Polymer sciences

Polymer molecular weight (Mw)

Mw controls many physical properties of polymers

A-Transition Temperature: From one phase to other

( From liquids to waxes to rubbers to solids )

B-Mechanical Properties:

(stiffness, strength, viscoelasticity, toughness,

and viscosity)

Thus Mw is low, the transition temperature and

mechanical strength low

Strength and molecular weight have approximate inverse relation.

A is a constant and M is the molecular weightS0 is strength at infinite molecular weight.

polymers property is rather a function of molecular distribution weight,P(M).

)]([/ MpFASS

MASS /

Or a function of average molecular weight.

MASS /

Effect of MW on Property of the Polymers

Tensile Strength as a function of MW

The tensile strength is the stress needed to break a sample (Pascals or psi). The tensile strength is an important property for polymers.

% Elongation to Break

The elongation-to-break is the strain on a sample when it breaks. This usually is expressed as a percent.

Young's Modulus

Young's modulus is the ratio of stress to strain. It also is called the modulus of elasticity or the tensile modulus.

Rigid materials, such as metals, have a high Young's modulus but low Mw polymers will have low modulus.

Degree of Polymerization and Molecular weights

Xn = ---------11-P

Mn = M0 ---------1

1-P

Xw = ---------1-P

Mw = M0 ---------1-P

1+P

1+P

Mw 1+PMn

PDI

Depending on statistical methods, the following molecular weights of polymer are determined

Weight average molar mass or Mw

Number average molar mass or Mn

Viscosity average molar mass or Mν

Z average molar mass or Mz

Typical molecular weights distribution curve

Mn < Mv < Mw < Mz

Polydisperse sample: having broad range of size,shape and mass characteristics

Monodisperse sample: uniform size, shape and mass distribution

CommonNot Common

Polydispersity of a sample is defined as ratio

of Mw/Mn

A-In step growth polymerization it is about 2

B- In addition polymerization it varies from

10- 20

C- In living polymerization its value is nearly 1

Polydispersity in polymer varies with mechanism of polymerization

The resistance to flow of polymer solution through a capillary is very informative as A- It provides information on the size of polymer chains.

B-Its flexibility and shape in solution.

C-Its interactions with solvent in which it is dissolved.

Viscosity of dilute polymer solution is higher than ordinary solutes.

Ubbelohde viscometer by German chemist (1877-1964).

Ubbelohde type viscometer or suspended-level viscometer is capillary based viscometer used to measure viscosity of polymers

Where, t0 and ρ0 are the elution time and density of the pure liquid. When the solution is very dilute

The so-called specific viscosity becomes:

This specific viscosity is related to the concentration of the analyte.

Concentration dependence of reduce viscosity.

This specific viscosity is related to the concentration of the analyte.

Where, ηsp/c is called the viscosity number

Or reduce viscosity

Concentration dependence of inherent viscosity

lnr

C k

2C + ........

k' - k'' should equal 0.5

Inherent and reduce viscosity are having common intersect

Typical Huggins and Kraemer Plots (note common intercept for both curves)

Intrinsic viscosity [η] is a measure of a solute's contribution to the viscosity η of a solution and related to the molecular weight of the polymers as

a and K, depend on the particular polymer-solvent system.

Also, the molecular weights of two different polymers in a particular solvent can be related using the Mark-Houwink equation when the polymer-solvent systems have the same intrinsic viscosity:

a a ~ 0.5 (randomly coiled polymers) ~ 0.8 (rod-like, extended chain polymers)K K between 10-3 and 0.5

K Ma Mark-Houwink equation

32

12

320

2

322

0 )()(

][

MM

r

M

r

[] intrinsic viscosity related to size (r0)

is Flory constant (3×1024 mol-1)

M

r 20 is a constant

At temperature, = 1 2

1

][ MK

At other conditions a

MK][

In the above equation the intrinsic viscosity is written along with expansion factor and the unperturbed end-to-end distance

Intrinsic viscosity and unperturbed dimension of polymer chains

In a theta solvent, the expansion factor () is 1

Thus [] proportional to the square root of molecule weight ( M½ ) and the 3/2 power of

[] = < r2>< r2>3/2< r0

2>M M M

< r2 > = r02

< r02>/ M

[] = < r02>

M

Effect of Mw on Intrinsic Viscosity of Polymer

The Ubbelohde capillary viscometer

The most useful kind of viscometer for determining intrinsic viscosity is the "suspended level" or Ubbelohde viscometer.

B

A: Plug while drawing fluid into capillary

D: Timing lines

C: Pressure equilibration arm

Little bulb, whose volume = V.Q = V/tflow

Capillary

Big Bulb/Reservoir

Single point estimation of intrinsic viscosity by Solomon and Ciuta is sufficiently accurate

The intrinsic viscosity is determined by extrapolation of the ratio ηsp/C through various concentrations to zero concentration . This is impractical for chromatographic detection and it also turns out to be unnecessary wastage of time.

