Dilution Theory Research Articles

Co-Ion Identity Affects Double Layer Structure and Reactivity Trends in the Hydrogen Evolution Reaction

The formation of an electric double layer is ubiquitous in electrolytes undergoing electrochemical reactions. Currently, models for the double layer rely on the assumptions of dilute electrolyte theory where ions in solution do not interact. Dilute electrolyte theory predicts that solely hydrated counterions, or ions opposing the surface charge, occupy the near surface region and impact reactivity. Since this theory does not account for conditions like high applied potentials and high ion concentrations, understanding the relationship between double layer structure and electrochemical reactivity is critical for opening new domains for electrochemical modulation.Notably, our recent work shows that co-ions, or ions with the same charge as the surface, can also have a definitive influence on reaction rates, particularly under conditions of high applied potential and large bulk ion concentrations. In this talk, I will discuss how to use the hydrogen evolution reaction as a model system to explore co-ion effects in electrocatalytic reactions. In our work, we systematically vary co-ion identity and track hydrogen evolution reactivity as a function of concentration to highlight how the co-ion becomes increasingly relevant in the concentrated regime. In particular, we highlight the unique ability of the tetrafluoroborate co-ion to undergo dynamic ligand exchange between hydroxide and fluoride. This allows tetrafluoroborate to act as a hydroxide sink to stabilize the hydrogen evolution byproduct. Furthermore, I will discuss our use of Raman spectroscopy to describe how co-ions impact interfacial hydrogen bonding networks, which can have a significant impact on aqueous electrochemistry. Our results highlight how co-ions influence double layer structures and have significant implications for tuning other aqueous reactions such as carbon dioxide and nitrate electroreduction.

Retinal Vascular Permeability in Diabetic Subjects without Retinopathy Compared with Mild Diabetic Retinopathy and Healthy Controls

ObjectivesTo investigate retinal vascular permeability mapping as a potential biomarker for diabetic retinopathy in subjects with diabetes with no signs of retinopathy and with mild non-proliferative retinopathy. DesignThis is a case-control study. SubjectsParticipants included seven healthy controls, twenty-two subjects with diabetes mellitus and no clinical signs of retinopathy (DMnoDR), and seven subjects with mild non-proliferative diabetic retinopathy (NPDR). MethodsAll participants underwent routine retinal fluorescein videoangiography (FVA). Each FVA dataset was analyzed with the dynamic tracer kinetic model (DTKM) method to estimate five parameters: extraction fraction, blood flow, arrival time, transit time, and rate constant defined via adiabatic solution. The DTKM method was based on indicator dilution theory, including sequential use of two prominent kinetic models: the plug flow model and the adiabatic approximation to the tissue homogeneity model. Main Outcome MeasuresExtraction fraction (E), i.e., the fluorescein dye leakage measured during one pass through surrounding retinal tissue, is extracted via DTKM method and directly relates to retinal vascular permeability. Thus, E represents the pre-clinical biomarker, retinal vascular permeability. ResultsThe three diagnostic groups were found to have significantly different permeability (p = 0.003). Despite having no clinical signs of retinopathy, the mean rank of average vascular extraction fractions (E) was significantly higher in DMnoDR subjects compared to healthy controls (p = 0.04), as was the mean rank of E for mild NPDR subjects (p = 0.002). The average E for mild NPDR, DMnoDR, and control subjects was 0.1 ± 0.04, 0.07 ± 0.04, and 0.04 ± 0.01, respectively. ConclusionsThe vascular permeability extracted from FVA datasets using the DTKM method is a promising biomarker for detecting preclinical retinal pathology in patients with diabetes. Longitudinal studies are ongoing to explore the ability of this biomarker to distinguish those subjects with diabetes who will progress to clinically apparent retinopathy from those who will not.

