PNC polymeric nanocomposites: fundamentals & technology

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PNC polymeric nanocomposites: fundamentals & technology

PNC

Polymeric

Nanocomposites:

fundamentals & technology

L. A. Utracki

NRCC/IMI, 75 de Mortagne, Boucherville, QC, Canada J4B 6Y4; Tel.: +1 (450) 641-5182; fax: -5105

2nd _{Conference on Nanotechnology in Petroleum Industry, Teheran,} 2004.10.11-10; Workshop lecture.

2

Outline

Introduction

Polymeric nanocomposites (PNC)

Applications Diversity of PNC’s

Clay and its intercalation & exfoliation methods

Fundamentals

Mathematical modeling Thermodynamics of PNC Rheology of PNC

Performance (mechanical, barrier, flammability)

Production of CPNC

Intercalation

Reactive exfoliation

Melt exfoliation in shear flow

Melt exfoliation in elongational flow

Conclusions

Plastics production in 2005:

184 million tons



US $700 billion

0.01 0.1 1 10 100 1000 1900 1940 1980 2020

1900-2010 world production of plastics (Mton)

production data sigmoidal fit Pl a st ic s pro du ct ion ( M to n) Year WP = 0.14151 + (2*0.042959/ )* tan-1((Year - 1947.262)/17.881) R = 0.99489

Annually produced

volume of plastics

is sufficient to:

Form a circular rod with diameter:

D = 76.5 m

all along Equator, or

Cover Iran with a

plastics sheet

h = 112 mm

thick.

4

Nanocomposites (NC) = matrix + dispersed in it nanometer-size

particles.

The matrix may be single- or multi-phase.

It may comprise additives that complement functionalities of the

system (reinforcement, electrical conductivity, toughness, etc.)

Depending on the nature of matrix, NC is:

Polymeric NC (PNC)

Ceramic NC (CNC) Metallic NC (MNC)

To generate high enhancement of properties, the nano-particles

ought to be anisometric, viz.

lamellar

, fibrillar, tubular, etc.

Spherical particles have been used to produce functional NC

(e.g., for electrical conductivity, optical or magnetic properties).

The reinforcing effects of nano-particles is related to the

particle-matrix interactions and aspect ratio, p:

For p > 500 the reinforcing effect is the same as of an infinitely large particle.

Since the absolute size of the reinforcement is not important, a small amount of nano-particles has a disproportionably large effect.

Because of small size, the nano-particles are invisible to the

naked eye and their surface energy is high. Hence, they may be

used to engender reinforced, but transparent composites.

In the absence of antagonistic interactions (e.g., hydrophilic

nano-particles in hydrophilic matrix) they do not require the interface

modification.

NC normally requires 1-2 vol% (or  6 wt%) of nano-particles,

behaving as a single phase and single component material

– it is

transparent and easily modified by additives.

6

Introduction 4

The most common PNC types are:

Clay-containing polymeric nanocomposites (

CPNC

) contain a layered material, mineral or synthetic clay, viz. montmorillonite (MMT),

vermiculite, synthetic fluoromica (FM) or hectorite. Especially MMT is of commercial interest.

Polyhedral oligomeric silsesquioxanes – POSS.

Prepared by a sol-gel method that leads to spherical, functional

particles.

Several plastics producing companies are involved in the development and production of PNC, viz. Honeywell, Bayer, BASF, Dow Plastics, DuPont/ICI,

Eastman, GM, Magna Intl., Mitsubishi, Montell, RTP Co., Showa Denko, Solutia, Toyota, Ube, Unitica, etc. Nanocor is focused on the CPNC technology.

By the year 2020 the world production of PNC is expected to reach 30 Mton/year worth over US$65 billion.

Clays Advantages Disadvantages

Mineral Traditional technology

Availability

Cost (in 2001 US$1,600/ton)

Variability of composition

Difficulty in removing amorphous

Poor reproducibility in PNC performance

Synthetic Control of composition High aspect ratio p  2000

Reproducible PNC performance

Developing technology Limited sourcing

Cost (in 2001 US$2,300/ton)

Question whether natural or synthetic clay is to be used has not been settled:

CPNC show improved properties, viz.

Mechanical (2-5 x modulus, strength and thermal expansion), resulting in reduced wall thickness

Barrier, HDT, Transparency, surface finish, etc., hence reduced molding cycle time

Flammability, low density, modification of matrix crystallinity, relative isotropicity.

Introduction 5

8

Diversity of PNC 1

Examples of commercially important NC with polymeric matrix.

Matrix Nano-particles Properties Application

Polyamide (Nylon), esp. poly-e-caprolactam (PA-6)

Major players: Toyota, AlliedSignal, Ube, Nanocor, Unitica, Showa Denko, Bayer, BASF, Solutia-Dow

Delaminated (or exfoliated) silicates, e.g., montmorillonite; 1-2 vol%. Exfoliation is critical, done either by a monomer or selected solvent.

In comparison to PA: similar density, transparency, 70oC higher heat deflection temperature, 70% higher tensile modulus, 130% higher flexural modulus, 1/2 lower oxygen

permeability, 70% lower flammability, etc.

Automotive (e.g., truck mirror housing, engine covers), tool housing, garden equipment, telecommunication,

aerospace, specialty application, barrier film for food packaging, etc.

Polyolefins, viz. polypropylene (PP) and its copolymers)

Major players: Montell, GM, Southern Clay Products Inc., Toyota, Ford, Dow Plastics, Magna International

Exfoliated smectite clay particles;  5 wt%. Compatibilizer is needed for these hydrophilic clay  hydrophobic PO systems. For example, Toyota uses maleic anhydride modified PP

Low density (0.91 g/mL) with high stiffness (equivalent to standard composites with 35 wt% talc), dimensional stability, low temperature impact strength, ductility to –35o

C, high heat aging, 75% lower flammability, excellent surface finish

Automotive: body panels, door panels, interior trim, instrument panels, pillars, consoles, etc.

Polystyrene (PS) and its blends with poly(styrene-co-vinlylmethyloxazoline) Major players: Toyota

Surface-treated clay particles; 4.8 wt%. High strength, tensile modulus increased by 37 % (over PS matrix), 43% smaller thermal expansion

Aerospace, automotive Polyethyleneterephthalate (PET)

Major players: Eastman, Bayer, BASF

Solution-expanded clay particles present during the polycondensation reaction

Transparency, low permeability, high strength, high stiffness, low density NC to be the central layer in co-formed products.

Food packaging, esp. as bottles for beer, juice and soft drink

Ethylene-vinyl alcohol copolymer (EVAl)

Major players: Nanocor, Mitsubishi

Exfoliated smectite clay particles;  5 wt%.

