The Stokes-Einstein-Sutherland Equation at the Nanoscale Revisited.

The Stokes-Einstein-Sutherland (SES) equation is at the foundation of statistical physics, relating a particle's diffusion coefficient and size with the fluid viscosity, temperature, and the boundary condition for the particle-solvent interface. It is assumed that it relies on the separation of scales between the particle and the solvent, hence it is expected to break down for diffusive transport on the molecular scale. This assumption is however challenged by a number of experimental studies showing a remarkably small, if any, violation, while simulations systematically report the opposite. To understand these discrepancies, analytical ultracentrifugation experiments are combined with molecular simulations, both performed at unprecedented accuracies, to study the transport of buckminsterfullerene C60 in toluene at infinite dilution. This system is demonstrated to clearly violate the conditions of slow momentum relaxation. Yet, through a linear response to a constant force, the SES equation can be recovered in the long time limit with no more than 4% uncertainty both in experiments and in simulations. This nonetheless requires partial slip on the particle interface, extracted consistently from all the data. These results, thus, resolve a long-standing discussion on the validity and limits of the SES equation at the molecular scale.

Single-Molecule Pycnometry and Shape Analysis of Ions in the Gas Phase.

The analysis of ions and clusters by mobility-classified mass spectrometry provides information on the mobility of analytes in the drift gas and the analyte mass. Mass equivalent and mobility equivalent diameters of globular analytes, such as ions, poly(ethylene glycol) (PEG), and ionic liquid nanodroplets, can be correlated with good accuracy by the Stokes-Millikan mobility model. A prerequisite to such an analysis is, however, the assumption of a globular analyte shape, which then allows determination of material density for globular ions. We show that the analyte density can be evaluated with high precision, independent of any assumptions on the analyte shape, by careful analysis of analyte-PEG-cluster ions following the concept of classical pycnometry. In particular, the analyte is entrapped in a globular PEG-analyte droplet. Based on the now independently derived mobility diameter and volume equivalent diameter, it is possible to attribute two parameters, size and shape, to the analyte molecule. We demonstrate the approach for lysozyme, cyano-cobalamin (vitamin B12), and glucose, which cover two orders of magnitude in analyte mass (180···14 300 Da). The derived densities for these analytes are highly accurate, i.e., they deviate less than 1% from literature values. Our method can be applied to newly synthesized molecules, supramolecular assemblies, isolated biomolecules, and molecular clusters, where only minor amounts of materials are available. The obtained shape parameters of lysozyme and cyano-cobalamin agree well with the expected molecular shapes. Data evaluation relies only on locations of the species in the mass-mobility plane and is in principle independent of any mobility theory. Our approach is thus robust with respect to experimental uncertainties and produces identical results irrespective of the type of mobility classification and drift gas.

Adsorption of CTAB on Sapphire-c at High pH: Surface and Zeta Potential Measurements Combined with Sum-Frequency and Second-Harmonic Generation.

The adsorption of cetyltrimethylammonium bromide (CTA+Br-) on sapphire-c surfaces was studied at pH 10 below the surfactants' critical micelle concentration. The evolution of interfacial potentials as a function of CTAB concentration was characterized by surface and zeta potential measurements and complemented by molecular dynamic (MD) simulations as well as by second-harmonic (SHG) and vibrational sum-frequency generation (SFG) spectroscopy. The changes in interfacial potentials suggest that the negative interfacial charge due to deprotonated surface aluminols groups is neutralized and can be even overcompensated by the presence of CTA+ cations at the interface. However, SFG intensities from strongly hydrogen-bonded interfacial water molecules as well as SHG intensities decrease with both increasing CTAB concentration and the magnitude of the surface potential. They do not suggest a charge reversal at the interface, while the change in zeta potential is actually consistent with an apparent charge inversion. This can be qualitatively explained by results from MD simulation, which reveal adsorbed CTA+ cations outside a first strongly bound hydration layer of water molecules, where they can locally distort the structural order and replace some of the interfacial water molecules adjacent to the first layer. This is proposed to be the origin for the significant loss in SFG and SHG intensities with increasing CTAB concentration. Moreover, we propose that CTA+ can act as a counterion and enhance the occurrence of deprotonated surface aluminols that is consistent with the decrease in surface potential.

