# UNASKED QUESTIONS — Q001–Q025

*Twenty-five questions whose absence has a structural cause. Each names the question, the reason it
does not get asked, and what would change if it were answered. The reason is always a property of the
measurement or of the division of the field — never a claim that someone suppressed the answer.*

### Q001 — Do the surface energies of a solid measured by contact angle and by contact mechanics agree?
**Question.** On one clean, smooth solid, is the surface free energy from probe-liquid contact angles equal to the work of adhesion from a JKR pull-off?
**Why nobody asks it.** The two values share a name, not a definition. The contact-angle number is a work of adhesion against a liquid, decomposed by a model whose polar and dispersive parts are not unique; the contact-mechanics number is a work of adhesion against the solid itself, inferred from a pull-off force with a roughness correction. One community is surface chemistry, the other contact mechanics; each publishes "the surface energy" of a material without needing the other's value. Comparing them needs a solid that is clean enough for wetting, smooth enough for JKR and elastic enough to analyse — a sample neither community routinely prepares.
**What changes if answered.** Agreement would make tabulated surface energies thermodynamic quantities and let adhesion be predicted from wetting. Systematic disagreement would make every surface-energy table a model output, and the design of adhesives, coatings and composites would rest on a number that was never a property.

### Q002 — Is the stress in a deposited film uniform through its thickness?
**Question.** Does the thickness-averaged stress obtained from wafer curvature equal the local stress at every depth in a vapour-deposited film?
**Why nobody asks it.** Curvature returns one number per film: the integral of stress over thickness. A depth profile needs X-ray sin²ψ, focused-ion-beam digital image correlation, or a sequence of etches — each destructive, slow, or dependent on a model of the substrate. Deposition is tuned against the average, so a film that runs from compressive at the interface to tensile at the surface is reported as a single "intrinsic stress" and modelled as uniform. The gradient is invisible because the standard metrology integrates it away.
**What changes if answered.** The interface stress, not the average, decides delamination and cracking; a measured gradient would change how adhesion and failure are predicted. It would also explain the thickness dependence of intrinsic stress without invoking a change in growth mechanism, and would turn stress engineering from a set point into a depth-resolved design problem.

### Q003 — Is the zeta potential a property of the surface or of the slipping plane?
**Question.** Does the zeta potential obtained from electrophoretic mobility measure the potential at the particle surface, or at a plane whose position is assumed rather than measured?
**Why nobody asks it.** Mobility is converted to zeta by the Smoluchowski or Henry equation, which assumes the slipping plane sits at a fixed distance from the surface and that the double layer is thin compared with the particle. Neither assumption is measured; the plane's position is a fit parameter, and the surface charge inferred from it depends on that choice. Colloid science reports zeta as a material property, while surface chemistry measures charge by titration, and the two are rarely compared on the same particles.
**What changes if answered.** A measured slipping-plane position would turn zeta potentials into surface potentials, and every colloid stability, protein mobility and flocculation prediction would shift by a known amount. If the plane's position varies with ionic strength and surface chemistry, then the "surface charge" of a particle is not a single number, and electrokinetic transport, membrane fouling and the Hofmeister series inherit a systematic.

### Q004 — Is the "modulus" of a soft gel the same quantity in indentation and in rheology?
**Question.** For one gel at one temperature, does the modulus reported by atomic-force indentation equal the shear modulus reported by rheology?
**Why nobody asks it.** Both numbers are called the modulus, but indentation measures a local, confined response under a probe, while rheology measures a bulk shear response at a controlled frequency. Converting one to the other assumes linear elasticity, incompressibility and a flat half-space; a poroelastic gel relaxes under the probe, so the apparent modulus depends on indentation rate and probe radius. The communities are mechanobiology and polymer physics, and the two values are rarely compared on the same sample.
**What changes if answered.** If they differ by more than the effect being reported, the substrate-stiffness experiments that underpin mechanobiology rest on a calibration that shifts with probe size. If they agree under a stated protocol, that protocol becomes the standard, and the "soft" and "stiff" gels of the literature become comparable.

