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June 8, 2010

DOE Makes Public Detailed Information on the BP Oil Spill

WASHINGTON – As part of the Obama Administration’s ongoing commitment to transparency surrounding the response to the BP oil spill, U.S. Energy Secretary Steven Chu announced today that Department is providing online access to schematics, pressure tests, diagnostic results and other data about the malfunctioning blowout preventer.

Secretary Chu insisted on making the data widely available to ensure the public is as informed as possible, and to ensure that outside experts making recommendations have access to the same information that BP and the government have. The site will be updated with additional data soon.

“Transparency is not only in the public interest, it is part of the scientific process,” said Secretary Chu. “We want to make sure that independent scientists, engineers and other experts have every opportunity to review this information and make their own conclusions.”

The information is posted at energy.gov/oilspilldata. It includes detailed raw data on the pressure readings within the blowout preventer, as well as rates and amounts of hydrocarbons captured by the top hat and by the riser insertion tube. There is also a timeline of key events and detailed summaries of the Deepwater well configuration, the blowout preventer stack tubes, and the containment system.

Media contact(s):
(202) 586-4940

http://www.energy.gov/news/9053.htm

***

Gulf Coast Oil Spill Update

Steven Chu participates in a meeting about the BP oil spill in Houston, TX

U.S. Energy Secretary Steven Chu listens to analysis of oil spill response efforts during his recent trip to Houston, TX.
As part of the Obama Administration’s ongoing commitment to transparency surrounding the response to the BP oil spill, the Department of Energy is providing online access to schematics, pressure tests, diagnostic results and other data about the malfunctioning blowout preventer. The information is posted at energy.gov/oilspilldata, which will be updated with additional data soon.

For the latest information on this effort, visit our Gulf Coast Oil Spill Resource Center.

http://www.energy.gov/

***

***

Adsorption
From Wikipedia, the free encyclopedia
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Not to be confused with Absorption.
Search Wiktionary     Look up Adsorption in Wiktionary, the free dictionary.
Brunauer, Emmett and Teller’s model of multilayer adsorption is a random distribution of molecules on the material surface.

Adsorption is the process of attraction of atoms or molecules (generically known as “monomers”) from an adjacent gas or liquid to an exposed solid surface. Such attraction forces (adhesion or cohesion) align the monomers into layers (“films”) onto the existent surface.

Note: not to be confused with absorption; also not to be confused with chemisorption which actually is a chemical reaction that generates a new chemical species at the exposed surface (e.g. metallic oxidation, like steel rusting – or any corrosion).

The deposition may be driven by

* long range weak forces among atomic or molecular electric multipoles (“van der Waals”, among induced and/or fluctuating dipoles or “London”, dipole-quadrupole etc.) will initiate the initial attraction;
* short range strong ionic or metallic forces may finalize the setting of new layers onto the solid surface (without generating new chemical species) — as salt deposits (crystalline growth) from super-saturated solutions OR as metal vapor deposition onto metallic surfaces.

Note: covalent forces at solid surfaces will always create new chemical species; the formation of covalent solids involves energy transfers that penetrate deep into the bulk, far beyond the surfaces – these are valence electron rearrangements (phase transitions) at the whole scale of the involved bulk.

Energetically the adsorbed species loses its internal kinetic energy (of thermal agitation) which it transfers into the solid surface to which it is being adsorbed – so the adsorption rates increase with an increasing temperature gap between a warmer monomer gas/ liquid and a cooler surface.

Adsorption is present in many natural physical, biological, and chemical systems, and is widely used in industrial applications such as activated charcoal, capturing and using waste heat to provide cold water for air conditioning and other process requirements (adsorption refrigerators), synthetic resins, increase storage capacity of carbide-derived carbons for tunable nanoporous carbon, and water purification. Adsorption, ion exchange, and chromatography are sorption processes in which certain adsorbates are selectively transferred from the fluid phase to the surface of insoluble, rigid particles suspended in a vessel or packed in a column.