Cerebral perfusion metrics calculated directly from a hypoxia-induced step change in deoxyhemoglobin

Resting cerebral perfusion metrics can be calculated from the MRI ΔR2* signal during the first passage of an intravascular bolus of a Gadolinium-based contrast agent (GBCA), or more recently, a transient hypoxia-induced change in the concentration of deoxyhemoglobin ([dOHb]). Conventional analysis follows a proxy process that includes deconvolution of an arterial input function (AIF) in a tracer kinetic model. We hypothesized that the step reduction in magnetic susceptibility accompanying a step decrease in [dOHb] that occurs when a single breath of oxygen terminates a brief episode of lung hypoxia permits direct calculation of relative perfusion metrics. The time course of the ΔR2* signal response enables both the discrimination of blood arrival times and the time course of voxel filling. We calculated the perfusion metrics implied by this step signal change in seven healthy volunteers and compared them to those from conventional analyses of GBCA and dOHb using their AIF and indicator dilution theory. Voxel-wise maps of relative cerebral blood flow and relative cerebral blood volume had a high spatial and magnitude congruence for all three analyses (r > 0.9) and were similar in appearance to published maps. The mean (SD) transit times (s) in grey and white matter respectively for the step response (7.4 (1.1), 8.05 (1.71)) were greater than those for GBCA (2.6 (0.45), 3.54 (0.83)) attributable to the nature of their respective calculation models. In conclusion we believe these calculations of perfusion metrics derived directly from ΔR2* have superior merit to calculations via AIF by virtue of being calculated from a direct signal rather than through a proxy model which encompasses errors inherent in designating an AIF and performing deconvolution calculations.

Study on the Determination of the Nature of Trademark Dilution--Taking the "Lao Gan Ma Case" as an Example

China's current legislation does not make clear provisions for the dilution of well-known trademarks, resulting in difficulties in identifying dilution cases in practice. One such notable instance is the "Lao Gan Ma" dispute, which serves as a telling example of this legal gray area. Consequently, it becomes imperative to delve into typical cases like the "Lao Gan Ma Case" to gain clarity on the disputed actions' legal nature, and then demonstrate how the dilution theory can be applied in the determination of specific cases. Utilizing the case study method, this paper aims to examine a particular case of trademark dilution in detail. The initial focus is on clarifying the concept of trademark dilution and its constituent elements of determination. This theoretical foundation is essential for accurately analyzing the nature of the complained-of infringing act. The significance of this paper is to theoretically solve the problem of determining the nature of dilution under the system of China's Trademark Law, to provide a reference for the determination of the same type of cases in the future, and hopefully to provide ideas for the future legislation on trademark dilution in China.

Stabilization versus Penetration Dynamics Induced by Localized Concentration Polarization in Solid Polymer Electrolytes

While the onset of dendrites found inside solid polymer electrolytes was typically analyzed by the dilute solution theory, nonideal behaviors such as dendrites at underlimiting current densities were often reported. Here, we consider two critical factors that were often neglected in existing studies, the severe heterogeneous current distribution and the dynamic change of modulus during the polarization process. Polymers with different dynamic mechanical properties were assessed, exploiting the recently discovered mechanism of phase transformation inside low-salt-concentration polymers. Analyses of the operando images revealed two characteristic points on the potential curve, the local and total concentration depletion which each corresponded to the starting and stopping point of dendrites. We further assess these dynamics at different degrees of heterogeneity controlled by different electrode sizes. The penetration dynamics and Sand’s time scaling exponent were heavily affected by both the initial concentration and the electrode size, which stress the significance of interfacial dynamic heterogeneity in working batteries.

