Glass transition and subphase anchoring govern the emergence of viscoelasticity in polymer interfaces

Determining the rheological properties and the interfacial structure-property relationships for complex fluid-fluid interfaces is crucial for understanding physiological systems, and for designing and engineering industrial processes. While it is well established that polymer-laden interfaces can exhibit viscoelastic properties, the relationship between polymer molecular characteristics and interfacial mechanical response remains insufficiently understood. In this work, we investigate the role of two fundamental polymer properties: dynamic flexibility as manifested by the glass transition temperature (T_g) and anchoring strength to the water subphase. We examine the relative importance of these two properties as they govern interfacial morphology and rheology. To this end, we systematically study six homopolymers - poly(dimethylsiloxane), poly(n-butyl acrylate), poly(methyl methacrylate), poly(tert-butyl methacrylate), poly(4-vinylphenol), and polystyrene, that span a range of T_g values and water subphase interaction strengths. Their interfacial behavior is characterized by Langmuir-Pockels trough isotherms, interfacial shear rheology, Brewster angle microscopy (BAM), and neutron reflectivity. Film thickness and homogeneity are evaluated. Our findings show two distinct interfacial regimes: polymers with T_g below room temperature exhibit a morphology composed of discrete globular domains. Quantitative analysis of film thickness shows large interfacial heterogeneity. Their Langmuir isotherms are fully reversible, showing no hysteresis nor relaxation upon compression. Interfacial rheology measurements yield no detectable shear moduli. In contrast, high-T_g polymers form 1-2 nm thick continuous interfacial films. Their isotherms display pronounced hysteresis, significant relaxation at high compression, and no recovery after the first compression. They exhibit measurable viscoelastic moduli, even at moderate surface concentrations below full coverage of the interface. Polystyrene, with no interfacial affinity, fails to form an interfacial film and thus produces inconsistent rheological footprint. Taken together, these results establish that the formation of a viscoelastic polymer interface requires both a glass transition temperature exceeding the operating temperature and some minimal level of interaction with the aqueous subphase.