Nanoscale Liquid Crystal Lubrication Controlled by Surface Structure and Film Composition
NNanoscale Liquid Crystal Lubrication Controlled by Surface Structure and FilmComposition
Pritam Kumar Jana , ∗ Wei Chen , Mikko J. Alava , and Lasse Laurson † COMP Centre of Excellence, Department of Applied Physics,Aalto University, P.O.Box 11100, FI-00076 Aalto, Espoo, Finland and State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering (IPE),Chinese Academy of Sciences (CAS), Beijing 100190, PR China.
Liquid crystals have emerged as potential candidates for next-generation lubricants due to theirtendency to exhibit long-range ordering. Here, we construct a full atomistic model of 4-cyano-4-hexylbiphenyl (6CB) nematic liquid crystal lubricants mixed with hexane and confined by micasurfaces. We explore the effect of the surface structure of mica, as well as lubricant compositionand thickness, on the nanoscale friction in the system. Our results demonstrate the key role of thestructure of the mica surfaces, specifically the positions of potassium (K + ) ions, in determining thenature of sliding friction with monolayer lubricants, including the presence or absence of stick-slipdynamics. With the commensurate setup of confining surfaces, when the grooves created betweenthe periodic K + ions are parallel to the sliding direction we observe a lower friction force as comparedto the perpendicular situation. Random positions of ions exhibit even smaller friction forces withrespect to the previous two cases. For thicker lubrication layers the surface structure becomes lessimportant and we observe a good agreement with the experimental data on bulk viscosity of 6CBand the additive hexane. In case of thicker lubrication layers, friction may still be controlled bytuning the relative concentrations of 6CB and hexane in the mixture. I. INTRODUCTION
Controlling friction, wear, and lubrication by under-standing the atomic-scale processes taking place at theinterfaces of interacting bodies in relative motion hasbeen a long-standing challenge, with applications, for ex-ample, in micro- and nanoelectromechanical systems [1–3]. Many classical laws of friction and lubrication in suchsystems are violated due to the high surface-to-volumeratio and the greater importance of molecular interac-tions and arrangements in determining the surface forces[4]. As a result, a number of fundamental questions inthis field are still unsolved [5].A practical design goal for applications is to reducestiction, friction and wear. To this end, one may thinkof two main strategies: either modulating the roughness,electrostatic interactions, crystal structure, edge orien-tations and other properties of the surfaces that comeinto contact or by using various types of lubricants be-tween the surfaces[6, 7]. Approaches with the idea oftuning the potential energy landscape between the inter-acting surfaces at the atomic scale have been proposed[6], including the use of aperiodic quasicrystal surfaces orintroducing a lattice mismatch between the two slidingcrystal surfaces, leading to the superlubricity mechanism[2, 8, 9]. However, a recent study shows that the du-ration of the superlubric state, i.e., the incommensurateconfiguration can be finite and therefore, ultralow frictiondoes not prevail. The possibility of rotation of the slid-ing surface stabilizes the high frictional commensurate ∗ pritam.jana@aalto.fi † lasse.laurson@aalto.fi configuration [10, 11]. The idea of aligning the crystallo-graphic orientation of confining layers is used in resonanttunneling diodes [12] and other novel devices [11]. It sug-gests to perform more investigations on reducing frictionconsidering energetically stabilized high frictional com-mensurate setup. Guo et al. have shown that interlayerfriction, in case of commensurate setup, can be reducedby functionalizing the sliding surfaces [13]. Several stud-ies have been performed focusing on the quest of perfectlubricants and their dynamical properties or the adsor-bate surface coverage while being sheared by the confin-ing surfaces in relative sliding motion [1, 14–16].Liquid crystals (LCs) have been explored as potentiallubricant due to ultra-low friction as a result of their long-range orientational ordering tendency [17]. Due to thehigh cost of pure LCs, various mixtures of LCs with othersubstances are typically considered, and more extensiveinvestigations are required to understand the effects dueto such additives [18–22]. There are open questions re-lated to details of the interactions of the LC moleculeswith the confining surfaces, and the phase behavior theyexhibit under applied shear. While experiments, coarse-grained simulations, and theoretical studies to under-stand the structural and dynamical properties of LC lu-bricants have been performed [18, 22–32], atomistic sim-ulations to establish a proper link between coarse-grainedmodels and experiments are still missing.In this article, we focus on the lubricating properties ofnematic 4-cyano-4-hexylbiphenyl (6CB) LCs in pure andin presence of hexane additives where mica serves as con-fining surfaces by using fully atomistic model simulations.We probe the influence of the relative orientation of thesurfaces including an incommensurate setup, and the ef-fect of the random ion distribution in the confining micasurfaces. We also inspect the impact of the thickness of a r X i v : . [ c ond - m a t . s o f t ] D ec the lubricant film, whether pure 6CB or a 6CB/hexanemixture, on frictional response. Our results show thatfriction in systems with monolayer lubricant films is sen-sitive to the arrangement of ions on the confining sur-faces or to the relative surface orientations. Moreover,we demonstrate friction control also for thicker lubricantlayers via tuning the composition of the LC-hexane mix-ture, including controlling the presence of stick-slip. II. MODEL
