annex a. theoretical background on the techniques

Annex A: Theoretical background of the techniques and experimental conditions

Elodie Bugnicourt, PhD INSA Lyon, 2005 191

ANNEX A. THEORETICAL BACKGROUND ON THE TECHNIQUES - EXPERIMENTAL

CONDITIONS .......................................................................................................................... 193

A.1. Processing and characterization of the silica suspensions.............................193

A.1.1. Standard procedure .......................................................................................... 193 A.1.1.a. Dispersion step using a high speed disk disperser/ dissolver....................... 193 A.1.1.b. “On-line” controls .......................................................................................... 194 A.1.1.c. Out gassing................................................................................................... 195

A.1.2. Other processes ............................................................................................... 195 A.1.3. Control of the final dispersion in the liquid state ............................................... 197

A.1.3.a. PharmaVision (PVS) ..................................................................................... 197 A.1.3.b. Liquid state rheology..................................................................................... 198

A.2. Characterization of the crosslinking step ........................................................202

A.2.1. Determination of the gelation time by chemio-rheology.................................... 202 A.2.1.a. Theoretical backgroud .................................................................................. 202 A.2.1.b. Experimental conditions of dynamic mechanical analysis (DMA)................. 203

A.2.2. Near Infra-Red Spectrometry (NIR) .................................................................. 204

A.3. Characterization of the interfacial interactions................................................204

A.3.1. Extraction of the amino-modified silica from epoxy suspension ....................... 205 A.3.1.a. Extraction process ........................................................................................ 205 A.3.1.b. Size Exclusion Chromatography (SEC) ........................................................ 205

A.3.2. Elemental analysis............................................................................................ 206 A.3.3. Medium Infra-Red spectroscopy (MIR)............................................................. 206 A.3.4. Gas chromatography Mass Spectroscopy coupled with Thermo Gravimetric

Analysis (GC/MS+TGA) .................................................................................................... 206 A.3.5. Solid state Nuclear Magnetic Resonance of carbon, proton and nitrogen (13C, 1H, 14N and 15N NMR) ............................................................................................................. 207

A.3.5.a. Solid state Carbon NMR ............................................................................... 207 A.3.5.b. High resolution solid state Proton and Nitrogen NMR .................................. 207

A.4. Morphological characterization.......................................................................208

A.4.1. Transmission Electron Microscopy (TEM) ........................................................ 208 A.4.2. Image analysis.................................................................................................. 208

A.4.2.a. Morphological parameters ............................................................................ 209 A.4.2.b. Procedure ..................................................................................................... 210



A.4.3. Small angle neutron scattering (SANS) ............................................................ 211 A.4.3.a. Background about neutron scattering ........................................................... 212 A.4.3.b. Experimental set up and configurations........................................................ 215 A.4.3.c. Treatment of the data.................................................................................... 216

A.4.4. Morphological changes during crosslinking ...................................................... 218 A.4.4.a. Small angle neutron scattering (SANS) ........................................................ 218 A.4.4.b. Confocal microscopy..................................................................................... 218

A.5. Mechanical characterization ...........................................................................220

A.5.1. Dynamic Mechanical Analysis (DMA)............................................................... 220 A.5.2. Tensile tests...................................................................................................... 220

A.5.2.a. Glassy systems............................................................................................. 220 A.5.2.b. Rubbery systems .......................................................................................... 221

A.5.3. Crack propagation measurements (LEFM)....................................................... 222

A.6. Characterization of the thermal and combustion behavior..............................223

A.6.1. Differential Scanning Calorimetry (DSC) .......................................................... 223 A.6.2. Thermo-gravimetric Analysis (TGA) ................................................................. 224 A.6.3. Cone calorimeter .............................................................................................. 224



ANNEX A. THEORETICAL BACKGROUND ON THE TECHNIQUES - EXPERIMENTAL CONDITIONS

In this first annex, the techniques, as well as the experimental conditions, are described step by

step from the dispersion of the silica into the reactive epoxy-amine medium to the final

characterization of the crosslinked samples. The only techniques of which backgrounds are

detailed are those which were not considered as “standard” in polymer science such as image

analysis and neutron scattering. The strategies for the optimization of the materials are quoted,

as well as the different devices used for the characterization of the final epoxy / silica

composites: morphological, mechanical, and thermal properties as well as the study of the

interactions developed in the system.

A.1. Processing and characterization of the silica suspensions

A.1.1. Standard procedure

A.1.1.a. Dispersion step using a high speed disk disperser/ dissolver

The silica dispersion into epoxy DGEBA DER 330 (respectively Jeffamine D2000®) is realized

using a dissolver Turbotest 33/300P from Rayneri, with a 65 mm diameter stirring disk (Figure

A-1 (a)). The shape of this disk is specially designed for the deflocculation and dispersion of

solid powders into liquid media. The maximum rate that can be reached with this device is 3,300

rpm, that is to say a peripherical speed of about 11 m/s, with a torque limited to 160 N.cm. This

dispersion method appeared to be the most effective and easy to carry out, for most of our

formulations of average to high viscosities (typically up to 15 wt. % of silica N20 into epoxy

resin).



(a) (b)

Figure A-1 (a) Dissolver with a disk shaped specifically for the dispersion of fillers into a liquid, (b) Right configuration for an efficient dispersion.

The desired amounts of liquid and silica are weighted in order to prepare 500 g batch. The

dispersion is realized in a can of adequate dimensions to have a good dispersing action (Figure

A-1 (b)), at room temperature, usually without heating device. However, due to the friction, a

self-warming of the suspension is noticed (generally up to 60 to 80°C).

The silica is introduced progressively into the batch, a mixing speed of about 500 rpm is first

applied, and after complete incorporation of the silica, the mixing is realized at maximum rate

(3,300 rpm) during a few minutes. Once all the silica is introduced into the batch, the dispersion

is carried out at the max speed during at least 1 hour from the moment no further evolution of

the dispersion state is observed.

Note: At the end of each dispersion, it has to be taken care not to have undispersed part of the

silica stuck on the wall of the can that could create macro defects in the material.

A.1.1.b. “On-line” controls

Some tests are realized in order to evaluate and optimize the quality of the dispersion and its

evolution all along the step of processing of the silica suspension (grindometer, standard optical

microscopy on a thin layer and viscosity measurements).

A Grindometer or grind gauge (Figure A-1) consists of a

metal bar with a rectangular milled depression of which

depth gradually decreases. The sample is spread off by the

second bar towards the shallower end in a single pass.

