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    RheologyRheology is the study of flow and deformation of materials under applied forces. The measurement of rheological properties is applicable to all materials from fluids such as dilute solutions of polymers andsurfactants through to concentrated protein formulations, to semi-solids such as pastes and creams, to

    molten or solid polymers. Rheological properties can be measured from bulk sample deformation usinga mechanical rheometer, or on a micro-scale by using a microcapillary viscometer or an opticaltechnique such as Microrheology.

    Many commonly-used materials and formulations exhibit complex rheological properties, whoseviscosity and viscoelasticity can vary depending upon the external conditions applied, such as stress,strain, timescale and temperature. Internal sample variations such as protein concentration andstability, and formulation type for biopharmaceuticals, are also key factors that determine rheologicalproperties.

    Rheological properties impact at all stages of material use across multiple industries from formulation

    development and stability to processing to product performance. Examples of rheologicalmeasurements include:

    Viscosity profiling for non-Newtonian shear-dependent behavior to simulate processing or useconditions.

    Viscoelastic fingerprinting for material classification to determine extent of solid-like or liquid-like behavior.

    Optimising dispersion stability. Determination of thixotropy of paints and coatings for product application and final finish


    Impact of molecular architecture of polymers on viscoelasticity for processing and end-useperformance.

    Benchmarking Food and Personal Care products for ability to pump or spread. Full cure profiling for bonding or gelling systems. Preformulation screening for therapeutics, particularly biopharmaceuticals. Concrete's and mortar's workability is related to the rheological properties of the fresh cement

    paste. The mechanical properties of hardened concrete increase if less water is used in theconcrete mix design, however reducing the water-to-cement ratio may decrease the ease of mixing and application. To avoid these undesired effects, superplasticizers are typically added todecrease the apparent yield stress and the viscosity of the fresh paste. Their addition highlyimproves concrete and mortar properties.

    Surface PropertiesA materials property is an intensive, often quantitative, property of a solid or quasi-solid. Quantitativeproperties may be used as a metric by which the benefits of one material versus another can beassessed, thereby aiding in materials selection.

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    A property may be a constant or may be a function of one or more independent variables, such astemperature. Materials properties often vary to some degree according to the direction in the materialin which they are measured, a condition referred to as anisotropy. Materials properties that relate twodifferent physical phenomena often behave linearly (or approximately so) in a given operating range,and may then be modeled as a constant for that range. This linearization can significantly simplify thedifferential constitutive equations that the property describes.

    Some materials properties are used in relevant equations to predict the attributes of a system a priori.For example, if a material of a known specific heat gains or loses a known amount of heat, thetemperature change of that material can be determined. Materials properties are most reliablymeasured by standardized test methods. Many such test methods have been documented by theirrespective user communities and published through ASTM International.

    1. Acoustical properties2. Atomic properties3. Chemical properties4. Electrical properties5. Environmental properties6. Magnetic properties7. Manufacturing properties8. Mechanical properties9. Optical properties10. Radiological properties11. Thermal properties

    Acoustical properties Acoustical absorption Speed of sound Atomic properties Atomic mass Atomic number - applies to pure elements only Atomic weight - applies to individual isotopes or specific mixtures of isotopes of a given


    Chemical properties Corrosion resistance Hygroscopy pH Reactivity Specific internal surface area Surface energy Surface tension

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    Electrical properties Dielectric constant Dielectric strength Electrical conductivity Permeability

    Permittivity Piezoelectric constants Seebeck coefficient

    Environmental properties Embodied energy Embodied water

    Magnetic properties Curie Point Diamagnetism Hysteresis Permeability

    Manufacturing properties Castability Extruding temperature and pressure Hardness Machinability rating

    Machining speeds and feeds

    Mechanical properties Compressive strength : Maximum stress a material can withstand before compressive failure

    (MPa) Ductility : Ability of a material to deform under tensile load (% elongation) Fatigue limit : Maximum stress a material can withstand under repeated loading (MPa) Flexural modulus Flexural strength

    Fracture toughness : Energy absorbed by unit area before the fracture of material (J/m^2) Hardness : Ability to withstand surface indentation (e.g. Brinell hardness number) Plasticity (physics) : Ability of a material to undergo irreversible deformations (-) Poisson's ratio : Ratio of lateral strain to axial strain (no units) Shear modulus : Ratio of shear stress to shear strain (MPa) Shear strain : Change in the angle between two perpendicular lines in a plane Shear strength : Maximum shear stress a material can withstand

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    Specific modulus : Modulus per unit volume (MPa/ m^3) Specific strength : Strength per unit density (Nm/kg) Specific weight : Weight per unit volume (N/m^3) Tensile strength : Maximum tensile stress a material can withstand before failure (MPa) Yield strength : The stress at which a material starts to yield (MPa) Young's modulus : Ratio of linear stress to linear strain (MPa) Coefficient of friction (also depends on surface finish) Coefficient of restitution Roughness

    Optical properties Absorptivity Color Luminosity Photosensitivity

    Reflectivity Refractive index Scattering Transmittance

    Radiological properties Neutron cross-section Specific activity

    Thermal properties Autoignition temperature Binary phase diagram Boiling point Coefficient of thermal expansion Critical temperature Curie point Emissivity Eutectic point Flammability

    Flash point Glass transition temperature Heat of fusion Heat of vaporization Inversion temperature Melting point Phase diagram

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    Pyrophoricity Solidus Specific heat Thermal conductivity Thermal diffusivity Thermal expansion Seebeck coefficient Triple point Vapor pressure Vicat softening point

    SurfactantsSurfactants are compounds that lower the surface tension between two liquids or between a liquid anda solid. Surfactants may act as detergents, wetting agents, emulsifiers, foaming agents, and dispersants.

    Etymology and definitionThe term surfactant/surfactants is a blend of surface active agents.

    In Index Medicus and the United States National Library of Medicine, surfactant/surfactants is reservedfor the meaning pulmonary surfactant. For the more general meaning, surface active agent/s is theheading.

    Composition and structureSurfactants are usually organic compounds that are amphiphilic, meaning they contain bothhydrophobic groups (their tails) and hydrophilic groups (their heads). Therefore, a surfactant containsboth a water insoluble (or oil soluble) component and a water soluble component. Surfactants willdiffuse in water and adsorb at interfaces between air and water or at the interface between oil andwater, in the case where water is mixed with oil. The insoluble hydrophobic group may extend out of the bulk water phase, into the air or into the oil phase, while the water soluble head group remains inthe water phase. This alignment of surfactants at the surface modifies the surface properties of water atthe water/air or water/oil interface.

    World production of surfactants is estimated at 15 Mton/y, of which about half are soaps. Othersurfactants produced on a particularly large scale are linear alkylbenzenesulfonates (1700 kton/y), ligninsulfonates (600 kton/y), fatty alcohol ethoxylates (700 ktons/y), and alkylphenol ethoxylates (500


    Structure of surfactant phases in waterIn the bulk aqueous phase, surfactants form aggregates, such as micelles, where the hydrophobic tailsform the core of the aggregate and the hydrophilic heads are in contact with the surrounding liquid.Other types of aggregates such as spherical or cylindrical micelles or bilayers can be formed. The shapeof the aggregates depends on the chemical structure of the surfactants, depending on the balance of the

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    sizes of the hydrophobic tail and hydrophilic head. This is known as the HLB, Hydrophilic-lipophilicbalance. Surfactants reduce the surface tension of water by adsorbing at the liquid-gas interface. Therelation that links the surface tension and the surface excess is known as the Gibbs isotherm.

    Dynamics of surfactants at interfacesThe dynamics of adsorption of surfactants is of great importance for practical applications such as

    foaming, emulsifying or coating processes, where bubbles or drops are rapidly generated and need to bestabilized. The dynamics of adsorption depends on the diffusion coefficient of the surfactants. Indeed, asthe interface is created, the adsorption is limited by the diffusion of the surfactants to the interface. Insome cases, there exists a barrier of energy for the adsorption or the desorption of the surfactants, thenthe adsorption dynamics is known as kinetically limited'. Such energy barrier can be due to steric orelectrostatic repulsions. The surface rheology of surfactant layers, including the elasticity and viscosityof the surfactant layers plays a very important role in foam or emulsion stability.

    Characterization of interfaces and surfactant layersInterfacial and surface tension can be characterized by classical methods such as the -pendant orspinning drop method. Dynamic surface tensions, i.e. surface tension as a function of time, can beobtained by the Maximum Bubble Pressure apparatus

    The structure of surfactant layers can be studied by ellipsometry or X-Ray reflectivity.

