Polymer chemistry

Hydrogels, biopolymers and biodegradable polymers

Relate network structure and solvent interactions to hydrogel swelling, connect natural biopolymers to their roles in tissues and materials, and analyse the chemical mechanisms and timescales of polymer biodegradation.

1 Lower secondary 2 Upper secondary 3 Undergraduate 4 Advanced 5 Research

IntuitionA network that drinks water

Soak a dried contact lens or an alginate bead and it swells many times its dry volume without dissolving. Water enters because mixing is favourable; the cross-linked chains resist because stretching them lowers conformational freedom. Equilibrium sits where osmotic suction and elastic recoil balance — a tug-of-war set by chemistry. Biopolymers and biodegradable polymers follow the same logic of structure–property relationships, drawn from sugars, amino acids and ester bonds instead of synthetic chains.

Flory–Rehner swelling ratio Q = V/V₀ versus cross-link density for three values of the polymer–solvent parameter χ. Better solvents (lower χ) swell more; denser cross-linking restricts swelling.

SchoolNetworks, water and biological chains

Definition: Hydrogel

A three-dimensional polymer network that absorbs large amounts of water (often >90 wt%) without dissolving, because permanent chemical cross-links or physical junction zones hold the chains together. Stiffness rises and swelling falls as the junction density increases.

Definition: Biopolymer and biodegradable polymer

A biopolymer is made by living organisms — cellulose, chitin, starch, DNA, proteins. A biodegradable polymer is defined by its fate, not its origin: its bonds can be cleaved by hydrolysis or microbial enzymes into small molecules under environmental or physiological conditions. The two sets overlap but are not identical — poly(lactic acid) is biodegradable but not biosynthesized.

Representative materials
Material	Origin / chemistry / Use or behaviour
Cellulose	β-1,4-glucan from plants; H-bonded microfibrils resist swelling.
Alginate	Brown-algae copolymer of guluronate and mannuronate; Ca²⁺ ionic cross-links (egg-box model).
Chitosan	Deacetylated chitin; protonated –NH₃⁺ groups make it pH-responsive.
PLA / PGA	Aliphatic polyesters made by ring-opening polymerization; ester bonds hydrolyse.
PHA	Polyhydroxyalkanoates accumulated as bacterial carbon storage; enzymatically degradable.

Example: Swelling and cross-link density

A hydrogel disk swells from a dry volume of 0.20 mL to 3.6 mL in water. What are the swelling ratio Q and the polymer volume fraction in the swollen gel?

Solution

Q = V/V₀ = 3.6/0.20 = 18. The polymer volume fraction φ₂ ≈ V₀/V = 1/Q ≈ 0.056, so the swollen gel is about 94% water by volume — typical of a loosely cross-linked, well-swollen gel.

UndergraduateFlory–Rehner theory and hydrolysis kinetics

\ln(1-\phi_{2})+\phi_{2}+\chi\phi_{2}^{2}+\nu_{e}V_{1}\!\left(\phi_{2}^{1/3}-\tfrac{\phi_{2}}{2}\right)=0

The Flory–Rehner equation balances two free-energy terms: mixing of water with chains (left-hand logarithmic and χ terms, which favour swelling when χ < ½) and elastic retractive force of the cross-linked strands (term in νₑV₁, which opposes swelling). Ionizable groups add a Donnan osmotic contribution that can make weak-acid or weak-base gels extremely sensitive to pH and ionic strength.

G=\nu_{e}RT\qquad\Rightarrow\qquad \nu_{e}=\frac{G}{RT},\quad M_{c}=\frac{\rho}{\nu_{e}}

Example: From modulus to mesh size

A swollen hydrogel has shear modulus G = 100 kPa at 298 K. Estimate the effective cross-link density νₑ and, for a polymer density ρ ≈ 1.0 × 10³ kg m⁻³, the average molecular weight between cross-links M_c (R = 8.314 J mol⁻¹ K⁻¹).

Solution

νₑ = G/RT = 100 000/(8.314 × 298) ≈ 40.4 mol m⁻³. Then M_c = ρ/νₑ = 1000/40.4 ≈ 24.8 kg mol⁻¹ ≈ 25 kg mol⁻¹. The classic rubber-elasticity expression assumes Gaussian chains and neglects trapped entanglements, so this is an upper-level estimate of the network strand length.

-\frac{d[\mathrm{ester}]}{dt}=k[\mathrm{ester}],\qquad t_{1/2}=\frac{\ln 2}{k}

Example: Hydrolysis timescale of a degradable polyester

A PLA implant follows pseudo-first-order ester cleavage with k = 0.050 week⁻¹ under physiological conditions. Estimate its half-life for ester-bond loss.

Solution

t½ = ln2/k = 0.693/0.050 ≈ 13.9 weeks. Bond cleavage halves in ~14 weeks; however, mass loss typically lags bond cleavage because chains must fragment enough to become water-soluble — bulk erosion vs surface erosion controls which curve the implant follows.

AdvancedStimuli-responsive gels and degradation design

Poly(N-isopropylacrylamide) shows a lower critical solution temperature near 32 °C in water: hydrogen bonding keeps it swollen below the LCST; heating favours polymer–polymer contacts and the gel collapses. Weak-acid gels swell when their groups ionize, so pH and added salt switch them via both electrostatics and Donnan partitioning. Degradation is engineered by choosing hydrolysable backbones (esters, carbonates, anhydrides), tuning crystallinity and hydrophilicity to control water access, and sometimes embedding enzyme-labile sites — the same chemistry can be a liability (premature degradation) or a feature (programmed resorption).

ResearchResearch frontier

References

Statistical mechanics of cross-linked polymer networks II. Swelling · P. J. Flory, J. Rehner, 1943
Hydrogels for biomedical applications · A. S. Hoffman, 2002
Biodegradable polymers for the environment · R. A. Gross, B. Kalra, 2002