Mechanical properties of Mechanical properties of Mechanical properties of Mechanical properties of polymers: an overviewpolymers: an overviewpolymers: an overviewpolymers: an overview

Suryasarathi BoseSuryasarathi BoseSuryasarathi BoseSuryasarathi BoseDept. of Materials Engineering, IISc, BangaloreDept. of Materials Engineering, IISc, BangaloreDept. of Materials Engineering, IISc, BangaloreDept. of Materials Engineering, IISc, BangaloreDept. of Materials Engineering, IISc, BangaloreDept. of Materials Engineering, IISc, BangaloreDept. of Materials Engineering, IISc, BangaloreDept. of Materials Engineering, IISc, Bangalore

UGCUGCUGCUGC----NRCM Summer School on Mechanical Property CharacterizationNRCM Summer School on Mechanical Property CharacterizationNRCM Summer School on Mechanical Property CharacterizationNRCM Summer School on Mechanical Property Characterization---- June 2012June 2012June 2012June 2012

• Overview of polymer scienceOverview of polymer scienceOverview of polymer scienceOverview of polymer science

• Thermal transitions in polymersThermal transitions in polymersThermal transitions in polymersThermal transitions in polymers

• StructureStructureStructureStructure----property relationship in polymersproperty relationship in polymersproperty relationship in polymersproperty relationship in polymers• StructureStructureStructureStructure----property relationship in polymersproperty relationship in polymersproperty relationship in polymersproperty relationship in polymers

• Dynamic mechanical properties of polymersDynamic mechanical properties of polymersDynamic mechanical properties of polymersDynamic mechanical properties of polymers

• RheologyRheologyRheologyRheology

Poly(isoprene)

Cellulose

nitrate

The first man made

polymer

What is a polymer ?What is a polymer ?What is a polymer ?What is a polymer ?

How big are polymers ?How big are polymers ?How big are polymers ?How big are polymers ?

CLASSIFICATIONCLASSIFICATIONCLASSIFICATIONCLASSIFICATIONStructural shape of polymer molecules, which may be:Structural shape of polymer molecules, which may be:Structural shape of polymer molecules, which may be:Structural shape of polymer molecules, which may be:

– LinearLinearLinearLinear

– BranchedBranchedBranchedBranched

– CrossCrossCrossCross----linkedlinkedlinkedlinked

THERMOPLASTICS and THERMOSETSTHERMOPLASTICS and THERMOSETSTHERMOPLASTICS and THERMOSETSTHERMOPLASTICS and THERMOSETS

ThermoplasticsThermoplasticsThermoplasticsThermoplastics� Soften when heated and harden when cooled irrespective of the Soften when heated and harden when cooled irrespective of the Soften when heated and harden when cooled irrespective of the Soften when heated and harden when cooled irrespective of the

number or times the process is repeatednumber or times the process is repeatednumber or times the process is repeatednumber or times the process is repeated� Flow with pressure and heatFlow with pressure and heatFlow with pressure and heatFlow with pressure and heat� Temperature of use limited to softening temperatureTemperature of use limited to softening temperatureTemperature of use limited to softening temperatureTemperature of use limited to softening temperature� No chemical changes upon heatingNo chemical changes upon heatingNo chemical changes upon heatingNo chemical changes upon heating

ThermosetsThermosetsThermosetsThermosets� Once heated they react irreversibly to give strong Once heated they react irreversibly to give strong Once heated they react irreversibly to give strong Once heated they react irreversibly to give strong

intermolecular bondingintermolecular bondingintermolecular bondingintermolecular bonding� Do not soften or flow upon application of heat and pressureDo not soften or flow upon application of heat and pressureDo not soften or flow upon application of heat and pressureDo not soften or flow upon application of heat and pressure� Use temperature is higher and is governed by degradation Use temperature is higher and is governed by degradation Use temperature is higher and is governed by degradation Use temperature is higher and is governed by degradation

temperaturetemperaturetemperaturetemperature

Polymer can be synthesized to yield desired Polymer can be synthesized to yield desired Polymer can be synthesized to yield desired Polymer can be synthesized to yield desired mechanical behavior by appropriate combination of:mechanical behavior by appropriate combination of:mechanical behavior by appropriate combination of:mechanical behavior by appropriate combination of:

� Glass Transition Temperature, TgGlass Transition Temperature, TgGlass Transition Temperature, TgGlass Transition Temperature, Tg� CrystallinityCrystallinityCrystallinityCrystallinity� Melting Temperature, TmMelting Temperature, TmMelting Temperature, TmMelting Temperature, Tm� Branching or Cross LinkingBranching or Cross LinkingBranching or Cross LinkingBranching or Cross Linking

These determine the use of a specific polymer asThese determine the use of a specific polymer asThese determine the use of a specific polymer asThese determine the use of a specific polymer as

� Elastomer (Rubber)Elastomer (Rubber)Elastomer (Rubber)Elastomer (Rubber)� Flexible Flexible Flexible Flexible PlasticPlasticPlasticPlastic� Rigid PlasticRigid PlasticRigid PlasticRigid Plastic� FiberFiberFiberFiber

Thermal transitions in polymersThermal transitions in polymersThermal transitions in polymersThermal transitions in polymers

G

B

Translation, Vibration, Rotation

Local segment mobility besides vibration &

rotation

Only Vibration

F

I

D

E

H

C

TemperatureTmTg

Specific

Volume

Amorphous

Semi-crystalline

Crystalline

FACTORS AFFECTING GLASS FACTORS AFFECTING GLASS FACTORS AFFECTING GLASS FACTORS AFFECTING GLASS TRANSITION TRANSITION TRANSITION TRANSITION TEMPERATURETEMPERATURETEMPERATURETEMPERATURE

1.1.1.1. Bulky side groupsBulky side groupsBulky side groupsBulky side groups

2.2.2.2. Long side chainsLong side chainsLong side chainsLong side chains

3.3.3.3. Intermolecular bonding forces of attractionIntermolecular bonding forces of attractionIntermolecular bonding forces of attractionIntermolecular bonding forces of attraction

4.4.4.4. Chain stiffnessChain stiffnessChain stiffnessChain stiffness4.4.4.4. Chain stiffnessChain stiffnessChain stiffnessChain stiffness

5.5.5.5. Copolymers Copolymers Copolymers Copolymers

6.6.6.6. BlendingBlendingBlendingBlending

7.7.7.7. PlasticizationPlasticizationPlasticizationPlasticization

8.8.8.8. CrystallinityCrystallinityCrystallinityCrystallinity

Molecular interpretation Molecular interpretation Molecular interpretation Molecular interpretation –––– Free volume Free volume Free volume Free volume theorytheorytheorytheory

Motions in the rubbery state require larger free volume Motions in the rubbery state require larger free volume Motions in the rubbery state require larger free volume Motions in the rubbery state require larger free volume than the short range order in the glassy state.than the short range order in the glassy state.than the short range order in the glassy state.than the short range order in the glassy state.

The rise in the relative free volume with increasing The rise in the relative free volume with increasing The rise in the relative free volume with increasing The rise in the relative free volume with increasing temperature above glass transition leads to higher temperature above glass transition leads to higher temperature above glass transition leads to higher temperature above glass transition leads to higher observed expansion coefficient in the region.observed expansion coefficient in the region.observed expansion coefficient in the region.observed expansion coefficient in the region.observed expansion coefficient in the region.observed expansion coefficient in the region.observed expansion coefficient in the region.observed expansion coefficient in the region.

