1
Piezo- and ferromagnetic properties of polyvinylidene fluoride
(PVDF) from a molecular perspective
David Johannes Schreuder BSc
Abstract
The polymer polyvinylidene fluoride (PVDF) exhibits piezoelectric activity which has a different nature from the classical inorganic piezoelectric materials (PEMs). The nature of the piezoelectric effect (dipole kinetics) is currently under debate and several physical models describing ferro- and piezoelectricity of inorganic materials are suggested to be apllicable to PVDF. From a different point of view, molecular mechanisms have been proposed in order to examine molecular reorientations occuring in PVDF. This literature study surveys both approaches with the goal of identifying in molecular attributes that influence ferro- and piezoelectric properties of PVDF. In present literature it was reported that kinetic dipoles in PVDF films most strongly resemble the extrinsic mechanism, in which the switching time can be expressed as an exponential function of the applied electric field (Merz’s equation). Switching time in thin films is well described by this equation, while domain wall motion appears to influence dipole kinetics in thicker films. PVDF molecules invert dipole direction from internal rotations through distinctive pathways depending on the crystalline phase. Additionally, the effect of the electrode in ferroelectric devices is emphasized which affects dipole kinetics in thin films through electrode-film interactions.
2
Introduction
Piezoelectric materials (PEMs) are a class of solid materials that can exert an electric field if strain or stress is applied and vice versa. This property is of great importance in mechanically controlled devices: if a mechanical force is exerted on this material a voltage can be generated. Devices that contain PEMs are, for instance, microphones and amplifiers. The latter underlines the reciprocal behaviour of piezoelectricity: induction of mechanical movement (causing sound waves) when an electric field is applied. Piezoelectricity is closely related to ferroelectricity; solid materials that possess spontaneous polarization that can be reversed in direction by applying an external electric field. The important difference is that in piezoelectricity, this reversal of polarization can occur by applying physical stress to the material.
In 1880, the brothers Jean and Pierre Curie first observed piezoelectricity for quartz crystals (SiO2).1 With the development of electrical devices piezoelectric materials garnered interest for electrical appliances. In the 50’s, BaTiO3 was used to fabricate multilayered capacitors (MLCs)2 and later other types of perovskites, such as Zincronium Titanate (PZT) were also identified to exhibit strong piezoelectric response. Despite their toxicity, such materials are currently used as actuators of high resolution academic devices such as atomic force microscopy (AFM).3 Further research in organic PEMs would contribute to avoiding usage toxic inorganic materials.
In 1924, it was found that organic polymers such as celluloid and hard paraffin were also shown to exhibit some piezoelectric activity, even though the piezoelectric performances were significantly lower compared to the traditional inorganic PEMs. Nearly half a century later, in 1969, polyvinylidene fluoride (PVDF) was introduced as a PEM showing promising piezoelectric properties (figure 1).4 Since then, extensive research has been performed on PVDF and its application within mechanical devices. The most important current industrial applications are insulating wrapping for electrical wiring and filtration membranes for water in chemical labs. Beside industrial applications,
PVDF finds its application in various physical and chemical research fields. For example, an important application of this material is in microphones due to its relatively low acoustic impedance,5,74 but has also gained attention in research as a resistance random-access memory (RRAM) material.6 More recently, PVDF has been applied as an energy storing device71,72 and as an electromagnetic absorber (EMA).73 Additionally, it was found that introducing a thin PVDF layer in organo photovoltaic (OPV) devices facilitated charge separation and can increased efficiency by 200%.75
Figure 1: structural representation of polymerisation of vinylidene fluoride (VDF) monomers to obtain the polymer consisting of n monomers. Note that only after polymerization a transverse dipole moment with respect to the chain appears
With different types of materials that exhibit piezoelectricity, the question of what requirements need to be met for materials to classify as a PEM arises. Broadhurst and Davis8 postulated four requirements that a material must possess:
(a) the presence of permanent dipole moment; (b) the ability to orient or align the dipole moment; (c) the ability to sustain this dipole alignment once it is achieved; and
(d) the ability of the material to undergo large strains when mechanically stressed.
Note that, for a material to be piezoelectric it must also be ferroelectric, but not vica versa. Inorganics, such as perovskites contain permanent oriented dipole moments in their unit cells, obeying rules (a to c). In the case of polymers, dipole orientation is dependent on the conditions under which the polymer is solidified from solution. If for instance, the solid phase contains crystals, which have a centre of symmetry, rule (a) is disobeyed and the material does not show piezoelectric activity. As is often the case, the morphology of polymers can be quite complex due to the presence of amorphous and (multiple) crystalline phases. By rational choice of molecular species and fabrication
3
methods properties (a-d) can be enhanced,9-12 for instance through the use of polar solvents and the introduction of different monomers (in copolymer films).13 The tunability of the piezoelectric properties from the fabrication method distinguishes the organic materials from the inorganic materials, and therefore piezoelectric properties of organic materials are more heavily tied to their fabrication method.
PEMs are generally compared in piezoelectric activity via a set of piezoelectric constants: dij and gij. The constants dij [C/N] (piezoelectric voltage constant) and gij [Vm/N] (piezoelectric strain constant) quantify the amount of charge and the electric field generated per unit stress, respectively. The subscripts i and j indicate the direction of the field and the stress, respectively. The numbers corresponding to the dimensions of stress and electric field are depicted in figure 2. Subscripts 1-3 can correspond to both electric field and stress vectors and 4-6 indicate (shear) stress. In practice, d is more frequently measured than the g coefficient, in particular d33 because it is the highest of all dij coefficients (table 1) and therefore most relevant in piezoelectric applications. Negative values of dij indicate that compression occurs when an electric field is applied, while positive values indicate expansion in that direction.
Currently, some of the most commonly used techniques for experimentally measuring these coefficients are as follows: The Berlincourt method, the frequency method, and laser interferometry.
The Berlincourt method measures the charge
generated when a force is exerted on a PEM which can be directly related to the piezoelectric coefficients. This method is most frequently used to determine d33.77 The frequency method measures the impedance spectrum of a PEM. This is a reliable method for the calculation of the d33 coefficient and additionally allows for the determination of the entire dij matrix. However, to obtain all dij coefficients, three different sample geometries with dictated dimensions are required (plate, disc and cylinder).14 These geometries are not accessible for all PEMs. Laser interferometry directly observes the mechanical movement of a sample under an applied voltage (reversed
piezoelectric effect) by measuring the change in deflection of light. The method requires nanometer-scale resolution and therefore suffers from vibrations occurring during the measurements. Although the techniques are of a different nature, they yield comparable magnitudes and standard deviations of piezoelectric constants for ceramic PEMs.14 Allthough all methods have been applied on PVDF in seperate publications, no comparison of the constants obtained from different methods is reported. Comparing the methods on different samples is meaningless, as the observed coefficient depends on the method of fabrication. coefficients of PVDF in different dimensions of electric field and stress (ij) are provided in table 1.15
Table 1 and figure 2: Piezoelectric strain coefficients for PVDF obtained from the Berlincourt method. dij indicates the
measured electric response in i-direction when stress (stretching or shearing) in the j-direction is applied on PVDF films.15
The intrinsic physical property related to these coefficients is the dipole orientation in a PEM. The extent to which the individual dipole moments are aligned within a solid determines the electric field strength that can be created by exerting external stress. The total polarization is the vector sum of all dipole moments in the sample as shown in Eq. (1).
