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Relative permittivity
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Relative permittivities of some materials at room temperature under 1 kHz
Material εr
Vacuum 1 (by definition)
Air 1.00058986±0.00000050
(at STP, 900 kHz),[1]
PTFE/Teflon 2.1
Polyethylene/XLPE 2.25
Polyimide 3.4
Polypropylene 2.2–2.36
Polystyrene 2.4–2.7
Carbon disulfide 2.6
BoPET 3.1[2]
Paper, printing 1.4[3] (200 kHz)
Electroactive polymers 2–12
Mica 3–6[2]
Silicon dioxide 3.9[4]
Sapphire 8.9–11.1 (anisotropic)[5]
Concrete 4.5
Pyrex (glass) 4.7 (3.7–10)
Neoprene 6.7[2]
Natural rubber 7
Diamond 5.5–10
Salt 3–15
Melamine resin 7.2–8.4[6]
Graphite 10–15
Silicone rubber 2.9–4[7]
Silicon 11.68
GaAs 12.4[8]
Silicon nitride 7–8 (polycrystalline, 1 MHz)[9][10]
Ammonia 26, 22, 20, 17 (−80, −40, 0, +20 °C)
Methanol 30
Ethylene glycol 37
Furfural 42.0
Glycerol 41.2, 47, 42.5 (0, 20, 25 °C)
Water 87.9, 80.2, 55.5
(0, 20, 100 °C)[11]
for visible light: 1.77
Hydrofluoric acid 175, 134, 111, 83.6
(−73, −42, −27, 0 °C),
Hydrazine 52.0 (20 °C),
Formamide 84.0 (20 °C)
Sulfuric acid 84–100 (20–25 °C)
Hydrogen peroxide 128 aqueous–60
(−30–25 °C)
Hydrocyanic acid 158.0–2.3 (0–21 °C)
Titanium dioxide 86–173
Strontium titanate 310
Barium strontium titanate 500
Barium titanate[12] 1200–10,000 (20–120 °C)
Lead zirconate titanate 500–6000
Conjugated polymers 1.8–6 up to 100,000[13]
Calcium copper titanate >250,000[14]
Temperature dependence of the relative static permittivity of water

The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field.

Permittivity is a material's property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum.

Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, compared with a similar capacitor that has vacuum as its dielectric. Relative permittivity is also commonly known as the dielectric constant, a term still used but deprecated by standards organizations in engineering[15] as well as in chemistry.[16]

Definition

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Relative permittivity is typically denoted as εr(ω) (sometimes κ, lowercase kappa) and is defined as

where ε(ω) is the complex frequency-dependent permittivity of the material, and ε0 is the vacuum permittivity.

Relative permittivity is a dimensionless number that is in general complex-valued; its real and imaginary parts are denoted as:[17]

The relative permittivity of a medium is related to its electric susceptibility, χe, as εr(ω) = 1 + χe.

In anisotropic media (such as non cubic crystals) the relative permittivity is a second rank tensor.

The relative permittivity of a material for a frequency of zero is known as its static relative permittivity.

Terminology

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The historical term for the relative permittivity is dielectric constant. It is still commonly used, but has been deprecated by standards organizations,[15][16] because of its ambiguity, as some older reports used it for the absolute permittivity ε.[15][18][19] The permittivity may be quoted either as a static property or as a frequency-dependent variant, in which case it is also known as the dielectric function. It has also been used to refer to only the real component ε′r of the complex-valued relative permittivity.[citation needed]

Physics

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In the causal theory of waves, permittivity is a complex quantity. The imaginary part corresponds to a phase shift of the polarization P relative to E and leads to the attenuation of electromagnetic waves passing through the medium. By definition, the linear relative permittivity of vacuum is equal to 1,[19] that is ε = ε0, although there are theoretical nonlinear quantum effects in vacuum that become non-negligible at high field strengths.[20]

The following table gives some typical values.

