Theoretical study on the motion of a La atom inside a C82 cage

The motion of a single lanthanum atom inside a C82 (C2v) fullerene cage has been investigated by means of the hybrid density functional method (B3LYP). The obtained potential energy surface (PES) suggests that the encapsulated La atom can oscillate only around the minimum energy potential well, which is apparently different from the scenario of a giant bowl-shaped movement at room temperature described by Nishibori et al. (Nishibori, E.; Takata, M.; Sakata, M.; Tanaka, H.; Hasegawa, M.; Shinohara, H. Chem. Phys. Lett. 2000, 330, 497-502.) Interestingly, our calculations show that the La atom may probably undergo a boat-shaped movement when the temperature is high enough. In addition, the computed 13C NMR spectrum of the C2v [La@C82]- is in an excellent agreement with the experimental nuclear magnetic resonance (NMR) spectrum (Tsuchiya, T.; Wakahara, T.; Maeda, Y.; Akasaka, T.; Waelchli, M.; Kato, T.; Okubo, H.; Mizorogi, N.; Kobayashi, K.; Nagase, S. Anew. Chem. 2005, 117, 3346-3349), which confirms that the isomer of La@C82 with the C2v symmetry is the most stable.     

Drop retention force as a function of drop size

The force, f, required to slide a drop past a surface is often considered in the literature as linear with the drop width, w, so that f/w = const. Furthermore, according to the Dussan equation for the case that the advancing and receding contact angles are constant with drop size, one can further simplify the above proportionality to f/V(1/3) = const where V is the drop volume. We show, however, that experimentally f/V(1/3) is usually a decaying function of V (rather than constant). The retention force increases with the time the drop rested on the surface prior to sliding. We show that this rested-time effect is similar for different drop sizes, and thus the change of f/V(1/3) with V occurs irrespective of the rested-time effect which suggests that the two effects are induced by different physical phenomena. The time effect is induced by the unsatisfied normal component of the Young equation which slowly deforms the surface with time, while the size effect is induced by time independent properties. According to the Dussan equation, the change of f/V(1/3) with V is also expressed in contact angle variation. Our results, however, show that contact angle variation that is within the scatter suffices to explain the significant force variation. Thus, it is easier to predict contact angle variation based on force variation rather than predicting force variation based on contact angle variation. A decrease of f/V(1/3) with V appears more common in the system studied compared to an increase.     

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.     

Critical Eotvos numbers for buoyancy-induced oil drop detachment based on shape analysis

Critical values of the Eotvos number, which is half the Bond number, above which buoyancy induced drop detachment occurs, are estimated based on force balance equations available in the literature [Colloids Surf. A: Physicochem. Eng. Aspects 178 (2001) 249]. Since there are two significantly different expressions of the capillary retention force responsible for holding oil drops on a solid substrate in an aqueous phase, the critical dimensionless number is estimated with these two distinct equations. The differential equation defining the drop shape, with the constraints of the drop volume and the 'pinned' or 'receding' contact line, is numerically solved. The equilibrium drop shapes predicted are shown to match the experimentally observed variations in drop shape. From the numerical solution, it is observed that for interfacial tension (IFT) values lower than a certain limit for a given drop size, no numerically estimated drop shape can fulfil the drop volume constraint. Similarly, for the dimensionless number above a critical value, no shape can meet all the constraints. These critical Eotvos numbers are estimated, based on the above numerical approach, for initial contact angles measured in oil varying from 20 degrees to 90 degrees. It is found that the critical Eotvos numbers estimated from the numerical shape analysis are between the critical values estimated from the two force-balance equations. Near 90 degrees, the critical values estimated from the drop shape analysis matches the values from one of the force balance estimates, but merges with the critical values of the dimensionless number, estimated from the other force balance model near 10 degrees. From this analysis, it appears that a combination of the two equations for the capillary retention force is required, with one dominating when the contact angles are high, while the other applies for low values of the contact angle.     