NC to be the central layer in multilayer, co-formed products

Packaging films, for moisture and oxygen sensitive foods and electronics Polyoxymethylene or acetal (POM)

Major players: Showa Denko, Bayer

Montmorillonite (?) Low warpage, low shrink, high surface quality, heat deflection temperature increased by 45o, 40% higher modulus

Automotive under-hood applications, electronics, etc.

Polyolefins (PO)

Major players: Toyota, Mitsui, Showa Denko, Mitsubishi

Nano-particles: Clays (e.g., MMT or vermiculite having the aspect

ratio p = 10 to 1000 or 1,000 to 15,000, respectively); synthetic

silanes (fluoromica, hectorite, tetra-ethoxysilane, POSS, SiO

₂

);

mineral salts (e.g., CuS, ZrO

₂

, Fe

₂

O

₃

, TiO

₂

, V

₂

O

₅

, Ag or Au); rigid

polymers (cellulosic whiskers, LCP, carbon nanotubes), etc.

Any polymer: viz. PE, PP, PS, PMMA, ionomers, PVE, PEG, PVP,

polypyrrole, SMA, PCL, PVAc, P(tBuA); PA-6, PET, PC, epoxy,

PDMS, dendrimers, polyaniline, polyacrylamide, lattices, LCP, etc.

Preparation, general:

Polymerization (any reaction in any medium). Dispersion in solvents

Melt compounding with organoclay; in TSE or internal mixer.

Diverse (complexing and immobilization of dendrimers with (CuS)_15,; sol-gel processing; solvent casting; electrochemical preparation of conductive NC), etc.

Strong effects of processing on performance!

10

Applications of CPNC’s

Unitica produces injection-molding grades of PA-6 based PNC used for production of car engine and converter covers for Mitsubishi & Toyota.

The same grade is also used for injection molding of highly rigid bases for the electronic control tray & cover.

Ube PNC is used for rear mirror and timing belt housing.

Bayer PA-6 based PNC for barrier film packaging.

Eastman Chem. and Nanocor used MDX-based PNC as an inner layer in PNC bottles to control permeability.

Kabelwerk Eupen: EVAc/organoclay for wire & cable. Drastic reduction of heat release at 3 to 5 wt% clay.

Showa Denko: PA-66 and POM based PNC’s for flame retardancy and rigidity at 0.4 mm thickness. The flex moduli are 30-80% higher, and HDT 30 to 80°C higher, than those of neat resins.

TPO Nanocomposites

4 years of collaboration of GM, Basell, Southern Clay Products, and

Blackhawk Automotive Plastics, resulted in introduction of PP with 2.5% MMT ―step-assist‖ for 2002 GMC Safari and Chevrolet Astro vans. The key to success is reactive exfoliation of MMT during polymerization [Modern Plastics, Oct. 2001].

By 2004 GMC expanded the use of CPNC to body side moldings

(Chevrolet Impala-2004) and load floor panels (Hummer H2 SUT).

12

Gasoline tank

Other applications of CPNC’s

PET

The two bottles after hot

filling with water at 95

o

_C,

closed and reopened

PET + 3% organoclay

Definitions

Exfoliated clay:

− individual

platelets dispersed in a matrix

with spacing d

₀₀₁

> 8.8 nm.

The platelets may form Short

stacks randomly dispersed.

Intercalated clay:

− having

organic or inorganic molecules

inserted between Platelets, thus

with d

₀₀₁

> 1.5 nm.

Intercalant:

− material sorbed between Platelets that binds with their

surfaces to form an Intercalate.

Interlayer, basal spacing or d-spacing, d

₀₀₁

is the thickness of the

repeating layers as seen by the XRD = mineral thickness

14

TEM of CPNC

HDPE melt compounded with intercalated clay (A)

HDPE polymerized onto the intercalated clay (B). Noteworthy, clay

reduced catalyst activity by ca. 100.

PNC performance of LLDPE > that of HDPE

[Heinemann et al.,1999]

.

Epoxy PNC (C) shows a better, but still not total exfoliation of MMT

[Giannelis, 1996]

.

X-ray diffraction

XRD is used to determine:

The mean interlayer spacing, d₀₀₁ (Bragg)

The number of platelets per stack (Scherer)

The relative amount of clay platelets in stacks and these exfoliated. Left Fig.: A = MMT intercalated with di-methyl-stearyl-benzyl

ammonium chloride; B = HDPE melt compounded with A; C = HDPE polymerized on A; D = HDPE [Heinemann et al., 1999].

Right Fig.: A = intercalated MMT; B = LLDPE melt compounded with A; C = LLDPE polymerized on A (LLDPE = polyethylene-co-octene).

16 0 2 4 6 8 10 RT = 62.7sec RT = 96.0sec RT = 148.5sec RT = 168.7sec RT = 228.6sec RT = 405.5sec In te n s it y 2

The 1

st

_{peak area decreases with increase of the residence time}

(RT), while that of the 2

nd

_{peak increases due to re-aggregation.}

Organoclay: 5 wt%

Barrel temp.: 200°C

Screw: high shear

Increase

of RT

0 5000 1 104 1.5 104 2 104 2.5 104 3 104 3.5 104 0 2 4 6 8 10 Int en si ty ( cps ) 2*Theta A 1 A 2

Definition of peak areas

Organoclay d-spacing

XRD of PA-6 with C15A

Interlayer spacing d001 (nm) N Platelets/stack C15 wt% Specimen

(EFM gap) Main peak Secondary peak Main peak Secondary peak XE; % Exfoliation 100 Cloisite 15A 3.21 1.95/1.22 3.34 3.23 - 4 Master-batch 4% 3.87 1.91 3.35 4.75 - 4 Stabilized master-batch 4% 3.93 1.92 3.40 5.31 10.4 4 TSE 3.97 1.94 3.16 4.87 20.6 4 TSE+GP 3.90 1.91 3.28 4.86 17.7 2 TSE 4.44 1.98 2.79 4.21 52.7 2 TSE+GP 4.42 2.02 2.89 3.80 64.7 4 (1000) 3.96 1.95 3.08 4.57 19.4 4 (250) 3.91 1.92 3.35 4.96 8.9 4 (60) 4.11 1.98 3.16 4.88 10.4 4 (30) 3.97 1.93 3.29 5.30 10.1 4 (5) 4.25 1.995 2.82 4.50 27.0 2 (1000) 4.26 2.02 2.92 4.20 56.1 2 (250) 4.30 2.04 2.86 4.16 60.8 2 (60) 4.36 2.06 2.83 4.02 65.4 2 (30) 5.29 2.00 2.83 4.84 76.0 2 (5) 4.39 1.94 2.78 2.53 83.3

d₀₀₁ decreases from 3.2 to 4.0 in 4% PNC, and to 4.3 - 5.3 nm in 2% PNC. The number of clay platelet per stack is ca. 3 for all.

