Nanomechanical properties and nanoscale deformation of PDMS nanocomposites

Introduction

A widely used elastomer, crosslinked polydimethylsiloxane (PDMS), has been used in several areas, such as thin films and coatings, soft lithography, biomedical applications, optical systems, nanotribology, micro- and nanofluidics, microelectromechanical systems/nanoelectromechanical systems, etc.1^–3 The PDMS is chemically inert, thermally stable (well performing over a wide range of temperatures), permeable to gases and simple to handle and manipulate. It exhibits isotropic and homogeneous properties, is less costly than silicon and can conform to submicrometre features to develop microstructures.3^–5 The mechanical properties of surfaces and interfaces are important for understanding the behaviour of adhesive and sliding contacts.6 More specifically, the mechanical response of elastomers has a major impact in some applications such as tunable microdoublet lenses and dielectric elastomer actuators.7 Nanoindentation technique with depth sensing has been widely used for the measurement of the mechanical properties of materials, such as thin films, coatings and nanostructures.8 The elastic modulus of polymeric materials creates difficulty for accurate measurement using indentation testing. This difficulty is due to force resolution, typically on the order of 100 nN.9 Considerable uncertainties arise when applying the nanoindentation technique to very soft (elastic modulus below 5 MPa) or adhesive samples, such as biological or polymeric surfaces. 10 , 11 In this study, the nanoindentation technique was used to characterise the nanomechanical properties (hardness and modulus) and time dependent properties due to the viscoelasticity (creep, loading rate effects) of PDMS as a function of different concentrations of nanoclay [0, 5 and 8 parts per hundred (phr)].

Experimental

Oliver and Pharr (O&P) method

A typical nanoindentation test provides load–displacement data that represent the deformation responses of a material. In general, traditional mechanical property parameters, such as H and E, can be determined. Attention has been paid on analysing the unloading curve to obtain contact area for the determination of H and E. Most analyses are based on the O&P method, which determines the contact area in the use of the unloading tangent together with the known area function.14 The key problem inherited in these methods is the determination of the contact area between the indenter and the sample being tested. It is believed that the contact area is underestimated by the O&P method for most ductile metals and soft polymers.15 Hainsworth et al.16 provided a model for establishing the relationship between the loading coefficient of Berkovich indentation and the material properties of H and E. However, significant errors existed in the predicted and experimental results of the soft materials used in their research.

The O&P derived expression for calculating the E from the indentation experiments based on Sneddon's17 elastic contact theory is (1) where S is the unloading stiffness, which is represented by the tangent value of the initial slope of the unloading load–displacement curve at the maximum displacement of penetration (or peak load), A_c is the projected contact area between the tip and the substrate at peak and β is a constant that depends on the geometry of the indenter (β = 1·167 for Berkovich tip).

The conventional nanoindentation hardness refers to the mean contact pressure; this hardness, which is the contact hardness H_C, actually depends upon the geometry of the indenter (equations (2)–(4)). (2) where (3) and (4) where h_m is the total penetration displacement of the indenter at peak load, P_m is the peak load at the indenter displacement h_m and ϵ is an indenter geometry constant, which is equal to 0·75 for spherical indenters.

A sharper indenter induces greater contact H and smaller elastic recovery; however, the contact H will approach a constant, i.e. the true hardness H_T, which is defined by a perfectly plastic contact pressure. The true H is the H_C obtained from an ideal indentation with zero elastic recovery.

Hertz linear elastic analysis

Based on classical Hertzian contact theory, 18 , 19 the load P applied to the indenter tip is related to the total penetration displacement in the substrate h. Owing to the spherical geometry of the indenter tip, this deformation is directly related to the contact radius a using the relationship (5) where E_r is the reduced elastic modulus, and R is the nominal radius of curvature of the conospherical tip. The reduced modulus E_r is related to the elastic modulus of the sample as20 (6) where E is the steady state elastic modulus, and ν is Poisson's ratio of the sample (subscript s) and the indenter (subscript i). In the current investigation, the E of the indenter tip is many orders of magnitude higher than the E of the sample (rigid body indenter condition). Accordingly, the second term in equation (6) was neglected. From Hertz elastic analysis, the stiffness S is related to the contact radius α as (7) Combining equations (5)–(7), the following expression for the elastic modulus for spherical indentation is derived (8) The classic Hertz's model is a hard contact model that does not take adhesive interactions into account (i.e. outside the Hertzian contact area).

