Dependencies of the Heat of Forma2on

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Dependencies of the Heat of Forma2on

Reference State: Elem ental ground state at STP has an enthalpy of form ation of 0 N², O², He etc.

Generally energy is released on form ation of a m olecule from the elem ents if the m olecule is stable, so the heat of form ation is generally negative. For unstable m olecules such as NO which is a radical form ed a high tem peratures, the heat of form ation is positive (endotherm ic).

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Relative magnitude of heat of formation from elements, oxides, heat of fusion, heat of transition

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Heats of formation for various titania oxides

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Values are alm ost iden3cal

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Electronegativity, the ability of an atom to attract electrons in a bond

Linus Pauling

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Factors involved in the heat of formation: electronegativiy and atomic size

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Difference in electronegativity between the two com pounds

Average

electronegativity of the two com pounds Van Arkel–Ketelaar triangle Jensen’s quan+ta+ve triangle Norm an’s quan+ta+ve triangle

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e.g. m olten Na and Cl² gas

Energetics of compound formation

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Energetics of compound formation

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Energetics of compound formation

Electrosta+c a-rac+on +- Electron electron repulsion

Van der Waals or dispersion (d+ m akes d- leads to net a-rac+on) Polariza+on (shi>ing within com pound of electrons)

Crystal ﬁeld eﬀects

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Electrostatic interactions in NaCl

Nearest neighbors of Na⁺ and Cl^-

Repulsive cationic term s, second nearest neighbors

Third nearest neighbors, attraction between M⁺ and X^-

Generally:

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Repulsion and Dispersion Terms

Leonard-Jones (6-12) Potential

12 is repulsive since dE/dr = F is positive (guessed) 6 is van der Waals attractive force (calculated)

Buckingham Potential

Exponential term works better for ceram ics

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Trends in Enthalpy of Formation Alkali Metals

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Transition Metal Enthalpy of Formation

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p-orbitals 6 valence electrons (m ore acidic to right) s-orbitals

2 valence electrons (m ore basic to right)

Acidic Basic

d-orbitals 10 valence electrons

Transi>on M etals

f-orbitals 14 valence electrons

Basic (at low oxidation state)

Acidic (at high oxidation state)

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Depending on the crystallographic environm ent the d-orbital energies split This im pacts the Enthalpy of Form ation

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Transition metal lattice stabilization due to d-orbital splitting

First series chlorides, oxides and ﬂuorides Increasing d electrons

Atom ization Com ponent

Ionization Com ponent

Lattice Com ponent

Crystal Field

Stabilization due to d- orbital splitting

(not for Ca, M n, Zn)

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Heat of Formation for Transition Metal Oxides in Different Oxidation States

Cr, M o, W 3d, 4d, 5d

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Acid-Base Model for Heat of Formation of Ternary Oxides

SiO² Na²O

Base transfers its oxygen s-block oxides

Acid accepts oxygen p-block oxides SiO^42- M gO < C aO < SrO < B aO

Basicity

A l < Si < P < S Acidity

SiNa²O³

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p-orbitals 6 valence electrons (m ore acidic to right) s-orbitals

2 valence electrons (m ore basic to right)

Acidic Basic

d-orbitals 10 valence electrons

Transition M etals

f-orbitals 14 valence electrons

Basic (at low oxidation state)

Acidic (at high oxidation state)

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M ost Basic Oxide BaO

Sulfate m ost stable since SO3 m ost acidic

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Ionic potential e^-/ionic radius (Å) q/r

<2 strong base 2-4 basic

4-7 am photeric

>7 acidic

From UV spectra of probe ion

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Atomic Size

Perovskite structure Calcium titanate CaTiO³

Em bed cations in the structure for engineered properties One is solar energy absorption in Graetzel cells

These are the m ost prom ising low-tem perature PV devices

(silicon solar cells require high tem perature reduction of silica and chem ical purification)

Cubic/Orthorhom bic-like structure

Can accom m odate m any transition m etals ABX³

A is m uch larger than B cations, X is anion (oxide) B has 6 fold coordination surrounded by

octahedron of anions

A has 12-fold cubahedral coordination Red O^2-

Blue Ti⁴⁺

Green Ca²⁺ or Ba²⁺

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t = 1 Perfect Cubic 0.8 < t < 1.1

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M ethyl Am m onium Lead Halide

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Schem atic of a sensitized perovskite solar cell in w hich the active layer consist of a layer of m esoporous TiO2w hich is coated w ith the perovskite absorber. The active layer is contacted w ith an n-type m aterial for electron extraction and a p- type m aterial for hole extraction. b) Schem atic of a thin-film perovskite solar cell. In this architecture in w hich just a flat layer of perovskite is sandw iched

betw een tw o selective contacts. c)

C harge generation and extraction in the sensitized architecture. After light

absorption in the perovskite absorber the photogenerated electron is injected into the m esoporous TiO² through w hich it is extracted. The concom itantly generated hole is transferred to the p-type m aterial.

d) C harge generation and extraction in the thin-film architecture. After light absorption both charge generation as w ell as charge extraction occurs in the perovskite layer.

