The time evolution of oxygen plasma treated polystyrene(PS)surfaces was investigated upon storing them in theair under controlled humidity conditions.The methods of water contact angle,X-ray photoelectron spectroscopy...The time evolution of oxygen plasma treated polystyrene(PS)surfaces was investigated upon storing them in theair under controlled humidity conditions.The methods of water contact angle,X-ray photoelectron spectroscopy(XPS),sumfrequency generation(SFG)vibrational spectroscopy,and atomic force microscopy(AFM)were used to infer the surfaceproperties and structure.Chemical groups containing oxygen were formed on the PS surface with the plasma treatment,demonstrated by water contact angle and XPS.The surface polarity decayed markedly on time,as assessed by steady increasein the water contact angle as a function of storage time,from zero to around 60°.The observed decay is interpreted as arisingfrom surface rearrangement processes to burying polar groups away from the uppermost layer of the surfaces,which is incontact with air.On the other hand,XPS results show that the chemical composition in the first 3 nm surface layer isunaffected by the surface aging,and the depth profile of oxygen is essentially the same with time.A possible change of PSsurface roughness was examined by AFM,and it showed that the increase of water contact angle during surface aging couldnot be attributed to surface roughness.Thus,it is concluded that surface aging is attributable to surface reorganization andthe motion of oxygen containing groups is confined within the XPS probing depth.SFG spectroscopy,which is intrinsicallyinterface-specific,was used to detect the chemical structure of PS surface at the molecular level after various aging times.The results are interpreted as follows.During the aging of the plasma treated PS surfaces,the oxygen containing groupsundergo reorientation processes toward the polymer bulk and/or parallel to the surface,while the CH_2 moiety stands up onthe PS surface.Our results indicate that the surface configuration changes do not require large length scale segmentalmotions or migration of macromolecules.Motions that are responsible for surface configuration changes could be relativelysmall rotational motions.The aging behaviors under different relative humidity conditions were shown to be similar from18% to 91%,whereas the kinetics of surface polarity decays were faster in higher relative humidity.Here,the surfacerearrangement of polystyrene films that were previously treated by oxygen plasma and aged,and was investigated in terms ofcontact angle after the water immersion.The contact angles of the water-immersed samples were found to change andapproach the initial values before the immersion asymptotically.展开更多
We establish the exponential stability of fast traveling pulse solutions to nonlinear singularly per-turbed systems of integral differential equations arising from neuronal networks.It has been proved that expo-nentia...We establish the exponential stability of fast traveling pulse solutions to nonlinear singularly per-turbed systems of integral differential equations arising from neuronal networks.It has been proved that expo-nential stability of these orbits is equivalent to linear stability.Let (?) be the linear differential operator obtainedby linearizing the nonlinear system about its fast pulse,and let σ((?)) be the spectrum of (?).The linearizedstability criterion says that if max{Reλ:λ∈σ((?)),λ≠0}(?)-D,for some positive constant D,and λ=0 is asimple eigenvalue of (?)(ε),then the stability follows immediately (see [13] and [37]).Therefore,to establish theexponential stability of the fast pulse,it suffices to investigate the spectrum of the operator (?).It is relativelyeasy to find the continuous spectrum,but it is very difficult to find the isolated spectrum.The real part ofthe continuous spectrum has a uniformly negative upper bound,hence it causes no threat to the stability.Itremains to see if the isolated spectrum is safe.Eigenvalue functions (see [14] and [35,36]) have been a powerful tool to study the isolated spectrum of the as-sociated linear differential operators because the zeros of the eigenvalue functions coincide with the eigenvaluesof the operators.There have been some known methods to define eigenvalue functions for nonlinear systems ofreaction diffusion equations and for nonlinear dispersive wave equations.But for integral differential equations,we have to use different ideas to construct eigenvalue functions.We will use the method of variation of param-eters to construct the eigenvalue functions in the complex plane C.By analyzing the eigenvalue functions,wefind that there are no nonzero eigenvalues of (?) in {λ∈C:Reλ(?)-D} for the fast traveling pulse.Moreoverλ=0 is simple.This implies that the exponential stability of the fast orbits is true.展开更多
We establish the optimal rates of decay estimates of global solutions of some abstract differential equations, which include many partial differential equations. We provide a general treatment so that any future probl...We establish the optimal rates of decay estimates of global solutions of some abstract differential equations, which include many partial differential equations. We provide a general treatment so that any future problem will enjoy the decay estimates displayed here as long as the general hypotheses are satisfied. The main hypotheses are the existence of global solutions of the equations and some growth control of the Fourier transform of the solutions. We establish the optimal rates of decay of the solutions for initial data in different spaces. The main ingredients and technical tools are the Fourier splitting method, the iteration skill and the energy estimates.展开更多
The equilibrium problem for the infinite elastic plane consisting of two different media is considered, in which the interface is a broken line, there is a straight crack touching the vertex of the broken line with ...The equilibrium problem for the infinite elastic plane consisting of two different media is considered, in which the interface is a broken line, there is a straight crack touching the vertex of the broken line with some symmetry and the same uniform pressures are applied to both of its sides. The problem is reduced to a uniquely solvable singular integral equation on the interface and the crack. The order of singularity at the vertex is considered, which may be determined by a transcendental equation.展开更多
基金This work was funded in part by NSF(DMR-0084301)Eastman Kodak Company.
