[madscientist]

Hi All,

Ive got a question i am trying to answer, its in 4 parts and i have been able to answer 3 of these. the question/s is/are:

(1)
What is the intrinsic viscosity of a polysaccharide of M = 96000 with Mark-Houwink parameters
(K = 1.4*10^-6 m³ / kg, and a = 0.69)?

[n] = KM^a = (1.4*10^-6 m³/kg)(96000)^0.69 = 3.8*10^-3 m³/kg

(2)
Calculate the hydrodynamic volume

V_H = [n]M/2.5N_A

     = KM^aM/2.5N_A

     = KM^a+1 / 2.5N_A
 
    = ((1.4*10^-6 m³/kg)(96kg/mol)^0.69+1) / ((2.5)(6.022*10²³mol^-1))

     = 2.1*10^-27m³/chain

(3)
What concentration of the polysaccharide is needed to completely fill a solution with polymer coils?

V_H = hydrodynamic volume = volume of one polymer chain = 2.1*10^-27m³ / chain = 2.1*10^-24L/chain

#of polymer chains per liter = 1 / (2.1*10^-24L / chain)= 4.8*10²³ chain /L

the concentration of polysacharide in a solution completely filled with polysacharide coils = conc. max = 4.8*10²³ chain /L

alternatively, conc. max = 1/(V_H*N_A)

                                             = 1/((2.1*10-24L/poly. chain)(6.022*10²³chain/mol))

                                             = 0.791mol/L

(4)
What might you expect to happen to the viscosity of the solution as the concentration increases beyond this level?

This has got me puzzled, this is what ive come up with.

There is a maximum concentration of 4.8*10²³ poly. chains / L, therefore the viscosity of the solution will not increase, this is the point of maximum viscosity.

Its got me puzzled because I cant understand how you could have a concentration higher than 4.8*10²³ poly. chains / L of this polysacharide when thats all you can fit in a liter? does that make sense?

Any help would be much appreciated (im starting to have nightmares about polymers)

cheers,

Mad

[madscientist]

This is the first time that i havn't got a response to a question on these forums. must be a hard question to answer, I don't feel so stupid not being able to answer it .  If anyone has any idea how to make sense of the last question in my previous post, (Q.4), please let me know.

Cheers,

Madscientist

[P]

Did you get a firm answer in the end??   I did not post because I did not know the answer - I had speculated though  -  Would the polymer start to fall out of the solution?  I'm interested to find out what the answer was if you know.