There are several efforts to reproduce the properties,for example, the so-called odd-even effect in nematic-isotropic transition, of liquid crystal homologues namely4-cyano-4-alkylbiphenyl (nCB) up to a satisfactory levelof accuracy in computer simulations[33, 34]. In thepresent study, we are specifically interested in the lubri-cating properties of liquid crystals because of its long-range ordering. To this end, we choose 4-cyano-4-hexylbiphenyl (6CB). There is experimental evidence onlubrication of 6CB confined between mica surfaces[35–37]. We could have chosen other homologues. However,we believe that the observed results will qualitatively re-main same. We consider hexane as an additive becauseof its low cost and is largely used as a lubricant. To con-struct the atomistic models of 6CB and hexane molecules,we use force field parameters from Refs. [38, 39]. As forthe confining mica surfaces, we consider 2M1-muscovitemica with the formula KAl (Al,Si )O (OH) , using theforce field parameters as described in Ref. [40]. Detailsof the force field parameters used in the simulations areprovided in the Supporting Information. To verify theaccuracy of the force field, we have calculated two fric-tion related quantities: (a) bulk viscosity for both 6CBliquid crystal and hexane and we see a good agreementwith experiments. See the inset of Fig. 3. (b) frictionforce for commensurate (confining surfaces are aligned)and the incommensurate surface (confining surfaces aremisaligned) and we observe a lower friction in case of theincommensurate surface which is also observed in exper-iments. Both results, we discuss in detail in Results anddiscussions section. It assures that the used force fieldparameters are good enough to study frictional proper-ties of 6CB and hexane.In an experiment, Atomic Force Microscope (AFM)cannot detect potassium ions (K + ) on mica surfaces. Aprobable reason of that is K + ions on mica are movedaround by the AFM cantilever-tip during the slidingmotion[41]. However, there are several efforts on under-standing the spatial arrangement of ions at the solid-liquid interface. Ricci et al. have shown that the mono-valent metal ions do not adsorb on mica surfaces im-mersed in water randomly but form preferential orderedstructures to minimize the surface energy at the mica-ion interface[42]. Most of the theoretical studies con-sider the periodic arrangement of K + ions[43]. However,due to the randomness of the cleaving process of mica, uniform distribution of K + ions is unlikely[44]. Thoseexperimental observations lead us to consider both peri-odic and random arrangements of K + ions and examinethe resulting effects on friction. Each surface consists of10 × L x = 103 . L y = 70 .
54 ˚A, respectively. Both surfaces arekept parallel to the xy plane, and the upper surface isdriven with a constant velocity of V = 0 . x direction. We do not consider the y directional mo-tion of any of the plates. As shown in Fig. 1(a), thelower surface is attached to a fixed point with a springconstant k/N p = 0 .
007 N/m, with N p the number ofatoms in the surface which is a basic tribological setup[45]. The spring constant is consistent with experimen-tal values as mentioned in Refs. [46, 47] and the slidingvelocity (here 0.1m/s) of the upper plate is smaller thanthe critical velocity defined as the limiting velocity afterwhich stick-slip motion disappears [48]. Therefore, underthe chosen values of parameters, we expect stick-slip dy-namics in the system with thin layer of lubricants so thatin addition to study the frictional effect of ions positionon mica surfaces, we can also characterise the dynamicalbehavior of nano-confined liquid crystals during the stickand the slip events.In the steady state, the upper surface is subject toa normal load corresponding to a 1 atm. We do notvary normal load. However, it could be an interestingdirection to explore the responses of nanoscale frictionfor different normal loads that usually disobey a simplelinear relation[5].Temperature of the lubricants is main-tained at T = 298 K using a Langevin thermostat, ap-plied only in the y direction to avoid streaming bias[14, 49, 50]. To make sure that thermostat does notaffect our main results, we use the temperature relax-ation time 10 − ns which is significantly smaller thanthe time required ( ∼ − ns) to finish a slip event. Theequations of motion are solved with the velocity Verletalgorithm implemented in the LAMMPS code[51], withan integration time step of 1 fs. Long-range electrostaticinteractions are computed by using the particle-particle-particle-mesh solver for the slab geometry [52, 53] with10 − accuracy [54] implemented in LAMMPS[51]. Ini-tially lubricant molecules are arranged in a simple cubiclattice and first equilibrate for 100 ps with both confin-ing surfaces fixed. During the following 100 ps, the topsurface is subject to a normal load corresponding to a 1atm pressure and is allowed to move along the z direc-tion. After that, the top surface is driven along the x axiswith a velocity V for 60 ns; in most cases the observablesof interest have been averaged over the last 20 ns of thesimulations, to ensure that a steady state is reached. III. RESULTS AND DISCUSSIONS