A stable intermediate wetting state after a water drop contacts the bottom of a microchannel or is placed on a single corner

It is considered that, after a water drop contacts the base of a roughness groove, water should immediately fill this roughness groove. Subsequently, Cassie-Baxter wetting state is transited to that of Wenzel. Accordingly, one of the criteria used to judge the transition from Cassie-Baxter to Wenzel states is whether a water drop has contact with the base of a roughness groove. In this work, through theoretical and experimental investigations, we show that this transition criterion does not always hold true in the case of microchannels. We first theoretically prove that, when an angle criterion is satisfied, there may exist an intermediate wetting state inside a microchannel after a water drop contacts the bottom of the microchannel. In this wetting state, water does not completely fill the microchannel, and air pockets still exist in its bottom corners. Also, the wetting state is stable in the sense that its energy state is lower than that of the Wenzel model. According to the angle criterion, such intermediate states may exist, for example, in microchannels with vertical sidewalls, when contact angles on the inner surfaces of these microchannels are larger than 135°. In addition to microchannels, the aforementioned intermediate state may also exist on a single corner (which is formed by a horizontal plate and an inclined plate), when the angle criterion is met. After theoretical modeling, we then conduct four types of tests on single corners and microchannels to validate the angle criterion. In these tests, once the angle criterion is met, stable intermediate states are observed on the corresponding samples. In addition, it is found from the two types of tests conducted on microchannels that, once Laplace pressure inside a water drop is gradually reduced, such an intermediate wetting state may be transited back to the original Cassie-Baxter state. On the other hand, the Wenzel state may not have such a reversal transition unless an additional force is applied to overcome energy barrier between Wenzel and Cassie-Baxter states.     

Shape analysis based critical Eotvos numbers for buoyancy induced partial detachment of oil drops from hydrophilic surfaces

Removal of oil drops from solid surfaces immersed in an aqueous medium is of interest in many applications. It has been shown that drop shape analysis can be used to predict conditions at which the stability limit of a lighter than water oil drop on a solid surface immersed in an aqueous bath is reached (Adv. Colloid Interface Sci. 98 (2002) 265). However the above analysis is restricted to cases where the contact angle made by the drop is below 90degrees and when the surface conditions result in a 'pinned' contact line. In this paper, it is shown that drop shape analysis can be used to predict the critical conditions at which drop stability limit is reached for drop contact angles of 90degrees and above, which is encountered with 'hydrophilic' surfaces. This critical condition can predict the occurrence of partial oil drop detachment, before complete removal due to 'roll-up', which occurs when the hydrophilic surface is adequately smooth which prevents 'pinning' of the contact line. The critical conditions at which partial drop detachment occurs can also be approximately predicted from simple force balances. It has been shown (Adv. Colloid Interface Sci. 98 (2002) 265) that for contact angles less than 90degrees, the critical limit based on shape analysis appears to resolve the differences that arise due to alternate expressions for capillary retention force. This paper shows that even for contact angles above 90degrees, the critical conditions predicted from the shape analysis resolves the differences in the predictions from the alternate force balances. Drop shape analysis used in this paper is based on the 'Arc-length' form of Young-Laplace or 'drop shape' equation, which is different from the 'Y vs X' form of the above equation that is used in Adv. Colloid Interface Sci. 98 (2002) 265. The above drop shape equation is solved by a fourth order Runge-Kutta technique and it is shown that for angles less than 90degrees, the two forms of the drop shape equation, predict almost identical values of the critical Eotvos number. This paper highlights the competing effects of interfacial tension lowering induced drop instability and 'roll-up', a term that is used to describe the retraction of the contact line of an oil drop on a surface, in being the primary c ause for drop detachment.     

Anomalously increased lifetimes of biological complexes at zero force due to the protein-water interface

A number of biological bonds show dramatically increased lifetimes at zero-force conditions, compared to lifetimes when even a small tensile force is applied to the ligand. The discrepancy is so great that it cannot be explained by the traditional receptor-ligand binding models. This generic phenomenon is rationalized here by considering the interaction of water with the receptor-ligand complex. It is argued that the water-protein interaction creates an energy barrier that prevents the ligand unbinding in the absence of the force. The properties of the interaction are such that even application of a relatively low force results in a dramatic drop of the bond lifetime due to the alteration of the water-receptor and water-ligand interaction network. The phenomenon is described by the presence of a second shallow interaction energy minimum for the bound ligand followed by a wide receptor-ligand dissociation barrier. The general analysis is applied quantitatively to the actin-myosin system, which demonstrates the gigantic drop of the bond lifetime at small forces and catch behavior (an increase in the lifetime) at moderate forces. The base hypothesis proposed to explain the small-force abnormal drop in the bond lifetime suggests that the majority of biological bonds may exhibit this phenomenon irrespectively whether they behave as slip or catch-slip bonds.     

