From nanotubes to nanoholes: scaling of selectivity in uniformly charged nanopores through the Dukhin number for 1:1 electrolytes

Scaling of the behavior of a nanodevice means that the device function (selectivity) is a unique smooth and monotonic function of a scaling parameter that is an appropriate combination of the system's parameters. For the uniformly charged cylindrical nanopore studied here these parameters are the electrolyte concentration, $c$, voltage, $U$, the radius and the length of the nanopore, $R$ and $H$, and the surface charge density on the nanopore's surface, $\sigma$. Due to the non-linear dependence of selectivites on these parameters, scaling can only be applied in certain limits. We show that the Dukhin number, $\mathrm{Du}=|\sigma|/eRc\sim |\sigma|\lambda_{\mathrm{D}}^{2}/eR$ ($\lambda_{\mathrm{D}}$ is the Debye length), is an appropriate scaling parameter in the nanotube limit ($H\rightarrow\infty$). Decreasing the length of the nanopore, namely, approaching the nanohole limit ($H\rightarrow 0$), an alternative scaling parameter has been obtained that contains the pore length and is called the modified Dukhin number: $\mathrm{mDu}\sim \mathrm{Du}\, H/\lambda_{\mathrm{D}}\sim |\sigma|\lambda_{\mathrm{D}}H/eR$. We found that the reason of non-linearity is that the double layers accumulating at the pore wall in the radial dimension correlate with the double layers accumulating at the entrances of the pore near the membrane on the two sides. Our modeling study using the Local Equilibrium Monte Carlo method and the Poisson-Nernst-Planck theory provides concentration, flux, and selectivity profiles, that show whether the surface or the volume conduction dominates in a given region of the nanopore for a given combination of the variables. We propose that the inflection point of the scaling curve may be used to characterize the transition point between the surface and volume conductions.Comment: arXiv admin note: substantial text overlap with arXiv:2012.1426

Oppositional culture revisited. Friendship dynamics and the creation of social capital among Turkish minority adolescents in Germany

Ethnic differences in the endowment with social capital can exacerbate intergroup inequalities. Pursuing this argument, we first compare the educational compositions of friendship networks between Turkish minority and native majority adolescents in Germany. Second, we pick up notions from Oppositional Culture Theory (OCT) to examine how ethnic differences in the composition of friendship networks come about. In a sample of 2,419 students in 74 secondary schools, we focus on the effort, achievement, and anti-school behaviour of peers and the role these play in adolescents’ friendship selection. Results from multilevel stochastic actor-oriented models reveal that Turkish minority adolescents prefer highly engaged and high-achieving peers as friends. Despite these preferences, Turkish minority adolescents’ social networks still provide lower levels of social capital on aggregate than majority members’ networks. We attribute this to systematic variation in the opportunity structure. Our results speak against the existence of anti-school norms among Turkish minority youth. Still, our study supports the OCT’s notion that an ethnic group’s structural positioning within society can result in selective acculturation processes and distinct patterns of social embeddedness

Social comparison effects on academic self-concepts-Which peers matter most?

Social comparisons with peers are important sources of self-development during adolescence. Many previous studies showed that students' academic self-concepts (ASC) form by contrasting one's own achievement with the average of one's class or school (the Big-Fish-Little-Pond Effect [BFLPE]). Based on social comparison theory, however, we would expect some peers to be more likely social comparison targets than other peers, for example, because they are more visible or students perceive them as similar to themselves. In this study, we used sociometric data to analyze which peers play the most important role for social comparison effects on ASC. We examined how the average achievement of friends, study partners, peers perceived as popular by the student, as well as same-gender and same-ethnic peers affect the general ASC and how these effects compare to the effect of the classroom's average achievement. The study was based on a German longitudinal sample of 2,438 students (44% no recent immigrant background, 19% Turkish immigrant background, 10% Eastern European immigrant background, 27% other immigrant background) from 117 school classes that were followed from grade 9 to 10. Results from longitudinal social network analysis do not confirm substantial incremental effects of specific types of peers, while class average achievement showed a stable negative effect (confirming the BFLPE). In addition, we could provide evidence for social selection effects based on ASC. We conclude that classrooms provide a specific setting that imposes social comparisons with the "generalized peer" rather than with specific subgroups of peers. (PsycInfo Database Record (c) 2022 APA, all rights reserved)

Scaling for selectivity in finite nanopores for 1:1 electrolytes: the dependence of predictability of device behavior on system parameters

