Stochastic theory of ultrathin lubricant film melting in the stick-slip regime

Melting of an ultrathin lubricant film under friction between atomically smooth surfaces is studied in terms of the Lorentz model. Additive noise associated with shear stresses and strains, as well as with film temperature, is introduced, and a phase diagram is constructed where the noise intensity of the film temperature and the temperature of rubbing surfaces define the domains of sliding, dry, and stick-slip friction. Conditions are found under which stick-slip friction proceeds in the intermittent regime, which is characteristic of selforganized criticality. The stress self-similar distribution, which is provided by temperature fluctuations, is represented with allowance for nonlinear relaxation of stresses and fractional feedbacks in the Lorentz system. Such a fractional scheme is used to construct a phase diagram separating out different types of friction. Based on the study of the fractional Fokker-Planck equation, the conclusion is drawn that stick-slip friction corresponds to the subdiffusion process.     

First-order phase transition between the liquidlike and solidlike structures of a boundary lubricant

A thermodynamic model for characterization of the first-order phase transition between the structural states of a boundary lubricant is suggested. It is shown that melting of the lubricant is due both to a rise in its temperature and to shear experienced by friction surfaces when elastic strains (stresses) exceed a critical value. A phase diagram with regions of dry and sliding friction is constructed. Using a mechanical analogue of the tribological system, the dependence of the friction force on the lubricant temperature and relative shear rate of the friction surfaces is analyzed. The observed conditions of stick-slip friction, which is the main reason for friction parts wear, are described. Reasons for stick-slip friction are revealed.     

Periodic intermittent regime of a boundary flow

Melting of an ultrathin lubricant film during friction between two atomically smooth surfaces is investigated using the Lorentz model for approximating the viscoelastic medium. Second-order differential equations describing damped harmonic oscillations are derived for three boundary relations between the shear stresses, strain, and temperature relaxation times. In all cases, phase portraits and time dependences of stresses are constructed. It is found that under the action of a random force (additive uncorrelated noise), an undamped oscillation mode corresponding to a periodic intermittent regime sets in, which conforms to a periodic stick-slip regime of friction that is mainly responsible for fracture of rubbing parts. The conditions in which the periodic intermittent regime is manifested most clearly are determined, as well as parameters for which this regime does not set in the entire range of the friction surface temperature.     

Effect of correlated temperature fluctuations on the phase dynamics in an ultrathin lubricant film

The melting of an ultrathin lubricant film at friction between atomically smooth surfaces is studied with allowance for fluctuations of its temperature, which are described by the Ornstein-Uhlenbeck process. The behavior of the most probable types of shear stresses arising in the lubricant is considered, and phase diagrams for second-and first-order phase transformations (the melting of an amorphous lubricant and that of a crystalline lubricant, respectively) are constructed. It is shown that, in the former case, lubricant temperature fluctuations lead to the formation of a stick-slip friction domain separating the domains of dry and sliding friction, which is typical of first-order transitions. In the latter case, three domains of stick-slip friction arise, which mark the transitions between dry friction and metastable and stable sliding friction. As the time of correlation of lubricant temperature fluctuations gets longer, the temperature of rubbing surfaces rises to the point where sliding friction sets in.     

Phenomenological description of phase transitions in thin BaTiO<Subscript>3</Subscript> films

Phase transitions in thin epitaxial films of BaTiO₃ are described phenomenologically in terms of Landau potentials with sixth-and eighth-order terms. It is established that the phase diagram depends on the electrostrictive constant Q ₁₂. The phase diagrams calculated for different values of Q ₁₂ available in the literature differ qualitatively. The dependence of the misfit strain of a film on the film tetragonality at room temperature is found, which makes it possible to determine the thermodynamic path in the phase diagram for a specific film. The dependences of the spontaneous polarization and dielectric constant of a film on the misfit strain at room temperature are constructed.     

参数修改对铁电薄膜相变性质的影响

在关联有效场理论的框架内, 利用微分算子技术, 详细地计算了基于横场伊辛模型描述的对称铁电薄膜系统的相变性质. 根据薄膜各层自旋平均值构成的一系列耦合方程, 推导出可以用来计算任意层的具有不同表面层的薄膜相图的解析通式方程, 讨论了参数修改对薄膜相互作用参数从FPD (铁电相占主导地位的相图)到PPD (顺电相占主导地位的相图)过渡值和参数空间中各相变区域的影响. 在与平均场近似进行比较的结果显示, 关联有效场理论所得到的铁电薄膜的铁电性在某种程度上比平均场近似下的结果减弱. 关键词： 铁电薄膜 横场伊辛模型 相图 居里温度     

Phenomenological theory for the melting of a thin lubricant film between two atomically smooth solid surfaces

A thermodynamic model is developed for the melting of an ultrathin lubricant film squeezed between two atomically smooth solid surfaces. To describe the state of lubricant, an excess volume parameter is introduced; it appears due to the chaos in the structure of a solid body induced by melting. This parameter increases with the total internal energy upon melting. Thermodynamic melting and shear melting are described. The dependences of the friction force on the lubricant temperature and the shear rate of friction surfaces are analyzed. The calculated results are compared to the experimental data.     

