Contaminant adsorption

(RefLink[Needs, paclet:ref/Needs])["PhysicalConstants`"]

molecular flux

partial pressure, p, for a species with molar mass, MW, to form a single monolayer thickness, d, in time, tml (10 yrs) ... or 0.1 ML/yr as mentioned in LIGO-E1000730:

tml=365*24*3600*10; (* 1 monolayer formation time *)
d=10^-9; (* molecule diameter, m *)
k = 1.3804 10^-23; (* Boltzman constant, J/K *)
T=273.15+20;
MW = 100; (* g/mol *)
Na=6.022 10^23; (* Avagadro's number, #/mol *)
m=MW/Na/1000; (* kg *)

impingement rate/flux used to set partial pressure p:

p=0.00750062 4/(tml d^2 Sqrt[8/(Pi k T m)]) (* Torr *)

adsorbed molecular hydrocarbon surface coverage, Nad

extrapolation of n

In the key paper (J. Hollenshead, L. Klebanoff & G. Delgado, 2019), the authors stated that they linearly extrapolated the n parameter fits to the NMA isotherms for their hydrocarbons based on “chain length”.
In the paper in which the NMA isotherm was proposed (T. Nitta, T. Shigetomi, M, Huro-oka and T. Katayame, 1984), the authors plotted n versus the “molecular area projected on a plane”, which is also labeled “molecular cross-sectional area”. The calculated the molecular areas by means of compiled values of the van der Waals radii and bond lengths. 
Searched for molecular size, area, cross-sectional area, van der Waals volume, bond length, etc. to no avail:
	database of polymer van der Waals volumes:
	https://polymerdatabase.com/polymer%20physics/vdWVolume.html
	hydrocarbon molecular weight, formula, density:
	https://www.engineeringtoolbox.com/hydrocarbon-boiling-melting-flash-autoignition-point-density-gravity-molweight-d_1966.html
	https://pubchem.ncbi.nlm.nih.gov/
Below I show the NMA n vs molecular area fit and the apparent molecular areas for the HCs used in the key paper (J. Hollenshead, L. Klebanoff & G. Delgado, 2019).
Next I show that plotting against molar mass, M (molecular weight), seems equally linear. Since M is readily obtained I use this for extrapolating n values for other HCs.

componentsNuxitAL={"CH4","C2H2","C2H4","C2H6","C3H6","C3H8","n-C4H10","CO2"};
nNuxitAL={3.69,3.38,3.55,3.63,4.30,4.45,5.22,2.69};
csAreaNuxitAL={.125,.17,.175,.18,.24,.25,.3,.13};
MNuxitAL={16.04,26.04,28.05,30.07,42.08,44.1,58.12,44.01};
componentsMSC5A={"CH4","C2H4","C2H6","C3H6","C3H8","n-C4H10","n-C5H12"};
nMSC5A={2.81,3.06,3.22,3.71,4.17,4.89,5.72};
csAreaMSC5A={.125,.175,.18,.24,.25,.3,.36};
MMSC5A={16.04,28.05,30.07,42.08,44.1,58.12,72.15};

lineArea=Fit[Transpose[{Join[csAreaNuxitAL,csAreaMSC5A],Join[nNuxitAL,nMSC5A]}],{1,x},x]

componentsEUV={"n-tetradecane","n-dodecane","n-decane","benzene"};
nEUV={11.06,9.860,8.656,6.248};
csAreaEUV=Flatten[Table[x/.Solve[lineArea==nEUV[[i]],x],{i,Length[nEUV]}]];
MEUV={198.39,170.34,142.282,78.11};

nvsAreaPlt=ListPlot[{Transpose[{csAreaNuxitAL,nNuxitAL}],Transpose[{csAreaMSC5A,nMSC5A}],Transpose[{csAreaEUV,nEUV}]},PlotRange->{{0,.9},{0,13}},PlotMarkers->"OpenMarkers"];
Show[nvsAreaPlt,Plot[lineArea,{x,0.1,.9}],PlotRange->All,Frame->True,FrameStyle->{Black,Bold},Grid->True,GridLines->Automatic,FrameLabel->{"molecular cross-sectional area (nm^2)","NMA Isotherm parameter, n"}]

