The Hydrophobic Effect

Drop a spoonful of olive oil into a glass of water and shake vigorously. For a few seconds you get a cloudy emulsion of tiny droplets. Within minutes, though, the oil reassembles into a single continuous layer on top. No enzyme did this. No covalent bond broke or formed. No obvious electrostatic attraction pulled the oil molecules together. What drove the reassembly is one of the most consequential phenomena in biochemistry: the hydrophobic effect. This is the tendency of nonpolar molecules to minimize their contact with water. They do this not because they attract each other strongly. Rather, water itself "prefers" not to touch them. This single physical tendency is the quiet architect of the cell. It builds the lipid bilayer that separates the inside of a cell from the outside. It drives the collapse of an unfolded polypeptide chain into a compact globular protein in milliseconds. It stabilizes the double helix alongside base stacking. It also organizes multiprotein complexes without any need for covalent glue. Unlike a hydrogen bond or an ionic bridge, the hydrophobic effect is not really an attraction between two solute molecules at all. Instead, it is a consequence of the extraordinary cohesive hydrogen-bonded network of liquid water. This network is built on the anomalous physical properties explored in Anomalous Physical Properties of Water. It also relies on the ordering behavior seen already in Solvation of Ions and Polar Solutes. The essential insight was first crystallized quantitatively by Frank and Evans in 1945. It was later given its modern biochemical framing by Kauzmann, Tanford, and others. The insight is thermodynamic: dissolving a nonpolar molecule in water is enthalpically nearly neutral or even favorable. But it costs a large amount of entropy. This happens because surrounding water molecules must adopt more ordered, cage-like hydrogen-bonding arrangements around the solute. This is the so-called "iceberg" or clathrate-like structuring. Aggregating the nonpolar solutes together shrinks the total nonpolar surface exposed to water. This releases many of those ordered water molecules back into the bulk liquid. It produces a large positive entropy change that makes the process spontaneous, even though nothing "attracts." This article works through the thermodynamics of nonpolar solvation and aggregation from first principles. It covers the free energy decomposition, the characteristic entropy–enthalpy signature, and its curious temperature dependence. It also explains the physical mechanism at the molecular level. Finally, it shows how this single effect scales up to explain micelle formation, bilayer self-assembly, and the hydrophobic core of folded proteins. It closes with worked numerical examples spanning a simple alkane transfer, micelle critical concentration, and protein folding. This way, the abstract entropy argument becomes something you can compute.

Key takeaways

Nonpolar solutes distort the hydrogen-bond network of water into more ordered, low-entropy cage-like shells around themselves.
Dissolving a nonpolar solute in water has ΔH ≈ small (sometimes negative) but ΔS strongly negative — an entropy-driven penalty, not an enthalpy one.
Aggregation of nonpolar surfaces reduces total solute–water contact area, releases ordered water back to bulk, and gives ΔG < 0 via +ΔS.
The free energy of transfer scales linearly with buried nonpolar surface area, roughly 25 cal·mol⁻¹·Å⁻².
Micelle and bilayer self-assembly occur cooperatively above a critical concentration set by this same ΔG per hidden CH₂ or aromatic ring.
Key idea: hydrophobic "attraction" is really water's entropic drive to minimize its own ordered shell around nonpolar surface — the solute molecules aggregate as a side effect of water maximizing its own entropy.

Where this lives today

The hydrophobic effect is not a historical curiosity confined to textbook thermodynamics tables — it is actively engineered and exploited across biochemistry and biotechnology today. In membrane biology, it is the entire reason phospholipids self-assemble into bilayers rather than requiring covalent scaffolding, and it governs the partitioning of membrane proteins, the insertion of transmembrane α-helices (quantified by hydrophobicity scales like Kyte-Doolittle, built directly on transfer free energy measurements), and the mechanism of lipid raft formation. In drug design, medicinal chemists routinely calculate logP (octanol-water partition coefficients), a direct experimental proxy for the hydrophobic transfer free energies derived here, to tune a drug candidate's membrane permeability, oral bioavailability, and binding affinity — a hydrophobic pocket in a protein active site can be exploited by adding a nonpolar substituent to a lead compound, gaining binding free energy at a predictable rate close to the γΔA surface-area law. In protein engineering and structural biology, computational tools that predict folding stability (e.g., FoldX, Rosetta) explicitly include a solvent-accessible-surface-area hydrophobic term parameterized almost exactly as derived here, and directed-evolution or rational design efforts routinely improve thermostability by increasing hydrophobic core packing. In detergent and surfactant technology, from dish soap to protein purification (SDS-PAGE, detergent solubilization of membrane proteins for cryo-EM and crystallography) the CMC framework derived above is used daily to choose detergents with the right aggregation number and micelle stability for a given application. In materials science and nanotechnology, self-assembling peptide amphiphiles, drug-delivery liposomes, and block-copolymer micelles are all designed using the same γΔA and CMC thermodynamics, extending the biochemical logic of the hydrophobic effect into synthetic supramolecular chemistry. The concept naturally continues into the broader landscape of Noncovalent Interactions in Biology and the general thermodynamic bookkeeping developed in Entropy and the Chemical Logic of the Cell.

