Nitrile butadiene rubber (NBR) crosslink density determination is a critical quality control and research procedure that quantifies the network structure of vulcanized rubber, directly governing hardness, tensile strength, compression set, and oil resistance. This article provides a comprehensive technical guide covering testing samples, measurable parameters, established methods such as equilibrium swelling (Flory–Rehner), Mooney–Rivlin stress–strain analysis, DMA, and low-field NMR, along with relevant international standards and practical applications.
Technical Overview
Nitrile butadiene rubber (NBR) is a copolymer of acrylonitrile and butadiene, typically containing 18–50% acrylonitrile by weight, valued for its excellent resistance to oils, fuels, and non-polar solvents. During vulcanization, crosslinks (sulfidic or carbon–carbon bonds) are formed between polymer chains, transforming the thermoplastic gum into an elastomeric network. Crosslink density, defined as the moles of elastically effective network chains per unit volume of rubber (commonly expressed in mol/cm³ or mol/g), or equivalently as the average molecular weight between crosslinks (Mc), is the single most informative structural parameter of a cured NBR compound.
For NBR, crosslink density directly determines hardness, tensile and tear strength, elongation at break, rebound resilience, compression set, low-temperature flexibility, and swelling behavior in oils and solvents. An under-cured seal will exhibit high compression set and excessive swelling, while an over-cured compound becomes brittle and loses elongation. Accurate determination of crosslink density is therefore essential for cure optimization, incoming compound inspection, aging and reversion studies, and failure analysis of finished components such as O-rings, oil seals, gaskets, hoses, and gloves.
Testing Samples
Standard Vulcanized Plaques and Sheets
Laboratory-cured NBR sheets of 1–2 mm thickness, prepared under controlled press-curing conditions, are the preferred reference material. Specimens are typically cut into small pieces of approximately 20–50 mg or strips of roughly 30 mm × 5 mm × 2 mm to ensure uniform and rapid solvent penetration during swelling tests.
Finished and Semi-Finished Products
Crosslink density can be evaluated directly on O-rings, radial shaft seals, diaphragms, fuel hose liners, molded gaskets, roller coverings, and nitrile gloves. Small sections cut from these products reveal through-cure uniformity, batch-to-batch consistency, and the state of cure at critical locations such as thick cross-sections or bonded interfaces.
Aged and Exposed Specimens
Specimens subjected to thermal aging, hot oil immersion, ozone or UV exposure, compression stress relaxation, or post-curing are frequently analyzed to quantify network changes. Comparing crosslink density before and after exposure distinguishes additional crosslinking (densification, hardening) from chain scission and reversion (softening), which is central to durability and shelf-life assessment.
Testing Items
Depending on the method selected, the following parameters can be reported for NBR compounds:
- Total effective crosslink density (νe), including trapped entanglements, in mol/cm³ or ×10⁻⁵ mol/cm³
- Chemical crosslink density, reflecting covalent sulfur or peroxide crosslinks only
- Physical (entanglement) crosslink density
- Average molecular weight between crosslinks (Mc, g/mol)
- Equilibrium swelling ratio and mass/volume change in a reference solvent
- Volume fraction of rubber in the swollen network (Vr or φ)
- Sol fraction (extractable content), indicating degree of cure and oligomer content
- Crosslink type distribution (polysulfidic versus mono-/disulfidic versus C–C), assessed by selective chemical probes
Testing Methods
Equilibrium Swelling Method (Flory–Rehner)
The equilibrium swelling method is the most widely used approach and forms the basis of ASTM D6814 and the swelling procedures of ISO 1817 and ASTM D471. The procedure involves the following steps:
- Cut approximately 0.2 g of cured NBR into small pieces and pre-extract soluble components (oils, accelerators, antioxidants) in acetone or toluene for 24 hours, then vacuum-dry to constant mass (m₀)
- Immerse the specimen in toluene at 23 ± 2 °C for 48–96 hours, replacing the solvent at least once, until the mass change between consecutive weighings is below 1%
- Quickly blot the surface and weigh the swollen sample (m₁) in a closed tared vessel to prevent solvent evaporation
- Vacuum-dry to constant mass (m₂) to determine the sol fraction, (m₀ − m₂)/m₀
- Calculate the rubber volume fraction in the swollen gel: Vr = (m₂/ρr) / [(m₂/ρr) + (m₁ − m₂)/ρs], where ρr is the NBR density (approximately 0.98–1.02 g/cm³) and ρs is the solvent density
The crosslink density is then obtained from the Flory–Rehner equation: νe = −[ln(1 − φ) + φ + χφ²] / [Vs(φ^(1/3) − φ/2)], where φ is the volume fraction of rubber in the swollen network, Vs is the molar volume of the solvent (106.3 cm³/mol for toluene), and χ is the Flory–Huggins rubber–solvent interaction parameter. For NBR–toluene systems, χ values of approximately 0.39–0.46 are applied depending on acrylonitrile content, and the chosen value has a significant effect on the calculated result. The average molecular weight between crosslinks is Mc = ρr/νe.
