A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are consid...A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are considered as the temperature-dependent parameters in the form of hyperbolical temperature function based on the theory of temperaturedependent potential parameters. With this modified model, the second virial coefficients of some homonuclear molecules（such as O2, Cl2, CH3CH3, and CF3CF3） and heteronuclear molecules（such as CO, NO, CH3 F, CH3 Cl, CH3CF3,CH3CHF2, and CF3CH2F） are calculated. Then the Lorentz–Berthelot mixing rule is modified with a temperaturedependent expression, and the second virial coefficients of the heteronuclear molecules（such as CH3 F, CH3 Cl, and CH3CF3） are calculated. Moreover, CO2 and N2O are also studied with the modified 3CLJDQP model. The calculated results from the modified 2CLJDQP model accord better with the experimental data than those from the original model.It is shown that the presented model improves the positive deviation in low temperature range and negative deviation in high temperature range. So the modified 2CLJDQP potential model with the temperature-dependent parameters can be employed satisfactorily in large temperature range.展开更多
Poincaré's formalism is used to develop a variant of the usual virial theorem in which the time average of the equation of motion of a certain function is expressed in terms of the generalized Poisson brackets.
In this paper a new relation between the second virial coefficients A_2, (?)_w and (dV_(es)/dC)_c→0=K_s was derived from proposed model theory of concentration effects in GPC for mono-and poly-dispersed polymers. Bas...In this paper a new relation between the second virial coefficients A_2, (?)_w and (dV_(es)/dC)_c→0=K_s was derived from proposed model theory of concentration effects in GPC for mono-and poly-dispersed polymers. Based on this relation a new method for determination of second vifial coefficients from the combination of (dV_(es)/dC)_c→0=K_3, (?)_w and K_H measurements was proposed.The values of A_2 for mono-and poly-dispersed polystyrenes with molecular weight range from 10~4 to 10~6 in good and theta solvents were determined by proposed method. Results show that their values of A_2 are in agreement with those obtained by light scattering.展开更多
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of vir...From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical(except the second virial coefficient, where the sign is different)when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1(J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose(Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose(Fermi) gas.展开更多
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinea...In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.展开更多
Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamilto...Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamiltonians then how the Virial theorem should be modified.We also discuss the energy contribution arising from thecoordinates-momentum coupling for a definite energy level.展开更多
The solventnatures are crucial to deeply reveal solution behavior of macromolecular chains,physical essence of condensed state structures formation of the film as well as the photoelectronic devices performance.Based ...The solventnatures are crucial to deeply reveal solution behavior of macromolecular chains,physical essence of condensed state structures formation of the film as well as the photoelectronic devices performance.Based on the second virial coefficient(A2),effect of the synergistic action of solvents and external electric field on both solution behavior and the film’s condensed state structure for the semi-rigid conjugated polymer,poly[2-methoxy-5-(2’-ethylhexoxy)-1,4-phenylvinylene](MEH-PPV)was investigated by dynamic/static light scattering,photoluminescence spectroscopy and transmission electron microscopy,etc.It was found that although the MEH-PPV solutions with different solvents(toluene,chlorobenzene,chloroform and tetrahydrofuran)all could generate a response to the external electric field,the degree of response varied significantly with the change of solvent nature.Furthermore,ordered degree of the film from the solutions was also obviously different.The essential reason for this responsive difference was firstly revealed in the research,which actually depended on the degree of interaction between the solute and solvent,and this degree of interaction could be quantitatively described by the second virial coefficient(A2).The bigger the A2,the stronger the interaction between solvent and solute in the solution,and the stronger the response to the external electric field.Further,under the induction of external electric field,chains aggregations with different sizes were formed accompanied by large-scale chains ordered structure in the solution.This ordered structure not only can effectively transfer to film prepared by the precursor solution but also is beneficial to enhance the carrier mobility and device efficiency of the photoelectronic film.展开更多
