Broadband nanodielectric spectroscopy by means of amplitude modulation electrostatic force microscopy (AM-EFM)

In this work we present a new AFM based approach to measure the local dielectric response of polymer films at the nanoscale by means of Amplitude Modulation Electrostatic Force Microscopy (AM-EFM). The proposed experimental method is based on the measurement of the tip–sample force via the detection of the second harmonic component of the photosensor signal by means of a lock-in amplifier. This approach allows reaching unprecedented broad frequency range (2–3×104 Hz) without restrictions on the sample environment. The method was tested on different poly(vinyl acetate) (PVAc) films at several temperatures. Simple analytical models for describing the electric tip–sample interaction semi-quantitatively account for the dependence of the measured local dielectric response on samples with different thicknesses and at several tip–sample distances

Nanodielectric mapping of a model polystyrene-poly(vinyl acetate) blend by electrostatic force microscopy

We present a simple method to quantitatively image the dielectric permittivity of soft materials at nanoscale using electrostatic force microscopy (EFM) by means of the double pass method. The EFM experiments are based on the measurement of the frequency shifts of the oscillating tip biased at two different voltages. A numerical treatment based on the equivalent charge method allows extracting the values of the dielectric permittivity at each image point. This method can be applied with no restrictions of film thickness and tip radius. This method has been applied to image the morphology and the nanodielectric properties of a model polymer blend of polystyrene and poly(vinyl acetate)

Nanoscale dielectric properties of insulating thin films: From single point measurements to quantitative images

Dielectric relaxation (DR) has shown to be a very useful technique to study dielectric materials like polymers and other glass formers, giving valuable information about the molecular dynamics of the system at different length and time scales. However, the standard DR techniques have a fundamental limitation: they have no spatial resolution. This is of course not a problem when homogeneous and non-structured systems are analyzed but it becomes an important limitation for studying the local properties of heterogeneous and/or nano-structured materials. To overcome this constrain we have developed a novel approach that allows quantitatively measuring the local dielectric permittivity of thin films at the nanoscale by means of Electrostatic Force Microscopy. The proposed experimental method is based on the detection of the local electric force gradient at different values of the tip-sample distance. The value of the dielectric permittivity is then calculated by fitting the experimental points using the Equivalent Charge Method. Even more interesting, we show how this approach can be extended in order to obtain quantitative dielectric images of insulating thin films with an excellent lateral resolution

Imaging dielectric relaxation in nanostructured polymers by frequency modulation electrostatic force microscopy

We have developed a method for imaging the temperature-frequency dependence of the dynamics of nanostructured polymer films with spatial resolution. This method provides images with dielectric compositional contrast well decoupled from topography. Using frequency-modulation electrostatic-force-microscopy, we probe the local frequency-dependent (0.1–100 Hz) dielectric response through measurement of the amplitude and phase of the force gradient in response to an oscillating applied electric field. When the phase is imaged at fixed frequency, it reveals the spatial variation in dielectric losses, i.e., the spatial variation in molecular/dipolar dynamics, with 40 nm lateral resolution. This is demonstrated by using as a model system; a phase separated polystyrene/polyvinyl-acetate (PVAc) blend. We show that nanoscale dynamic domains of PVAc are clearly identifiable in phase images as those which light-up in a band of temperature, reflecting the variations in the molecular/dipolar dynamics approaching the glass transition temperature of PVAc

Measuring dielectric properties at the nanoscale using Electrostatic Force Microscopy

Several electrostatic force microscopy (EFM) - based methods have been recently developed to study the nanoscale dielectric properties of thin insulating layers. Some methods allow measuring quantitatively the static dielectric permittivity whereas some others provide qualitative information about the temperature-frequency dependence of dielectric properties. In this chapter, all these methods are described and illustrated by experiments on pure and nanostructured polymer films. A section is dedicated to EFM probe - sample models and especially to the Equivalent Charge Method (ECM)

Dielectric properties of thin insulating layers measured by Electrostatic Force Microscopy

