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The Journal of Adhesion Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gadh20

Influence of Nanoparticles on the Coupling Between Optical Dipoles in Epoxy-Silica Nanocomposites During Network Formation a

a

a

Martine Philipp , Ulrich Müller , Pierre-Colin Gervais , Carsten b

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Wehlack , Wulff Possart , Roland Sanctuary , Joachim E. Klee & Jan K. Krüger

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Lehrstule für Funktionelle Materialien, Physik Department, Technische Universität München, Garching, Germany b

Chair for Adhesion and Interphases in Polymers, Universität des Saarlandes, Saarbrücken, Germany c

DENTSPLY, Konstanz, Germany

Version of record first published: 28 Jun 2012

To cite this article: Martine Philipp, Ulrich Müller, Pierre-Colin Gervais, Carsten Wehlack, Wulff Possart, Roland Sanctuary, Joachim E. Klee & Jan K. Krüger (2012): Influence of Nanoparticles on the Coupling Between Optical Dipoles in Epoxy-Silica Nanocomposites During Network Formation, The Journal of Adhesion, 88:7, 566-588 To link to this article: http://dx.doi.org/10.1080/00218464.2012.682875

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The Journal of Adhesion, 88:566–588, 2012 Copyright # Taylor & Francis Group, LLC ISSN: 0021-8464 print=1545-5823 online DOI: 10.1080/00218464.2012.682875

Influence of Nanoparticles on the Coupling Between Optical Dipoles in Epoxy-Silica Nanocomposites During Network Formation

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¨ LLER1, PIERRE-COLIN GERVAIS1, MARTINE PHILIPP1, ULRICH MU CARSTEN WEHLACK2, WULFF POSSART2, ROLAND SANCTUARY1, ¨ GER1 JOACHIM E. KLEE3, and JAN K. KRU 1

¨ r Funktionelle Materialien, Physik Department, Technische Universita¨t Lehrstule fu ¨ nchen, Garching, Germany Mu 2 Chair for Adhesion and Interphases in Polymers, ¨ cken, Germany Universita¨t des Saarlandes, Saarbru 3 DENTSPLY, Konstanz, Germany

High-performance refractometry and infrared spectroscopy are combined in order to elucidate the gelation process and the glass transition during the network formation of epoxies and epoxy-based nanocomposites. Whereas infrared spectroscopy yields the chemical conversion due to the opening of oxirane rings during the covalent network formation, high-performance refractometry is extremely sensitive to the accompanying changes of the arrangement of the molecular network. In accordance with the Lorentz-Lorenz relationship, the evolution of the refractive index seems to reflect that of the mass density during polymerization of the epoxy-based systems within the limits of a few percent. The slight deviations from the Lorentz-Lorenz relationship, which occur during the gelation of the epoxy-based systems, are attributed to long-ranged dipoledipole interactions, which respond at optical frequencies. This point of view is supported by the fact that chemically inert silica nanoparticles embedded in the pure epoxy matrix as disturbances for these dipole-dipole interactions are able to diminish or even to suppress totally this excess contribution of the refractive index. Received 22 July 2011; in final form 22 November 2011. One of a Collection of papers honoring Wulff Possart, the recipient in February 2012 of The Adhesion Society Award for Excellence in Adhesion Science, Sponsored by 3M. Address correspondence to Martine Philipp, Lehrstuhl Fu¨r Funktionelle Materialien, Physik Department, Technische Universita¨t Mu¨nchen, Garching, Germany. E-mail: martine. [email protected] 566

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KEYWORDS Covalent network formation; Dipole-dipole interactions; Epoxy; Gelation; Refractive index

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1. INTRODUCTION The transformation of liquid materials into amorphous solids during polymerization is of high technological relevance [1–5]. Typical examples are structural adhesives, like epoxies, which change during curing from an initially liquid state to rigid adhesive joints so as to support significant mechanical loads during their lifetime [1–5]. The important variations of mechanical properties during polymerization [3–7] are due to the increasing number of network knots formed within the adhesive. This formation of covalent bonds is accompanied by a modification of molecular interactions and densification. For many adhesives during the polymeric network formation the sol-gel transition precedes the vitrification. One frequent definition of the gel state, which is also adopted in this article, claims that the gel state is reached when for the first time the polymeric network spreads throughout the whole sample and, thus, confers static shear stiffness to the adhesive [6,8–10]. The high mechanical stability of cured adhesive joints premises that the structural adhesive has also undergone a chemically induced glass transition during polymerization. Note that in the glassy state often only local motion and vibrations of molecular chains or chain segments are possible. Only if a concurrent driving force, like a chemical potential related to chemical reactions, exists, molecules can diffuse over macroscopic distances and may lead to a slowly ongoing polymerization in the glassy state [6,8–10]. (The diffusion of solvents of low molecular weight is not considered in the following.) The evolution of mass density during polymerization of epoxy adhesives has been the topic of several experimental studies (e.g., [11–13]). Essential experimental challenges were encountered during these investigations, as densitometers are usually either well-suited for low-viscous liquids or for solids, but not for sticky, jelly-like substances [11]. In line with this, the self-built densitometer setups introduced by different research groups [11,12] lead to controversial mass density evolutions during polymerization of epoxies. To our assessment, the most reliable investigations have been made by Holst et al. [11]. In their opinion, a linear evolution of mass density versus chemical conversion holds true until the occurrence of the chemically induced glass transition for the studied anhydride cured epoxy [11]. The motivation for the current study results from the question of how far optical refractometry is suited as an alternative to densitometry in the case of curing epoxies. Indeed, a simple relationship, the Lorentz-Lorenz relation [14–18], is a commonly used and elegant method for estimating the mass density from the refractive index of many simple liquids and polymers within a margin of error of less than one percent [19–22]. The Lorentz-Lorenz relation