This paper focuses on a very important point which consists in evaluating experimental data prior to their use for chemical process designs. Hexafluoropropylene P, ρ, T data measured at 11 temperatures from 263 to 36...This paper focuses on a very important point which consists in evaluating experimental data prior to their use for chemical process designs. Hexafluoropropylene P, ρ, T data measured at 11 temperatures from 263 to 362 K and at pressures up to 10 MPa have been examined through a consistency test presented herein and based on the use of a methodology implying both neural networks and Virial equation. Such a methodology appears as very powerful to identify erroneous data and could be conveniently handled for quick checks of databases previously to modeling through classical thermodynamic models and equations of state. As an application to liquid and vapor phase densities of hexafluoropropylene, a more reliable database is provided after removing out layer data.展开更多
The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this pape...The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.展开更多
A correlation between maxima in virial coefficients (Bn), and “kissing” numbers for hard hyper-spheres up to dimension D = 5, indicates a virial equation and close-packing relationship. Known virial coefficients up ...A correlation between maxima in virial coefficients (Bn), and “kissing” numbers for hard hyper-spheres up to dimension D = 5, indicates a virial equation and close-packing relationship. Known virial coefficients up to B7, both for hard parallel cubes and squares, indicate that the limiting differences Bn – Bn-1 behave similar to spheres and disks, in the respective expan-sions relative to maximum close packing. In all cases, the difference Bn – Bn-1 is approaching a negative constant with similar functional form in each dimen-sion. This observation enables closed-virial equa-tions-of-state for cubes and squares to be obtained. In both the 3D and 2D cases, the virial pressures begin to deviate from MD thermodynamic pressures at densities well below crystallization. These results consolidate the general conclusion, from previous papers on spheres and disks, that the Mayer cluster expansion cannot represent the thermodynamic fluid phases up to freezing as commonly assumed in statistical theories.展开更多
Resultant gradient-information is introduced and applied to problems in chemical reactivity theory. This local measure of the structural information contained in (complex) wavefunctions of electronic states is related...Resultant gradient-information is introduced and applied to problems in chemical reactivity theory. This local measure of the structural information contained in (complex) wavefunctions of electronic states is related to the system overall kinetic energy combining the modulus (probability) and phase (current) contributions. The grand-ensemble representation of thermodynamic equilibria in open systems demonstrates the physical equivalence of the variational energetic and information principles. It is used and to relate the populational derivatives of ensemble-average functionals in both these representations, which represent reactivity criteria for diagnosing the charge-transfer (CT) phenomena. Their equivalence is demonstrated by using the in situ potential and hardness descriptors to predict the direction and optimum amount of CT. The virial theorem is generalized into thermodynamic quantities and used to extract the kinetic energy component from qualitative energy profiles in the bond-formation and (exo/endo)-ergic reactions. The role of electronic kinetic energy in such chemical processes is reexamined, the virial theorem implications for the Hammond postulate of reactivity theory are explored, and variations of the structural-information in chemical processes are addressed. The maximum thermodynamic information rule is formulated and "production" of the gradient-information in chemical reactions is addressed. The Hammond postulate is shown to be indexed by the geometric derivative of resultant gradient-information at transition-state complex.展开更多
The virial theorem is written by using the canonical equations of motion in classical mechanics. A moving particle with an initial speed in an n-particle system is considered. The distance of the moving particle from ...The virial theorem is written by using the canonical equations of motion in classical mechanics. A moving particle with an initial speed in an n-particle system is considered. The distance of the moving particle from the origin of the system to the final position is derived as a function of the kinetic energy of the particle. It is thought that the considered particle would not collide with other particles in the system. The relation between the final and initial distance of the particle from the origin of the system is given by a single equation.展开更多
The scattering of electron by a photon is a well-known reaction in physics. In this study, the change in the electron’s energy after the scattering is taken into account. The previous works are searched. In order to ...The scattering of electron by a photon is a well-known reaction in physics. In this study, the change in the electron’s energy after the scattering is taken into account. The previous works are searched. In order to take into account this change in the electron’s energy in the equation of motion of the electron, the Dirac equation is used with the virial theorem. The scattered electron kinetic energy which is given to the electron by the loss in photon’s energy is related to the potential energy of the electron by the virial theorem which states that the potential energy is two times of the kinetic energy in minus sign. A first time application of the virial theorem on a scattered electron by a photon is included to the Dirac equation.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.51106129)the Fundamental Research Funds for the Central University,China(Grant No.XJTU-HRT-002)