We divide our results into two subsections. First, wediscuss the effects of surface structure and orientation onfriction. Next, we show how additives’ concentration can (c) (d) (b) (a) cyanobiphenyl alkyl 1 2 k F n V Fixed x z Lubricant y (e)(g) (f) XY FIG. 1. (a) A schematic of the model. Lower plate is at-tached with a spring to a fixed point. The upper surface issubject to a normal load F n and driven along the + x directionwith a constant velocity V . (b) A snapshot of the system isdepicted, with 144 6CB molecules confined by the two micaplates. (c) and (d) correspond to the molecular structuresof 6CB (consisting of cyanobiphenyl and alkyl groups) andhexane, respectively. Pink, red, yellow, cyan, green, grey andblue colored atoms are potassium, oxygen, silicon, aluminum,carbon, hydrogen and nitrogen, respectively. (e), (f) and (g)show the different arrangements of the K + ions at the sur-faces considered in the simulations (only a small part of thesurface shown, with red and black dots corresponding to up-per and lower faces of the mica sheet, respectively), i.e., withgrooves perpendicular and parallel to the sliding direction,and a random arrangement of the ions, respectively. tune the resulting friction forces. A. Effects of surface structure and orientation onfriction
As we are interested in understanding the boundary lu-brication, where friction between the confining surfacesdepends on the surface properties and the properties ofthe thin layer of lubricants, first we consider the systemwith monolayer of 6CB and hexane molecules. For thesystem geometry considered here, monolayer systems areobtained by considering 72 6CB or 144 hexane molecules,respectively. To construct a monolayer we choose thenumber of molecules to be such that the total area oc- F S ( p N )
10 20 30 40 50 60t (ns) 468 D ( Å ) S | c o s f | F S ( p N )
10 20 30 40 50 60t (ns)468 D ( Å )
10 20 30 40 50 60t (ns) 20406080 N H (b)(a)(c) random (cid:244)(cid:244) ^ (d) FIG. 2. Time evolution of the friction force F s and film thick-ness D for monolayers of (a) 6CB and (b) hexane, consideringthe three different arrangements of the K + ions at the surfacesdepicted in Fig. 1. (c) Order parameter S and the angle φ between the 6CB director and the sliding direction, quantifiedhere by cos φ , are shown in the top and the bottom panel, re-spectively. (d) Time evolution of the number N H of hydrogenbonds between the 6CB and bottom mica, illustrating thatthe bonds tend to break during the slip events. cupied by them is smaller than the area of the confiningsurfaces. To characterize the dynamics, we compute thefriction force F s (the average force exerted on each atomof the bottom plate by the lubricant and the top micaplate along the + x direction), film thickness D (distancebetween the two plates), and the order parameter S ofthe LCs, i.e., the maximum eigenvalue of the average or-dering tensor Q α,β defined as Q α,β = 1 N N (cid:88) i (cid:18) u iα u iβ − δ α,β (cid:19) , (1)where u iα ( α, β = x, y, z ) are the Cartesian components ofthe unit vector of the LC molecule i , N is the numberof LC molecules, and δ α,β is the Kronecker delta. Here,the unit vector of the LC molecule is taken to be parallelto the line connecting the nitrogen atom and the endcarbon of the cyanobiphenyl group of 6CB, denoted by1 and 2 in Fig. 1(c), respectively. We also compute thedirector (eigenvector of the maximum eigenvalue) of theLC molecules (the average molecular orientation), andcharacterize it by the angle φ with the x -axis.The monolayer results are summarized in Fig. 2, con-sidering three different arrangements of the K + ions onthe mica surfaces: Figs. 1(e) and (f) display two differentperiodic arrangements of the ions [the structure in (f) isobtained by rotating the surface in (e) by 90 ◦ ], while Fig.1(g) shows an example with randomly positioned ions. Itis important to notice that in the case of the two periodicarrangements, grooves are generated along the x [Fig.1(f)] or y direction [Fig. 1(e)] in between stripes of ions,resulting in an anisotropic surface structure, while in thecase of randomly positioned ions, such features are absent[Fig. 1(g)]. To examine the effect of surface structure onboundary lubricated friction, we plot in Figs. 2 (a) and(b) the time-dependence of the friction force F s and thefilm thickness D for those three different structures of theconfining mica surfaces for 6CB and hexane, respectively;see also example movies (Videos SM1, SM2, and SM3)provided as Supporting Information. We observe regu-lar stick-slip dynamics for both 6CB and hexane for theordered surfaces. The maximum friction force (and thusthe magnitude of the stick-slip oscillations) as well as themaximum film thickness during the “jumps” of the topplate associated with the slip events are larger in the casewhere the grooves of the mica surfaces are perpendicularto the sliding direction. In case of 6CB lubricated system,this effect is visible also when considering the time evolu-tion of the number of hydrogen bonds, N H , formed be-tween 6CB hydrogens and the bottom mica plate (i.e., thenumber of 6CB hydrogens closer than 3 ˚A from the bot-tom mica surface [50]. A typical hydrogen bond lengthis 1.5 ˚A to 2.5 ˚A which is smaller than the distance, 3 ˚A, that we consider as the breakage of hydrogen bonds.),see Fig. 2 (d): bonds break as the system evolves fromstick to the slip state. In the case of the randomly po-sitioned ions, 6CB exhibits more irregular stick-slip dy-namics, with