(1) 𝑃⃗ = ∫ 𝑑𝑉 𝜌(𝑟 )𝑟
Where 𝑃⃗ is the total polarization of the sample (V), and 𝜌(𝑟 ) the seperate dipole moments as a function of the position vector. The total polarization usually determined via experiments that make use of the ferroelectric effect, where
4
interaction of electric field with individual dipoles can change the dipole orientation. By applying an alternating current (AC), PEMs can subsequently
switch their dipole moments, meaning the dipole
moment will end up facing in the opposite direction, illustrated in figure 3. The total polarization of the sample can be extracted from the current during a (PE) hysteresis loop. This loop has a central role in the performance of PEMs, as it reveals quantitative information of polarization in a PEM. A more detailed description of the hysteresis loop will be provided later on.
Figure 3: Schematic representation of dipole switching in ferroelectric materials. The arrows indicate the individual dipole vectors (𝜌(𝑟 )) in the sample. Applying an alternating current (AC) to the ferroelectric results in allignment of dipole moment with the applied field, resulting in switching. The mechanism of dipole switching is discussed later on.
To this date, there is no clear understanding of the kinetic model by which dipoles reorient in PVDF. While some research groups take a rather physical approach (that is, an approach were several models that apply to inorganic PEMs are used to describe dipole kinetics in PVDF.),23,33-35 several molecular mechanisms have been proposed as well, taking the molecular motions into account.21,24-26,59-61,63-65 As we shall see later on, the approaches are focused on different aspects, and the characteristic quantities of a PEM (such as the total dipole switching time, polarization values, the electric field necessary to induce such dipole reorientations) are derived from physical methods. Depending on the method of preparation, PVDF films can strongly alter in their morphology due to the complexity of the molecular structure. Such molecular subtle differences can have a significant effect on the aforementioned physical constants. This literature study will focus on the fundamental piezoelectric properties of PVDF. The following text is structured as following: First an introduction to several physical models for dipole kinetics will be described, and relevant physical properties of ferroelectric materials will be introduced. Then, the molecular model related to the piezoelectricity in
PVDF will be discussed. Lastly, the molecular properties significant for the ferro- and piezoelectric properties of PVDF will be summarized.
Dipole switching
Thermodynamic approach
The thermodynamic approach to describe the polarization (P) of a crystal is through the Landau formalism. The Gibbs free energy as a function of the polarization is expressed as a Taylor expansion as in Eq. (2). (2) 𝐺(𝑃) = 𝛼(𝑇 − 𝑇0) ( 𝑃2 2) + 𝛽 ( 𝑃4 4) + 𝛾(𝑃 6/6) + 𝐸𝑃
The direction of polarization does not influence the Gibbs free energy, thus G(P) = G(-P) and therefore only even powers appear in Eq. (1). For a stable phase, 𝑑𝐺
𝑑𝑃= 0 and 𝑑2𝐺
𝑑𝑃2> 0 should be considered. The Landau plot represents the Gibbs free energy as a function of the polarization. Below the Curie temperature Tc, Eq. (1) is expected to contain two minima located at 𝑑𝐺
𝑑𝑃= 0 (𝐺(𝑃) = 𝐺(−𝑃)), which represent the values of remnant polarisation of the ferroelectric component (the polarization in the absence of a field, Pr). A transition from Pr to -Pr (and vica versa) would require energy as 𝐺(𝑃 = 0) is the maximum (figure 4).27 Above the Curie temperature, 𝐺(𝑃) has a minimum at 𝑃 = 0 (loss of polarization).
Figure 4: Gibbs free energy as a function of the polarization for T = Tc and T > Tc (dashed lines) and T < Tc (solid line).27
AC (alternating current)
5
From the derivative 𝑑𝐺
𝑑𝑃= 0 a relation between P and E (electric field) can be extracted (Eq. (3)).
(3) 𝛿𝐺/𝛿𝑃 = −𝛼(𝑇 − 𝑇0) − 𝛽𝑃3− 𝛾𝑃5 + 𝐸 = 0
This relation describes the ferroelectric effect (change of polarization in the presence of an electric field). It is the well known (PE)-plot/hysteresis loop (figure 5), and it visualizes the polarization response of the sample to the applied electric field, i.e. the switching the orientation of dipole moments induced by an electric field. From
this plot, three important parameters describing the performance of a ferroelectric (and piezoelectric) material can be determined:
Ec : The Coercive field strength, describing the magnitude of the electric field necessary to induce a dipole switching transition. In the (PE)-loop Ec is defined as 𝐸(𝑃 = 0).
Pr : The remnant polarization: The polarization magnitude when the electric field is absent.
Ps : The saturated polarization: The maximum obtainable polarization if the sample is exposed to an electric field.
Figure 5: (a) Representation of a hysteresis loop in ferroelectric materials predicted by Eq. (3). Points A (Ec, Ps) , B (0, Pr),
and C ((-Ec, P(-Ec), and O (0, 0) indicate physical relevant points in the the ferroelectric effect. (b) Experimentally obtained
hysteresis loops of ferroelectrics. The commonly reported ferroelectric parameters related to the PE loop are shown, with Ek = Ec.28
Figure 5a shows a theoretical (PE)-loop from Eq.
