in many areas of process 
 engineering such as pharmaceutical or 
 food technology industry powders are manipulated in big containers . 

the flowability of granular dry powders is usually prone to strong 
 shear stresses , which depend on particle shape , particle roughness , 
 adsorbates or chemical impurities on the particle surfaces , and plastic 
 or elastic deformations in the particle surface layers .
a principal 
 understanding of the particle interactions on the microscopical scale 
 can help to figure out the causes of the shear stresses to use this 
 knowledge to reduce them . in this
paper ultrafine powders in the nanometers 
 range consisting of amorphous silica spheres were studied . because 
 of the high hydrophilicity of the material , under ambient conditions 
 water vapor is the most frequent chemi- and physisorbed substance 
 on the amorphous silica surface .
moisture drastically changes the 
 adhesion between silica particles , leading to agglomeration of particles 
 into large clusters , thereby hindering the flowability of powders 
 in process containers which is considered undesirable .
hence , it is 
 essential to study particle adhesion for varying relative humidity . for macroscopic bodies
laplace 
 and kelvin equation are conventionally used to describe the capillary 
 force which originates from liquid bridges that form between the particles 
 by the condensation of water vapor from the atmosphere .
the young  laplace 
 equation assumes that capillary pressure and surface tension can be 
 defined by two principal radii giving the curvature of the meniscus , 
 while the kelvin equation requires that the liquid behaves like a 
 continuum on the length scales of the so - called kelvin length ( 0.52 
 nm for water ) . over the years
the standard equations have been further 
 developed by many groups to account for surface roughness and chemical 
 composition : rabinovich et al .
developed 
 a model to calculate adhesion forces between a particle and a plane 
 with nanoroughness .
butt and fashchi - tabrizo 
 et al . presented an analytical model for 
 the adhesion forces between rough particles .
moreover , butt and kappl as well as efremov et al . gave extended reviews of the theoretical treatment of capillary 
 forces along with afm measurements .
numerically calculated the exact meniscus profile between 
 smooth nanoparticles from the kelvin equation , demonstrating that 
 the standard equations are only applicable for particles larger than 
 1 m .
many theories assume that the particle radius or the horizontal 
 extent of the contact area is much larger than the curvature radius 
 of the liquid bridge .
moreover , line tensions caused by the shrinkage 
 or expansion of the liquid meniscus normally not accounted for by 
 many theories are typically in the range of 1 nn like the capillary 
 forces of nanoparticles themselves ; i.e. , they are not negligible . 
 because of the introduced approximations in macroscopic theories
, 
 they can fail to predict the correct adhesion forces , especially when 
 either the particles themselves or the surface roughness of larger 
 particles are on the nanometer scale .
this is especially problematic 
 at low relative humidity when the surfaces are partly wetted by water ; 
 then the liquid film is not able to fill the whole contact area between 
 the particles , but rather the water meniscus appears where surface 
 asperities on the particles which are usually on the nanometers scale 
 approach each other . since gravitational forces
play no role for nanoparticle 
 interaction which is dominated by van der waals and coulomb forces , 
 the smallness of the investigated particles together with the requirement 
 to determine highly accurate adhesion forces predestines the system 
 for molecular dynamic simulations . to our knowledge
the calculation 
 of capillary forces between realistic 
 silica particles has not yet been done by molecular simulation techniques . 

however , the wetting of crystalline silica plates applying molecular 
 dynamic simulations has been studied by berendsen and co - workers , who looked at the qualitative agreement of their 
 calculated capillary forces with surface tension forces deduced from 
 macroscopic relations .
have 
 carried out molecular dynamic simulations aiming to determine realistic 
 adhesion energies of amorphous silica wafers in dependence of a predefined 
 amount of adsorbed water .
conventionally the grand canonical monte 
 carlo ( gcmc ) molecular simulation approach is used to study the behavior of particles under ambient atmosphere . 

jang et al . used gcmc to simulate force versus distance 
 curves of a humid hydrophilic nanoparticle close to a wall applying 
 simple lennard - jones interactions to study the influence of varying 
 hydrophilicity on the adhesion forces .
puibasset and pellenq have calculated adsorption isotherms for water 
 on different faces of -cristobalite ; moreover , they studied 
 the filling of hydrophilic mesopores using 
 gcmc . moreover , ramachandran et al . applied 
 gcmc to calculate adsorption isotherms for conventional water models 
 in silicalite pores , desbien et al . did 
 the same for zeolite , and shirono et al . investigated the phase behavior of confined water in silica nanopores . 

