# Morally Indiscriminate Pedophiles and Invisible Ring: Psychopaths That Cause Suicide Or Murder Thru Targeting And Harassment

### To The Police, Mayor, And FBI

We have prisons for a reason, I have given you more than enough data to show that my experiences are real, and I expect you to do a proper covert investigation. My personal experiences, especially considering my knowledge in chemical engineering and biological sciences, should be weighted heavily when evaluating the below data.

## Summary

Sadly, Targeting[1-3;5] and gang stalking is real, and some psychopaths are using the dark web, computer hacking[Quotes, 19,11,12],

Video: Gang Stalking, Electronic Harassment – How the System Works[1]

Quote: “But some simple software lets just about anyone sitting next to you at your local coffee shop watch you browse the Web and even assume your identity online.”[19]

Quote: “Until recently, only determined and knowledgeable hackers with fancy tools and lots of time on their hands could spy while you used your laptop or smartphone at Wi-Fi hot spots. But a free program called Firesheep, released in October, has made it simple to see what other users of an unsecured Wi-Fi network are doing and then log on as them at the sites they visited.”[19]

Pedophile Quote: “Barry Ardolf, 46, repeatedly hacked into his next-door neighbors’ Wi-Fi network in 2009, and used it to try and frame them for child pornography, sexual harassment, various kinds of professional misconduct and to send threatening e-mail to politicians, including Vice President Joe Biden.”[11]

Pedophile Quote: “Within three days, investigators determined the homeowner had been telling the truth: If someone was downloading child pornography through his wireless signal, it wasn’t him. About a week later, agents arrested a 25-year-old neighbor and charged him with distribution of child pornography. The case is pending in federal court.”[12]

“Voice to Skull” and other Radio Frequency equipment to affect people and neighbors[Quotes, 1-15]. Your neighbor could very well be a sociopath, psychopath–serial killer included, or an average citizen with the “invisible ring,” that is trying to cause your suicide, murder, or other violent act. In the latter case, I think psychologist would classify them as a sociopath or psychopath as well. They could be just like Internet trolls[6].

I am experiencing electronic harassment by my neighbors, gang stalking and electronic harassment by Eugene, Oregon, community, I have written about it, Secret Service has visited me because of my experiences, Secret Service has called both my brothers and said I am not dangerous and trying to help them, and, personally, I believe it is the ethical dilemma of the invisible ring–Would you be a psychopath or network with one or many if invisible? In my case, it is because I blew the whistle on Abbott Laboratories[8].

## Electronic Harassment

1962 Abstract Quote: “The intent of this paper is to bring a new phenomenon to the attention of physiologists. Using extremely low average power densities of electromagnetic energy, the perception of sounds was induced in normal and deaf humans. The effect was induced several hundred feet from the antenna the instant the transmitter was turned on, and is a function of carrier frequency and modulation. Attempts were made to match the sounds induced by electromagnetic energy and acoustic energy. The closest match occurred when the acoustic amplifier was driven by the rf transmitter’s modulator. Peak power density is a critical factor and, with acoustic noise of approximately 80 db, a peak power density of approximately 275 mw/ cm2 is needed to induce the perception at carrier frequencies of 425 mc and I ,31 o mc. The average power density can be at least as low as 400 pw/cm2. The evidence for the various possible sites of the electromagnetic energy sensor are discussed and locations peripheral to the cochlea are ruled out.” [4]

Pins and Needles Quote: “With somewhat different transmitter parameters, we can induce perception of severe buffeting of the head, without such apparent vestibular symptoms as dizziness of nausea. Changing transmitter parameters again, one can induce a “pins-and-needles” sensation.”[4]

Quote:“A significant amount of research has been concerned with the effects of radio-frequency (rf) energy on organisms (electromagnetic energy between 1 kc and 100 Gc). Typically, this work has been concerned with determining damage resulting from body temperature increase. The average power densities used have been on the order of 0.1 – 1 w/cm^2 used over many minutes to several hours.”[4]

Microwatt Quote: “In contrast, using average power densities measured in microwatts per square centimeter, we have found that other effects, which are transient, can be induced with this energy. Further, these effects occur the instant the transmitter is turned on. With appropriate modulation, the perception of various sounds can be induced in clinically deaf, as well as normal human subjects at a distance of inches up to thousands of feet from the transmitter.” [4]

Note, I have experienced “Pins-and-Needles,” gastrointestinal discomfort, feelings that my brain is expanding and contracting, and audio. Reference [4] shows that each is possible, and the technology has been around prior to 1962. I believe Kip Kinkle was affected by the same “foundation” of Eugene psychopaths that is affecting me. I have read that Kip Kinkle does not hear voices and thinks Eugene/Springfield is evil. I must agree because citizens know electronic harassment happens and they turn a blind eye.

## The Technology Can Be Built Easily[3], And Can Be Small

Video Time: 17:35-18:40: Spark Gap can send out a broad range of frequencies[3].

Video Time: 18:38 – 19:08: Wider the gap, the lower the frequency; broad range of frequencies by adjusting gap[3]. Frequencies can affect physiological functioning[3,7].

