Effective Geometry Parameter Research Articles

Empirical Calibration of a Cylindrical Ion Trap for Mass-Selected Gas-Phase Fluorescence Spectroscopy.

The ion motion in a quadrupole ion trap of hyperbolic geometry is well described by the Mathieu equations. A simpler cylindrical ion trap has also gained significance and has been used by us for fluorescence-spectroscopy experiments. This design allows for the easy replacement of the end-cap with a mesh, enhancing the photon collection. It is crucial to obtain a firm understanding of the ion motion in cylindrical ion traps and their capability as mass spectrometers. We present here an empirical method of calibrating a cylindrical ion trap based on fluorescence detection. This can be done nearly background-free in a pulsed experiment. The ions are located at the center of the trap, where the field is primarily quadrupolar, and here an effective Mathieu description is found through an effective geometry parameter. In spectroscopy experiments, high buffer-gas pressures are needed to efficiently cool the ions, which complicates the ions' motion and hence their stability. Still, simulations show that the stability diagram closely aligns with the Mathieu diagram, albeit shifted due to collisions. We map the stability diagram for six molecular ions by fluorescence collection from four cations and two anions spanning m/z from 212 to 647. The stability diagram is parametrized through the Mathieu functions with an m/z-dependent effective geometry parameter and a q-dependent shrinkage of the diagram. Based on the calibration, we estimate the mass resolution to be +7/-3 Da for ions with masses in the hundreds of Da.

Temperature-dependent optical properties of some mixtures nematic liquid crystal

The presence of optical anisotropy in liquid crystals (LCs) has caused these materials to have dual refractive indices: ordinary (no) and extra-ordinary (ne). Many fundamental information about LCs can be found by looking at these refractive indices. In this work, the refractive indices of four mixtures nematic liquid crystal (NLC) have been studied as a function of temperature, and the relevant functions were then calculated. Subsequently, the order parameter of mentioned LCs was determined using three methods: Vuks, Haller, and the effective geometry parameter method. It was concluded that the obtained values are not significantly different and exhibit the same temperature dependence. The obtained results were evaluated in relation to the approach utilized.

Temperature effects on optical parameters of liquid crystal binary mixtures exhibiting induced smectics phases

Temperature dependent optical properties like birefringence, temperature gradients of refractive indices, molecular polarizabilities, effective geometry parameter, order parameter and cross over temperatures have been investigated for nine different liquid crystal mixtures. These mixtures are prepared by mixing two pure nematic liquid crystal compounds, namely, 4-n-pentyl phenyl 4-n′-hexyloxybenzoate (ME6O.5) and 4-cyanophenyl 4′-n-pentyl benzoate (CPPB) where, ME6O.5 is a monotropic compound and CPPB is an enantiotropic compound. The mixtures however are found to be exhibit induced smectic phases. The theoretical fitting values obtained by using Hallers’ extrapolated method of birefringence values agree quite well with the experimental values. It is observed that the normalized polarizability behaves exactly as refractive indices when it is plotted against temperature. The effective geometry parameter (αeg) of the mixture having highest birefringence shows highest value of αeg at certain temperature. Finally, order parameters of the mixtures have been calculated using five different techniques and for all mixtures the order parameters shows characteristics range from 0.3–0.9. The abrupt changes in order parameter before nematic phases are due to the existence of the induced smectic phases in the liquid crystal mixtures.

Optical Properties of Liquid Crystalline Alkoxy Benzoic Acids with Dispersed Citrate-Capped Gold Nanoparticles

