where, p(alkylbenzene) denotes the thermochemical property (heat of atomization, enthalpy of formation and boiling points) of alkylbenzenes; X1CC and X1CH are the eigenvalues of the C–C and C–H σ bond orbital-connection matrices, respectively. X1π is the eigenvalue of the conjugated π bond orbital-connection matrix. NC–C and NC–H are the number of C–C and C–H σ bonds in the alkylbenzene, respectively, and a, b, c, d, e, and k are coefficients.  相似文献   

13.
Mixed Monolayers of Amphiphilic Cyclodextrins and Phospholipids: II. Surface Potential–Area Behavior of Per-(6-amino-2,3-di-O-hexyl) β-CD Hydrochloride Salt and 1,2 Dipalmitoyl, 3-sn-Phosphatidic Acid Mixed Monolayers     
Athena Kasselouri  Anthony William Coleman  Genevive Albrecht  Adam Baszkin 《Journal of colloid and interface science》1996,180(2):398
The dielectric properties of mixed monolayers of per-(6-amino-2,3-di-O-hexyl) β-CD hydrochloride (NH3-β-CD-OC6) and 1,2 dipalmitoyl, 3-sn-phosphatidic acid (DPPA) have been assessed using surface potential measurements at constant area. From the comparison of these surface potential (ΔV) versus surface density (δ) relationships with those of surface pressure (π) against surface density (δ) it was apparent that the increase in the NH3-β-CD-OC6 content in mixed films gave rise to a gradual increase in the saturation value of the surface potential (ΔVmax). This potential for pure DPPA was found to be equal to 396 mV and for pure CD 554 mV. The ΔVmaxvalues reflect the onset of reorientation effects that arrive at molar areas before the collapse of these films. Independently of reorientation effects, the obtained results strongly indicate that the dipolar term contributing to the overall ΔVvalue was for NH3-β-CD-OC6 due to the hydration of its NH+3group. For both DPPA and NH3-β-CD-OC6 molecules the contribution of the electric double layer (Ψ) was calculated and was found for DPPA and NH3-β-CD-OC6 to be equal to −249 and +252 mV, respectively. These calculated Ψ values made possible the evaluation of dipole moments for NH3-β-CD-OC6 and DPPA monolayers which revealed a marked difference in dipolar properties between these two film forming components. In contrast to DPPA which exhibited a decrease in the surface dipole moment (μ) with the decrease inA, NH3-β-CD-OC6 displayed an increase in μwith the decrease inAforAvalues above 580 Å2. Below this value μdecreases with decreasing molecular area and this variation arises from a change in the polarity of the electric double layer arising from interactions with the complementary anion. The differences in dielectric properties between the two film forming molecules have been attributed to modification, during compression, in the structure of the interfacial water bound to the cyclodextrin.  相似文献   

14.
Theoretical studies of uracil–(H2O)n (n = 1–7) clusters by ab initio and ABEEMσπ/MM fluctuating charge model     
Fang-Fang Wang  Dong-Xia Zhao  Zhong-Zhi Yang   《Chemical physics》2009,360(1-3):141-149
Uracil–(H2O)n (n = 1–7) clusters were systemically investigated by ab initio methods and the newly constructed ABEEMσπ/MM fluctuating charge model. Water molecules have been gradually placed in an average plane containing uracil. The geometries of 38 uracil–water complexes were obtained using B3LYP/6-311++G** level optimizations, and the energies were determined at the MP2/6-311++G** level with BSSE corrections. The ABEEMσπ/MM potential model gives reasonable properties of these clusters when comparing with the present ab initio data. For interaction energies, the root mean square deviation is 0.96 kcal/mol, and the linear coefficient reaches 0.997. Furthermore, the ABEEMσπ charges changed when H2O interacted with the uracil molecule, especially at the sites where the hydrogen bond form. These results show that the ABEEMσπ/MM model is fine giving the overall characteristic hydration properties of uracil–water systems in good agreement with the high-level ab initio calculations.  相似文献   

