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Chemical Systems Prone to Complexity

The science of chemistry – chemistry, the whole thing – is analysed in terms of systems thinking over three pages of this web book. This third page deals with non-linear (unpredictable, complex, chaotic) chemistry systems.

Real Compounds, Broken Terrains

Image by Erik Tanghe from Pixabay

Consider the first 36 main group elements, hydrogen to barium, not as gas-phase mono-atomic species, but as chemicals in bottles: as reagent chemicals in their standard (thermodynamically most stable) state at 298 Kelvin and 100 kPa (25°C & 1.0 atm) pressure:

The bulk properties: structure, melting/boiling points, electrical & thermal conductivity conductivity, reactivity, etc., of the main group elements as materials are not predictable from first principles, and neither are they periodically related in a general way.

Consider the elements N, P, O & S in the standard state. All exist as molecules, but:

Nitrogen exists as N2
Phosphorus exists as P4
Oxygen exists as O2
Sulfur exists as S8

Indeed, where is the regular change?, in:

Al (metal)
Si (network)
P4 (molecular)
S8 (molecular)
Cl2 (molecular)
Ar (single atom molecular)

These are complicated materials.

At 25° and 1.0 atm (std. conditions, 298K & 100kPa), sulfur, due to bond length, bond angle, van der Waals radius, electronic and crystal packing considerations, prefers to exist in rings of exactly eight sulfur atoms, hence S8.

Phosphorus prefers to exists as four atom, P4, tetrahedra. Etc.

While it is relatively easy to explain after the fact "why" a particular allotropic form is stable under a particular set of conditions using the phase diagram, valence and molecular orbital theory... these arguments are invariably based on empirical (experimental) evidence and always end up being circular:

Sulfur exists in S8 rings because sulfur exists in S8 rings.

Hey sports fans! Have you noticed how much easier to explain why the team won the game, than it is to predict which team is going to win? Hindsight is a wonderful thing; it gives 20:20 vision in sport, and also with chemical science.

Should it have been the case that sulfur existed in S10 rings... well, we would have been able to explain that as well...

Remove the standard state (298 Kelvin and 100 kPa) constraint, and things get far more involved as different elemental allotropes can be found which are stable (or meta-stable) under various conditions:

Generally, it is not possible to deduce an element's equation of state or phase diagram from first principles; they must be experimentally determined.

As expected, chemical compounds are far more involved than the chemical elements. [At least they are usually are: the main group hydrides and congeneric series used in the chemogenesis analysis are notable exceptions.]

Oxides are particularly difficult. Consider, for example, the oxides of the period 2 elements: Li, Be, B, C, N, O, F & Ne. According to webelements, the set of period 2 oxides consists of:

This set of chemical compounds clearly presents as an unpredictable "broken terrain". It is not possible to predict which period 2 oxides will exist from first principles. Indeed, it is not an impossible scenario that a new Period 2 oxide will be discovered. Should this is be the case, theory will be used to explain why the new compound is stable and how it is able to exist.

I predict that the carbon oxide C2O2, O=C=C=O, should exist from my knowledge of carbon dioxide, CO2 (O=C=O), and carbon suboxide, C3O2 (O=C=C=C=O), both of which are known. I can generate all three homologs in Spartan, a molecular modeling package employing high level (QM/HF/DF) theory. However, I know that chemists will take little or no notice of my prediction until it is verified by experiment, the new carbon oxide is made and its melting point determined.

Prof. Harry Kroto predicted the existence of fullerene, C60 (Wikipedia), in 1985 after he observed an ion at m/e 720 by mass spectrometry, in a molecular beam experiment which created carbon clusters. This cluster had to contain 60 carbon atoms and he assigned the "football" structure, but scientists only took note – and awarded the Nobel prize – after the substance had been prepared in relative bulk in 1991.

Thinking further... I suspect C2O2 will be susceptible to fragmentation, yielding two molecules of carbon monoxide, CO. Bother...

The set of all possible compounds is a huge, complex, broken terrain. It has been estimated that there are more that 1060 possible organic molecules with a molecular mass of 500 or less. Bohacek et. al., Med. Res. Rev. 16, 3-50, 1996

Amazingly, if just one molecule of each compound were to be produced, the total mass would nearly equal that of a million suns. Do the math:

The set of known compounds is strongly biased towards issues of biological, medical, military, commercial and/or academic interest. The three largest on-line chemical databases are:

CAS (the Chemical Abstracting Service) has a database of close to 127 million substances (as of June 2024), and about 10,000 more are added per day, that is more than three million a year.
: 9 million organic substances
Gmelin: 2 million inorganic compounds

The chemical industry produces vast numbers of compounds for testing, particularly in the areas of drug discovery and flavoring/fragrance. Industry probably has proprietary (secret) information on [intelligent guess here] half a billion chemical substances/compounds.

The set of commercially available chemicals is represented by on-line databases.

The CAS developed CHEMCATS is a database of chemicals and suppliers. The database lists 8 million commercially available chemicals, 750 suppliers of commercial chemicals and 900 chemical catalogs

In the UK, the Available Chemicals Directory, hosted by the Chemical Database Service, lists 437,790 unique substances from 680 supplier catalogs, and the Screening Compounds Database lists 3.6 million compounds, but these are usually only available in very small quantities, down to 10 microgram quantities, from 20 or so specialist suppliers.

Of course, if you require a chemical that is not currently commercially available, somebody will happily make it for you, for a fee.


Matter is complicated stuff and the sets of possible, known and available chemical compounds/substances form a broken terrain.

Chemistry is an experimental science. The existence of a compound can be predicted from theory, but until somebody actually makes the stuff, nobody will be interested.