Low-frequency relative permittivity of some common solvents
Solvent Relative permittivity Temperature
C6H6 benzene 2.3 298 K (25 °C)
Et2O diethyl ether 4.3 293 K (20 °C)
(CH2)4O tetrahydrofuran (THF) 7.6 298 K (25 °C)
CH2Cl2 dichloromethane 9.1 293 K (20 °C)
NH3(liq) liquid ammonia 17 273 K (0 °C)
C2H5OH ethanol 24.3 298 K (25 °C)
CH3OH methanol 32.7 298 K (25 °C)
CH3NO2 nitromethane 35.9 303 K (30 °C)
HCONMe2 dimethyl formamide (DMF) 36.7 298 K (25 °C)
CH3CN acetonitrile 37.5 293 K (20 °C)
H2O water 78.4 298 K (25 °C)
HCONH2 formamide 109 293 K (20 °C)

The relative low frequency permittivity of ice is ~96 at −10.8 °C, falling to 3.15 at high frequency, which is independent of temperature.[21] It remains in the range 3.12–3.19 for frequencies between about 1 MHz and the far infrared region.[22]

Measurement

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The relative static permittivity, εr, can be measured for static electric fields as follows: first the capacitance of a test capacitor, C0, is measured with vacuum between its plates. Then, using the same capacitor and distance between its plates, the capacitance C with a dielectric between the plates is measured. The relative permittivity can be then calculated as

For time-variant electromagnetic fields, this quantity becomes frequency-dependent. An indirect technique to calculate εr is conversion of radio frequency S-parameter measurement results. A description of frequently used S-parameter conversions for determination of the frequency-dependent εr of dielectrics can be found in this bibliographic source.[23] Alternatively, resonance based effects may be employed at fixed frequencies.[24]

Applications

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Energy

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The relative permittivity is an essential piece of information when designing capacitors, and in other circumstances where a material might be expected to introduce capacitance into a circuit. If a material with a high relative permittivity is placed in an electric field, the magnitude of that field will be measurably reduced within the volume of the dielectric. This fact is commonly used to increase the capacitance of a particular capacitor design. The layers beneath etched conductors in printed circuit boards (PCBs) also act as dielectrics.

Communication

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Dielectrics are used in radio frequency (RF) transmission lines. In a coaxial cable, polyethylene can be used between the center conductor and outside shield. It can also be placed inside waveguides to form filters. Optical fibers are examples of dielectric waveguides. They consist of dielectric materials that are purposely doped with impurities so as to control the precise value of εr within the cross-section. This controls the refractive index of the material and therefore also the optical modes of transmission. However, in these cases it is technically the relative permittivity that matters, as they are not operated in the electrostatic limit.

Environment

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The relative permittivity of air changes with temperature, humidity, and barometric pressure.[25] Sensors can be constructed to detect changes in capacitance caused by changes in the relative permittivity. Most of this change is due to effects of temperature and humidity as the barometric pressure is fairly stable. Using the capacitance change, along with the measured temperature, the relative humidity can be obtained using engineering formulas.

Chemistry

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The relative static permittivity of a solvent is a relative measure of its chemical polarity. For example, water is very polar, and has a relative static permittivity of 80.10 at 20 °C while n-hexane is non-polar, and has a relative static permittivity of 1.89 at 20 °C.[26] This information is important when designing separation, sample preparation and chromatography techniques in analytical chemistry.

The correlation should, however, be treated with caution. For instance, dichloromethane has a value of εr of 9.08 (20 °C) and is rather poorly soluble in water (13 g/L or 9.8 mL/L at 20 °C); at the same time, tetrahydrofuran has its εr = 7.52 at 22 °C, but it is completely miscible with water. In the case of tetrahydrofuran, the oxygen atom can act as a hydrogen bond acceptor; whereas dichloromethane cannot form hydrogen bonds with water.

This is even more remarkable when comparing the εr values of acetic acid (6.2528)[27] and that of iodoethane (7.6177).[27] The large numerical value of εr is not surprising in the second case, as the iodine atom is easily polarizable; nevertheless, this does not imply that it is polar, too (electronic polarizability prevails over the orientational one in this case).

