Article pubs.acs.org/Macromolecules
Viscoelasticity of Inhomogeneous Polymers Characterized by Loss Tangent Measurements Using Atomic Force Microscopy Hung K. Nguyen, Makiko Ito, So Fujinami, and Ken Nakajima* WPI-Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan ABSTRACT: The viscoelastic response of inhomogeneous rubbery blends upon interacting with an atomic force microscopy (AFM) cantilever is characterized in both the contact and intermittent contact states. In particular, loss tangent spectra and images are measured in tapping mode AFM at relatively high frequencies (>105 Hz) and in an AFMbased method in the contact state recently developed for the characterization of the viscoelasticity of soft materials in a frequency range of 100−104 Hz. Comparing the measured data to that from a bulk technique reveals that a combination of these two methods can qualitatively characterize the nanoscale viscoelastic behavior of inhomogeneous rubbers over an unprecedented frequency range. However, the loss tangent measured in the tapping mode is overestimated compared to those measured in the contact state and the bulk technique, which is attributed to the existence of the adhesion energy hysteresis during the approach and withdrawal of the tip from the sample in the tapping mode. Such an overestimation becomes less pronounced near the glass transition region of the materials.
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INTRODUCTION Over the past three decades, atomic force microscopy (AFM) has been extensively used to observe surface nanostructures in a variety of inhomogeneous polymeric materials (IPMs) such as polymer blends, copolymers, and polymer nanocomposites.1 In parallel, a number of AFM-based methods have been developed to characterize the mechanical,2−5 dielectric,6 and electric7 properties of individual nanometer-sized domains in IPMs. Such measurements are becoming more important due to the rapid increase in the practical implications of nanostructural IPMs in various areas ranging from flexible biodevices,8 microelectronics,9 to tire industry,10 in which the size of some components in IPMs is continuously reduced to improve the material’s performance. Despite efforts to advance AFMbased methods, quantitative measurements of the nanoscale physical properties of IPMs remain challenging due to difficulties in precisely quantifying the characteristic parameters of the AFM cantilever and the lack of a suitable model covering all the aspects of the tip/sample interaction.11,12 However, in many cases, the structural relaxation response of the individual components under external perturbation from an AFM cantilever over a wide frequency or temperature range can provide valuable information about a material’s properties without requiring a detailed understanding of the cantilever’s characteristics.6,13−17 Among many approaches, the methods based on loss tangent measurements have recently been the subject of great interest.6,16−19 Generally, each component of an IPM has a different response to external dynamic perturbations (e.g., electric voltage, stress, or strain) over a wide range of frequency or temperature. The presence of multicomponents with © XXXX American Chemical Society
different physical properties can provide a large variation in the mechanical, optical, and electric responses of a material.6,7,10 For example, rubber materials having cross-linked network and filler dispersion are widely used in a tire, and hence they frequently receive mechanical stimuli over a broad range of frequencies and temperatures.10,16 Understanding the influence of the filler on the mechanical performance of the rubber would make it easier to design new materials with improved performances. In bulk materials, dynamic responses have been well characterized using standard macroscopic techniques, such as dielectric spectroscopy20 or dynamic mechanical analysis (DMA),21 providing critical information about the dielectric and viscoelastic relaxations, glass transition, and molecular structure of various polymers. However, for IPMs, measurements based on macroscopic techniques could only provide an average response of all the components, making interpretation of measured data complicated.17,22 Recent reports have demonstrated the ability of AFM to obtain similar responses to an external perturbation for nanometer-sized domains as bulk techniques, but with a resolution as small as tens of nanometers.16,17,23 For example, the mechanical relaxation of rubbery polymers has been characterized by a modified AFM method in the contact state using a soft cantilever with a fundamental resonant frequency of ∼70 kHz.16 In this study, loss and storage modulus and loss tangent were obtained over a wide frequency range of 1 Hz−20 kHz. The results were nicely consistent with the data obtained Received: July 30, 2014 Revised: October 15, 2014
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dx.doi.org/10.1021/ma501562q | Macromolecules XXXX, XXX, XXX−XXX
Macromolecules
Article
Loss Tangent Measurements by AFM. Loss tangent measurements were performed at ambient conditions (Troom ∼ 25 °C) using a modified commercial AFM (Nanoscope V with MultiMode 8, Bruker AXS) in both the intermittent contact (i.e., TM-AFM) and contact states. In the contact state, a soft silicon cantilever (OMCL-AC240TS-C2, Olympus, Japan) with spring constant of 1.7 N/m (calibrated) was used. Details of this method are described elsewhere.16 Here we only briefly describe the principle for the loss tangent measurements. When the tip approaches contact with the sample, a tiny piezoelectric actuator placed between the sample holder and the AFM scanner is mechanically vibrated by applying a sinusoidal driven voltage Ap cos(ωpt), in which the applied frequency f p = ωp/2π ranges from 1 Hz to 20 kHz. Consequently, the cantilever vibrates at the same frequency as the actuator but has a phase lag ϕs due to the viscoelastic behavior of the tip/sample interaction. During the oscillation, the cantilever maintains contact with the sample until the frequency sweep is complete using surface delay control. It is noteworthy that a systematic small phase lag ϕpm always exists between the cantilever and the driven voltage, which is independent of the sample properties. To eliminate the effect of ϕpm, before conducting measurements on the polymers, the value of ϕpm was calculated on a mica substrate at each applied frequency. Assuming that the oscillation of the cantilever on mica is Acm cos(ωpt + ϕcm) and that on the polymer is Acs cos(ωpt + ϕcs), these amplitudes Acm and Acs, and phase lags ϕcm and ϕcs of the cantilever oscillation can be detected using a lock-in amplifier, allowing the amplitude and phase lag between the photodiode deflection signal and the driven signal to be measured. Thus, the deformation of the sample can be calculated as
by DMA for the bulk sample. In principle, using harder cantilevers can extend the upper limit of this frequency range, but a higher force may be necessary to maintain a similar degree of the cantilever deflection to that of the soft cantilever,16 which can damage soft polymers. Therefore, high-frequency measurements are limited using this contact AFM in the current state. On the other hand, some AFM-based methods can measure the viscoelastic response of polymers in the high frequency range of 105−106 Hz by utilizing the resonant frequency of the cantilever itself at various harmonics.24,25 While the contact resonance AFM method is only suitable for relatively hard materials,25 loss tangent measurements in tapping mode AFM (TM-AFM) recently introduced by Proksch et al.24 can be a viable candidate to obtain the viscoelastic response of soft polymeric materials (e.g., rubbers and biomaterials) in a high frequency range ∼105−106 Hz due to the small force (