Gases, Liquids, Solids and the Phase Interaction Matrix

We learn about the solid, liquid & gaseous states of matter during in our very first science classes:


• atomic, ionic, molecular particles bonded together in a lattice
• particles are tightly packed, usually in a regular pattern
• condensed phase
• particles vibrate – jiggle about – but generally do not move from place to place
• samples retain a fixed volume and shape
• not easily compressed
• not free flowing (unless granular, which is a special case)


• discrete atomic or molecular particles
• particles are packed closely together, but with no regular arrangement
• condensed phase
• particles vibrate, and they are able to move about by "sliding past" each other
• samples are fluids able assume the shape of the part of the container which it occupies
• not easily compressed
• free flowing fluid: Navier-Stokes


• discrete atomic or molecular particles
• particles are well separated and have no regular arrangement
• particles are able to move freely at high speeds, colliding with container walls and each other
• samples are fluids able assume the shape and volume of the container
• compressible: PV = nRT
• free flowing fluid: Navier-Stokes

Later we learn to understand the physics and chemistry of gas, liquid and solid phases in terms of kinetic theory, thermodynamics and solution theory, as discussed in the section on linear chemistry here, and solid structure in terms of bonding theory, here and here.

So it is surprising to find out just how quickly complexity emerges in the gas-liquid-solid system when phases are mixed together.

Consider the Phase Interaction Matrix ('interaction table', a type of Karnaugh map):       

At first sight, there appear to be just six possibilities:

Gas/Gas A mixture of two gases
Gas/Liquid Mixture of a gas and a liquid
Liquid/Liquid Mixture of two liquids
Gas/Solid Mixture of a gas & a solid
Liquid/Solid Mixture of a liquid & a solid
Solid/Solid Mixture of two solids

But this is an illusion because phase interactions usually – but not always – lead to the formation of phase boundaries, heterogeneous systems and emergent complexity that is critically dependent upon the nature of the phase boundary surface.

Some points before we begin:

However, using turbulent mixing to produce homogeneity is somewhat ironic because turbulence is itself a complex non-linear process that is here being used to smooth out the chaos and complexity associated with unstirred mixtures. One type of chaos destroying another.

Milk and smoke are both colloids.

Gas/Gas: A mixture of two or more gases such as air.

Mixtures of gases are always homogeneous if they are at thermal equilibrium. The mixing time can be determined by Graham's law of diffusion/effusion which is mass dependent: low mass gases like hydrogen and helium diffuse into each and mix with other more quickly than heavy gases like xenon and krypton. Turbulent mixing efficiently scrambles gaseous samples to a distance scale where Graham's law can take over and render a system homogeneous.

The mixing of gases is seldom an issue in the lab where containers are small. However, the Earth's atmosphere very large and it is not at thermal equilibrium due to differential heating by the Sun. The is atmosphere is decidedly heterogeneous gaseous system, as we experience with the changing weather.

Mixtures of gases – such as air or natural gas (methane + ethane + propane) – can be separated by low temperature fractional distillation.

Differential diffusion separates by mass rather than boiling point. The method has been used to separate uranium 235U and 238U isotopes by diffusing gaseous uranium hexafluoride, UF6, through porous material.

Uranium hexafluoride is used for two reasons. Firstly, UF6 is a molecular solid that sublimes to gas at 56°C. More importantly, fluorine only has one isotope, 19F, so there is no blurring the uranium's isotopic mass by the six attached F ligands.

Gas/Liquid: Mixture of a gas and a liquid: clouds, foams, aerosols, sprays

Mixtures of gases and liquids are always heterogeneous. Clouds, aerosols and sprays consist liquid droplets dispersed in a gas. Foams consist of surfactant stabilised bubbles of liquid filled with gas. Clouds, aerosols, sprays and foams are unstable states, and the gas and liquid components are usually separated by gravity within a short time. Clouds may be charge stabilised with individual droplets having a net charge, the result is that droplets repel each other and the rate of condensation is slowed.

It is likely that the gas will have some solubility in the liquid, and that the liquid will exert a vapour pressure "into" the gas phase.

Supercritical fluids are materials in a state above their critical temperature, Tc, and critical pressure, Pc, a regime where gases and liquids "coexist" in a state of matter outside our usual everyday experience. Decaf coffee is made by removing the caffeine using a solvent of supercritical CO2.

Gas liquid chromatography, GLC, involves vapour phase analyte species differentially partitioning between the vapour phase and a liquid phase bound to a solid carrier phase support. As the carrier gas moves with respect to the stationery phase, analyte species are separated and assayed by some sort of detector.

Liquid/Liquid: Mixture of two liquids, which may be miscible or immiscible

Immiscible: oil and water

Mixtures of immiscible liquids are always heterogeneous, with a phase boundary, although the two liquids will always be partially soluble in each other.

The two phases will separate by differential density and gravity. In the laboratory the separation of immiscible liquids is conveniently carried out using a separating funnel:

Solute molecules can partition between the two immiscible phases. In pharmaceutical science the partitioning of medicinal agents between immiscible octan-1-ol and water is a common measure of overall polarity. (There is a JAVA partition calculator here.) Turbulent mixing by "shaking the sep' funnel" will maximise the phase boundary surface area and will speed up partition equilibrium.

Miscible: methanol and water

Mixtures of miscible liquids are homogeneous if completely stirred. Turbulent mixing is particularly efficient at thoroughly mixing miscible liquids together.

However, at high concentrations – close to 1:1 molar ratios – classic homogeneous systems like methanol and water are actually considerably more involved than may be assumed. A recent paper says:

"When a simple alcohol such as methanol or ethanol is mixed with water, the entropy of the system increases far less than expected for an ideal solution of randomly mixed molecules. Our data indicate that most of the water molecules exist as small hydrogen bonded strings and clusters in a 'fluid' of close packed methyl groups, with water clusters bridging to neighbouring methanol -OH functions through hydrogen bonding. "Molecular Segregation Observed in Concentrated Alcohol-Water Solution by Dixit et. al., Nature, 416, 829-832 (2002), abstract.