Hydrodynamic simulations of sedimenting dilute particle suspensions under repulsive DLVO interactions.

We present guidelines to estimate the effect of electrostatic repulsion in sedimenting dilute particle suspensions. Our results are based on combined Langevin dynamics and lattice Boltzmann simulations for a range of particle radii, Debye lengths and particle concentrations. They show a simple relationship between the slope K of the concentration-dependent sedimentation velocity and the range χ of the electrostatic repulsion normalized by the average particle-particle distance. When χ → 0, the particles are too far away from each other to interact electrostatically and K = 6.55 as predicted by the theory of Batchelor. As χ increases, K likewise increases as if the particle radius increased in proportion to χ up to a maximum around χ = 0.4. Over the range χ = 0.4-1, K relaxes exponentially to a concentration-dependent constant consistent with known results for ordered particle distributions. Meanwhile the radial distribution function transitions from a disordered gas-like to a liquid-like form. Power law fits to the concentration-dependent sedimentation velocity similarly yield a simple master curve for the exponent as a function of χ, with a step-like transition from 1 to 1/3 centered around χ = 0.6.

Structure and Dynamics of Interfacial Peptides and Proteins from Vibrational Sum-Frequency Generation Spectroscopy.

Proteins at interfaces play important roles in cell biology, immunology, bioengineering, and biomimetic material design. Many biological processes are based on interfacial protein action, ranging from cellular communication to immune responses and the protein-driven mineralization of bone. Despite the importance of interfacial proteins, comparatively little is known about their structure. The standard methods for studying crystalline or solution-phase proteins (X-ray diffraction and NMR spectroscopy) are not well-suited for studying proteins at interfaces, and for these proteins we still lack a corresponding technique that can provide the same level of structural resolution. This is not surprising in view of the challenges involved in probing the structure of proteins within monomolecular films assembled at a very thin interface in situ. Vibrational sum-frequency generation (SFG) spectroscopy has the potential to overcome this challenge and investigate the structure and dynamics of proteins at interfaces at the molecular level with subpicosecond time resolution. While SFG studies were initially limited to simple model peptides, the past decade has seen a dramatic advancement of experimental techniques and data analysis methods that has made it possible to also study interfacial proteins and their folding, binding, orientation, hydration, and dynamics. In this review, we first explain the principles of SFG spectroscopy and the experimental and theoretical methods to measure and analyze protein SFG spectra. Then we give an extensive overview of the interfacial proteins studied to date with SFG. We highlight representative examples to demonstrate recent advances in probing the structure of proteins at the interfaces of liquids, membranes, minerals, and synthetic materials.

Characterization of Electrospray Drop Size Distributions by Mobility-Classified Mass Spectrometry: Implications for Ion Clustering in Solution and Ion Formation Pathways.

One of the outcomes of electrospray ionization is the size distribution of the droplets, which determines, together with the solvent composition and the source gas temperature, the minimum distance from the sprayer tip to the mass spectrometer inlet and therefore the ion transfer efficiency. Even more importantly, the average number of analyte molecules and, if present, contaminant species per droplet depend on the drop size. Consequently, the drop size distribution is a key parameter in nonspecific ion clustering in solution and ion suppression. The finding that small droplet sizes improve the mass spectral quality led to the development of nanoelectrospray sources, which dispense liquid flow rates below 0.1 µL/min and can generate drops with diameters smaller than 100 nm. However, current discussions on the effect of drop size on ion formation pathways and efficiencies remain qualitative because the exact drop size distributions are unknown. Here, we show that ion mobility-classified mass spectrometry of raffinose cluster ions allows us to determine very precisely the drop size distribution generated by the electrospray source in positive- and negative-ion modes. Based on the derived drop size distributions, we can quantitatively predict nonspecific ion clustering and can extract accurate probabilities for emission of species from parent drops upon Coulomb fission.

Effect of Surfactants on the Molecular Structure of the Buried Oil/Water Interface.

