POLYMER TECHNOLOGY AND SUSTAINABILITY AA2010-2011

Review of physical principles (solubility, diffusivity, wettability)

Principles of mixing

Degradation and stabilization

Classification of additives

Compounding of thermoplastics

Rubber technology (vulcanization, reinforcement)

Biodegradation and bioplastics

Polymer recycling

Life cycle assessment

Polymer technology and sustainability

• Frontal lessons

• Exercitations (numerical exercises, experimental techniques with lab, case hystories)

• Seminars led by industrial experts

• Visit to an industrial plant (production of recycled PET nonwovens for roofing)

Final oral exam (in italian or english)

Bibliography:

Copy of all the slides/presentations + (consultation only)

• H. Zweifel, Plastics Additives Handbook, Hanser, Munich 2001

• C. Rauwendaal, Polymer Mixing, Hanser, Munich 1998

• I. Manas-Zloczower, Z. Tadmor, Polymer Mixing and Compounding, Hanser, Munich

1994

• L. Mascia, The Role of Additives in Plastics, Arnold, London 1974

• H.H. Jellinek, Aspects of Degradation and Stabilization of Polymers, Elsevier,

Amsterdam 1978

• F. La Mantia, Handbook of Plastics Recycling, RAPRA, Shawbury 2002

Introduction to the concept of “polymer formulation”

A polymer molecule becomes polymeric materials only when formulated (mixed) with suitable additives

Compounding is the term indicating the industrial process of mixing the raw polymers with additives

Additives are used for the following purposes:– To modify (improve) the material properties (durability, mechanical,

optical etc)– To improve processing– Cost reduction

Additives can be miscible (homogeneous, like stabilizers) as well as heterogeneous (like fillers and pigments)

Classification of additives

Polymer modifiers and processing aids

see for ex. L. Mascia, The Role of Additives in Plastics, Hanser (1985)

1. Additives which assist processing

2. Additives which modify mechanical properties

3. Surface property modifiers

4. Optical properties modifiers

5. Anti-ageing additives

6. Others

Examples of property modifiers (mechanical, electric conductivity, fire retardancy)

Function Structure

Fillers / reinforcing agents Oxides (glass, MgO, SiO2, Al2O3)Hydroxides (Al(OH)3)Salts (CaCO3, BaSO4, CaSO4, fosfati)Silicates (talc, mica, kaolin, clay)Metals

Organics Carbon-graphite, polymeric fibres

Plasticizers Esters, chlorinated paraffins, oxidized vegetal oils

Tougheners Rubbers (EPR, EPDM, NBR, NR, EVA)

Crosslinkers Peroxides, sulphur, silanes.

Fire retardants and smoke suppressants Sb2O3, chlorinated paraffins, Al(OH)3, Mg(OH)2, phosphates, brominted organics

Conductive c. black, graphite, metals

Examples of processing aids and antiageing

Function Examples

Heat stabilizers Primary antioxidants (sterically hindered phenols), hydroperoxide decomposers (organophosphites, thioesters)

Lubricants Fatty acids and their derivatives, paraffin waxes, metallic soaps, ester and amide waxes, silicones, fluoropolymers

AntiagingAntioxidants Phenols, arylamines, phosphites

Metal deactivators Chelants

Photostabilizers Pigments (c. black, TiO2), UV adsorbers, radical scavengers (HALS)

Biocides Thiocompounds, organometallic compounds

Function ExamplesSurface modifiersAntistatics Ethoxylated amines, ammonium salts, non-ionic

surfactants

Antifog Non-ionic surfactants

Antiwear Graphite, PTFE, MoS2

Adhesion promoters Silanes, block and grafted copolymers

Optical properties modifiersPigments

Soluble dyes

Nucleants

Inorganics: oxides (Ti, Fe, Cr), sulfides, chromatesOrganics: c. black, phtalocyanines, azo compounds etc.

Antraquinones, azo and bis-azo compounds

SiO2, talc, benzoates

Blowing agentsPhysical actionChemical action

Hydrocarbons, halocarbons, N2, CO2

NaHCO3, azocarbonamide etc.

Physical principles

Solubility and compatibility

Solubility has a thermodynamic meaning and it involves molecular mixing and formation of single-phase systems.

Compatibility is a technological term which may involve formation of both single-phase and stable multi-phase systems (like most polymer compounds).