Abstract Citrate-capped gold nanoparticles (Gnps) have multiple applications in all optical devices and influence the properties of birefringence in liquid crystalline (LC) molecules. In the present paper, systematic studies have been carried out on LC compounds p-n-undecyloxy benzoic acid (11oba) and p-n-dodecyloxy benzoic acid (12oba) with dispersed citrate-capped Gnps in different low molar concentrations. The phase transition temperatures of the LC nanocomposites obtained from polarizing thermal microscopy (POM), differential scanning calorimetry (DSC) and modified spectrometry are found to be reduced with the increase in concentration of dispersed citrate-capped Gnps. The information was obtained from textural data utilizing the simple technique gradient measurement of standard deviation (GMSD) using the MATLAB tool, which is analogous to DSC. Further, the existence of citrate-capped Gnps in 11oba and 12oba was determined by spectroscopic techniques like ultraviolet-visible spectrometry and scanning electron microscopy. The birefringence measurements were carried out at different wavelengths (460, 500, 570 and 635 nm) using a wedge-shaped cell with a modified spectrometer. The birefringence (δ n) increases with increase in weight concentration of citrate-capped Gnps in the nematic thermal range. Further, the order parameter S values obtained from the Kuczynski internal field model, the Vuks model, the Haller extrapolation model and the effective geometry parameter methods are in good agreement. It is found that the order parameter S increases with increase in dispersion of concentration of citrate-capped Gnps. This is due to strong Van der Waal’s interaction between the LC molecules and citrate-capped Gnps, which increases the alignment of the LC molecules.

A Plant Leaf Geometric Parameter Measurement System Based on the Android Platform.

Automatic and efficient plant leaf geometry parameter measurement offers useful information for plant management. The objective of this study was to develop an efficient and effective leaf geometry parameter measurement system based on the Android phone platform. The Android mobile phone was used to process and measure geometric parameters of the leaf, such as length, width, perimeter, and area. First, initial leaf images were pre-processed by some image algorithms, then distortion calibration was proposed to eliminate image distortion. Next, a method for calculating leaf parameters by using the positive circumscribed rectangle of the leaf as a reference object was proposed to improve the measurement accuracy. The results demonstrated that the test distances from 235 to 260 mm and angles from 0 to 45 degrees had little influence on the leafs’ geometric parameters. Both lab and outdoor measurements of leaf parameters showed that the developed method and the standard method were highly correlated. In addition, for the same leaf, the results of different mobile phone measurements were not significantly different. The leaf geometry parameter measurement system based on the Android phone platform used for this study could produce high accuracy measurements for leaf geometry parameters.

Optical and dielectric parameters of a laterally difluorinated phenylbicyclohexane liquid crystalline compound

The temperature variation of the refractive indices in the nematic range of a laterally difluorinated phenylbicyclohexane liquid crystalline compound was determined using the thin prism technique. Birefringence and effective geometry parameter of this LC compound was calculated from the measured refractive indices. Using a four-parameter model, the temperature variation of the refractive indices and birefringence was theoretically fitted. The compound is found to have low value of birefringence and high value of effective geometry parameter. Using refractive index data, three different methods were used in this work to obtain temperature dependence of order parameter, namely Vuks’ method, Haller approximation method, and method based on effective geometry parameter. All of them show the same trend. The temperature variation of dielectric permittivities of the compound was done at frequency 1 kHz by an LCR meter. The temperature variation of dielectric anisotropy of the compound was calculated from the experimentally measured values of dielectric permittivities. The compound shows moderate negative dielectric anisotropy.

Study of effective geometry parameter, order parameter, temperature gradients and crossover temperatures of three nematic liquid crystals having highly different clearing temperature

The temperature dependent properties of three liquid crystals (LC) namely effective geometry parameter, order parameter and temperature gradients of refractive indices of two fluorinated isothiocyanato nematic liquid crystal (NLC) compounds 4′-pentylcyclohexyl-3,5-difluoro-4-isothiocyanatobiphenyl, 4'−butylcyclohexyl−3, 5− difluoro− 4− isothiocyanato-biphenyl of high clearing temperature (TC) and low TC LC compound 4 (trans-4/-n-hexycyclohexyl) isothiocyanatobenzene (6CHBT) have been studied. In this paper, the effective geometry parameters of the three LC compounds are calculated. The order parameters of three LC compounds are also calculated from the effective geometry parameter. From the available data, it is found that the two fluorinated NLC compounds exhibit moderately high value of birefringence (∼0.24–0.26) and 6CHBT exhibits a lower value of birefringence (∼0.16). From the study, it is found that the order parameter is found to be higher in higher birefringence and higher TC LC compounds. The values of temperature gradient of ordinary refractive index (dno/dT) are found to be showing negative to positive value while increasing temperature which gives the crossover temperature (TCO). The crossover temperature has been calculated from the temperature gradient at the value (dno/dT) = 0. LC compounds with lower TC are found to have larger TCO value which gives narrower temperature between TCO and TC. The TCO value of compound having larger alkyl group is found to be smaller. The Lorentz field factors for both compound are also reported which can be used for order parameter calculation by different aspects.