lineMass=Fit[Transpose[{Join[MNuxitAL,MMSC5A],Join[nNuxitAL,nMSC5A]}],{1,x},x]

nvsMassPlt=ListPlot[{Transpose[{MNuxitAL,nNuxitAL}],Transpose[{MMSC5A,nMSC5A}],Transpose[{MEUV,nEUV}]},PlotRange->{All,All},PlotMarkers->"OpenMarkers"];
Show[nvsMassPlt,Plot[lineMass,{x,10,500}],PlotRange->All,Frame->True,FrameStyle->{Black,Bold},Grid->True,GridLines->Automatic,FrameLabel->{"modal mass (g/mol)","NMA Isotherm parameter, n"}]

replicating steady-state adsorption fractional surface coverage calculations for 4 hydrocarbons on Ru

Replicating Figure 12 from J.T. Hollenshead, L.E. Klebanoff and G. Delgado, “Predicting radiation-induced carbon contamination of EUV optics”, J. Vac. Sci. Technol., B 37, 021602 (2019)

dNad/dt = impingement rate - molecular reflection-thermal desorption+surface diffusion
impingement rate = s Γmol
	s = condensation coefficient
	Γmol = impingement rate of molecules from the gas phase from the kineticgas theory
	Γmol = (P/(4 kb T) Sqrt[8 kb T/(π M)]
	p = partial pressure of the hydrocarbon molecule
	T = optic surface temperature
	M = molecular weight of the HC molecule
	kb = Boltzmann’s constant
molecular reflection = - (Nad(t)/Nad,max) s Γmol
thermal desorption = -Nad(t) v0 exp[-Ea/(R T)]
	v0 = escape frequency == 1 x 10^13 1/s
	R = universal gas constant
	Ea = binding energy of the molecular species to the optic surface material, in this case Ruthenium (Ru)
surface diffusion is negligible for large molecules

kb=Entity["PhysicalConstant","BoltzmannConstant"]["Value"] //N;
R=Entity["PhysicalConstant","MolarGasConstant"]["Value"] //N;
Nav=Entity["PhysicalConstant","AvogadroConstant"]["Value"] //N;
v0=Quantity[10^13,"s^-1"];
s=1;

The NMA isotherm parameter, K - the equilibrium constant for adsorption, is defined by matching to the NadSS/NadMax calculation at the following temperature and partial pressure for each hydrocarbon:

T=Quantity[273.15+20,"K"] //N;
p=Quantity[10^-12,"Torr"] //N;

Γmol[p_,T_,m_]:=p/(4 kb T) Sqrt[8 kb T/(π m)];

pp = partial pressure list for generating NMA isotherm plot (evenly spaced in log space):

b=10;
factor=10^(1/b);
pp=Quantity[Table[10^-12 factor^i,{i,0,11 b}],"Torr"] //N;
npp=Length[pp];

HClabels={"n-tetradecane (C14H30)","n-dodecane (C12H26)","n-decane (C10H22)","benzene (C6H6)","n-tetradecane Langmuir","n-dodecane Langmuir","n-decane Langmuir","benzene Langmuir"};

n-tetradecane

Ea=Quantity[96.35,"kJ/mol"]; 
M=Quantity[198.39,"grams/mol"] ;
ρ=Quantity[0.767,"grams/cc"];
n=11.06;
m=M/Nav;
v=M/(ρ Nav);
ml=v^(1/3)
NadMax=v^(-2/3)

UnitConvert[Sqrt[8 kb T/(π m)],"m/s"]

source=UnitConvert[Γmol[p,T,m],"m^-2 s^-1"]

Steady-state number density of adsorbed molecules on the optic surface @ p,T

NadSS=source/(v0 Exp[-Ea/(R T)]+source/NadMax)