Ordering Mechanisms in Confined Diblock Copolymers

We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of confining flat surfaces. The surfaces are chemically patterned where different regions attract different parts of the copolymer chain. The surface pattern or template is decomposed into its Fourier modes, and the decay of these modes is analyzed. The propagation of the surface pattern into the disordered bulk is given for several types of patterns (e.g. uniform and striped surface). It is further shown that complex morphology can be induced in a thin film even though the bulk is disordered. We next consider lamellar diblock copolymers (low temperature regime) in the presence of a striped surface. It is shown that lamellae acquire a tilt with respect to the surface, if the surface periodicity is larger than the bulk one. The lamellae close to the surface are strongly distorted from their perfect shape. When the surface and lamellar periodicities are equal, the lamellae are perpendicular to the surface. Lastly, the transition from parallel to perpendicular lamellae in a thin film is presented. The transition between the two states depends on the surface separation and strength of surface interactions. We further calculate the phase diagram in the presence of perpendicular electric field favoring perpendicular ordering. In the strong segregation limit we introduce a simple model to calculate the phase diagram of the fully parallel, fully perpendicular and mixed (parallel and perpendicular) states.     

Hysteresis phenomena during melting of an ultrathin lubricant film

The influence of a deformational defect of the shear modulus on the melting of an ultrathin lubricant film was investigated in the framework of the Lorenz model used for describing a viscoelastic medium. It was established that the film can undergo both stepwise and continuous melting. Analysis of the lubricant behavior revealed that there are three modes corresponding to a zero shear stress, a Hookean portion in the loading diagram, and a plastic-flow portion. The hysteresis in the dependences of the stationary shear stress on the strain and the friction surface temperature is examined.     

Investigation of the crossover properties for the interaction parameters of a ferroelectric thin film

The crossover feature, from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD), for the interaction parameters of a ferroelectric thin film described by the transverse Ising model have been calculated in detail by the use of the mean-field approximation. The crossover values of the exchange interactions and the transverse fields for a thin film with certain layers are displayed as a curved surface in the three-dimensional parameter space. The numerical results show that for thin films with different numbers of layers there exists a common intersection line for the curved surfaces of the crossover values. Meanwhile the layer-independent equation for the intersection line is obtained for the first time.     

Phase diagram of a wide current-carrying superconducting film

A model of current heating of a wide superconducting film is suggested assuming nonlinearity of the film conductance. Within this model, the parameters of the film can be characterized by a single dimensionless coefficient of thermal balance which includes both thermal and resistive parameters of the system. The stability of the state of the current-carrying film is analyzed. A phase diagram of the film is constructed in terms of the coefficient of thermal balance and the average current density. The propagation velocity of a stationary nonuniform temperature distribution in the film is calculated as a function of current density at various values of the coefficient of thermal balance.     

Binary separation in very thin nematic films: thickness and phase coexistence

The behavior as a function of temperature of very thin films (10 to 200 nm) of pentylcyanobiphenyl on silicon substrates is reported. In the vicinity of the nematic-isotropic transition we observe a coexistence of two regions of different thicknesses: thick regions are in the nematic state while thin ones are in the isotropic state. Moreover, the transition temperature is shifted downward following a 1/h(2) law ( h is the film thickness). Microscope observations and small-angle x-ray scattering allowed us to draw a phase diagram which is explained in terms of a binary first-order phase transition where thickness plays the role of an order parameter.     

On a moving liquid film and its instability on textured surfaces

Recently, two regimes of viscous friction on textured surfaces were proposed in the context of penetration of liquid film into the texture (EPL 79, 56005 (2007)): the Poiseuille and Stokes regimes. With this idea on viscous friction, we theoretically discuss instabilities on a liquid film on textured surfaces when the film is forced to move with external forces. When a film recedes due to a pressure drop, we find scaling laws for instabilities to be checked in future experiments. When a circular film expands due to centrifugal force we find that the expanding film is stable against rim fluctuations (within the linear stability analysis) with its radius determined by a simple equation. Our discussion sheds light on the curvature of the front of the moving liquid film on textured surfaces and how the film thickness is kept fixed to the texture height on textured surfaces, aspects which have not been discussed in previous studies.     