Particles having a diameter nearly equal or larger than the

depth of the depression rise up through the surface. Figure A-1 Grindometer



Vacuum

pump

Oil bath at 80°C

This device is mainly used in the field of paints and more adapted to low viscosities. It is easy

and fast to use, however the results are subject to important variability.

The tests were realized using two grind gages: first from 100 to 0 µm, and then, if the dispersion

is fine enough, from 25 to 0 µm. The resolution is limited to the visual acuity (~ 5 µm). This

device only allows detecting the biggest particles with no indication on the size distribution.

A.1.1.c. Out gassing

The mixture is finally out-gassed in a vacuum reactor for 30 minutes

to 1 hour at 80°C, with a slow mixing rate (Figure A-2).

Figure A-2 Out gassing device

A.1.2. Other processes

We had to resort to other processes for extreme viscosities and/ or in order to optimize the

dispersion, especially in case of amino-modified silica that happened to be difficult to disperse

uniformly.

A bead mill and a 3-roll mill (Figure A-3) were used at Wacker Co., after a first step of

incorporation of the silica in the liquid medium using a dissolver, in order to reduce the size of

the agglomerates. The two devices are adapted to low viscosities (paint, ink, adhesives,

cosmetics…), thus they were only tested in order to optimize amino-modified silica dispersions

into Jeffamine at low concentration.

A bead mill acts through the crushing action of the beads on the agglomerates, whereas for 3-

roll mill, shearing and compressing forces work on the clusters of particles when the suspension

passes through the clearance between the three rolls (10-15 µm), which rotate at different

speeds.



Figure A-3 Processes adapted for the preparation of formulations of low viscosities

For products displaying very high viscosities (master-batches containing up to 25 wt. % of silica,

such as 25A-D330), and / or high yield stress (such as 15H-D330), the dissolver is no more

effective to carry out the dispersion. To replace the dissolver, a kneader (Figure A-4 (a)) of

capacity 50 g was used at INSA (HAAKE Rheomix). The kneading was carried out at 200 rpm,

during 30 minutes, at 100°C (after optimization of the conditions).

In the same objective, a micro twin-screw extruder (Figure A-4 (b)) of capacity 15g (DSM

Microcompounder) was used at INSA for 20 minutes, at 200 rpm, and 80°C.

Adapted for wide range of viscosities, a planetary mixer (Figure A-4 (c)) is a quite versatile and

convenient device, which was used at Wacker Co. The vessel has a revolutionary motion and it

works under vacuum conditions. Several interchangeable blades are used to combine

dispersing, kneading and mixing actions; it was tested in configuration butterfly / dissolver.

Figure A-4 Processes used for high viscosities (a and b) and large range of viscosities (c)

All these devices were tested alone or in combination between each other in order to try to

optimize the dispersion with amino-modified or highly hydrophobic silica (see Annex C.1.1.e. for

the morphologies resulting from the different techniques).

(b) Micro-twin screw extruder (a) Kneader

(c) Planetary mixer

(a) Bead mill (b) 3-roll mill



A.1.3. Control of the final dispersion in the liquid state

A.1.3.a. PharmaVision (PVS)

The PharmaVision 830® device from Malvern was used at the head quarter of Malvern France

in Orsay in collaboration with Stéphane Rouquette.

Principle

The PharmaVision 830 enables the characterization of particle size and particle shape using

automated microscopy and image analysis techniques (Figure A-5). Information is generated

from the analysis of thousands of particles and is supported by images of all the particles. A

number of shape and size parameters are calculated for each particle.

This device is designed for measurements of dry powders from 0.7 µm to 2,000 µm (depending

on the magnification). However, it could be adapted for the analysis of a thin layer of our

viscous suspensions coated onto a glass plate.

Sample on a glass slide

Images

Segmentationof the particles

Calibration reticule

Mobile video camera in XY

Movingtransmissionlighting

Sample on a glass slide

Images

Segmentationof the particles

Calibration reticule

Mobile video camera in XY

Movingtransmissionlighting

Figure A-5 Principle of the Phamavision Malvern

Example of result

An example of result obtained for a suspension of 5 wt. % of amino-modified silica into epoxy

prepolymer (5A-D330) is presented in the Figure A-6 to Figure A-8.



(a) (b)

Figure A-6 Example of results for amino-modified silica: (a) Image of the area scanned (350 x 500 µm²) and (b) individual image of each particle detected (image truncated, 1000 particles analyzed in total)

(a) (b)

Figure A-7 Example of results for amino-modified silica: size distributions of the particles detected within the suspension (a) by number and (b) by volume

Figure A-8 Example of results for amino-modified silica: statistical data provided by the software

about the size distribution

A.1.3.b. Liquid state rheology

A few theoretical elements on the rheology of suspensions are reminded briefly in this

paragraph, first in dynamic regime, second in steady shear regime and then about thixotropy.

Dynamic regime (low strain): theory

When a sinusoidal strain )t(*γ is applied to a material displaying a linear viscoelastic behavior,

the stress )t(*τ resulting is also sinusoidal but presents a dephasing δ. This behavior can be



written as follow:

)t(i0

ti0

e.)t(e.)t(

δ+ω

ω

τ=τγ=γ Equation A-1

The complex modulus is defined by:

δ

γτ=

γτ= i

0

0 e.)t()t(*G

Equation A-2 It can also be expressed as:

"iG'G*G += Equation A-3 where G’ is the storage and G” is the loss moduli respectively:

δγτ= cos.'G

0

0

δ

γτ= sin."G

0

0

The loss factor (or damping factor) is defined by:

'G"Gtan =δ Equation A-4

The complex viscosity is then defined as: "i'* η−η=η Equation A-5

where ω

=η "G' and ω

=η 'G" .

In steady regime: theory

The newtonian viscosity (in Pa.s) is defined as follow:

γτ=η&

Equation A-6

where :τ is the shear stress (in Pa), γ& is the shear rate (in s-1).

When the material presents a threshold stress, i.e. it does not deform up to the application of a

certain stress:

)(lim 0y γ=τ →γ &&

Equation A-7

Traditionally, the following types of behavior are distinguished for liquids (Figure A-9):

− Newtonian behavior:

γη=τ &. Equation A-8 The viscosity is then independent upon the shear rate applied.

− Shear thinning (respectively thickening) behavior.

γ=τ &n.K Equation A-9

where K is the consistency index.

and



The steady shear viscosity changes as a function of the shear rate: for shear thinning

behavior the viscosity decreases as a function of the shear rate. In contrast, it increases

in case of shear thickening behavior, but this behavior is more seldom.