θ=NadSS/NadMax

K=θ/(n p (1-θ)^n)

tetradecaneNMA=Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]-n Log[1-θNMA]==Log[n K pp[[i]]],θNMA,Reals][[1]]},{i,npp}] //N;

tetradecaneLA=Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]- Log[1-θNMA]==Log[ K pp[[i]]],θNMA,Reals][[1]]},{i,npp}] //N;

n-dodecane

Ea=Quantity[85.13,"kJ/mol"]; 
M=Quantity[170.34,"grams/mol"] ;
ρ=Quantity[0.753,"grams/cc"];
n=9.86;
m=M/Nav;
v=M/(ρ Nav);
ml=v^(1/3)
NadMax=v^(-2/3)

UnitConvert[Sqrt[8 kb T/(π m)],"m/s"]

source=UnitConvert[Γmol[p,T,m],"m^-2 s^-1"]

Steady-state number density of adsorbed molecules on the optic surface @ p,T

NadSS=source/(v0 Exp[-Ea/(R T)]+source/NadMax)

θ=NadSS/NadMax

K=θ/(n p (1-θ)^n)

dodecaneNMA=Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]-n Log[1-θNMA]==Log[n K pp[[i]]],θNMA,Reals][[1]]},{i,npp}] //N;

dodecaneLA=Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]- Log[1-θNMA]==Log[ K pp[[i]]],θNMA,Reals][[1]]},{i,npp}] //N;

n-decane

Ea=Quantity[73.90,"kJ/mol"]; 
M=Quantity[142.282,"grams/mol"] ;
ρ=Quantity[0.734,"grams/cc"];
n=8.656;
m=M/Nav;
v=M/(ρ Nav);
ml=v^(1/3)
NadMax=v^(-2/3)

UnitConvert[Sqrt[8 kb T/(π m)],"m/s"]

source=UnitConvert[Γmol[p,T,m],"m^-2 s^-1"]

Steady-state number density of adsorbed molecules on the optic surface @ p,T

NadSS=source/(v0 Exp[-Ea/(R T)]+source/NadMax)

θ=NadSS/NadMax

K=θ/(n p (1-θ)^n)

decaneNMA=Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]-n Log[1-θNMA]==Log[n K pp[[i]]],θNMA,Reals][[1]]},{i,npp}] //N;

decaneLA=Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]- Log[1-θNMA]==Log[ K pp[[i]]],θNMA,Reals][[1]]},{i,npp}] //N;

benzene

Ea=Quantity[85.07,"kJ/mol"]; 
M=Quantity[78.11,"grams/mol"] ;
ρ=Quantity[0.879,"grams/cc"];
n=6.248;
m=M/Nav;
v=M/(ρ Nav);
ml=v^(1/3)
NadMax=v^(-2/3)

UnitConvert[Sqrt[8 kb T/(π m)],"m/s"]

source=UnitConvert[Γmol[p,T,m],"m^-2 s^-1"]

Steady-state number density of adsorbed molecules on the optic surface @ p,T

NadSS=source/(v0 Exp[-Ea/(R T)]+source/NadMax)

θ=NadSS/NadMax

K=θ/(n p (1-θ)^n)

benzeneNMA=Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]-n Log[1-θNMA]==Log[n K pp[[i]]],θNMA,Reals][[1]]},{i,npp}] //N;

benzeneLA=Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]- Log[1-θNMA]==Log[ K pp[[i]]],θNMA,Reals][[1]]},{i,npp}] //N;

NMA isotherm plot on Ru

The two plots below showing the NMA adsorption isotherms for 4 hydrocarbons match Figure 12 in
J.T. Hollenshead, L.E. Klebanoff and G. Delgado, “Predicting radiation-induced carbon contamination of EUV optics”, J. Vac. Sci. Technol., B 37, 021602 (2019)

ListLogLinearPlot[{tetradecaneNMA,dodecaneNMA,decaneNMA,benzeneNMA,tetradecaneLA,dodecaneLA,decaneLA,benzeneLA},Joined->True,Frame->True,FrameStyle->{Black,Bold},FrameLabel->{"Partial Pressure (Torr)","Monolayer (%)"},PlotStyle->{Black,Red,Blue,Green,{Black,Dashed},{Red,Dashed},{Blue,Dashed},{Green,Dashed}},PlotRange->{All,{0,100}},PlotLegends->HClabels,GridLines->Automatic]

