Dielectric fluctuations in force microscopy: noncontact friction and frequency jitter

Electric force microscopy, in which a charged probe oscillates tens to hundreds of nanometers above a sample surface, provides direct mechanical detection of relaxation in molecular materials. Noncontact friction, the damping of the probe's motions, reflects the dielectric function at the resonant frequency of the probe, while fluctuations in the probe frequency are induced by slower molecular motions. We present a unified theoretical picture of both measurements, which relates the noncontact friction and the power spectrum of the frequency jitter to dielectric properties of the sample and to experimental geometry. Each observable is related to an equilibrium correlation function associated with electric field fluctuations, which is determined by two alternative, complementary strategies for a dielectric continuum model of the sample. The first method is based on the calculation of a response function associated with the polarization of the dielectric by a time-varying external charge distribution. The second approach employs a stochastic form of Maxwell's equations, which incorporate a fluctuating electric polarization, to compute directly the equilibrium correlation function in the absence of an external charge distribution. This approach includes effects associated with the propagation of radiation. In the experimentally relevant limit that the tip-sample distance is small compared to pertinent wavelengths of radiation, the two methods yield identical results. Measurements of the power spectrum of frequency fluctuations of an ultrasensitive cantilever together with measurements of the noncontact friction over a poly(methylmethacrylate) film are used to estimate the minimum experimentally detectable frequency jitter. The predicted jitter for this polymer is shown to exceed this threshold, demonstrating the feasibility of the measurement.     

Dynamics in disordered block copolymers and miscible blends composed of poly(vinyl ethylene) and polyisoprene

We investigated the segmental and terminal relaxation dynamics of a well‐characterized disordered diblock copolymer, poly(isoprene‐b‐vinyl ethylene) (PI‐PVE), and miscible blends of polyisoprene (PI)/poly(vinyl ethylene) (PVE), using dielectric and viscoelastic spectroscopies. Generally, the concentration fluctuation (CF) amplitude of a disordered diblock copolymer is smaller than that of the miscible blend, especially in a length scale longer than the size of the whole block chain. To test whether the difference in the CF amplitudes causes the difference in the segmental relaxation spectra, we compared the shape of the dielectric loss curves between PI‐PVE and PI/PVE with the same composition (PI/PVE ratio = 17:83). However, no appreciable difference was observed, indicating that the CF amplitudes in PI‐PVE and PI/PVE are not so different in the length scale of the segmental motions. We also examined the effect of distinct friction coefficients of the PI and PVE chains on the terminal relaxation dynamics by comparisons of the viscoelastic and dielectric normal mode relaxations in PI‐PVE. The former probes the whole chain motion and the latter probes motions of the PI block. Shift factors (a_T) for the viscoelastic and dielectric relaxations were compared. The dielectric normal mode a_T was found to have weaker temperature dependence than the viscoelastic a_T, which indicates that the friction for the PI block chain is lower than the average friction for the PI‐PVE chain. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4084–4094, 2004     

Triboelectrification between smooth metal surfaces coated with self-assembled monolayers (SAMs)

Using a modified surface forces apparatus, we have simultaneously measured the friction and triboelectrification between both similar and dissimilar molecularly smooth hexadecanethiol-coated metal surfaces on mica substrates. On shearing dissimilar surfaces, the tribocurrent increases dramatically as the load or pressure is increased, with large fluctuations about the mean. Neither charge transfer nor fluctuations are observed when the symmetric surfaces are sheared against each other. We also find that the type of friction, i.e., stick-slip or smooth sliding, the load and friction force, the sliding distance, and recent previous history have additional fine influences on the triboelectrification. Our results suggest that frictional dissipation induces electron-hole formation and charge transfer between two shearing surfaces due to molecular-level roughness and defects and local dielectric constant changes, giving rise to the observed tribocurrents.     

Glass transition cooperativity from broad band heat capacity spectroscopy

Molecular dynamics is often studied by broad band dielectric spectroscopy (BDS) because of the wide dynamic range available and the large number of processes resulting in electrical dipole fluctuations and with that in a dielectrically detectable relaxation process. Calorimetry on the other hand is an effective analytical tool to characterize phase and glass transitions by its signatures in heat capacity. In the linear response scheme, heat capacity is considered as entropy compliance. Consequently, only processes significantly contributing to entropy fluctuations appear in calorimetric curves. The glass relaxation is a prominent example for such a process. Here, we present complex heat capacity at the dynamic glass transition (segmental relaxation) of polystyrene (PS) and poly(methyl methacrylate) (PMMA) in a dynamic range of 11 orders of magnitude, which is comparable to BDS. As one of the results, we determined the characteristic length scale of the corresponding fluctuations. The dynamic glass transition measured by calorimetry is finally compared to the cooling rate dependence of fictive temperature and BDS data. For PS, dielectric and calorimetric data are similar but for PMMA with its very strong secondary relaxation process some peculiarities are observed.     