    Surface rheology can be characterized by the oscillating drop method or shear surface rheometers suchas double-cone, double-ring or magnetic rod shear surface rheometer.

    Detergents in biochemistry and biotechnologyIn solution, detergents help solubilize a variety of chemical species by dissociating aggregates and

    unfolding proteins. Popular surfactants in the biochemistry laboratory are SDS and CTAB. Detergents arekey reagents to extract protein by lysis of the cells and tissues: They disorganize the membrane's lipidicbilayer (SDS, Triton X-100, X-114, CHAPS, DOC, and NP-40), and solubilize proteins. Milder detergentssuch as (OctylThioGlucosides) are used to solubilize sensible proteins (enzymes, receptors). Non-solubilized material is harvested by centrifugation or other means. For electrophoresis, for example,proteins are classically treated with SDS to denature the native tertiary and quaternary structures,allowing the separation of proteins according to their molecular weight.

    Detergents have also been used to decellularise organs. This process maintains a matrix of proteins thatpreserves the structure of the organ and often the microvascular network. The process has beensuccessfully used to prepare organs such as the liver and heart for transplant in rats. Pulmonarysurfactants are also naturally secreted by type II cells of the lung alveoli in mammals.

    Classification of surfactantsThe "tail" of most surfactants are fairly similar, consisting of a hydrocarbon chain, which can be branch,linear, or aromatic. Fluorosurfactants have fluorocarbon chains. Siloxane surfactants have siloxanechains.

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    Many important surfactants include a polyether chain terminating in a highly polar anionic group. Thepolyether groups often comprise ethoxylated (polyethylene oxide-like) sequences inserted to increasethe hydrophilic character of a surfactant. Polypropylene oxides conversely, may be inserted to increasethe lipophilic character of a surfactant.

    Surfactant molecules have either one tail or two; those with two tails are said to be double-chained.

    Most commonly, surfactants are classified according to polar head group. A non-ionic surfactant has nocharge groups in its head. The head of an ionic surfactant carries a net charge. If the charge is negative,the surfactant is more specifically called anionic; if the charge is positive, it is called cationic. If asurfactant contains a head with two oppositely charged groups, it is termed zwitterionic. Commonlyencountered surfactants of each type include:

    AnionicSulfate, sulfonate, and phosphate estersAnionic surfactants contain anionic functional groups at their head, such as sulfate, sulfonate,

    phosphate, and carboxylates. Prominent alkyl sulfates include ammonium lauryl sulfate, sodium laurylsulfate (SDS, sodium dodecyl sulfate, another name for the compound) and the related alkyl-ethersulfates sodium laureth sulfate, also known as sodium lauryl ether sulfate (SLES), and sodium myrethsulfate.

    Docusates: dioctyl sodium sulfosuccinate, perfluorooctanesulfonate (PFOS), perfluorobutanesulfonate,linear alkylbenzene sulfonates (LABs).

    These include alkyl-aryl ether phosphates and the alkyl ether phosphate

    CarboxylatesThese are the most common surfactants and comprise the alkyl carboxylates (soaps), such as sodiumstearate. More specialized species include sodium lauroyl sarcosinate and carboxylate-basedfluorosurfactants such as perfluorononanoate, perfluorooctanoate (PFOA or PFO).

    Cationic head groupspH-dependent primary, secondary, or tertiary amines: Primary and secondary amines become positivelycharged at pH < 10:

    Octenidine dihydrochloride;

    Permanently charged quaternary ammonium cation: Alkyltrimethylammonium salts: cetyl trimethylammonium bromide (CTAB) a.k.a. hexadecyl

    trimethyl ammonium bromide, cetyl trimethylammonium chloride (CTAC) Cetylpyridinium chloride (CPC) Benzalkonium chloride (BAC) Benzethonium chloride (BZT)

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    5-Bromo-5-nitro-1,3-dioxane Dimethyldioctadecylammonium chloride Cetrimonium bromide Dioctadecyldimethylammonium bromide (DODAB)

    Zwitterionic surfactantsZwitterionic (amphoteric) surfactants have both cationic and anionic centers attached to the samemolecule. The cationic part is based on primary, secondary, or tertiary amines or quaternary ammoniumcations. The anionic part can be more variable and include sulfonates, as in CHAPS (3-[(3-Cholamidopropyl)dimethylammonio]-1-propanesulfonate). Other anionic groups are sultaines illustratedby cocamidopropyl hydroxysultaine. Betaines, e.g., cocamidopropyl betaine. Phosphates: lecithin

    Nonionic surfactant Many long chain alcohols exhibit some surfactant properties. Prominent among these are the fattyalcohols cetyl alcohol, stearyl alcohol, and cetostearyl alcohol (consisting predominantly of cetyl andstearyl alcohols), and oleyl alcohol.

    Polyoxyethylene glycol alkyl ethers (Brij): CH3 (CH2)10 16 (O-C2H4)1 25 OH:o Octaethylene glycol monododecyl ethero Pentaethylene glycol monododecyl ether

    Polyoxypropylene glycol alkyl ethers: CH3 (CH2)10 16 (O-C3H6)1 25 O Glucoside alkyl ethers: CH3 (CH2)10 16 (O-Glucoside)1 3 OH:

    o Decyl glucoside,o Lauryl glucosideo Octyl glucoside

    Polyoxyethylene glycol octylphenol ethers: C8H17 (C6H4) (O-C2H4)1 25 OH:o Triton X-100

    Polyoxyethylene glycol alkylphenol ethers: C9H19 (C6H4) (O-C2H4)1 25 OH:o Nonoxynol-9

    Glycerol alkyl esters:o Glyceryl laurate

    Polyoxyethylene glycol sorbitan alkyl esters: Polysorbate Sorbitan alkyl esters: Spans Cocamide MEA, cocamide DEA Dodecyldimethylamine oxide

    Block copolymers of polyethylene glycol and polypropylene glycol: Poloxamers Polyethoxylated tallow amine (POEA).

    According to the composition of their counter-ionIn the case of ionic surfactants, the counter-ion can be:

    Monoatomic / Inorganic:o Cations: metals : alkali metal, alkaline earth metal, transition metal

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    includes Emulsan produced by Acinetobacter calcoaceticus, Sophorolipids produced by several yeastsbelonging to candida and starmerella clade, and Rhamnolipid produced by Pseudomonas aeruginosaetc.

    Biosurfactants enhance the emulsification of hydrocarbons, have the potential to solubilise hydrocarboncontaminants and increase their availability for microbial degradation. The use of chemicals for the

    treatment of a hydrocarbon polluted site may contaminate the environment with their by-products,whereas biological treatment may efficiently destroy pollutants, while being biodegradable themselves.Hence, biosurfactant-producing microorganisms may play an important role in the acceleratedbioremediation of hydrocarbon-contaminated sites. These compounds can also be used in enhanced oilrecovery and may be considered for other potential applications in environmental protection. Otherapplications include herbicides and pesticides formulations, detergents, healthcare and cosmetics, pulpand paper, coal, textiles, ceramic processing and food industries, uranium ore-processing, andmechanical dewatering of peat.

    Several microorganisms are known to synthesise surface-active agents; most of them are bacteria andyeasts. When grown on hydrocarbon substrate as the carbon source, these microorganisms synthesise awide range of chemicals with surface activity, such as glycolipid, phospholipid, and others. Thesechemicals are synthesised to emulsify the hydrocarbon substrate and facilitate its transport into thecells. In some bacterial species such as Pseudomonas aeruginosa, biosurfactants are also involved in agroup motility behavior called swarming motility.

    Safety and environmental risksMost anionic and nonionic surfactants are nontoxic, having LD50 comparable to sodium chloride. Thesituation for cationic surfactants is more diverse. Dialkyldimethylammonium chlorides have very lowLD50's (5 g/kg) but alkylbenzyldimethylammonium chloride has an LD50 of 0.35 g/kg. Prolonged

    exposure of skin to surfactants can cause chaffing because surfactants (e.g., soap) disrupts the lipidcoating that protects skin (and other) cells.

    Biosurfactants and Deepwater HorizonThe use of biosurfactants as a way to remove petroleum from contaminated sites has been studied andfound to be safe and effective in the removal petroleum products from soil. Biosurfactants were notused by BP after the Deepwater Horizon oil spill. However, unprecedented amounts of Corexit (activeingredient: Tween-80), were sprayed directly into the ocean at the leak and on the sea-water's surface,the theory being that the surfactants isolate droplets of oil, making it easier for petroleum-consumingmicrobes to digest the oil.