The Application Dilemma and Perfection of Trademark Dilution Theory

The theory of trademark dilution originated in German courts and was gradually adopted by American legislation in the process of practice. The birth of desalination theory also reflects the value pursued by law. Although China has not clarified the theory of trademark dilution, some courts have applied the trademark dilution theory in the process of handling actual cases. As the provisions of the trademark dilution theory are too abstract, without clear concepts and identification criteria, there are large differences in the legal application of "trademark dilution" in judicial practice. And in the actual application process, the application of relevant provisions still exists ambiguity. By analyzing the case of anti-dilution protection of Jinritoutiao, a well-known trademark registered in China, this paper draws out the problems existing in the current environment of application of trademark dilution theory. Using the methods of case analysis and normative research, this paper analyzes the defects of trademark dilution theory and its application, and gives corresponding improvement measures.

The Legal Practice of Trademark Dilution Theory in Protecting Brand Value in China

Trademark dilution theory aims to further develop and protect the trademark's own value and its new function, and to provide protection for well-known trademarks on non-identical or non-similar goods. Trademark dilution theory has not yet been systematically and clearly stipulated in Chinese trademark law, but it has increasingly become the basis for references and judgments in the cross-class protection of well-known trademarks. This paper explores and summarizes the novel function of trademarks in protecting brand value through the methods of literature research and theoretical study, citing the case of trademark right dispute between Hunan Yong He Food Co. and Beijing Byte Dance Technology Co. Ltd, as a case, the paper analyzes the design of legal rules to regulate the dilution in judicial practice. It is concluded that although the object of trademark dilution protection in China is relatively clear at present, which is limited to well-known trademarks, there are problems such as unclear boundaries between dilution and confusion, inconsistent determination standards, and generalized reasoning process of judges.

EC conversion for 1:5 extracts and standard saturated soil–water pastes in the assessment of arid land salinization: Classical methodologies revisited

The common assessment of soil salinity posits a linear function, which transfers the electrical conductivity (EC) of highly diluted extracts to the standard state of soil paste. Our study examines this assumption and explains its limitations in a wide range of EC for highly saline soils of the Aral region in Uzbekistan. For a comparative EC assessment in the liquid phase from standard soil pastes and 1:5 aqueous extracts we used portable EC–meters. The dependences of EC, total dissolved solids (TDS), and soil–water potential on the pore water content were evaluated using centrifugation to separate the liquid phase from the soil matrix. The non-linearity of the relationship between the EC of water from soil pastes and 1:5 water extracts for both average and median data over a broad (0.4–160 dS/m) range of their variation is detected. A strong retention and concentration of electrolytes in fine pores and water films resistant to vacuum extraction, as well as the nonlinear EC versus TDS relationship in highly saline soils are attributed to this nonlinearity. A comprehensive statistical analysis showed that despite the general non-linearity, in the EC range from 0 to 30–35 dS/m, the results for 1:5 extract can be reliably converted to the standard state using the dilution model for the liquid phase of the soil with one basic parameter of soil bulk density. For hypersaline soils (EC > 30–35 dS/m), conversion based on the dilution theory is unacceptable due to a strong underestimation of TDS.

Comparing Experimentally-Measured Sand’s Times with Concentrated Solution Theory Predictions in a Polymer Electrolyte

We compare the electrochemically measured Sand’s time, the time required for the cell potential to diverge when the applied current density exceeds the limiting current, with theoretical predictions for a 0.47 M poly(ethylene oxide) (5 kg mol−1)/LiTFSI electrolyte. The theoretical predictions are made using concentrated solution theory which accounts for both concentration polarization and polymer motion, using independently measured parameters that depend on concentration, c: conductivity (κ), salt diffusion coefficient (D), cationic transference number with respect to the solvent velocity (), thermodynamic factor and partial molar volume of the salt (); is the mean molar activity coefficient of the salt. We find quantitative agreement between experimental data and theoretical predictions. We derive a generalized analytical expression for Sand’s time for electrolytes based on dilute solution theory. This expression correctly predicts the divergence of the Sand’s time at the limiting current, in agreement with experimental data and concentrated solution theory predictions. When the applied current is large compared to the limiting current, the analytical expression approaches the standard expression for Sand’s time used in the literature.