Above Tg the segments can move, rearrange and relieve Above Tg the segments can move, rearrange and relieve Above Tg the segments can move, rearrange and relieve Above Tg the segments can move, rearrange and relieve stress and the polymer will flowstress and the polymer will flowstress and the polymer will flowstress and the polymer will flow

Upon application of stressUpon application of stressUpon application of stressUpon application of stress

Above Tg Above Tg Above Tg Above Tg ---- the segments can move, rearrange and relieve stress the segments can move, rearrange and relieve stress the segments can move, rearrange and relieve stress the segments can move, rearrange and relieve stress and the polymer will flow.and the polymer will flow.and the polymer will flow.and the polymer will flow.

Physical state Physical state Physical state Physical state –––– soft, rubbery, sticky & can flow easily.soft, rubbery, sticky & can flow easily.soft, rubbery, sticky & can flow easily.soft, rubbery, sticky & can flow easily.

Below Tg Below Tg Below Tg Below Tg –––– the segments are frozen, the polymer will not flow. It the segments are frozen, the polymer will not flow. It the segments are frozen, the polymer will not flow. It the segments are frozen, the polymer will not flow. It will show ductile will show ductile will show ductile will show ductile behavior, behavior, behavior, behavior, resulting in cohesive brittle failure.resulting in cohesive brittle failure.resulting in cohesive brittle failure.resulting in cohesive brittle failure.

Physical state Physical state Physical state Physical state –––– hard, brittle, rigid & not easily deformable.hard, brittle, rigid & not easily deformable.hard, brittle, rigid & not easily deformable.hard, brittle, rigid & not easily deformable.

DYNAMIC mechanical analysis (DMA)DYNAMIC mechanical analysis (DMA)DYNAMIC mechanical analysis (DMA)DYNAMIC mechanical analysis (DMA)----is a thermal analysis techniqueis a thermal analysis techniqueis a thermal analysis techniqueis a thermal analysis techniquethat measures the properties of materials as they are deformed underthat measures the properties of materials as they are deformed underthat measures the properties of materials as they are deformed underthat measures the properties of materials as they are deformed underperiodic stress.periodic stress.periodic stress.periodic stress.

Specifically, in DMA a variable sinusoidal stress is applied, and the Specifically, in DMA a variable sinusoidal stress is applied, and the Specifically, in DMA a variable sinusoidal stress is applied, and the Specifically, in DMA a variable sinusoidal stress is applied, and the resultant sinusoidal strain is measured. resultant sinusoidal strain is measured. resultant sinusoidal strain is measured. resultant sinusoidal strain is measured.

If the material being evaluated is purely elastic, the phase difference between If the material being evaluated is purely elastic, the phase difference between If the material being evaluated is purely elastic, the phase difference between If the material being evaluated is purely elastic, the phase difference between

DYNAMIC mechanical analysis (DMA)DYNAMIC mechanical analysis (DMA)DYNAMIC mechanical analysis (DMA)DYNAMIC mechanical analysis (DMA)

If the material being evaluated is purely elastic, the phase difference between If the material being evaluated is purely elastic, the phase difference between If the material being evaluated is purely elastic, the phase difference between If the material being evaluated is purely elastic, the phase difference between the stress and strain sine waves is 0the stress and strain sine waves is 0the stress and strain sine waves is 0the stress and strain sine waves is 0°°°° (i.e., they are in phase). If the material (i.e., they are in phase). If the material (i.e., they are in phase). If the material (i.e., they are in phase). If the material is purely viscous, the phase difference is 90is purely viscous, the phase difference is 90is purely viscous, the phase difference is 90is purely viscous, the phase difference is 90°°°°. However, most real. However, most real. However, most real. However, most real----world world world world materials including polymers are viscoelastic and exhibit a phase difference materials including polymers are viscoelastic and exhibit a phase difference materials including polymers are viscoelastic and exhibit a phase difference materials including polymers are viscoelastic and exhibit a phase difference between those extremes.between those extremes.between those extremes.between those extremes.