Corrections for Filled Compounds (Kraus Correction)
Carbon black and silica reinforce NBR through chain adsorption and occluded rubber, which artificially raises the apparent crosslink density from swelling data. The Kraus correction, or equivalently the Lorentz–Parks approach, adjusts the measured swollen volume fraction using the filler loading and a filler-specific constant to recover the true rubber network density. For compounds containing more than approximately 20 phr of reinforcing filler, applying such a correction is strongly recommended.
Stress–Strain Method (Mooney–Rivlin Analysis)
Tensile testing per ASTM D412 or ISO 37 provides stress–strain data that can be analyzed with the Mooney–Rivlin equation: σ/(λ − λ⁻²) = 2C1 + 2C2/λ, where σ is the engineering stress and λ is the extension ratio. Plotting the reduced stress against 1/λ and extrapolating to zero gives the constants C1 and C2. The elastic constant 2C1 relates to the chemical crosslink density through 2C1 = νc·RT, while C2 is associated with chain entanglements and filler effects, enabling separate evaluation of chemical and physical network contributions.
Dynamic Mechanical Analysis (DMA)
In DMA, the storage modulus is measured in the rubbery plateau region, typically 60–120 °C (well above the NBR glass transition of approximately −40 to −20 °C depending on acrylonitrile content). The plateau modulus is converted to crosslink density using rubber elasticity theory, νe ≈ E′/(3RT) for small-strain conditions, where E′ is the storage modulus, R is the gas constant, and T is absolute temperature. DMA offers small specimen requirements and simultaneous information on Tg and damping, though entanglement contributions must be considered when comparing with chemical methods.
Low-Field Solid-State NMR (Multiple-Quantum Method)
Proton multiple-quantum (MQ) NMR at low magnetic fields measures residual dipolar couplings that are directly proportional to segmental orientation constraints in the network. This technique quantifies total (chemical plus topological) crosslink density, the sol fraction, and the fraction of dangling chains within minutes, requires no solvent or χ parameter, and can be applied to finished parts with minimal sample preparation. It is increasingly regarded as the most information-rich method for network characterization, with results typically calibrated and cross-verified against equilibrium swelling.
Method Selection Considerations
- Swelling: lowest equipment cost, best for routine QC; sensitive to χ selection and filler corrections
- Mooney–Rivlin: uses standard tensile equipment; limited to unfilled or lightly filled systems for reliable interpretation
- DMA: fast, small specimens, additional thermal transitions data; includes entanglement contribution
- MQ-NMR: non-destructive, distinguishes network defects and sol fraction; highest equipment investment
Applications
- Cure system optimization: balancing sulfur/accelerator ratio, peroxide dosage, and cure time to achieve target hardness and compression set
- Incoming compound verification and batch-to-batch consistency control for purchased NBR compounds
- State-of-cure audits on thick-walled or thermally demanding molded parts to detect under-cure in core regions
- Aging, reversion, and oil-immersion studies that quantify network degradation versus post-crosslinking
- Failure analysis of leaking seals, O-rings with excessive compression set, or embrittled rubber components
- Fuel hose and oil field equipment qualification, where crosslink density correlates with volume swell in ASTM fuels and IRM oils
- Research on NBR blends, reclaimed rubber, and HNBR comparisons where network homogeneity is critical
- Medical and food-contact nitrile glove manufacturing, ensuring uniform crosslinking and extractable limits
FAQ
What is a typical crosslink density value for cured NBR?
Conventional sulfur-vulcanized NBR compounds typically exhibit total effective crosslink densities of approximately 2–10 × 10⁻⁵ mol/cm³, corresponding to Mc values of roughly 3,000–10,000 g/mol. Efficient vulcanization (EV) systems and peroxide-cured compounds can reach higher densities, while under-cured articles may fall below 2 × 10⁻⁵ mol/cm³. Exact values depend on formulation, filler loading, and the measurement method applied.
Which solvent is best for NBR swelling tests?
Toluene is the standard choice because it sufficiently swells NBR across the common acrylonitrile range and well-documented interaction parameters exist. Cyclohexane and chloroform are also used in specific studies. Highly polar solvents should be avoided for NBR swelling measurements because the polar acrylonitrile units yield unreliable or non-equilibrium behavior.
How long does equilibrium swelling take?
For standard 2 mm thick specimens at room temperature, 48–96 hours is generally sufficient. Thicker sections cut from finished parts may require up to one week. Equilibrium is confirmed when consecutive daily weighings differ by less than 1%.
Does higher crosslink density always improve oil resistance?
Higher crosslink density reduces equilibrium swelling in oils and fuels, but excessive density sacrifices elongation, tear strength, low-temperature flexibility, and fatigue life. Optimal performance is a compromise, which is why crosslink density targets are established for each specific application.
Can finished O-rings be tested without destroying the part?
Swelling and tensile methods require cutting small specimens from the product, making them destructive. Low-field MQ-NMR can evaluate complete components non-destructively, which is valuable for prototype validation and retained samples.
Which standards govern NBR crosslink density testing?
ASTM D6814 covers crosslink density determination by the swelling method. ISO 1817 and ASTM D471 govern liquid resistance and volume change, which are adapted for swelling-based network analysis. Tensile-based Mooney–Rivlin evaluation relies on ASTM D412 and ISO 37, while GB/T 1690 provides the equivalent Chinese national procedure for liquid immersion testing.