Hydrodynamic permeability of circular-inclusion-doped Brinkman media

Theory and computations are applied to assess the hydrodynamic permeability of cavity- doped hydrogels, central to a variety range of contemporary technological applications. Direct volume-averaging is undertaken in a two-dimensional, Brinkman-hydrodynamic context to test an ensemble-averaging methodology recently proposed for the ion permeability of such media. In two dimensions, the ensemble-averaging integral furnishes a pre-factor $2$ linking the pressure dipole strength of a single inclusion in an unbounded continuum to the effective hydrodynamic permeability of a composite with small inclusion area fraction. The factor is verified by direct computations for dilute simple-square arrays of (cylindrical) inclusions. At area fractions up to the close-packing limit, computations address the hydrodynamic interactions. The theory is shown to accurately predict the effective hydrodynamic permeability of physically relevant composites (Brinkman length of the continuous phase $\ell$ smaller than the inclusion radius $a$ ) for area fractions $\phi \lesssim {\rm \pi}/ 9 \approx 0.3$ . Computations for random ensembles demonstrate that the dilute theory may be extended to higher area fractions by drawing on Rayleigh's self-consistent approximation when the continuous-phase permeability places the continuous-phase flow well into the Darcy regime ( $a / \ell \gtrsim 10$ ). Computations also demonstrate, similarly to Rayleigh theories for scalar diffusion, that microstructural order has a very weak influence on the effective permeability when $\phi \lesssim {\rm \pi}/ 9$ with $\ell / a \lesssim 1$ (Darcy hydrodynamic interactions). Finally, a cursory examination is undertaken of the fluid velocity and its fluctuations arising from shear-viscosity heterogeneity in media with perfectly uniform permeability $\ell ^2$ .

Research on Dissipation Dilution Mechanism and Boundary Dissipation Suppression Technique for High-Stress Graphene Nanoelectromechanical Resonator

The low-quality factor is a key bottleneck for the engineering and commercial application of graphene nanoelectromechanical resonators at room temperature. The hypothesis in dissipation dominated by the ohmic loss is difficult to cover this phenomenon. Mechanical loss may still be on the list of the main causes for the quality factor stress-modulation characteristics of graphene resonators. The dissipation dilution theory reveals the intrinsic energy and dissipation mechanism of the traditional high-stress silicon-based resonator, which may also be applied to two-dimensional (2D) materials if dominated by mechanical loss. Based on Zener’s model of anelasticity, combined with the edge-corrected mode shape, the stress dilution mechanism of the bending potential dissipation of the graphene resonator is revealed. On this basis, the resonator dissipation is decomposed into boundary dissipation and non-boundary dissipation parts, and the steep rise phenomenon of the bending dissipation density (curvature) in the boundary region is analyzed through theoretical calculation. The analysis reveals that boundary dissipation is dominant in bending dissipation. To effectively suppress the boundary dissipation, a novel design of a graphene resonator via soft-clamped phononic crystal (PnC) is proposed. The existence of localized mode (LM) and effective suppression of boundary dissipation are verified in the simulations of both triangular and honeycomb PnC lattices. The theoretical model developed in this paper provides a new window into the dissipation properties of graphene nanoelectromechanical resonators, and the design of graphene resonators via soft-clamped PnC is expected to provide a new route toward high-quality factors at room temperature.

Hemodialysis access flow measurement: Comparison of ultrasound dilution and ultrafiltration method on NIKKISO DBB-EXA™ dialysis machine.