The oil/water interface, for instance in emulsions, is often stabilized by surfactants. Hence, the co-existence of oil, water, and surfactant molecules at the buried oil/water interface determines macroscopic properties such as surface tension or emulsion stability. Utilizing an inherently surface sensitive spectroscopic method, sum frequency generation (SFG) spectroscopy, we show that adsorption of an anionic surfactant to the buried oil/water interface increases the magnitude of the interfacial electric field. Meanwhile, the degree of ordering of the interfacial oil molecules increases with the surfactant concentration owing to the intercalation of aliphatic chains of interfacial oil and surfactant molecules. At sufficiently high surfactant concentrations, the interfacial charge reaches a maximum value and the interfacial oil molecules arrange in a fully ordered conformation, a state which coincides with the significant decrease in interfacial tension and increased emulsion stability.

Measurement of length distribution of beta-lactoglobulin fibrils by multiwavelength analytical ultracentrifugation.

The whey protein beta-lactoglobulin is the building block of amyloid fibrils which exhibit a great potential in various applications. These include stabilization of gels or emulsions. During biotechnological processing, high shear forces lead to fragmentation of fibrils and therefore to smaller fibril lengths. To provide insight into such processes, pure straight amyloid fibril dispersions (prepared at pH 2) were produced and sheared using the rotor stator setup of an Ultra Turrax. In the first part of this work, the sedimentation properties of fragmented amyloid fibrils sheared at different stress levels were analyzed with mulitwavelength analytical ultracentrifugation (AUC). Sedimentation data analysis was carried out with the boundary condition that fragmented fibrils were of cylindrical shape, for which frictional properties are known. These results were compared with complementary atomic force microscopy (AFM) measurements. We demonstrate how the sedimentation coefficient distribution from AUC experiments is influenced by the underlying length and diameter distribution of amyloid fibrils.In the second part of this work, we show how to correlate the fibril size reduction kinetics with the applied rotor revolution and the resulting energy density, respectively, using modal values of the sedimentation coefficients obtained from AUC. Remarkably, the determined scaling laws for the size reduction are in agreement with the results for other material systems, such as emulsification processes or the size reduction of graphene oxide sheets.

Probing particle heteroaggregation using analytical centrifugation.

The controlled aggregation of colloidal particles is not only a widespread natural phenomenon but also serves as a tool to design complex building blocks with tailored shape and functionalities. However, the quantitative characterization of such heteroaggregation processes remains challenging. Here, we demonstrate the use of analytical centrifugation to characterize the heteroaggregation of silica particles and soft microgels bearing similar surface charges. We investigate the attachment as well as the stability of the formed heteroaggregates as a function of particle to microgel surface ratio, microgel size and the influence of temperature. The attachment of microgels onto the colloidal particles induces a change in the sedimentation coefficient, which is used to quantitatively identify the number of attached microgels. We corroborate the shift in sedimentation coefficient by computer simulations of the frictional properties of heteroaggregates via a modified Brownian dynamic algorithm. The comparison between theoretical investigations and experiments suggest that the microgels deform and flatten upon attachment.

Effect of the Counteranion on the Formation Pathway of Cu2ZnSnS4 (CZTS) Nanoparticles under Solvothermal Conditions.

Cu2ZnSnS4 and Cu2ZnSnSe4 (CZTS and CZTSe, respectively) and their mixed chalcogenide phase Cu2ZnSnSxSe4-x (CZTSS(e)) are benign and cheap photovoltaic absorber materials that represent a valuable alternative to the more expensive chalcogenide systems: i.e., Cu(In,Ga)SS(e)2 (CIGSS(e)). One of the main challenges related to the fabrication of CZTS(e) layers is the control over both the crystalline phase (tetragonal, cubic, or hexagonal) and the formation of binary (MS, M = Cu(II), Zn(II), Sn(II); M'2-xS, M'= Cu(I), x = 0, 0.2; M″S2, M″ = Sn(IV)) and ternary products (CTS phases, Cu2SnS3, Cu3SnS4) that hinder the performance of the corresponding devices. In the present work, we rationalize the formation pathway of the CZTS phase through binary and ternary products when salt precursors with chloride and acetate as counteranions, respectively, are employed. The results show that the counteranions have a remarkable influence on the formation pathway of CZTS nanoparticles. The use of chloride precursors leads to the predominant formation of CTSs ternary phases (Cu2SnS3, Cu3SnS4), whereas the formation of the CZTS phase is not observed even for higher temperature and longer reaction time (250 °C, 24 h). In the case of acetates the copresence of CZTS as the main product, together with binary and ternary phases, is observed in the early stages of the reaction even at lower temperature and shorter reaction time (200 °C, 2 h), while when the reaction time and temperature are increased, only the CZTS phase is observed. In addition to a careful microstructural characterization of the as-synthesized materials by Raman spectroscopy, X-ray diffraction (XRD), Energy dispersive X-ray spectroscopy (EDX), X-ray photoelectron spectroscopy (XPS), and high-resolution transmission electron microscopy (HRTEM), we shed light on the reactivity among the metal precursors, the organic ligand oleylamine, and the sulfur precursor carbon disulfide (CS2) by 13C nuclear magnetic resonance (13C NMR) and investigate in depth the effect on particle surfaces by Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), and XPS. A rationale for the formation pathway of CZTS nanoparticles is proposed and supported by experimental evidence.