(3) and figure 5b one that is experimentally obtained, where Ec (Ek in image) is the coercive field strength and Pr is the polarization of the sample when E = 0. Therefore, the normalized points E/Ec (point C, C’) and P/Ps indicate at what point the coercive field strength and the remnant polarization is applied. A PEM in the absence of an electric field located is in point B (or equivalently B’) the net polarization equals the remnant polarization of the sample. Applying a field will
cause the polarization to switch, moving along the B-C (or B’-C’) line. The regions A-B (and A’-B’) are stable regions, while B-C (and B’-C’) are metastable regions. Starting from point B, if a field is applied E < Ec, point C is not reached and after the field is switched off the PE loop will return to stable point B. If, however, a field with strength E > Ec is applied, the polarization will be switched and line A’ - B’ will be reached.28
The Landau formalism described above is solely applicable to single crystals, which have a unique domain (corresponding to a unique Ps value) over the entire crystal. Ferroelectrics, however, consist of many different domains with different
spontaneous polarisation magnitudes. Therefore,
this sample is consisting of an ensemble of Landau potentials, or in other words: an ensemble of spontaneous
polarisation vectors.27 Such areas within the sample that contain different Landau potentials are called domains and they are separated by a
Polariaztion
Electric Field
6
domain wall. A complete change of the total
polarization (the piezoelectric effect) can occur by motion of these walls, whereby the domain polarisation is changed. This is a process referred to as extrinsic switching of dipoles. A domain is correlated to a critical volume, which means below a certain sample thickness such walls do not exist.23 In that case, the dipoles are switched, not due to wall motions, but rather switch homogeneously; this is referred to as intrinsic
dipole switching.
For the extrinsic mechanism, where domains in the sample subsequently switch, a gradual transition along the vertical line (B-C-A’-B’) is observed in
figure 5a. This can be thought of as a first order
(continuous) phase transition. For a homogeneous switching mechanism, the polarization is switched in a discontinued fashion (second order phase transition), and if E>Ec, the polarization switches simultaneously. Theoretically, the switching trajectory would then evolve along the dynamically unstable B-C-O-C’-B line. However, such a hysteresis loop is not experimentally observed because the C’-O-C line is dynamically unstable and a graph similar to figure 5b is obtained in both mechanisms.27,28 Equivalently, the polarization is inverted and located in point B’ when the field is removed, but the coercive field value and time in order to switch the polarization will be fundamentally different.
In the following section, the mechanisms related to the dipole inversion will be discussed in more detail. An important notion is that these mechanisms have been derived from inorganic ferroelectrics, which have a very different origin of the piezoelectric effect; In PVDF, molecular orientation is responsible for the ferroelectric effect, while for perovskite it is the displacement of ions. As we shall see, the mechanism for dipole switching in PVDF is a topic which is currently debated over,28-32 as the thin films show experimental values for dipole switching that can’t be correctly described by one mechanism.
Models for dipole inversion
Extrinsic mechanism
The most widely applied dipole kinetic model is the extrinsic mechanism. The fundamental principle of the model is that the change of total polarization occurs gradually, determined by two factors:
1. Nucleation (phase transition) of domains with opposite polarization in the presence of an applied electric field.
2. Growth of this domain, accompanied by the domain wall motion.
When applying an electric field (in the opposite direction of initial polarization) some regions in the sample will align to the electric field creating a domain which can expand during the time the field is applied. The result is that, after a certain exposure time to an electric field, the polarization will have switched for the entire material. There are two known variations to this mechanisms called the Kolmogrov-Avrami-Ishibashi (KAI)-model and the nucleation-limited-switching (NLS)-model.33,34
In the KAI-model, nucleation sites are assumed to be homogeneously distributed over the sample. The model states that switching the dipole moment at local domains in the sample corresponds to an unique switching time (and coercive field). In the extrinsic mechanism, the time it takes to switch from the remnant polarization to a stable point in opposite polarization is defined as 𝜏ex. The relation between the time constant and electric field changes for varying field strength. For lower electric fields, the switching is mainly determined by nucleation (consideration (1)) via Merz’s equation (Eq. (4)),
(4) 𝜏𝑒𝑥= 𝜏∞𝑒(𝐸′/𝐸)𝑛
where n is the dimension of domain growth, E is the applied electric field, E’ is the coercive field strength and 𝜏∞ is the switching time constant when E = E’, for PVDF usually in the range of 2-5 ns.39,40
When the ferroelectric is exposed to a high field strength the mobility of the wall growth is rate determining for the switching time, described by Eq. (5),
7
(5) 𝜏𝑒𝑥= 1 𝜇(𝐸 − 𝐸′)
where μ is the mobility of domain walls, E’ is the coercive field strength. Additionally, E’ is a value that determines the range/validity of the equation (E must be larger than E’).
While this predicts the dipole kinetics of relatively bulk material appropriately, it fails to describe the longer switching times in thinner inorganic films (below d~150 nm).35
To account for the latter observation many authors refer to the NLS-model.34 The model describes thinner films, where the amount of nucleation sites is significantly reduced. For this reason, the nucleation (1) is assumed to be much slower than the wall domain motions (2), i.e. (1) determines the switching time rather than (2).7,34
The mathmatical description of dipole switching in the NLS-model (Eq. 6,7) is similar to the KAI-model. The most important difference in the two models is that for the NLS model, a distribution of time constants is involved due to inhomogeneous regions in the sample.34,36,37 Such a distribution can be attributed to the crystal defects that causes a discrapancy in energy barriers for nucleation in different local regions in the film. Under the assumption of mean field theory, time constant distribution might be described by Gaussian functions. Von Seggern et al. fitted PZT switching time distributions to Gaussian functions but observed deviations.80 Alternatively, Lorentzian functions fitted the time scale distribution of thin PZT films more properly.35 A better fitting of the time scale distribution to Lorentzians might be attributed to the fact that magnetic line broadning due to dipole defects also follows a Lorentzian distribution.78 Distribution of time constants get to be more pronounced in thin films, as the variation in film thickness at local spots in the film (the roughness of the film) is larger relative to the total thickness, creating inhomogeneous locations in the sample, which affect the locally observed switching times.38
As stated above, the extrinsic time constant is assumed to be unique for a sample in the KAI-model, while the NLS-model predicts an ensemble of time constants in the sample. Consequently, the time constant correlated to the NLS-model is Gaussian-distributed (Eq. (5)) or Lorentz-distributed (Eq. (6)).35
(6) 𝜏𝑒𝑥= (𝜏∞𝑒(𝐸′/𝐸)𝑛)(𝐺(𝜏𝑒𝑥)) (7) 𝜏𝑒𝑥= (𝜏∞𝑒(𝐸′/𝐸)𝑛)(𝐹(𝜏𝑒𝑥))
For thin PVDF:TrFE (copolymer) films, the coercive field strength of domain wall growth is an order of magnitude smaller than the coercive field strength in its nucleation.38,41-43 Because the latter has a much stronger coercive field, the observed time constant is mainly dependent on nucleation rather than domain wall growth (see NLS model).40 Note that Eq. (5) only applies to dipole kinetics that are not solely determined by nucleation (Eq. (5, 6, 7)) and therefore Eq. (5) only applies to dipole kinetics that follow the KAI-model.
