Calculation of number and free energy of the conformers of linear alkanes with medium and long chains. Implications for catalysis

A method for calculating the number of rotamers of a linear alkane and of the number of rotamers with a given number of gauche conformations along the chain as a function of the total number of atoms in the chain, using general equations, is presented. A graphical method for generating individual rotamers was applied to the homologs up to decane, which has 1134 rotamers. The steric energies calculated by molecular mechanics (MM2 force field) were used as measures of the heat of formation for the coiled conformations relative to the anti conformer for each molecule, whereas the statistical entropy differences were calculated for classes of coiled rotamers grouped by the number of gauche bonds and steric energy. The free energy values calculated from these components show that already at 400 K hexane exists preferentially in conformations containing gauche bonds. For larger chains the free energy advantage for the coiled chains increases very steeply. The implications for the question of reactions of linear alkanes occurring on the surface or inside the channels of small- and medium-pore zeolites are briefly examined.     

Fragmentation processes of methylbutyl trifluoroacetates studied by tandem quadrupole mass spectrometry and isotope labeling

The fragmentation patterns of 3-methyl-2-butyl trifluoroacetate and 2-methyl-2-butyl trifluoroacetate were investigated by GC/MS/MS, with electron impact and collision-induced dissociation, on regular and isotope-labeled (deuterium and ¹⁸O) esters. The atoms found in various fragments could be traced back to specific positions in the parent molecules. In this way, molecular rearrangements potentially occurring during the formation of esters by trifluoroacetolysis of 3-methyl-2-butyl p-toluenesulfonate or trifluoroacetic acid addition to various 2-methylbutenes could be shown. Rearrangements also occurred during the fragmentation, particularly during the expulsion of the small fragments CO, C₂H₄ and F₂CO. For the decompositions of oxygen-containing ions these rearrangements were highly specific. By contrast, alkyl cations lead to fragments that are fully scrambled (statistical label distribution). Alkene radical cations ([C_nH_2n]^{+ ˙}) fragment to daughter ions that are extensively, but less than statistically scrambled. Hydrogen scrambling may also occur in fluoroalkyl cation fragments.     

Single and double hydrogen migration in the fragmentation of 3-methyl-2-butyl trifluoroacetate

Three of the main oxygen-containing fragments resulting from 3-methyl-2-butyl trifluoroacetate (11) had been identified previously as the 1-triflnoroacetoxyethyl cation (m/z 141, 12, product of simple cleavage), and the products of single (m/z 142) and double hydrogen transfer (m/z 143, protonated ethyl trifluoroacetate). Collisionally activated dissociation of m/z 142 and the isotopomers resulting from 11-2-d, 11-1-d₃, 11-5,6-d₆, and 11-¹⁸O₂ has established that m/z 142 is the oxygen protonated 1-trifluoroacetoxyethyl free radical (17) formed by hydrogen shift irom a γ-methyl group to oxygen in the molecular ion, rather than in a complex (18) between 12 and the 2-propyl free radical, as expected based on a mechanistic model existing in the literature. The second hydrogen transferred originates in the other γ-methyl group; its migration may occur, but does not have to, in the complex between 17 and a molecule of propene, prior to dissociation of the two fragments. Collision-activated dissociation has now shown that the m/z 140 ion observed in the spectrum is the molecular ion of vinyl trifluoroacetate, possibly formed by a hydrogen transfer from 12 to the 2-propyl radical in the complex 18. The hydrogen migration to oxygen exhibits no isotope effect, whereas the transfers to carbon atoms exhibit small primary and α secondary kinetic isotope effects. Exclusive migration of the tertiary hydrogen from C(3) occurs in the formation of 2-methylbutene cation radical (m/z 70) from the molecular ion. The hydrocarbon ion fragments and the heteroatom-containing fragments are formed from 11 by disjoint pathways.     

近炸引信炮口保险距离的计算

该文以国外某舰炮弹药无线电近炸引信为例,分析研究了该无线电近炸引信炮口安全保险距离有关的参量,通过对火药燃烧时间和电路延迟时间的计算推出了几种不同情况下该无线电近炸引信炮口保险距离,分析计算方法具有普遍性。     

用^1H—NMR测定纤维素的摩尔取代度

用＾１Ｈ－ＮＭＲ测定羟丙基纤维素的摩尔取代度,根据纤维素在ＤＣｌ中水解后的＾１Ｈ－ＮＭＲ谱峰面积来计算ＭＳ值。同时还应用铬酸氧化蒸馏法测定了羟丙基纤维素的ＭＳ值,以及利用ＭＳ与羟丙基含量的关系得到ＭＳ值,可以发现ＮＭＲ的方法是可行的。     

Further on Set-Valued Equilibrium Problems and Applications to Browder Variational Inclusions

In this paper, we introduce some concepts of convexity and semicontinuity for real set-valued mappings similar to those of real single-valued mappings. Then, we obtain different results on the existence of solutions of set-valued equilibrium problems generalizing in a common way several old ones for both single-valued and set-valued equilibrium problems. Applications to Browder variational inclusions, with weakened conditions on the involved set-valued operator, are given.     

Associating divisors with quadratic differentials on Klein surfaces

We extend the notion and basic properties of quadratic differential divisors to a Klein surface, using the corresponding form’s divisors from the double cover of the Klein surface.