The methods of estimating vascular access (VA) flow rates are usually based on the indicator dilution theory by measuring recirculation during dialysis sessions. This is an observational study comparing the VA flow rates measured by NIKKISO DBB-EXA™ and Transonic®. Sixty-five patients (38 M/27 F, mean age 72 ± 10 years) participated in the study. We measured the VA flow rates during dialysis twice with each method and repeated the procedure 7 days later. In 130 double measurements for each method on the same day, mean flow with Transonic® was 1413±715 ml/min and with DBB-EXA™ 1297 ± 664 ml/min. In Bland-Altman analysis, the mean difference between the two methods was 159 ± 211 ml/min (limits of agreement: -274 and 572 ml/min). Eighty-one out of the 130 DBB-EXA™ measurements were within 25% of the Transonic® measurements (62% accuracy). Regarding reproducibility of each method on different days, mean difference in the Bland-Altman analysis was 29 ± 620 ml/min (limits of agreement: -1186 and 1244 ml/min) for the Transonic® measurements and 132 ± 625 ml/min (limits of agreement: -1092 and 1356 ml/min) for the DBB-EXA™ measurements. The measurements on two different days were within 25% of each other for 52 of the 65 patients (80%) with the Transonic® method, and for 35 of the 65 patients (54%) with the DBB-EXA™ method. In conclusion, the DBB-EXA™ method underestimates VA flow rates compared to the Transonic® technique, resulting in a limited accuracy of 62%. There was poor reproducibility for both methods in different day measurements with better performance of the Transonic® technique. The DBB-EXA™ method could be used as a simple tool for a rough estimate of VA flow rates but cannot replace the Transonic® reference method.

Imaging human lung perfusion with contrast media: A meta-analysis

PurposeTo pool and summarise published data of pulmonary blood flow (PBF), pulmonary blood volume (PBV) and mean transit time (MTT) of the human lung, obtained with perfusion MRI or CT to provide reliable reference values of healthy lung tissue. In addition, the available data regarding diseased lung was investigated. MethodsPubMed was systematically searched to identify studies that quantified PBF/PBV/MTT in the human lung by injection of contrast agent, imaged by MRI or CT. Only data analysed by ‘indicator dilution theory’ were considered numerically. Weighted mean (wM), weighted standard deviation (wSD) and weighted coefficient of variance (wCoV) were obtained for healthy volunteers (HV), weighted according to the size of the datasets. Signal to concentration conversion method, breath holding method and presence of ‘pre-bolus’ were noted. ResultsPBV was obtained from 313 measurements from 14 publications (wM: 13.97 ml/100 ml, wSD: 4.21 ml/100 ml, wCoV 0.30). MTT was obtained from 188 measurements from 10 publications (wM: 5.91 s, wSD: 1.84 s wCoV 0.31). PBF was obtained from 349 measurements from 14 publications (wM: 246.26 ml/100 ml ml/min, wSD: 93.13 ml/100 ml ml/min, wCoV 0.38). PBV and PBF were higher when the signal was normalised than when it was not. No significant differences were found for PBV and PBF between breathing states or between pre-bolus and no pre-bolus. Data for diseased lung were insufficient for meta-analysis. ConclusionReference values for PBF, MTT and PBV were obtained in HV. The literature data are insufficient to draw strong conclusions regarding disease reference values.

A study on the combustion performance and NOx emissions characteristics of a novel U-type radiant tube based on MILD combustion theory

Based on the theory of moderate or intense low-oxygen dilution (MILD) combustion, a 3D steady-state CFD model coupling dual flue gas recirculation and dispersion combustion was developed to describe the flow field, combustion temperature field, wall temperature distribution, and NOx concentration field during the operation of a novel U-type radiant tube (N-URT). A user-defined function (UDF) method was implemented to simulate the dilution of O2 concentration in the combustion air due to external flue gas recirculation (E-FGR). The effects of the E-FGR ratio on combustion characteristics and NOx emission were evaluated. The simulated results were consistent with experimental results. The simulated NOx concentration at the outlet was reduced to 105.5 mg/m3 at 8% O2, which was about 35.2% lower than the conventional combustion method. The study found that when the E-FGR ratio was increased from 0 to 25%, the standard deviation of wall temperature decreased from 30.3 °C to 23.3 °C, and the non-uniformity coefficient decreased from 0.2598 to 0.2183, indicating an improvement in temperature uniformity. However, the thermal efficiency decreased from 82.1% to 76.2%. Moreover, at higher E-FGR ratios, the volume of the high-temperature region (above 1500 ℃) gradually decreased, and both the maximum flame temperature and the outlet NOx concentration decreased sharply. Regression equations for the E-FGR ratio (β) on the maximum combustion temperature (Tmax) and the outlet NOx concentration (CNOx) were obtained, and an E-FGR ratio greater than 13.4% was recommended to meet the emission requirements.