Models for dipole inversion
Intrinsic mechanism
The intrinsic mechanism is a much more rare mechanism, in which the polarization is switched homogeneously (as a “single domain”) rather than domain by domain. In order to induce this switching mechanism, a coercive field of great magnitude is necessary (order of 𝐸 𝑐 = 1 𝐺𝑉/𝑚). The process is further known to be of a threshold nature; below the coercive field strength, no dipole switching is observed. To observe this theoretical possible mechanism, many efforts have been made to suppress the extrinsic mechanism. One of these methods is to reduce sample thickness to ~10 nm thick films. As ß-phase PVDF chains are separated by ~0.5 nm, such samples consist of only ~20 PVDF chains.39 Such samples would be too small for stable domains to form, which inhibit the extrinsic switching mechanism. For PVDF:TrFE copolymer films of this size the deviation from extrinsic switching kinetics has been attributed to the intrinsic switching model, but this claim has been disputed.28,30,31,45
8
As the switching kinetics inorganic films with thickness 𝑑 < 150 nm deviate severely from the extrinsic model, Ducharme et al. suggested that organic films like PVDF also contain a critical thickness at which the intrinsic mechanism would dominate. In their work, they have tried to induce this switching mechanism by preparing LB-films of various sample thickness (down to a few nm).28,29,32 It was demonstrated that for thick films the thickness of PVDF films scales with the coercive field, comparable to earlier experiments 𝐸𝑐 = 𝑑−2/3 , while below a critical thickness (𝑑 < 10 nm), the coercive field is independent of the sample thickness. The saturation in the coercive field strength lead to the conclusion that it is the intrinsic switching mechanism that occurs below this thickness.29
The inverse of the time constant that relates to the intrinsic dipole switching, is derived from the Landau formalism and given as following;
(8) 𝑅𝑎𝑡𝑒 = (1/𝜏𝑖𝑛) = (1/𝜏ℎ (𝑇)
)√(𝐸/𝐸𝑐− 1)
Where 𝜏𝑖𝑛 and 𝜏ℎ represent the intrinsic switching time and a temperature dependent factor that approaches the Curie temperature, respectively.32 This is quite surprising, as in the extrinsic mechanism increased temperature accelerates the dipole switching rate. Interestingly, the time scale in which intrinsic switching would occur is in the order of seconds, which can be 6 orders of magnitude slower than the extrinsic mechanism.29
Table 2 presents switching time values attributed
to intrinsic and extrinsic switching mechanism. Both samples where similiar fabricated 70:30 PVDF:TrFE films with a thickness of 5 nm (intrinsic) and 50 nm (extrinsic).28 It should be noted that the time constant are dependant on experimental parameters such as pulse time and electric field strength. The purpose of this table is only to point out the difference in order of magnitude for the different mechanisms.
Switching mechanism Switching time (s)
Extrinsic (d = 50 nm) 1.0 Intrinsic (d = 5 nm) 100
Table 2: Comparison of switching time constants in literature for the which are attributed to the intrinsic and extrinsic switching mechanism. The switching times correspond to electric field strengths of E/Ec ~ 1.1. Both samples were
Langmuir Blodgett fabricated 70:30 PVDF:TrFE.28
Although several authors later reported intrinsic dipole switching in PVDF,45,53 this kinetic model is not widely accepted; Bralovksy and Levanyuk state in a reply to Ducharme et al. that the observation for this mechanism in PVDF that some misinterpretations have been made, most importantly that the use of the Gibbs free energy is invalid because the phase transition is a strong first order phase transition, rather than a weak one.31 Consequently, Eq. (8) would not be appropriate to be used to describe the dipole kinetics of this system.54 They support this statement by mentioning the mixed character of a PVDF (copolymer) film, i.e. a crystalline and amorphous mixture. In their defence, Ducharme et al. claim that the ferroelectric material actually can be considered as a single domain, since they are annealed in a proper manner and therefore the sample would consist of only one homogeneous crystalline phase. However, the authors did not provide a quantitative crystalline characterization of their thin films to prove this statement. This raises the question whether the intrinsic model is applicable to organic ferroelectrics or wheter the observed coervive field is affected by a different mechanism.
9
Time constants and coercive field
The time constants are experimentally determined via the time-domain induced polarization method, in which the PVDF thin film is connected to two electrodes. When pulsed voltages are applied, the current is measured as a function of time after the pulses. The current can be related to the polarization of the sample by Eq. (9):
(9) 𝑃(𝑡) = (𝑄1(𝑡) − 𝑄2(𝑡)) 1 𝐴
Where Q1 and Q2 are the measured currents in two different directions and A is the area of the electrodes.50 To avoid long waiting times between applying pulses, the time constant 𝜏exis defined as the time at which the polarization is 90% of its maximal value; 𝑃(𝜏𝑒𝑥) = 0.9𝑃𝑠. It should be noted that with this method the pulse duration (i.e. the time in which the electric field is applied) is of influence for the polarization switching. Applying the coercive field over too short of a pulse duration, the polarization does not switch to a stable (inverted) polarization, but the initial polarization value is regenerated. Therefore, the coercive field should be applied for at least as long as the switching time when obtaining the time constant of polarization switching.51 A similar but more sophisticated method to measure the polarization is the three pulse method, in which several effects causing a bias when determining the time constant (high-frequency polarization, Kohlrausch relaxational polarization, space charge polarization and leakage currents) can be eliminated.52
Another way to look at this is that the AC-frequency affects coercive field. Analytical expressions are provided in ref. 44 but are beyond the scope of this literature study. It is shown that the coercive field increases that the with increasing AC-frequency.44 The observed coercive field for ferroelectric films therefore can vary (within the same sample), usually in the range of Ec ~ 70-250 MV/m. For inorganic PEMs it was shown that AC frequency depends different on Ec in different frequency domains, attributed to a competing nucleation process with domain wall motion.44
Later, the same phenomenon has been observed for PVDF films within sample thickness 𝑑 = 160 − 500 nm.45 Note that this observation disputes the the NLS model that assumes nucleation is rate-determining for polarization switching. Another general property of the coercive field is that it increases with reducing sample thickness as 𝐸𝑐 = 𝑑−2/3, derived from a model describing energetics of stable (opposite) domain formation.70 Such behaviour is especially problematic in the application of (ultra)thin PVDF films in electric devices. Interestingly, it has been shown that the coercive field strength can be reduced by simply reducing the sample area of thin PVDF films. This is attributed to a decrease in interchain van der Waals interactions that inhibit nucleation.46 Experimental values for the coercive field of PVDF are usually in the range of 70-250 MV/m. Such values are approximately 3 orders of magnitude larger than the inorganic BaTiO3. However, applying fields of 70-250 MV/m to inorganic materials such as BaTiO3 (with the desire to reduce switching time) would not be possible, as the breakdown field would be exceeded.79
Sharma et al. have investigated wall domain motion in thin PVDF films.37 By including a built-in potential in PVDF:TrFE (75:25) films, the energy profile in figure 4 could be desymmetrized, i.e. stabilizing a particular direction for polarization. It was visualized with AFM that domain walls in such PVDF films grow differently depending on the direction of polarization; switching polarization to the stabilized direction grow anisotropically (figure
6a) and isotropically to the other polarization
direction (figure 6b). The difference is attributed to the fact that in the former the energy barrier in the image is lowered upon applying a pulse (15 V). Consequently, random crystal defects give a more significant contribution to the total energy required, causing anisotropic domain growth through the film. When a pulse in the opposite direction is applied (-20 V), the energy barrier increases and structural defects have relatively little influence on the growing process, resulting in more isotropic domain wall growth.37 Other
10
research has observed similar rough domain wall structures in PVDF films.47-49 The results point out that microscopic wall domain kinetics are deviating through the domain when the energy barrier between the two polarization states is lowered. Such inhomogenicity in domain propagation might be related to the NLS model, which states that switching times are dispersed due to crystal defects. It would imply that switching time is distributed to a higher degree if the energy barrier between the polarization states is reduced.