− Viscoplastic behavior presenting a yield stress (Bingham-type):

γη+τ=τ ⋅ &.plb Equation A-10

where: τb is the yield stress of Bingham, and ηpl is the plastic viscosity

Once the yield stress is reached, the behavior is newtonian.

− Shear thinning (respectively thickening) behavior presenting a yield threshold:

γ+τ=τ &n.Ky Equation A-11

where τy is the yield stress, K is the consistency index, n is the flowing index.

Once τy is reached, the behavior is a shear thinning (respectively thickening).

τ b

τ y

τ b

τ y

τ

γ'

Bringham type fluid

Shear thinning behavior with a yield stress

Shear thinning behavior

Newtonian behavior

Figure A-9 Evolution of the shear stress as a function of the

shear rate for traditional rheological behaviors

Thixotropic behavior: theory

A thixotropic behavior describes the systems for which the viscosity depends on the time. It is

often evidenced experimentally by the existence of a hysteresis loop for the viscosity during a

loading (increasing shear rate), unloading (decreasing shear rate) experiment, various answers

can be observed (Figure A-10 (a)).

It can also be evaluated by the time needed for the viscosity to recover its initial value after

shearing (Figure A-10(b)) [BAR97]. Indeed, equilibrium can never be reached with an increasing

shear rate. So, after measuring viscosity at a low shear rate, a high shear rate is applied till the

sample reaches equilibrium. Then, the low shear rate is applied again, and the time for the

viscosity to return to its initial value, directly linked to the thixotropic behavior, is measured.



τ τ y

τ

γ'

Thixotropic behavior with a yield stress

Thixotropic behavior

γ1’ γ1

’ γ2’

tthixo

t

η

(a) (b)

Figure A-10 Thixotropic behavior evidenced by two types of experiments: (a) hysteresis loop, (b) shearing at various rates (γ1

’ << γ2’), the time for the viscosity to recover is measured (tthixo)

Experimental conditions

These experiments were realized on the unreacted silica suspensions into epoxy (respectively

Jeffamine) in the liquid state using a rheometer AR1000 from the Thermal Analysis company

with controlled stress and thermoregulated by Peltier effect.

A plate / plate geometry (20 mm diameter, gap = 0.8 mm) was selected due to several reasons:

i) the really high viscosities of some of the silica suspensions studied; ii) to follow the same

procedures as the ones commonly used by Wacker Co. and iii) a cone/plate geometry would

not have been adequate in case of really poor dispersion because big silica agglomerates could

generate a friction within the gap.

The procedures systematically used were the following:

− For the measurement of the steady shear viscosity: a shear rate sweep from 0.1 to

100 s-1 was applied.

− In order to characterize the dynamic behavior in oscillation, a strain sweep from

0.001 to 10 was performed

The measurements were carried out at room temperature (respectively at 80°C in order to

simulate the processing temperature).

Note: Each characterization was made on a newly installed sample and no pre-shearing step

was realized because of the really long time needed for the total re-structuration of the silica

aggregates within the suspensions after shearing.

A 10 minutes rest was waited after installation of the sample between the plates in order to

allow the product to reach an equilibrium (tests were realized to adjust this duration).



A.2. Characterization of the crosslinking step

The basics of the chemio-rheology for the study of the crosslinking of epoxy networks,

especially at the gelation point, are summarized in this paragraph. Then the conditions of the

two techniques that were used in order to investigate pyrogenic silica effect on the kinetics of

epoxy-amine reaction are detailed: Dynamic Mechanical Analysis and Near Infra Red

spectroscopy.

A.2.1. Determination of the gelation time by chemio-rheology

A.2.1.a. Theoretical backgroud

The formation of a chemical three-dimensional network leads to the appearance of elastic

properties for the materials (Figure A-11). The gelation point can be determined through

rheological dynamical tests.

Figure A-11 Schematic evolution of the molecular weight, viscosity, sol part and elastic modulus during the crosslinking process of a thermosetting network, xgel: conversion at gelation point

At the gelation point, the storage and loss modulus can be described by a power law as a

function of the pulsation: ∆ω∝ω∝ω )( G” )( G' (Figure A-12), where ∆ is the relaxation exponent

that can predicted by Rouse’s percolation theory (about 0.7).

So, at the gelation, the loss factor G'G"tan =δ is independent on the frequency and its value is:

2.gel

∆π=δ Equation A-12

0 0.25 0.5 0.75 1

conversion

AU Mw

Viscosity

wsol

G

xgel



Figure A-12 Log-log plot of the dynamic modulus as a function of the pulsation at the gelation time: ♦ G’, ■ G” for a neat MDEA-based system

Experimentally, the gelation point is determined by the crossover of the curves of the loss factor

at various frequencies. Using this method, Eloundou et al. obtained a value of ∆=0.69 for a

diepoxy / diamine systems (DGEBA / MCDEA), in good agreement with Rouse theory [ELO96,

98]. Examples of evolution of the damping factor, of the loss and storage moduli during a

conventional chemio-rheological experiment allowing the evaluation of the gelation time are

presented in the Figure A-13.

1E-2

1E-1

1E+0

1E+1

1E+2

3500 4000 4500 5000 5500t (s)

tan(

δ)

1 rad/s2.15 rad/s4.64 rad/s10 rad/s21.5 rad/s46.4 rad/s100 rad/s

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

1E+6

3500 4000 4500 5000 5500t (s)

G',

G" (

Pa)

G' 1 rad/sG' 2.15rad/sG' 4.64 rad/sG' 10 rad/sG' 21.5 rad/sG' 46.4 rad/sG' 100 rad/sG'' 1rad/sG" 2.15 rad/sG" 4.64 rad/sG" 10 rad/sG" 21.5 rad/sG" 46.4 rad/sG" 100 rad/s

(a) (b) Figure A-13 (a) Evolution of the loss factor as a function of time during crosslinking of an epoxy-amine

network; and (b) of the storage and loss moduli for a MDEA-based system filled with 5 wt. % of hydrophilic silica (5N-D330-M)

A.2.1.b. Experimental conditions of dynamic mechanical analysis (DMA)

Gelation times of the reactive epoxy-amine systems, were measured using a Rheometric

Dynamic Analyser (RDAII) device allowing the measurement of the storage G', loss G" moduli

and loss factor tan δ as a function of frequency.

Pulsation sweep from 1 to 100 rad/s were applied to the systems, with a strain applied around

10-15% for MDEA-based systems and 20-25% for Jeffamine-based systems. The tests were

performed during an isothermal curing process (respectively at 135°C for MDEA-based systems

tgel

log(G") = 0.78.log(ω) + 1.42

log (G') = 0.77.log(ω) + 2.22

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5log (ω) (rad/s)



and 120°C for Jeffamine corresponding with the first segment of the cure schedule) using a

geometry consisting of parallel plates of 40 mm diameter, with a gap included between 0.5 and

0.8 mm. Before the introduction of the reactive mixture, the plates were heated at the

polymerization temperature.

