16) U,(17,18) and Pu,(19) are summarized in eq 1,

I added the bold.

Trimethylsilyl versus Bis(trimethylsilyl) Substitution in Tris(cyclopentadienyl) Complexes of La, Ce, and Pr: Comparison of Structure, Magnetic Properties, and Reactivity (Chad T. Palumbo, Lucy E. Darago, Cory J. Windorff, Joseph W. Ziller, and William J. Evans, Organometallics 2018 37 (6), 900-905)

Most surprising in this equation is the fact that this holds true for three actinides, thorium, uranium and plutonium. Weird.

I'm glad I found that out before I died.

I was going to plant my summer vegetables and herbs seeds this weekend, but...

...we're having a midweek freeze here in central New Jersey.

That sucks. It's beautiful weather today.

Beto O'Rourke: Leadership on the Front Lines

This is a virtual online event. If you sign up and are unable to attend at the time it runs, they usually send you a recording.

Sign up here for the March 29 event: Tuck Life Long Learning.

One scientist showing appreciation of another in the comments section of a journal.

We often don't think of the social aspects of a scientific life, but in fact, all human strengths and flaws, particularly those involved simply with personality are there. It is a pleasure to work with most scientists, but it is also true that some are oppressive cranks with a nasty edge, including, to be sure, arrogance, contempt and, in many cases, a sense of malignant superiority and dismissiveness.

Of course, most people can display these flaws from time to time; I'm hardly immune myself.

At the end of most issues of scientific journals there'll often be short section in which comments on previous papers are offered. This is particularly true of ACS Journals, which tend to dominate my reading.

Often these comments are critical of the published paper under discussion, sometimes highly critical, even to the point of barely disguised hostility, even contempt.

I was very pleased to see one today that praised a paper and then simply asked for more information.

It's here:

Comment: The Novelty of a Two-Step Aromatization Process (Pulkit Bajwa, Industrial & Engineering Chemistry Research 2021 60 (10), 4189-4190)

An excerpt:

The problems of environmental pollution and limited oil reserves have drawn several scientists and engineers to look for alternate routes for producing petroleum-like products. One important route is the conversion of renewable materials to aromatic hydrocarbons. In search of literature on this topic, I came across the work of Fegade Swapnil that was published in I&EC Research.(1) The title of the paper is “Novel Two-Step Process for the Production of Renewable Aromatic Hydrocarbons from Triacylglycerides”. I read this article with great interest because the novelty is very high. Almost all of the previous research was focused on one step involving either thermal or catalytic conversion of plant oils to hydrocarbons. No previous work aimed particularly at aromatic hydrocarbons, BTEX...

...A design of experiments strategy was briefly mentioned in the beginning of section 3.2 of this article. Statistical analysis was not provided in the Supporting Information. Variations in reaction conditions may significantly change the outcome of the reaction. As explained in the other study(2) interactions between factors generally provide additional important information. Was this true for this two-step study? Statistical details such as main effects, interactions, or contour plots could reveal more information on this topic, particularly the second step. Therefore, I would like to ask for more information on statistical analysis and answers to questions that are asked above. Researchers would be interested in this information, which will certainly add value to the current study. Perhaps it would encourage engineers and scientists to conduct more detailed studies on aromatization of hydrocarbons from renewable sources and coke characterization, and use statistical data for optimization.

"Design of Experiments," often abbreviated as "DOE" is a statistical approach to evaluating parameters in a process to understand how these parameters interact to delineate a path to a desired outcome.

After these kind remarks, the authors of the paper under discussion replied:

Reply to “The Novelty of a Two-Step Aromatization Process” (Swapnil Fegade, Brian Tande, Alena Kubátová, Wayne Seames, and Evguenii Kozliak Industrial & Engineering Chemistry Research 2021 60 (10), 4191-4191)

The authors greatly appreciate these comments on this paper and highlighting the importance of this potential process pathway to aromatics production.

Further information about the statistical work performed during the study is available in Fegade(1) appendix C which contains all of the raw statistical data generated as well as additional statistical results from the Minitab program. These details were not included in the paper due to publication space limitations. Additional details can also be found in a patent by Seames and Tande.(2)

I can certainly appreciate when scientists "greatly appreciate" each other and be helpful to one another.

Science is a very human activity, and it's a joy when science can include graciousness. This is not always possible, but when it is, and is exercised, I certainly applaud it.

A trade-off between plant and soil carbon storage under elevated CO2

The paper I'll discuss in this post is this one: Terrer, C., Phillips, R.P., Hungate, B.A. et al. A trade-off between plant and soil carbon storage under elevated CO2. Nature 591, 599–603 (2021).