Figure 6a/b: AFM visualized domain wall growth in (free energy-polarization)-desymmetrized PVDF:TrFE (75:25) films where the polarization down (Pd) is lower in free energy thenupward polarization (Pu). The time values indicate the delay
between the pulse and the measurement. (a) Polarization switching to the energetically favoured direction (Pd) creates a
lower energy barrier. (b) Polarization switching to the energetically unfavourable direction (Pu) creating a higher energy
barrier. The consequence is that (a) grows significantly more anisotropic than (b).37
Finite size effects
Electrode-film interface interactions
The results of Ducharme et al. interpreted as intrinsic dipole switching contained samples with a significantly reduced thickness (~10 nm). In such films, local effects can affect the dipole switching behaviour severely. For instance, Domain wall
pinning55 is a mechanism that might explain the observations that are related to the intrinsic mechanism for PVDF films. Structural defects can cause a domain wall to be stabilized at a predetermined region (pinning). (Electrical) energy is required in order to destabilize the wall and
induce further depolarization.56 In relatively thick samples this effect does not significantly influence the observed coercive field. However, it becomes more pronounced at thinner samples as the nucleation volume is reduced, i.e. with a significantly reduced thickness.
Beside structural defects in the film, the type of electrode significantly affects the observed coercive field. At the PVDF-electrode interface compensation charges are present that stabilize the polarization of PVDF molecules. Such charges cause depolarization fields and contribute to the observed magnitude of the polarization and Ec.57
11
This suggests that the electrodes rather than the material could determine the correlation between sample thickness and Ec. Dependent on the type of electrode, these interactions can be either small (perfect electrode without significant screening length) or larger (imperfect electrode with finite screening length). Kliem et al. observed a different sample thickness dependence on Ec of PVDF films (i.e., no saturation of Ec observed for films down to 2.5 nm thick)50, and De Leeuw et al. suggested that the different behaviour of Ec could be attributed to the electrodes rather than the PVDF films.30 Interestingly, it was demonstrated that similar prepared PVDF films connected to gold electrodes revealed saturation of Ec at a thickness of 60 nm. The results underline that saturation of Ec is not an intrinsic material property and that Ducharme et al. have not observed a threshold coercive field for PVDF. In conclusion, it was shown that electrode-film interactions play a crucial role in the saturation behaviour of Ec in thin PVDF films. Remarkably, the conclusion drawn by De Leeuw et al. had already been published in a more general theoretical model for charge compensation in ferroelectrics in 1972.58
Molecular conformations related to
piezo- and ferroelectricity
Despite a dipole moment being present in the molecular structure of polyvinylidene fluoride (PVDF) (figure 1), the material itself is not piezoelectric after crystallization under standard conditions. In the first observation of piezoelectric response of polyvinylidene fluoride (PVDF) by Kliem et al., it was found that PVDF would exhibit
piezoelectric activity after the polymer undergoes a process called poling, which means that an electric field is used to align the dipole moments PVDF.1 The fact that a PVDF can be modified to a PEM was a breakthrough of major significance, because polymers have some advantages in comparison with inorganic materials: The film thickness can reduced to several nanometers while maintaining their molecular properties. Additionally, polymers are generally more flexible materials. However, polymers often contain a relatively low piezoelectric coefficients compared to that of inorganic PEMs (for instance, d33 of PZT and PVDF are 153 and -32.5 pC/N respectively). Numerous research has been conducted in order to enhance the piezoelectric effect (i.e. to increase the piezoelectric coefficients) of PVDF.13,16,17
PVDF units in the polymer contain a dipole moment due to the relatively high electronegativity of the fluoride atoms. For an individual monomer in the PVDF chain, there exist two dipole moments; one in the transverse and one in the longitudinal direction of the chain. The total dipole moment of a PVDF sample quantifies to what extent these individual components are aligned. Different solid phases have different contributions to the dipole moment of PVDF. Beside an amorphous phase, PVDF is known to exist in five different crystal structures (the α-, ß- δ-, ɛ-, and ɣ-phase).18 The different crystalline phases are depicted schematically in figure 7a. The α-phase is thermodynamically the most stable and predominantly formed when the polymer is crystallized under standard conditions. The α-phase and ɛ-α-phase are undesired in
Figure 7a: The molecular structures of a single PVDF chain (containing 5 monomeric units) in 5 crystal phases. Based on this single-chain representation, Two sets of crystal phases can’t be distinguished basesd on this single chain representations (see figure 7b below).
12
Figure 7b: the non-polar α-phase (black structure) and polar
δ-phase (red structure) of PVDF.
