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❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙

❱✳ ❊✳ ❆s❛❞❝❤✐❦♦✈✱ ❨✉✳ ❖✳ ❱♦❧❦♦✈✱ ■✳ ❱✳ ❑♦③❤❡✈♥✐❦♦✈✱ ❇✳ ❙✳ ❘♦s❤❝❤✐♥✱ ❆✳ ▼✳ ❚✐❦❤♦♥♦✈∗

❙❤✉❜♥✐❦♦✈ ■♥st✐t✉t❡ ♦❢ ❈r②st❛❧❧♦❣r❛♣❤② ❘❆❙

∗ ❑❛♣✐t③❛ ■♥st✐t✉t❡ ❢♦r P❤②s✐❝❛❧ Pr♦❜❧❡♠s ❘❆❙

➽❙②♥❝❤r♦tr♦♥ ❛♥❞ ❋❊▲ r❛❞✐❛t✐♦♥✿ ❣❡♥❡r❛t✐♦♥ ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s➾ ◆♦✈♦s✐❜✐rs❦✱ ✹✕✼ ❏✉❧② ✷✵✶✻

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶ ✴ ✷✶

❈❡❧❧ ♠❡♠❜r❛♥❡ ♠♦❞❡❧ ✖ ♣❤♦s♣❤♦❧✐♣✐❞ ❜✐❧❛②❡r

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✷ ✴ ✷✶

▼♦❞❡❧ ❧✐♣✐❞s

✶✱✷✲❞✐st❡❛r♦②❧✲s♥✲❣❧②❝❡r♦✲✸✲♣❤♦s♣❤♦❝❤♦❧✐♥❡ ✭❉❙P❈✮ ✶✲st❡❛r♦②❧✲✷✲♦❧❡♦②❧✲s♥✲❣❧②❝❡r♦✲✸✲♣❤♦s♣❤♦❝❤♦❧✐♥❡ ✭❙❖P❈✮

❚❛❜✉❧❛r ♣r♦♣❡rt✐❡s✿ ▲✐♣✐❞ ❋♦r♠✉❧❛ ▼♦❧✳ ✇❡✐❣❤t Γ Tc✱ ◦❈ ❈❆❙ ■♥❞❡① ❉❙P❈ ❈✹✹❍✽✽◆❖✽P ✼✾✵✳✶✹✺ ✹✸✽ ✺✺ ✽✶✻✲✾✹✲✹ ❙❖P❈ ❈✹✹❍✽✻◆❖✽P ✼✽✽✳✶✷✾ ✹✸✻ ✻ ✺✻✹✷✶✲✶✵✲✹

❉✳ ▼✳ ❙♠❛❧❧✱ P❤②s✐❝❛❧ ❈❤❡♠✐str② ♦❢ ▲✐♣✐❞s✱ ◆❨✱ P❧❡♥✉♠ Pr❡ss✱ ✶✾✽✾✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✸ ✴ ✷✶

❍♦✇ ❝❛♥ ♦♥❡ ♣r❡♣❛r❡ ❛ ♠❛❝r♦s❝♦♣✐❝ ❧✐♣✐❞ ♠✉❧t✐❧❛②❡r❄

▲❛♥❣♠✉✐r✲❇❧♦❞❣❡tt t❡❝❤♥✐q✉❡ P❘❖✿ ✇✐❞❡❧② ✉s❡❞ ❛♥❞ r❡❧❛t✐✈❡❧② ❡❛s② t♦ ✐♠♣❧❡♠❡♥t❀ P❘❖✿ ❤✐❣❤❧② ❤♦♠♦❣❡♥❡♦✉s ❧✐♣✐❞ ❧❛②❡rs❀ ❈❖◆✿ s♦❧✐❞ s✉❜str❛t❡ ❞♦❡s ♥♦t ❝♦rr❡s♣♦♥❞ t♦ ❛❝t✉❛❧ ❝❡❧❧ ❜♦❞②✦ ❈❖◆✿ ❝♦♠♣r❡ss✐♦♥ ❦❡❡♣s ❧✐♣✐❞ ✜❧♠ ❤♦♠♦❤❡♥✐t② ✉♣ t♦ t❤❡ ♠♦♥♦❧❛②❡r ♦♥❧②✳ ✏❋r❡❡✑ ✜❧♠ ♦♥ ❧✐q✉✐❞ s✉❜str❛t❡ ❘❡❧❛t✐✈❡❧② ❧♦✇ ❤♦♠♦❣❡♥✐t② ♦❢ t❤❡ ❧❛②❡rs ♦♥ ❝❧❡❛♥ ✇❛t❡r s✉r❢❛❝❡✳ P♦ss✐❜✐❧✐t✐❡s t♦ ✉s❡ ❞✐✛❡r❡♥t ✇❛t❡r s♦❧✉t✐♦♥s ❛s ❛ s✉❜str❛t❡s❄