Ask the tutor: How does the hydrophobic effect quantitatively combine with electrostatic and hydrogen-bonding terms to set the overall free energy landscape of protein folding?

The physical picture

Liquid water at 25 °C is not a random jumble of molecules; each water molecule participates, on average, in roughly 3.5 hydrogen bonds, in a dynamic network that reforms every few picoseconds. This network has enormous configurational freedom — many geometrically distinct ways to arrange hydrogen bonds while keeping nearly all of them intact. When a nonpolar solute (say, a methane molecule or the hydrocarbon side chain of leucine) is inserted into this network, it cannot hydrogen-bond to water at all. The water molecules touching its surface cannot bond outward into the cavity, so they compensate by reorienting to preserve hydrogen bonds tangential to the solute surface — forming a partial cage, sometimes loosely called a "clathrate-like" or "iceberg" shell. This reorganization is not a stronger network in an absolute sense — the enthalpy of hydrogen bonding at the interface is often nearly as favorable as in bulk water, which is why ΔH for dissolving small alkanes in water is close to zero or even negative at room temperature. The real cost is entropic: the constrained geometry needed to maintain hydrogen bonds around a curved nonpolar cavity restricts the number of accessible water configurations, lowering the entropy of that shell of water relative to bulk. The bigger the exposed nonpolar surface area, the more shell water is constrained, and the larger this entropy penalty becomes. Now bring two nonpolar solutes together, or fold a nonpolar surface into the interior of a protein or bilayer. The total solute–water interfacial area shrinks — two spheres merging into contact hide the "equatorial" patch where they touch, exactly as two soap bubbles merging reduce total surface area. Water molecules that had been constrained in the shell around each separate patch are released back into the bulk liquid, free to sample the full hydrogen-bond configuration space again. This entropy gain in the water — not any new attractive force between the solutes — is what makes aggregation spontaneous. The hydrophobic "attraction" is a solvent-entropy effect wearing the clothing of an intersolute force.

Figure

Ordered water shell around a nonpolar solute, and its release upon aggregation

The consequence of this shell-release picture is a distinctive signature in the thermodynamics: transferring a nonpolar solute from water into a nonpolar (oil-like) phase, or burying it in a folded protein, is characterized by a large positive ΔS and a small, often near-zero, ΔH, so that ΔG = ΔH − TΔS is dominated by the −TΔS term. This is the opposite of the "obvious" intuition that nonpolar molecules "stick together" because of some new attraction — dispersion (van der Waals) forces between nonpolar groups do exist and contribute a modest favorable ΔH, but the dominant driving force at room temperature is the entropy of water. A second layer of subtlety, essential for the protein-folding and membrane literature, is the strong temperature dependence of hydrophobic hydration, which shows up as a large positive heat capacity change, ΔCp > 0, for transferring nonpolar solute from oil into water (equivalently, ΔCp < 0 for water-to-oil transfer, i.e., for burial/aggregation). This large ΔCp means ΔH and ΔS are themselves strongly temperature-dependent, producing the famous phenomenon that hydrophobically driven processes (protein folding, micelle formation) can have an enthalpy-driven regime at high temperature and an entropy-driven regime near room temperature, and can even show cold denaturation — proteins unfolding upon cooling — because burial of nonpolar surface becomes less favorable at low temperature.

Figure

Entropy–enthalpy signature and cold denaturation from ΔCp>0 of nonpolar hydration

The core ideas

The whole framework rests on decomposing the free energy of transferring a nonpolar solute between two environments — typically bulk water and a nonpolar reference phase (liquid alkane, cyclohexane, or the interior of a folded protein) — into enthalpic and entropic terms, and then relating that free energy to solvent-exposed surface area.

\Delta G_{tr} = \Delta H_{tr} - T\Delta S_{tr}

where: ΔG_tr, ΔH_tr, ΔS_tr are the standard free energy, enthalpy, and entropy of transfer of the solute from water into the nonpolar phase; T is absolute temperature. For small alkanes at 25 °C, ΔH_tr is small (often within a few hundred cal/mol of zero) while −TΔS_tr is large and negative (favoring transfer out of water), so ΔG_tr is dominated by the entropy term.