Phase behaviour of <Emphasis Type="Italic">n</Emphasis>-hexane/perfluoro-<Emphasis Type="Italic">n</Emphasis>-hexane binary thin wetting films

We present X-ray reflectivity investigations of the concentration distribution in binary liquid thin films on silicon substrates. The liquid-vapor coexistence of the binary mixture investigated, hexane and perfluorohexane, is far from criticality. Therefore, a sharp interface separates the liquid film from the vapor. The data reveal a separation of the film in layers parallel to the substrate. A phase diagram is constructed as a projection to the (composition difference, temperature) space, covering a temperature range corresponding to the one-phase and the two-phase regime of the bulk liquid. Although the composition data indicate a mixing gap similar to that of the bulk system, there are two major differences: i) only the near-surface phase changes its composition significantly, and ii) a composition gradient in the film exists also at higher temperatures where in the bulk system the one-phase regime exists.Received: 28 April 2004, Published online: 21 September 2004PACS: 61.10.Kw X-ray reflectometry (surfaces, interfaces, films) - 64.75. + g Solubility, segregation, and mixing; phase separation - 68.15. + e Liquid thin films     

Modeling of soft phase transfer to the surface of multicomponent aluminum alloy in friction

A model for calculating the dependence of the amount of solid lubricant formed on the surface of a multicomponent aluminum alloy in friction is proposed. The constructed model is applied to analyze how the properties of the matrix and soft structural components as well as the alloy structure influence the amount of the soft phase transferred to the friction zone which provides for self-lubrication. Recommendations are given concerning the structural composition of the alloy (size and density of phase inclusions) in order to increase the thickness of formed lubricant film in specified friction modes.     

Study on effect of dimples on friction of parallel surfaces under different sliding conditions

The influence of rectangle dimples with flat bottom on the friction of parallel surfaces at different sliding conditions is investigated based on lubrication equations. The elastic deformation of rough surfaces is evaluated using continuous convolution fast Fourier transform (CC-FFT). The friction coefficients for dimpled and non-dimpled parallel surfaces by simulation are compared with experimental results. Results show that this kind of dimples can reduce the friction coefficient for cases with the smaller ratio of film thickness to roughness (h/R_q), small roughness or large applied load. The friction force for the parallel surfaces can decrease due to the dimple effect over the range of the larger sliding speed, larger load or smoother surfaces.     

Energy dissipation in solid friction

Dissipation in solid friction is studied as a function of the elastic properties of the two sliding surfaces. The two surfaces have been constructed by embedding macroscopic asperities in an elastic layer. It is shown that when the surfaces are rigid the energy dissipation is smaller than in the elastic case. The scaling of the friction force as a function of the asperity number is also studied. Received 9 November 1998     

Spontaneous transformations of the magnetic structure of a film nanocontact

The magnetization distributions in a symmetric magnetic film nanocontact for oppositely magnetized ferromagnetic electrodes are analyzed based on numerically solving the Landau-Lifshitz and magnetostatic equations as a function of magnetic and geometrical factors. It is found that a symmetric magnetic configuration is unstable when the head-to-head domain wall dividing the regions with opposite orientations of magnetization is located at the center of the nanocontact. The instability arises when the uniaxial magnetic anisotropy constant reaches a certain critical value K _c below which it spontaneously leaves the center of the nanocontact. The transition from the symmetric state (wall at the center) to an asymmetric one can be continuous (second order) or discrete (first order), depending on the geometrical and physical parameters of the nanocontact (length to width ratio, anisotropy constant, and saturation magnetization). The phase diagram is constructed in terms of the variable’s nanocontact length vs. anisotropy constant. This diagram divides the symmetric and asymmetric magnetic configurations of the system. The occurrence of a tricritical point in the phase diagram is its characteristic feature.     

衬底温度对类金刚石薄膜力学性能的影响

 采用脉冲激光沉积方法在不同衬底温度下制备了最高硬度与弹性模量分别达45 GPa和290 GPa,且表面十分光滑的类金刚石薄膜。在相对湿度为80%的条件下,薄膜最低的摩擦系数与磨损率分别为0.045与5.74×10^-10 mm³·N^-1·m^-1。实验结果表明,硬度与弹性模量随衬底温度升高而降低,摩擦系数与磨损率随衬底温度升高而增大。拉曼光谱表明:在室温下制备的薄膜为典型类金刚石结构,sp³含量高达76.8%,而随温度升高,薄膜结构逐渐经无定形碳结构向纳米晶石墨结构方向发展,sp³含量也随之降低,力学性能变差。