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is only exactly valid for very simple fluids [15,16]. Remember that the refracto the dielectric properties measured at optical fretive index, nD, is related pffiffiffiffiffiffiffiffiffiffiffiffiffiffi quencies (nD ðxopt Þ ¼ eðxopt Þ, xopt: optical frequency, e: relative dielectric permittivity), which stem from the electronic polarizability, the molecular bond polarizability, and the molecular arrangement [14–16]. This means that different factors account for the refractive index, more precisely for the electronic polarizability at optical frequencies: the electronic dipole number density (being roughly proportional to the mass density), the strength of the electronic dipoles, interactions between electronic dipoles, the conformations and the arrangement of the polymeric network chains, etc. [14–16,19–22]. In the frame of the Lorentz-Lorenz relationship, all of these contributions, except of the first one which is linked to the mass density, are described by one common material-dependent parameter, the specific refractivity. This implies that changes of the refractive index caused by the influence of external or internal thermodynamic variables can be used for the unique determination of the related mass density variations, only if the accompanying variation of the specific refractivity can be neglected. If, on the other hand, for a given material the changes of the mass density and the refractive index are determined independently, variations of molecular bond polarizabilities, dipole-dipole interactions, spatial molecular arrangements, etc., can be estimated. More technical advantages of commercial refractometers compared with densitometers are related to the high accuracy of high-performance refractometers, which is better than one part in 104, and their comparably easy handling. Moreover, refractometry is an invasive, non-destructive technique that permits fast data accumulation with a time resolution of seconds. Technologically relevant epoxy compositions were studied for this article. The resin diglycidyl ether of bisphenol A and the liquid hardener diethylene triamine were used to produce room temperature-cured epoxies. To assess the progress of polymerization, the temporal evolution of the formation of covalent bonds was analyzed by infrared spectroscopy [23]. In order to record the datasets under similar experimental conditions, the refractive indices and the degrees of curing were always determined simultaneously for one given sample batch at the same temperature. Based on the representation of the refractive index versus chemical conversion, a discussion follows about how far the refractive index evolution represents that of the mass density for the chosen epoxy systems. Deviations from the Lorentz-Lorenz behavior, which were already observed during the chemically induced gelation of epoxies based on the same resin and hardener [24], are recapitulated. In this context, the role of electronic dipoles related to molecular interactions and polymeric chain conformations during the epoxy network formation is elucidated. More recent investigations described in the following concentrate on the role of widely investigated chemically inert silica nanoparticles [25–29] on the curing process of the nanocomposites. As the nanoparticles are assumed to modify already by their

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mere presence the topology of the epoxy network around the nanoparticles, a central question is in how far this topological effect affects the mass density and the refractive index of the nanocomposite. Moreover, it is unclear how far the interphase regions between nanoparticles and epoxy contribute in an additional manner to the refractive index, for instance by means of induced electronic polarizabilities.

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2. SAMPLES AND SAMPLE PREPARATION As an excellent transparency of the nanocomposites in the visible and midinfrared ranges of the electromagnetic spectrum is a prerequisite for the investigations, we chose highly transparent, commercially available products. Nanopox1 A410 from Nanoresins AG, Geesthacht, Germany, was used as an epoxy resin. The average molecular weight of the resin equals to 354 g=mol, corresponding to a high concentration of diglycidyl ether of bisphenol A (DGEBA) monomers. This material consists of DGEBA filled with silica nanoparticles according to the mass ratio DGEBA=silica (100=67). According to the manufacturer these amorphous silica nanoparticles have an average diameter of 20 nm [25] and possess a hydrophobic silane coating on their surfaces. Due to the almost complete absence of particle clustering, optical Mie scattering cannot be observed for the filled resin. In contrast to other silica nanoparticles, these hydrophobically coated nanoparticles were shown not to modify the reaction pathways between DGEBA and the hardener diethylene triamine (DETA) [25,30,31]. DETA, which is liquid at room temperature, was obtained from Fluka Chemie GmbH, Buchs, Switzerland. The refractive indices of these materials are indicated in Table 1. Four mass ratios of DGEBA=silica nanoparticles were chosen: (100=0), (100=11), (100=25), and (100=67), respectively, by diluting the Nanopox A410 with the same type of DGEBA (purchased from Nanoresins AG, Geesthacht, Germany), if necessary. For these four samples a slightly overstoichiometric mass ratio of 100 g DGEBA to 14 g DETA was selected, which corresponds to a technologically relevant mixture of DGEBA and DETA [6,7,24,32,33]. Note that the stoichiometric DGEBA=DETA mass ratio equals to (100=11.6) [24]. According to the model of Bansal and Ardell [34], for the selected nanocomposites the mean surface-to-surface interparticle distance between the silica nanoparticles varies between roughly 25 and 6 nm TABLE 1 Refractive Indices of the Components of the Nanocomposites at Room Temperature

nD

Nanopox1 A410

DGEBA

Silica nanoparticlesa

DETA

1.545
0.001

1.571
0.001

1.48
0.02

1.482
0.001

a Estimated nD using a linear mixing rule for Nanopox1 A410 and DGEBA. The term ‘‘silica particle’’ should be understood as the pure silica core and its silane shell.

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TABLE 2 Some Properties of the Samples at 295 K Sample

Vol%a

Interparticle distance=nmb

Extrapolated nD for a ¼ 0%c

Calculated nD for a ¼ 0%

EP EP EP EP

0 5
1 11
1 25
1

= 23
3 14
2 6
1

1.556
0.001 1.553
0.001 1.549
0.001 1.537
0.001

1.556
0.001 1.553
0.001 1.548
0.001 1.537
0.001

(100=0=14) (100=11=14) (100=25=14) (100=67=14)

a

Absolute increase of volume percentage estimated to be below 1% during the curing. According to the model of Bansal and Ardell [34]. c Gained by linear extrapolation of nD towards a ¼ 0% in Fig. 6a.

