Torsion Balance Research Articles

Effect of the starting azimuth uncertainty in Eötvös-torsion balance measurements

The magnitude of the impact of the incorrect setting of the starting azimuth on the gradients established by the Eotvos torsion balance was tested at two different kind of area. According to the results, gradients measured by the Eotvos torsion balance are extremely sensitive regarding the precise adjustment of the starting azimuth if the vectors of gradients are high. Furthermore, the worst deviances were experienced in the case of curvature gradients i.e. the most important gradients for geodetic use.

Partitioning Solvophobic and Dispersion Forces in Alkyl and Perfluoroalkyl Cohesion

AbstractFluorocarbons often have distinct miscibility properties compared to their nonfluorinated analogues. These differences may be attributed to van der Waals dispersion forces or solvophobic effects, but their contributions are notoriously difficult to separate in molecular recognition processes. Here, molecular torsion balances were used to compare cohesive alkyl and perfluoroalkyl interactions in a range of solvents. A simple linear regression enabled the energetic partitioning of solvophobic and van der Waals forces in the self‐association of apolar chains. The contributions of dispersion interactions in apolar cohesion were found to be strongly attenuated in solution compared to the gas phase, but still play a major role in fluorous and organic solvents. In contrast, solvophobic effects were found to be dominant in driving the association of apolar chains in aqueous solution. The results are expected to assist the computational modelling of van der Waals forces in solution.

Partitioning solvophobic and dispersion forces in alkyl and perfluoroalkyl cohesion.

Fluorocarbons often have distinct miscibility properties compared to their nonfluorinated analogues. These differences may be attributed to van der Waals dispersion forces or solvophobic effects, but their contributions are notoriously difficult to separate in molecular recognition processes. Here, molecular torsion balances were used to compare cohesive alkyl and perfluoroalkyl interactions in a range of solvents. A simple linear regression enabled the energetic partitioning of solvophobic and van der Waals forces in the self-association of apolar chains. The contributions of dispersion interactions in apolar cohesion were found to be strongly attenuated in solution compared to the gas phase, but still play a major role in fluorous and organic solvents. In contrast, solvophobic effects were found to be dominant in driving the association of apolar chains in aqueous solution. The results are expected to assist the computational modelling of van der Waals forces in solution.

A 3D model of the Wathlingen salt dome in the Northwest German Basin from joint modeling of gravity, gravity gradient, and curvature

In the past few decades, numerous attempts have been made on modeling of salt tectonics and deciphering the geometry of salt domes, which is a key challenge in petroleum exploration. We have derived a 3D density model of the Wathlingen salt dome, situated in the southern part of the Northwest German Basin from joint modeling of reprocessed torsion balance measurements. Gravity, gravity gradients [Formula: see text], curvature derived from horizontal gravity gradients [Formula: see text], and horizontal directive tendency are jointly modeled to decipher the geometric structure of the salt dome. The model was constrained by geologic and borehole information. We found that the Wathlingen salt dome is a mushroom-structured salt body, which is 14-km long, 4–8-km wide extending up to [Formula: see text] depth. The top mushroom structure of the salt is horizontally spread up to [Formula: see text]. It would not have been possible to derive the complex 3D structure from modeling of gravity data alone.

Twisted ultrathin silicon nanowires: A possible torsion electromechanical nanodevice

Nanowires have been considered for a number of applications in nanometrology. In such a context, we have explored the possibility of using ultrathin twisted nanowires as torsion nanobalances to probe forces and torques at molecular level with high precision, a nanoscale system analogous to the Coulomb's torsion balance electrometer. In order to achieve this goal, we performed a first-principles investigation on the structural and electronic properties of twisted silicon nanowires, in their pristine and hydrogenated forms. The results indicated that wires with pentagonal and hexagonal cross-sections are the thinnest stable silicon nanostructures. Additionally, all wires followed a Hooke's law behavior for small twisting deformations. Hydrogenation leads to spontaneous twisting, but with angular spring constants considerably smaller than the ones for the respective pristine forms. We observed considerable changes on the nanowire electronic properties upon twisting, which allows to envision the possibility of correlating the torsional angular deformation with the nanowire electronic transport. This could ultimately allow a direct access to measurements on interatomic forces at molecular level.

