Lecture 4: 14/09

Question 1

What is the difference between regular (affine) and irregular (nonaffine) network deformations?

Answer 1

• 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

Question 2

What is the function of crosslinks?

Answer 2

• 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

Question 3

Define percolated network

Answer 3

When there is a direct mechanical connection between all of the filaments in a system (polymers connected via crosslinks)

Question 4

What is the percolation condition?

Answer 4

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).

Question 5

Describe crosslinker valency?

Answer 5

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)

Question 6

What is the maximum number of filaments that can bind to an existing bound crosslinker?

Answer 6

= Valency - 1

Question 7

What is the minimal percolation condition?

Answer 7

r > 1/(f-1)
Ratio of crosslinkers to polymer > 1 / (valency - 1)

Question 8

What does the Pc (percolation constant) tell you about stress within the system?

Answer 8

Pc > 1 elastic solid, stores stress
Pc < 1 incomplete elastic solid, dissipates stress

Question 9

What happens to the stiffness if you heat an elastic cross-linked network?

Answer 9

Temperature goes up, entropy goes up, stiffness increases

Increasing temperature increases tension in rubber bands

Question 10

What happens to the stiffness if you heat an uncross-linked entangled network?

Answer 10

Increasing the temperature reduces the viscosity (higher flow), the stiffness decreases

Question 11

What is the Tube Model?

Answer 11

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

Question 12

What happens if you heat a biopolymer network?

Answer 12

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

Question 13

How does stress affect the storage modulus for crosslinked and entangled conditions?

Answer 13

Crosslinked: increasing stress increases G’ (stress stiffening)

Entangled: increasing stress decreases G’ (stress softening)

Question 14

What is the differential elastic modulus?

Answer 14

Measures stiffness as a function of stress

Question 15

Instead of temperature, what do biological systems use to alter the mechanical properties of a system?

Answer 15

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)

Question 16

What’s unique about polyacrylamide?

Answer 16

It is a linear elastic system, as when the strain increases the storage modulus remains constant (i.e., hookean)

Question 17

How do crosslinker mechanics impact strain stiffening?

Answer 17

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

Question 18

How do you stiffen a polymer network?

Answer 18

• 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)

Question 19

Why does understanding the mechanics of active biopolymers matter?

Answer 19

It explains the observed mechanics of cells