The multi-frequency crossover point was used as criterion in order to estimate the gelation time.

A.2.2. Near Infra-Red Spectrometry (NIR)

Kinetics analyses by near infrared spectroscopy (NIR) were realized on a spectrophotometer

NIR-TF Equinox 55 from Bruker.

The experimental set up (Figure A-14) consists in an aluminum mould of dimensions 50 x 30 x 3

mm3 warmed by two electric plates connected to a temperature regulator. Each face of the

mould has a circular hole in the middle of, 1 cm diameter, into which is inserted a glass window

to allow the IR beam to cross the preparation. Spectra are recorded each minute for 4 hours at

135°C for MDEA-based systems and 120°C for Jeffamine-based systems.

Figure A-14 Experimental set up for the in situ monitoring of the epoxy-amine kinetics by NIR

A.3. Characterization of the interfacial interactions

The extraction process of silica from epoxy suspension, as well as the conditions of the different

techniques of characterization carried out in order to evidence the reaction at the interface

between amino-modified silica and epoxy (in the second chapter of the manuscript II.4.2.), are

reported in this paragraph.

Reactive system

Detector

Emitter

Thermocouple Insulator

Silicone joint

Mold

Heating plateGlass windows



A.3.1. Extraction of the amino-modified silica from epoxy suspension

A.3.1.a. Extraction process

The unreacted part of the epoxy prepolymer has to be separated from the epoxy that reacted

with amino-modified silica. Several successive washings / extractions were realized on an

amino-modified silica suspension diluted into THF in order to remove, by centrifugation at 5000

rpm, the most part of adsorbed epoxy (filtrate) from the silica with convalently bonded epoxy,

thanks to the difference of densities.

A.3.1.b. Size Exclusion Chromatography (SEC)

A Size Exclusion Chromatography (SEC) device for low molar mass equipped with two columns

and with a refractometric detector Viscotek VE 3580 was used with THF as solvent with an

output flow of 1ml.min-1. The aim of SEC experiments was to measure the residual

concentration on epoxy in the filtrate after each centrifugation (example of result given in the

Figure A-15). The initial epoxy concentration in the solution was c.a. 100 mg of epoxy per ml of

THF, 5 successive extractions of 6-8 hours were regarded as efficient to remove most

unreacted epoxy “desadsorbable” from amino-modified silica surface, as residual epoxy

concentration in the filtrate became then negligible.

Figure A-15 Evolution of the concentration of epoxy in the sol vs. the number of centrifugations,

elution time for epoxy DGEBA DER 330 ~17-18 min, concentration of the standard: 50 mg/ml

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0,2

10 12 14 16 18 20

0

20

40

60

80

100

0 1 2 3 4 5 6n° of centrifugation

dgeb

a co

ncen

trat

ion

(mg/

ml)

Number of

centrifugations:

RI

Elution time (min)



A.3.2. Elemental analysis

Elemental analyses were realized by the Service Central d’Analyses (SCA) of Solaize, in order

to quantify Carbon, Oxygen, Hydrogen and Nitrogen contents in the different amino-modified

silica samples extracted from epoxy.

A.3.3. Medium Infra-Red spectroscopy (MIR)

The device used is a Magma-IRTM 550 from Nicolet. The spectrum is acquired in absorbance

between 4,000 and 400 cm-1 with a resolution of 4 cm-1 and averaged on 16 scans. A sample of

the powder of each amino-modified silica samples extracted from epoxy is mixed into KBr in

order to prepare a thin sample. The background is systematically corrected.

A.3.4. Gas chromatography Mass Spectroscopy coupled with Thermo

Gravimetric Analysis (GC/MS+TGA)

These experiments were realized with Jean-Marie Letoffé and Catherine Sigala at the

Laboratory “Multimatériaux et Interfaces”, UMR CNRS 5615 of UCB Lyon 1. The specifications

of the TGA and GCMS are given in the Figure A-16.

The TGA measurements were carried out on a device Mettler Toledo 851 from 30 to 600°C at

10°C/min, or in maximal resolution mode. In this latter, the temperature increase rate is

controlled in real time as a function of the weight loss rate in order to evidence isothermal

degradation processes. The min and max heating rate imposed were 1°C/min to 15°C/min with

corresponding losses of weight of 3 to 1 µg/s. The samples analyzed weighted 10 to 15 mg.

The gas effluents produced by the processes of degradation of the material were probed by

GCMS at different temperatures bellow and above isothermal degradation processes previously

determined by maximal resolution TGA. The TGA is coupled via a " home made " interface with

an analyzer GC (6890) / MS (5973) from Agilent Technologies. During each experiment, four

samplings were realized, and stored in loops of 1 ml. The capillary column of the GC/MS is a

VOC (volatile organic components) column working with a "solvent delay" of 1 minute to allow

detecting the VOC only from the CO2. The column is regulated following the temperature

program: isotherm at 36°C during 2 minutes followed by an increase at 5°C.min-1 up to 260°C.

This method allows obtaining a good compromise between the separation of the peaks and an



an acceptable duration of the analysis (46.8 minutes for each gas effluent sample). The

identification of the VOC was made with the library NIST, with a reliability greater than 90%.

Figure A-16 Experimental set up GC/MS + TGA

A.3.5. Solid state Nuclear Magnetic Resonance of carbon, proton and nitrogen

(13C, 1H, 14N and 15N NMR)

A.3.5.a. Solid state Carbon NMR 13C and 1H solid state NMR were realized at CPE Lyon with Anne Baudouin. The spectrometer

used was a Bruker 500 MHz, with a 4 mm Bruker probe. The rotation of the sample was carried

out at 10 kHz. For the 13C spectra in CP/MAS (Cross Polarization Magic Angle Spinning:

irradiation of the protons and transfer of the magnetization on the carbons), the contact time

was 2 ms, the relaxation time was 1 s except for the samples D330 and D330-J that were

recorded in direct irradiation of the carbons.

A.3.5.b. High resolution solid state Proton and Nitrogen NMR

High resolution 1H and 14;15N solid state NMR were realized at the CRMHT (Centre de

Recherche sur les Matériaux à Haute Température) in Orléans in collaboration with Bruno

Alonso using a Bruker Avance WB 750 MHz (17.6 T) spectrometer with a boron nitride stator

and a 4 mm probe.

