Activation-Induced Volume Change

• Activation-induced volume change is defined as the reversible or irreversible alteration in a system’s volume due to activation events like chemical, physical, or biological triggers.
• The phenomenon is quantified by activation volume parameters and explored through theoretical, experimental, and computational approaches across various scales and disciplines.
• Its practical applications include optimizing battery electrode stability, understanding earthquake precursors in geophysics, and elucidating cellular morphodynamics in biological systems.

Activation-induced volume change refers to any reversible or irreversible alteration in the volume of a material, structure, or system that is directly associated with an activation event—such as chemical, physical, or biological activation. In both materials science and biological contexts, such changes are intimately connected to phase transitions, redox reactions, mechanical or electrochemical strain, or cellular signaling. The phenomenon may involve atomic, molecular, mesoscopic, or even multicellular scales, and is characterized by intricate dependencies on external variables such as pressure, temperature, or stress. The following sections synthesize theoretical models, experimental findings, and applications as they pertain to activation-induced volume change across solid-state physics, complex fluids, electrochemistry, and biological systems.

1. Theoretical Frameworks and Key Variables

Activation-induced volume change is usually quantified by the "activation volume" $v_{\rm act}$ or $V_{\rm act}$, which measures the derivative of an activation barrier (e.g., Gibbs free energy, migration energy) with respect to applied pressure at constant temperature:

$$v_{\rm act} = \left(\frac{\partial \Delta G_{\rm act}}{\partial P}\right)_T$$

For a thermally activated process with relaxation time $\tau$ expressed as

$$\tau(P,T) = (2\nu)^{-1} \exp\left(\frac{\Delta G_{\rm act}}{k_B T}\right)$$

the pressure derivative becomes

$$\frac{\partial \ln \tau}{\partial P}\Big|_T = -\frac{\gamma}{B} + \frac{v_{\rm act}}{k_B T}$$

with $\gamma$ as the Grüneisen parameter and $B$ the isothermal bulk modulus (Papathanassiou et al., 2010). In the field of solid-state diffusion, an analogous activation volume tensor can be defined as the (logarithmic) derivative of the diffusivity tensor with respect to the stress tensor (Trinkle, 2016).

In glass-forming materials, the isothermal equation of state (EOS) formalism for the activation volume is

$$\left(\frac{V_{\text{act}}(T,p_0)}{V_{\text{act}}(T,p)}\right)^{Y_{\text{act}}} = 1 + Y_{\text{act}} \frac{p-p_0}{B_{\text{act}}(T,p_0)}$$

with $Y_{\text{act}}$ as the scaling exponent and $B_{\text{act}}$ as the isothermal bulk modulus for the activation volume (Grzybowski et al., 2012).

In biological and cellular contexts, activation-induced volume changes are described using dynamical systems that combine osmotic, electrochemical, and mechanical forces (Taloni et al., 2015, Adar, 3 Nov 2024, Ron et al., 22 May 2025).

2. Negative Activation Volume and Its Physical Origin

Negative activation volumes are rare and counterintuitive, signifying that increasing pressure accelerates the relaxation or transport process instead of retarding it. Theoretical and experimental studies on hydrated rocks (leukolite, limestone) demonstrated that the dielectric relaxation time $\tau$ decreases with pressure, corresponding to $v_{\rm act} < 0$ (Papathanassiou et al., 2010, Papathanassiou, 22 May 2025). This is interpreted as increased dipole (defect) mobility under compression. The physical origin is linked to pressure-driven enhancements of charge carrier mobility along hydrated pore networks or at solid/fluid interfaces, especially when water's conductivity sharply increases with pressure—overwhelming the pressure dependence of pure dielectric permittivity (Papathanassiou, 22 May 2025).

Thermodynamic models quantify the condition for negative defect activation volumes:

$$v^i = \frac{2h^i}{B} \left(\frac{dB}{dP} - 1\right)$$

where $h^i$ is defect enthalpy. For $dB/dP < 1$, $v^i$ becomes negative—this regime is realized near the glass transition or in solids with low Grüneisen parameters (Katsika-Tsigourakou, 2017). In hydrated or impure ionic crystals, the activation volume may be negative when the relevant transverse optical mode Grüneisen parameter $\gamma_{\rm TO} < 1/3$.

In effective medium models of mesoscopic heterogeneous systems, interfacial polarization between a solid and water yields a negative activation volume when the logarithmic pressure derivative of water's conductivity dominates that of the dielectric constants (Papathanassiou, 22 May 2025).

3. Experimental Evidence and Measurement Protocols

Experimental observation of activation-induced volume change employs techniques tailored to the system scale. In dielectric relaxation studies, Broadband Dielectric Spectroscopy (BDS) measures the frequency shift of the loss tangent ($\tan \delta$) peak as a function of hydrostatic pressure. The activation volume is then extracted from the pressure derivative of the peak frequency $f_{\rm max}$ or the associated relaxation time (Papathanassiou et al., 2010, Papathanassiou, 22 May 2025).

Key findings include:

System	Measured $v_{act}$ (GPa$^{-1}$)	Interpretation
Polycrystalline calcite + water	$-4.3$ to $-8.8$	Strong interfacial polarization, water conductance dominates
Magnesite (leukolite) + water	$\sim -20$	Enhanced conductivity of water in pores
Hydrated limestone	Similar to above	Several mechanisms possible

In glass-formers, dielectric spectroscopy paired with pressure-tuned relaxation measurements is used to determine how the effective activation volume varies across the supercooled domain (Drozd-Rzoska, 2018, Grzybowski et al., 2012). The activation volume shows marked pressure and temperature dependence, especially near the glass transition.

