CY 1050
Macromolecules as Engineering Materials
Dr. R.L. Gardas
Office: CB 214 (First Floor)
E-mail: gardas@iitm.ac.in
Phone: 4248
9 credits
A slot
Mon: 8:00 am
Tue: 1:00 pm
Thu: 11:00 am
Quiz - I & II
End-Sem
Concepts
–
(6-7 hours)
Synthesis, Thermodynamics and kinetics
–
(12-14 hours)
Characterization
–
(9-10 hours)
Applications
–
(9-10 hours)
References:
1. Polymer Science and Technology by Joel R. Fried, Prentice Hall of India Pvt. Ltd.
1999.
2. Textbook of Polymer Science, by Fred W. Billmeyer Jr. Fourth Edition, 1999. WileyInterscience, New York.
3. Principle of Polymerization by George Odian, Fourth Edition, Wiley-Interscience,
New York 1999.
4. Polymer Science, By V.R. Gowarikar, N.V. Viswanathan and S. Jayadev.
Concepts - Small molecules to macromolecules. Definitions and nomenclature.
Classification of polymers, types of polymerizations (chain growth, step growth and
living), molecular weights and distribution. An elementary tour of physical methods
of determining molecular weights and distribution. (6-7 hours)
Synthesis of Macromolecules - Thermodynamics and kinetics of chain
polymerization with reference to industrially important polymers such as
polyethylene, polypropylene, polystyrene, poly(vinyl chloride). Thermodynamics
and kinetics of step polymerization with reference to specialty polymers such as PET,
Nylon, PC, and PU. Step growth polymerizations involving crosslinking (gelation) or
formation of insoluble polymer mass. Determination of polymer structure via IR and
NMR spectroscopies. (12-14 hours)
Characterization of polymer structure in the solid state - Characteristics of
Amorphous and semicrystalline polymers.
Viscoelasticity.
Glass transition
temperature and elementary theories of glass transition. Rubber elasticity and
thermodynamic theory of rubber elasticity. (9-10 hours)
Applications – Engineering and specialty polymers, high performance fibres
(Kevlar), Composite materials (BMC and SMC), conducting plastics. Polymers for
separation science, biomedical devices, electronics and photonics. (9-10 hours)
Class – 1
Engineering materials
The science of macromolecules is divided
between biological and nonbiological materials.
This course is concerned primarily with the
chemistry nonbiological polymers.
These are the synthetic materials used for
plastics, fibers, and elastomers, with a few
naturally occurring polymers, such as rubber,
wool, and cellulose, included
A polymer is a large molecule built up by the repetition of
small, simple chemical units (held together by chemical bonds).
In some cases the repetition is linear, much as a chain is built
up from its links.
In other cases the chains are branched or interconnected to form
three dimensional networks.
The repeat unit of the polymer is usually equivalent or nearly
equivalent to the monomer, or starting material from which
the polymer is formed.
Repeat unit of poly(vinyl chloride) is –CH2CHCl –
Its monomer is vinyl chloride, CH2=CHCI
The repeating units constituting the polymer molecule are
called constitutional repeat units (or CRU).
Convert Monomer to Polymer
A monomer needs to have at least bifunctionality,
which may arise from one double bond or two reactive functional groups to
undergo polymerisation.
Two major types of polymerisation methods are used to convert small
molecules (monomers) into polymers.
(i) Addition polymerisation
(chain-, chain growth-, or chain reaction polymerisation)
(ii) Condensation polymerisation
(step-, -step growth, or step reaction polymerisation
polycondensation)
Unsaturated monomers usually follow Addition polymerisation while those,
containing functional groups undergo Polycondensation.
For example, polyethylene and polypropylene are addition polymers (as the
monomers undergo addition polymerisation).
Each carbon has three sp2 hybridised orbitals
that form three sigma (σ) bonds and the
remaining p orbital forms the pi (π) bond.
The double bond between 2 C consists of one
sigma bond and one pi bond.
C=C bond length
dissociation energy
1.34 Å
611 kJ/mol
nylons, terylene etc. are condensation polymers
(as the monomer pairs undergo condensation).
Addition polymerisation
(Chain-growth polymerisation)
Polycondensation
(Step-growth polymerisation)
1
Monomers are unsaturated
Monomers contain two or more
functional groups
2
Involves opening of double bond by
active species like free radical or ion
Involves reaction between functional
groups
3
Nothing is eliminated as a result of
this type of polymerisation
Usually small molecules like H2O,
CH3OH, HCI, etc. are eliminated
4
Polymer molecular weight is equal to
DP x molecular weight of monomer
Not so, some small molecules often
get eliminated
5
High molecular weight in polymer is
attained at once
High molecular weight is attained only
at very high conversions
6
Only monomers and polymers are
present during the course of
polymerisation
All possible molecular weight species
viz. dimers, trimers, tetramers and
multimers etc. are present
7
Examples: polyolefins, polydienes,
vinylpolymers and acrylic polymers
Examples: polyesters, polyamides and
polycarbonates
Addition polymerisation
(Chain-growth polymerisation)
Polycondensation
(Step-growth polymerisation)
8
Can be done by bulk, solution,
suspension, and emulsion
polymerisation techniques
Polycondensation can be achieved in
melt, solution as well as at interfacial
boundary between two liquids
9
Can quickly lead to a polymer with
very high molecular weight
Slow stepwise addition process
Addition polymerisation (Chain-growth polymerisation)
Important characteristics of chain polymerisation are:
(i) once the initiation occurs, the polymer chains form very quickly
i.e. in the time scale of 10-1 to 10-6 s
(ii) the catalyst concentration needed is very low and that means during the
course of polymerisation only monomers and polymer are present
(iii) the process is usually exothermic
(iv) high polymers with molecular weights of 10,000 to >10 million can be
obtained.