The degree of exfoliation ranges from 10 in MB to 83% in EFM-compound!

1 2 001 peak height hkl t 0.9 N 1 ; t d W cos l      



1

0



100

A

A

X

_E





Bragg:

Scherer

:

Exfoliation %:

00 n 001

d

n /( 2 sin )

d

8.8253 / 2 ( nm )

l











18

Methods of CPNC preparation

The three principal

methods for CPNC

preparation are:

1. REACTIVE (in situ

polymerization)

2. SOLUTION (dispersing

organoclay in polymer

solution)

PNC Performance

4 main reasons for the development of PNC:

Enhanced rigidity (100% at 5 wt% clay)

Improved barrier properties (by a factor of 100 at 10 wt%) Reduced flammability (PHRR reduced by 2/3 at 5 wt% clay)

Improved heat deflection temperature (HDT)

Examples of published data for various systems are

tabulated for PA-

6 and its CPNC’s with 2 wt% organoclay:

Mechanical properties of PA-6 and based on it PNC.

Data from [Ube Industries, Ltd., 2002, and Unitika Plastics, 2004].

Property ASTM Units Ube Unitika

PA-6 PNC PA-6 PNC Tensile strength,  D-638 kg/cm2 800 910 810 930 Tensile elongation, eb D-638 % 100 75 100 4 Flexural strength, f D-790 kg/cm 2 1100 1390 1080 1580 Flexural modulus, Ef D-790 kg/cm2 28,500 35,900 29,000 45,000

Impact strength, NIRT D-256 kg cm/cm

6.5 5 4.9 4.5

HTD (18.56 kg/cm2) D-648 oC 75 140 70 172 HTD (4.6 kg/cm2) D-648 oC 180 197 175 193 H2O permeability, PH2O JIS Z208 G/m2 24

h

203 106 -- --

Both companies use reactive

exfoliation.

Ube starts with MMT/ODA

Unitika uses

synthetic clay for reproducibility & color control.

20

Clays 1

Clays are classified as

:

Crystalline: kaolin's, serpentines, smectites, vermiculites, micas, etc. Amorphous: allophane, imogolities, hydrated alumina, ...

Crystalline clays are layered, with large specific surface area, esp. for d  2 mm. Clays are chemically complex, with properties that change from one deposit layer to another.

At T < 500°C smectites (e.g., montmorillonite, MMT) are composed of 4 layers:

Three-layer, 0.956 nm thick sandwich: octahedral central with excess charge, and two tetrahedral: SiO₂-(Al/Mg)-SiO₂, with negative charges and –OH groups on the surfaces and edges.

Water absorbing, expandable (by H₂O, alcohols, glycol, glycerol, etc.) layer with charge compensating Na+_{, K}+_{, Ca}++_{, Mg}++ _ions.

Clay uses: for bonding (sand), catalysis, water clarification; in ceramics, drilling fluids, oil refining and decolorization, paper-making, viscosity controllers in motor oils, greases, adhesives, paints, cosmetics, pharmaceuticals, polymers, etc.

In polymers clays have been used as fillers, thermoset h-controllers, nano-reinforcer's, etc.

Clays 2

Clay (MMT) contaminants are: silica, feldspar, gypsum, orthoclase, apatite, halite, dolomite, muscovite, pyrite, etc. Ca-MMT content is > 50 wt%.

Purification: grounding to < 200 mm, dispersing to 10 –15 wt%, sedimenting, hydrocycling to remove impurities of d > 50 mm, and amorphous clay.

The resulting suspension that contains

3-7 wt% of MMT (d = 5-10 mm) is cation exchanged, giving > 95 wt% Na-MMT.

Centrifugation removes d > 5 mm particles, filtration to 12 wt% solids, spray drying to powder with 9 wt% H₂O.

Product is then conveyed to holding tanks, then to the bagging area.

22 Cell unit MW (g/mol.) 540.46

Density (g/mL) 2.3 to 3.0 Mohs Hardness @20°C 1.5- 2.0

Cleavage Perfect in one direction, lamellar Characteristic Expands up to 30 times in volume

in H2O

Appearance Light yellow with dull luster Field Indicators Softness, and soapy feel

Montmorillonite (MMT)

TEM of MMT

At T < 500°C smectites have 4 layers:

Outer layer with H₂O and Na+_{, K}+_{, Ca}++_{, Mg}++ _ions.

3-layer sandwich: octahedral central between two tetrahedral: SiO₂-(Al/Mg)-SiO₂; 0.956 nm thick.

MMT: monoclinic, contains ca.:

(Na,Ca)(Al,Mg)₆(Si₄0₁₀)₃(OH)₆-nH₂0], has:

Al = 10, Si = 21, H = 4. and O = 65 (wt%);

aspect ratio, p  100 to 300; sp. surface area,

A_sp  750 m2_{/g; Cation exchange capacity:}

CEC  1.0 ± 0.2 meq/g.

Reactive sites: anions and –OH groups on the surface and cations and –OH groups at the rim.

Intercalation 1

Intercalation

− diffusion of intercalant into clay galleries.

The intercalant binds to the platelet surface.

The aim of intercalation: to expand the interlayer space,

facilitating diffusion of macromolecules (exfoliation).

Intercalation depends on the balance of forces: positive

that drives the molecules to bond with the solid surface

and negative that requires breaking the solid-solid

interaction and loss of entropy.

Intercalation is a process of expansion of ca. 200 clay

platelets that form a tactoid. The layers are elastic, but

there is a limit to the amount of bending they can undergo.

The efficient strategy of intercalation involves reduction of

the stack size and a progressive increase of the penetrant

size, starting with H

₂

O, then an alkonium cation, ....

24

Intercalation 2

Intercalation of MMT started in the 1930’s [Maloney, US Pat. 2,158,987]. For

hydrophilic applications, H₂O + Na₄P₂O₇ + compounds with -OH groups

(e.g., alcohols, glycols, PEG) were prepared at high stresses.

For reinforcing elastomers [Carter et al., US Pat. 2,531,396; 1950] MMT

intercalated with dodecyl amine, tri-phenyl-dodecyl phosphonium or lauryl

pyridinium was used.

For hydrophobic applications [Hoffman, 1956] fatty quarternary alkonium

was recommended, viz. methyl and/or benzyl tri-hydrogenated tallow

ammonium chloride. Two onium cations replace 2Na+_{, then these}

complex with 2 amines, causing  orientation;

d

= 3.9 (which decreases

to 2.9 nm when heated to 75°C). Disadvantages: (1) thermal instability above 180°C and (2) plasticating effect that reduced HDT.