Results and discussion

In the FTIR spectra of the pristine PDMS and the PDMS nanocomposites (Fig. 1), the characteristic peaks of PDMS with symmetric [ν_s(CH₃)] and asymmetric [ν_a(CH₃)] stretching and deformation [ν_δ(CH₃)] vibrations of the methyl groups at 2963, 2906 and 1258 cm⁻¹ are respectively revealed. The methyl rocking and Si–C vibrations appeared at ∼800 cm ⁻¹, while the Si–O–Si asymmetric stretching vibrations emerged between 930 and 1200 cm⁻¹. Comparison of the pristine and modified PDMS samples with their spectral values and corresponding group assignments revealed no significant differences.21^–23

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Figure 1

a Fourier transform infrared spectroscopy and b XRD spectra of PDMS (0, 5 and 8 phr)

The XRD measurements were performed in 30% organically modified Cloisite 30B [2θ angle is 4·88°, corresponding to the space between the montmorillonite platelets (d = 1·80 nm)] and the PDMS with 0, 5, 8 and 10 phr (Fig. 1). The penetration of the polymer chains in the nanoclay structure caused the increase in its thickness, and the initial distinctive peak of the intercalated structure of the nanoclays is confirmed by decreased θ angles. This confirmed the expansion of the space between the montmorillonite platelets, which was caused by the siloxane surfactant intercalating agent. A disordered arrangement of siloxane surfactant grafted onto the surface of the montmorillonite clay platelets. The XRD pattern of the silicone/montmorillonite composite shows that all of the peaks attributed to siloxane modified montmorillonite clay disappeared, meaning that the silicone rubber macromolecules are fully embedded in the clay layer spacing.24

Several studies on PDMS samples via nanoindentation have revealed various nanomechanical properties.25^–33 Hou et al.26 investigated PDMS samples (surface E = 19 MPa, bulk region E = 8 MPa) with average surface roughness of ∼15 nm (0–3000 nm) with conical tip (tip radius = 20 nm). Wahl et al.29 confirmed the increase in E of PDMS with higher crosslinking agent concentrations due to the polymerisation degree decrease (E = 8·7 MPa). The interfacial friction on the contact boundary increases due to the increasing normal stress when the indenter propagates further in displacement. In most of the cases, the contact boundary is where the relative slip exists, with the increase in the contact area while indenting. The shear stress created by the indenter (for an adhesive contact boundary between PDMS and diamond) is likely to be balanced in case the applied load exceeds a critical value. For lower indentation loads than this value, the contact area increases, leading to increased contact stiffness values. At a further step, the tip locally sticks with the sample (invariant contact area and contact stiffness). A sharp indenter creates a highly concentrated stress beneath the indenter, where the plastic deformation zone mainly exists (beneath the contact region). In the case of the sticky approach, the plastic zone is smaller because strong adhesion affects the contact area. This explains why the initial contact stiffness behaviour is reversible in the unloading segment (Fig. 2b).30 Figure 2 presents the typical load–unload curves, where the applied load is plotted in accordance with the displacement of the indenter. The H and E of the PDMS samples (with an average surface roughness of ∼100 nm) with surface topography through SPM for 0, 5 and 8 phr nanocomposites are presented in Figure 3 Figs. 3 and 4. The increase in the nanoclay amount in the PDMS matrix creates surface incongruity (SPM images). The higher H and E values in the surface area are caused probably by the higher crosslink density in the low displacement range (0–300 nm) (combined with exposure of the PDMS samples in atmospheric air). The mechanical behaviour of polymers is usually described by the viscoelastic and/or viscoplastic characteristics, depending on the time (or frequency) as well as the temperature, which makes the mechanical response of the polymer systems complicated. The related literature reveals that significant initial penetration displacements can be created during the finding surface process. 34 , 35 For soft nanocomposite surfaces, the initial contact load can create an initial penetration displacement in the order of nanometres so that the contact area tends to be underestimated, which leads to an overestimation of the H and E values.

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Figure 2

Load–unload curves for 0, 5 and 8 phr PDMS samples at different applied loads

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Figure 3

Hardness and elastic modulus (O&P model) versus displacement for 0 phr PDMS samples: 5 and 8 phr PDMS samples exhibited similar behaviour of nanomechanical properties

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Figure 4

Average hardness and elastic modulus of surface/near surface (0–300 nm) and bulk (300–2600 nm) regions for 0, 5 and 8 phr PDMS samples, calculated through O&P model

The H/E ratio is of significant interest in tribology. Higher stresses are expected in high H/E, hard materials, and high stress concentrations develop towards the indenter tip, whereas in the case of low H/E, soft materials, the stresses are lower and are distributed more evenly across the cross-section of the material. 36 , 37 The high ratio of hardness to elastic modulus (H/E) is indicative of the good wear resistance in a disparate range of materials:37 ceramic, metallic and polymeric (e.g. c-BN, tool steel and nylon respectively), which are equally effective in resisting attrition for their particular intended application. In Fig. 5, the change of H/E slope reveals that the addition of nanoclay amount strengthens the PDMS–montmorillonite nanocomposite.

