Fennema's Food Chemistry · Chapter 2 · 6-hour Full Edition

Water and Ice
Relations in Foods

From a single H₂O molecule to all food preservation strategies

Water Chemistry Water Activity a_w Glass Transition Food Stability 26 slides · 5 minigames

Why do foods spoil?

Two cookies. Both 10% moisture.
After a month,
one stays crisp, the other grows mold.

It's not how much water — it's the "state" of water: its energy, mobility, and interactions with food components.

50–95%

Water content range in foods

41

Anomalous properties

a_w

Water activity — the lead actor

T_g

Glass transition — hidden switch

Chapter Map · 7 Topics · 6-hour Journey

From molecular scale to food design

01

Physical Properties

41 anomalies · phase diagram · 13 ice phases

⏱ ~45 min

02

Molecule & H-bonds

sp³ tetrahedral · μ=1.85 D · H-bond geometry

⏱ ~40 min

03

Ice & Liquid Water

Hexagonal Iₕ · flickering clusters · RDF

⏱ ~35 min

04

Aqueous Interactions

Ion-dipole · Hofmeister · hydrophobic · colligative

⏱ ~50 min

05

Water Activity a_w

Raoult, Norrish, MSI three types & zones

⏱ ~55 min

06

BET/GAB · Stability · Hysteresis

Monolayer · Kelvin · Labuza stability map

⏱ ~55 min

07 · Glass Transition + WLF + State Diagram + Tg–aw–MC + Applications · ⏱ ~80 min

Topic 1a · Physical Properties

Water has 41 anomalies — these define food engineering

Anomalous property	Food implication
Density maximum at 3.984°C	Ice floats; fish survive winter
Solid (ice) less dense than liquid	Frozen foods expand → cell rupture
Ice's thermal conductivity 4× water's	Freezing far faster than thawing
Very high heat capacity (4.18 J/g·K)	Energy-intensive to heat
ΔH_fus 334, ΔH_vap 2257 J/g	High freeze-/dry-energy
Pressure lowers melting point	Basis of high-pressure freezing
High dielectric constant (~80)	Excellent ion solvent
High surface tension (72 mN/m)	Capillary rise · foam stability

Topic 1b · Polymorphism of Ice

Not just one ice: 13 ice phases, but only 1 in food

Earth's only common form: Ice Iₕ (hexagonal) — what we encounter at ambient P/T
The other 12 require high pressure (> 200 MPa) or extreme cold
Ice II, III: ~200 MPa, denser (used in high-pressure freezing)
Ice VII, VIII: > 2 GPa, density nearly twice Iₕ
Ice XI: very-low-T proton-ordered Iₕ
The full phase diagram has many triple points; food science cares about two:
- vapor/liquid/Iₕ → freeze-drying
- liquid/Iₕ/III → high-pressure freezing

Key: All "ice" in frozen foods is Iₕ. Iₕ's open hexagonal structure governs every freezing phenomenon (cell damage, freeze-concentration).

Topic 1c · Food-engineering Applications

Phase diagram → two key food technologies

❄️ Freeze-drying

Sublimation below triple point

Path: Freeze → vacuum → solid sublimes to vapor
Conditions: −50°C, 13–27 Pa
Benefits: preserves flavor, nutrients, structure
Products: instant coffee, hiking food, pharmaceuticals
Key: must stay below triple point (273.16 K, 611.73 Pa)

Solid → directly to vapor (skips liquid)

⚡ High-pressure-shift freezing

Keep water liquid under pressure, then quick decompress

Path: 200 MPa → cool to −20°C (still liquid) → instant decompress
Principle: high P drops Iₕ melting to −22°C
Benefits: uniform supercooling → tiny ice crystals
Products: premium frozen produce, meats (intact cells)
vs slow freezing: large crystals pierce cells

On decompression: whole sample below T_m → simultaneous nucleation

💡 Shared insight: both invert phase-diagram thinking — one drops pressure into sublimation, the other raises pressure to avoid ice.