ΔG = ΔH − TΔS
Class – 2
Quick Revision of Class -1
• To get polymerised, a monomer needs to have at least bifunctionality.
• Two major types of polymerisation methods:
(i) Addition polymerization (chain-, chain growth-, or chain reaction)
(ii) Condensation polymerisation (step-, -step growth, or step reaction
polycondensation)
Addition polymerisation
(Chain-growth polymerisation)
Polycondensation
(Step-growth polymerisation)
1
Monomers are unsaturated
Monomers contain two or more
functional groups
2
Involves opening of double bond by
active species like free radical or ion
Involves reaction between functional
groups
3
Nothing is eliminated as a result of
this type of polymerisation
Usually small molecules like H2O,
CH3OH, HCI, etc. are eliminated
4
Polymer molecular weight is equal to
DP x molecular weight of monomer
Not so, some small molecules often
get eliminated
5
High molecular weight in polymer is
attained at once
High molecular weight is attained only
at very high conversions
6
Only monomers and polymers are
present during the course of
polymerisation
All possible molecular weight species
viz. dimers, trimers, tetramers and
multimers etc. are present
7
Examples: polyolefins, polydienes,
vinylpolymers and acrylic polymers
Examples: polyesters, polyamides and
polycarbonates
Addition polymerisation
(Chain-growth polymerisation)
Polycondensation
(Step-growth polymerisation)
8
Can be done by bulk, solution,
suspension, and emulsion
polymerisation techniques
Polycondensation can be achieved in
melt, solution as well as at interfacial
boundary between two liquids
9
Can quickly lead to a polymer with
very high molecular weight
Slow stepwise addition process
Addition polymerisation (Chain-growth polymerisation)
Important characteristics of chain polymerisation are:
(i) once the initiation occurs, the polymer chains form very quickly
i.e. in the time scale of 10-1 to 10-6 s
(ii) the catalyst concentration needed is very low and that means during the
course of polymerisation only monomers and polymer are present
(iii) the process is usually exothermic
(iv) high polymers with molecular weights of 10,000 to >10 million can be
obtained.
ΔG = ΔH − TΔS
Mechanism of polymerization
(Addition polymerisation )
If monomers containing at least a double bond participates in the
polymerisation reaction, the polymerisation will consists of three steps:
Initiation
Propagation
Termination
Initiation step comprises of the reaction of the active species generated from
an initiator (or catalyst by its decomposition) and adds to the C=C bond of the
monomer.
The active species generated from an initiator may be a free radical, a cation,
an anion or a coordination complex.
These species on reaction with the monomer form new free radicals such as a
carbocation, a carbanion or a coordination complex.
Mechanism of polymerization
Initiation
(Addition polymerisation )
Propagation
Termination
After the initiation, the second step is propagation, where the newly
generated 'active species' adds to another monomer in the same manner as in
the initiation step.
This procedure is repeated over and over again until the final step of the
polymerisation process 'termination', occurs.
The termination step is one when the growing chain with active species reacts
with other growing chain or by the spontaneous decomposition of the active
site.
Termination types : (a) Combination; and (b) Disproportionation.
Addition polymerisation (Chain-growth polymerisation)
The initiators for chain polymerisation may be different depending upon
the nature of initiation.
Free raidical chain polymerisation
Cationic chain polymerisation
Anionic chain polymerisation
The initiators commonly used for generating various active species are
listed below;
General Considerations of Polymerizability
• Whether a particular monomer can be converted to polymer depends on both
thermodynamic and kinetic considerations.
• Polymerization is possible only if the free-energy difference ΔG between
monomer and polymer is negative.
ΔG = ΔH − TΔS
• However, the ability to carry out a thermodynamically feasible polymerization
depends on its kinetic feasibility—on whether the process proceeds at a
reasonable rate under a proposed set of reaction conditions (type of initiation,
temperature, etc.).
• Thus, whereas the polymerization of a wide variety of unsaturated monomers is
thermodynamically feasible, very specific reaction conditions are often required
to achieve kinetic feasibility in order to accomplish a particular polymerization.
Kinetics of polymerization
Kinetics:
the speed of a reaction under a given set of conditions
How these conditions will influence the
• polymer molecular weight
• molecular weight distribution
• chemical composition
• extent of polymer conversion etc.
Kinetics of chain polymerization
3 Steps:
Initiation
Propagation
Termination
The carbon–carbon double bond in alkene monomers and the carbon–oxygen
double bond in aldehydes and ketones are the two main types of linkages that
undergo chain polymerization.
The polymerization of the carbon–carbon double bond is by far the most
important of the two types of monomers.
The carbonyl group is not prone to polymerization by free radical initiators
because of its polarized nature:
Aldehydes and ketones are polymerized by both anionic and cationic initiators
Kinetics of chain polymerization
The carbonyl group is not prone to polymerization by free radical initiators
because of its polarized nature:
Aldehydes and ketones are polymerized by both anionic and cationic initiators.
Unlike the carbonyl linkage, the carbon–carbon double bond undergoes
polymerization by both radical and ionic initiators.
The difference arises because the p-bond of a vinyl monomer can respond
appropriately to the initiator species by either homolytic or heterolytic bond
breakage:
Kinetics of chain polymerization
Whether a vinyl (−CH=CH2) monomer polymerizes by radical, anionic, or
cationic initiators depends on the inductive and resonance characteristics of
the substituent(s) present.
Effects of Substituents
3 Steps:
Initiation
Propagation
Termination
Free Radical Chain Polymerisation
To initiate the reaction, there must be free-radicals available,
which are usually generated by the homolytic decomposition of an initiator:
----- (1)
I is initiator, R• is free-radicals formed, kd is initiator decomposition rate constant.