    ApplicationsSurfactants play an important role as cleaning, wetting, dispersing, emulsifying, foaming and anti-foaming agents in many practical applications and products, including:

    Detergents Fabric softeners

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    liquids, conduction is due to the collisions and diffusion of molecules during their random motion.Photons in this context do not collide with one another, and so heat transport by electromagneticradiation is conceptually distinct from heat conduction by microscopic diffusion and collisions of material particles and phonons. In condensed matter, such as a solid or liquid, the distinction betweenconduction and radiative transfer of heat is clear in physical concept, but it is often notphenomenologically clear, unless the material is semi-transparent. In a gas the distinction is both

    conceptually and phenomenologically clear.

    In the engineering sciences, heat transfer includes the processes of thermal radiation, convection, andsometimes mass transfer. Usually more than one of these processes occurs in a given situation. Theconventional symbol for the material property, thermal conductivity, is .

    OverviewOn a microscopic scale, conduction occurs within a body considered as being stationary; this means thatthe kinetic and potential energies of the bulk motion of the body are separately accounted for. Internalenergy diffuses as rapidly moving or vibrating atoms and molecules interact with neighboring particles,

    transferring some of their microscopic kinetic and potential energies, these quantities being definedrelative to the bulk of the body considered as being stationary. Heat is transferred by conduction whenadjacent atoms or molecules collide, or as several electrons move backwards and forwards from atom toatom in a disorganized way so as not to form a macroscopic electric current, or as phonons collide andscatter. Conduction is the most significant means of heat transfer within a solid or between solid objectsin thermal contact. Conduction is greater in solids because the network of relatively close fixed spatialrelationships between atoms helps to transfer energy between them by vibration.

    Fluids (and especially gases) are less conductive. This is due to the large distance between atoms in agas: fewer collisions between atoms means less conduction. Conductivity of gases increases with

    temperature. Conductivity increases with increasing pressure from vacuum up to a critical point that thedensity of the gas is such that molecules of the gas may be expected to collide with each other beforethey transfer heat from one surface to another. After this point conductivity increases only slightly withincreasing pressure and density.

    Thermal contact conductance is the study of heat conduction between solid bodies in contact. Atemperature drop is often observed at the interface between the two surfaces in contact. Thisphenomenon is said to be a result of a thermal contact resistance existing between the contactingsurfaces. Interfacial thermal resistance is a measure of an interface's resistance to thermal flow. Thisthermal resistance differs from contact resistance, as it exists even at atomically perfect interfaces.Understanding the thermal resistance at the interface between two materials is of primary significancein the study of its thermal properties. Interfaces often contribute significantly to the observed propertiesof the materials.

    The inter-molecular transfer of energy could be primarily by elastic impact as in fluids or by free electrondiffusion as in metals or phonon vibration as in insulators. In insulators the heat flux is carried almostentirely by phonon vibrations.

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    Metals (e.g. copper, platinum, gold,etc.) are usually good conductors of thermal energy. This is due tothe way that metals are chemically bonded: metallic bonds (as opposed to covalent or ionic bonds) havefree-moving electrons which are able to transfer thermal energy rapidly through the metal. The"electron fluid" of a conductive metallic solid conducts most of the heat flux through the solid. Phononflux is still present, but carries less of the energy. Electrons also conduct electric current throughconductive solids, and the thermal and electrical conductivities of most metals have about the same

    ratio. A good electrical conductor, such as copper, also conducts heat well. Thermoelectricity is causedby the interaction of heat flux and electrical current. Heat conduction within a solid is directly analogousto diffusion of particles within a fluid, in the situation where there are no fluid currents.

    To quantify the ease with which a particular medium conducts, engineers employ the thermalconductivity, also known as the conductivity constant or conduction coefficient, k. In thermalconductivity k is defined as "the quantity of heat, Q, transmitted in time (t) through a thickness (L), in adirection normal to a s urface of area (A), due to a temperature difference (T) *...+." Thermalconductivity is a material property that is primarily dependent on the medium's phase, temperature,density, and molecular bonding. Thermal effusivity is a quantity derived from conductivity which is a

    measure of its ability to exchange thermal energy with its surroundings.

    Steady-state conductionSteady state conduction is the form of conduction that happens when the temperature difference(s)driving the conduction are constant, so that (after an equilibration time), the spatial distribution of temperatures (temperature field) in the conducting object does not change any further. Thus, all partialderivatives of temperature with respect to space may either be zero or have nonzero values, but allderivatives of temperature at any point with respect to time are uniformly zero. In steady stateconduction, the amount of heat entering any region of an object is equal to amount of heat coming out(if this were not so, the temperature would be rising or falling, as thermal energy was tapped or trapped

    in a region).

    For example, a bar may be cold at one end and hot at the other, but after a state of steady stateconduction is reached, the spatial gradient of temperatures along the bar does not change any further,as time proceeds. Instead, the temperature at any given section of the rod remains constant, and thistemperature varies linearly in space, along the direction of heat transfer.

    In steady state conduction, all the laws of direct current electrical conduction can be applied to "heatcurrents". In such cases, it is possible to take "thermal resistances" as the analog to electricalresistances. In such cases, temperature plays the role of voltage, and heat transferred per unit time(heat power) is the analog of electrical current. Steady state systems can be modelled by networks of such thermal resistances in series and in parallel, in exact analogy to electrical networks of resistors. Seepurely resistive thermal circuits for an example of such a network.

    Transient conductionIn general, during any period in which temperatures are changing in time at any place within an object,the mode of thermal energy flow is termed transient conduction. Another term is "non steady-state"conduction, referring to time-dependence of temperature fields in an object. Non-steady-state

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    situations appear after an imposed change in temperature at a boundary of an object. They may alsooccur with temperature changes inside an object, as a result of a new source or sink of heat suddenlyintroduced within an object, causing temperatures near the source or sink to change in time.

    When a new perturbation of temperature of this type happens, temperatures within the system willchange in time toward a new equilibrium with the new conditions, provided that these do not change.

    After equilibrium, heat flow into the system will once again equal the heat flow out, and temperaturesat each point inside the system no longer change. Once this happens, transient conduction is ended,although steady-state conduction may continue if there continues to be heat flow.

    If changes in external temperatures or internal heat generation changes are too rapid for equilibrium of temperatures in space to take place, then the system never reaches a state of unchanging temperaturedistribution in time, and the system remains in a transient state.

    An example of a new source of heat "turning on" within an object which causes transient conduction, isan engine starting in an automobile. In this case the transient thermal conduction phase for the entiremachine would be over, and the steady state phase would appear, as soon as the engine had reached

    steady-state operating temperature. In this state of steady-state equilibrium, temperatures would varygreatly from the engine cylinders to other parts of the automobile, but at no point in space within theautomobile would temperature be increasing or decreasing. After establishment of this state, thetransient conduction phase of heat transfer would be over.

    New external conditions also cause this process: for example the copper bar in the example steady-stateconduction would experience transient conduction as soon as one end was subjected to a differenttemperature from the other. Over time, the field of temperatures inside the bar would reach a newsteady-state, in which a constant temperature gradient along the bar will finally be set up, and thisgradient would then stay constant in space. Typically, such a new steady state gradient is approached

    exponentially with time after a new temperature-or-heat source or sink, has been introduced. When a"transient conduction" phase is over, heat flow may still continue at high power, so long astemperatures do not change.

    An example of transient conduction which does not end with steady-state conduction, but rather noconduction, occurs when a hot copper ball is dropped into oil at a low temperature. Here thetemperature field within the object begins to change as a function of time, as the heat is removed fromthe metal, and the interest lies in analyzing this spatial change of temperature within the object overtime, until all gradients disappear entirely (the ball has reached the same temperature as the oil).Mathematically, this condition is also approached exponentially; in theory it takes infinite time, but inpractice it is over, for all intents and purposes, in a much shorter period. At the end of this process withno heat sink but the internal parts of the ball (which are finite), there is no steady state heat conductionto be reached. Such a state never occurs in this situation, but rather the end of the process is whenthere is no heat conduction at all.

    Analysis of non steady-state conduction systems is more complex than steady-state systems, and(except for simple shapes) calls for the application of approximation theories, and/or numerical analysisby computer. One popular graphical method involves the use of Heisler Charts.

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    Occasionally transient conduction problems may be considerably simplified if regions of the object beingheated or cooled can be identified, in which thermal conductivity is very much greater than that for heatpaths leading into the region. In this case, the region with high conductivity can often be treated in thelumped capacitance model, as a "lump" of material with a simple thermal capacitance consisting of itsaggregate heat capacity. Such regions show no temperature variation across their extent duringwarming or cooling (as compared to the rest of the system) due to their far higher conductance. During

    transient conduction, therefore, their temperature changes uniformly in space, and as a simpleexponential in time. An example of such systems are those which follow "Newton's law of cooling"during transient cooling (or the reverse during heating). The equivalent thermal circuit consists of asimple capacitor in series with a resistor. In such cases, the remainder of the system with high thermalresistance (comparatively low conductivity) plays the role of the resistor in the circuit.