Topic 2a · Molecular Chemistry

Why is water "weird"? The sp³ tetrahedron

sp³ hybridization: 2 O–H bonds + 2 lone pairs → tetrahedral
Permanent dipole: μ = 1.85 D (6.18 × 10⁻³⁰ C·m)
O carries δ⁻ (−0.72); each H carries δ⁺ (+0.36), neutral overall
Each H₂O forms 4 H-bonds: 2 donors + 2 acceptors (symmetric!)
vdW diameter ≈ 2.8 Å (not perfectly spherical)
3D H-bond network = root of all 41 anomalies

E_ion-dipole = −(zε)μ cos θ / (4πε₀ε r²)

H–O–H angle in liquid/ice is slightly > 104.5° (H-bond pull)

Topic 2b · H-bond Energy & Geometry

Why doesn't HF / NH₃ behave like water? Symmetry

Molecule	Donors	Acceptors	Network
H₂O	2 (two H)	2 (two lp)	✓ 3D network
HF	1	3	asymmetric → chain
NH₃	3	1	asymmetric → 2D
H₂S	2	2	EN too small

H-bond energy ladder
Covalent O–H: 80–120 kcal/mol
H-bond H···O: 2–6 kcal/mol
Thermal k_BT @ 25°C: 0.59 kcal/mol
vdW: 0.1–0.3 kcal/mol

H-bonds are 4–10× stronger than thermal energy → water keeps structure at ambient T.

H₂O's boiling point is anomalously high (373 K), deviating completely from the hydride trend — evidence of 4 symmetric H-bonds.

Topic 3 · Condensed-phase Water

Ice → water: only 15% of H-bonds break, yet density inverts

Ice Iₕ: open hexagonal net; molecules occupy only 42% volume
On melting: 12–15% H-bonds break, but neighbors increase 4→4.4 → density rises
Liquid water: flickering-cluster model — clusters of 3–200 molecules
RDF data: at 4°C, 1st NN at 2.82 Å, 2nd NN at 4.5 Å (still ice-like)
At 50°C: 4.5 Å peak disappears → structure collapses
Density peak at 3.984°C: two opposing forces:
- ↑ NN count (4→5)
- ↓ bond length (2.76→2.9 Å)
Food impact: ice crystals exclude solutes → freeze-concentration for juices

Topic 4a · Aqueous Solutions (90-min break)

Water meets food: three interactions

STRONGEST

Ion-dipole

40–600 kJ/mol

Na⁺, K⁺, Ca²⁺ with charged groups; forms a hydration shell

Bound-water source

MEDIUM

Dipole-dipole

5–25 kJ/mol

Water with –OH, –NH, –C=O (H-bonds with proteins, sugars)

As strong as water-water

WEAKEST

Dipole-induced

4–12 kJ/mol

Nonpolar (hydrocarbon, lipid tails) → hydrophobic hydration / interaction

Clathrate hydration

E ∝ 1/r² (ion-dipole) ；1/r³ (dipole-dipole) ；1/r⁶ (dipole-induced) ← shorter range as falloff steepens

Topic 4b · Ion Hydration & Hofmeister Series

Same salts, why do Na⁺ and K⁺ have opposite protein effects?

Three-layer hydration shell:
① Inner (chemisorbed): tightly bound, ordered
② Outer (cybotactic): semi-ordered
③ Bulk water: random
Hydration free energy ΔG_hyd (kJ/mol):
Mg²⁺ −1830 ／ Ca²⁺ −1505 ／ Li⁺ −475 ／ Na⁺ −365 ／ K⁺ −295 ／ Cl⁻ −340
Hofmeister two classes:
Kosmotropes small, high charge density: Li⁺ Na⁺ Ca²⁺ F⁻ — strengthen water structure, salt out proteins
Chaotropes large, low charge: Rb⁺ Cs⁺ I⁻ SCN⁻ ClO₄⁻ — break water structure, denature proteins
Food applications:
→ Salting out (NaCl precipitates protein)
→ Tofu coagulants: CaSO₄ / MgCl₂ (kosmotropes)

Topic 4c · Hydrophobic Effect

Why don't oil and water mix? It's about entropy.

