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Universal features in "stickiness" criteria for soft adhesion with rough surfaces

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper shows that three stickiness criteria for rough soft contacts collapse to the same macroscopic law, so stickiness can be predicted from large-scale roughness and material properties alone.

desk verdict The BAM stickiness criterion rests on an algebraic error (Eq. 13 multiplies by la/ε instead of dividing), and once corrected the claimed near-universality with Persson-Tosatti largely disappears. read the letter →

arxiv 1908.06380 v1 pith:EXRBJEEZ submitted 2019-08-18 cond-mat.soft cond-mat.mtrl-sci

Michele Ciavarella This is my paper · ORCID
classification cond-mat.softcond-mat.mtrl-sci
keywords adhesionstickinessroughsurfacespowerspectraldensitybearingareamodelJKRDMTsoftmatter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Soft surfaces stick to rough counterfaces only when the roughness is mild enough. This paper shows that three stickiness criteria derived from different starting points—an energy-balance argument, a bearing-area geometric model, and a DMT-type adhesion theory—give nearly the same threshold when the roughness spectrum is a power law. In all three, stickiness is controlled by the longest wavelength of roughness, the rms amplitude of roughness, and the ratio of the work of adhesion to the plane-strain modulus; atomic-scale details drop out. If this is right, predicting stickiness requires only macroscopic surface and material properties, and the elastic modulus is the main practical control, consistent with the old empirical rule that tacky materials need a low modulus.

What carries the argument

The machinery is a pure power-law power-spectral-density model $C(q)=Z q^{-2(1+H)}$ with Hurst exponent $H=0.8$ (fractal dimension $D=2.2$), cut off at the low wavevector $q_0=2\pi/\lambda_L$. Because $H>0.5$, the elastic energy per unit area needed to flatten the surface converges to $E^*\pi h_{\mathrm{rms}}^2/\lambda_L \cdot H/(2H-1)$ as the short-wavelength cutoff is removed. Setting the effective work of adhesion $\Delta\gamma - E^*\pi h_{\mathrm{rms}}^2/\lambda_L \cdot H/(2H-1)$ to zero yields the energy-balance criterion. The bearing-area criterion instead computes the adhesive area from a constant-traction adhesive law (constant adhesive traction up to range $\varepsilon$) and defines stickiness as the pull-off traction falling to $10^{-8}$ of the theoretical strength; after power-law fits the dependence on $\varepsilon$ cancels and the same square-root form appears. All three are then compared on the axis $(\Delta\gamma/(E^*\varepsilon))(\lambda_L/\varepsilon)$ versus $h_{\mathrm{rms}}/\varepsilon$, where $\Delta\gamma/E^*$ sets the adhesion length.

What would settle it

Take a soft material and two surfaces with the same longest wavelength $\lambda_L$ and the same rms height $h_{\mathrm{rms}}$ but different short-wavelength content, e.g. one filtered below a few nanometres and one retaining atomic-scale roughness. The paper's three criteria predict identical stickiness. If pull-off measurements, or simulations with band ratio up to $10^7$, show stickiness changing when only the atomic-scale tail is altered, the universal claim is false.

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Extended reading notes

Core claim

Stickiness—whether a soft elastic body pressed against a hard rough surface holds on at pull-off—is claimed to be governed by three macroscopic quantities: the low-wavevector cutoff $q_0=2\pi/\lambda_L$, the rms roughness amplitude $h_{\mathrm{rms}}$, and the ratio $\Delta\gamma/E^*$ of the work of adhesion to the plane-strain elastic modulus. Two new criteria are derived: an energy-balance criterion that sets the effective surface energy to zero gives $h_{\mathrm{rms}} < \sqrt{0.24\,(\Delta\gamma/E^*)\,\lambda_L}$, and a bearing-area-model criterion with a constant-traction adhesive law and a numerical pull-off threshold gives $h_{\mathrm{rms}} < \sqrt{0.6\,(\Delta\gamma/E^*)\,\lambda_L}$. A third, DMT-based criterion gives $h_{\mathrm{rms}} < \varepsilon^{-1/5}\,[0.36\,(\Delta\gamma/E^*)\,\lambda_L]^{3/5}$, differing only by a weak dependence on the range of attraction. For power-law roughness with $H=0.8$, the three curves nearly coincide over many decades of wavelength. The paper concludes that small-scale roughness features such as local slopes and curvatures do not affect stickiness, while a numerical-interpolation criterion that does depend on them is regarded as an artifact of its limited roughness band.

