polymer chemistry sem-6, dse-b3 transition phenomena in

POLYMER CHEMISTRY

SEM-6, DSE-B3

Transition Phenomena in PolymersPART-1, PPT-13

Dr. Kalyan Kumar Mandal

Associate Professor

St. Paul’s C. M. College

Kolkata

Transition Phenomena in GlassPart-1: Glass Transitions-I

Contents

• Glass-Rubber Transition Behaviour

• Mechanical Relationships

• Five Regions of Viscoelastic Behaviour

• Thermal Transitions in Polymers: Tg and Tm

Glass-Rubber Transition Behaviour

• The state of a polymer depends on the temperature and on the time allotted to the experiment.

At low enough temperatures, all amorphous polymers are stiff and glassy. This is the glassy

state, sometimes called the vitreous state, especially for inorganic materials. On warming, the

polymers soften in a characteristic temperature range known as the glass - rubber transition

region. Here, the polymers behave in a leathery manner.

• The importance of the glass transition in polymer science was stated by Eisenberg (1993):

“The glass transition is perhaps the most important single parameter that determines the

application of many noncrystalline polymers now available.” The glass transition is named

after the softening of ordinary glass. On a molecular basis, the glass transition involves the

onset of long-range coordinated molecular motion, the beginning of reptation (Figure 1).

• The glass transition is a second order transition. Rather than dicontinuities in enthalpy and

volume, their temperature derivatives, heat capacity, and coefficients of expansion shift. By

difference, melting and boiling are first-order transitions, exhibiting discontinuities in

enthalpy and volume, with heats of transition.

This Lecture is prepared by Dr. K. K. Mandal, SPCMC, Kolkata

Glass-Rubber Transition Behaviour

• Reptation: Reptation is the thermal motion of very long

linear, entangled macromolecules in polymer melts or

concentrated polymer solutions.

• Reptation is derived from the word reptile. It suggests the

movement of entangled polymer chains as being analogous to

snakes slithering through one another. Reptation is used as a

mechanism to explain viscous flow in an amorphous polymer.

• For amorphous polymers, the glass transition temperature, Tg, constitutes their most

important mechanical property. In fact, upon synthesis of a new polymer, the glass transition

temperature is among the first properties measured. The transition describes the behavior of

amorphous polymers in the glass transition range, emphasizing the onset of molecular

motions associated with the transition.

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Mechanical Relationships

• Terms such as “glassy,” “rubbery,” and “viscous” imply a knowledge of simple material

mechanical relationships. The modulus of elasticity is simply the ratio between stress and

strain. Elastic Moduli can be of three types, Young's modulus, Shear modulus, and Bulk

modulus.

• Young’s Modulus: Hook’s law assumes perfect elasticity in a material body. Young’s

modulus, E, may be written

𝑬 =𝝈

𝜺−−− −𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟏

where σ and ε represent the tensile (normal) stress and strain, respectively.

• Young’s modulus is a fundamental measure of the stiffness of the material. The higher its

value, the more resistant the material is to being stretched.

• The tensile stress is defined in terms of force per unit area. If the sample’s initial length is L0

and its final length is L, then the strain is, 𝜺 =(𝑳−𝑳𝟎)

𝑳𝟎=

∆𝑳

𝑳𝟎−−−−𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟐



• Modulus is usually expressed in dynes/cm2, in terms of force per unit area. Frequently the

Pascal unit of modulus is used, 10 dynes/cm2 = 1 Pascal.

• Stress: Stress is defined as a force applied per unit area. When a body is subjected to a

deforming force, a restoring force occurs in the body which is equal in magnitude but

opposite in direction to the applied force. This restoring force per unit area is known as

stress. It is given by the formula, 𝝈 =𝑭

𝑨, where 𝝈 is the stress applied, F is the force applied

and A is the area of force application. The SI unit of stress is N/m2. Stress applied to a

material can be of two types. They are:

• Tensile Stress: It is the force applied per unit area which results in the increase in length (or

area) of a body. Objects under tensile stress become thinner and longer.

• Compressive Stress: It is the force applied per unit area which results in the decrease in

length (or area) of a body. The object under compressive stress becomes thicker and shorter.



• Strain: It is defined as the amount of deformation experienced by the body in the direction of

force applied, divided by initial dimensions of the body. Strain is simply the measure of how

much an object is stretched or deformed. The relation for deformation in terms of length of a

solid is given below.

𝜺 =(𝑳 − 𝑳𝟎)

𝑳𝟎=∆𝑳

𝑳𝟎

ε is the strain due to stress applied, ∆L is the change in length of the material.