have studies the 
 water meniscus formation between an afm tip and a surface using gcmc 
 simulations .
in one of our most recent papers we calculated the forces between silica plates in dependence of 
 the relative humidity applying gcmc simulations , and now we want to 
 adopt the approach for the investigation of humid silica particles .
zhuravlev has given a detailed description 
 of the chemistry of amorphous silica , defining a maximal number of 
 hydroxyl groups on the surface and categorizing them into subgroups 
 according to their chemical reactivity with water molecules .
gsele 
 and tong have determined surface energies 
 for silica wafer bonding under moist and dry conditions condensing 
 the surface hydroxyls to water , thereby establishing siloxane bonds 
 across the interface .
adhesion energies of 
 contacting silica surfaces exposed to different relative humidity 
 applying crack and atomic force microscopy ( afm ) measurements have 
 been proposed by wan et al .
, by michalske 
 et al . , and by chikazawa and co - workers , who moreover have given adsorption isotherms for water on silica 
 particles with varying silanol density .
lahtinen and co - workers , butt , 
 rabinovich et al . , and fashchi - tabrizi et al . have measured pull - off forces of silica particles 
 on walls in dependence of relative humidity applying afm .
to 
 produce force over distance curves of realistic silica nanoparticles , 
 the choice of the atomic interaction potentials is crucial . in the 
 current study the model of goddard and co -
it is based on a simple morse - type short - range potential including 
 the long - range electrostatic interactions via a coulomb term . despite 
 its simplicity
, it reproduces the amorphous silica structure very 
 accurately and moreover predicts the correct crystal - glass transition 
 temperature . for the water  silica interface we decided to use 
 the conventional clay force field which 
 has shown a reasonably well described 
 hydrogen - bond network on the silica surface as well as adhesion energies 
 in agreement with experiments .
the paper is organized as follows : 
 first , the simulation details 
 and the creation of the silica nanoparticles are described .
this is 
 followed by the results and discussion section where simulated adsorption 
 isotherms , force  distance curves , and pull - off forces in dependence 
 of the relative humidity are presented in comparison to experiments , theories , and simulations .
the silica particles 
 with a diameter of 4 nm are cut out of an amorphous bulk which was 
 created as described in a former paper using the silica potential developed by demiralp et al .
the particles were then annealed for 100 ps 
 at 300 k to reduce the number of dangling bonds on the freshly cleaved 
 surfaces .
the structures in terms of radial pair distribution functions 
 and angle distribution functions agree very well with the ones found 
 by hoang applying the same silica potential . 
 also ,
the atomic coordination numbers of silicon and oxide as well 
 as the fraction of silicon and oxide atoms on the surface found in 
 over- , under- , or chemically saturated coordination match well with 
 the values given in ref ( 29 ) . to receive a silanol density of 4.2/nm on the surface of the nanoparticles , siloxane bonds ( so - called bridging 
 oxygens )
have been randomly broken . according to zhuravlev s 
 model describing the surface chemistry 
 of amorphous silica , the silanol density ranges from 2.6 to 4.6/nm , where the silanol groups can be divided into isolated ( single 
 silanols ) , geminal ( two hydroxyl groups per silicon ) , and vicinal 
 or bridged hydroxyl ( oh ) groups . for a hydroxyl density of 3.55/nm on silica at room temperature
, zhuravlev has found a portion 
 of isolated , geminal , and vicinal silanols of 0.46 , 0.14 , and 0.40 , 
 respectively , in good agreement with our created particles which can 
 be seen on the left in figure 1 .
the clay force field along with 
 the spc water model was chosen to describe the water 
although the clay force field 
 was parametrized for bulk water only and not for its liquid 
vapor 
 interface treated in this work , it was shown in a previous paper that the water - mediated interactions are able 
 to reproduce measured surface energies of silica wafers given by experiments 
 of wan et al .
moreover , we showed that the hydrogen bond structure of water on 
 silica is reasonably well described in comparison to nuclear magnetic 
 resonance measurement and ab initio calculations .
thus , the clay force field with the parameters 
 given in table 1 was applied here to study 
 humidity - induced interactions of silica nanoparticles . for the 
 lennard - jones interactions the standard lorentz 
berthelot 
 combining rules were used for unlike pairs , where the cutoff was set 
 to 10  .
the long - range electrostatic interactions have been 
 accounted for applying the particle  particle particle - mesh 
 solver , which is faster than the traditional 
 ewald summation .
the equations of motion are integrated using the 
 velocity - verlet algorithm with an integration step of 2 fs .
all hydrogen 
 bonds and angles have been frozen , applying the shake algorithm . since for the clay force field the parameters 
 for bond
hs bonds and si  os  hs angles , the remaining bond and angle parameters in table 2 were taken from the cwca force field .
in the course of the simulations the bulk of 
 the particles was kept rigid ; only the silanol groups were allowed 
 to move .
uijlj = 4ij[(ij / rij )  ( ij / rij ) ] , uijcoul = qiqj/4rij .
the subscripts b , h , and 
 w stand for bridging 
 oxygens and for atoms part of hydroxyls and water , respectively . in the presence of water vapor 
 in the surrounding atmosphere a 
 certain amount of water molecules is chemisorbed ( silanol groups ) 
 and physisorbed ( hydrogen bonded ) on the silica surface .
the number 
 of adsorbed water molecules changes in dependence of the air s 
 relative water - vapor pressure p / p0 ( relative humidity ) with p0 = 0.044 bar the saturation water - vapor 
 pressure of spc water and in dependence of the particle separation . 
 to model silica particles under ambient conditions ,
the grand canonical 
 ensemble is applied since it allows fluctuations in the number of 
 water molecules during the simulation .
along with the grand canonical 
 ensemble the inhomogenous phase given by the adsorbed water molecules 
 on the silica surfaces is in equilibrium with an infinite reservoir 
 of water vapor molecules , imposing its chemical potential and temperature . 

the saturation pressure of water is extremely low such that only a 
 few water molecules are present in the gas phase of the simulation 
 box ; most of them are physically adsorbed on the particle surface . 