Precision torsion balance experiments and its applications

As an old and classical scientific instrument, the torsion balance was widely used in the field of precision measurement and fundamental physical experiments because of its extremely high sensitivity. In this paper, we briefly describe the basic principle of the torsion balance and the essential properties determining the accuracy of a torsion balancey experiment, and then introduce its typical applications at our laboratory, such as precision measurement of the gravitational constant <italic>G</italic> by the time-of-swing method, testing of the Newtonian gravitational inverse square law at short ranges by the dual-frequency modulation method, and measuring the upper limit on the photon mass by a rotating torsion balance.

Additivity of substituent effects in aromatic stacking interactions.

The goal of this study was to experimentally test the additivity of the electrostatic substituent effects (SEs) for the aromatic stacking interaction. The additivity of the SEs was assessed using a small molecule model system that could adopt an offset face-to-face aromatic stacking geometry. The intramolecular interactions of these molecular torsional balances were quantitatively measured via the changes in a folded/unfolded conformational equilibrium. Five different types of substituents were examined (CH3, OCH3, Cl, CN, and NO2) that ranged from electron-donating to electron-withdrawing. The strength of the intramolecular stacking interactions was measured for 21 substituted aromatic stacking balances and 21 control balances in chloroform solution. The observed stability trends were consistent with additive SEs. Specifically, additive SE models could predict SEs with an accuracy from ±0.01 to ±0.02 kcal/mol. The additive SEs were consistent with Wheeler and Houk's direct SE model. However, the indirect or polarization SE model cannot be ruled out as it shows similar levels of additivity for two to three substituent systems, which were the number of substituents in our model system. SE additivity also has practical utility as the SEs can be accurately predicted. This should aid in the rational design and optimization of systems that utilize aromatic stacking interactions.

Laboratory test of Newtonʼs law of gravity for small accelerations

The rotation curves of spiral galaxies suggest that either a considerable fraction of the galactic mass must be dark matter, or that one of Newtonʼs laws needs revision at accelerations less than . We have endeavored to search for evidence of the latter in a terrestrial laboratory. A sensitive torsion balance was employed to measure small accelerations due to gravity. No deviations from the predictions of Newtonʼs law were found down to 1 × 10−12 m s−2.

A measurement of noise created by fluctuating electrostatic charges on dielectric surfaces using a torsion balance

Future gravitational wave detectors could have their sensitivity significantly limited, at frequencies below 10 Hz, by the presence of fluctuating electrostatic charges on the dielectric surfaces of the detector optics. A confirmed observation of the effect of fluctuating charges, or charging noise, in a gravitational wave detector has still to be made and it has never been experimentally verified by any other means. This paper presents a direct measurement of the fluctuating force noise created by moving charges on a dielectric surface using a servo controlled torsion balance. The results confirm that the fluctuating force noise caused by excess charges can be best described by a Markov process with a single correlation time and has a frequency dependence of .

Experimental Study of the Cooperativity of CH−π Interactions

A series of new torsional molecular balances was designed to study the cooperativity of CH-π interaction in the solid state and in solution. The measured interaction energies correlated better to the number of participating alkyl carbons than to the number of CH-π contacts. The methyl and ethyl groups displayed additive interaction energies. However, the branched isopropyl group displayed strong positive cooperativity with higher than predicted interaction energies.

Experimental measurements and numerical simulations of the Knudsen force on a non-uniformly heated beam

Rarefied thermally-induced flows generate Knudsen thermal force on structures immersed in a gas and are significant for vacuum microbalances as well as for microsystem sensors and actuators. We study experimentally and numerically the influence of transverse thermal gradients on the Knudsen thermal force. A Peltier device provided the thermal gradient in a beam located in close proximity of a large reaction plate, whose displacement has been sensed using a torsional balance. The pressure in the vacuum chamber varied between 1 and 100 Pa giving a range of Knudsen numbers from the slip to nearly free molecular regimes, based on the gap between the beam and the movable plate. Switching polarity of the Peltier heater produces reversal of the Knudsen thermal force, from repulsive to attractive. The numerical solution of Ellipsoidal Statistical Bhatnagar–Gross–Krook (ESBGK) kinetic model of the Boltzmann equation agrees well with experimental data. The obtained non-dimensional Knudsen force coefficient, dependent on the Knudsen number, temperature ratio and the gap height to beam width aspect ratio, quantifies the magnitude of the force for a wide range of generic conditions and could be used for design and analysis of sensors and actuators exploiting this rarefied flow effect.

Precision measurement of the Newtonian gravitational constant using cold atoms.