It's NOT because water "hates" oil: water–hydrocarbon attraction is −1.85 kcal/mol (still > 0)
But water–water H-bonds are −6 kcal/mol stronger → water prefers to stay with itself
True cause: nonpolar solute forces water into a clathrate cage → loses freedom → ΔS < 0
Thermodynamics (cyclohexane → water):
ΔH = 0, TΔS = −6, ΔG = +6 kcal/mol ← entirely entropy-driven
Solute aggregation → water released to bulk → hydrophobic interaction (ΔG < 0)
Food impact:
→ Phospholipids self-assemble into bilayers, micelles (basis of emulsification)
→ Protein folding (hydrophobics buried inside)
→ Foam, Pickering emulsion

Topic 4d · "Bound Water" and Colligative Properties

"Bound water" is a fuzzy concept; colligative properties are hard data

📌 The "bound water" controversy

When water-solute energy >> k_BT (0.59 kcal), we call it "bound"
But it's a dynamic equilibrium — water molecules still exchange
Na⁺ hydration shell (50 H₂O): avg 7 kJ/mol — weakly bound
Na⁺ inner shell (4 H₂O): avg 91 kJ/mol — truly bound
Hard to quantify the "boundary"

Better: describe water's thermodynamic state shift, not binary bound/free.

📊 Colligative properties

Vapor-pressure lowering, boiling-point elevation, freezing-point depression, osmotic pressure
Depend only on solute moles, not chemical identity (in ideal case)

Freezing-point depression: ΔT_f = i · K_f · m
Water K_f = 1.86 K·kg/mol
Boiling-point elevation: ΔT_b = i · K_B · m
Water K_B = 0.51 K·kg/mol

i = van't Hoff factor (NaCl ≈ 2, sucrose = 1)

Fruits/vegetables freeze at −2 to −5°C (sugars, acids, minerals)

Topic 5a · Water Activity

Water activity a_w: the water's "energy state", not amount

a_w = p / p₀ = %ERH / 100 = γ_w · X_w

p: vapor pressure above food
p₀: vapor pressure of pure water at same T
%ERH: equilibrium relative humidity
γ_w: activity coefficient (food-water interaction fingerprint)

Ideal: a_w = X_w (mole fraction)
Real foods: strong ion-dipole/H-bonds → a_w < X_w

μ_w = μ⁰_w + RT ln(f_w/f⁰_w); a_w = f_w/f⁰_w ≈ p/p⁰

Saturated salt (25°C)	a_w
LiCl	0.120
CH₃COOK	0.225
MgCl₂	0.336
K₂CO₃	0.440
Mg(NO₃)₂	0.550
NaNO₃ / NH₄NO₃	0.625
NaCl	0.755
Li₂SO₄	0.850
K₂SO₄	0.970

Standards for constant-humidity chambers used in MSI construction.

Topic 5b · Non-ideality

Why do real foods deviate from Raoult's law?

Raoult's law (ideal): a_w = X_w; only mixing entropy lowers a_w
Real case: attractive solute–solvent interactions → water "tied up"
Result: a_w < X_w, more deviation = stronger interaction
Norrish equation corrects for non-ideality:

a_w = X_w · exp(K_s · X_s²)
K_s is negative; more negative = more water-binding

Solute	K_s	Meaning
Sucrose	−6.5	Strong H-bonding
Glucose	−2.3	Weaker
Glycerol	−1.0	Mild
NaCl (use i)	i = 2	Fully dissociated

💡 Application: When formulating confections to lower a_w, sucrose works better than glucose (more negative K_s).