Lossy medium

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Again, similar as for absolute permittivity, relative permittivity for lossy materials can be formulated as:

in terms of a "dielectric conductivity" σ (units S/m, siemens per meter), which "sums over all the dissipative effects of the material; it may represent an actual [electrical] conductivity caused by migrating charge carriers and it may also refer to an energy loss associated with the dispersion of ε′ [the real-valued permittivity]".[17]: 8  Expanding the angular frequency ω = 2πc / λ and the electric constant ε0 = 1 / μ0c2, which reduces to:

where λ is the wavelength, c is the speed of light in vacuum and κ = μ0c / 2π = 59.95849 Ω ≈ 60.0 Ω is a newly introduced constant (units ohms, or reciprocal siemens, such that σλκ = εr remains unitless).

Metals

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Permittivity is typically associated with dielectric materials, however metals are described as having an effective permittivity, with real relative permittivity equal to one.[28] In the high-frequency region, which extends from radio frequencies to the far infrared and terahertz region, the plasma frequency of the electron gas is much greater than the electromagnetic propagation frequency, so the refractive index n of a metal is very nearly a purely imaginary number. In the low frequency regime, the effective relative permittivity is also almost purely imaginary: It has a very large imaginary value related to the conductivity and a comparatively insignificant real-value.[29]

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Relative permittivity

View on Grokipedia
from Grokipedia
Relative permittivity, often denoted as ε_r and commonly referred to as the dielectric constant, is a that measures a material's ability to store electrical energy in an relative to . It is defined as the ratio of the of the material (ε) to the permittivity of free space (ε_0), expressed as ε_r = ε / ε_0, where ε_0 ≈ 8.85 × 10^{-12} F/m. In physical terms, relative permittivity quantifies the reduction in strength within a compared to for the same free , arising from the polarization of bound charges in the . For non-lossy materials, ε_r is a greater than or equal to 1, with having ε_r = 1 and typical engineering materials ranging from about 2 (e.g., Teflon) to over 60 (e.g., certain ceramics). In lossy dielectrics, it becomes complex, ε_r = ε_r' - j ε_r'', where the imaginary part accounts for dissipation as . Relative permittivity plays a fundamental role in electromagnetics and , influencing the of devices—where scales directly with ε_r—and the propagation speed and attenuation of electromagnetic waves in materials. It is critical for designing components such as capacitors, antennas, circuits, and transmission lines, as well as in applications like high-frequency dielectrics and sensing. Accurate measurement of ε_r is essential across frequencies, from static fields to s, using techniques like cavity resonators or transmission lines to ensure performance in technologies ranging from to .

Fundamentals

Definition

Relative permittivity, denoted as ϵr\epsilon_r, is defined as the ratio of the permittivity of a (ϵ\epsilon) to the permittivity of (ϵ0\epsilon_0), mathematically expressed as ϵr=ϵϵ0\epsilon_r = \frac{\epsilon}{\epsilon_0}. This quantity characterizes a 's response to an in terms of charge storage capacity relative to . As a dimensionless scalar, ϵr\epsilon_r quantifies the degree of polarization induced in the by an external , which effectively reduces the net inside the compared to that in . with ϵr>1\epsilon_r > 1 exhibit enhanced , allowing them to support greater electric displacement for a given field intensity. The concept emerged in the 19th century from investigations into dielectrics, with coining the term "specific inductive capacity" in his 1837 studies to describe this property. By definition, ϵr=1\epsilon_r = 1 for ; typical values include 5–10 for and approximately 80 for at .

Terminology

Relative permittivity is also known as the dielectric constant, relative dielectric constant, and—particularly in historical contexts—specific inductive capacity. The term dielectric constant, first documented in scientific literature around 1875, became a standard descriptor for the property in the late . Specific inductive capacity, introduced by in the 1830s, referred to the material's ability to store relative to and laid the groundwork for modern understandings. In notation, the SI standard uses the symbol ε_r to denote relative permittivity, distinguishing it clearly from the absolute permittivity ε, defined as ε = ε_r ε_0 where ε_0 is the (8.854 × 10^{-12} F/m). Older texts frequently employ κ for the dielectric constant, while in German-language literature, the equivalent term Dielektrizitätskonstante is abbreviated as DK. Contextually, relative permittivity is sometimes called simply "" in discussions, though this can lead to ambiguity with absolute permittivity. In optics, for non-magnetic materials where the relative permeability μ_r ≈ 1, it relates to the n through the approximation n ≈ √ε_r, connecting electromagnetic properties across disciplines. The evolution of terminology reflects a shift toward precision: while "dielectric constant" remains in widespread use, IUPAC recommendations favor "relative permittivity" to emphasize its dimensionless, relative nature and avoid implying a true constant independent of or conditions.