Free Radical Chain Polymerisation
Formation of
Free Radicals
from the Initiator:
BPO
(Benzoyl peroxide)
AIBN
(Azo bis isobutyro
nitrile)
3 Steps:
Initiation
Propagation
Termination
Class – 3
Quick Revision of Class -2
• Whether a particular monomer can be converted to polymer depends on both
thermodynamic and kinetic considerations.
• Kinetics of polymerization: speed of a reaction under a given set of conditions
3 steps:
Initiation
Propagation
Termination
• C=C (alkene/ vinyl) and C=O (aldehydes and ketones) monomers undergo chain
polymerization.
• Initiators: Free radical / cation / anion
Free Radical Chain Polymerisation
Decomposition
Initiation
Propagation
Termination
3 Steps:
Initiation
Propagation
Termination
Free Radical Chain Polymerisation
To initiate the reaction, there must be free-radicals available,
which are usually generated by the homolytic decomposition of an initiator:
----- (1)
I is initiator, R• is free-radicals formed, kd is initiator decomposition rate constant.
The rate of decomposition (Rd) of the initiator is related
to the concentration of the initiator (I) :
----- (2)
A factor of 2 is used as a pair of radicals is produced
by decomposing one molecule of the initiator.
3 Steps:
Initiation
Propagation
Termination
Free Radical Chain Polymerisation
From the Arrhenius equation, the rate constant is related to temperature as:
----- (3)
where A is frequency factor; E is activation energy; R is gas constant and T is absolute
temperature.
Substituting kd , from Eqn (3); Eqn (2) can be written as
----- (4)
the rate of decomposition of an initiator increases with the temperature and
concentration of the initiator.
Free Radical Chain Polymerisation
Step 0. Decomposition
The free-radical generated by
the decomposition of the initiator (Eqn 1),
can attack the monomer to give a new free radical:
----- (5)
where M is the monomer, ki is initiation rate constant.
Rate of initiation (Ri) can be written as
----- (6)
Free Radical Chain Polymerisation
Step 1. Initiation
The free-radicals have such a high reactivity that as soon as they are formed by the
decomposition of the initiator, they attack the monomer and start the initiation
process.
We can assume, therefore, that the rate of formation of free-radicals is equal
to the rate of the disappearance of the same according to Eqn (5).
Therefore, we can write Ri is equal to Rd,
----- (7)
Eqn (7) is correct when all the free-radicals produced are effective in initiating the
polymer growth. Actually, some of them are not effective since they are lost as side
products by way of processes such as recombination.
So, Ri should be further modified as
----- (8)
where f is the fraction of the free-radicals produced that
is effective in initiating the chain growth
The value of f is usually between 0.6 and 1.0
Free Radical Chain Polymerisation
Step 2. Propagation
Initiation is followed by a propagation step which can be represented as
Eqn (5).
----- (9 a)
----- (9 b)
----- (9 c)
where kp is propagation rate constant.
Rate of propagation (Rp) can be written as
----- (10)
Propagation rate is proportional to [M]•, the concentration of reactive free-radical
sites (i.e., concentration of growing chains) as well as [M], the concentration of the
monomer.
Free Radical Chain Polymerisation
Step 3. Termination
The final step in polymerlsation is termination.
If termination occurs by the combination of two growing chains (i.e., coupling),
it can be represented as
----- (11)
where kt is termination rate constant.
Rate of termination (Rt) can be written as
----- (12)
However, when the steady state prevails (i.e., when the number of chain growths
initiated equals the number of chain growths arrested),
the rate of initiation is equal to the rate of termination, i.e.
----- (13)
Free Radical Chain Polymerisation
From Eqn (8)
Step 3. Termination
and Eqn (12)
----- (14)
Now, from Eqn (10)
get the value of [M]•
----- (15)
and substitute this value of [M]• in Eqn (14)
or
----- (16)
Rate of polymer formation is proportional to the monomer concentration
and also to the square-root of the initiator concentration.
Class – 4
Quick Revision of Class -3
Free Radical Chain Polymerisation
Degree of Polymerisation (DP)
decreases
➢ with an increase of T and [I]
➢ with a decrease of [M]
Extent of conversion (p) increases
➢ increases with an increase of
T , t , [I] , [M]
Free Radical Chain Polymerisation
Step 3. Termination
The final step in polymerlsation is termination.
If termination occurs by the combination of two growing chains (i.e., coupling),
it can be represented as
----- (11)
where kt is termination rate constant.
Rate of termination (Rt) can be written as
----- (12)
However, when the steady state prevails (i.e., when the number of chain growths
initiated equals the number of chain growths arrested),
the rate of initiation is equal to the rate of termination, i.e.
----- (13)
Free Radical Chain Polymerisation
From Eqn (8)
Step 3. Termination
and Eqn (12)
----- (14)
Now, from Eqn (10)
get the value of [M]•
----- (15)
and substitute this value of [M]• in Eqn (14)
or
----- (16)
Rate of polymer formation is proportional to the monomer concentration
and also to the square-root of the initiator concentration.
The kinetic chain length ()
can be defined as the average number of monomer molecules consumed by
each effective free-radical generated by the initiator.
Degree of Polymerisation (DP)
As the kinetic chain length gives the average number of monomer molecules present
in a growing chain at the time of termination, the average degree of polymerisation,
, can be correlated as follows:
N=0.5 when Termination by Coupling
N=1 when Termination by Disproportionation
General Statements, from Free Radical Chain Polymerisation
Degree of Polymerisation (DP) decreases
➢ with an increase of T and [I]
➢ with a decrease of [M]
Extent of conversion (p) increases
➢ increases with an increase of T , t , [I] , [M]
Chain Transfer
Termination
Termination of growing polymer chain can take place through chain transfer:
where ktr is the chain transfer rate constant and RH is the chain transfer agent
Many initiators (not all) can encourage the chain transfer reaction.