In order to measure the dielectric permittivity of thin insulting layers, we developed a method based on electrostatic force microscopy (EFM) experiments coupled with numerical simulations. This method allows to characterize the dielectric properties of materials without any restrictions of film thickness, tip radius and tip-sample distance. The EFM experiments consist in the detection of the electric force gradient by means of a double pass method. The numerical simulations, based on the equivalent charge method (ECM), model the electric force gradient between an EFM tip and a sample, and thus, determine from the EFM experiments the relative dielectric permittivity by an inverse approach. This method was validated on a thin SiO2 sample and was used to characterize the dielectric permittivity of ultrathin poly(vinyl acetate) and polystyrene films at two temperatures

High and low molecular weight crossovers in the longest relaxation time dependence of linear cis-1,4 polyisoprene by dielectric relaxations

The dielectric relaxation of cis-1,4 Polyisoprene [PI] is sensitive not only to the local and segmental dynamics but also to the larger scale chain (end-to-end) fluctuations. We have performed a careful dielectric investigation on linear PI with various molecular weights in the range of 1 to 320 kg/mol. The broadband dielectric spectra of all samples were measured isothermally at the same temperature to avoid utilizing shift factors. For the low and medium molecular weight range, the comparisons were performed at 250 K to access both the segmental relaxation and normal mode peaks inside the available frequency window (1 mHz–10 MHz). In this way, we were able to observe simultaneously the effect of molecular mass on the segmental dynamics—related with the glass transition process—and on the end-to-end relaxation time of PI and thus decouple the direct effect of molecular weight on the normal mode from that due to the effect on the monomeric friction coefficient. The latter effect is significant for low molecular weight (M w < 33 kg/mol), i.e., in the range where the crossover from Rouse dynamics to entanglement limited flow occurs. Despite the conductivity contribution at low frequency, careful experiments allowed us to access to the normal mode signal for molecular weights as high as M w = 320 kg/mol, i.e., into the range of high molecular weights where the pure reptation behavior could be valid, at least for the description of the slowest chain modes. The comparison between the dielectric relaxations of PI samples with medium and high molecular weight was performed at 320 K. We found two crossovers in the molecular weight dependence of the longest relaxation time, the first around a molecular weight of 6.5 ± 0.5 kg/mol corresponding to the end of the Rouse regime and the second around 75 ± 10 kg/mol. Above this latter value, we find a power law compatible with exponent 3 as predicted by the De Gennes theory

Propriétés dielectriques et mecaniques des polymeres aux échelle macroscopiques et nanoscopique