the chemical potential is directly related to the pressure of the 
 surrounding gas phase , such that with 
 the choice of a fixed chemical potential a constant water - vapor pressure 
 and with that a constant relative humidity is set , where the relation 
 between chemical potential and water - vapor pressure was determined 
 in a former publication .
the bond and 
 angle functions 
 are harmonic with kb the force constant 
 in kcal/(mol  ) and r0 the equilibrium distance in  , ka the force constant in kcal/(mol rad ) , and r0 the equilibrium angle in degrees . at the beginning of the simulations 

a single silica particle was 
 completely dissolved in bulk water to establish an equilibrated water 
 profile from which the number of water molecules adsorbed in the first 
 monolayer ( ml ) could be deduced .
the simulations treating the dissolved 
 particle have been carried out in the isothermal , isobaric ( npt ) ensemble for 1 ns at a 
 temperature of 300 k and a pressure of 1 bar , to allow for the adjustment 
 of the simulation box dimensions .
the wetted silica particles 
 were then prepared by removing water 
 molecules from the box of the dissolved particle configuration , leaving 
 only those that form the appropriate portions of water ml around the 
 particles given by the adsorption isotherm corresponding to the selected 
 relative humidity .
the adsorption isotherm of spc water on a single 
 silica particle was calculated applying grand canonical monte carlo 
 ( gcmc ) simulations which consisted of at least 600  000 cycles 
 for equilibration followed by a production run of a further 300  000 
 cycles to deduce the ensemble average for the number of water molecules . 
 at each cycle
n particle displacement , rotation , 
 insertion , and deletion attempts have been executed , where n corresponds to the number of water molecules in the simulation 
 box .
when two humid silica particles were brought into closer 
 contact 
 for the force calculations , capillary condensation set in and the 
 number of water molecules were allowed to adjust for at least 600  000 
 cycles for each selected particle  particle distance . to measure 
 the forces in dependence of particle distance and relative humidity , 

the silica particles are kept at fixed center of mass distances with 
 respect to each other along the z - axis .
the simulations 
 started at a center - of - mass distance of around 70  , which was 
 successively reduced by 0.5  until the repulsive forces onto 
 the silica particles became dominant .
after a stable water meniscus 
 and a constant water molecule number has been established the simulations 
 were continued in the canonical ensemble to save computation time 
 during the collection of the forces , where at each constant distance 
 the system is equilibrated for 1 ns , followed by a production run 
 of 3 ns to collect the center - of - mass forces onto each silica particle .
the mean force1acting between particles a and b 
 at a certain 
 center - of - mass separation along the z - axis is deduced 
 by an arithmetic average over the total center of mass forces fa and fb collected at the single simulation steps .
assuming ergodicity , the arithmetic average corresponds 
 to the canonical ensemble average denoted by the    
 in eq 1 . to keep the simulation box at 
 a reasonable small size , preserving 
 the performance of the mpi simulations , reflecting hard walls
were 
 established perpendicular to the z - axis , each wall 
 30  away from the surface of the closest particle .
thus , the 
 long - range electrostatic interactions have been treaded in the slab 
 configuration , i.e. , periodic in the x , y direction and nonperiodic with respect to z.
on the right in figure 1 the water density 
 profile around a dissolved amorphous silica particle is depicted . 
 to clarify the onset of bulk silica indicated by the vertical line , 

the origin of the coordinate system has been shifted 
 along the r - axis in the following figures depicting 
 the particle forces , such that it coincides with the surface of the 
 first silica particle . as a consequence of the surface roughness of 
 about 2  , on the amorphous particle the first water density 
 peak
counting 
 all the water molecules from the interior of the particle to the first 
 minimum in the water density profile in figure 1 gives a number of water molecules in the first ml of 9.95/nm ( compared to the number of 9.6/nm found for a 
 silica plate with an oh density of 3/nm ) .
water molecules are able to penetrate the silica surface 
 up to 3  , which could explain the higher number of water molecules 
 in the first monolayer in comparison to early assumptions of 9.52 
 water molecules / nm made in ref ( 39 ) for the quartz surface . left : created 4 nm silica 
 particle with silanol density of 4.2/nm .
right : number 
 density plot of water on the silica particle , 
 where the vertical line indicates the onset of bulk silica . left : adsorption isotherm of the silica particle 
 with oh density 
 of 4.2/nm in comparison to experiments ( oh density of 4.6 and 5.8/nm ) and simulations ( oh density of 7.0/nm ) .
right : isosteric 
 heat of adsorption for the nanosphere , in comparison to simulations on vycor and an amorphous plane .
on the left in figure 2 the 
 adsorption isotherm 
 for water on the silica nanoparticle is presented in comparison to 
 the adsorption isotherm simulated by puibasset and pellenq for a silica surface composed of different faces 
 of the -cristobalite crystal and experiments done by chikazawa 
 and co - workers on nonporous amorphous silica 
 1.7 m spheres .
the silica plates treaded in ref ( 12 ) had the highest hydroxyl 
 density of 7/nm and thus show the largest amount of adsorbed 
 water molecules among the displayed systems in figure 2 . only for relative humidities above 0.7 the simulated adsorption 
 isotherm agrees with the experimental one measured for a hydroxyl 
 density of 4.6/nm , which is comparable with the oh density 
 on the simulated particles . for low and intermediate relative humidity , 