Physical Principles

Relation to and Fields

In the context of , the relative permittivity ϵr\epsilon_r describes the response of a material to an applied E\mathbf{E} at the macroscopic level. In , where no material is present, ϵr=1\epsilon_r = 1, and the D\mathbf{D} is simply D=ϵ0E\mathbf{D} = \epsilon_0 \mathbf{E}, with ϵ0\epsilon_0 being the . When a material is introduced, the material polarizes, inducing a P\mathbf{P} that modifies the displacement field according to D=ϵ0E+P\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}. For linear isotropic dielectrics, the polarization is proportional to the , P=ϵ0χeE\mathbf{P} = \epsilon_0 \chi_e \mathbf{E}, where χe\chi_e is the of the material. Substituting this into the expression for D\mathbf{D} yields D=ϵ0(1+χe)E=ϵE\mathbf{D} = \epsilon_0 (1 + \chi_e) \mathbf{E} = \epsilon \mathbf{E}, where ϵ=ϵ0ϵr\epsilon = \epsilon_0 \epsilon_r is the absolute permittivity and ϵr=1+χe\epsilon_r = 1 + \chi_e. This relation highlights how ϵr\epsilon_r quantifies the enhancement of the displacement field beyond the case due to material polarization. The role of ϵr\epsilon_r becomes evident in practical devices such as parallel-plate capacitors. The capacitance CC of such a device filled with a dielectric is given by C=ϵrϵ0A/dC = \epsilon_r \epsilon_0 A / d, where AA is the plate area and dd is the separation distance. Compared to the vacuum capacitance C0=ϵ0A/dC_0 = \epsilon_0 A / d, the factor ϵr>1\epsilon_r > 1 increases the stored charge for a given voltage, enhancing capacity. For example, in materials like (ϵr≈80\epsilon_r \approx 80), this effect dramatically boosts relative to air (ϵr≈1\epsilon_r \approx 1). At interfaces between dielectrics with different ϵr\epsilon_r, boundary conditions from govern field behavior. The tangential component of E\mathbf{E} is continuous across the interface, while the normal component of D\mathbf{D} is continuous in the absence of charge. These conditions lead to refraction of lines, analogous to in but involving the tangents of the angles θ\theta with the normal: tan⁡θ1tan⁡θ2=εr1εr2\frac{\tan \theta_1}{\tan \theta_2} = \frac{\varepsilon_{r1}}{\varepsilon_{r2}}. Thus, field lines bend away from the normal when entering a higher-εr\varepsilon_r medium, reflecting the material's greater ability to support displacement.

