Polymer Chemistry

The word polymer is derived from the classical Greek words poly meaning "many" and meres meaning "parts".

Simply stated, a polymer is a long-chain molecule that is composed of a large number of repeating units of identical structure.

Certain polymers, such as proteins, cellulose, and silk, are found in nature, while many others, including polystyrene, polyethylene, and nylon, are produced only by synthetic routes.

In some cases, naturally occurring polymers can also be produced synthetically.

An important example is natural (Hevea) rubber, known as polyisoprene in its synthetic form.

Polymers that are capable of high extension under ambient conditions find important applications as elastomers.

In addition to natural rubber, there are several important synthetic elastomers including nitrile and butyl rubber.

Other polymers may have characteristics that enable their fabrication into long fibers suitable for textile applications.

The synthetic fibers, principally nylon and polyester, are good substitutes for naturally occurring fibers such as cotton, wool, and silk.

In contrast to the usage of the word polymer, those commercial materials other than elastomers and fibers that are derived from synthetic polymers are called plastics.

A typical commercial plastic resin may contain two or more polymers in addition to various additives and fillers.

These are added to improve a particular property such as process ability, thermal or environmental stability, or mechanical properties.

The birth of polymer science may be traced back to the mid-nineteenth century.

In the 1830s, Charles Goodyear developed the vulcanization process that transformed the sticky latex of natural rubber into a useful elastomer for tire use. In 1847, Christian F. Schönbein reacted cellulose with nitric acid to produce cellulose nitrate. This was used in the 1860s as the first man-made thermoplastic, celluloid. In 1907, Leo Hendrik Baekeland produced Bakelite (phenol−formaldehyde resin). Glyptal (unsaturated-polyester resin) was developed as a protective coating resin by General Electric in 1912

Examples :

1. Proteins are built from many amino acids. Proteins are polymers, amino acids are the monomers.

2. Polyethylene : n CH2 = CH2⟶ (CH2-CH2)n

3. Polystyrene:

4. Polymethyl Methacrylate

Degree of Polymerization:

Represents the number of structural or monomeric units contained in polymer

P = M/m

M = Molar mass of polymer,

m = Molar mass of monomeric units

Molecular Weight

Number Average Molar Mass:

Each molecule contribute account to its mass.

Used in Osmotic pressure, End group analysis, Colligative properties

Used in light Scattering

Compared to Mn, Mw takes into account the molecular weight of a chain in determining contributions to the molecular weight average.

The more massive the chain, the more the chain contributes to Mw.

Mw is determined by methods that are sensitive to the molecular size rather than just their number, such as light scattering techniques.

If Mw is quoted for a molecular weight distribution, there is an equal weight of molecules on either side of Mw in the distribution.

z-Average Molar Mass:

Used in sedimentation equilibrium.

Viscosity Average Molar Mass:

a is characterized by system under study and value lies between 0.5 and 1:

Used in intrinsic viscosity

a= Mark Houwink exponent when a= 1

a is depend on the temperature, nature of solvent and polymer sample.

Polydispersity Index (P.D.I) or heterogeneity index:

The polydispersity index is used as a measure of the broadness of a molecular weight distribution of a polymer, and is defined by ratio of weight average molecular weight and number average molecular weight.

For Monodisperse system P.D.I =1 and for polydisperse system greater than one (>1)

Kinetic Chain Length:

It is the ratio of overall rate to the rate of initiation.

It can also be defined as number of repeating chain units in polymer chain.

Kinetic chain length = (Rate of formation of product)/(Rate of intition reaction)

Probability (P) for addition of another monomer to growing chain is given by:

Kinetics of condensation polymerization:

f = fraction of reaction that has occurred at time t.

[M1]0 = initial concentration of monomer

Mm + Mm ⟶ M(m+n)

Net rate of disappearance is given by :

Net rate of production of dimer Mm+n :

Concentration of n.mers is :

[Mn] = [[M1]0fn-1(1-f)2]

Condensation polymerization also known as "Step Growth Polymerization".

For condensation poly relation between :

P = probability or extent of reaction.

Probability of forming K mers is given by:

Pk = Pk-1 (1-P)

mole fraction of K mers is:

xk =(1-P)P(k-1)

Number average or mean value of k [ or number average degree of polymerization] is given by:

Mass fraction of molecules having k units is given

Maximum in the plots shifts to larger value of k with increasing value of P

where M1= molar mass of repeating unit

Contour Length [RC]:

Length of macromolecule measured along is backbone from atom to atom

RC = Nl

N = number of monomer unit or number of bonds

l = length of monomer units

Mean Squar end to end Distance of Chain:

Rrms = N1/2 l

Mean End to End Distance of Chain:

Most Probable End to End Distance:

Rmp =(2/3 )(1/2) N(1/2) l

For a linear Coil Polymer Chain:

Rg = 1/√6 Rrms

Rg = radius of gyration

For Constrained Chain:

A factor "F" is multiplied to above obtained relations

For tetrahedral bonds θ = 109°5 ∴ F= √2

Solvents in Polymer Chemistry

Good Solvent:

Strong interaction between solvent and polymer than between solvent or between segments of polymer and polymer uncoil is good solvent.