In other words, the concentrated methanol/water mixture only appears to be homogeneous and on a molecular scale the mixing is incomplete. It follows that the methanol/water phase diagram is more complex than expected.

As a rule of thumb, linear behaviour should only at less than < 0.1 molar... water in methanol or methanol in water.

It should be said that water is a particularly complex material due to its polar, hydrogen bonding nature. Mixtures of – for example – dichloromethane, CH2Cl2, and trichloromethane (chloroform), CHCl3, are far more predictable than concentrated aqueous solutions.

Miscible liquids can be separated by fractional distillation or by 'freezing out' one of the components. For example, the ethanol concentration an ethanol-water mixture can be increased by cooling the mixture to about -10°C and removing the crystals of pure water ice. (This method was/is used to produce vodka during the cold Russian winter.)

Solvent Types

There are several types of liquid phase solvent:

Non-polar Organic Solvents
immiscible with water
van der Waals interactions
cyclohexane to ethylacetate, MIBK, etc.

Dipolar, Weakly Protic Solvents
miscible with water
van der Waals interactions not Brønsted acidic, but form an equilibrium with hydroxide ion
pKa 15-25
acetone, acetonitrile, etc.

Dipolar Aprotic Solvents
miscible with water
van der Waals interactions
not Brønsted acidic
pKa > 30

Protic Solvents
miscible with water
Brønsted acidic
pKa < 20
hydrogen bonding
water, alcohols, acetic acid

Exotic Solvents
van der Waals interactions
Liquid SO2, liquid NH3

Liquid Metals
Liquid Hg

Ionic Liquids
Molten NaCl

A few observations:

  • All liquids dissolve in themselves.
  • Within a given type, solvents *tend* to be infinitely miscible with each other (if they don't react).
  • There is a profound and useful difference between the non-polar organic solvents and water that is exploited in solvent extraction, etc.
  • The useful dipolar aprotic solvents like DMF lie between the non-polar organic solvents and the polar protic solvents.
  • Methyl isobutyl ketone is the most polar of the organic solvents that is immiscible with water. Indeed, MIBK is an important industrial extraction solvent used to pull polar organic molecules and complexes into the organic phase.
  • Sucrose and other sugar molecules are covered with hydroxy groups able to hydrogen bond with water and so are very soluble in water.
  • Gold, Au, dissolves in mercury, Hg.
  • Aluminium oxide, Al2O3, dissolves in liquid cryolite, Na3[AlF6].
  • From these observations the general conclusion can be drawn that: "like dissolves like".
  • However... every solvent is unique with its own spectrum of properties and reactivity.

In terms of chromatography, solvents an be can be collected into an eluotropic series, non-polar-to-polar:

acetic acid

Gas/Solid: The mixture of a gas and a solid can take two forms: foam or smoke.

Gas/solid systems are always heterogeneous.

Pumice stone (a volcanic material), bread and Styrofoam® are all solid foams in which a gas is held in solid matrix with an open structure. Much modern technology uses gas/solid foams because they can be engineered to be strong, energy adsorbing and very light.

Smoke consists of low density solid particles suspended in a gas.

Properties of smokes and foams are controlled by the surface area of the solid, which may be small or very large. Activated carbon has a huge surface area, a paper here reports 500 square meters per gram. Aerogels can have surface areas up to 4000 square meters per gram, here.

Solid foams can be separated by crushing/cutting and gravity, or the gas may diffuse out and away if the foam structure is open enough. The solid components of smokes can be filtered out.

Fluidized beds use moderate density, granular solids supported by high pressure flow of gas.

Gas phase reaction systems commonly employ heterogeneous solid phase catalyst systems. For example, hydrogenation reactions often use Ni/Pd/Pt transition metals dispersed over the large surface area of an activated carbon or ceramic materials.

Liquid/Solid: The solid may be insoluble in the liquid, or it may be soluble, or an emulsion may form.

Insoluble: sand and water

The two phase mixture is by definition heterogeneous. There may be some solubility of the solid into the liquids phase. (The range from soluble to insoluble is, of course, continuous.)

Solids and liquids can be separated by filtration.

Column chromatography and HPLC, involves analyte species differentially partitioning between a mobile liquid phase and a stationary solid phase. As the carrier solvent moves with respect to the stationary phase, analyte species are separated before being assayed by some sort of detector.

Soluble: sugar and water

Solubility of a solid in a liquid – or more technically, a solute in a solvent – is temperature dependent. Generally gases become less soluble in solvents with increasing temperature and they are "out gassed" at the boiling point, where as solids become more soluble, but there exceptions, ie sodium sulfate, Na2SO4.

Experimentally determined solubilities curves are linear, but individual curves cannot be predicted from first principles and the set of solubility curves is complex:

There is a discussion about the thermodynamics of solubility, and an insight as to why it is so difficult to predict solubility, on the ChemGuide site.

Stirred solutions are homogeneous, and the rate of dissolution is dramatically increased by turbulent mixing.

The stirred solid-dissolved-in-liquid system is the preferred reaction environment for practical chemistry. Many components can exist in the solution. The system can be controlled in terms of relative and absolute concentration, temperature, time, etc. With turbulent stirring there is intimate mixing of all components.

The solid and liquid components of a solution can be separated by cooling, crystallisation and filtering off the solid phase and moving it away from the liquid phase. Alternatively, the solvent can be evaporated away from the solid and condensed. The final stage this latter process is usually referred to as drying.

Temperature controlled cycles of dissolution followed by crystallisation represent a very efficient way of purifying solid.