15.
Relaxation phenomena in phospholipid monolayers at the air–water interface     
Mª. Rosario Rodríguez Nio  Ana Lucero  Juan M. Rodríguez Patino 《Colloids and surfaces. A, Physicochemical and engineering aspects》2008,320(1-3):260-270
In this work we are concerned with the study of long-term relaxation phenomena in dipalmitoyl phosphatidylcholine (DPPC) and dioleoyl phosphatidylcholine (DOPC) monolayers spread at the air–water interface as a function of the surface pressure and the aqueous phase pH (pH 5, 7, and 9). Long-term relaxation phenomena were determined in an automated Langmuir-type film balance at constant temperature (20 °C). Two kinds of experiments were performed to analyze relaxation mechanisms. In one, the surface pressure (π) was kept constant, and the area (A) was measured as a function of time (θ). In the second, the area was kept constant at monolayer collapse and the surface pressure was decreased. This decrease was measured as a function of time. Various relaxation mechanisms, including monolayer molecular loss by dissolution, collapse, and/or organization/reorganization changes, can be fitted to the results derived from these experiments. These relaxation mechanisms are pH and phospholipid dependent. In the discussion, special attention will be given to the effect of the relaxation phenomena on the hysteresis in πA isotherms before and after the relaxation experiment. At π lower than the equilibrium spreading pressure (πe) the relaxation phenomena are mainly due to the loss of DPPC or DOPC molecules by desorption into the bulk aqueous phase. The formation of interfacial macroscopic vesicles, which are dissolved into the bulk phase, makes the phospholipid monolayer molecular loss irreversible. At the collapse point (at π > πe), the relaxation phenomena may be due either to collapse for DPPC and/or to a complex mechanism including competition between desorption and monolayer collapse for DOPC.  相似文献   

16.
Crystal structure of the 1 : 1 : 6 complex between 18-crown-6, hydroquinone and water     
Bachir Belamri  Claude Bavoux  Alain Thozet 《Journal of inclusion phenomena and macrocyclic chemistry》1990,8(4):383-388
Hydroquinone forms a 1 : 1 : 6 complex with 18-crown-6 and water. Crystals of this complex are monoclinic, space groupP21/a witha = 14.289(1),b = 7.972(1),c = 11.596(1) Å, = 97.72(1)°,Z = 2,D c = 1.22 g cm–3. The hydroquinone and crown ether molecules lie on centres of symmetry with the crown in theD 3d conformation. The water molecules act as a bridge between hydroquinone and the crown ether. The structure consists of molecules linked by a 3-dimensional network of hydrogen bonds: the hydroquinone and two water molecules lie roughly in the (001) plane; the crown ether and four water molecules form bipyramidal structures which are stacked in layers alternating with the previous planes.  相似文献   

17.
Structural and magnetic properties of “one-dimensional” barium vanadium triselenide     
J. Kelber  A. H. Reis  Jr.  A. T. Aldred  M. H. Mueller  O. MassenetG. DePasqualiG. Stucky 《Journal of solid state chemistry》1979,30(3)
BaVSe3 has been synthesized and its crystal structure determined at 293(2)°K. The structure was solved in the hexagonal space group P63/mmc (D46h), with a = 6.9990(11) and c = 5.8621(13) Å. Scans (2 Θ) of a polycrystalline sample revealed that BaVSe3 undergoes a transition to an orthorhombic unit cell (b′ 31/2 a, aa, cc) at 303(5)°K. Magnetic susceptibility measurements between 4 and 300°K indicate that BaVSe3 is paramagnetic down to 41(1)°K, where magnetic ordering occurs, with a magnetic moment in the ordered phase of 0.2 μB per vanadium atom. The orthorhombic lattice distortion may be caused by the “freezing in” of “soft” vibrational modes.  相似文献   

18.
Structure,Z′ = 2 Crystal Packing Features of 3-(2-Chlorobenzylidene)-5-(p-tolyl)furan-2(3H)-one     
Vyacheslav S. Grinev  Oksana A. Mayorova  Tatyana V. Anis&#x;kova  Alexandra S. Tikhomolova  Alevtina Yu. Yegorova 《Molecules (Basel, Switzerland)》2021,26(8)
3-(2-Chlorobenzylidene)-5-(p-tolyl)furan-2(3H)-one (1), C18H13ClO2, crystallizes with Z = 8 and Z′ = 2, and the structure at 100 K has orthorhombic (Pna21) symmetry. Each kind of molecule takes part in π–π stacking interactions to form infinite chains parallel to the c axis. We believe that the existence of two forms can be explained by the probable rotation around a single C–C bond. The quantum chemical modeling reveals that these molecules are almost equivalent energetically, and they can be described as the two most stable conformers (rotamers) with a minor rotational barrier of about 0.67 kcal/mol.  相似文献   