(and lookup fractional distillation – my note)

http://en.wikipedia.org/wiki/Adsorption

***

(from this page – although it is about scanning tunneling microscopes – STM – it has some very interesting basic information that can be used in this –  )

http://www.iap.tuwien.ac.at/www/surface/stm_gallery/electronwaves

Interference phenomena of surface and bulk states

As mentioned in the introduction to scanning tunneling microscopy, STM does not only show the geometric structure but it is strongly influenced by the electronic structure of the sample, i.e., the density of electronic states (DOS). Since electrons not always behave like particles but rather propagate as waves, we can see electron wave phenomena in STM images. These phenomena are very subtle, however, since the change of DOS is only a few percent, corresponding to apparent heights of a few pm (picometers). Compare this to the size of metal atoms, which are some 250 to 350 pm in diameter.

Surface states – waves

If there are electrons in a solid restricted to a region close to the surface (typically a few atomic layers deep), we call their states surface states. A good example for surface states can be observed on (111)-oriented Cu surfaces, where the wavelength of the surface state electrons at the Fermi energy (the energy probed by the STM in case of small sample voltage) equals approximately 14 interatomic distances. Since the STM is sensitive to the square of the wavefunction psi, we see both maxima and minima of the wavefunction psi as maxima of current or apparent height in the STM image, and, hence, the wavelength looks only half as long:

Cu(111) surface with atomic resolution and surface state electrons scattered at a defect

Only standing waves can be imaged by STM. In the above image a standing wave is created by scattering of the surface state electrons by at an impurity of unknown nature, which is probably situated above the surface (the white blob). Standing waves can also occur if the impurity atoms are located in the surface layer such as two substitutional Pb atoms in the following image, or even if the impurities are in deeper layers (as the impurity atoms responsible for the two rings in the top part of this image presumably are).

standing-wave patterns on Cu(111)

Image size is 10×8 nm (similar scale as the previous one, but no atomic resolution).

All these images were obtained at room temperature. At low temperatures the waves are much more pronounced (not smeared out by contributions of different energies), as shown in several great images obtained in Don Eiglers’s group at IBM Almaden Research Center.

Surface states – orbitals

Surface states do not always look like waves, however. Have a look at the following STM image of a (100)-oriented surface consisting of nearly equal amounts of iron (some with white circles superimposed) and silicon atoms (red), created by Segregation of Impurity Atoms of Si out of bulk Fe. In most parts of the surface like the one marked ©, Fe and Si form a checkerboard-like structure of alternating Fe and Si called c(2×2) superstructure, with Si appearing dark in the STM image. There are also zigzag rows of Fe atoms (b), which form domain boundaries of the c(2×2) structure. (When you cross a domain boundary, Fe and Si atoms are exchanged with respect to their arrangement on the other side.) Finally, there are also small patches of pure Fe (a) not related to domain boundaries (one could also say, a few Si atoms replaced by Fe).

FeSi surface with bright domain boundaries

The striking feature of this image is the large brightness (high tunneling current) in regions (a) and (b) not covered by silicon. This is not a geometric effect, since it occurs only in a certain range of positive tunneling voltages. Hence, it must be rather due to the electronic structure of the surface.

(etc.)

The solution to the puzzle can be found by calculations of the electronic structure of these surfaces: On pure Fe, a surface state reaching far into the vacuum (where the STM tip is probing the electronic structure) consisting of d-orbitals is found at just the energy observed in the tunneling spectra (+0.3 eV in spectrum (a), above). In domain boundaries of the c(2×2) structure shown above, the d-orbitals become tilted in such a way that the resulting density of the surface state reaching into the vacuum looks more like a band (and not like the zigzag row of the iron atoms), as you can see in the calculated density of states (white represents high density of the electronic state):

Calculation of the orbitals imaged by STM

This not only explains the bright bands in the STM image above, but we also find good agreement with tunneling spectrum (b), showing that the peak is shifted to higher energies as the surface state is confined along the zigzag rows.

Of course, without the calculations, there is no way to see that the STM image actually shows tilted d-orbitals. The electronic structure inside the solid, which you see in this image, is not accessible to the STM tip.

