Water, adhesion, and how a tree drinks

Water evaporates from the wet cell walls inside a leaf and escapes through the stomata. Losing it curves the remaining water into tiny menisci, and a curved water surface pulls: the pressure just under it drops below zero. Because the water in the xylem is one continuous, hydrogen-bonded thread all the way to the root, that negative pressure is transmitted straight down the column, and water is pulled — not pushed — out of the soil. The theory is named for the two properties doing the work: cohesion holds the thread together, and tension is what the thread is under.

Driving energy

Sunlight, at the leaf

ATP spent lifting

None

Typical xylem tension

−0.5 to −2 MPa

Water taken up that is then transpired

≈ 97 %

Xylem conducting cells — tracheids and vessel elements — are dead at maturity. Their end walls are perforated or gone, their cytoplasm is cleared out, and their side walls are reinforced with lignin so they cannot be crushed by the tension inside them. What is left is an open, rigid, water-filled tube. Phloem, running just outside the xylem in the same bundle, is alive, and it moves sugar the other way by a completely different mechanism (pressure flow, which costs ATP). Only one of the two is plumbing.

Vessel diameter

10 – 500 µm

Tracheid diameter

10 – 15 µm

Sap velocity

1 – 45 m/h

Tallest measured tree

115.55 m (coast redwood)

Every part of cohesion–tension depends on there being no break anywhere between the soil and the stomata. A single gas bubble in a vessel and the tension on either side of it is no longer connected: that vessel stops conducting. This is why the stage you are about to reach matters — the entire mechanism is a claim about how strongly water molecules hold on to each other and to the wall, and that claim can be checked at the scale where it is made.

Cellulose is a polymer of β-glucose linked carbon 1 to carbon 4. Every second monomer is flipped 180°, which is what makes the chain a flat ribbon rather than a helix (compare amylose, which is α-linked and coils). Each glucose keeps free hydroxyl groups at C2, C3 and C6, and on the ribbon's surface those point outward into the vessel lumen. So the surface a water molecule meets is a regular array of δ− oxygens and δ+ hydrogens spaced a few tenths of a nanometre apart.

Linkage

β-1,4 glycosidic

Free −OH per glucose

3 (C2, C3, C6)

Sheet stacking distance

≈ 0.39 nm

Surface

Strongly hydrophilic

There is no separate adhesion force. The same δ+ hydrogen that would have hydrogen-bonded to a neighbouring water molecule bonds instead to a hydroxyl oxygen in the wall, and the wall's own δ+ hydrogens bond to water's lone pairs. Cohesion and adhesion are the same interaction with different partners — which is exactly why water wets cellulose so completely, and why the contact angle of water on clean cellulose is close to 0°.

Cohesion

H₂O ··· H₂O

Adhesion

H₂O ··· HO–cellulose

Interaction

Hydrogen bond, either way

Contact angle on cellulose

≈ 0° (fully wetting)

Water touching a hydrophilic surface is not bulk water. The first two or three molecular layers are held at a preferred orientation, with their hydrogens turned toward the surface oxygens, and they exchange with the bulk far more slowly than bulk molecules exchange with each other. The strip along the bottom of the viewport measures the hold itself: for each slice of the liquid it plots the share of molecules still joined to the wall by an unbroken chain of hydrogen bonds. It is near 90 % against the surface and falls to nothing by about two nanometres out. Take the hydroxyls away and the whole profile drops to zero, because there is no longer anything to be joined to — and heat the water and it retreats toward the wall, because the far end of every chain breaks first.

Adhesion pins the edge of the water to the wall. Cohesion means the middle of the column cannot stay behind while the edge climbs, so surface tension pulls the whole meniscus up together. Capillary rise is that argument repeated all the way up a tube, and it is the subject of the last stage.

Electronegativity is how strongly an atom in a bond pulls on the shared pair. Oxygen is 3.44 on the Pauling scale; hydrogen is 2.20. The difference, 1.24, sits squarely in the polar covalent range: the electrons are genuinely shared — this is not an ionic bond — but they spend more of their time near the oxygen. That leaves a partial negative charge on the oxygen and a partial positive charge on each hydrogen. Partial, not full: δ, not +1 and −1.

ΔEN = 3.44 (O) − 2.20 (H) = 1.24

ΔEN < 0.4

Nonpolar covalent

ΔEN 0.4 – 1.7

Polar covalent ← water is here

ΔEN > 1.7

Ionic

O–H bond enthalpy

459 kJ/mol

Oxygen has four electron domains around it: two bonding pairs and two lone pairs. That is a tetrahedral electron geometry, and it would give 109.5° — but lone pairs are held closer to the nucleus and repel more strongly than bonding pairs, so they squeeze the two O–H bonds down to 104.5°. The molecular shape is therefore bent, the two bond dipoles do not point in opposite directions, and they add up to a net molecular dipole. Carbon dioxide is the control experiment: its C=O bonds are more polar than water's O–H bonds, but the molecule is linear, the two dipoles cancel exactly, and CO₂ is nonpolar.