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✹ ✴ ✷✶

❳✶✾❈ ❜❡❛♠❧✐♥❡ ❛t ◆❙▲❙✱ ❇r♦♦❦❤❛✈❡♥

Φ = ✶✵✶✹ ♣❤♦t♦♥s✴s✱ E = ✶✺✵✵✵ ❡❱✱ ∆E/E ∼ ✶✵−✸

✶ ✕ t❤♦r♦✐❞❛❧ ❳✲r❛② ♠✐rr♦r❀ ✷ ✕ s✐♥❣❧❡✲❝r②st❛❧ ♠♦♥♦❝❤r♦♠❛t♦r❀ ✸ ✕ ✈✐❜r♦✲❞❛♠♣✐♥❣ ♣❧❛t❢♦r♠ ❛♥❞ s❛♠♣❧❡ ❝❤❛♠❜❡r❀ ✹ ✕ ✷θ✲r♦t❛t✐♦♥ ♣❧❛t❢♦r♠❀ ✺ ✕ t✇♦✲s❧✐t ❝♦❧❧✐♠❛t♦r❀ ✻ ✕ β✲r♦t❛t✐♦♥ ♣❧❛t❢♦r♠ ✇✐t❤ ❞❡t❡❝t♦r s❧✐t✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✺ ✴ ✷✶

▼♦❞❡❧✲✐♥❞❡♣❡♥❞❡♥t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❡❧❡❝tr♦♥ ❞❡♥s✐t② ♣r♦✜❧❡

❊①tr❛♣♦❧❛t✐♦♥ ♦❢ t❤❡ r❡✢❡❝t✐✈✐t② ❛s②♠♣t♦t✐❝

❇❛s✐❝ ❛ss✉♠♣t✐♦♥s✿ ▲❡t δ(z) = ❘❡ ✶ − ε(z) ❞✐str✐❜✉t✐♦♥ ❝♦♥t❛✐♥s m s♣❡❝✐❛❧ ♣♦✐♥ts ♦❢ n✲t❤ ♦r❞❡r✱ ✇❤❡r❡ ❢✉♥❝t✐♦♥ δ(z) ❛♥❞ ✐ts n − ✶ ❞❡r✐✈❛t✐✈❡s δ′(z) . . . δ(n−✶)(z) ❛r❡ ❝♦♥t✐♥✉♦✉s ❜✉t n✲t❤ ❞❡r✐✈❛t✐✈❡ s✉✛❡rs ❛ st❡♣✲❧✐❦❡ ✈❛r✐❛t✐♦♥✳ ❉✐❡❧❡❝tr✐❝ ♣❡r♠✐tt✐✈✐t✐② ♦❢ ❡①t❡r♥❛❧ ♠❡❞✐✉♠ ❡q✉❛❧s t♦ ✈❛❝✉✉♠ ✭δ(z < zmin) ≡ ✵✮ ✇❤✐❧❡ ♣❡r♠✐tt✐✈✐t② ♦❢ s✉❜str❛t❡ ✐s ❝♦♥st❛♥t ✭δ(z > zmax) ≡ δ+ = ✵✮✳ ❆❧❧ ❞✐s❝♦♥t✐♥✉✐t② ♣♦✐♥ts z✶ < z✷ < · · · < zm ❛r❡ ♦❢ t❤❡ s❛♠❡ ♦r❞❡r✳ ❆❜s♦r♣t✐♦♥ ♦❢ t❤❡ ❳✲r❛②s ✐♥ ❛ ♠❛tt❡r ✐s ♥❡❣❧❡❝t❡❞✿ ■♠ ε(z) ≡ ✵✳ ❘❡✢❡❝t✐✈✐t② ❛s②♠♣t♦t✐❝ ✐♥ t❤❡ ❢r❛♠❡s ♦❢ ✜rst✲♦r❞❡r ❇♦r♥ ❛♣♣r♦①✐♠❛t✐♦♥✿