Bulk states

On Aluminum surfaces (and probably on several other metals as well), a nice electron interference phenomenon can be observed: We create subsurface Argon bubbles by ion bombardment with Ar+ and subsequent annealing, which makes the implanted Ar atoms diffuse around and coagulate. Similar to the single impurity atoms in the examples above, these “large” objects can also scatter electrons, but in this case the “usual” electron states of the bulk electrons are affected.

What we see in STM images of Al(111) looks like this:

STM image of an Al(111) surface with subsurface Ar bubbles

The reason for the hexagonal shape of the interference patterns is the shape of the subsurface Ar bubbles, which minimize their surface energy. This leads to hexagonal (111) facets, as the Wulff construction for Al shows:

Wulff-shape calculated for Al

Since our surface is (111)-oriented, the top of each bubble is a small hexagon parallel to the surface, causing a hexagonal interference pattern. Scattering of electrons at the edges causes fringes, which are not waves propagating parallel to the surface as one might think looking at the STM image above. In a very simplified view, it rather looks like this:

schematic view of electron interference at a subsurface Ar bubble

Since both the (outer) surface of the crystal and the top of the Ar bubbles are very efficient reflectors, standing waves of electrons form between them. Such an arrangement is called a quantum well.

( . . . )

For further information

A textbook on surface physics, including surface states, the Wulff construction etc.
Andrew Zangwill
Physics at surfaces
Cambridge University Press 1988.

Scattering of Cu(111) surface states by Pb
C. Nagl, O. Haller, E. Platzgummer, M. Schmid and P. Varga
Submonolayer growth of Pb on Cu(111): Surface alloying and de-alloying
Surf. Sci. 321 (1994) 237-248. Full text*

Scattering of surface states by subsurface impurities (theoretical)
S. Crampin
Surface states a probes of buried impurities

J. Phys. Condens. Matter 6 (1994) L613-L618.

Surface states of Fe and FeSi/Fe (d-orbitals)
A. Biedermann, O. Genser, W. Hebenstreit, M. Schmid, J. Redinger, R. Podloucky, and P. Varga
Scanning tunneling spectroscopy of one-dimensional surface states on a metal surface
Phys. Rev. Lett. 76 (1996) 4179-4182. Full text

Bulk electron scattering by Ar bubbles
M. Schmid, W. Hebenstreit, P. Varga, S. Crampin
Quantum wells and electron interference phenomena in Al due to subsurface noble gas bubbles
Phys. Rev. Lett. 76 (1996) 2298-2301. Full text

M. Schmid, S. Crampin, P. Varga
STM and STS of bulk electron scattering by subsurface objects
J. Electron Spectrosc. Relat. Phen. 109 (2000) 71-84. Full text*

(from)

http://www.iap.tuwien.ac.at/www/surface/stm_gallery/electronwaves

***

Back to the entry from wikipedia about Adsorption –

The probability of adsorption occurring from the precursor state is dependent on the adsorbate’s proximity to other adsorbate molecules that have already been adsorbed. If the adsorbate molecule in the precursor state is in close proximity to an adsorbate molecule which has already formed on the surface, it has a sticking probability reflected by the size of the SE constant and will either be adsorbed from the precursor state at a rate of kEC or will desorb into the gaseous phase at a rate of kES. If an adsorbate molecule enters the precursor state at a location that is remote from any other previously adsorbed adsorbate molecules, the sticking probability is reflected by the size of the SD constant.These factors were included as part of a single constant termed a “sticking coefficient,” kE, described below:

k_\mathrm{E}=\frac{S_\mathrm{E}}{k_\mathrm{ES}.S_\mathrm{D}}.

As SD is dictated by factors that are taken into account by the Langmuir model, SD can be assumed to be the adsorption rate constant. However, the rate constant for the Kisliuk model (R’) is different to that of the Langmuir model, as R’ is used to represent the impact of diffusion on monolayer formation and is proportional to the square root of the system’s diffusion coefficient. The Kisliuk adsorption isotherm is written as follows, where Θ(t) is fractional coverage of the adsorbent with adsorbate, and t is immersion time:

\frac{d\theta_\mathrm{(t)}}{dt}=\R'(1-\theta)(1+k_\mathrm{E}\theta).