The interlamellar gallery in dry MMT is

d

= 0.35 nm (d₀₀₁ = 1.31 nm);

swollen with 3 molecular layers of H₂O it expands to

d

= 1.2 - 1.4 nm.

Any organic cation with the smallest dimension d  0.6 nm can be

Intercalation 3

Okada et al., [US Pat. 4,739,007; 19.04.1988] dispersed clay in aqueous solution

of

w

-amino-C_12-18 acid. The organoclay was then mixed with e-caprolactam and reacted.

Water-soluble polymers, viz. oligo(oxy-propylene)₂₅-(2-Et)Me-N+_Cl- _were reported superior to fatty acid onium salts [Beall et al., US 5,760,121, 1998].

Several routes have been used to intercalate clay particles:

Low-MW solvents and solutions, viz. water, alcohols, glycols, monomers. Freeze-drying of expanded clay.

Organic cations, viz. ammonium, phosphonium or sulfonium.

Complexing of aromatic or cyclical (crown ether) compounds by Cu++ _{or Ag}+_.

Compounding with organic liquids, viz. monomers, epoxies, PEG, PVAl, PDMS, PVP, and their solutions.

Inorganic compounds that form inter-layer pillars – stable porosity, but no

exfoliation.

26

Intercalation 4

Molecular modeling of clay layers

intercalated with alkyl-ammonium

cations [

Vaia et al., 1994

].

The generated structures were

confirmed by FTIR and the XRD

d

₀₀₁

spacing measurements.

As the alkyl length increases

(from the top):

a) isolated, short chains in a

monolayer

b) intermediate chains disordered,

forming a quasi-bilayer

c) long chains with increased order

and multi-layer spacing.

Intercalation 5

The d

₀₀₁

-spacing depends on: (

1

) intercalant, its

(

2

) concentration, (

3

) temperature and (

4

) pressure.

1.0 3.0 5.0 7.0

0 10 20

In te rc alatio n w ith w  am in o a cid = N H 2(C H2)n-1CO O H (AA ) an d e  cap rolactam only am in o acid (A A) A A a nd ca pr ola ctam I n te rl a y e r S p a c in g ( n m )

# of C-atoms per m olecule, n

da ta: O kad a & Usuki, 1995

1.4 1.6 1.8 2 Ca -smectite Na -smectite Ca-vermiculite Na-vermiculite d -s p a c in g ( n m )

d e Siqu ira et al., 199 9

4 .2 4 .6 5 B e id e llit e : Al 2.17[Al0.33N a0.33Si3.17] O10(O H )2 w ith : te t rad e c y l a m m o n iu m - te t rad ec y l a m in e ( TA T A) o r d im e th y ld it e tra d e c yl am m o n iu m ( D M T A) T AT A D MT A d 0 0 1 ( n m ) 1 2 3 4 5 0 4 0 8 0

In terc a la tio n o f N a M M T w ith

p o lyvin ylp y ro llid o n e (P V P ) o r p o lyvin yla lc o h o l (PV A l)

PVP PVA l X R D b a s a l s p a c in g , d 001 ( n m ) C o n c e n tra tio n o f P V P o n d ry we ig h t o f N a -M M T (w t% ) O p tim u m ra n g e : 3 - 4 .5 n m

data: Beall et al., 1996

1

₂

28

Intercalation 6

The 12 ammonium ions were used to intercalate MMT.

The organoclay was incorporated into PCvia melt compounding using TSE-CORI at 260o_{C; evidence of thermal degradation.}

The mechanical properties were measured [Yoon et al., 2003].

Symbols: M = methyl, T = tallow, (HT) = hydrogenated tallow, (HE) = 2-hydroxy-ethyl, B

= benzyl, (C18) = octadecyl hydrocarbon, (EO) = ethylene oxide, (PO) = propylene oxide, (12-ALA) = 12-amino lauric acid, and H = hydrogen.

Intercalation 7

Three ammonium ions were used to intercalate MMT.

The organoclay was incorporated into PA via melt compounding using TSE-CORI at 240o_C.

The mechanical properties were measured [Fornes et al., 2004]. d₀₀₁ for M₄, M₃(HT), and M₂(HT)₂, was: 1.36, 1.80, and 2.42 nm, respectively.

30 Commercial intercalated clays

contain quarternary amines

(Southern Clay Products, 2000). The cation exchange capacity of MMT: CEC = 100 ± 20 meq/100 g. Equilibrium of NaMMT reaction with ammonium salt is shifted left,

hence excess of onium salt is often used, i.e., 0.9 to 1.4 meq/g or 23 to 40 % of the organic modifier.

Intercalated clay contains 2 to 4 % water and up to 40 wt% of organic compounds.

Intercalation increases the cost of clay from US$2 to 7/kg.

Organoclays 1

d₀₀₁ = 3.59; 2.96; 2.39 nm

d₀₀₁ = 1.93 nm

d₀₀₁ = 1.87 nm

Organoclays 2

Synthetic clays, e.g., fluorohectorite, are produced from talk

and Na

₂

SiF

₆

by Co-op Chemical Co., Ltd., Japan.

Organoclays based on quarternary ammonium are thermally

unstable above 180

o

_C.

Organoclays from Süd-Chemie AG, based on Na-MMT

Organoclay Cation Intercalant (wt%) Bulk density (g/L) d001 spacing (nm) Recommended for matrix Nanofil 15 DSDM 35 440 2.8 EVAc, PP Nanofil 948 DSDM 45 440 3.5 EVAc, PP Nanofil 32 SBDM 30 300 1.8 PET, PBT Nanofil 919 SBDM 35 460 2.0 PET, PBT

Nanofil 848 SA 25 180 1.8 EVAc, PA-6. PA-66, PP Nanofil 804 SDHE 30 130 1.8 PET, PBT, TPU

Nanofil 784 AC12A 20 180 1.7 PA-6. PA-66, PA-12

Notes: 1. moisture content < 2 wt%; 2. Thermal stability up to 200oC; 3. Cation codes: DSDM = di-stearyl di-methyl ammonium chloride, SBDM = stearyl-benzyl di-methyl ammonium chloride, SA = stearyl amine, SDHE = stearyl di-hydroxyethyl ammonium

32

Thermal instability

The onium intercalant is thermally instable.

Stability decreases with the degree of substitution.

The decomposition occurs in steps, from 125

o

_{C on.}

Oxygen and shear accelerate the degradation.

Branched alkyl chains are more stable than linear.

Aromatic substituents provide better stability than paraffins.

2MBHT degradation proceeds by Hofmann elimination:

CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 N CH2 CH3 H3C H3C CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH H3C CH2 CH2 N H3C H3C + + H SiO -out

Hofmann elimination (1851)

Degradation of polymeric nanocomposite intercalants at

T > 125

o

_{C is a major problem in CPNC technology}

Phosphonium ions are more stable than ammonium.