Chain transfer reactions are of greater significance with the solvents.
Chain transfer constant (C)
is used to asses the ability of solvent/substance to act as chain transfer agent
ktr
𝑪=
kp
where ktr and kp are the rate constants for
the chain transfer and propagation reaction
Chain Transfer
Chain transfer constant (C) increases with temperature.
ktr
𝑪=
kp
Extent of MW or DP decrease by chain transfer agent can be obtained by
measuring MW or DP as function of concentration of chain transfer agent
Chain Transfer
ktr
𝑪=
kp
Chain Transfer
where
Mayo Equation
DP0 is the DP in the absence of chain transfer agent
DP is the same in the presence of chain transfer agent
DP0 will always greater than DP
Kinetics of Copolymerisation
The process of polymerising two or more than two monomers together is called
copolymerisation.
The term copolymer is better referred to as addition polymers.
The copolymers often possess the properties shown by the homopolymers made
from the constituent monomers of the copolymer. Instead of searching new
monomers for the production of polymers with desired properties, it is often desired
to achieve this by copolymerisation using the well known inexpensive monomers like
styrene, ethylene, propylene, butadiene, vinyl chloride and other common vinyl and
acrylic monomers etc.
Kinetics of Copolymerisation
Some very useful and commercially important copolymers are SBR and NBR- the
copolymers of butadiene with styrene or acrylonitrile. These copolymers are ideal
elastomers and possess properties superior to polybutadiene rubber.
Block copolymers of styrene and butadiene are excellent thermoplastic elastomers.
The kinetics of copolymerisation is well understood and on its basis one can predict
the composition of a copolymer and its nature when the two different monomers are
copolymerised in different mole ratios in the feed.
Kinetics of Copolymerisation
The kinetics of copolymerisation is described below:
When two monomers say M1 and M2 are simultaneously polymerised, both will
form free radicals RM1*; and RM2*; as a result of the initiation reaction between the
initiator free radical R *. Now there are four propagation steps described below
which will determine the reactivity of a monomer free radical with the same
monomer or the other.
Assuming that all the four types of addition take place, the growing chains ending
with M1* or M2* will have the possibility of all the four types of propagation. Now,
the ra!esofthesefour propagation reactions are as follows,
CY 1050
Macromolecules as Engineering Materials
Dr. R.L. Gardas
Office: CB 208 (First Floor)
E-mail: gardas@iitm.ac.in
Phone: 4248
Classes – 5 & 6
Quick Revision of Class -4
Chain transfer constant (C)
ktr
𝑪=
kp
Mayo Equation
DP0 will always greater than DP
Kinetics of Copolymerisation
The kinetics of copolymerisation is described below:
When two monomers say M1 and M2 are simultaneously polymerised,
both will form free radicals RM1*; and RM2*;
as a result of the initiation reaction between the initiator free radical R*.
Now there are four propagation steps will determine the reactivity of a monomer
free radical with the same monomer or the other.
Kinetics of Copolymerisation
Assuming that all the four types of addition take place,
the growing chains ending with M1* or M2* will have the possibility of all the
four types of propagation.
Now, the rates of these four propagation reactions are as follows,
Kinetics of Copolymerisation
rates of four propagation reactions
The basic assumption is that the reactivity of any growing chain depends only
on the end monomer unit carrying the free-radical site and not on the
number of type of monomer units already added to the chain.
Kinetics of Copolymerisation
rates of four propagation reactions
The rate at which the monomers M1 and M2 are consumed
during the course of propagation can be expressed as follows:
Kinetics of Copolymerisation
Now, assuming a steady state wherein the rate of particular chain end (say, M1)
disappearing is equal to the rate of formation of the same chain end, we can write
A combination of all the foregoing equations gives the 'copolymer equation',
Kinetics of Copolymerisation
𝑘11
𝑘22
The terms 𝑘12 (denoted by r1) and 𝑘21 (denoted by r2) appearing in this equation are
two important terms, known as the reactivity ratios for any given pair of monomers
MI and M2.
Reactivity ratios r1 and r2 indicate whether a growing chain carrying a free
radical on a particular monomer unit would prefer to add its own monomer
species or the co-monomer species.
Kinetics of Copolymerisation
In other words,
the composition of the copolymer formed at any given instance is dependent
not only on the concentration of the monomer species present in the system at
that instance but also on their reactivity ratios.
The point to be noted is that r1 and ,2 for any given pair of monomers are dependent
purely on the nature of other parameters such as the solvent, initiator and chain
transfer agent.
The latter, however, will have a pronounced influence on the molecular weight and
the molecular weight distribution of the copolymer formed.
Kinetics of Copolymerisation
The chemical composition of the copolymer formed depends exclusively on the
monomer concentration and the reactivity ratios, by the eqn:
where [m1]/[m2] gives the ratio of the monomers M1 and M2 entered into the
copolymer formed.
If we express the monomer components [m1] and [m2] in terms of mole fraction
instead of molar concentration,
the mole fraction of monomer M1 in the copolymer can be given by
Kinetics of Copolymerisation
where n1 and n2 are the mole fractions of monomers M1 and M2, respectively, in the
copolymer formed.
Similarly, the mole fractions of monomer M1 in the monomer feed can be given by
where, N1 and N2 are the mole fractions of the monomers M1 and M2, respectively in
the monomer feed.