Mobility-Classified Mass Spectrometry Reveals a Complete Picture of the Electrospray Outcome.

Electrospray ionization mass spectrometry supported by mobility classification (ESI-DMA-MS) is a strong technique for a comprehensive analysis of organic and inorganic clusters and small nanoparticles. In-depth understanding and optimization of the electrospray process are key for unlocking new fields of application and for extension of the accessible range of data. We show that the combination of mobility-classified mass spectrometry (DMA-MS) with an electrospray operated in a well-defined cone-jet mode is capable of providing a full picture of the outcome of the electrospray process including the evaporation residues of the parent droplets. Based on ESI-DMA-MS measurements of lysozyme, we find that clusters up to almost 1 MDa (around 60 lysozyme molecules per cluster) formed as evaporation residues of the parent droplets can be detected. The escape probability of lysozyme molecules from the parent droplets is polarity-dependent. A quantitative analysis of clusters is possible at analyte concentrations where the likeliness of finding more than a single molecule in the generated droplet is low. At higher concentrations, one can, however, quantify the analyte concentration from the detected size of the droplet evaporation residues. The approach is widely applicable for organic and inorganic nanostructures. The results allow clear statements on the conditions under which mixtures of larger molecules, clusters, and nanoparticles are accessible to quantitative analysis by mass spectrometry.

Isoelectric Points of Proteins at the Air/Liquid Interface and in Solution.

Electrostatic interactions play essential roles in determining the function, colloidal stability, and adsorption of proteins on different surfaces and interfaces. Therefore, a molecular-level understanding of the charge state of the proteins under different conditions is required to explain their macroscopic properties. In this study, we have employed an inherently surface-sensitive spectroscopic tool, sum frequency generation spectroscopy, to determine the charge state of a wide range of proteins as a function of pH at the air/liquid interface via measurement of the degree of orientation of water molecules. We compared the isoelectric point (IEP) of the 12 investigated proteins at the air/liquid interface with that in the bulk solution obtained through zeta potential measurements. Ellipsometry is performed to determine the film thickness at the air/liquid interface at different charge states. In particular, protein aggregation at the IEP is reflected by increased film thickness. For all proteins, the interfacial point of zero charge is close (with less than 1 pH unit variation) to that in the bulk solution.

A Comprehensive Brownian Dynamics Approach for the Determination of Non-ideality Parameters from Analytical Ultracentrifugation.

Brownian dynamics (BD) has been applied as a comprehensive tool to model sedimentation and diffusion of nanoparticles in analytical ultracentrifugation (AUC) experiments. In this article, we extend the BD algorithm by considering space-dependent diffusion and solvent compressibility. With this, the changes in the sedimentation and diffusion coefficient from altered solvent properties at increased pressures are accurately taken into account. Moreover, it is demonstrated how the concept of space-dependent diffusion is employed to describe concentration-dependent sedimentation and diffusion coefficients, in particular, through the Gralen coefficient and the second virial coefficient. The influence of thermodynamic nonideality on diffusional properties can be accurately simulated and agree with well-known evaluation tools. BD simulations for sedimentation equilibrium and sedimentation velocity (SV) AUC experiments including effects of hydrodynamic and thermodynamic nonideality are validated by global evaluation in SEDANAL. The interplay of solvent compressibility and retrieved nonideality parameters can be studied utilizing BD. Finally, the second virial coefficient is determined for lysozyme from SV AUC experiments and BD simulations and compared to membrane osmometry. These results are in line with DLVO theory. In summary, BD simulations are established for the validation of nonideal sedimentation in AUC providing a sound basis for the evaluation of complex interactions even in polydisperse systems.