Organo-metallic complexes show high stability.

Bulky, aromatic ammonium (e.g., dyes) form stable organoclays.

Thermal degradation in the presence of O₂ of ammonium intercalant in PS (or PP) matrix resulted in formation of peroxy-radicals and subsequent degradation of the PS (or PP) matrix.

34

The Figure illustrate these two

processes: melt exfoliation (

#1

)

and degradation (

#2

)

Variation of the XRD with the

mixing time for PS/Cloisite10A

at T = 200 to 210°C under a

shear rate of 65 (1/s)

[Yoon et al., 2001; Tanoue et al., 2004].

Shear compounding results in two parallel processes:

Mechanical intercalation/exfoliation

Thermal degradation via Hofmann elimination reaction

The result is a complex variation of the interlayer spacing as

a function of mixing time and temperature.

Degradation effects

Usuki’s classification

Exfoliation methods

with increasing difficulties:

1. Hydrophilic matrix with strong polar groups, e.g., P2VP:

2. Hydrophobic matrix with strong polar groups, e.g., PA-6:

3. Hydrophobic matrix with strong polar groups, e.g., PA-6:

4. Hydrophobic non-polar matrix, e.g., PP:

water polar organic compound

clay swollen clay CPNC

int ercalant (s) monomer

polymerization

clay int ercalated clay

exp anded clay CPNC

 



int ercalant (s)

compounding

clay int ercalated clay

polar polymer CPNC



 

int ercalant (s)

compounding

clay int ercalated clay compatibilizer

non polar polymer CPNC

 

36

Exfoliation

– general 1

Exfoliation transforms an intercalate into dispersion of individual

platelets. The system is considered exfoliated when d₀₀₁ > 8.8 nm, or when there is no peak attributable to the d₀₀₁ on the XRD trace.

In exfoliated systems > 90% clay is dispersed in stacks that contain  2 individual platelets randomly distributed in the matrix.

There are several methods that may lead to exfoliation, e.g.:

Polymerization of a monomer in the presence of organo-clay. Combining the organo-clays with a polymeric latex.

Melt compounding a polymer in a TSE with a suitable organo-clay complex. Melt compounding polymer with layered particles in a kinetic energy mixer, e.g., Gelimat.

Ultrasonically exfoliating suspensions of organo-clay particles in a low MW polar liquid, followed by either polymerization or melt compounding.

Exfoliation

– general 2

The two principal exfoliation methods for the production of PNC with olefinic thermoplastic matrix are:

(1) Reactive, and (2) Mechanical.

Re 1. Reactive methods start with a suitably intercalated clay and

monomer or monomer mixture.

The polymerization may be of any type (radical, ionic, Z-N, metallocene) in bulk, solution, suspension or emulsion.

The growing macromolecular coils force the platelets apart.

Re 2. The mechanical exfoliation method starts with suitably intercalated clay (often modified by other compounds, e.g., surface modifiers or

compatibilizers).

The principal controlling factors are:

Chemical interactions between organo-clay and polymer, e.g., in PA-6 an easy

exfoliation of methyl tallow bis-hydroxy ammonium-MMT while very difficult of di-methyl di-hydrogenated tallow ammonium-MMT (Cloisite 30B and 15A, respectively).

Residence time in the processing equipment [Dennis et al., 2000]. Type and intensity of stress fields.

38

Assuming that clay platelets are circular discs with diameter,

d, and thickness, h (aspect ratio p = d/h), the geometric

calculation for freely rotating platelets gives:

Exfoliation

– general 3

0 40 80 120 0 10 20 RDX TEM d = 100/w d -spa cing (nm) MMT content, w(wt%)

data: Okada & Usuki, 1995

Ratio of the encompassed to

actual volume = 2p/3.

The maximum packing volume

fraction

f

_max

= 0.93/p.

The distance between

exfoliated platelets should be:

At

f

>

f

_max

platelets are not

able to rotate freely. As they

are aligned, they have greater

tendency for stacking, hence a

decrease of separation.

Intercalation with w-amino acid, NH₂-(CH₂)₁₁-COOH (AA) and

e-caprolactam

001

223/

(

%)

Grafted clay platelets

Properties of end-grafted polymers on solid surface have been studied

for nearly 30 years.

In melt of polymer P clay grafted with chemically identical, end-terminated polymer N is dispersed; N  P.

For low



, the phase diagram show swollen (S) and ideal (I) mushrooms

(M), at higher S-, and I-stretched brush, as well as non-stretched brush (NSB); for high



> N-½_{, and high P > N the brush is non-penetrating} –

Immiscible

mushrooms

40

Aggregation of grafted clay

Consider two clay platelets grafted at the grafting density



with chains of length L.

The energy of interaction free energy between such two

platelets at a separation H is F = F(H).

Computations

[Ferreira et al., 1998; Wang et al., 2003]

indicate

repulsion for low



and L, but

aggregation

at higher values of

Nanothermodynamics

In the early 1960’s Hill noted that the equilibrium thermodynamic properties of sufficiently small systems differ from these predicted by the classical thermodynamics.

The treatment considers a system such as, e.g., colloidal particles, each composed of

n

-elements. For

n

  the classical behavior is recovered.

For small

n

there are at least two significant contributions:

the first depends on the surface energies, and

the second on the entropy related to the dynamic state of particles.

As an example, a MMT platelet has the specific surface area of ca. 800

m2_{/g, and about 36% of its atoms are on the surface, thus the surface} effects are expected to dominate the thermodynamics, especially the miscibility and phase equilibria in CPNC’s.

Hill formally wrote the total (subscript

t

) energy of a macro-system as:

S is the entropy, m is the chemical potential, N is the number of molecules of species i , and

  , , , , / t t i t t t t i i t i t _{S V N} dE TdS PdV dN edn e E n m       



, , , , ( / ) ; ( / ) ; ( / ) i i j i i i P T i i T P de SdT VdP N d S e T _m V e P _m N e _m m m              



42 -10 -5 0 5 10 0 1 2 3  F A ( m J/ m 2 ) h - h o(nm) e sp, sa = 0 e sp, sa = - 4 e sp, sa = - 8 e sp, sa = - 10

Vaia’s model

Vaia’s PhD thesis of 1995 provided the first thermodynamic

description of PNC: a sandwich of two brushes comprising:

(1) silicate, s, (2) intercalant, a, and (3) polymer, p:

Intercalant entropy gain only up to full stretch (Dolan-Edward). Macromolecule entropy loss within the sandwich (Huggins-Flory). Enthalpy taken from van Opstal et al. (1991).