Kinetics of Copolymerisation
Now, the 'copolymer equation' can be expressed as,
By knowing r1 and r2 and also the monomer feed ratio, one can easily predict the
instantaneous molar composition of the copolymer formed.
There are experimental methods by which the reactivity ratios can be determined.
Determination of Reactivity Ratios
In order to predict composition of the monomers in the copolymer formed,
the values of r1 and r2 for a given pair of monomers are required.
Mayo-Lewis scheme
where A = [M1]/[M2] and B = [m1]/[m2]
Determination of Reactivity Ratios
Finemann-Rose Method
where A = [M1]/[M2] and
B = [m1]/[m2]
Linear plot :
A–(A/B)
vs
(A2/B)
intercept equal to - r2
slope equal to r1
Determination of Reactivity Ratios
Alfrey and Price Method (Q-e scheme)
Assume that a monomer M2 adds onto a radical M1* and the rate constant for the
propagation reaction after the addition can be written as,
k12 = P1Q2 exp(− e1e2)
where P1 is a factor that characterises the state of the radical M1* at the growing
chain and Q2 is the resonance stability in the structure of monomer M2, i.e. reactivity
measure of M2.
e1 and e2 refer to the polarisation characteristics of monomer M1 and M2 as well as
radicals M1* and M2*.
The rate of propagation or addition of a M1 to its non radical i.e. k11 can be defined as
k11 = P1Q1 exp(− e1e1)
Determination of Reactivity Ratios
Alfrey and Price Method (Q-e scheme)
By definition r1=k11/k12 and r2 = k22/k21 or
thus, r1 = Q1/Q2 exp [-e1(e1–e2)]
and
r2 = Q2/Q1 exp [-e2(e2–e1)]
The values Qi and ei have been assigned to several monomers based on styrene
(which is considered as reference)
Given monomer (M1) & styrene (M2) with Standard values
Q2 = 1 & e2 = -0.8
Alfrey and Price Method (Q-e scheme)
By knowing Q-e values for different monomer pairs, r1 and r2 values can be
calculated.
The general conclusions drawn from the Q-e scheme are,
(i) monomers do not copolymerise when the values of Q for individual monomer
differ largely,
(ii) when the e values for a given pair of monomer differ widely, alternating
copolymers are formed,
(iii) the ideal or azeotropic copolymerisation is achieved with monomer pairs, when
the Q values and e values are roughly equal or identical.
Class – 7 & 8
Quick Revision of Classes – 5 & 6
Kinetics of Copolymerisation
Reactivity ratios: r1 = 𝑘11/𝑘12
r2 = 𝑘22/𝑘21
Mayo-Lewis scheme
Finemann-Rose Method
where
A = [M1]/[M2] and
B = [m1]/[m2]
Alfrey and Price Method (Q-e scheme)
Determination of Reactivity Ratios
Alfrey and Price Method (Q-e scheme)
By definition r1=k11/k12 and r2 = k22/k21 or
thus, r1 = Q1/Q2 exp [-e1(e1–e2)]
and
r2 = Q2/Q1 exp [-e2(e2–e1)]
The values Qi and ei have been assigned to several monomers based on styrene
(which is considered as reference)
Given monomer (M1) & styrene (M2) with Standard values
Q2 = 1 & e2 = -0.8
Alfrey and Price Method (Q-e scheme)
By knowing Q-e values for different monomer pairs, r1 and r2 values can be
calculated.
The general conclusions drawn from the Q-e scheme are,
(i) monomers do not copolymerise when the values of Q for individual monomer
differ largely,
(ii) when the e values for a given pair of monomer differ widely, alternating
copolymers are formed,
(iii) the ideal or azeotropic copolymerisation is achieved with monomer pairs, when
the Q values and e values are roughly equal or identical.
Kinetics of Copolymerisation
Copolymer composition be predicted based on monomer reactivity ratios.
When r1 = r2 = 0
Here propagation reactions 11 and 22 would not occur and therefore M1*
will react with M2 to form M2* which in turn would react with M1. Thus
an alternating copolymer would form irrespective of the monomer ratio
taken in the feed.
Kinetics of Copolymerisation
Copolymer composition be predicted based on monomer reactivity ratios.
When r1 = r2 = 1
Here all the four propagation steps are equally possible.
Thus the copolymer formed will have the same ratio as the monomers in the feed.
Thus the copolymer composition can be adjusted by changing the monomer ratio in
the feed. It can thus be said as an ideal polymerisation.
Also, since the copolymer composition is uniform through out the process and it is
called azeotropic copolymerisation.
Kinetics of Copolymerisation
Copolymer composition be predicted based on monomer reactivity ratios.
When r1 > 1 and r2 < 1
In such a case the copolymer will be richer in M1.
furthermore, if the two reactivity ratios differ much, it would be difficult to
incorporate M2 in the growing chain and the copolymer will essentially be
homopolymer of M1.
For the reverse case i.e. when r1 < 1 and r2 > 1, the copolymer would be rich in M2.
Kinetics of Copolymerisation
Copolymer composition be predicted based on monomer reactivity ratios.
When r1 > 1 and r2 > 1
In such cases the mixture of two homopolymers can be expected.
Step-growth Polymerisation (Polycondensation)
nylons, terylene etc. are condensation polymers
(as the monomer pairs undergo condensation).
Step-growth Polymerisation (Polycondensation)
Kinetics of Polycondensation
Kinetics of Polycondensation
Kinetics of Polycondensation
Class – 9 & 10
Quick Revision of Classes – 7 & 8
Step-growth Polymerisation
(Polycondensation)
Kinetics of Polycondensation
Non-catalysed
Acid-catalysed
Kinetics of Polycondensation
Non-catalysed
Acid-catalysed
Schematic plot of DP versus time for the reaction between
ethylene glycol and terephthalic acid
(a) non-catalysed
and
(b) acid catalysed poly condensation
Control of Polymer Molecular Weight
The mechanical properties of a polymer remains almost constant after a
critical molecular weight and the melt viscosity increase exponentially.
