despite its ubiquity 
 in cell membranes , there is little quantitative 
 information on the effects of small mole fractions of cholesterol 
 on the phase diagrams , molecular organization , and surface viscosity 
 of mixtures of phospholipids and cholesterol .
understanding 
 cholesterol s effects in altering the local molecular organization 
 and rheology of lipid monolayers may give clues to the mechanisms 
 that stabilize nanometer - scale  rafts  in complex lipid - cholesterol 
 mixtures ; the raft hypothesis has emerged in recent years as a general 
 organizing principle for the structure of eukaryotic cell membranes .
rafts are hypothesized to result from nanometer - scale phase separation 
 of ordered and viscous domains in which cholesterol , saturated lipids , 
 and membrane proteins preferentially accumulate , surrounded by a sea 
 of less viscous , unsaturated lipids with greater protein diffusivity .
however , the fundamental physics underlying raft formation is still 
 being developed , especially how interactions between saturated phospholipids 
 and cholesterol determine membrane phase behavior , viscosity and diffusivity .
the interactions of cholesterol and saturated 
 phospholipids also 
 play an important , but poorly understood , role in the properties of 
 human lung surfactant ( ls ) , a lipid - protein monolayer necessary to 
 reduce the surface tension in the lung alveoli . at present ,
even the existence of cholesterol in native 
 ls is questioned , as the lung lavage required to harvest ls inevitably 
 causes blood and cell debris to be coextracted , potentially contaminating 
 ls with cholesterol .
this lack of consensus is reflected in the composition 
 of replacement lung surfactants , which are used to treat neonatal 
 respiratory distress syndrome ( nrds ) , which occurs in 20  00030  000 
 premature infants each year in the u.s .
survanta and 
 curosurf , two clinically approved animal extract replacement surfactants 
 for treatment of nrds , have all cholesterol removed after harvesting . 

infasurf , the third clinically approved surfactant , retains 4 - 5 wt 
 % cholesterol . resolving
this controversy 
 is difficult , as there is little information on the effects of small 
 cholesterol fractions on the organization and dynamics of phospholipid 
 monolayers .
our previous work has shown that the surface viscosity 
 of dipalmitoylphosphatidylcholine ( dppc ) monolayers decreases by an 
 order of magnitude per wt % cholesterol , up to about 3 wt % , suggesting that the cholesterol - containing infasurf 
 would have significantly different monolayer dynamics than cholesterol - free 
 survanta and curosurf .
interfacial viscosity is believed to have a 
 significant effect on monolayer collapse , surfactant spreading during breathing , and transport from the type 
 ii epithelial cells , where surfactant is produced , to the alveolar 
 air  water interface .
interfacial 
 viscosity may also be important during the instillation of replacement 
 surfactant and the reopening of bronchial airways .
however , the origin of this dramatic effect of cholesterol 
 on dppc viscosity is not yet known .
cholesterol may also play 
 a role in lung surfactant inactivation 
 in acute lung injury ( ali ) and acute respiratory distress syndrome 
 ( ards ) .
ards occurs as a rapid onset of respiratory failure and affects about 150  000 people per year in the u.s . with 
 a mortality rate of 3040% .
the 
 pathogenesis of ards is not fully understood , but in both ali and 
 ards , surfactant is  inactivated  by some primary pathogenesis 
 such as lung inflammation , trauma , pulmonary infection , near - drowning , 
 etc .
the cholesterol content of ards 
 patients shows an increase in cholesterol content and in vitro , cholesterol levels greater than 10 mol % increase 
 the minimum surface tension at monolayer collapse , which may exacerbate 
 lung damage .
grazing incidence x - ray diffraction ( gixd ) shows 
 that up to 7 mol 
 % added cholesterol does not change the basic alkane packing of dppc , 
 but does decrease the extent of ordering , or coherence area , suggesting 
 an increased number of lattice defects .
we postulate that the free 
 area available for diffusive transport in a two - dimensional analog 
 of the classic cohen and turnbull free volume model of viscosity is inversely proportional to the number of molecules 
 in a coherence area . using this relationship
, the surface viscosity data for 
 all surface pressures and cholesterol fractions collapses to a simple 
 logarithmic relation with no adjustable parameters .
this suggests 
 that the decreased molecular ordering caused by the incompatibility 
 of cholesterol with the alkane chain lattice is the origin of the 
 orders of magnitude decrease in surface viscosity .