Video Time: 22:07: Cell Phone jammer made (approximately $40.00 cost) made with copper pipe and automotive spark plug as spark gap. Size of cavity controls frequency.[3] Video Time: 24:21–25:01: RBoC: Radio Blast Cannon is a high energy device to cause a computer to be destroyed.[3] Video Time: 59:50: Ten amps will kill a person easily, and it only takes a dozen milliamps to stop the heart.[3] Video Time: 1:04:36: Laws against energy weapons. There are laws against cell phone jammers.[3] Video Time: 1:10:06–1:12:12: Radio weapons can generate biological effects. Tail end, no body will admit to experimenting on humans.[3] Video Time: 1:12:32–1:13:35: Ultrasonic weapons, ear, me having ringing in the ears.[3] Video Time: 1:13:25: He says he does all things with ultrasonic weapons, but he also says it is hypothetical. Above, he says nobody would admit to it. He also talks about the gut-buster and producing a sound that is resonate with gastrointestinal tracts, it works, it is not to hard, and it is real close to 16 Hz but he did not say that.[3] Video Time: 1:14:30: His discussion was about low frequency applications.[3] Video: Defcon 8: Radio Energy Weapons (Complete)[3] ## Serial Killers On The Loose–Pedophile and Sexual Trafficking Network Frequency of Serial Killers Gender by Date Quote (Year, Number):1900-Men: 18; Women: 11; 1910-Men: 30; Women: 12; 1920-Men: 43; Women: 12; 1930- Men: 43; Women: 8; 1940-Men: 54; Women: 8; 1950-Men: 66; Women: 12; 1960-Men: 198; Women: 18; 1970-Men: 536; Women: 33; 1980-Men: 706; Women: 59; 1990-Men: 673; Women: 53; 2000-Men: 410; Women: 29; 2010-Men: 93; Women: 5.”[9] Note, the internet seemed to help reduce the number of serial killers. Likely because of incriminating data. Quote:Average IQ: 94.1; Median IQ: 86.5; Lowest: 54; Highest: 165.”[9] Quote:Type: Organized: 112; Disorganized: 66; Mixed: 8″[9] Quote:Number of Kills: Two: 50; Three: 47; Four: 20; Five: 15; More than five: 86″[9] Note, some research has shown that the average IQ of a pedophile is below 100 (average) as well, but not every pedophile is a serial killer and not every serial killer is a pedophile. As seen below, the Morally Indiscriminant pedophile/sexual trafficker is the likely serial killer[Quote, 10]. ## Pedophiles: I Believe Eugene, Oregon, Has Serial Killers Please note that I am an ex-Federal Law Enforcement Agent with the FDA, I have taken a basic criminal profiling class with the “Reids” called “The Reid Technique of Interviewing and Interrogation,” which is taught to FBI, FDA, NSA, and CIA, and an Eugene cop, he called himself “Lars,” harassed me in 2010 and said he knew a bunch of “Reids.” I had said in my home that the Reids could catch them in lies because the psychopaths using Radio Frequency said they could not be caught in lies. I also know, from my Reid training, that psychopaths are caught in lies just as easily as normal people. The difference, though, is that psychopaths get mad at their intellectual failure instead of worrying about the consequence of serving a prison term or receiving the death penalty. The people gang-stalking and electronic harassing me in Eugene, I have heard their audio at the Eugene YMCA, West 11th Walmart, and other places in Eugene, Oregon. They have bragged that they are sexual traffickers/pedophiles and they have corrupt police on their side. I-5 is the only North/South interstate, The Oregonian said Portland was one of the worse sexual trafficking locations in the US, and one can easily deduce that sexual trafficking is a main source of business in Eugene, Oregon, too[Quote, 16]. The average age of a child is 13 to 15. They also record audio in my home and hacked my computer[Quotes, 11, 12]. February 2016 Quote: “Rewind. Oregon, as a state has a the 9th highest amount of strip clubs per capita at 63,806.17. Portland itself has 50, whereas Seattle has about 4. So? Well, Oregon also comes in at 19th for called in cases sex trafficking through the National Human Trafficking Resource Center (NHTRC). That’s only the reports that are called in, or reported. There are many more found after the fact.”[16] Pedophiles, sexual traffickers included, are using the dark web and targeting innocent people for practice in the USA/World. They are practicing to kidnap your child, make you seem crazy if they molest your child, if they photograph your child, etc [Quote, 10]. My ex-coworkers from Abbott Laboratories-Eric Nielsen, Sara, Chase, Kathy Ford, Roger Quan-connected with a criminal enterprise (traffickers) to murder me via suicide, cancer, or other abnormal death[Quote, 13,14]. Note, corporations have pedophiles and child molesters too, and the FBI specifies that not all pedophiles actually molest[10]. Still, I believe I have been affected by a Morally Indiscriminate[Quote, 10] that probably found each other on the dark web[See End Quotes]. FBI Pedophile Quote: “Their victims tend to be targeted based primarily on availability and opportunity. They are more likely to use practical tools (e.g., weapons, lock picks, gloves, masks) and learn from and then modify their criminal sexual behavior. Their patterns of criminal sexual behavior are more likely to involve the previously discussed concept of method of operation (MO).[10, Page 34] Abbott Laboratories Quote: “I called David Pacitti, vice president of global marketing for Abbott Laboratories’ cardiac-plumbing division, to ask why he seems to want goons to beat me up in the newspaper parking lot. “Don’t you have connections in Baltimore?????” Pacitti e-mailed a subordinate regarding a January column I wrote on heart-artery stents. “Someone needs to take this writer outside and kick his ass! Do I need to send in the Philly mob?”[13] Abbott Laboratories Quote: “Corporations, such as General Electric, Abbot Laboratories, and Halliburton, as been pointed out, have had an extensive history of illegal practices. Other corporations have a reputation of ethical standards and behavior such as Proctor and Gamble, Hewlett-Packard, and Borg Warner.”[14] Whistleblower Quote: “For at least eight insiders, the financial consequences were reportedly devastating. One said, “I just wasn’t able to get a job. It went longer and longer. Then I lost — I had a rental house that my kids were [using to go] to school. I had to sell the house. Then I had to sell the personal home that I was in. I had my cars repossessed. I just went — financially I went under. Then once you’re financially under? Then no help. Then it really gets difficult. I lost my 401[k]. I lost everything. Absolutely everything” (Relator 17).” [Relator = pharmaceutical whistleblower] [10] Pedophile Quote: “Barry Ardolf, 46, repeatedly hacked into his next-door neighbors’ Wi-Fi network in 2009, and used it to try and frame them for child pornography, sexual harassment, various kinds of professional misconduct and to send threatening e-mail to politicians, including Vice President Joe Biden.”[11] Pedophile Quote: “Within three days, investigators determined the homeowner had been telling the truth: If someone was downloading child pornography through his wireless signal, it wasn’t him. About a week later, agents arrested a 25-year-old neighbor and charged him with distribution of child pornography. The case is pending in federal court.”[12] FBI Pedophile Quote: “Morally Indiscriminate: For this offender the sexual victimization of children is simply part of a general pattern of abuse in his life. Mental-health clinicians refer to this type of individual as a psychopath or having anti-social personality disorder. He is a user and abuser of people. He abuses his wife, friends, and coworkers. He lies, cheats, or steals whenever he thinks he can get away with it. He molests children for a simple reason — “Why not?” His primary victim criteria are vulnerability and opportunity. He has the urge, a child is available, and so he acts. He typically uses force, lures, or manipulation to obtain his victims. He may abduct his victims using trickery or physical force. Although his victims frequently are strangers or acquaintances, his victims can also be his own children or those of his live-in girlfriend. An incestuous father (or mother) might be this morally indiscriminate offender. Because he is an impulsive person whose conscience is inconsistent with society standards, he is an especially high risk to molest pubescent children. Such acts may be criminal but not necessarily sexually deviant. He frequently collects detective magazines or adult pornography of a violent nature. He may collect some child pornography especially that which depicts pubescent children. Even when his child victims are acquaintances, he may still use threats and force to overpower or control those victims.”[10] # Churchill Triad Murders Before the death of Churchill High school students, my neighbors told me via Radio Frequency they knew a shooting would happen. The community near my home placed two dead ducks on my roadway that leads to Bailey Hill Road. I called the dead ducks in, one duck disappeared, and then there were three dead ducks. Within a month, there were three murders. When I was here between 2008-2010, a news agency had announced that Eugene, police, was ordering citizens to quit killing and using dead animals in code. During that same period, I saw three dead cats on my bike route at different times, and some were disemboweled. I was being retaliated against during this period as well, and a corrupt cop told me to quit talking about “The Nielsens”, which happens to be a prominent family in Eugene. I blew the whistle on Eric Nielsen from Abbott Laboratories. As mentioned in other notes, my niece was hit by a hit and run driver after I was told family would die because I blew the whistle. One “set” of recent (2015) murders was teens at Churchill high school by a shooter. I believe that shooter was targeted[1-9] by psychopaths in Eugene, Oregon. After this death, the other death was a “set’ that included a man who was found in a city culvert that was locked. I believe corrupt cops were involved with both sets. The culvert man had blocked the flow of fluids. I believe the group of psychopaths, because they “gang bully/gang stalk” and include people with the invisible ring who actually have empathetic feeling, murdered this person to shut others up. It is a way for a group of maybe 10-15 psychopaths to threaten larger numbers. Also, some empathetic people are likely to commit suicide, and this would make the psychopaths happy. Since three deaths have happened near a month period, the group, larger number included, can be classified as serial killers. ## Some Pedophiles Cook And Eat Children My neighbors have bragged that they are cannibals[Quote, 15]. If I die from cancer, heart attack, murder, or a suicide that looks like murder, contact my brothers and tell them to contact the Secret Service. They are to tell the Secret Service the truth. My brothers were contacted by the Secret Service because of me and told that I am not dangerous and trying to help them. The Secret Service is to contact the FBI and force an investigation into my death–cancer, heart attack, or suicide included. See, these very stupid people said they wanted to sexually traffic the President’s children and then make a snuff film. You must know that sexual traffickers and some pedophiles will grind children up and feed them to animals, humans included. They will cook children[Quote, 15]. Quote: “A Boston-area man, who was planning to kidnap children, lock them in a basement dungeon, rape and eat them, should be imprisoned for at least 27 years, federal authorities said in court documents filed this week.”[15] Quote: “When his home in Worcester was searched last year, authorities found tens of thousands of computer images and videos of child pornography and 4,500 exchanges of child pornography between Portway and the people he chatted with online. The images included children being cooked and prepared to be eaten, court documents said. Those photographs are sealed.”[15] ## Dark Web Quote: “It’s not out of the question to suggest that the part of the web that hasn’t been indexed is actually bigger than the part that has.” [17] Quote: “If you’re a terrorist, paedophile, gun-runner, drug dealer, sex trafficker or serious criminal of that ilk then the shadows of the Deep Web, and particularly the Dark Web, offer a safer haven then the part occupied by, say, Naked Security or Wikipedia.”[17] Quote: “Although Memex will eventually have a very broad range of applications, the project’s initial focus is on tackling human trafficking and slavery.” [17] Quote: “In September 2014, sex trafficker Benjamin Gaston was sentenced to a minimum of 50 years in prison having been found guilty of “Sex Trafficking, as well as Kidnapping, Criminal Sexual Act, Rape, Assault, and Sex Abuse – all in the First Degree”.[17] Quote: “For example, an ad attempting to sell the sexual services of a woman or child in one locale might pop up in another location and include a regional address or phone number. White says this kind of data has been used by investigators to find women who were being trafficked.[18] “You can imagine a scenario where people are moving around the country with women and are interested in advertising them—they post ads in different places. It can involve the same women and some of the same info like phone numbers.”[18] Quote: “To achieve this goal, Memex will not only scrape content from the millions of regular web pages that get ignored by commercial search engines but will also chronicle thousands of sites on the so-called Dark Web—such as sites like the former Silk Road drug emporium that are part of the TOR network’s Hidden Services.”[18] ## Referencecs: [1] Targeting Must End. (2015, Nov. 04). Gang Stalking, Electronic Harassment – How the System Works. Retrieved (2016, Feb. 14). Available from: https://youtu.be/plrHU4VKbRM [2] Targeting Must End. (2015, Sep. 26). Electronic Harassment and Gang Stalking – Yet Another Point of View. Retrieved (2016, Feb. 14). youtube[online]. Available from: https://youtu.be/dVZnGYrqnkY [3] GBPPR2. (2011, Jan 23). Defcon 8: Radio Energy Weapons (Complete). Retrieved (2012). Available from: https://youtu.be/6fu9M6f59j0 [4] Kitteh, Miss. (2013, Jan. 20). Dr. Joe Pompei explains audio spotlight on Mad Labs. Retrieved (2016, Feb. 15). Available from: https://youtu.be/P5Tv9Wmcbf4 [5] OSIInformers. (2012, Oct. 06). Organized Stalking And Mind Control. Retrieved (2011). youtube[online]. Available from: https://youtu.be/BZJLqVgulZQ [6] Golbeck, Jennifer, PhD. (2014, Sep. 18). Internet Trolls Are Narcissists, Psychopaths, and Sadists. Trolls will lie, exaggerate, and offend to get a response. Retrieved (2016, Feb. 17). Available from: https://www.psychologytoday.com/blog/your-online-secrets/201409/internet-trolls-are-narcissists-psychopaths-and-sadists [7] Frey, A.H., General Electric (1962): Human Auditory system response to modulated electromagnetic energy. J. Appl Physiol. 17, 689-692. Available from: https://drive.google.com/file/d/0BxgSPGHH3R4aSldGcWIzRFQ3M3M/view?usp=sharing [7a] Golbeck, Jennifer, PhD. (2014, Sep. 18). Internet Trolls Are Narcissists, Psychopaths, and Sadists. Trolls will lie, exaggerate, and offend to get a response. Retrieved (2016, Feb. 17). Available from: https://www.psychologytoday.com/blog/your-online-secrets/201409/internet-trolls-are-narcissists-psychopaths-and-sadists [8] Harding, Byron. (2016, Feb. 17). Schizoaffective or Whistleblower Retaliation? New Trusted Scientific Evidence Suggests Retaliation. Retrieved (2016, Feb. 18). Facebook[online]. Available from: https://www.facebook.com/notes/byron-harding/schizoaffective-or-whistleblower-retaliation-new-trusted-scientific-evidence-sug/10153561522753477 [9] Aamodt, M. G. (2013, October 19). Serial killer statistics. Retrieved (insert date of retrieval) skdb.fgcu[online]. Available from http://skdb.fgcu.edu/public/Serial%20Killer%20Statistics%2019OCT2013.pdf [10] Kesselheim, Aaron S., MD, JD, MPH; Studdert, David M., LL.B., Sc.D., MPH; Mello, Michelle M., JD, PhD, M.Phil.; Whistle-Blowers’ Experiences in Fraud Litigation against Pharmaceutical Companies. The New England Journal of Medicine[online]. 2010. vol. 362, pp. 1832-1839. Available from: New England Journal of Medicine: http://www.nejm.org/doi/full/10.1056/NEJMsr0912039 [11] Kravets, David. (2011, July 12). WI-FI-Hacking Neighbor From Hell Sentenced To 18 Years. Retrieved (2016, Feb. 19). wired[online]. Available from: http://www.wired.com/2011/07/hacking-neighbor-from-hell/ [12] Associated Press. (2011, June 24). Innocent Man Accused Of Child Pornography After Neighbor Pirates His WiFi. Retrieved (2016, Feb. 20). huffingtonpost[online]. Available from: http://www.huffingtonpost.com/2011/04/24/unsecured-wifi-child-pornography-innocent_n_852996.html [13] Hancock, Jay. Threat betrays big medicine’s profit obsession. Baltimore Sun[online]. 2010. Available from: < a href=”http://www.baltimoresun.com/health/bs-bz-hancock-stents-abbott-20101206,0,5226901.column&#8221; Target=”_blank”>http://www.baltimoresun.com/health/bs-bz-hancock-stents-abbott-20101206,0,5226901.column [14] Marshall, Clinard B.; Yeager, Peter C. Corporate Crime. Transaction Publishers[online]. 2006. Available from: http://books.google.com/books?id=uNM9ybnZxj8C&pg=PR38&dq=”Abbott+Laboratories”+corporate Google Books. ISBN: 1-4128-0493-0 [15] Mungin, Lateef; Cannold, Julie. (2013, Sep. 13). Massachusetts man plotted to kill and eat children, feds say. Retrieved (2016, Jan. 28). cnn[online]. Available from: http://www.cnn.com/2013/09/12/justice/cannibal-eat-children-case/index.html [16] Rieckmann-James, Morgan. (2016, Feb. 16). Sex Trafficking in the Pacific Northwest. Retrieved (2016, Feb. 20). ccrampart[online]. Available from: http://ccrampart.org/788/news/sex-trafficking-in-the-pacific-northwest/ [17] Stockley, Mark. (2015, Feb. 16). Memex – DARPA’s search engine for the Dark Web. Retrieved (2016, Feb. 08). nakedsecurity.sophos[online]. Available from: https://nakedsecurity.sophos.com/2015/02/16/memex-darpas-search-engine-for-the-dark-web/ [18] Zetter, Kim. (2015, Feb. 02). Darpa IS Developing A Search Engine For The Dark Web. Retrieved (2015, Feb.). Available from: http://www.wired.com/2015/02/darpa-memex-dark-web/ [19] Murphy, Kate. (2011, Feb. 16). New Hacking Tools Pose Bigger Threats to Wi-fi Users. Retrieved (2016, Feb. 19). nytimes[online]. Available from: http://www.nytimes.com/2011/02/17/technology/personaltech/17basics.html # Numerical Method Reviews Hello, This note will be a collection of my personally created numerical method reviews. I will be reviewing topics from two books[B1;B2].I have uploaded my PDFs to scribd because I have had hit and miss experience with LaTeX in WordPress. Also, the PDFs can be accessed, downloaded, and printed easily. I have chosen books [B2; B5] because they are used in courses at MIT that are freely available online. Since I am using Octave, I found a great book for that environment too[B1]. I plan to study both books. Purpose Most books have an initial chapter that discusses pertinent topics to be successful for the rest of the book. The topics are briefly discussed, and the authors [B1;B2] really expect the reader to have full knowledge or gain full knowledge of the material before proceeding. I am entering a learning phase and a review phase. I am reviewing calculus [B3] and algebra[B4], but I am learning linear algebra[B5]. This note will be a place that I categorize my reviews. I am writing these reviews with LaTeX, so that takes time as well. Still, LaTeX lets me easily write in the language of mathematics once I learn it well. Numerical Methods Using MATLAB Reviews[B2] Quote: It is assumed that the reader is familiar with the notation and subject matter covered in undergraduate calculus sequence. This should have included topics of limits, continuity, differentiation, integration, sequences, and series. Throughout the book we refer to the following results.”[B2] Quote: “Example 1 is about as easy a limit proof can get; most limit proofs require a little more algebraic and logical ingenuity. (sic: read basic knowledge should be well understood.) The reader who finds “δ – ε ” discussions hard going should not become discouraged; the concepts and techniques are intrinsically difficult. In fact, a precise understanding of limits evaded the finest mathematical minds for centuries.”[B3]”[B2,1] Reviews For Numerical Methods Using MATLAB[B2]: [B2,1] Harding, Chris. (2015, Dec. 21). Review of Limits. Retrieved (2015, Dec. 21). Available from: https://www.scribd.com/doc/293834966/Review-of-Limits Scientific Computing With MATLAB And Octave[B1] Quote: “In this book we will systematically use elementary mathematical concepts which the reader should know already, yet he or she might not recall them immediately. We will therefore use this chapter to refresh them and we will condense notions which are typical of courses in Calculus, Linear Algebra and Geometry, yet rephrasing them in a way that is suitable for use in Scientific Computing.”[B1] Reviews For Scientific Computing with MATLAB and Octave[B1]: [B1,1] Harding, Chris. (2015, Dec. 26). Chapter 1, What Can’t Be Ignored: Section 1.1 To Addition And Multiplication Review Of Matrices.(Octave) Retrieved (2015, Dec. 26). Scribd[online]. Available from: https://www.scribd.com/doc/294069551/Chapter-1-What-Can-t-Be-Ignored-1-Section-1-1-To-Addition-And-Multiplication-Review-Of-Matrices Books: [B1] Quarteroni, Alfio; Saleri, Fausto; Gervasio, Paola. Scientific Computing with MATLAB and Octave. Fourth Edition. Retrieved (2015, Dec. 18). Shannon[online] [B2] Mathews, John H.; Fink, Kurtis, D. (1999). Numerical Methods Using Matlab. (Third Edition). Prentice Hall [B3] Anton, Howard. Calculus with Analytic Geometry. Fifth Edition. [B3a] Barker, William H.; Ward, James E. (1995). The Calculus Companion to Accompany Calculus with Analytic Geometry. Fifth Edition by Howard Anton. John Wiley [B4] Grossman, Stanley I. (1992) Algebra and Trigonometry, Second Edition. Saunders College [B5] Strang, Gilbert. (2009). Introduction to Linear Algebra. South Asian Edition. Cambridge University Press India Pvt. Ltd. # Limits Review: A Rigorous Approach Hello, Dr. Anton–Calculus Textbook–Quote: “Example 1 is about as easy a limit proof can get; most limit proofs require a little more algebraic and logical ingenuity. (sic: read basic knowledge should be well understood.) The reader who finds “δ – ε” discussions hard going should not become discouraged; the concepts and techniques are intrinsically difficult. In fact, a precise understanding of limits evaded the finest mathematical minds for centuries.”[3]”[1] Purpose I have hopes to learn some Numerical Methods[2] to allow me to contribute to PLOTS (http://publiclab.org). Numerical methods are often used by engineers to mathematically solve problems that do not have “exact” solutions. In truth, they can be used to solve problems that have exact solutions where the solution is quite difficult as well. Also, the studying of math and engineering help me mentally by providing the psychotherapy methods of mindfulness and compensatory cognitive training for my schizoaffective disorder (bipolar type). Here, I have provided my first LaTeX created PDF on this topic– LaTeX is great for writing mathematics and is free–that reviews limits and absolute values. I am writing such documents because it is likely that I will lose focus or be hospitalized since that has happened in the past. I can then read a document I made to provide an understanding to move forward. In this case, one of my numerical methods Books started with a vague and abstract definition of the rigorous limits approach[1;2], and I wanted a better understanding[1]. I plan to do similar PDFs for other “review” topics in Section 1.1[2]. By the way, I picked[2] because MIT has a free course that uses the same textbook. In my reference[1], I also provide a great book that covers the use of Octave and MATLAB when doing numerical methods. Great Video and Special Note This MIT video on the Rigorous approach has great information of absolute values, etc. In fact, I suggest the reader pay particular attention, within the video[3], of the power of a simple absolute value property of “Triangle inequality” $|a + b| \leq |a| + |b|$ that is discussed during the problem solving near video time of 35:12 to end at 46 minutes. The professor is being kind. To be good, one must have an amazing memory and an amazing grasp of the fundamentals of mathematics. Really, I believe one should obviously begin this grasp in each math class, but, if one is intelligent enough to grasp future fundamentals ahead of the curve, then he or she can go back and review past sections as they pertain to the current set of problems. I am not that person, but hope to gain enough of a “working” knowledge that I can be competent and useful in the world of PLOTS. With that said, all the video[Embedded; 3] is important and a good test of one’s knowledge on this topic[1]. References: [1] Harding, Chris. (2015, Dec. 21). Review of Limits. Retrieved (2015, Dec. 21). Available from: https://www.scribd.com/doc/293834966/Review-of-Limits; Google URL: goo.gl/vd5XAe [2] Mathews, John H.; Fink, Kurtis, D. (1999). Numerical Methods Using Matlab. (Third Edition). Prentice Hall [3] MIT OpenCourseWare. (2011, May 05). Unit I: Lec 5 | MIT Calculus Revisted: Single Variable Calculus, Unit !: Lecture 5: A More Rigorous Approach to Limits. Retrieved (2015, Dec. 28). youtube[online]. Available from: https://youtu.be/9tYUmwvLyIA?list=PLLEGnvlQMshG_TaCu75GpVOeXHiVe0JP2 # An investment opportunity : For those interested in OxiGene (OXGN)–a developer of novel anti-cancer drugs Disclosure First, I own OxiGene (OXGN) stock. Also, I have two STEM degrees: chemical engineering and biological sciences, so I have some understanding of the science behind OxiGene drugs. As such, I am not an expert, but I can provide a somewhat educated evaluation. History OxiGene once traded at near$8,000 per share, $5,000 per share,$3,000 per share, and from $1,000 per share to the current, December 26, 2013, near$2.60 per share[6]. It is a small cap company with no current product on the market[3;7]. As such, its stock dropped over the years because of the recession and negative Earnings Per Share, EPS. What should be noted is that small-cap stocks are the usual winners of a recession recovery[4]. Also, the splits make the share price less.

