Determination of molecular weight of polymers by viscometry

Presented by:Udhay Kiron

13305017

Contents

• Introduction• Determination of molecular weight• Polymer solutions• Viscometry• References

Introduction• In simple compounds there is some

definiteness about the molecular weight, hence we can say the simple compounds have fixed molecular weight.

• Example Hydrogen: 2 Ethylene: 28

• Since a polymer sample is a mixture of molecules of same chemical type with different molecular weight it is expressed in terms of an average value.

Number Average and Weight Average Molecular Weight The molecular weight of polymers  

a. Some natural polymer (monodisperse) : All polymer molecules have same molecular weights. b. Synthetic polymers (polydisperse) : The molecular weights of polymers are distributed c. Mechanical properties are influenced by molecular weight much lower molecular weight ; poor mechanical property much higher molecular weight ; too tough to process optimum molecular weight ; 105 -106 for vinyl polymer, 15,000 - 20,000 for polar functional group containing polymer (polyamide)

Determination of molecular weight

a. Absolute method : mass spectrometry

colligative property

end group analysis

light scattering

ultracentrifugation.

b. Relative method : solution viscosity

c. Fractionation method : GPC

Definition of average molecular weight

a. number average molecular weight ( Mn ) Mn= (colligative property and end group analysis)

b. weight average molecular weight ( Mw) Mw=

(light scattering)

i i

Ni

MN

Wi

Wi Mi

c. z average molecular weight ( MZ )

M Z= (ultracentrifugation)

d. general equation of average molecular weight :

M = ( a=0 , Mn a=1 , Mw a=2 , Mz ) e. Mz > Mw > Mn

NiMi3

NiMia+1

NiMia

NiMi2

Definition of average molecular weight

polydispersity index (PI) = Mw / Mn ≥ 1

Polydispersity index : width of distribution

Example of molecular weight calculation

a. 9 moles, molecular weight ( Mw) = 30,000 5 moles, molecular weight ( Mw) = 50,000

Mn=9 mol + 5 mol

(9 mol x 30,000 g/mol) + (5 mol x 50,000 g/mol)= 37,000 g/mol

Mw = 9 mol(30,000 g/mol) + 5 mol(50,000 g/mol)

9 mol(30,000 g/mol)2 + 5 mol(50,000 g/mol)2

= 40,000 g/mol

b. 9 grams, molecular weight ( Mw ) = 30,000 5 grams, molecular weight ( Mw ) = 50,000

Example of molecular weight calculation

= 35,000 g/molMn =9 g + 5 g

(9 g/30,000 g/mol) + (5 g/50,000 g/mol)

Mw =(9 g/30,000 g/mol) + (5 g/50,000 g/mol)

9 g + 5 g= 37,000 g/mol

Polymer Solutions

A. Process of polymer dissolution : two step First step : The solvent diffuses into polymer masses to make a swollen polymer gel

Second step : Swollen polymer gel breaks up to solution

B. Thermodynamics of solubility : Gibb's free energy relationship

G =H - TS

ΔG < 0 : spontaneously dissolve T and ΔS are always positive for dissolving process. Conditions to be negative ΔG, ΔH must be negative or smaller than TΔS.

Polymer Solutions

C. Hydrodynamic volume of polymer molecules in solution depend on the following:

a. polymer-polymer interaction b. solvent-solvent interaction c. polymer-solvent interaction d. polymer structure ( branched or not ) e. brownian motion r = end-to-end distance s = radius of gyration

Figure : Coil molecular shape

The greater the value of α, the ‘better’ the solvent α = 1, 'ideal' statistical coil.

r 2 = ro22

s2= so22

= (r2)1/2

(ro2)1/2

D. theta(θ) temperature and theta(θ) solvent The lowest temperature at which α=1 : theta(θ) temperature blink The solvent satisfied this condition : theta(θ) solvent point

E. Flory-Fox equation : The relationship among hydrodynamic volumes, intrinsic viscosity and molecular weight [η] : intrinsic viscosity M : average molecular weight : Flory constant (3×1024/mol) r : end-to-end distance

[η] =(r2)3/2

M

Polymer Solutions

F. Mark-Howink-Sakurada equation : The relationship between intrinsic viscosity and molecular weight [η] : intrinsic viscosity K , a : constant for specific polymer and solvent M : average molecular weight

G. Important properties of polymer solution : solution viscosity a. paint spraying and brushing b. fiber spinning

[η] = KMa

Polymer Solutions

SOLUTION VISCOSITY AND MOLECULAR SIZE

• The usefulness of solution viscosity as a measure of polymer molecular weight has been recognized ever since the early work of Staudinger (1930).