Le but de cette thèse était tout d'abord de comprendre les théories physiques qui décrivent la dynamique des polymères à l'échelle macroscopique. Le modèle de Rouse et la théorie d'enchevêtrement de De Gennes décrivent la dynamique des polymères non enchevêtrés et enchevêtrés, respectivement. Nous avons étudiés les différentes transitions entre ces deux régimes en utilisant deux techniques expérimentales: Broadband Dielectric Spectroscopy (BDS) et rhéologie. Les effets d'enchevêtrement sur les spectres diélectriques ont été discutés. Un test complet du modèle de Rouse à été effectué sur en comparant les prédictions de ce modèle pour la dépendance en fréquence de la permittivité diélectrique et du module de cisaillement aux données expérimentales. Ensuite nous avons développés des méthodes bas"s sur la microscopie à force électrostatique afin d'étudier les propriétés diélectriques locales. En utilisant la simulation numérique de la Méthode des Charges Equivalentes la constante diélectrique a été quantifiée à partir de la mesure du gradient de force crée par un potentiel statique entre une pointe et un diélectrique. Cette méthode permet d'imager la constante diélectrique avec une résolution spatial de 40 nm. Le retard de phase de la composante en 2ω de la force ou du gradient de force crée par un voltage alternatif est relié aux pertes diélectriques. En mesurant cette quantité nous avons montré que la dynamique était plus rapide proche d'une interface libre et nous avons développé un mode d'imagerie des pertes diélectriques. Cette méthode simple pourrait être appliqué en biologie ou matière molle en générale afin d'étudier des variations locales de constantes diélectriques.The aim of this thesis was first to understand the physical theories that describe the dynamics of linear polymers at the macroscopic scale. Rouse and the reptational tube theory describe the large scale dynamics of unentangled and entangled polymers respectively. Using Broadband Dielectric Spectroscopy (BDS) and rheology we have studied the different transition between these two regimes. Effects of entanglement on dielectric spectra will be discussed (Rheologica Acta. 49(5):507-512). Avoiding the segmental relaxation contribution and introducing a distribution in the molecular weight we have been able to perform a comparison of the Rouse model with experiment dielectric and rheological data (Macromolecules 42(21): 8492-8499) Then we have developed EFM-based methods in order to study the local dynamics. Using the numerical simulation of the Equivalent Charge Method, the value of the static dielectric permittivity has been quantified from the measurement of the force gradient created by a VDC potential between a tip and a grounded dielectric (Journal of Applied Physics 106(2):024315). This method allows a quantitative mapping of dielectric properties with a 40 nm spatial resolution and is therefore suitable for the study of nano-defined domains (Physical Review E 81(1): 010801). The electrical phase lags in the 2ω components of the force or force gradient created by VAC voltage, ΔΦ2ω, are related with dielectric losses. Measuring the frequency dependence of ΔΦ2ω Crieder et al (Applied Physics Letters 91(1):013102) have shown that the dynamics at the near free surface of polymer films is faster than the one in bulk. We have used this method in order to visualize the activation of the segmental relaxation with temperature and frequency (Applied Physics Letters 96(21): 213110). All this measurements can be achieved using standard Atomic Force Microscope (and a lock-in) for VAC measurements

Propriétés diélectrique et mécanique des polymères aux échelles macro et nanoscopiques

The idea was first to understand the physical theories that describe the dynamics of linear polymers at the macroscopic scale. Rouse and the reptational tube theory describe the large scale dynamics of unentangled and entangled polymers respectively. Using Broadband Dielectric Spectroscopy (BDS) and rheology we have studied the different transition between these two regimes. Avoiding the segmental relaxation contribution and introducing a distribution in the molecular weight we have been able to perform a detailed comparison of the Rouse model with dielectric and rheological data. Effects of entanglement on dielectric spectra have been discussed. BDS and rheology are commonly used techniques to measure dielectric and mechanical properties but they do not have spatial resolution. Therefore the study of the local dynamics or heterogeneous system is always model dependant. We have developed EFM-based methods in order to study this local dynamics. Using the numerical simulation of the Equivalent Charge Method, the value of the static dielectric permittivity has been quantified from the measurement of the force gradient created by a Vdc potential between a tip and a grounded dielectric. This method allows a quantitative mapping of dielectric properties with a 40 nm spatial resolution and is therefore suitable for the study of nano-defined domains. The electrical phase shift in the 2 omega component of the force gradient created by Vac voltage is related with dielectric losses. We have developed a method to image the temperature-frequency dependence of the dielectric losses. These methods would allow the study of soft matter or biological phenomena at the local scale.Le but de cette thèse était tout d'abord d'étudier les théories physiques qui décrivent la dynamique des polymères à l'échelle macroscopique. Le modèle de Rouse et la théorie d'enchevêtrement de P-G. de Gennes décrivent la dynamique des polymères non enchevêtrés et enchevêtrés, respectivement. Nous avons étudié les différentes transitions entre ces deux régimes en utilisant deux techniques expérimentales : Spéctroscopie dielectrique large bande et rhéologie. Un test complet du modèle de Rouse à été effectué en comparant les prédictions de ce modèle pour la dépendance en fréquence de la permittivité diélectrique et du module de cisaillement aux données expérimentales. Les effets d'enchevêtrement sur les spectres diélectriques ont été discutés. Nous avons ensuite développé des méthodes basées sur la microscopie à force électrostatique afin d'étudier les propriétés diélectriques locales. En utilisant une simulation numérique basée sur la Méthode des Charges Equivalentes, nous avons quantifié la constante diélectrique à partir de la mesure du gradient de force crée par un potentiel statique entre une pointe et un diélectrique. Cette méthode permet d'imager la constante diélectrique avec une résolution spatial de 40 nm. Le retard de phase de la composante en 2 omega de la force ou du gradient de force crée par un voltage alternatif est relié aux pertes diélectriques. Nous avons développé un mode d'imagerie des pertes diélectriques. Cette méthode simple pourrait être appliqué en biologie ou matière molle en générale afin d'étudier des variations locales de constantes dielectriques

