Block copolymer/homopolymer blends exhibit rich phase behavior due to the interplay between molecular interactions, chain architecture, and self-assembly mechanisms. These systems are widely studied for their ability to form well-defined nanostructures through microphase separation, where the balance between enthalpic and entropic contributions dictates morphology. The introduction of homopolymers into block copolymer matrices further modifies self-assembly pathways, leading to tunable structural features influenced by swelling behavior, miscibility, and interfacial thermodynamics.

In miscible blends, homopolymers selectively swell the compatible block of the copolymer, altering domain spacing and inducing order-order or order-disorder transitions. The degree of swelling depends on the molecular weight ratio between the homopolymer and the corresponding copolymer block. When the homopolymer is shorter than the copolymer block, it uniformly disperses within the domain, increasing its effective volume fraction. Conversely, long homopolymers may localize near the domain center, reducing conformational entropy penalties. The Flory-Huggins interaction parameter (χ) governs miscibility, with lower χ values favoring homogeneous mixing. For example, a polystyrene-block-polyisoprene (PS-b-PI) blend with low-molecular-weight PS homopolymer swells the PS domain, increasing its periodicity while maintaining lamellar order.

Immiscible blends, where homopolymers are incompatible with both blocks, lead to macrophase separation or localization at interfaces. The wet brush and dry brush theories describe interfacial behavior in such systems. In the wet brush regime, homopolymers penetrate the compatible block, stretching copolymer chains and increasing interfacial width. This occurs when the homopolymer molecular weight is lower than that of the corresponding block. The dry brush regime arises when homopolymers are larger, expelling them from the brush layer and sharpening the interface. The transition between wet and dry brushes is determined by the ratio of homopolymer chain length (Nh) to copolymer block length (Nc), with wet brush behavior typically observed when Nh/Nc < 1.

Morphology modification in these blends is highly sensitive to composition. For a diblock copolymer with a minority block volume fraction (f), adding a homopolymer that swells the majority phase can drive transitions from spheres to cylinders or lamellae. In poly(ethylene oxide)-block-polypropylene oxide (PEO-b-PPO) blends, PEO homopolymer addition shifts the effective volume fraction of PEO, leading to hexagonal-to-lamellar transitions at critical concentrations. The critical swelling ratio, defined as the maximum homopolymer content before macrophase separation, depends on χ and chain architecture. Beyond this limit, homopolymer-rich domains form, disrupting long-range order.

The interplay between entropic and enthalpic effects also dictates domain spacing (D). For miscible blends, D scales with the total degree of polymerization (N) as D ~ N^(2/3) in the strong segregation limit, following self-consistent field theory predictions. Experimental studies on poly(styrene-block-methyl methacrylate) (PS-b-PMMA) blends with PS homopolymers confirm this scaling, with deviations occurring near order-disorder transitions due to fluctuations. In immiscible systems, domain spacing remains largely unchanged, but interfacial defects increase due to homopolymer aggregation.

Temperature further modulates self-assembly. Upper critical solution temperature (UCST) behavior is common in weakly interacting systems, where heating enhances miscibility and reduces domain contrast. Lower critical solution temperature (LCST) behavior, observed in hydrogen-bonded blends like poly(vinylpyridine)-block-polyol systems, leads to thermally induced phase separation. The temperature dependence of χ, often approximated as χ = A/T + B, plays a key role in these transitions.

Kinetic effects are equally important. Homopolymer addition slows down self-assembly dynamics due to increased viscosity and altered diffusion coefficients. In symmetric diblock blends, the order-disorder transition temperature (TODT) decreases with homopolymer content, following mean-field predictions. However, asymmetric blends exhibit complex kinetic pathways, with metastable states appearing during annealing.

Applications of these blends exploit their tunable nanostructures. Membrane technologies utilize homopolymer-induced pore formation in block copolymer templates, while photonic materials rely on precise control over domain spacing for optical bandgap engineering. The absence of nanoparticle fillers in these systems ensures uniformity in property-structure relationships, making them ideal for fundamental studies.

In summary, block copolymer/homopolymer blends offer a versatile platform for nanostructure design through controlled self-assembly. Swelling behavior, wet/dry brush transitions, and miscibility govern morphological outcomes, with chain length ratios and interaction parameters serving as key tuning parameters. These systems bridge the gap between polymer physics and materials engineering, enabling tailored functionalities without nanoparticle incorporation. Future work may explore dynamic reconfiguration via external fields or multi-component blends for higher-order hierarchical structures.