Emulsions (colloids): milk and butter

Solid fats can emulsify with water in two ways: fat in water and water in fat.

Dairy products are of biological origin and have many components present, but they illustrate this point rather nicely: Whole milk is a colloidal emulsion largely consisting of fat particles suspended in water, and butter is a emulsion largely consisting of a suspension of water droplets in fat.

Solid/Solid: A mixture of two solids can result in a heterogeneous mixture or a homogeneous alloy.

Alloys: brass

The two phases are intimately mixed together in a melt to give a solid homogeneous mixture on cooling. However – and it should be said somewhat confusingly – there are several types of alloy, some of which are actually heterogeneous mixtures.

• Substitutional alloys: homogeneous
• Solid solution alloys: homogeneous
• Eutectic alloys: heterogeneous
• Partial solubility alloys: heterogeneous

For example, heterogeneous eutectic alloys are formed from a homogeneous melt of two or more metals, which partially phase separate on cooling. Metallic alloys are discussed here, with reference to their positions with respect to the Laing tetrahedron of material type.

Polymer alloys are formed by turbulently mixing two or more thermoplastic polymers in the liquid state. The polymer alloy is formed on cooling. Dye can be added to a polymer which is evenly dispersed throughout the material.

It is very difficult to separate the individual components from an alloy. It may be necessary to dissolve the alloy in a solvent and chemically separate the individual components from a liquid phase environment. For polymer alloys, it may be necessary to crack the individual polymer components back to the starting monomers and separate these by distillation.

Heterogeneous mixture: iron filings + sand or granite

There will always be two (or more) distinct solid phases, although this may only be apparent under microscopic examination.

Separation is by physical means which always starts with mechanical crushing, followed by:

• selective dissolution
• separation by size
• separation by density
• froth floatation
• iron is a special case because magnetic separation is possible

In solid/solid alloys and heterogeneous mixtures it is not possible for mixing to occur because there is no mobile fluid phase. Therefore the only chemical reactions that can occur are temperature and/or pressure induced phase changes. Geologists and geochemists are particularly interested in how rocks are metamorphosed over geological time. The ice-water-steam system is exceedingly involved.

This type of analysis is not new. Here is an old "like-dissolves-like" diagram from 1751 using old alchemical symbols:

A facsimile English edition of Gellert's Metallurgic Chymistry. First published in German in 1751, with an intro by Fathi Habashi. ISBN: 2-980-3247-3-6


The rule of thumb is that homogeneous solutions are simple, whereas heterogeneous systems are complicated because they are dominated by the nature of the phase boundary. However, solutions – particularly aqueous solutions – can only be expected to be ideal (linear) when solute concentrations are below 0.1 molar. This situation is restricted to:

• Mixtures of gases (stirred)
• Mixtures of miscible liquids (stirred and where one component is < 0.1 molar)
• Solution of a solid in a solvent (stirred and where the solute is < 0.1 molar)
• Solid solutions (where one component is < 0.1 molar)

At high concentrations, activity and fugacity "fiddle factors" have to be employed.

Linear behaviour is rare. Most phase interactions are non-linear, inherently complex and emergence abounds.

Isomers and Emergent Structure

As molecular size increases, so does complexity, and emergent new properties appear. Consider the linear and branched alkane alcohols, the alkanols. Above, it was argued that there is:

However, some of the alkanols – the first example is 2-butanol, CH3CHOHCH2CH3 – have a chiral centre with four different groups attached about a tetrahedral carbon. The implication is that there are two ways (configurations) that the groups can attach to the tetrahedral centre and the molecule can exist as a pair of "handed" enantiomers or "stereoisomers". So, actually there is:

Enantiomers can only be distinguished in a chiral environment, but biology is very, very chiral and with just one exception (glycine): all amino acids, all nucleic acids, all sugars, all peptides, all proteins, all DNA strands and all organisms are chiral and are enantiomer selective. Biologically, (2R)-2-butanol is completely different to (2S)-2-butanol.

Molecules with more than one chiral centre exist as diastereoisomers (diastereomers), which unlike enantiomers are chemically distinguishable in an achiral (non-chiral) environment. Diastereomers have different melting points, different IR spectra, different reaction chemistry as well as different biology.

Consider the biologically important D-aldohexose sugars, a set which includes glucose. Each D-aldohexose has three variable chiral centres, which leads to a set of eight (23) D-diastereomers, each with a unique and distinct melting point, IR and H-NMR spectra, reaction chemistry and biochemistry:

As molecular size and complexity increases, further degrees of freedom emerge. For example, molecular structure cannot be fully described in terms of bond lengths, three atom [X-Y-Z] bond angles and chiral centre configurations. As illustrated by hydrogen peroxide, HOOH, here and specifically, here, the four atom dihedral angle emerges as an ever more important parameter:

Variations in dihedral angle lead to conformational isomers, and variations in dihedral angle with time lead to rotormers and dynamic molecular structures. For example, at room temperature, cyclohexane, C6H12, exists as dynamic mixture of interchanging chair, boat and in-between twisted boat conformations, with attached groups adopting axial or equatorial positions:

Most pharmaceutical agents are smallish molecules (GFW = 50 - 300) that are able to enter enzyme active sites or hormone receptor sites where they "mimic" – more technically, agonise (positive effect) or antagonise (negative effect) – the local biosystem in some way.

These days much drug discovery research involves modelling how substrate molecules and synthetic agonists & antagonists interact with and effect the active site, a process that involves understanding the conformation(s) and dynamic conformational changes adopted by molecules while in or bound to the active site.

An example of the software available to pharma industry scientists is Omega by OpenEye Scientific Software. Omega is able to "generate multi-conformer structure databases so that conformational expansion of drug-like molecules can be performed". Below are two [of thousands of possible] overlaid conformers of the cholesterol-lowering medication Lipitor:


As molecular structures grow in size and complexity, emergent properties like diastereoisomerism and dynamic conformation become ever more important.