\Delta G_{tr} = \gamma \, \Delta A

where: γ is an empirical "microscopic surface tension" or atomic solvation parameter (roughly 20–25 cal·mol⁻¹·Å⁻² for aliphatic carbon transfer from water to a nonpolar phase; higher, up to ~45–50, for aromatic carbon), and ΔA is the solvent-accessible nonpolar surface area removed from water contact. This linear surface-area relationship, established empirically by Chothia, Reynolds, and others from alkane solubility data, is the workhorse formula for estimating hydrophobic burial free energies in protein folding and ligand binding.

\Delta C_{p,tr} = \left(\frac{\partial \Delta H_{tr}}{\partial T}\right)_P = -T\left(\frac{\partial^2 \Delta G_{tr}}{\partial T^2}\right)_P

where: ΔC_p,tr is the heat capacity change of transfer, large and positive for water-to-oil transfer of nonpolar surface (equivalently negative for burial). This large ΔCp is the diagnostic fingerprint of hydrophobic hydration; polar and ionic solvation, by contrast, gives small or even negative ΔCp.

\Delta G_{tr}(T) = \Delta H_{tr}(T_H) + \Delta C_p\,(T - T_H) - T\left[\Delta S_{tr}(T_H) + \Delta C_p \ln\!\left(\frac{T}{T_H}\right)\right]

where: T_H is a reference temperature (often chosen where ΔH_tr = 0, the "enthalpy convergence temperature," empirically near 25 °C for nonpolar transfer); ΔC_p is assumed roughly constant over the relevant range. This integrated Gibbs–Helmholtz form is what produces the characteristic parabolic ΔG(T) curve — small ΔG over a wide temperature window, rising sharply toward both high and low temperature — and explains cold denaturation of proteins. Finally, for self-assembly of many amphipathic monomers into a micelle or bilayer, the relevant free energy comparison is between a monomer free in solution and a monomer in an aggregate of average size N:

\Delta G^{\circ}_{mic} = RT\ln(\mathrm{CMC})

where: ΔG°_mic is the standard free energy of transferring one surfactant monomer from free solution into a micelle, R is the gas constant, T is temperature, and CMC is the critical micelle concentration expressed as mole fraction (or molarity, with appropriate reference-state care). A more negative ΔG°_mic (stronger hydrophobic driving force, e.g., longer acyl chains) corresponds to a lower CMC.

Derivation AFrom nonpolar hydration entropy to the surface-area law ΔG = γΔA

Goal. Show how the microscopic picture of ordered water shells around nonpolar solute leads to a free energy of transfer that scales linearly with exposed nonpolar surface area, and extract the physically meaningful sign and magnitude of γ.

Step 1 — Define the reference process. Consider transferring a single nonpolar solute molecule (or, for a protein, a nonpolar side chain) from an aqueous environment into a nonpolar reference phase (bulk liquid hydrocarbon). This transfer free energy is measured experimentally from mutual solubility data: if a solute has mole-fraction solubility $x_w$ in water and $x_o$ in the nonpolar phase, at equilibrium the chemical potentials are equal, $\mu_w^\circ + RT\ln x_w = \mu_o^\circ + RT\ln x_o$ , giving

\Delta G_{tr}^{\,w\to o} = \mu_o^\circ - \mu_w^\circ = RT\ln\!\left(\frac{x_w}{x_o}\right)

Step 2 — Interpret molecularly. In the aqueous phase, each solute molecule sits in a cavity surrounded by a hydrogen-bonded water shell whose configurational entropy is reduced relative to bulk water, because the water molecules at the cavity surface must maintain their hydrogen bonds tangentially rather than freely in all directions. Denote the entropy loss per unit area of cavity surface as $-\sigma_S$ (a negative quantity per Å², since order is imposed). In the nonpolar reference phase, no such reorganization occurs (no hydrogen-bond network to distort), so the entropy of the surrounding oil is essentially unaffected by the solute's presence.

Step 3 — Assume additivity over surface area. Because the ordering effect is local — it happens at the water molecules directly contacting the solute surface, and dies off within roughly one hydration shell — the total entropy of hydration for a solute of exposed area $A$ is approximately

\Delta S_{hyd}(A) \approx \sigma_S \, A

for some negative constant $\sigma_S$ (entropy per unit area), independent of the detailed shape of the solute to a good approximation. This additivity is what makes surface area — rather than volume or molecular weight — the natural predictive variable; it is confirmed empirically because the solubilities of a homologous series of n-alkanes (methane through octane) show ΔG_tr increasing almost perfectly linearly with added CH₂ surface area.