Optical anisotropy, order parameter and its critical behavior in temperature-dependent refractive indices of nematic liquid crystals

The temperature dependence of optical birefringence, order parameter, effective geometry parameter, and normalized polarizability was determined for nematic liquid crystal mixtures by measuring the refractive indices. The effects of the adjustable parameters obtained from temperature-dependent refractive indices were analyzed appropriately for the crossover temperature and order parameter values. Besides, a four-parameter power law expression method was used for the optical birefringence measurement to address inappropriate fits in the weak first-order phase transition region. From this method, the effective second order phase transition temperature T⁎⁎ was determined by showing the slightly higher values than phase transition temperature. The value of the order parameter critical exponent λ obtained from this method showed a good agreement with the mean field theory by demonstrating closeness to the tricritical hypothesis (β = 0.25). As a consequence, the measurement of the temperature-dependent optical birefringence was successfully verified the pre-transitional phenomena accurately, and it can facilitate an insightful description of that region.

Order parameter and crossover temperature from temperature-dependent refractive indices for low birefringence liquid crystals

Abstract The temperature dependencies of three low birefringence ( ∆n ) liquid crystals (LCs) at similar clearing temperatures ( T NI ) were investigated to characterize the order parameter S ( T ) and crossover temperature ( T co ). Three different methods were used to determine the S ( T ) property, including the Vuks model, the Haller approximation model, and a model based on the effective geometry parameter ( α eg ). In our low ∆n LCs with relatively analogous T NI , three parameters ( B , ( ∆n ) o , and β ) that originated from the modified four-parameter model were analyzed to increase the T co condition. A larger absolute value for the B parameter and a smaller β parameter were also needed to reduce the temperature dependence of ∆n . In particular, a lower ( ∆n ) o value was found to be beneficial for increasing the T co value, which resulted in a higher T co value for the low ∆n LCs, compared with that of a high ∆n LC with a similar T NI value. This led to a narrower temperature range between T co and T NI for the low ∆n LCs compared to that of the high ∆n LC, which could result in appropriate temperature properties for LCs for practical display applications, including a lower temperature dependence of ∆n and wider operational temperature regime.

Birefringence and temperature-gradient refractive index study of a laterally Fluorinated Terphenyl LC compound.

The temperature behaviour of the refractive indices in the nematic range of a laterally fluorinated terphenyl LC compound, viz, 2,3-difluoro-I,4 bis(4’,4”-dipropyl phenyl) benzene was determined using the thin prism experiment. Birefringence of this LC compound was calculated from the measured refractive indices. Using the four parameter model, the temperature variation of the refractive indices and birefringence were theoretically fitted. The compound is found to have high value of birefringence. The temperature gradients of refractive indices i.e, and dne/dT and dne/dT were determined, as a result, a cross over temperature was also found.The values of order parameter were obtained in two ways one by direct calculation using the effective geometry parameter αeg. and the other by using the modified Vuks’ method. Both show the same trend. It has been observed also αeg changes almost linearly with the birefringence.

Thermotropic, refracting and birefringent properties in homogeneous mixtures of 4-n-alkyl-4′-cyanobiphenyl mesogens

In this work, studies of the thermotropic and thermo-optical properties in five homogeneous mixtures of 4-n-alkyl-4′-cyanobiphenyl mesogens have been carried out. Temperature behavior of the mean refractive index n, ordinary no and extraordinary ne refractive indices has been investigated. The principal polarizabilities α0 and αe, effective geometry parameter αeg and average polarizability αave were calculated using the internal field model (Vuks approach). Behavior of the birefringence Δn and the anisotropy of polarizability Δα as a function of temperature, and the order parameter in regions of the smectic A–nematic, nematic–isotropic liquid and smectic A–isotropic liquid phase transitions are discussed.

