The chain length dependency of molar association constant K_a of polymer in solution was investigated theoretically. K_a is proportional to the effective hydrodynamic volume V_ eff of polymer chain in solution. V_ eff...The chain length dependency of molar association constant K_a of polymer in solution was investigated theoretically. K_a is proportional to the effective hydrodynamic volume V_ eff of polymer chain in solution. V_ eff is the product of a shape factor and hydrodynamic volume. On the basis of these results, the observed enhancement of Huggins coefficient for short chain and branched polymer could be satisfactorily interpreted.展开更多
In this paper we propose and analyze a second order accurate numericalscheme for the Cahn-Hilliard equation with logarithmic Flory Huggins energy potential. A modified Crank-Nicolson approximation is applied to the lo...In this paper we propose and analyze a second order accurate numericalscheme for the Cahn-Hilliard equation with logarithmic Flory Huggins energy potential. A modified Crank-Nicolson approximation is applied to the logarithmic nonlinear term, while the expansive term is updated by an explicit second order AdamsBashforth extrapolation, and an alternate temporal stencil is used for the surface diffusion term. A nonlinear artificial regularization term is added in the numerical scheme,which ensures the positivity-preserving property, i.e., the numerical value of the phasevariable is always between -1 and 1 at a point-wise level. Furthermore, an unconditional energy stability of the numerical scheme is derived, leveraging the special formof the logarithmic approximation term. In addition, an optimal rate convergence estimate is provided for the proposed numerical scheme, with the help of linearizedstability analysis. A few numerical results, including both the constant-mobility andsolution-dependent mobility flows, are presented to validate the robustness of the proposed numerical scheme.展开更多
In this paper, we propose and analyze a second order accurate in time, masslumped mixed finite element scheme for the Cahn-Hilliard equation with a logarithmic Flory-Huggins energy potential. The standard backward dif...In this paper, we propose and analyze a second order accurate in time, masslumped mixed finite element scheme for the Cahn-Hilliard equation with a logarithmic Flory-Huggins energy potential. The standard backward differentiation formula (BDF)stencil is applied in the temporal discretization. In the chemical potential approximation,both the logarithmic singular terms and the surface diffusion term are treatedimplicitly, while the expansive term is explicitly updated via a second-order Adams-Bashforth extrapolation formula, following the idea of the convex-concave decompositionof the energy functional. In addition, an artificial Douglas-Dupont regularizationterm is added to ensure the energy dissipativity. In the spatial discretization, the masslumped finite element method is adopted. We provide a theoretical justification of theunique solvability of the mass lumped finite element scheme, using a piecewise linearelement. In particular, the positivity is always preserved for the logarithmic argumentsin the sense that the phase variable is always located between -1 and 1. In fact, thesingular nature of the implicit terms and the mass lumped approach play an essentialrole in the positivity preservation in the discrete setting. Subsequently, an unconditionalenergy stability is proven for the proposed numerical scheme. In addition, theconvergence analysis and error estimate of the numerical scheme are also presented.Two numerical experiments are carried out to verify the theoretical properties.展开更多
羟基磷灰石微粒人工骨(Hydroxylapati- te Particle Artificial Bone,HA)是一种生物相容性良好的骨替代材料。其异位诱导成骨细胞生长的研究国内尚未见报导。本实验用Wistar大鼠40只,按Reddi和Huggins建立的异位诱导模型作胸大肌肌袋移...羟基磷灰石微粒人工骨(Hydroxylapati- te Particle Artificial Bone,HA)是一种生物相容性良好的骨替代材料。其异位诱导成骨细胞生长的研究国内尚未见报导。本实验用Wistar大鼠40只,按Reddi和Huggins建立的异位诱导模型作胸大肌肌袋移植。组织学作HE,AB/HE染色;组化作ALP、钙质染色法。展开更多