DMA continuously monitors material modulus with temperature and, hence, DMA continuously monitors material modulus with temperature and, hence, DMA continuously monitors material modulus with temperature and, hence, DMA continuously monitors material modulus with temperature and, hence, provides a better indication of longprovides a better indication of longprovides a better indication of longprovides a better indication of long----term, elevated temperature performance.term, elevated temperature performance.term, elevated temperature performance.term, elevated temperature performance.

DMADMADMADMA- Measure response of material to periodic stressMeasure response of material to periodic stressMeasure response of material to periodic stressMeasure response of material to periodic stress

---- Can apply stress (strain) in tension, compression, shear, Can apply stress (strain) in tension, compression, shear, Can apply stress (strain) in tension, compression, shear, Can apply stress (strain) in tension, compression, shear, bendbendbendbend

- Also measure the phase difference or “lag” (Also measure the phase difference or “lag” (Also measure the phase difference or “lag” (Also measure the phase difference or “lag” (δδδδ) between two sine waves) between two sine waves) between two sine waves) between two sine waves

material responseapplied stress

phase angle (δδδδ)

amplitude

Fdynamic

Force

E’

E”δ

Temperature

Fdynamic

Fstatic ((((δδδδ) ) ) ) phase difference, phase lag or “dissipation factor”phase difference, phase lag or “dissipation factor”phase difference, phase lag or “dissipation factor”phase difference, phase lag or “dissipation factor”

E”E*

There are several components that are critical to the design and There are several components that are critical to the design and There are several components that are critical to the design and There are several components that are critical to the design and resultant performance of a dynamic mechanical analyzer. resultant performance of a dynamic mechanical analyzer. resultant performance of a dynamic mechanical analyzer. resultant performance of a dynamic mechanical analyzer.

Those components are Those components are Those components are Those components are

� the drive motor (which supplies the sinusoidal the drive motor (which supplies the sinusoidal the drive motor (which supplies the sinusoidal the drive motor (which supplies the sinusoidal deformation force to the sample material), deformation force to the sample material), deformation force to the sample material), deformation force to the sample material),

� the drive shaft support and guidance system the drive shaft support and guidance system the drive shaft support and guidance system the drive shaft support and guidance system � the drive shaft support and guidance system the drive shaft support and guidance system the drive shaft support and guidance system the drive shaft support and guidance system (which transfers the force from the drive motor to (which transfers the force from the drive motor to (which transfers the force from the drive motor to (which transfers the force from the drive motor to the clamps that hold the sample), the clamps that hold the sample), the clamps that hold the sample), the clamps that hold the sample),

� the displacement sensor (which measures the the displacement sensor (which measures the the displacement sensor (which measures the the displacement sensor (which measures the sample deformation that occurs under the sample deformation that occurs under the sample deformation that occurs under the sample deformation that occurs under the applied force), applied force), applied force), applied force),

� the temperature control system (furnace), and the temperature control system (furnace), and the temperature control system (furnace), and the temperature control system (furnace), and the sample clamps.the sample clamps.the sample clamps.the sample clamps.

DYNAMIC MECHANICAL DYNAMIC MECHANICAL DYNAMIC MECHANICAL DYNAMIC MECHANICAL THERMALTHERMALTHERMALTHERMAL ANALYSIS (DMTA)ANALYSIS (DMTA)ANALYSIS (DMTA)ANALYSIS (DMTA)

Can detect weaker thermal transitions:Can detect weaker thermal transitions:Can detect weaker thermal transitions:Can detect weaker thermal transitions:

� At sufficiently low temperatures when chainAt sufficiently low temperatures when chainAt sufficiently low temperatures when chainAt sufficiently low temperatures when chain----and chain segment and chain segment and chain segment and chain segment mobility are fro�zen in, that is below the glassmobility are fro�zen in, that is below the glassmobility are fro�zen in, that is below the glassmobility are fro�zen in, that is below the glass----transition temperature, transition temperature, transition temperature, transition temperature, polymers behave like common elastic materials.polymers behave like common elastic materials.polymers behave like common elastic materials.polymers behave like common elastic materials.