1,2-dipalmitoyl - sn - glycero-3-phosphocholine ( dppc , r - enantiomer ) and dihydrocholesterol 
 ( avanti , alabaster , al ) with 0.1 wt % texas - red dhpe ( n-(texas red sulfonyl)-1,2-dihexadecanoyl - sn - glycero-3-phosphoethanolamine , 
 invitrogen , grand island , ny ) were mixed in the appropriate ratios 
 and diluted to 0.2 mg / ml in hplc - grade chloroform ( fisher 
 scientific , st .
dihydrocholesterol 
 ( chol ) was used instead of cholesterol to minimize oxidation but has 
 little impact on phase behavior .
surface 
 pressure  area isotherms were recorded at 25 c using a 
 teflon trough ( nima , coventry , england ) with custom designed stainless 
 steel ribbons which reduce film leakage at high surface pressures . 

a filter paper wilhelmy plate ( riegler and kirstein , gmbh ; potsdam , 
 germany ) was used to measure surface pressure .
the open area of the 
 trough used was 125 cm and each complete compression / expansion 
 cycle took about 8 min ( 0.42 cm / s ) .
for fluorescence imaging , 
 the langmuir trough was mounted on a nikon optiphot optical microscope 
 with a custom designed stage equipped with long working distance objectives 
 designed for fluorescent light .
a dichroic mirror / barrier filter assembly 
 directed the excitation light onto the monolayer films at a normal 
 angle of incidence and filtered the emitted light and the images were 
 detected by a silicon intensified ccd camera .
videos of the monolayer 
 film were recorded during the compression - expansion cycle directly 
 onto the computer using the pinnacle studio capture software .
the 
 continuous , fluid lipid phase appears bright due to the preferential 
 segregation of the texas red dye , while the better ordered domains 
 exclude the dye molecules and appear dark .
two - dimensional 
 gixd experiments were carried out at the chemmatcars station at beamline 
 15-id at the advanced photon source , argonne national laboratory .
dppc / chol at the appropriate ratios were dissolved 
 in chloroform solution at 1 mg / ml and spread dropwise onto 
 the air / deionized water interface in a custom langmuir trough , which was temperature - controlled at 22 c. after waiting 30 min for solvent evaporation , 
 the monolayers were compressed to the desired surface pressure ( 20 , 
 30 , or 40 mn / m ) and annealed for an additional 30 min .
the trough 
 was enclosed in a helium - filled chamber and the oxygen level was constantly 
 monitored during exposure to the x - ray beam .
the analysis of gixd 
 data for two - dimensional films at the air - water interface follows 
 that of kaganer et al . it is well established 
 that the bragg peaks correspond to ordering within the alkane chains 
 of the lipid tailgroups ; the organization 
 of the headgroups is inferred from changes in the tailgroup lattice 
 in response to changes in surface pressure and cholesterol fraction .
circular ferromagnetic probes 
 ( microbuttons ) of diameter 20 m , thickness 1 m , with 
  button holes  of diameter 3.5 m were fabricated 
 by photolithography .
. a uniform magnetic field of magnitude , b , and orientation ,  , was generated by the output 
 of two independent pairs of electromagnets controlled by a custom 
 labview code to exert a controlled torque , l , on a microbutton 
 of moment m and orientation . to measure the 
 frequency - dependent linear viscoelastic response , a sinusoidal magnetic 
 field was applied to generate a time varying applied torque .
the microbutton 
 orientation was determined from bright field images of the holes in 
 the microbuttons as a function of applied torque , to determine the 
 rotational resistance . from the rotational resistance
, the linear 
 viscoelastic surface moduli were obtained from the solution of the 
 hydrodynamic problem of a rotating cylinder within a viscoelastic 
 monolayer atop a viscous subphase . in terms of measured experimental properties , the surface loss modulus
, g is the out of phase component of the rotational 
 resistance , the surface storage modulus , g , 
 is in the in - phase component as in conventional 3-d rheology ( figure 6b ) . the surface viscosity for the newtonian response 
 we observed over the frequency range of 0.110 hz is s = g/ , or 
 for the 1 hz frequency used in figure 6 , s = g/2. the 
 same exponential dependence of surface viscosity on surface pressure 
 was obtained using a 100 m probe showing that continuum values 
 of elasticity and viscosity were being measured .
the 100 m 
 probe is more than an order of magnitude larger than the domain sizes 
 we have seen ( figures 5 and 6 ) .
