bi 109 6 amorphous phase of polymers

8/10/2019 BI 109 6 Amorphous Phase of Polymers

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INTRODUCTION

AMORPHOUS POLYMERS

Amorphous polymers are frozen polymer liquids

At low temperatures, amorphous polymers are

glassy, hard, and brittle.

As the temperature is raised, they go through the

glass-rubber transition.

Glass transition temperature (Tg): temperature at

which the polymer softens because of the onset of

long range coordinated molecular motion; a second

order transition.

First order transition: transition that involves anabrupt change in a fundamental thermodynamic

property(e.g. enthalpy or volume). Melting point

(Tm).


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AMORPHOUS POLYMERS

AMORPHOUS POLYMERS


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AMORPHOUS POLYMERS

The various molecular motion occurring in an

amorphous polymer

1. Translational motion of the entire molecule

2. Wriggling and jumping of segment ofmolecules ( 40- 50 carbons) permitting flexing anduncoiling which lead to elasticity.

3. Motion of few atoms(5 or 6) along the mainchain.

4. Vibration of atom about equilibrium positions

Activation energy 1>2>3>4 Tg is the temperature where 1 and 2 are frozen

out

AMORPHOUS POLYMERS


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YOUNGS MODULES (E) Youngs modulus is defined by theequation: !=E"

where: =tensile stress (in terms

of force per unit area) =tensile strain (no units,

remember?)

E=Youngs modulus (in dynes/cm2, or force per unit area)

NOTE: 10 dynes/cm-1 Pascal

E is a measure of the stiffness ofthe material

The higher the E, the more

resistant the material to stretching.

=(L-L0)/L0if initial length isL0and final length = L

one dyne of force through 1 cmgives 1 erg (amount of work done)

Mechanical deformation of solid bodies.(a)Triaxial stresses on a material body Undergoingelongation. (b) Simple shear deformation.

SHEAR MODULUS (G)Instead of elongating (or compressing) a sample, it may also be

subjected to shearing or twisting motions.

The ratio of the shear stress (f) to the shear strain (s) defines the

shear modulus (G):G=f/s

The table below summarizes some mechanical terms wide used in

the literature:

Variable Definition

Stress

Strain

E Youngs modulus

G Shear modulus

B Bulk modulus

Poissons ratio

Coefficient of viscosityJ Tensile compliance

s Shear strain

f Shear stress

R Gas constant=8.31x107

(dynes.cm)/(mol.K)

t Time


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SHEAR MODULUS (G)

Instead of elongating (or compressing) a sample, it may also be subjected to

shearing or twisting motions. The ratio of the shear stress (f) to the shear

strain (s) defines the shear modulus (G):

G=f/s

SHEAR MODULUS (G)The table below summarizes some mechanical terms widely used in the

literature:Variable Definition

Stress

Strain

E Youngs modulus

G Shear modulus

B Bulk modulus

Poissons ratio

Coefficient of viscosity

J Tensile compliance

s Shear strain

f Shear stress

R Gas constant=8.31x107

(dynes.cm)/(mol.K)

t Time


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POISSONS RATIO ($)

Values of Poissons Ratio

Value Interpretation

0.5 No volume change during stretch

0.0 No lateral contraction

0.49-0.499 Typical values for elastomers

0.20-0.40 Typical values for plastics

d lnV( )d ln x( )

=d lnx( )d lnx( )

"d ln y( )d ln x( )

+d lnz( )d ln x( )

and

"d lny( )d lnx( )

= "d lnz( )d ln x( )

=#

Since d ln x/ d ln x= 1, for no volume change #=0.5

On extension, plastics exhibit considerable volume increases

BULK MODULUS (B) AND COMPRESSIBILITY (%)

B = -V("P/"V)T P= hydrostatic pressure

A body usually shrinks in volume on being exposed toincreasing external pressures, therefore ("P/"V)T isnegative

The inverse of the bulk modulus is the compressibility

%

= 1/B

true only for a solid or liquid in which there is no time-dependent response


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RELATIONSHIPS BETWEEN E, G, B, AND $

The following equation relates the four basic mechanicalproperties:

E=3B(1-2$)=2(1+$)G

When $=0.5, then E=3 G, which defines the relationshipbetween Eand Gto a good approximation for elastomers.