Microscopic Origins

The relative permittivity of a material arises from the polarization response of its atoms and molecules to an applied electric field, where polarization PP represents the dipole moment per unit volume induced by the field. This response originates at the microscopic level through several distinct mechanisms that shift or align charges within the material. The primary types of polarization include electronic, atomic (also known as ionic), orientational, and interfacial. Electronic polarization occurs due to the displacement of electron clouds relative to atomic nuclei, creating induced dipoles in all materials; this mechanism is fast and dominates at high frequencies up to the optical range (~10^{15} Hz). Atomic polarization involves the relative displacement of positively and negatively charged ions in crystalline lattices, such as in ionic solids, and is effective up to infrared frequencies (~10^{13} Hz). Orientational polarization arises from the alignment of permanent electric dipoles in polar molecules, like water, under the field; this is prevalent in liquids and gases. Interfacial polarization, also called space-charge polarization, results from the accumulation of free charges at material boundaries or defects, leading to charge separation; it is the slowest mechanism and significant at low frequencies below the kilohertz range. These microscopic polarizabilities link to the macroscopic relative permittivity ϵr\epsilon_r through relations like the Clausius-Mossotti equation, which accounts for the local field experienced by molecules in a dense medium: ϵr−1ϵr+2=Nα3ϵ0\frac{\epsilon_r - 1}{\epsilon_r + 2} = \frac{N \alpha}{3 \epsilon_0} Here, NN is the of molecules, α\alpha is the molecular , and ϵ0\epsilon_0 is the . This equation connects the bulk response to atomic-scale properties, assuming non-interacting induced dipoles, and is particularly applicable to nonpolar dielectrics where electronic polarization dominates. The temperature dependence of relative permittivity is primarily influenced by orientational polarization, which decreases with increasing temperature due to thermal agitation randomizing alignments, as described by Debye's theory of polar molecules (1929). In this model, the orientational contribution to polarization follows P∝1/TP \propto 1/T, leading to a Curie-like behavior in the static constant for polar liquids. Electronic and atomic polarizations are largely temperature-independent. Frequency effects cause dispersion in ϵr\epsilon_r, where the value drops at higher frequencies because slower polarization mechanisms—such as orientational and interfacial—cannot follow rapid field oscillations, while electronic polarization persists. For instance, orientational effects cease beyond frequencies due to molecular rotational . Detailed analysis of this frequency-dependent complex permittivity, including losses, is covered in the section on complex permittivity.

Measurement

Experimental Techniques

The measurement of relative permittivity, denoted as ϵr\epsilon_r, has evolved from early electrostatic experiments to precise modern techniques. In 1837, conducted pioneering work using Leyden jars to investigate the inductive capacity of materials, effectively measuring how insulators enhanced charge storage in capacitors, laying the foundation for quantitative assessments of dielectric properties. These historical methods relied on observing charge accumulation and discharge, but lacked the standardization seen today. Modern protocols, such as ASTM D150 established in 1922, provide standardized procedures for AC-based permittivity measurements on solid insulators, ensuring reproducibility across laboratories. Capacitance methods remain the cornerstone for low-frequency and static measurements of ϵr\epsilon_r. In the parallel-plate setup, a sample is inserted between two conductive plates separated by distance dd, with plate area AA. The CC is measured using an , and ϵr\epsilon_r is computed via the formula ϵr=Cdϵ0A\epsilon_r = \frac{C d}{\epsilon_0 A}, where ϵ0\epsilon_0 is the (8.85×10−128.85 \times 10^{-12} F/m). This approach assumes uniform fields and negligible fringing effects, achieving accuracies suitable for many engineering applications. Variations, such as the guarded configuration, incorporate a surrounding guard ring to minimize and stray , enhancing precision for thin or irregular samples. For instance, in ASTM D150 procedures, samples are typically thin films or sheets under controlled voltage (e.g., 1 V), with measurements at frequencies from 60 Hz to 1 MHz. At higher frequencies, resonance techniques like cavity perturbation are employed to probe ϵr\epsilon_r without direct contact in some setups. A small dielectric sample is introduced into a resonant microwave cavity, perturbing its resonant frequency f0f_0. The frequency shift Δf\Delta f relates to ϵr\epsilon_r approximately through Δff0∝(ϵr−1)\frac{\Delta f}{f_0} \propto (\epsilon_r - 1) times a geometric factor involving sample and cavity volumes, allowing extraction of ϵr\epsilon_r from calibration curves. This method excels for frequencies in the GHz range, such as 1-10 GHz using rectangular or cylindrical cavities, and is particularly useful for low-loss materials where broadband coverage is not required. Systems often automate the perturbation via vector network analyzers for rapid, non-destructive testing. For broadband characterization spanning DC to GHz, time-domain methods utilize dielectric spectroscopy with pulse propagation. Short electrical pulses are launched into a (e.g., or stripline) loaded with the sample, and the reflected or transmitted waveform is analyzed to derive time-dependent responses, from which frequency-domain ϵr\epsilon_r is obtained via . This approach, often implemented with time-domain reflectometry, captures dispersive effects over wide frequency bands (up to 100 GHz) by measuring pulse delay and , making it ideal for heterogeneous or samples. Common error sources in these techniques include poor electrode-sample contact, which introduces air gaps altering effective dd, and non-uniform sample thickness, leading to averaged ϵr\epsilon_r values that deviate from bulk properties. Fringing fields and exacerbate inaccuracies in setups, while cavity methods are sensitive to sample positioning. With careful preparation, such as vapor-deposited electrodes and micrometer-controlled spacing, precision can reach 0.1% for solid samples at low frequencies. These methods primarily yield the real part of ; complex aspects, including losses, are addressed in specialized frequency-domain analyses.