About 300 experiments have tried to determine the value of the Newtonian gravitational constant, G, so far, but large discrepancies in the results have made it impossible to know its value precisely. The weakness of the gravitational interaction and the impossibility of shielding the effects of gravity make it very difficult to measure G while keeping systematic effects under control. Most previous experiments performed were based on the torsion pendulum or torsion balance scheme as in the experiment by Cavendish in 1798, and in all cases macroscopic masses were used. Here we report the precise determination of G using laser-cooled atoms and quantum interferometry. We obtain the value G = 6.67191(99) × 10(-11) m(3) kg(-1) s(-2) with a relative uncertainty of 150 parts per million (the combined standard uncertainty is given in parentheses). Our value differs by 1.5 combined standard deviations from the current recommended value of the Committee on Data for Science and Technology. A conceptually different experiment such as ours helps to identify the systematic errors that have proved elusive in previous experiments, thus improving the confidence in the value of G. There is no definitive relationship between G and the other fundamental constants, and there is no theoretical prediction for its value, against which to test experimental results. Improving the precision with which we know G has not only a pure metrological interest, but is also important because of the key role that G has in theories of gravitation, cosmology, particle physics and astrophysics and in geophysical models.

Dispersion-corrected DFT study of methano and ethano bridged Wilcox torsion balances

Wilcox torsion balances with well-defined “folded” and “unfolded” configurations provide a facile experimental probe of noncovalent interactions in solution. Recent modifications to the torsion balance bridgehead (Bhayana and Ams in J Org Chem 76:3594, 2011) provide new insights into the distance dependence of noncovalent interactions. We explore these systems using dispersion-corrected density functional theory calculations and continuum model solvents. The results quantify the role of bridgehead flexibility and point to the importance of folding entropy and noncovalent interactions in the unfolded configuration.

Structures and Properties of Molecular Torsion Balances to Decipher the Nature of Substituent Effects on the Aromatic Edge‐to‐Face Interaction

Various recent computational studies initiated this systematic re-investigation of substituent effects on aromatic edge-to-face interactions. Five series of Tröger base derived molecular torsion balances (MTBs), initially introduced by Wilcox and co-workers, showing an aromatic edge-to-face interaction in the folded, but not in the unfolded form, were synthesized. A fluorine atom or a trifluoromethyl group was introduced onto the edge ring in ortho-, meta-, and para-positions to the C-H group interacting with the face component. The substituents on the face component were varied from electron-donating to electron-withdrawing. Extensive X-ray crystallographic data allowed for a discussion on the conformational behavior of the torsional balances in the solid state. While most systems adopt the folded conformation, some were found to form supramolecular intercalative dimers, lacking the intramolecular edge-to-face interaction, which is compensated by the gain of aromatic π-stacking interactions between four aryl rings of the two molecular components. This dimerization does not take place in solution. The folding free enthalpy ΔG(fold) of all torsion balances was determined by (1)H NMR measurements by using 10 mM solutions of samples in CDCl3 and C6D6. Only the ΔG(fold) values of balances bearing an edge-ring substituent in ortho-position to the interacting C-H show a steep linear correlation with the Hammett parameter (σ(meta)) of the face-component substituent. Thermodynamic analysis using van't Hoff plots revealed that the interaction is enthalpy-driven. The ΔG(fold) values of the balances, in addition to partial charge calculations, suggest that increasing the polarization of the interacting C-H group makes a favorable contribution to the edge-to-face interaction. The largest contribution, however, seems to originate from local direct interactions between the substituent in ortho-position to the edge-ring C-H and the substituted face ring.

Testing the weak equivalence principle with macroscopic proof masses on ground and in space: A brief review

General relativity is founded on the experimental fact that in a gravitational field all bodies fall with the same acceleration regardless of their mass and composition. This is the weak equivalence principle, or universality of free fall. Experimental evidence of a violation would require either that general relativity is to be amended or that another force of nature is at play. In 1916 Einstein brought as evidence the torsion balance experiments by Eötvös, to 10-8–10-9. In the 1960s and early 70s, by exploiting the "passive" daily rotation of the Earth, torsion balance tests improved to 10-11 and 10-12. More recently, active rotation of the balance at higher frequencies has reached 10-13. No other experimental tests of general relativity are both so crucial for the theory and so precise and accurate. If a similar differential experiment is performed inside a spacecraft passively stabilized by 1 Hz rotation while orbiting the Earth at ≃ 600 km altitude the test would improve by 4 orders of magnitude, to 10-17, thus probing a totally unexplored field of physics. This is unique to weakly coupled concentric macroscopic test cylinders inside a rapidly rotating spacecraft.