ListLogLogPlot[{tetradecaneNMA,dodecaneNMA,decaneNMA,benzeneNMA,tetradecaneLA,dodecaneLA,decaneLA,benzeneLA},Joined->True,Frame->True,FrameStyle->{Black,Bold},FrameLabel->{"Partial Pressure (Torr)","Monolayer (%)"},PlotStyle->{Black,Red,Blue,Green,{Black,Dashed},{Red,Dashed},{Blue,Dashed},{Green,Dashed}},PlotRange->{{10^-12,10^-9},{10^-6,10^2}},PlotLegends->HClabels,GridLines->Automatic]

S. Hill, C. Tarrio, R. Berg and T. Lucatorto, EUV study - coverage data

digitization of the zero intensity coverage (in monolayers) of tetradecane (calculation), using https://apps.automeris.io/wpd/, from Figure 6 of
S. Hill, C. Tarrio, R. Berg and T. Lucatorto, “Extreme-ultraviolet-induced carbon growth at contaminant pressures between 10-10 and 10-6 mbar: Experiment and model”, J. Vac. SCI. technol., A 38(6), Nov/Dec 2020.

mlTetradecane={2.078931417619599 10^-11,0.10916497916650791,
2.3798503116571752 10^-11,0.11057320651577195,
2.7243262850776208 10^-11,0.11171285679744196,
3.118664090430388 10^-11,0.11310561706399425,
3.5700810737003656 10^-11,0.11436905484777746,
4.0868392693855744 10^-11,0.11564660576824588,
4.678396615929015 10^-11,0.11683854630240385,
5.3555800591165833 10^-11,0.11834576260572338,
6.130783711656674 10^-11,0.1195655226718189,
7.018195695745938 10^-11,0.12115967134380858,
8.034057820395166 10^-11,0.12267020809842899,
9.196962846245145 10^-11,0.1242526527918011,
1.0528194778545074 10^-10,0.12607078190218496,
1.2052118416487646 10^-10,0.12737016180290883,
1.3796625288605573 10^-10,0.12912352474865,
1.579364413593809 10^-10,0.13095696367953197,
1.807972528605671 10^-10,0.13236324432730895,
2.0696709613424605 10^-10,0.13418534147075692,
2.3692494329699554 10^-10,0.13591633129159708,
2.7121909619814374 10^-10,0.13719989941937263,
3.104772216842007 10^-10,0.13980351547460923,
3.55417839436778 10^-10,0.14142559128098584,
4.0686347263953243 10^-10,0.1433724396465812,
4.657557021634668 10^-10,0.14522194295966354,
5.331723997990262 10^-10,0.14867488698789483,
6.178945491698634 10^-10,0.14969470995941592,
7.073328744518687 10^-10,0.1523400506399719,
8.037685090751846 10^-10,0.15568262660802867,
9.269211700957269 10^-10,0.1567639134839048,
1.0385134746283666 10^-9,0.15934684554329948,
1.2161733481300329 10^-9,0.16248524552876917,
1.3819827610316573 10^-9,0.16417396822629904,
1.89060965979123 10^-9,0.17016574123368897,
2.0604517551276144 10^-9,0.17118663747671897,
2.7334972012301624 10^-9,0.17797340795129046,
2.9608104060158066 10^-9,0.18069337167578137,
3.903895368165463 10^-9,0.18598032358753938,
4.25460010823138 10^-9,0.18805780279644357,
5.644362921510758 10^-9,0.19476308390917713,
6.2274856176692556 10^-9,0.19766362269201382,
8.160780396298526 10^-9,0.20606277323798025,
8.893900548789698 10^-9,0.20854270550786483,
1.1799088329845588 10^-8,0.21718131970869645,
1.2701991112966518 10^-8,0.21857764961211826,
1.6954953408430016 10^-8,0.23058071292144477,
2.51239437541356 10^-8,0.24582872118785026,
5.3496722129313 10^-8,0.28527693357616946,
7.010453785399889 10^-8,0.30803794179140725,
1.1046468775353743 10^-7,0.35574214801936216,
1.4565018482462598 10^-7,0.38780810261081006,
2.3091757674999746 10^-7,0.45480776416747765,
3.007511777825618 10^-7,0.4992575599548488,
4.7975764140885 10^-7,0.6077761177964333,
6.644439830909153 10^-7,0.6807524286159482,
7.196980697345609 10^-7,0.6880626848970308,
9.258986650377572 10^-7,0.7283626873540741};
mlTetradecane=Partition[mlTetradecane,2];
d1=UnitConvert[Quantity[Transpose[mlTetradecane][[1]],"mbar"],"Torr"];
d2=Transpose[mlTetradecane][[2]] 100;
mlTetradecane=Transpose[{d1,d2}];