-4 -2 0 2 0 1 2 3  S A /R ( 1 0 6 /m 2 ) h - h o (nm) In te rc alant Po lym er Total









1 2 , 2 1 2 2 1 2 1

ˆ ˆ

2

/

/

ˆ ˆ

ˆ

1

1 ( / ) ( /

)

sp sa o ap v o

h

r

e

r r

r h

j j e

e

j j e

j



 

 







G = H –TS

Balazs SCF model 1

The self-consistent field (SCF) lattice model considers

adsorption on a solid surface hence the properties change with

the short range interactions,

e

, and the distance from clay

surface, h

_o

< z < h :

Free energy per unit area as a function of surface separation for five different values of the polymer-intercalant interaction parameter, c_ap. Other parameters are: N = 100; N_i = 25 and c_sa = c_sp = 0. In the LHS and the RHS Figures the grafting density: r = 0.04 and 0.12, respectively. The cartoons, left and center, show the initial and final state, respectively, where the surfaces are separated by macromolecules [Balazs et al., 1998].

( ) _i( ) ln _i( ) (1/ 2) _ij ( ') ( ) ( ')_{i j} '

i ij

44

Balazs SCF model 2

Thus, the theory predicts that clay intercalation/exfoliation is reduced

by high grafting density,



, the latter being related to:

Clay CEC (CEC = 0.02 for kaolin, 1 for MMT, 2.5 meq/g for hectorite),

Intercalant structure, viz. PA-6 with Cloisite-15A (2xC₁₈) or -30B (1xC₁₈).

SCF shows that as the packing density increases it becomes harder

for the macromolecules to diffuse into the gallery and mix with the

intercalant chains

‒

there is an optimum



for intercalation

.

SCF was also used to explore two compatibilization strategies:

Compatibilizer between intercalant and polymer, c_ac = c_pc < c_ap .

Compatibilizer to bind directly to the clay surface: N_p = 100, N_c = 75,

c_sc = -75, other interaction parameters c_ij = 0.

The SCF computations indicate that it is advantageous to use a

macromolecular

―sticker‖ compatibilizer with highly interactive

end-group (see next slide). This prediction agrees with the

Balazs SCF model 3

-0 .8 -0 .4 0 0 1 0 2 0 0 % 5 % 1 0% 3 0% 7 0%  F /A h a fte r: B a la z s et al., 1 99 8 0 4 8 0 1 0 2 0 N p = 5 0, 10 0 N p = 1 0 N p = 1  (h ) h

Free energy vs. gallery

height for

clay-polymer-‖sticker‖ system (its

content is indicated).

Thus, 5 wt% of ―sticker‖ is

sufficient for exfoliation.

The amount of adsorbed

functionalized ―sticker‖ polymer

with N = 75 and concentration

f

= 0.05 for four chain lengths of

the non-functionalized polymer,

N

_p

= 1, 10, 50 and 100

F/A

5% is sufficient

46

Phase diagrams

Phase structures for CPNC:

(a) isotropic, (b) nematic, (c) smectic, (d) columnar, (e) plastic solid (house of cards), and (f) crystal. The nematic director is in the Z direction, platelets in X-Y.

Computed phase diagrams of

polymer-clay mixtures: (a)  = 0.04,

PNC with telechelic sticker

The scaling (non-lattice) theory was used to compute phase diagram of two pre-intercalated clay platelets immersed in a polymer melt of telechelic N-polymer (

f

 and regular P-polymer (1-

f

). The energy per sticker–clay contact was e [Kuznetsov and Balazs, 2000].

N-macromolecules are either free (f), anchored by one (t for ―tails‖) or two ends (l or b for ―loops" or "bridges", respectively). The Huggins-Flory interaction parameters are:

c

_NN =

c

_PP = 0, and

c

_NP =

c

.

Left

:

Phase diagram for PNC containing f of functionalized polymer (

N

= 1000) and (1-

f

) of non-functionalized polymer (

P

= 100).

The phases are: intercalated (In), exfoliated (Ex), and immiscible (Im).

48

Confirmation of theory 1

1.At least two US patents (AMCOL, Exxon) support Balazs et al. theoretical predictions.

2. Hoffmann et al. [2000] intercalated in THF/H₂O at

T = 40o_{C synthetic fluoromica (Somasif) with:}

1.2-phenyl-ethyl amine (M_n = 121 g/mol) – C-PEA.

2.amine-terminated PS (M_n = 5.8 kg/mol) – C-APS.

Dried organoclays were compounded with the PS

at 200o_C

The intercalation expanded the interlayer spacing

d₀₀₁ to 1.4 nm with PEA and to > 4 nm with APS.

Compounding with PS produced large aggregates for C-PEA and full exfoliation for C-APS.

In C-APS clay platelets were ca. 600 nm long and

100 nm wide hence the aspect ratio: p ≅ 245.

C-APS C-PEA

Confirmation of theory 2

The dynamic rheological measurements of C-PEA (5 wt% clay)

caused

G’ = G’(

w

) to parallel the dependence of the matrix with a

slight increase caused by the filler effect.

The dynamic rheological measurements of C-APS (5 wt% clay) the

low frequency slope in the terminal zone was about 0.5 (instead of 2,

as in the former case), as predicted by the LCP theories.

50

Fundamentals 1



F =



H - T



S

System

:

1. Clay platelet (s); 2. Host polymer (h);

3. Compatibilizer (g); 4. Organic modifier (o).

Conformational Entropy,



S:

Number of ways to occupy free lattice site

Mixing Enthalpy,



H:

Huggins-Flory short-range

parameters

solid-liquid :

c

hs,

c

hs ,

c

os

Long-range interactions for

solid-solid

:

Van der Waals force between clay plates

with Hamaker constant, A:

liquid-liquid :

c

_hg,

c

_hg,

c

_ho d s 2

12

A s

F

d







K. Kim, L. A. Utracki and M. R. Kamal, ―Numerical Simulation of Polymer Nanocomposites using

Fundamentals 2

Enthalpy

Solid energy

Entropy

Low area-lattice ratio Poor solubility

Short chain Thin gap

High area-lattice ratio

Unfavorable



F

(+)

Favorable



F

()

Long chain

Thick gap Good solubility

d

s

52

The system: clay

+ compatibilizer, N

_g

= 100,

+ polymer N

_h

= 100; at the

grafting density of



_g

= 0.04

1D computational model

Computed effects of the binary

intercalation parameter on the

chemical composition of the

lattice layers, z = 1

– 20.

Results:

For c_hg > 0 compatibilizer is

immiscible with h-polymer

For c_hg = 0 the system is miscible.

The miscibility increases with c_hg

and N_gr .