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b

depending on the filler content (see Table 2). In the following, the samples are all designated by their respective DGEBA=silica=DETA mass ratio. In addition to these four sample types, an epoxy with a high excess of amine was used: (100=0=61). To produce well-mixed epoxies and nanocomposites, the hardener DETA was added to the glass vessels containing the different resins; afterwards the samples were stirred at room temperature for 5 minutes. The moment of adding the hardener to the resin was taken as the start time of the curing. The relevant groups of the epoxy reaction are the oxirane groups of DGEBA and the primary and secondary amine groups of DETA [32,33]. During curing at 295 K, the epoxy (100=0=14) successively undergoes the sol-gel transition and the glass transition [24]. If a 1-hour postpolymerization step at 393 K is applied to the room temperature cured epoxy (100=0=14), in order to consume all oxirane groups, the glass transition temperature of the epoxy lies at about 403 K [32,33]. On the contrary, the sample (100=0=61) remains liquid after room temperature polymerization and can be considered as a solution of amino-terminated epoxide-amine addition products [24]. Sample droplets of a volume of some microliters were investigated simultaneously on the prisms of both experimental techniques. The evolution of the refractive index and the degree of curing was, thus, always determined simultaneously for one given sample batch at 295
0.5 K, in order to record the two datasets for each adhesive under similar experimental conditions. Due to technical reasons concerning the infrared spectrometer, the investigations had to be performed at 295 K and not at 298 K as in reference [29]. After the polymerization, the glassy adhesives were removed from the prisms by swelling the epoxy networks with dimethyl formamide.

3. EXPERIMENTAL TECHNIQUES AND THEORETICAL BACKGROUND 3.1. Abbe Refractometry The high-precision, computer-controlled Abbe-type refractometer Abbemat1 from Anton Paar OptoTech, GmbH, Seelze, Germany, allowed recording the

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refractive index every minute during the maximal 18 hours of isothermal curing of the samples. The optical wavelength is equal to 589 nm (sodium D-line). This refractometer possesses the high absolute accuracy of 2  105 and a relative accuracy of 106. The measurement chamber was specially sealed against moisture [35] in order to avoid water-induced demixing processes of the reacting epoxies [36]. The temperature of the prism made of yttrium aluminum garnet was stabilized at 295 K with an absolute precision of 0.03 K using a Peltier thermostat. The amplitude of long-time fluctuations is estimated to be smaller than 0.01 K. In the following, the link between the measured refractive indices of the samples and their molecular dielectric properties is presented [15,17–19]. The refractive index, nD equals the square root of the relative dielectric permittivity, e, as measured at optical frequencies xopt: nD ðxopt Þ ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi eðxopt Þ:

ð1Þ

The relative dielectric permittivity reflects the properties of the molecular electric dipoles, averaged on a macroscopic level. Note that, in the present case, only the electric dipoles which are relevant at optical frequencies play a role. These are the electronic dipoles, which result from the shifting of the electron cloud versus the positively charged nuclei. It should be stressed that different factors account for the relative dielectric permittivity at optical frequencies. It is indeed not only the electronic dipole number density, which is roughly proportional to the mass density. In addition, the strengths of the various electronic dipoles, interactions between electronic dipoles, their arrangement related to the conformations of the polymeric network chains, etc., can play a significant role [15,16,19–22]. From these explanations it follows that in general no simple algebraic relationship exists between the molecular electronic dipoles and the phenomenological quantity ‘‘refractive index’’. Only for very simple systems like non-interacting gases is an exact algebraic expression, the Lorentz-Lorenz relation, valid. It relates the mass density, qLL, to the refractive index, nD, whereas other contributions to the electronic polarizability are considered by the material-dependent parameter ‘‘specific refractivity’’ r: 1 n2  1 : qLL ¼  D r n2D þ 2

ð2Þ

Albeit, the Lorentz-Lorenz relation is frequently used as an elegant method for estimating the mass density from the refractive index of many liquids and polymers within a margin of error of less than one percent. In this approach, the contributions to the electronic polarizability related to the strength and interactions between dipoles as well as the conformations

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and the arrangement of the polymeric network chains are also incorporated in the specific refractivity. A commonly adopted strategy for estimating the specific refractivity relies on the group contribution method proposed by Goedhart [37]. For this purpose, tables containing approximate values of the molar refractivities of a large number of molecular groups were introduced [38]. In order to estimate the molar refractivity of a given material, only the molar refractivities of the involved molecular groups are summed up. The group contribution method, thus, neglects the contribution to the electronic polarizability arising from possible interactions between different molecular groups. The group contribution method was applied to estimate the specific refractivities of the unreacted DGEBA=DETA mixtures (100=0=14) and and r ¼ (0.2894
(100=0=61), yielding r ¼ (0.2853
0.0005) cm3=g 3 0.0005) cm =g, respectively. As expected, these values lie in between those of pure DGEBA monomers, r ¼ (0.2833
0.0005) cm3=g, and DETA, r ¼ (0.2993
0.0005) cm3=g. Within the margin of error, the specific refractivity values estimated for the unreacted epoxy mixtures agree well with the respective values determined by experimental methods [29]. In a next step, the specific refractivities of the room temperature cured epoxy mixtures were estimated, by taking into account the finally achieved chemical conversion of the epoxies (see Section 4). For the epoxies, the specific refractivities, as determined by the group contribution method, rise only slightly during polymerization, as the specific refractivities of the room temperature-cured epoxies EP (100=0=14) and EP (100=0=61) equal r ¼ (0.2855
0.0005) cm3=g and r ¼ (0.2897
0.0005) cm3=g, respectively. Hence, in the framework of the group contribution method, the specific refractivities of the selected epoxies remain constant during room temperature curing within the margin of error.

3.2. Attenuated Total Reflection Infrared Spectroscopy All measurements were performed on a modified FTS 3000 Excalibur1 infrared spectrometer from Bio-Rad=Digilab, Mu¨nchen, Germany, in the mid-infrared range in the geometry of attenuated total reflection. The prism was made of zinc selenide. The modification of the spectrometer consists in the automated cooling system of the detector. During the first 18 hours of isothermal curing of the epoxies, a software-controlled recording of the infrared spectra took place every 15 minutes. In all experiments, the angle of incidence of the s-polarized incident beam equals 60. Both prism and sample were enclosed in a measurement chamber under nitrogen atmosphere. The temperature of the measurement chamber may be subjected to longterm fluctuations of 0.5 K around 295 K. The calculation of the chemical conversion from the measured infrared spectra is described below [32,33]. First, the temporal diminishing of the