### Q005 — Is the adsorption energy measured in ultrahigh vacuum the energy at reaction conditions?
**Question.** Does the binding energy of an adsorbate measured on a single crystal at low coverage and ultrahigh vacuum equal the binding energy of that intermediate at the coverage and pressure of a working catalyst?
**Why nobody asks it.** Temperature-programmed desorption gives a clean number at low coverage, on a well-defined facet, with no gas phase; the working catalyst is a nanoparticle at high coverage under a bar of reactant. The binding energy is coverage-dependent through lateral interactions and the reconstruction the gas induces, and the two conditions are studied by different communities — surface science and catalysis — with different apparatus and different definitions of "clean." The vacuum number is the benchmark for every computed binding energy and every volcano plot.
**What changes if answered.** A measured coverage dependence would change the Sabatier analysis that ranks catalysts, since the optimum is set by a binding energy that may move with coverage. It would also explain part of the pressure gap between model surfaces and real catalysts, and would turn the volcano plot from a single-point correlation into a function of the operating condition.

### Q006 — Is the phonon density of states measured on a powder the density of states?
**Question.** For a crystal with more than one element, is the spectrum extracted from inelastic neutron scattering the phonon density of states, or a cross-section-weighted projection of it?
**Why nobody asks it.** The intensity is weighted by the neutron scattering cross-sections of the constituent atoms, by the Debye–Waller factor and by the instrument's wavevector range, so the result is a generalized, element-weighted density of states. It is routinely plotted against a first-principles density of states, and the mismatch is absorbed in a scale factor or a small adjustment of the force constants. Recovering the true density needs isotopic substitution or polarization analysis — a different experiment from the one that produced the data.
**What changes if answered.** If the weighting explains a substantial part of the measured–calculated disagreement, then phonon-derived heat capacities, thermal conductivities and electron–phonon couplings inherit a systematic error. Some "anomalous" phonon softening would be a cross-section effect rather than physics.

### Q007 — What fraction of the protein molecules in a crystal has the ligand bound?
**Question.** In a co-crystal structure, is the refined ligand occupancy the fraction of molecules that are actually occupied, or a number chosen to fit the density?
**Why nobody asks it.** Occupancy and atomic displacement parameters are almost perfectly correlated in refinement: raising occupancy and raising B-factors produce nearly the same calculated map, and the residual barely distinguishes them. The reported occupancy is therefore set by restraints and convention, while the crystal is treated as a homogeneous population. Measuring the real fraction needs single-crystal absorption or fluorescence microspectroscopy on the same crystal — a different technique, usually a different laboratory.
**What changes if answered.** If occupancies are systematically overestimated, binding modes are being interpreted from a minority species, and the thermodynamic quantities attached to a structure are not properties of the crystal that was solved. A measured occupancy would turn the structure into a population measurement and make co-crystal structures quantitative.

### Q008 — Is the pH inside a protein crystal the pH of the mother liquor?
**Question.** Does the proton activity inside a protein crystal equal the value measured in the drop it grew from?
**Why nobody asks it.** A protein crystal is a charged porous medium: fixed charges on the lattice create a Donnan potential, so small ions — protons included — partition unequally between crystal and bath. Crystallisation is reported at the bath pH, and pH-dependent binding, catalysis and conformation are interpreted against that number. Measuring the internal value needs a ratiometric dye or a pH-sensitive label inside the crystal, a technique from another field, and the answer would vary with the crystal's own charge.
**What changes if answered.** Every "the structure was determined at pH 7" statement would carry an internal value, and ligand affinities measured in crystals would be corrected to the environment the protein actually experienced. It would also explain part of the irreproducibility of crystallisation screens, since the internal pH would depend on the protein's charge rather than on the buffer alone.

### Q009 — Is the Coulombic efficiency of an electrode a property of that electrode?
**Question.** In a two-electrode half cell, how much of the measured Coulombic efficiency belongs to the working electrode and how much to the counter electrode it is measured against?
**Why nobody asks it.** The standard half cell uses a lithium-metal counter that is also the reference, and that electrode reacts with the electrolyte on its own. The cycle therefore reports a cell efficiency, but it is tabulated as a material property, and electrolytes and additives are ranked by it. Separating the two needs a third electrode or a symmetric cell, which changes the geometry and is not the community's standard protocol.
**What changes if answered.** If the counter electrode contributes a significant, drifting share, part of the reported efficiency is an artefact of the test cell, and the ranking of electrolytes and additives is contaminated by a variable nobody controls. It would also change what a high efficiency means for an anode-less cell, where the lithium inventory is the quantity of interest.