• Solution viscosity is basically a measure of the size or extension in space of polymer molecules. It is empirically related to molecular weight for linear polymers

• Viscosity is an internal property of a fluid that offers resistance to flow.

• It is due to the internal friction of molecules and mainly depends on the nature & temperature of the liquid.

• Many methods are available for measuring viscosity of polymer solution.

• Example Ostwald viscometry

Ostwald viscometry

• The Ostwald method is a simple method for the measurement of viscosity, in which viscosity of liquid is measured by comparing the viscosity of an unknown liquid with that of liquid whose viscosity is known. In this method viscosity of liquid is measured by comparing the flow times of two liquids of equal volumes using same viscometer.

• The molecular weight of the polymer is measured by using viscometer and the molecular weight obtained by this technique is called viscosity average molecular weight.

• The molecular weight of the polymer solution is very high so the viscosity of polymer solution is very high compared to that of pure solvent.

• Consider two liquids are passing through a capillary of same viscometer. Then the coefficient of viscosity of liquid (η2) is given by equation

Viscometry

IUPAC suggested the terminology of solution viscosities as following. Relative viscosity : : solution viscosity o: solvent viscosity t : flow time of solution t o: flow time of solvent Specific viscosity :

Reduced viscosity :

Inherent viscosity :

Intrinsic viscosity :

rel = o

=

to

t

rel - 1sp = o

- o =to

t - to =

rel = csp = c

rel - 1

inh = cIn rel

[] = (csp )c=o=(ηinh)C = 0

Mark-Houwink-Sakurada equation [η] = KMa

log[η] = logK + alogMv

(K, a : viscosity-Molecular weight constant, )

Mv is closer to Mw than Mn

Mw > Mv > Mn

TABLE . Representative Viscosity-Molecular Weight Constants

Polymer

Polystyrene(atactic)

Polyethylene(low pressure)Poly(vinyl chloride)

Polybutadiene98% cis-1,4, 2% 1,297% trans-1,4, 3% 1,2Polyacrylonitrile

Poly(methyl methacrylate-co-styrene)30-70 mol%71-29 mol%Poly(ethylene terephthalate)Nylon 66

Solvent

CyclohexaneCyclihexaneBenzeneDecalin

Benzyl alcoholCyclohexanone

TolueneTolueneDMFg

DMF

1-Chlorobutane1-ChlorobutaneM-CresolM-Cresol

Temperature, oC35 5025135

155.420

30302525

30302525

Molecular WeightRange 10-4

8-424-1373-613-100

4-357-13

5-505-165-273-100

5-554.18-810.04-1.21.4-5

K 103

80 26.9 9.52 67.7

156 13.7

30.5 29.4 16.6 39.2

17.6 24.9 0.77240

a

0.500.5990.740.67

0.501.0

0.7250.7530.810.75

0.670.630.950.61

Image taken from Textbook of Polymer Science by Fred. W. BillMeyer

• For measuring intrinsic viscosity of polymer sample, solutions of known concentrations are prepared, the flow times of solvent ( ) and the solutions ( ) are measured using viscometer.

• Double extrapolation plots of reduced viscosity against concentration and inherent viscosity against concentration is plotted by calculating the corresponding reduced viscosity and inherent viscosity. The intrinsic viscosity is given by the common ordinate intercept of these graphs.

Determining the Intrinsic Viscosity of the Polymer- solvent system:• Select the Polymer and Select the Solvent.• Determine the Time of flow of the solvent (t0).• Determine the time of flow of polymer-solvent system at different

concentrations.• From the concentration and time of flow, the inherent viscosity and

reduced viscosity are calculated using the equations; Inherent Viscosity = Reduced Viscosity = • A graph is drawn by plotting reduced viscosity against concentration

and inherent viscosity against concentration.• Intrinsic viscosity can be obtained by extrapolating the graph to zero

concentration.• From the value of intrinsic viscosity, the viscosity average molecular

weight of the polymer can be calculated by using the equation.

References:

Books:• Polymer Science by V R Gowarikar, N V Viswanathan, Jayadev

Sreedhar.• Textbook of Polymer Science by Fred. W. BillMeyer. Webliography:• www.udel.edu/pchem/C446/Experiments/exp5.pdf• www.ias.ac.in/initiat/sci_ed/resources/chemistry/Viscosity.pdf• www.isasf.net/fileadmin/files/Docs/Colmar/Paper/T19.pdf• en.wikipedia.org/wiki/Polymer Image Source:• t1.gstatic.com/images