    Relativistic conductionThe theory of relativistic heat conduction is a model that is compatible with the theory of specialrelativity. For most of the last century, it was recognized that Fourier equation is in contradiction withthe theory of relativity because it admits an infinite speed of propagation of heat signals. For example,

    according to Fourier equation, a pulse of heat at the origin would be felt at infinity instantaneously. Thespeed of information propagation is faster than the speed of light in vacuum, which is physicallyinadmissible within the framework of relativity. Alterations to the Fourier model provided for arelativistic model of heat conduction, avoiding this problem.

    Quantum conductionSecond sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion,rather than by the more usual mechanism of diffusion. Heat takes the place of pressure in normal soundwaves. This leads to a very high thermal conductivity. It is known as "second sound" because the wavemotion of heat is similar to the propagation of sound in air.

    Fourier's lawThe law of heat conduction, also known as Fourier's law, states that the time rate of heat transferthrough a material is proportional to the negative gradient in the temperature and to the area, at rightangles to that gradient, through which the heat is flowing. We can state this law in two equivalentforms: the integral form, in which we look at the amount of energy flowing into or out of a body as awhole, and the differential form, in which we look at the flow rates or fluxes of energy locally.

    Newton's law of cooling is a discrete analog of Fourier's law, while Ohm's law is the electrical analogueof Fourier's law.

    Differential formThe differential form of Fourier's Law of thermal conduction shows that the local heat flux density, ,is equal to the product of thermal conductivity, , and the negative local temperature gradient,. The heat flux density is the amount of energy that flows through a unit area per unit time.

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    where (including the SI units)

    is the local heat flux, W m2

    is the material's conductivity, W m1 K1,

    is the temperature gradient, K m1.

    The thermal conductivity, , is often treated as a constant, though this is not always true. While thethermal conductivity of a material generally varies with temperature, the variation can be small over asignificant range of temperatures for some common materials. In anisotropic materials, the thermalconductivity typically varies with orientation; in this case is represented by a second-order tensor. Innon-uniform materials, varies with spatial location.

    For many simple applications, Fourier's law is used in its one-dimensional form. In the x-direction,

    Integral formBy integrating the differential form over the material's total surface , we arrive at the integral form of Fourier's law:

    where (including the SI units)

    : is the amount of heat transferred per unit time (in W) and

    : is an oriented surface area element (in m2)

    The above differential equation, when integrated for a homogeneous material of 1-D geometry betweentwo endpoints at constant temperature, gives the heat flow rate as:

    Where A is the cross-sectional surface area,

    is the temperature difference between the ends,

    is the distance between the ends.

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    From the electrical formula: , where is resistivity, x is length, and A is cross -sectional

    area, we have , where G is conductance, k is conductivity, x is length, and A is cross-sectional area.

    For Heat,

    where U is the conductance.

    Fourier's law can also be stated as:

    analogous to Ohm's law: or

    The reciprocal of conductance is resistance, R, given by:

    analogous to Ohm's law:

    The rules for combining resistances and conductances (in series and in parallel) are the same for bothheat flow and electric current.

    Cylindrical shellsConduction through cylindrical shells (e.g. pipes) can be calculated from the internal radius, , theexternal radius, , the length, , and the temperature difference between the inner and outer

    wall, .

    The surface area of the cylinder is

    When Fo uriers equation is applied:

    and rearranged:

    then the rate of heat transfer is:

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    the thermal resistance is:

    and , where . It is important to note that this is thelog-mean radius.

    SphericalThe conduction through a spherical shell with internal radius, , and external radius, , can becalculated in a similar manner as for a cylindrical shell.

    The surface area of the sphere is:

    Solving in a similar manner as for a cylindrical shell (see above)


    Transient Thermal ConductionInterface Heat TransferThe heat transfer at an interface is considered a transient heat flow. To analyze this problem, the Biotnumber is important to understand how the system will behave. The Biot number is determined

    by: The heat transfer coefficient, h, is introduced in this formula, and is measured

    in . If the system has a Biot number of less than 0.1, the material behaves according toNewtonian cooling, i.e. with negligible temperature gradient within the body. If the Biot number isgreater than 0.1, the system will behave as a series solution. The temperature profile in terms of timecan be determined by the function can be derived from the equation:

    Which will become:

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    The heat transfer coefficient, h, is measured in , and represents the transfer of heat at aninterface between two materials. This value is different at every interface, and is an important conceptin understanding heat flow at an interface.

    The Series Solution can be analyzed with a nomogram. A nomogram has relative temperature as the y

    coordinate and the Fourier number, which is calculated by: The Biot number increases asthe Fourier number decreases. There are 5 steps to determine a temperature profile in terms of time.

    Step 1. Calculate the Biot numberStep 2. Determine which relative depth matters, either x or L.Step 3. Convert time to the Fourier number.Step 4. Convert to relative temperature with the boundary conditions.Step 5. Compared required point to trace specified Biot number on the nomogram.

    Thermal Conduction ApplicationsSplat CoolingSplat cooling is a method for quenching small droplets of molten materials by rapid contact with a coldsurface. The particles undergo a characteristic cooling process, with the heat profile at for initialtemperature as the maximum at and at and , and the heat

    profile at for as the boundary conditions. Splat cooling rapidly ends in asteady state temperature, and is similar in form to the Gaussian diffusion equation. The temperatureprofile, with respect to the position and time of this type of cooling, varies with:

    Splat cooling is a fundamental concept that has been adapted for practical use in the form of thermal

    spraying. The thermal diffusivity coefficient, represented as alpha, can be written as . Thisvaries according to the material.

    ColloidsA colloid is one of the three main types of mixtures, with the other two being a solution or suspension. Acolloid is a solution that has particles ranging between 1 and 1000 nanometers in diameter, yet is stillable to remain evenly distributed throughout the solution. These are also known as colloidal dispersionsbecause the substances remain dispersed and don't settle to the bottom. In a colloid one substance isevenly dispersed in another. The substance being dispersed is referred to as being in the dispersedphase, while the substance in which it is dispersed is in the continuous phase.

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    Classifying ColloidsAn easy way of determining whether a mixture is colloidal or not is through use of the Tyndall Effect.When light is shined through a true solution, the light passes cleanly through the solution, howeverwhen light is passed through a colloidal solution, the substance in the dispersed phases scatters the lightin all directions, making it readily seen. An example of this is shining a flashlight into fog. The beam of light can be easily seen because the fog is a colloid.

    Light being shined through water and milk. The light is not reflected when passing through the waterbecause it is not a colloid. It is however reflected in all directions when it passes through the milk, whichis colloidal.

    Another method of determining whether a mixture is a colloid is by passing it through a semipermeablemembrane. The dispersed particles in a colloid would be unable to pass through the membrane. Dialysistakes advantage of the fact that colloids cannot diffuse through semipermeable membranes to filter

    them out of a

    Practice ProblemsQ 1) Is dust a colloid? If so, what type is it?Q 2) Is whipped cream a colloid? if so, what type is it?Q 3) What does Sol mean?Q 4) When hit by light what happens to a colloidal mixture?Q 5) What is the mixture considered if the particles are larger than the particles of a colloidalsubstance

    AnswersA 1) Dust is a colloid. It consists of a solid in a gas, so it is a aerosol.A 2) Whipped cream is a colloid. It consists of a gas in a liquid, so it is a foam.A 3) Sol is a colloidal suspension with solid particles in a liquid.A 4) The light is reflected off the large particles and spread out.A 5) It's considered a suspension if the particles are larger than 1000 nanometers.

    Work Hardening or Strain HardeningWork hardening, also known as strain hardening or cold working, is the strengthening of a metal byplastic deformation. This strengthening occurs because of dislocation movements and dislocationgeneration within the crystal structure of the material. Many non-brittle metals with a reasonably highmelting point as well as several polymers can be strengthened in this fashion. Alloys not amenable toheat treatment, including low-carbon steel, are often work-hardened. Some materials cannot be work-hardened at normal ambient temperatures, such as indium,however others can only be strengthenedvia work hardening, such as pure copper and aluminum.

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    TheoryBefore work hardening, the lattice of the material exhibits a regular, nearly defect-free pattern (almostno dislocations). The defect-free lattice can be created or restored at any time by annealing. As thematerial is work hardened it becomes increasingly saturated with new dislocations, and moredislocations are prevented from nucleating (a resistance to dislocation-formation develops). Thisresistance to dislocation-formation manifests itself as a resistance to plastic deformation; hence, theobserved strengthening.

