Boltzmann distribution
A formula describing the statistical distribution of particles in a system among different energy levels.
Applications of the Boltzmann-distribution I.: Nernst equation
- P.E = Charge * Voltage
- Has long formula
Applications of the Boltzmann-distribution II.: equilibrium and rate of chemical reactions. (The Arrhenius plot)
- In chemical reactions atoms must transition from one energy state A, to state B.
- In equilibrium the distribution between the states can be calculated with formula.
- na/nb = K (equi. Constant)
- Arrhenius plot, Graph K / 1/t and the slope gibes the energy distribution between 2 states.
Applications of the Boltzmann-distribution III.: barometric formula
- In thermal equilibrium we can measure decreases in atmospheric density vs altitude by this formula.
Applications of the Boltzmann-distribution IV. electric conductivity of semiconductors.
- Depends on number of electrons which are able to transition from valence band through gap to the conduction band.
- Number increases with T.
- Using Boltzmann distribution we can calculate fraction of electrons that are able to cross the gap.
(Delta e)
Macrostate and microstate in thermodynamics
- Microstate: Examination of molecular state of system and instant state. (Location of particles, velocity of particles, momentum)
- Macrostate: Examine whole system (Pressure, Temperature)
- In Thermal equilibrium the macro states stay constant whole microstate always changes.
Boltzmann’s definition of entropy
S = k * ln
S = entropy (extensive quantity of heat)
- Number of micro states which belong to a macrostate
Kinetic gas theory
- Particles are small compared to volume
- Constant random motion
- Collision of particles is elastic
- Particles exert pressure when colliding with container wall
- Molecular speed is proportional to temperature
Maxwell-Boltzmann velocity distribution
- Upon increasing temperature, average absolute value of molecular speed increases
- Width of distribution increases due to increase in interactions between molecules
The Ideal gas
- Non realistic gas
- Composed of molecules which follow the kinetic gas theory
- Pv = nrt
The real gas
- Contrary to ideal gas
- Particles are not point like
- Volume is not negligible
- Less volume available for motion
- Interaction between particles arise and pressure becomes reduced
- Explains possibility of condensartion
State equation of real gases
() () = nkt
Pressure of ideal gases
Pv=nRt
The crystalline state (unit cell, crystal defects)
- Unit cells arrange to form crystal lattice.
- Ideal crystals: Infinite periodic spatial sequences of identical structural elements.
- Real crystals: Microcrystaline, keep their identical spatial sequence only in microscopic scale and instead have various sizes and orientations in structure.
- Defects: Point defect, Line defect, Surface defect
Optical properties of crystalline materials
Anisotropic, their physical properties are dependent on direction of measurement related to orientation of atoms in the crystal.
Thermotropic liquid crystals
Liquid crystal: Substance that possesses properties of both liquid and crystalline solid.
- Transitional order (Center mass point forms plane), Orientational order (axes of molecule align parallel)
Thermotropic: Order of structure depends on temperature.
- Applied to contact tomography: Changing colors of film on patients body indicates inflammation (higher temp, different color)
Lyotropic liquid crystals
- Order is affected by concentration of components
- Components are amphiphilic molecules that form ordered structures in presence of solvent
- Phospholipids
Energy levels of electrical insulators
- Insulators have valence band and conduction band
- Gap between bands called forbidden band
- Electrons are not able to cross it to get to conduction band
The function of the semiconductor diode.
- Acts as one way valve for electricity
- n and p type semiconductors
- In semiconductors increasing temperature gives more energy for electrons to reach conductance band so therefore more conductance.
Energy levels of electrical conductors.
- Conduction and valence band only
- No forbidden band
- Increasing temp here causes vibration which disturbs electron flow.
The liquid state
- Lacks spatial order of solid
- Isotropic, no directional dependence
- Take shape of container
- Not compressible
Electro- and thermo optical phenomena in liquid crystals
- Electro: Nematic liquid crystal (characterized only by orientation). Orientation can be controlled by electric field, manipulates optical transmission. Can be used to manufacture displays.
- Thermo: Choleric liquid crystal (twisted nematic) color of layer will change with different temperature. Contact thermography.
Energy levels of intrinsic semiconductors
- There is valence band and conduction band
- Gap between them so electrons cant pass freely
- But not too big of a gap so that excited electrons can cross into conduction band
- electricity conducted!
Types of doped semiconductors
- P-type (boron, acceptor, holes)
- N-type (Phosphorus, donor, electrons)