Temperature variation of effective geometry parameter, αg, refractive indices and the determination of orientational orders in three room temperature nematic liquid crystal mixtures

ABSTRACTOrientational order parameter, S and effective geometry, αg are calculated from the refractive index in three nematic room temperature liquid crystal mixtures, blOO3, blOO6, and blO38. The method due to Kuczynski et al. used to determine S from birefringence. The effective geometry parameter is αg = no/ne. (no and ne are the ordinary and extraordinary refractive indices of the liquid crystal material.) The behavior of αg as a function of temperature and order parameter has also been reported. The S value calculated from αg is identically equal to the value obtained from Kuczynski et al method, i.e., from birefringence, δn. Finally, dne/dT and dno/dT are obtained and the crossover temperatures, TCO the characteristic temperature, which is in fact the temperature of minimum in the ordinary index of refraction in three mixtures for different wavelengths are calculated from dno/dT.

Orientational order parameter, S, in N-(p-n-ethoxy benzylidene)-p-n-alkoxy anilines, 2O.Om LC compounds

The orientational order parameter, S, is estimated in N-(p-n-ethoxy benzylidene)-p-n-alkoxy anilines, 2O.Om liquid crystalline (LC) compounds with alkoxy chain number, m = 3, 4, and 6–10 using four different methods. The methods employed are (1) from birefringence, where ne and no are extraordinary and ordinary refractive indices, (2) from effective geometry parameter, αg, where α = no/ne, (3) from the Haller approximation (1 − T/TNIβ where β is obtained from method (1), and (4) the Maier and Saupe method from density. In the four methods proposed no field is chosen to explain the nematic liquid crystal and provides the S values obtained are identical to one another except in the case of 2O.O9 compound where the S values are higher when compared to the others. All the methods are explained in detail.

Thermotropic, refracting and thermo-optical properties in three homologs of 4-n-alkyl-4’-cyanobiphenyls

Investigations of temperature behaviour of the mean refractive index n, ordinary no and extraordinary ne refractive indices, and birefringence Δn have been carried out for three homologues of 4-n-alkyl-4’-cyanobiphenyls (n = 8, 10, 12). The principal polarizabilities α0 and αe, effective geometry parameter αeg and average polarizability αave have been calculated using the isotropic internal field model (Vuks approach). Temperature behaviour of the order parameter in regions of the smectic A–nematic, nematic–isotropic liquid and smectic A–isotropic liquid is discussed. All of the optical and orientational parameters, which have been obtained in this work, are in good agreement with the theoretical approach.

Orientational order in three nO.m liquid crystalline compounds

Refractive index and density measurements have been carried out on three nO.m liquid crystalline compounds, namely, 4O.2, 4O.3 and 1O.10 belonging to the N-(p-n-alkoxybenzylidene)-p-n-alkylaniline series. From the data, the orientational order parameter has been estimated using Vuks and Neugebauer local field models. Furthermore, the orientational order parameter has been calculated directly from refractive index data employing the Vuks scaling factor method, Neugebauer f(B) parameter, effective geometry parameter and a method proposed by Kuczyński et al. It is observed that order parameter values estimated from different methods agree well near the nematic–isotropic transition and diverge as the nematic phase attains equilibrium. The temperature gradient of refractive indices and the nematic crossover temperatures have also been estimated for these compounds. The results obtained are compared and discussed.

Orientational order parameter studies on 3.Om and 3O.Om liquid crystals

Orientational order parameter S is evaluated in the nematic phase of six liquid crystal compounds, N-(p-n-propyl benzylidene)-p-n-alkoxy anilines, 3.Om and N-(p-n-propyloxy benzylidene)-p-n-alkoxy anilines, 3O.Om compounds with m = 6, 7 and 8, using different methods. The techniques employed are S from birefringence δn, Haller's approximation from (1−T/Tc) β, effective geometry parameter αg and Vuks’ scaling factor SC. The values of S obtained using the above methods are compared with one another and with the results on a number of liquid crystals; the liquid crystals favor isotropic Vuks’ method.