[] = C

[2 ( sp-ln(sp + 1)) ]1/2

Dimension of polymer chains and intrinsic viscosity

1- Root-mean-squared end-to-end distance of

Polymer Chains < r2>1/2

2-Hydroynamic Radius of Polymer Chains (Rh)

3-Root mean squared radius of gyration < rg2>1/2

4- The simplest conformation of polymer chain is fully extended

chain.The end to end distance in this idealized model for chain

length is  

r = n l

Root mean square end-to-end distance and root mean square radius of gyration

The average root mean square end-to-end distance for the chain, <r2>1/2, turns out to be l times the square root of N. In other words, the average distance scales with N0.5.

Average end-end distance of polymer (<r2>1/2 )

A quantity frequently used in polymer physics is the radius of gyration <rg

2>1/2 . it is root-mean-square (r.m.s.) distance of all the bonds from the centre-of-mass of the chain, averaged over all possible conformations.

< r2> 1/2 = N l

< rg2> 1/2 = ------

N l

6

Root-mean-squared end-to-end distance of

Polymer Chains and Intrinsic Viscosity

Flory-Fox expression for the root-mean-squared end-

to-end distance of polymer molecules in solution.

The constant for polymer molecules in a good solvent has been found experimentally to be of

2.1 × 1021 dl / mol cm3.

< r2> 1/2

< r2> 1/2 = [] M/

Hydroynamic Radius of Polymer Chains ( Rh)

and Intrinsic viscosity.

Based on Einstein viscosity relation

The hydrodynamic radius Rh may be calculated using

Einstein viscosity relation, considering hydrated polymer molecules as hydrodynamic spheres that would increase the viscosity to the same extent as solid spherical particles of volume Ve:

where M = polymer molecular weight (g/mol), N = Avogadro's number, and Ve = the volume of an

equivalent spherical particle (cm3). Since

Thus, for each polymer is

simply 3.1- fold greater than Rh.

< r02>

[] = M

2.5 NVe

Rh = ------------ (cm)3[]M

10 N

1/3

Ve = 4/3 Rh3

The and M are proportional to the number of bonds or n.

Therefore, is a constant for a particular polymer that is independent of molecular weight.

Thus above equation is simplified to Where , K is a constant

For polymers in non-theta solvents, will no longer be one hence [] will not be square-root dependence on molecular weight.

where may have molecular weight dependence of its own. Thus for non theta condition it is written as

[

[

[a

< r02>/ M

< r02>

Effect of branching on pervaded volume between a linear chain and a branched chain with the same total chain length

The hydrodynamic volume is smaller with the same mass of polymer molecule with high density, producing a lower Intrinsic Viscosity.

The Mark-Houwink plot is the central plot of polymer structure analysis. It reflects structural changes in the polymer, such as polymer branching and chain rigidity.

Mark-Houwink constant (a) related to the structure of polymer. If its value varies from 0 to 0.1 = spherical, 0.35 to 0.80 = random coil, and 1.5 to 2 = rigid rod structure.

More Precise information about the values of

‘a’ in Mark-Houwink Equation

1- Value of a = 0 Sphere shape polymer molecules

2- = 0.5 - 0.8 Random coil structure

(0.5 Flory temperature and

0.8 for thermodynamically good solvent

3- = 1.0 Stiff coil structure

4- = 2.0 Rod shape structure

[a

Branching index

The branching index measures the effect of long-chain branches on the size of a macromolecule in solution.

It is defined as:

g = <sb2>/<sl

2>

where sb is the mean square radius of gyration of the branched macromolecule in a given solvent, and sl is the mean square radius of gyration of an otherwise identical linear macromolecule in the same solvent at the same temperature.

A value greater than 1 indicates an increased radius of gyration due to branching.

Intrinsic viscosity and degree of long chain branching in polymers

Intrinsic viscosity is related to the degree of long chain branching in polymers through the following factor (g’), which is analogous to ratio of mean square radius of gyration ‘g’.

Where, [η]M,br denotes the intrinsic viscosity of the branched polymer at molecular weight M

and [η]M,lin is the intrinsic viscosity of the corresponding linear polymer at the same molecular weight M.

ε is a structure value having an average value of approximately 0.8

g' =[

[

br

lin

Intrinsic viscosity versus molecular weight plots (‘Mark-Houwink’ plots) for linear and branched PVA polymers.

Branching distribution overlaid with the weight fraction distribution of the branched PVA sample.

Left hand axis shows the number of branches

Zimm and Stockmayer equations for degree of branching

R a n do m , T ri-fu n ctio n al m o n o dis p erse

gM = 1 + MB

7

1/2

+BM4

9

1/2-

Sta r b ra n ch m o n o disp erse

gM =

MB6

BM+ 1( ) BM

+ 2( )

In each of these equation, the nu m ber of braches (B M ) is related to an entity ,which in turn related to as,

gM' = g

Mb

where b is structure factor for the polym er

gM' =

[ br

[ lin

gMb

gM

To determine the branching number( BM) for a branched polymer, we need to know its structure factor ‘b’ , to decide which branching calculation has to be made. The average value of b is 0.8. This can be determined either from the Mark-Houwink constants ‘a’ of the polymer, or by inspection from a linear reference sample.