    In metallic crystals, irreversible deformation is usually carried out on a microscopic scale by defectscalled dislocations, which are created by fluctuations in local stress fields within the material culminatingin a lattice rearrangement as the dislocations propagate through the lattice. At normal temperatures thedislocations are not annihilated by annealing. Instead, the dislocations accumulate, interact with oneanother, and serve as pinning points or obstacles that significantly impede their motion. This leads to anincrease in the yield strength of the material and a subsequent decrease in ductility.

    Such deformation increases the concentration of dislocations which may subsequently form low-angle

    grain boundaries surrounding sub-grains. Cold working generally results in a higher yield strength as aresult of the increased number of dislocations and the Hall-Petch effect of the sub-grains, and adecrease in ductility. The effects of cold working may be reversed by annealing the material at hightemperatures where recovery and recrystallization reduce the dislocation density.

    A material's work hardenability can be predicted by analyzing a stress-strain curve, or studied in contextby performing hardness tests before and after a process

    Hollomon's equation is a power law relationship between the stress and the amount of plastic strain:

    where is the stress, K is the strength index, p is the plastic strain and n is the strain hardening


    Advantages and Disadvantages

    Advantages No heating required Better surface finish Superior dimensional control Better reproducibility and interchangeability Directional properties can be imparted into the metal

    Contamination problems are minimized

    Disadvantages Greater forces are required Heavier and more powerful equipment and stronger tooling are required Metal is less ductile Metal surfaces must be clean and scale-free

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    Intermediate anneals may be required to compensate for loss of ductility that accompaniesstrain hardening

    The imparted directional properties may be detrimental Undesirable residual stress may be produced

    CapillarityThe phenomenon in which water rises above the ground water table against the pull of gravity, but is incontact with the water table as its source, is referred to as Capillary rise with reference to soils. Thewater associated with capillary rise is called capillary moisture. The phenomenon by virtue of w hich aliquid rises in capillary tubes is, in general, called Capillarity.

    Capillary action can be defined as the ascension of liquids through slim tube, cylinder or permeablesubstance due to adhesive and cohesive forces interacting between the liquid and the surface. Whenintermolecular bonding of a liquid itself is substantially inferior to a substances surface it is interacting,capillarity occurs. Also, the diameter of the container as well as the gravitational forces will determineamount of liquid raised. While, water possesses this unique property, a liquid like mercury will notdisplay the same attributes due to the fact that it has higher cohesive force than adhesive force.

    Forces in Capillary ActionThree main variables that determine whether a liquid possesses capillary action are:

    Cohesive force: It is the intermolecular bonding of a substance where its mutual attractivenessforces them to maintain a certain shape of the liquid.

    Surface tension: This occurs as a result of like molecules, cohesive forces, banding together toform a somewhat impenetrable surface on the body of water. The surface tension is measuredin Newton/meter.

    Adhesive force : When forces of attraction between unlike molecules occur, it is called adhesiveforces.

    Capillary action only occurs when the adhesive forces are stronger than the cohesive forces, whichinvariably becomes surface tension, in the liquid.

    A good way to remember the difference between adhesive and cohesive forces is that with adhesiveforces you add another set of molecules, the molecules of the surface, for the liquid to bond with. Withcohesive forces, the molecules of the liquid will only cooperate with their own kind. Decreased surfacetension also increases capillary action. This is because decreased surface tension means that the

    intermolecular forces are decreased, thus decreasing cohesive forces. As a result, capillary action will beeven greater.

    Applications:Practical use of capillary action is evident in all forms of our daily lives. It makes performing our tasksefficiently and effectively. Some applications of this unique property include:

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    The fundamental properties are used to absorb water by using paper towels. The cohesive andadhesive properties draw the fluid into the paper towel. The liquid flows into the paper towel ata certain rate.

    A technique called thin layer chromatography uses capillary action in which a layer of liquid isused to separate mixtures from substances.

    Capillary action helps us naturally by pumping out tear fluid in the eye. This process cleanses the

    eye and clears all of the dust and particles that are around the ducts of the eye. To generate energy: A possible use for capillary action is as a source of renewable energy. By

    allowing water to climb through capillaries, evaporate once it reaches the top, the condensateand drop back down to the bottom spinning a turbine on its way to create the energy, capillaryaction can make electricity! Although this idea is still in the works, it goes to show the potentialthat capillary action holds and how important it is.

    Formula and MathematicsFormula for the Height of a Meniscus

    When measuring the level of liquid of a test tube or buret, it is imperative to measure at the meniscusline for an accurate reading. It is possible to measure the height (represented by h) of a test tube, buret,or other liquid column using the formula:

    In this formula, represents the surface tension in a liquid -air environment, is the angle of contact orthe degree o f contact, is the density of the liquid in the representative column, g is the accelerationdue to the force of gravity and r is the radius of the tube in which the liquid is presented in. At optimum

    level, in which a glass tube filled with water is present in air, this formula can determine the height of aspecific column of water in meters (m):

    However, the following conditions must be met for this formula to occur.

    = 0.0728 N/m (when water is at a temperature of 20C) = 20

    is 1000 kg/m3 g= 9.8 m/s2

    Formula for Volume of Liquid Transport in Medium:When certain objects that are porous encounter a liquid medium, it will begin to absorb the liquid at arate which actually decreases over a period of time. This formula is written as:

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    In this specific formula, A is the wet area (cross-section), S is the sorptivity (capacity of medium toabsorb using the process of capillary action), V is the volume of liquid absorbed in time, t.

    Rise of Water in Capillary Tubes

    This equation helps one in computing the capillary rise of water in a glass capillary tube.

    Conceptual and Mathematical QuizQ 1) Name one way to increase capillary action, and one way to decrease it.Q 2) If cohesion is greater than adhesion, will the meniscus be convex or concave?Q 3) What would be the height of a liquid in a column, on earth, with a liquid-air surface tension 0f

    .0973 N/m, contact angle of 30 degrees, density of 1200 kg/m3? Note that the radius of thetube is 0.2 meters.

    Q 4) What would be the height of water in a glass tube with a radius of .6mm?

    Answers to QuizA 1) Increase capillary action: Increase temperature, decrease capillary tube diameter, perform any

    number of actions to decrease surface tension, etc! Decrease capillary action: Th e opposite of the steps you would take to increase, also, increasing the density of the liquid you're workingwith.

    A 2) The meniscus will result in a convex formation.

    A 3) Using the formula above, the height of the liquid will be 7.165* 10-5m high.A 4) Using the formula above, the height of the water in the glass tube would be .014m high.

    Workout in CapillarityQ 1) To what height would water rise in a glass capillary tube of 0.01 mm diameter? What is the

    water pressure just under the meniscus in the capillary tube?Q 2) The D10 size of a soil is 0.01 mm. Assuming (1/5) D10 as the pore size, estimate the height of

    capillary rise assuming surface tension of water as 75 dynes/cm.Q 3) The effective sizes of two soils are 0.05 mm and 0.10 mm, the void ratio being the same for

    both. If the capillary rise in the first soil is 72 cm, what would be the capillary rise in the second


    Atomic BondingAtomic bonding is chemical bonding. Chemical bonding is the physical process that is responsible for theinteractions between atoms and molecules. Bonds vary widely. There are covalent, ionic, hydrogen,metallic, as well as many other types of bonds, and all have a working connection in all living things.

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    In the simplest view of a so -called 'covalent' bond, one or more electrons (often a pair of electrons) aredrawn into the space between the two atomic nuclei. Here the negatively charged electrons areattracted to the positive charges of both nuclei, instead of just their own. This overcomes the repulsionbetween the two positively charged nuclei of the two atoms, and so this overwhelming attraction holdsthe two nuclei in a fixed configuration of equilibrium, even though they will still vibrate at equilibriumposition. Thus, covalent bonding involves sharing of electrons in which the positively charged nuclei of

    two or more atoms simultaneously attract the negatively charged electrons that are being sharedbetween them. These bonds exist between two particular identifiable atoms, and have a direction inspace, allowing them to be shown as single connecting lines between atoms in drawings, or modeled assticks between spheres in models. In a polar covalent bond, one or more electrons are unequally sharedbetween two nuclei. Covalent bonds often result in the formation of small collections of better -

    connected atoms called molecules, which in solids and liquids are bound to other molecules by forcesthat are often much weaker than the covalent bonds that hold the molecules internally together. Suchweak intermolecular bonds give organic molecular substances, such as waxes and oils, their soft bulkcharacter, and their low melting points (in liquids, molecules must cease most structured or orientedcontact with each other). When covalent bonds link long chains of atoms in large molecules, however

    (as in polymers such as nylon), or when covalent bonds extend in networks though solids that are notcomposed of discrete molecules (such as diamond or quartz or the silicate minerals in many types of rock) then the structures that result may be both strong and tough, at least in the direction orientedcorrectly with networks of covalent bonds. Also, the melting points of such covalent polymers andnetworks increase greatly.

