Laboratory of Magnetic Soft Materials

Magnētisku Mīkstu Materiālu Laboratorija (MMML; Laboratory of Magnetic Soft Materials) is a research group in the Chair of Theoretical Physics, which is a part of the Faculty of Physics, Mathematics and Optometry of the University of Latvia. Our research interests cover various aspects in the field of magnetic soft materials, magnetism and soft matter, including material synthesis, characterization and rheology, investigation of different phenomena connected with these materials and development of new methods and applications for use in biotechnology.

Dynamics of a flexible magnetic chain in a rotating magnetic field.

2004

The model of an elastic magnetic rod is applied for a study of a behavior of the flexible magnetic particle chain in a rotating magnetic field. By numerical simulation it is shown that behavior of a flexible magnetic chain is characterized by the existence of a critical frequency beyond which the dynamics of the rod is periodic with subsequent stages of bending and straightening. The value of the critical frequency found is explained by a simple model. Below the critical frequency the chain is bent and rotates synchronously with a field. It is illustrated that in particular cases the considered model reproduces phenomena observed experimentally and numerically for the magnetic particle chai…

Hydrodynamics with spin in bacterial suspensions

2016

We describe a new kind of self-propelling motion of bacteria based on the cooperative action of rotating flagella on the surface of bacteria. Describing the ensemble of rotating flagella in the framework of the hydrodynamics with spin the reciprocal theorem of Stokesian hydrodynamics is generalized accordingly. The velocity of the self-propulsion is expressed in terms of the characteristics of the vector field of flagella orientation and it is shown that unusually high velocities of \textit{Thiovulum majus} bacteria may be explained by the cooperative action of the rotating flagella. The expressions obtained enable us to estimate the torque created by the rotary motors of the bacterium and …

The cage elasticity and under-field structure of concentrated magnetic colloids probed by small angle X-ray scattering

2013

International audience; In the present study we probe the bulk modulus and the structure of concentrated magnetic fluids by small angle X-ray scattering. The electrostatically stabilized nanoparticles experience a repulsive interparticle potential modulated by dipolar magnetic interactions. On the interparticle distance length scale, we show that nanoparticles are trapped under-field in oblate cages formed by their first neighbours. We propose a theoretical model of magnetostriction for the field-induced deformation of the cage. This model captures the anisotropic features of the experimentally observed scattering pattern on the local scale in these strongly interacting colloidal dispersions

Time-resolved velocity measurements in a magnetic micromixer

2015

Abstract Mixing efficiency is lower in passive micromixers due to viscous forces and substantial research effort is focused on designing high performance micromixers. Active micromixers make use of external forces to enhance mixing efficiency. Among these, magnetic forces are popular because they are non-contact and therefore the micromixer design can be kept simple. Laser-based diagnostic tools have great potential in providing multi-parameter information in microfluidics research on mixing. MicroPIV experiments are performed to investigate the transient flow field in a magnetic micromixer undergoing labyrinthine instability. Velocity and interface front information is extracted from a seq…

Magnetic field driven micro-convection in the Hele-Shaw cell: the Brinkman model and its comparison with experiment

2015

International audience; The micro-convection caused by the ponderomotive forces of the self-magnetic field in a magnetic fluid is studied here both numerically and experimentally. The theoretical approach based on the general Brinkman model substantially improves the description with respect to the previously proposed Darcy model. The predictions of both models are here compared to finely controlled experiments. The Brinkman model, in contrast to the Darcy model, allows us to describe the formation of mushrooms on the plumes of the micro-convective flow and the width of the fingers. In the Brinkman approach, excellent quantitative agreement is also obtained for the finger velocity dynamics …

Gravity effects on mixing with magnetic micro-convection in microfluidics.

2018

Mixing remains an important problem for development of successful microfluidic and lab-on-a-chip devices, where simple and predictable systems are particularly interesting. One is magnetic micro-convection, an instability happening on the interface of miscible magnetic and non-magnetic fluids in a Hele-Shaw cell under applied field. Previous work proved that Brinkman model quantitatively explains the experiments. However, a gravity caused convective motion complicated the tests. Here we first improve the experimental system to exclude the gravitational convective motion. Afterwards, we observe and quantify how gravity and laminar flow play an important role in stabilizing the perturbations …

Flexible ferromagnetic filaments and the interface with biology

2009

Flexible ferromagnetic filaments are studied both theoretically and experimentally. Two main deformation modes of the filament at magnetic field inversion are theoretically described and observed experimentally by using DNA-linked chains of ferromagnetic particles. Anomalous orientation of ferromagnetic filaments perpendicular to AC field with a frequency which is high enough is predicted and confirmed experimentally. By experimental studies of magnetotactic bacteria it is demonstrated how these properties of ferromagnetic filaments may be used to measure the flexibility of the chain of magnetosomes.