Propriétés dielectriques et mecaniques des polymeres aux échelle macroscopiques et nanoscopique

Le but de cette thèse était tout d'abord de comprendre les théories physiques qui décrivent la dynamique des polymères à l'échelle macroscopique. Le modèle de Rouse et la théorie d'enchevêtrement de De Gennes décrivent la dynamique des polymères non enchevêtrés et enchevêtrés, respectivement. Nous avons étudiés les différentes transitions entre ces deux régimes en utilisant deux techniques expérimentales: Broadband Dielectric Spectroscopy (BDS) et rhéologie. Les effets d'enchevêtrement sur les spectres diélectriques ont été discutés. Un test complet du modèle de Rouse à été effectué sur en comparant les prédictions de ce modèle pour la dépendance en fréquence de la permittivité diélectrique et du module de cisaillement aux données expérimentales. Ensuite nous avons développés des méthodes bas"s sur la microscopie à force électrostatique afin d'étudier les propriétés diélectriques locales. En utilisant la simulation numérique de la Méthode des Charges Equivalentes la constante diélectrique a été quantifiée à partir de la mesure du gradient de force crée par un potentiel statique entre une pointe et un diélectrique. Cette méthode permet d'imager la constante diélectrique avec une résolution spatial de 40 nm. Le retard de phase de la composante en 2ω de la force ou du gradient de force crée par un voltage alternatif est relié aux pertes diélectriques. En mesurant cette quantité nous avons montré que la dynamique était plus rapide proche d'une interface libre et nous avons développé un mode d'imagerie des pertes diélectriques. Cette méthode simple pourrait être appliqué en biologie ou matière molle en générale afin d'étudier des variations locales de constantes diélectriques.The aim of this thesis was first to understand the physical theories that describe the dynamics of linear polymers at the macroscopic scale. Rouse and the reptational tube theory describe the large scale dynamics of unentangled and entangled polymers respectively. Using Broadband Dielectric Spectroscopy (BDS) and rheology we have studied the different transition between these two regimes. Effects of entanglement on dielectric spectra will be discussed (Rheologica Acta. 49(5):507-512). Avoiding the segmental relaxation contribution and introducing a distribution in the molecular weight we have been able to perform a comparison of the Rouse model with experiment dielectric and rheological data (Macromolecules 42(21): 8492-8499) Then we have developed EFM-based methods in order to study the local dynamics. Using the numerical simulation of the Equivalent Charge Method, the value of the static dielectric permittivity has been quantified from the measurement of the force gradient created by a VDC potential between a tip and a grounded dielectric (Journal of Applied Physics 106(2):024315). This method allows a quantitative mapping of dielectric properties with a 40 nm spatial resolution and is therefore suitable for the study of nano-defined domains (Physical Review E 81(1): 010801). The electrical phase lags in the 2ω components of the force or force gradient created by VAC voltage, ΔΦ2ω, are related with dielectric losses. Measuring the frequency dependence of ΔΦ2ω Crieder et al (Applied Physics Letters 91(1):013102) have shown that the dynamics at the near free surface of polymer films is faster than the one in bulk. We have used this method in order to visualize the activation of the segmental relaxation with temperature and frequency (Applied Physics Letters 96(21): 213110). All this measurements can be achieved using standard Atomic Force Microscope (and a lock-in) for VAC measurements