Solubility is influenced by m.w., chemical nature, additive amount, matrix morphology etc.

For binary systems at constant pressure we have:

∆Gm = ∆Hm – T ∆Sm

Solubility occurs when ∆Gm < 0.

∆Sm is always positive (mixing increases disorder)

From classical thermodynamics we know:

∆Hm / Vtot = [(∆E1/V1)0.5 – (∆E2/V2)0.5]2 Φ1 Φ2 =(δ1 – δ2)2 Φ1 Φ2

∆Ei vaporization energies, Vi molar volumes, Φi volume fractions

∆Ei/Vi = cohesive energy density CED

(∆Ei/Vi)0.5 = δi solubility parameter

∆Hm is always positive or eventually = 0 (athermal mixing), therefore unfavourable for solubility

Flory-Huggins theory (recall): 2D lattice model

1 = diluent and 2 = polymer

The lattice is made by N1 + xN2 dots

Φ1 = N1 V / (N1 V + x N2 V) = N1/(N1+xN2)

Φ2 = xN2 V / (N1 V + xN2 V) = xN2/(N1+xN2)

The overall change in free energy upon mixing is

∆Gm = -T∆Smid + non ideal contribution

According to Boltzman we have

∆Smid = R lnΩ

with Ω = number of configurations accessibile to the system = No!/(N1!N2!)

We obtain

-T∆Smid = RT (N1 lnΦ1 + N2 lnΦ2)

Interaction parameter χ, = interaction energy between chain segment and diluent (non ideal part, enthalpic contribution)

∆Hm = RTχN1Φ2

Therefore we obtain:

∆Gm/N = RT(Φ1 lnΦ1 + (Φ2/x) lnΦ2 + Φ1 Φ2 χ)

∆Gm / RT = N1 lnΦ1 + N2 lnΦ2 + N1 Φ2 χ

Extension to the case of polymer blends (V/Vr is the number of lattice sites)

∆G’m / RT = (∆Gm / RT) (Vr/V) = ΦA/XA lnΦ1 + ΦB/XB lnΦ2 + ΦA ΦB χ

Mixing entropy tends to zero with increasing m.w.

χ varies from 0 (good miscibility) e 0.5 (theta temperature).

By comparing Flory-Huggins equation and solubility paramater we obtain

χ = V/(NRT) (δ1-δ2)2 = Vr/(RT) (δ1-δ2)2

V/N = molar volume of the solution

Solubility parameter δ

The cohesive energy density is

CED = (∆Hvap – RT)/V

(∆E = ∆H –RT).

The solubility parameter is:

δ = CED0.5 in cal0.5/cm3/2 = 0.4888 MPa0.5

As a general rule materials with similar δ are mutually miscible (solubility).

In case of polymers an experimental determination of δ is unfeasible (distillation).

Indirect methods:• Solubility tests• Swelling tests after crosslinking (better)

Numerical methods (group contribution method, see B. Van

Krevelen, Properties of Polymers, Elsevier,1990):

δ= ΣFi/(Mi/ρ) = ΣFi/Vi

F = molar attraction constant for the solubility parameter

ρ= density.

Chemical group F, in (J.cm3)0.5.mol-1

CH3- 420

-CH2- 280

CH (tertiary) 140

C (quaternary) 0

-CH=CH- 444

-phenyl 1517

-NHCO- 1228

-NHCOO- 1483

-CO- 685

-COO- 512

Hansen solubility parameters: there are various contributions (dispersive, polar, hydrogen bonding) of VdW forces to the overall CED, they must be treated separately.

δ2tot= δ2

d + δ2p + δ2

h

Hansen solubility parameters can be represented graphically in a 3D space

R is the interaction radius of a given polymer; for each additive to be added we can calculate a R’ point

R’ = (2δd,p – 2δd,s)2 + (δp,p – δp,s)2 + (δh,p – δh,s)2

if R’/R < 1 solubility is predicted, this occurs when each ∆δi is < 25%.

Polymer regular solutions theory applied to binary polymer/additive systems

Regular solutions = ∆H whatsoever, ∆S ideal.