also some visible jumps in D accompanyingthe slip events, while no clear signature of stick-slip is ob-served for hexane. Due to the incommensurate nature ofthe confining surfaces with randomly positioned K + ions,the average film thickness D is larger and the maximum F s is lower than with ordered mica surfaces. A similar ob-servation is depicted in an experiment where surface ioninduced tribological properties have been studied. It hasbeen shown that when the ions are strongly bound andrandomly distributed on mica irregular stick-slip occurs[41]. Several experimental studies have been performedto understand the dynamical or mechanical properties oforganic liquids when they are confined to few layers bysolid surfaces such as mica [55]. A common phenomenonis the observation of stick-slip motion depending on thesliding velocity and the normal load [56, 57]. Althoughthere are several efforts, molecular origin of stick-slip cy-cle in sheared solid-like lubricants is not well understoodbecause of the difficulties to capture the behaviour of lu-bricants during the slip events, precisely mainly for tworeasons: (a) slip events occur in nanometrically confinedfilm (b) slip events are of very short duration and occupya tiny fraction of the stick-slip cycle [57]. Therefore, a lotof understanding has been derived from theoretical andcomputer simulations. To this end, we also explore thebehaviour of confined LCs during the stick and the slipevents.For 6CB LCs, the time-evolution of the order param-eter S and the angle φ between the LC director and thesliding direction ( x axis) [Fig. 2 (c)] encode additional in-formation about the dynamics. In particular, 6CBs havea tendency to orient along both the grooves of the confin- ing surfaces (due to formation of hydrogen bonds betweenthe biphenyl hydrogen and the surface oxygen exposedalong the grooves), as well as along the sliding direction: S is larger and φ is smaller when the grooves and thesliding direction are parallel [both along x , see Fig. 1(f)].For the perpendicular case, in the steady state the 6CBspoint mostly along y (i.e., along the grooves), but S is alittle smaller than in the parallel case due to the compet-ing ordering mechanism of the sliding along x . It showsthat the monolayer of LCs prefers to orient along themicrogrooves instead of aligning along the sliding direc-tion due to the presence of strong chemical interactions.In contrast, for the random arrangement of K + ions onmica, the 6CBs exhibit clearly less orientational order(smaller S ), and φ also fluctuates significantly in time,see Fig. 2 (c). The alignment of LCs along the groovesis not a complete surprise. Vegt et al. have investigatedthe orientation of 4-cyano- 4-octylbiphenyl (8CB) liquidcrystals on anisotropic polyimide surfaces by performingmolecular dynamics simulations where they have shownthat a single molecule of 8CB prefers to orient along themicrogrooves because of the strong binding between po-lar cyano groups from LCs and the carbonyl groups fromthe polyimide surface[58]. In general, understanding theorientation of LCs on the surface is interesting becauseof its application in liquid crystal display.To explore more about the dynamics of LCs and theirresponse during the stick-slip cycle we measure the meansquare displacement (MSD) of 6CB molecules. It showsthat while the molecules move ballistically along x fortime scales longer than the stick-slip period for all micasurface structures (Fig. SM2 (a) in the Supporting Infor-mation) they exhibit diffusive dynamics in the y directionin the long-time limit only for random ion arrangementand grooves perpendicular to the sliding direction (Fig.SM2 (c) in the Supporting Information). In contrast, forgrooves parallel to the sliding direction, MSD saturatesto a value comparable to the groove spacing, suggest-ing that in that case the grooves act as barriers for the y -directional diffusion of 6CBs. However, the slip is con-fined to the lubricant close to the lower plate, and hap-pens in the direction of sliding. Details are shown in theSupporting Information. Thus, for monolayer lubricants,the structure of the confining surfaces plays a decisiverole in the frictional response. So far, we have discussedthe system where confining surfaces are aligned with eachother- thus commensurate. When we consider the incom-mensurate setup, i.e, two surfaces are misaligned with re-spect to each other, we see a frictional response which iseven somewhat lower than the situation where K+ ionsare randomly positioned on the surface. See Fig. SM7in the Supporting Information. Experiments show thesimilar observations as misaligned mica surfaces exhibitlower friction forces as compared to the commensuratesetup [8, 9].To understand the effect of the confining films’ thick-ness on friction, we study here the periodic pattern of theK + ions with the grooves perpendicular to the sliding di- ‘ D (Å)00.40.81.21.622.4 ‘ F S ( p N ) ‘ D (Å)10 h ( m P a S ) LCHexanebulk LC (exp)bulk Hexane (exp)
FIG. 3. Average friction force ¯ F s as a function of the averagefilm thickness ¯ D , obtained by considering different numbersof molecules confined by the mica surfaces, with the film con-sisting of pure 6CB or pure hexane. The inset shows thecorresponding dynamic viscosities η , which approach in bothcases the experimental bulk viscosity values (Refs. [59, 60]and [61] for 6CB and hexane, respectively), indicated by thedashed horizontal lines. Solid lines are fits of the form of η ( ¯ D ) ∝ exp( − ¯ D/λ ) + η , yielding λ = 0 .
