Temperature-Dependent van der Waals Adhesion

• Temperature-dependent van der Waals adhesion is defined by the interplay of fixed dispersion forces and thermal renormalizations from fluctuations, electromagnetic resonances, and mechanical dissipation.
• Research highlights include analyses in supported graphene, near-field Casimir–Polder regimes, and anisotropic media where temperature alters both the effective adhesion energy and the interaction coefficients.
• Understanding these mechanisms aids in designing material interfaces and accurately interpreting experimental adhesion data where thermal effects do not directly reflect changes in microscopic bonding.

Searching arXiv for recent and foundational papers on temperature-dependent van der Waals adhesion and closely related mechanisms. Temperature-dependent van der Waals adhesion denotes the variation with temperature of either the underlying dispersion interaction itself or of experimentally observed adhesion quantities that are built on dispersion forces but renormalized by thermal fluctuations, dissipation, or bulk mechanics. The literature considered here spans several distinct regimes. In supported graphene, the bare van der Waals potential is taken to be temperature independent, while thermal rippling generates an entropic repulsion that increases mean separation and reduces effective adhesion (Wang et al., 2015). In the near-field Casimir–Polder regime, by contrast, the nonretarded potential itself is written as $U(z,T)=-C_3(T)/z^3$, so the van der Waals coefficient can become strongly temperature dependent through resonant coupling to thermally populated surface polariton modes (Silans et al., 2014). In pressure-sensitive adhesives, measured peel adhesion may vary strongly with temperature even when the interfacial surface contribution is unchanged, because the temperature dependence resides predominantly in bulk viscoelastic dissipation rather than in the interfacial van der Waals bonding potential (Street et al., 10 Jul 2025).

1. Conceptual scope and definitions

A central distinction in this subject is the difference between bare interaction parameters and effective adhesion observables. For monolayer graphene on a rigid substrate, the $T=0$ interaction per unit area is modeled as

$$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$

with $\Gamma_0$ the adhesion energy per unit area at $T=0$ K and $h_0$ the equilibrium separation at $T=0$ K; in that treatment, $\Gamma_0$ and $h_0$ are intrinsic, temperature-independent parameters of the bare van der Waals interaction (Wang et al., 2015). The temperature dependence of adhesion is then an emergent statistical-mechanics effect.

In the near-field atom–surface problem, the nonretarded Casimir–Polder interaction is itself expressed as

$U(z,T)=-\frac{C_3(T)}{z^3},$

so the coefficient $T=0$0 directly parametrizes a temperature-dependent van der Waals attraction or repulsion at nanometric separations (Silans et al., 2014). In anisotropic media, the corresponding nonretarded free energy is obtained from a Matsubara sum over surface modes,

$T=0$1

and temperature enters both through Matsubara spacing and through explicit $T=0$2-dependence of the dielectric tensor (Kornilovitch, 2012).

A third definition arises in adhesion mechanics. For a $T=0$3 peel geometry, the adhesive failure energy per unit area is written as

$T=0$4

so that $T=0$5 at $T=0$6, and the standard decomposition

$T=0$7

separates interfacial bond energy $T=0$8 from bulk dissipation $T=0$9 (Street et al., 10 Jul 2025). This decomposition is indispensable when interpreting “temperature-dependent van der Waals adhesion,” because a strongly temperature-dependent peel force need not imply a strongly temperature-dependent interfacial van der Waals potential.

2. Entropic weakening of adhesion by thermal rippling in two-dimensional membranes

For supported graphene, temperature dependence emerges from the coupling between membrane fluctuations and an anharmonic substrate potential. The out-of-plane profile is decomposed as

$$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$0

where $$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$1 is the normalized average separation and $$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$2 is a dimensionless fluctuation field with $$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$3 under the harmonic approximation (Wang et al., 2015). The membrane has bending rigidity $$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$4, biaxial modulus $$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$5, and possible biaxial pre-strain $$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$6.