∆Gm = ∆Hm – T∆Sm

If the additive are solid crystalline (i.e. stabilizers) with T < Tf, an additional term must be considered:

∆Gf = ∆Hf – T ∆Sf = ∆Hf (1-T/Tf)

since at equilibrium Tf = ∆Hf/∆Sf and ∆Sf = ∆Hf/Tf

The solubility equation is given by the sum of three positive terms

-lnΦa = ∆Hf/RT (1 – T/Tf) + (1-Vp/Va) + χ

with Φa volume fraction of additive

1° term: dipends only on the solid character of the additive2° term: volume ratio (entropic non combinatorial)3° term: polymer-additive interaction parameter (enthalpic)

Solubility Φa will increase on decresing those 3 contributions.

Temperature dependence of solubility (Van’t Hoff plot, assuming V indepedent over T)

-dlnΦa/d(1/T) ≅ ∆Hf/R + dχH/d(1/T) = ∆Hf/R + ∆Hm/R = ∆Hsol/R

Normally solubility increases with T

The experimental determination of additive solubility in apolymer matrix can be carried out putting in contact thetwo materials in form of thin films and measuring the time-dependent diffusion process

Examples, Van’t Hoff plot for 3 stabilizers in PP (the slope is proportional to ∆Hsol) and solubility tables

Physical state of additives in polymers:

Various cases are feasible as shown by phase diagrams

Horizontal line: temperature quenching after compounding

Curve A : the additive is always insoluble (es. fillers and pigments)Curve B: additive is always soluble (es. plasticizer)Curve C: solubility at high temperature with following phase separation when the

polymer is still molten (microparticle formation, they act as reservoirs)Curve D: solubility at high temperature with following phase separation only when the

polymer is already solid (metastabile states, blooming)

Diffusion

Diffusion is a mass transfer driven by a concentration gradient.

It is important for the following features:

• mechanisms of loss of additives (leaching, blooming, food contamination etc)

• mechanism of action of some additives which need to move for being effective (i.e. stabilizers)

• formulation of barrier polymers (packaging)

Hp: one molecule, monodirectional flow through a isotropic surface A

1° Fick’s law: Flux = J = 1/A dm/dt = - D (dC/dx) (J in kg/m2 s)

This is the law concerning steady diffusion (J constant with time)D = diffusion coefficient (in m2/s)The concentration gradient is given by

dC/dx = (CA-CB)/(xA-xB)

2° Fick’s law: dC/dt = D (d2C/dx2)

It can be applied for cases when both J and dC/dX can change over time.Only approximated solutions with known boundary conditions are feasible

We can determine D by measuring the amount of additivepermeated into the polymer film Mt vs. time (sorption curves)

Mt / M∞ = K tn

1. case I, or fickian diffusion, with n = 0.5. The rate of diffusion is << polymer relaxation times.

2. case II, with n=1. The rate of diffusion is >> relaxation times (solvent stress crazing)

3. anomalous diffusion, with n comprised between 0.5 and 1.

In case of fickian diffusion (frequent) we draw the Mt-t1/2 curve

Various anomalies are feasible

Determination of D (simplified 2° Fick’s law solution): from theslope k of the initial part of the sorption curve (for M / M∞ < 0.4)

b = film thickness

M / M∞ = 4/b (D t/π)0.5

k = 4M∞/b (D/π)0.5

Determination of S (solubility coefficient): from the limiting, asymptotic value of the sorption curve

The permeability coefficient P will be given by

P = D· S

S is thermodynamic and will depend mainly on ∆δ

D is kinetic and will depend on free volume /Tg

Morphology effect on D: diffusion involves only amorphous phases

Temperature effect:D = Do exp(-ED/RT)

Effect of polymer type:

D = Do exp(-ED/RT) exp(-Bd/f)

f = fractional free volume of the polymer (related to T-Tg) Bd = volumetric parameter proper of the additive

Effect of molecular weight:

D = KM-a a = 1.5 – 2.5Increasing the m.w. of the additive means lower solubility but also less migration

Wettability

The property is important for the following features:

• property modification: development of polimeric compounds with tailored surface properties – (lower wettability means hyprophobic treatmants, antistick-

release etc.)– (higher wettability means better inkability, adhesivity etc)

• processing aid: better wetting of solid additives (pigments) during mixing, work of adhesion etc.