however , the simulated adsorption isotherm lies above the experimental 
 one and mostly coincides with the asorption isotherm measured for 
 a hydroxyl density of 5.8/nm . as already discussed in 
 our last paper
, this could be an indication 
 that the silica  water interactions are too strong in the clay 
 force field while the water  water interactions agree better 
 with experiments .
the strong increase in the amount of adsorbed water 
 molecules at low relative humidity explains the large adhesion forces 
 down to very low relative humidity which will be discussed later . 
 for a hydroxyl density as low as 4.2/nm ( not shown in 
 figure 2 ) ,
puibasset and pellenq predicted a water adsorption on amorphous silica 
 plates that starts as from a relative humidity of 0.2 , whereas experiments 
 of fuji et al .
show that water already 
 adsorbs strongly at very low relative humidity which was also confirmed 
 by the current simulations . to have more insight into the water  silica 
 interaction , 
 the isosteric heat of adsorption
was calculated on the right in figure 2 by use of the cross - fluctuations2with u the 
 potential energy contributions for the water 
n the number of water molecules , r the ideal gas constant , and t the temperature . 
 within the statistical error of 15% the isosteric heat of adsorption 
 for
the amorphous nanosphere agrees well with the one calculated by 
 puibasset and pellenq for a vycor pore 
 and an amorphous surface represented by the superposition of different 
 faces of cristobalite , both at an average silanol density of 7.0/nm .
the isosteric heat of the particle is in shape similar to 
 the one for vycor , characteristic for curved surfaces .
when around 
 one monolayer ( 16.5 mol / m ) of water is adsorbed , 
 which corresponds to a relative humidity of 0.85 , the heat of adsorption 
 becomes nearly equal to the heat of liquefaction of spc bulk water 
 of 10.5 kcal / mol given by the horizontal line on the right picture 
 in figure 2 .
this indicates that the interaction 
 with the silica surface has become negligible as soon as the silica 
 surface is covered with water molecules .
for very low relative humidity , 
 on the other hand , the isosteric heat of adsorption for the nanosphere 
 is at least 16 kcal / mol , i.e. , well above the heat of liquefaction 
 of spc bulk water , which characterizes the strong hydrophilicity of 
 the silica particle .
puibasset and pellenq have shown that for extremely low relative humidity amorphous surfaces 
 can have considerably higher isosteric heat of adsorption than perfect 
 crystal surfaces with comparable silanol density .
they argued that 
 in this case the hydrophilicity of the surface is not directly related 
 to the silanol density but rather to locally very favorable arrangements 
 of hydroxyl groups that can maximize the number of hydrogen bonds . 
 on corrugated surfaces
the water molecules can easier adsorb on highly 
 energetic sites created by small hole - like defects .
besides surface 
 curvature and defects real amorphous 
 surfaces consist of a considerable large number of low - membered siloxane 
 rings .
bridging oxygens in low - membered rings show a high affinity 
 to hydrogen bond to water molecules if they are close to destabilizing 
 silanol groups .
those single hydrogen - bonded water molecules finally 
 serve as adsorption centers for further water with rising humidity , 
 which leads to the observed steep ascend of the adsorption isotherm 
 in figure 2 for very low relative humidity .
when two humid particles approach each other close enough , the 
 adsorbed layers around the particles become instable due to the attractive 
 surface forces , in addition , water from the atmosphere starts to condense 
 into the gap between the particles , which finally leads to the formation 
 of a connecting liquid bridge seen in figure 3 . at every given particle separation the capillary neck between the 
 particles grows in size over time until its curvature has decreased 
 such that evaporation and condensation are in equilibrium . with decreasing 
 particle distance
the meniscus becomes broader and less elongated . 
 at narrow gaps finally , water molecules are squeezed out between the 
 particles , and the system can not compensate for the loss of water 
 molecules by forming a broader meniscus ; the water content in the 
 capillary then shrinks . in figure 3 , 
 water number contour plots 
 for silica nanoparticles exposed to air of 0.9 relative humidity are 
 shown , where the water number is given by the sum of water molecules 
 in small volume elements on the particle surface .
the amount of adsorbed 
 water molecules on the noninteracting particles according to the adsorption 
 isotherm in figure 2 gives 1.15 ml for a relative 
 humidity of 0.9 .
as one can see , the water molecules are not equally 
 distributed on the silica particle surfaces but concentrated on areas 
 of high hydroxyl density .
even when 16.5 mol / m is 
 adsorbed , which corresponds to one monolayer of water , small hydrophobic 
 domains on the surface stay free of water molecules while on hydrophilic 
 regions the water molecules start to form a second layer . in 
 figure 4 , the water meniscus is displayed 
 for different relative humidities of 0.1 , 0.5 , and 0.9 , all at the 
 same particle  particle distance of 9  . at low relative 
 humidity
no meniscus is formed between the particles , at intermediate 
 relative humidity the particles are bridged by single water molecules 
 forming connecting chains , while at high relative humidity a continuous 
 water meniscus is formed .
the onset of capillary condensation at large 
 particle separations is visible in the step in the mean forces acting 
 between the humid particles in figure 5 for 
 high and intermediate relative humidity .
the sudden increase in the 
 attractive forces , resulting from the negative capillary pressure 
 inside the meniscus , pulls the particles together . for small nanoparticles 
 and especially for low relative humidity , one can not strictly speak 
 of a continuous capillary bridge , but rather of single hydrogen - bonded 
 water chains linking the silanol groups at opposite particles to each 
 other . for decreasing relative humidity
the step in the onset of the 
 mean forces at large distances thus disappears and becomes smooth 
 as can be seen in the bottom image of figure 5 .
sketch for the water capillary formation at 0.9 relative humidity 
 for particle distances of 3.0 , 7.0 , 13.0 , 15.0 , and 21  .
shown 
 are the water densities in small volume elements on the particle surface 
 ( the color code ranges from blue ( no waters ) , to white ( 0.025/ ) , yellow ( 0.033/ ) , and red ( 0.04/ ) ) . on the vertical axis the particle separation and on the 
 horizontal axis the radial distance from the particle s centers 
 of mass
the relative humidities are 0.1 , 0.5 , and 0.9 ( from left to right ) , 
 and the particle separation is 9  . shown are the water densities 
 in small volume elements on the particle surface ( the color code ranges 
 from blue ( no waters ) to white ( 0.025/ ) , yellow 
 ( 0.033/ ) and red ( 0.04/ ) ) .
on 
 the vertical axis the particle separation and on the horizontal axis 
 the radial distance from the particle s centers of mass are 
 displayed in  .
left : mean force split off into its contributions coming from the 
 capillary and sphere  sphere interactions for 0.9 , 0.5 , and 
 0.1 relative humidity ( from top to bottom ) .
right : number of water 
 molecules adsorbed on the particles and in the liquid bridge .
the mean forces in figure 5 have been split 
 off into their contributions origin from capillary and direct sphere 
sphere interactions contribute 
 only up to 7  to the total mean forces which are dominated by 
 the capillary forces .
the total interactions are of considerably longer 
 range than the forces between dry particles .
the range of the capillary 
 forces increases with relative humidity , so for instance in figure 5 the range is 11 , 12 , and 21  at 0.1 , 0.5 , 
 and 0.9 relative humidity , respectively . while for large particle 
 separations the mean force is a smooth 
 gently rising function , it exhibits strong oscillations when the surface 
 distances come into the range of a few angstroms .
the oscillations 
 at close distances originate from the ordering of the water molecules 
 in the gap between the approaching curved surfaces and show three 
 distinct maxima , at separations of 3.0 , 5.0 , and 7.0  , which 
 indicate water layers formed between the particles .
the mean forces 
 are less attractive here since it is not favorable for the particles 
 to penetrate into the water layer . at the equilibrium distance of 
 around 4.0  the particles are separated by a single water layer , 
 at 6.0  by two water layers , and at 8.0  by three water 
 layers , for instance ( as we will discuss in detail later ) . with increasing 
 relative humidity
the mean forces become less attractive at small 
 particle separations because of the increasing amount of water molecules 
 which have to be accommodated between the particles . on the right 
 in figure 5 the number of adsorbed water molecules 
 in dependence of particle distance and relative humidity
is depicted , 
 where the horizontal line in the plots indicates the adsorbed amount 
 of water for isolated particles .
as soon as capillary condensation 
 sets in , the number of water molecules jumps due to the formation 
 of a connecting water bridge . moving the particles closer to each 
 other ,
the meniscus ( or for low relative humidity more and more shorter 
 water chains span the gap between the particles ) becomes broader , 
 and the number of water molecules constantly rises until at a certain 
 particle distance the removal of water molecules from the region between 
 the particles can not be compensated by a broadening of the water neck . 
 at that separation
the number of water molecules starts to decrease , 
 as can be seen on the right in figure 5 .
this 
 separation depends , like the range of the capillary forces , on the 
 relative humidity . for low relative humidity it lies at around 4.0 
  , for intermediate at around 6.0  , and for high relative 
 humidity at around 9.0  . in agreement with simulations of shinto 
 et al . , the volume of the water bridge 
 is changing with particle distance ; thus , the constant volume approach 
 used in many theories can not be applied .
right : capillary forces for relative humidities between 0.05 and 0.95 . to discuss the force curves in 
 dependence of relative humidity , 
 total and capillary mean
as can be seen in figure 5 , the capillary forces start to become repulsive 
 with decreasing particle 
particle distance at significantly 
 lower distance values than the pure silica  silica forces ; i.e. , 
 they are still attractive at distances smaller than the equilibrium 
 distance of 4.2  for the pure silica  silica interaction . 
 what can be followed from that
is that humid particles can approach 
 each other closer than dry ones . in the insets of figure 6
one can see that the equilibrium distance of the 
 particles is slightly shifted to smaller values for low and intermediate 
 relative humidity in comparison to high relative humidity and dry 
 particles .
the increase of the equilibrium distance with rising relative 
 humidity is intuitively clear because of the hydrophilicity of the 
 silica particles which usually leads to good dispersion in water solution . 

