Simple Linear Plot Research Articles

Determination of the pKa and Concentration of NMR-Invisible Molecules and Sites Using NMR Spectroscopy.

NMR spectroscopy is a very powerful tool for measuring the dissociation constants (pKa) of molecules, requiring smaller quantities of samples of lower purity relative to potentiometric or conductometric methods. However, current approaches are generally limited to those molecules possessing favorable pH-dependent NMR properties. Typically, a series of 1D experiments at varying pH are performed, and the pKa is obtained by fitting the observed chemical shift of the analyte as a function of pH using nonlinear routines. However, the majority of polymers, biomolecules, and inorganic species do not present favorable NMR resonances. Either the resonances are not observable or too broad, or the unambiguous interpretation of the NMR data is impossible without resorting to complex 2D experiments due to spectral overlap. To overcome these fundamental limitations, we present a method to obtain the pKa values and concentrations of acidic species without their direct observation by NMR. We instead determine the quantity of acidic protons removed from the species along a concentration gradient of an organic base in a single 1H chemical shift imaging experiment that can be run under automation. The pKa values are determined via simple linear plots, avoiding complex and potentially unreliable nonlinear fitting routines.

History, Cultural Memory and Intermediality in Radu Jude’sAferim!

AbstractA historical drama that can be interpreted at the juncture of theoretical discourses (heritage film, auteur film), genres (historical film, western, road movie) and representational modes (connecting to, but subverting the master narrative of Romanian historical cinema), Radu Jude’sAferim!(2015) has attracted the attention of the international public by the unique response that it gives to the tradition of representation of the (Romanian) historical past. Its unmatched character even within New Romanian Cinema can be attributed to the fact that it does not focus on tensions of the post-communist condition or their antecedents in the recent communist past; instead, it goes back in history to a much earlier period, to the Romanianancien régime, after the Ottoman occupation and before the abolition of Gypsy slavery, only to point at the historical roots of current social problems. Through its ingenuous (inter)medial solutions (black-and-white film, with an implied media-archaeological purport; periodmise en scènebut with an assumed artificiality and constructedness; a simple linear plot infused with a dense dialogue in archaic Romanian, drawn from a multitude of literary and historical sources; a sweeping panorama of 19th-century Wallachian society presented in a succession oftableaucompositions), Radu Jude’s ironical-critical collage defetishizes the traditional historical iconography and debunks the mythical national imaginary, unveiling the traumatic history of an ethnic and racial mix.1

The Interaction of Bioactive Peptides with an Immobilized Phosphatidylcholine Monolayer

The interaction of three bioactive peptides, bombesin, β-endorphin, and glucagon with a phosphatidylcholine monolayer that was immobilized to porous silica particles and packed into a stainless steel column cartridge, has been studied using dynamic elution techniques. This immobilized lipid monolayer provides a biophysical model system with which to study the binding of peptides to a lipid membrane. In particular, the influence of temperature and methanol concentration on the affinity of each peptide for the immobilized lipid surface was assessed. For all test peptides, nonlinear retention plots were observed at all temperatures that contrasted sharply with the simple linear plots observed for the small unstructured control molecules N-acetyltryptophanamide and diphenylalanine. An analysis of the thermodynamics of the interaction of peptides with the immobilized monolayer was also carried out. The results revealed that while the peptides interacted with the monolayer predominantly through hydrophobic interactions, the relative contribution of ΔH assoc O and ΔS assoc O to the overall free energy of association was dependent on the temperature and methanol concentration. In particular, it was evident that under most conditions, the binding of the peptides to the immobilized lipid monolayer was enthalpy-driven, i.e., mediated by nonclassical hydrophobic interactions. Significant band-broadening and asymmetric and split peaks were also observed for bombesin, β-endorphin, and glucagon at different temperatures and methanol concentrations. These changes in affinity and peak shape are consistent with the formation of multiple conformational species during the interaction of these peptides with the lipid monolayer. In addition, the binding behavior of the three test peptides on an n-octylsilica surface that lacked the phospho headgroups of the phospholipid was significantly different from that observed with the immobilized phosphatidylcholine surface, indicating a specificity of interaction between the peptides and the lipid surface. Overall, these experimental results demonstrate that the biomimetic phosphatidylcholine monolayer provides a stable and sensitive system with which to explore the molecular mechanism of peptide conformational changes during membrane interactions.