Wetting of a solid involves the displacement of air by the action of a liquid (like a molten polymer)

Surface = interphase between solid and gasInterface = interphase between solids and/or liquids

An interphase can be represented thermodynamically as the reversibile work dW spent to create it, as in the case of formation of a soap film

Surface energy Γ

dW = Γ.l.dX

Γ = ∆Es/∆A (in J/m2)

∆Es = energy spent to increase the interfacial area of ∆A.

Surface tensioni s the tangential stress opposed by the liquid to the creation of a new surface (in N/m)

For liquid systems surface energy and surface tension are equivalent and the term are used interchangeably in polymer technology.

Surface tension = the surface atoms are in an energetically anisotropic state and tend to return in the bulk putting the material in a state of tension.

The surface tension depend on the intensity of cohesive forces (polarity of material)

High surface tension solid = easy wettabilityLow surface tension solid = difficult wettability

Typical Γ for polymers 20-50 mN/mTypical Γ for ionic solids (fillers, pigments) >200 mN/m

Surface tension of a solid can be estimated through measurements of contact angle θ.

Contact anglethe angle at which a liquid/vapor interface meets a solid surface

Young equation (thermodynamic equilibrium, ideal case for rigid, homogenous and flat surfaces):

Γlv cos θ = Γsv – ΓslΓlv = surface tension of the liquid in equilibrium with vapour (known)Γsv = surface tension of the solid in eq. with vapour (unknown)Γsl = interfacial tension

Vectorial form of Young equation:

Better surface wetting for cos θ → 1, favored by high Γsv and low ΓlvComplete wetting when Γsv > Γsl + Γlv

vapour

liquid

solid

Γsv

θ Γsl

Γlv

Critical surface tension of wetting Γc (Zisman) Estrapolation of Γ to zero angle (cos θ=1) from measurements with homologousseries of liquids

Note = the extrapolated value will depend on the choice of the solvent series

It’s better to separate dispersive and polar contributions of surface tension.

Fowkes:

Γ = Γd + Γp + Γh + …

Owens-Wendt method: calculation of the interfacial tension Γsl according to a geometric mean approximation, to be used in the Young equation:

Γsl = Γsv + Γlv -2(Γsvd. Γlv

d)0.5 – 2(Γsvp. Γlv

p)0.5

Measurements with at least two liquids with known surface tension components are needed to solve the equation system, generally waterand diiodomethane are used.

The final result will be Γsv = Γsvd + Γsv

p , generally higher than Γc

Polymer wettability depend on their polarity.Fluoropolymers show the least wettability values, while polymers with polar bonds (like polyamides) are those with highest surface tension

Contact angle hysteresis

Real surfaces show difference in advancing and receding contact angle during dynamic experiments

Hysteresis is due to roughness and/or chemical heterogeneity.Time-dependent hysteresis is due to sorption or surface enrichment

of specific functional groups (see antifog additives).

Work of adhesion

A good wetting is needed but not enough to achieve a efficient pigment/filler dispersion in a polymer compound. We need also avery high interfacial adhesion

Duprè equation (work of adhesion Wa)

Wa = Γ1 + Γ2 - Γ12 = Γsv - Γsl + Γlv

Young-Duprè equation:

Wa = Γlv (1 + cos θ)

Best adhesion is achieved for high surface tension liquids capable togive low contact angle with the surface

How to estimate interfacial tension?

Γ12 = Γ1 + Γ2 -2Φ(Γ1 Γ2)0.5 ≅ (Γ10.5 – Γ2

0.5)2

with Wa = 2Φ(Γ1 Γ2)0.5

Φ = interaction parameter of Good-Girifalco→ 1 per materials with comparable polarity→ 0 for materials with different polarity

polarity = Γp / (Γp + Γd).

Example: dispersing agents/compatibilizers for polymer compounding

Several compatibilizers are also used to lower interfacial tension ion polymer blends.

method example

Functionalized polymers giving strong interactions/chemical bonds

PVC/NBR, PVC/MBSPA6/EPR-g-MA

Copolymer with miscible segmentEPDM/PMMA + EPDM-g-MAPS/EPDM + S-EB-SPVC/PS + PCL-b-PS

Copolymer with reactive groupsPA6,6/EPM + EPM-g-MAPA6/PP + PP-g-AA

Low molecular weight chemicalsPA6,6/PET + p-TSOHNR/PA6 + peroxides