Clinical Phases, Orphan Drugs, and Pipeline

With that said, Zybrestat, its leading drug, was in phase 3 for Anaplastic Thyroid Cancer (ATC)[12] and designated an orphan drug by the United States (US)[14;15], but, according to information from an OxiGene source, Zybrestat will not currently enter continued phase III trials for  ATC in the USA because of funding. As such, I assume OxiGene will not be marketing Zybrestat for ATC in the USA. Still, according to FDA website, OxiGene’s combretastatin drugs have been designated Orphan drugs for “Treatment of anaplastic thyroid cancer, medullary thyroid cancer, and stage IV papillary or follicular thyroid cancer”, “Treatment of ovarian cancer”, and “Treatment of acute myelogenous leukemia.”[16, search: combretastatin]. US Orphan drug status guarantees OxiGene exclusive marketing rights for seven years and various significant tax breaks[15]. According to the US Food and Drug Administration, Phase 3 can take from 1 to 4 years[13]. At the OxiGene website, a graphic indicates that the Zybrestat Phase 3 for ATC is half way completed, but I received a phone call from an OxiGene representative that said phase 3 for ATC will not continue in the USA due to FDA requirements for a large population of patients, near  300, in a future phase III trial. The FDA required number of subjects is, at this time, to costly for OxiGene. The representative did say that OxiGene is still planning to continue USA clinical trials for ovarian cancer. Once Zybrestat is approved by the FDA, assuming phase 3 trials continue to go well[5], a physician, oncologist as an example, can prescribe Zybrestat for other cancers, which is called “off-label” use[2], in ethical situations. In truth, I assume FDA mandates on ATC clinical trials could be an indication of future FDA mandate on ovarian cancer trials. OxiGene is also expecting early marketing of Zybrestat in the European Union, EU. Also, Zybrestat has been designated an EU orphan drug for Anaplastic Thyroid Cancer, ATC, and ovarian cancer. The OxiGene representative that contacted me also said OxiGene is still planning to market Zybrestat in the European Union once approved. Eventually, I have hope the stock will stabilize at a new price significantly greater than where I bought it.

As an example, current and past phase I thru III drug trials of OxiGene drugs, Zybrestat and OXi4503, show promise with Anaplastic Thyroid Cancer (ATC)[12], Ovarian Cancer[12], Acute Myeloid Leukemia (AML)[10;11], myelodysplastic syndrome (MDS)[10;11], and other abnormal vascular diseases such as macular degeneration[12]. Zybrestat has shown success against Pancreatic Neuroendocrine Tumor Model as well[9], and Zybrestat has had mixed results with non-small cell lung cancer[12]. This is important because investment companies look at “how many” people a drug will serve to earn profits per share. Remember, a physician can prescribe for “off-label use,” but the additional prescriptions might or might not affect the overall share price. Finally, Zybrestat has a good safety profile so far[5]. According to reference [5], Zybretsat did show some myocardial ischemia, but the OxiGene representative told me the ischemia problem has been eliminated by prescribing a drug that helps with hypertension. As the reader may know, the US FDA denies the approval of many drugs because of heart issues, but I cannot definitively say this is why the US FDA required near 300 subjects for a Zybrestat phase III trial for anaplastic thyroid cancer, ATC. As mentioned previously, an OxiGene representative told me that OxiGene will not currently be completing ATC phase 3 clinical trials in the USA because of funding.

Research Pipeline

OxIGene also has an effective research pipeline. One of OxiGene’s drugs in the research pipeline is benzosuberenes[1], which have shown success for prostate, ovarian, and non-small cell lung cancers[1] in the pico-molar range. OxiGene owns the rights to all of Baylor Universities studies on benzosuberenes. If you notice, the Division of Cancer Treatment and Diagnosis, National Cancer Institute at Frederick, National Institutes of Health, Frederick, Maryland, United States was apart of the following journal article too[1]. In truth, I do not believe the US Government wants OxiGene to fail. I believe the science behind OxiGene’s drugs is strong[1;3;5;7;8;9;10;11;12]. For a nice video of Zybrestat in action within a biologically active cancer tumor[8].

