Table 1 Parameters characterising the different MESs (metastable elastocapillary systems) considered in this work

From: Bubbles enable volumetric negative compressibility in metastable elastocapillary systems

System

pint

pext

a0

\(\frac{\Delta {a}_{{{{{{{{\rm{NC}}}}}}}}}^{{{{{{{{\rm{int}}}}}}}}}}{{a}_{0}}\)

\(\frac{\Delta {a}_{{{{{{{{\rm{NC}}}}}}}}}^{{{{{{{{\rm{ext}}}}}}}}}}{{a}_{0}}\)

\(\frac{\Delta {a}_{{{{{{{{\rm{p}}}}}}}}}^{{{{{{{{\rm{int}}}}}}}}}}{{a}_{0}}\)

\(\frac{\Delta {a}_{{{{{{{{\rm{p}}}}}}}}}^{{{{{{{{\rm{ext}}}}}}}}}}{{a}_{0}}\)

\(\frac{\Delta {a}_{\gamma }}{{a}_{0}}\)

\({\beta }_{{{{{{{{\rm{1D}}}}}}}}}^{{{{{{{{\rm{int}}}}}}}}}\)

\({\beta }_{{{{{{{{\rm{1D}}}}}}}}}^{{{{{{{{\rm{ext}}}}}}}}}\)

ZIF-67

23

8.72

17.053

0.29

− 0.28

− 0.059

0.032

− 0.23

− 286

− 269

ZIF-8

31

20.3

17.09

0.34

− 0.34

− 0.090

0.074

− 0.25

− 841

− 487

Laminae

0.45

0.985

2.18 ⋅ 107

17.9

− 8.3

− 3.2

-

− 14.7

− 5.8 ⋅ 105

− 4.1 ⋅ 107

MscL

>40

-

25.23

>40

-

−0.2

-

-

− 1 ⋅ 104

-

BK

100

-

39.4

16.8

-

−0.6

-

-

− 1680

-

  1. The reported 1D compressibilities are defined as β1D = − Δa/a0/Δp, where Δp refers to the pressure drop needed to achieve the displacement Δa; this monodimensional definition is chosen to facilitate comparison of different systems and underestimates NC as compared to the conventional one based on the maximum derivative da/dp, used, e.g., in Ref. 8. ZIF-67 values at 5° C. ZIF-8 data from8, with β recomputed according to the present definition. Biological pores data (MscL and BK channels) are inferred from different works and are reported for comparison, see Supplementary Text 2 for details. Missing data are denoted by a dash. Table units: pint/ext (MPa), a0(Å), Δa/a0 (%), \({\beta }_{{{{{{{{\rm{1D}}}}}}}}}^{{{{{{{{\rm{int}}}}}}}}/{{{{{{{\rm{ext}}}}}}}}}\,({{{{{{{{\rm{TPa}}}}}}}}}^{-1})\).
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