Interface Agilent Technologies

GC HP 6890 / MS HP 5973

TGA Mettler Toledo 851



A.4. Morphological characterization

Two main experimental approaches were followed for the study of the final morphologies: image

analysis of TEM micrographs and neutron scattering experiments which is a powerful technique

for the study of colloidal systems. Then the procedure of image analysis of the morphology is

presented. The morphological evolution during the polymerization was also studied as

explained finally.

A.4.1. Transmission Electron Microscopy (TEM)

The TEM observations were realized at the Centre of Electron Microscopy of UCB University

Lyon 1 with help from Pierre Alcouffe.

The samples were prepared in pyramidal shape and then cut as thin layer (between 60 and 80

nm for MDEA-based systems that are glassy at room temperature, and 80 and 100 nm for

Jeffamine-based system that are rubbery at room temperature) using an ultra-microtome with a

diamond knife. It was realized at room temperature for MDEA-based systems and about 50°C

bellow Tg for Jeffamine-based systems (about -80°C), under liquid nitrogen flow. The thin layers

were then placed between copper grids and then observed using a transmission electronic

microscope Philips CM120.

A.4.2. Image analysis

The image analyses were performed at the Centre Commun de Quantimétrie of Université Lyon

1 in collaboration with Jean-Claude Bernengo.

The image analyses of TEM micrographs were carried out on frames measuring 512 pixels x

512 pixels using Quantimet 570 and 600 from Leica.



A.4.2.a. Morphological parameters

The morphological parameters worked out by image analysis are illustrated in the Figure A-17

and are defined as follows:

− Position and number of aggregates

− Ferets: lengths intercepted in 8 directions (0; 22.5; 45; 67.5; 90; 112.5; 135; 157.5 and

190°) on the object

Geometric mean of Ferets: L.WF =

where L is the longest Feret and W is the shortest Feret

Note: This value is regarded as the size of the object in our calculations.

− Area A: a.NA =

where N is the number of pixels covering the object and a is the single pixel area

− Perimeter P: c65.0V2H2P −+=

where H is the horizontal projection, V the vertical projection and c the corners number

− Convex Perimeter: ∑

π=8

1iFc F . ).n

2( 2.tan P

where nF is the Ferets number and Fi the Feret length in each direction

− Convex Area: ²F.

4 A c

π=

− Roundness: A4²P R

π=

The roundness is 1 for a sphere

− Aspect ratio (or shape factor): b/a for the equivalent ellipsoid

− Bulkiness: AA

B c=

Figure A-17 Schemes of the morphometric descriptor worked out by image analysis

Initial aggregate

Binary aggregate

a

b

Convex perimeter

Convex area

Perimeter

Area

Equivalent ellipsoid

Feret at 0°



A.4.2.b. Procedure

The data treatment procedure consisted in the following steps:

1. Colours inversion

2. Background subtraction

3. Contrast increase

4. Binarization

Note: the threshold must to be adapted for each micrograph, this is a very sensitive

parameter, especially in case of large distribution of the sizes of the agglomerates.

5. Noise filtration (by area selection/ or erosion followed by dilatation)

After this stage (Figure A-18), the first calculation concerning the shape and size of the

aggregates are realized.

From the step 3, the following steps are necessary in order to realize the image of the skeleton

(illustrated in the Figure A-19):

6. Dilatation(s)

7. Smoothing(s)

8. Binarization

9. Skeletonization

The skeleton is defined as the locus of equidistance from the edges, it is obtained via a critical

erosion process Therefore it gives an illustration of the structure of the aggregates where the

primary particles appeared substituted by segments. The skeletonized picture enables

calculations concerning the branching (parameters provided: number of joins, forks and ends).

(a) (b)

Figure A-18 Illustration of image analyses procedure for a Jeffamine-based crosslinked sample filled with 5 wt. % of amino-modified silica (a) initial frame, (b) improved and inverted frame (after step 1- 3)



(a) (b)

(c) (d)

Figure A-19 Illustration of image analyses procedure for skelotonization on a Jeffamine-based crosslinked sample filled with 5 wt. % of amino-modified silica (a) after step 7, (b) after step 8, (c) skeleton

overlaid on the image (a), and (d) zoomed examples of skeletonized aggregates

A.4.3. Small angle neutron scattering (SANS)

Small angle neutron scattering (SANS) experiments were realized at the Laboratoire Léon

Brillouin (laboratoire commun CEA-CNRS) at the CEA Saclay, France, in collaboration with

François Boué.

In this paragraph, the background of scattering measurements is presented, as well as a few

elements on the theoretical calculations related to this technique. Then, the experimental set up

used is presented, as well as the procedure for the treatment of the data obtained.



A.4.3.a. Background about neutron scattering

Introduction

From scattering measurements, information can be obtained about the shape, size and

organization of the dispersed phase.

Basically, during a scattering experiment, a neutron beam, of wavelength λ, presenting a small

angular divergence, is sent on a sample and the resulting scattered intensity I(θ) is measured as

a function of the scattering angle θ (Figure A-20).

Figure A-20 Schematic view of a general scattering experiment [DRE05]

The scattering vector q allows assembling the data obtained at various configurations on the

same plot I(q) (Figure A-21):

θλ

π= sin.4q0

Equation A-13

where θ is the scattering angle (small, typically < 5°) and λ is the wavelength of the incident

radiation

The scattering vector is a spatial variable in the reciprocal space, so that, large structures

scatter at low-q and reciprocally. Typically, small angle neutron scattering gives access to sizes

between 0.5 and 100 nm.

In order to obtain information about the structure of the sample, the following conditions should

be fulfill: i) the particle diameter, φ, must be in the range: 1< q.φ <20, the limits of the scattering

vector being fixed by the experimental setup (due to the geometry), and ii) the contrast between

the scattering densities of the particles and continuous medium should be large enough.

Note: Why SANS?

The differences between the 3 types of scattering experiments directly lie on the specificity of

the beam / material interactions. X-ray and light beam are electromagnetic waves (of really

different λ), so the scattering level is correlated to the number of electron Z (low scattering for

every organic systems). On the contrary, neutrons interact directly with the nucleus, depending

http://www-drecam.cea.fr/



on the scattering length of the atoms composing a scattering centre, but with no dependence on

Z. SAXS and SANS give information about the same range of sizes, whereas the distances

reachable are larger through light scattering. Therefore these 3 techniques are complementary.

