Concept:
The modulus of rubber depends on the reinforcement (fillers) and the degree of softening (plasticizers). Carbon black increases modulus (stiffens), while DOP (Plasticizer) decreases it (softens).
Step 1: Evaluate the effect of each additive.
• A (NR + 30 phr HAF): Carbon black is a reinforcing filler that significantly increases the stiffness and modulus of the vulcanizate. This will have the highest modulus.
• D (NR + 10 phr DOP + 30 phr HAF): The HAF stiffens the rubber, but the DOP plasticizer softens it simultaneously. The net modulus will be high due to the HAF but lower than option A.
• C (Vulcanized NR): Pure vulcanized rubber with no fillers or plasticizers represents the baseline modulus.
• B (NR + 10 phr DOP): Plasticizers increase the free volume between chains, making the rubber much softer and reducing the modulus below the baseline. This is the lowest modulus.
Step 2: Final Sequence.
Descending order of modulus: A (Reinforced) $>$ D (Reinforced + Softened) $>$ C (Baseline) $>$ B (Softened).