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height of a band, which corresponds to a molecular group that reacts during curing, must be determined. As usual, the oxirane band at 915 cm1 is chosen for this purpose (see Fig. 1). For each spectrum, the height of the oxirane band hoxirane(t) is divided by the height of the phenylene band hphenylene(t) at 1510 cm1. This band acts as a reference band, which is independent of the polymerization process. The division of the height of both bands allows for excluding atmospheric influences on the evaluation, which could result, for instance, from small temperature fluctuations inside the measurement chamber. Moreover, it takes into account that the refractive index of the epoxies grows continuously during polymerization (see Fig. 5a) and, hence, the penetration depth of the beam into the sample as well as the studied sample volume. The chemical conversion, given in percent, equals to: "

#  hoxirane ðtÞ hphenylene ðtÞ   100: aðt Þ ¼ 1  hoxirane ðt ¼ 0hÞ hphenylene ðt ¼ 0hÞ

ð3Þ

The heights of the bands related to the oxirane group hoxirane(t ¼ 0h) and the phenylene group hphenylene(t ¼ 0h) of the unreacted liquid mixtures are estimated by a superposition of the infrared spectra of the reactants [32,33]. It ensues from the infrared spectra of the epoxy=silica nanocomposites depicted in Fig. 1 that in the mid-infrared range the spectral features of the

FIGURE 1 Detail of the infrared spectra of the pure epoxy (100=0=14) and the three epoxy-silica nanocomposites in the mid-infrared range recorded after 11 min of polymerization. The vertical lines specify the wavenumbers chosen for the definition of the baselines for the oxirane band (949 cm1 and 892 cm1) and the phenylene band (1547 cm1 and 1400 cm1), respectively. (Color figure available online.)

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silica nanoparticles are especially pronounced around 1100 cm1. However, the spectral features of the nanoparticles lie neither significantly in the wavenumber interval of the oxirane band, nor in that of the phenylene band. Hence, the usual data evaluation for the pure epoxy (100=0=14) described above can also be applied to the nanocomposites [32,33]. Irrespective of the samples, and accounting for all sources of uncertainties, the absolute error for the chemical conversion is estimated to lie below 5%.

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3.3. Theoretical Background of the Experimental Techniques Both experimental techniques, the Abbe refractometry and the attenuated total reflection infrared spectroscopy benefit from the total internal reflection of the incident electromagnetic wave to access the desired information about the refractive index and the infrared absorption spectrum, respectively [16,23]. In order to elucidate the phenomenon of total internal reflection, first the behavior of a light beam incident on a planar surface is discussed as a function of its angle of incidence, u. As shown in Fig. 2, in general the incident light beam impinging on an interface between two media is split at the interface into two beams: a reflected and a refracted light beam. The angle of the refracted  beam, h, is related to the incident angle by Snell’s law: h ¼ Arc sin

nk0 prism nk0 sample

sin u , where nk0 prism and nk0 sample represent the real

part of the refractive indices of the prism or the sample. The absorption of light by the sample and the prism is accounted for by using complex refractive indices, nk0 :

FIGURE 2 Schematic representation of the reflection and refraction of a light beam impinging onto the interface between two media under an angle of incidence u. h: angle of refraction; nk0 prism , nk0 sample : real part of the refractive index of the prism or the sample.

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nk0 ¼

qffiffiffiffiffiffi ek0 ¼ nk0 þ i  Kk0 ;

575

ð4Þ

with k0 representing the vacuum wavelength of the light beam, ek0 ¼ e0k0 þ i  e00k0 the complex relative dielectric permittivity, and Kk0 the extinction index. The extinction index considers the different types of intensity losses of the electromagnetic wave, like absorption and scattering processes. Note that absorption of the infrared light by the sample is crucial for the measurement principle of infrared spectroscopy. Actually, the intensity of the incident infrared beam which is absorbed by the sample needs to be exactly determined in dependence of the wavelength (or wavenumber). The measured infrared spectrum finally yields information about the relevant absorption mechanisms in the sample, regarding different types of molecular vibrations and rotations [23]. On the contrary, the absorption in the visible range of the electromagnetic spectrum is almost negligible for the studied samples. Hence, only the real part of the refractive index needs to be considered in the case of optical refractometry. The reflection and transmission coefficients of the reflected and transmitted light beams resulting from the incident beam impinging on the interface between both media depicted in Fig. 2 are described by Fresnel’s equations [16,39]. The reflection coefficients, Rp and Rs, for p- or s-polarized incident light beam under an angle of incidence, u, are given by: 

Rp u; k0 ; nk0 P=S





qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 nk02P=S  sin2 u ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 nk02P=S cos u þ nk02P=S  sin2 u nk02P=S cos u 

ð5Þ

and  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2   cos u  nk02P=S  sin2 u Rs u; k0 ; nk0 P=S ¼  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 : cos u þ nk02P=S  sin2 u

ð6Þ

n

Here nk0 P=S ¼ nk0 sample describes the quotient of the complex refractive k prism indices of the sample0 and the prism. Because of energy conservation the transmission coefficients are given by: Tp ¼ 1  Rp and Ts ¼ 1  Rs. For a sample being optically less dense than the prism, i.e., nk0 sample < nk0 prism , the critical angle of total internal reflection is defined by:   utotal reflection ¼ Arc sin nk0 P=S :

ð7Þ

If the angle of incidence is larger than utotal reflection, the intensity of the transmitted beam equals zero. Hence, all light of the incident beam, which

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has not been absorbed by the prism or the sample, is reflected. This explains the choice of the expression ‘‘total internal reflection’’ for this phenomenon. In the case of Abbe refractometers the intensity of the reflected light beam is determined versus the angle of incidence, u. Actually, the principle of measurement is based on the exact determination of the borderline between the bright zone (total internal reflection) and dark zone (reflection and transmission) of the light beam reflected at the interface between the prism and the sample. Knowing the refractive index of the prism, Fresnel’s equations, Eqs. (5) and (6), allow one to determine the refractive index of the sample with high precision. In the case of total internal reflection a so-called evanescent wave propagates a distance of the order of the wavelength along the interface between the prism and the sample before leaving the prism as the reflected light beam (Goos-Ha¨nchen effect [16,39]). Within the sample, the evanescent wave decays exponentially in the direction perpendicular to the interface. The penetration depth of the evanescent wave into the sample, ddepth, depends on the wavelength, k0, of the incident beam, the angle of incidence, u, and on the refractive indices of the prism and sample: ddepth ¼

k0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : 2p  nk0 Pr ism sin2 u  n2k0 P=S

ð8Þ

The penetration depth of the evanescent wave, hence, co-determines the information volume within the sample, which is probed by the experimental technique. The thickness of the information volume lies in the 100 nm range for refractometry and in the micron range for infrared spectroscopy. Consequently, both Abbe refractometry and attenuated total reflection infrared spectroscopy are rather surface-sensitive techniques. The question then arises as to how far the bulk properties of the samples coincide with their near-interface properties as determined in the vicinity of the prism. For both experimental techniques it was actually verified that the prism does not induce any relevant molecular orientation or segregation of DGEBA, DETA, epoxy oligomers, and silica nanoparticles within the samples.