Molecular dynamics of grafted PBLG in the swollen and in the dried state

A novel technique to contact (ultra‐) thin polymer layers is presented which enables to compare the molecular dynamics in grafted films of poly(γ‐benzyl‐L ‐glutamate) (PBLG) to that of the bulk polymer by means of dielectric spectroscopy. Two relaxation processes are observed which are assigned to restricted fluctuations of the helical main chains and to the dynamic glass transition of the side chains. Furthermore, the swelling behavior of PBLG is studied.     

Dielectric relaxation in some polyacrylate solutions

The dielectric constant ?′ and loss factor ?″ of poly(butyl acrylate), poly(butyl methacrylate), and poly(isobutyl methacrylate) solutions are reported in the frequency region of 1 kHz to 24.42 GHz at four different temperatures of 27, 40, 50, and 60°C. Cole–Cole plots are plotted to obtain the distribution parameter and relaxation time. The activation energies are evaluated assuming dielectric relaxation to be a rate process in these solutions. A possible relaxation mechanism is discussed.     

Interconversion between mechanical and dielectric relaxations for poly(cyclohexyl acrylate)

Storage E′ and loss E″ relaxation moduli are reported as functions of frequency for poly(cyclohexyl acrylate) (PCA) at several temperatures. The possibility that these results, in conjunction with the dipolar correlation coefficient, can be used to predict the frequency dependence of the real ε and loss ε″ and the components of the complex dielectric permittivity ε* of PCA is studied. A relation between ε* and the complex relaxation modulus E* is obtained by assuming that the lag of the rotating dipoles in the electric field is caused by both dielectric and mechanical friction. The values of ε* obtained from mechanical results by means of this expression are very close to those obtained from other relations based on the assumption that the lag of the dipoles is caused exclusively by mechanical friction. © 1993 John Wiley & Sons, Inc.     

Effective charge of polyelectrolytes as a function of the dielectric constant of a solution

The combination of diffusion and electrophoresis NMR is applied to determine the effective charge of poly(styrene sulfonate) in solution. While electrophoresis NMR yields the electrophoretic mobility of the molecules in solution, the hydrodynamic friction is determined from diffusion NMR. From the force balance between electrostatic force and hydrodynamic friction, the effective charge of the molecule is determined free of any model. In the present study poly(styrene sulfonate) has been investigated in mixtures of water and methanol of varying composition. The lower dielectric constant in the mixtures with high methanol content results in a drastically reduced effective charge of the polyelectrolytes. The reduced effective charge along the polymer chain is the reason for a much more compact conformation of the polyelectrolyte, which is seen in a smaller hydrodynamic size of the molecule.     

Influence of the solvent environment on the contact mechanics of tip-sample interactions in friction force microscopy of poly(ethylene terephthalate) films

Friction force microscopy measurements have been carried out on free-standing films of poly(ethylene terephthalate) in a variety of different media. In ethanol, the adhesion force was small, and the friction-load relationship was linear. In perfluorodecalin, nonlinearity was observed in the friction-load relationship, and the data have been found to fit the Johnson-Kendall-Roberts model of contact mechanics. The behavior in hexadecane was also characterized by a single-asperity contact model, but in this case, the data were found to fit the Derjaguin-Müller-Toporov model. It is suggested that these differences are due to the different strengths of tip-sample adhesion, which arise from the differences in the dielectric constants of the media: in ethanol, which has a high dielectric constant, the friction force varies linearly with the load, whereas in media of low dielectric constant, adhesion-limited behavior is observed.     

General properties of secondary relaxations in polymers as determined by the thermally stimulated current method

The method of thermally stimulated current (TSC) has been used to study the low-temperature dielectric β relaxations of several polymers including especially poly(vinyl chloride), poly(vinyl acetate), polyamide 6, 6,6,poly(t-butyl acrylate), poly(methyl methacrylate), poly(ethyl methacrylate), poly(phenyl methacrylate), and poly(t-butyl methacrylate). The distribution characteristics of the relaxation processes have been determined from the corresponding TSC peaks by a fractional polarization technique which consists of applying the electric field in several discrete steps during a slow cooling. Several common features have been found in all the polymers investigated: the β peaks are characterized by a distribution of relaxation times resulting from a distribution in activation energy and this distribution is quasisymmetrical and continuous. These facts are in agreement with the hypothesis of a relaxation involving local motions of small polar groups undergoing various interactions with the environment. Some discrepancy remains, however, between our calculated values of the mean activation energy and those obtained from the dielectric loss.     