19.
Distribution of Co(II) between immiscible phases formed in water + 1-butanol system     
Muhammad Shahid Ansari  Arifa Aslam  Hafiz-ur-Rehman 《Fluid Phase Equilibria》2009,280(1-2):129-131
Heterogeneous equilibria for the distribution of Co2+ between the two layers formed in water + 1-butanol (1-BuOH) system have been investigated at ambient conditions. The study (confined to only 28 °C) reveals an interesting feature of the distribution equilibrium for the system whereby Co2+ has been found to exist in both the phases as the same species namely its aqua-complex thus directly demonstrating strong selective solvation of Co2+ by the water molecules. Almost constant values of refractive indices and densities were exhibited by the two layers regardless in which ratio the component liquids were mixed together. However, relative volumes of the layers varied smoothly on gradually changing the ratio of the two liquids in the overall “solvent system”. Also the Co2+ distribution coefficient (KD) changed appreciably on going to alcohol-richer “solvent systems” but KD remained fairly constant on adding different amounts of cobalt dichloride to any given “solvent system”.  相似文献   

20.
Monolayer properties of fatty acids : II. Surface vapor pressure and the free energy of compression     
A. K. Rakshit  G. Zografi  I. M. Jalal  F. D. Gunstone 《Journal of colloid and interface science》1981,80(2):466-473
The properties of monolayers spread at the air-water interface were measured for saturated, unsaturated, and hydroxy fatty acids, differing in the type and degree of unsaturation, geometric isomerism, and position of unsaturated and hydroxy groups. Surface vapor pressures, reflecting the equilibrium between “gaseous” and “liquid” monolayer states were determined, as were the free energies of compression, ΔFc, from essentially infinite dilution (100,000 Å2/molecule) to the area per molecule, Ae at the equilibrium spreading pressure, πe. Surface vapor pressures and free energies of compression for saturated and unsaturated fatty acids with a double bond, or bonds, change in a manner expected because of chain-chain interactions. Hydroxy and acetylenic acids produce relatively high surface vapor pressures, despite their tendency for strong chain-chain interaction. It is concluded that chain-water interactions are very significant for the acetylenic and hydroxy acids and less so for the saturated and ethylenic acids.  相似文献   

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1.
The title compound, cobalt 4′,7-diethoxylisoflavone-3′-sulfonate([Co(H2O)6](X)2⋅8H2O, X = C19H17O4SO3) was synthesized and its structure was determined by single-crystal X-ray diffraction analysis. It crystallizes in the triclinic space group P-1 with cell parameters a = 9.026(3) Å, b = 16.431(5) Å, c = 18.195(6) Å, α = 72.289(4), β = 87.498(4), γ = 82.775(5), V = 2550.1(13) Å−3, Dc = 1.419 Mg m−3, and Z = 2. The results show that the title compound consists of one cobalt cation, six coordinated water molecules, eight lattice water molecules, and two 4′,7-diethoxylisoflavone-3′-sulfonate anions, C19H17O4SO3. Two anions have different conformations. Twelve H atoms of six coordinated water molecules, as donors, form hydrogen bonds with four oxygen atoms of sulfo-groups of two anions and eight oxygen atoms of eight lattice water molecules. In addition, π < eqid1 > ⋅ < eqid2 > π stacking interactions exist in the crystal structure, which together with hydrogen bonds lead to supramolecular formation with a three-dimensional network.  相似文献   