r (q) ∼ = −k✷ i ✷q ✷+n

m

• j=✶

∆(n) zj

• ❡①♣
• ✷iqzj
• ,

∆(n) zj

• ≡ dnδ

dzn (zJ + ✵) − dnδ dzn (zJ − ✵) ,

■✳ ❱✳ ❑♦③❤❡✈♥✐❦♦✈✱ ◆✉❝❧✳ ■♥str✉♠❡♥ts ❛♥❞ ▼❡t❤♦❞s ✐♥ P❤②s✳ ❘❡s✳ ❆ ✭✷✵✵✸✮ ✺✵✽✿✺✶✾

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✻ ✴ ✷✶

▼♦❞❡❧✲✐♥❞❡♣❡♥❞❡♥t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❡❧❡❝tr♦♥ ❞❡♥s✐t② ♣r♦✜❧❡

❙❡❛r❝❤✐♥❣ ❢♦r ❞✐s❝♦♥t✐♥✉✐t② ♣♦✐♥ts

❘❡❣✉❧❛r✐③❡❞ ❋♦✉r✐❡r✲❢r❛♥s❢♦r♠ ♦❢ t❤❡ r❡✢❡❝t✐✈✐t② ❝✉r✈❡

F (x) = ✷✷n+✹ k✹ (qmax − qmin)

qmax

• qmin
• q✷n+✹R (q) − C
• ❝♦s (✷qx) dq

C = ✶ qmax − qmin

qmax

• qmin

q✷n+✹R (q) dq, q = k s✐♥ θ Reflectivity

10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100

qz, Å-1

0.1 0.2 0.3 0.4 0.5

F(x)*1015

−8 −6 −4 −2 2 4 6 8

x

50 100 150 200 250 300 350 400 450 500 ■✳ ❱✳ ❑♦③❤❡✈♥✐❦♦✈✱ ◆✉❝❧✳ ■♥str✉♠❡♥ts ❛♥❞ ▼❡t❤♦❞s ✐♥ P❤②s✳ ❘❡s✳ ❆ ✭✷✵✵✸✮ ✺✵✽✿✺✶✾

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✼ ✴ ✷✶

▼♦❞❡❧✲✐♥❞❡♣❡♥❞❡♥t r❡❝♦♥str✉❝t✐♦♥ ♦❢ ❡❧❡❝tr♦♥ ❞❡♥s✐t② ♣r♦✜❧❡

❘❡❣✉❧❛r✐③❡❞ ♠❡r✐t ❢✉♥❝t✐♦♥ ❢♦r ♥✉♠❡r✐❝❛❧ ♦♣t✐♠✐③❛t✐♦♥✿

▼❋ = ✶ N

• j
• Rexp
• θj
• − Rcalc
• θj
• Rexp
• θj
• ✷

+ Q✶

• i=✷,...,N

i=i✶,...,im

• δi+✶ − ✷δi + δi−✶

✷ + Q✷  

• i=i✷,...,im
• δi+✶ − δi

✷ + δ✷

✶

 

❊①tr❛❝t✐♦♥ ♦❢ str✉❝t✉r❛❧ ♣❛r❛♠❡t❡rs ρe(z) = πδ(z) r✵λ✷ , A = Γ

z✷

• z✶

ρ(z)dz ✇❤❡r❡ r✵ = ✷.✽✶✹ × ✶✵−✺ ✝ ❆✱ Γ ✕ q✉❛♥t✐t② ♦❢ ❡❧❡❝tr♦♥s ♣❡r str✉❝t✉r❡ ✉♥✐t✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✽ ✴ ✷✶