S. Hill, C. Tarrio, R. Berg and T. Lucatorto, EUV study - comparison plots

ListLogLinearPlot[{tetradecaneNMA,dodecaneNMA,decaneNMA,benzeneNMA,tetradecaneLA,dodecaneLA,decaneLA,benzeneLA,mlTetradecane},Joined->True,Frame->True,FrameStyle->{Black,Bold},FrameLabel->{"Partial Pressure (Torr)","Monolayer (%)"},PlotStyle->{Black,Red,Blue,Green,{Black,Dashed},{Red,Dashed},{Blue,Dashed},{Green,Dashed},{Black,Dotted}},PlotRange->{All,{0,100}},PlotLegends->Append[HClabels,"n-tetradecane Alt. isotherm"],GridLines->Automatic]

ListLogLogPlot[{tetradecaneNMA,dodecaneNMA,decaneNMA,benzeneNMA,tetradecaneLA,dodecaneLA,decaneLA,benzeneLA,mlTetradecane},Joined->True,Frame->True,FrameStyle->{Black,Bold},FrameLabel->{"Partial Pressure (Torr)","Monolayer (%)"},PlotStyle->{Black,Red,Blue,Green,{Black,Dashed},{Red,Dashed},{Blue,Dashed},{Green,Dashed},{Black,Dotted}},PlotRange->{{10^-12,10^-9},{10^-6,10^2}},PlotLegends->Append[HClabels,"n-tetradecane Alt. isotherm"],GridLines->Automatic]

adsorption energy vs molar mass

linear alkanes with 5 to 60 Carbon atoms, H(CH2)nH

MlinearAlkanes[n_]:=n 12.0107+(2 n+2) 1.00784;
Malkanes=Table[MlinearAlkanes[n],{n,5,60}];

Ead[n_]:=-29+42 n^0.5;
Ealkanes=Table[Ead[n],{n,5,60}];

ListPlot[Transpose[{Malkanes,Ealkanes}]]

S. Margariti, I. Bassiotis and F. Roubani-Kalantzopoulou, “Physicochemical characterization of interfaces”, Journal of Colloid and Interface Science, 274 (2004), p 413-420.
Ea = binding (adsorption) energy on SiO2
1-butene (C4H8), 56.108 g/mol, 0.620 g/cc, 113 kJ/mol
acetylene (C2H2), 26.04 g/mol, 0.0011 g/cc, 106 kJ/mol

P. Voumard, R. Zenobi, “Laser-induced thermal desorption of aniline from silica surfaces”, J. Chem. Phys. 103, 6795 (1995); https://doi.org/10.1063/1.470358
aniline (C6H5NH2), 93.13 g/mol, 1.02 g/cc, 100 kJ/mol

A.C. Ferraz, R. Miotto, “A comparative study of the interaction of cyclopentene, cyclohexene, and 1,4-cyclohexadiene with silicon (001) surface”, Surface Science, 566-568 (2004).
Ea = binding (adsorption) energy on Si
N.B.: This is a theoretical study only. The claim is made that the predicted (theoretical) adsorption energies compare well with experiment, but I could not determine if this was true or not. Not used below.
cyclopentene (C5H8), 68.11 g/mol, 0.744 g/cc, 146 kJ/mol
cyclohexene (C6H10), 82.143 g/mol, 0.811 g/cc, 96 kJ/mol
1,4-cyclohexadiene (C6H8), 80.129 g/mol, 130 kJ/mol

Ludmilla Derr, Nils Hildebrand, Susan Köppen, et al.,”Physisorption of α-chymotrypsin on SiO2 and TiO2: A comparative study via experiments and molecular dynamics simulations”, Biointerphases 11, 011007 (2016); https://doi.org/10.1116/1.4940701
G W SCHWERT, S KAUFMAN, “The molecular size and shape of the pancreatic proteases. III. alpha-Chymotrypsin”, J Biol Chem
. 1951 Jun;190(2):807-16.
α-chymotrypsin (C23H25N5O8), 499.5 g/mol or >21,600 g/mol ??, 35 kJ/mol
I’m confused by references in the literature to extremely large AMU proteins named α-chymotrypsin and the adsorption energy seems far too low. Not used below.