Load-bearing premise

The agreement rests on representing real surfaces as a pure power-law roughness spectrum with Hurst exponent $H=0.8$ and on defining stickiness as the pull-off traction falling below $10^{-8}$ of the theoretical strength; if real surfaces deviate from that spectrum or the threshold is set differently, the quantitative coincidence among the criteria may not persist.

Editorial extensions

If this is right

  • Predicting stickiness no longer requires resolving roughness at or near atomic scale: the threshold is fixed by the longest wavelength $\lambda_L$, the rms height $h_{\mathrm{rms}}$, and the adhesion length $\Delta\gamma/E^*$.
  • The elastic modulus becomes the dominant practical control: lowering $E^*$ raises the stickiness threshold, in quantitative agreement with the empirical rule that soft materials around 1 MPa are tacky.
  • For surfaces whose roughness spans seven or more decades of wavelength, the three convergent criteria should be preferred over the numerical-interpolation criterion, which predicts a residual short-wavelength dependence.
  • The adhesion experiments on soft polymer hemispheres against rough diamond cited by the paper are consistent with the criteria: the estimated roughness parameter lies below the predicted stickiness threshold, so the surfaces are expected to stick.
  • Surface engineering for stickiness can focus on long-wavelength topography, increasing $\lambda_L$ by polishing, rather than on removing nanoscale roughness.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The closeness of the prefactors 0.24 and 0.6 hints at an asymptotic identity between the energy-balance and bearing-area routes that the paper does not derive; finding it would remove the remaining factor-of-two uncertainty.
  • The universality is established only for $H=0.8$ power-law surfaces. A testable extension is whether it survives for $H\le0.5$, where the elastic flattening energy diverges and the same derivation breaks down.
  • Because the criteria depend only on $h_{\mathrm{rms}}$ and $\lambda_L$, experimental data across materials and roughnesses could be collapsed onto a single master curve of $h_{\mathrm{rms}}^2/((\Delta\gamma/E^*)\lambda_L)$ against stickiness; the paper does not perform this test.
  • The comparison with the cited sphere experiments is indirect because the criteria are derived for nominally flat contacts; a flat-punch adhesion experiment with controlled power-law roughness would be a cleaner check.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The manuscript proposes two new "stickiness" criteria for soft adhesion of rough surfaces, one derived from the Persson-Tosatti energy balance and one from the bearing-area model (BAM), and compares them with the earlier DMT-based criterion of Violano et al. For a power-law roughness spectrum with Hurst exponent H = 0.8, the Persson-Tosatti criterion reduces to h_rms < sqrt(0.24 l_a lambda_L), the BAM criterion is fitted to numerical solutions and written as h_rms < sqrt(0.6 l_a lambda_L), and Violano's criterion is h_rms < epsilon^{-1/5} (0.358 l_a lambda_L)^{3/5}. The paper argues that the closeness of these three criteria is surprising and that stickiness is controlled by macroscopic quantities (the long-wavelength cutoff, the rms height, and the ratio of work of adhesion to plane-strain modulus) rather than by atomic-scale details. The conclusion is applied to the recent Dalvi et al. adhesion experiments, for which all surfaces are predicted to be sticky.