Low Stock Price

Although OxiGene has performed a reverse stock-split, which indicates a distressed company that is possibly facing NASDAQ delisting if the stock does not increase, I believe the strong science and importance of cancer therapy make the risky company a good buy. Still, I am not a financial analyst. With that said, I would ask a potential financial analyst to strongly consider the science behind OxiGene’s drugs when making a decision.

References:

[1] Tanpure, Rajendra P; George, Clinton S; Sriram, Madhavi; Strecker, Tracy E; Tidmore, Justin K; Hamel, Ernest; Charlton-Sevcik, Amanda K; Chaplin, David J; Trawick, Mary Lynn; Pinney, Kevin G. An Amino-Benzosuberene Analogue That Inhibits Tubulin Assembly and Demonstrates Remarkable Cytotoxicity, Jun 2012. Medchemcomm[online]. 2012. vol. 3(6). pp. 720-724. Available from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3682772/ PMCID: PMC3682772; NIHMSID: NIHMS386131; doi: 10.1039/C2MD00318J

[2] Cancer.org. Off-label Drug Use: What is off-label drug use? cancer.org[online]. 2013. Available From: http://www.cancer.org/treatment/treatmentsandsideeffects/treatmenttypes/chemotherapy/off-label-drug-use

[3] Murphy, Bryan. Yes, This Time Really is Different for OxiGENE (OXGN), Nov 6, 2013. smallcapnetwork.com[online]. 2013. Available from: http://www.smallcapnetwork.com/Yes-This-Time-Really-is-Different-for-OXiGENE-OXGN/s/via/1789/article/view/p/mid/3/id/454/

[4] Consumer Reports Money Advisor. Post-recession investing: No matter which kind of economic recovery we get, diversification still wins, Oct 2009. consumerreports.org[online]. 2013. Available from: http://www.consumerreports.org/cro/money/personal-investing/post-recession-investing/overview/index.htm

[5] Kanthou, Chryso; Tozer, Gillian M. Microtubule depolymerizing vascular disrupting agents: novel therapeutic agents for oncology and other pathologies, Jun 2009. Int J Exp Pathol[online]. 2009. vol. 90(3). pp. 284-294. Available from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2697551/ PMCID: PMC2697551; doi: 10.1111/j.1365-2613.2009.00651.x

[6] NASDAQ. OxiGene, Inc (OXGN) Interactive Chart Analysis. nasdaq.com[online]. 2013. Available from: http://www.nasdaq.com/symbol/oxgn/interactive-chart

[7] Oxigene. Clinical Trails. oxigene.com[online]. 2013. Available from: http://www.oxigene.com/pipeline/clinical_trials/

[8] OxiGene. How Our Drugs Work. How do ZYBRESTAT (fosbretabulin) and OXI4503 work? oxigene.com[online]. 2013. Available from: http://oxigene.com/our_science/how_our_drugs_work/

[9] Wall Street Journal. OxiGene Presents Preclinical Data Demonstrating Significant Antitumor Activity of Zybrestat ® in Pancreatic Neuroendocrine Tumor Model, Oct. 21, 2013. online.wsj.com[onlne]. 2013. Available from: http://online.wsj.com/article/PR-CO-20131021-905345.html

[10] Turner, Daniel BS; Gonzalez, Andres BS; Pettiford, Leslie RN; Meacham, Amy MS; Wise, Elizabeth BS; Bosse, Raphael C BS; Chaplin, Dai PhD; Hsu, Jack W. MD; Brown, Randy A. MD; Hiemenz, John W. MD; Norkin, Maxim MD, PhD; Wingard, John R. MD; Cogle, Christopher R. MD. 1463 A Phase I Study Of The Vascular Disrupting Combretastatin, OXi4503, In Patients With Relapsed and Refractory Acute Myeloid Leukemia (AML) and Myelodysplastic Syndromes (MDS), Dec 7, 2013. American Society of Hematology[online]. 2013. Available from: https://ash.confex.com/ash/2013/webprogram/Paper65534.html

[11] OxiGene. Pipeline. OXi4503 in Onocology. oxigene.com[online]. 2013. Available from: http://www.oxigene.com/pipeline/OXi4503_in_oncology/

[12] Oxigene. Pipeline. oxigene.com[online]. 2013. Available from: http://www.oxigene.com/pipeline/

[13] US Food and Drug Administration. Step 3 Clinical Research. patientnetwork.fda.gov[online]. 2013. Available from: http://www.patientnetwork.fda.gov/learn-how-drugs-devices-get-approved/drug-development-process/step-3-clinical-research

[14] Landes Bioscience. Oxigene breathes life into cancer treatments. Cancer Biology & Therapy[online]. vol 6(8). Available from: https://www.landesbioscience.com/journals/cbt/article/5015/

[15] US Food and Drug Administration. Orphan Drugs. fad.gov[online]. 2013. Available from: http://www.fda.gov/downloads/Drugs/DevelopmentApprovalProcess/SmallBusinessAssistance/UCM311928.pdf

[16] US Food and Drug Administration. Search Orphan Drug Designations and Approvals. accessdata.fda.gov[online]. 2013. Available from: http://www.accessdata.fda.gov/scripts/opdlisting/oopd/

# Drop Evaporation at 10 degrees C, 1 atmosphere, and 71% relative humidity (January in Iraq and near Baghdad): Sarin (Nerve Agent) versus Water

Note: Sadly, I have noticed that the code of LaTex changes in WordPress. As an example, the text “\textdegree” use to provide the ˚ symbol but now provides “$\textdegree$“. As such, please be patient and do not blame me for all editor faults! 🙂 It truly is an experiment in progress and I am dependent upon LaTex and WordPress consistency.

Title: Drop Evaporation at 10 degrees C, 1 atmosphere, and 71% relative humidity (January in Iraq and near Baghdad): Sarin (Nerve Agent) versus Water

Conclusion: The molar flux of water is greater than sarin. As such, I assume the evaporation of water is greater than sarin. The latter is supported by a relative volatility (water:sarin) that is 12.6 at the specified conditions. Also, the boiling point of sarin is greater than water.

1991 Gulf War Illness

Before I continue, I would like the reader to know that more than 250,000 United States 1991 Gulf War veterans are suffering from 1991 Gulf War Illnesses. The illness can be psychologically and medically debilitating. For more information and to provide support, please please read the  December 2012 scientific journal articles that connect chemical weapons to potential cause of illnesses[7;8]. Also, I wrote a post about differing hypotheses and 1991 Gulf War Illness[17].

Actual mathematical properties of a potential  drop

Equation: $z = 1-\frac{1}{8}(x^2 + y^2)$

The base: $y = \sqrt{2.3^2 - x^2}$

The base radius: 2.3 millimeters; The height: 1 millimeter

Drop volume: Double integration in polar coordinates

$Volume = \iint_R z \ \mathrm{d}A = \iint_R f(x,y) \ \mathrm{d}A = \iint_R f(rcos(\theta), rsin(\theta)) \ r \ \mathrm{d}r \ \mathrm{d}\theta$

In polar coordinates

$r^2 = x^2 + y^2$

$z = 1 - \frac{1}{8}(x^2 + y^2) = 1 - \frac{1}{8}(r^2)$

$Volume =\iint_R (1 - \frac{1}{8}(x^2 + y^2)) \mathrm{d}A = \iint_R (1 - \frac{1}{8}(r^2)) \ r\mathrm{d}r \ \mathrm{d}\theta$

R is a unit disk in the xy plane and one reason I can use polar coordinates.

(i) For fixed $\theta$, r range: 0 ≤ r ≤ 2.3 millimeters

(ii) Angle range: 0 ≤ $\theta$ ≤ 2$\pi$

$Volume = \int_0^{2\pi} \int_0^{2.3} (1-\frac{1}{8}(r^2)) \ r\mathrm{d}r \ \mathrm{d}\theta$

From TI-92:

$Volume = \int_0^{2\pi} [\frac{-(r^2-8)^2}{32}]_{r=0}^{r=2.3} \ \mathrm{d}\theta = \int_0^{2\pi}(1.77) \ \mathrm{d}\theta$

$Volume = \int_0^{2\pi}(1.77) \ \mathrm{d}\theta = [1.77\theta_{\theta = final} - 1.77\theta_{\theta = initial}]_0^{2\pi} = (1.77(2\pi) - 1.77(0)) =$

$Drop \ volume = 11.12 \ mm^3$

Convert to cubic centimeters for calculations

$\frac{1 \ cm}{10 \ mm} \ and \ \frac{1^3 \ cm^3}{10^3 \ mm^3} = \frac{1 \ cm^3}{1000 \ mm^3}$

$Drop \ volume = 11.12 \ mm^3(\frac{1 \ cm^3}{1000 \ mm^3}) = 0.011 \ cm^3$

Density of fluids

Sarin[12-14]: ChemSpider: 1.07; Noblis: 1.096 at 20 deg C; WISER: 1.0887 at 25 deg C

Note: Difficult finding density data on sarin. As such, will assume the density changes little between above values and 10 deg Celsius.

Sarin average: $Density \ average =\frac{(1.07+1.096+1.0887)}{3} = 1.09 = 1.1 \ \frac{g}{cm^3}$

Water at 10 deg C[3;15]: Perry’s: 999.699; Engineering Tool Box: 999.7

Water average: $Density \ average = \frac{(999.699 + 999.7)}{2} = 999.699 \frac{kg}{m^3}$

Conversion: $(999.699 \frac{kg}{m^3}) (\frac{1 m^3}{100^3cm^3})(\frac{1000 g}{1 kg}) = 1.0 \frac{g}{cm^3}$

Water average: $Density \ average = 1.0 \ \frac{g}{cm^3}$

Evaporation mass: Drop Volume x density

Sarin: $Mass = 0.011cm^3(1.1 \frac{g}{cm^3}) = 0.012 \ grams$

Water: $Mass = 0.011cm^3(1.0 \frac{g}{cm^3}) = 0.011 \ grams$

Evaporation moles: Mass divide by molecular weight

Sarin: $Moles_{C_4H_{10}FO_2P} = \frac{0.012 \ grams}{(\frac{140.1 \ grams}{mole})} = 8.6 x 10^{-5} \ moles$

Water: $Moles_{H_2O} = \frac{0.011 \ grams}{\frac{18 \ grams}{mole}} = 6.11 x 10^{-4} \ moles$

Mass transfer: Evaporation

Sarin

The moles of sarin evaporated per square centimeter per unit time may be expressed by[1]

$N_{A,z} = \frac{cD_{AB}}{(z_2-z_1)} \frac{(y_{A1} - y_{A2})}{y_{B,lm}}$

Total molar concentration, c

$PV = nRT; c =\frac{n}{V} = \frac{P}{RT} = \frac{cm^3}{mol}$

The gas constant “R” will be calculated at standard temperature and pressure, “STP”

$Temperature = 273 K; Pressure = 1 atm; Molar \ volume: \ \frac{L}{mol} = 22.4 \frac{L}{mol}$

Conversion: $22.4 \frac{L}{mol}(\frac{1000 \ cm^3}{1\ Liters}) = 2.24x10^4 \ \frac{cm^3}{mol}$

$R = \frac{PV}{nT} = \frac{(1 \ atm)(2.24x10^4\frac{cm^3}{mol})}{273 \ K} = 82.05 \frac{atm \ cm^3}{mol \ K}$

$c = \frac{moles}{cm^3} = \frac{P}{RT} = \frac{1 \ atm}{(82.05 \frac{atm cm^3}{mol K})(283 \ K)} = 4.31x10^{-5} \ \frac{mol}{cm^3}$