4. RESULTS AND DISCUSSION In the framework of the Flory-Stockmayer theory [24,40], the (100=0=14) epoxy is expected to undergo a chemically induced sol-gel transition close to a degree of curing of a ¼ 57%. The strongly rising shear viscosity observed by Baller et al. [25] in the vicinity of a ¼ 38% during rheological investigations of this technologically relevant epoxy composition are consistent with these findings. Moreover, during room temperature curing a chemically induced glass transition was observed for this epoxy at a  62%, as witnessed by

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the kink-like evolution of the reaction rate versus chemical conversion curve [24]. This kink-like evolution is interpreted as follows: in the glassy state the polymerization is highly decelerated, but still leads to an increase in the degree of polymerization of a few percent in the course of some hours. The step-like evolution of the specific heat capacity during curing, as given by temperature modulated differential scanning calorimetry, supports the occurrence of the glass transition at about 62% of curing [25]. As the chemically induced sol-gel transition and the glass transition are only separated by about 5% of chemical conversion, it was unclear as to how far both transition phenomena influence each other during curing. The possible interdependence of both transitions was studied in an article by Mu¨ller et al. [24], where the curing and transition behavior of strongly varying epoxy compositions was analyzed. In the following, the polymerization and transition behavior of the almost stoichiometric epoxy will be compared with that of a highly overstoichiometric epoxy, which does actually not undergo any transition at all during polymerization. This (100=0=61) epoxy system only evolves from a low-viscosity liquid to a highly viscous liquid, which can be described as a solution of amino-terminated epoxide-amine structures [24]. For these two epoxy systems, Fig. 3 depicts the corresponding refractive indices, nD(a), versus the chemical conversion, a, during room temperature

FIGURE 3 Refractive index, nD(a) (solid symbols), and mass density, qLL(a) (calculated using the Lorentz-Lorenz relation; open symbols), versus chemical conversion during isothermal curing of two epoxies. R1, R2, and R3: liquid, gelatinous, and glassy ranges, separated in the graph by vertical lines. Two solid straight lines: display the linearity of the range R1 for both epoxies. Two dashed straight lines: indicate the expected true evolution of the mass density for both epoxies.

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curing. Obviously, the refractive index behaves strongly nonlinear versus chemical conversion for both epoxy compositions. This nonlinear evolution of the refractive index is in contrast to observations for different polyurethane systems, for which the authors recorded an almost linear nD(a)-relationship [41]. First, a mere description of the nD(a)-curves for the epoxies will be given, prior to an in-depth discussion of these findings. The initial linear part of the curves shown in Fig. 3, reaching until a ¼ 22% for the (100=0=14) epoxy and until a ¼ 70% for the (100=0=61) epoxy, is assigned to a first range, R1. Subsequently, both nD(a)-curves significantly deviate from linearity. The upwards bending of nD(a) is allocated to a second range, R2. In accordance with the observations made in [24], this second range is called the ‘‘range of gelation’’. Indeed, increasingly large epoxy structures develop for the (100=0=14) epoxy during the range of gelation and the sol-gel transition, which occurs at a  57%, lying in the strongest upward bending of R2. In the case of the (100=0=61) epoxy, larger amino-terminated epoxideamine structures are created in range R2, which corresponds to the formation of mesoscopic gelatinous epoxy structures. Note that for the (100=0=61) epoxy, about 50% of the total increase in refractive index unexpectedly occurs within R2, i.e., during the last 30% of curing. This fact appears quite astonishing, but is experimentally well-established as the experiments were repeated several times. For the (100=0=61) epoxy, the strong upwards bending of nD(a) stops at a degree of polymerization of 100% when all oxirane groups (but not all primary and secondary amine groups) have been consumed. On the contrary, for the (100=0=14) epoxy the range of gelation is finalized by the glass transition. As soon as the glass transition has occurred at a chemical conversion of about 62%, the refractive index remains almost constant versus the degree of curing. Hence, the slowly ongoing polymerization in the glassy state, leading to a maximal degree of curing of about 65% in this experiment, does not lead to a significant modification of the refractive index. This third range, R3, is called the ‘‘glassy range.’’ To the best of the authors’ knowledge, no investigations about the evolution of the refractive index upon solidification of epoxies have been carried out by other research groups. Even though little is known about the evolution of the mass density of epoxies during curing because of the inherent experimental difficulties mentioned in the Introduction, at least some datasets for the evolution of mass density upon curing exist. In order to compare our data with the density data from the literature, the applicability of the Lorentz-Lorenz relationship with specific refractivities estimated on the base of the group contribution method (see Section 3.1) is first assumed. As discussed in Section 3, for many liquids and polymers the Lorentz-Lorenz relationship [see Eq. (2)] allows us to estimate the mass density from the refractive index in an elegant manner; the error made is actually often less than one percent. Using these calculated specific refractivities and the measured refractive indices, the Lorentz-Lorenz relationship leads to the mass