Main Role of New High Strength, Toughness and Low-Density Steel in Artillery Lightweight

The new high strength, toughness and low density steel is a new generation of lightweight material with high protection, which is based on the theory of lattice dilution and lattice distortion and is manufactured by adding light elements to reduce its density. Furthermore, after impact process, the composite effects such as transformation induced plasticity (TRIP) effect, twinning induced plasticity (TWIP) effect, microbands induced plasticity (MBIP) effect and phase transformation precipitation occur in the microstructure. The specific strength and specific stiffness are better than those of aluminum, magnesium and titanium alloys, and the modulus is 3 times that of aluminum alloy and 2 times that of titanium alloy. Preliminary research shows that the application of low density steel in artillery system can greatly reduce the production cost. On the basis that all technical and tactical indexes meet the design requirements, it can realize lightweight, long-distance strategic delivery and battlefield real-time repair.

Solubility of ibrutinib in supercritical carbon dioxide (Sc-CO2): Data correlation and thermodynamic analysis

Ibrutinib (PCI-32765), marketed under the trade name IMBRUVICA, is a first-in-class irreversible inhibitor drug of Bruton tyrosine kinase (BTK). In the current research, its solubility was measured at operational conditions 120–270 bar and 308–338 K, for the first time. The drug solubility has been reported between 3.90×10-6 to 1.30×10-5 based on mole fraction. Analysis of the curves confirms strong dependency of ibrutinib solubility to operational conditions due to their direct effect on solvating power of solvent. Also, pressure effect was more pronounced at the higher temperatures and the cross-over point was located around 170 bar. Besides, theoretical investigation and computational approach were carried out to correlate and extrapolate the experimental solubility of this medicine using thermodynamic models based on different approaches; semi-empirical models, activity coefficient (modified model of Margules), fugacity coefficient (mPR and mRK cEoSs) and dilute solution theory by the model of Wang-Tavlarides. Best correlation results were obtained by the modified model of Margules (AARD = 6.68%) and the empirical model of Jouybanet al., (9.62%). Additionally, different enthalpies of ibrutinib-Sc-CO2 system were estimated.

Impacts of sibling and gender on supplementary education opportunities in China

Supplementary education, which is different from the formal education system, is more likely to reflect the other form of inequality in educational opportunities through the process of education. In China, supplementary education is generally divided into two sorts: academic-oriented classes and hobby-oriented classes. Using the dataset of China Family Panel Studies 2018 and analysing with the Logit Regression models (LR), this study analyses how gender and sibling structure impact the students’ supplementary education participation opportunities. Applying the “resource dilution theory” and “budget constraint theory” in Chinese modern families, siblings might have a competitive relationship with each other in obtaining limited family resources, while parents would assess the lifetime cost of raising a child when deciding the investment in supplementary education. According to the results, an increase in sibling numbers and density dilutes the family resources of supplementary education for each child on average. Females have more opportunities to participate in supplementary education than males, especially in hobby-oriented supplementary education. The “female advantage” is significant in the supplementary education opportunity of the first-born child and the “gender minority” child. This study claims that the family allocation of supplementary educational resources is influenced by economic motives. This study supports both the “resource dilution theory” and the “budget constraint theory” in supplementary education in contemporary China, while the issues of gender inequality regarding family resources allocation seem still remain.