The geometry of individual chains is equivalent, but the α-phase contains chains in which the fluoride are oriented in- and out of plane alternating, while the fluorine atoms in the δ-phase are oriented in one direction (here out of plane). The ɣ- and ɛ-phase are distinguished via the interchain packing as well.19,76
the development of piezoelectric PVDF films, because no dipole moment is present. Despite the polarity, the ɣ-phase has not been extensively studied because it is relatively hard to obtain. Of all the other phases, the ß- and δ-phase are the phases which contain a net dipole moment (D) in their crystal lattice. The highest piezoelectric effect is generally observed for PVDF with a high ß-phase crystalline content (𝐷ß= 7 ∙ 10−30Cm per monomer). Although the crystal structure of the single chains is the same for the α- and δ-phase, the packing of multiple chains is different.19 This difference in packing equivalently discriminates the polar ɣ-phase from the nonpolar ɛ-phase.76 The consequence is that PVDF films containing the α-phase do not contain a net dipole moment whereas the ones containing δ-phase do (𝐷δ = 4 ∙ 10−30 Cm per monomer). The difference between the α- and δ-phase is illustrated in figure 7b. The existence of so many different phases in this material result in a complex morphology of PVDF films. Numerous techniques are developed to obtain films with the desired ß-phase, and protocols for developing PVDF films up to high content ß-phase have been obtained,13,16,20 and recently 100% ß-phase PVDF films have been developed.17 Obtaining the ß-phase can be modulated via the crystallization of PVDF. It was shown that polarity of the solvent can induce the ß-phase formation in PVDF crystallization. This can be attributed to dipole-dipole interactions between the polar C-F group and the solvent.21 Similarly,
presence of ions can increase the ß-phase formation via stabilizing ion-dipole interactions.13 After the ß-phase has been obtained and the sample consist of polarized crystals, which are oriented in different directions. A valuable contribution to the piezoelectric effect requires that these dipole moments are aligned (requirement (b)). Alignment of dipole moments can be achieved via two common procedures: stretching and poling. The former is less practical because it can’t be applied to thin films. Poling is a post-fabrication process that ensures this dipole alignment through application of an electric field in a certain direction. The dipoles can interact to orient in the same direction as the applied electric field. Because molecules need to undergo motions in order to change the direction of polarization, such processes require an elevated temperature (T>Tg). After this the sample is cooled below Tg (glass transition temperature), the dipole moments “freeze” in a particular direction and the dipole moments will remain in this direction when the electric field is removed (requirement (c)).59 In practice, poling is often executed in the out-of-plane direction because this generally yields the highest piezoelectric strain constant (when stress is applied in the same direction as the electric field that is observed, d33).22
Besides the orientation of dipole moments, phase transitions between different crystal structures occur during the poling process. The crystalline
13
phases of PVDF (figure 7a/b) are interconvertible in the presence of an electric field; at E~150 MV/m, α- → δ-phase transitions can occur, which increases the overall dipole moment. At higher fields (~ 500 MV/m), the transition of the δ- to the ß-phase can be achieved. The net result is a two-stage transformation of the apolar α-phase to the polar ß-phase.26 Such transformations are of major significance, as they allow for extra polarization of a PEM at any time after the film has been synthesized.
The glass transition temperature Tg, however, is a limiting factor in the above described induction of polarization. As Tg can vary for different fabricated PVDF materials (containing a different composition of phases), it is possible that the Curie temperature Tc (temperature at which ferromagnetic properties of solid disappear) is lower than Tg. For such a system, it would not be possible to create piezoelectric activity, since Tg needs to be exceeded in the poling process but before this temperature is reached the material has lost its ferromagnetism.
Fabrication of ferroelectric films
In practice, PVDF could be used as a thin film to reduce the volume occupance in electronic devices. Therefore, optimization of PVDF as a PEM are mainly focussed on two properties; piezoelectric (strain) coefficient (dij) and film thickness. Some classical techniques and novel methods to obtain a thin film from PVDF will be discussed shortly. For a more detailed description the reader is directed to literature.9-13
Spin coating is the most traditional way of
depositing PVDF; a solution of PVDF is deposited over a surface while being spun, resulting in the solution being spread out over the surface and eventually the solvent evaporates. With this approach, a thin PVDF film with thickness down to ~10 nm can be obtained.9,10 Thickness of such a film can be controlled by spinning conditions and solvent type and concentrations.7
A more sophisticated method is the
electrospinning method, in which high voltage
droplets are immersed on a surface. The high voltage in the droplets causes crystallization mainly in the ß-phase. The interaction of the salt with the electric field causes alignment of the dipole moments and therefore allows for fabrication without poling.13
Another frequently used method to fabricate thin films is via the Langmuir-Blodgett (LB) technique, in which PVDF solution in H2O is deposited on a surface. The amphiphilic character of the organic fragment, PVDF in this case, ensures ß-phase formation through fluoride-hydrogen interactions. Using this method, layers might be immersed on the substrate layer-by-layer, allowing for a well regulated thickness of films. Generally, the method allows for synthesis of films of a single monolayer of organic molecules. In the case of PVDF, however, obtaining a single monolayer of film containing a single monolayer is not easy because of the relative weak amphiphilic character of PVDF.11 Due to the conformationally organized deposition of PVDF, alignment with poling is not necessary using this technique.12
Beside these fabrication methods for obtaining thin films, some additional efforts have been made in the enhancement of the ß-phase in PVDF. One of the most important developments is the inclusion of ‘additives’ to PVDF; these are ions or small molecules that influence the morphology of PVDF. While ions are not covalently bonded, smaller molecules are introduced in the synthesis of the polymer, resulting in a polymer consisting of alternating monomers of VDF and other small molecules (copolymer). One example of such small molecules is trifluoroethylene (TrFE). TrFE has a very similar structure to the VDF monomer units; one hydrogen atom is replaced by a fluoride atom. Van der Waals interactions of VDF and TrFE cause that a conformation similar to the ß-phase is lowered in energy sufficiently to predominantly form. The zig-zag structure in the ß-phase is maintained in the copolymer, but the net dipole moment is reduced with respect to PVDF due to inclusion of the third fluorine atom in part of the monomers.62 Most of the reported copolymer containing films are in the range of (80:20)-(70:30) PVDF-TrFE ww% composition because it leads to
14
the highest piezoelectric strain coefficient. Similarly, salts can give rise to polar interactions that have the same effect.7,13
15
Molecular models for PVDF dipole
inversion
In the following section, it should be taken into account that kinetic models for ferroelectricity discussed above are derived from inorganic materials, for which ferroelectricity has a different origin from the organic molecule PVDF. In order to obtain a change in dipole moment PVDF molecules must reorient to achieve 180º rotation, which is energetically characterized by van der Waals interactions.45 Such a mechanism for the ferroelectric effect differs from inorganic materials, in which ionic displacements in the lattice induce a change in polarization. This next paragraph attempts to investigate in the reorientation of PVDF molecules during the ferroelectric effect.
To describe PVDF films on a molecular level, molecular reorientations during the ferroelectric effect must be considered. It should be taken into consideration that two phases contribute to the net polarization (reversal), namely the δ- and ß-inversion. Additionally, the α → δ phase transition will be treated, since it occurs in the poling process and the molecular mechanism is very similar to δ-inversion.
