B. N. J. Persson

Crack propagation in rubber-like materials

Crack propagation in rubber-like materials is of great practical importance but still not well understood. We study the contribution to the crack propagation energy (per unit area) G from the viscoelastic deformations of the rubber in front of the propagating crack tip. We show that G takes the standard form G(v,T) = G0[1+f(v,T)] where G0 is associated with the (complex) bond-breaking processes at the crack tip while f(v,T) is determined by the viscoelastic energy dissipation in front of the crack tip. As applications, we discuss the role of crack propagation for adhesion, rolling resistance and sliding friction for smooth surfaces, and for rubber wear.

Adsorbate motions induced by inelastic-tunneling current: Theoretical scenarios of two-electron processes

We discuss how the excitation of high-frequency modes in adsorbed molecules may result in motion (e.g., rotation, translation, or dissociation) of the molecules. Our study is based on rate equations and considers one- and two-vibrational excitation processes, corresponding to linear and quadratic dependences of the reaction rate on the tunneling current in the case the scanning tunneling microscopy is used to excite the vibrations (inelastic tunneling). From the results reported in this paper it should be possible to obtain intramolecular transition rates directly from the experimental data, and gain some understanding on how these important quantities depend on the modes involved and on the substrate.

Heat transfer between graphene and amorphous SiO2

We study the heat transfer between graphene and amorphous SiO(2). We include both the heat transfer from the area of real contact, and between the surfaces in the non-contact region. We consider the radiative heat transfer associated with the evanescent electromagnetic waves which exist outside of all bodies, and the heat transfer by the gas in the non-contact region. We find that the dominant contribution to the heat transfer results from the area of real contact, and the calculated value of the heat transfer coefficient is in good agreement with the value deduced from experimental data.

Heat transfer between weakly coupled systems: Graphene on a-SiO2

We study the heat transfer between weakly coupled systems with flat interface. We present a simple analytical result which can be used to estimate the heat transfer coefficient. As an application we consider the heat transfer between graphene and amorphous SiO2. The calculated value of the heat transfer coefficient is in good agreement with the value deduced from experimental data.

Heat transfer between adsorbate and laser-heated hot electrons

Strong short laser pulses can give rise to a strong increase in the electronic temperature at metal surfaces. Energy transfer from the hot electrons to adsorbed molecules may result in adsorbate reactions, e.g. desorption or diffusion. We point out the limitations of an often used equation to describe the heat transfer process in terms of a friction coupling. We propose a simple theory for the energy transfer between the adsorbate and hot electrons using a newly introduced heat transfer coefficient, which depends on the adsorbate temperature. We calculate the transient adsorbate temperature and the reaction yield for a Morse potential as a function of the laser fluency. The results are compared to those obtained using a conventional heat transfer equation with temperature-independent friction. It is found that our equation of energy (heat) transfer gives a significantly lower adsorbate peak temperature, which results in a large modification of the reaction yield. We also consider the heat transfer between different vibrational modes excited by hot electrons. This mode coupling provides indirect heating of the vibrational temperature in addition to the direct heating by hot electrons. The formula of heat transfer through linear mode–mode coupling of two harmonic oscillators is applied to the recent time-resolved study of carbon monoxide and atomic oxygen hopping on an ultrafast laser-heated Pt(111) surface. It is found that the maximum temperature of the frustrated translation mode can reach high temperatures for hopping, even when direct friction coupling to the hot electrons is not strong enough.

Comment on "Diffusion and dimer formation of CO molecules induced by femtosecond laser pulses".

In a recent Letter [1], Mehlhorn et al. reported on femtosecond-laser induced diffusion yield YðFÞ of a single CO molecule on Cu(111) using a scanning tunneling microscope. As a function of the absorbed fluence F, they observed that YðFÞ exhibits a linear increase at low F followed by a strongly nonlinear increase at high F. They proposed that the linear increase is induced by single electronic transitions, while the strong increase can be described using a friction model where hot electrons transfer energy to the frustrated translation (FT) mode. They assumed the electronic friction e to depend on the electron temperature TeðtÞ, in accordance with earlier suggestions [2]. However, it was proved that frictional coupling is temperature independent if it originates from electron-hole pair excitation [3]. The electronic friction is defined as el 1⁄4 w1!0 w0!1, where the decay rate w1!0 and the thermal excitation rate w0!1 between the vibrational excited state and the ground state are given by eðnB þ 1Þ and enB, respectively, and where nB 1⁄4 1⁄2expð@!=kBTÞ 1 1 is the Bose-Einstein distribution function. It is clear that e is temperature independent, even when w1!0 and w0!1 depend on the temperature. Here we show how one can understand the experimental results of Ref. [1] without using a temperature-dependent friction. We propose an indirect heating of the FT mode via the mode coupling to the frustrated rotation (FR) mode in addition to a direct heating of the FT mode by laser excitation [4]. We note that for CO diffusion on a Pt(111) indirect heating of the FT mode by the FR mode reproduced the experimental results of the real-time monitoring [4,5] and two-pulse correlation [6,7]. In the mode-coupling model we have two coupled equations: dUFT=dt 1⁄4 1⁄2 FT þ ð FT;FR=@!FRÞUFR ðUel UFTÞ and dUFR=dt 1⁄4 1⁄2 FR þ ð FR;FT=@!FTÞUFTÞ ðUel UFRÞ, where Ux 1⁄4 @!=1⁄2expð@!=kBTxÞ 1 denotes the energy of a harmonic oscillator corresponding to the FT and FR modes at the temperature Tx (where x 1⁄4 FT, FR, and el). Without intermode coupling (i.e., FT;FR 1⁄4 0), neither heating of the FTor FR mode can explain the experimental data of Ref. [1]. However, using the measured FT and FR [8] and a suitably chosen FT;FR the calculated YðFÞ agrees very well with the experimental result (see Fig. 1). In this calculation we have used the diffusion barrier height Eb 1⁄4 87 meV, which is close to the value (97 4 meV) deduced from diffusion data for CO on Cu(110) [9]. Also, the prefactor we use (R0 1⁄4 3 10 s ) is close to what one expects from Kramers theory of activated processes, which in the present case gives R0 !FT=2 10 s . To summarize, in the friction model for heat transfer one should use a temperature-independent electronic friction. If the friction model cannot describe the experimental data with a temperature-independent electronic friction, the surface reaction involves more complex processes, e.g., involving two anharmonically coupled adsorbate modes as assumed above. We believe that our model with intermode coupling between the FT and FR modes captures the essential elementary process behind CO diffusion [10].