Significance. If correct, the paper would provide a practical and simple design rule for soft adhesion and would strengthen the Persson-Tosatti energy-balance picture against magnification-dependent criteria such as Pastewka-Robbins and Muser. The PT derivation in Section 2.1 is transparent and easy to reproduce, and the comparison with the Dalvi et al. experiments is a useful quantitative check. The BAM criterion, however, is essential to the claimed universality and is not derived in closed form: it is obtained by solving a numerical equation at an arbitrary threshold and then fitting power laws. Its validity therefore depends entirely on the correctness of Eq. (13). Because the central conclusion of quantitative agreement among the three criteria rests on this BAM criterion, the significance of the paper hinges on whether that equation is correct and on how sensitive the fitted exponent and prefactor are to the threshold choice.

major comments (2)
  1. [Section 2.2, Eq. (13)] The normalized repulsive term in Eq. (13) appears to be algebraically inverted. From Eq. (7), the repulsive term is q0 h_rms (E*/sigma0) exp(-u/(gamma h_rms)). With q0 = 2 pi / lambda_L and E*/sigma0 = epsilon / l_a, the term in the reduced variables used in Eq. (13) is 2 pi (h_rms/epsilon) / [(lambda_L/epsilon)(l_a/epsilon)], so it must be divided by l_a/epsilon. As printed, Eq. (13) places l_a/epsilon in the numerator, making the repulsive coefficient too small by a factor (l_a/epsilon)^{-2}, which is 400 for the representative Lennard-Jones value l_a/epsilon = 0.05. Since the power-law fits (14)-(15) and the final criterion (16) are extracted from Eq. (13), the BAM branch in Fig. 4 and the central claim of quantitative agreement between BAM and Persson-Tosatti in Section 5 are directly affected; for example, re-solving the zero-threshold balance for l_a/epsilon = 0.05 and lambda_L/epsilon = 10^7 gives a stickiness threshold near h_rms/epsilon ~ 180, not the value near 550 implied by Eq. (16).
  2. [Section 2.2, Eqs. (13)-(16)] The BAM stickiness criterion is not derived in closed form but is obtained by solving Eq. (13) at the arbitrary threshold -sigma_min/sigma0 = 10^-8 and then fitting the results to power laws (14)-(15). The value beta_BAM = 0.6 in Eq. (16) therefore encodes both the threshold choice and the fitting range. A sensitivity analysis, for example using thresholds 10^-6 or 10^-10 and different ranges of lambda_L/lambda_L0, is needed before the close agreement with the Persson-Tosatti criterion can be presented as a universal feature rather than as a consequence of the chosen numerical definition of stickiness.
minor comments (4)
  1. [Fig. 1 caption] The caption writes lambda_L0 = q0/2 pi = 2048 epsilon, which is dimensionally inconsistent; since q0 = 2 pi / lambda_L, the intended expression is lambda_L0 = 2 pi / q0 = 2048 epsilon.
  2. [Throughout] The surname of the experimental group is spelled "Dalvi" in the abstract and references but appears as "Davli" in several places in Sections 3 and 4; please correct.
  3. [Section 3 and Fig. 4] The comparison of the three criteria is presented only for H = 0.8 (D = 2.2); the Persson-Tosatti prefactor depends on H through (2H-1)/(pi H), and the Violano criterion is stated for D ~ 2.2. The abstract and conclusions should avoid implying universality over all Hurst exponents until other values of H are examined.
  4. [Section 4.2, Eq. (30)] The symbol delta_gamma_rrs should presumably be delta_gamma_rss to match Eq. (29); please check the notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: BAM coefficient is a curve-fit to the paper's own BAM model; PT and Violano are independent criteria, and self-citation is not load-bearing.