recent results using macroscopic wire rings ( 10 cm diameter 
 ring , 0.7 mm diameter wires ) showed identical trends with surface 
 pressure and good agreement for similar monolayers . the maximum surface viscosity that we could measure with 

our rheometer was 100 pams ; the surface 
 viscosity of pure dppc at 40 mn / m was greater than this and was not 
 measured .
freshly - cleaved 
 mica substrates ( s&j trading inc . ; glen oaks , ny ) connected to 
 a computer - controlled dipping mechanism in a commercial circular nima 
 l - b trough ( biolin scientific , inc . , linthicum heights , md ) were pulled 
 through the monolayer at 5 mm / min at a constant surface pressure of 
 20 mn / m .
transfer ratios were determined by recording the interfacial 
 area change of the trough during transfer and comparing this to the 
 surface area of the mica substrate . a transfer ratio of 1 means that 
 these areas are equal ; only films with transfer ratios of 1 
 were examined .
the mica substrates were glued to stainless steel discs 
 and affixed to the magnetic holder of an mmafm-2 afm ( digital instruments ; 
 santa barbara , ca ) with a cantilever tip ( asylum research , ac160ts ; 
 santa barbara , ca ) designed for tapping mode operation .
two - dimensional gixd was carried out at chemmatcars , 
 sector 15-id 
 at the advanced photon source , argonne national laboratory on dppc 
 monolayers with various mole fractions of dihydrocholesterol ( chol ) . 

figure 1 shows the gixd intensity maps for 
 ( a ) pure dppc at 20 mn / m and ( b ) 6.4 mol % chol / dppc monolayers at 
 40 mn / m .
figure 2 shows the qz - integrated intensity 
 profiles ( arbitrary units ) for dppc / chol monolayers at 20 , 30 , and 
 40 mn / m for 0 to 7 mol % chol ( each spectra offset by 1000 ) .
two - dimensional 
 x - ray maps of ( a ) pure dppc at  = 20 mn / m 
 and ( b ) 6.4 mol % chol in dppc at  = 40 mn / m .
two bragg reflections 
 are visible , the degenerate   reflection at positive qz and lower qxy and the   at higher qxy and qz = 0 , indicating nearest neighbor tilt .
the   peak remains at the same location for all cholesterol or 
 surface pressures ( dotted lines ) .
the basic motif of the dppc lattice 
 is unchanged by cholesterol , although the tilt is reduced with increasing 
 cholesterol .
cholesterol broadens both peaks consistent with a decrease 
 in the size of the correlated areas in the monolayer .
we assign the bragg peak in figure 1 at 
 lower qxy and positive qz as due to the degenerate ( 11 ) 
 and ( 11 ) reflections of distorted hexagonal packing ; the second peak at higher qxy and qz = 0 is due 
 to the nondegenerate ( 02 ) reflection .
as the ( 11 ) reflection is located 
 at qz > 0 , and the ( 02 ) 
 reflection 
 is centered at qz = 0 , the 
 alkane chains are tilted in the nearest neighbor ( nn ) direction .
regardless of composition or surface pressure , 
 all ordered areas in the monolayers had the same distorted hexagonal 
 packing with nn tilt ( figure 3b , inset ) .
( a ) d11 and ( b ) d02 as 
 a function of cholesterol and surface pressure . d11 decreases with increasing surface pressure 
 and cholesterol fraction .
this is consistent with 
 a decrease in tilt , which decreases d11 , while the alkane chain packing normal to the chain axis , hence d02 remains the same .
one gray 
 and one white circle are the two alkane chains in a rectangular unit 
 cell of dimensions a and b. translation 
 of the pair of gray and white circles by a and/or b generates the lattice .
the spacing between the dotted 
 lines corresponds to the d - spacings in table 2 and a , b. the qz - integrated 
 intensity 
 profiles ( figure 2 ) show that the ( 11 ) bragg 
 peak broadens and moves to higher qxy with increasing cholesterol content ( dotted lines ) for all 
 surface pressures , while the ( 02 ) peak also broadens with increasing 
 cholesterol content but remains at constant qxy . from the qij values in table 1 ,
the real space lattice 
 dimensions are dij = 
 2/qij ( table 2 and figure 3 ) .
the tilt angle ,  , for nearest neighbor 
 tilt is given by tan  = qz[q112  ( q02/2 ) ] .