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density curves, qLL(a), given in Fig. 3. In this section, the notation ‘‘LL’’ marks that the mass densities were determined using the Lorentz-Lorenz relationship. Both mass density curves of Fig. 3 are strongly nonlinear and possess qualitatively the same characteristics as the refractive index curve of the respective epoxy composition. The definition of the three ranges can, hence, be maintained. Note that for the (100=0=61) epoxy qLL(a) shows about 50% of the total increase of mass density during the last 20% of polymerization! Such a strong increase of the mass density in the liquid state seems quite implausible. For the (100=0=14) epoxy a pronounced qLL(a)-increase appears in the gelation range, R2, between 20% and 60% which amounts to more than 60% of the total increase of mass density. As soon as the glass transition has occurred at a  62 %, qLL(a) saturates in this sample. According to Holst et al. [11], for epoxies an almost linear evolution of the mass density, q(a), at least until the occurrence of the glass transition, is expected. Since the epoxy reactants studied in that paper are different from the ones in the present article, the claimed linearity of q(a) until the occurrence of the glass transition can, of course, not be considered as a generally valid statement, independent of the exact nature of the curing epoxy system. But at least it can be judged as a strong hint for the linear mass density evolution in the range of gelation. Furthermore, it appears hardly understandable why the mass density, q(a) should increase with an almost vertical tangent at the end of polymerization for the (100=0=61) epoxy, as this system remains liquid until the end of polymerization (provoked by the consumption of all oxirane groups). Indeed, how should the molecular packing improve so much as to lead to an as pronounced volume shrinkage of the liquid epoxy? Based on these two arguments, the authors surmise that the nonlinear increase of the refractive index in the gelation range R2 of both epoxies is not caused by an increase in mass density. In that case, the question is which optically relevant phenomenon is responsible for the excess refractive index contribution in range R2. In accordance with literature data [11], the almost horizontal evolution of the mass density, qLL(a), in range R3 for the (100= 0=14) epoxy is attributed to the existence of a rigid and dense polymeric network. In line with these arguments, the dashed lines displayed in Fig. 3 are tentatively attributed to the true evolution of the mass density, q(a), in the liquid and gelatinous state. Notice that the mass density curves qLL(a) deviate for each degree of curing by less than 2% from the dashed lines for both epoxy systems. Hence, the Lorentz-Lorenz relation seems to be also applicable for the current epoxies with the usually surmised accuracy of, at maximum, a few percent. A higher precision for the estimated mass densities qLL(a) seems to be only attained for sure for the linear part of the nD(a)curves in the first range, R1. As the nonlinear increase of the nD(a)-curves in the second range is not attributed to an effect related to mass density, it must be clarified what contributes to this nonlinear increase of the refractive

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index, or this excess electronic polarizability. Assuming that the LorentzLorenz relationship is exactly applicable in dependence of the degree of curing for the epoxies, the specific refractivity, r, must vary upon gelation. According to the group contribution method, the pure modification of chemical groups upon the reaction of oxirane groups with primary or secondary amine groups is not responsible for any significant change in the specific refractivity. Hence, the interactions between the molecular groups and chains within the curing epoxies should be at the origin of the excess polarizability. That is why, in the following, the impact of a modification of the dielectric properties on a local scale will be studied for the epoxy (100=0=14). To this end, chemically inert nanoparticles, which do not modify the reaction pathways between DGEBA and DETA, were inserted into the epoxy prior to polymerization. The same hydrophobically silanized silica nanoparticles as studied in [25] were used, for which chemical inertia concerning the epoxy reaction mechanisms was demonstrated [25]. The impact of these particles on the excess polarizability will be the focus of interest. Figure 4 shows the smooth temporal evolution of the chemical conversion, a(t), for the (100=0=14) epoxy and the three related epoxy-silica nanocomposites during the isothermal polymerization. All curves steeply increase at the beginning of the experiment and start to saturate after about 5 h. In the limit of the experimental accuracy of better than 5%, all a(t)-curves represented in Fig. 4 can be interpreted as coinciding. This feature clearly underlines the assumed negligible effect [25] of the silica nanoparticles on the temporal evolution of the reaction mechanisms, e.g., catalysis does not play a role. As no different spectral features arise during polymerization in the infrared spectra of the

FIGURE 4 Temporal evolution of the chemical conversion, a(t), for the pure epoxy (100= 0=14) and the three related epoxy-silica nanocomposites during isothermal polymerization. (Color figure available online.)

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nanocomposites compared with those of the pure epoxy (not shown), the network formation seems to proceed in a similar way for all samples. A remarkable aspect of the four curves in Fig. 4 is that about 35% of the oxirane groups do not react, although a chemical conversion of 100% oxirane groups is possible by considering the stoichiometry of the samples. The chemically induced glass transition, occurring at a  62%, is in fact responsible for a strong deceleration of the chemical reaction. Within the margin of error of the present measurements, and in concordance with the literature [25], the degree of polymerization at which the chemically induced glass transition appears is not modified by the filler concentration. The investigations of Baller et al. [25] strongly suggest that not only for the pure epoxy (100=0=14), but also for the related nanocomposites, the glass transition is preceded by the sol-gel transition. However, the percolation threshold of the nanocomposites, which may depend on the nanoparticles, could not be quantified until now [25]. The temporal development of the refractive indices, nD(t), indicated in Fig. 5a, was measured simultaneously with the infrared spectra for each of the four sample batches. Using a linear volume mixing rule for the refractive indices of the freshly prepared epoxy mixture, nD epoxy(a ¼ 0%) ¼ 1.556
0.001, and of the silica particles, nD silica ¼ 1.48
0.02 (see Table 1), the experimentally determined refractive indices at a ¼ 0% can be well reproduced by calculation for the nanocomposites (see Table 2). As the refractive index of the nanoparticles does not change during the polymerization of the epoxy, the temporal increase of the refractive index accompanying the polymeric network formation can be written as follows: DnD ðt; cÞ ¼ nD ðt; cÞ  nD ðt ¼ 0h; cÞ;

ð9Þ

FIGURE 5 Temporal evolution of (a) the refractive indices, nD(t), and (b) DnD(t) ¼ nD(t)  nD(t ¼ 0h), for the pure epoxy (100=0=14), and the three related epoxy-silica nanocomposites during isothermal polymerization. (Color figure available online.)