Gelation of semiflexible polyelectrolytes by multivalent counterions

2012

Filamentous polyelectrolytes in aqueous solution aggregate into bundles by interactions with multivalent counterions. These effects are well documented by experiment and theory. Theories also predict a gel phase in isotropic rodlike polyelectrolyte solutions caused by multivalent counterion concentrations much lower than those required for filament bundling. We report here the gelation of Pf1 virus, a model semiflexible polyelectrolyte, by the counterions Mg(2+), Mn(2+) and spermine(4+). Gelation can occur at 0.04% Pf1 volume fraction, which is far below the isotropic-nematic transition of 0.7% for Pf1 in monovalent salt. Unlike strongly crosslinked gels of semiflexible polymers, which stif…

Salmon fibrinogen and chitosan scaffold for tissue engineering: in vitro and in vivo evaluation

2018

3D fibrous scaffolds have received much recent attention in regenerative medicine. Use of fibrous scaffolds has shown promising results in tissue engineering and wound healing. Here we report the development and properties of a novel fibrous scaffold that is useful for promoting wound healing. A scaffold made of salmon fibrinogen and chitosan is produced by electrospinning, resulting in a biocompatible material mimicking the structure of the native extracellular matrix (ECM) with suitable biochemical and mechanical properties. The scaffold is produced without the need for enzymes, in particular thrombin, but is fully compatible with their addition if needed. Human dermal fibroblasts culture…

Magnetically enhancing the Seebeck coefficient in ferrofluids.

2019

The influence of the magnetic field on the Seebeck coefficient (Se) was investigated in dilute magnetic nanofluids (ferrofluids) composed of maghemite magnetic nanoparticles dispersed in dimethyl-sulfoxide (DMSO). A 25% increase in the Se value was found when the external magnetic field was applied perpendicularly to the temperature gradient, reminiscent of an increase in the Soret coefficient (ST, concentration gradient) observed in the same fluids. In-depth analysis of experimental data, however, revealed that different mechanisms are responsible for the observed magneto-thermoelectric and -thermodiffusive phenomena. Possible physical and physico-chemical origins leading to the enhancemen…

Magnetic microrods as a tool for microrheology

2015

International audience; Dynamics of superparamagnetic rods in crossed constant and alternating magnetic fields as a function of field frequency are studied and it is shown that above the critical value of the amplitude of the alternating field the rod oscillates around the direction of the alternating field. The fit of the experimentally measured time dependence of the mean orientation angle of the rod allows one to determine the ratio of magnetic and viscous torques which act on the rod. The protocol of microrheological measurements consists of recording the dynamics of the orientation of the rod when the magnetic field is applied at an angle to the rod and observing its relaxation due to …

Dynamics of Magnetotactic Bacteria in a Rotating Magnetic Field

2007

The dynamics of the motile magnetotactic bacterium Magnetospirillum gryphiswaldense in a rotating magnetic field is investigated experimentally and analyzed by a theoretical model. These elongated bacteria are propelled by single flagella at each bacterial end and contain a magnetic filament formed by a linear assembly of approximately 40 ferromagnetic nanoparticles. The movements of the bacteria in suspension are analyzed by consideration of the orientation of their magnetic dipoles in the field, the hydrodynamic resistance of the bacteria, and the propulsive force of the flagella. Several novel features found in experiments include a velocity reversal during motion in the rotating field a…

Nonlinear dynamics of semiflexible magnetic filaments in an ac magnetic field

2006

Flexible spontaneously magnetized filaments exist in the living world (magnetotactic bacteria) and arise in magnetic colloids with large magnetodipolar interaction parameter. We demonstrate that these filaments possess variety of novel nonlinear phenomena in an ac magnetic field: orientation of the filament in the direction perpendicular to the field and the development of the oscillating U-like shapes, which presumably can lead to the formation of rings of magnetic filaments. It is found that these phenomena are determined by the development of the localized boundary modes of the filament deformation. We have illustrated by qualitative estimates that the phenomena found may be useful for i…