2.
In this work we have analyzed the topography by atomic force microscopy (AFM) of dipalmitoyl-phosphatidyl-choline (DPPC) monolayers previously spread at the air–water interface and penetrated by β-casein. AFM images of β-casein–DPPC monolayers were taken from Langmuir–Blodgett films deposited onto hydrophilic mica substrates at different initial surface pressures (πi) and after the compression of the mixed films. The monolayer topography depends on the initial structure of the phospholipid:liquid expanded (LE) at 3 mN/m, coexistence between LE and liquid condensed (LC) structures at 7 mN/m, at the end of the LE–LC transition at 10 mN/m, and with a LC structure at 15 mN/m. The area occupied by DPPC domains in the mixed film increases with the πi value, especially for DPPC with a LC structure at 15 mN/m. At this surface pressure the thickness of the film is at a maximum. After the film compression at 25 mN/m, which is above the equilibrium spreading pressure of β-casein (), this protein is displaced from the interface by DPPC and the topography of the mixed monolayer depends on the initial structure of the DPPC monolayer. A notable feature of the topography of these mixed monolayers is the presence of multilayers of β-casein and DPPC of high thickness (50–70 nm) at the lower πi values. Although the film is dominated by DPPC at the highest surface pressures (at 25 mN/m), β-casein is not displaced totally from the interface and coexists as β-casein collapsed domains within the network of the DPPC structure.  相似文献   

3.
The energy barrier of [9.] extended to globular protein adsorption and denaturation, equal to the work ΠδA, where Π is the film pressure and δA the “hole area” formed by the adsorbing protein, is in fact related to the water activity at the interface and not to the size of the adsorbing molecules. The possibility that a reaction takes place between the adsorbed protein molecules and n water molecules is postulated, which allows to predict values of n from the values of δA.  相似文献   

4.
The structure of cobalt formate dihydrate, Co(HCO2)2 · 2H2O, was determined using single-crystal X-ray diffraction data. The crystals are monoclinic, space groupP21/c, with unit-cell dimensionsa=8.680(2),b=7.160(2),c=9.272(2) Å,=97.43(2)°,V=571.4(3) Å3 Z=4.R obs=0.038 for 1282 unique reflections withI>3(I). The crystal structure is found to be isomorphous with those of other divalent metal formates. This structure is interesting crystallographically because the Patterson map is homometric with respect to the positions of the heavy atoms. The asymmetric unit consists of two independent cobalt atoms on special positions, two formate ions (HCOO), and two water molecules. The two cobalt atoms are each coordinated to six oxygen atoms in an octahedral arrangement. One of the cobalt octahedra contains only oxygen atoms from six formate ions. The second cobalt ion is surrounded by four water molecules and an oxygen atom from each of two formate ions. The two different octahedra are bridged by one of the formate ions and by hydrogen bonds. This network extends in a three-dimensional polymeric manner throughout the crystal structure. Each of the four oxygen atoms in the two independent formate ions forms a hydrogen bond to water and is coordinated to a metal ion. It is found that the metal ions lie in the plane of the formate carboxyl group to which they are coordinated, while molecules to which the formate ion is hydrogen bonded lie more out of this plane.  相似文献   

5.
The rates of change of film pressure (π) and surface concentration (Γ) of protein during the adsorption of β-casein, bovine serum albumin (BSA), and lysozyme at the air-water interface have been monitored by the Wilhelmy plate and surface radioactivity methods, respectively. The increases in π and Γ for the relatively flexible β-casein molecule occur simultaneously with both parameters attaining their steady-state values at about the same time. In contrast, π and Γ follow different time courses for the globular lysozyme molecule; Γ can reach a steady state value while π is still increasing significantly. The kinetics indicate that initially adsorption is diffusion-controlled but at higher surface coverages there is an energy barrier to adsorption. Under these conditions, the ability of the protein molecules to create space in the existing film and penetrate and rearrange in the surface is rate-determining. Two kinetic regions exist: the relaxation time τ1 (typically 2 hr when Γ 2 mg m−2) describes the adsorption when both π and Γ are increasing whereas τ2 (in the range 1–8 hr for all three proteins) relates to the situation when π is increasing at constant Γ because the protein molecules are changing conformation in the surface.  相似文献   

6.
Critical surface tensions γc of poly(vinyl butyral) and poly(vinyl benzal) multilayers built up by the Langmuir-Blodgett method were measured with polyhydric alcohols and n-alkanes. The γc values of both polymer multilayers increased with increasing pressures of the piston oils used to control pressures of polymers on the water surface during deposition. The γc value of poly(vinyl butyral) multilayers built up to lower pressure of the piston oil was approximately consistent with a crystalline hydrocarbon surface, while the γc value of the multilayer built up to higher pressure of the piston oil was approximately consistent with a—CH3 rather than a ? CH2 ? CH2? surface. All results for γc values of poly(vinyl benzal) multilayers were very close to the γc value of benzene ringrich surface. The γc value of the multilayer built up to lower pressure of the piston oil almost coincided with the γc value for amorphous polystyrene, while the γc value for the multilayer built up to higher pressure of the piston oil was in fair agreement with γc for an aromatic ring edge in the crystalline state. Values of γsd, the dispersion force contribution to the surface free energy of multilayers calculated by Fowkes' relation, were in fair agreement with the corresponding observed γc values, respectively. It is concluded from these measurements that orientations and surface structures in both polymer multilayers are affected by pressure change of piston oils. The properties on monolayers of two polymers at a air-water interface and on barium stearate multilayers are also presented.  相似文献   