73 ˚A and 3.36 ˚A forhexane and 6CB, respectively. rection; for thicker lubricant films, stick-slip dynamicsgradually disappears with increasing D (see Fig. SM3 inthe Supporting Information), and the surface structureof mica becomes less important, with all the three surfacestructures from above yielding similar results for the fric-tion force. A similar observation is reported when wateris confined between mica surfaces [50]. We consider var-ious systems with the number of 6CBs ranging from 72to 600, and the number of hexane molecules from 144 to640, and also systems with a smaller area of the confin-ing mica plates to reach a larger D for a given number oflubricant molecules. We compute the resulting averagefriction force ¯ F s as a function of the average thickness¯ D (Fig. 3; see also Supporting Information Video SM4for an example movie of a thick 6CB system). The insetof Fig. 3 displays the corresponding dynamic viscosities η , defined via ¯ F s N p = ηA ( V / ¯ D ), where A is the surfacearea [62]. Under strong confinement (small ¯ D ), both sys-tems exhibit a high dynamic viscosity which decreaseswith increasing ¯ D , and approaches the known bulk vis-cosity values at T = 298 K, i.e., 31 . . · s for6CB [59, 60] and hexane [61], respectively. Notice thatin general η is expected to depend on V (or the shearrate) [63], but our results indicate that V = 0 . η approachesa value close to that of the bulk viscosity in the limitof large ¯ D . We fit the data by η ( ¯ D ) ∝ exp( − ¯ D/λ ) + η ,yielding a decay length λ = 0 .
73 ˚A and 3.36 ˚A for hexaneand 6CB, respectively. This slower approach to bulk be-havior for 6CBs may be understood via the competitionbetween screening of the mica-mica interaction and the inherent “stickiness” of the 6CB lubricant, with the lat-ter manifested also as the higher bulk viscosity value for6CB. Due to their larger dielectric constant ( (cid:15) ≈ (cid:15) ≈ + ions and the highly electronegative ni-trogen atoms, as well as from the hydrogen bonding be-tween phenyl hydrogen and mica oxygen atoms, hindersthe rapid reduction of friction as ¯ D increases. The differ-ence in the screening properties of the two lubricants canalso be seen by noticing that η LCbulk /η Hbulk ≈ .