Step 4 — Combine into the free energy. Since ΔH_tr for small nonpolar solutes is close to zero at room temperature (the hydrogen-bond enthalpy in the shell is nearly as favorable as in bulk water — the "iceberg" is enthalpically cheap, only entropically expensive), the free energy of transfer from water to oil is dominated by the entropy term:

\Delta G_{tr}^{\,w\to o} \approx -T\Delta S_{hyd}(A) = -T\sigma_S A \equiv \gamma A

with $\gamma = -T\sigma_S > 0$ since $\sigma_S < 0$ . This reproduces the empirical surface-area law with a positive γ: transfer out of water is favorable (ΔG_tr < 0 is what we want for water→oil since oil is more stable for a nonpolar solute — sign conventions must be tracked carefully, and by the more common convention used in protein folding, γ is defined so that burying area (removing it from water) lowers the free energy, ΔG_burial = −γΔA with γ ≈ 20–25 cal·mol⁻¹·Å⁻²).

Step 5 — Extract the number from data. Fitting the water-to-cyclohexane (or water-to-vapor) transfer free energies of the n-alkane series (methane, ethane, propane, butane...) against their calculated solvent-accessible surface areas gives a slope of about 20–25 cal·mol⁻¹·Å⁻² for aliphatic carbon and an intercept close to zero, confirming that surface area — not chain length or volume per se — is the controlling variable, exactly as the shell-additivity argument in Step 3 predicts. This derivation shows why doubling the buried nonpolar area (e.g., two leucines instead of one buried in a protein core) roughly doubles the hydrophobic stabilization, a rule of thumb used constantly in protein engineering and drug design.

Go deeper · Derivation B · 2 minMicelle formation as a cooperative phase-transition-like equilibrium, and the CMC

Derivation BMicelle formation as a cooperative phase-transition-like equilibrium, and the CMC

Goal. Derive how the hydrophobic free energy per monomer, ΔG°_mic, sets the critical micelle concentration (CMC), and show why micelle formation is sharply cooperative rather than gradual.

Step 1 — Model micellization as a multiple equilibrium. Consider N identical amphipathic monomers (S) associating into a micelle $S_N$ :

N\,S \rightleftharpoons S_N, \qquad K_N = \frac{[S_N]}{[S]^N}

The standard free energy change per mole of micelle formed is $\Delta G^\circ_{N} = -RT\ln K_N$ , but the more useful quantity is the free energy change per monomer transferred from free solution into the aggregate, since that is what is comparable across different aggregate sizes:

\Delta G^\circ_{mic} = \frac{\Delta G^\circ_N}{N} = -\frac{RT}{N}\ln K_N

Step 2 — Mass balance and the total monomer concentration. Let $C_T$ be the total stoichiometric surfactant concentration and $[S]$ the free monomer concentration. Then

C_T = [S] + N[S_N] = [S] + N K_N [S]^N

For large N (typical micelles have N ≈ 40–100), the term $NK_N[S]^N$ is a very steep function of $[S]$ : below a threshold value of $[S]$ it is negligible, and above it, it grows explosively. This steepness is the mathematical origin of the "sharp" CMC — a phase-transition-like onset rather than gradual aggregation.

Step 3 — Locate the threshold. Define the CMC as (approximately) the free monomer concentration at which micelle-bound surfactant becomes comparable to free surfactant, i.e., where $N K_N [S]^N \sim [S]$ , giving

K_N [S]^{N-1}_{CMC} \sim 1 \quad\Rightarrow\quad [S]_{CMC} \sim K_N^{-1/(N-1)}

For large N, $[S]_{CMC} \to K_N^{-1/N}$ , and substituting $K_N = e^{-\Delta G^\circ_N/RT} = e^{-N\Delta G^\circ_{mic}/RT}$ gives

[S]_{CMC} \approx e^{\Delta G^\circ_{mic}/RT} \quad\Rightarrow\quad \Delta G^\circ_{mic} = RT\ln(\mathrm{CMC})

recovering the standard working formula, where CMC is expressed as a mole fraction (or, loosely, molarity referenced to a 1 M standard state, a common simplification in the biochemical literature).

Step 4 — Why cooperativity, not gradual aggregation. Because $\Delta G^\circ_{mic}$ accumulates additively per monomer (Step 1 of the surface-area derivation shows each CH₂ contributes roughly the same increment, about −0.7 to −1.0 kcal/mol per methylene group buried from water), the aggregate free energy scales as N times a nearly constant per-monomer term. This means the equilibrium constant $K_N = e^{-N\Delta G^\circ_{mic}/RT}$ depends on monomer concentration as the Nth power — for N = 60 amphiphiles, a mere 5% increase in free monomer concentration changes $[S]^N$ by a factor of $(1.05)^{60} \approx 18.7$ , an enormous amplification that produces the essentially step-function onset of micellization observed experimentally (surface tension, dye solubilization, and light scattering all show sharp inflections at the CMC rather than smooth curves).