The very high melt viscosity of high molecular weight polymers offers
problems in its processing and therefore they are not often desired.
Techniques of Polymerisation
(Phase systems in polymerisation)
1.
Bulk (or mass) polymerisation
2.
Solution polymerisation
3.
Precipitation polymerisation
4.
Suspension polymerisation
5.
Emulsion polymerisation
1.
Bulk (or mass) polymerisation
2.
Solution polymerisation
3.
Precipitation polymerisation
4.
Suspension polymerisation
5.
Emulsion polymerisation
Comparison of various polymerisation techniques
CY 1050
Macromolecules as Engineering Materials
Dr. R.L. Gardas
Office: CB 214 (First Floor)
E-mail: gardas@iitm.ac.in
Phone: 4248
Class – 10
Techniques of Polymerisation
(Phase systems in polymerisation)
1.
Bulk (or mass) polymerisation
2.
Solution polymerisation
3.
Precipitation polymerisation
4.
Suspension polymerisation
5.
Emulsion polymerisation
1.
Bulk (or mass) polymerisation
Polymerisation reaction is carried out within the monomer itself.
The reaction is catalysed by additives (like initiator, transfer agents etc.) or under
the influence of heat or light.
Since polymerisation is a highly exothermic process is difficult to carry out and
the polymer obtained is generally non-uniform molecular mass distribution
(as polymerisation proceeds, viscosity increases and mixing becomes difficult).
If the polymer is insoluble in its monomer, it is obtained as a powder of porous
solid.
Since the recipe contains primarily the monomers, the polymer formed is usually
pure.
Bulk polymerisation on large scale is carried out with vinyl chloride, vinyl acetate
and acrylic esters.
2.
Solution polymerisation
When both monomer and polymer produced are soluble in a suitable solvent,
the polymerisation reaction is carried out with the monomer in solution is referred
to as 'solution polymerisation’.
It has the advantage of easy dissipation of heat evolved as a result of exothermic
polymerisation reaction.
The polymers so formed have low degree of branching and relatively uniform
molecular weight, but the disadvantage is that solid polymeric product can only be
isolated in pure form from the solution with great difficulty or some times not at all.
It is because the solvent is occluded and firmly traps the polymer.
For this reason solution polymerisation is mainly applied when solutions of
polymers are required (for ready-made use) for technical applications e.g. as
lacquers, adhesives etc. The products obtained by this method are usually relatively
low molecular weight because of the possibility of chain transfer to solvents.
Polyacrylonitrile by free-radical ploymerisation.
Block copolymers preferred to be made by this technique.
3.
Precipitation polymerisation
Monomer is soluble in the solvent and polymer will precipitates out as a result of
polymerisation (polymer being insoluble in 'solvent unlike solution polymerisation).
Precipitated polymer can be separated in the form of a gel or powder by
centrifugation or simple filtration.
There is no problem in heat dissipation and the degree of polymerisation is also
high.
Polyethylene, polyvinyl esters, polyacrylic esters are obtained commercially using
hydrocarbons as solvents.
Polyacrylonitrile is prepared using water as solvent.
4.
Suspension polymerisation
In suspension polymerisation, the monomer containing initiator, modifier etc. is
dispersed in a solvent (generally water) by vigorous stirring.
Polymer should be water insoluble.
For a stable suspension of monomer in the solvent, some stabilisers are added.
Size of the monomer droplets formed depends on the monomer-water ratio, type
and conc of stabiliser, type and speed of agitation employed.
Ploymerisation takes place within the dispersed (or suspended) monomer
particles. Agglomeration of which is prevented by stabiliser.
Polymer is separated by centrifugation or filtration, washed and dried.
Polystyrene beads, styrene-divinyl benzene copolymer beads, polyvinyl acetate
beads are produced using suspension polymerization technique.
5.
Emulsion polymerisation
In emulsion polymerisation, the liquid monomer is dispersed in an insoluble
liquid, which in turn gives an emulsion.
Mostly the dispersion medium is water. So the monomer-in-water emulsion
(containing catalyst and stabilised by emulsifying agents e.g. surface active
agents) is then used as the polymerising mixture.
A typical recipe for emulsion polymerisation is monomer, water (monomer is
immiscible with water), emulsifier (a surfactant at concentration above critical
micelle concentration) and a water soluble initiator.
Once the polymensation is complete, the polymer can be isolated either by
product contains emulsifier, catalyst, modifier and other foreign substances; the
separated product can be washed before drying.
The degree of polymerisation is usually high since there exists only a few
possibilities of chain termination of a growing polymer chain within the micelles.
5.
Emulsion polymerisation
Heat transfer is very efficient and viscosity build-up of the polymerization is quite
low.
Suspension and Emulsion technique, both have monomer droplets, the emulsion
has (additionally) micelles (in which the monomer solubilised).
If the conc. of emulsifier added is less than the CMC, the system becomes
suspension polymerization; only when there is enough emulsifier to form the
micelle, an emulsion system obtained.
Emulsion polymerization is most widely used industrial technique to polymerise
the various monomers, such as vinyl chloride, vinyl acetate, acrylates, butadiene
etc.
Comparison of various polymerisation techniques
Class – 11
Quick Revision of Class - 10
Critical molecular weight
Techniques of Polymerisation
(Phase systems in polymerisation)
1. Bulk (or mass) polymerisation
2. Solution polymerisation
3. Precipitation polymerisation
4. Suspension polymerisation
5. Emulsion polymerisation
Comparison of various polymerisation techniques
Thermodynamic Aspects
of
Polymerisation
Thermodynamic Aspects of Polymerisation
The polymerisation process can be explained thermodynamically.