After quadratic expansion of the interaction, bending, and in-plane strain energies, Fourier decomposition of $$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$7, and Gaussian evaluation of the partition function, the mean-square rippling amplitude becomes

$$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$8

Within the harmonic approximation, $$V(z)=\Gamma_0\left[\frac{1}{2}\left(\frac{h_0}{z}\right)^9-\frac{3}{2}\left(\frac{h_0}{z}\right)^3\right],$$9 grows linearly with $\Gamma_0$0 and is suppressed by bending rigidity, tension, and the curvature of the substrate potential (Wang et al., 2015). The average normal traction is

$\Gamma_0$1

so the second term is an entropic correction. Because the potential is anharmonic, this term is nonzero and acts as an effective repulsion near equilibrium (Wang et al., 2015).

The principal predictions are coupled. The equilibrium average separation $\Gamma_0$2 increases approximately linearly with temperature at low to moderate $\Gamma_0$3. The effective adhesion energy,

$\Gamma_0$4

decreases monotonically with temperature and is approximately linear in $\Gamma_0$5 up to about $\Gamma_0$6 K for the baseline parameter set. For $\Gamma_0$7 eV, $\Gamma_0$8 J/m$\Gamma_0$9, $T=0$0 nm, and $T=0$1, the harmonic theory gives $T=0$2 K and $T=0$3 at $T=0$4; it also yields an out-of-plane coefficient of thermal expansion $T=0$5 around room temperature to $T=0$6 K (Wang et al., 2015).

Pre-strain modifies the same mode spectrum. Tensile pre-strain suppresses rippling and reduces entropic repulsion, whereas compressive pre-strain enhances rippling and can eliminate the bound state beyond a critical compressive strain $T=0$7. Molecular dynamics confirms the predicted trends for rippling amplitude, separation, interaction energy, and thermal stress up to about $T=0$8 K, while also showing that harmonic theory overpredicts rippling at higher amplitudes and fails to capture full anharmonic stabilization near instability (Wang et al., 2015).

3. Intrinsic temperature dependence from near-field electromagnetic fluctuations

In the near-field Casimir–Polder regime, temperature can modify the dispersion interaction itself through resonant coupling between atomic transitions and thermally populated surface polariton modes. For an atom in state $T=0$9, the van der Waals coefficient is written as a sum over dipole-allowed transitions,

$h_0$0

and the resonant image coefficient for an upward transition is

$h_0$1

with $h_0$2 and $h_0$3 (Silans et al., 2014). The mechanism therefore requires both a suitable dielectric response and thermal occupation of the relevant surface mode.

This produces large and even sign-changing effects. For Cs$h_0$4 near CaF$h_0$5, the calculated total $h_0$6 changes from $h_0$7 kHz·$h_0$8m$h_0$9 at $T=0$0 K to $T=0$1 kHz·$T=0$2m$T=0$3 at $T=0$4 K; for BaF$T=0$5, it changes from $T=0$6 kHz·$T=0$7m$T=0$8 at $T=0$9 K to $\Gamma_0$0 kHz·$\Gamma_0$1m$\Gamma_0$2 at $\Gamma_0$3 K. By contrast, for Cs$\Gamma_0$4 near sapphire, the temperature variation is modest, from $\Gamma_0$5 to $\Gamma_0$6 kHz·$\Gamma_0$7m$\Gamma_0$8 over the same range (Silans et al., 2014). For Cs$\Gamma_0$9 near sapphire, selective-reflection spectroscopy yields a measured increase of $h_0$0 from approximately $h_0$1 to approximately $h_0$2 kHz·$h_0$3m$h_0$4 between $h_0$5 K and $h_0$6 K, in agreement with the predicted coupling to sapphire surface polaritons (Silans et al., 2014).

This regime differs fundamentally from entropic weakening in graphene. Here, the temperature dependence is not merely a fluctuation-induced renormalization of a fixed substrate potential; it is a temperature dependence of the van der Waals coefficient itself. The same study also shows a stringent experimental caveat: surface quality and chemical stability can dominate the outcome. In the Cs–CaF$h_0$7 configuration, degradation of the CaF$h_0$8 tube in hot Cs vapor altered the effective dielectric response and prevented clean observation of the predicted strong thermal variation, whereas sapphire remained robust up to about $h_0$9 K (Silans et al., 2014).