The abstract is open sourced, but it is useful to excerpt here to get some abbreviations understood:

Terrestrial ecosystems remove about 30 per cent of the carbon dioxide (CO2) emitted by human activities each year1, yet the persistence of this carbon sink depends partly on how plant biomass and soil organic carbon (SOC) stocks respond to future increases in atmospheric CO2 (refs. 2,3). Although plant biomass often increases in elevated CO2 (eCO2) experiments4,5,6, SOC has been observed to increase, remain unchanged or even decline7. The mechanisms that drive this variation across experiments remain poorly understood, creating uncertainty in climate projections8,9. Here we synthesized data from 108 eCO2 experiments and found that the effect of eCO2 on SOC stocks is best explained by a negative relationship with plant biomass: when plant biomass is strongly stimulated by eCO2, SOC storage declines; conversely, when biomass is weakly stimulated, SOC storage increases.

It currently seems likely to me that this Sunday, a new weekly average record for concentrations of the dangerous fossil fuel waste carbon dioxide will be set at the Mauna Loa CO2 observatory, probably near, at, or above 418 ppm. (The previous all time record was established in the week beginning February 28 of this year, 417.97 ppm.)

Last year, for the week beginning March 22, 2020, the weekly average reading at Mauna Loa was 415.52. The high for the year, which established a new record until this year, was 417.43, 1.89 ppm higher, observed for the week beginning May 24, 2020. All this suggests that we may see a weekly average reading of close to 420 ppm this year, possibly above it.

We are doing nothing to address climate change. Nothing beyond reciting the usual myths on our side of the political spectrum (so called "renewable energy" will save us) or simply engaging in lying and denial on the right ("climate change is not happening" or " it is not driven by human actions" or "it can be addressed by 'market' solutions."

We may think if we plant a lot of trees, we can ameliorate the problem, but the fact is that we are destroying forests and other wildernesses at an alarming rate, and many pristine areas are now being rendered into industrial parks for land intensive and material intensive "renewable energy," which has not worked to address climate change, is not working to address climate change, and will not work to address climate change. But even if we were not engaged in these massive efforts to destroy forests, it appears, if this paper is correct, that improvements in the mass of biomass on the surface will be offset by decreased soil carbon storage.

From the introduction to the paper:

The future of the land sink, especially of SOC, is particularly uncertain9. Soils can become either sources or sinks of carbon with rising levels of atmospheric CO2, depending on the prevalence of gains via photosynthesis or losses via respiration9,10. This uncertainty in terrestrial ecosystem model projections reflects uncertainty in both the mechanisms and the parameter values controlling SOC cycling under eCO211.

Plant growth generally increases in response to eCO24,12, with soil nutrients identified as the dominant factor explaining variability across experiments12,13,14,15. The effect of eCO2 on SOC stocks (βsoil) is more equivocal. Although the expectation is that SOC will accrue as eCO2 increases plant growth16, a few experiments show increases in βsoil, many show no change, and some even show losses7. The observed variation in βsoil across experiments is puzzling, and there is wide disagreement regarding the dominant mechanisms explaining this variation7,17,18.

A positive relationship between the effects of eCO2 on plant biomass and SOC pools is expected if increased plant production under eCO2 increases carbon inputs (litter) into the soil. Indeed, a positive relationship between inputs and SOC storage is formalized in first-order kinetics16 and is applied in most terrestrial ecosystem models19,20. Because the effect of eCO2 on plant aboveground biomass (βplant) is strongly correlated with the effect of eCO2 on litter production (Extended Data Fig. 1a, r = 0.81) and on root production21, a positive relationship between βplant and βsoil can thus be expected from first-order kinetics. This hypothesis, however, ignores SOC losses associated with accelerated soil organic matter decomposition sometimes observed under eCO27,18. Plants acquire limiting resources from soils through carbon investment belowground in root growth, exudates and symbiotic bacteria and fungi. Accelerated decomposition of soil organic matter fuelled by plant carbon inputs can enable plant nutrient uptake (the “priming effect”22). The return on this belowground carbon investment is an increase in aboveground biomass production15. However, the priming effect can decrease SOC5. A negative relationship between βplant and βsoil may thus emerge through the economics of plant resource acquisition.

Here, we evaluate the mechanisms of βsoil, including its relationship with βplant, by synthesizing 268 observations of βsoil from 108 eCO2 experiments spanning the globe with coupled βplant−βsoil data (Supplementary Table 1) using meta-analysis techniques...

Some graphics from the paper:

Fig. 1: Meta-analysis of the effect of eCO2 on percentage SOC across different factors.

The caption:

n = 108. Overall means and 95% confidence intervals are given; we interpret CO2 effects when the zero line is not crossed by the confidence intervals. Arrows represent 95% confidence intervals that extend beyond the limits of the plot. Soil carbon stocks represent values in ambient CO2 plots as a continuous variable, here expressed as intervals of equal sample size for illustration purposes. Values in parentheses are sample sizes. CO2 effects represent, on average, an increase in CO2 from 372 parts per million (ppm) to 616 ppm. FACE, Free Air CO2 Enrichment; OTC, Open Top Chamber; AM-ER, mix of AM and ericoid mycorrhizal; N-fixer, fixation of atmospheric nitrogen.

The authors state that overall, higher CO2 levels result, according to their meta analysis, in higher soil organic carbon (SOC).