High-Frequency Dynamical Behavior of Poly(ethylene glycol)+H2O Mixtures by Brillouin Spectroscopy

Brillouin spectroscopy has been used to examine high-frequency dynamical behavior of aqueous solutions of poly(ethylene glycol) (Mw ≈ 400g/mol) at 298K in the entire concentration region. It was found that a relaxation process takes place in the experimental frequency window that significantly affects the shape of experimentally recorded spectrum of the density fluctuations (dynamical structure factor). The process detected was attributed to segmental motion of the flexible polymeric chain. The full spectrum analysis of Brillouin spectra has been performed taking advantage of the relaxation function previously used in describing a single relaxation process in dielectric examination of water solutions of PEG 400. The proposed data processing procedure permits a qualitative reproduction of concentration dependencies of the hypersonic wave velocity and absorption measured. The shapes of the concentration dependencies of the relaxation times obtained from the Brillouin and the dielectric spectroscopies are in good agreement over a very broad concentration range, although their absolute values are scaled by the factor of 3. This result indicate that the two processes revealed independently by dielectric and Brillouin spectroscopies, apparently separated in time-scale, are just the same relaxation process.     

Effect of chemical structure on the volume-phase transition in neutral and weakly charged poly(N-alkyl(meth)acrylamide) hydrogels studied by ultrasmall-angle x-ray scattering

Neutral poly(N-isopropylacrylamide) (PIPAAm), poly(N,N-diethylacrylamide) (PDEAAm), and poly(N-isopropylmethacrylamide) (PIPMAm) hydrogels and their weakly charged counterparts prepared by copolymerizing with sodium methacrylate (x(MNa)=0,0.025,0.05) were studied using ultrasmall-angle x-ray scattering. The volume-phase transition in hydrogels was observed as an increase in the inhomogeneity correlation length of the networks. The change in inhomogeneity correlation length was abrupt in neutral PIPAAm and PIPMAm gels with increase in temperature but was continuous in neutral PDEAAm gels. Addition of ionic comonomer to the network backbone suppressed the volume-phase transition in poly(N-alkylacrylamide)s but not in PIPMAm. The observed differences in temperature-induced volume change of these three polymers in water cannot be rationalized based on their relative hydrophobicity and are instead explained by considering the hydrogen-bonding constraints on their thermal fluctuations. Both PIPAAm and PDEAAm undergo volume collapse since their thermal fluctuations are constrained by hydrogen bonding with water to an extent that beyond a critical temperature they seek entropic compensation. Although thermal fluctuations in both PIPAAm and PIPMAm are equally constrained, thermal energy of the latter can be relaxed via the rotation of alpha-methyl groups allowing it greater flexibility. Compared to N-alkylacrylamides, N-alkylmethacrylamide can thus sustain hydrogen bonding to relatively higher temperatures before seeking entropic compensation by undergoing volume collapse.     

Electrophoretic mobilities of large organic ions in nonaqueous solvents: determination by capillary electrophoresis in propylene carbonate, N,N-dimethylformamide, N,N,-dimethylacetamide, acetonitrile and methanol

The mobilities of the monocharged permanent tertraphenylphosphonium cation and tetraphenylborate anion are determined by capillary zone electrophoresis in different organic solvents as a function of the ionic strength, I, of the background electrolyte. The nonaqueous solvents are propylene carbonate (PC), N,N-dimethylformamide (DMF), N,N,-dimethylacetamide (DMA), acetonitrile (MeCN) and methanol (MeOH). The ionic strength is between 5 and 50 mmol/L. The mobility as a function of I is in good agreement with the theory of Debye, Hückel and Onsager (DHO), extended by the ion size parameter as introduced by Falkenhagen and Pitts. The values of the limiting DHO slopes of the mobility vs. I curves (the slopes express the influence of the solvent on the reduction of the mobility with increase of I) decrease in the order MeCN > MeOH > DMF > DMA > PC. Absolute mobilities (obtained by extrapolation to I = 0) of a particular ion differ by a factor of about 7 between the solvents. However, constancy within 10% is observed for their Walden products (the absolute mobility multiplied with the solvent's macroviscosity). The role of dielectric friction on the mobility of the present monocharged, large analyte ions is discussed according to the theory of Hubbard and Onsager. Based on the radii of the ions, the static permittivity of the solvent and its permittivity at infinite frequency, and the relaxation time of polarization, an equal contribution of dielectric and hydrodynamic friction is predicted in MeOH as solvent. Experimental data are in contrast to this prediction, indicating the overestimation of dielectric friction, and the dominance of hydrodynamic friction on the migration of the analyte ions in all solvents under consideration.     