4. Anisotropic media, orientational dependence, and thermal tuning of Hamaker amplitudes

In uniaxial anisotropic media, temperature dependence enters nonretarded van der Waals adhesion through the full dielectric tensor rather than through a single scalar permittivity. The nonretarded electrostatic problem is governed by

$U(z,T)=-\frac{C_3(T)}{z^3},$0

with $U(z,T)=-\frac{C_3(T)}{z^3},$1 evaluated at imaginary Matsubara frequencies $U(z,T)=-\frac{C_3(T)}{z^3},$2 (Kornilovitch, 2012). For the liquid crystal 5CB, the dielectric tensor components $U(z,T)=-\frac{C_3(T)}{z^3},$3 and $U(z,T)=-\frac{C_3(T)}{z^3},$4 are represented by a temperature-dependent three-band model, while the static limits are modeled as

$U(z,T)=-\frac{C_3(T)}{z^3},$5

with $U(z,T)=-\frac{C_3(T)}{z^3},$6 and $U(z,T)=-\frac{C_3(T)}{z^3},$7 (Kornilovitch, 2012).

For a single isotropic slab immersed in the anisotropic liquid crystal, the free energy per unit area is written as

$U(z,T)=-\frac{C_3(T)}{z^3},$8

where $U(z,T)=-\frac{C_3(T)}{z^3},$9 is a tilt Hamaker constant. For two semi-infinite slabs separated by an anisotropic liquid crystal layer of thickness $T=0$00, the adhesion free energy takes the form

$T=0$01

with $T=0$02 obtained from the Matsubara sum over anisotropic reflection-like factors and directional propagation terms (Kornilovitch, 2012).

Two distinct orientational phenomena follow. First, a solid slab immersed in a liquid crystal experiences a van der Waals torque that aligns the surface normal relative to the optical axis of the medium, and the preferred orientation is different for different materials. All studied materials except Teflon favor planar alignment in the single-slab geometry. Second, for two slabs in close proximity, the van der Waals attraction is strongest for homeotropic alignment of the intervening liquid crystal for all the materials studied (Kornilovitch, 2012). As temperature approaches the nematic–isotropic transition, the birefringence decreases, the orientational dependence of $T=0$03 and $T=0$04 weakens, and the torque disappears. This places temperature-dependent van der Waals adhesion in anisotropic media within a Lifshitz-type framework where geometry, orientation, and dielectric criticality are inseparable.

5. Dynamic, apparent, and continuum descriptions of thermal adhesion

Dynamic force microscopy shows that van der Waals interactions can control a conservative potential landscape without being the immediate dissipative channel. In frequency-modulation AFM, the dissipated energy due to tip–sample interaction is obtained from the extra drive required to maintain the oscillation amplitude, and the standard adhesion-hysteresis interpretation attributes dissipation to bistable structural configurations induced by the conservative tip–surface interaction (0806.1106). On PTCDA, the dissipated energy decreases from $T=0$05 eV/cycle at $T=0$06 K to $T=0$07 eV/cycle at $T=0$08 K, giving a negative temperature coefficient consistent with adhesion hysteresis. On KBr, the stated values change from approximately $T=0$09 eV/cycle at $T=0$10 K to $T=0$11 eV/cycle at $T=0$12 K, implying the opposite sign and pointing to a different dissipation mechanism; the source itself notes a typographical inconsistency between abstract and detailed discussion (0806.1106). The important distinction is that temperature-dependent dissipation in a vdW-dominated junction need not track the intrinsic temperature dependence of the conservative van der Waals force.

Pressure-sensitive adhesion in side-chain liquid crystal elastomers makes the same distinction at larger scales. The adhesive failure energy is decomposed as $T=0$13, where $T=0$14 is the interfacial bond energy and $T=0$15 is bulk dissipation. Contact-angle measurements show that the surface contribution is identical within experimental error for homeotropic, planar $T=0$16, planar $T=0$17, and isotropic films, so the interfacial van der Waals bonding potential is effectively the same across geometries (Street et al., 10 Jul 2025). The temperature dependence from $T=0$18C to $T=0$19C is instead captured by the adhesion factor

$T=0$20

which exhibits two relaxation-driven peaks. At $T=0$21C, $T=0$22 is approximately $T=0$23, $T=0$24, $T=0$25, and $T=0$26 MPa$T=0$27 for homeotropic, isotropic, planar $T=0$28, and planar $T=0$29 films, respectively, and the measured peel forces follow the same ordering: $T=0$30, $T=0$31, $T=0$32, and $T=0$33 N mm$T=0$34 (Street et al., 10 Jul 2025). This is a direct demonstration that strong temperature dependence of measured adhesion can arise while the interfacial van der Waals term remains unchanged.