all the forces in figure 6 show the same trend , 
 irrespective of the relative humidity the force maxima all lie at 
 nearly the same distances of 3 , 5 , and 7  ; the forces , however , 
 shifted to higher values with rising relative humidity .
this 
 behavior is in qualitative agreement with simulations of shinto et 
 al . and
hydrogen bond network for 0.1 relative humidity at 2.0 , 4.0 , and 
 6.0  particle distance ( from left to right ) .
the formation of water layers in the meniscus connecting 
 the particles 
 will be discussed in figure 7 . for
the system 
 with 0.1 relative humidity one can not strictly speak of a continuous 
 meniscus but rather of hydrogen - bonded water chains that span the 
 gap between the particles . at a larger distance of 6.0  ( rightmost 
 plot ) water chains consisting of at least ( because of the curvature ) 
 two water molecules connecting the surfaces by forming hydrogen bonds 
 with silanol groups on opposite particles .
then those hydrogen bonds 
 are broken by moving the particles closer together , squeezing out 
 the water molecules from the region between the particles , visible 
 in the decrease of the attractive forces at 5.0  in the bottom 
 plot of figure 5 . at the equilibrium distance 
 close to 4.0 
at least single water molecules link the particles 
 together ; at 2.0  finally the surfaces directly approach each 
 other in the center of the contact area seen in the snapshot on the 
 left in the same figure .
the water molecules then form a circumventing 
 ring around the particle contact . for high relative humidity 
 of 0.9 we analyzed the water layers 
 in the meniscus and their correlation to the oscillations in the mean 
 forces in a similar way as has been done by kim et at . to display the water density and the charge 
 density close to the particles and in the water bridge in figure 8 ,
the water molecules have been counted in volumes 
 of cylinder rings centered around the particle  particle axis 
 of width dr and height dz of 1  , 
 where the density is then gained by dividing the number of water molecules 
 or the sum of the charges by the cylinder ring volume .
the densities 
 are shown for particle separations of 4 , 5 , 6 , 7 , and 8  , corresponding 
 to the minima and maxima of the capillary forces in figure 5 .
all the graphs in figure 8 have in common that the water density is elevated with respect to 
 the water bulk density of 0.033/ near the surfaces 
 of the particles , while in the interior of the water bridge the water 
 density hardly deviates from the bulk one .
this behavior could already 
 be seen in the density profile on the right in figure 1 . with increasing distance from the vertical axis
for very narrow cavities as for the particle distance of 4 
  the density is zero for small r since a full 
 water layer is not able to be formed in the gap between the particles . 
 for the particle distance of 5 
two density maxima lying close 
 to 20.36 and 22.7  can be seen with a separation between them 
 of 2.34  , which is slightly smaller than the water molecular 
 diameter of 2.7  , indicating that a second water layer is not 
 yet fully developed . at a distance of 6
 the maxima lie at 21.6 
 and 24.3  with a difference that corresponds to a water molecular 
 diameter . at 7 
the maxima can be found at 21.5 , 22.8 , and 24.9  , 
 indicating that a third layer in the middle of the capillary is not 
 yet formed . at 8 
finally the maxima are at 21.4 , 23.6 , and 
 26.23  with distance between the maxima of 2.2 and 2.5  , 
 indicating the presence of a not yet fully developed third water layer
. 
 the charge density in figure 8 can give information 
 about the orientation of the water molecules in the water bridge . 