Determination of the numerical value of the gravitational constant in the case of a complicated form of interacting bodies

An example of extending the functionality of methods for calculating the gravitational constant for the spherical shape of interacting bodies is presented. The results that were obtained using an apparatus in which the working body is in the form of quartz box are analyzed. A bad choice of the form and material of the working medium for a torsion balance in a vacuum chamber with non-equilibrium flows led to a systematic measurement error.

Feedback control of torsion balance in measurement of gravitational constant G with angular acceleration method

The performance of the feedback control system is of central importance in the measurement of the Newton's gravitational constant G with angular acceleration method. In this paper, a PID (Proportion-Integration-Differentiation) feedback loop is discussed in detail. Experimental results show that, with the feedback control activated, the twist angle of the torsion balance is limited to [Formula: see text] at the signal frequency of 2 mHz, which contributes a [Formula: see text] uncertainty to the G value.

Constraints on noncommutative spectral action from Gravity Probe B and torsion balance experiments

Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the gravitational, the electroweak and the strong forces are all described as purely gravitational forces on a unified noncommutative space-time. In this study, we infer a constraint on one of the three free parameters of the model, namely the one characterising the coupling constants at unification, by linearising the field equations in the limit of weak gravitational fields generated by a rotating gravitational source, and by making use of recent experimental data. In particular, using data obtained by Gravity Probe B, we set a lower bound on the Weyl term appearing in the noncommutative spectral action, namely β≳10−6m−1. This constraint becomes stronger once we use results from torsion balance experiments, leading to β≳104m−1. The latter is much stronger than any constraint imposed so far to curvature squared terms.

A microNewton thrust stand for average thrust measurement of pulsed microthruster

A torsional thrust stand has been developed for the study of the average thrust for microNewton pulsed thrusters. The main body of the thrust stand mainly consists of a torsional balance, a pair of flexural pivots, a capacitive displacement sensor, a calibration assembly, and an eddy current damper. The behavior of the stand was thoroughly studied. The principle of thrust measurement was analyzed. The average thrust is determined as a function of the average equilibrium angle displacement of the balance and the spring stiffness. The thrust stand has a load capacity up to 10 kg, and it can theoretically measure the force up to 609.6 μN with a resolution of 24.4 nN. The static calibrations were performed based on the calibration assembly composed of the multiturn coil and the permanent magnet. The calibration results demonstrated good repeatability (less than 0.68% FSO) and good linearity (less than 0.88% FSO). The assembly of the multiturn coil and the permanent magnet was also used as an exciter to simulate the microthruster to further research the performance of the thrust stand. Three sets of force pulses at 17, 33.5, and 55 Hz with the same amplitude and pulse width were tested. The repeatability error at each frequency was 7.04%, 1.78%, and 5.08%, respectively.

Radiative forces on macroscopic porous bodies in protoplanetary disks: laboratory experiments

In optically thin parts of protoplanetary disks photophoresis is a significant force not just for dust grains, but also for macroscopic bodies. The absolute strength on the supposedly highly porous objects is not known in detail as yet. We set up a low pressure torsion balance and studied photophoretic forces. We investigated the dependence on plate dimensions and on ambient pressure and considered the influence of channels through the plates. As samples for full (no channel) plates we used tissue with 2mm thickness and circular shape with diameters of 10mm, 30mm and 50mm. The influence of channels was probed on rectangular-shaped circuit boards of 35mm x 35mm area and 1.5mm thickness. The number of channels was 169 and 352. At low pressure, the absolute photophoretic force is proportional to the cross section of the plates. At high pressure, gas flow through the channels enhances the photophoretic force. The pressure dependence of the radiative force can (formally) be calculated by photophoresis on particles with a characteristic length. We derived two characteristic length scales l depending on the plate radius r_1, the channel radius r_2, and the thickness of the plate which equals the length of the channel d as l=r^{0.35} x d^{0.65}. The highest force is found at a pressure p_max = 15 x l^{-1}Pa mm. In total, the photophoretic force on a plate with channels can be well described by a superposition of the two components: photophoresis due to the overall size and cross section of the plate and photophoresis due to the channels, both with their characteristic pressure dependencies. We applied these results to the transport of large solids in protoplanetary disks and found that the influence of porosity on the photophoretic force can reverse the inward drift of large solids, for instance meter-sized bodies, and push them outward within the optically thin parts of the disk.