▲✐♣✐❞ ♠♦♥♦❧❛②❡r ♦♥ ❛ ✇❛t❡r s✉❜str❛t❡

❉❡♥s✐t② ♣r♦✜❧❡s ♥♦r♠❛❧✐③❡❞ ❜② ρH✷O ≈ ✵.✸✸✸ ✝ ❆−✸

Reflectivity

10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102

qz, Å-1

0.1 0.2 0.3 0.4 0.5 0.6

DSPC SOPC

×100

DSPC

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

20 40 60 80 100 120

A = 55.7±0.7 Å2 SOPC

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

20 40 60 80 100 120

A = 63.8±1.3 Å2

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✾ ✴ ✷✶

❈♦❧❧♦✐❞❛❧ s✐❧✐❝❛ ♥❛♥♦♣❛rt✐❝❧❡s s♦❧✉t✐♦♥s

❉✱ ♥♠ ρ✱ ❣✴❝♠✸ ❈SiO✷✱ ✪ ❈NaOH✱ ✪ ♣❍ ❋▼ ✺ ✶✳✶ ✶✻ ✵✳✸ ✾ ❙▼✲✸✵ ✶✵ ✶✳✷✷ ✸✵ ✵✳✺ ✶✵ ❍❙✲✹✵ ✶✷ ✶✳✷✼ ✹✵ ✵✳✸ ✾✳✺ ❚▼✲✹✵ ✷✷ ✶✳✸✵ ✹✵ ✵✳✵✸ ✾

❏✳ ❉❡♣❛ss❡✱ ❆✳ ❲❛t✐❧❧♦♥✱ ❏✳ ❈♦❧❧♦✐❞✳ ■♥t❡r❢❛❝❡ ❙❝✐✳ ✸✸✿✹✸✵ ✭✶✾✼✵✮

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✵ ✴ ✷✶

❙✉r❢❛❝❡ ❡✛❡❝ts ♦♥ ❛ ❝❧❡❛♥ s✐❧✐❝❛ s♦❧

❊①❛♠♣❧❡✿ s♦❧ ❙▼✲✸✵✱ ρH✷O ≈ ✵.✸✸✸ ✝ ❆−✸

Reflectivity

10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100

qz, Å-1

0.1 0.2 0.3 0.4 0.5 0.6 0.7

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

100 200 300 400 500 600

✐♠❛❣❡✲❝❤❛r❣❡ ❡✛❡❝t ✐♥✢✉❡♥❝❡s t❤❡ ♣❛rt✐❝❧❡s ♥❡❛r ❛✐r✴s♦❧ ✐♥t❡r❢❛❝❡ ❉❡❜②❡ s❝r❡❡♥✐♥❣ ❧❡♥❣t❤ ΛD =

• ε✵ε✷kB

c−NAe✷ ∼ ✸✵✵ . . . ✺✵✵✝

❆✳ ❛✐r✴✏❧❡✈✐t❛t✐♥❣ ✐♦♥s✑✴❞❡♣❧❡t❡❞ ❧❛②❡r✴❙✐❖✷ ♣❛rt✐❝❧❡s✴s♦❧ ✈♦❧✉♠❡ ❆♣♣r♦①✐♠❛t❡ ◆❛+ s✉r❢❛❝❡ ❞❡♥s✐t② ✭✹.✽ ± ✵.✸✮×✶✵✶✽♠−✷

❱✳ ❊✳ ❆s❛❞❝❤✐❦♦✈✱ ❨✉✳ ❖✳ ❱♦❧❦♦✈✱ ❆✳ ▼✳ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✴✴ ❏❊❚P ▲❡tt✳ ✾✹✭✼✮✿✻✷✺ ✭✷✵✶✶✮

