In apolar dielectrics, polarization can be understood as a slight displacement of the electron cloud of each atom with respect to its positively charged nucleus; this type of polarization is known as electronic polarization. In biological materials, the corresponding relative permittivity values are typically low, usually in the range εr ≈ 2–4; for example, the hydrophobic core of biological membranes, composed of lipid acyl chains, represents a prototypical apolar dielectric with a relative permittivity in this range [6].

The second type of polarization is atomic (or ionic) polarization [7]. Here, ions (nuclei together with their bound electrons) are displaced relative to each other under the applied field. This can be viewed as an elastic displacement of charged entities within the material. Typical contributions lie in the range of ε_r ≈ 2–10, depending on material structure.

The third type of polarization is dipolar orientational polarization, which occurs in materials with permanent dipoles. A classic example is water, where molecular dipoles tend to rotate and align with the applied field. This leads to a stronger dielectric response, with ε_r ≈ 80.

The fourth type of polarization is interfacial polarization, also known as Maxwell–Wagner polarization [8]. It occurs in heterogeneous systems due to charge accumulation at interfaces between regions with different electrical properties (e.g., conductivity and/or permittivity). In biological cells, charge separation occurs mainly across the cell membrane, which acts as a thin insulating layer between conductive intracellular and extracellular media. Charges accumulate on both sides of the membrane, producing a strong interfacial polarization. Consequently, the effective permittivity can reach values of ε_r ≈ 10³–10⁴. In tissues, this effect is exacerbated by the presence of many cells and interfaces. The accumulation of charge at multiple boundaries leads to even higher effective permittivity values, typically ε_r ≈ 10⁵–10⁶. It is worth noting, however, that strictly speaking, these permittivity values do not depend on the dielectric nature of the material, but rather on the mobility of internal mobile charges.

The characteristic time of a polarization mechanism, τ, is defined as the time required for the polarization to adjust to a change in the applied electric field [9]. When the field is switched on or varies, the system does not respond instantaneously but relaxes toward equilibrium over a finite time.

For electronic polarization, the moving charges are electrons. The relevant scale is atomic, with very small mass and strong Coulomb forces, leading to τ≈10−16 s.

For atomic polarization, the motion involves ions (nuclei with bound electrons). The system behaves like an elastic lattice with much larger masses and restoring forces, giving τ≈10−14−10−13 s.

For dipolar orientational polarization, the moving entities are polar molecules such as water. The process involves rotational motion in a viscous environment, influenced by thermal collisions, with τ≈10−11−10−9 s.

For interfacial polarization, charge accumulation occurs at boundaries. The mechanism is governed by charge transport processes such as conduction and diffusion in heterogeneous media, typically with τ≈10−3−10−1 s.

The permittivity of a biological organ or tissue results from the combined contribution of all these polarization mechanisms.

When an alternating electric field is applied, the characteristic relaxation times τ of the dielectric polarization mechanisms described above lead to frequency-dependent responses. Each mechanism is associated with a characteristic relaxation frequency fc=12πτ, as described by Debye-type relaxation models (see Section 5). For frequencies f≪fc, polarization can follow the applied field and contribute fully to the permittivity. For f≫fc, the mechanism cannot respond effectively, and its contribution to the dielectric constant decreases. At f=fc the system undergoes a transition between the low-frequency and high-frequency regimes, giving rise to so-called dielectric dispersion centered around the characteristic relaxation frequency. Overall, the frequency dependence of these polarization mechanisms underlies dielectric dispersion in materials [10,11].

When a dielectric is placed between the plates of a capacitor, its capacitance changes; these variations can be used experimentally to determine the permittivity. Under a sinusoidal applied field, the response is characterized by amplitude and phase. For this reason, a complex representation is required. Without entering mathematical details, the dielectric permittivity at a given frequency is described by two measurable quantities: ε′ and ε″. ε′ is the real part (reactive component), representing energy stored in the material. It quantifies how effectively polarization follows the applied field and corresponds to reversible (elastic) energy storage. In the static limit, ε_r = ε′ because no losses are present (ε″ = 0). Thus, ε′ describes how strongly the material polarizes in phase with the field; ε″ is the imaginary part (dissipative component), associated with energy losses. It accounts for frictional motion of dipoles, finite conductivity, and delays in charge transport, all of which convert electrical energy into heat. It therefore quantifies the energetic cost for the material to follow the field.

A useful physical picture is to compare an ideal capacitor, where energy is stored without loss, with a resistor, where charge motion leads to Joule heating and energy dissipation.

