3. Macromolecules in solution

Macromolecules

Large molecules built up by small molecules (monomers), that are covalently linked 

Examples: 

Biological polymers: 

• Polysaccharides such as starch, cellulose etc.

  • Sugar monomers

• Lignin

  • Phenolic monomers

Proteins: Not strictly polymers

• Amino acid monomers

Synthetic polymers:

• Polyethylene (PE)

• Polyethylene glycol (PEG)

• Polyvinylalcohol (PVA)

• Polystyrene (PS)

• Polyacrylamide etc.

What is homopolymer, copolymer, block copolymer and branched homopolymer?

Homopolymer- same type of monomer

Copolymer- alternating monomer

Block copolymer- alternating in block→ making them surface-active 

Branched homopolymer- branching can occur for others

Polymer size - Hydrodynamic radius

Hydrodynamic radius is obtained from the Stokes-Einstein equation. It describes how diffusion of a particle or polymeric structure depends on its radius.

D= diffusion coefficient [m²/s]

k= Boltzmann constant (J/K)=1.38×10⁻²³ J/K

T= temperature (K)

η=dynamic viscosity of continuous phase [Pa•s]

d=hydrodynamic diameter of particle [m]

Polymer size - Radius of gyration

 Based on the distance of each monomer unit to the polymer’s center of mass. Used for random coil polymer 

Debey’s definition of radius of gyration

It is most common one. Distance of every mass to the center of mass. The average distance is r_g

r_g=average distance

M_i=molar mass 

r_i=distance to the center of mass

Polymer conformation in solutions depends on

• Interactions with solvent molecules

• pH

• Salt 

• Temperature

• Interactions with other polymer molecules

Really likes solvent: polymer swell

Doesn’t like it as much: polymer minimises

Conformation in dilute solutions

Rod: stiff

Double helix: two molecules 

Flory-Huggins theory

Describes solubility of a polymer and thermodynamics of macromolecular solutions.

Flory-Huggins parameter (χ)

– 0.1< χ<0.5 ”Good” solvent (molecule swell)

– χ ≈ 0.5 ”θ-solvent” (transition between good and poor solvents) (reduce it bellow to precipitate, increase to allow it dissolve)

– χ > 0.5 ”Poor” solvent (molecule shrink)

– χ >> 0.5 Insoluble

• χ can change with temperature, pH, ionic strength etc.

Phase behaviour of macromolecule solutions (miscibility, segregative phase separation and associated phase separation)

Polymer 1 and polymer 2 are chemically different 

Miscibility: polymers like the solvent, don’t care about each other 

Segregative phase separation: Polymers don’t like each other but like solvent 

• The rule for mixtures of non-ionic polymers

Associated phase separation: Polymers like each other better than solvents (e.g polymer could have opposite charges)

• Polyelectrolytes of opposite charge, proteins-polysaccharides

Applications of macromolecules

• Thickening to increasing viscosity to preferred value and flow properties in liquid formulations. Example: Pharmaceutics, Foods and Paints and coatings

• Stabilization of dispersions

Rheology

Rheology is the study of the flow and deformation of matter, including liquids, solids, and soft materials, under applied forces or stresses.

Shear stress

Shear stress is the external force applied parallel to the surface, which causes deformation. 

σ=shear stress [Pa]

F=applied external force [N]

A=cross-sectional area [m²]

Shear rate

Shear rate 𝛾 is the rate at which strain changes over time, which is the rate of deformation. 

γ=shear rate [1/s]

v=velocity [m/s]

y=distance between moving plates [m]

Describe viscosity is in pure liquid and solution of polymer

In a pure liquid: friction between molecules

In a solution of polymers: resistance to a deforming flow compared to pure solvent → increase in viscosity

Dynamic viscosity

γ=shear rate [1/s]

σ=shear stress [Pa]

η=dynamic viscosity [Pa・s=N・s/m²]

Newtonian flow

• Shear stress proportional to shear rate → viscosity independent of shear rate.

• Low molar mass liquids (water, organic solvent etc.).

What happens viscosity from flow field is distrub?

Viscosity increase in dispersions arises from disturbances in the flow field

Non-Newtonian flow

• The viscosity is shear rate dependant.

• Pseudo-plastic flow: The viscosity decreases with increasing shear rate (as known as shear-thinning). For example paint 

• Dilatent flow: The viscosity increases with increasing shear rate. For example wet sand (particle volume fraction increase locally)

• Apparent viscosity

Herschel-Bulkley flow

• Above the yield stress the system starts to flow.

• Below the yield stress the system appears solid (i.e. gel)

Example: Tooth paste, tomate ketchup 

Overlap concentration (c*)

The point where solution viscosity increases sharply

with polymer concentration

• c* depends on the volume occupied by polymer in the solution.

– Large volume → lower c*

– Small volume → higher c*

• Note that the volume is 3D!

– i.e. rod-like conformation occupies a large volume

Relation to overlap concentration (c*) for different concentrations

c correlation to c*

Thixotropy

Thixotropic fluids are a type of non-Newtonian liquids that exhibit shear thinning during increased shear rate and a slow recovery to the original viscosity after the shear rate is removed.

• Time-dependent viscosity decrease during constant shear

• Obtained with associative thickeners – dissociation and orientation give a decrease in viscosity

• The viscosity is recovered when shearing/deformation stops

• Example: Important for controlling paint viscosity and application

Associative thickeners

Hydrophobic interaction can play a role in polymer network formation

Surfactant micelles can associate with hydrophobic groups