Diffusion Flashcards
Define diffusion.
Spontaneous spreading of particles in other medium, does not require any energy.
Explain Brownian motion and the formula.
Brownain motion is what is called random walk of a particle, it is the kinetic energy of the particle related to the surrounding thermal energy.
E_kin = 1/2mv^2 = 3/2kT
Explain Fick’s 1st law.
Conc. gradient and brownian motion drives even distribution of gas particles.
The particle flux is j_N = -D*dc/dx
which means that the flux is in the opposite direction of the conc. gradient.
When dc/dt=0 for some dx, there is no change in conc. over time in one position, but when dc/dt!=0 there can also be change over time.
Derive Fick’s 2nd law.
Mass conservation: dc/dt = -dj_N/dx and Fick’s 1st law
–> dc/dt = D* d^2c/dt^2
The behavior is not linear any more, the conc. in one point is changed over time.
When measuring the mobility of a process and finds
x prop. sqrt(t) –> is diffusion process
Explain the Stokes-Einstein relation.
Connecting the macroscopic (temp., viscousity) and microscopic (part. radius) properties.
D = kT/(6pietaR) eta is vicsousity
This says that the diffusion increases when temp. rises, or viscosity of radius decreases.
How is the relation between particle radius and radius of gyration related to the diffusion speed?
When the particle radius is much smaller than the radius of gyration of the polymer is the diffusion very fast, up to 250 times faster than SE behavior. Because the particle can just go through the polymer and don’t feel the viscous drag.
When the particle radius and radius of gyration are of the same size does the particle need to go in between the polymers and it bumps into them and feels the viscosity, and the diffusion follow SE behavior.
How can the diffusion of Ag be slowed down?
Normally polymers need to be heated up to allow metals to diffuse in them, but Ag can diffuse in some polymer at room temp. But when adding thin film of Cr between Ag and polymer this slows down the diffusion into the polymer.
What are the dominant interactions during self-assembly of metal aggregates in polymer?
In metal-metal interaction can der Waals and electrostatic interactions are occurring. Because of enthalpy does metal want to aggregate because they like each other more.
If atoms of course diffuse faster, Stokes-Einstein and also the amount of metal affects the aggregation speed.
Is dominated by van der Waals interactions.
Give examples of how entropy and enthalpy affect the aggregation of metal in polymer.
Ex. 1: Entropy.
Have Si wafer with PMMA layer containing nanoparticles and on top SiOx. When it is heated the surface cracks because of different thermal expansion. Then nanoparticles accumulate in these cracks because their radius is comparable in size to the radius of gyration of the PMMA and then it is more entropically favorable to leave the PMMA.
Ex. 2: Enthalpy.
When have nanoparticles covered in alkane in PMMA they aggregate because PMMA and alkane is incompatible and than it is more enthalpically favorable for the particles to accumulate so less particles are in contact with PMMA.
Ex. 3: Enthalpy.
Particles grafted with PS favors to be in PS domains.
Ex. 4: Entropy.
When have particles in a lamellar block copolymer structure and the polymer has to stretch itself around the particles, it is more entropically favorable to rearrange the structure to eg. cylinder so there is more space for the polymer to arrange itself around the particles.