The Electronic Absorption Spectrum of Molecular Iodine: A New Fitting Procedure for the Physical Chemistry Laboratory

This paper presents a different approach to the data treatment for the electronic absorption spectrum of molecular iodine, a standard experiment in the undergraduate physical chemistry laboratory. Traditionally, students analyze the transitions originating from the υ' ' = 0 level using a Birge-Sponer plot and thereby determine the various molecular constants and energies. Our treatment involves simply fitting the transition frequencies to a second-order polynomial. This fit then yields a direct determination of the important molecular constants along with the various energy terms. With the availability of common graphing programs such as Excel, Kaleidagraph, and SigmaPlot, students can take advantage of more advanced fitting techniques and no longer have to rely on simple linear plots. Additionally, students find this new approach more satisfying and we believe it has pedagogical advantages over the Birge-Sponer treatment.

Elastoplastic trouser tear testing of sheet materials

An elastoplastic analysis of trouser tear testing is presented and differences from the Mai-Cotterell rigid-plastic analysis [1] are highlighted. In particular, the simple linear plot of the latter for tearing force per unit thickness against leg width proves to be a curve with a lower intercept for fracture toughness, since the radius of tearing increases with leg width. Furthermore, the curve passes through a maximum and the tearing force decreases at very large leg widths owing to the effects of elasticity. Experiments on NS4 aluminium alloy and on 64/36 brass sheet (including the effects of anisotropy) confirm these results.

Thermodynamics of coupled reactions by the method of dynamic titration: the Nickel(II)-salicylate ion system

Amplitudes of chemical relaxation signals can provide useful information as to the thermodynamics of coupled chemical reactions. The temperature-jump technique has been used to investigate the thermodynamic behavior of the Nickel(II)-3,5-dinitrosalicylate system in buffer solution, where complex formation steps are coupled to proton transfer steps. The analysis of the relaxation curves is based on the transformation of a set of coupled elementary reactions into a set of uncoupled ‘normal reactions.’ By analogy with classical titrations, the experiments have been performed by changing the metal ion concentration at constant ligand concentration and pH. Each measured amplitude is associated in this way to a point of a ‘dynamic titration’ and a procedure is formulated by which the values of the equilibrium constants and enthalpies of the normal reactions are simultaneously obtained by simple linear plots. From the dependence of these parameters on suitable functions of the concentrations of the reactants the values of ΔG° and ΔH° of the individual steps are derived. It is shown that the addition of a buffer (instead of an indicator) influences the stoichiometric coefficients of the normal reaction in such a way that measurable amplitudes are produced in systems that, as the presently investigated, in unbuffered solution would remain insensitive to the external perturbation. The circumstances under which the dynamic method offers advantages over the classical techniques are discussed.

The trousers tearing test with ductile metal sheets

A general elastoplastic analysis for the tearing of sheet materials is applied to the well-known “trousers tearing test” which is used to determine R, the specific work of fracture (the fracture toughness), of materials. It is shown that the Cotterell-Mai rigid-plastic analysis for the testpiece [3] has to be modified to take account of differences in local sheet curvature at the tear tip. In consequence, their simple linear plot (back extrapolation of which gives the toughness R) is really a curve with a lower intercept giving the true toughness according to our model. Differences are also revealed at large widths of torn material, where the normalised pulling force at constant R decreases. Experiments over a wide range of tear widths confirm the analysis and also explain why the linear plot of the earlier Cotterell-Mai analysis appeared to be satisfactory.

A SIMPLE METHOD OF DETERMINING PORE AND SURFACE DIFFUSIVITIES IN ADSORPTION STUDIES

In this paper, a new graphical method of determining pore and surface diffusivities in adsorption systems is presented. The method involves only a simple linear plot of the inverse of half time of adsorption versus a concentration factor. The pore diffusivity and the surface diffusivity are determined directly from the intercept and the slope of the straight line, respectively. Experimental data of n-butane on Ajax activated carbon are used to illustrate the potential application of this new technique in the diffusivity parameter determination.

On the mechanics of guillotining ductile metals

Guillotining is the cropping of offcuts from plates using an inclined blade and the action is a steady-state composite of the actions occurring progressively in orthogonal bar shearing. Deformation patterns under the blade are discussed and forces, displacements and work inputs are investigated in terms of rigid-plastic fracture mechanics. The major work inputs concern shear and fracture in the plane of the cut face, and bending of the offcut to the inclination of the blade; other work inputs (e.g. for offcut twist and friction) may be neglected. Simple relations for cropping force versus offcut width are derived and confirmed by experiment. The effective fracture toughness (including work of flow) in the plane of cut, and the flow stress of the material may be determined from a simple linear plot of guillotining force versus offcut overhang width.