For battery electrodes, atomic force microscopy (AFM) and multi-beam optical sensor (MOS) techniques are used in-situ to measure film thickness and stress during (de)intercalation cycles. Activation, such as initial sodiation of Ge, produces irreversible volume expansion of more than 300%, with subsequent cycles displaying repeatable, reversible stress–strain–volume responses (Rakshit et al., 2020).

In cellular and biological systems, time-resolved 3D imaging measures volume fluctuations during morphology changes, as in bleb formation (Taloni et al., 2015). Osmotic shock and activation protocols in single cells validate the predicted two-phase volume adjustment—fast passive (Cl$^-$-leakage/water flux) followed by slow active (Na$^+$-leakage/membrane potential adaptation) (Adar, 3 Nov 2024).

4. Consequences Across Materials and Biological Systems

Activation-induced volume change impacts:

• Dielectric Transients and Seismoelectric Signals: Rapid, pressure-driven reorientation of dipoles in rocks with negative activation volumes leads to pressure-stimulated currents (PSC) that may underlie the observed seismic electric signals (SES) preceding earthquakes (Papathanassiou et al., 2010).
• Heterogeneous Dielectrics: Water-saturated polycrystalline minerals with strong interfacial polarization show negative activation volume, leading to faster relaxation and practical implications for subsurface fluid detection and earthquake monitoring (Papathanassiou, 22 May 2025).
• Battery Electrode Stability: Large irreversible activation-induced volume changes during initial cycling (e.g., sodiation/lithiation in Ge) result in significant stress evolution and mechanical dissipation. Designing "zero-strain" or "strain-less" materials through structural/chemical modifications addresses mechanical degradation (Rakshit et al., 2020, Baumann et al., 2023, Maréchal et al., 7 Jun 2024).
• Muscle Physiology: Muscle contraction cycles produce lattice volume oscillations in the sarcomere, generating advective fluid motion that enhances metabolite transport—critical for high-frequency muscle operation (Cass et al., 2019).
• Cell Locomotion and Morphodynamics: Cellular volume loss during spreading and swelling upon signaling (RVI) crucially alters contact area and motility. Theoretical models establish that a critical contact area, set via activation-induced volume changes, determines the onset of persistent cell migration. Volume regulation operates through coupled mechanisms involving membrane potential, ion transport, and active mechanical forces (Taloni et al., 2015, Adar, 3 Nov 2024, Ron et al., 22 May 2025).

5. Theoretical and Computational Approaches

The modeling of activation-induced volume change spans multiple levels:

• Condensed Matter and Defect Models: Thermodynamic relations connect defect energetics and elastic properties to activation volumes, incorporating parameters such as $B$, $dB/dP$, and Grüneisen constants (Katsika-Tsigourakou, 2017, Grzybowski et al., 2012).
• Effective Medium and MWS Theory: The dielectric response of composite media is modeled using DEMA and Maxwell–Wagner–Sillars approaches, capturing how polarization and conductivity synergies determine the pressure dependence of interfacial relaxation (Papathanassiou, 22 May 2025).
• Molecular Simulation and DFT: First-principles calculations facilitate a decomposition of activation-induced volume changes into ionic, electronic, and host structural contributions, with tailored DFT+U and van der Waals corrections critical for accurate volume prediction in electrode materials (Baumann et al., 2023, Maréchal et al., 7 Jun 2024).
• Continuum and Dynamical Systems in Biology: Cell volume is treated via dynamical pump–leak models with timescale separation and coupling to mechanical spreading via viscoelastic geometric relations, linking activation-induced volume change to cell polarization and motility (Adar, 3 Nov 2024, Ron et al., 22 May 2025).

6. Applications and Future Research Directions

Activation-induced volume change underpins advances in:

• Geophysical Monitoring: Laboratory validation of negative activation volumes supports the physical basis for SES as earthquake precursors, suggesting targeted field and laboratory studies on heterogeneous, hydrated crustal rocks (Papathanassiou et al., 2010, Papathanassiou, 22 May 2025).
• Materials Design: Control of activation-induced volume variation via electronic structure tuning, doping, polymorphism, and mechanical hardening is central to developing strain-less battery electrodes with improved longevity (Baumann et al., 2023, Maréchal et al., 7 Jun 2024).
• Cellular Engineering: Quantitative understanding of activation-induced volume changes enables manipulation of cellular shape and migratory behavior, with implications for immunology, cancer invasion, and tissue engineering (Taloni et al., 2015, Ron et al., 22 May 2025).
• Dynamic Systems in Physiology: Elucidating the interplay between ionic permeability, osmotic water flow, and cytoskeletal activation informs models of morphodynamics, motility, and adaptive responses in diverse cell types (Taloni et al., 2015, Adar, 3 Nov 2024).

Further research is poised to address the influence of more complex morphologies, multiscale defect structures, and emergent collective effects in both synthetic and biological systems. Extended theoretical frameworks may be necessary to capture coupled chemo-mechanical and electromechanical responses in next-generation functional materials and living matter.