as can be seen the positively charged hydrogen atoms are preferentially 
 orientated toward the particle surface while the oxygens point into 
 the water bridge . for larger distances from the particles
the charge 
 distribution becomes nearly uniform , giving evidence that the water 
 molecules adopt no special orientation with respect to the silica 
 surface in the interior of the water meniscus .
water density plots ( in 
 1/ ) for 0.9 relative 
 humidity at particle distances of 4.0 , 5.0 , 6.0 , 7.0 , and 8.0  . 

the rightmost plot in the second line shows the charge density ( in 
 e /  ) for a distance of 8.0  . on the horizontal 
 axis the particle separation and on the vertical axis the radial distance 
 from the particle s centers of mass
experimentally , the adhesion forces 
 between particles can be determined 
 by atomic force microscopy measurements . the so - called pull - off or 
 adhesion forces
are given by the global minimum in the mean forces 
 and correspond to the force dedicated to separate two humid silica 
 particles from their pull - off distance .
the pull - off distance gives 
 the location of the global force minimum , so for instance in figure 5 it is at 8  for high , at 6  for intermediate , 
 and at 5  for low relative humidity , where the pull - off distances 
 for total and capillary forces do not necessarily coincide .
the pull - off 
 forces at different water coverage can be seen in table 3 and figure 9 .
total and capillary pull - off 
 forces for relative humidities between 
 0 and 1 .
the forces in figure 9 are normalized with 
 respect to the particle radius r = 20  and 
 compared with the laplace - pressure contribution to the forces in the 
 limit of very small meniscus radius3with  = 73 mn / m the water - vapor surface 
 tension and  = 30 the contact angle of water on silica . 

