Article pubs.acs.org/Macromolecules
Sulfur-Cured Natural Rubber Elastomer Networks: Correlating CrossLink Density, Chain Orientation, and Mechanical Response by Combined Techniques Arnaud Vieyres,† Roberto Pérez-Aparicio,*,† Pierre-Antoine Albouy,‡ Olivier Sanseau,† Kay Saalwac̈ hter,§ Didier R. Long,† and Paul Sotta† †
Laboratoire Polymères et Matériaux Avancés, CNRS/Rhodia-Solvay, UMR 5268, 85 avenue des Frères Perret, F-69192 Saint Fons, France ‡ Laboratoire de Physique des Solides, CNRS/Université Paris-Sud, UMR 8502, 91405 Orsay Cedex, France § Institut für Physik-NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str. 7, D-06120 Halle, Germany ABSTRACT: We present a combination of independent techniques in order to characterize vulcanized natural rubber elastomer networks. We combine solid state proton multiplequantum NMR, equilibrium swelling, mechanical experiments, and in-situ tensile X-ray scattering measurements, all of them giving access to the segmental orientation effects in relation to the cross-linking of the systems. By means of the combination of these techniques, we investigate a set of unfilled natural rubber networks with different levels of cross-linking. The relevance of this work is the application of this approach in order to study the reinforcement effect in filled elastomers with nanoparticles in a following work.
I. INTRODUCTION Elastomers are very important polymeric materials since they present unique mechanical properties. For practical applications, they generally need to be reinforced by adding solid particles or aggregates (fillers) of nanometric sizes like carbon black or silica,1−3 which brings qualitatively new mechanical behavior and drastically improves the properties of the obtained materials.4 Reinforcement is complex and eventually involves several distinct mechanisms, related with the structure and dynamics at the molecular level.5−8 Local strain amplification in the elastomer matrix due to the filler volume effect, filler−filler networking, filler−rubber interactions, and long-range modification of the molecular dynamics within the elastomer matrix have been identified as the most important ones. The relative quantitative importance of these various factors in various elastomer materials is still frequently debated. For these reasons, it is essential to be able to discriminate and quantify each of these factors. In this sense, it is important to use techniques or combinations of techniques which may allow to characterize the behavior of the elastomer matrix in both pure (unfilled) and filled materials.9 In this paper we present an innovative combination of various experimental techniques which allows to gain precise insight into the molecular characterization of elastomer networks. The aim of this article is to introduce our approach, which combines proton multiple-quantum (MQ) NMR, equilibrium swelling experiments, mechanical experiments, © 2013 American Chemical Society
and amorphous phase orientation measurements under strain by wide-angle X-ray diffraction. All these techniques give access to segmental orientation effects and/or chain elastic response, measured in different ways. Therefore, all techniques give results which can be related essentially to one main parameter, which is the average cross-link density (or equivalently the average length of network chains). Here we describe in detail the various experimental techniques and show how their results are correlated to each other. We present a study on welldefined sulfur vulcanized unfilled natural rubber (NR) elastomers, prepared with standard procedures and with various cross-link densities. Indeed, one purpose of this paper is to check the concordance of all these measurements. Specifically, we introduce a new correlation between amorphous phase anisotropy measurements by X-ray scattering and other techniques (equilibrium swelling and proton MQ-NMR). Our ultimate interest lies in reinforced materials, and we argue that transposing the same combination of techniques to reinforced systems shall give some new pieces of information on reinforcement mechanisms, by comparing to pure (nonreinforced) materials with similar elastomer matrices. This is a prerequisite to study reinforced materials because it is the way in which these correlations will be affected which shall give Received: December 13, 2012 Revised: January 15, 2013 Published: January 31, 2013 889
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elasticity theory. In section III we describe in detail the samples, the experimental techniques which have been used, and the way in which results have been analyzed. Results are shown in section IV and discussed in section V.
some hints on reinforcement mechanisms. Studying reinforced samples will be the subject of another publication. In unfilled elastomers, the mechanical behavior is essentially related to the complex topology of the cross-link network and the conformation of chains within this network. Besides mechanical measurements, many different experimental approaches have been used in order to study elastomer networks. These include techniques to measure segmental orientation, such as fluorescence polarization,10 infrared dichroism,11 and 2 H NMR.12−16 Small-angle scattering techniques have been used as well.17−20 More recently, innovative time-domain NMR techniques such as proton MQ experiments, which can be applied on lowresolution, low-field spectrometers, have been developed.21,22 These measurements are based on the quantitative determination of partially averaged residual dipolar couplings between protons, under the effect of the induced local order due to the orientation dependence of the chain segments constrained by cross-links and entanglements. These residual dipolar couplings are responsible for a buildup signal dominated by spin-pair double-quantum (DQ) coherences. MQ-NMR is one of the most quantitative and reliable methods for the measurement of residual dipolar couplings and thus to characterize elastomer networks. The advantage of MQ as compared to other NMR techniques is that, without invoking any specific model, the temperature-independent effects of the network structure can be quantitatively separated from the temperature-dependent segmental dynamics, just by following a normalization procedure. Moreover, by a suitable data analysis, it is possible to access the whole distribution of residual dipolar couplings and from them calculate the average cross-link density of networks and its distribution (heterogeneities) in relation to the physicochemical characteristics of the elastomer network.23,24 Equilibrium swelling experiments in a good solvent have been widely used as well to characterize elastomer network structures in rubber science and technology. The classical Flory−Rehner equation,25−27 based on the elastic response of polymer chains to the osmotic stress of the solvent, directly relates the rubber volume fraction at swelling equilibrium to the average molecular weight between cross-links. Thus, the average molecular weight between cross-links can be determined in a simple way, even though experiments must be conducted and analyzed very precisely. 