Mechanistic Pathways

All reaction mechanisms can be deconstructed into sequences of STAD (substitution-transfer-abstraction-displacement) steps, as discussed here, although it is usually more useful to consider reaction mechanisms in terms of unit mechanistic steps and sequences of unit steps, as discussed here:

Pericyclic processes
Name Reactions

Many factors determine when an particular mechanism is able to come into play, and mechanisms can compete with each other. This is nicely illustrated by the common undergraduate laboratory preparation of tertiary butyl chloride (2-chloro-2-methylpropane), (CH3)3CCl:

Method: Tertiary butanol (2-methylpropan-2-ol), (CH3)3COH, is carefully mixed with concentrated hydrochloric acid in a separating funnel. After a few minutes an upper organic layer appears. After 30 minutes the lower aqueous layer is discarded, and the upper organic layer is washed with aq. base/water, dried and distilled to give tertiary butyl chloride, (2-chloro-2-methylpropane), (CH3)3CCl.

The yield of tertiary butyl chloride is always low. One reason is because the reaction proceeds via a first order nucleophilic substitution, SN1, mechanism, a pathway that has a tertiary carbenium ion (3° carbocation, R3C+) species as an intermediate. The 3° carbenium ion can react in two ways: either it can complex with chloride ion nucleophile, Cl, to give (CH3)3CCl, or it can lose a proton, H+, to form methylpropene.

The ratio of alkyl chloride to alkene is dependent on everything: temperature, solvent polarity, mode of addition, relative and absolute concentrations, rate of stirring, etc.

Reactions can give fast forming kinetic products, or the more stable thermodynamic products. This effect is illustrated with the sulfonation of naphthalene giving 1-naphthalene sulfonic acid and/or 2-naphthalene sulfonic acid:

Under moderate temperature conditions (~80°C) and short reaction times the 1-naphthalene sulfonic acid is formed. This is the kinetic or "fastest forming" product.

At higher temperatures (~160°C), the less sterically hindered and more stable the 2-naphthalene sulfonic acid is formed.

Molecular conformation can influence chemical reactivity.

Alkyl chlorides can undergo base catalysed E2 elimination to give an alkene and HCl. The base commonly used is ethoxide ion in a solvent of ethanol.

There is a rule – explainable in terms of frontier molecular orbital (FMO) theory – that the H and the Cl atoms must be "diaxial" (at 180° with respect to each other) before the E2 mechanism can occur. This constraint is not an issue with small molecules like 2-chloropropane, CH3CHClCH3, where bonds are free to rotate, but things are rather more involved with chlorocyclohexanes.

Consider neomenthyl chloride (below). There is a large, bulky isopropyl group, –CH(CH3)2, that prefers to sit in an equatorial position about the cyclohexane ring, an influence that dominates the ring conformation. One effect of this conformation is that the H and the Cl are forced into axial positions that are 1,2 relative to each other. The result is fast base mediated E2 elimination to give 1-isopropyl-4-methylcyclohexene:

However, in menthyl chloride, a diastereoisomer of neomenthyl chloride, the chlorine is held in an equatorial position by the bulky isopropyl function. In this situation, it is only when the ring (occasionally) flips into another conformation that the chlorine finds itself 1,2-diaxial with respect to a hydrogen. The result is that menthyl chloride undergoes base mediated E2 elimination at only 1/600th of the rate of neomenthyl chloride, and the product is a different isomer, 3-isopropyl-6-methylcyclohexene:

Ph.D. students with research projects looking at target synthesis or synthetic methodology learn to explore how configuration and conformation influence competing mechanistic pathways.


The previous page of this web book, here, introduced the idea of the mechanism matrix. However, the proposed schema – which looked plausible – simply cannot be mapped to the complex terrain of reaction chemistry space.

Also, the chemistry presented in textbooks simply does not reflect the reality of low yield reactions where products are often accompanied by large quantities of ill defined black gunk.

Non-Equilibrium Thermodynamics

While systems at equilibrium and approaching equilibrium are predictable and linear, as discussed here, non-equilibrium systems are a rich source of complexity, emergent behaviour and chaos.

There are two main ways of producing a non-equilibrium thermodynamic state in a chemical system: use electrical or photon stimulation rather than thermal (heat) energy to excite the system, or, heat a system locally, but do not stir.

Photon Stimulation

One of the central ideas of equilibrium thermodynamics is that of the Boltzmann distribution of particles between two (or more) states, i and j. The rule is that at thermal equilibrium there will always be more species in the lower energy state i than the higher energy state j, here.

However, if species are excited from i to j is by a light source with a wave length/energy that exactly matches the energy difference i and j (j i), then a population inversion will be set up with more species in the higher energy state j. This is a non-equilibrium system, and the Boltzmann equation does not hold.

Laser operation requires population inversion. The laser "works" by species in the higher energy state falling to the lower state and emitting a photon of energy j i. This photon stimulates adjacent species in the higher state to emit their photon as well – as predicted by Einstein – producing a cascade of coherent light, where "coherent" light is all of the same frequency and is in phase.

• According to classical equilibrium thermodynamics, it should not be possible to form ozone, O3, from dioxygen, O2:

3O2   →    2O3

because the Gibbs free energy for this process is positive and anti- spontaneous at all temperatures. The reaction is thermodynamically "disallowed" on both enthalpy and entropy grounds. In fact, the reverse ozone to oxygen process, 2O3 →  3O2, has a negative Gibbs free energy at all temperatures.

However, ozone can be formed when O2 is exposed to short wavelength UV light, the process generates the ozone layer high in the atmosphere.