it assumes an adhesion force that is independent of the relative humidity 
 and a particle radius that is much larger than the radius of the mensicus . 
 for a particle radius of 20 
this is hardly fulfilled . that 
 the adhesion force of nano - sized particles is not independent of humidity 
 has been shown by afm measurements as 
 well as by more advanced macroscopic theories .
equation 3 states 
 therefore a crude estimation for the capillary forces and thus conventionally 
 only serves as convergence limit , indicated by the horizontal line , 
 for the adhesion force at high relative humidity . at 0.95 relative 
 humidity the pull - off force , however , falls below this limiting value , 
 which could be caused by the known underestimation of the water surface 
 tension by the spc water model .
the normalization of the pull - off 
 forces with respect to r is conventionally done in 
 experiments to make the forces 
 independent of particle size .
this works fine when the particle radius 
 is at least in the range of several 100 nm ; for smaller particles , however , the pull - off forces are still size 
 dependent even after normalization .
so , for instance , normalized water - capillary 
 forces calculated by pakarinen et al . applying 
 a macroscopic model for smooth nanoparticles of different sizes have 
 shown that with decreasing radius the maximum of the pull - off force 
 curve is shifted to lower values and lower relative humidity . in figure 9 , the total and the capillary 
 part of the pull - off forces are displayed in dependence of the relative 
 humidity .
both curves run through a flat maximum between 0.1 and 0.8 
 relative humidity , exhibiting smaller pull - off forces for nearly dry 
 and very humid particles .
contact adhesion measurements of wan et 
 al . gave surface energies between wetted 
 silica plates which are nearly constant over the whole range of investigated 
 relative humidities between 0.05 and 0.95 .
the surface energy they 
 found was 105 mj / m , which corresponds to an adhesion force 
 between curved surfaces of 990 mn / m applying the derjaguin equation 
 2f / r = 3 , where this 
 approximation relates the surface energy  between deformable 
 flat surfaces to the forces between spherical particles separated 
 by the same surface to surface distance . moreover , surface energies 
 for amorphous silica surfaces simulated in a former publication varied between 82 and 100 mj / m ( which 
 translates to particle forces between 772 and 942 mn / m ) for relative 
 humidities between 0.8 and 0.3 , respectively , which agrees reasonably 
 well with the force values in figure 9 .
moreover , with respect to principal shape and maximum value of 
 the force  humidity curve good agreement in comparison to afm 
 experiments and macroscopic theories was achieved .
afm measurements 
 of a silicon nitride tip on a silica wafer under ambient conditions gave a force  humidity curve with a steep 
 maximum of 820 mn / m around 0.7 relative humidity .
moreover , butt calculated water capillary forces for rough microspheres 
 at zero separation and contact angle with a maximum of around 820 
 mn / m at very high relative humdity , by describing the roughness of 
 5  by a rectangular asperity distribution .
got water capillary forces running 
 through a maximum of 720 mn / m at 0.8 relative humidity applying their 
 model to a hydrophilic smooth 15 nm sphere at a distance of 3  
 from a smooth hydrophilic wall .
all those force values lie in the 
 same range as the pull - off forces in table 3 and figure 9 , certainly with their maximum 
 at different relative humidity than the current simulations suggest .
one may , however , not forget to mention that there are afm measurements 
 that predict a complete different shape of the force 
so for instance afm measurements executed 
 by rabinovich et al . for silica microspheres 
 on a rough silica surface of root - mean - square roughness of 2.2  
 showed a continuous increase of the adhesion force ending in a broad 
 plateau of around 650 mn / m between 0.4 and 0.8 relative humidity ; 
 even somewhat smaller maximum adhesion forces have been measured between 
 humid hydrophilic silica nanospheres by paajaninen et al .
moreover , for relative humidities lower than 
 0.2 the capillary force vanished completely in those experiments in 
 contradiction to our simulations .
furthermore , adhesion forces measured 
 by fuji et al . between silica microspheres 
 of varying silanol density ( hydrophilicity ) gave a completely different 
 shape of the force curve which did not exhibit a maximum or a plateau 
 at a certain relative humidity but instead increased monotonically 
 having a similar shape as the adsorption isotherm in figure 2 .
what can be followed from the aforesaid 
 is that the adhesion force 
 can either increase monotonically , remain relatively constant by encountering 
 a plateau , or run through a maximum with changing relative humidity 
 even on very similar surfaces or particles from the same batch of 
 a nearly monodisperse powder . besides the chemical heterogeneity of 
 the surface which can lead to variations in the energy of adhesion 
 in dependence of which regions on the two particle surfaces are in 
 direct contact ,
the reason why a force plateau or a maximum in the adhesion 
 force is established with respect to the relative humidity was investigated 
 by molecular dynamic simulations of jang et al .
they changed the hydrophilicity of the tip by varrying 
 its chemical composition and showed that for weakly hydrophilic tips 
 on strongly hydrophilic surfaces the adhesion force is nearly zero 
 for low relative humidity and steadily rises with increasing humidity 
 forming a plateau , while for high hydrophilicity the capillary force 
 is already observable at very low relative humidity and becomes a 
 nonmonotonic function of humidity where the maximum in the adhesion 
 force moves to lower relative humidity .
this was also confirmed by 
 simulations with nanoparticles on planes by shinto et al .
have shown that moreover , particle 
 size and tip geometry can explain the ambiguity in the shape of the 
 force  humidity curves .
humidity 
 curves which they gained from afm measurements for a silicon nitride 
 tip on a silicon wafer , on a mica surface , and on an iron particle 
 under ambient conditions , by systematically studying the influence 
 of variations in particle size , roughness , and tip geometry in their 
 theoretical model .
they showed that the curve for a perfectly 
 smooth large sphere 
 on a smooth surface ( or a second smooth sphere ) is nearly flat down 
 to very low relative humidity , while for very high relative humidity 
 it slowly descends . only if some surface roughness is included into 
 the model the force  humidity curve 
 gradually decreases for low humidity exhibiting a force maximum , where 
 the region of zero - capillary force increases with higher surface roughness . 

besides the surface roughness also the particle size has an effect 
 on the formation of a force maximum .
showed that a maximum in the force curve calculated for 
 hydrophilic nanoparticles can be observed only as from a certain particle 
 radius downward and that it moves to lower relative humidity with 
 decreasing radius .
finally , it was shown by pakarinen et al . and fashchi - tabrizi et al .
that the particle shape has a major influence on the force  humidity 
 curve .
the increase of the adhesion force with relative humidity found 
 by fuji et al .
for instance could be 
 explained by the use of a cone - like instead of a sphere - like tip . to summarize the above , the agreement with afm meansurements 
 and 
 theoretical predictions is good as far as the principal shape of the 
 force  humidity curve and the value of its maximum are concerned .
the discrepancies in comparison to some experiments could be attributed to differences 
 in the hydrophilicity ( in terms of surface roughness or chemistry ) 
 or geometry between the investigated sample in the lab and simulations . 