### Q010 — Is electrochemically active surface area measured, or defined by the constant used to calculate it?
**Question.** When a catalyst's activity is normalised per electrochemically active area, is that area an independent measurement or the double-layer capacitance divided by an assumed specific capacitance?
**Why nobody asks it.** The capacitance is measured, but converting it to area requires a specific capacitance per real area, usually inherited from mercury or from a flat single crystal of a different material. Since the real area is the unknown, that constant cannot be calibrated against it; it is a convention embedded in the methods. The circularity is invisible because the result is reported as a number with units of area.
**What changes if answered.** A primary measurement of the specific capacitance — on a surface whose area is known from a crystal facet or a stepped single crystal — would either validate the normalisation or show that "intrinsic activity" comparisons between catalysts are comparisons of roughness. Since most electrocatalysis claims are per-area, this decides whether the field's central normalisation is a measurement at all.

### Q011 — How much does the elastic wave speed of a rock disperse between hertz and megahertz?
**Question.** Is the velocity measured in the laboratory at ultrasonic frequency the velocity a seismic wave samples at seismic frequency?
**Why nobody asks it.** Rock physics measures at ultrasonic frequencies because specimens are centimetres; seismology measures at hertz because the Earth is large. Dispersion from fluid flow in pores and from cracks is expected in the intermediate band, but the two communities calibrate their own velocities and meet through a velocity model, not through a shared sample. A few percent of dispersion is the same size as the difference between two plausible mineralogies.
**What changes if answered.** If dispersion is that large, every laboratory-to-seismic extrapolation carries a systematic currently assigned to composition, porosity or saturation. A measured dispersion curve on one sample, spanning seismic to ultrasonic frequencies, would let the two datasets be merged honestly — and would change what a seismic velocity anomaly is allowed to mean.

### Q012 — Is the liquid permeability of a tight rock the gas permeability corrected for slip?
**Question.** Does the Klinkenberg-corrected gas permeability of a low-permeability rock equal its permeability to water?
**Why nobody asks it.** Gas is used because water swells clays and because a steady water flow through a tight core takes weeks; the correction for gas slip is a single-coefficient model. But water flow in the same rock carries electrokinetic and interfacial effects that gas does not, and the two measurements belong to different communities — petrophysics and hydrogeology — which rarely share a core. The corrected number is reported as "the" permeability.
**What changes if answered.** If the two permeabilities differ systematically in tight rocks, flow models, caprock seals and contaminant transport are calibrated on a quantity measured with the wrong fluid. A paired measurement on the same core would establish the conversion, or show that permeability in tight formations is fluid-specific and should be reported as such.

### Q013 — Is the nucleation rate per unit volume the same in a picolitre droplet as in a bulk melt?
**Question.** Does the steady-state nucleation rate measured in thousands of small droplets equal the rate measured in a bulk sample, once both are normalised by volume?
**Why nobody asks it.** Droplet methods are used precisely because they divide a sample into many independent volumes and make rare nucleation events countable; the analysis then assumes each droplet nucleates independently, at a rate proportional to its volume. At small volumes the interface is a large fraction of the sample, so surface nucleation and container effects enter exactly where the volume is smallest. Bulk and droplet measurements are made in different communities and compared through the volume normalisation.
**What changes if answered.** A measured deviation would mean nucleation rates cannot be extrapolated between volumes, which is what every polymorph screen and crystalliser design does. It would also separate homogeneous from surface nucleation without assuming which dominates, and would tell process engineers the smallest volume at which a rate measurement still predicts a plant.

### Q014 — Is the fracture toughness obtained from an indentation crack a measurement?
**Question.** Does the toughness calculated from the length of a crack around a hardness indent equal the toughness measured on a macroscopic specimen of the same material?
**Why nobody asks it.** The indentation formula contains an empirical constant calibrated on a small set of materials, and the crack is measured in a complex residual-stress field that depends on the indentation load, the modulus-to-hardness ratio and the crack geometry. The fracture-mechanics community measures on beams; the ceramics community screens with indents; the two values are compared rarely, and a discrepancy is attributed to R-curve behaviour or surface condition rather than to the conversion.
**What changes if answered.** If indentation toughness is systematically offset, a large fraction of the ceramics and coating literature is on a relative scale that cannot be compared with design data. A cross-calibration would either validate the screening method or restrict it to ranking within a material family, and would change how thin-film and small-specimen toughness is reported.