文摘The time evolution of oxygen plasma treated polystyrene(PS)surfaces was investigated upon storing them in theair under controlled humidity conditions.The methods of water contact angle,X-ray photoelectron spectroscopy(XPS),sumfrequency generation(SFG)vibrational spectroscopy,and atomic force microscopy(AFM)were used to infer the surfaceproperties and structure.Chemical groups containing oxygen were formed on the PS surface with the plasma treatment,demonstrated by water contact angle and XPS.The surface polarity decayed markedly on time,as assessed by steady increasein the water contact angle as a function of storage time,from zero to around 60°.The observed decay is interpreted as arisingfrom surface rearrangement processes to burying polar groups away from the uppermost layer of the surfaces,which is incontact with air.On the other hand,XPS results show that the chemical composition in the first 3 nm surface layer isunaffected by the surface aging,and the depth profile of oxygen is essentially the same with time.A possible change of PSsurface roughness was examined by AFM,and it showed that the increase of water contact angle during surface aging couldnot be attributed to surface roughness.Thus,it is concluded that surface aging is attributable to surface reorganization andthe motion of oxygen containing groups is confined within the XPS probing depth.SFG spectroscopy,which is intrinsicallyinterface-specific,was used to detect the chemical structure of PS surface at the molecular level after various aging times.The results are interpreted as follows.During the aging of the plasma treated PS surfaces,the oxygen containing groupsundergo reorientation processes toward the polymer bulk and/or parallel to the surface,while the CH_2 moiety stands up onthe PS surface.Our results indicate that the surface configuration changes do not require large length scale segmentalmotions or migration of macromolecules.Motions that are responsible for surface configuration changes could be relativelysmall rotational motions.The aging behaviors under different relative humidity conditions were shown to be similar from18% to 91%,whereas the kinetics of surface polarity decays were faster in higher relative humidity.Here,the surfacerearrangement of polystyrene films that were previously treated by oxygen plasma and aged,and was investigated in terms ofcontact angle after the water immersion.The contact angles of the water-immersed samples were found to change andapproach the initial values before the immersion asymptotically.
基金This project is partly supported by the Reidler Foundation
文摘We establish the exponential stability of fast traveling pulse solutions to nonlinear singularly per-turbed systems of integral differential equations arising from neuronal networks.It has been proved that expo-nential stability of these orbits is equivalent to linear stability.Let (?) be the linear differential operator obtainedby linearizing the nonlinear system about its fast pulse,and let σ((?)) be the spectrum of (?).The linearizedstability criterion says that if max{Reλ:λ∈σ((?)),λ≠0}(?)-D,for some positive constant D,and λ=0 is asimple eigenvalue of (?)(ε),then the stability follows immediately (see [13] and [37]).Therefore,to establish theexponential stability of the fast pulse,it suffices to investigate the spectrum of the operator (?).It is relativelyeasy to find the continuous spectrum,but it is very difficult to find the isolated spectrum.The real part ofthe continuous spectrum has a uniformly negative upper bound,hence it causes no threat to the stability.Itremains to see if the isolated spectrum is safe.Eigenvalue functions (see [14] and [35,36]) have been a powerful tool to study the isolated spectrum of the as-sociated linear differential operators because the zeros of the eigenvalue functions coincide with the eigenvaluesof the operators.There have been some known methods to define eigenvalue functions for nonlinear systems ofreaction diffusion equations and for nonlinear dispersive wave equations.But for integral differential equations,we have to use different ideas to construct eigenvalue functions.We will use the method of variation of param-eters to construct the eigenvalue functions in the complex plane C.By analyzing the eigenvalue functions,wefind that there are no nonzero eigenvalues of (?) in {λ∈C:Reλ(?)-D} for the fast traveling pulse.Moreoverλ=0 is simple.This implies that the exponential stability of the fast orbits is true.
文摘We establish the optimal rates of decay estimates of global solutions of some abstract differential equations, which include many partial differential equations. We provide a general treatment so that any future problem will enjoy the decay estimates displayed here as long as the general hypotheses are satisfied. The main hypotheses are the existence of global solutions of the equations and some growth control of the Fourier transform of the solutions. We establish the optimal rates of decay of the solutions for initial data in different spaces. The main ingredients and technical tools are the Fourier splitting method, the iteration skill and the energy estimates.
文摘The equilibrium problem for the infinite elastic plane consisting of two different media is considered, in which the interface is a broken line, there is a straight crack touching the vertex of the broken line with some symmetry and the same uniform pressures are applied to both of its sides. The problem is reduced to a uniquely solvable singular integral equation on the interface and the crack. The order of singularity at the vertex is considered, which may be determined by a transcendental equation.