The frequency-dependent behavior of ε′ and ε″ defines the dielectric spectrum of the material. Often, instead of ε″, the loss tangent tanδ = ε″/ε′ is reported as a function of frequency.

In summary, ε′ and ε″ together provide a complete description of the electromagnetic response of a material.

In the frequency range from quasi-static conditions up to ~10 GHz, permittivity measurements in biological systems rely on techniques that combine broadband capability with compatibility with hydrated and heterogeneous samples. At low frequencies (Hz–MHz), lumped-element methods such as parallel-plate capacitors and impedance spectroscopy are commonly used, treating the sample as an equivalent circuit element [12].

At higher frequencies (MHz–GHz), transmission and reflection techniques are preferred, including coaxial probes and transmission-line or waveguide configurations, where permittivity is extracted from scattering parameters (S-parameters). Open-ended coaxial probes are particularly suitable for biological tissues because they require minimal sample preparation and can be applied directly to hydrated materials [13]. However, their accuracy depends critically on the quality of contact between the probe aperture and the sample. A small air gap between the probe and the tissue introduces a low-permittivity layer at the measurement interface and can therefore bias the extracted permittivity, usually toward lower apparent values. This issue is particularly relevant for heterogeneous plant surfaces (see Table 1), such as leaves, stems, bark, fruits, and roots, where curvature, roughness, epidermal structures, trichomes, or waxy layers may prevent complete contact. For this reason, the probe is commonly pressed gently against the sample to eliminate air gaps and improve repeatability. Nevertheless, excessive pressure can deform soft biological tissues, alter the local water distribution, squeeze intercellular or extracellular fluid, and change the volume effectively sensed by the evanescent field. Contact pressure should therefore be minimized, standardized, and reported when possible, for example, by using a mechanical holder or spring-loaded fixture. This limitation is especially important for plant tissues with high turgor pressure, large intercellular spaces, or easily deformable parenchyma, because compression may modify the dielectric response being measured. Resonant methods provide high accuracy at discrete frequencies but are less suited to heterogeneous samples, while time-domain techniques offer broadband characterization [8]. Overall, method selection is constrained by the need to preserve physiological conditions, avoid sample deformation, and account for high water content, conductivity, and tissue heterogeneity [13,14,15].

Beyond methodological aspects, the measured dielectric permittivity is affected by a combination of physical parameters and biological factors, including temperature, hydration status, and structural features, as summarized in Table 2.

In plant tissues, water does not behave as a single homogeneous dielectric phase. Instead, it exists in different physical states that contribute differently to the measured complex permittivity. A useful distinction can be made among free water, bound water, and hydration water associated with ions and charged macromolecular surfaces.

Free water is the fraction of water that is relatively mobile within vacuoles, cytoplasm, apoplast, xylem vessels, intercellular spaces, and extracellular aqueous compartments. Its dielectric behavior is closest to that of bulk liquid water, described above, with a high real permittivity at low microwave frequencies and a dominant dipolar relaxation in the GHz range. Because of its high dielectric strength, changes in free-water content strongly affect ε′, especially in radiofrequency and microwave measurements. Thus, tissue dehydration, drought stress, reduced irrigation, or loss of turgor generally decrease the contribution of free water and therefore reduce the apparent permittivity. Conversely, rehydration or tissues with high succulence usually show larger dielectric loading.

Bound water refers to water molecules whose rotational mobility is restricted by hydrogen bonding, adsorption, confinement, or interaction with macromolecular surfaces. In plants, bound water is associated with cell-wall polysaccharides such as cellulose, hemicellulose and pectins, proteins, membranes, starch granules, and other hydrophilic or charged structures. Compared with free water, bound water has a lower effective dielectric strength and a broader, slower relaxation because its dipoles cannot rotate as freely. In leaf tissues, bound water has been associated with water physically or chemically bound to cell walls and organic compounds, and its characteristic relaxation has been reported at a much lower frequency than that of free water [16]. Therefore, an increase in the relative fraction of bound water, as can occur during dehydration or osmotic adjustment, does not simply reproduce the dielectric behavior of bulk water. Instead, it broadens the dielectric spectrum and shifts part of the water-related response toward lower frequencies. This is one reason why plant tissues rarely follow a single-Debye relaxation model (see Section 5).