O2   +   UV photon   →    2O•
O•  +  O2     →      O3

Photochemistry, here, and other methods of non-thermal excitation are widely exploited.

Local Heating

If a layer of fluid is heated from below, the density at the bottom layer becomes less than at the top layer due to thermal expansion. Experiments, carried by Bernard in 1900, showed that hexagonal convection cells develop, here:

An image of Bernard cells, captured of from Georgia Tech:

The appearance of Bernard cells is an example of order out of chaos. The local heating causes entropy to increase, but the density inversion induces complex & non-linear behaviour: convection cells that arrange into a regular hexagonal lattice, classic emergent behaviour. This is exactly analogous to the one dimensional waves of slowing and speeding found on highways at high traffic densities. As discussed in the intro to this section here.

The implication of Bernard convection is that local heating can cause complex emergent behaviour. To eliminate such effects it is necessary to stir (turbulently mix) the fluid and render the system homogeneous.

The Sun also heats our planet with thermal radiation, but the atmosphere is large and it has a spherical geometry, so it cannot be mixed to homogeneous. Indeed, on Earth, the Bernard cells present as ocean currents and weather systems.

Life on Earth

Our planet is in a non-equilibrium thermodynamic situation with respect to the Sun.

The Sun heats us and bombards us with high energy photons (light) that are exploited by photosynthetic systems in cyanobacteria and plants to convert carbon dioxide into glucose and oxygen.

The implications of non-equilibrium thermodynamic systems generating complexity are both extraordinary and profound, as eloquently summed up by Prof. Peter Atkins of Physical Chemistry textbook fame on the BBC:

"The driving force [for complexity on Earth] is the Sun. It dissipates its energy and drives the processes of life on Earth. An analogy. Imagine you were sitting in front of a screen and there was a weight on the floor, and you saw the weight rise up. You would think it was a miracle. But if you looked behind the screen and see there is a heavier weight that is falling down and pulling the front weight upwards, you realise there is a rational explanation. That is, the dispersing energy [of the falling weight] is driving the events that give rise to complexity [the weight rising]. Overall there is increasing disorder, but locally there is increasing complexity."

The BBC has a listen again facility, and you can hear this fascinating discussion about the second law of thermodynamics on the BBC web site and clicking the "Listen Again" link. Real Player is required as the download file is .RAM format, not .MP3.

The simplest living cells consists of just a few hundred chemicals: amino acids, sugars, metabolites, intermediates etc., as well as the molecular biology apparatus for replication and protein synthesis. However, the various enzyme catalysed biochemical processes are not at thermodynamic equilibrium. The emergent complexity of the cell is due to it being a non-equilibrium system. A dead cell that is at equilibrium.

For a technical discussion of non-equilibrium thermodynamics go to the Wikipedia page, here.


Non-equilibrium systems are prone to develop in complex ways that exhibit emergent behaviour.

Diffusion Controlled Processes

If the following reagents are added together in a flask:

• Malonic acid - 0.2 M/L
• Sodium bromate - 0.3 M/L
• Sulfuric acid - 0.3 M/L
• Ferroin - 0.005 M/L

and the reaction mixture is stirred vigorously, an oscillating Belousov-Zhabotinsky reaction (BZR) is set up:

The BZ reaction is an auto-catalytic reduction-oxidation (redox) process. Each step of the multi-step reaction sequence generates a catalyst that speeds up the counter reaction:

As the reduction step proceeds it produces more and more catalyst to speed up the oxidation, and vice versa.

The reduced state reaction is red while the oxidised state is a pale brown.

But if the reaction system is not stirred, diffusion control takes over. This can be observed when the reaction mixture is prepared as a thin film, 0.5 - 1 mm deep, to avoid any vertical mixing, and waves of reaction can be seen propagating through the unstirred mixture:

For a chemical reaction between X and Y to proceed, the chemical species first have to meet each other in the reaction medium. In an unstirred reaction medium, the rate at which the various chemical species move, meet and react is limited – and so controlled – by the speed that the species diffuse through the reaction medium. The effect the BZ type auto-catalysis is to cause the rather dramatic moving waves, and these are made visible by the colour change.

There are many resources about the BZ reaction and other non-linear process on the web:

An example of order out of chaos, is a mercury 'beating heart' where the various processes lead to a regular pulse. Such processes are exceeding rare in chemistry space, and are always of interest:


Molten materials and super saturated solutions have a thermodynamic tendency for form crystals, however, crystal growth can be highly complex.

The following images and accompanying text are captured from

"Many pure metals, alloys [and other materials] solidify by the growth of complex crystals called dendrites. Unlike most inorganic crystal which display a faceted interface, dendrites exhibit a smooth, continuously variable interface, which displays multiple branching. This leads to the formation highly complex growth patterns."

The left image shows a theoretically modelled dendritic crystallisation that is is described as "seaweed". The image to the right shows the "as-solidified microstructure of Cu undercooled by 280 K". From here.

"Dendrites may undergo a kinetically induced instability which results in repeated multiple tip splitting, or doublon formation":

Heterogeneous catalyst efficiency can be boosted if the active material is deposited on a solid support with a fractal surface:

"Surface render of Ru10Pt2 catalyst particles (shown in red) anchored on and within a disordered porous silica support (grey). Data was obtained via tomography, an electron microscopy technique that generates a three-dimensional volume from a series of two-dimensional projections taken at different angles. A fractal analysis (performed using standard box-counting algorithms) revealed that the fractal dimension of the surface to be 2.4 +/- 0.1. The number of catalyst particles accessible to reactant gas molecules will therefore depend on their size according to this fractal distribution of surface sites, strongly influencing catalytic activity and selectivity." EPW Ward, T J V Yates and P A Midgley, Department of Materials Science, University of Cambridge.