• The strain is a dimensionless quantity as it just defines the relative change in shape.

Depending on stress application, strain experienced in a body can be of two types. They are:

• Tensile Strain: It is the change in length (or area) of a body due to the application of tensile

stress.

• Compressive Strain: It is the change in length (or area) of a body due to the application of

compressive strain.


Mechanical Relationships• Shear Modulus: It is a measure of the elastic shear stiffness of a material. Instead of

elongating (or compressing) a sample, it may be subjected to various shearing or twisting

motions. The ratio of the shear stress, τ, to the shear strain, γ, defines the shear modulus, G:

𝑮 =𝝉

𝜸−−−−𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟑

• The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in

gigapascals (GPa). The shear modulus is concerned with the deformation of a solid when it

experiences a force parallel to one of its surfaces while its opposite face experiences an

opposing force (such as friction).

• The Bulk Modulus and Compressibility: The bulk modulus describes the material's response to

(uniform) hydrostatic pressure. The bulk modulus, B, is defined as

𝑩 = −𝑽𝝏𝑷

𝝏𝑽 𝑻−−−−𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟒, 𝜷 =

𝟏

𝑩−−−−𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟒

where P is the hydrostatic pressure. Usually a body shrinks in volume on being exposed to increasing

external pressures, so the term𝝏𝑷

𝝏𝑽 𝑻is negative. The inverse of the bulk modulus is considered as the

compressibility, β.

Five Regions of Viscoelastic Behaviour

• Viscoelastic materials simultaneously exhibit a combination of elastic and viscous behavior.

While all substances are viscoelastic to some degree, this behaviour is especially prominent

in polymers. Generally, viscoelasticity refers to both the time and temperature dependence of

mechanical behaviour. The states of matter of low-molecular-weight compounds are well

known: crystalline, liquid, and gaseous. The first-order transitions that separate these states

are equally well known: melting and boiling.

• Another well-known first-order transition is the crystalline - crystalline transition, in which a

compound changes from one crystalline form to another. By contrast, no high-molecular-

weight polymer vaporizes to a gaseous state; all decompose before the boiling point. In

addition no high-molecular-weight polymer attains a totally crystalline structure, except in

the single-crystal state.



• In fact many important polymers do not

crystallize at all but form glasses at low

temperatures. At higher temperatures they

form viscous liquids. The transition that

separates the glassy state from the viscous

state is known as the glass - rubber

transition. This transition attains the

properties of a second-order transition at

very slow rates of heating or cooling.

• The five regions of viscoelastic behavior

are briefly discussed to provide a broader

picture of the temperature dependence of

polymer properties.



• The five regions of viscoelastic behavior for linear amorphous polymers are shown in

Figure 2.

• Region 1: The glassy Region: In this region the polymer is glassy and frequently brittle.

Typical examples at room temperature include polystyrene (plastic) drinking cups and

poly(methyl methacrylate) (Plexiglas® sheets).

• Young’s modulus for glassy polymers just below the glass transition temperature is

surprisingly constant over a wide range of polymers, having the value of approximately

3x1010 dynes/cm2 (3x109 Pa). In the glassy state, molecular motions are largely restricted to

vibrations and short-range rotational motions.

• Region 2: The Glass Transition Region: Typically the modulus drops a factor of about 1000

in a 20 to 30°C range in this region. The behavior of polymers in this region is best described

as leathery, although a few degrees of temperature change will obviously affect the stiffness

of the leather.



Table 1: Glass transition parameters

Polymer Tg, °C Number of chain atoms involvedPoly(dimethyl siloxane) -127 40

Poly(ethylene glycol) -41 30

Polystyrene 100 40-100

Polyisoprene -73 30-40

• For quasi-static measurements (Quasi-static term means semi static. It is an infinitely slow

process which means change from its original position is not at all significant.) such as

illustrated in Figure 2, the glass transition temperature, Tg, is often taken at the maximum

rate of turndown of the modulus at the elbow, where E ≈ 109 Pa.

• The glass transition temperature is defined as the temperature where the thermal expansion

coefficient undergoes a discontinuity. Qualitatively, the glass transition region can be

interpreted as the onset of long-range, coordinated molecular motion. While only 1 to 4

chain atoms are involved in motions below the glass transition temperature, some 10 to 50

chain atoms attain sufficient thermal energy to move in a coordinated manner in the glass

transition region (Table 2).



• The number of chain atoms, 10-50, involved in the coordinated motions was deduced by

observing the dependence of Tg on the molecular weight between cross-links, Mc . When Tg

became relatively independent of Mc in a plot to Tg versus Mc, the number of chain atoms

was counted.