Complex Permittivity and Losses

In materials subjected to alternating , the relative permittivity ε_r becomes frequency-dependent and is generally represented as a complex , ε_r(ω) = ε_r' - j ε_r'', where ω is the , ε_r' is the real part associated with and polarization, and ε_r'' is the imaginary part representing or losses. The real part ε_r' determines the material's ability to store electric , while the imaginary part ε_r'' quantifies the conversion of into heat through various relaxation and conduction mechanisms. The extent of these losses is often characterized by the loss tangent, defined as tan δ = ε_r'' / ε_r', which provides a dimensionless measure of the of dissipated to stored ; low values of tan δ (e.g., < 0.01) indicate low-loss dielectrics suitable for high-frequency applications. Frequency dispersion in the complex relative permittivity arises from the delayed response of molecular dipoles or charges to the oscillating field, leading to variations in ε_r' and ε_r'' across different frequencies. A foundational model for this behavior is the Debye relaxation model, which describes a single relaxation process as εr(ω)=ε∞+εs−ε∞1+jωτ,\varepsilon_r(\omega) = \varepsilon_\infty + \frac{\varepsilon_s - \varepsilon_\infty}{1 + j \omega \tau}, where ε_s is the static (low-frequency) relative permittivity, ε_∞ is the high-frequency relative permittivity (approaching the optical limit), and τ is the relaxation time constant governing the transition between these limits. In this model, ε_r' decreases from ε_s to ε_∞ with increasing frequency, while ε_r'' peaks near the relaxation frequency ω = 1/τ, reflecting maximum energy loss. This single-relaxation approximation is particularly effective for polar liquids like water, though more complex materials may require multi-relaxation extensions. Losses in dielectrics are quantified through several methods that relate measurable quantities to the complex permittivity. Power dissipation, derived from the time-averaged Poynting theorem, is proportional to ω ε_0 ε_r'' |E|^2 / 2, where ε_0 is the vacuum permittivity and |E| is the electric field magnitude, allowing losses to be inferred from temperature rise or calorimetric measurements in the material. In resonant structures, such as cavities or transmission lines, the quality factor Q (ratio of stored to dissipated energy) provides another metric, with dielectric losses contributing to 1/Q_d = ε_r'' / ε_r' = tan δ at the resonant frequency. Impedance analysis, often using vector network analyzers with coaxial or waveguide fixtures, extracts ε_r' and ε_r'' from reflection or transmission coefficients via fitting to transmission line models, enabling broadband characterization of lossy media. Representative values of ε_r' and tan δ for common materials illustrate the range of behaviors, from high-loss polar substances to low-loss insulators. The following table summarizes data at room temperature (~20–25°C) for water (a high-permittivity, lossy dielectric) and polytetrafluoroethylene (PTFE, a low-loss polymer), highlighting frequency dependence:
MaterialFrequencyε_r'tan δNotes
Water~1 Hz (static)~80~0.0001High storage, negligible conduction loss at DC.
Water10 GHz~61~0.53Significant dispersion near relaxation frequency.
Water2.45 GHz~78~0.16Microwave regime, balanced storage and dielectric heating potential.
PTFE10 GHz~2.1~0.0002Stable low-loss behavior across microwaves.
These values underscore how polar materials like water exhibit strong frequency dispersion due to dipole reorientation, while non-polar PTFE maintains consistent low losses. The losses captured by ε_r'' enable practical applications, notably dielectric heating in microwave systems, where absorbed power P = (1/2) ω ε_0 ε_r'' ∫ |E|^2 dV generates uniform volumetric heating in materials with moderate tan δ, such as foods or polymers, without surface overheating common in conductive heating. This process, governed by the penetration depth δ ≈ 1 / (ω √(μ_0 ε_0 ε_r' / 2) √(√(1 + tan² δ) - 1)), is widely used in industrial drying, chemical synthesis, and medical therapies, with water's high ε_r'' at 2.45 GHz making it ideal for microwave ovens.