Rearranging this equation to evaluate Poissons ration forelastomers:

1-2$=E/3B=%E/3

The quantity 1-2$is close to zero for elastomers

Values in the literature for elastomers vary from 0.49 to 0.49996

Therefore, in contrast to plastics, separation of the atoms playsonly a small role in the internal storage of energy

COMPLIANCE VERSUS MODULUS

Modulus is a measure of the stiffness or hardness of an object,

Elongational compliance (J) is a measure of softness. J=1/E

This equation applies to regions far from transitions

For regions in or near transitions, the relationship is more complex.

Nu me ri ca l Va lues for E

Material E (dyne/cm

2

) E (Pa)Copper 1.2 x 1012 1.2 x 1011

Polystyrene 3 x 1010 3 x 109

Soft Rubber 2 x 107 2 x 106


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STORAGE AND LOSS MODULIEand Grefer to quasistatic measurements

In reference to cyclical or repetitive motions of stress

and strain, use dynamic mechanical moduli (E* ):

E*=E + iE

where: E= storage modulus the energy stored

elastically during deformation

E= loss modulus, the energy converted to heat

Note that E=|E*| i = !1

REGIONS OF VISCOELASTIC BEHAVIOR

Viscoelastic materials exhibit a combination ofelastic and viscous behavior.

Viscoelasticity refers to both the time andtemperature dependence of mechanical behavior.

The states of matter for low molecular weightcompounds are well known: crystalline, liquid,and gaseous.

The first order transitions (melting and boiling)separate these 3 states.

These small compounds exhibit crystalline-crystalline transitions (also first order).


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No high molecular weight polymer vaporizes. Alldecompose before the boiling point.

No high molecular weight polymer attains a 100%crystalline structure, except in the single-crystalstate.

Many polymers do not crystallize at all, but formglasses at low temperatures. At highertemperatures, they form viscous liquids. The

transition that separates the glassy and viscousliquid states is known as the glass-rubbertransition



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Region 1: Glassy region

Polymer is glassy andfrequently brittle (e.g.polystyrene drinking cupsand Plexiglas(PMMA)at room temperature)

Youngs modulus forpolymers just below theTgis surprisingly constantover a wide range ofpolymers

(~3 x 1010dynes/cm2or 3x 109Pa)

Region 2: Glass transition regionModulus drops a factor of about 1000 over

a 20-30C range

Tgdefined as the temperature when the thermal

expansion coefficient ( ) undergoes a discontinuity.

! =1

V

"V

"T

#

$%&

P

where V= the volume of the material

Qualitatively, this region can be interpreted as the onset of long-range,

coordinated molecular motion. While only 1-4 chain atoms are in motion

below the Tg, some 10-50 chain atoms move above the Tg.

Polymer Tg (C) No. of chain atoms involved

Poly( dimethyl siloxane -127 40

Poly(ethylene glycol) -41 30

Polystyrene +100 40-100

Polyisoprene -73 30-40


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Region 3: Rubbery plateau region

Modulus becomes almost constant again, typically

2 x 107dynes/cm2or 2 x 106Pa.

Polymers exhibit long-range rubber elasticity, which means that the elastomer

can be stretched, perhaps several hundred percent, and snap back to its

original length when released.Two cases: linear polymer or cross-linked polymer


Case 1: Linear polymer

Modulus drops off slowly

The higher the molecular weight, the longer the plateau.

When Columbus came to America, he found the native Americans playing

ball with natural rubber. This product, a linear polymer of very high

molecular weight retains its shape for short durations of time. However, upon

standing overnight, it creeps, first forming a flat spot on the bottom, ad

eventually flattening out like a pancake.