Solving for Θ(t) yields:

\theta_\mathrm{(t)}=\frac{1-e^{-R'(1+k_\mathrm{E})t}}{1+k_\mathrm{E}e^{-R'(1+k_\mathrm{E})t}}.

Henderson-Kisliuk

The Henderson-Kisliuk adsorption equation prediction of normalised impedance as a function of adsorption time, where the first peak corresponds to the formation of an adsorbent surface that is saturated with MPA in its “lying down” structure. The curve then tends to an impedance value that is representative of an adsorbent saturated with “standing up” structure.

This adsorption isotherm was developed for use with the new field of Self Assembling Monolayer (SAM) adsorption. SAM molecules adsorb to the surface of an adsorbent until the surface becomes saturated with the SAM molecules’ hydrocarbon chains lying flat against the adsorbate. This is termed “lying down” structure (1st structure). Further adsorption then occurs, causing the hydrocarbon chains to be displaced by thiol groups present on the newly adsorbed SAM molecules. When this adsorption step takes place, electrostatic forces between the newly adsorbed SAM molecules and the ones previously adsorbed, causes a new structure to form, where all of the SAM molecules are occupying a “standing up” orientation (2nd structure). As further adsorption takes place, the entire adsorbent becomes saturated with SAM in a standing up orientation, and no further adsorption takes place.

The SAM adsorbate is usually present in a liquid phase and the adsorbent is normally a solid. Hence, intermolecular interactions are significant and the Kisliuk adsorption isotherm applies. The sequential evolution of “lying down” and “standing up” mercaptopropionic acid (MPA) SAM structures on a gold adsorbent, from a liquid MPA-ethanol adsorbate phase, was studied by Andrew P. Henderson (b. 1982) et al. in 2009. Henderson et al. used electrochemical impedance spectroscopy to quantify adsorption and witnessed that the 1st structure had different impedance properties to the 2nd structure and that both structures evolved sequentially. This allowed four rules to be expressed:

  • That the amount of adsorbate on the adsorbent surface was equal to the sum of the adsorbate occupying 1st structure and 2nd structure.
  • The rate of 1st structure formation is dependent on the availability of potential adsorption sites and intermolecular interactions.
  • The amount of 1st structure is depleted as 2nd structure is formed.
  • The rate of second structure formation is dictated by the amount of adsorbate occupying 1st structure and intermolecular interactions at immersion time, t.

From these statements, Henderson et al. used separate terms to describe rate of fractional adsorption for 1st structure [Θ1(t)] and 2nd structure [Θ2(t)] as a function of immersion time (t). Both of these terms were dictated by the Kisliuk adsorption isotherm, where variables with a subscript of 1 relate to 1st structure formation and a subscript of 2 relates to 2nd structure formation.

These terms were combined in the Henderson adsorption isotherm, which determines the total normalised impedance detection signal strength caused by the adsorbate monolayer (z(t)) as a function of Θ1(t), Θ2(t), φ1 and φ2. Values of φ are weighting constants, which are normalized signal values that would result from an adsorbent covered entirely with either 1st structure or 2nd structure. This isotherm equation is shown below:

z_\mathrm{t}=\theta_\mathrm{1(t)}.[\varphi_\mathrm{1}.(1-\theta_\mathrm{2(t)})+\varphi_\mathrm{2}.\theta_\mathrm{2(t)}].

Although the Henderson-Kisliuk adsorption isotherm was originally applied to SAM adsorption, Henderson et al. hypothesised that this adsorption isotherm is potentially applicable to many other cases of adsorption and that Θ1(t) and Θ2(t) can be calculated using other adsorption isotherms, in place of the Kisliuk model (such as the Langmuir adsorption isotherm equation).

Adsorption enthalpy

Adsorption constants are equilibrium constants, therefore they obey van ‘t Hoff’s equation:

\left( \frac{\partial \ln K}{\partial \frac{1}{T}} \right)_\theta=-\frac{\Delta H}{R}.