    In a simplified view of an ionic bond, the bonding electron is not shared at all, but transferred. In thistype of bond, the outer atomic orbital of one atom has a vacancy which allows addition of one or moreelectrons. These newly added electrons potentially occupy a lower energy -state (effectively closer tomore nuclear charge) than they experience in a different atom. Thus, one nucleus offers a more tightly

    bound position to an electron than does another nucleus, with the result that one atom may transfer anelectron to the other. This transfer causes one atom to assume a net positive charge, and the other toassume a net negative charge. The bond then results from electrostatic attraction between atoms, andthe atoms become positive or negatively charged ions. Ionic bonds may be seen as extreme examples of polarization in covalent bonds. Often, such bonds have no particular orientation in space, since theyresult from equal electrostatic attraction of each ion to all ions around them. Ionic bonds are strong (andthus ionic substances require high temperatures to melt) but also brittle, since the forces between ionsare short -range, and do not easily bridge cracks and fractures. This type of bond gives rise to the physicalcharacteristics of crystals of classic mineral salts, such as table salt.

    A less often mentioned type of bonding is the metallic bond. In this type of bonding, each atom in ametal donates one or more electrons to a "sea" of electrons that reside between many metal atoms. Inthis sea, each electron is free (by virtue of its wave nature) to be associated with a great many atoms atonce. The bond results because the metal atoms become somewhat positively charged due to loss of their electrons, while the electrons remain attracted to many atoms, without being part of any givenatom. Metallic bonding may be seen as an extreme example of de -localization of electrons over a largesystem of covalent bonds, in which every atom participates. This type of bonding is often very strong

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    (resulting in the tensile strength of metals). However, metallic bonds are more collective in nature thanother types, and so they allow metal crystals to more easily deform, because they are composed of atoms attracted to each other, but not in any particularly -oriented ways. This results in the malleabilityof metals. The sea of electrons in metallic bonds causes the characteristically good electrical andthermal conductivity of metals, and also their "shiny" reflection of most frequencies of white light.

    All bonds can be explained by quantum theory, but, in practice, simplification rules allow chemists topredict the strength, directionality, and polarity of bonds. The octet rule and VSEPR theory are twoexamples. More sophisticated theories are valence bond theory which includes orbital hybridization andresonance, and the linear combination of atomic orbitals molecular orbital method which includesligand field theory. Electrostatics is used to describe bond polarities and the effects they have onchemical substances.

    Valence bond theoryIn 1927, valence bond theory was formulated and it argues that a chemical bond forms when twovalence electrons, in their respective atomic orbitals, work or function to hold two nuclei together, by

    virtue of effects of lowering system energies. Building on this theory, the chemist Linus Paulingpublished in 1931 what some consider one of the most important papers in the history of chemistry:"On the Nature of the Chemical Bond". In this paper, elaborating on the works of Lewis, and the valencebond theory (VB) of Heitler and London, and his own earlier works, Pauling presented six rules for theshared electron bond, the first three of which were already generally known:

    1. The electron -pair bond forms through the interaction of an unpaired electron on each of twoatoms.

    2. The spins of the electrons have to be opposed.3. Once paired, the two electrons cannot take part in additional bonds.

    His last three rules were new:

    4. The electron -exchange term for the bond involves only one wave function from each atom.5. The available electrons in the lowest energy level form the strongest bonds.6. Of two orbitals in an atom, the one that can overlap the most with an orbital from another atom

    will form the strongest bond, and this bond will tend to lie in the direction of the concentratedorbital.

    Building on this article, Pauling's 1939 textbook: On the Nature of the Chemical Bond would becomewhat some have called the "Bible" of modern chemistry. This book helped experimental chemists to

    understand the impact of quantum theory on chemistry. However, the later edition in 1959 failed toadequately address the problems that appeared to be better understood by molecular orbital theory.The impact of valence theory declined during the 1960s and 1970s as molecular orbital theory grew inusefulness as it was implemented in large digital computer programs. Since the 1980s, the more difficultproblems of implementing valence bond theory into computer programs have been solved largely, andvalence bond theory has seen resurgence.

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    Comparison of valence bond and molecular orbital theoryIn some respects valence bond theory is superior to molecular orbital theory. When applied to thesimplest two-electron molecule, H 2, valence bond theory, even at the simplest Heitler -London approach,gives a much closer approximation to the bond energy, and it provides a much more accuraterepresentation of the behavior of the electrons as chemical bonds are formed and broken. In contrastsimple molecular orbital theory predicts that the hydrogen molecule dissociates into a linearsuperposition of hydrogen atoms and positive and negative hydrogen ions, a completely unphysicalresult. This explains in part why the curve of total energy against interatomic distance for the valencebond method lies below the curve for the molecular orbital method at all distances and mostparticularly so for large distances. This situation arises for all homonuclear diatomic molecules and isparticularly a problem for F2, where the minimum energy of the curve with molecular orbital theory isstill higher in energy than the energy of two F atoms.

    The concepts of hybridization are so versatile, and the variability in bonding in most organic compoundsis so modest, that valence bond theory remains an integral part of the vocabulary of organic chemistry.However, the work of Friedrich Hund, Robert Mulliken, and Gerhard Herzberg showed that molecular

    orbital theory provided a more appropriate description of the spectroscopic, ionization and magneticproperties of molecules. The deficiencies of valence bond theory became apparent when hypervalentmolecules (e.g. PF 5) were explained without the use of d orbitals that were crucial to the bondinghybridisation scheme proposed for such molecules by Pauling. Metal complexes and electron deficientcompounds (e.g. diborane) also appeared to be well described by molecular orbital theory, althoughvalence bond descriptions have been made.

    In the 1930s the two methods strongly competed until it was realised that they are both approximationsto a better theory. If we take the simple valence bond structure and mix in all possible covalent andionic structures arising from a particular set of atomic orbitals, we reach what is called the full

    configuration interaction wave function. If we take the simple molecular orbital description of theground state and combine that function with the functions describing all possible excited states usingunoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configurationinteraction wavefunction. It can be then seen that the simple molecular orbital approach gives too muchweight to the ionic structures, while the simple valence bond approach gives too little. This can also bedescribed as saying that the molecular orbital approach is too delocalised, while the valence bondapproach is too localised.

    The two approaches are now regarded as complementary, each providing its own insights into theproblem of chemical bonding. Modern calculations in quantum chemistry usually start from (but

    ultimately go far beyond) a molecular orbital rather than a valence bond approach, not because of anyintrinsic superiority in the former but rather because the MO approach is more readily adapted tonumerical computations. However better valence bond programs are now available.

    Bonds in chemical formulasThe fact that atoms and molecules are three -dimensional makes it difficult to use a single technique forindicating orbitals and bonds. In molecular formulas the chemical bonds (binding orbitals) between

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    atoms are indicated by various methods according to the type of discussion. Sometimes, they arecompletely neglected. For example, in organic chemistry chemists are sometimes concerned only withthe functional groups of the molecule. Thus, the molecular formula of ethanol may be written in a paperin conformational, three-dimensional, full two-dimensional (indicating every bond with no three-dimensional directions), compressed two -dimensional (CH 3 CH2 OH), separating the functional groupfrom another part of the molecule (C 2H5OH), or by its atomic constituents (C 2H6O), according to what is

    discussed. Sometimes, even the non -bonding valence shell electrons (with the two -dimensionalapproximate directions) are marked, i.e. for elemental carbon .'C'. Some chemists may also mark therespective orbitals, i.e. the hypothetical ethene 4 anion (\

    /C=C/\ 4) indicating the possibility of bond


    Strong chemical bondsStrong chemical bonds are the intramolecular forces which hold atoms together in molecules. A strongchemical bond is formed from the transfer or sharing of electrons between atomic centers and relies onthe electrostatic attraction between the protons in nuclei and the electrons in the orbitals. Althoughthese bonds typically involve the transfer of integer numbers of electrons (this is the bond order, which

    represents one transferred electron or two shared electrons), some systems can have intermediatenumbers of bonds. An example of this is the organic molecule benzene, where the bond order is 1.5 foreach carbon atom, meaning that it has 1.5 bonds (shares three electrons) with each one of its twoneighbors.