### Q015 — Is a working catalyst at the temperature the thermocouple reports?
**Question.** During an exothermic reaction on a supported metal catalyst, what is the temperature of the metal nanoparticle, and how far is it from the temperature the thermocouple reports?
**Why nobody asks it.** The thermocouple sits in the gas or in the reactor wall, not on the nanoparticle; the surface temperature is inferred from a heat balance with assumed heat-transfer coefficients, or from anti-Stokes Raman thermometry, which is another community's technique. A local rise large enough to change the apparent activation energy would be invisible in every rate table, because the table records the reactor temperature.
**What changes if answered.** Measured particle temperatures would let rates be plotted against the temperature the catalyst experiences rather than the reactor's, changing activation energies, comparisons between catalysts, and the interpretation of hot spots and oscillations. It would also decide whether some reports of non-Arrhenius behaviour are kinetics or thermometry.

### Q016 — What is the concentration of active enzyme in a purified preparation?
**Question.** Of the protein molecules in a purified enzyme stock, what fraction is catalytically competent?
**Why nobody asks it.** The turnover number is the maximal rate divided by the total protein concentration, which comes from A280 and an extinction coefficient computed from the sequence; both steps assume every molecule is the intended protein and every molecule is active. The direct measurement is active-site titration with a tight-binding inhibitor, available only for enzymes that happen to have one, and the result is a property of the batch rather than the molecule — so it appears as a caveat, not as a result.
**What changes if answered.** A routine active-fraction measurement would rescale a large part of enzymology: turnover numbers, catalytic efficiencies, and the many engineering claims that compare a mutant with a wild type through a rate ratio. Some "improvements" would turn out to be purification differences, and the kinetic constants used in metabolic models would acquire a denominator that was measured.

### Q017 — Is a protein as stable inside a cell as it is in a test tube?
**Question.** For the same protein, is the free energy of folding measured in dilute buffer the free energy that governs its folded fraction in the cytoplasm?
**Why nobody asks it.** In vitro stability comes from chemical or thermal denaturation and a two-state extrapolation; in-cell measurements use NMR, FRET or fluorescence lifetime, which report a folded fraction rather than a free energy and need labels that may perturb the protein. The two communities — biophysical chemistry and cell biology — rarely study the same protein, and crowding theory predicts a stabilisation that is not always observed. The dilute value is used as if it transferred.
**What changes if answered.** Drug design that targets stability, the interpretation of destabilising mutations in disease, and every model of proteostasis depend on whether the test-tube number is the cellular one. A measured transfer would also say which osmolytes and crowders matter, turning macromolecular crowding from a correction into a calibrated environment.

### Q018 — What is the pressure inside a sealed hydrothermal vessel?
**Question.** In a hydrothermal synthesis run at "autogenous pressure", what is the actual pressure in the vessel?
**Why nobody asks it.** The vessel is not instrumented at the sample, so pressure is not measured; it is computed from the fill fraction and the vapour pressure of the pure solvent. The reaction consumes and produces species, the solvent activity changes with dissolved solids, and the fill fraction is set by the experimenter. The phrase "autogenous pressure" hides the assumption inside a name, and temperature is the only reported variable.
**What changes if answered.** Pressure shifts phase selection, solubility and particle size; if the real value departs from the assumed one, hydrothermal phase diagrams are drawn against the wrong axis. A gauge or an in-situ pressure measurement would make syntheses reproducible between vessels and would explain batch differences now attributed to seeding or stirring.

### Q019 — At what concentration do trace impurities control crystal nucleation?
**Question.** In a "pure" solution, are the impurities at a concentration that changes the nucleation rate?
**Why nobody asks it.** Nucleation is measured on the purest available reagent, whose certificate of analysis lists a few elements at detection limits chosen by the vendor; the species that matters may be unlisted. Measuring it needs inductively coupled plasma mass spectrometry or a clean-room protocol, a different technique from the nucleation assay, and the answer would make the measurement a study of the reagent rather than of the crystal.
**What changes if answered.** If nucleation is impurity-controlled at trace levels, much of the irreproducibility of crystallisation is a hidden variable, and polymorph selection by "additives" is a special case of a general effect. It would also give a recipe for making nucleation measurements comparable between laboratories: report the impurity budget.

### Q020 — Is the molecular mass of a glycoprotein measured by light scattering the mass of its protein?
**Question.** When size-exclusion chromatography with light scattering reports the mass of a glycoprotein, is the value the total mass, given that both the refractive-index increment and the extinction coefficient are taken from the protein alone?
**Why nobody asks it.** Light scattering needs a refractive-index increment, normally assumed to be the protein value; a glycan has a different increment, and the concentration is computed from A280, to which the glycan does not contribute. The two assumptions multiply, and the error grows with glycosylation. Measuring the increment requires dialysed solutions and a refractometer, and the glycan composition is measured by a different community.
**What changes if answered.** Masses, stoichiometries and conjugation ratios of glycoproteins — antibodies, glycopeptide hormones, industrial enzymes — would carry a measured correction rather than a systematic one. It would also explain why values from light scattering, sedimentation and mass spectrometry disagree for the same molecule, and would make the disagreement informative.