Poor Solvent :

Strong interaction between segment of polymer and no interaction between polymer and solvent.

polymer coil is poor solvent.

Effectiveness of solvent is given by value of 2nd virial coefficient B.

=18 cm3/mol

M = molar mass

Good Solvents :

B > Bideal

B ≈10-5 to 10-3

Poor Solvents :

B ≤ 0

Determination of Molar mass of macromolucules


Unit of Viscosity= (dyne/cm2)/(cms-1/cm)

So Unit = dyne / (cm2 x sec )

Unit of Viscosity= gm/cm/sec and 1poise = 1 gm/cm/sec

In SI units:

Unit of Viscosity = Nm-2 sec

1 N m-2 sec = 1 kg m-1 sec-1

1 Kg m-1 sec-1 = 10 g cm-1 sec-1

1 Kg m-1 sec-1 = 10P

Relative Viscosity: [ or Viscosity Ratio]

Specific Viscosity:

Reduced Viscosity: [or Viscosity Number]

Intrinsic Viscosity: Also known as limiting viscosity number.

also called as : Viscosity Number, Staudinger Index

C = concentration of polymer

Note: None of the above quantities have units of viscosit

Relation between viscocity of dilute solution and volume fraction

η = η0(1 + 2.5 Φ)

Φ= Volume fraction of solute molucule

η/η0 - 1 = nsp = 2.5 Φ

ηrel - 1 + 2.5Φ


[η]= (2.5Φ)/C

Relation between [η] and Molar of Polymer

This is Mark Houwink Sakurada equation or staudiger

Mvisc = Viscosity average molar mass of polymer

k = Mark Houwink constant

a = 0.8 ⇒ random coils

a =0 0.5 ⇒ globular proteins a = 0.92 i.e. max for PVC in THF solvent

a = 0.50 (min) for polyisobutylene in C6H6

Graph between (ηsp/C) vs. concentration (C)

Unit of [η] = cm3/gm, unit of K = dL/gm

If a = 1 and C ⟶ 0


Only colligative property useful for investigating macromolecules.

Not good for studying solutes of low molar mass because membranes are impermiable to such solutes.

Van't Hoff Equation

Π/C = reduced osmotic pressure

For a polydisperse solute

B = 2nd Virial coefficient

Graph between Π/C2RT v/s C2 gives number average molar mass


(a) Sedimentation Velocity

for spherical molecules only

v = Partial specific volume

S = Sedimentation coefficient [Unit= Svedberg IS= 10-13 sec]

ŋ = Coefficient of viscosity

r = radius of spherical polymer particle

For any other type of polymer molecule

p = density

D = Diffusion coefficient

Here sedimentation coefficient is independent of w i.e.angular velocity.

Unit of v = rotation per minute , w = radians / sec , r = in cm and t = in sec

S = (dr/dt)/ w2r

(b)Sedimentation Equilibrium

Better Method no prior knowledge of shape of macro molecule is required

Sedimentation velocity ⇒ gives number average molar mass [Mn]

Sedimentation equilibriu ⇒ gives mass average molar mass [Mm]

These two apply only when M is not given in option.

Light Scattering Method: Based on Tyndall effect

Rayleigh Equation:

ratio of scattered light intensity ( I θ) to incident light intensity (I0)

r = distance of observer from sample

a = number of scattering particles I unit vol

a = electrical polarizability

Iθ α 1/λ4

Therefore, blue light is scattered more than red light

This accounts for colour of sky when viewed in any direction except towards sun.

Rθ is independent of θ

For non-ideal polymer solution, there are interactions between the polymer molecules, Random Brownian motion causes fluctuations in concentration .

So equation becomes:

Turbidity: Turbidity is given by :

Diffusion :

K = R / NA

f = 6π η r

⇒ functional coefficient

During Diffusion: Average Distance < x > = 0

Root mean square distance is :

frictional ratio (f /fo) is useful for ascertaining the shape of biomolecule

f / f0 ≈ 1

⇒spherical shape

f / f0 > 1

⇒ rod like shape


a = variable depnds upon the system under investigation/study