2nd n-decane reference is from [73] from Hollenshead 2019

labelsEad={"n-tetradecane (C14H30)","n-dodecane (C12H26)","n-decane (C10H22)","benzene","1-butene (C4H8)","acetylene (C2H2)","aniline (C6H5NH2)","n-decane (C10H22)"};
Eadsorption={96.35,85.13,73.90,85.07,113,106,100,37};
MolarMassAd={198.39,170.34,142.282,78.11,56.108,26.04,93.13,142.282};

ListPlot[{Transpose[{Malkanes,Ealkanes}],Transpose[{MolarMassAd,Eadsorption}]},Frame->True,FrameLabel->{"Molar Mass (g/mol)","Adsorption Energy (kJ/mol)"},GridLines->Automatic,PlotLegends->Placed[{"straight chain alkanes","other literature"},Above],PlotRange->{{0,500},{0,250}}]

Malkanes[[10]]

Ealkanes[[10]]-Eadsorption[[1]]

EadMOD[n_]:=-29-31.7996+42 n^0.5;
EalkanesMOD=Table[EadMOD[n],{n,5,60}];

S. Tait, et. al., “n-alkanes on MgO(100). II. Chain length dependence of kinetic desorption parameters for small n-alkanes”, J. of Chemical Physics 122, 164708 (2005).
Indicates significant adsorption energy decrease as the coverage increases from zero to ~0.2 ML. This is the asymptotic value of Ead = E0 < 1 ML for 1 < n < 10

EadMgO[n_]:=5.4+7.2n;
EalkanesMgO=Table[EadMgO[n],{n,1,10}];
MalkanesMgO=Table[MlinearAlkanes[n],{n,1,10}];

ListPlot[{Transpose[{Malkanes,Ealkanes}],Transpose[{MolarMassAd,Eadsorption}],Transpose[{Malkanes,EalkanesMOD}],Transpose[{MalkanesMgO,EalkanesMgO}]},Frame->True,FrameLabel->{"Molar Mass (g/mol)","Adsorption Energy (kJ/mol)"},GridLines->Automatic,PlotLegends->Placed[{"alkanes, θ = 0","other literature","shifted alkanes","alkanes, ~0.1 < θ < 1"},Right],PlotRange->{{0,500},{0,250}},PlotMarkers->{{●,10},{■,10},{○,10},{△,10}}]

general hydrocarbon adsorption isotherms - linear alkanes

pp = partial pressure list for generating NMA isotherm plot (evenly spaced in log space):

b=10;
factor=10^(1/b);
pp=Quantity[Table[10^-16 factor^i,{i,0,12 b}],"Torr"] //N;
npp=Length[pp];

Limit the HC molar mass to 500 AMU:

index=First[Position[Floor[Malkanes],Nearest[Floor[Malkanes],500][[1]]][[1]]];

Malkanes=Malkanes[[1;;index]];
Ea=Quantity[Ealkanes[[1;;index]],"kJ/mol"];
EaMOD=Quantity[EalkanesMOD[[1;;index]],"kJ/mol"];
nalkanes=lineMass/.x->Malkanes;

Use power law fit to approximate epoxy monolayer thickness (nm) from molar mass (g/mol) (see Excel listing/plot):

m=Quantity[Malkanes,"g/mol"]/Nav;
ml=Quantity[0.1913 Malkanes^0.2757,"nm"];
v=ml^3;
NadMax=v^(-2/3);

source=UnitConvert[Γmol[p,T,m],"m^-2 s^-1"];

Steady-state number density of adsorbed molecules on the optic surface @ p,T

NadSS=source/(v0 Exp[-Ea/(R T)]+source/NadMax);