### Q021 — Is the piezoelectric coefficient of a thin film the bulk crystal's coefficient?
**Question.** When a film's piezoelectric response is measured with the substrate attached, is the reported coefficient the free strain per unit field of the material, or the clamped response of a film on an elastic foundation?
**Why nobody asks it.** The film is bonded to a substrate that resists in-plane strain, so the measured displacement is a clamped response; converting it to the free coefficient needs the elastic constants of film and substrate, which are assumed or taken from the bulk. The bulk and thin-film communities report values under the same name, and the difference is absorbed into an "effective" coefficient that is quoted without its boundary condition.
**What changes if answered.** A measured clamping correction would make the "giant piezoelectricity" claims of thin films comparable with bulk data, and would tell device designers whether the coefficient they use is the one the film actually has under an electrode. It would also separate an intrinsic material improvement from a measurement geometry.

### Q022 — Does the dielectric constant of water change when it is confined to a nanometre pore?
**Question.** Is the dielectric constant of water in a pore a few nanometres wide the bulk value?
**Why nobody asks it.** Dielectric spectroscopy of a confined liquid is limited at low frequency by electrode polarization, a huge capacitance in series with the sample; removing it requires a circuit model whose parameters are not measured. Simulations give a dielectric profile that depends on the force field, and the experimental and simulation communities rarely compare on the same pore. The bulk permittivity is then used in every electrostatic model of the pore.
**What changes if answered.** A measured permittivity profile would change ion selectivity, surface charge, and the free energy of a charged species inside a nanopore. It would also decide whether the bulk dielectric constant is admissible in the Poisson–Boltzmann equations used for membranes, colloids and confined water.

### Q023 — What happens in the first millisecond of a stopped-flow experiment?
**Question.** At early times in a stopped-flow experiment, is the observed signal kinetics or a convolution of kinetics with mixing?
**Why nobody asks it.** The dead time is measured with a test reaction whose rate is assumed known, so the calibration inherits that reaction's own uncertainty; mixing is not instantaneous, and the earliest data are a convolution of the reaction with the concentration gradient in the observation cell. The convolution is usually avoided by discarding early points, which is exactly where a burst or a transient intermediate would appear.
**What changes if answered.** A measured instrument response function would let the early signal be deconvolved rather than discarded, changing burst amplitudes, transient intermediate concentrations and the rate constants extracted from rapid kinetics. It would also make the many "burst" phases in enzymology comparable across instruments, instead of being partly a property of the mixer.

### Q024 — Is the optical gap the transport gap?
**Question.** In a disordered or molecular semiconductor, is the gap measured by absorption the energy needed to create a free carrier, or the energy of an exciton?
**Why nobody asks it.** Absorption measures an exciton; transport and device models need a free-carrier gap; the two differ by a binding energy that is rarely measured and is instead absorbed into a fitted band tail or a disorder width. The optical and transport communities report "the gap" from their own measurement, and the device literature uses whichever number makes the curve fit.
**What changes if answered.** A measured exciton binding energy on the same film would fix the energy scale of every device model and decide whether the band tail needed to fit transport is real disorder or a mislabelled exciton. It would also change design rules for organic photovoltaics and light-emitting diodes, where the two gaps are close to the energies being engineered.

### Q025 — Does an X-ray microanalysis of a grain boundary measure the boundary?
**Question.** When an electron beam is placed on a grain boundary, what fraction of the detected X-ray signal comes from the boundary itself rather than from the adjacent grains?
**Why nobody asks it.** The beam can be a nanometre wide, but the excitation volume is tens of nanometres, so the spectrum averages the boundary with the matrix on both sides. The measured segregation is diluted by an amount that depends on foil thickness, beam energy and boundary inclination — all estimated, not measured. Quantification uses a thin-foil assumption, and the correction for beam spreading is a model imported from another community.
**What changes if answered.** A measured excitation-volume correction would rescale every grain-boundary segregation measurement and every core-shell composition in the electron-microscopy literature. It would say which reported boundaries are genuinely enriched and which are matrix signal, changing the input to grain-boundary engineering and to embrittlement models.