8, whilein the monolayer case η LC /η H ≈ η LCbulk and η Hbulk the measured η -values of LCs and hexane, respectively),suggesting (in relative terms) a stronger surface-surfaceinteraction through a thin layer of hexane as comparedto the LC case. We note that a similar evolution with ¯ D of the viscosity of LC lubricants has been observed ex-perimentally [67]. The MSD of the 6CB molecules showsthat in thicker systems they exhibit ballistic motion along x and diffusive dynamics in the y direction independentof the structure of the confining surfaces (Figs. SM2 (b)and (d) in the Supporting Information).We also investigate the molecular orientation forthicker lubrication films. In contrast to the monolayercase with grooves perpendicular to the sliding direction(see Fig. 1 (e)), we observe that the director fields forthicker LC films tend to orient along the sliding motionas shown in Fig. SM5 (a) in the Supporting Information.Due to larger distances between the confining plates, theyalso display a z -directional degree of freedom which is ab-sent in the monolayer cases, see Fig. SM5 (b) in the Sup-porting Information. We do not see homeotropic align-ment, i.e., a perpendicular arrangement with respect tothe confining surfaces. Experiments also exhibit that incase of untreated mica, LCs have a tendency to be in theplane of the surface [68]. In these studies of LCs as alubricant we have not paid any direct attention to thegeneral structural properties of the LC films. This con-cerns both eventual smectic order in thicker systems (andthe corresponding dislocations) and the point defects ordisclination lines in the presence of nematic order de-pending on the lubrication layer thickness. B. Effect of film composition on friction
Finally, to explore the potential film composition ofLCs and hexane mixtures at which a reduced friction canbe observed, we add various concentrations of hexane tothe LC lubricant and compute the friction forces for dif-ferent mixtures of 6CB LCs and hexane, see Fig. 4 (a).We fix the total number of molecules N to 144, and varythe fraction ρ H = N H /N of hexane from 0 to 1, where N H is the number of hexane molecules. Interestingly, theaverage friction force ¯ F s displays a non-monotonic depen- A D (Å) η ( m P a s ) ρ H D ( Å ) A6 8 10 D (Å)0.11 F S ( p N ) A ρ H = (a) f il m t h i c kn e ss f il m c o m po s iti on (b)(c) FIG. 4. (a) Average friction force ¯ F s as a function of the filmthickness ¯ D for films with different mixtures of 6CB and hex-ane. (b) shows the corresponding dynamic viscosity η , while(c) displays the film thickness as a function of the hexaneconcentration ρ H dence on ρ H (and on ¯ D ). While the general trend is that¯ F s decreases with decreasing ρ H and increasing ¯ D , for thesmallest ρ H (corresponding to the pure and almost pureLC cases), ¯ F s increases with decreasing ρ H and increas-ing ¯ D . As LCs are larger in size and stickier in nature as
12 15 18Z (Å)00.40.8 ·r ( z ) ( Å - )
12 15 18Z (Å)cyanobiphenylalkylhexane 12 15 18Z (Å) 012 ·r ( z ) ( Å - ) (b) r H =0 r H =0.5 r H =1.0 (c)(a) FIG. 5. Probability density profiles ρ ( z ) describing the prob-ability per unit volume of finding a molecule with a given z coordinate, for 6CB (shown separately for cyanobiphenyl andalkyl groups) and hexane for three different mixtures, (a) 144pure 6CB, (b) 72 6CB and 72 hexane mixture, and (c) 144pure hexane. The cyanobiphenyl groups of the 6CBs tendto stay adjacent to the confining mica plates, while the 6CBalkyl groups as well as hexane occupy the space also in themiddle of the gap. compared to hexane, reduction of ρ H or addition of LCsin the LC-hexane mixture renders a competing effect onfriction. A larger size of LC will lead to the thickeningof the film and thus decrease of friction while the stickiernature will oppose the effect. When ρ H = 1, hexane isconfined to a monolayer between mica surfaces (see Fig.5 (c)) and stick-slip motion is observed as shown in Fig.2 (b), thus high friction. With the addition of LCs upto 1:1 ratio, film thickness increases as shown in Fig. 4(c) and friction decreases rapidly (see Fig. 4 (a)) because of the gradual disappearance of stick-slip. See Fig. SM4and Video SM5 in the Supporting Information. Thus,film thickness dominates on controlling the friction. Notethat, when N LC : N H = 1 : 1 ( N LC is the number of LCs)probability density of the confined mixtures along the z direction exhibits the formation of two layers (See Fig.5 (b)). Due to the strong attractive interaction betweencyanobiphenyl group of 6CB and mica (K + ions and oxy-gens), cyanobiphenyl groups are attracted to the micasurfaces while alkyl parts as well as hexane occupy thespace in the middle in between the confining surfaces asshown in Fig. 5 (b). Further addition of LCs leads to theweak changes of thickness and in that region, sticky na-ture of LCs plays a key role and thus a gradual increase offriction. Density profile ρ ( z ), when ρ H = 0, exhibits sim-ilar probability distribution as observed when ρ H = 0 . η [Fig. 4 (b)].In precise, this non-monotonic behavior of friction is aresult of the cross-over from a film thickness controlledfriction regime (shown in Fig. 4(a) as a gray region; inthis regime we observe gradual disappearance of stick-slip dynamics with decreasing ρ H ) to a film composition dependent regime (orange colored region; stick-slip notobserved due to larger ¯ D ). When we characterize theslip at surface depending on the amount of hexane, wesee that both slip length and slip position increase as weapproach the pure hexane case (See Fig. SM10 in theSupporting Information). The slip in confined LCs fol-lows the surface-slip coherently. However, slip length atsurface is larger as compared to the LCs. When the sliplength at the surface is small, we do not see any slip inthe LCs (See Fig. SM9 in the Supporting Information). IV. CONCLUSIONS
To summarize, we have presented an extensive study ofnanoscale LC lubrication using a full atomistic model. Inthe boundary lubricated regime we show that nanoscalefriction can be tuned by controlling the distribution ofion positions on muscovite mica. In case of commensu-rate setup, when ions are periodic we observe a largerfriction force as compared to the case where ions arerandomly placed on mica. In the latter case, the di-rector field of the confined LCs fluctuates while in theformer case, director field orients along the grooves cre-ated between periodically arranged ions. When groovesand the sliding direction are parallel, LCs exhibit higherorder and the friction is lower as compared to the per-pendicular case. In case of incommensurate setup, thefriction force is smaller than the commensurate setupwhere ions are randomly arranged on mica and the con-fined LCs orient along the sliding direction. Tuning thecharge distribution and modifying the surface geometry,one can reduce the friction in commensurate structures[13]. The experimental probe of the ion arrangement [44]can open up novel directions in controlling nanoscale fric-tion. However, at the limit of a large thickness, surfaceeffects disappear and we predict that effective viscosityof the confined LC and hexane exponentially decays tothe bulk viscosity that exhibits a good agreement withexperimental values.On the quest of potential lubricant from LC-hexanemixtures, our results show that increase of LC and hex-ane concentration in the hexane [69] and the liquid crys-tal dominated regions, respectively both lead to the re-duction of friction. It suggests that instead of pure LCsaddition of impurity results better lubrication and it canbe thought of potential lubricant in applications. By tun-ing the film composition, we also observe the possibilityof controlling the stick-slip motion which is a major rea-son of wear in sliding surfaces.