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with c ¼ 0, 11, 25, 67 characterizing the loading of silica nanoparticles. A basic assumption made at this point is that the increase of the volume concentration of the silica within the epoxy matrix, caused by the epoxy shrinkage during polymerization, is insignificant, i.e., even below one percent for the highest load (see Table 2). Indeed, as the refractive index is a volume averaged quantity, a volume average of the contributions to the refractive index of the epoxy matrix and the nanoparticles needs to be done. The result shown in Fig. 5b is striking: in contrast to the chemical conversion, a(t) the temporal evolution of the refractive index does depend on the silica concentration! As a matter of fact, the increase of the refractive index of the epoxy network depends on the amount of nanoparticles at any given reaction time. Keeping in mind that at the beginning of the chemical reaction process DnD is zero for all nanoparticle concentrations, it is amazing that after 18 h of isothermal polymerization the relative DnD-difference between the pure epoxy c¼0ÞDnD ðt¼18h; c¼67Þ and the most loaded nanocomposite DnD ðt¼18h; amounts to DnD ðt¼18h; c¼0Þ 37%. Hence, the silica concentration of the nanocomposite affects different quantities in unequal ways: whereas the chemical conversion and the heat produced per gram of epoxy [25] during the polymerization of the nanocomposites are not sensitive to the nanoparticle concentration, the refractive index and, thus, the optical polarizability, obviously is. At this stage, different possible influences of the silica nanoparticles on the optical polarizability of the epoxy matrix may be considered. First, as the nanoparticles are impenetrable for the epoxy, because of geometrical reasons the epoxy network must possess, at least close to the nanoparticles, different conformations compared with those in the bulk. The silica particles may, thus, change the optical polarizability in this interphase region of the epoxy network, due to modified or additional physicochemical bonds between chain segments, like hydrogen bonds or dipole-dipole interactions. Second, in addition to this purely geometrical argument, the silica nanoparticles possibly lead to the adsorption of epoxy chains at the surfaces of the nanoparticles. If the surfaces of the silica nanoparticles were not completely hydrophobized by the silane coating, Si-OH groups at the surface of the silica particles could react with the oxirane groups. However, the thermal effect of debonding of DGEBA molecules and rebonding of epoxy molecular segments and their effect on the consumption of oxirane groups must be small compared with the accuracy of calorimetry [25] and infrared spectroscopy (and is, thus, probably negligible, in accordance with the literature [42,43]). The drawback of the time-dependent representation of the refractive index in Fig. 5 is that these curves give only little information about the progress of the chemical reaction process as measured by the chemical conversion, a since the time and the chemical conversion depend in a strongly nonlinear manner on each other. In Fig. 6a are represented the refractive indices, nD(t), of the pure epoxy and the three nanocomposites versus the

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FIGURE 6 (a) Refractive index versus chemical conversion, nD(a), for the (100=0=14) epoxy and the related nanocomposites; reaction rate versus chemical conversion, r(a), for the (100=25=14) nanocomposite. (b) Excess refractive index versus chemical conversion, Dnexcess ðaÞ, for the four systems. Grey rectangles: region between a ¼ 55% and 60% where D the sol-gel transition is supposed to occur. The vertical lines indicate the changeover between the three ranges R1 to R3. Straight lines in (a) indicate the linearity of the nD(a)-curves in range R1. (Color figure available online.)

chemical conversion, a(t). As all four nD(a)-curves show a similar evolution, the sub-division into three ranges, which was introduced for the pure epoxies in Fig. 3, also applies to the nanocomposites. In the range R1 shown in Fig. 6a only oligomers and small epoxy network fragments can be formed for these four samples as the degree of polymerization is at maximum 23%. The nD(a)-linearity of range R1 means that on average the same increase of the refractive index is obtained during the formation of a covalent bond. The grey rectangle in range R2 of Fig. 6a marks the conversion range 55% to 60%, for which the sol-gel transition is expected to occur. The nD(a)-curves for the nanocomposites (100=11=14) and (100=25=14) show an excess contribution going beyond linearity in range R2. But this excess optical polarizability decreases with an increasing content of silica nanoparticles. Within the margin of error, for the sample (100=67=14) the excess optical polarizability does even not develop at all in range R2. Since the chemical reaction evolves almost identically for all nanoparticle concentrations, the reaction rate r(a) ¼ da=dt given for the (100=25=14) sample in Fig. 6a is representative for all samples. While the increase of the reaction rate, r(a), in range R1 results from the autocatalysis of the epoxy reaction, its reduction for chemical conversions larger than about a ¼35% is caused by the decreasing local molecular mobility within the samples. Note that the strong change in slope at 62% is statistically relevant, while taking into account the experimental error. Hence, the important deceleration of the polymerization starting at a ¼ 62% is a clear sign for the occurrence of the glass transition, which happens for the same degree of polymerization for all nanoparticle concentrations. Thus, the third range can be assigned

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to the glassy range, starting at about a ¼ 62%, independently of the silica concentration in all samples. This interpretation is in line with the caloric investigations of Baller et al. [25] performed on the same type of nanocomposites. The dynamic vitrification of the nanocomposites at mHz frequencies, as reflected by calorimetry, is indeed almost independent of the concentration of silica particles and occurs at about 55% [25], i.e., earlier than the static vitrification determined by the reaction rate [24]. Hence, the silica particles virtually do not change the macroscopic freezing behavior of the polymeric matrix although they influence at least the topology of the epoxy network in the vicinity of the particles. If, in addition, the epoxy network may be covalently bonded at a few sites to the surfaces of the hydrophobically coated silica nanoparticles, any interaction must be of the nature that it does not significantly change the thermo-mechanical properties of the matrix material; otherwise, the glass transition properties would be modified. We surmise that the occurrence of the sol-gel transition is also little influenced by the particles and, thus, located close to a ¼ 57% for all four samples. In fact, as the epoxy network probably is not much attached by covalent bonds to the nanoparticles [26–28], the latter are not expected to behave as large binding sites, or network knots, for the overall system. Therefore, the chemical conversion of the epoxy network, at which the sol-gel transition happens, should not be considerably affected by the concentration of nanoparticles (although, for instance, the zero-shear viscosity is [25]). In the first and the third ranges the slopes of all nD(a)-curves are almost identical. The respective parts of the curves basically vary by vertical refractive index shifts caused by the direct contribution of the refractive indices of the nanoparticles (nD  1.48) to those of the epoxy matrix (see Table 1). The almost flat evolution of nD(a) in range R3 of the four samples is assigned to a tiny increase of mass density or electronic dipole number density in the glassy state. This viewpoint seems plausible, as in the glassy state the slowly ongoing polymerization can no longer lead to an as important shrinkage of the system as in the liquid or gelatinous state since the network is already dense and rigid. Of course, slight variations of other contributions to the electronic polarizability, like that of optical dipole-dipole interactions, cannot be excluded. Revisiting the ranges R1 and R2, it is first remarkable that the higher the filler content, the more extended is the linear behavior of nD(a), typical for R1, into the range R2. For the maximum loaded nanocomposite this linear behavior even almost extends until R3. Second, the slope of nD(a) in R1 is remarkably independent of the nanoparticle concentration. This observation supports the statement that in R1 a volume average of the refractive indices of the pure epoxy matrix (100=0=14) and the nanoparticles applies well. In particular, the slight increase in silica volume concentration upon polymerization (because of the shrinkage of the epoxy matrix) can be neglected.