The intrinsic viscosity [η], Huggins constant （Ku）, [η]0, α^3 and flow activation energy values of nylon 6 have been measured in wateηm-cresol （0/100-20/80） systems at different temperatures （20-60℃）. It ha...The intrinsic viscosity [η], Huggins constant （Ku）, [η]0, α^3 and flow activation energy values of nylon 6 have been measured in wateηm-cresol （0/100-20/80） systems at different temperatures （20-60℃）. It has been found that the intrinsic viscosity, [η]0 and α^3 increase with the increase in water contents in m-cresol up to 15% and then decrease. They increase with the increase in temperature irrespective of solvent composition. It has been noted that the percent increase of α^3 is the highest at 60℃ and the lowest at 20℃ for a particular solvent system. The intrinsic viscosity data obey Arrhenius equation over the considered conditions. The activation energy and the KH values decrease very sharply with the addition of water, giving a minimum value at 15% of water and then increase slowly. The variation of all the parameters has been explained in terms of variation in thermodynamic quality of solvent with the addition of water to m-cresol and change in temperature, resulting in the change of conformational and orientational properties of polymer molecules. This change of solvent quality also results in variation of selective sorption of solvent over the polymer, such as hydrogen bonding, etc.展开更多
The reduced viscosity of polymer guar gum solutions containing a certain concentration of sodium dodecyl benzene sulfonate （SDBS） was measured. It has been found that the Huggins coefficient kH of polymer solutions ...The reduced viscosity of polymer guar gum solutions containing a certain concentration of sodium dodecyl benzene sulfonate （SDBS） was measured. It has been found that the Huggins coefficient kH of polymer solutions is very sensitive to the concentration of the surfactant, CSDBS, in solutions. If CSDBS is lower than CMC, the critical micelle concentration of SDBS, kH increases rapidly with CSDBS. On the other hand, if CSDBS is larger than CMC, kH decreases rapidly with CSDBS. Comparatively, the intrinsic viscosity of polymer solution does not show a notable change with CSDBS. The experimental results indicate that the interchain association of polymer guar gum in solution is greatly associated with SDBS interacted with polymer chains through hydrogen bonds. However, the effect of SDBS upon the intrachain association of polymer guar gum solution is negligible, presumably due to the fact that guar gum is a slightly stiffened random-coil chain polymer.展开更多
文摘The chain length dependency of molar association constant K_a of polymer in solution was investigated theoretically. K_a is proportional to the effective hydrodynamic volume V_ eff of polymer chain in solution. V_ eff is the product of a shape factor and hydrodynamic volume. On the basis of these results, the observed enhancement of Huggins coefficient for short chain and branched polymer could be satisfactorily interpreted.
基金This work is supported in part by the grants NSFC 12071090(W.Chen)NSF DMS-2012669(C.Wang)+2 种基金NSFC 11871159Guangdong Provincial Key Laboratory for Computational Science and Material Design 2019B030301001(X.Wang)NSF DMS-1719854,DMS-2012634(S.Wise).C.Wang also thanks the Key Laboratory of Mathematics for Nonlinear Sciences,Fudan University,for the support.
文摘In this paper we propose and analyze a second order accurate numericalscheme for the Cahn-Hilliard equation with logarithmic Flory Huggins energy potential. A modified Crank-Nicolson approximation is applied to the logarithmic nonlinear term, while the expansive term is updated by an explicit second order AdamsBashforth extrapolation, and an alternate temporal stencil is used for the surface diffusion term. A nonlinear artificial regularization term is added in the numerical scheme,which ensures the positivity-preserving property, i.e., the numerical value of the phasevariable is always between -1 and 1 at a point-wise level. Furthermore, an unconditional energy stability of the numerical scheme is derived, leveraging the special formof the logarithmic approximation term. In addition, an optimal rate convergence estimate is provided for the proposed numerical scheme, with the help of linearizedstability analysis. A few numerical results, including both the constant-mobility andsolution-dependent mobility flows, are presented to validate the robustness of the proposed numerical scheme.