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Case 1: Linear polymer

Modulus drops off slowly


Case 2: Cross-linked polymer

Dotted line in figure on page 6-13 is followed.

Cross-linked polymers remain in region 3 until decomposition.

Improved rubber elasticity with creep suppressed.

The dotted line follows the equation E= 3nRT where nis the

number of active chain segments in the network.

Example: rubber bands


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Region 4: Rubbery flow region

For linear polymers only

Polymer has both rubbery and flow properties, depending on the time

scale of the experiment.

Example: Silly Putty

Region 5: Liquid flow region

Polymer flows readily, often behaving like molasses.

Increased energy allotted to the chains permits them to reptate out through

entanglements rapidly, and flow as individual molecules.


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The loss quantities behave somewhat like the

absorption spectra in IR spectroscopy, where the

energy of the EM radiation is just sufficient to

cause a portion of the molecule to go to a higher

energy state.

Measurements by DMS (dynamic mechanical

spectroscopy) refers to any one of several methods

where the sample undergoes repeated small-

amplitude strains in a cyclic manner. The

molecules store a portion of the imparted energy

elastically and dissipate some in the form of heat.

The Youngs storage modulus (E) i s ameasure of the energy store elastically andthe Youngs loss modulus (E) is a measureof the energy lost as heat.


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Simplified definition of E and E.hen a viscoelastic ball is dropped onto a perfectly elastic floor, it bounces

back to a height E, a measure of the energy stored elastically during thecollision. The quantity Erepresents the energy lost as heat.

Another equation is

wide use is:

E/E= tan &

Tan &is called the

loss tangent, with &

being the angle

between the in-phase

and out-of-phase

components in the

cyclic motion.


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.

The quantities E and tan &

display maxima at Tg, with the

tan &peak several degrees (C)

higher than the Epeak.

The areas under the peaks is

related to the chemical structure

of the polymer. The width of the

transitions and shifts in the peak

temperatures of E and tan &

are sensitive guides to the exact

state of the material and

molecular mixing in blends.

:

The maxima in Eandtan &are sometimes usedas the definition of T g.

The dynamic mechanicalbehavior of an idealpolymer is shown below:


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THE AMORPHOUS POLYMER STATE

Amorphous polymers areusually dense. The density ofthe amorphous phase isapproximately 85-95% that ofthe crystalline phase.

Amorphous polymers do not:

(1) exhibit crystalline x-raydiffraction pattern (topfigure)

(crystalline-left, amorphous-right)

Or (2)have first order meltingtransition (bottomfigure)

GLASS TO RUBBER TRANSITION

Rubber: liquid-like state with rapid

molecular motion

Crystalline: solid state with regular order and restricted molecularmotion

Glass: solid state without regular order and restricted molecularmotion; formed when the polymer will not crystallize or if Tc< Tg

A glass and rubber are then two states of the same material, with the

glassy state being a non-equilibrium state. The glassy state is a dynamic state. The specific volume continues to

relax towards the equilibrium value.

Time-dependent volume relaxation of poly(vinyl acetate) at varioustemperatures is shown below at various temperatures below its Tgof32C.


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Where V = volume

Tg = 32

V

# = equilibrium volume

determined from a linearextrapolation of the rubbertime-volume data into theglassy state

The volume-relaxation occursover exceedingly long timescales. The rate of volume

relaxation decreasesdramatically when the polymeris cooled below 5-10C belowits T g.


The volume-temperature curve onheating is differentthan on cooling. Thisdifference is referredto as hysteresis.


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The coefficient ofthermal expansion alsoshows both anundershoot and overshoot on heating whichis absent on cooling.