Dynamics of terrace formation in a nanostructured thin block copolymer film

We have used dynamic self-consistent field (DSCF) theory to investigate the structural evolution of an ABA block copolymer thin film placed between a solid substrate and a free surface. In line with the few existing theoretical studies for pure homopolymers and mixtures, the free interface is introduced by a void component. In our calculations, the free surface experiences surface roughening and eventually the formation of terraces, as in the experiments. The kinetic pathway of the microstructures was compared to findings of an existing detailed experimental study (Knoll, A.; Lyakhova, K. S.; Horvat, A.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Nat. Mater. 2004, 3, 886) and was found to be equivalent in detail. This corroborates our assumption in this earlier work that the pathway due to changing film thickness is similar to a pathway due to changing surface energetics. Moreover, our calculations show for the first time that microstructural transitions are a driving force of polymer/air interface curving and the formation of terraces.     

界面现象与液滴聚并

报导了一个受溶质Marangoni效应影响的液滴聚结的迟缓现象．采用示踪液滴法，对滴加在正戊醇水溶液表面、受自发界而流控制的硝基乙烷液滴的运动和存在状态进行了研究．结果显示，在一定体系中溶质Marangoni效应可导致液滴的悬浮态，并对液滴的聚并产生显著影响．由于界面状态的不同，示踪液滴也表现出完全不同的动力学特征．基于以上认识对液滴运动速率的计算得到了合理的结果．     

Hydrodynamically induced formation of cellulose fibers. III. Coagulation of droplets of cellulose solution in extensional flow

The formation of cellulose fibers by coagulation of drops of cellulose solution in extensional flow was studied theoretically and experimentally. In the theory, which applies for slow-motion conditions, homogeneity of the drop is assumed. The drop deforms according to a previously established deformation mechanism and becomes solid when a critical concentration of coagulant is reached at a certain position inside the drop. The theoretical predictions for the variation of fiber length with various parameters were tested experimentally in a four-roller mill for cellulose/dimethyl sulfoxide/paraformaldehyde with glycerol as coagulant. In agreement with the theoretical predictions, it was found that fiber length increases with shear rate and original droplet size, but decreases with the diffusion coefficient of the coagulant in the cellulose solution.     

Membrane emulsification using membranes of regular pore spacing: Droplet size and uniformity in the presence of surface shear

During membrane emulsification it is shown that the size of the drops formed at the membrane surface may increase with increasing dispersed phase injection rate through the membrane, or it may decrease, depending on the prevailing conditions. This is illustrated using a paddle stirrer positioned above flat disc membranes with regular arrays of pores of 20 μm diameter and spacing between the pores of 80 and 200 μm. In the former case an additional mechanism for drop detachment is the push-off force, which is determined by the geometry of the drops as they deform at the membrane surface. When dispersing sunflower oil in to aqueous solutions containing Tween 20, drop sizes between 60 and 200 μm were produced, and in the case of the membrane when the push-off force was working the Coefficient of Variation of the drops formed was below 10%. The push-off force may be added to the shear-drag force to predict drop detachment. For the 200 μm pore spaced membrane this force is much less prominent than the 80 μm spaced membrane. The capillary-shear model has been modified to include this push-off force. The experimental study required the use of very low dispersed phase injection rates as well as very high rates. Hence, two different types of pumps were used to provide these: a peristaltic and syringe pumps. A small study comparing the drop size, and size distributions, showed that the pump type did not influence the drops produced by the membrane emulsification process.     