• Region 3: The Rubbery Plateau Region: After the sharp drop that the modulus takes in the

glass transition region, it becomes almost constant again in the rubbery plateau region, with

typical values of 2x107 dynes/cm2 (2x106 Pa). In this region, polymers exhibit long-range

rubber elasticity, which means that the elastomer can be stretched several hundred percent,

and snap back to substantially its original length on being released. Two cases in region 3

need to be distinguished:

1. The polymer is linear. In this case the modulus will drop off slowly, as indicated in

Figure 2. The width of the plateau is governed primarily by the molecular weight of the

polymer; the higher the molecular weight, the longer is the plateau.



• The polymer is cross-linked. In this case the dotted line in Figure 2 is followed, and

improved rubber elasticity is observed, with the creep portion suppressed. The dotted line

follows the equation E = 3nRT, where n is the number of active chain segments in the

network and RT represents the gas constant times the temperature. An example of a cross-

linked polymer above its glass transition temperature obeying this relationship is the ordinary

rubber band.

• If a polymer is semicrystalline, the dashed line in Figure 2 is followed. The height of the

plateau is governed by the degree of crystallinity. This is so because of two reasons: first, the

crystalline regions tend to behave as a filler phase, and second, because the crystalline

regions also behave as a type of physical crosslink, tying the chains together. The crystalline

plateau extends until the melting point of the polymer. The melting temperature, Tm, is

always higher than Tg, Tg being from one-half to two-thirds of Tm on the absolute

temperature scale.



• Region 4: The Rubbery Flow Region: As the temperature is raised past the rubbery plateau

region for linear amorphous polymers, the rubbery flow region is reached. In this region the

polymer is marked by both rubber elasticity and flow properties, depending on the time scale

of the experiment. For short time scale experiments, the physical entanglements are not able

to relax, and the material still behaves rubbery.

• For longer times, the increased molecular motion imparted by the increased temperature

permits assemblies of chains to move in a coordinated manner (depending on the molecular

weight), and hence to flow. However, region 4 does not occur for cross-linked polymers. In

that case, region 3 remains in effect up to the decomposition temperature of the polymer

(Figure 2).

• Region 5: The Liquid Flow Region: At still higher temperatures, the liquid flow region is

reached. The polymer flows readily, often behaving like molasses. The increased energy

allotted to the chains permits them to reptate out through entanglements rapidly and flow as

individual molecules.



• For semicrystalline polymers, the modulus depends on the degree of crystallinity. The

amorphous portions go through the glass transition, but the crystalline portion remains hard.

Thus a composite modulus is found. The melting temperature is always higher than the glass

transition temperature. At the melting temperature the modulus drops sharply to that of the

corresponding amorphous material, now in the liquid flow region.

• Effect of Plasticizers: Polymers are frequently plasticized to “soften” them. These

plasticizers are usually small, relatively nonvolatile molecules that dissolve in the polymer,

separating the chains from each other and hence making reptation easier. The glass transition

temperature is lowered, and the rubbery plateau modulus is lowered.

• If the polymer is semicrystalline, the plasticizer reduces the melting temperature and/or

reduces the extent of crystallinity. An example is poly(vinyl chloride), which has a Tg of

+80 °C. Properly plasticized, it has a Tg of about +20 °C or lower. A typical plasticizer is

dioctyl phthalate, with a solubility parameter of 8.7 (cal/cm3)1/2, fairly close to that of

poly(vinyl chloride), 9.6 (cal/cm3)1/2.


Thermal Transitions in Polymers

• The term “transition” refers to a change of state induced by changing the temperatures or

pressure. Two major thermal transitions are the glass transition and the melting, the respective

temperatures being called Tg and Tm.

• Glass transition: The term “glass transition” refers to the temperature in which ordinary glass

softens and flows. Glass transitions occur in all amorphous or semicrystalline materials and

lead to significant changes in material properties such as thermal expansion, the specific heat

capacity or modulus. Because the glass transition is very sensitive to chemical and physical

structure, it can be used to characterize materials. Thermal Analysis provides different

methods to measure the glass transition and the glass transition temperature.

• The glass transition provides information about molecular dynamics in the supercooled melt.

It defines the upper temperature limit for the use of solid amorphous materials; for rubbery

materials, it is the lower temperature limit.


Thermal Transitions in Polymers• Glass Transition Temperature: Glass transition temperature is the temperature at which a

hard glassy state of an amorphous material is converted to a rubbery state. Each polymer with

an amorphous structure has its own unique glass transition temperature. This term is

discussed regarding polymer compounds since polymers, especially thermosetting polymers,

can undergo this glass transition.

