## 1 Introduction  
Recent developments in medical devices, including artificial organs and biosensors, have focused on the inhibition of protein accumulation or adsorption. This is because the deposition of protein on the surface often leads to the deterioration of artificial organs due to surface contamination or the development of human amyloidosis. For example, the dialyzer, an artificial organ, is used to filter \(\beta_{2}\)-microglobulin (\(\beta_{2}\)-mg) in dialysis-related amyloidosis (DA) [1, 2] and amyloid \(\beta\) peptides (A\(\beta\)) in Alzheimer's disease (AD) [3] from the bloodstream. However, \(\beta_{2}\)-mg and A\(\beta\) accumulate on the surface of dialyzing membranes to induce amyloidosis [1]. Likewise, the biosensor also requires the suppression of adsorption of pathological proteins such as \(\beta_{2}\)-mg, A\(\beta\), and \(\alpha\)-synuclein (\(\alpha\)-syn) in [PERSON]'s disease, as well as serum albumin. Therefore, robust operation of medical devices requires effective inhibition of protein adsorption. Many hydrophilic polymers developed for this purpose are biocompatible. Poly (vinylpyrrolidone) (PVP) [4, 5], poly(L-lactic acid) (PLLA) [6, 7], poly(methyl methacrylate)(PMMA) [8], poly(sulfonate) (PSf) [9], and others [10] are well-known examples. Several homopolymers have been used to produce blends [11; 12] and block copolymers [13]. Nanoscopic architectures using these polymers, viz., planar membranes [7], membranes with asymmetric pore structures [14], (nano)particles [15], polymer brushes [16], and vesicles (polymersomes) [13] have been reported. From the perspective of biocompatibility, the surfaces of these polymeric materials require hydrophilicity or the reduction in protein adsorption [16]. With the development of polymer engineering, the pathological mechanisms of amyloidosis, such as DA [2], AD [17; 18], and Parkinson's disease [19], have been revealed in the past two decades. Furthermore, amyloid fibril formation, as the key process in amyloidosis, has been clarified at the molecular level [2; 20]. The mechanisms of fibril formation for \(\beta_{2}\)-mg, A\(\beta\), and \(\alpha\)-syn are similar, i.e., fibril formation proceeds by nucleation and subsequent elongation [2]. Of these, only A\(\beta\) is addressed in this study. A\(\beta\) is a soluble protein with a 4.5 kDa peptide related to AD [20]. A\(\beta\) aggregation on neuronal cell membranes is a hallmark of AD [18]. Recent studies have demonstrated a variety of molecular self-assembles of A\(\beta\), including oligomers [21], micellar aggregates [22], protofibrils [23], and fibrillar aggregates, including spherulitic fibrillar aggregates (spherulite) [24; 25; 26; 27]. At most, ten monomeric A\(\beta\) form an oligomer on the biomembrane, and indicate strong cytotoxicity [21]. Oligomers bind with monomeric A\(\beta\) to grow up to protofibrils, eventually forming mature fibrils (fibrillar aggregates) [21]. In addition, spherulites have a structure similar to senile plaques on neuronal cell membranes [24]. These morphologies can be induced on the phospholipid membranes, polymer membranes, and others [21; 24; 25; 26; 27; 28; 29]. Hence, interaction of external factors with A\(\beta\) fibril formation affords a variety of morphologies of A\(\beta\) aggregates. Thus, A\(\beta\) fibril formation is the result of the contribution of external environments, including the interfaces of lipid and polymer membranes, i.e., the partitioning of A\(\beta\) into the interfaces. Electrostatic interaction [30; 31], hydrophobic interaction [27; 32], or topological interaction [33; 34] are possible mechanisms of A\(\beta\) partitioning into the interfaces. For polymer-based interfaces, the topological interaction between A\(\beta\) peptides and polymers should be considered. This is because, in an earlier study, the partitioning behavior of peptides in the biphasic water/polymer solution system was determined by the entanglement of peptides with the polymer [34].