As can be seen in the formula, the variation of K must be isosteric, that is, at constant coverage. If we start from the BET isotherm and assume that the entropy change is the same for liquefaction and adsorption we obtain ΔHads = ΔHliqRTlnc, that is to say, adsorption is more exothermic than liquefaction.

Adsorbents

Characteristics and general requirements

Activated carbon is used as an adsorbent

Adsorbents are used usually in the form of spherical pellets, rods, moldings, or monoliths with hydrodynamic diameters between 0.5 and 10 mm. They must have high abrasion resistance, high thermal stability and small pore diameters, which results in higher exposed surface area and hence high surface capacity for adsorption. The adsorbents must also have a distinct pore structure which enables fast transport of the gaseous vapors.

Most industrial adsorbents fall into one of three classes:

  • Oxygen-containing compounds – Are typically hydrophilic and polar, including materials such as silica gel and zeolites.
  • Carbon-based compounds – Are typically hydrophobic and non-polar, including materials such as activated carbon and graphite.
  • Polymer-based compounds – Are polar or non-polar functional groups in a porous polymer matrix.

Silica gel

Silica gel is a chemically inert, nontoxic, polar and dimensionally stable (< 400 °C or 750 °F) amorphous form of SiO2. It is prepared by the reaction between sodium silicate and acetic acid, which is followed by a series of after-treatment processes such as aging, pickling, etc. These after treatment methods results in various pore size distributions.

Silica is used for drying of process air (e.g. oxygen, natural gas) and adsorption of heavy (polar) hydrocarbons from natural gas.

(etc.)

http://en.wikipedia.org/wiki/Adsorption

***

My Note –

But that’s not exactly what I wanted because the Gulf of Mexico is not a flat surface nor a consistent equilibrium – all these equations take into account that three or four assumptions are made of restricted dimensionality and restrictions of these – (more or less) which cannot even come close to the dynamic dimensional systems of the Gulf of Mexico oil slick and oil plumes –

It is a semi-empirical isotherm derived from a proposed kinetic mechanism. It is based on four assumptions:

  1. The surface of the adsorbent is uniform, that is, all the adsorption sites are equivalent.
  2. Adsorbed molecules do not interact.
  3. All adsorption occurs through the same mechanism.
  4. At the maximum adsorption, only a monolayer is formed: molecules of adsorbate do not deposit on other, already adsorbed, molecules of adsorbate, only on the free surface of the adsorbent.

These four assumptions are seldom all true: there are always imperfections on the surface, adsorbed molecules are not necessarily inert, and the mechanism is clearly not the same for the very first molecules to adsorb as for the last. The fourth condition is the most troublesome, as frequently more molecules will adsorb on the monolayer; this problem is addressed by the BET isotherm for relatively flat (non-microporous) surfaces. The Langmuir isotherm is nonetheless the first choice for most models of adsorption, and has many applications in surface kinetics (usually called Langmuir-Hinshelwood kinetics) and thermodynamics.

(etc.)

Hmmmmm………..

– cricketdiane

have to find something else to add to it – but I’m actually looking for something else that coordinates with what the STM article shows – (about a potential propagating wave of change that could occur within volumes using something like adsorption principles or orbital exchanges propagated throughout the hydrocarbon chains – not like the dispersants are doing but rather like a chain reaction does.)

Hmmmm……..

It’s just a thought.

***

I can see something but it isn’t here in the words and equations that I’m finding – and therefore – I must be looking in the wrong place.

Going to my encyclopedias and notes –

Encyclopedia Britannica, vols. 6 and 5

In vol. 6, pp. 851 – entry, “Energy”

In vol. 5, pp. 345 – entry, “Crystallography”

Starting with the second one first in the right hand paragraph —

“Certain general information can be obtained from the indices of planes reflecting and not reflecting. If atoms are arranged with a face-centred cubic unit cell, for example, the only reflections that will appear are those with h, k, l all even or all odd. The (111), (200), ans (220) reflections occur, but not the (100) and (110). Furthermore, the positions of reflections can be calculated with a single parameter, the edge of the unit cell. Other unit cells express themselves differently. Certain symmetry elements give rise to specific absences of reflections. A glide plane halves the spacing of planes perpendicular to it, and this requires h to be even for a reflection; for h odd, the molecules on the plane at half the spacing cancel the reflection. Such rules are tabulated for different symmetries and the different structures for easy reference.” – pp. 345, vol.6; Encyclopedia Britannica, 1978

(etc.)