ACKNOWLEDGEMENT
PKJ, MJA and LL are supported by the Academy ofFinland through project no. 251748 (Centres of Excel- lence Programme, 2012-2017). PKJ acknowledges sup-port from the Academy of Finland FiDiPro program,project no. 13282993. LL acknowledges the support ofthe Academy of Finland via an Academy Research Fel-lowship (project no. 268302). WC is grateful to thefinancial support by the National Natural Science Foun-dation of China (Grant No. 11504384). We acknowledgethe computational resources provided by the Aalto Uni-versity School of Science “Science-IT” project, as well asthose provided by CSC (Finland). We thank Jens Smi-atek for useful discussions and suggestions. [1] B. Bhushan, J. N. Israelachvili, and U. Landman, Nature , 607 (1995).[2] J. Y. Park, D. F. Ogletree, M. Salmeron, R. A. Ribeiro,P. C. Canfield, C. J. Jenks, and P. A. Thiel, Science ,1354 (2005).[3] B. Bhushan, Wear , 1507 (2005).[4] A. M. Smith, K. R. J. Lovelock, N. N. Gosvami, T. Wel-ton, and S. Perkin, Phys. Chem. Chem. 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Force field
For 4-cyano-4-hexylbiphenyl (6CB) liquid crystals the force field has the following functional form 𝐸 𝑓 = 𝐸 𝑠𝑡𝑟𝑒𝑡𝑐ℎ𝑖𝑛𝑔 + 𝐸 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 + 𝐸 𝑡𝑜𝑟𝑠𝑖𝑜𝑛𝑎𝑙 + 𝐸 𝑣𝑑𝑤 + 𝐸 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐 (1) where 𝐸 𝑠𝑡𝑟𝑒𝑡𝑐ℎ𝑖𝑛𝑔 = ∑ 𝑘 𝑙 (𝑙 − 𝑙 ) (2) 𝐸 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 = ∑ 𝑘 𝜃 (𝜃 − 𝜃 ) (3) 𝐸 𝑡𝑜𝑟𝑠𝑖𝑜𝑛𝑎𝑙 = ∑ [ 𝑘 (1 + cos 𝜑 𝑖 ) + 𝑘 (1 − cos 2𝜑 𝑖 ) + 𝑑𝑖ℎ𝑒𝑑𝑟𝑎𝑙𝑠12 𝑘 (1 + cos 3𝜑 𝑖 ) + 𝑘 (1 − cos 4𝜑 𝑖 )] (4) 𝐸 𝑣𝑑𝑤 = ∑ 4𝜀 𝑖𝑗𝑖,𝑗 [( 𝜎 𝑖𝑗 𝜀 𝑖𝑗 ) − ( 𝜎 𝑖𝑗 𝜀 𝑖𝑗 ) ] (5) 𝐸 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐 = ∑ 𝑖,𝑗 𝑞 𝑖 𝑞 𝑗 𝑟 𝑖𝑗 (6) Here kl , 𝑘 𝜃 , and kn are the force constants for bond stretching, bond angle bending, and torsional force rotations, respectively. l and 𝜃 are the equilibrium bond lengths and angles, 𝜎 𝑖𝑗 and 𝜀 𝑖𝑗 are the collision distance at which E vdw = 0 and potential well depth, respectively. qi is the atomic charge. l , 𝜃 , and 𝜑 are the bond lengths, bond angles, and torsional angles, respectively. Force field parameters used in the simulations are summarized below. FIG. SM1. Structural details of 6CB molecule. All digits stand for the identity of the atoms. C A and H A are aromatic carbon and aromatic hydrogen. C P is the ring joining carbon atom. C n and H represent aliphatic carbon and hydrogen. C z and N z are the carbon and nitrogen from the cyano group. When we define the atoms using digits as suffix we consider C A, C P, C n, C Z ≡ C or H A ≡ H. C A C A C A C A C A C P C A C A C A C A C P C n C n C n C n C n C n HHH H H HH HHH H H H C Z N Z H A H A H A H A H A H A H A H A C A Table 1. Bond stretching force constants ( 𝒌 𝒍 ) and equilibrium bond lengths ( 𝒍 ). Table 2. Bond angle bending force constants ( 𝒌 𝜽 ) and equilibrium bond angle ( 𝜽 ) for 6CB used in the simulations. Table 3. Torsional force constants ( 𝒌 , 𝒌 , 𝒌 , 𝒌 ) for LCs used in simulations. Bond 𝑘 𝑙 (eV Å -2 ) 𝑙 ( Å ) C A -H A A -C A A -C P P -C P A -C Z Z -N Z A -C n n -C n n -HC 31.65 1.09 Angle 𝑘 𝜃 ( × 10 −5 eV/deg ) 𝜃 (degree) C A -C A -H A A -C A -C A A -C P -C P A -C A -C Z A -C Z -N Z n -C n -C n n -C n -HC 116.98 112 HC-C n -HC 147.25 107 C n -C A -C A A -C n -HC 92.466 109.5 C A -C n -C n 𝑘 𝑘 𝑘 𝑘 C A -C A -C A -C A n -C n -C n n -C n -HC 0.0 0.0 0.14 0.0 C A -C P -C P -C A A -C n -C n -C n n -C n -C n -C n A -C A -C n -C n Table 4. Partial charges for all atoms of 6CB molecule used in simulations.