� The (elastic) deformations in that state are character�ised by changes of The (elastic) deformations in that state are character�ised by changes of The (elastic) deformations in that state are character�ised by changes of The (elastic) deformations in that state are character�ised by changes of bond length and bond angles. The only in macromolecular sub�stances bond length and bond angles. The only in macromolecular sub�stances bond length and bond angles. The only in macromolecular sub�stances bond length and bond angles. The only in macromolecular sub�stances observed rubber elasticity is not caused by an energetic distortion of observed rubber elasticity is not caused by an energetic distortion of observed rubber elasticity is not caused by an energetic distortion of observed rubber elasticity is not caused by an energetic distortion of bond length or bond angles but by entropic effects: perturbation of a bond length or bond angles but by entropic effects: perturbation of a bond length or bond angles but by entropic effects: perturbation of a bond length or bond angles but by entropic effects: perturbation of a random coil leads to a state of lower entropy since the number of random coil leads to a state of lower entropy since the number of random coil leads to a state of lower entropy since the number of random coil leads to a state of lower entropy since the number of random coil leads to a state of lower entropy since the number of random coil leads to a state of lower entropy since the number of random coil leads to a state of lower entropy since the number of random coil leads to a state of lower entropy since the number of accessible quantum states (conforma�tions) is restricted by e. g. an accessible quantum states (conforma�tions) is restricted by e. g. an accessible quantum states (conforma�tions) is restricted by e. g. an accessible quantum states (conforma�tions) is restricted by e. g. an extension. extension. extension. extension.

� Rubber elasticity can be observed at tem�peratures higher than the glass Rubber elasticity can be observed at tem�peratures higher than the glass Rubber elasticity can be observed at tem�peratures higher than the glass Rubber elasticity can be observed at tem�peratures higher than the glass transition temperature if the polymer chains are long enough and if transition temperature if the polymer chains are long enough and if transition temperature if the polymer chains are long enough and if transition temperature if the polymer chains are long enough and if crosscrosscrosscross----links of any kind are present. The crosslinks of any kind are present. The crosslinks of any kind are present. The crosslinks of any kind are present. The cross----links can be permanent links can be permanent links can be permanent links can be permanent or temporary, chemical or physical of nature. They cause phenomena or temporary, chemical or physical of nature. They cause phenomena or temporary, chemical or physical of nature. They cause phenomena or temporary, chemical or physical of nature. They cause phenomena like relaxation and creep (retardation). like relaxation and creep (retardation). like relaxation and creep (retardation). like relaxation and creep (retardation).

Rheology of polymer meltsRheology of polymer meltsRheology of polymer meltsRheology of polymer melts

-Deformation and flowDeformation and flowDeformation and flowDeformation and flow- Gives information on the structureGives information on the structureGives information on the structureGives information on the structure

Mechanical Spectroscopy:Mechanical Spectroscopy:Mechanical Spectroscopy:Mechanical Spectroscopy:to study polymer morphologyto study polymer morphologyto study polymer morphologyto study polymer morphologyand structure and relate these and structure and relate these and structure and relate these and structure and relate these to endto endto endto end----use performance. use performance. use performance. use performance.

Rheological propertiesRheological propertiesRheological propertiesRheological propertiescan be measured continuouslycan be measured continuouslycan be measured continuouslycan be measured continuouslyas the material undergoes as the material undergoes as the material undergoes as the material undergoes temperaturetemperaturetemperaturetemperature----induced changes induced changes induced changes induced changes from amorphous to crystallinefrom amorphous to crystallinefrom amorphous to crystallinefrom amorphous to crystalline

RheologyRheologyRheologyRheologyThe study of deformation and flow characteristics of substances is called The study of deformation and flow characteristics of substances is called The study of deformation and flow characteristics of substances is called The study of deformation and flow characteristics of substances is called rheologyrheologyrheologyrheology