In the cited material – there are (111) planes diagrams – starting with the first on the right hand side and (110) planes – first of the series on the page group – which show an interesting possibility for interpreting the three-dimensional aspects of a molecular body of systems like the oil spill and ocean water constituents with the dispersants that have been added plus whatever other unnaturally occurring pollutants already existed in concentrations, such as the fixed nitrogen runoff, etc. (my note)

This is the diagram from that page I was describing above –

Encyclopedia Britannica - vol 5 - pp 345 - crystallography

Encyclopedia Britannica - vol 5 - pp 345 - crystallography

Using the top (110) and the top (111) visual descriptions for the equations –

(my note)

And then going to the Encyclopedia Britannica, vol. 6, pp. 851 – entry “Energy” (and then using the vol. 5 entry “Deformation and Flow” – after that)

From section titled –

Energy of interaction between charged particles –

and starting briefly in a paragraph on the opposite side of pp. 851 –

“Understanding the distribution of energy in its various forms in a physical problem can often be facilitated by constructing an appropriate graphical energy diagram. If a mass is suspended from a spring in a gravity-free space, displacement of the spring (or molecules, my note) from its equilibrium position stores potential energy in the spring. When the spring is released, the restoring force accelerates the mass, giving it kinetic energy. At the moment it is released, the potential energy stored in the spring is at its maximum value, while the kinetic energy is zero. As the system moves toward the equilibrium position, the stored energy decreases while the force tending to restore the system to equilibrium imparts to the mass a kinetic energy until, at the equilibrium displacement, the potential energy is zero, but the kinetic energy has reached a value that is equal in magnitude to the potential energy at the point of maximum displacement. As the mass moves past the equilibrium position, the spring exerts a retarding force on it, which tends to slow the mass down and thus decrease its kinetic energy. Concurrently, the displacement of the spring from equilibrium again results in energy being stored in the spring. Thus, in an ideal system the total kinetic plus potential energy remains unchanged but is being transformed continually from one to the other. This transfer of energy from one form to another is shown graphically in the Figure. The total energy in the oscillating system remains constant, but at specific times is completely in the form of kinetic energy, while at other times it is completely in the form of potential energy.

(etc.)

Energy of interaction between charged particles.

In considering the interaction between charged particles in electrostatcs, the force is given by Coulomb’s law – (etc.)

The value of 1 divided by 4 piE(0) – which is determined experimentally to be 9 x 10 (to the ninth power) newton-metre squared per coulomb squared. (etc.)

In applying Coulomb’s law, it is useful to introduce the concept of an electrical field E, the force per unit charge acting on a charge at a point as a result of all the other charges – (etc.)

Thus, the electric field at point 1 due to the charge at point 2 would be, using the equation above – (I’ll have to go do it on my other computer or find on wikipedia)

so that the force on a charge q1, located at point 1 is (by substituting for q2 divided by r2) the product of charge and field:

F(1)  =  q(subscript 1)E(1).

The real advantage to the concept of the electric field is in investigations into the effect of a complicated array of charges.

(etc. – about energy densities)

pp. 851 – 852, vol. 6; Encyclopedia Britannica, 1978

Now – I’m going online to Co9ulomb’s law electric field (Google search) and then popping into the vol. 5 for Deformation and Flow, pp. 555 – 558, vol.5; Encyclopedia Britannica, 1978

http://en.wikipedia.org/wiki/Electric_field

In physics, an electric field is a property that describes the space that surrounds electrically charged particles or (etc.)