Overdamped dynamics of paramagnetic ellipsoids in a precessing magnetic field

2009

We report on the dynamical behavior of paramagnetic ellipsoidal particles dispersed in water and floating above a flat plane when subjected to an external precessing magnetic field. When the magnetic field and the long axis of the particles are on the same plane, two clear regimes are distinguished in which the particles follow the magnetic modulation synchronously or asynchronously. Both regimes are also observed when the field precesses at an angle $\ensuremath{\vartheta}l90\ifmmode^\circ\else\textdegree\fi{}$ with respect to the normal to the confining plane, while the transition frequency increases with decreasing precession angle. We combine experimental observations with a theoretical…

Magnetic dipole with a flexible tail as a self-propelling microdevice.

2012

By numerical simulations, it is illustrated that a magnetic dipole with a flexible tail behaves as a swimmer in AC magnetic fields. The behavior of the swimmer on long time scales is analyzed and it is shown that due to the flexibility of the tail two kinds of torques arise, the first is responsible for the orientation of the swimmer perpendicularly to the AC field and the second drags the filament in the direction of the rotating field. Due to this, circular trajectories of the swimmer are possible; however, these are unstable. The self-propulsion velocity of this swimmer is higher than the velocities of other magnetic microdevices for comparable values of the magnetoelastic number.

Electrohydrodynamic instabilities and orientation of dielectric ellipsoids in low-conducting fluids.

2000

We study the dynamics of an ellipsoidal particle in a weakly conducting dielectric liquid when submitted to a dc electric field. At low field intensities, the particle long axis is aligned in the field direction. When the field strength is increased, we show that, depending on the initial orientation of the particle, there exist two stable orientations: the one with the long axis parallel to the field direction remains possible while a spinning state with the long axis perpendicular to the field appears. This last striking orientation is due to the finite Maxwell-Wagner polarization relaxation time. For sufficiently high field intensities, each state loses its stability and the particle dyn…

Parametric excitation of bending deformations of a rod by periodic twist

2013

A model of a semiflexible magnetic filament with magnetization frozen in the direction perpendicular to the tangent of its center line is formulated. It is shown that if the rod is magnetized at its ends in opposite directions, an AC magnetic field causes parametric excitation of bending deformations. Neutral curves of parametric excitation are calculated both analytically and numerically. The shapes arising upon parametric excitation of bending deformations are chiral. Periodic rotation of the chiral filament due to nonhomogeneous twist in a nonhomogeneous AC field causes its unidirectional motion.

Spontaneous order in ensembles of rotating magnetic droplets

2019

Ensembles of elongated magnetic droplets in a rotating field are studied experimentally. In a given range of field strength and frequency the droplets form rotating structures with a triangular order - rotating crystals. A model is developed to describe ensembles of several droplets, taking into account the hydrodynamic interactions between the rotating droplets in the presence of a solid wall below the rotating ensemble. A good agreement with the experimentally observed periodic dynamics for an ensemble of four droplets is obtained. During the rotation, the tips of the elongated magnetic droplets approach close to one another. An expression is derived that gives the magnetic interaction be…

Dynamics of a flexible ferromagnetic filament in a rotating magnetic field.

2017

Flexible magnetic filaments have garnered considerable attention as prospective materials for the creation of different microdevices. We describe a theoretical model of a ferromagnetic filament and derive its equations of motion by variational techniques. The numerical algorithm used to solve the filament dynamics in magnetic fields of different configurations is described. It is found that in a rotating field the filament transitions between synchronous and asynchronous regimes with respect to the rotating field, similarly to a rigid magnetic dipole. The mean angular velocity of the filament is well described by a relation valid for a rigid magnetic dipole with quantitative differences att…

Polyelectrolyte properties of filamentous biopolymers and their consequences in biological fluids.