    The types of strong bond differ due to the difference in electro negativity of the constituent elements. Alarge difference in electro negativity leads to more polar (ionic) character in the bond.

    Metallic BondMetallic bonds are a metal, and share outer bonds with atoms in a solid. Each atom gives off a positive

    charge by shedding its outer electrons, and the negatively charges electrons hold the metal atomstogether.

    In a metallic bond, bonding electrons are delocalized over a lattice of atoms. By contrast, in ioniccompounds, the locations of the binding electrons and their charges are static. The freely-moving ordelocalization of bonding electrons leads to classical metallic properties such as luster (surface lightreflectivity), electrical and thermal conductivity, ductility, and high tensile strength.

    Ionic BondAtoms are filled with an outer shell of electrons. Electron shells are filled by transferring electrons fromone atom to the next. Donor atoms will take on a positive charge, and the acceptors will have a negativecharge. They will attract each other by being positive and negative, and bonding will then occur.

    Ionic bonding is a type of electrostatic interaction between atoms which have a large electronegativitydifference. There is no precise value that distinguishes ionic from covalent bonding, but a difference of electronegativity of over 1.7 is likely to be ionic, and a difference of less than 1.7 is likely to be covalent.Ionic bonding leads to sepa rate positive and negative ions. Ionic charges are commonly between 3e to+3e. Ionic bonding commonly occurs in metal salts such as sodium chloride (table salt). A typical feature

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    of ionic bonds is that the species form into ionic crystals, in which no ion is specifically paired with anysingle other ion, in a specific directional bond. Rather, each species of ion is surrounded by ions of theopposite charge, and the spacing between it and each of the oppositely charged ions near it, is the samefor all surrounding atoms of the same type. It is thus no longer possible to associate an ion with anyspecific other single ionized atom near it. This is a situation unlike that in covalent crystals, wherecovalent bonds between specific atoms are still discernible from the shorter distances between them, as

    measured by with such techniques as X-ray diffraction.

    Ionic crystals may contain a mixture of covalent and ionic species, as for example salts of complex acids,such as sodium cyanide, NaCN. Many minerals are of this type. X-ray diffration shows that in NaCN, forexample, the bonds between sodium cations (Na +) and the cyanide anions (CN -) are ionic, with nosodium ion associated with any particular cyanide. However, the bonds between C and N atoms incyanide are of the covalent type, making each of the carbon and nitrogen associated with just one of itsopposite type, to which it is physically much closer than it is to other carbons or nitrogens in a sodiumcyanide crystal.

    When such crystals are melted into liquids, the ionic bonds are broken first because they are non-directional and allow the charged species to move freely. Similarly, when such salts dissolve into water,the ionic bonds are typically broken by the interaction with water, but the covalent bonds continue tohold. For example, in solution, the cyanide ions, still bound together as single CN - ions, moveindependently through the solution, as do sodium ions, as Na +. In water, charged ions move apartbecause each of them are more strongly attracted to a number of water molecules, than to each other.The attraction between ions and water molecules in such solutions is due to a type of weak dipole-dipole type chemical bond. In melted ionic compounds, the ions continue to be attracted to each other,but not in any ordered or crystalline way.

    Covalent BondsAtoms like to share their electrons and this causes their outer shell to be complete. A covalent bond isproduced by the sharing of atoms and electrons. This produces a strong covalent bond.

    Covalent bonding is a common type of bonding, in which the electronegativity difference between thebonded atoms is small or nonexistent. Bonds within most organic compounds are described as covalent.See sigma bonds and pi bonds for LCAO-description of such bonding.

    A polar covalent bond is a covalent bond with a significant ionic character. This means that the electronsare closer to one of the atoms than the other, creating an imbalance of charge. They occur as a bondbetween two atoms with moderately different electronegativities, and give rise to dipole -dipole

    interactions. The electronegativity of these bonds is 0.3 to 1.7 .

    A coordinate covalent bond is one where both bonding electrons are from one of the atoms involved inthe bond. These bonds give rise to Lewis acids and bases. The electrons are shared roughly equallybetween the atoms in contrast to ionic bonding. Such bonding occurs in molecules such as theammonium ion (NH 4

    +) and are shown by an arrow pointing to the Lewis acid. Also known as non -polarcovalent bond, the electronegativity of these bonds range from 0 to 0.3.

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    Molecules which are formed primarily from non -polar covalent bonds are often immiscible in water orother polar solvents, but much more soluble in non -polar solvents such as hexane.

    One- and three-electron bondsBonds with one or three electrons can be found in radical species, which have an odd number of electrons. The simplest example of a 1-electron bond is found in the dihydrogen cation, H 2+. One-

    electron bonds often have about half the bond energy of a 2-electron bond, and are therefore called"half bonds". However, there are exceptions: in the case of dilithium, the bond is actually stronger forthe 1-electron Li 2

    + than for the 2-electron Li 2. This exception can be explained in terms of hybridizationand inner-shell effects.

    The simplest example of three-electron bonding can be found in the helium dimer cation, He 2+. It isconsidered a "half bond" because it consists of only one shared electron (rather than two) in addition toone lone electron on each atom; in molecular orbital terms, the third electron is in an anti -bondingorbital which cancels out half of the bond formed by the other two electrons. Another example of amolecule containing a 3-electron bond, in addition to two 2-electron bonds, is nitric oxide, NO. The

    oxygen molecule, O 2 can also be regarded as having two 3-electron bonds and one 2-electron bond,which accounts for its paramagnetism and its formal bond order of 2. Chlorine dioxide and its heavieranalogues bromine dioxide and iodine dioxide also contain three -electron bonds.

    Molecules with odd-electron bonds are usually highly reactive. These types of bond are only stablebetween atoms with similar electronegativities.

    Electron-deficient bondingIn three-center two-electron bonds ("3c 2e") three atoms share two electrons in bonding. This type of bonding occurs in electron deficient compounds like diborane. Each such bond (2 per molecule indiborane) contains a pair of electrons which connect the boron atoms to each other in a banana shape,with a proton (nucleus of a hydrogen atom) in the middle of the bond, sharing electrons with bothboron atoms. In certain cluster compounds, so-called four-center two-electron bonds also have beenpostulated.

    In certain conjugated (pi) systems, such as benzene and other aromatic compounds (see below), andin conjugated network solids such as graphite, the electrons in theconjugated system of -bonds are spread over as many nuclearcenters as exist in the molecule, or the network.

    Aromatic bonding

    In organic chemistry, certain configurations of electrons and orbitalsinfer extra stability to a molecule. This occurs when orbitalsoverlap and combine with others on different atomic centres,forming a long range bond. For a molecule to be aromatic, it mustobey Hckel's rule, where the number of electrons fit the formula4n + 2, where n is an integer. The bonds involved in the aromaticity are all planar.

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    In benzene, the prototypical aromatic compound, 18 (n = 4) bonding electrons bind 6 carbon atomstogether to form a planar ring structure. The bond "order" (average number of bonds) between thedifferent carbon atoms may be said to be (18/6)/2=1.5, but in this case the bonds are all identical fromthe chemical point of view. They may sometimes be written as single bonds alternating with doublebonds, but the view of all ring bonds as being equivalently about 1.5 bonds in strength, is much closer totruth.

    In the case of heterocyclic aromatics and substituted benzenes, the electronegativity differencesbetween different parts of the ring may dominate the chemical behaviour of aromatic ring bonds, whichotherwise are equivalent.

    Hypervalent bondingIn hypervalent molecules, there exist bonds which have significant non-bonding ionic quality to them.This manifests as non-bonding orbital levels in molecular orbital theory, while in valence bond theory itis analyzed as a form of resonant bonding.

    Resonant bonding

    Secondary BondsSecondary bonds are significantly weaker than primary bonds in that they often produce weak links, andcreate deformations in the bond. Secondary bonds include hydrogen and van der waals bonds.

    Hydrogen BondsA common bond is a hydrogen bond. They are most common in covalently bonded molecules thatcontain hydrogen. Hydrogen bonds share between covalent and oxygenated atoms. This leads to verysmall electrical charges around the hydrogen bond, and negative charges around the oxygenated bonds.

    Van der Waals BondsVan der waals bonds are the weakest bond, but are incredibly important gases, that are cooled at lowtemperatures. These bonds are created by small charges of positive and negative electron that producea weak bond. Van der waals bonds are overwhelmed by thermal energy, causing them to malfunction.

    Intermolecular bondingThere are four basic types of bonds that can be formed between two or more (otherwise non-associated) molecules, ions or atoms. Intermolecular forces cause molecules to be attracted or repulsedby each other. Often, these define some of the physical characteristics (such as the melting point) of asubstance.