Ideal solids deform elasticallyIdeal solids deform elasticallyIdeal solids deform elasticallyIdeal solids deform elastically---- energy required to deform is fully recoveredenergy required to deform is fully recoveredenergy required to deform is fully recoveredenergy required to deform is fully recovered

Ideal fluids (liquids/gases) deform irreversiblyIdeal fluids (liquids/gases) deform irreversiblyIdeal fluids (liquids/gases) deform irreversiblyIdeal fluids (liquids/gases) deform irreversibly---- they flow; energy required to deform they flow; energy required to deform they flow; energy required to deform they flow; energy required to deform is dissipated within the fluid as heat (viscous).is dissipated within the fluid as heat (viscous).is dissipated within the fluid as heat (viscous).is dissipated within the fluid as heat (viscous).

In realityIn realityIn realityIn reality---- bodies are somewhere between ideal solids and ideal fluidsbodies are somewhere between ideal solids and ideal fluidsbodies are somewhere between ideal solids and ideal fluidsbodies are somewhere between ideal solids and ideal fluids

PolymersPolymersPolymersPolymers---- viscous and elasticviscous and elasticviscous and elasticviscous and elastic---- viscoelasticviscoelasticviscoelasticviscoelastic

Time scale of any deformation processTime scale of any deformation processTime scale of any deformation processTime scale of any deformation process

Characteristic time factor: Characteristic time factor: Characteristic time factor: Characteristic time factor: λ (infinite for ideal elastic solids and almost 0 for liquids)(infinite for ideal elastic solids and almost 0 for liquids)(infinite for ideal elastic solids and almost 0 for liquids)(infinite for ideal elastic solids and almost 0 for liquids)

Deformation process is related to a characteristic value: tDeformation process is related to a characteristic value: tDeformation process is related to a characteristic value: tDeformation process is related to a characteristic value: t

Deborah No.: Deborah No.: Deborah No.: Deborah No.: λ/t (high Deborah No. indicates solid/t (high Deborah No. indicates solid/t (high Deborah No. indicates solid/t (high Deborah No. indicates solid----like and low D No. indicates liquid like and low D No. indicates liquid like and low D No. indicates liquid like and low D No. indicates liquid like)like)like)like)

Dynamic Viscosity: As a fluid moves, a shear stress is developed in it, the magnitude of Dynamic Viscosity: As a fluid moves, a shear stress is developed in it, the magnitude of Dynamic Viscosity: As a fluid moves, a shear stress is developed in it, the magnitude of Dynamic Viscosity: As a fluid moves, a shear stress is developed in it, the magnitude of which depends on the viscosity of the fluid.which depends on the viscosity of the fluid.which depends on the viscosity of the fluid.which depends on the viscosity of the fluid.

Shear stress, denoted by the Greek letter (tau), Shear stress, denoted by the Greek letter (tau), Shear stress, denoted by the Greek letter (tau), Shear stress, denoted by the Greek letter (tau), τ, can , can , can , can be defined as the force required to be defined as the force required to be defined as the force required to be defined as the force required to slide one unit area layer of a substance over another.slide one unit area layer of a substance over another.slide one unit area layer of a substance over another.slide one unit area layer of a substance over another.

Thus, Thus, Thus, Thus, τ is a force divided by an area and can be measured in the units of N/mis a force divided by an area and can be measured in the units of N/mis a force divided by an area and can be measured in the units of N/mis a force divided by an area and can be measured in the units of N/m2222 (Pa)(Pa)(Pa)(Pa)

The fact that the shear stress in the fluid is directly proportional to the velocity gradient can be statedmathematically as:

τ = µ γ

Newtonian Fluids and NonNewtonian Fluids and NonNewtonian Fluids and NonNewtonian Fluids and Non----Newtonian FluidsNewtonian FluidsNewtonian FluidsNewtonian Fluids

�Any fluid that behaves in accordance with called a Any fluid that behaves in accordance with called a Any fluid that behaves in accordance with called a Any fluid that behaves in accordance with called a Newtonian fluid.Newtonian fluid.Newtonian fluid.Newtonian fluid.