Advanced Multiwavelength Detection in Analytical Ultracentrifugation.

This work highlights significant advancements in detector hardware and software for multiwavelength analytical ultracentrifugation (MWL-AUC) experiments, demonstrating improvement in both the spectral performance and UV capabilities of the instrument. The hardware is an extension of the Open AUC MWL detector developed in academia and first introduced in 2006 by Bhattacharya et al. Additional modifications as well as new analytical methods available for MWL data have since been reported. The present work describes new and continuing improvements to the MWL detector, including mirror source and imaging optics, UV sensitive acquisition modes and revised data acquisition software. The marked improvement of experimental data promises to provide access to increasingly complex systems, especially semiconductor nanoparticles, synthetic polymers, biopolymers, and other chromophores absorbing in the UV. Details of the detection system and components are examined to reveal the influences on data quality and to guide further developments. The benchmark comparisons of data quality across platforms will also serve as a reference guide for evaluation of forthcoming commercial absorbance optics.

Synergy of Catechol-Functionalized Zinc Oxide Nanorods and Porphyrins in Layer-by-Layer Assemblies.

Catechol-functionalized, positively charged ZnO nanorods (NRs) and anionic porphyrins were integrated into layer-by-layer (LbL) assemblies. In general, this study focuses on the impact that different porphyrins, varying in size and number of negative charges, exert on the LbL architecture in terms of morphology and spectroscopy. In particular, through a combination of analytical methods, including UV/Vis spectroscopy, SEM, and profilometry, valuable insights into LbL assembly formation were gathered. A key feature was the surface coverage in the resulting films. Denser films and surface coverages were realized when highly negatively charged and sterically demanding porphyrins were employed. As a complement to basic characterization, the LbL assembled films were used to fabricate proof-of-concept solar cells.

Simple and Reliable Method for Studying the Adsorption Behavior of Aquivion Ionomers on Carbon Black Surfaces.

A better understanding of the interactions of carbon black and perfluorinated sulfonic acid (PFSA) ionomer helps to improve the effectiveness of polymer electrolyte membrane fuel cells. We present a simple and fast method for quantitative PFSA ionomer analysis based on suspension density measurements. After validation of the reliability of our method by thermogravimetric analysis and isothermal titration calorimetry (ITC), we investigate the adsorption equilibrium of short-side-chain PFSA ionomers of different equivalent weights (EW) and polarities on carbon black. The measured adsorption isotherms exhibit a plateau in the ionomer surface concentration for ionomer equilibrium concentrations ≤2 g/L. In this concentration range, the adsorption isotherms are described by the Langmuir model, whereby the surface concentrations in the plateau region are between 0.041 and 0.070 g/g. The plateau value of the ionomer surface concentration increases with EW and therefore with decreasing number of side chains with terminal sulfonic acid group per ionomer molecule, while the amount of adsorbed sulfonic acid groups remains constant for all investigated ionomers, resulting in similar ζ-potentials and sedimentation stability of the suspensions. The free energies of adsorption Δ G calculated from the association constants of the adsorption isotherms agree well with Δ G values obtained by isothermal titration calorimetry (ITC) and thus validate the adsorption isotherm measurement method. From the values of adsorption enthalpy Δ H ((-7.3 ± 0.8) kJ/mol) and entropy Δ S (ca. 100 J/(mol K)), which were extracted from ITC, we conclude that the ionomer adsorption on carbon black is a spontaneous physisorption process.

Ionomer and protein size analysis by analytical ultracentrifugation and electrospray scanning mobility particle sizer.

By combining analytical ultracentrifugation (AUC) in liquid phase and scanning mobility particle sizer (SMPS) in the gas phase, additional information on the particle size and morphology has been obtained for rigid particles. In this paper, we transfer this concept to soft particles, allowing us to analyze the size and molar mass of the short side chain perfluorosulfonic acid ionomer Aquivion® in a dilute aqueous suspension. The determination of the primary size and exact molar mass of this class of polymers is challenging since they are optically transparent and due to the formation of different aggregate structures depending on the concentration and solvent properties. First, validation of AUC and SMPS measurements was carried out using the well-defined biopolymers bovine serum albumin (BSA) and lysozyme (LYZ) to confirm the reliability of the results of the two unique and independent classifying methods. Then, the ionomer Aquivion® was studied using both techniques. From the mean molar mass of 185 ± 14 kDa obtained by AUC, a mean hydrodynamic diameter of 7.6 ± 0.5 nm was calculated. The particle size obtained from SMPS (7.1 nm) agrees very well with the results from AUC showing that the molecule was transferred into the gas phase without significantly changing its structure. In conclusion, the Aquivion® is molecularly dispersed in the used aqueous buffer solution without any aggregate formation in the investigated concentration range (< 2 g l-1).

