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Two series of lactone-terminated alkanethiol adsorbates with five- and six-membered lactone groups, γ-COCnSH and δ-COCnSH (n = 11, 12), were synthesized and employed to create nanoscale self-assembled monolayers (SAMs) on gold substrates to mimic the properties of commercially available poly(lactic-co-glycolic acid) (PLGA) and poly(glycolic acid) (PGA) surfaces. 1H and 13C nuclear magnetic resonance (NMR) were employed to characterize the adsorbate molecules. The thicknesses of the corresponding self-assembled monolayers (SAMs) were evaluated by ellipsometry. The conformational characteristics of the SAMs were analyzed using polarization modulation infrared reflection adsorption spectroscopy (PM-IRRAS), with a focus on the C-H antisymmetric stretching vibrations of the alkyl spacers. To evaluate the packing densities of the monolayers, X-ray photoelectron spectroscopy (XPS) measurements were performed. Separately, contact angle measurements provided insights into the wettability of the surfaces. Remarkably, the contact angle data across a broad range of probe liquids for the γ-COC11SH and γ-COC12SH SAMs were consistently similar to each other and to the contact angle values of the PLGA surface, rather than to PGA. This finding suggests that the lactone-terminated SAMs investigated in this study effectively mimic nanoscale polyester surfaces, enabling the exploration of interfacial properties of polyesters in the absence of swelling and/or surface reconstruction phenomena. 

Abstract We study the effective front associated with first-order front propagations in two dimensions ($n=2$) in the periodic setting with continuous coefficients. Our main result says that that the boundary of the effective front is differentiable at every irrational point. Equivalently, the stable norm associated with a continuous $${\mathbb{Z}}^{2}$$-periodic Riemannian metric is differentiable at irrational points. This conclusion was obtained decades ago for smooth metrics [ 4, 6]. To the best of our knowledge, our result provides the first nontrivial property of the effective fronts in the continuous setting, which is the standard assumption in the literature of partial differential equations (PDE). Combining with the sufficiency result in [ 15], our result leads to a realization type conclusion: for continuous coefficients, a polygon could be an effective front if and only if it is centrally symmetric with rational vertices and nonempty interior. 

We study a class of second-order degenerate linear parabolic equations in divergence form in ( − ∞ , T ) × R + d (-\infty , T) \times {\mathbb {R}}^d_+ with homogeneous Dirichlet boundary condition on ( − ∞ , T ) × ∂ R + d (-\infty , T) \times \partial {\mathbb {R}}^d_+ , where R + d = { x ∈ R d : x d > 0 } {\mathbb {R}}^d_+ = \{x \in {\mathbb {R}}^d: x_d>0\} and T ∈ ( − ∞ , ∞ ] T\in {(-\infty , \infty ]} is given. The coefficient matrices of the equations are the product of μ ( x d ) \mu (x_d) and bounded uniformly elliptic matrices, where μ ( x d ) \mu (x_d) behaves like x d α x_d^\alpha for some given α ∈ ( 0 , 2 ) \alpha \in (0,2) , which are degenerate on the boundary { x d = 0 } \{x_d=0\} of the domain. Our main motivation comes from the analysis of degenerate viscous Hamilton-Jacobi equations. Under a partially VMO assumption on the coefficients, we obtain the well-posedness and regularity of solutions in weighted Sobolev spaces. Our results can be readily extended to systems.