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✶ ✴ ✷✶

P❤♦s♣❤♦❧✐♣✐❞ ❧❛②❡r ♦♥ ❛ s♦❧ s✉❜str❛t❡

❉❙P❈ ♦♥ ❙▼✲✸✵✱ ♠❡❛s✉r❡♠❡♥ts ♦✈❡r ❞✐✛❡r❡♥t t✐♠❡✱ ρH✷O ≈ ✵.✸✸✸ ✝ ❆−✸

Reflectivity

10−8 10−6 10−4 10−2 100 102 104

qz, Å-1

0.0 0.1 0.2 0.3 0.4 0.5

1-3 h ≈24 h ≈96 h

×104 ×102

1-3 h

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

100 200 300 400 500 600

A = 55.7±0.7 Å2 ✶✕✸ ❤rs✿ s✐♥❣❧❡ ❧❛②❡r✱ d ≈ ✶✸✷ ✝ ❆❀ ❙✐❖✷ ♣❛rt✐❝❧❡s ❛r❡ ❞✐s❛♣♣❡❛r❡❞✦ ✷✹ ❤rs✿ ♣❡r✐♦❞✐❝ str✉❝t✉r❡✱ ✻✽ ✵ ✷ ✶ ✝ ❆❀ ✽ ◆❛ ✐♦♥s✴❧✐♣✐❞ ♠♦❧❡❝✉❧❡✳ ✾✻ ❤rs✿ ♠✉❧t✐❧❛②❡r✱ ✻✽ ✶ ✵ ✾ ✝ ❆❀ ✶✵ ◆❛ ✐♦♥s✴❧✐♣✐❞ ♠♦❧❡❝✉❧❡✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✷ ✴ ✷✶

P❤♦s♣❤♦❧✐♣✐❞ ❧❛②❡r ♦♥ ❛ s♦❧ s✉❜str❛t❡

❉❙P❈ ♦♥ ❙▼✲✸✵✱ ♠❡❛s✉r❡♠❡♥ts ♦✈❡r ❞✐✛❡r❡♥t t✐♠❡✱ ρH✷O ≈ ✵.✸✸✸ ✝ ❆−✸

Reflectivity

10−8 10−6 10−4 10−2 100 102 104

qz, Å-1

0.0 0.1 0.2 0.3 0.4 0.5

1-3 h ≈24 h ≈96 h

×104 ×102

≈ 24 h

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

100 200 300 400 500 600

A = 35.3±1.5 Å2 ✶✕✸ ❤rs✿ s✐♥❣❧❡ ❧❛②❡r✱ d ≈ ✶✸✷ ✝ ❆❀ ❙✐❖✷ ♣❛rt✐❝❧❡s ❛r❡ ❞✐s❛♣♣❡❛r❡❞✦ ≈ ✷✹ ❤rs✿ ♣❡r✐♦❞✐❝ str✉❝t✉r❡✱ L = ✻✽.✵ ± ✷.✶ ✝ ❆❀ Φ ≈ ✽ ◆❛+ ✐♦♥s✴❧✐♣✐❞ ♠♦❧❡❝✉❧❡✳ ✾✻ ❤rs✿ ♠✉❧t✐❧❛②❡r✱ ✻✽ ✶ ✵ ✾ ✝ ❆❀ ✶✵ ◆❛ ✐♦♥s✴❧✐♣✐❞ ♠♦❧❡❝✉❧❡✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✷ ✴ ✷✶

P❤♦s♣❤♦❧✐♣✐❞ ❧❛②❡r ♦♥ ❛ s♦❧ s✉❜str❛t❡

❉❙P❈ ♦♥ ❙▼✲✸✵✱ ♠❡❛s✉r❡♠❡♥ts ♦✈❡r ❞✐✛❡r❡♥t t✐♠❡✱ ρH✷O ≈ ✵.✸✸✸ ✝ ❆−✸

Reflectivity

10−8 10−6 10−4 10−2 100 102 104

qz, Å-1

0.0 0.1 0.2 0.3 0.4 0.5

1-3 h ≈24 h ≈96 h

×104 ×102

≈ 96 h

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

100 200 300 400 500 600

A = 34.4±1.9 Å2 ✶✕✸ ❤rs✿ s✐♥❣❧❡ ❧❛②❡r✱ d ≈ ✶✸✷ ✝ ❆❀ ❙✐❖✷ ♣❛rt✐❝❧❡s ❛r❡ ❞✐s❛♣♣❡❛r❡❞✦ ≈ ✷✹ ❤rs✿ ♣❡r✐♦❞✐❝ str✉❝t✉r❡✱ L = ✻✽.✵ ± ✷.✶ ✝ ❆❀ Φ ≈ ✽ ◆❛+ ✐♦♥s✴❧✐♣✐❞ ♠♦❧❡❝✉❧❡✳ ≈ ✾✻ ❤rs✿ ♠✉❧t✐❧❛②❡r✱ L = ✻✽.✶ ± ✵.✾ ✝ ❆❀ Φ ≈ ✶✵ ◆❛+ ✐♦♥s✴❧✐♣✐❞ ♠♦❧❡❝✉❧❡✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✷ ✴ ✷✶