    A large difference in electronegativity between two bonded atoms will cause a permanentcharge separation, or dipole, in a molecule or ion. Two or more molecules or ions withpermanent dipoles can interact within dipole-dipole interactions. The bonding electrons in amolecule or ion will, on average, be closer to the more electronegative atom more frequentlythan the less electronegative one, giving rise to partial charges on each atom, and causingelectrostatic forces between molecules or ions.

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    A hydrogen bond is effectively a strong example of an interaction between two permanentdipoles. The large difference in electronegativities between hydrogen and any of fluorine,nitrogen and oxygen, coupled with their lone pairs of electrons cause strong electrostatic forcesbetween molecules. Hydrogen bonds are responsible for the high boiling points of water andammonia with respect to their heavier analogues.

    The London dispersion force arises due to instantaneous dipoles in neighbouring atoms. As the

    negative charge of the electron is not uniform around the whole atom, there is always a chargeimbalance. This small charge will induce a corresponding dipole in a nearby molecule; causing anattraction between the two. The electron then moves to another part of the electron cloud andthe attraction is broken.

    A cation pi interaction occurs between a pi bond and a cation.

    Electrons in chemical bondsIn the (unrealistic) limit of "pure" ionic bonding, electrons are perfectly localized on one of the twoatoms in the bond. Such bonds can be understood by classical physics. The forces between the atomsare characterized by isotropic continuum electrostatic potentials. Their magnitude is in simple

    proportion to the charge difference.

    Covalent bonds are better understood by valence bond theory or molecular orbital theory. Theproperties of the atoms involved can be understood using concepts such as oxidation number. Theelectron density within a bond is not assigned to individual atoms, but is instead delocalized betweenatoms. In valence bond theory, the two electrons on the two atoms are coupled together with the bondstrength depending on the overlap between them. In molecular orbital theory, the linear combination of atomic orbitals (LCAO) helps describe the delocalized molecular orbital structures and energies based onthe atomic orbitals of the atoms they came from. Unlike pure ionic bonds, covalent bonds may havedirected anisotropic properties. These may have their own names, such as sigma bond and pi bond.

    In the general case, atoms form bonds that are intermediates between ionic and covalent, depending onthe relative electronegativity of the atoms involved. This type of bond is sometimes called polarcovalent.

    Bond EnergyIn chemistry, bond energy (E) is the measure of bond strength in a chemical bond. It is the heat requiredto break one Mole (unit) of molecules into their individual atoms. For example, the carbon-hydrogenbond energy in methane E(C H) is the enthalpy change involved with breaking up one molecule of methane into a carbon atom and 4 hydrogen radicals divided by 4.

    Chemical bonds that form do so at differing strengths (or, bond energies) based on the electronegativityof the atoms involved. Atoms like carbon (C), hydrogen (H), nitrogen (N) and oxygen (O) consistentlyform bonds and break to form new compounds. The carbon-oxygen double bond, as seen in carbondioxide (CO 2), has the highest bond energy (hardest to break) of these atoms. The carbon-nitrogen singlebond has the lowest bond energy (easiest to break).

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    Bond energy (E) should not be confused with bond-dissociation energy. It is a roughly transferableproperty, and enthalpy of formation can typically be roughly approximated by simply adding tabulatedvalues for bond energies for all bonds in a molecule, with an error of sometimes just a few percent.However, to get a better approximation is much more difficult.

    Bond energy/distance correlationBond strength (energy) can be directly related to the bond length/bond distance. Therefore, we can usethe metallic radius, ionic radius, or covalent radius of each atom in the molecule to determine the bondstrength. For example, the covalent radius of boron is estimated at 83.0 pm, but the bond length of B Bin B2Cl4 is 175 pm, a significantly larger value. This would indicate that the bond between the two boronatoms is a rather weak single bond. In another example, the metallic radius of rhenium is 137.5 pm, witha Re Re bond length of 224 pm in the compound Re2Cl8. From this data, we can conclude that the bondis a very strong bond or a quadruple bond. This method of determination is most useful for covalentlybonded compounds.

    Factors affecting ionic bond energyThere are several contributing factors but usually the most important is the difference in theelectronegativity of the two atoms bonding together.

    Crystal structureIn mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in acrystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in aparticular way, and a lattice exhibiting long-range order and symmetry. Patterns are located upon thepoints of a lattice, which is an array of points repeating periodically in three dimensions. The points canbe thought of as forming identical tiny boxes, called unit cells, that fill the space of the lattice. Thelengths of the edges of a unit cell and the angles between them are called the lattice parameters. Thesymmetry properties of the crystal are embodied in its space group.

    A crystal's structure and symmetry play a role in determining many of its physical properties, such ascleavage, electronic band structure, and optical transparency.

    Unit cellThe crystal structure of a material (the arrangement of atoms within a given type of crystal) can bedescribed in terms of its unit cell. The unit cell is a small box containing one or more atoms arranged in3-dimension. The unit cells stacked in three-dimensional space describe the bulk arrangement of atomsof the crystal. The unit cell is given by its lattice parameters, which are the length of the cell edges andthe angles between them, while the positions of the atoms inside the unit cell are described by the setof atomic positions (xi , yi , zi) measured from a lattice point.

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    Within the unit cell is the asymmetric unit, smallest unit the crystal can be divided into using thecrystallographic symmetry operations of the space group. The asymmetric unit is also what is generallysolved when solving a structure of a molecule or protein by X-ray crystallography.

    Miller indicesVectors and atomic planes in a crystal lattice can be described by a three-value Miller index notation

    (mn ). The , m, and n directional indices are separated by 90, and are thus orthogonal. In fact,the component is mutually perpendicular to the m and n indices.

    By definition, ( mn ) denotes a plane that intercepts the three points a 1/, a 2/m, and a 3/n, or somemultiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the planewith the unit cell (in the basis of the lattice vectors). If one or more of the indices is zero, it means thatthe planes do not intersect that axis (i.e., the intercept is "at infinity"). A plane containing a co-ordinateaxis is translated so that it no longer contains that axis before its Miller indices are determined. TheMiller indices for a plane are integers with no common factors. Negative indices are indicated withhorizontal bars, as in (123). In an orthogonal co-ordinate system, the Miller indices of a plane are the

    Cartesian components of a vector normal to the plane.

    Considering only ( mn ) planes intersecting one or more lattice points (the lattice planes), theperpendicular distance d between adjacent lattice planes is related to the (shortest) reciprocallattice vector orthogonal to the planes by the formula:

    Planes and directionsThe crystallographic directions are geometric lines linking nodes (atoms, ions or molecules) of a crystal.

    Likewise, the crystallographic planes are geometric planes linking nodes. Some directions and planeshave a higher density of nodes. These high density planes have an influence on the behavior of thecrystal as follows:

    Optical properties: Refractive index is directly related to density (or periodic densityfluctuations).

    Adsorption and reactivity: Physical adsorption and chemical reactions occur at or near surfaceatoms or molecules. These phenomena are thus sensitive to the density of nodes.

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    New Technologies and Materials CIV558 Surface tension: The condensation of a material means that the atoms, ions or molecules are

    more stable if they are surrounded by other similar species. The surface tension of an interfacethus varies according to the density on the surface.

    Microstructural defects: Pores and crystallites tend to have straight grain boundaries followinghigher density planes.

    Cleavage: This typically occurs preferentially parallel to higher density planes.

    Plastic deformation: Dislocation glide occurs preferentially parallel to higher density planes. Theperturbation carried by the dislocation (Burgers vector) is along a dense direction. The shift of one node in a more dense direction requires a lesser distortion of the crystal lattice.

    Some directions and planes are defined by symmetry of the crystal system. In monoclinic, rombohedral,tetragonal, and trigonal/hexagonal systems there is one unique axis (sometimes called the principal axis)which has higher rotational symmetry than the other two axes. The basal plane is the planeperpendicular to the principal axis in these crystal systems. For triclinic, orthorhombic, and cubic crystalsystems the axis designation is arbitrary and there is no principal axis.

    Cubic structuresFor the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length(usually denoted a); similarly for the reciprocal lattice. So, in this common case, the Miller indices (mn)and *mn+ both simply denote normals/directions in Cartesian coordinates. For cubic crystals withlattice constant a, the spacing d between adjacent (mn) lattice planes is (from above):

    Because of the symmetry of cubic crystals, it is possible to change the place and sign of the integers and

    have equivalent directions and planes: Coordinates in angle brackets such as denote a family of directions that are equivalent

    due to symmetry operations, such as [100], [010], [001] or the negative of any of thosedirections.

    Coordinates in curly brackets or braces such as {100} denot