2014

Anionic polyelectrolyte filaments are common in biological cells. DNA, RNA, the cytoskeletal filaments F-actin, microtubules, and intermediate filaments, and polysaccharides such as hyaluronan that form the pericellular matrix all have large net negative charge densities distributed over their surfaces. Several filamentous viruses with diameters and stiffnesses similar to those of cytoskeletal polymers also have similar negative charge densities. Extracellular protein filaments such collagen, fibrin and elastin, in contrast, have notably smaller charge densities and do not behave as highly charged polyelectrolytes in solution. This review summarizes data that demonstrate generic counterion-…

3D motion of flexible ferromagnetic filaments under a rotating magnetic field.

2020

Ferromagnetic filaments in a rotating magnetic field are studied both numerically and experimentally. The filaments are made from micron-sized ferromagnetic particles linked with DNA strands. It is found that at low frequencies of the rotating field a filament rotates synchronously with the field and beyond a critical frequency it undergoes a transition to a three dimensional regime. In this regime the tips of the filament rotate synchronously with the field on circular trajectories in the plane parallel to the plane of the rotating field. The characteristics of this motion found numerically match the experimental data and allow us to obtain the physical properties of such filaments. We als…

Relaxation of the field-induced structural anisotropy in a rotating magnetic fluid

2009

The relaxation of field-induced anisotropy in a magnetic fluid with dominant repulsion is theoretically modeled and experimentally measured by small angle neutron scattering on a sample rotating at angular velocity ω. The scattered pattern distortion scales as the Mason number Mn=ω·τq, τq being the q-dependent diffusion time of nanoparticles. The model accounts for the magnetophoretical drift in the non-homogeneous self-magnetic field of the assembly, continuously created by the thermal noise. The Mn-dependence of the pattern distortion is well described without any adjustable parameter.

Evaluation of Physicochemical Properties of Amphiphilic 1,4-Dihydropyridines and Preparation of Magnetoliposomes

2021

This study was focused on the estimation of the targeted modification of 1,4-DHP core with (1) different alkyl chain lengths at 3,5-ester moieties of 1,4-DHP (C12, C14 and C16)

Bending of flexible magnetic rods.

2004

The flexible inextensible magnetic rod model is applied for the study of bending and buckling deformations of the paramagnetic particle chains linked by polymer molecules. It is shown that the existing experimental results can be reasonably well described by this model which takes into account the normal magnetic forces arising at chain bending deformation. By matching the experimentally observed shapes with our numerical simulation results different physical properties of the linked paramagnetic particle chains are determined.

Dynamic fluctuations of dipolar semiflexible filaments

2005

On the basis of the model of a flexible magnetic filament, the characteristics of their thermal fluctuations are considered. The crossover of the time dependence of the mean quadratic displacement from t(3/4) to t(1/2) at the magnetic field increase is found. Two characteristic mechanisms of the magnetization relaxation time distribution--straightening of the thermal undulations and excitation of the bending modes of the free ends under the action of an ac magnetic field--are described. In both cases, the characteristic scaling law omega(-3/4) of the magnetic susceptibility in a high-frequency range is found.

Rotating-field-driven ensembles of magnetic particles.

2019

Vortex patterns in ensembles of magnetic particles driven by a rotating field are studied. The driving arises due to the lubrication forces between the rotating particles acting in the direction perpendicular to the radius vector between the particles. Since the lubrication forces cannot be equilibrated by the radial forces due to the dipolar attraction and steric repulsion, the ensemble is in a nonequilibrium state. Different regimes are found for the dynamics of the driven ensembles---solid-body rotation at low frequency of the rotating field and stick-slip motion of the external layers of the aggregate with respect to the internal structure as the frequency is increased. The relation obt…

Dispersion of magnetic susceptibility in a suspension of flexible ferromagnetic rods

2020

Abstract The properties of suspensions of magnetosomes extracted from magnetotactic bacteria are investigated. By using dynamic light scattering and measuring the dispersion of magnetic susceptibility it is shown that sonicated samples with broken magnetosome chains have qualitatively different behavior in comparison with native samples. This is explained by the presence of flexible chains of magnetosomes in non-sonicated samples which have the qualitative features of magnetic susceptibility predicted by the model of flexible magnetic rods.