Step 5 — Chain-length dependence. Since each additional CH₂ group buried in the micelle core contributes roughly $\delta = -0.7$ to $-1.0$ kcal/mol to $\Delta G^\circ_{mic}$ (consistent with the γΔA surface law: a CH₂ group buries roughly 21 Å² of surface, so $\delta \approx \gamma \times 21\,\text{Å}^2 \approx 25\,\text{cal}\,\cdot\,\text{mol}^{-1}\text{Å}^{-2} \times 21\,\text{Å}^2 \approx 525\ \text{cal/mol}$ , in reasonable accord), the CMC should fall roughly by a constant factor for each added methylene:

\ln(\mathrm{CMC}_{n+1}) - \ln(\mathrm{CMC}_n) \approx \frac{\delta}{RT}

This is exactly Stauff's/Klevens' empirical rule that the CMC of a homologous surfactant series decreases by a factor of roughly 2–3 per added CH₂ group, quantitatively linking micelle thermodynamics back to the same γ extracted from alkane solubility in the first derivation.

Worked examples

Example 1 — Foundational: transfer free energy of n-butane from water to its own liquid phase. The aqueous solubility of n-butane at 25 °C is about $x_w = 1.0 \times 10^{-5}$ (mole fraction), and its "solubility" in itself (i.e., the reference liquid phase is essentially pure butane, $x_o = 1$ ). Using

\Delta G_{tr}^{\,w\to o} = RT\ln\!\left(\frac{x_w}{x_o}\right) = (1.987\ \text{cal}\,\cdot\,\text{mol}^{-1}\text{K}^{-1})(298\ \text{K})\ln(1.0\times10^{-5})

= 592.1\ \text{cal/mol} \times (-11.51) = -6815\ \text{cal/mol} \approx -6.8\ \text{kcal/mol}

So transferring one mole of butane from water into pure liquid butane releases about 6.8 kcal/mol — this is the thermodynamic drive for nonpolar aggregation to "escape" water. Using the calculated solvent-accessible surface area of butane, roughly $A \approx 240\ \text{Å}^2$ , the implied surface tension coefficient is

\gamma = \frac{|\Delta G_{tr}|}{A} = \frac{6815\ \text{cal/mol}}{240\ \text{Å}^2} \approx 28\ \text{cal}\,\cdot\,\text{mol}^{-1}\text{Å}^{-2}

which sits squarely in the expected 20–25 (here slightly higher, consistent with butane's branching/rounding uncertainties in surface area estimates) range for aliphatic carbon, confirming the surface-area law derived above. Limiting case check: as chain length → 0 (a point solute with no surface), $\Delta G_{tr} \to 0$ ; this matches the trend that methane, the smallest alkane, has by far the smallest (least negative) transfer free energy of the series, approaching but never reaching zero.

Example 2 — Applied: burial of a leucine side chain in a folding protein. Suppose a leucine side chain (isobutyl group, roughly 140 Å² of solvent-accessible surface area when fully exposed in the unfolded state) becomes completely buried in the hydrophobic core upon folding, losing essentially all solvent contact. Using $\gamma \approx 25\ \text{cal}\,\cdot\,\text{mol}^{-1}\text{Å}^{-2}$ for aliphatic carbon:

\Delta G_{burial} = -\gamma A = -(25\ \text{cal}\,\cdot\,\text{mol}^{-1}\text{Å}^{-2})(140\ \text{Å}^2) = -3500\ \text{cal/mol} = -3.5\ \text{kcal/mol}

A single buried leucine contributes roughly 3.5 kcal/mol of stabilization to the folded state. For comparison, the total conformational entropy cost of fixing that same side chain's rotamer freedom upon burial is typically 0.5–1 kcal/mol unfavorable (a smaller opposing term), so the net contribution remains strongly stabilizing, of order −2.5 to −3 kcal/mol. Given that a typical small globular protein (e.g., a 100-residue domain) has total folding stability of only about 5–15 kcal/mol, it is immediately clear why even one or two badly designed hydrophobic-core mutations (e.g., Leu → Ala, which removes about 100 Å² of buried surface, costing roughly $25 \times 100 = 2500$ cal/mol $\approx 2.5$ kcal/mol of stability) can measurably or catastrophically destabilize a protein — this is the molecular basis of countless disease-causing missense mutations that swap a buried hydrophobic residue for something smaller or polar. Limiting case check: if burial were only partial, say 50 Å² instead of 140 Å² (a side chain that remains half-exposed at a protein surface pocket), $\Delta G_{burial} = -25 \times 50 = -1250$ cal/mol, a proportionally smaller stabilization, exactly as expected from linear scaling with buried area — this is why surface-exposed hydrophobic patches contribute far less to stability than fully buried core residues, and why protein engineers target core, not surface, positions to boost stability.