moreover , it is a size effect since with smaller particle size the 
 maximum of the adhesion force moves to lower relative humidity and 
 lower values and the region of zero capillary 
 force at low relative humidity shrinks .
adsorption 
 isotherms calculated for silica nanoparticles were nearly 
 in perfect agreement with experiments of fuji et al . at high relative humidity , while for low relative humidity 
 the amount of adsorped water molecules was considerably higher than 
 in the experiments .
the 
 isosteric heat of adsorption adopts high values for very low humidity , 
 in agreement with other simulations which 
 can not be explained in dependence of the hydroxyl density , but by 
 surface defects and the presence of low membered siloxane rings typically 
 found on amorphous surfaces which create energetically favorable sites 
 for the adsorption of water molecules which serve as adorption centers 
 for further water with rising relative humidity .
thus , the adsorption 
 isotherm of amorphous surfaces can show a nonzero amount of adsorbed 
 water , even at lower relative pressures than necessary for the water 
 adsorption on perfect crystalline surfaces of comparable oh density . 

with rising number of adsorbed water molecules the isosteric heat 
 of adsorption decreases , since more and more water molecules hydrogen 
 bind to adsorbed water molecules and not directly to hydroxyls on 
 the silica surface .
when around one full monolayer of water covers 
 the particle surface , the heat of adsorption is thus close to the 
 heat of liquefaction of bulk water .
when two particles approach 
 each other close enough to enable capillary 
 condensation , a water bridge is formed between the particles which 
 causes an additional attractive force to the van der waals interactions . 
 in agreement with other simulations , the capillary 
 force becomes longer ranged but gentler in slope with higher humidity 
 and shows oscillations for very small particle distances indicating 
 the layering of water molecules in the interparticle gap .
the volume 
 of water in the capillary is not constant as assumed by many theories . 

it slowly rises with the onset of capillary condensation , runs through 
 a maximum , and finally decays when the broadening of the water bridge 
 with decreasing distance can not compensate for the number of squeezed 
 out water molecules . for small nanoparticles one can not speak of a 
 continuous water mensicus but rather of hydrogen - bonded water chains 
 that connect the particles . the pure silica 
silica interactions 
 between dry particles 
 are of considerable shorter range , weaker in magnitude and stronger 
 repulsive at very close contact than the capillary forces .
it is thus 
 not surprising that particles under humid conditions can approach 
 each other closer .
moreover , the presence of water has the effect 
 that the particles are much more tightly bound to each other than 
 the same particles in perfect vacuum . only for very high relative 
 humidity
the water layers lead to weaker attractive interactions at 
 close particle approach such that the equilibrium distance shifts 
 to bigger values , which is characteristic for strongly hydrophilic 
 particles in solution .
the forces needed to detach two particles 
 from contact are called 
 pull - off forces , and their strength depends on the relative humidity 
 of the air .
simulated force  humidity curves exhibit a broad 
 maximum at intermediate relative humidities and decrease for very 
 low and high relative humidities .
what can be followed by that is 
 that the flowability of nanosilica powders is best for very dry air 
 or in solution , while for low and intermediate relative humidity the 
 particles tend to cluster , which hampers the flowability . as has been 
 demonstrated by pakarinen et al . and farshchi - tabrizi 
 et al .
, the observed shape of the simulated 
 force  humidity curve is characteristic for atomistically rough , 
 strongly hydrophilic sphere - shaped bodies .
a lower hydrophilicity 
 would shift the force maximum to higher relative humidity or replace 
 it by a force plateau . moreover , the appearance of a maximum is also 
 a size effect , where an existing maximum moves to lower relative humidity 
 with decreasing particle radius .
regardless of the location of the 
 force maximum and the exact shape of the force  humidity curve 
 many experiments and theories are in reasonable good agreement with 
 our simulated force  humidity curves giving maxima of around 
 850 mn / m ( 750 mn / m for the capillary part alone ) . at very high relative 
 humidity ,
however , the pull - off force is underestimated by the spc 
 water model .
 adhesion forces between nanoparticles 
 strongly depend on the amount 
 of adsorbed condensed water from ambient atmosphere . 
 liquid water 
 forms bridges in the cavities separating the particles , giving rise 
 to the so - called capillary forces which in most cases dominate the 
 van der waals and long - range electrostatic interactions . 
 capillary 
 forces promote the undesirable agglomeration of particles to large 
 clusters , thereby hindering the flowability of dry powders in process 
 containers . in process engineering macroscopic theories based on the 
 laplace pressures are used to estimate the strength of the capillary 
 forces . 
 however , especially for low relative humidity and when the 
 wetting of rough or small nanoparticles is studied , those theories 
 can fail . 
 molecular dynamic simulations can help to give better insight 
 into the water  particle interface . 
 the simulated force versus 
 distance curve as well as adhesion forces and the adsorption isotherm 
 for silica nanoparticles at varying relative humidity will be discussed 
 in comparison to experiments , theories , and simulations . 
Introduction
Methods
Results and Discussion
Conclusion