Based on Coulomb’s Law for interacting point charges, the contribution to the E-field at a point in space due to a single, discrete charge located at another point in space is given by the following:

\mathbf{E}= {1 \over 4\pi\varepsilon_0}{q \over r^2}\mathbf{\hat{r}} \

where

q is the charge of the particle creating the electric force,
r is the distance from the particle with charge q to the E-field evaluation point,
 \mathbf{\hat{r}} is the unit vector pointing from the particle with charge q to the E-field evaluation point,
\varepsilon_0 is the electric constant.

The total E-field due to a quantity of point charges, nq, is simply the superposition of the contribution of each individual point charge:

\mathbf{E} = \sum_{i=1}^{n_q} {\mathbf{E}_i} = \sum_{i=1}^{n_q} {{1 \over 4\pi\varepsilon_0}{q_i \over r_i^2}\mathbf{\hat{r}}_i}.

If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results:

\mathbf{E} = \frac{1}{4\pi\varepsilon_0} \int\frac{\rho}{r^2} \mathbf{\hat{r}}\,\mathrm{d}V

where

ρ is the charge density, or the amount of charge per unit volume.

from pp. 554, vol 5; Encyclopedia Britannica, 1978 –

“When forces are applied to some materials they assume a deformed shape in equilibrium and return to their original shapes after the forces are removed. Such materials are called solids. Other materials can maintain an equilibrium shape only when subjected to hydrostatic pressures (the force is perpendicular to the surface). These materials, both liquid and gaseous, are known as fluids. Under other types of forces, they deform indefinitely as long as the forces are applied and do not return to their original form when these forces are removed. Such an irrecoverable deformation is called flow.”

“An important part of continuum mechanics is the formulation of constitutive equations – that is, relations between force and deformation – that describe the mechanical behaviour of a given material. Rheology is the part of continuum mechanics that deals with constitutive equations. Such equations provide an approximate description of behaviour over a certain range of circumstances.”

“For example, a metal under a light load might be considered rigid: under a heavier load or with more accurate measurement of length, a linearly elastic solid; under a very large load, a plastic solid; and under a small oscillatory motion, a linearly viscoelastic solid.” (etc.)

(from pp. 555 – middle of the first column, left-hand side, vol. 5 – Deformation and Flow, entry from Encyclopedia Britannica, 1978)

under the heading –

Kinematics –

1. In uniform expansion, all volume elements of the body are transformed to geometrically similar elements of greater dimensions. Such deformation occurs when a body is uniformly deformed in all directions so that any arbitrary particle, originally having the coordinates (x1, x2, x3) moves to a point whose coordinates are (ax1, ax2, ax3), in which a is a multiplicative factor (Figure 1). The displacement of the particle may be represented by the vector u whose components (u1, u2, u3) are [(a – 1)x subscipt i], i = i, 2, 3.

Any physical quantity that has direction, such as displacement, velocity, force, electric field, can be represented in magnitude and direction by a vector. The vector u, for instance, can be represented by an arrow that points in the direction of the motion of the particle with the length representing the displacement or distance moved.

Each component is the length of the axis intersected by lines drawn perpendicular to it from the head and tail of the vector. For example, the tail interects the X1-axis in the Cartesian coordinate system (X1, X2, and X3 coordinates mutually perpendicular) at x subscript 1 and the head intersects at axsubscript 1, so that the displacement along the X1-axis is a component of u1 of length ax1  —  x1, or (a – 1)x1.

(etc.)

Parts 3 and 4 also on this page – 555 and 556, vol. 5; Encyclopedia Britannica

3. General Infinitesimal Strain. (see 6 spatial derivatives.) – can’t write them on this computer with software I have, my note

4. For Finite Strains, the infinitesimal strain is no longer a valid measure of deformation (for example, a zero value does not necessarily mean that the material is undeformed.) – etc.

***

Illustration of the electric field surrounding a positive (red) and a negative (blue) charge.
(from)

http://en.wikipedia.org/wiki/Electric_field

***

Adsorption enthalpy

Adsorption constants are equilibrium constants, therefore they obey van ‘t Hoff’s equation:

\left( \frac{\partial \ln K}{\partial \frac{1}{T}} \right)_\theta=-\frac{\Delta H}{R}.