Free-volume Theory

Introduces free volume in the form ofsegment-size voids as a requirement for theonset of coordinated molecular motion

Provides relationships between coefficientsof expansion below and above Tgand yieldsequations relating viscoelastic motion to thevariables of time and temperature


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Kinetic theory

Thermodynamic Theory


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SUMMARY OF GLASS TRANSITION THEORIES

Theory Advantages Disadvantages

Free-volume

theory

1. Time and temperature

of viscoelastic events

related to Tg

1. Actual molecular

motions poorly

defined

2. Coefficients of

expansion above and

below Tg related

Kinetic

theory

1. Shifts in Tgwith time

frame quantitativelydetermined

1. No Tgpredicted at

infinite time scales

2. Heat capacities

determined

SUMMARY OF GLASS TRANSITION THEORIES

Theory Advantages Disadvantages

Thermodynamic

theory

1. Variation of Tg with

molecular weight,

diluent, and cross-link

density predicted

1. Infinite time scale

required for

measurements

2. Predicts true second-

order transition

temperature

2. True second-order

transition temperature

poorly defined


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FREE VOLUME THEORY OF T g

The specific volume of

a liquid or solid is

composed of a part

occupied by molecules

(V0)

and unoccupied space,

or free volume (Vf).

FREE VOLUME THEORY OF T g

This free volume is essential

for molecular motion. When

the free volume is less than a

critical value, there is

insufficient room for the

polymer molecules to move.

At this point the polymer will

fall out of thermodynamic

equilibrium and we will

observe the rubber to glass

transition.


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Schematic illustration of the temperature

dependence of free volume:

Variables are defined as

follows:

Vr= volume of rubber

Vg= volume at Tg

V0 = volume occupied

at 0K

Vf = free volume

The slopes of the lines above and below the Tgare defined as:

(dV/dT)r above the Tg(dV/dT)gbelow the Tg

Vg = V0 +Vf +dV

dT

!"

#$

g

Tg = V0 + Vf+ Vg%gTg

and

Vr =Vg +dV

dT

!"

#$

r

T& Tg( ) = Vg + Vg%r T& Tg( )

where %g =1

Vg

dV

dT

!"

#$g

= thermal expansion of glass


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The slopes of the lines above and below the Tgare defined as:

(dV/dT)r above the Tg(dV/dT)gbelow the Tg

And ! r =1

Vg

dV

dT

"#

$%r

= thermal expansion of rubber

Solving the first equation for Vf gives:

Vf = Vg 1 &! gTg( )& V0 V0cannot be measured directly, but is usually estimated by extrapolating therubber volume-temperature curve to a temperature of zero degrees Kelvin.

Using this assumption,

Vf = Vg'!Tg w h e r ew h r '! = !r & ! g


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THERMODYNAMIC THEORY OF Tg

THERMODYNAMIC THEORY OF Tg

A second order transitionbelow Tgis needed toresolve KauzmannsParadox: uponextrapolating to lowertemperatures theexperimentally measuredentropy in the rubber, anegative entropy is

calculated.

T2= Second order transitiontemperature 0


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THERMODYNAMIC THEORY OF T g

THERMODYNAMIC BASIS FOR Tg

By linearly extrapolating

the experimentally

measured entropy to

temperatures lower than

Tg, negative entropies are

obtained:


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If there existed a secondorder transition below theTg, only zero and positiveentropies would be found,even at lowertemperatures. Therefore,they make the assumptionthat such as transition

exists.


The effects of chemical

composition, molecular

weight, plasticizers, etc.

on this transition have

been calculated.


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Effects of Chemical Structure:

Block and graft copolymers have multiple glass transitions,

Corresponding to the different homopolymers

Random or statistical copolymers have a single glass transition.

If wAand wB are the weight fractions of the comonomers Aand B, the glasstransition of the copolymer could be given by either a linear equation:

Tgco = TgAwA + TgBwBor a more complex relation:

1

Tgco=

wA

TgA+

wB

TgB

These equations are plotted for copolymers of various ratios when TgA= 100

and TgB= 200:

Effects of Molecular Weight:

Tg!= Tg +

K

M whereK =

2"NA#

$fMnTg!

is defined as the value of Tg for a polymer sample of infinite molar

mass, is the contribution of one chain end to the free volume, and $fis thethermal expansion coefficient of the free volume, is the density, and NAis

Avogadros number, as before.