Material-Specific Behavior

Dielectrics and Lossy Media

Dielectrics are broadly classified into linear and nonlinear types based on their polarization response to an applied electric field. Linear dielectrics exhibit a constant relative permittivity independent of field strength, resulting in a proportional relationship between electric displacement and field, with minimal energy dissipation. In contrast, nonlinear dielectrics display field-dependent permittivity, often characterized by hysteresis in the displacement-electric field loop due to reversible domain reorientation or phase changes. Ferroelectric materials, a subset of nonlinear dielectrics, such as , achieve exceptionally high relative permittivities exceeding 1000, enabling applications in high-capacitance devices but introducing losses from hysteresis during polarization switching. In lossy dielectrics, energy dissipation mechanisms contribute to the imaginary component of the complex relative permittivity, particularly through finite conductivity. The conductivity σ adds to the effective dielectric loss via the term ϵr′′=σωϵ0\epsilon_r'' = \frac{\sigma}{\omega \epsilon_0}, where ω\omega is the angular frequency and ϵ0\epsilon_0 is the vacuum permittivity, representing conduction currents that convert electromagnetic energy to heat. Moisture absorption exacerbates losses in polymers by introducing polar water molecules that enhance both real and imaginary permittivity components, often increasing overall dielectric losses due to interfacial polarization and ionic conduction./03%3A_Wave_Propagation_in_General_Media/3.04%3A_Complex_Permittivity) Environmental factors significantly influence relative permittivity in dielectrics. Temperature variations alter molecular alignment and vibrational modes; for instance, the relative permittivity of water reaches a maximum of approximately 88 at 0°C, decreasing monotonically to about 55 at 100°C due to reduced hydrogen bonding strength. Humidity absorption in polymer composites can elevate relative permittivity by 10-20% through water ingress, which boosts polarizability while simultaneously raising losses via enhanced conductivity pathways. Representative examples illustrate the range of behaviors in dielectrics and lossy media. Ceramics, such as titanates and zirconates, typically exhibit relative permittivities spanning 10 to 10,000, with high-ε_r variants like BaTiO₃ suited for capacitors despite elevated losses. Insulating liquids, including mineral and vegetable transformer oils, possess low relative permittivities of 2-4, minimizing losses in high-voltage insulation while providing thermal management. Recent advances since 2020 have focused on polymer-ceramic hybrids for 5G applications, achieving tunable relative permittivities of 2-10 with ultralow losses below 0.001 through optimized filler dispersion and core-shell structures that suppress interfacial polarization.

Conductors and Metals

In conductors and metals, the relative permittivity ϵr\epsilon_r is generally complex and frequency-dependent due to the presence of free charge carriers, which dominate the response over bound charges. Unlike dielectrics, where ϵr\epsilon_r is typically positive and real at low frequencies, in highly conductive materials, the imaginary part ϵr′′\epsilon_r'' becomes significant, reflecting energy dissipation through conduction. This behavior arises from the collective motion of free electrons, modeled classically by the Drude theory, which treats electrons as a gas subject to damping collisions. The Drude model yields the complex relative permittivity as ϵr(ω)=1−ωp2ω2+jγω,\epsilon_r(\omega) = 1 - \frac{\omega_p^2}{\omega^2 + j \gamma \omega}, where ωp=ne2/(ϵ0m)\omega_p = \sqrt{n e^2 / (\epsilon_0 m)}
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