Chemists usually like to work with turbulently mixed, homogeneous solutions so as to avoid diffusion controlled artifacts. Materials scientists are not so lucky, and they often have to work under diffusion controlled conditions.

Experiential Design: Time, Gravity, Geometry, Temperature, Chemical Potential, Physical Separation

Chemists use clever experimental design – implemented using laboratory equipment constructed from glass, stainless steel, rubber tubing and Teflon – that exploit time, gravity, geometry, differential temperature, chemical potential, physical separation, etc., to influence the outcome of reaction and separation processes, usually to maximise the % yield or separation of a particular material or compound and/or to minimise the formation of unwanted by-products and contaminants.

There as a number of standard pieces of laboratory equipment: flasks, condensers, syringes, pipettes, burettes, separating funnels, filters, Bunsen burners, Dean & Stark traps, etc., (in different sizes). Bespoke equipment is developed as well. This lab apparatus dramatically increases the complexity of reaction chemistry space.

As a first approximation, the reaction system is the system universe, here. But as soon as the reaction system is constrained to a physical experiment, the reaction system is bound by the experimental design.

Some examples – taken from literally thousands of possible examples – of how intelligent design is used to optimise a reaction system space in various ways:

The Bunsen Burner

Methane burns in air, but in the Bunsen burner, methane is premixed with air to create a mixture that burns with a hot, smokeless flame. The Bunsen burner is carefully designed and constructed to maximise localised heating.


The Dean & Stark Trap

Benzaldehyde reacts with ethylene glycol (1,2-dihydroxyethane) to form the cyclic acetal (2-phenyl-1,3-dioxolane). The reaction is an equilibrium process, and the cyclic acetal product can be formed in 100% yield if the water by-product is removed as it is formed:

One very convenient and elegant method for removing the water from the reaction is to use an azeotroping solvent, such as toluene, with a Dean & Stark trap:

The water produced in the reaction is co-distilled with the refluxing toluene solvent with which it forms a vapour phase azeotrope. The toluene/water vapour phase complex rises into the condenser where it cools and condenses. However, as liquids toluene and water are immiscible and they separate into two phases. The denser water (containing a blue dye in the photo above) collects in the "trap", and the toluene - with water removed - returns to the main reaction vessel.

With this experimental design: gravity, temperature are geometry are exploited.

• Gravity is required to set up two density gradients:

• The hot vapour phase azeotrope rises into the condenser.
• Immiscible water and toluene separate in the trap.

Indeed, the Dean & Stark apparatus would not work in the zero gravity of the International Space Station.

• Temperature and temperature differences are required to:

  • Overcome the activation energy and speed up the reaction.
  • Form the refluxing reaction mixture and produce the vapour phase azeotrope.
  • Condense the vapour phase azeotrope into the two immiscible liquids, water and toluene.

• The geometry of the Dean & Stark trap physically separates the water generated in the reaction and so drives the equilibrium position to the formation of the acetal.

A experimental set up with a simple reflux condenser would not drive the equilibrium to the right by removing the water.


Temporal (time) considerations usually involve exploiting differential rates of reaction, where "rate" is measures of moles of material transformed per unit time.

Cyclopentadiene is a reagent commonly used in the study cycloaddition chemistry (here), and organotransition metal chemistry.

However, the cyclopentadiene monomer is in equilibrium with the dimer. At room temperature the dimer is stable and over just a few hours the cyclopentadiene monomer will completely dimerise.

Therefore, before use the cyclopentadiene dimer must be cracked to the cyclopentadiene monomer:

To use cyclopentadiene in a reaction it is necessary to heat the dimer at reflux (170°C) for a couple of hours to "crack" the dimer to the monomer. The pure monomer is distilled off and used immediately, and before it has time to re-dimerise. The rate of dimerisation can also be reduced by dilution in a suitable solvent.

Chemical Potential (Reagent Strength)

Benzene is nitratrated to nitrobenzene with nitrating mixture, a mixture of concentrated sulfuric acid and concentrated nitric acid. Nitrating mixture produces as equilibrium concentration of nitronium ion, [NO2]+, the electrophilic agent which partakes in the electrophilic aromatic substitution of benzene.

However, vary in their reactivity towards nitration. Activated aromatics like phenol are nitrated far more easily than benzene and the reaction can be carried out with dilute nitric acid. Other aromatic compounds require more forcing conditions (or are not stable in nitrating mixture) and for these situations the highly potent nitronium tetrafluoroborate can be used. This ionic reagent consists of the tetraborate ion, [BF4], stabilised salt or nitronium ion, [NO2]+.

The chemical potential of the nitrating agents increases:

dilute nitric acid << nitrating mixture << NO2BF4

Another example. It is a common procedure in synthetic chemistry carry out the nucleophilic substitution of a nucleofugal leaving group at an acyl carbon centre. (This mechanism is also referred to as addition-followed-by-elimination and the tetrahedral mechanism.) It is known that leaving group ability – the ease with which X is lost – correlates with the pKa of the leaving group's conjugate Brønsted acid. With this knowledge in mind it is possible to develop a range of substituted acyl species which under go ever more facile substitution with a nucleophile.

Below are shown methyl ester (least reactive), anhydride, mixed anhydride & acid chloride (most reactive):

Reagents with greater chemical potential partake in more exothermic reactions. For example, a methyl ester can be converted into an ethyl ester by adding excess ethanol and a bit of H+ catalyst (a couple of drops of conc. H2SO4 or 0.1g of para toluene sulfonic acid). No heat will be generated as the Keq is about 1.0. However, if ethanol is added directly to acid chloride will be a great fizzing as the reaction gets hot because it is very exothermic.


Reaction process environments can be designed chemically, spatially, thermally and temporally.