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spiro Om etad p-type sem i-conductor

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Enthalpy of Formation versus Number of Valence Electrons

TiC w ith ne = 4 has a high enthalpy of form ation since the Ferm i level falls in a pronounced gap in density of electronic states separating bonding and anti- bonding electron bands.

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Zeolites (Natural are aluminosilicate rocks, synthetic can be a variety of materials usually based on SiO

²

)

M icroscopic structure of a zeolite (m ordenite) fram ework, assem bled from tetrahedra.

Sodium is present as an extra-fram ework cation (in green).

Can form m eso or m icro pores (colloidal- or nano-scale) (These are term s from gas adsorption field.)

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Synthetic Zeolites can have m eso (colloidal) or m icro (nano) pores depending on the tem plating m aterial and synthesis conditions. Usually start with TEOS and a

surfactant or block copolym er Reference 29

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M olar Volum e Enthalpy relative

to quartz

Surface effect as we saw earlier except that this is on a m olecular/nano scale

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Energy of Forma-on for Subs-tu-onal Solid Solu-ons

Atom ic Radii => Volum e of com pounds

Hum e-Rothery Rule lim ited solubility if size difference exceeds 15%

Electronegativity

Large difference in binary system leads to negative enthalpy of m ixing Pd-Zr and is sm all for system s with low or no electronegativity and size difference Ti-Zr

Valence electron density

Binary com ponents have the sam e crystal structure

Large enthalpy of m ixing is related to large num ber of interm etallic phases

Elastic contribution to the enthalpy of m ixing, sm all m ixes well with large

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Energy of Formation for Interstitial Solid Solutions

Elastic interactions Electronic interactions

Gas solubility in m etals Tem perature

Pressure solubility for H² x ~ √p

Sievert’s Law

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6 kJ/m ole diﬀerence in form a3on enthalpy

Reduc3on tem perature is 600K higher for hexagonal Cubic reduced SrM nO^2.5 is m ore stable

Octahedral corners shared in cubic, faces shared in hexagonal High vacancies in faces m ake reduced hexagonal unfavorable

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Liquid-Liquid Miscibility

M ixing of acidic (SiO²) and Basic (CaO) oxides Si⁴⁺has coordination num ber 4 and Ca²⁺ has 6 SiO² m ixes well with CaO but CaO has a harder tim e m ixing with SiO²

Increasing basicity

Ortho-silicate Ca²SiO⁴

ZrF⁴ strong acid

Increasing basicity

ZrF^62-

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Liquid Salt Mixtures

Size param eter, d = (d^A – d^B)/(d^A + d^B)

Com m on Anions m ix with negative enthalpy of m ixing Com m on cations do not m ix due to anion-anion repulsion

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Conformational Enthalpy of Polymers

The Rotational Isom eric State M odel of Volkenstein and Paul Flory (Nobel Prize)

Carbon has a tetrahedral bonding arrangem ent

For a chain of carbon the two side groups interact with the side groups of neighboring carbons

“Trans” is sterically the m ost favorable arrangem ent

“Gauche +” and “Gauche -” are less favorable

The Boltzm ann equation gives the probability of a particular conform ation, Z is the partition

function or the sum of all of the different Boltzm ann expressions in an ensem ble For Butene

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Conformational Enthalpy of Polymers

function or the sum of all of the different Boltzm ann expressions in an ensem ble

Neum ann Projection

For Butene

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Conformational Enthalpy of Polymers

function or the sum of all of the different Boltzm ann expressions in an ensem ble For Butene

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Conformational Energy of Polymers

Helmholtz Free Energy and Entropy

Boltzm ann equaHon where Z is num ber of states (which depend on tem perature and energy barriers)

For Butene

U = F P + S P T

^-SUV_{H A(F)}

-pGT

Internal Energy

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Conformational Enthalpy of Polymers

For a polym er with N carbons there are N-2 covalent bonds

The num ber of discrete conform aGon states per chain is n^N-2 where n is the num ber of discrete rotaGonal states for the chain, II, g^-g^-g^-g^-,g⁺g⁺g⁺g⁺,g⁺It, etc. for N = 4; N¹=1, N⁴=4, etc. assum ing no end eﬀects

Average rotational angle

Characteristic Ratio

Q is the bond angle 180°-109° = 71°

E^g+-= 2100 J/m ole C^∞ = 3.6

Exp. 6.7

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