Testing of nonlinear electrofrictiophoresis in agarose gel

It was theoretically predicted earlier that if a periodic force without constant component is applied to a particle, then the particle can produce a directed drift in some direction. The effect is named nonlinear electrofrictiophoresis, because it is crucial for its appearance that the friction force depends on the particle's velocity in a nonlinear manner. We test a possibility to observe this effect when a mixture of fragments of DNA (the DNA ladder) moves in the agarose gel. For this purpose, we study the nonlinear characteristics of a DNA ladder movement in the gel. The gels with the ladder were run under various electric field strengths. It was found that the friction coefficient for each DNA fragment in the ladder depends on the migration velocity, suggesting that energy dissipation during migration is a nonlinear function of velocity. This nonlinearity makes the system under consideration suitable for observing nonlinear electrofrictiophoresis. A possible velocity of directed drift under periodic electric drive without constant component was estimated numerically for experimentally observed dependencies. The velocity appeared to be comparable with that of migration under a constant field of moderate strength. A possible mechanism of energy dissipation during movement of DNA through the gel is discussed.     

超疏水表面上冷凝液滴发生弹跳的机制与条件分析

使用液滴合并前后的体积和表面自由能守恒作为两个限制条件,确定了合并液滴的初始形状,即为偏离平衡态的亚稳态液滴,具有缩小其底半径而向平衡态液滴转变的推动力.进而分析了液滴变形过程中的推动力和三相线(TPCL)上的滞后阻力,建立了液滴变形的动态方程并进行了差分求解.如果液滴能够变形至底半径为0mm的状态,则根据该状态下液滴重心上移的速度确定液滴的弹跳高度.不同表面上冷凝液滴合并后的变形行为的计算结果表明,光滑表面上的液滴合并后,液滴只能发生有限的变形,一般都在达到平衡态之前就停止了变形,因此冷凝液滴不会发生弹跳;粗糙表面上的Wenzel态液滴的三相线上的滞后阻力更大,因而液滴更难以变形和弹跳;具有微纳二级结构表面上只润湿微米结构,但不润湿纳米结构的部分Wenzel态液滴能够变形至Cassie态,但没有明显的弹跳;只有在纳米或微纳二级结构表面上的较小Cassie态液滴合并后,液滴易于变形至底半径为0mm的状态并发生弹跳.因此,Cassie态合并液滴处于亚稳态,并且其三相线上的移动阻力很小,是导致冷凝液滴弹跳的关键因素.     

Dead-end street of protein folding: thermodynamic rationale of amyloid fibril formation

An increasing number of diseases, including Alzheimer's, have been found to be a result of the formation of amyloid aggregates that are practically independent of the original primary sequence of the protein(s). (Eakin, C. M.; Berman, A. J.; Miranker, A. D. Nat. Struct. Mol. Biol. 2006, 13, 202-208.) Consequently, the driving force of the transformation from original to disordered amyloid fold is expected to lie in the protein backbone, which is common to all proteins. (Nelson, R.; Sawaya, M. R.; Balbirnie, M.; Madsen, A. O.; Riekel, C.; Grothe, R.; Eisenberg, D. Nature 2005, 435, 773-778. Wright, C. F.; Teichmann, S. A.; Clarke, J.; Dobson, C. M. Nature 2005, 438, 878-881.) However, the exact explanation for the existence of such a "dead-end" structure is still unknown. Using systematic first principle calculations on carefully selected but large enough systems modeling the protein backbone we show that the beta-pleated sheet structure, the building block of amyloid fibers, is the thermodynamically most stable supramolecular arrangement of all the possible peptide dimers and oligomers both in vacuum and in aqueous environments. Even in a crystalline state (periodical, tight peptide attechment), the beta-pleated sheet assembly remains the most stable superstructure. The present theoretical study provides a quantum-level explanation for why proteins can take the amyloid state when local structural preferences jeopardize the functional native global fold and why it is a beta-pleated sheetlike structure they prefer.     