Chain Dynamics of Polymers with Highly Flexible Side Groups

Summary: The relaxation behaviour of poly(5-acryloxy-5-methyl-2,3-dioxacyclohexne), poly(2,3-dichlorobenzyl methacrylate) and poly(3-chlorobenzyl methacrylate) was thoroughly studied by broadband dielectric spectroscopy with the aim of investigating how the chemical structure affects the response of polymers to electric perturbation fields over a wide temperature window. Retardation spectra calculated from dielectric isotherms utilizing linear programming regularization parameter techniques were used to deconvolute strongly overlapped absorptions. Special attention is paid to both the splitting region and the fitting of the Williams ansatz to the experimental results. Attempts are made to explain the molecular origin of the relaxations observed in the retardation spectra of the polymers.     

Tribological properties of hydrophilic polymer brushes under wet conditions

This article demonstrates a water‐lubrication system using high‐density hydrophilic polymer brushes consisting of 2,3‐dehydroxypropyl methacrylate (DHMA), vinyl alcohol, oligo(ethylene glycol)methyl ether methacrylate, 2‐(methacryloyloxy)ethyltrimethylammonium chloride (MTAC), 3‐sulfopropyl methacrylate potassium salt (SPMK), and 2‐methacryloyloxyethyl phosphorylcholine (MPC) prepared by surface‐initiated controlled radical polymerization. Macroscopic frictional properties of brush surfaces were characterized by sliding a glass ball probe in water using a ball‐on‐plate type tribotester under the load of 0.1–0.49 N at the sliding velocity of 10^?5–10^?1 m s^?1 at 298 K. A poly(DHMA) brush showed a relatively larger friction coefficient in water, whereas the polyelectrolyte brushes, such as poly(SPMK) and poly(MPC), revealed significantly low friction coefficients below 0.02 in water and in humid air conditions. A drastic reduction in the friction coefficient of polyelectrolyte brushes in aqueous solution was observed at around 10^?3–10^?2 m s^?1 owing to the hydrodynamic lubrication effect, however, an increase in salt concentration in the aqueous solution led to the increase in the friction coefficients of poly(MTAC) and poly(SPMK) brushes. The poly(SPMK) brush showed a stable and low friction coefficient in water even after sliding over 450 friction cycles, indicating a good wear resistance of the brush film. © 2010 The Japan Chemical Journal Forum and Wiley Periodicals, Inc. Chem Rec 10: 208–216; 2010: Published online in Wiley InterScience ( www.interscience.wiley.com ) DOI 10.1002/tcr.201000001     

Dielectric response of polar liquids in narrow slit pores

Based on molecular dynamics (MD) simulations and a simple (Stockmayer) model we investigate the static and dynamic dielectric response of polar liquids confined to narrow slit pores. The MD simulations are used to calculate the time-dependent polarization fluctuations along directions parallel and perpendicular to the walls, from which the components of the frequency-dependent dielectric tensor can be derived via linear response theory. Our numerical results reveal that the system's response is strongly anisotropic. The parallel dielectric function, epsilonparallel(omega), has Debye-like character very similar to the corresponding isotropic bulk function, epsilonbulk(omega), at the same chemical potential. Indeed, the main confinement effect on epsilonparallel(omega) consists in a shift toward smaller values relative to the bulk function. On the other hand, in the perpendicular direction we observe a characteristic peak in the absorption part of the dielectric function, epsilonperpendicular(omega). This peak is absent in the bulk system and reflects strongly pronounced, damped oscillations in the polarization fluctuations normal to the walls. We discuss two possible origins of the oscillations (and the resulting absorption peak), that is collective oscillations of dipoles in clusters formed parallel to the walls, and the existence of a "dipolaron mode" previously observed in MD simulations of bulk polar fluids.     