Thermodiffusion anisotropy under a magnetic field in ionic liquid-based ferrofluids

2021

International audience; Ferrofluids based on maghemite nanoparticles (NPs), typically 10 nm in diameter, are dispersed in an ionic liquid (1-ethyl 3-methylimidazolium bistriflimide - EMIM-TFSI). The average interparticle interaction is found to be repulsive by small angle scattering of X-rays and of neutrons, with a second virial coefficient A2 = 7.3. A moderately concentrated sample at Φ = 5.95 vol% is probed by forced Rayleigh scattering under an applied magnetic field (up to H = 100 kA m-1) from room temperature up to T = 460 K. Irrespective of the values of H and T, the NPs in this study are always found to migrate towards the cold region. The in-field anisotropy of the mass diffusion c…

Three dimensional dynamics of ferromagnetic swimmer

2011

It is shown that a flexible ferromagnetic filament self-propels perpendicularly to the AC magnetic field during a limited period of time due to the instability of the planar motion with respect to three dimensional perturbations. The transition from the oscillating U-like shapes to the oscillating S-like shapes is characterized by the calculated Wr number.

Electrostatic Contribution to the Surface Pressure of Charged Monolayers Containing Polyphosphoinositides

2008

Structural and functional studies of lateral heterogeneity in biological membranes have underlined the importance of membrane organization in biological function. Most inquiries have focused on steric determinants of membrane organization, such as headgroup size and acyl-chain saturation. This manuscript reports a combination of theory and experiment that shows significant electrostatic contributions to surface pressures in monolayers of phospholipids where the charge spacing is smaller than the Bjerrum length. For molecules with steric cross sections typical of phospholipids in the cell membrane (approximately 50 A(2)), only polyphosphoinositides achieve this threshold. The most abundant s…

Magnetic micro-droplet in rotating field: numerical simulation and comparison with experiment

2017

Magnetic droplets obtained by induced phase separation in a magnetic colloid show a large variety of shapes when exposed to an external field. However, the description of shapes is often limited. Here we formulate an algorithm based on three dimensional boundary-integral equations for strongly magnetic droplets in a high-frequency rotating magnetic field, allowing us to find their figures of equilibrium in three dimensions. The algorithm is justified by a series of comparisons with known analytical results. We compare the calculated equilibrium shapes with experimental observations and find a good agreement. The main features of these observations are the oblate-prolate transition, the flat…

Magnetic field driven micro-convection in the Hele-Shaw cell

2013

AbstractMicro-convection caused by ponderomotive forces of the self-magnetic field of a magnetic fluid in the Hele-Shaw cell under the action of a vertical homogeneous magnetic field is studied both experimentally and numerically. It is shown that a non-potential magnetic force at magnetic Rayleigh numbers greater than the critical value causes fingering at the interface between the miscible magnetic and non-magnetic fluids. The threshold value of the magnetic Rayleigh number depends on the smearing of the interface between fluids. Fingering with its subsequent decay due to diffusion of particles significantly increases the mixing at the interface. Velocity and vorticity fields at fingering…

Swarming of micron-sized hematite cubes in a rotating magnetic field -- Experiments

2020

Energy input by under-field rotation of particles drives the systems to emergent non-equilibrium states. Here we investigate the suspension of rotating magnetic cubes. Micron-sized hematite cubes are synthesized and observed microscopically. When exposed to a rotating magnetic field, they form rotating swarms that interact with each other like liquid droplets. We describe the swarming behaviour and its limits and characterize swarm size and angular velocity dependence on magnetic field strength and frequency. A quantitative agreement with a theoretical model is found for the angular velocity of swarms as a function of field frequency. It is interesting to note that hematite particles with p…

Elastic properties of DNA linked flexible magnetic filaments.

2011

Elastic properties of magnetic filaments linked by DNA in solutions of univalent and bivalent salts with different pH values are investigated through their deformation in an external field. A strong dependence of the bending modulus in bivalent salt solution on the pH is shown. Experimental results are interpreted on the basis of the magnetic elastica.

Coupled stochastic dynamics of magnetic moment and anisotropy axis of a magnetic nanoparticle

2012

An algorithm is developed for numerical simulation of coupled stochastic dynamics of magnetic moment and magnetic anisotropy axis of a nanoparticle. Time-correlation functions of the magnetic moment and its components longitudinal and transverse to the magnetic anisotropy axis are calculated by averaging along the stochastic trajectory. The longitudinal and transverse relaxation times are found by fitting the time correlation functions. Existing theoretical relations derived by the effective field approach in the limit of small fields are confirmed. The time-correlation functions of magnetic moments of nanoparticles in dependence on their properties are calculated numerically for arbitrary …