ß-phase inversion
The ß-phase contains a distinctive zig-zag structure (figure 7a) and contributes most significantly to the polarization. The first mechanism for polarization inversion of the ß-phase introduced by Aslaksen et al. in 1972 considered the most intuitive conformational chnge: a simple 180° rotation of the entire chain around its molecular axis.59 It is argued, however, that the macromolecule would never be able to reorient itself in one motion because of the high moment of inertia. Therefore, a PVDF chain is considered as an ensemble of N monomers, which rotate independently; a model that is known as the
kink propagation model. However, because of
movement of all atoms in the crystal lattice, this rotation is expected to require a high energy and therefore seems unlikely.60 The same calculations could not exclude a variation of this model,
introduced by Kepler and Anderson, who proposed in 1978 that a set of 60° rotations could lead to the same final structure.61 This is based on the fact that the lattice structure of the ß-phase is a ~1% distorted hexagonal symmetric structure. By applying an electric field, 60° increment rotations of CH2-CF2-CH2 units will lead to an energetically more favourable change of polarization (figure 8). Later reported PFM measurements on PVDF convincing evidence for this hypothesis.45 The model has been extended by the inclusion of trapped charges on the surface.51 Additionally, it can be explained why ferroelectric materials containing copolymers show faster switching behaviour; beside induction of the ß-phase crystal structure in copolymer films, the increased interchain distances causes the rotation of chains to be energetically more favourable.62
Figure 8: Schematic representation of kink propagation model
for dipole inversion of ß-phase in PVDF suggested by Kepler and Anderson.61 The left structure depicts the ß-phase with
aligned individual dipole moments along the chain (Pi). R
groups indicate rest of chain, for which PR has an equal
orientation along the rest of the chain. Right image shows the kink along 4 monomers, where CH2-CF2-CH2 planes are
rotated by a torsional angle of 60°. As the kink propagates through the chain, the individual dipole moments are inverted (PR→ PR).
16
Without enhancement of the ß-phase through fabrication methods, PVDF polymers are predominantly solidified in the α-phase due to its thermodynamic stabilltiy. This phase does not possess a dipole moment. By interacting with a relatively weak electric field (~150 MV/cm), the δ-phase can be obtained from the α-phase. When looking at the initial and final structures, it can be concluded that for two chains, one of the two is twisted 180°, which leads to an effective dipole moment (defined per two chains).13 This process can be expected to be similar to the inversion of the δ-phase, which requires 180° rotation of both chains, resulting in an inversion of the dipole moment. Two models have been proposed to explain this transition.
180° rotation
When the δ-phase was first discovered it was observed that it contributes to the ferroelectric effect and the dipole inversion of this phase was speculated to occur by 180° rotation around the molecular axis. The rotation is accompanied by some small translational motion of the backbone. It was argued that the minimal atomic distances of hydrogen and fluoride atoms (2.76 for F 2.78
F-H for and 2.73 Å for F-H-F-H) imply that such reorientations can occur without a significant change in lattice dimensions.63 Later, it was argued that van der Waals forces did not favor 180° rotation at once, and similar to ß-inversion it was shown that the subsequent rotation of monomers (kink propagation model) could be applied to α → δ phase transitions.24,64,65
90° rotation
More recently, McGaughey et al.24 have investigated the same α → δ phase transition by simulating various chains that undergo molecular motions, that were predicted to be dynamically favourable.64 The important difference with the former described mechanism is that the carbon atoms are not displaced during the rotation. McGaughey et al. concluded that in the presence of an electric field (E~150 MV/m), a CH2-CF2 bond rotates 90°, after which the next CH2-CF2 bond rotates 90° in the opposite direction (internal rotation). If this alternating rotation is performed along the entire chain, the α → δ phase transition is achieved. All these rotations are correlated to a certain energy barrier (with a transition state around 45°), as is depicted in the figure 9.24
17
Figure 9: Computational model of the inversion of dipole moment of a single PVDF chain (4 monomers). Every monomer undergoes internal rotations (90°) around the CH2-CF2 bond in four subsequent steps which result in inversion of the
polarization of a single chain.24
Comparison of the δ- and ß-inversion
In all mechanisms, a 180° rotation of PVDF is required, which raises the question: What are the differences between the two mechanisms? In the first place, the rotation is of a different nature in the sense that ß-inversion occurs through torsional rotations while δ-inversion occurs through internal rotations. Additionally, it was shown by Furukawa
et al. that the coercive field strength necessary to
induce a δ-inversion is much higher than that of the ß-inversion (Ec = 240 MV/m and 70 MV/m, respectively).66 Besides, it becomes apparent from the shape of the hysteresis loop that rates at which the inversions occur are clearly different for the two
phases (although not quantified).66 The authors attribute the difference in reversal of the two phases of relative stability of the two chains after nucleation; in the ß-phase, chains are packed much closer (the density in the ß-phase ~3 times higher)67, which leads to an unfavourable state after nucleation has occurred. Consequently, the propagation of reversal will be relatively fast, making the time scale of this process nucleation-limited (Eq. (4)). The δ-inversion, however, is much lower in energy after nucleation, and the domain walls will not move as quickly. The authors conclude that the δ-inversion leads to a much more gradual change in polarization, limited by domain wall motion (Eq. (7)).66
18
Ionic-dipole interactions
Trapped charge model
Previously described molecular mechanisms concern the contribution of the dipole moment to the ferroelectric properties of the material. As has been discussed, electrode-film interactions can strongly influence these properties in thin films. For instance, the stability of remnant polarization is governed by interactions of dipole moments with ions in the film. Such ions (H+, F-) originate from gas evolution reactions that occur at the electrode interface in the poling process.68 In dipole reorientations, the ions configure to the system and are displaced in the film. Most importantly, the timescale in which dipole reversal and ionic displacement occurs is different. The consequence is that for relatively short pulses, dipole moments can reorient but ions lack sufficient time to reorient to the new structure. This results in an unstable polarization reversal: The polarization returns to its initial value and is again stabilized by the ions (that have also adopted their initial position in the film).69
The nature of the ion distribution in the sample is dependent on the strength of the field that is used to pole the sample; for low field strengths charges will be oriented around the dipoles homogeneously, while for high field strengths the charges will be located at the electrode-film interface. These two situations are illustrated in
figure 10.
Figure 10: Graphical representation of the trapped charge model for PVDF films. The dipolar PVDF chains are represented as elliptical shapes while the thick lines indicate electrodes. In the upper case (high E-field), all polar crystals are surrounded by stabilizing countercharges (ionic). On the contrary, in the case below (low E-field) countercharges only appear at the electrode-film interface.
Because of absence of (a stabilizing) ion-dipole interaction, reversal of a dipole moment requires less energy for the middle chain segments in the lower case in figure 10. In fact, the likelihood for reversal of central units in PVDF films (nucleation) has been experimentally observed.69 Interestingly, the effect on the coercive field is similar to that of depolarization fields of (imperfect) electrodes, as pointed out by De Leeuw et al.58 The most important difference is that in the trapped charge model, there is a pulse time dependance in the (PE)-measurements due to the ion mobility.