Molecular structure of octadecylphosphonic acids during their self-assembly on α-Al2O3(0001).

The formation of octadecylphosphonic acid (ODPA) self-assembled monolayers (SAMs) from 2-propanol solutions on hydroxylated α-Al2O3(0001) surfaces was studied in situ and in real time at the solid/liquid interface. Time-resolved vibrational spectra from sum-frequency generation (SFG) of C-H stretching modes revealed contributions from ODPA's alkyl backbone and the terminal methyl group as well as vibrational bands that originated from the presence of 2-propanol molecules at the α-Al2O3 surface. 2-Propanol signatures in SFG spectra decreased during SAM formation. This is due to adsorption of ODPA molecules which trigger desorption of 2-propanol from the α-Al2O3(0001) surface, so that these sites can be occupied by ODPA molecules. SAM formation was studied for different bulk concentrations of ODPA which changed substantially both the quality and the coverage of the final SAM. At initial stages of SAM growth, SFG spectra are dominated by methylene contributions and are indicative for a low molecular order and coverage of ODPA molecules. For concentrations of ODPA ≤2 mM this situation did not change within reasonable adsorption times (∼16 h) while for 5 and 30 mM concentrations a dramatic increase in molecular order and coverage within the first 2 h of adsorption is observed. Thermodynamic analysis using Langmuir adsorption kinetics provided equilibrium constants and the Gibbs free energy of adsorption between -24 and -28 kJ mol-1.

Synthesis and characterization of manganese containing mesoporous bioactive glass nanoparticles for biomedical applications.

Mesoporous bioactive glass (BG) nanoparticles based in the system: SiO2-P2O5-CaO-MnO were synthesized via a modified Stöber process at various concentrations of Mn (0-7 mol %). The synthesized manganese-doped BG nanoparticles were characterized in terms of morphology, composition, in vitro bioactivity and antibacterial activity. Scanning electron microscopy (SEM), transmission electron microscopy (TEM) and Brunauer-Emmett-Teller (BET) analysis confirmed that the particles had spherical morphology (mean particle size: 110 nm) with disordered mesoporous structure. Energy dispersive X-ray spectroscopy (EDX) confirmed the presence of Mn, Ca, Si and P in the synthesized Mn-doped BG particles. Moreover, X-ray diffraction (XRD) analysis showed that Mn has been incorporated in the amorphous silica network (bioactive glass). Moreover, it was found that manganese-doped BG particles form apatite crystals upon immersion in simulated body fluid (SBF). Inductively coupled plasma atomic emission spectroscopy (ICP-OES) measurements confirmed that Mn is released in a sustained manner, which provided antibacterial effect against Bacillus subtilis, Pseudomonas aeruginosa and Staphylococcus aureus. The results indicate that the incorporation of Mn in the bioactive glass network is an effective strategy to develop novel multifunctional BG nanoparticles for bone tissue engineering.

Singlet Fission for Photovoltaics with 130 % Injection Efficiency.

A novel pentacene dimer (P2) and a structurally analogous monomer (P1) were synthesized for use in n-type dye-sensitized solar cells. In P2, the triplet excited states formed by the rapid, spin-allowed process singlet fission were expected to enable carrier multiplication in comparison to the slow, spin-forbidden intersystem crossing seen in P1. A meta-positioning of the two pentacenes and the carboxylate anchor were chosen in P2 to balance the intramolecular dynamics of singlet fission and electron injection. Electron injection from energetically low-lying triplet excited states of pentacene units necessitated the intrinsic and extrinsic lowering of the Fermi level of the semiconductor. Indium-zinc oxide in the presence of Li+ was found to be the optimum choice for the photoelectrodes. Efficient electron injection from the triplet excited states of P1 and P2 was found, with a carrier multiplication of nearly 130 %.