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However, the explanation of the physical mechanisms responsible for the first observation is not straightforward. As argued at the beginning of this section, it seems highly implausible that the strong nonlinear nD(a)-growth observed for the pure epoxy (100=0=14) in R2 is related to a nonlinear increase of the mass density. This interpretation is particularly reinforced by the fact that for the most loaded nanocomposite, such a nonlinear evolution of nD(a) is not observed at all. Actually, for the (100=67=14) nanocomposite, nD(a) seems to represent in essence the evolution of q(a). For some reason, the excess contribution of the refractive index probably cannot develop during the gelation of the most loaded nanocomposite. In other words, only for the nanocomposite (100=67=14) does the Lorentz-Lorenz relation allow one to estimate the evolution of mass density, q(a), from the refractive index, nD(a), with an accuracy of much better than a few percent in all three ranges, R1 to R3. In return, for all samples, the contribution to the refractive index given by the mass density via the Lorentz-Lorenz relationship is estimated using the DnD-evolution of the nanocomposite (100=67=14): ndensitydominated ða; cÞ ¼ nD ða ¼ 0%; cÞ þ DnD ða; 67Þ; D

ð10Þ

with c ¼ 0, 11, 25, 67 and DnD being defined by Eq. (9). In Fig. 6b are shown the resulting excess refractive indices: densitydominated

Dnexcess ða; cÞ ¼ nD ða; cÞ  nD D

ða; cÞ;

ð11Þ

for c ¼ 0, 11, 25, 67. By definition, the excess refractive index is zero for the ðaÞ is nanocomposite (100=67=14). Moreover, Fig. 6b confirms that Dnexcess D the most important for the pure epoxy for which it equals to 0.011 at most. Note that this value is really considerable for a refractive index. Close to the sol-gel transition at a  57%, a percolated network is forming for all systems. Apparently, the cooperative excess contributions of optical polarizability are especially pronounced close to this percolation threshold for the pure epoxy and the nanocomposites (100=11=14) and ðaÞ-curves qualitatively results (100=25=14). The similar shape of their Dnexcess D from the interplay between different factors. First, the excess polarizability grows while larger epoxy network fragments are formed. Second, the interaction of the silica nanoparticles with the epoxy network fragments plays a ðaÞ is reduced. role as the higher is the nanoparticle content, the more Dnexcess D Finally, at the static glass transition the excess polarizability does not increase anymore, but rather seems to freeze at the given value (see also [24]). The ðaÞ, ensuing from this viewpoint could be excess refractive index, Dnexcess D linked to extended dipole-dipole interactions generated in the larger epoxy network fragments created in the range R2. As to how far long-ranged Van der Waals interactions, like Keesom interactions, could be relevant at optical

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frequencies and be the underlying reasons for the observed excess refractive index, is uncertain. As discussed above, the thermo-elastic properties must for sure be quite unaffected by the relevant interactions and structural changes within the molecular network. An obvious question concerns the length scale at which the nanoparticles hinder these extended dipole-dipole interactions to build up in the epoxy network. Apparently, the excess polarizability is not a very local phenomenon related to the epoxy morphology just next to the particles. Only in the most loaded composite, which contains about 25 vol% silica nanoparticles and for which the average interparticle surface-to-surface distance is of about 6 nm (see Table 2), the excess polarizability does not arise. Apparently, for larger average interparticle distances varying between 14 and 23 nm, as present in the less loaded nanocomposites (100=11=14) and (100=25=14), the development of this contribution is only partially hindered. While the perturbing role of the nanoparticles for the development of the excess polarizability is established, their specific action on the epoxy matrix is not. It is plausible that they perturb with their own dielectric properties the internal electric field and, thus, the presumed extended dipole-dipole interactions of the epoxy matrix. Another depression of the excess polarizability could stem from the necessary topological modifications of the epoxy network around the silica nanoparticles. In this context, the question remains why these topologically forced network changes do not significantly influence the chemically induced glass transitions of the nanocomposites.

5. CONCLUSION The network formation of epoxies and epoxy-based nanocomposites, as well as the accompanying transitions, could be elucidated by combining high performance refractometry with infrared spectroscopy. In accordance with the Lorentz-Lorenz relationship, the behavior of the refractive index versus the degree of polymerization seems to reflect the evolution of the mass density of the epoxy-based systems within the limit of a few percent. From the technological point of view, this may be of importance as refractive indices are much easier to measure than mass densities of sticky, highly viscous materials, like curing epoxy adhesives. The slight deviations from the LorentzLorenz relationship, which are observed during the gelation of the chosen epoxy-based systems, are tentatively attributed to long-ranged dipole-dipole interactions. It is speculated whether long-ranged Van der Waals interactions, which are relevant at optical frequencies, are the underlying reasons for this excess contribution of the refractive index. Adding chemically inert silica nanoparticles to the pure epoxy matrix prior to curing leads to a decrease, or even a total suppression, of these dipole-dipole interactions within the larger epoxy fragments created during gelation.

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ACKNOWLEDGMENT This work was financially supported by the University of Luxembourg through the project ‘‘Static and Dynamic Properties of Nanocomposites’’. MP would like to thank the National Research Fund of Luxembourg for the AFR Ph.D. grant and, in addition, the European Commission for the Marie Curie cofounded AFR Postdoc grant.

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