Inject a series of Narrow Standards of known Molecular Weight. Measure the Retention Volume (RV) of the resulting peak apex. Construct a calibration curve of Log(MW) vs. Retention Volume.

GPC Theory : In Gel Permeation Chromatography

Intermolecular forces:

1-The intermolecular forces for polymers are the

same as for small molecules.

2-Though, the magnitude of their intermolecular

forces can vastly exceed those between small

molecules.

3-The presence of strong intermolecular forces is

one of the main factors leading to the unique

physical properties of polymers.

4-These intermolecular forces are following types.

A-Dispersion Forces:

B-Dipole-Dipole Forces:

C-Hydrogen Bonds:

A-Dispersion Forces

1-Dispersion forces are due to instantaneous dipoles that form as the charge clouds in the molecules fluctuate. 2-Dispersion forces, the weakest of the intermolecular forces.

3-These only forces possible for non-polar polymers such as polyethylene.

4-Dispersion forces depend on the polarizability of a molecule.

5- Large polymers with high molecular weights can have significant dispersion forces.

Ultra high molecular weight polyethylene (UHMWPE), which has a molecular weight in excess of 3,000,000 g/mole, is used to make bulletproof vests. 

B-Dipole-Dipole Forces

Dipole-dipole forces result from the attraction between polar groups,such as those in

1- polyesters and,

polyester called poly(ethylene terephthalate) (PET)

2- Vinyl polymers with chlorine pendant groups.

Polyvinyl chloride.

C-Hydrogen Bonding

Hydrogen bonding can take place when the polymer molecule contains -OH or -NH groups.

Hydrogen bonding is the strongest of the intermolecular forces.

Polymers such as

1-Poly(vinyl alcohol) and,

polyamide(nylon)

2-Polyamides, polpeptides have hydrogen

bonding

D-Electrostatic interactions

In addition to hydrogen bonding, there are electrostatic interactions, such as those between COO− and NH3+ groups of the side chains.

1-Interactions between polymers influence the

physical properties,

both in equilibrium and

nonequilibrium conditions.

Manifestation of Molecular Interactions in Polymers

2-Most thermoplastics are polymers with

high molecular weight that are associated

through the van der waals forces, dipole-

dipole interactions etc

Physical properties

1- Solution properties.

(Interactions with the solvents:

solubility, viscosity etc)

2- Phase Transition Temperatures.

Glass Transition Temperature(Tg)

3- Mechanical Properties.

(Tensile strength, elongation, retraction

forces, thermo mechanical behavior)

4- Stability toward heat and chemicals.

(Decomposition on heating, and

corrosive effect of solvent)

5- Miscibility with other polymers

(Extent of Blending or mixing)

Retraction forces in elastomers

They return to original shape due to intermolecular forces

State of material is also influenced by these Intermolecular forces

Textbooks:

1. Billmeyer Jr.(FW).Text book of Polymer Science. 3rd Ed. 1994, Wiley Interscience, New York.

2. Fried (JR). Polymer Science and Technology. 2002, Prentice-Hall ofIndia

3. Stevens(MP), Polymer Chemistry: An Introduction. 3rd Ed. 1999, OxfordUniversity Press, New York.

4. Seymour (RB). Carraher Jr (CE). Polymer Chemistry.1991, Marcel-Dekker,NewYork.

S.N. Particulars Contact

    Hrs

1. Introduction: General idea of the polymers and their 4

  classifications, molecular forces and chemical bonding; Polymers in  

  technological and biomedical fields.  

2. Polymer chains and molecular weights: Degree of  

  polymerization, Number and weight average molecular weights. 6

  Molecular weight dispersity and characteristics of polymers, Weight  

  and composition heterogeneity in polymers. Polymer chain  

  dimension and solution viscosity. Thermal and spectral  

  characteristics of polymers.  

3. Methods of polymer synthesis: Synthesis of polymers using bulk, 6

  solution, emulsion, suspension and interfacial route of  

  polymerization and characteristics of polymers. Addition and step  

  growth polymers.  

4. Technological polymers: Polymer blends, Polymers Composites, 6

  Polymer films, Resins, Foams, Polymer Liquid Crystals and  

  Engmeering Plastics, Smart and Responsive Polymers. Polymers for  

  Device Applications, Biodegradable Polymers. Conducting polymers  

5. Industrial Polymers: Vinylic and Phenolics, Polyesters, 6

  Polyamides, Polyphosphazenes, Polysilanes, Polysiloxanes,  

  Coordination and Organometallic polymers, Polyacrylates