文摘A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are considered as the temperature-dependent parameters in the form of hyperbolical temperature function based on the theory of temperaturedependent potential parameters. With this modified model, the second virial coefficients of some homonuclear molecules（such as O2, Cl2, CH3CH3, and CF3CF3） and heteronuclear molecules（such as CO, NO, CH3 F, CH3 Cl, CH3CF3,CH3CHF2, and CF3CH2F） are calculated. Then the Lorentz–Berthelot mixing rule is modified with a temperaturedependent expression, and the second virial coefficients of the heteronuclear molecules（such as CH3 F, CH3 Cl, and CH3CF3） are calculated. Moreover, CO2 and N2O are also studied with the modified 3CLJDQP model. The calculated results from the modified 2CLJDQP model accord better with the experimental data than those from the original model.It is shown that the presented model improves the positive deviation in low temperature range and negative deviation in high temperature range. So the modified 2CLJDQP potential model with the temperature-dependent parameters can be employed satisfactorily in large temperature range.
文摘Poincaré's formalism is used to develop a variant of the usual virial theorem in which the time average of the equation of motion of a certain function is expressed in terms of the generalized Poisson brackets.
基金The project supported by National Natural Science Foundation of China.
文摘In this paper a new relation between the second virial coefficients A_2, (?)_w and (dV_(es)/dC)_c→0=K_s was derived from proposed model theory of concentration effects in GPC for mono-and poly-dispersed polymers. Based on this relation a new method for determination of second vifial coefficients from the combination of (dV_(es)/dC)_c→0=K_3, (?)_w and K_H measurements was proposed.The values of A_2 for mono-and poly-dispersed polystyrenes with molecular weight range from 10~4 to 10~6 in good and theta solvents were determined by proposed method. Results show that their values of A_2 are in agreement with those obtained by light scattering.
文摘From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical(except the second virial coefficient, where the sign is different)when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1(J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose(Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose(Fermi) gas.
基金Supported in part by National Natural Science Foundation of China under Grant No. 11171164
文摘In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
基金the Specialized Research Fund for the Doctorial Progress of Higher Education of China under Grant No.20070358009
文摘Usually the Virial theorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings inHamiltonians then how the Virial theorem should be modified.We also discuss the energy contribution arising from thecoordinates-momentum coupling for a definite energy level.
基金financially supported by the National Natural Science Foundation of China(Nos.91333103 and 21574053)。
文摘The solventnatures are crucial to deeply reveal solution behavior of macromolecular chains,physical essence of condensed state structures formation of the film as well as the photoelectronic devices performance.Based on the second virial coefficient(A2),effect of the synergistic action of solvents and external electric field on both solution behavior and the film’s condensed state structure for the semi-rigid conjugated polymer,poly[2-methoxy-5-(2’-ethylhexoxy)-1,4-phenylvinylene](MEH-PPV)was investigated by dynamic/static light scattering,photoluminescence spectroscopy and transmission electron microscopy,etc.It was found that although the MEH-PPV solutions with different solvents(toluene,chlorobenzene,chloroform and tetrahydrofuran)all could generate a response to the external electric field,the degree of response varied significantly with the change of solvent nature.Furthermore,ordered degree of the film from the solutions was also obviously different.The essential reason for this responsive difference was firstly revealed in the research,which actually depended on the degree of interaction between the solute and solvent,and this degree of interaction could be quantitatively described by the second virial coefficient(A2).The bigger the A2,the stronger the interaction between solvent and solute in the solution,and the stronger the response to the external electric field.Further,under the induction of external electric field,chains aggregations with different sizes were formed accompanied by large-scale chains ordered structure in the solution.This ordered structure not only can effectively transfer to film prepared by the precursor solution but also is beneficial to enhance the carrier mobility and device efficiency of the photoelectronic film.