Sarin diffusivity in air at 10 deg Celsius and 1 atmosphere[16]

$D_{AB} = 0.070 \frac{cm^2}{s}$

Assume the gas film

$(z_2 - z_1) = 0.5 cm$

Mole fraction Sarin

$y_{A1} = \frac{p_{A1}}{P_{total}}; y_{A2} = 0$

From[13a]:

Sarin vapor pressure:

$log \ p_A(Torr) = 9.4(\pm 0.1) - \frac{2700 (\pm 40) }{T(K)} \ from \ 0 \ to \ 147 \ deg \ C$

$log \ p_A(Torr) = 9.4 - \frac{2700}{283} = -0.1406; 10^{log \ p_A} = 10^{-0.1406} = 0.723 \ Torr$

Conversion: $0.723 \ Torr(\frac{1 \ atm}{760 \ Torr}) = 9.51x10^{-4} \ atm$

$y_{A1} = \frac{9.51x10^{-4} \ atm}{1 \ atm} = 9.51x10{-4}$

Assume no sarin in the air at a distance away from drop, $y_{A2} = 0$

For a binary system

$y_{B1} = 1 - y_{A1} = 1 - 9.51x10^{-4} = 0.9991;y_{B2} = 1 - y_{A2} = 1 - 0 = 1$

$y_{B,lm} = \frac{(y_{B2} - y_{B1})}{ln(\frac{y_{B2}}{y_{B1}})} = \frac{(1-0.9991)}{ln(\frac{1}{0.9991})} = \frac{9.0x10^{-4}}{9.52x10^{-4}} = 0.946$

The sarin flux

$N_{A,z} = \frac{cD_{AB}}{(z_2-z_1)}\frac{(y_{A1}-y_{A2})}{y_{B,lm}} = \frac{(4.31x10^{-5})(0.070)}{0.5}\frac{(9.51x10^{-4} - 0)}{0.946} =2.18x10^{-5} \frac{mol}{cm^2 \ hr}$

Water

The moles of water evaporated per square centimeter per unit time may be expressed by[1]

$N_{A,z} = \frac{cD_{AB}}{(z_{2}-z_{1})}\frac{(y_{A1}- y_{A2})}{y_{B,lm}}$

Total molar concentration, c

$PV = nRT; c = \frac{n}{V} = \frac{P}{RT} = \frac{cm^3}{mol}$

As before, the gas constant “R” will be calculated at standard temperature and pressure, “STP”

$Temperature = 273K; Pressure = 1atm; Molar \ volume= \frac{L}{mol} = 22.4\frac{L}{mol}$

Conversion: $22.4 \frac{L}{mol}(\frac{1000 \ cm^3}{1 \ Liters}) = 2.24x10^4 \frac{cm^3}{mol}$

$R = \frac{PV}{nT} = \frac{(1 \ atm)(2.24x10^4\frac{cm^3}{mol})}{273 \ K} = 82.05 \frac{atm \ cm^3}{mol \ K}$

$c = \frac{moles}{cm^3} = \frac{P}{RT} = \frac{1 \ atm}{(82.05 \frac{atm \ cm^3}{mol \ K})(283 \ K)} = 4.31x10^{-5} \ \frac{mol}{cm^3}$

Water diffusivity in air at 10 deg Celsius and 1 atmosphere[16]

$D_{AB} = 0.193 \frac{cm^2}{s}$

Assume the gas film

$(z_2-z_1) = 0.5 \ cm$

Mole fraction of water

$y_{A1} = \frac{p_{A1}}{P_{total}}; y_{A2}= \frac{p_{A2}}{P_{total}}$

From[4]:

Water vapor pressure:

$log_{10} \ P_{vp} = A - \frac{B}{T + C - 273.15}$

Constants A, B, C[Appendix A;4], T in kelvins, and pressure is in bar

$log_{10} \ P_{vp} = 5.11564 - \frac{1687.537}{283+230.17-273.15} = -1.91518$

$P_{vp} = 10^{-191518} = 0.0122 \ bars$

Conversion: $\frac{1 \ atm}{1.01325 bars}(0.0122 \ bars) = 0.012 \ atm; \frac{760 \ mmHg}{1 \ atm}(0.012 \ atm) = 9.11 mmHg$

$y_{A1} = \frac{p_{A1}}{P_{total}} = \frac{0.012 \ atm}{1 atm} = 0.012$

From[2] and relative humidity of 71% (January weather in Iraq)[9]

Partial pressure of water in flowing stream

Relative humidity[2]:

$s_r(h_r) = \frac{p_{v}}{p_v^*(T)}x 100\% = 71\%$

At 283 K, previous equation gave: $p_v^* = 0.012 \ atm$

$\frac{71\%}{100}(0.012 \ atm) = p_v = p_{A2} = 0.0085 \ atm$

$y_{A2} = \frac{p_{A2}}{P_{total}} = \frac{0.0085 \ atm}{1 \ atm} = 0.0085$

For a binary system

$y_{B1} = 1 - y_{A1} = 1 - 0.012 = 0.988; y_{B2} = 1 - y_{A2} = 1 - 0.0085 = 0.992$

$y_{B,lm} = \frac{(y_{B2} - y_{B1})}{ln(\frac{y_{B2}}{y_{B1}})} = \frac{(0.992 - 0.988)}{ln(\frac{0.992}{0.988})} = 0.990$

Molar flux of water

$N_{A,z} = \frac{cD_{AB}}{(z_2-z_1)} \frac{(y_{A1} - y_{A2})}{y_{B,lm}} = \frac{(4.31x10^{-5})(0.193)}{0.5} \frac{(0.012 - 0.0085)}{0.990} = 5.88x10^{-8} \ \frac{mol}{cm^2 \ s}$

Conversion:

$N_{A,z} = 5.88x10^{-8} \frac{mol}{cm^2 \ s}\frac{3600 \ s}{1 \ hr} = 2.12x10^{-4} \ \frac{mol}{cm^2 \ hr}$

Molar Flux: Sarin versus water comparison

Sarin: $N_{A,z} = 2.18x10^{-5} \ \frac{mol}{cm^2 \ hr}$

Water: $N_{A,z} = 2.12x10^{-4} \ \frac{mol}{cm^2 \ hr}$

Ratio: $\frac{Water}{Sarin} = \frac{2.12x10^{-4}}{2.18x10^{-5}} = 9.71$

Although the above is a simple evaluation based on “diffusion through a stagnant gas film”[1] and not the most rigorous, the ratio makes since because the ratio of vapor pressures at 10 deg Celsius, “relative volatility”[18], is

$\alpha_{water-sarin} = \frac{p_{H_2O}}{p_{C_4H_{10}FO_2P}} = \frac{0.012 \ atm}{9.51x10^{-4} \ atm} = 12.6$

Per US Department of Energy[19]

“The evaporation of a liquid depends upon its vapor pressure — the higher the vapor pressure at a given temperature the faster the evaporation — other condition being equal.

The higher/lower the boiling point the less/more readily will a liquid evaporate.”[19]

The boiling points are:

Sarin[14]: 147 deg Celsius; Water[15a]: 100 deg Celsius

Conclusion:

The evaporation of water is greater than the evaporation of sarin.

References:

[1] Welty, James R.; Wicks, Charles E.; Wilson, Robert E. (1984) Fundamentals of Momentum, Heat, and Mass Transfer, Third Edition. New York: John Wiley & Sons.

[2] Felder, Richard M; Rousseau, Ronald W. (1986) Elementary Principles of Chemical Processes, Second Edition. New York: John Wiley & Sons.

[3] Perry, Robert H; Green, Don W. (1997) Perry’s Chemical Engineers’ Handbook, Seventh Edition. New York. McGraw-Hill.

[4] Poling, Bruce E.; Prausnitz, John M.; O’Connell, John P. (2001) The Properties of Gases and Liquids, Fifth Edition. New York: Mcgraw-Hill.

[5] Anton, Howard. Calculus with Analytic Geometry, Fifth Edition. New York: John Wiley & Sons.

[6] Barker, William H; Ward, James E. (1995) The Calculus Companion. Calculus: Howard Anton, Fifth Edition.

[7] Haley, Robert W.; Tuite, James J. Meteorological and Intelligence Evidence of Long-Distance Transit of Chemical Weapons Fallout from Bombing Early in the 1991 Persian Gulf War, December 2012. karger.com[online]. 2012. vol. 40. pp. 160-177. Available from: http://content.karger.com/ProdukteDB/produkte.asp?Aktion=ShowFulltext&ArtikelNr=345123&Ausgabe=257603&ProduktNr=224263 DOI: 10.1159/000345123

[8] Haley, Robert W.; Tuite, James J. Epidemiologic Evidence of Health Effects from Long-Distance Transit of Chemical Weapons Fallout from Bombing Early in the 1991 Persian Gulf War, December 2012. karger.com[online]. vol. 40. pp. 178-189. Available from: http://content.karger.com/ProdukteDB/produkte.asp?Aktion=ShowFulltext&ArtikelNr=345124&Ausgabe=257603&ProduktNr=224263 DOI: 10.1159/000345124

[9] Wikipedia. Baghdad. en.wikipedia.org[online]. 2013. Available from: http://en.wikipedia.org/wiki/Baghdad#Geography_and_climate

[10] Harding, Byron. Diffusivity of Water versus Sarin (Nerve Agent) in Air at 10 Degrees Celsius (50 Degrees Fahrenheit) and 1 Atmosphere, January 2013. chrisbharding.wordpress.com[online]. 2013. Available from: https://chrisbharding.wordpress.com/2013/01/07/test/

[11] Removed

[12] ChemSpider. The free chemical database. Sarin. chemspider.com[online]. 2013. Available from: http://www.chemspider.com/Chemical-Structure.7583.html

[13] Noblis. Chemistry of GB (Sarin). noblis.org[online]. 2013. Available from: http://www.noblis.org/MissionAreas/nsi/ChemistryofLethalChemicalWarfareAgents/Pages/Sarin.aspx

[13a] Noblis. Parameters for Evaluation of the Fate, Transport, and Environmental Impacts of Chemical Agents in Marine Environments. noblis.org[online]. 2012. Available from: http://pubs.acs.org/doi/pdf/10.1021/cr0780098

[14] Wireless Information System for Emergency Responders. WISER. Sarin, CAS RN: 107-44-8. webwiser.nlm.nih.gov[online]. 2013. Available from: http://webwiser.nlm.nih.gov/getSubstanceData.do?substanceID=151&displaySubstanceName=Sarin&UNNAID=&STCCID=&selectedDataMenuItemID=30

[15] The Engineering ToolBox. Water-Density and Specific Weight. engineeringtoolbox.com[online]. 2013. Available from: http://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html

[15a] The Engineering Toolbox. engineeringtoolbox.com[online]. 2013. Available from: http://www.engineeringtoolbox.com/

[16] Harding, Byron. Diffusivity of Water versus Sarin (Nerve Agent) in Air at 10 Degrees Celsius (50 Degrees Fahrenheit) and 1 Atmosphere, January 2013. chrisbharding.wordpress.com[online]. 2013. Available from: https://chrisbharding.wordpress.com/2013/01/07/test/

[17] Harding, Byron. 1991 Gulf War Illnesses and Differing Hypotheses: Nerve and Brain Death Versus Stress, December 2012. gather.com[online] 2012. Available from: http://www.gather.com/viewArticle.action?articleId=281474981824775

[18] Chopey, Nicholas P. (1994). Handbook of Chemical Engineering Calculations, Second Edition. Boston Massachusetts: Mc Graw Hill.