■♥✢✉❡♥❝❡ ♦❢ t❤❡ s✉❜str❛t❡ ♦♥ ♠✉❧t✐❧❛②❡r ♣r♦♣❡rt✐❡s

Reflectivity

10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 104

qz, Å-1

0.1 0.2 0.3 0.4 0.5 0.6 DSPC on FM DSPC on HS-40 DSPC on TM-40

×102 ×102 ×104

DSPC on FM

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2

z, Å

100 200 300 400 500 600

ΛD ≈ 450 Å L = 72.2±1.8 Å A = 39.0±1.3 Å2

DSPC on HS-40

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

100 200 300 400 500 600

ΛD ≈ 400 Å L = 66.7±2.0 Å A = 33.7±1.3 Å2

DSPC on TM-40

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

100 200 300 400 500 600

ΛD ≈ 300 Å L = 68.3±1.8 Å A = 35.4±1.6 Å2

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✸ ✴ ✷✶

❙✉❜str❛t❡ ❞♦♣❛t✐♦♥ ✇✐t❤ ❛❧❦❛❧✐ ✐♦♥s

❙♦❧ ❋▼✲✶✻ ❞♦♣❡❞ ✇✐t❤ ◆❛+✱ ♣❍≈✶✶✳✺

Reflectivity

10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102

qz, Å-1

0.1 0.2 0.3 0.4 0.5 0.6 0.7

DSPC SOPC

×100

DSPC

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

z, Å

20 40 60 80 100 120 140

SOPC

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

z, Å

20 40 60 80 100 120 140

∆♣❍ = ✶ ❞❡❝r❡❛s❡s ΛD ❜② √ ✶✵ t✐♠❡s❀ L✶ ≈ ✸✺✝ ❆✱ ADSPC = ✹✹.✾ ± ✶.✼✝ ❆✷ ✖ ❝r②st❛❧❧✐♥❡ ♠♦♥♦❧❛②❡r❀ ASOPC = ✻✺.✸ ± ✷.✺✝ ❆✷ ✖ ❧✐q✉✐❞ ✜❧♠❀ d✷ ≈ ✷✵✝ ❆< dSiO✷ ✖ ♣r♦❜❛❜❧② ❧✐♣✐❞ ✈❡s✐❝✉❧❛❡ ✇✐t❤ ◆❛+ ✐♦♥s❄

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✹ ✴ ✷✶

■♦♥ s❝r❡❡♥✐♥❣ ❡✛❡❝t✿ ❤❡❛✈② ❛❧❦❛❧✐ ✐♦♥s

❉❙P❈ ♦♥ s♦❧ ❙▼✲✸✵ ❞♦♣❡❞ ✇✐t❤ ❈s+✱ ♣❍≈ ✶✶

Reflectivity

10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100

qz, Å-1

0.1 0.2 0.3 0.4 0.5 0.6 0.7

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z, Å

50 100 150 200 250 300 350

❙✐❖✷ ♣❛rt✐❝❧❡s ❧❛②❡r ✐s ♣r❡s❡♥t✦ L✶ = ✸✺ ± ✵.✼✝ ❆✱ A = ✹✵.✷ ± ✷.✵✝ ❆✷ ✖ ❛❧♠♦st ✐❞❡❛❧ ❧✐♣✐❞ ♠♦♦♥♦❧❛②❡r✳ ❆♣♣r♦①✐♠❛t❡ ❈s+ s✉r❢❛❝❡ ❞❡♥s✐t② ✭✹.✹ ± ✵.✷✮×✶✵✶✼♠−✷