the 
 coherence length is determined from the full width at half - maximum 
 ( fwhmij ) of each peak after correction 
 for the instrumental resolution , lij = ( 0.92)/(fwhmij ) ( table 2 ) .
q02 and q11 are the lattice parameters in fourier space 
 for the two strong reflections from the qz averaged data .
all d - spacings are referenced 
 to a two molecule rectangular unit cell with a = d10 = [ d112  ( 2d02 ) ] and b = 2d02= d01 ( see inset to figure 3b ) .
the error in a is larger than b as the ( 11 ) reflection is much broader than the ( 02 ) reflection 
 ( see figure 2 ) .
 is the tilt angle of 
 the alkane chains in degrees with respect to the water surface , tan 
  = qz[q112 (q02/2 ) ] from table 1 ( see inset to figure 3b ) .
the chain area 
 is the cross sectional area of the chains in the direction perpendicular 
 to the chains , or ( ab cos )/2 .
l02 and l11 are the coherence 
 lengths in the ( 02 ) and ( 11 ) directions , lij  ( 0.92)/(fwhmij ) .
figure 3a shows that , at a fixed surface 
 pressure , adding chol decreases d11 while 
 figure 3b shows that d02 remains constant . for pure dppc
, d11 decreases from 4.79 to 4.58  as the surface pressure 
 increases from 20 to 40 mn / m ; d02 is constant 
 at 4.30  ( table 1 ) .
cholesterol and surface 
 pressure influence the lattice in a similar way ; the same linear relationship 
 between d11 and the tilt angle  
 holds over the range of surface pressures and cholesterol fractions 
 examined ( figure 4 ) .
 decreases with 
 increasing surface pressure , and with some scatter , increasing cholesterol 
 fraction from 35 for pure dppc at 20
mn / m to 18 for 7 mol % chol at 40 mn / m .
this change in tilt causes 
 a decrease in the area per dppc molecule at the air  water interface 
 from 49.9  1 to 43.9  1  .
molecular tilt 
 angle measured from the monolayer normal ,  , 
 decreases in the same manner with increasing cholesterol fraction 
 as with increasing surface pressure ( over this range of  , sin 
 tilt  tilt ; to convert 
 to degrees of tilt ,  = 180(tilt/ ) ) . 

black symbols 20 mn / m surface pressure , open symbols 30 
 mn / m and gray symbols 40 mn / m . with some scatter , the tilt 
 decreases with increasing cholesterol fraction .
this linear relationship 
 between d11 and  is the same for 
 changes in cholesterol fraction and surface pressure , which suggests 
 that the local alkane packing of dppc does not change with added cholesterol , 
 but that both surface pressure and cholesterol act to decrease the 
 mismatch between the lipid headgroup and tailgroup area in the same 
 way . from the values in table 2 , we determine 
 a rectangular two - molecule unit cell of dimensions , a = d10 = [ d112  
 ( 2d02 ) ] and b = 2d02 = d01 ( figure 3b inset ) , 
 with a decreasing from 5.8  0.1 at 20 mn / m , 
 to 5.4  0.1  at 40 mn / m ; b remains constant 
 at 8.6  0.05  .
these unit cell dimensions are consistent 
 with a hexagonal packing of the alkane chains , which are tilted to accommodate the mismatch in projected 
 area between the dppc headgroup and the close - packed chains .
as is the case for other lipids , accommodation of the larger dppc 
 headgroup area occurs by dilation of the alkane chain area via an 
 increase in the tilt angle .
tilt costs little favorable alkane chain 
 contact energy , as tilt occurs without changing the distances between 
 the alkane chains .
tilt in the nn direction 
 causes a , which is measured in the plane of the monolayer , 
 to increase .
however , b remains constant as this 
 spacing does not change with tilt if the alkane chains retain their 
 close - packed configuration . increasing the surface pressure
provides 
 a uniform compression of the dppc headgroup , which results in a decrease 
 in the headgroup - chain incompatibility , and hence the tilt , without 
 altering the alkane chain packing .
the area per alkane chain perpendicular to the alkane chains , 20.5 
  0.3  = ( ab cos )/2 , 
 is constant within the experimental error for all surface pressures 
 and also for all cholesterol fractions .
pure chol has an untilted 
 hexagonal lattice with a d spacing of 5.7  , 
 and an area per molecule of 35  , much larger than the 20.5  area per alkane chain we measure .