Table 5. 𝜺 and 𝝈 for all atoms of 6CB molecule used in simulations. Table 6. Partial charges for all atoms of mica surfaces used in simulations. See Ref. 40 in the main text. Same force field parameters are used in Ref. 50 in the main text.
Atom Charge (e) Nz -0.43 C -0.122 C -0.12 C -0.18 H A 𝜖 (eV) 𝜎 ( Å ) Nz C C C C C C H A H Atom Charge (e) K 1.0 Si surface surface octahedral octahedral surface -0.55 O apical -0.758 O hydroxyl -0.683 H hdroxyl FIG. SM2. Mean square displacement (MSD) of liquid crystals for different surface structures. Left panel is for monolayer and the right panel is for multi-layer lubricant.
Here, we consider the incommensurate system. To construct the incommensurate setup, we misalign the confining surfaces with respect to each other as shown in Fig. SM6.
FIG. SM6. Confining plates are misaligned (incommensurate). Grooves from the upper and lower plates make an angle of -30 and +30 with respect to x axis, respectively. Friction force Fs for the incommensurate case is compared with the commensurate structure, where we probe three different arrangements of ions on the surface (shown in Figure 1 (e), (f), and (g) in the main manuscript), in Fig. SM7. FIG. SM7. Friction force Fs for incommensurate case is compared with commensurate surfaces where we study three different patterns of ions ’ position on the confining surfaces as shown in Figure 1 (e), (f), and (g) in the main manuscript. FIG. SM8. Orientation of the director field of LCs where (cid:84) is the angle between the director field and the x-axis for misaligned surfaces . To understand the effect of misaligned surfaces on LCs’ orientation we have plotted the alignment of director field in Fig. SM8. In contrast to the commensurate cases, we observe that the director field orients along x axis, not along any of the groov es’ direction from two surfaces
In Fig. SM9 we have shown the time evaluation of stick-slip dynamics for the following systems: (a) a mixture of 72 hexane and 72 LCs, and (b) a mixture of 84 hexane and 60 LCs. In the latter case, we see clear slip events in the surface (X surface vs t) and LCs response coherently which is observed in the mean square displacement ( 2 LC >: Mean square displacement of LCs along x axis. |dx LC |: Average displacement magnitude for LCs along x axis. Slip length is defined as the distance slipped by the center of mass of the lower plate during the motion from the stick to the slip state which is shown as a black dotted line in the top panel of (b) . In Fig. SM10, we characterize the slip events as a function of the amount of hexane. We could not analyze the systems where (cid:85) H < 0.5 because of the disappearance of stick-slip events. It shows that as we increase the amount of hexane starting from equal amount of hexane and LCs mixture, slip length increases and slip happens at a larger displacement of the lower plate. FIG. SM10 . Slip in the surface as a function of hexane concentrations. Title of file: Video SM1 Video caption: Dynamics of 72 liquid crystals forming a monolayer nanoconfined between are not shown in the video for clarity. Color codes of the atoms are same as in Fig. 1 (b).