❆✳ ▼✳ ❚✐❦❤♦♥♦✈✱ ❏✳ ❈❤❡♠✳ P❤②s✳ ✶✸✵✿✵✷✹✺✶✹ ✭✷✵✵✾✮

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✺ ✴ ✷✶

■♦♥ s❝r❡❡♥✐♥❣ ❡✛❡❝t✿ s❛t✉r❛t❡❞ ❧✐♣✐❞ s❛❧t

❉❙P❈✲◆❛ s❛❧t ♦♥ ❚▼✲✹✵

Reflectivity

10−10 10−8 10−6 10−4 10−2 100

qz, Å-1

0.1 0.2 0.3 0.4 0.5 0.6

ρ/ρH2O

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

z, Å

75 150 225 300 375 450 525 600 675 750

❙✐❖✷ ♣❛rt✐❝❧❡s ❧❛②❡r ✐s ♣r❡s❡♥t❀ d✶ ≈ ✻✹✝ ❆ ✖ ❧✐♣✐❞ ❜✐❧❛②❡r✳ A = ✸✸.✶ ± ✶.✻✝ ❆ ✖ ✷✲❞✐♠❡♥s✐♦♥❛❧ ❧✐♣✐❞ ❝r②st❛❧✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✻ ✴ ✷✶

❈✉♠✉❧❛t✐✈❡ t❛❜❧❡ ♦❢ ❧✐♣✐❞ ❧❛②❡r ♣❛r❛♠❡t❡rs

❆♣♣r♦①✳ str✉❝t✉r❡ s✉❜str❛t❡ ♣❍ ♣❤♦s♣❤♦❧✐♣✐❞ L ✭✝ ❆✮ A ✭✝ ❆✷✮ ♠♦♥♦❧❛②❡r ✇❛t❡r ✼ ❉❙P❈ ✸✼ ± ✷ ✺✺.✼ ± ✵.✼ ♠♦♥♦❧❛②❡r ✇❛t❡r ✼ ❙❖P❈ ✸✻ ± ✷ ✻✸.✽ ± ✶.✸ ❜✐❧❛②❡r ✐♥ st❛❝❦ ❋▼ ✾ ❉❙P❈ ✼✷ ± ✷ ✸✾.✵ ± ✶.✸ ❜✐❧❛②❡r ✐♥ st❛❝❦ ❙▼✲✸✵ ✶✵ ❉❙P❈ ✻✽ ± ✶ ✸✹.✹ ± ✵.✾ ❜✐❧❛②❡r ✐♥ st❛❝❦ ❍❙✲✹✵ ✾✳✺ ❉❙P❈ ✻✼ ± ✷ ✸✸.✼ ± ✶.✸ ❜✐❧❛②❡r ✐♥ st❛❝❦ ❚▼✲✹✵ ✾ ❉❙P❈ ✻✽ ± ✶ ✸✺.✹ ± ✶.✻ ♠♦♥♦❧❛②❡r ❋▼✲✶✻ ✶✶✳✺ ❉❙P❈ ≈ ✸✺ ✹✹.✾ ± ✶.✼ ♠♦♥♦❧❛②❡r ❋▼✲✶✻ ✶✶✳✺ ❙❖P❈ ≈ ✸✺ ✻✺.✸ ± ✷.✺ ♠♦♥♦❧❛②❡r ❚▼✲✹✵✴❈s+ ✶✶ ❉❙P❈ ✸✺ ± ✵.✼ ✹✵.✷ ± ✷.✵ ❜✐❧❛②❡r ❚▼✲✹✵ ✾ ❉❙P❈✲◆❛ ✻✹ ± ✺ ✸✸.✶ ± ✶.✻

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✼ ✴ ✷✶

❖✛✲s♣❡❝✉❧❛r ❣r❛③✐♥❣ ✐♥❝✐❞❡♥❝❡ ❞✐✛r❛❝t✐♦♥ ❢r♦♠ ❉❙P❈ ♠✉❧t✐❧❛②❡r

Pr❡❧✐♠✐♥❛r② ❞❛t❛ t❛❦❡♥ ✇✐t❤ ❧❛❜♦r❛t♦r② s♦✉r❝❡ ✭E = ✽✵✹✽ ❡❱✮✱ ✷✺✕✸✵ ❏✉♥❡ ✷✵✶✻

Π

10−4 10−2 100 102 104 1 2 3 4 5

Π

10−4 10−3 10−2 10−1 100 101 1 2 3 4 5

Π

10−4 10−3 10−2 10−1 100 101 1 2 3 4 5

Π

10−4 10−3 10−2 10−1 100 1 2 3 4 5

Π

10−3 10−2 10−1 100 101 1 2 3 4 5

R

10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 1 2 3 4 5 ❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✽ ✴ ✷✶