Hydrated ions provide an additional contribution. Dissolved ions such as K⁺, Ca²⁺, Mg²⁺, Cl⁻, nitrate, phosphate, and organic counterions are surrounded by hydration shells in which water mobility is reduced by ion–water interactions. Dielectric relaxation studies of aqueous electrolyte solutions show that ions modify both the relaxation behavior and the static permittivity of water, with solvation effects contributing to the concentration dependence of the dielectric response [17]. When salts are added to pure water, only moderate changes in ε′ and ε″ are observed. In particular, the low-frequency plateau of ε′ decreases, and the peak of ε″ is reduced. For example, at 1.42 M KCl, the maximum value of ε′ decreases from ~78 to ~65, while the peak of ε″ decreases from ~35 to ~30 [18]. At the same time, ions increase electrical conductivity, introducing an additional contribution to ε″ at low and intermediate frequencies. Therefore, salinity, nutrient status, membrane leakage, and stress-induced changes in ion transport can modify dielectric spectra through two coupled mechanisms: changes in dipolar water relaxation and changes in conductive/interfacial losses [16,17]. In living tissues, these effects are difficult to separate because water content, ion concentration, membrane integrity, and tissue structure change simultaneously.

From a physiological perspective, drought and water-stress responses alter all three water fractions. Loss of free water reduces dielectric strength; osmotic adjustment and accumulation of soluble compounds increase the fraction of hydration water; membrane damage or altered ion-channel activity changes ionic conductivity; and changes in root water uptake or hydraulic redistribution modify spatial water distribution. Consequently, dielectric measurements can provide a non-invasive signature of plant water status, but the measured permittivity should be interpreted as an integrated response of water amount, water mobility, ion content, and tissue compartmentalization rather than as a direct measurement of total water content alone [19,20,21].

Interestingly, the frequency-dependent permittivity of water has enabled novel antenna designs in the microwave domain. At microwave frequencies, water exhibits a relatively high dielectric permittivity, which makes it suitable as a radiating or loading material for compact antenna structures. Simultaneously, water is optically transparent in the visible spectrum, allowing for the transmission of light through the antenna volume.

This unique combination of electromagnetic and optical properties enables the integration of photovoltaic cells beneath water-based antennas, leading to compact multifunctional systems. In contrast, conventional metallic antennas fabricated from conductive materials such as copper are opaque to visible light, preventing the placement of solar cells directly underneath the radiating element without significantly blocking incident illumination. Therefore, water-based antennas provide a promising approach for co-locating wireless communication and solar-energy-harvesting functionalities within the same physical footprint [22,23].

Comparative analyses among species further suggest that dielectric behavior is strongly influenced by plant functional and anatomical traits. Parameters such as leaf thickness, water content, tissue compactness, cuticle properties, venation density, stomatal distribution, surface roughness, trichome presence, mesophyll organization, conductivity, ionic composition, and the proportion of intercellular air spaces may all contribute to variations in dielectric response across frequencies [34,35,36]. Functional traits related to stress adaptation, including leaf dry matter content, succulence, sclerophylly, tissue hydration dynamics, and nitrogen concentration, may further modulate polarization mechanisms associated with membranes, interfaces, ionic transport, and water organization within tissues [37,38].

Among these factors, water content likely plays a dominant role because of the high dielectric permittivity and dielectric loss associated with dipolar relaxation processes. At the same time, tissue thickness and conductivity may influence dielectric loading and electromagnetic interactions in radiofrequency applications [16,31,32,33]. Overall, dielectric spectra should therefore not be interpreted only phenomenologically, but also in relation to the structural and functional traits underlying dielectric diversity among plant tissues and their responses to environmental conditions.

In addition to studies reporting complete dielectric spectra across broad frequency ranges, many investigations have focused on selected frequency windows associated with specific biological or technological applications, including hydration monitoring, stress detection, fruit ripening assessment, root activity estimation, and microwave sensing. Consequently, the dielectric parameters reported in the literature span different species, tissues, physiological conditions, and frequency domains. Together, these studies highlight the large variability in dielectric properties among plant taxa and support the hypothesis that structural and functional traits contribute substantially to the observed dielectric diversity.

From a general point of view, the spectrum of ε′ as a function of frequency (Figure 2) shows a sequence of step-like decreases. These steps correspond to the progressive deactivation of different polarization mechanisms: as the frequency increases, each polarization process is no longer able to follow the oscillations of the external electric field and therefore progressively drops out of the dielectric response.

The dashed vertical lines indicate representative frequency windows (from ~10² to ~10¹² Hz) where different polarization mechanisms dominate, including interfacial (Maxwell–Wagner), ionic, dipolar (water-related), and high-frequency molecular contributions. The overall behavior highlights the broadband and multi-relaxation nature of plant dielectric response, which deviates from single-Debye behavior due to structural heterogeneity and water content distribution within tissues.