A simple method to determine high-accuracy refractive indices of liquid crystals and the temperature behavior of the related optical parameters via high-resolution birefringence data

We report new high-resolution experimental data for the optical birefringence over the temperature range spanning the nematic (N) and smectic A (Sm A) phases of various liquid crystals (LCs) by means of a rotating-analyzer method. In this work we proposed a simple procedure to determine high-accuracy extraordinary (ne) and ordinary (no) refractive indices of LCs both in the N and Sm A phases based on the birefringence measurements. We then show that, apart from the birefringence data, the procedure needs only a single value for the refractive index which is the value of that in the isotropic (I) phase just above the N–I transition temperature. The consistency of our approximation has been checked under the framework of the Vuks model using the criteria found in the literature. We then conclude that our proposal is self-consistent for obtaining the extraordinary and ordinary refractive indices of LCs with high accuracy and seems to be readily applied as compared to the other methods reported to date and also that temperature variation of ne and no refractive indices is well portrayed by the fit expression presented here for the first time contrary to the Haller extrapolation method. Furthermore, we then show that, without addressing density measurements, the proposed method allows one to obtain the temperature dependence of normalized molecular polarizabilities for extraordinary and ordinary rays, and the effective geometry parameter αeg. It has been observed that αeg changes linearly with the order parameter and the same slope value has been obtained for all investigated samples, which can be ascribed to the global behavior of the nematic phase, which has been reported most recently.

Estimation of order parameter from different models in symmetric dimeric liquid crystals

The birefringence measurements with the temperature are carried out employing the wedge technique at the wavelength λ = 5893Å on symmetric dimeric liquid crystalline compounds of α,ω-bis(4-alkylanilinebenzylidene-4′-oxy) alkanes which are popularly known as m.OnO.m’s with m = 3, 4 and 5 and spacer length n = 8, 9 and 10. The studied compounds are mono variant with long range of nematic phase. The birefringence data δn = (ne–no) along with the density results are employed to estimate the molecular polarisabilty anisotropy, δα = (αe–αo) assuming a particular local field (due to Vuks and Neugebauer) the nematic molecule experiences and the order parameter S is estimated from δα and Δα, i.e., polarisabilty anisotropy which is estimated employing different methods. Further, S can also be obtained from Kuczynski model and also using the effective geometry parameter, αg. Further, it is observed that from our analysis the S value obtained from Δn and αg are identical. The results are analysed and compared with the data available in the literature.

Texture transformations and thermo-optical properties of nematic mesogen at nematic–isotropic liquid phase transition

Study of the thermo-morfologic, thermotropic and thermo-optical properties of monomorphic nematic mesogen has been carried out. Temperature behavior of the mean the refractive index n, ordinary no and extraordinary ne refractive indexes, and birefringence Δn have been investigated. The principal polarizabilities α0 and αe, effective geometry parameter αeg, average polarizability αave and polarizability anisotropy Δα were estimated. Peculiarities of the biphasic regions of the direct nematic mesophase–isotropic liquid and inverse isotropic liquid–nematic mesophase have been investigated.

Temperature and Wavelength Dependence of Effective Geometry Parameter and a Comparative Study of Orientational Order

Temperature and wavelength dependence of effective geometry parameter, the ratio of ordinary and extraordinary refractive indices, is reported. A modified four-parameter model and the Cauchy equations are opted to explain the temperature and wavelength dependence of effective geometry parameter, respectively. Additionally, the order parameter variation of effective geometry parameter is also studied. Influence of effective geometry parameter on the deflection of light by the liquid crystal compounds is also discussed. Different methods for the determination of order parameter from the optical data are compared. The order parameter is determined by using the birefringence, Vuks, and Neugebauer methods. The fitting results, obtained by the application of four-parameter model and Cauchy equations, are validated using the experimental data available in literature. A fine agreement is obtained between the experimental data and fitting results.