Magnetic particle mixing with magnetic micro-convection for microfluidics

2015

International audience; In this paper we discuss the magnetic micro-convection phenomenon as a tool for mixing enhancement in microfluidics systems in cases when one of the mis-cible fluids is a magnetic particle colloid. A system of a water-based magnetic fluid and water is investigated experimentally under homogeneous magnetic field in a Hele-Shaw cell. Subsequent image analysis both qualitatively and quan-titatively reveals the high enhancement of mixing efficiency provided by this method. The mixing efficiency dependence on the magnetic field and the phys-ical limits is discussed. A suitable model for a continuous-flow microfluidics setup for mixing with magnetic micro-convection is als…

Counterion-mediated attraction and kinks on loops of semiflexible polyelectrolyte bundles.

2006

The formation of kinks in a loop of bundled polyelectrolyte filaments is analyzed in terms of the thermal fluctuations of charge density due to polyvalent counterions adsorbed on the polyelectrolyte filaments. It is found that the counterion-mediated attraction energy of filaments depends on their bending. By consideration of curvature elasticity energy and counterion-mediated attraction between polyelectrolyte filaments, the characteristic width of the kink and the number of kinks per loop is found to be in reasonable agreement with existing experimental data for rings of bundled actin filaments.

Synchronized rotation in swarms of magnetotactic bacteria.

2017

Self-organizing behavior has been widely reported in both natural and artificial systems, typically distinguishing between temporal organization (synchronization) and spatial organization (swarming). Swarming has been experimentally observed in systems of magnetotactic bacteria under the action of external magnetic fields. Here we present a model of ensembles of magnetotactic bacteria in which hydrodynamic interactions lead to temporal synchronization in addition to the swarming. After a period of stabilization during which the bacteria form a quasiregular hexagonal lattice structure, the entire swarm begins to rotate in a direction opposite to the direction of the rotation of the magnetic …

Relaxation of polar order in suspensions with Quincke effect

2014

The Quincke effect---spontaneous rotation of dielectric particles in a liquid with low conductivity under the action of an electric field---is considered. The distribution functions for the orientation of particle rotation planes are introduced and a set of nonlinear kinetic equations is derived in the mean field approximation considering the dynamics of their orientation in the flow induced by rotating particles. As a result the nonequilibrium phase transition to the polar order, if the concentration of the particles is sufficiently high, is predicted and the condition of the synchronization of particle rotations is established. Two cases are considered: the layer of the Quincke suspension…

Quincke rotation driven flows

2020

In density-matched suspensions of Quincke particles, macroscopic flow arises due to the synchronization of their rotations at electric-field values smaller than the threshold field for the spontaneous rotation of a single particle.

Rotating hematite cube chains

2023

Recently a two-dimensional chiral fluid was experimentally demonstrated. It was obtained from cubic-shaped hematite colloidal particles placed in a rotating magnetic field. Here we look at building blocks of that fluid, by analyzing short hematite chain behavior in a rotating magnetic field. We find equilibrium structures of chains in static magnetic fields and observe chain dynamics in rotating magnetic fields. We find and experimentally verify that there are three planar motion regimes and one where the cube chain goes out of the plane of the rotating magnetic field. In this regime we observe interesting dynamics -- the chain rotates slower than the rotating magnetic field. In order to ca…

Magnetic Soft Matter: Book of Abstracts, 79th Scientific Conference of the University of Latvia, February 11, 2021

2021

Seminar chair is Professor Andrejs Cēbers. Seminar organizing committee includes Dārta Antāne, Ivars Driķis and Guntars Kitenbergs.

3D motion of flexible ferromagnetic filaments under rotating magnetic field

2020

This repository contains experimental data and numerical results related to the publication: A. Zaben, G. Kitenbergs, A. Cēbers (2020), 3D motion of flexible ferromagnetic filaments under rotating magnetic field. Soft Matter, https://doi.org/10.1039/D0SM00403K / https://arxiv.org/abs/2003.03737. Figs_data.xlsx contains the data presented in the figures. Experimental_Data.rar contains experimental images used to obtain the results for Fig. 3 and 9. The files are named with the operating frequency, field strength and filament length. Numerical.rar contains numerical results used in Fig.6, 8 and 9. The files are named with Cm values. The results are in .dat files named with Cm values follo…