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Figure 5

Relationship between H and E for 0, 5 and 8 phr of nanoclays in PDMS matrix

In Fig. 6, H and E as a function of loading rate and holding time are presented. The effect of loading rate on the H and E values was studied for loading rates of 0·1, 0·8, 1·2, 1·5, 8, 20 and 40 μΝ s⁻¹ in PDMS (8 phr) with a maximum load of 80 μΝ through a three-segment process (hold time of 3 s between loading and unloading segments). The nanoindentation creep tests were performed on pristine PDMS samples. Hold times in the range from 5 to 2000 s were selected. The loading and unloading time periods (segments) were carefully chosen regarding a similar study presented in the literature (4 and 15 s respectively).19

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Figure 6

Hardness and elastic modulus values calculated for different loading rates and creep (hold) periods

In Fig. 7, comparison between tensile test modulus and E values from nanoindentation using the standard O&P method (unloading stiffness analysis) and Hertzian analysis of the PDMS samples is presented. The tensile experiment of Sirghi and Rossi25 revealed an E value of 1·63 MPa.

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Figure 7

Comparison between tensile test modulus and elastic modulus values via nanoindentation testing of 0, 5 and 8 phr: elastic modulus values correspond to penetration depths of ∼300 nm, using standard O&P method (unloading stiffness analysis), assuming incompressible (ν = 0·5) linear elastic behaviour of samples

The E values obtained via the O&P method were found to be significantly higher than the data obtained from performing a classical Hertzian contact analysis.38 This difference appears due to the assumption in the Hertz formulation that the contact depth h_c is related to the total penetration depth h by h = 2h_c. Only for ideal elastic contact (i.e. h = 2h_c) will both analyses compute the same moduli. The trends in tensile test modulus and E of PDMS appear similar (close to linear behaviour). It is important to note that nanoindentation and tensile tests do not measure the same properties. Generally, the nanoindentation modulus (E) values, using the standard O&P method, are higher than the results from standard tensile tests. Several reasons have been invoked to explain this: surface effects (the initial part of the load–displacement curve is affected by the surface roughness, surface oxidation39 and other surface phenomena), the type of loading is compressive in nanoindentation (not tensile), the test frequencies are quite different (70 Hz for nanoindentation, compared to a much lower frequency in the tensile test) and hydrostatic pressure generated below the Berkovich indenter.40

Conclusions

A number of problems exist with the application of the nanoindentation technique to polymeric materials. In general, the values of the E tend to increase with decreasing penetration displacement, often referred to as an indentation size effect. Thus, either E(surface)>E(bulk) for a large number of materials, which seems unlikely, or these trends result from the increased uncertainties for shallow depth indents that are likely due to tip defects near the apex and decreased signal/noise ratios at low load and displacement levels. For some studies, the E values measured using nanoindentation have been compared to handbook or manufacturer values. However, such comparisons can often be misleading, because the quoted values of E for many polymer systems can cover a large range due to potential variations in microstructure, semicrystalline morphology, anisotropy, molecular weight, crosslink density, etc. Thus, comparisons of E values are most appropriate for polymer samples with identical chemistry, molecular weight and processing history.

Additionally, several ways of analysing data were used, and the exact surface region (with higher values of H and E) was clearly defined. Consideration of the adhesion energy at the tip–sample interface is requisite for determining the accurate elastic moduli of PDMS samples and other soft, elastomeric materials from nanoindentation experiments, since soft material samples are expected to have significant adhesive forces. Thus, the work of adhesion must be included in the experimental protocol and evaluated when determining the mechanical properties with nanoindentation. The reduced modulus values may be similarly overestimated due to hysteresis, since the unloading curves clearly have a higher initial unloading stiffness than the loading curves. The increase in montmorillonite nanoclay amount leads to an increase in surface hardness and bulk elastic modulus of the elastomeric nanocomposite. The slope change of H/E reveals that the addition of nanoclay amount strengthens the PDMS–montmorillonite nanocomposite.

Further investigation of the mechanical exfoliation of the nanoclays in PDMS will be performed, varying the content of the crosslinking agent and the catalyst amount, in order to improve the overall mechanical performance of the nanocomposites.