NadSSMOD=source/(v0 Exp[-EaMOD/(R T)]+source/NadMax);

θ=NadSS/NadMax

θMOD=NadSSMOD/NadMax

Malkanes[[1;;9]]

K=θ[[1;;9]]/(nalkanes[[1;;9]] p (1-θ[[1;;9]])^nalkanes[[1;;9]])

Malkanes[[1;;14]]

KMOD=θMOD[[1;;14]]/(nalkanes[[1;;14]] p (1-θMOD[[1;;14]])^nalkanes[[1;;14]])

alkanesNMA=Table[Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]-nalkanes[[j]] Log[1-θNMA]==Log[nalkanes[[j]] K[[j]] pp[[i]]],θNMA,Reals][[1]]},{i,npp}],{j,9}] //N;

alkanesNMAMOD=Table[Table[{pp[[i]],100 θNMA/.NSolve[Log[θNMA]-nalkanes[[j]] Log[1-θNMA]==Log[nalkanes[[j]] KMOD[[j]] pp[[i]]],θNMA,Reals][[1]]},{i,npp}],{j,14}] //N;

ListLogLinearPlot[{alkanesNMA[[1]],alkanesNMA[[2]],alkanesNMA[[3]],alkanesNMA[[4]],alkanesNMA[[5]],alkanesNMA[[6]],alkanesNMA[[7]],alkanesNMA[[8]],alkanesNMA[[9]]},Joined->True,Frame->True,FrameLabel->{"Partial Pressure (Torr)","Monolayer (%)"},PlotStyle->{Automatic},PlotRange->{All,{0,100}},GridLines->Automatic,PlotLabels->Round[Malkanes[[1;;9]]]]

ListLogLogPlot[{alkanesNMA[[1]],alkanesNMA[[2]],alkanesNMA[[3]],alkanesNMA[[4]],alkanesNMA[[5]],alkanesNMA[[6]],alkanesNMA[[7]],alkanesNMA[[8]],alkanesNMA[[9]]},Joined->True,Frame->True,FrameLabel->{"Partial Pressure (Torr)","Monolayer (%)"},PlotStyle->{Automatic},PlotRange->{{10^-16,10^-11},{10^-5,10^2}},GridLines->Automatic,PlotLabels->Round[Malkanes[[1;;9]]]]

general hydrocarbon adsorption isotherms - linear alkanes Ea MODIFIED

ListLogLinearPlot[{alkanesNMAMOD[[1]],alkanesNMAMOD[[2]],alkanesNMAMOD[[3]],alkanesNMAMOD[[4]],alkanesNMAMOD[[5]],alkanesNMAMOD[[6]],alkanesNMAMOD[[7]],alkanesNMAMOD[[8]],alkanesNMAMOD[[9]],alkanesNMAMOD[[10]],alkanesNMAMOD[[11]],alkanesNMAMOD[[12]],alkanesNMAMOD[[13]],alkanesNMAMOD[[14]]},Joined->True,Frame->True,FrameLabel->{"Partial Pressure (Torr)","Monolayer (%)"},PlotStyle->{Automatic},PlotRange->{All,{0,100}},GridLines->Automatic,PlotLabels->Round[Malkanes[[1;;14]]]]

ListLogLogPlot[{alkanesNMAMOD[[1]],alkanesNMAMOD[[2]],alkanesNMAMOD[[3]],alkanesNMAMOD[[4]],alkanesNMAMOD[[5]],alkanesNMAMOD[[6]],alkanesNMAMOD[[7]],alkanesNMAMOD[[8]],alkanesNMAMOD[[9]],alkanesNMAMOD[[10]],alkanesNMAMOD[[11]],alkanesNMAMOD[[12]],alkanesNMAMOD[[13]],alkanesNMAMOD[[14]]},Joined->True,Frame->True,FrameLabel->{"Partial Pressure (Torr)","Monolayer (%)"},PlotStyle->{Automatic},PlotRange->{{10^-16,10^-11},{10^-5,10^2}},GridLines->Automatic,PlotLabels->Round[Malkanes[[1;;14]]]]