�Conversely, a fluid that does not behave in accordance with the Conversely, a fluid that does not behave in accordance with the Conversely, a fluid that does not behave in accordance with the Conversely, a fluid that does not behave in accordance with the above equation is called a above equation is called a above equation is called a above equation is called a nonnonnonnon----Newtonian fluid.Newtonian fluid.Newtonian fluid.Newtonian fluid.

Two major classifications of nonTwo major classifications of nonTwo major classifications of nonTwo major classifications of non----Newtonian fluids are Newtonian fluids are Newtonian fluids are Newtonian fluids are timetimetimetime----Two major classifications of nonTwo major classifications of nonTwo major classifications of nonTwo major classifications of non----Newtonian fluids are Newtonian fluids are Newtonian fluids are Newtonian fluids are timetimetimetime----independent and timeindependent and timeindependent and timeindependent and time----dependent fluids.dependent fluids.dependent fluids.dependent fluids.

�As their name implies, timeAs their name implies, timeAs their name implies, timeAs their name implies, time----independent fluids have a independent fluids have a independent fluids have a independent fluids have a viscosity at any given shear stress that does not vary with time.viscosity at any given shear stress that does not vary with time.viscosity at any given shear stress that does not vary with time.viscosity at any given shear stress that does not vary with time.

�The viscosity of time dependent fluids, however, changes with The viscosity of time dependent fluids, however, changes with The viscosity of time dependent fluids, however, changes with The viscosity of time dependent fluids, however, changes with time.time.time.time.

Drop breakDrop breakDrop breakDrop break----upupupup

CoalescenceCoalescenceCoalescenceCoalescence

α

γη &RCa m=

capillary number capillary number capillary number capillary number CaCaCaCa that represents the ratio of deforming viscous to restoring that represents the ratio of deforming viscous to restoring that represents the ratio of deforming viscous to restoring that represents the ratio of deforming viscous to restoring interfacial stresses. interfacial stresses. interfacial stresses. interfacial stresses. ηηηηmmmm the matrix viscosity, the matrix viscosity, the matrix viscosity, the matrix viscosity, γ the shear rate, the shear rate, the shear rate, the shear rate, RRRR the droplet radius, the droplet radius, the droplet radius, the droplet radius, αααα the interfacial the interfacial the interfacial the interfacial tension and tension and tension and tension and ηηηηdddd the droplet viscositythe droplet viscositythe droplet viscositythe droplet viscosity

viscosity ratio, viscosity ratio, viscosity ratio, viscosity ratio, λλλλm

d

η

ηλ = If If If If λ >4, no break>4, no break>4, no break>4, no break----upupupup

Drops can break when 1< Ca <2Drops can break when 1< Ca <2Drops can break when 1< Ca <2Drops can break when 1< Ca <2

Thank You !Thank You !Thank You !Thank You !

sbose@materials.iisc.ernet.insbose@materials.iisc.ernet.insbose@materials.iisc.ernet.insbose@materials.iisc.ernet.in

For deformed droplets and fibrils, the interfacial tension drives retraction towards a For deformed droplets and fibrils, the interfacial tension drives retraction towards a For deformed droplets and fibrils, the interfacial tension drives retraction towards a For deformed droplets and fibrils, the interfacial tension drives retraction towards a spherical shape. In the case of ellipsoidal Newtonian droplets in a Newtonian matrix, spherical shape. In the case of ellipsoidal Newtonian droplets in a Newtonian matrix, spherical shape. In the case of ellipsoidal Newtonian droplets in a Newtonian matrix, spherical shape. In the case of ellipsoidal Newtonian droplets in a Newtonian matrix, the characteristic time the characteristic time the characteristic time the characteristic time ττττdddd for this process can be obtained from the linear viscoelastic for this process can be obtained from the linear viscoelastic for this process can be obtained from the linear viscoelastic for this process can be obtained from the linear viscoelastic model of Palierne:model of Palierne:model of Palierne:model of Palierne:

)25(2)1(10

))1(232)(1619(

4 +−+

−−++⋅

⋅

⋅=

λϕλ

λϕλλ

α

ητ m

d

R

If the droplet elongation exceeds a certain critical value, the droplet or fibril will break up after If the droplet elongation exceeds a certain critical value, the droplet or fibril will break up after If the droplet elongation exceeds a certain critical value, the droplet or fibril will break up after If the droplet elongation exceeds a certain critical value, the droplet or fibril will break up after cessation of the flowcessation of the flowcessation of the flowcessation of the flow

The increase of the dimensions of the dispersed phase are caused by coalescence and Ostwald The increase of the dimensions of the dispersed phase are caused by coalescence and Ostwald The increase of the dimensions of the dispersed phase are caused by coalescence and Ostwald The increase of the dimensions of the dispersed phase are caused by coalescence and Ostwald ripening.ripening.ripening.ripening.

Ostwald ripening is purely caused by thermodynamics, which drives the content of small droplets Ostwald ripening is purely caused by thermodynamics, which drives the content of small droplets Ostwald ripening is purely caused by thermodynamics, which drives the content of small droplets Ostwald ripening is purely caused by thermodynamics, which drives the content of small droplets Ostwald ripening is purely caused by thermodynamics, which drives the content of small droplets Ostwald ripening is purely caused by thermodynamics, which drives the content of small droplets Ostwald ripening is purely caused by thermodynamics, which drives the content of small droplets Ostwald ripening is purely caused by thermodynamics, which drives the content of small droplets to diffuse through the matrix into the bigger droplets . The dynamics of droplet growth by Ostwald to diffuse through the matrix into the bigger droplets . The dynamics of droplet growth by Ostwald to diffuse through the matrix into the bigger droplets . The dynamics of droplet growth by Ostwald to diffuse through the matrix into the bigger droplets . The dynamics of droplet growth by Ostwald ripening obeys the following kinetics as a function of time ripening obeys the following kinetics as a function of time ripening obeys the following kinetics as a function of time ripening obeys the following kinetics as a function of time tttt::::

RRRR0000 is the initial droplet radius and is the initial droplet radius and is the initial droplet radius and is the initial droplet radius and bbbb is a factor that depends, among others, on the diffusion is a factor that depends, among others, on the diffusion is a factor that depends, among others, on the diffusion is a factor that depends, among others, on the diffusion coefficient of the molecules of the dispersed phase in the matrix material. In cocoefficient of the molecules of the dispersed phase in the matrix material. In cocoefficient of the molecules of the dispersed phase in the matrix material. In cocoefficient of the molecules of the dispersed phase in the matrix material. In co----continuous blends, continuous blends, continuous blends, continuous blends, the rate of coarsening the rate of coarsening the rate of coarsening the rate of coarsening drdrdrdr////dtdtdtdt is given by:is given by:is given by:is given by:

Due to the large viscosity and matched densities of polymers, the driving forces for droplet approach Due to the large viscosity and matched densities of polymers, the driving forces for droplet approach Due to the large viscosity and matched densities of polymers, the driving forces for droplet approach Due to the large viscosity and matched densities of polymers, the driving forces for droplet approach are rather limited, which makes that quiescent coalescence is mainly observed in blends with a are rather limited, which makes that quiescent coalescence is mainly observed in blends with a are rather limited, which makes that quiescent coalescence is mainly observed in blends with a are rather limited, which makes that quiescent coalescence is mainly observed in blends with a large volume fraction of dispersed phase. large volume fraction of dispersed phase. large volume fraction of dispersed phase. large volume fraction of dispersed phase.

tbRR ⋅+= 3

0

3

blend

a

dt

dr

η

α⋅=