full rationale

The derivation chain is self-contained with respect to the central comparison. The Persson-Tosatti criterion (Eq. 12) follows directly from the energy balance in Eqs. (1)-(11) with no fitted parameters. The Violano criterion (Eq. 8) is imported from an independent DMT-based derivation. The BAM criterion (Eq. 16) is obtained by numerically solving the BAM force-separation equation (Eq. 13) for a stated stickiness threshold and then curve-fitting that threshold in Eqs. (14)-(15); the fit is to the paper's own model output, not to the Persson-Tosatti or Violano thresholds or to the Dalvi experimental data. Thus the coefficient beta_BAM = 0.6 is not a fitted parameter disguised as an external prediction. Self-citations to the author's earlier BAM papers introduce the model, but the model equation is restated in the paper, so the argument does not reduce to an unverified self-citation. The skeptical algebraic concern about Eq. (13) (whether 2*pi*(la/eps) should be 2*pi*(eps/la)) is a correctness issue, not a circularity issue: even if the BAM threshold shifted, its derivation would remain independent of the PT and Violano criteria it is compared with. The paper's own caveats about needing further experiments and about the Pastewka-Robbins magnification dependence concern empirical adequacy, not circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. It does rely on two fitted quantities in the BAM criterion: the arbitrary stickiness threshold and the prefactor of the power-law fit. The remaining axioms are standard contact-mechanics assumptions inherited from Persson-Tosatti and from the author's BAM model.

free parameters (3)
  • BAM stickiness threshold = −σmin/σ0 = 10^−8
    Defines when the BAM model counts as sticky; arbitrary choice that sets the numerical threshold in eq (13).
  • BAM power-law fit prefactor α = α ≈ 35 (la/ε)^0.5 (eq 15)
    Fitted to BAM numerical solutions for the hrms/ε threshold across four decades of la/ε; this fit produces the final β_BAM = 0.6 in eq (16).
  • Reference long-wavelength cutoff λL0 = λL0 = 2048 ε
    Normalization used in eq (14); the fitted α absorbs this choice, so the final criterion should ideally be independent of it.
assumptions (4)
  • domain assumption Surface roughness is described by a pure power-law PSD C(q) = Z q^(−2(1+H)) with H=0.8 in the comparison.
    Used in eqs (9)-(12) and throughout; real surfaces are only approximately power-law, and the universality claim is tested for this one spectrum.
  • domain assumption Persson-Tosatti effective energy balance (eq 1) is valid and the A/A0 term can be neglected in the first derivation.
    The new PT criterion (12) sets Δγ_eff = 0 without the area ratio; the correction is deferred to Section 4.1.
  • domain assumption BAM model assumptions: Dugdale force-separation law, superposition of repulsive and attractive forces, and Persson's repulsive pressure relation (eqs 3-7).
    The BAM criterion inherits these model assumptions, and the criterion is a fit to this model, not an independent measurement.
  • domain assumption Gaussian height distribution for the bearing area calculation in BAM.
    Eq (5) uses Gaussian statistics for the bearing area; real surfaces may differ.

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Cite this review

Pith. "Pith review of Universal features in "stickiness" criteria for soft adhesion with rough surfaces." pith.science (2026). https://pith.science/paper/EXRBJEEZ

@misc{pith2026190806380,
  author       = {Pith},
  title        = {Pith review of: Universal features in "stickiness" criteria for soft adhesion with rough surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EXRBJEEZ}},
  note         = {Machine review of arXiv:1908.06380}
}
read the original abstract

A very interesting recent paper by Dalvi et al. has demonstrated convincingly with adhesion experiments of a soft material with a hard rough material that the simple energy idea of Persson and Tosatti works reasonably well, namely the reduction in apparent work of adhesion is equal to the energy required to achieve conformal contact. We demonstrate here that, in terms of a stickiness criterion, this is extremely close to a criterion we derive from BAM (Bearing Area Model) of Ciavarella, and not very far from that of Violano et al. It is rather surprising that all these criteria give very close results and this also confirms stickiness to be mainly dependent on macroscopic quantities.

Figures

Figures reproduced from arXiv: 1908.06380 by the authors.