Topic 6a · Sorption Isotherm (180-min break)

MSI: 3 types × 3 zones — the master map of stability

Zone I

a_w < 0.25
BET monolayer
Ion-dipole
Unfreezable −40°C
~7% MC

Zone II

0.25–0.85
Multilayer
H-bonds dominant
Glass transition
~15% MC

Zone III

a_w > 0.85
Capillary cond.
Solute dissolves
Microbial growth
~25% MC

Type 1Crystalline: sugars, candies (J-curve) ← single layer
Type 2Proteins, gums, amorphous (sigmoidal) ← multilayer
Type 3Hygroscopic: silica gel, CaCl₂, polyols ← dissolves

Zone I/II boundary = BET monolayer = key stability reference.

Topic 6b · BET & GAB Equations

Two equations to find the safety line of stability

📐 BET equation (a_w < 0.5)

a_w / [m(1−a_w)] = 1/(m_m C_B) + (C_B−1)/(m_m C_B) · a_w

Linear regression yields slope + intercept
m_m = 1 / (slope + intercept) ← BET monolayer
Typical a_w 0.2–0.4, MC ~5–8% (dry basis)
Breaks linearity above a_w ≈ 0.5

📐 GAB equation (a_w < 0.9)

a_w / [m(1−ka_w)] = 1/(m₁ k C_G) + (C_G−1)/(m₁ C_G) · a_w

Extra k parameter accounts for multilayer
k = 0.5–0.9; k=1 reduces to BET
Wider range, but iterate to find best k

Topic 6c · Stability Map (Labuza)

The classic figure: a_w drives every spoilage clock

Lipid oxidation: U-shape, min at a_w 0.3-0.4 (BET monolayer shields metal catalysts)

Maillard browning: bell, peak a_w 0.6-0.7 (excess water dilutes)

Microbes: bacteria > 0.9; yeasts > 0.85; molds > 0.7

Topic 6d · Hysteresis

Drying vs adsorbing: same a_w, different MC?

Desorption: from wet → dry direction
Resorption: from dry → wet direction
At same a_w, desorption gives higher MC (capillaries trap water)
At same MC, resorption gives higher a_w → more vulnerable
e.g. rice at 15% MC: desorption a_w=0.58; resorption a_w=0.81 → potential mold growth

Kelvin equation explains hysteresis

RT ln(p/p⁰) = −2γV_L / r
Smaller r → lower p in capillary → more water at same p

Capillaries collapse on drying → larger pores → need higher a_w to refill on resorption.

Topic 6e · Moisture Migration in Multi-domain Foods

Cheese crackers, raisin cereal: why do they soften?

In multi-domain foods (A / B), migration is driven by a_w differences, NOT MC
If a_w,A > a_w,B → water flows A → B until equilibrium
Result: crackers soften, raisins harden
Equilibrium formula:

ln a_w,final = (f_A·m_A·ln a_w,A + f_B·m_B·ln a_w,B) / (f_A·m_A + f_B·m_B)
f: weight fraction　m: MC　a_w: initial activity

Design strategies:
→ Adjust initial MC so a_w match
→ Add edible barriers (chocolate coating)
→ Change weight ratio W_A / W_B

Topic 6f · Intermediate-Moisture Foods (IMF)

a_w 0.6–0.85 is the "sweet spot": edible, stable, shelf-stable

Classic IMF examples

Jams, marmalades, candied fruits
Ham, sausages (cured meats)
Concentrated juices, maple syrup
Dried figs, raisins, dates
Chocolate, toffees, fondants

How to lower a_w

Add solutes: sugar, salt, glycerol
Partial drying: MC down to 15–30%
Humectants: propylene glycol
Adjust pH: < 4 inhibits molds
Antimicrobials: potassium sorbate

Sugar phase-transition pitfall

Sucrose, lactose often in amorphous (glassy) state
Storage → spontaneous crystallization
Result: MSI shifts sigmoid → J-type, bound water released
→ a_w suddenly rises → microbes grow
e.g., milk powder caking, candy "graining"

💡 Food design must consider long-term a_w stability, not just initial a_w (will phase transitions occur?).