Additionally, SANS allows the study of thick samples (contrary to SAXS) as well as opaque

samples (contrary to light scattering experiments). Another specificity of SANS consists in the

possibility of contrast variation by substitution of selected atoms by isotopes (same Z, so no

variation for X-ray, but different scattering lengths for neutrons) as it is often used to obtain

further information on complex organic systems. For instance, one can resort to the mixing with

a deuterated solvent in order to extinguish one selected specie by matching the scattering

densities [ESP90 , QIU05].

Theoretical calculations related to SANS

The scattering intensity is generally written as [TEI88]:

)().(..².)( qSqPVqI ppφρ∆= Equation A-14

where ∆ρ is the difference between the scattering densities of the scattering object and of the

medium; φp is the volume fraction of scattering objects and Vp is the volume of the scattering

objects. P(q) is the form factor including information on the morphology of the scattering objects

and S(q) is the structure factor including information on the spatial correlation between the

scattering objects (Figure A-21).

1- High-q domain: the window is very small: there is a contrast

only at the interface between the two media.

2- Intermediary zone: the window is in the range of the size of the

elementary scattering unit in the systems. The form factor can be

measured (size, shape and internal structure of one particle).

3- Low-q domain: the observation window is large, and show the

structural order in the system, the structure factor can be obtained

allowing characterizing the interactions.

Figure A-21 Schematic windows analysed in a sample vs. scattering vector q and position of the

signal of each structure on the typical intensity profile [adapted from DRE05]

Often, two main simplified regions are distinguished within a scattering pattern:

− The “Guinier region” (Figure A-22), observed at low-q values (large distances), rather gives

information about the structuration in the sample. The scattering intensity can be written as:

I(q)

1

2

3





)q(S.3

²R².qexp)q(I g

⎟⎟⎠

⎞⎜⎜⎝

⎛−∝ Equation A-15

for q.Rg <<1, where Rg is the gyration radius of the object, and S(q) is the structure factor.

Note that the gyration radius is generally defined as the radius of the compact sphere where

all the weight of the aggregate has to be distributed to keep the same momentum of inertia.

Figure A-22 Schematic scattering curve in the Guinier region [CHE91]

− The “Porod region”, observed at high-q values (small distances), rather gives information

about the interfaces in the sample. The Porod behavior can be written as: α−∝ q)q(I , for q.Rg >>1 Equation A-16

For self-similarly rough surfaces (fractal), α is generally included between 3 and 4. The

surface fractal dimension can be deduced as: α= -6D s, with 2< Ds<3.

Ds=2 for a smooth and sharp surfaces.

If the particle distribution is statistically self-similar, the mass fractal dimension α=mD : with

Dm smaller than 3.

Thus, in first approximation, Ds and Dm can be obtained by the slope from the log-log plot of

the intensity as a function of the scattering vector.

Beaucage proposed unified equations to describe both Guinier and Porod domains [BEA95]:

( )( ) P3

gig

q6/R.qerf

.B3

²R².qexp.G)q(I

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛−= Equation A-17

in case of a mono-disperse distribution.

( )( )∑

=

+

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

n

1i

Pi3

gi)1i(gi

gii q

6/R.qerf.

3²R².q

exp.B3

²R².qexp.G)q(I Equation A-18

in case of n structural levels observed in the scattering pattern.

As the calculations connected with neutron scattering are not detailed furthermore here; the

reader can refer to other papers [ESP90, COT99, TEI86, 88] for additional information.



A.4.3.b. Experimental set up and configurations

Various small angle spectrometers were used (PACE, PAXE, PAXY) supplied respectively with

an isotropic detector for the former, and anisotropic detectors for the two latters. Since most

experiments were realized on the spectrometer PAXE, the experimental details are given here

only for this spectrometer (Figure A-23, Table A-1) but the reader can find additional details on

the LLB web site [LLB05].

Figure A-23 Experimental set up of the spectrometer PAXE [LLB05] (on the left); Automatic sample

changer for measurements carried out at room temperature (on the right)

Table A-1 Specifications of the spectrometer PAXE [LLB05]

Cold neutrons of wave lengths included between 6 and 25 A° were used in 3 configurations (so-

called c1, c2 and c3 and described in the Table A-2).The resulting q range was included

between 2. 10-3 and 0.15 A°-1. The spectra acquisition lasted about 20 minutes for each

configuration; it was rather fast due to the large scattering contrast between the organic medium

and silica particles.



λ (A°) Dsample-detect (m) qmin (A°-1) qmax (A°-1) c2 25 5 1,5E-03 7,0E-03 c1 13 5 4,0E-03 3,5E-02 c3 6 2,5 3,0E-02 1,5E-01

Table A-2 3 configurations used on the SANS spectrometer PAXE. λ: wave length, Dsample-detect: distance between the sample and the detector, and resulting scattering vector range (qmin-qmax)

A.4.3.c. Treatment of the data

The treatment of the data followed standard procedures in order to make the appropriate

corrections and calculate the absolute intensity (in cm-1), the softwares used were LLB-made:

1. Visualization and determination of the beam stop position and size using VISU (data

type Figure A-24)

2. Removal of the data of the beam stop using XYmasq

3. Gathering of the data of the cells corresponding to the same q-values (since our

samples are isotropic, an isotropic assembling of the cells was realized) using REGISO

4. Plotting of the pattern of the intensity as a function of the scattering vector I(q) and

realization of the corrections for each configuration (Figure A-25, Figure A-26) using

PASIDUR

The corrections realized allowed obtaining of the following spectra:

Equation A-19

Where: Isample is the signal of the sample after the 3 first steps, Iref is the signal of the reference

accounting for the incoherent scattering background i.e. matrix for the composites, solvent for

the suspensions, Iemptycell is the signal for the sample holder.

The thickness (e), transmission (T), and volume concentration (C) of the sample was taken into

account to adjust the level of each signal.

Solid samples of epoxy / silica composites were plates of about 1 mm thickness, and 20 mm

diameter and were observed directly without sample holder, whereas the suspensions were

observed into Helma quartz cells of 1 mm path length. The samples for kinetical measurements

were placed between two glass plates settled in an aluminum sample holder.

Eventually, for each sample, the 3 spectra obtained (after correction, step 4) were matched

using Origin or Excel by calculating a translation factor for the three configurations in order to

compensate the lowering of the neutron flow as wave length increases (Figure A-27).

),,(),,(

),,(),,(

2

1 )(CTeemptycellCTeOH

CTerefCTesample

IIII

cmI−

−=−

Ann

ex A

: The

oret

ical

bac

kgro

und

of th

e te

chni

ques

and

exp

erim

enta

l con

ditio

ns

Elo

die

Bug

nico

urt,

PhD

INS

A L

yon,

200

5 21

7

Step

by

step

illu

stra

tion

of th

e re

cons

titut

ion

of a

SA

NS

patte

rn I(

q)

for a

cro

sslin

ked

MD

EA-b

ased

sam

ple

fille

d w

ith 5

wt.