Figure 4
Figure 4. Fig.4. A comparison of the three derived stickiness criteria: Persso [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Fig.5. The coefficient [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Fig.6. A further comparison of the three derived stickiness criteria [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

8 extracted references · 8 canonical work pages

  1. [1]

    , 2010, Autumn et al

    Introduction The role of adhesion in contact mechanics has seen an explosion of int er- est in recent years, due to the enormous interest in soft materials technology, nano-systems, cell adhesion, and the understanding of bio-atta chments and the idea to imitate their solutions (Creton et al., 1996, Kendall, 2001, Kendall et al. , 2010, Autumn et al. , 20...

    work page 2018

  2. [2]

    A new Persson-Tosatti stickiness criterion Let us start from obtaining a stickiness criterion from the Persson -Tosatti’s idea of the effective surface energy (1)

    New stickiness criteria 2.1. A new Persson-Tosatti stickiness criterion Let us start from obtaining a stickiness criterion from the Persson -Tosatti’s idea of the effective surface energy (1). If we take a typical powe r law PSD C (q) = Zq −2(1+H) for q > q 0 = 2π λL , where H is the Hurst exponent (equal to 5 3 − D where D is the fractal dimension of the ...

    work page 2019

  3. [3]

    BAM makes an independent estimate for the repulsive and adhesive component s of the load

    ≃ σth (the theoretical strength of the material, for a crystalline solid, and anyway the peak of tensile stress in a true Lenn ard- Jones potential), ǫ is the range of attraction, and ∆ γ = σ0ǫ. BAM makes an independent estimate for the repulsive and adhesive component s of the load. It has the big advantage to be very simple to implement, particu larly f...

    work page 2014

  4. [4]

    Persson-Tosatti and BAM even closer when considering s urface area increase Dalvi et al

    Discussion 4.1. Persson-Tosatti and BAM even closer when considering s urface area increase Dalvi et al. (2019) make a discussion about the term true surface area, which they estimate as A (ζ) A0 = 1 + √π 2 h′2 rms exp ( 1 h′2rms ) Erf c ( 1 h′ rms ) /h′ rms which complicates the model slightly. This terms will modify the Persso n- Tosatti criterion intro...

    work page 2019

  5. [5]

    Comparison between the three stickiness criteria We have obtained, for the example case of a pure power law PSD roug h- ness (for the typical case of H ≃ 0.8) that Persson-Tosatti and BAM predict stickiness (12) (16) with exactly the same qualitative form hrms < √ βlaλL (17) where βP T = 0.24 and βBAM = 0.6 which are even quantitatively close — even close...

    work page 2019

  6. [6]

    Linking energy loss in soft adhesion to surface roughness

    References Afferrante, L., Bottiglione, F., Putignano, C., Persson, B. N. J., & Ca r- bone, G. (2018). Elastic Contact Mechanics of Randomly Rough Sur faces: An Assessment of Advanced Asperity Models and Persson’s Theory . Tribol- ogy Letters, 66(2), 75. Autumn, K., Sitti, M., Liang, Y. A., Peattie, A. M., Hansen, W. R., Sponberg, S., Kenny, T.W., Fearing,...

    work page Pith review arXiv 2018

  7. [7]

    Conclusions We have obtained two new stickiness criteria, originated from the th eories of Persson-Tosatti, and from BAM. These two, which have complet ely differ- ent origin (one being a simple energy balance concept, and the other a mix of Persson’s adhesiveless solution with a geometric estimate of adhesiv e forces), together with the DMT criterion of V...

    work page 2016

  8. [2018]

    This result may be in contrast with the theory by Joe et al

    so this theory would predict that such surfaces could never adhere, even for arbitrarily small rms height hrms. This result may be in contrast with the theory by Joe et al. (2017, 2018), and should be further investi- gated. By contrast, for D < 2.5 the energy converges in the fractal limit ζ → ∞ and hence full contact is expected to be possible regardles...

    work page 2019

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