Example 3 — Exam/competition-level: CMC shift with chain length and temperature-driven cold denaturation check. (a) CMC and chain length. Sodium dodecyl sulfate (SDS, C12 tail) has a CMC of about $8.2\times10^{-3}$ M at 25 °C. Estimate the CMC of the C14 homolog (sodium myristyl sulfate), assuming each additional CH₂ contributes $\delta \approx -650$ cal/mol to $\Delta G^\circ_{mic}$ (a typical experimental value, between the 525 cal/mol estimate from pure surface-area scaling and the ~700–800 cal/mol sometimes quoted, reflecting additional chain-packing/conformational contributions in the micelle interior). Two extra CH₂ groups (C12 → C14) add $2 \times (-650) = -1300$ cal/mol to $\Delta G^\circ_{mic}$ . From $\Delta G^\circ_{mic} = RT\ln(\mathrm{CMC})$ :

\ln(\mathrm{CMC}_{14}) - \ln(\mathrm{CMC}_{12}) = \frac{\Delta(\Delta G^\circ_{mic})}{RT} = \frac{-1300\ \text{cal/mol}}{592.1\ \text{cal/mol}} = -2.196

\mathrm{CMC}_{14} = \mathrm{CMC}_{12}\times e^{-2.196} = (8.2\times10^{-3}\ \text{M})(0.1112) \approx 9.1\times10^{-4}\ \text{M}

This predicts roughly a 9-fold drop in CMC for two additional methylenes, in good agreement with the well-documented experimental trend that CMC falls by roughly a factor of 2–4 per CH₂ group for ionic surfactants (so a factor of ~4–16 for two groups) — our estimate of 9× sits comfortably inside that range, validating the additivity assumption of Step 5 in the second derivation. (b) Cold denaturation sanity check. A protein has ΔH_unfold(25°C) = +60 kcal/mol, ΔS_unfold(25°C) = +180 cal·mol⁻¹K⁻¹ (typical values for a small globular protein at its temperature of maximal stability), and ΔCp,unfold = +1.5 kcal·mol⁻¹K⁻¹ (positive because unfolding exposes nonpolar core to water — matching the ΔCp>0 signature of hydrophobic hydration described above). Using the integrated Gibbs–Helmholtz relation with $T_H$ as reference (take $T_H = 298$ K where these values are quoted):

\Delta G_{unfold}(T) = \Delta H(T_H) + \Delta C_p(T-T_H) - T\left[\Delta S(T_H) + \Delta C_p\ln\!\left(\frac{T}{T_H}\right)\right]

Evaluate at T = 278 K (5 °C) to check for cold denaturation:

\Delta H(278) = 60{,}000 + 1500(278-298) = 60{,}000 - 30{,}000 = 30{,}000\ \text{cal/mol}

\Delta S(278) = 180 + 1500\ln\!\left(\frac{278}{298}\right) = 180 + 1500(-0.0693) = 180 - 104.0 = 76.0\ \text{cal}\,\cdot\,\text{mol}^{-1}\text{K}^{-1}

\Delta G(278) = 30{,}000 - 278\times76.0 = 30{,}000 - 21{,}128 = 8872\ \text{cal/mol} \approx +8.9\ \text{kcal/mol}

Still positive (folded state favored) but much smaller than at 25 °C, where $\Delta G(298) = 60{,}000 - 298(180) = 60{,}000-53{,}640=6360$ cal/mol — interestingly smaller than the 5°C value in this parameter set, illustrating that the maximum stability temperature lies between them; continuing to cool toward, say, 263 K would eventually drive ΔG through zero, producing cold denaturation, precisely because burying nonpolar surface (equivalently, the reverse of ΔCp > 0 hydration) becomes progressively less entropically favorable as temperature drops and the −TΔS term shrinks. Limiting case check: if ΔCp were zero (no hydrophobic-effect temperature dependence, as for a purely polar/ionic-driven folding), ΔH and ΔS would be temperature-independent, ΔG(T) would be a straight, monotonic line in T with no minimum, and cold denaturation could never occur — confirming that ΔCp > 0, the fingerprint of nonpolar hydration, is mechanistically required for cold denaturation to be possible.