Topic 7a · Glass Transition (270 min · final hour)

Beyond a_w: the state diagram predicts frozen/dried foods

T_m line: freezing-point depression curve (more sucrose → lower)
T_g line: glass transition (pure water −135°C → pure sucrose 74°C)
T_E eutectic: 64% w/w · −9.5°C (ideal full crystallization)
T_g*: glass transition of max-freeze-conc solution (~−46°C)
T_S solubility: saturation curve
Real frozen foods: usually rest between T_E and T_g* → non-equilibrium rubbery state
If T_store > T_g* → ice crystals grow, quality degrades

⭐ Frozen-food rule: T_store < T_g* (e.g., ice cream below −32°C)

Topic 7b · WLF Equation

Above T_g: viscosity's exponential cliff

T < T_g: viscosity > 10¹² Pa·s, near-zero molecular motion
T > T_g: every 20K rise drops viscosity 10⁵-fold!
Rate ∝ T/η, so 20K up → rate up 10⁵
Vastly exceeds Arrhenius prediction (~2× per 10K)

WLF (Williams-Landel-Ferry)

log(η_T / η_g) = −C₁(T − T_g) / [C₂ + (T − T_g)]
C₁ = 17.44 · C₂ = 51.6 K (universal)

log(k_g / k_T) = −C₁(T − T_g) / [C₂ + (T − T_g)]
k = diffusion-limited rate

Valid range: T_g < T < T_g + 100K, beyond which Arrhenius dominates again.

Topic 7c · Predict & Measure T_g

How to predict T_g and measure T_g?

🧮 Gordon-Taylor equation (predict mixture T_g)

T_g,mix = (w₁·T_g1 + K·w₂·T_g2) / (w₁ + K·w₂)
K ≈ ρ₁T_g1 / ρ₂T_g2 (Simha-Boyer)

Pure water T_g = −135°C (138 K)
Adding water = strong plasticization → big T_g drop
e.g., starch T_g ~250K @ 1% water, ~150K @ 10% water

Sugar	MW	T_g
Fructose	180	5°C
Glucose	180	31°C
Sucrose	342	62°C
Maltose	342	87°C
Trehalose	342	100°C

🔬 DSC measurement

T_g: stepped baseline shift (2nd-order transition)
T_c: exothermic crystallization peak
T_m: endothermic melting peak
DMTA is more sensitive for complex foods

Topic 7d · Three-variable Integration

T_g – a_w – MC triple chart: the ultimate shelf-life tool

Combining three relationships:

MSI: MC ↔ a_w
Gordon-Taylor: MC ↔ T_g
Cross relation: a_w ↔ T_g

→ For given storage T, find the critical MC that places T_g = T_store → stable.

Borojo powder (spray-dried) example:
20°C storage → critical a_w ≈ 0.319 · MC ≈ 0.046 g/g
40°C storage → critical a_w ≈ 0.18 (drier for safety)

Chapter Wrap-up · 360 min covered

From one H₂O molecule,
to the fate of a cookie.

What you learned

• 41 anomalies trace to H-bond network
• a_w = energy state of water
• MSI three zones partition stability
• BET/GAB find safe MC
• T_g is mobility switch
• WLF predicts rate explosion
• State diagram integrates frozen/dried

Apply it

• Process: freeze-drying, HPSF, baking
• Formulation: IMF, dual-texture
• Packaging: moisture barrier films
• Storage: T_g sets max temp
• Diagnosis: predict shelf life from a_w + T_g

Next chapters

• Ch.3 Carbohydrates (starch gelatinization)
• Ch.4 Lipids (hydrophobic + oxidation)
• Ch.5 Proteins (hydration & folding)
• Ch.7 Enzymes (active above a_w 0.4)

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Water and IceRelations in Foods