the invariance of d02 ( or b ) , and the linear relationship 
 between d11 and  is consistent 
 with the bulk of the chol not intercalating uniformly into the dppc 
 lattice as it does at higher mole fractions , but separating primarily into a second phase .
figure 5 shows afm images of 
 dppc / chol monolayers transferred to mica substrates at 20 mn / m showing 
 two distinct morphologies . at 0.8 mol % chol ,
dark gray , 10100 
 nm circular areas are dispersed in extended light gray domains .
the 
 dark gray nanodomains localize preferentially at the boundaries of 
 the light gray domains ( arrows ) .
increasing 
 the chol fraction causes the circular nanodomains to percolate into 
 linear structures ( 3.7 mol % ) , although the width of the linear structures 
 remains 10100 nm . the linear structures eventually 
 break up the light gray domains ( 5 mol % ) .
afm force spectroscopy 
 showed that the nanodomains were more compliant and easier to deform 
 than the dppc domains , suggesting that 
 the nanodomains are disordered and do not contribute to the gixd signature 
 of the monolayer .
the alkane chains of dppc prefer to be untilted 
 to maximize the 
 van der waals contact between the chains , but are frustrated by the conflicting cross - sectional area requirements 
 of the phosphocholine headgroup .
this mismatch requires the tailgroup 
 lattice to dilate , which responds by the lower energy tilt deformation 
 in order to fill space efficiently .
however , chol has a complementary 
 shape to dppc , with a relatively small alcohol headgroup and a relatively 
 large sterol ring tailgroup .
hence , this shape complementarity suggests 
 that chol can relieve the packing frustration of dppc by making up 
 some of the mismatch between the headgroups and alkane chains .
palmitic 
 acid ( pa ) and hexadecanol ( hd ) , which also have complementary shapes 
 with dppc , also lead to a decreased tilt at a given surface pressure , but do not show nanodomains in afm images .
hd is the same as 
 the c16 alkane chain of dppc , which allows pa and hd to 
 be incorporated into the dppc lattice .
pa and hd increase the correlation 
 length of the mixed crystal and the surface 
 viscosity .
tapping - mode afm images 
 of dppc / cholesterol monolayers transferred 
 by langmuir - blodgett deposition to mica substrates at 20 mn / m .
for 
 0.8 mol % cholesterol , dispersed , circular 10100 nanodomains 
 appear ( darker gray indicates more compliant relative to the lighter 
 gray background phase ) , which preferentially 
 locate at the boundaries of the light gray domains ( arrows ) . for 3.7 
 mol % chol ,
the circular nanodomains have condensed into linear features 
 begin to break up the light gray domains , but the light gray domains 
 remain continuous . for 5.0 mol %
chol the nanodomains make up a cocontinuous 
 network separating the light gray domains , while decreasing the size 
 of the light gray domains to 100200 nm .
fluorescence images of dppc monolayers with 0.0 , 0.2 , 
 and 0.4 mol 
 % cholesterol at coexistence between the disordered le ( light ) and 
 ordered lc ( dark ) phases at 10 mn / m .
contrast is due to doping the 
 monolayer with 0.1 wt % of the fluorescent ( n-(texas 
 red sulfonyl)-1,2-dihexadecanoyl - sn - glycero-3-phosphoethanolamine , 
 ( invitrogen ) which segregates to the more fluid le phase .
the domain 
 width decreases with increasing cholesterol , indicative of a decrease 
 in line tension .
although the shape of cholesterol 
 can relieve the frustration between 
 the area of the headgroup and alkane chains of dppc , the sterol rings 
 can not efficiently pack into the alkane chain lattice .
this leads 
 to a second type of frustration ; the decrease in tilt due to the accommodation 
 of the area mismatch results in disrupting the alkane chain lattice , 
 which is likely higher in energy than decreasing the tilt .
the combination of the sterol rings 
 of chol and more disordered dppc chains gives the nanodomain phase 
 excess tailgroup area , which may relieve part of the packing frustration 
 of the headgroups in the adjacent ordered dppc domains , albeit at 
 longer range than if the cholesterol intercalated within the dppc 
 lattice .
the size of domains in typical phase - separated monolayers 
 is governed 
 by a competition between line tension ,  , which leads to larger 
 domains , and entropy and electrostatic interactions , which favor smaller 
 domains .
fluorescence 
 images ( figure 6 ) at the coexistence surface pressure ( 910 mn / m ) show that 
 increasing chol leads to a dramatic decrease in the width of the domains , 
 which means a large decrease in . this decrease may be sufficient to stabilize 
 the nanodomains against coalescence .
an additional factor stabilizing 
 the nanodomains may be the energy of reducing the tilt in the adjacent 
 dppc domains .
the time for diffusive mixing of the nanodomains with 
 the bulk is of order seconds over the 100 nm length scales 
 of the nanodomains , so even with electrostatic 
 interactions slowing bulk coalescence , molecular diffusion should 
 eliminate the nanodomains in minutes if this structure were not stable . 