文摘This paper focuses on a very important point which consists in evaluating experimental data prior to their use for chemical process designs. Hexafluoropropylene P, ρ, T data measured at 11 temperatures from 263 to 362 K and at pressures up to 10 MPa have been examined through a consistency test presented herein and based on the use of a methodology implying both neural networks and Virial equation. Such a methodology appears as very powerful to identify erroneous data and could be conveniently handled for quick checks of databases previously to modeling through classical thermodynamic models and equations of state. As an application to liquid and vapor phase densities of hexafluoropropylene, a more reliable database is provided after removing out layer data.
文摘The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.
文摘A correlation between maxima in virial coefficients (Bn), and “kissing” numbers for hard hyper-spheres up to dimension D = 5, indicates a virial equation and close-packing relationship. Known virial coefficients up to B7, both for hard parallel cubes and squares, indicate that the limiting differences Bn – Bn-1 behave similar to spheres and disks, in the respective expan-sions relative to maximum close packing. In all cases, the difference Bn – Bn-1 is approaching a negative constant with similar functional form in each dimen-sion. This observation enables closed-virial equa-tions-of-state for cubes and squares to be obtained. In both the 3D and 2D cases, the virial pressures begin to deviate from MD thermodynamic pressures at densities well below crystallization. These results consolidate the general conclusion, from previous papers on spheres and disks, that the Mayer cluster expansion cannot represent the thermodynamic fluid phases up to freezing as commonly assumed in statistical theories.
文摘Resultant gradient-information is introduced and applied to problems in chemical reactivity theory. This local measure of the structural information contained in (complex) wavefunctions of electronic states is related to the system overall kinetic energy combining the modulus (probability) and phase (current) contributions. The grand-ensemble representation of thermodynamic equilibria in open systems demonstrates the physical equivalence of the variational energetic and information principles. It is used and to relate the populational derivatives of ensemble-average functionals in both these representations, which represent reactivity criteria for diagnosing the charge-transfer (CT) phenomena. Their equivalence is demonstrated by using the in situ potential and hardness descriptors to predict the direction and optimum amount of CT. The virial theorem is generalized into thermodynamic quantities and used to extract the kinetic energy component from qualitative energy profiles in the bond-formation and (exo/endo)-ergic reactions. The role of electronic kinetic energy in such chemical processes is reexamined, the virial theorem implications for the Hammond postulate of reactivity theory are explored, and variations of the structural-information in chemical processes are addressed. The maximum thermodynamic information rule is formulated and "production" of the gradient-information in chemical reactions is addressed. The Hammond postulate is shown to be indexed by the geometric derivative of resultant gradient-information at transition-state complex.
文摘The virial theorem is written by using the canonical equations of motion in classical mechanics. A moving particle with an initial speed in an n-particle system is considered. The distance of the moving particle from the origin of the system to the final position is derived as a function of the kinetic energy of the particle. It is thought that the considered particle would not collide with other particles in the system. The relation between the final and initial distance of the particle from the origin of the system is given by a single equation.
文摘The scattering of electron by a photon is a well-known reaction in physics. In this study, the change in the electron’s energy after the scattering is taken into account. The previous works are searched. In order to take into account this change in the electron’s energy in the equation of motion of the electron, the Dirac equation is used with the virial theorem. The scattered electron kinetic energy which is given to the electron by the loss in photon’s energy is related to the potential energy of the electron by the virial theorem which states that the potential energy is two times of the kinetic energy in minus sign. A first time application of the virial theorem on a scattered electron by a photon is included to the Dirac equation.