[19] US Department of Energy. Newton: Ask A Scientist.Evaporation and Vapor Pressure. newton.dep.anl.gov[online]. 2012. Available from: http://www.newton.dep.anl.gov/askasci/phy00/phy00130.htm

# Diffusivity of Water versus Sarin (Nerve Agent) in Air at 10 Degrees Celsius (50 Degrees Fahrenheit) and 1 Atmosphere

Diffusivity of Water versus Sarin in Air at 10 Degrees Celsius (50 Degrees Fahrenheit) and 1 Atmosphere[see bottom of post]

1991 Gulf War veterans are suffering from 1991 Gulf War Illness[3;References]. Scientific research suggests the combination of experimental medication, pyridostigmine bromide as an example, over use of pesticides, chemical weapon-sarin as an example-destruction at plants and football sized bunkers, oil fires, etc as the potential cause[6-9].

Dr. Robert Haley, MD, UT SouthWestern Medical Center, and Intelligence Analyst James Tuite have reported how 1991 Gulf War veterans might have been contaminated with chemical weapons prior to the ground war, “Desert Storm”[9]. In fact, their work provides data proving that sophisticated equipment detected chemical weapons in Saudi Arabia prior to the ground war[9a]. It is also hypothesized that the “toxic cocktail” has caused autonomic dysfunction, nerve death, and brain death[9-14].

As a 1991 Gulf War veteran, I have been affected. I am also a chemical engineer with a degree in biological sciences. Like most educated, I have lost much of my knowledge in chemical engineering and biological sciences, but I can, if I find a good example, still “plug and chug” by using “tested and trusted” equations, which is advised anyhow. 🙂 Here, I compare the diffusivity of sarin vapor and water vapor in air by using Chapman and Enskog equation with Brokaw relations for polar gases correction. I have shown that the equation can be used when considering the diffusivity of polar in a non-polar matrix[19]. After performing the latter calculation, I noticed that reference [1] also suggests Brokaw relations to be used for diffusivity of one polar gas molecule in a non-polar matrix[1].

I will be comparing the diffusivity of polar sarin = A in non-polar air = B at 10$\textdegree$C and 1 atmosphere. I chose 10$\textdegree$C because I discovered data, possibly experimental, that stated that 90% volume of 1 mm sarin drop on a non-absorbable surface at 10$\textdegree$C evaporated in 0.24 hours[17].

Equations

Chapman and Enskog Equation[1]. Reference [1] reports that this equation has a “Average absolute error” of 7.9% when used without Brokaw relations. The range is from 0% to 25%. The authors[1] did not provide an average for Browkaw relations but do provide specific absolute error values. When I averaged the Brokaw values[1], I obtained a 10.9% average absolute error with a range from 0% to 33%.

Chapman and Enskog Equation[1]

$D_{AB} = \frac{3}{16} \frac{(\frac{4 \pi \kappa T}{M_{AB}})^{1/2}}{n \pi \sigma_{AB}^2 \Omega_D} f_D$

Neufield, et al. Equation

$\Omega_D = \frac{A}{(T^*)^B} + \frac{C}{\exp{((D)(T^*))}} + \frac{E}{\exp{((F)(T^*))}} + \frac{G}{((H)(T^*))}$

Polar Gases: Brokaw Relations

$\Omega_D(Neufield) + \frac{0.19 \delta_{AB}^2}{T^*}$

$T^* = \frac{\kappa T}{\epsilon_{AB}}$

$\delta = \frac{1.94x10^3 \mu_p^2}{V_bT_b}$

$\mu_p = dipole \ moment, \ debyes$

$V_b = liquid \ molar \ volume \ at \ the \ normal \ boiling \ point, \ \frac{cm^3}{mol}$

$T_b = normal \ boiling \ point \ (1 \ atm), K$

$\frac{epsilon}{\kappa} = 1.18(1 + 1.3\delta^2)T_b$

$\sigma = (\frac{1.585V_b}{1 + 1.3 \delta^2})^{1/3}$

$\delta_{AB} = (\delta_A \delta_B)^{1/2}$

$\frac{\epsilon_{AB}}{\kappa} = (\frac{\epsilon_A}{\kappa} \frac{\epsilon_B}{\kappa})^{1/2}$

$\sigma_{AB} = (\sigma_A \sigma_B)^{1/2}$

When $f_D$ is chosen as unity and “n” is expressed by the ideal-gas law, the Chapman-Enskog Equation

$D_{AB} = \frac{0.00266 T^{3/2}}{PM_{AB}^{1/2} \sigma_{AB}^2 \Omega_D}$

Brokaw Diffusivity: Water in Air at 10$\textdegree$C and 1 Atmosphere

Molecular Weight

Water:

$M_A = M_{H_2O} = 2(MW_H) + 1(MW_O) = 2(1.008) + 1(16.00) = 18 \frac{g}{mol}$

Air: 1 mole basis

$21\% \frac{molO_2}{mol} \ O_2 \ and \ 79\% \frac{molN_2}{mol}\ N_2$

$Moles \ O_2 = 0.21 \frac{molO_2}{mole}(1 \ mol) = 0.21 \ molO_2; Moles \ N_2 = 0.79 \frac{molN_2}{mol} (1 \ mol) = 0.79 \ molN_2$

Grams oxygen:

$0.21 \ molO_2(MW_{O_2}) = 0.21 molO_2(\frac{32 \ grams \ O_2}{mol \ O_2}) = 6.72 \ grams \ O_2$

Grams nitrogen:

$0.79 \ molN_2(MW_{N_2}) = 0.21 molO_2(\frac{ 28 \ grams \ N_2}{mol \ O_2}) = 22.12 \ grams \ N_2$

Air: $M_B = M_{air} = \frac{(6.72 + 22.12)}{1mol} = 28.8 \frac{g}{mol}$

$M_{AB} = 2[\frac{1}{M_A} + \frac{1}{M_B}]^{-1} = 2[\frac{1}{18} + \frac{1}{28.8}]^{-1} = 22.2$

Need: $\sigma; \delta; \Omega_D$

Note: I will only be calculating a delta value for water because air is non-polar[1;19].

$\delta_A = \delta_{H_2O} = \frac{1.94x10^3 \mu_p^2}{V_bT_b}$

From [16]: $V_b \frac{cm^3}{mol} = 18.045 \frac{cm^3}{mol}$

From [20]: $\mu_{p_{H_2O}} = 1.855$

$T_b = 373 K$

$\delta_{A_{H_2O}} = \frac{1.94x10^3(1.855)^2}{(18.045)(373)} = \frac{6.68x10^3}{6.73x10^3} = 0.992$

$\frac{\epsilon_{A}}{\kappa} = 1.18(1 + 1.3 \delta_{A}^2)T_b = 1.18(1 + 1.3(0.992)^2)373 K = 1003 K$

$\sigma_A = (\frac{1.585V_b}{1 + 1.3\delta_A^2})^{1/3} = (\frac{1.585 (18.045)}{1 + 1.3(0.992)^2})^{1/3} = (12.55)^{1/3} = 2.32 \AA$

Need $T^*$ to calculate $\Omega_D$

$T^* = \frac{\kappa T}{\epsilon_{AB}}$

$\frac{\epsilon_{AB}}{\kappa} = (\frac{\epsilon_A}{\kappa} \frac{\epsilon_B}{\kappa})^{1/2}$

Water: $\frac{\epsilon_A}{\kappa} = 1003 K; Air[1, Appendix B]:78.6 K$

$\frac{\epsilon_{AB}}{\kappa} = \sqrt{\frac{\epsilon_A}{\kappa} \frac{\epsilon_B}{\kappa}} = \sqrt{(1003 K)(78.6 K)} = 280.8 K$

$T^* = \frac{\kappa T}{\epsilon_{AB}}$

$\frac{\epsilon_{AB}}{\kappa T} = \frac{280.8 K}{283 K} = 0.992$

$T^* = \frac{\kappa T}{\epsilon_{AB}} = \frac{1}{0.992} = 1.01$

Neufield, et al.:

$\Omega_D = \frac{A}{(T^*)^B} + \frac{C}{\exp{((D)(T^*))}} + \frac{E}{\exp{((F)(T^*))}} + \frac{G}{\exp((H)(T^*))} =$

$\Omega_D = \frac{1.06036}{1.01^{0.15610}} + \frac{0.19300}{\exp{((0.47635)(1.01))}} + \frac{1.03587}{\exp{((1.52996)(1.01))}} + \frac{1.76474}{\exp{((3.89411)(1.01))}} =$

$\Omega_D = 1.43$

$\Omega_D = \Omega_D(Neufield) + \frac{0.19 \delta_{AB}^2}{T^*}$ changed to $\Omega_D(Neufield) + \frac{0.19 \delta_A^2}{T^*}$

$\Omega_D = 1.43 + \frac{0.19(0.992)^2}{1.01} = 1.62$

Need $\sigma_{AB} = \sqrt{\sigma_A \sigma_B}$

Water: 2.32 $\AA$; Air (Appendix B[1]): 3.711 $\AA$

$\sigma_{AB} = \sqrt{\sigma_A \sigma_B} = \sqrt{(2.32)(3.711)} = 2.93 \AA$

Diffusivity: Polar water in non-polar air at 10$\textdegree$C and 1 atmosphere

$D_{AB} = \frac{0.00266 T^{3/2}}{PM_{AB}^{1/2} \sigma_{AB}^2 \Omega_D} = \frac{0.00266 (283)^{3/2}}{1 (22.2)^{1/2} (2.93)^2 (1.62)} = \frac{12.66}{65.53} =$

$D_{AB} = 0.193 \frac{cm^2}{s}$

Brokaw Diffusivity of Sarin in Air at 10$\textdegree$C and 1 Atmosphere

Molecular Weight

Sarin, $C_4H_{10}FO_2P$:

$M_A = M_{C_4H_{10}FO_2P} = 4(MW_C) + 10(MW_H) + 1(MW_F) + 2(MW_O) + 1(MW_P) =$

$M_{C_4H_{10}FO_2P} = 4(12.01) + 10(1.008) + 1(19.00) + 2(16.00) + 1(30.97) = 140.1 \frac{g}{mol}$

Air: 1 mole basis

$21\% \frac{molO_2}{mol} \ and \ 79\% \frac{molN_2}{mol}$

0.21 $\frac{molO_2}{mol}$(1 mol) = 0.21 mol oxygen gas; 0.79 $\frac{molN_2}{mol}$(1 mol) = 0.79 mol nitrogen gas

Grams oxygen:

$0.21 (molO_2)(32 \frac{gO_2}{molO_2}) = 6.72 grams \ O_2$

Grams nitrogen:

$0.79 (molN_2)(28 \frac{gN_2}{molN_2}) = 22.1 grams \ N_2$

Air: $M_B = M_{air} = \frac{(6.72 + 22.12)}{1 mol} = 28.8 \frac{g}{mol}$

$M_{AB} = 2[\frac{1}{140.1} + \frac{1}{29.0}]^{-1} = 48.1$

Need: $\delta; \sigma; \Omega_D$

Note: I will only be calculating the delta value for the polar gas sarin because air is non-polar[1;19].