this stability may also be an indication that we are seeing an example 
 of the recently proposed 2-d analogs of 3-d microemulsions , in which 
 compositional variations within a single phase are due to coupling 
 between monolayer curvature ( i.e. incompatible area requirements of 
 headgroups and tails ) and composition . the evolution 
 of the structure between discrete circular nanodomains ( analogous 
 to spherical micelles in 3-d ) to extended linear structures ( rod - like 
 micelles ) to an interconnected network ( bicontinuous microemulsion ) 
 suggests this possibility .
figure 7a 
 shows that the coherence length , l02 , 
 in the untilted direction for pure dppc 
 is about 70 lattice repeats , or > 300  , more than five times 
 that in the tilted direction , l11  
 60  or about 12 lattice repeats ( table 2 ) . for both 20 and 30 mn / m
, l02 decreases 
 monotonically with increasing cholesterol fraction to 20 lattice 
 repeats , but l11 only decreases to 10 
 lattice repeats . at 40 mn / m , l02 does 
 not monotonically decrease with cholesterol fraction , the scatter 
 in l02 is much greater than at lower surface 
 pressures , and l02 is always less than 
 expected from the results for the lower surface pressures .
this is 
 likely due to a decrease in film stability caused by a combination 
 of leakage under the trough barriers and slow monolayer collapse during 
 the 3 - 5 h required for gixd .
the afm images in figure 5 show that the average dppc ( light gray ) domain size decreases 
 from microns to 100200 nm with cholesterol .
even with the 
 decreasing domain size , the positional ordering given by the coherence 
 lengths are orders of magnitude smaller than the domain size for a 
 given cholesterol fraction .
however , the orientational order extends 
 for tens of microns as shown by the spiral domain textures in figure 6 .
dppc / chol monolayers 
 have nanometer - range positional order and micron - range orientational 
 order , similar to tilted smectic c liquid crystals and other langmuir films that are classified 
 as hexatics .
( a ) coherence lengths , l11 , in the 
 ( 11 ) or tilt direction , and l02 , in the 
 ( 02 ) or untilted direction , normalized by their respective lattice 
 constants , d11 and d02 .
l02 decreases significantly 
 with cholesterol fraction , but is less affected by surface pressure .
l02 for 40 mn / m has more scatter and is nonmonotonic 
 with cholesterol fraction , likely the result of film instabilities 
 due to trough leakage and monolayer collapse at higher surface pressure . 

( b ) the surface viscosity of dppc / chol monolayers measured with a 
 microbutton magnetic rheometer decreases exponentially with cholesterol 
 fraction for a given surface pressure for small mole fractions of 
 cholesterol , then plateaus in the same fashion as l02 .
( surface viscosity for pure dppc at 40 mn / m was too 
 high for the viscometer to measure . ) ( c ) free area model for dppc / chol 
 monolayers ( eqs 6 - 8 ) provides 
 an excellent correlation between the surface viscosity and the number 
 of correlated molecules , ( l02l11)/ab , over the entire range 
 of cholesterol fraction .
the lines are linear regression fits of eq 7 to the data ( p < 0.01 ) .
( d ) 
 normalizing to a reference state ( taken to be that of pure dppc for 
 20 and 30 mn / m and 0.4% chol for 40 mn / m surface pressures ) , collapses 
 the data onto a single universal curve relating surface viscosity 
 to the molecular organization .
the line is a linear regression fit 
 of eq 8 to the data with p < 
 .001 showing that the data is well described by the free area model .
figure 7b shows that the surface viscosity , 
 s , of dppc / chol monolayers decreases exponentially with increasing 
 cholesterol fraction at a given surface pressure . in previous work
, we found that the exponential dependence of 
 surface viscosity on surface pressure was well - correlated by a  free 
 area 
the free - volume model was developed to explain the divergence in the 
 viscosity of a liquid at the glass transition .