7.
Plots of surface pressuer (π) vs surface area (A) are taken from mixed monolayers of dipalmitoylphosphatidylcholine (DPPC) and “egg” phosphatidylglycerol (egg PG) with the concentration of egg PG (X) ranging from 0 to 100%, the temperatures (T) from 37 to 41°C, and the compression rate (dA/dt) from −13.6 to −688 mm2s, and at a relative humidity of over 90%. Between limiting values of X, T, and dA/dt the π-A plots of compression show regions of nearly constant π (plateaus) which start at values of π (πpb) of 48 ± 2 mN m−1, and which can be followed by an increase in π until collapse occurs at 70 mN m−1. πpb is independent of X, T, and dA/dt. The plateau is correlated with a loss of molecules from the monolayer, which increases strongly with X and T and decreases with dA/dt. The quantitative results are not in agreement with separate collapse of the components. A model is presented stating that plateaus occur when the transition from the liquid-expanded (LE) to the liquid-condensed phase (LC) is incomplete at πpb. During plateau formation a mixed LE phase is squeezed out at its collapse pressure. The remaining LC phase can be compressed to 70 mN m−1. Results of calculations based on this model are in agreement with the experimental results and predict slight enrichment of the squeezed-out phase with respect to egg PG.  相似文献   

8.
The mixed lead nitrate oxalate, Pb2(NO3)2(C2O4).2H2O, has been obtained in a polycrystalline form in the course of a study on precursors of nanocrystalline PZT-type oxides. Its crystal structure has been solved from powder diffraction data collected using a monochromatic radiation from a conventional X-ray source. The symmetry is monoclinic, space group P21/c (No. 14), the cell dimensions are a=10.623(2) Å, b=7.9559(9) Å, c=6.1932(5) Å, β=104.49(1)° and Z=4. The structure consists of a stacking of complex double sheets parallel to (1 0 0), forming layers held together by hydrogen bonds. The sheets result from the condensation of PbO10 polyhedra, in which the oxalate and nitrate groups, as well as water molecules, play a major role. The structure is discussed in terms of Pb---O distances, polyhedra shape and lead coordination, with emphasis on the dimensional polymerisation role of water molecules. The thermal behaviour of this layered compound is carefully described from temperature-dependent powder diffraction and thermogravimetric measurements. The enthalpy, ΔrH=232(3) kJ mol−1, and entropy, ΔrS=532(8) J K−1 mol−1, of the dehydration reaction have been determined. The high value of ΔrH demonstrates that the water molecules are strongly bonded in the structure. The complex decomposition proceeds through the crystallisation and decomposition of Pb(NO3)2(C2O4) into Pb(NO3)2 and PbC2O4, and, finally, various lead oxides.  相似文献   

9.
A new cobalt phosphates (trans-1,4-dach)0.5Co3(H2O)(OH)(PO4)(HPO4)·(3+x)H2O (1), has been synthesized under a hydrothermal condition and structurally characterized by single-crystal X-ray diffraction. It consists of cobalt phosphates layers and coordinated bis-N-donor ligands, trans-1,4-diaminocyclohexane, which are interlinked to form a 3-D framework structure with 1-D tunnel occupied by water molecules. When its channel water is fully removed at a relatively low temperature, the pillars fold up, and no porosity can be detected by sorption. However, the structural integrity of the compound is retained, and the pillar can still rise to its original upright position after contact with water vapor. This implies that some channel water molecules play a wedge function to control the up and down positions of the organic bis-N-donor ligands. When 1 is partially dehydrated, it revealed adsorption of various linear organic molecules, although the fully dehydrated one did not adsorb any organic molecules. Magnetic susceptibility measurements showed that 1 is an antiferromagnet with a canted interaction at a transition temperature of about 10 K. Crystal data: monoclinic, C2/c, a=28.653(10) Å, b=12.874(4) Å, c=8.266(3) Å, β=97.257(7), V=3025(2) Å3, Z=8.  相似文献   