Quantification of shunt fraction using contrast ultrasound and indicator dilution in an in vitro model

Transthoracic saline contrast echocardiography is commonly used to assess intrathoracic shunt flow in vivo. Though the technique has many advantages (safe, simple, repeatable), the measurement technique lacks specificity, and the contrast agent has limited stability. This study sought to determine if the indicator dilution modeling technique could be applied to ultrasound contrast data to quantify shunt fraction and to determine if buoyant force has a significant effect on microbubble pathway determination at a “vascular” bifurcation. A model of the pulmonary circuit was perfused with blood at three distinct flow rates (low, medium and high) over shunt fractions ranging from ∼2–10 %. The buoyancy effect on contrast was quantified using a simplified in vitro model of a vascular bifurcation that had an upper and lower outflow tract where saline contrast formed from carbon monoxide (CO) gas passed through the bifurcation, was collected and quantified. The indicator dilution model was found to have a mean bias of − 3.2 % for the low flow stage, − 2.6 % for the medium flow stage and − 1.4 % for the high flow stage compared to volumetric measurements, suggesting agreement increases with increasing flow rate. Investigations of the buoyant effects revealed that at lower flow rates, contrast bubbles that encounter a bifurcation will favor the upper outflow tract over the lower. However, this effect is reduced by increasing the flow rate two-fold. These data identify that application of indicator dilution theory to contrast ultrasound data and the pathway ultrasound contrast travels in a network of tubules is flow dependent.

Quality factor comparison between graphene and SiN with triangular lattice phononic crystal structure based on dissipation dilution theory

Nanomechanical resonators attract interests both in fundamental and applied fields, offering outstanding mass and force sensitivity, relying on both the low mass m and high quality factor Q. However, the quality factor typically does not exceed the inverse of the material loss angle φ, related to resonant energy dissipation. Recently, some exceptions breaking the 1/φ limiting rule in a great extent have been reported in use of highly stressed silicon nitride material. Up to now it is interpreted that the pre-stress seems to ‘dilute’ the intrinsic energy dissipation according to Zener model. Dissipation dilution effect could be better if the device dimension is reduced, which implies that the smaller the resonator, the higher the quality factor. Single-layer graphene's thickness is 0.335 nm, which is one hundredth of silicon nitride’ typical thickness about 30 nm, indicating that the dissipation dilution effect of graphene could be much better than that of silicon nitride. Through theoretical calculation, the quality factor amplification coefficient defining the dissipation dilution effect quantitatively of graphene is 2272 times that of SiN. By COMSOL finite element simulation, we further confirm this conclusion. Take the first defect mode for example, the amplification coefficient of graphene and SiN is about 3.02 × 105 and 151 respectively, with the division result about 2004 times. As the overall size increases, the division results gradually converge to a stable value about 2260.

The influence of cross-interactions between dilute cosolutes upon liquid interfaces.

We employ a statistical mechanical dilute solution theory (DST) and lattice Monte Carlo simulations to investigate the interfacial properties of ternary solutions with a dominant solvent and two dilute cosolutes. We consider cosolutes with weak interfacial preferences in order to focus on the impact of cross-interactions between the two cosolute species. When the cross-interaction is properly balanced, the two cosolutes make independent, additive contributions to both bulk and interfacial properties. Conversely, repulsive cross-interactions slightly enhance the interfacial preference of both solutes. In contrast, attractive cross-interactions reduce interfacial preferences and can convert weak surfactants into weak depletants. We observe a particularly interesting transition in the symmetric case of two equivalent self-repelling cosolutes with attractive cross-interactions. In this regime, the major cosolute acts as a weak surfactant in order to avoid repulsive self-interactions, while the minor cosolute acts as a weak depletant in order to form attractive cross-interactions. The two equivalent cosolutes switch roles depending upon their relative concentration. DST very accurately describes the surface tension and surface excess of simulated lattice solutions up to molar concentrations. More importantly, DST provides quantitative and qualitative insight into the mechanism by which cosolute interactions modulate interfacial preferences.