On the mechanics of guillotining ductile metals

Guillotining is the cropping of offcuts from plates using an inclined blade and the action is a steady-state composite of the actions occurring progressively in orthogonal bar shearing. Deformation patterns under the blade are discussed and forces, displacements and work inputs are investigated in terms of rigid-plastic fracture mechanics. The major work inputs concern shear and fracture in the plane of the cut face, and bending of the offcut to the inclination of the blade; other work inputs (e.g. for offcut twist and friction) may be neglected. Simple relations for cropping force versus offcut width are derived and confirmed by experiment. The effective fracture toughness (including work of flow) in the plane of cut, and the flow stress of the material may be determined from a simple linear plot of guillotining force versus offcut overhang width.

Substituent Effects. XX. Highly Electron-Deficient Carbocation Solvolyses

Abstract The solvolysis rates of 1-aryl-2,2,2-trifluoroethyl tosylates (1-OTs) and m-nitrobenzenesulfonates (1-ONs) were determined conductometrically in aqueous ethanol and aqueous TFE. While the Brown ρ+σ+ equation does not give a simple linear plots, but a remarkably split pattern, there is a linear free energy relationship between the solvolyses of 1-OTs and 1-aryl-1-(trifluoromethyl)ethyl tosylates (2) with a slope of unity over a wide range (108 in reactivity) of substituents from p-MeO to unsubstituted derivatives. The substituent effect on the solvolysis of 1 should be closer to that on the solvolysis of 2, rather than to the σ+ substituent effect. The ρ value for this system was estimated to be identical to the value of −6.3 assigned for 2, and the r value in the LArSR correlation to be comparable with or even higher than the r=1.4 of 2. The enhanced r value of this system must be caused from a strong destabilization of the transition state by the α-CF3 substituent. Extremely high ρ+ values have recently been pointed out for many solvolyses generating highly electron-deficient carbocations; however, in no case is the ρ+ value equally high for the electron-attracting region of the substituent. In fact, they all resulted in significantly concave σ+ plots, suggesting a mechanistic transition. All of the conflicts must be attributed to the inadequacy of the simple application of σ+. The use of the Brown σ+ scale must be the only cause of a curve break in the correlation plot of such a system having a significantly different resonance demand.

Substituent Effects. XXI. Solvolysis of Benzyl Tosylates

Abstract The rates of solvolyses of a series of substituted benzyl tosylates were determined in 80% aqueous acetone, and the substituent effect was analyzed based on the Yukawa–Tsuno LArSR Eq. The LArSR Eq. as well as Hammett–Brown treatment failed to give any simple linear plot for the effect of the full range of substituents, indicating a significant mechanistic shift. The σ+ plot gave a split pattern of parallel curvatures with significant gaps for strong π-donors, weak π-donors, and non-conjugative substituents, respectively. The widely split σ+ plot conflicts with the accepted interpretation in terms of the kc–ks mechanistic transition, since the kc–ks mechanistic change should result in a single smooth-curved plot, only if plotted against an appropriate substituent constant scale. The plots of para π-donors against an appropriate \barσ scale with r=1.3 coalesced into a single smooth curve including the meta correlation curve. A sufficiently linear LArSR plot with r=1.3 for the reactive substituents down to 4-MeS-3-CN group can be referred to the substituent effect correlation for the kc mechanism of this system. The result of a correlation analysis confirmed this conclusion, giving a best ρ value of −5.23 and an r value of 1.28 for a range of substituents more activating than 4-MeS-3-CN. The r value for the kc solvolysis of activated range of substituents was found to be identical with the r value obtained for the gas-phase stability of benzyl cation. The enhanced resonance demand (r=1.28) obtained in the benzyl solvolysis must be an intrinsic feature characterizing the nature of the transition state of kc solvolysis of benzyl tosylate, rather than a correlational artifact of the nonlinearity caused from mechanistic complexity.