Data: K. Kim & LAU, 2003

c_hg

Compatibilizer content

Fig. 1;

c

_hg

= 0.02

Fig. 2;

c

_hg

= 0.00

Fig. 3;

c

_hg

= -0.02



_max

 0.02



_max

 0.07



_max

 0.05

Optimization of compatibilizer content

The 1D free energy (h  ) for homopolymer with N

_h

= 200

depends on:

Compatibilizer N_g  [25, 200],



_g  [0.02, 1],

Binary interaction parameter: c_hg  [0.02, 0.02].

Following Balazs et al. publications, the 1D model assumes

clay platelet enrobed by intercalant.

54

The binary interactions are taken for the PNC with PP as the

matrix, i.e., for PP/compatibilizer/intercalant/clay.

The influence of the solid area-lattice ratio (

e

) and binary

interaction (

c

_hg

) on the excess free energy

Statistical chain lengths:

N_g = 200, N_h = 400, N_o = 10

Surface grafting density:



_g = 020%,



_o = 70%,



_v = 25% Solid-solid interactions: A = 20(k_BT),

e

 [0,50] Binary interaction parameters:

c

_hg = 0,

c

_ho = 0,

c

_go = 0,

c

_hs = 0.01,

c

_gs =



0.01,

c

_os =



0.02

1D-SCF model

2

Comparing with the preceding graph one may conclude that

doubling the void fraction significantly improved miscibility (



F <0).

The influence of the solid area-lattice ratio (

e

) and binary

interaction (

c

_hg

) on the excess free energy

(higher vacancy

fraction)

Statistical chain lengths:

N_g = 200, N_h = 400, N_o = 10

Surface grafting density:



_g = 020%,



_o = 70%,



_v = 510%

Solid-solid interactions:

A = 20(k_BT),

e

 [0,50]

Binary interaction parameters:

c

_hg = 0.0,

c

_ho = 0,

c

_go = 0,

c

_hs = 0.01,

c

_gs =



0.01,

c

_os =



0.02

56

Favorable polymer/compatibilizer interactions, along with

favorable solid grafting interactions and high vacancy fraction are expected to lead to easy exfoliation.

Statistical chain lengths:

N_g = 200, N_h = 400, N_o = 10

Surface grafting density:



_g = 020%,



_o = 70%,



_v = 510%

Solid-solid interactions:

A = 20(k_BT),

e

 [0,50]

Binary interaction parameters:

c

_hg = -0.02,

c

_ho = 0,

c

_go = 0,

c

_hs = 0.01,

c

_gs =



0.01,

c

_os =



0.02

1D vs. 2D or 3D models

In principle, the lattice model of PNC is 3D

In 1D simulations it is assumed that

properties of any lattice cell on a

X-Y plane are identical, varying only

with platelet separation in Z.

In 2D simulation it is assumed that

properties depends on X and Z.

In 3D simulation variation of properties in all three dimensions

is computed.

The computed differences between 1D, 2D and 3D originate

from the different probability for segment placement

(center-edge) hence the configurational entropy and enthalpy (where

pertinent).

x

z

o

Lattice

Clay

x

y

z

o

Lattice

Clay

58 -0.006 -0.004 -0.002 0 0 10 20 z=2 z=3 z=4 z=6 z=8 z=10  F M x 1D

Results for 1D & 2D

The 2D model assumes finite size of clay platelets in the x-direction, and

invariance in the y-direction; the variation with respect to the lateral dimension, y, is averaged,

The Figure displays variation of the excess free energy with the number of cells in x-direction. The data are computed at different distance from the clay surface z = 2 to 10 for: N_g= 25, N_h= 100, _g= 0.04, and c_hg= 0

The 1D prediction is indicated by a horizontal red line.

The 1D model assumes presence of two parallel platelets immersed in a molten polymeric matrix.

In this model the platelets are infinitely large, thus only in the

vertical z-direction the properties may change.

The 1D data of Kim et al. (2004) reproduced results by Balazs et al. (1998).

2D result for 4-components 1

x z

0.0,

0.01,

0.01,

0.02

hg hs gs os

c



c 

c  

c  

Influence of the binary interaction parameters on the

concentration profiles for:

A = 20(k_BT),

N

_h

= 400, N

_g

= 200,

N_o = 100,

60

The influence of the bare-solid

area-lattice ratio (

e

) and grafting

density (



_g

,



_o

) on the excess free

energy (h = z  ).

Statistical chain length

N_g = 200, N_h = 400, N_o = 10

Surface properties



_g  [0, 0.2];



_o  [0.5, 0.9]; and



_v  [0.02, 0.05]

Influence of solid-solid

interactions

A = 20(k_BT),

e

 [0, 20]

Binary interaction parameters

c

_hg = 0,

c

_ho = 0,

c

_go = 0,

c

_hs = 0.01,

c

_gs =



0.01,

c

_os =



0.02

Effect of

intercalant degradation

on the concentration

profiles in 2D lattice with:

N_g = 200, N_h = 400, N_o = 100,



_g = 15%,



_o = 80%,



_v = 25%, A = 20(k_BT),

c

_hg = 0,

c

_ho = 0,

c

_go = 0,

c

_hs = 0.01,



_o

= 100 %



_o

= 0.0 %

x z

Degradation effect 1

62

Statistical chain length

N_g = 200, N_h = 400, N_o = 10

Surface property



_g = 020%,



_o = 70%,



_v = 25%

Solid influence

A = 20(k_BT),

e

= 10,

g

_o[0.2,1.0]

Binary Interaction parameter

c

_hg = 0,

c

_ho = 0,

c

_go = 0,

c

_hs = 0.01,

c

_gs =



0.01,

c

_os =



0.02

Degradation of intercalant can readily be compensated by incorporation of compatibilizer, capable of forming stable bonds with clay surface.

Grafting density of ca. 6% would compensate for the degradation.

Problem Suggested solution

The absence of specific interaction between host and grafted polymer

(c_hg = 0)

Higher grafting density, and/or higher MW of compatibilizer and organic modifier

(_o, _g, N_o and N_g)

Increased bare surface area

(unfavorable solid-solid interactions)

Higher favorable interactions between clay and compatibilizer or intercalant

(stronger negative values for c_gsand c_os)

Thermal degradation of organic modifier

(increasing g_o)

- Better attraction between compatibilizer

and solid surface and bigger _g

- Less unfavorable interaction between host polymer and solid

Unfavorable host polymer-solid

interaction (c_hs > 0)

Decrease _v as well as saturate the clay

surface with compatibilizer and organic modifier, both miscible with polymer

Solutions of practical

problems

64

Summary of

Mathematical modeling

To reduce surface energy crystalline solids adsorb molecules.

For optimum dispersion of solid there is MW-dependent grafting

density

– above it the grafted particles aggregates (immiscibility).

The Kim et al. SCF model reproduces previous 1D results.