$\Omega_D = \Omega_D(Neufield) + \frac{0.19 \delta_{AB}^2}{T^*}$ changed to $\Omega_D(Neufield) + \frac{0.19 \delta_A^2}{T^*}$

$T^* = \frac{\kappa T}{\epsilon_{AB}}$

$\frac{\epsilon_i}{\kappa} = 1.18(1 + 1.3\delta_i^2)T_b$

Sarin: $\frac{\epsilon_A}{\kappa} = 1.18(1 + 1.3(0.418)^2)(420) = 608.2 K$

$\frac{\epsilon_{AB}}{\kappa} = (\frac{\epsilon_A}{\kappa} \frac{\epsilon_B}{\kappa})^{1/2}$

Sarin: $\frac{\epsilon_A}{\kappa} = 608.2 K$

Air[Appendix B;1]: $\frac{\epsilon_B}{\kappa} = 78.6 K$

$\frac{\epsilon_{AB}}{\kappa} = \sqrt{\frac{\epsilon_A}{\kappa} \frac{\epsilon_B}{\kappa}} = \sqrt{(608.2)(78.6)} = 216.1 K$

$T^* = \frac{\kappa T}{\epsilon_{AB}}$

$\frac{\epsilon_{AB}}{\kappa T} = \frac{216.1}{283} = 0.764$

$T^* = \frac{\kappa T}{\epsilon_{AB}} = \frac{1}{0.764} =1.31$

$\delta_A = \frac{1.94x10^3 \mu_p^2}{V_bT_b}$

$\mu_p =$ dipole moment, debyes

$V_b =$ liquid molar volume at the normal boiling point, $\frac{cm^3}{mol}$

$T_b =$ normal boiling point (1 atm), K

Sarin[18;16a]: $\delta_A = \frac{1.94x10^3(3.44)^2}{(130.9)(420)} = 0.418$

$\sigma_i = (\frac{1.585V_b}{1 + 1.3\delta_i^2})^{1/3}$

Sarin[16a]: $\sigma_A = (\frac{1.585(130.9)}{1 + 1.3(0.418)^2})^{1/3} = 5.5 \AA$

$\sigma_{AB} = (\sigma_A \sigma_B)^{1/2}$

Sarin: $\sigma_A = 5.5 \AA$

Air[Appendix B;1}: $\sigma_B = 3.711 \AA$

$\sigma_{AB} = \sqrt{(\sigma_A)(\sigma_B)}= \sqrt{(5.5)(3.711)} = 4.52 \AA$

$\Omega_D = \frac{A}{(T^*)^B} + \frac{C}{\exp{((D)(T^*))}} + \frac{E}{\exp{((F)(T^*))}} + \frac{G}{\exp{((H)(T^*))}} =$

$\Omega_D = \frac{1.06036}{(1.31)^{0.15610}} + \frac{0.19300}{\exp{((0.47635)(1.31))}} + \frac{1.03587}{\exp{((1.52996)(1.31))}} + \frac{1.76474}{\exp{((3.89411)(1.31))}} =$

$\Omega_D = 1.24$

$\Omega_D = \Omega_D(Neufield) + \frac{0.19 \delta_A^2}{T^*} = 1.24 + \frac{0.19(0.418)^2}{1.31} = 1.27$

Chapman-Enskog equation after polar correction

Diffusivity of Sarin in Air:

$D_{AB} = \frac{0.00266T^{3/2}}{PM_{AB}^{1/2}\sigma_{AB}^2 \Omega_D} = \frac{0.00266(283)^{3/2}}{1(48.1)^{1/2}(4.52)^2(1.27)} = \frac{12.66}{180.0} = 0.070 \frac{cm^2}{s}$

Diffusivity Comparison in Air: Water Versus Sarin in Descending Order

Water: $D_{AB} = 0.193 \frac{cm^2}{sec}$

Sarin: $D_{AB} = 0.070 \frac{cm^2}{sec}$

Diffusivity Ratio: $\frac{Water}{Sarin} = \frac{0.193}{0.070} = 2.74$

References:

[1] Poling, Bruce E.; Prausnitz, John M.; O’Connell, John P. (2001) The Properties of Gases and Liquids, Fifth Edition. New York: Mcgraw-Hill.

[2] Welty, James R.; Wicks, Charles E.; Wilson, Robert E. (1984) Fundamentals of Momentum, Heat, and Mass Transfer, third edition. New York: John Wiley & Sons.

[3] Harding, Byron. 1991 Gulf War Illnesses and Differing Hypotheses: Nerve and Brain Death Versus Stress, December 2012. gather.com[online] 2012. Available from: http://www.gather.com/viewArticle.action?articleId=281474981824775

[4] Removed

[4a] Removed

[5] National Academies.News.Gulf War Service Linked to Post-traumatic Stress Disorder, Multisymptom Illness, Health Problems, But Causes Unclear. nationalacademies.org[online].April 2010. Available from: http://www8.nationalacademies.org/onpinews/newsitem.aspx?RecordID=12835

[6] National Academies Press. Institute of Medicine. Committee on Gulf War and Health: Health Effects of Serving in the Gulf War, Update 2009. Board on Health of Select Populations. Gulf War and Health, Volume 8. nap.edu[online]. 2010. pp. 320. Available from: http://www.nap.edu/catalog.php?record_id=12835 ISBN-10: 0-309-14921-5; ISBN-13: 978-0-309-14921-1

[7] Research Advisory Committee on Gulf War Veterans’ Illnesses. Gulf War Illness and Health of Gulf War Veterans. Scientific Findings and Recommendations, 2008. va.gov[online]. 2012. Available from: http://www.va.gov/RAC-GWVI/docs/Committee_Documents/GWIandHealthofGWVeterans_RAC-GWVIReport_2008.pdf

[8] Research Advisory Committee on Gulf War Veterans’ Illnesses. Research Advisory Committee on Gulf War Veterans’ Illnesses Findings and Recommendation, June 2012. va.gov[online]. 2012. Available from: http://www.va.gov/RAC-GWVI/docs/Committee_Documents/CommitteeDocJune2012.pdf

[9] Kennedy, Kelly. Study: Wind blew deadly gas to U.S. troops in Gulf War, December 2012. ustoday.com[online]. 2012. Available from: http://www.usatoday.com/story/news/world/2012/12/13/sarin-gas-gulf-war-veterans/1766835/

[9a] Haley, Robert W.; Tuite, James J. Meteorological and Intelligence Evidence of Long-Distance Transit of Chemical Weapons Fallout from Bombing Early in the 1991 Persian Gulf War, December 2012. karger.com[online]. 2012. vol. 40. pp. 160-177. Available from: http://content.karger.com/ProdukteDB/produkte.asp?Aktion=ShowFulltext&ArtikelNr=345123&Ausgabe=257603&ProduktNr=224263 DOI: 10.1159/000345123

[9b] Haley, Robert W.; Tuite, James J. Epidemiologic Evidence of Health Effects from Long-Distance Transit of Chemical Weapons Fallout from Bombing Early in the 1991 Persian Gulf War, December 2012. karger.com[online]. vol. 40. pp. 178-189. Available from: http://content.karger.com/ProdukteDB/produkte.asp?Aktion=ShowFulltext&ArtikelNr=345124&Ausgabe=257603&ProduktNr=224263 DOI: 10.1159/000345124

[10] Oswal, DP; Garrett, TL; Morris, M; Kucot, JB. Low-dose sarin exposure produces long term changes in brain neurochemistry of mice. Neurochem Res[online]. 2013. vol. 1. pp. 108-116. Available from: http://www.ncbi.nlm.nih.gov/pubmed/23054072 doi: 10.1007/s11064-012-0896-9

[11] Shewale, SV.; Anstadt, MP; Horenziak, M; Izu, B.; Morgan, EE.; Lucot, JB.; Morris, M. Sarin causes autonomic imbalance and cardiomyopathy: an important issue for military and civilian health, July 2012. J. Cardiovasc Pharmacol.[online]. 2012. vol 60(1). pp. 76-87. Available from: http://www.ncbi.nlm.nih.gov/pubmed/22549449 doi: 10.1097/FJC.0b013e3182580b75

[12] DTIC. Online Information for the Defense Community.Chan, Victor T; Soto, Armando; Wagner, Jessica A; Watts, Brandy S.; Walters, Amy D.; Hill, Tiffany M. Mechanisms of Organophosphates (OP) Injury: Sarin-Induced Hippocampal Gene Expression Changes and Pathway Perturbation, Jan 2012. dtic.mil[online]. 2012. Available from: http://www.dtic.mil/docs/citations/ADA560343

[13] Medical News Today. Low-Level Exposure to Organophosphate Pesticides Damage Brain and Nervous System, December 2012. medicalnewstoday.com[online]. 2012. Available from: http://www.medicalnewstoday.com/releases/253534.php

[14] Fulco, Carolyn E; Liverman, Catharyn T.; Sox, Harold C. National Academy Press. Committee on Health Effects Associated with Exposures During the Gulf War. Gulf War and Health: Volume 1. Depleted Uranium, Sarin, Pysidostigmine Bromide, Vaccines, 2000. Effects of Long-Term Exposure to Organophosphate Pesticides in Humans. nap.edu[online]. 2012. Available from: http://www.nap.edu/openbook.php?record_id=9953&page=R1

[15] NCBI.PubChem. Sarin-Compound Summary (CID 7871). pubmed.ncbi.nlm.nih.gov[online]. 2012. Available from: http://pubchem.ncbi.nlm.nih.gov/summary/summary.cgi?cid=7871

[16] ChemSpider. The free chemical database. Water. chemspider.com[online]. 2013. Available from: http://www.chemspider.com/Chemical-Structure.937.html?rid=01a81689-c122-434f-a0a1-b4e6e3ca8109

[16a] ChemSpider. The free chemical database. Sarin (isopropyl methylphosphonofluoridate). chemspider.com[online]. 2013. Available from: http://www.chemspider.com/Chemical-Structure.7583.html?rid=8885b92c-43db-4dbf-a9fd-280d32df0450

[17] US National Library of Medicine. WISER: Wireless Information System for Emergencey Responders. Sarin, CAS RN: 107-44-8. Volatilization. webwiser.nlm.nih.gov[online]. 2012. Available from: http://webwiser.nlm.nih.gov/getSubstanceData.do;jsessionid=E6C28B95977867F872631D36CDD61D42?substanceID=151&displaySubstanceName=Sarin&UNNAID=&STCCID=&selectedDataMenuItemID=81

[18] Lee, Ming-Tsung; Vishnyakov, Aleksey; Gor, Gennady Yo.; Neimark, Alexander V. Interactions of Phosphororganic Agents with Water and Components of Polyelectrolyte Membranes, October 2011. J. Physical Chemistry[online]. 2012. Available from: http://www.princeton.edu/~ggor/Gor_JPCB_2011.pdf

[19] Harding, Byron. Chapman and Enskog Versus Hirschfelder Equation when Compared to Experimental Value at 25 Degree C and 1 Atm, and Non-Polar Versus Brokaw Polar Method, January 2013. Available from: https://chrisbharding.wordpress.com/2013/01/04/chapman-and-enskog-versus-hirschfelder-equation-and-compared-to-experimental-value-at-25c-and-1-atm/

[20] Gregory, J.K.; Clary, D.C.; Liu, K.; Brown, M.G.; Saykally, R.J. The Water Dipole Moment in Water Clusters, February 1997. science[online]. vol. 275. pp. 814. Available from: http://www.cchem.berkeley.edu/rjsgrp/publications/papers/1997/187_gregory_1997.pdf

# Temporary Divergence: Diffusivity: That Smell-Methyl Mercaptan (Methanethiol), Odorless Natural Gas, Odorless Propane, and Even Flatulence

Temporary Divergence: Diffusivity: That Smell-Methyl Mercaptan (Methanethiol), Odorless Natural Gas, Odorless Propane, and Even Flatulence

Lynyrd Skynyrd. That Smell. youtube.com[online]. 2013. Available from: http://youtu.be/ZDB-yswOrzc

Diffusivity of Methyl Mercaptan Versus Methane and Propane

Methyl mercaptan[3-6], “methanethiol”, is the byproduct of many natural processes. Flatulence is one example[7]. Because of its odor threshold, 1 ppb has been reported[4], methanethiol is also added to odorless natural gas, methane, and odorless propane for detection purposes. Apparently, it is used as a communication warning system in mining operations as well[4].