The scaling properties of a cation selective nanopore mean that the device function (selectivity) depends on the input parameters (pore radius, pore length, surface charge density, electrolyte concentration, voltage) via a single scaling parameter that is a simple analytical function of the input parameters. In our previous study (Sarkadi et al., J. Mol. Liq., 357 (2022) 119072.), we showed that a parameter inspired by the Dukhin number (therefore, we also call it a Dukhin number) is an appropriate scaling parameter for infinitely long nanopores. Here, we extend that study to finite pores in a membrane and provide a detailed analyzes over a large parameter space for 1:1 electrolytes obtained from the Nernst-Planck transport equation coupled either to the Local Equilibrium Monte Carlo method or to the Poisson- Botzmann theory. Scaling is exact in a limiting case, where an analytical solution, such as Linearized Poisson-Boltzmann, is available (infinite pore). Here we show that scaling can work even if the solution is numerical or provided by computer simulations (finite pore). We discuss how these cases approach the limiting case as functions of the system parameters

Scaling for rectification of bipolar nanopores as a function of a modified Dukhin number: the case of 1:1 electrolytes

The scaling behaviour for the rectification of bipolar nanopores is studied using the Nernst-Planck equation coupled to the Local Equilibrium Monte Carlo method. The bipolar nanopore’s wall carries σ and − s surface charge densities in its two half regions axially. Scaling means that the device function (rectification) depends on the system parameters (pore length, H, pore radius, R, concentration, c, voltage, U, and surface charge density, σ) via a single scaling parameter that is a smooth analytical function of the system parameters. Here, we suggest using a modified Dukhin number, mDu = | s |l B ∗ l D HU/(RU 0 ), where l B ∗ = 8 p l B , l B is the Bjerrum length, l D is the Debye length, and U 0 is a reference voltage. We show how scaling depends on H, U, and σ and through what mechanisms these parameters influence the pore’s behaviour

The Dukhin number as a scaling parameter for selectivity in the infinitely long nanopore limit: extension to multivalent electrolytes

Scaling of the behavior of a nanodevice means that the device function (selectivity, in this work) is a unique function of a scaling parameter that is an appropriate combination of the device parameters. Although nanopores facilitate the transport of ions through a membrane of finite length if the pore is long compared to the pore radius, we deal with an important limiting case, the infinitely long nanopore (nanotube). While in our previous study (Sarkadi et al., J. Chem. Phys. 154 (2021) 154704.) we showed that the Dukhin number is an appropriate scaling parameter in the nanotube limit for 1:1 electrolytes, in this work we obtain the Dukhin number from first principles on the basis of the Poisson-Boltzmann (PB) theory and generalize it to electrolytes containing multivalent ions as well. We show that grand canonical Monte Carlo simulations for charged hard spheres in an implicit solvent give results that are similar to those obtained from the PB theory with deviations that are the consequences of ionic correlations (including finite size of ions) beyond the mean-field level of the PB theory. Such a deviation occurs when charge inversion is present, in 2:2 and 3:1 electrolytes, for example

Calcium versus potassium selectivity in a nanopore: the effect of charge inversion at localized pore charges

The Anomalous Mole Fraction Effect (AMFE) in negatively charged pores has been considered as a signature of Ca2+ vs. monovalent ion (K+ , in this study) selectivity. Increasing the mole fraction of CaCl2 in the KCl/CaCl2 mixture, the total conductance first declines as Ca2+ ions replace K+ ions inside the pore, then it increases as Ca2+ becomes the main charge carrier. While the AMFE was first pointed out in calcium selective ion channels, in a previous study Gillespie et al., Biophys. J. 95 (2008) 609–619.) we showed that it is also present in synthetic nanopores. Here we use the Local Equilibrium Monte Carlo method coupled to the Nernst-Planck transport equation to study a simple model of a finite nanopore in a membrane with ions being explicitly modeled as charged hard spheres and water as an implicit continuum. The novel component of the model is the treatment of the pore charges that are present in localized COO− groups on the wall of the nanopore. Therefore, we study the effect of localizing the pore charges instead of smearing them as a continuous surface charge. Localized charges profoundly influence Ca2+ vs. K+ selectivity because they enhance charge inversion at the pore wall. Ca2+ ions overcharge the pore wall at which the K+ ions have a disadvantage in the K+ vs. Ca2+ competition because the overcharged pore wall does not attract them so strongly

The Link between Social and Structural Integration: Co- and Interethnic Friendship Selection and Social Influence within Adolescent Social Networks

Assimilation theories argue that social ties with majority-group members enhance the structural integration of ethnic minority members, whereas under certain conditions, coethnic social ties can also benefit minority members’ socioeconomic outcomes. We examine these propositions through a social network perspective, focusing on friendship networks and educational expectations in adolescence, during which peer socialization is crucial. Longitudinal data from 1,992 adolescents in 91 classrooms allow us to investigate co- and interethnic social selection and social influence processes as well as their aggregated outcomes. In terms of friendship selection, we find that Turkishorigin minority adolescents in Germany have distinct preferences for friends with high educational expectations, among both co- and interethnic peers. In contrast, social influence on Turkish-minority adolescents’ educational expectations is not uniform: only majority-group friends exert a significant (positive) influence. Our results emphasize that bridging social capital gained from social ties with majority-group members enhances ethnic minority adolescents’ educational integration