Limiting cases, scope & common traps

Regime	Behavior	Why
Very small nonpolar solute (methane)	Small but nonzero ΔG_tr, ΔCp still large per unit volume	Even minimal surface area distorts local H-bond network
Large nonpolar surface / long alkane chains	ΔG_tr, ΔCp scale linearly with buried/exposed area	Additivity of local water-shell perturbation (surface-area law)
High temperature (~60–100 °C)	Hydrophobic effect weakens; ΔH_tr dominates, water shell "melts"	Bulk water itself becomes less structured; shell/bulk entropy gap shrinks
Low temperature (near 0–10 °C)	Hydrophobic driving force weakens too — can cause cold denaturation	−TΔS term shrinks faster than ΔH via ΔCp; net ΔG can flip sign
Charged/polar solutes	Hydrophobic-effect framework does not apply directly	Electrostatic/H-bond solvation dominates; see solvation of ions article
Micelle/bilayer self-assembly	Sharp cooperative CMC threshold	K_N ∝ [S]^N amplifies small concentration changes enormously

Common trapCommon misconception: "hydrophobic molecules attract each other"

It is tempting to picture two oil droplets as if they feel a mutual pull, analogous to gravity or van der Waals attraction. In reality the dominant driving force is not an attraction between the nonpolar solutes at all — it is the entropy gain of the water that is released from ordered shells when nonpolar surface area is buried. Van der Waals (London dispersion) forces between nonpolar groups are real and contribute a modest favorable enthalpy, but they are present between essentially any two atoms in contact (polar or nonpolar) and are far too weak, alone, to explain the strength or the entropy-dominated signature of hydrophobic aggregation. The correct statement is that water pushes nonpolar surfaces together to minimize its own ordering, not that nonpolar surfaces pull each other in.

The chemist behind it

Walter Kauzmann (1916–2009) was the biochemist and physical chemist most responsible for framing the hydrophobic effect as the central force in protein folding, in his landmark 1959 review article synthesizing decades of solubility and calorimetry data into the entropy-driven "iceberg" model. Trained under Linus Pauling at Caltech, Kauzmann brought a rigorous physical-chemistry sensibility to a problem — why proteins fold into stable, unique three-dimensional structures — that had previously been discussed mostly in vague structural terms. He recognized that the anomalously large, negative entropy of dissolving small hydrocarbons in water, first quantified by Henry Frank and Marjorie Evans in 1945, was not a curiosity of hydrocarbon chemistry but the very same physics that must drive nonpolar side chains to bury themselves in a protein's interior during folding. His 1959 synthesis explicitly connected alkane solubility thermodynamics to protein stability, coining much of the vocabulary — "hydrophobic bond," later refined by others to "hydrophobic effect" to emphasize its non-bonded, solvent-driven nature — that biochemists still use. Charles Tanford extended and quantified this picture through the 1960s and 1970s, using surfactant micelle thermodynamics (exactly the CMC framework derived above) as a clean, well-controlled model system to extract the free energy, enthalpy, and entropy of transferring hydrocarbon chains between water and nonpolar environments, and applied these numbers directly to estimate protein folding stabilities — his 1973 monograph The Hydrophobic Effect remains a foundational text. Together, Kauzmann's conceptual framing and Tanford's quantitative thermodynamic machinery transformed the hydrophobic effect from a qualitative "oil and water don't mix" observation into a load-bearing, numerically predictive pillar of modern structural biochemistry.

Origins · 1 minWalter Kauzmann and how this was discovered

Walter Kauzmann

1916–2009 · Princeton University; protein thermodynamics and the physical chemistry of folding

Kauzmann's 1959 Advances in Protein Chemistry review is among the most cited papers in the history of structural biochemistry, explicitly proposing that burial of nonpolar side chains, driven by the same entropy-of-hydration effect seen in simple hydrocarbon solubility, was the dominant force organizing the folded protein structure — a claim later confirmed repeatedly by calorimetric and mutagenesis studies.

History

- 1945 — Henry S. Frank and Marjorie W. Evans quantify the large negative entropy of dissolving nonpolar gases in water, proposing the "iceberg" model of ordered hydration shells.

- 1959 — Walter Kauzmann publishes his landmark review connecting nonpolar hydration thermodynamics to protein folding, coining "hydrophobic bond."

- 1973 — Charles Tanford publishes The Hydrophobic Effect, using micelle CMC data to quantify transfer free energies and apply them to protein stability.

- 1974–1980s — Chothia, Richards, Lee, and others establish the empirical linear surface-area law (ΔG ≈ γΔA) from protein and alkane solubility data.

- 1990s–2000s — Calorimetric measurements (Privalov, Makhatadze, and others) establish ΔCp signatures and cold denaturation as direct experimental confirmations of the entropy/heat-capacity picture.

Why is it called an "effect" rather than a "force" or "bond"?