Mechanisms describing film-electrode effects might provide plausible explanations for saturation of the coercive field in ultrathin (<15 nm) samples. Possibly, the saturation below certain sample thickness could mean that at this critical thickness PVDF molecules are mainly consisting of film-electrode stabilized molecules (because all PVDF units are close to the electrode in thin films). Lowering the thickness would then not change the film-electrode interactions in the sample, resulting in the same observed coercive field.
19
Concluding remarks and outlook
In conclusion, this research has focused on the fundamental piezoelectric properties of PVDF. A proper understanding of dipole kinetics in organic piezo- and ferroelectrics could lead to rational design of films. First, it should be noted that this approach only considers a fraction of the factors that influence the performance of a PEM. However, since the fabrication optimized of thin films, inclusion of additives and other performance-enhancing techniques have been reported widely elsewhere, the focus here is to address theoretical considerations for further developments in PVDF as a PEM. Concluding from the discussed literature some findings are summarized:
- Inversion of polarization occurs through nucleation at the defects in the crystalline structure, being heterogeneously distributed through the film. Domains of opposite polarization from the initial direction propagate recursively through a PVDF chain. The frequency dependence on the observed coercive field shows that the two processes occur at different time scales, namely nucleation and domain wall motion. The former one is rate determining for polarization switching in thin films (below ~150 nm thick) - The effects of the electrode-film interface
appear to have a significant effect of the observed Ec in thin film PVDF samples. Therefore, saturation of the coercive field below a certain thickness does not prove a transition from the extrinsic mechanism to the
intrinsic mechanism, as has been suggested
in literature. The depolarization field induced by imperfect electrodes lead to stabilized polarization states at the film electrode interface. Such interactions that cause bias in the observed switching time might be avoided by using more perfect electrodes such as Au. Additionally, interactions arise from ions created during the poling process that stabilize remnant polarization either through the entire film or at the film-electrode interface. Both interactions at the electrode-film interface are less pronounced when the sample thickness is increased.
- The non-polar-to-polar phase transition, α → δ, induces additional polarization, which will lead to a higher Pr. This phase transition occurs through internal rotations (CH2-CF2 bonds) rather than rotations of the entire chain (around its molecular axis). Such transformations occur at an electric field strength of E ~ 150 MV/m. Although the δ inversion is mechanistically similar to the α → δ transition, it requires a higher electric field (240 MV/m).
- The ß-inversion is a process that occurs through a set of 60° rotations, attributed to the near-hexagonal symmetry of the ß-unit cell. Similar to α → δ transition, it occurs through subsequent rotations groups in the polymer chain. The most important difference is that it does not occur via internal rotations, but through rotations of [CH2-CF2-CH2] units. Both processes are characterized by subsequential inversion of individual dipole moments (monomer by monomer) through the PVDF chain. The electric field required to induce such a transformation is in the order of E ~ 70-250 MV/m. This value is most relevant for ferroelectric dipole switching, assuming that the predominant phase in the sample is the ß-phase. This field is significantly larger when compared to the inorganic PEMs, which can exhibit the same switching time for electric fields of three orders of magnitude lower. Finally, molecular models related to ferroelectricity in PVDF will be connected to the physical models. The piezoelectric effect is accompanied by molecular (internal) rotations, thereby inversing the dipole moment direction. The process of dipole inversion in PVDF films is governed by heterogeneously distributed nucleation sites and domain wall growth of nucleated areas in the case of relatively thick films (d > 150 nm). When films become thinner the nucleation sites are reduced, which result in the fact that dipole switching kinetics are determined by nucleation processes (NLS-model). Domain wall growth can be thought of as subsequent rotations, which cause ß- and δ-inversion (δ-inversion of polarization). Electric fields of ~150 MV/m can facilitate α → δ phase transitions give rise to supplemental polarization. Additives in the PVDF film (salts, copolymers) can
20
cause the lattice cell dimensions to increase, facilitating the molecular rotations by less steric interactions. Finally, in the case of thin films not only molecular properties of PVDF are of importance but also the interactions of PVDF with the electrodes; during the poling process ions are created at the film-electrode interface that stabilize remnant polarization in PVDF films.
Based on these findings, a device with increased ferroelectric response (Pr) and simultaneously decreased switching time is suggested (figure 11). A ferroelectric device that operates (i.e. can switch dipole moment) in the order of ns is demanded for novel memory devices such as NVRAMs. We consider a thin film, in which the switching time is assumed to be determined by nucleation processes. If the ferroelectric material consists of pure ß-phase PVDF, the density of dipole moments is maximum due to the smaller lattice dimensions in pure ß-phase PVDF and a higher dipole moment of a ß-phase VDF unit compared to the TrFE unit. However, such films suffer from structural defects to induce nucleation in the film. If, however, at the film-electrode interface a local copolymer film solid phase is present, this would allow for nucleation at the relevant position of the film; from the insulating character of PVDF, it is expected that the highest charge density is located at the position close to the electrode. Thus, the presented device would exist of two PVDF:TrFE
copolymer layers sandwiching a PVDF layer; in the PVDF:TrFE layer nucleation is and in the PVDF layer which density of dipole moments is relatively large (pure ß-phase PVDF), depicted in figure 11. Theoretically, a relatively large ferroelectric response would be expected owing to the high density of molecular dipoles, while the switching time would be kept minimal due to induction of nucleation in the PVDF:TrFE layers. A possible drawback to this device might be that the syntehsis of the desired composition of layers is demanding and might perform differently than expected because of complexity in the morphology. Spin coating is not expected to be a suitable fabrication method; the deposition of multiple (chemically different) layers is expected to result in a blend of polymers rather than a layer-by-layer composition because of the rigorous deposition process. Films like this might be fabricated using the LB-technique, because thin layers can be deposited on the substrate in a controlable manner. It would be required to expose the substrate to a PVDF:TrFE solution, a PVDF solution and finally another PVDF:TrFE solution in the LB trough. Additionally, the different piezoelectric responses of the different layers might lead to decomposition of the ferroelectric device due to external force between the layers (the layers might fall apart). This bottleneck might be resolved by including thin interfacial layers in the device.
Figure 11: Suggested organic ferroelectric device structure with expected low switching time and relatively high ferroelectric responses. A layer of PVDF (grey) is sandwiched between copolymer PVDF:TrFE (orange). The latter one exhibits a lower coercive field. Thick arrows indicate the domain within PVDF (black arrows) and PVDF:TrFE (blue).