the premise underlying 
 the model is that in order to diffuse , a molecule in a liquid or other 
 condensed phase has to have sufficient  free volume 
, 
 that is , volume not occupied by other molecules , in order to escape 
 the cage formed by its neighboring molecules .
each molecule has a 
 minimum van der waals volume , v0 , and 
 moves randomly with thermal velocity u , within confining 
 cages of diameter d0 defined by its nearest 
 neighbors .
cohen and turnbull calculated 
 the probability for fluctuations in free volume relative to the average 
 free volume , v. if the local fluctuation in 
 free volume exceeds v0 , a hole is created 
 in the confining cage sufficiently large to allow a diffusional jump 
 of the solute molecule into the hole .
diffusion occurs if another 
 molecule fills the hole left by the solute molecule before the original 
 molecule returns to its starting position .
the probability p(v0 ) that the  free  volume , vf , rearranges to give a void volume , v0 , large enough for a molecule to diffuse ( at constant energy ) is 
 given by1thus giving a diffusivity2 in which g is a geometric 
 factor .
the parameter b in eqs 1 and 2 is to 
 take into account overlaps of free volume , and cohen and turnbull 
 suggest a range from 1/2  b  1 . in three dimensions , the diffusivity can 
 be related to the bulk 
 viscosity ,  , via a generalized stokes - einstein relationship , d = kt / f . for
spherical 
 particles , the friction factor , f , is given by the 
 stokes drag on a sphere of diameter a : f = 3a .
this leads to the free volume 
 model for the viscosity:3 in applications of the model , the free volume 
 is the difference between the measured volume per molecule , v , and v0 : vf = v  v0 . in applications of the model
, v0 is a fitting parameter ; theoretically , v0 is related to the volume per molecule at the glass transition where 
 the viscosity diverges . for a 2-dimensional film of constant 
 thickness , l:4 in analogy to the free volume , af( )
a0 , in which a( ) is the 
 area per molecule determined at a surface pressure ,  , from 
 a surface pressure - area isotherm and a0 is taken to be a fitting parameter . in 2-dimensions , the diffusivity 
 and free area can be related to the surface viscosity , s , via the saffmann - delbrck model for a cylinder diffusing within a viscous monolayer , 
 surrounded by a viscous subphase , to give an equation analogous to 
 eq 3 in terms of the free area:5from fitting dppc 
 viscosity data , we found 
 that a0  40  , which is roughly equal to ab cos 
  , the molecular area of a dppc molecule in a close - packed , 
 untilted lattice ( table 2 ) .
however , 
 cohen and turnbull did not speculate on the molecular 
 origins of af(19 ) as they were modeling an unstructured liquid
. however , for semicrystalline 
 monolayers , we postulate that the free area is proportional to the 
 number of defects in the lattice , which is inversely proportional 
 to the number of correlated molecules at that composition and surface 
 pressure:6 lattice defects , such as dislocations , 
 vacancies , and grain boundaries 
 decorrelate the lattice , which creates free area and pathways for 
 diffusion .
we define  as the free area ( or number of defects 
 times the area per defect ) per number 
 of correlated molecules ; we take  to be constant , independent 
 of concentration . combining eqs 5 and
6:7 in which  = ba0/. linear 
 regression to eq 7 ( figure 7c ) shows that for 20 , 30 , and 40 mn / m , the slopes , 
  = 0.0134  0.0007 , 0.0131  0.002 and 0.0196  
 0.007 are the same within the experimental error .
s0( = 20 mn / m ) 
 = 0.09  0.02 , s0( = 30 mn / m ) = 0.37  0.2 , and 
 s0( 
 = 40 mn / m ) = 0.6  0.5 pms , although the physical 
 significance of the surface pressure variation of s0 is not given by 
 our model . the pearson correlation coefficient , r , for the three lines are 0.99 , 0.95 and 0.81 , respectively , 
 giving a statistically significant fit of eq 7 to the data with p < 0.001 , 0.001 , and 0.05 , 
 respectively . to better compare the data at different surface pressures , 
 the surface viscosity and correlated area are normalized relative 
 to a reference composition , xref , at the 
 same :8ref(xref, ) is 
 the surface viscosity and ( ( l02l11)/ab)ref is the 
 number of molecules in the coherence area 
 at xref ( taken to be pure dppc for  
 = 20 and 30 mn / m and 0.4% chol for  = 40 mn / m ) .
linear regression to eq 8 gives  = 0.0133  0.007 , which is the same as 
 the fits to eq 7 .