A theory of electrolyte friction on translating polyelectrolytes

Enormous increases in friction factors of isolated polyelectrolytes have been observed when the concentration of added monovalent salt is decreased below 10^?2M. Electrolyte friction on translating polyions, analogous to dielectric friction on translating small ions, is postulated to account for this effect. A quantitative theory of this electrolyte friction is developed, based on the fluctuating force formulation of Kirkwood and Previous development of the author for the dynamics of smallion concentration fluctuations. By modelling the flexible linear polyelectrolyte as a charged gel sphere of constant radius equal to the measured hydrodynamic radius in 1.0 M NaBr, where electrolyte friction is negligible, and employing the theory of Harris and Rice to determine the net charge on the sphere, remarkably good agreement with the data is obtained using no adjustable parameters. Polyion expansion of only a few percent would make the agreement perfect. Diffusion of polyions at finite concentration is discussed in the light of the present work, and it is suggested that an appropriate reinterpretation of parameters in the existing theories can account for the observed dependence of the measured diffusion coefficients on salt and polyion concentration in the linear range.     

Dynamics of water in partially crystallized polymer/water mixtures studied by dielectric spectroscopy

The dielectric relaxation process of water was investigated for polymer/water mixtures containing poly(vinyl methyl ether), poly(ethyleneimine), poly(vinyl alcohol), and poly(vinylpyrrolidone) with a polymer concentration of up to 40 wt % at frequencies between 10 MHz and 10 GHz in subzero temperatures down to -55 degrees C. These polymer/water mixtures have a crystallization temperature TC of water at -10 to -2 degrees C. Below TC, part of the water crystallized and another part of the water, uncrystallized water (UCW), remained in a liquid state with the polymer in an uncrystallized phase. The dielectric relaxation process of UCW was observed, and reliable dielectric relaxation parameters of UCW were obtained at temperatures of -26 to -2 degrees C. At TC, the relaxation strength, relaxation time, and relaxation time distribution change abruptly, and their subsequent changes with decreasing temperature are larger than those above TC. The relaxation strength of UCW decreases, and the relaxation time and dynamic heterogeneity (distribution of relaxation time) increase with decreasing temperature. These large temperature dependences below TC can be explained by the increase in polymer concentration in the uncrystallized phase C(p,UCP) with decreasing temperature. C(p,UCP) is independent of the initial polymer concentration. In contrast to the relaxation times above TC, which vary with the chemical structure of the polymer and its concentration, the relaxation times of UCW are independent of both of them. This indicates that the factor determining whether the water forms ice crystals or stays as UCW is the mobility of the water molecules.     

The Vinyl Homopolymerization of Norbornene

A full literature and patent account (about 100 references) is given on work describing vinyl polymerization to form the homopolymer poly(norbornene). The interest in vinyl‐poly(norbornene) is driven by its dielectric and mechanical properties for the technical application as an interlevel dielectric in microelectronics applications. For comparison, the norbornene/olefin copolymerization is discussed also. The metal catalysts are introduced and important polymer product properties are emphasized. The six possible isomers for stereoregular poly(norbornene) are presented.     

Dielectric friction as a mechanism for selectivity alteration in capillary electrophoresis using acetonitrile-water media

The mobilities of a series of aromatic carboxylates and sulfonates, ranging in charge from -1 to -4, were investigated as a function of acetonitrile concentration in the electrophoretic buffer. Absolute mobilities were determined by extrapolation of the effective mobilities to zero ionic strength according to the Pitts' equation. In general, anions of higher charge were more strongly influenced by ionic strength, with similarly charged anions experiencing ionic strength effects that were not significantly different at the 95% confidence level. Furthermore, the relative magnitudes of the Onsager slopes varied with acetonitrile content according to the z/(etaepsilon(1/2)) dependence in the electrophoretic effect of the Pitt's equation. Addition of acetonitrile to the electrophoretic media resulted in changes in the absolute mobilities of the anions. These acetonitrile-induced selectivity alterations were attributed to dielectric friction. As predicted by the Hubbard-Onsager model of dielectric friction, changes in sulfonate mobility were shown to correlate to changes in solvent viscosity (eta), dielectric constant (epsilon), and relaxation time (tau). The combined effects of ionic strength and dielectric friction caused analytes with higher charge-to-size ratios to be slowed to a greater extent upon addition of acetonitrile compared to those with lower charge-to-size. For example, at 75% acetonitrile and 20 mM ionic strength, a migration order reversal occurred between the triply and singly charged sulfonates.