A process may occur spontaneously at constant temperature and pressure if
the free energy change is negative i.e. the free energy of polymer is less than the
free energy of monomer.
The free energy change is given by the relation
ΔG = ΔH − TΔS
The formation of macromolecules from randomly arranged monomers results in
their ordering i.e. the entropy of a polymer is less than the entropy of
monomers.
For most of the chain polymerisations, S falls in a narrow range of -25 to -30
cal mo1-1 K-1 (thus does not favor polymerisation).
Polymerisation of monomers with double bonds involves breaking up of the
double bond and formation of two single bonds e.g. in ethylene
CH2 = CH2 ➔ -[CH2-CH2]-
Ceiling Temperature
Now since
C=C bond energy is 145.5 kcal mol-1 and
C-C bond energy is 84 kcal mol-1
the enthalpy of polymerisation can be calculated as
145.5 - 2(84) = - 22.5 kcal mol-1
ΔG = ΔH − TΔS
An increase in polymerisation temperature increases TS term whereas H does
not change significantly. This decreases the magnitude of G and at a certain
temperature a condition is achieved when H = TS, i.e. G = 0.
This means that above this temperature, no polymerisation can occur.
The temperature at which G = 0 is called ceiling temperature Tc.
Polymer
Dissolution
Polymer dissolution
Polymer dissolution
Swelling of polymers
Swelling of polymers is a slow process involving the penetration of solvent
molecules into the polymer matrix there by increasing its mass and volume.
Swelling may be limited or unlimited.
The diffusion of solvent molecules into polymer solute structures depends upon
polymer-solvent interaction, which leads to expanding of the polymer surface
and allows the penetration of the solvent molecules. Thus the polymer chain
containing diffused solvent molecules is known as swollen chain.
The swelling may reach a thermodynamic equilibrium.
For solutes which form molecular solutions in solvents the swelling is unlimited
and continues infinitely until the chains are completely separated from each other
and finally acquire mobility and diffuse back into the bulk of solvent state (forming
molecular solutions).
For limited swelling i.e. when thermodynamic equilibrium exists between polymer solvent systems, the polymer does not dissolve to form molecular solution.
Polymer dissolution
Swelling of polymers
Swelling can be treated thermodynamically as the phenomenon involving two
processes namely mixing and expansion.
The diffusion of solvent into the polymer matrix is a type of mixing phenomenon
where as the expansion due to swelling is similar to an elastic deformation.
For systems showing limited swelling, a parameter known as degree or amount of
swelling can be defined. It is expressed as the amount of liquid sorbed by unit mass
or volume of the polymer and is determined both gravimetrically and
volumetrically.
For example, a known mass of a polymer is kept in a solvent till equilibrium is
established. The mass of the swollen polymer gel is measured after separating it
from the bulk solvent. Then the amount of the swelling can be expressed as
(m - m0)/m0
where mo is the mass of the solid polymer and m is that of swollen polymer.
Polymer dissolution
Swelling of polymers
Swelling and dissolution of polymers in suitable solvents constitute very
important phenomenon in solution chemistry and applications of polymers.
These two successive process are influenced by several factors
viz.
chemical nature of polymer and solvent,
molecular weight of polymer,
chain flexibility of polymer,
packing density in solid polymer,
phase state and
temperature etc.
The nature of polymer/solvent system is often described in terms of
polymer- polymer,
polymer-solvent and
solvent-solvent
interactions.
Polymer dissolution
Amorphous polymers containing bulky polar substituents readily swell in polar
solvent but do not form solutions at room temperature.
Crystalline polymers with close packing between the chain segments do not easily
dissolve and need high temperatures so the crystalline order is broken to facilitate
individual segment-solvent contacts.
Crystalline polymers usually form solutions above their melting temperatures.
Highly cross-linked polymers do not show swelling even above their melting
temperatures.
Class – 12 & 13
Quick Revision of Class - 11
Thermodynamic Aspects of Polymerisation
ΔG = ΔH − TΔS
The temperature at which G = 0 (i.e. H = TS) is called
ceiling temperature Tc.
Polymer dissolution
Polymer dissolution
Swelling of polymers
Swelling and dissolution of polymers in suitable solvents constitute very
important phenomenon in solution chemistry and applications of polymers.
These two successive process are influenced by several factors
viz.
chemical nature of polymer and solvent,
molecular weight of polymer,
chain flexibility of polymer,
packing density in solid polymer,
phase state and
temperature etc.
The nature of polymer/solvent system is often described in terms of
polymer- polymer,
polymer-solvent and
solvent-solvent
interactions.
Polymer dissolution
Amorphous polymers containing bulky polar substituents readily swell in polar
solvent but do not form solutions at room temperature.
Crystalline polymers with close packing between the chain segments do not easily
dissolve and need high temperatures so the crystalline order is broken to facilitate
individual segment-solvent contacts.
Crystalline polymers usually form solutions above their melting temperatures.
Highly cross-linked polymers do not show swelling even above their melting
temperatures.
Polymer dissolution
Polymer dissolution
Polymer dissolution
For linear polymers, the
size of the polymer coil
can be expressed by any
of these two quantities;
as they are related:
Polymer dissolution
Flory–Huggins Solution Theory
Flory-Huggins Theory
for
Polymer Solutions
➢
To develop the classical Flory-Huggins theory for the free
energy of mixing of polymer solutions based on a
statistical approach on a regular lattice.
➢
To describe the criteria for phase stability and illustrate
typical phase diagrams for polymer blends and solutions.