However SOC is negatively correlated with surface biomass:

Fig. 2: Elevated CO2 experiments show an inverse relationship between the effects of eCO2 on plant biomass and SOC stocks due to plant nutrient-acquisition.

The caption:

This inverse relationship (a) can be explained by the different efficiencies in plant nutrient uptake (c) between AM and ECM nutrient-acquisition strategies driving opposite effects on plant biomass and SOC pools (b), including MAOM stocks (d). The regression line in a is based on a quadratic mixed-effects meta-regression model and 95% confidence interval (R2 = 0.67, P < 0.0001, n = 38). Dots in a represent the individual experiments in the meta-analysis, with dot sizes proportional to model weights. Dots in b−d represent overall effect sizes from a meta-analysis and 95% confidence intervals. Data shown here are for non-fertilized experiments (see Extended Data Fig. 3 for nutrient-fertilized experiments).

Fig. 3: Effect of eCO2 (about 240 ppm) on SOC stocks scaled up from 108 CO2 experiments.

The caption:

a, b, Relative effect of elevated CO2 on SOC scaled up on the basis of a meta-forest approach with data from CO2 experiments, with the spatial distribution shown on a map (a) and aggregated by ecosystem type (b). c shows the standard error in a, and d shows the standard error in b. Green dots in c represent the location of the CO2 experiments included in the analysis. e, f, Difference between expected CO2 effects on SOC stocks based on CMIP5 models and scaled up on the basis of experiments (shown in a) with the spatial distribution shown on a map (e) and aggregated by ecosystem type (f). Expected values result from the relationship between βsoil and βplant coded in models. Positive values (reddish colours) indicate an overestimation by models; negative values (bluish colours) indicate an underestimation by models. Shaded areas between –15 to 15 and from 60° to 90° in latitude represent ecosystems not well sampled by experiments that we excluded from the analysis. Boxplots show the median, the first to third quartile, the 1.5× interquartile ranges, and outliers. On average, the difference between elevated CO2 and control plots in the experiments is 240 ppm.

Fig. 4: Comparison of modelled and measured relationships between aboveground biomass and SOC responses to CO2.

The caption:

a, Relationship observed (blue) and modelled (red) across six eCO2 experiments. Model results are based on 12 models applied to the same six experiments with a common forcing and initialization protocol. The experiments included are: Duke FACE (DUKE), Kennedy Space Center (KSCO), Nevada Desert FACE (NDFF), Oak Ridge FACE (ORNL), Prairie PHACE (PHAC), and Rhinelander (RHIN). The regression line across observations in a is based on a quadratic meta-regression model. Modelled simulations averaged in a for each experiment are from the FACE-MDS project phase 2 (ref. 34). b, c, Global-scale relationship simulated by ecosystem models from the TRENDY ensemble for the historical increase in CO2 since the year 1700 (b) and from the CMIP5 ensemble for an increase in CO2 from 372 ppm to 616 ppm as in eCO2 experiments (c). Dotted lines are the 1:1 line.

Some conclusions from the paper:

In summary, our synthesis of experiments shows that SOC stocks can increase by approximately 5% in response to a 65% step increase in CO2 concentrations, with a strong coupling between CO2-driven changes in plant aboveground biomass and SOC. However, the coupling between plant biomass and soils is an inverse relationship (Fig. 2a, Extended Data Fig. 1b), opposite to that simulated by many ecosystem models (Fig. 4). The effect of eCO2 on SOC storage is dependent on a fine balance between changes in inputs and changes in turnover18, where the latter is dependent on root−microbe−mineral interactions in the rhizosphere. Our results suggest that rhizosphere responses, and especially priming, explain much of the variation in βsoil across experiments (Fig. 2). Most models focus on carbon inputs and underestimate rhizosphere effects11,20,35, probably explaining the disagreement in βsoil between observations and models (Figs. 3, 4). We propose a framework to explain βsoil based on nutrient acquisition strategies15,36,37. On one end of the spectrum, substantial acquisition of soil N is possible via priming5 in ECM-associated plants, causing a stronger plant biomass sink at the expense of SOC accrual. On the other end, low nutrient availability strongly constrains the plant biomass sink38 in AM-associated plants.

This all suggests that forests have a limited capacity to address ever increasing carbon dioxide concentrations. The authors suggest that in terms of soil carbon, grasslands are more efficient than forests.

I note that it took many millions of years for the carbon we've released in the last century to be sequestered by photosynthesis and decay. This should be a sobering thought, given our propensity to believe sunlight alone can save the world. It won't be a sobering thought, but it should be.

Have a nice day tomorrow.

The National Mag Lab: The World's Strongest Magnet.

The video shows the 21 Tesla Magnet, the highest field magnet in the world. (The ion source seems surprisingly generic, but hey, at that field strength, who cares?)

If you go, leave your wallet outside.

The National Ignition Facility.

The world's largest laser is at Lawrence Livermore Laboratory. Cool video.

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