Early literature did use "hydrophobic bond," but this phrasing implies a direct attractive interaction between two nonpolar solute atoms analogous to a covalent or hydrogen bond. The modern, mechanistically accurate view is that the driving force is the entropy of the surrounding water, not an intrinsic attraction between the solutes. Removing nonpolar surface from water contact releases ordered water molecules back into the bulk, raising total system entropy; the solutes end up close together as a side effect, not a cause. Calling it an "effect" — a solvent-mediated phenomenon — avoids the misleading implication of a new fundamental force and correctly centers water's own thermodynamics as the driver.

Does the hydrophobic effect involve van der Waals forces at all?

Yes, but as a secondary, not primary, contributor. Van der Waals (London dispersion) attractions do exist between any two atoms in contact, nonpolar or polar, and contribute a modest, generally favorable enthalpic term when nonpolar surfaces come into contact (partly explaining why ΔH_tr for larger, more polarizable nonpolar solutes can become somewhat negative). However, these dispersion forces are far too weak and too generic (they act on all matter) to explain either the magnitude or, crucially, the strong entropy-dominated signature and large ΔCp characteristic of hydrophobic aggregation. The dominant driving force remains the release of ordered water, not intersolute dispersion attraction.

How does the hydrophobic effect relate to protein folding cooperativity?

Because ΔG_burial scales with total buried surface area (the γΔA law), and folding buries hundreds to thousands of Å² simultaneously as the whole hydrophobic core forms at once, the folding transition tends to be highly cooperative — partially folded states with only some core residues buried gain only partial hydrophobic stabilization, often not enough to compensate for the conformational entropy lost by the rest of the chain. This creates a thermodynamic bias toward two-state (fully folded vs. fully unfolded) behavior for many small, single-domain proteins, directly paralleling the N-th power cooperativity of micelle formation derived above — both are consequences of the additive, area-proportional nature of the hydrophobic driving force acting on many groups at once.

Why do detergents disrupt membrane proteins and native protein structure?

Detergents (like SDS) are amphipathic molecules whose nonpolar tails can compete directly with a protein's own hydrophobic core or with lipid tails for burial away from water. Above the CMC, detergent monomers partition into and coat nonpolar surfaces — inserting between lipid tails to solubilize membranes, or wrapping around a denatured polypeptide chain's exposed hydrophobic residues in SDS-PAGE — because doing so lowers free energy by the same γΔA logic that drives micelle formation. This effectively substitutes detergent-hydrocarbon contacts for protein-protein or lipid-lipid hydrophobic contacts, unfolding or extracting the protein/lipid assembly, which is exactly why SDS denatures proteins into extended, uniformly charged rods for electrophoretic separation by size.

Is the hydrophobic effect the same as hydrophobic hydration?

"Hydrophobic hydration" specifically refers to the process and thermodynamics of dissolving an individual nonpolar solute in water — the ordered-shell formation, negative entropy, near-zero enthalpy, and large positive ΔCp discussed here. "The hydrophobic effect" more broadly refers to the consequence of hydrophobic hydration: the tendency of nonpolar solutes or surfaces to aggregate, or of amphipathic molecules to self-assemble, in order to minimize total hydrophobic hydration (i.e., minimize total nonpolar surface exposed to water). So hydrophobic hydration is the microscopic cause; the hydrophobic effect (aggregation, folding, self-assembly) is the macroscopic, thermodynamically favorable consequence.

Why does the hydrophobic effect weaken at high temperature?

Bulk liquid water itself becomes progressively less hydrogen-bonded and less "structured" as temperature rises toward the boiling point — the anomalous ordering that makes cold water special (as explored in the broader context of water's physical anomalies) diminishes. Since the entropic penalty of hydrophobic hydration arises from the difference between ordered shell water and bulk water, and bulk water is itself becoming more disordered at high T, that difference — and hence the driving force for burial — shrinks. This is captured quantitatively by the large positive ΔCp: as T rises, ΔH_tr becomes more positive and ΔS_tr less negative, so ΔG_tr for water-to-oil transfer decreases, meaning the entropic drive to escape water weakens (though it typically remains favorable until near the boiling point for most biological temperature ranges).

How is the hydrophobic effect measured experimentally?

Several independent, converging methods are used: (1) mutual solubility of hydrocarbons in water and in nonpolar solvents, giving ΔG_tr directly via the mole-fraction ratio; (2) calorimetry (isothermal titration or differential scanning calorimetry) on model compounds or on protein unfolding, giving ΔH_tr and ΔCp directly from heat measurements; (3) micelle CMC measurements via surface tension, dye solubilization, or conductivity, giving ΔG°_mic through the CMC relation; and (4) systematic protein mutagenesis (replacing buried hydrophobic residues with smaller or polar ones) combined with measured changes in folding stability (ΔΔG), which validates the γΔA surface-area law directly in the biological context of interest.