% o

f hyd

roph

ilic

silic

a of

spe

cific

sur

face

are

a 30

0m²/g

(5T-

D33

0-M

):

Fi

gure

A-2

4 S

chem

atic

illu

stra

tion

of th

e ro

ugh

data

ob

tain

ed fr

om a

n an

isot

ropi

c sp

ectro

met

er ty

pe P

AX

E:

inte

nsity

leve

l of t

he 6

4 x

64 c

ells

(1cm

² for

eac

h on

e), s

tep

1

Fi

gure

A-2

5 R

ough

I(q)

cur

ves

for t

he 3

con

figur

atio

ns b

efor

e st

ep 4

Figu

re A

-26

I(q) p

atte

rns

for t

he 3

con

figur

atio

ns a

fter s

tep

4, n

orm

aliz

atio

n re

aliz

ed u

sing

wat

er a

s st

anda

rd a

nd e

poxy

-am

ine

mat

rix a

s re

fere

nce.

The

co

rrec

tion

by th

e m

atrix

allo

ws

rem

ovin

g th

e in

cohe

rent

bac

kgro

und

at h

igh-

q.

Figu

re A

-27

Rec

onst

itutio

n of

the

over

all s

catte

ring

curv

e I(q

) in

abs

olut

e in

tens

ity

0.00

1

0.010.1110

1E-3

1E-2

1E-1

1E+0

q (A

-1)

I (AU)

c1 c2 c3

1E-3

1E-2

1E-1

1E+0

1E+1

1E+2

1E-3

1E-2

1E-1

1E+0

q (A

-1)

I (cm-1

)

c1 c2 c3

1E-2

1E-1

1E+0

1E+1

1E+2

1E+3

1E-3

1E-2

1E-1

1E+0

q (A

°-1)

I (cm-1

)

c1 c2 c3



A.4.4. Morphological changes during crosslinking

A.4.4.a. Small angle neutron scattering (SANS)

The SANS monitoring of the kinetics were realized in a thermo-regulated oven at 110°C (Figure

A-28). The other experimental details are the same as for the room temperature scattering static

measurements (A.4.3).

Figure A-28 Experimental setup for in situ monitoring of the kinetics by SANS

A.4.4.b. Confocal microscopy

The confocal microscope from Leica DMR was used at the Centre Commun de Quantimétrie of

Université Lyon 1 in collaboration with Yves Tourneur and Batoule Smatti.

Principle

In a confocal microscope, due to the conjugation between the focal image plan and a pinhole,

the contribution of afocal beams due to the neighboring plans in the sample, responsible for the

creation of noise, is removed from the image. From the recording of images of a thin sample at

various heights in the sample, one can rebuild a 3D-image with a high transversal resolution

(Figure A-29(a)).

This technique was used in order to try to elucidate the morphological evolution during the

crosslinking following a given zone in the sample with a higher resolution compared to

conventional microscopy. An acquisition mode called “time-laps” allowed programming the

recording of the images after given delays. A special set up was developed (Figure A-29(b)) in

order to allow carrying out the observations during the crosslinking in situ in an heating stage. A

special long working distance objective had to be used in order not to suffer from the heat.

Sample

Neutron beam

Thermo-regulated oven



UV laser at 352 nm

Fluorescence

Heating device at 135°C

Reactive system

Long-working distance objective x 500

Confocalmicroscope

Sample stage

Insulating quartz windows (a) (b)

Figure A-29 (a) Principle of the reconstitution of a 3D image of the sample from serial cuts using a confocal microscope, (b) experimental set up developed for the in situ observation of the morphological

evolution during polymerization by confocal microscopy, in fluorescent mode

Grafting of a fluorescent probe on the silica surface

In order to increase the contrast between the dispersed phase and the matrix, a fluorescent

probe was grafted on the silica surface (Figure A-30). In fluorescent mode, a UV laser excites

the emission of the chromophore at a lower wave length, and the image of the fluorescence of

the sample is recorded. The fluorescent probe might either react with the residual silanols on

silica surface, or just strongly physisorb. The grafting process consisted in a dissolution of the

fluorescent probe into THF, the silica was then added and stirred using a dissolver. The epoxy

was then mixed, and the THF was finally evaporated (Figure A-31).

Note: If the solvent removal is realized after the first step (i.e. without epoxy), upon drying the

silica strongly agglomerates and a really coarse silica dispersion into epoxy is finally obtained.

Figure A-30 Fluorescent probe used: O-4-methylcoumarinyl-N-[3-(triethoxysilyl)propyl]carbamate] from Gelest. UV max: 223, 281, and 319.5 nm, soluble in THF

Figure A-31 Process for the grafting of the fluorescent probe on the silica surface; fluorescent probe

content: 10-3 g/ g of silica

The fluorescence was then checked at room temperature, on a crosslinked sample (Figure

A-32), the morphology appears quite consistent with the usual agglomerated silica structures (~

5-10 µm) found in the amino-modified silica filled systems.

Fluorescent probe into THF

+ Amino-modified silica

Addition of the

DGEBA DER330

Extraction

of the THF Dispersion Dispersion

voxel pixel

Focal plan conjugated with the sample

Focal beam

Afocal beams

Pinhole



Figure A-32 Room temperature image of confocal microscopy in fluorescent mode of the crosslinked system 3A-D330-M modified with a fluorescent probe

However, unexpected problems arose at high temperature: loss of a part of the fluorescence as

well as difficulties faced to realize the proper alignment of the long-working distance objective

needed in confocal mode. Unfortunately, these problems could not be solved by lack of time.

Therefore, the only observations presented in the manuscript were finally realized in

transmission mode.

A.5. Mechanical characterization

A.5.1. Dynamic Mechanical Analysis (DMA)

The dynamic thermo-mechanical behavior was characterized using a Rheometric Dynamic

Analyser (RDAII), device allowing to measure the conservation modulus G', loss modulus G"

and loss factor tan δ as a function of the temperature requested, at a given strain. The samples

were rectangular bars measuring roughly 2-3 x 5-6 x 40 mm3. The temperature sweeps were

performed at a rate of 2°C.min-1 and a frequency of 1 Hz, generally between 80 and 230°C for

MDEA-based systems, and between -100 and 30°C for Jeffamine-based systems. The strain

applied was checked to belong to the linear domain in all the temperature range, it was typically

1% for Jeffamine-based systems and 0.5% for MDEA-based systems.