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EFFECT OF COPOLYMERIZATION ON T g

For one-phase systems:

Tg !M1"Cp1Tg1 + M 2"Cp2 Tg2

M 1"C p1 + M 2"C p2(8.77)

1

Tg=

M1

Tg1+

M2

Tg2(8.78)

ln Tg = M 1ln Tg 1 +M2ln Tg2 (8.79)

Tg = M1Tg1 + M2 Tg2 (8.80)

EFFECT OF COPOLYMERIZATION ON T g

Figure 8.28 Glass transition temperatures, Tg, of poly(2,6-dimethyle-1,4-phenylene oxide)-blend-polystyrene (PPO/PS) blends vs. mass fraction oPPO, MPPO. The full curve was calculated from equation 8.76 as circles. PPOwas designated as component 2.


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DEPENDENCE OF Tg ON CHEMICAL

STRUCTURE

Increase Tg Decrease Tg

Intermolecular forces In-chain groups promoting

flexibility(double-bonds and ether

linkages)

High CED Flexible side groups

Intrachain steric hindrance Symmetrical substitution

Bulky, stiff side groups

Effect of Aliphatic Side Groups on Tg


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Effect of Aliphatic Side Groups on Tg

Tg(C)

Polyacrylates Polymethacrylates

Side chain Atactic

Dominantly

Syndiotactic Isotactic

Dominantly

Syndiotactic

100%

Isotactic

methyl 10 8 43 105 160

ethyl -25 -24 8 65 120n-propyl --- -44 --- 35 ---

iso-propyl -11 -6 27 81 139

n-butyl --- -49 -24 20 88

iso-butyl --- -24 8 53 120sec-butyl -23 -22 --- 60 ---

cyclo-

hexyl

12 19 51 104 163

SUB-Tg TRANSITIONS

The glass is not a static structure,but a dynamic state where the molecular

motion is just retarded.

There are numerous relaxation processesthat can occur below Tg.

e.g. Poly(methyl methacrylate)