In this blog post, I will be comparing the diffusivity of the polar chemical methanethiol to the non-polar chemicals methane and propane in air. I have heard reports that the diffusivity of methanethiol is significantly greater than methane and propane. See bottom of post for diffusivities.Since reference[1] has tabular values for methane and propane in appendix B, I will use the tabular values and the Chapman-Enskog equation to calculate diffusivity values for methane and propane. For methanethiol, I will use Fuller, et al equation and tabular values for the atoms making up methanethiol, $CH_3-SH$

Chapman-Enskog Equation. From reference[1], the average absolute error of this “theoretical equation” is 7.9%

$D_{AB} = \frac{3}{16} \frac{(\frac{4 \pi \kappa T}{M_{AB}})^{1/2}}{n \pi \sigma_{AB}^2 \Omega_D} f_D$

If $f_D$ is chosen as unity and “n” expressed by ideal-gas law

$D_{AB} = \frac{0.00266 T^{3/2}}{P M_{AB}^{1/2} \sigma_{AB}^2 \Omega_D}$

For Non-polar gases: Methane and Propane

Methane $CH_4$ in air at 25$\textdegree$C and 1 atmosphere (atm)

$M_{AB} = 2[\frac{1}{M_A} + \frac{1}{M_B}]^{-1}$

$M_A = M_{CH_4} = 1(MW_C) + 4(MW_H) = 1(12.01) + 4(1.008) = 16.0 \frac{g}{mol}$

$M_B = M_{air} = 29.0 \frac{g}{mole}$

$M_{AB} = 2[\frac{1}{M_A} + \frac{1}{M_B}]^{-1} = 2[\frac{1}{16.0} + \frac{1}{29.0}]^{-1} = 20.6$

Need $\Omega_D$

Neufield, et al.: $\Omega_D = \frac{A}{(T^*)^B} + \frac{C}{\exp{((D)(T^*))}} + \frac{E}{\exp{((F)(T^*))}} + \frac{G}{\exp{((H)(T^*))}}$

$T^* = \frac{\kappa T}{\epsilon_{AB}}$

From appendix B[1]

Methane: $\sigma = 3.758 \AA; \frac{\epsilon_A}{\kappa} = 148.6 K$

Air: $\sigma = 3.711 \AA; \frac{\epsilon_B}{\kappa} = 78.6 K$

$\sigma_{AB} = \frac{\sigma_A + \sigma_B}{2} = \frac{3.758 + 3.711}{2} = 3.735 \AA$

$\frac{\epsilon_{AB}}{\kappa} = \sqrt{(148.6)(78.6)} = 108.1 K$

$\frac{\epsilon_{AB}}{\kappa T} = \frac{108.1 K}{298 K} = 0.363$

$T^* = \frac{\kappa T}{\epsilon_{AB}} = \frac{1}{0.363} = 2.76$

$\Omega_D = \frac{A}{(T^*)^B} + \frac{C}{\exp{((D)(T^*))}} + \frac{E}{\exp{((F)(T^*))}} + \frac{G}{\exp{((H)(T^*))}} =$

$\Omega_D =\frac{1.06036}{(2.76)^{0.15610}} + \frac{0.19300}{\exp{((0.47635)(2.76))}} + \frac{1.03587}{\exp{((1.52996)(2.76))}} + \frac{1.76474}{\exp{((3.89411)(2.76))}} =$

$\Omega_D = 0.972$

Diffusivity of Methane in Air:

$D_{AB} = \frac{0.00266 T^{3/2}}{P M_{AB}^{1/2} \sigma_{AB}^2 \Omega_D} = \frac{0.00266 (298)^{3/2}}{1(20.6)^{1/2} (3.735)^2 (0.972)} = \frac{13.68}{61.54} = 0.222 \frac{cm^2}{s}$

Propane $CH_3CH_2CH_3$ in air at 25$\textdegree$C and 1 atmosphere (atm)

$M_{AB} = 2[\frac{1}{M_A} + \frac{1}{M_B}]^{-1}$

$M_A = M_{CH_3CH_2CH_3} = 3(MW_C) + 8(MW_H) = 3(12.01) + 8(1.008) = 44.1 \frac{g}{mol}$

$M_B = M_{air} = 29 \frac{g}{mol}$

$M_{AB} = 2[\frac{1}{44.1} + \frac{1}{29}]^{-1} = 35.0$

Need $\Omega_D$

Neufield, et al.: $\Omega_D = \frac{A}{(T^*)^B} + \frac{C}{\exp{((D)(T^*))}} + \frac{E}{\exp{((F)(T^*))}} + \frac{G}{\exp{((H)(T^*))}}$

$T^* = \frac{\kappa T}{\epsilon_{AB}}$

From appendix B[1]

Propane: $\sigma_A = 5.118 \AA; \frac{\epsilon_A}{\kappa} = 237.1 K$

Air: $\sigma_B = 3.711 \AA; \frac{\epsilon_B}{\kappa} = 78.6 K$

$\sigma_{AB} = \frac{\sigma_A + \sigma_B}{2} = \frac{5.118 + 3.711}{2} = 4.42 \AA$

$\frac{\epsilon_{AB}}{\kappa} = \sqrt{(\frac{\epsilon_A}{\kappa})(\frac{\epsilon_B}{\kappa})} = \sqrt{(237.1)(78.6)} = 136.5 K$

$\frac{\epsilon_{AB}}{\kappa T} = \frac{136.5}{298} = 0.458$

$T^* = \frac{\kappa T}{\epsilon_{AB}} = \frac{1}{0.458} = 2.18$

$\Omega_D = \frac{A}{(T^*)^B} + \frac{C}{\exp{((D)(T^*))}} + \frac{E}{\exp{((F)(T^*))}} + \frac{G}{\exp{((H)(T^*))}} =$

$\Omega_D = \frac{1.06036}{(2.18)^{0.15610}} + \frac{0.19300}{\exp{((0.47635)(2.18))}} + \frac{1.03587}{\exp{((1.52996)(2.18))}} + \frac{1.76474}{\exp{((3.89411)(2.18))}} =$

$\Omega_D = 1.05$

Diffusivity of Propane in Air:

$D_{AB} = \frac{0.00266T^{3/2}}{PM_{AB}^{1/2} \sigma_{AB}^2 \Omega_D} = \frac{0.00266(298)^{3/2}}{1 (35.0)^{1/2} (4.42)^2 (1.05)} = \frac{13.68}{121.36} =$

$D_{AB} = 0.113 \frac{cm^2}{s}$

For polar molecule $CH_3-SH$, will use Fuller, et al. equation. From reference[1], the absolute relative error of this equation is 5.4%. Authors report an average absolute error of about 4% when using

Fuller, et al.

$D_{AB} = \frac{0.00143 T^{1.75}}{PM_{AB}^{1/2}[(\sum \nu)_A^{1/3} + (\sum \nu)_B^{1/3}]^2}$

T = 25$\textdegree$C = 298 K; P = 1 atm

$M_{AB} = 2[\frac{1}{M_A} + \frac{1}{M_B}]^{-1}$

$M_A = M_{CH_3SH} = 1(C) + 4(H) + 1(S) = 1(12.01) + 4(1.008) + 1(32.07) = 48.11 \frac{g}{mol}$

$M_B = M_{air} = 29 \frac{g}{mol}$

$M_{AB} = 2[\frac{1}{48.11} + \frac{1}{29}]^{-1} = 18.1$

Summation of “Atomic and Structural Diffusion Volume Increments from table 11-1[1]

$(\sum \nu)_A = (\sum \nu)_{CH_3SH} = 1 (C) + 4(H) + 1(S) = 1(15.9) + 4(2.31) + 1(22.9) = 40.04$

$(\sum \nu)_B = (\sum \nu)_{air} = 19.7$

$D_{AB} = \frac{0.00143T^{1.75}}{PM_{AB}^{1/2}[(\sum \nu)_A^{1/3} + (\sum \nu)_B^{1/3}]^2} = \frac{0.00143(298)^{1.75}}{1(18.1)^{1/2}[(40.0)_A^{1/3} + (19.7)_B^{1/3}]^2} =$

Diffusivity of methanethiol in air

$D_{AB} = \frac{30.56}{159.38} = 0.192 \frac{cm^2}{s}$

Diffusivities in air in decreasing order

Methane: $D_{AB} = 0.222 \frac{cm^2}{s}$

Methanethiol: $D_{AB} = 0.192 \frac{cm^2}{s}$

Propane: $D_{AB} = 0.113 \frac{cm^2}{s}$

At a detection threshold of 1 part per billion (ppb) and the above diffusivities, one might detect methanethiol prior to experiencing propane. In truth, there is an equation that takes “mixture” into account but I do not know the percent mixture of each component[2].

Equation for mixture

$D_{1-mixture} = \frac{1}{\frac{z_2}{D_{1-2}} + \frac{z_3}{D_{1-3}} + .... + \frac{z_n}{D_{1-n}}}$

$z_n$ is the mole fraction of component “n” in the gas mixture evaluated on a component-1-free basis

$z_2 = \frac{y_2}{y_2 + y_3 + ... + y_n}$

ihatemyhate. Friends Selection – Ross Flirts. youtube.com[online]. 2013. Available from: http://youtu.be/kH5JhYsfNMA

• Wait until 2nd attempt

References:

[1] Poling, Bruce E.; Prausnitz, John M.; O’Connell, John P. (2001) The Properties of Gases and Liquids, Fifth Edition. New York: Mcgraw-Hill.

[2] Welty, James R.; Wicks, Charles E.; Wilson, Robert E. (1984) Fundamentals of Momentum, Heat, and Mass Transfer, third edition. New York: John Wiley & Sons.

[3] ScienceBlogs. Molecule of the day. Methanethiol (They put that in, you know), March 2009. scienceblogs.com[online]. 2013. Available from: http://scienceblogs.com/moleculeoftheday/2009/03/18/methanethiol-they-put-that-in/

[4] Wikipedia. Methanethiol. Also known as methyl mercaptan. en.wikipedia.org[online]. 2013. Available from: http://en.wikipedia.org/wiki/Methanethiol

[5] NCBI.PubChem Substance. Methanethiol-Substance Summary (SID 3699). Also known as Methylmercaptan (CAS: 74-93-1). pubchem.ncbi.nlm.nih.gov[online]. 2013. Available from: http://pubchem.ncbi.nlm.nih.gov/summary/summary.cgi?sid=3699

[6] US National Institute of Standards and Technology. NIST. Methanethiol. webbook.nist.gov[online]. 2013. Available from: http://webbook.nist.gov/cgi/cbook.cgi?ID=74-93-1&Units=SI

[7] Wikipedia. Flatulence. en.wikipedia.org[online]. 2013. Available from: http://en.wikipedia.org/wiki/Flatulence