Electron geometry

Tetrahedral

Molecular shape

Bent

H–O–H angle

104.5°

O–H length

0.0957 nm

Dipole moment

1.85 D

A hydrogen already covalently bonded to nitrogen, oxygen or fluorine is left so exposed and so positive that it is attracted to a lone pair on a nearby N, O or F. That attraction is a hydrogen bond. It is about one twentieth the strength of the O–H covalent bond it hangs off, and in liquid water each bond survives only a picosecond or two before breaking and re-forming somewhere else. What makes it powerful is not any individual bond but that there are always billions of them, and that they are directional: the geometry criterion used in this simulation is an H···O distance under 0.245 nm and an O–H···O angle over 130°, which is the same test used on real molecular-dynamics trajectories.

O—H ··· O donor — hydrogen ··· acceptor

Energy

≈ 21 kJ/mol

Compared with O–H covalent

1/22 as strong

H···O distance

≈ 0.18 nm

Max per molecule

4 — donates 2, accepts 2

Average in liquid water, 25 °C

≈ 3.4

Lifetime

1 – 2 picoseconds

Cohesion is the attraction of water to water. Adhesion is the attraction of water to a different substance. Both are hydrogen bonding here. When adhesion to the surface is stronger than cohesion within the liquid, the liquid spreads out and climbs — water on glass or cellulose. When cohesion wins, the liquid beads up and the meniscus curves the other way — mercury in a glass tube, or water on a waxed leaf. Everything the last stage shows is decided by which of the two is larger.

The molecules on this stage are not animated along a path. Each one carries three point charges (−0.834 e on the oxygen, +0.417 e on each hydrogen) and a Lennard-Jones core on the oxygen, and every pair of molecules exchanges a Coulomb force between all nine site pairs plus a 12-6 dispersion-repulsion term, integrated with a Langevin thermostat so the temperature control means something. Nothing in the code says 'hydrogen bond': the bonds you see are what falls out of the charges. That includes the equilibrium O···O separation of about 0.28 nm, which nobody put there.

The height a liquid climbs in a narrow tube is set by a balance: the upward pull of surface tension acting around the line where water meets wall, against the weight of the column it is holding up. Solve it and the radius ends up on the bottom, so halving the radius doubles the rise. The cos θ on the top is the contact angle — the term that encodes adhesion. When water wets the wall perfectly, θ is 0 and cos θ is 1. Switch adhesion off in the controls and θ goes toward 90°, cos θ goes toward zero, and so does the rise.

h = 2γ·cos θ / (ρ · g · r)

γ, surface tension at 20 °C

0.0728 N/m

ρ, density

998 kg/m³

θ on cellulose

≈ 0°

r = 5 µm

h ≈ 2.97 m

r = 200 µm

h ≈ 7.4 cm

The wall can only hold water where water touches wall, and that contact is a circle: it scales with the circumference, 2πr. The load being held is the column's weight, and that scales with the cross-sectional area, πr². Divide one by the other and the grip-to-load ratio goes as 1/r. A narrow vessel is not lifting less water because it is narrow — it is lifting far less water for each unit of wall it has to hold on with.

grip / load ∝ 2πr / πr² = 2/r

Run the slider to its narrowest and the rise tops out around three metres. A coast redwood is 115 metres. Capillary action is not what lifts water up a tall plant — it is what keeps the water gripping the wall and keeps the meniscus curved. The lifting is done by evaporation at the leaves, which puts the entire column under tension, and that tension is only transmissible because cohesion holds the thread together. Take away adhesion and the thread lets go of the wall; take away cohesion and the thread snaps.

Best capillary rise, 10 µm vessel

≈ 3 m

Height of a coast redwood

115.55 m

Tension needed at that height

≈ 2 MPa

Supplied by

Evaporation at the stomata

Water in xylem is under negative pressure — it is being stretched. Pure water in a clean tube can take a remarkable amount of that, but a real vessel contains nucleation sites, and past a threshold a bubble forms out of nothing, expands to fill the vessel and breaks the column. That is cavitation, and the gas-filled vessel it leaves behind is an embolism: that pipe is out of service. Plants manage the risk structurally. Narrow conduits resist it better, which is why the tallest trees have the narrowest tracheids, and pit membranes between vessels stop a bubble spreading to its neighbours. In the simulation, raise the temperature and the transpiration rate together in a wide vessel and you can make it happen.

Cavitation threshold, typical xylem

−2 to −4 MPa

Effect of a wider vessel

Cavitates more easily

Effect of heat

Lowers the threshold

Result

That vessel stops conducting

Three things at once, and they all point the same way. Molecules gain kinetic energy, so a given hydrogen bond survives less time before thermal motion breaks it. Surface tension falls — about 0.15 mN/m for every degree — because surface tension is just the hydrogen-bond network resisting being opened up, so a weaker network pulls less hard. And evaporation at the leaf speeds up, raising the tension in the column at exactly the moment the column is least able to take it.

γ(T) ≈ 0.0728 − 0.00015 · (T − 20) N/m