A simple approach for improving the hybrid MMVB force field: application to the photoisomerization of s-cis butadiene

MMVB is a QM/MM hybrid method, consisting of a molecular mechanics force field coupled to a valence bond Heisenberg Hamiltonian parametrized from ab initio CASSCF calculations on several prototype molecules. The Heisenberg Hamiltonian matrix elements Q(ij) and K(ij), whose expressions are partitioned here into a primary contribution and second-order correction terms, are calculated analytically in MMVB. When the original MMVB force field fails to produce potential energy surfaces accurate enough for dynamics calculations, we show that significant improvements can be made by refitting the second-order correction terms for the particular molecule(s) being studied. This "local" reparametrization is based on values of K(ij) extracted (using effective Hamiltonian techniques) from CASSCF calculations on the same molecule(s). The method is demonstrated for the photoisomerization of s-cis butadiene, and we explain how the correction terms that enabled a successful MMVB dynamics study [Garavelli, M.; Bernardi, F.; Olivucci, M.; Bearpark, M. J.; Klein, S.; Robb, M. A. J Phys Chem A 2001, 105, 11496] were refitted.     

Non-aqueous phase liquid drop formation within a water saturated fracture

This work focuses on the mechanisms of non-aqueous phase liquid (NAPL) drop formation within a single fracture fed from a NAPL reservoir by way of a circular orifice, such as a pore. The fracture is assumed to be fully saturated, the relative wettability of the system is assumed water-wet, and the water velocity profile within the fracture is described by a Poiseuille flow. The size of the NAPL drops is investigated for various water flow velocities and NAPL entrance diameters. A force balancing method was used to determine the radii of detached drops. The drop sizes calculated from the model developed here are shown to be in agreement with available experimental drop size data. It is shown that at low Reynolds numbers the buoyancy force is the dominant force acting on the drop during the formation process and at high Reynolds numbers the viscous forces dominate. A simplified expression relating the geometry of the fractured system to the drop radii is developed from the model equations, and it is shown to predict drop radii that match well with both the model simulations and the available experimental data.     

Liquid crystal phases of charged colloidal platelets

The liquid crystal phase behavior of a suspension of charged gibbsite [Al(OH)3] platelets is investigated. By variation of the ionic strength, we are able to tune the effective thickness-to-diameter ratio of the platelets in suspension. This enables us to experimentally test the liquid crystal phase transition scenario that was first predicted a decade ago by computer simulations for hard platelets (Veerman, J. A. C.; Frenkel, D. Phys. Rev. A 1992, 45, 5632), that is, the isotropic (I) to nematic (N) and isotropic to columnar (C) phase transitions in one colloidal suspension. In addition to the shape-dependent thermodynamic driving force, the effect of gravity is important. For example, a biphasic (I-N) suspension becomes triphasic (I-N-C) on prolonged standing. This effect is described by a simple osmotic compression model.     

Investigating the quartz (1010)/water interface using classical and ab initio molecular dynamics

Two different terminations of the (1010) surface of quartz (α and β) interacting with water are simulated by classical (CMD) (using two different force fields) and ab initio molecular dynamics (AIMD) and compared with previously published X-ray reflectivity (XR) experiments. Radial distribution functions between hydroxyl and water show good agreement between AIMD and CMD using the ClayFF force field for both terminations. The Lopes et al. (Lopes, P. E. M.; Murashov, V.; Tazi, M.; Demchuk, E.; MacKerell, A. D. J. Phys. Chem. B2006, 110, 2782-2792) force field (LFF), however, underestimates the extent of hydroxyl-water hydrogen bonding. The β termination is found to contain hydroxyl-hydroxyl hydrogen bonds; the quartz surface hydroxyl hydrogens and oxygens that hydrogen bond with each other exhibit greatly reduced hydrogen bonding to water. Conversely, the hydroxyl hydrogen and oxygens that are not hydrogen bonded to other surface hydroxyls but are connected to those that are show a considerable amount of hydrogen bonding to water. The electron density distribution of an annealed surface of quartz (1010) obtained by XR is in qualitative agreement with electron densities calculated by CMD and AIMD. In all simulation methods, the interfacial water peak appears farther from the surface than observed by XR. Agreement among AIMD, LFF, and XR is observed for the relaxation of the near-surface atoms; however, ClayFF shows a larger discrepancy. Overall, results show that for both terminations of (1010), LFF treats the near-surface structure more accurately whereas ClayFF treats the interfacial water structure more accurately. It is shown that the number of hydroxyl and water hydrogen bonds to the bridging Si-O-Si oxygens connecting the surface silica groups to the rest of the crystal is much greater for the α than the β termination. It is suggested that this may play a role in the greater resistance to dissolution of the β termination than that of the α termination.