plot of volume-temperature data


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SUB-Tg TRANSITIONS

Alkyl methacrylates - plot of thermal expansion vs. temperature

SUB-Tg TRANSITIONS

CH3!- relaxation of long range order |"- relaxation due to ester group rotation

~~~~CH2C~~~~~~~

#- a-methyl group relaxation |$- side-chain methyl group rotation C=O

|O|CH3


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RESIDUAL ORDER IN AMORPHOUS

POLYMERS?

Amorphous polymers are often described as a bowl of spaghetti, where the

spaghetti strands weave randomly in and out among each other.

Closer examination shows that they have short regions where the chains

appear to lie more or less parallel.

Our knowledge of the amorphous state is incomplete and is the subject of

intensive research at this time.

EXPERIMENTAL METHODS

There are two categories of methods to study amorphous polymers.

Those which study:

(1) short range interactions (non-random vs. random chain positions) < 20

(2) long range interactions

The data that can be obtained by these methods is summarized in thefollowing table:


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EXPERIMENTAL METHODSfollowing table:

EXPERIMENTAL METHODS

SHORT-RANGE INTERACTIONS

measure the orientation of monomer residues along the axialdirection of a chain

(or) measure the order between chains in the radial direction

Methods include: Birefringence Rayleigh scattering Brillouin scattering Raman scattering

Axial Correlation

Radial Correlation


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LONG-RANGE INTERACTIONS

Most powerful method is small angle neutron scattering (SANS)

This technique can be used to determine the actual chain radius of gyration inthe bulk state.

Similar to the light scattering methods described in the section on polymersolutions and solubility:

Hc

R(!) " R(solvent)=

1

M wP(!)+ 2A2c

where

R(!) =I!#

2

I0Vs where I = scattered radiationintensity

I0 = initial radiation intensityVs = scattering volume = sample-detector distance

P()= scattering form factor = 1 for small particles or molecules

For this type of study,

LONG-RANGE INTERACTIONS

(1) A deuterated polymer solution is dissolved in an ordinary hydrogen-bearing polymerof the same type

(2) Background originates from the protonated sample and will be subtracted

(3) Scattering of interest comes from the deuterated sample


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ELECTRON AND X-RAY DIFFRACTION

Amorphous materials diffract x-rays and electrons, but the pattern is morediffuse, sometimes called halos

Questions to be resolved center about:

Do chains lie parallel for any distance?

If so, what is the distance?

X-ray diffraction studies are often called wide-angle x-ray scattering (WAXS)


Typical WAXS data for polytetrafluoroethylene (Teflon) are shown in thefollowing figure:


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The scattering maxima indicate chain spacing distances.

The x axis (s) is sometimes called inverse space and is equal to 4!sin!/"inunits of -1

The diffracted intensity is plotted on the y-axis multiplied by s to permit the

features to be more evenly weighted.


(1) conformational orientation in the axial direction which is a measure ofhow ordered or straight a chain might be(2) organization in the radial direction, which is a direct measure of

intermolecular order.WAXS measures both of these parameters.

For example:The axial direction of molten polyethylene could be described as a chain withthree rotational states (0, +180, and -180) with an average trans sequencelength of 3-4 backbone bonds.

Polytetrafluoroethylene (Teflon) was found to have more or less straightchains in the axial direction for distances of at least 24


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The following table shows the first interchain spacing of typical amorphouspolymers:

Table 5.5 Interchain spacing in selected amorphous polymers

Polymer Spacing, Reference

Polyethylene 5.5 (a)

Silicone rubber 9.0 (a)Polystyrene 10.0 (b)

Polycarbonate 4.8 (c)

References: (a) Y.K. Ovchinnikov, G.S. Markova, and V.A. Kargin, Vysokomol. Soyed.,A11, 329 (1969). (b) A. Bjornhaug, O. Ellefsen, and B.A. Tonnesen,J. Polym. Sci., 12,621 (1954). (c) A. Siegmann and P.H. Geil,J. Macromol. Sci. (Pys.), 4(2), 239 (1970).

THE FREELY JOINTED CHAIN

The simplest mathematical model describing the conformation of a polymerchain in space is the freely jointed chain model.

This model uses a chain with x links, each with length l, joined in a linearsequence with no restrictions on the angle between successive bonds.


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By analogy with Brownian motion statistics, the root-mean-square end-to-enddistance would be given by:

rf2( )

1 / 2

= lx1/ 2

where the fsubscript indicates free rotation.

A more general equation yielding the average end-to-end distance is given by:

r02= l

2x

1! cos"( ) 1+ cos#( )1+ cos"( ) 1! cos#( )

where = bond angle between atoms = conformation angle


This model underestimates the end-to-end distance since it omits severalissues:

Regular bond angles of 109 (such as in polyethylene) expands the chain by a

factor of [(1-cos!)/(1+cos!)]1/ 2

= 21/ 2

Other short-range interaction include steric hindrances which work to expand

the chain.

Long-range interactions include excluded volume, which eliminatesconformations in which two widely-separated segments would occupy thesame space.