the pearson correlation coefficient 
 is 0.91 , giving p < 0.001 , showing that eq 8 gives a statistically significant representation 
 of the surface viscosity over the almost three orders of magnitude 
 change in surface viscosity ( figure 7b ) .
for a0  40  ,   1500  ( for b = 1/2 ) 
3000  ( for b = 
 1 ) . for pure dppc , ( l02l11)/ab  450 ,
giving af  36  from eq 6 , which is consistent with the variation in area 
 per molecule , a(x, ) = a0 + af(x, ) , measured from dppc isotherms . adding cholesterol decreases ( l02l11)/ab to 100 , thereby 
 increasing the free area per molecule to 1530  , resulting in the dramatic decrease in surface viscosity .
these 
 values of af are in agreement with the 
 assumptions behind the cohen and turnbull free volume theory , which 
 postulates that vf  v0 , hence af  a0 .
in summary , gixd shows 
 that increasing the chol fraction at constant 
 surface pressure , or increasing the surface pressure at constant chol 
 fraction , decreases the tilt of the dppc lattice , while leaving the 
 alkane chains close - packed with an invariant area per molecule normal 
 to the alkane chain direction .
this confirms afm images that show 
 cholesterol does not intercalate homogeneously into the dppc lattice 
 but is expelled to disordered nanodomains that break up the dppc domains . 

the nanodomains evolve from isolated , circular 10100 nm diameter 
 domains to 1050 nm wide linear nanodomain aggregates 
 to an interconnected network structure with increasing cholesterol . 
 however , the monolayer is homogeneous at micron - scale optical images ; 
 macroscopic phase separation does not occur as at lower surface pressure 
 ( figure 6 ) .
hence , the dppc / cholesterol monolayer 
 is better described as a nanostructured , single - phase monolayer , rather 
 than a mixture of two distinct phases , similar to recently proposed 
 two - dimensional microemulsions . as such , this system 
 is analogous to 3-d nanostructured surfactant - oil - water bicontinuous 
 microemulsions , or copolymer systems that separate into nanometer - scale 
 regions more enriched in one or the other monomer , which are considered 
 single phase . adding cholesterol does not change the local hexagonal 
 dppc chain 
 packing , but does reduce the molecular tilt , suggesting that cholesterol 
 relieves some of the packing frustration between the dppc headgroup 
 and tailgroups .
most important to the monolayer dynamics , the extent 
 of order , or the number of correlated molecules , decreases with increasing 
 cholesterol fraction at all surface pressures , suggesting an increased 
 number of lattice defects that create free area for visco - diffusive 
 transport . at all cholesterol fractions ,
the positional order is much 
 shorter ranged than the orientational order , consistent with an overall 
 hexatic organization .
we show that a 
 simple model that proposes that the  free  area available 
 for visco - diffusive transport is inversely 
 proportional to the number of correlated molecules , which collapses 
 the surface viscosity data for all surface pressures and cholesterol 
 fractions onto a single universal curve .
molecular defects and the 
 associated decrease in domain size caused by the incompatibility of 
 cholesterol packing into the alkane chain lattice enhance visco - diffusive 
 transport in monolayers . our model and data show that the extent of 
 molecular correlations is an excellent predictor of the effects of 
 the cholesterol on the surface viscosity of model lung surfactant 
 monolayers .
 adding small fractions of cholesterol 
 decreases the interfacial 
 viscosity of dipalmitoylphosphatidylcholine ( dppc ) monolayers by an 
 order of magnitude per wt % . 
 grazing incidence x - ray diffraction shows 
 that cholesterol at these small fractions does not mix ideally with 
 dppc but rather induces nanophase separated structures of an ordered , 
 primarily dppc phase bordered by a line - active , disordered , mixed 
 dppc - cholesterol phase . 
 we propose that the free area in the classic 
 cohen and turnbull model of viscosity is inversely proportional to 
 the number of molecules in the coherence area , or product of the two 
 coherence lengths . 
 cholesterol significantly reduces the coherence 
 area of the crystals as well as the interfacial viscosity . using this 
 free area collapses the surface viscosity data for all surface pressures 
 and cholesterol fractions to a universal logarithmic relation . 
 the 
 extent of molecular coherence appears to be a fundamental factor in 
 determining surface viscosity in ordered monolayers . 
Introduction
Materials and
Methods
Results
and Discussion
Conclusions