Substituent Effects. XIX. Solvolysis of 1-Aryl-1-(trifluoromethyl)ethyl Tosylates

Abstract The rates of solvolysis of 1-aryl-1-(trifluoromethyl)ethyl tosylates were determined in 80% aqueous ethanol for a series of substituents. The Brown ρ+σ+ treatment fails to give a simple linear plot, but all the p-π-donors deviate upward from the meta-correlation line. On the other hand, the Yukawa–Tsuno LArSR Eq. gives a linear correlation over the whole range of substituents, log(k⁄k0)=−6.287(σ°+1.388Δ\barσR+), with excellent precision. Strong destabilization of the carbocation intermediate by α-CF3 appears to be reflected only in the extremely high r value, but not in the ρ value of the substituent effect. This conflicts seriously with the conclusion in the literature given for this reaction based on a simple Brown σ+ treatment. This reaction, having an extremely high resonance demand r=1.4, should be far beyond the scope of the simple Brown σ+ analysis. Varying resonance demand should be a basic requirement for adequately describing the substituent effect regarding conjugative carbocation reactions.

Shear-thinning of ‘random coil’ polysaccharides: Characterisation by two parameters from a simple linear plot

The shear-thinning behaviour of solutions of conformationally disordered (‘random coil’) polysaccharides, at concentrations above the onset of coil-overlap and entanglement (i.e. above c∗), can be matched, with reasonable precision, by the equation: η=η= 0⧸[1 + ( λ λ 1 2 ) 0.76] Thus viscosity (η) at any shear rate (γ) can be characterised by two parameters: the maximum ‘zero-shear’ viscosity ( η 0) and the shear rate ( γ ̇ 1 2 ) at which viscosity is reduced to η 0 2 . The values of η 0 and γ ̇ 1 2 can be derived from, respectively, the intercept and slope of a simple linear plot of η versus η γ ̇ 0·76 . The method can also be applied to other ‘random coil’ polymers of reasonably high polydispersity, and to the analysis of the frequency (ω) dependence of dynamic viscosity (η∗) from small-deformation oscillatory measurements.

Two kinetic methods to study the regulation of mammalian hexokinases

Two new kinetic analyses for mammalian hexokinases are presented, which permit one to study the regulation of these enzymes by product inhibition. One method uses the pyruvate kinase-coupled assay and the other the glucose-6-phosphate dehydrogenase-coupled assay. Both methods give simple linear plots, which indicate that the magnesium-ATP complex overcomes the glucose 6-phosphate inhibition competitively, but by atypical kinetics. A new regulation coefficient ( K r ) was defined and it was shown that, with both assay methods, the reciprocals of the slopes of the simple linear plots are proportional to K r ·[Mg·ATP]. NADP, but not NAD, was found to be a powerful inhibitor of pig heart hexokinase.

Analysis of a batch adsorber with rectangular adsorption isotherms

This paper deals with an analysis of a batch adsorber with a rectangular adsorption isotherm (i.e., a system operating at the flat part of a Langmuir isotherm). This situation is common in many systems of adsorption of organic solutes from aqueous solution onto activated carbon. The theoretical solutions reveal that the transport parameters, the effective diffusivity and the external mass transfer coefficient, can be easily extracted from two simple linear plots. Two systems of adsorption of phenol onto activated carbon and Victoria Blue dye onto activated carbon are employed to demonstrate the versatility of the theoretical solutions.

Determination of km and De from a one‐shot experiment of enzyme immobilization

Although, the quadrature-form solution of immobilized enzyme penetration depth was given in the work of Do', the integral in the LHS of eq. ( 1 ) is possible and is given in the appendix. The purpose of this communication is to show that two important dynamic parameters, k, and D, , can be determined very easily via two simple linear plots using the one-shot experiment of immobilization of enzyme into porous solid supports. The information that one can get from experiments is the data of Eb vs. real time, t. As we shall show below, the external mass transfer coefficient, k, , can be determined from the initial data of Eb vs. time and the effective diffusivity of enzyme, D,, can be determined from the full transient data of Eb vs. time.

Memory mechanisms and the psychophysical scaling of duration.

Two experiments were performed to examine the suggestion that underlying memory mechanisms may be revealed in the form of the psychophysical function for duration. In experiment 1 a broad range of durations, with fine spacing at the lower end, was employed to bring out any transition in function that might reflect a change from 'ionic' memory to short-term memory. Estimation in conventional time-units (Verbal Estimation) was also compared with unit-free estimation (Magnitude Estimation). In experiment 2 Verbal Estimation was compared with the Production method, for a different range of stimulus values, and with varying interval content. Contrary to earlier claims, memory mechanisms were not found to be reflected in the values of power exponents for subjective duration. The value of the search for such functions is questioned, as simple linear plots fit the data at least as well.