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Incorporating these considerations into a constant (C) and squaring both sidesof the equation giving root-mean-square end-to-end distance gives:

rf2=Cl

2x

Typical values forCare:

Polymer CPolyethylene 6.8Polystyrene 9.85Isotactic polypropylene 5.5Poly(ethylene oxide) 4.1Nylon 66 5.9Polybutadiene(98% cis) 4.75

RANDOM COIL

Random coil is often used to describe the unperturbed shape of polymerchains in both dilute solutions and in the bulk amorphous state.

In this model, chains are permitted to wander in a space-filling way as long asthey do not pass through themselves or another chain. That is, this modelconsiders the constraint of excluded volume.

This model was developed by x-ray and mechanical studies.

In dilute solutions, the random coil dimensions are present under the Flory !-solvent conditions where the polymer-solvent interactions and the excludedvolume terms just cancel each other.


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RANDOM COIL

In the bulk amorphous state, the monomers are surrounded entirely byidentical monomers, and the sum of all interactions is zero. (i.e. monomer-monomer contacts between monomers on the same chain is the same as theinteraction between monomers on different chains)

In the limit of high molecular weight, the end-to-end distance of the randomcoil divided by the square root of 6 yields the radius of gyration. The radiusof gyration is defined as the root-mean-square distance of a segment from thecenter of mass for the molecule.

Since the number of links (x) is proportional to the molecular weight,Rg

Mis

a constant.

This models advantage is its simplicity

The vast bulk of research to date strongly suggests that the random coil mustbe at least close to the truth for many polymers of interest.


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MACROMOLECULAR DYNAMICSPolymer motion can take two forms:(1) The chain can change its overall conformation (relaxation after strain)

or

(2) It can move relative to its neighbors

Both motions can be considered in terms of self-diffusion, a subcase ofBrownian motion.

While polymer chains can and do move sideways by simple translation

(as simple liquids do), such motion is exceedingly slow for long, entangledchains. A sideways translation would involve the coordinated movements ofmany such chains.

Two theories describing motion for linear chains will be discussed (theRouse-Bueche Theory and the de Gennes Reptation Theory) followed by abrief section on nonlinear chains.


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ROUSE-BUECHE THEORYThis theory uses a bead and spring model for the polymer chain:

The segments move in a viscous medium (other polymer chains and

segments) in which they are immersed.

This viscous medium exerts a drag force on the system, damping out the

motions.

The force is assumed to be proportional to the velocity of the beads

This assumption is equivalent to assuming that the bead behaves as a

macroscopic bead in a continuous viscous medium.

DE GENNES REPTATION THEORY

This model describes the polymer chain (P) as being trappedinside a three-dimensional network (G) such as a polymeric gel:

The chain P is not allowed to cross any of the obstacles (O) but may move ina snake-like fashion among them.

This snake-like motion is called reptation.


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When the defects move, the chain progresses:


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Using scaling concepts, the diffusion coefficient (D) of a chain in the geldepends upon the molecular weight as:

D!M-2

Numerical values for Drange from 10-12

to 10-6

cm2/sec

Experimental methods for determining Dare:

(1) measure the broadening of concentration gradients versus time

and(2) measure the translation of molecules directly using local probes

such as nuclear magnetic resonance (NMR)

The relaxation time () depends on molecular weight as:

"!M3

NONLINEAR CHAINS

Two possibilities exist for translational movement in branched polymers:

(1) One end may move forward, pulling the other end and branch through

the same tube

(2) An entangled branched polymer may renew its conformation by

retracting a branch so that it retraces its path along the confining tube to a

position of the center monomer.

The second possibility is energetically cheaper and is depicted by the

following figure:


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GENERAL REMARKS

The amorphous state is defined as condensed, non-crystalline state of matter.

Many polymers are amorphous under normal use conditions

e.g. PolystyrenePoly(methyl methacrylate)Poly(vinyl acetate)

Crystalline polymers become amorphous above their melting point

e.g. PolyethylenePolypropyleneNylon

GENERAL REMARKS

In the amorphous state, the position of one chain segment relative to itsneighbors is relatively disordered.

In the relaxed condition, the polymer chains form random coils.

The chains are highly entangled, with physical crosslinks appearing aboutevery 600 backbone atoms.

Physical properties of the amorphous polymer change dramatically from the

rubbery to the glassy state.

The glassy state is a non-equilibrium state where molecular motion is highlyrestricted.


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bi 109 6 amorphous phase of polymers

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