For most reaction systems, chemists are able to prepare (or buy) a reagent of suitable power and reactivity.


For a chemical species to "exist", two conditions must hold:

A pertinent paper titled "What Is the Smallest Saturated Acyclic Alkane that Cannot Be Made?" (de Silver & Goodman, J. Chem. Inf. Model. 2005, 45, 81-87), examines this very question with respect to branched alkanes, exemplified by the structures below:

The C5 (five carbon) molecule above, neopentane, is well known but the C17 homolog (3,3-bis-(1,1-dimethylethyl)-2,2,4,4-tetramethylpentane) is unknown. The paper's authors write: "[The C17 molecule] has never been synthesized, and studies show that it must be extremely strained. However, this is not a proof that it is impossible to prepare. Indeed, molecules which include this carbon framework have been synthesized.. and their existence suggests preparation [of C17] may be possible."

It was argued above that the set of compounds is a complex, broken terrain. That being the case, the synthetic route to a specific compound must involve a complex path through the broken terrain exploiting intermediate compounds to act as way points up the mountain.

Synthesis is analogous with the well known children's game of Snakes & Ladders – or Chutes & Ladders – where ability to produce a material or compound is a synthetic ladder, and lack of stability is an anti-synthetic snake. In reaction chemistry space there are few ladders but many, many snakes.

Consider a couple of related examples from industrial inorganic chemistry: the extraction of the metals iron, Fe, and titanium, Ti, from their oxide ores, Fe2O3 and TiO2. Both oxide ores are common and both can be reduced by carbon at high temperature.

Extraction of Iron

The overall iron(III) oxide plus carbon reduction reaction is:

This reaction process represents a "synthetic ladder": at high temperature (1200°C) the reducing ability of the carbon and the entropy driven loss of gaseous CO2 is able to drive a redox reaction to give liquid iron metal. (The pig iron produced by a blast furnace must be further purified to steel and wrought iron, but this is not the issue here.)


Extraction of Titanium

Titanium(IV) oxide can also be reduced by carbon to titanium metal and carbon dioxide, however, the hot titanium reacts with carbon to form titanium carbide, TiC.

Even small amounts of TiC impurity make titanium metal very brittle and unusable. The titanium carbide cannot be removed, and its formation is an "anti-synthetic snake". As a result, the simple, direct carbon reduction reaction pathway cannot be used.

An alternative pathway is employed by industry, the Kroll process. The carbon reduction reaction is carried out in the presence of chlorine, Cl2, to form titanium(IV) chloride, TiCl4, and carbon dioxide. A great advantage of this method is that titanium tetrachloride is a low boiling point molecular liquid, bp 136°C, which can be distilled to very high purity. In the second synthetic step, titanium tetrachloride is reduced with sodium or magnesium metal to give high purity titanium metal and sodium (or magnesium) chloride.

That is not quite the end of the story because there are other anti-synthetic snakes: titanium tetrachloride is readily hydrolysed by water, at elevated temperature the titanium metal is rapidly oxidised by air back to titanium(IV) oxide and hot titanium even reacts with nitrogen, N2, to form titanium(III) nitride, TiN. As a result, air and moisture have to be rigorously excluded, and the second-step processes are carried out under an atmosphere of inert argon.

The major downside of the two-step synthetic route to titanium is that it is expensive, not because of the use of argon which can be recycled, but because two moles of chlorine and four moles of sodium are consumed for each mole of metal produced; the process is said to have a poor atom economy. However, titanium is so useful as a material that the expense of the extraction process can be adsorbed.

The thirteen-step synthesis of vitamin A, by O. Isler et al (1947), shows a long and complex synthetic pathway:

O. Isler et al, Helv. Chima. Acta, 30, 1911(1947)

R. O. C. Norman, Principles of Organic Synthesis, Chapman and Hall, 1978, pp 711

The reason why the total synthesis of natural products is so tantalising to the cognoscenti is that Nature throws up some extraordinary structures, and the biosynthetic route –  if known – is usually little guide to developing a successful laboratory route.

And, of course, the beauty of the natural product is that there can be no doubt that the species really does exist, so lack of stability arguments cannot be used!

R.B.Woodward, the greatest synthetic chemist of the 20th century, was heard to say while his research group was attempting a particularly difficult synthesis "If we can't make strychnine, we'll take strychnine."

Or, as more put generally by the scientific philosopher, and advocate of Darwin, T.H. Huxley (1825-1895): "The great tragedy of science - the slaying of a beautiful hypothesis by an ugly fact"


The set of possible compounds is a broken terrain, and the individual species that occupy this space can act as stepping stones or way points, from which multi-step synthetic routes are constructed.

Within the broken terrain there will be compounds which in principle exist but which in practice cannot be made, however, this can never be proved.

This brings in some philosophy. Karl Popper introduced the idea of falsifiability in science, the notion that a scientific idea can only proved to be false, not true: "All crows are black because [insert your theory here]". Find one white crow, and the black crow theory is false.

Synthesis of unnatural target compounds turns this idea round because there are many ways not to make something. It follows that it is impossible to prove that a compound cannot be synthesized, only that it can.

Finding a synthetic route – a series of synthetic ladders – in reaction chemistry space that avoids all of the anti-synthetic snakes is very difficult, and in the 20th century target synthesis represented the pinnacle of chemical science. Will this continue in the 21st century?

Chemistry & Complexity: Summing Up

Chemistry is – and will remain – an experimental science because predictions can seldom be made from first principles due to the inherent complexity.

When predictions are made from theory they always need to be verified in the laboratory.

There is an excellent & recent RSC paper (2008) that discusses these matters:

R. Frederick Ludlow & Sijbren Otto
Systems Chemistry
Chem. Soc. Rev., 2008, 37, 101-108

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