• The glassy state of a thermosetting polymer is very hard and rigid. The rubbery state is very

viscous and pliable. Only amorphous polymers and semi-crystalline polymers show this

property. Pure amorphous polymers have only the glass transition temperature. Pure

crystalline polymers do not have a glass transition temperature.

• If a polymer in its molten state is cooled it will at some point reach its glass transition

temperature (Tg). At this point the mechanical properties of the polymer change from those of

an elastic material to those of a brittle one due to changes in chain mobility. The heat capacity

of the polymer is different before and after the glass transition temperature. The heat capacity

Cp of polymers is usually higher above Tg.


Thermal Transitions in Polymers• Hard plastics like polystyrene and poly(methyl methacrylate) are used well below their glass

transition temperatures, i.e., when they are in their glassy state. Their Tg values are both at

around 100 °C (212 °F). Rubber elastomers like polyisoprene and polyisobutylene are used

above their Tg, that is, in the rubbery state, where they are soft and flexible. Crosslinking

prevents free flow of their molecules, thus endowing rubber with a set shape at room

temperature (as opposed to a viscous liquid).

• Melting Temperature: Melting temperature is the temperature at which a solid material is

converted into its liquid form. In other words, this is the temperature that causes a solid to

melt. Here a phase transition of matter occurs. In this melting temperature or the melting

point of a substance, the solid phase and the liquid phase exist in equilibrium. At the melting

temperature of a substance, the entropy increases since the tightly packed molecules of that

solid substance are released.


Thermal Transitions in Polymers

• Glass transition temperature can be observed in amorphous and semi-crystalline polymer

compounds. Melting temperature can be observed in crystalline compounds. But the main

difference between glass transition temperature and melting temperature is that glass

transition temperature describes the transition of a glass state into a rubbery state whereas

melting temperature describes the transition of a solid phase into a liquid phase.

• The crystalline melting temperature is the melting temperature of the crystalline domains of a

polymer sample. The glass transition, is the gradual and reversible transition in amorphous

materials (or in amorphous regions within semicrystalline materials) from a hard and

relatively brittle “glassy” state into a viscous or rubbery state as the temperature is increased.

Therefore, glass transition temperature (Tg) is always lower than the melting temperature, Tm,

of the crystalline state of the material, if one exists.


Thermal Transitions in Polymers: Tg and Tm

• The different types of thermal response in

the transition of a thermoplastic polymer

from the rigid solid to an eventually liquid

state can be illustrated in several ways. One

of the simplest and most satisfactory is to

trace the change in specific volume, as

shown schematically in Figure 3.

• The volume change in amorphous polymers

follows the curve ABC. In the region C-B,

the polymer is a glassy solid and has the

characteristics of a glass, including

hardness, stiffness, and brittleness.



• As the sample is heated, it passes through a temperature Tg, called the glass transition

temperature, above which it softens and becomes rubberlike. This is an important

temperature and marks the beginning of movements of large segments of the polymer chain

due to available thermal energy (RT energy units/mol). This is reflected in marked changes in

properties, such as specific volume, refractive index, stiffness, and hardness.

• Above Tg, the material may be more easily deformed. A continuing increase in temperature

along B-A leads to a change of the rubbery polymers to a viscous liquid without any sharp

transition.

• In a perfectly crystalline polymer, all the chains would be contained in regions of three

dimensional order, called crystallites, and no glass transition would be observed. Such a

polymer would follow the curve G-F-A, melting at Tom to become a viscous liquid. Perfectly

crystalline polymers are, however, rarely seen in practice and real polymers may instead

contain varying proportions of ordered and disordered regions in the sample.



• The semicrystalline polymers usually exhibit both Tg and Tm (not Tom) corresponding to the

disordered and ordered regions, respectively, and follow curves similar to E-H-D-A. Tm is

lower than Tom and more often represents a melting range, because the semicrystalline

polymer contains crystallites of various sizes with many defects which act to depress the

melting temperature.

• Both Tg and Tm are important parameters that serve to characterize a given polymer. While Tg

sets an upper temperature limit for the use of amorphous thermoplastics like poly(methyl

methacrylate) or polystyrene and a lower temperature limit for rubbery behavior of an

elastomer like SBR rubber or 1,4-cis-polybutadiene, Tm or the onset of the melting range

determines the upper service temperature for semicrystalline thermoplastics.

• Between Tm and Tg, these polymers tend to behave as a tough and leathery material. They are

generally used at temperatures between Tg and a practical softening temperature that lies

above Tg and below Tm.


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