Flory-Huggins Free Energy of Mixing:
General Case
Gm = Hm − TSm
Hm = N1 2 RT
 = 0 For athermal mixtures
 > 0 For endothermic mixing
 < 0 For exothermic mixing
Sm = −R[x1 ln 1 + x2 ln 2 ]
[
]
Gm = RT N1 2  + (x1 ln 1 + x2 ln  2 )
Converting the expression from molecules N1 and N2 to moles n1 and n2 by
transferring the Avogadro constant N0 to the gas constant R=kNA
The value of the interaction parameter can be estimated from the
Hildebrand solubility parameters δa and δb
where Vseg is the actual volume of a polymer segment.
Hildebrand solubility parameter is the square root of the cohesive
energy density:
The cohesive energy density is the amount of energy needed to
completely remove unit volume of molecules from their
neighbours to infinite separation (an ideal gas).
Substance
The conventional units for
the solubility parameter are
(calories per cm3)1/2, or cal1/2 cm−3/2.
The SI units are
J1/2 m−3/2, equivalent to the pascal1/2.
n-Pentane
n-hexane
Diethyl Ether
Ethyl Acetate
Chloroform
Dichloromethane
Acetone
2-propanol
Ethanol
PTFE
Poly(ethylene)
Poly(propylene)
Poly(styrene)
Poly(phenylene oxide)
PVC
Polyurethane (PU/PUR)
PET
Nylon 6,6
Poly(methyl methacrylate)
δ [cal1/2 cm−3/2]
7.0
7.24
7.62
9.1
9.21
9.93
9.77
11.6
12.92
6.2
7.9
8.2
9.13
9.15
9.5
8.9
10.1
13.7
9.3
δ [MPa1/2]
14.4
14.9
15.4
18.2
18.7
20.2
19.9
23.8
26.5
16.6
19.5
20.5
28
19.0
(Hydroxyethyl)methacrylate
25–26
poly(HEMA)
Ethylene glycol
26.93
29.9, 33.0
By convention, these values are always positive and irrespective of their magnitude; the
term (δs - δp)2 will also be positive. Thus, Hmix will always be positive.
Now as discussed before TSmix is very small in magnitude;
for the condition favouring polymer solubility, i.e. Hmix < TSmix , a minimum positive
value of Hmix can be upset by matching the polymer and solvent such that their
solubility parameters are as close as possible.
To a rough approximation a polymer and solvent differing in solubility parameter
(δs - δp) < 0.5
will form the solution.
Flory interaction parameter X is dimensionless
and thus Hmix may lead to large positive values
which would not favour dissolution (or phase
separation would result).
Small positive or negative values of X
would explain the spontaneity of dissolution process.
Quick Revision of Class - 12
Flory–Huggins Solution Theory
Boltzmann Equation
S = k ln 
Hm = N1 2 RT
 = 0 For athermal mixtures
 > 0 For endothermic mixing
 < 0 For exothermic mixing
Solubility parameter
is the square root of the
cohesive energy density
By convention, these values are always positive and irrespective of their magnitude; the
term (δs - δp)2 will also be positive. Thus, Hmix will always be positive.
Now as discussed before TSmix is very small in magnitude;
for the condition favouring polymer solubility, i.e. Hmix < TSmix , a minimum positive
value of Hmix can be upset by matching the polymer and solvent such that their
solubility parameters are as close as possible.
To a rough approximation a polymer and solvent differing in solubility parameter
(δs - δp) < 0.5 will form the solution.
Gm = Hm − TSm
Flory interaction parameter X is dimensionless
and thus Hmix may lead to large positive values
which would not favour dissolution (or phase
separation would result).
Small positive or negative values of X
would explain the spontaneity of dissolution process.
Gm = Hm − TSm
Substance
The conventional units for
the solubility parameter are
(calories per cm3)1/2, or cal1/2 cm−3/2.
The SI units are
J1/2 m−3/2, equivalent to the pascal1/2.
n-Pentane
n-hexane
Diethyl Ether
Ethyl Acetate
Chloroform
Dichloromethane
Acetone
2-propanol
Ethanol
PTFE
Poly(ethylene)
Poly(propylene)
Poly(styrene)
Poly(phenylene oxide)
PVC
Polyurethane (PU/PUR)
PET
Nylon 6,6
Poly(methyl methacrylate)
δ [cal1/2 cm−3/2]
7.0
7.24
7.62
9.1
9.21
9.93
9.77
11.6
12.92
6.2
7.9
8.2
9.13
9.15
9.5
8.9
10.1
13.7
9.3
δ [MPa1/2]
14.4
14.9
15.4
18.2
18.7
20.2
19.9
23.8
26.5
16.6
19.5
20.5
28
19.0
(Hydroxyethyl)methacrylate
25–26
poly(HEMA)
Ethylene glycol
26.93
29.9, 33.0
CY 1050
Macromolecules as Engineering Materials
Dr. R.L. Gardas
Office: CB 214 (First Floor)
E-mail: gardas@iitm.ac.in
Phone: 4248
Class – 14 & 15
Quick Revision of Class - 13
Flory–Huggins Solution Theory
Boltzmann Equation
S = k ln 
Hm = N1 2 RT
 = 0 For athermal mixtures
 > 0 For endothermic mixing
 < 0 For exothermic mixing
Solubility parameter
is the square root of the
cohesive energy density
Thermal Behaviour
Distinct features
of
low and high
molecular weight
substances
on heating
Thermal Behaviour
Temperature
effect
on
Amorphous
and
Crystalline
polymer
Stress – Elongation behavior of polymer
Industrial Scenario
% composition
of
commercial
polymers
Resin Identification Code
ASTM International (American Society for Testing and Materials)
Resin Identification Code