10.
The structure of 5-nitraminotetrazole sodium salt sesquihydrate was determined by X-ray diffraction. The crystals are monoclinic, space group P21/c;a = 3.551(1) Å, b = 21.834(4) Å, c = 9.075(2) Å; = 110.68(3)°; V = 658.3(2) Å3; Z = 4; calc = 1.807 g/cm3. The anion is planar and has an intramolecular hydrogen bond. The negative charge of the anion is localized on one of the oxygens of the nitro group. The sodium cation (c.n.6) is coordinated by three oxygen atoms of different anions and three oxygens of crystallization water. One of the crystallization water molecules is disordered in the unit cell. The anions are hydrogen-bonded with each other and with crystallization water molecules.Original Russian Text Copyright © 2004 by A. M. Astakhov, A. D. Vasiliev, M. S. Molokeev, L. A. Kruglyakova, A. M. Sirotinin, and R. S. StepanovTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 3, pp. 562–565, May–June 2004.  相似文献   

11.
The 17O-NMR spin-lattice relaxation times (T 1) of water molecules in aqueous solutions of n-alkylsulfonate (C1 to C6) and arylsulfonic anions were determined as a function of concentration at 298 K. Values of the dynamic hydration number, (S-) = nh - (tc- /tc0 - 1)(\mathrm{S}^{-}) = n_{\mathrm{h}}^{ -} (\tau_{\mathrm{c}}^{-} /\tau_{\mathrm{c}}^{0} - 1), were determined from the concentration dependence of T 1. The ratios (tc -/tc0\tau_{\mathrm{c}}^{ -}/\tau_{\mathrm{c}}^{0}) of the rotational correlation times (tc -\tau_{\mathrm{c}}^{ -} ) of the water molecules around each sulfonate anion in the aqueous solutions to the rotational correlation time of pure water (tc0\tau_{\mathrm{c}}^{0}) were obtained from the n DHN(S) and the hydration number (nh -n_{\mathrm{h}}^{ -} ) results, which was calculated from the water accessible surface area (ASA) of the solute molecule. The tc -/tc0\tau_{\mathrm{c}}^{ -}/\tau_{\mathrm{c}}^{0} values for alkylsulfonate anions increase with increasing ASA in the homologous-series range of C1 to C4, but then become approximately constant. This result shows that the water structures of hydrophobic hydration near large size alkyl groups are less ordered. The rotational motions of water molecules around an aromatic group are faster than those around an n-alkyl group with the same ASA. That is, the number of water–water hydrogen bonds in the hydration water of aromatic groups is smaller in comparison with the hydration water of an n-alkyl group having the same ASA. Hydrophobic hydration is strongly disturbed by a sulfonate group, which acts as a water structure breaker. The disturbance effect decreases in the following order: $\mbox{--} \mathrm{SO}_{3}^{-} > \mbox{--} \mathrm{NH}_{3}^{ +} > \mathrm{OH}> \mathrm{NH}_{2}$\mbox{--} \mathrm{SO}_{3}^{-} > \mbox{--} \mathrm{NH}_{3}^{ +} > \mathrm{OH}> \mathrm{NH}_{2}. The partial molar volumes and viscosity B V coefficients for alkylsulfonate anions are linearly dependent on their n DHN(S) values.  相似文献   

12.
The properties of alkylbenzenes were estimated, using the contributions of the σ bonds, the conjugated π bond and the steric effect in alkylbenzene molecule. And a novel bond orbital-connection matrix, conjugated π bond orbital-connection matrix in aromatic molecules, was proposed. The eigenvalues of the conjugated π bond orbital-connection matrix can well express the contribution of the conjugated π bond to the properties of aromatic molecules. Using this eigenvalue together with the parameters proposed in our early works, the bond orbital-connection matrix method was extended successfully to the QSPR studies of alkylbenzenes and a general model was obtained to evaluate the thermochemical properties of alkylbenzenes, that is,
p(alkylbenzene)=aNC–C+bX1CC+cNC–H+dX1CH+eSZ/E+kX1π,
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