28 Different expressions are available, according to whether the swelling is assumed to be described by an affine or phantom network model. Note that these determinations are quite sensitive to the precise value of the Flory−Huggins interaction parameter χ29,30 which describes elastomer−solvent interactions. X-ray diffraction has been used for decades to characterize strain-induced crystallization (SIC) in NR.31−34 SIC is generally considered to be responsible for the high mechanical and ultimate performances of NR. In addition to characterizing the onset, equilibrium value, and kinetics of SIC, it has been shown recently that quantitative measurements of the amorphous phase orientation can be obtained by analysis of X-ray diffraction patterns obtained in samples stretched in situ.35 Indeed, under uniaxial stretching, an anisotropy is observed in the amorphous scattering, which can be related to the average orientation of network chain segments in the amorphous phase. The paper is organized as follows. In section II we give some general, basic background on the analysis of the results of the various techniques which are used, based on basic rubber
II. GENERAL BACKGROUND A. Mechanical Experiments. The linear regime of rubber elasticity under constant volume uniaxial elongation is characterized by the following relationship between the true stress σ and the elongation ratio λ = l/l0, where l0 (l) is the initial (elongated) length of the sample:36 σ = RTρψ n(λ 2 − λ−1) r
(1) −1
where n is the number density of elastic chains (in mol g ), R is the ideal gas constant, and ρr is the rubber density (expressed here in g m−3 in order to have σ in Pa). The cross-link density ν is related to n or equivalently to the average chain molecular weight Mc between consecutive cross-links by ν = n/2 = 1/2Mc (assuming tetrafunctional cross-links). The factor RTρrψn is the shear modulus G. The factor ψ depends on the way in which cross-link positions move under the applied strain. Under the hypothesis of affine deformation ψ = 1, for a phantom network model, ψ = (f − 2)/f, where f is the network functionality,37 taken here to be typically f = 4, leading to ψ = 1/2. Basic statistical theory of rubber elasticity leading to eq 1 is based on the assumption that the system may reach equilibrium, i.e., have a fast dynamics, subject to a given set of permanent constraints, namely chemical cross-links and other topological constraints, generically denoted as trapped entanglements. Thus, the effective cross-link density ν should be understood here as comprising both chemical cross-links and trapped entanglements which have a permanent elastic effect. B. Time-Domain Proton Solid-State NMR Spectroscopy. Time-domain proton NMR spectroscopy is based on the measurement of the residual tensorial interactions, which originate from incomplete motional averaging of chain segments fluctuating rapidly between topological constraints, such as cross-links or chain entanglements. The local anisotropy of reorientational motions is described by a nonzero dynamical orientation of the polymer backbone ⟨P2(cos θ)⟩ defined as the time average of the second-order Legendre polynomial:31 ⟨P2(cos θ )⟩t =
1 t
∫0
t
⎛ 3 cos2 θ(τ ) − 1 ⎞ ⎜ ⎟ dτ 2 ⎝ ⎠
(2)
in which θ is the time-dependent angle between the local chain direction (segmental orientation) and a reference direction. At high enough temperature (with respect to Tg), reorientational motions are fast and the above time average stabilizes rapidly at short times t. For a network chain, however, longer-range or slower motions of the segments are hindered by the presence of permanent topological constraints such as entanglements and cross-links. This leads to a nonzero permanent time average, which gives a dynamic average orientation of the polymer backbone, related to the length R and orientation α of the endto-end vector. In a freely jointed rigid rod chain model, the average segment orientation is ⟨P2(cos θ )⟩ ≈
3 R2 3 cos2 α − 1 3 cos2 α − 1 ≈ S b 5 N 2b2 2 2 (3)
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where N is the number of statistical segments (freely jointed rigid rods) between constraints and b the statistical segment length. The overall NMR signal is then the sum of individual monomer or segment signals, which are at least partially timeaveraged over the distribution of end-to-end vectors. From this, an average value of the local backbone orientation with respect to the end-to-end vector arises, which corresponds to Sb (see eq 3). Using the usual result for ideal chains R2 ≈ Nb2, it may be written 3 R2 1 Sb ≈ ∝ ≈ν 2 2 5Nb N
deformation are mainly used to describe the behavior of crosslinked rubbers: (i) the affine deformation model which states that the deformation applied to cross-link positions is the same as the macroscopic deformation imposed to the overall network and (ii) the phantom model which assumes that the positions of the cross-links are not fixed and can fluctuate. For the affine deformation model, the classical Flory−Rehner equation which relates the rubber volume fraction ϕr at swelling equilibrium (or equivalently the degree of swelling Q = V/V0 = 1/ϕr) to Mc is ln(1 − ϕr) + ϕr + χϕr 2 = −
(4)
(6)
where ρr is the rubber density, Vs the solvent molar volume, χ the Flory−Huggins polymer−solvent interaction parameter, and f the cross-link functionality. On the other hand, for the phantom model, the equations reads
Since the proton dipolar coupling, which is the NMR observable, depends on molecular orientation, the nonzero dynamic orientation of the polymer backbone Sb is detected in NMR because it gives a nonzero residual dipolar coupling. Sb is calculated from the experimental average residual dipolar coupling constant Dres, by comparison with its static counterpart, Dstatic, as (k is a correction factor