A continuum thermoviscoelastic formulation extends this logic. In the Frémond-type contact model, adhesion is represented by a surface damage parameter $T=0$35, with free-energy terms such as $T=0$36 and a temperature-dependent cohesion term $T=0$37; friction enters through a coefficient $T=0$38, and bulk–surface heat exchange through $T=0$39 (Bonetti et al., 2012). The reconstructed interpretation explicitly states that the paper does not mention van der Waals interactions, but that the framework is compatible with representing adhesion as arising from microscopic van der Waals bonds if the interfacial energetic terms are chosen consistently with van der Waals energetics (Bonetti et al., 2012). This suggests that continuum models of temperature-dependent adhesion can absorb van der Waals physics either into a temperature-dependent work of adhesion or into a traction–separation law, while keeping the thermomechanical coupling explicit.

6. Registry dependence, material specificity, and interpretive issues

Graphite cleavage under an adhesive nanoasperity provides a sharp comparison between a purely pairwise interlayer description and a registry-dependent one. In classical molecular dynamics with a Lennard–Jones interlayer potential, complete removal of the upper graphene layer occurs throughout the range $T=0$40 K to $T=0$41 K. With the registry-dependent Kolmogorov–Crespi-type potential, which supplements the van der Waals term with a short-range contribution associated with $T=0$42-orbital overlap and electronic delocalization,

$T=0$43

exfoliation occurs for temperatures higher than $T=0$44 K, while from $T=0$45 K down to $T=0$46 K there is no cleavage (Prodanov et al., 2010). The analytical estimates in that study indicate that the effective $T=0$47-overlap repulsion increases with temperature more strongly than the van der Waals attraction decreases, so the qualitative transition is governed primarily by the electronic registry-dependent term rather than by the van der Waals part itself (Prodanov et al., 2010).

Several recurring misconceptions can therefore be rejected. First, a temperature-dependent adhesion measurement does not by itself demonstrate a temperature-dependent microscopic van der Waals pair potential: the graphene, PSA, AFM, and continuum-contact results all show mechanisms in which entropy, viscoelasticity, hysteresis, or damage dominate the observed temperature dependence while the bare interfacial dispersion potential is fixed or only weakly varying (Wang et al., 2015, Street et al., 10 Jul 2025, 0806.1106, Bonetti et al., 2012). Second, the sign of the temperature effect is not universal. Resonant near-field Casimir–Polder coupling can increase $T=0$48, decrease it, or even reverse its sign depending on the relation between atomic transitions and surface polaritons (Silans et al., 2014). Entropic rippling in supported graphene weakens effective adhesion with increasing temperature (Wang et al., 2015). Dynamic dissipation in AFM can decrease with temperature on one material and increase on another (0806.1106). Third, surface quality and constitutive fidelity are often decisive: degraded CaF$T=0$49 surfaces obscure intrinsic thermal Casimir–Polder effects, harmonic rippling theory loses accuracy at large amplitudes, and simple Lennard–Jones models can miss the strong temperature dependence introduced by registry-dependent electronic structure (Silans et al., 2014, Wang et al., 2015, Prodanov et al., 2010).

Possible experimental signatures follow the same mechanistic partition. For supported two-dimensional materials, temperature-dependent blister or peel tests, high-resolution separation measurements by AFM, STM, or x-ray reflectivity, and strain-controlled wrinkling or buckling experiments can probe the predicted entropic weakening of adhesion and temperature-dependent stability boundaries (Wang et al., 2015). For atom–surface dispersion forces, selective-reflection spectroscopy near polaritonic materials directly accesses $T=0$50 (Silans et al., 2014). For anisotropic hosts, measurements of torque, orientation, and colloidal stability across the nematic–isotropic transition probe the temperature dependence of tensorial Hamaker amplitudes (Kornilovitch, 2012). Taken together, these results define temperature-dependent van der Waals adhesion not as a single effect but as a family of temperature-coupled phenomena whose dominant mechanism depends on scale, geometry, material anisotropy, and the observable used to define adhesion.