2D computations predict lower miscibility than 1D.

To achieve exfoliation in 4-component system:

Clay: Intercalated (f_o  70-80 %), but with surface partially bare for interacting with a compatibilizer (functionalized polymer)

Stable intercalant – no thermal degradation or extraction by melt

Bare clay surface, caused by inadequate intercalation or degradation can be compensated by compatibilization

Compatibilizer (f_g  6 vol%)

Strongly interacting with clay surface

High molecular weight (N  P)

With non-positive F of mixing with host polymer

Molecular adsorption 1

The specific surface energy of crystalline

solids is unusually high, e.g., freshly cleaved

in mica has

n

₁

= 4,500 mN/m, crystalline

CaO

n

₁

= 1,310 mN/m, but amorphous SiO

₂

only

n

₁

= 130 mN/m.

Any interphase induces

changes of properties.

1/ 2 2 g r  s_ 1/ 2 2 t  s_

Theories and experiments point out polymer adsorption from

solution or melt on solid surfaces (e.g., on mica flakes).

As shown in the Figure above, neutron scattering indicate

exponential decline of PS concentration in z-direction.

The thickness of the adsorbed layer depends on the system; e.g.,

the rms thickness , viz. 3.6 vs. 4.8 nm for copolymer and

6.8 vs. 9.0 nm for PS, respectively.

0.2 0.6 1

0 4 8 12

Adsorption of PEG from aq. solution

M_w = 25 M w = 100 M w = 900 V olu me fr a ct ion of ad sor b e d po lym er, f(-)

66

Molecular adsorption 2

Adsorption of polymer on solid

surface was predicted by numerical methods.

Klein experimentally showed that on

mica flake a layer of PS is adsorbed

from toluene solution to a thickness of 110 nm!

Luengo et al., [1997] observed a 3-layer structure of PBD on mica:

z < 6 nm – solid-like

6 < z < 100 – elastomeric z > 100 nm – bulk behavior

Thickness of the adsorbed solid-like layer, z_s, depends on M_w: Surface Force Analyzer (SFA) 2

6.46 6.75log

;

0.99996

s w

z

 



M

r



Molecular adsorption 3

PBD (M

_w

= 6.95 kg/mol) was

studied in a SFA at:

g

< 30%,

n

(Hz) = 0.03 to 80

and gap, 2z = 10 to 250 nm.

As shown in the Figures

(right), three regions of

dynamic behavior were

identified:

1. For 2z > 200 nm the angle between strain and stress

d  /2, and - the bulk behavior.

2. At smaller gaps d < /2, and G'

and G'' increased, showing an ―elastomeric-plateau‖, i.e., a 3D structure.

3. At gaps, 2z  12 nm, d = 0, or a

Left Fig. Effect of frequency on the

shear moduli for PBD at T = 25°C, 2z = 10, 30, 180 and 250 nm.

Right Fig. Effect of surface separation

(D = 2z) on the rheological properties of PBD at T = 25°C, n = 13 Hz

68

Clay surface energy

The surface energy,



s

₌

n

1

A, depends on the

nature and

structure

of material.

Polymer surface tension coefficients at 20°C:

n

₁

=

10 to 49 mN/m

The surface tension coefficient of crystalline solid:

n

₁

= 1-8 N/m

The high surface energy causes molecular adsorption

n₁ of freshly cleaved mica is 4,500 that exposed to air is 375 mN/m.

Molecular adsorption causes solidification of organic molecules on the clay surface.

The solid layer is ca. 6 nm thick, thus it increases clay platelet thickness from 1 to about 13 nm (see next slide).

Molecular mobility is retarded up to ca. 100 nm from the clay surface.

Another consequence of high surface energy is the aggregation of solid powders.

According to Johnson et al. [1971], the force between two interacting spheres of radius R is:





2

11

/ 2

11

/

V const

N

R

R

Gnomix

®

PVT

instrument

T =

25-400°C, P = 10- 200

70

Raw data from Gnomix

®

PVT diagrams for glassy (PS) and semi-crystalline (PP)

polymers (P = 0.1 to 190 MPa)

PVT of PP (RUN 287) Temperature, T( K) 250 300 350 400 450 500 550 S pe ci fic V ol um e -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Col 112 vs Col 114

PVT Diagram for PS Nano HS 17

Temperature, T(K) 250 300 350 400 450 500 550 S pe ci fic V ol um e -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Col 112 vs Col 114

General notes

PVT measurements offer an easy access to the thermodynamic

properties of a variety of materials.

The direct information is accessed through the temperature and

pressure dependent specific volume changes, e.g.,



and

k

.

Experimentally, S-S eos offers precise description of the PVT

dependence for any liquid tested to date

–

n-paraffins, polymer

melts, blends, composites, foams, nanocomposites.

S-S theory leads to computation of the free volume parameter, h,

as well as the internal energy hence cohesive energy density

(CED) and the solubility parameter,

d

.

The theory has been extended to the glasses, treated as a

pseudo-equilibrium state. However, large effort is still required for the

72

Free volume - definitions

Free volume is that part of space that is left after

subtracting the occupied volume, defined by the atomic

dimensions.

Considering that a molecule or its segment moves in a

cage created by surrounding molecules, its free volume

is defined by the space within which its center can freely

move:

Total specific volume, V

Occupied volume is defined as: V at T = 0 K

→

V

_o

≡ V(T = 0).

Free volume: V

_f

= V - V

_o

Free volume fraction:

f = V

_f

/ V = 1 - (V

_o

/V)

Note that f is only a function of V = V(P, T)

S-S Quasi-lattice

Vacancy (hole) fraction: h = 1

– y(V, T)

(excess « free volume ») is a measure of

structural disorder.

Occupied sites Vacant sites









V,T T F F V, T; y(V, T); c / s Minimization : F / y 0 Equation of state : P F / V            

Free energy

For s-mer:

Scaling parameters: P* = qz

e

*/sv*; V* = v*/M_o; T* = qz

e

*/cR → (P*V*/T*)M_o = Rc/s

v*: segmental repulsion volume

e

*: segmental attraction energy

3c/s: number of external modes (volume-dependent

degrees of freedom) per segment:

Ideal flexible linear chain: 3c/s → 1 Rigid chain: 3c/s → 0

74

S-S Lattice model

2D lattice containing two types

of molecules and holes or

vacancies (open circles). The

binary interaction parameters,

e

_ij

, are also indicated.

Lattice model is a base for many

theories, e.g., free volume,

cell-hole, tunnel, etc. For example:

In 1941 Huggins & Flory

calculated the configurational

entropy of mixing.

In 1969 Simha and Somcynsky (S-S) published the lattice-hole theory, deriving PVT equation of state, cohesive energy