Lecture 4: 14/09 Flashcards
What is the difference between regular (affine) and irregular (nonaffine) network deformations?
- Affine deformations are well understood and easily calculated
- Nonaffine deformations are more common, scales with the square of the concentration
These deformations are scaled in different ways
What is the function of crosslinks?
- Without cross-links, polymers can be easily moved or manipulated
- Crosslinks elastically couple polymers within a system
With crosslinks, the individual polymers cannot slide past each other
Define percolated network
When there is a direct mechanical connection between all of the filaments in a system (polymers connected via crosslinks)
What is the percolation condition?
How many crosslinkers need to be added in order to create a percolated network.
The percolation condition describes how well the crosslinkers are working (>1 is satisfied).
Describe crosslinker valency?
How available the crosslinker is for binding at different locations; how many binding spots are in the configuration of the crosslinker (similar to atomic valency)
What is the maximum number of filaments that can bind to an existing bound crosslinker?
= Valency - 1
What is the minimal percolation condition?
r > 1/(f-1)
Ratio of crosslinkers to polymer > 1 / (valency - 1)
What does the Pc (percolation constant) tell you about stress within the system?
Pc > 1 elastic solid, stores stress
Pc < 1 incomplete elastic solid, dissipates stress
What happens to the stiffness if you heat an elastic cross-linked network?
Temperature goes up, entropy goes up, stiffness increases
Increasing temperature increases tension in rubber bands
What happens to the stiffness if you heat an uncross-linked entangled network?
Increasing the temperature reduces the viscosity (higher flow), the stiffness decreases
What is the Tube Model?
Surrounding chains restrict transverse motion of a polymer
Each polymer is confined to a tube region
This is defined for polymers with permanent topological interactions in networks
Polymers must slide along their length
What happens if you heat a biopolymer network?
Example: cooking egg, adding heat increases stiffness
Cooking is temperature-induced denaturation and crosslinking of proteins which is irreversible
Because its irreversible, using heat to alter mechanics is not biologically favorable; biological systems use dynamic crosslinking which is reversible
How does stress affect the storage modulus for crosslinked and entangled conditions?
Crosslinked: increasing stress increases G’ (stress stiffening)
Entangled: increasing stress decreases G’ (stress softening)
What is the differential elastic modulus?
Measures stiffness as a function of stress
Instead of temperature, what do biological systems use to alter the mechanical properties of a system?
Increasing applied stress stiffens crosslinked networks
Increasing ratio of crosslinkers to polymers increases stiffness
Biological systems use stress systems to alter mechanical properties (i.e., stiffness)
What’s unique about polyacrylamide?
It is a linear elastic system, as when the strain increases the storage modulus remains constant (i.e., hookean)
How do crosslinker mechanics impact strain stiffening?
The strain stiffening is impacted by the size and rigidity of the cross-link; the scaling is different in each condition
Stiffer crosslinks stress-stiffen networks more for a given stress
How do you stiffen a polymer network?
- Make it harder for polymers to move
- Increasing the amount of crosslinkers (i.e., ratio C:P)
- Increasing the valency of the crosslinkers
- Apply a stress generator (i.e., motor protien)
- Select more rigid crosslinkers
- Increase the length of the polymer
- Heat it (if crosslinked non biopolymer)
- Cool it (if entangled system)
- Apply stress or strain (if crosslinked system)
Why does understanding the mechanics of active biopolymers matter?
It explains the observed mechanics of cells