基金NSFC(No.12071090)the National Key R&D Program of China(No.2019YFA0709502)+2 种基金Z.R.Zhang is partially supported by NSFC No.11871105 and Science Challenge Project No.TZ2018002C.Wang is partially supported by the NSF DMS-2012269S.M.Wise is partially supported by the NSF DMS-1719854,DMS-2012634.
文摘In this paper, we propose and analyze a second order accurate in time, masslumped mixed finite element scheme for the Cahn-Hilliard equation with a logarithmic Flory-Huggins energy potential. The standard backward differentiation formula (BDF)stencil is applied in the temporal discretization. In the chemical potential approximation,both the logarithmic singular terms and the surface diffusion term are treatedimplicitly, while the expansive term is explicitly updated via a second-order Adams-Bashforth extrapolation formula, following the idea of the convex-concave decompositionof the energy functional. In addition, an artificial Douglas-Dupont regularizationterm is added to ensure the energy dissipativity. In the spatial discretization, the masslumped finite element method is adopted. We provide a theoretical justification of theunique solvability of the mass lumped finite element scheme, using a piecewise linearelement. In particular, the positivity is always preserved for the logarithmic argumentsin the sense that the phase variable is always located between -1 and 1. In fact, thesingular nature of the implicit terms and the mass lumped approach play an essentialrole in the positivity preservation in the discrete setting. Subsequently, an unconditionalenergy stability is proven for the proposed numerical scheme. In addition, theconvergence analysis and error estimate of the numerical scheme are also presented.Two numerical experiments are carried out to verify the theoretical properties.
文摘羟基磷灰石微粒人工骨(Hydroxylapati- te Particle Artificial Bone,HA)是一种生物相容性良好的骨替代材料。其异位诱导成骨细胞生长的研究国内尚未见报导。本实验用Wistar大鼠40只,按Reddi和Huggins建立的异位诱导模型作胸大肌肌袋移植。组织学作HE,AB/HE染色;组化作ALP、钙质染色法。
文摘The intrinsic viscosity [η], Huggins constant （Ku）, [η]0, α^3 and flow activation energy values of nylon 6 have been measured in wateηm-cresol （0/100-20/80） systems at different temperatures （20-60℃）. It has been found that the intrinsic viscosity, [η]0 and α^3 increase with the increase in water contents in m-cresol up to 15% and then decrease. They increase with the increase in temperature irrespective of solvent composition. It has been noted that the percent increase of α^3 is the highest at 60℃ and the lowest at 20℃ for a particular solvent system. The intrinsic viscosity data obey Arrhenius equation over the considered conditions. The activation energy and the KH values decrease very sharply with the addition of water, giving a minimum value at 15% of water and then increase slowly. The variation of all the parameters has been explained in terms of variation in thermodynamic quality of solvent with the addition of water to m-cresol and change in temperature, resulting in the change of conformational and orientational properties of polymer molecules. This change of solvent quality also results in variation of selective sorption of solvent over the polymer, such as hydrogen bonding, etc.
文摘The reduced viscosity of polymer guar gum solutions containing a certain concentration of sodium dodecyl benzene sulfonate （SDBS） was measured. It has been found that the Huggins coefficient kH of polymer solutions is very sensitive to the concentration of the surfactant, CSDBS, in solutions. If CSDBS is lower than CMC, the critical micelle concentration of SDBS, kH increases rapidly with CSDBS. On the other hand, if CSDBS is larger than CMC, kH decreases rapidly with CSDBS. Comparatively, the intrinsic viscosity of polymer solution does not show a notable change with CSDBS. The experimental results indicate that the interchain association of polymer guar gum in solution is greatly associated with SDBS interacted with polymer chains through hydrogen bonds. However, the effect of SDBS upon the intrachain association of polymer guar gum solution is negligible, presumably due to the fact that guar gum is a slightly stiffened random-coil chain polymer.