In parallel, the ε″ spectrum exhibits a series of peaks, each one associated with a dielectric dispersion process. These peaks correspond to energy dissipation mechanisms linked to the relaxation of the different types of polarization.

Overall, the dielectric response of plant tissues can be divided into several frequency-dependent regimes, commonly referred to as the α, β, and γ dispersions, each reflecting a different physical scale of interaction between the electromagnetic field and the biological structure (see Table 3).

In the low-frequency range (Hz–kHz), corresponding to the α-dispersion, the response is dominated by large-scale interfacial polarization processes, typically described as Maxwell–Wagner polarization at the organ or tissue level. In this regime, charge carriers have sufficient time to accumulate at interfaces such as cell walls, cell–cell boundaries, and extracellular spaces, as well as along complex conductive pathways within the tissue. Therefore, a strong charge separation builds up at macroscopic heterogeneities, leading to very large effective permittivity values (ε′), which can range from 10² up to 10⁴ or even higher depending on structural complexity and hydration.

When moving to intermediate frequencies (kHz–MHz range), corresponding to β-dispersion, the dielectric response becomes dominated by processes occurring at the cellular level. This regime is generally associated with Maxwell–Wagner polarization across cell membranes and is strongly related to the electrical properties of individual cells. The cell membrane plays a central role here and can be modeled as a capacitor due to the amphipathic nature of phospholipids. These molecules form a bilayer structure in which hydrophobic tails face inward, creating an insulating layer that allows for charge accumulation on both sides of the membrane. In this frequency range, ε′ decreases with respect to the α-regime but remains relatively high (typically between ~10² and 10³ depending on tissue type and physiological state). β-dispersion is therefore closely linked to membrane properties and, more generally, to cell integrity and viability.

At higher frequencies (GHz range), corresponding to γ-dispersion, the dielectric response is mainly governed by the orientational relaxation of water molecules. In this regime, dipolar rotation of free and bound water becomes the dominant mechanism. The real part of the permittivity (ε′) decreases further, while the imaginary part (ε″) exhibits a pronounced peak associated with strong dielectric losses due to water relaxation processes.

In plant tissues, a distinct δ-dispersion is only rarely resolved experimentally. When reported in biological materials, this intermediate water-related relaxation is generally located between the β- and γ-dispersion ranges, broadly from the high-MHz region to the low-GHz region, although the exact frequency depends strongly on tissue hydration, temperature, ionic composition, and the type of macromolecular or interfacial environment [16,25,39]. Its possible molecular origins include rotational relaxation of bound or weakly bound water at cell-wall polysaccharides, proteins, membranes, starch granules, and other hydrophilic surfaces; water confined within cell-wall nanopores or intracellular compartments; hydration shells of ions and charged macromolecules; and exchange processes between bound and free water populations.

The difficulty in assigning a unique δ-dispersion arises because bound water does not have a single relaxation time. Instead, plant tissues contain a distribution of water environments, from nearly bulk-like vacuolar water to strongly restricted hydration water at charged or polymeric surfaces. As a result, the corresponding dielectric loss is broad and often appears as a shoulder rather than as a well-defined ε″ peak. Moreover, the upper tail of β-dispersion, which is associated mainly with membrane and interfacial Maxwell–Wagner polarization, can extend into the MHz region, while the low-frequency side of the γ-dispersion of free water can extend down toward the GHz region. The bound-water contribution is therefore frequently masked by the overlap between these two stronger processes. Ionic conductivity and electrode or contact effects at lower frequencies can further obscure this spectral region. For this reason, the interpretation of bound-water relaxation in plants remains challenging and usually requires broadband measurements, careful control of hydration and temperature, and multi-relaxation models such as multi-Debye or Cole–Cole representations (see Section 5).

Finally, in the high-frequency range (THz to optical frequencies), only the fastest polarization mechanisms remain active, namely electronic and atomic (ionic) polarization. All slower contributions, including α, β, and γ processes, are no longer able to follow the field variations. As a result, the dielectric constant decreases further, typically reaching values in the range of approximately 2–5.

In summary, the dielectric spectrum of plant tissues can be interpreted as a hierarchical signature of their structure: from macroscopic organization (α-dispersion) to cellular membranes (β-dispersion), molecular water dynamics (γ-dispersion), and finally intrinsic atomic and electronic polarization processes. This hierarchical framework provides the basis for interpreting the dielectric behavior observed in different plant organs and physiological conditions.