The temperature of the main mechanical relaxation, Tα, was evaluated at the temperature of the

peak of loss factor and the rubbery modulus was measured at Tα + 50K.

A.5.2. Tensile tests

A.5.2.a. Glassy systems

In order to characterize MDEA-based systems, which are glassy at room temperature, tensile

tests were performed using straight strain gages (from Vishay Micro-measurements) (Figure

250 µm250 µm



A-33). Stress- strain curves in the elastic region at low strain (typically < 0.5 %) were recorded

using a tensile machine of the INSTRON company, at 1 mm.min-1 (samples ~ 3 x15 x120 mm3).

Figure A-33 Experimental set up for tensile tests using gages for the glassy samples

A.5.2.b. Rubbery systems

Theory of rubber elasticity

The theory of rubber elasticity was applied in order to obtain the values of the elastic modulus.

This theory is based on two main hypotheses: the material is regarded as ideal (i.e. the chains

are dynamically flexible, do not present a preferred orientation, are long enough to be described

by a gaussian statistic, are ended by crosslinks and elastically active). The second hypothesis

lies in the affinity of the macroscopic deformation as a function of the motions of the crosslinks.

From these hypothesis, the variation of the true stress as a function of the extension ratio λ can

be expressed as follow:

)-(σ* 2 λλ −ρ= 1

McRT Equation A-20

where: σ∗=F/S is the true stress in the sample, F being the strength measured using tensile

tests and S= S0/λ is the true section at any time to take into account the reduction of the section

during the test, S0 being the initial section of the sample. λ=1+ε=l/l0, is the extension ratio of the

sample where ε=∆l/l0 is the sample elongation, l0 being the initial length of the sample. Mc is the

average molar mass between crosslinks.

For low deformations (typically < 20 %), the true stress can be approximated by the formula:

)(3ε*McρRTσ*= Equation A-21

where the Young modulus can be identified from the Hook’s law in “uniaxial” tensile test as:

McρRT3E= Equation A-22



Assuming that the Poisson coefficient is 0.5 for rubbery materials above their glass transition

temperature, the Coulomb modulus can be calculated as:

McRT

)1(2EG ρ≈

υ+≈

Equation A-23

Thus, the Coulomb’s modulus, G, can be obtained from the slope of the plot of the true stress σ*

as a function of λ²-λ-1, and the Young modulus E is then equal to 3G as it is illustrated in the

Figure A-34(b). An example of rough stress strain curve is also given in the Figure A-34(a).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1

ε (∆l/l0)

σ (M

Pa)

εmax

σmax

y = 0.522x

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3

λ²-λ-1

σ∗ (M

Pa)

(a) (b)

Figure A-34 Examples of tensile results test for the neat matrix (a) rough stress/ strain plot: εmax and σmax: respectively elongation and stress at break, (b) plot of the true stress σ* vs. λ²-λ-1 (slope: G~E/3)

Experimental conditions

Tensile tests on Jeffamine-based samples were realized on normalized samples (cut using a

dye type H3 which dimensions are given in the Table A-3, with a thickness included between 2

and 3 mm, using a tensile machine 2/M from MTS. The measurements were performed at room

temperature, at 10 mm.min-1, and continued till the sample fracture. The samples were

maintained using pneumatic clamping tools with a clamping pressure of 3 bars.

Table A-3 Dimensions (mm) of the samples used for tensile tests in the rubbery state

A.5.3. Crack propagation measurements (LEFM)

Linear Elastics Fracture Mechanics measurements characterize the resistance of the sample to

crack propagation; it assumes that fracture behavior of the materials is due to the larger defect

Sample



bBbafPKIc

.)/(.=

Figure A-35 Specifications of the samples used for toughness measurement in mode I (KIc), approximate dimensions of the samples: thickness B = 5-6 mm, height b ~ 2B, length

between knives L = 4B, total length ~ 80 mm

present in the sample. The procedure is based on the creation of a well-defined defect that will

be responsible for the fracture of the sample. First, the sample is notched at room temperature

using a diamond saw, a fine crack is then generated thanks to the impact of a thin blade, the

radius at the crack-tip must be very small. The fracture strength is then measured by 3-point

bending tests on these pre-notched samples (Figure A-35).

The mode I critical stress intensity factor, KIc can be calculated using the following formula: Equation A-24

where: a is the crack length, b is the sample width, P is the strength measured at fracture

(Newton), and f(a/b) is the shape factor defined from an empirical model.

Various models can be found in the literature for the shape factor, as the one used in this study:

Equation A-25

The results were the average of c.a. 8 measurements with 0.3<a/b<0.6.

A.6. Characterization of the thermal and combustion behavior

A.6.1. Differential Scanning Calorimetry (DSC)

Calorimetric measurements were realized on an instrument DSC30 Mettler Toledo under inert

atmosphere (argon flow at 10 ml.min-1), using a scan rate of 10K.min-1, between 25 and 250°C

for MDEA-based systems, and between -120 and 80°C for Jeffamine-based systems.

2/3

22/1

121

7.293.315.2199.16

)/(

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛

=

ba

ba

ba

ba

ba

ba

ba

baf

P 10 mm.min-1

B

b~2B

L=4B



A.6.2. Thermo-gravimetric Analysis (TGA)

The experiments were realized on a device TGA2950 from the company Thermal Analysis

Instruments. The loss of mass of samples was measured either under inert atmosphere

(helium), or under oxidizing atmosphere (air) using a heating rate of 10°C per minute between

room temperature and 600°C.

A.6.3. Cone calorimeter

Fire resistance measurements were realized in collaboration with Aleberto Fina and Giovanni

Camino from “Centro di Cultura per l'Ingegneria delle Materie Plastiche”, Politecnico Torino,

Sede di Alessandria using a cone calorimeter from the Fire testing Technology Ltd company.

The sample is submitted to a constant heat flux emitted by a conical heater (Figure A-36). From

the measurement of the oxygen consumption, the heat released rate (HRR) can be calculated

taking into account that the quantity of heat released vs. the quantity of oxygen consumed is a

constant for almost every material. By integration of HRR curve during the whole combustion

process, the total heat released can be obtained.

Figure A-36 Schematic description of a cone calorimeter

Samples consisted of square plates measuring c.a. 65 x 65 x 3 mm3 and the external heat flux

used was 35 kW/m², which corresponds to the level of a moderated home fire. The values

obtained can be compared between each other but not directly to a standard because the

conditions selected were not exactly alike ASTM standards (smaller samples used).

annex a. theoretical background on the techniques

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