As can be seen in the formula, the variation of K must be isosteric, that is, at constant coverage. If we start from the BET isotherm and assume that the entropy change is the same for liquefaction and adsorption we obtain ΔHads = ΔHliqRTlnc, that is to say, adsorption is more exothermic than liquefaction.

http://en.wikipedia.org/wiki/Adsorption

Nobel Lecture Osmotic Pressure and Chemical Equilibrium from Nobelprize.org website

http://en.wikipedia.org/wiki/Jacobus_Henricus_van_%27t_Hoff

Jacobus Henricus van ‘t Hoff (30 August 1852 – 1 March 1911) was a Dutch physical and organic chemist and the winner of the inaugural Nobel Prize in chemistry. His research on chemical kinetics, chemical equilibrium, osmotic pressure and stereochemistry are among his most notable achievements. Through these achievements, Van ‘t Hoff helped found the discipline of physical chemistry as it is known today.

Nobel laureates in Chemistry | People from Rotterdam | University of Amsterdam faculty

Hornix WJ, Mannaerts SHWM, Van’t Hoff and the emergence of Chemical Thermodynamics, Delft University Press, 2001, ISBN 90-407-2259-5

***

Lunch Break – watching World Cup

10.33 am

Very Nifty – Great Goal by South Africa – and Great football –

The coverage is great across CNN and CNNI =- on ESPN , getting to see the whole game – very cool. Never thought I would see that day in the US, where soccer would be available on the tele and especially the World Cup. It is great to see the celebrations, the people, that the children across South Africa and throughout the World are being inspired by it to play football and team play – it is wonderland and very awesome. And, the US is going to kick those Brits butts tomorrow – yepper. Too fun.

France playing Uruguay in just a bit – 2 pm – very nifty, can’t wait. That will be a good game.

Rio de Janeiro playing Tuesday, they are saying on CNNI right now – very cool to see they are getting ready to scream and holler and party with children running around playing soccer.

Oh, yeah – ESPN had a super great soccer montage from Nike – that was great and the CNN mention about the interactive tweet site that shows info on the different teams – and the best was to see the iReport videos passing the ball from one to another across the world – that was very nifty. I’ve got to go find that and see it.

Yep, quickly getting back to work that I was trying to post earlier – and also saw something from UK PM Cameron awhile ago that I want to look up online right quick.

– cricketdiane

***

UPDATE 1-UK PM stresses importance of strong BP

Fri Jun 11, 2010 12:47pm EDT

* Stresses importance of strong BP

* Cameron to discuss issue with Obama on Saturday

By Keith Weir

LONDON, June 11 (Reuters) – British Prime Minister David Cameron said on Friday it was in everyone’s interests for BP (BP.L) to remain a financially strong and stable company following the Gulf of Mexico oil spill.

Cameron, who is on his way home from Afghanistan, spoke to BP Chairman Carl-Henric Svanberg and expressed his frustration about the environmental damage caused by the massive leak.

“Mr Svanberg made clear that BP will continue to do all that it can to stop the oil spill, clean up the damage and meet all legitimate claims for compensation,” a spokesman for the prime minister said, adding this issue would be raised by the premier in a call with U.S. President Barack Obama on Saturday.

( . . . )

He is under fire at home for not doing enough to protect a company that provides more than 12 percent of all dividends paid by British companies.

(etc.)

http://www.reuters.com/article/idUSLDE65A20L20100611

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Hydrocarbon

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Ball-and-stick model of the methane molecule, CH4. Methane is part of a homologous series known as the alkanes, which contain single bonds only.

In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon.[1] Hydrocarbons from which one hydrogen atom has been removed are functional groups, called hydrocarbyls.[2] Aromatic hydrocarbons (arenes), alkanes, alkenes, cycloalkanes and alkyne-based compounds are different types of hydrocarbons.

The majority of hydrocarbons found naturally occur in crude oil, where decomposed organic matter provides an abundance of carbon and hydrogen which, when bonded, can catenate to form seemingly limitless chains.[3][4]

http://en.wikipedia.org/wiki/Hydrocarbon

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