❘❡s✉❧ts ❛♥❞ ❞✐s❝✉ss✐♦♥

❆✳ ❚✐❦❤♦♥♦✈✱ ❱✳ ❆s❛❞❝❤✐❦♦✈✱ ❨✉✳ ❱♦❧❦♦✈ ✴✴ ❏❊❚P ▲❡tt✳ ✷✵✶✺✱ ✶✵✷✭✼✮✿✺✸✻✕✺✹✶✱ ❛r❳✐✈✿✶✺✶✶✳✵✸✺✹✸✈✶

P❤♦s♣❤♦❧✐♣✐❞ ❧❛②❡r ♦♥ t❤❡ s✉r❢❛❝❡ ♦❢ s✐❧✐❝❛ s♦❧ ❝♦♠♣❡♥s❛t❡s ♠✐rr♦r ❝❤❛r❣❡ ❡✛❡❝t✱ ♣r❡s✉♠❛❜❧② ❞✉❡ t♦ t❤❡ ❛❜s♦r♣t✐♦♥ ♦❢ ◆❛+ ✐♦♥s ❜② ❧✐♣✐❞ ♠♦❧❡❝✉❧❡s ❢r♦♠ s♦❧ ✈♦❧✉♠❡✳ ▲✐♣✐❞ ♠♦❧❡❝✉❧❡s ✇✐t❤✐♥ t❤✐❝❦ ♠✉❧t✐❧❛②❡r ✉♥❞❡r❣♦ s♣♦♥t❛♥❡♦✉s ♦r❞❡r✐♥❣ ❡✛❡❝t ✉♥❞❡r t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❛ s✉r❢❛❝❡ ❡❧❡❝tr✐❝ ✜❡❧❞✱ ❧❡❛❞✐♥❣ t♦ t❤❡ ❢♦r♠❛t✐♦♥ ♦❢ r❡❣✉❧❛r ❜✐❧❛②❡r st❛❝❦ ❛❢t❡r ❛ ❢❡✇ ❞❛②s✳ ◗✉❛♥t✐t② ♦❢ ❜✐❧❛②❡rs ❞❡♣❡♥❞s ♦♥ ΛD ❛t t❤❡ s✉r❢❛❝❡ ❛♥❞✱ ❝♦♥s❡q✉❡♥t❧②✱ s✉❜str❛t❡ ♣❍✳ ❚❤✉s ♦♥❡ ❝❛♥ r❡❞✉❝❡ ❜✐❧❛②❡r ♥✉♠❜❡r ❜② ✐♥❝r❡❛s✐♥❣ ♦❢ s♦❧ ♣❍✳ ❇✐❧❛②❡r ✉♥✐❢♦r♠✐t② ❞❡♣❡♥❞s ♦♥ s✉r❢❛❝❡ ❡❧❡❝tr✐❝ ✜❡❧❞ ❣r❛❞✐❡♥t ❛♥❞✱ ❝♦♥s❡q✉❡♥t❧②✱ s✐③❡ ♦❢ ❙✐❖✷ ♥❛♥❛♣❛rt✐❝❧❡s ✐♥ s♦❧✉t✐♦♥✳ ▲❛②❡r ♦❢ ✏❧❡✈✐t❛t✐♥❣ ✐♦♥s✑ ♦♥ t❤❡ ❛✐r✴s♦❧ ✐♥t❡r❢❛❝❡ ♣r♦❤✐❜✐ts t❤❡ ✐♦♥ ❛❜s♦r♣t✐♦♥ ❢r♦♠ s♦❧ ✈♦❧✉♠❡✱ ❡✛❡❝t✐✈❡❧② s❝r❡❡♥✐♥❣ ❧✐♣✐❞ ❧❛②❡r ❢r♦♠ t❤❡ s✉❜str❛t❡✳ ❚❤✐s ❧❡❛❞s t♦ t❤❡ ❢♦r♠❛t✐♦♥ ♦❢ t❤✐♥ ♠♦♥♦❧❛②❡r ✐♥st❡❛❞ ♦❢ ❜✐❧❛②❡r st❛❝❦✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✶✾ ✴ ✷✶

❋✉rt❤❡r ❣♦❛❧s ❛♥❞ ♣❡rs♣❡❝t✐✈❡s

❖✛✲s♣❡❝✉❧❛r ❛♥❞ ♦✛✲♣❧❛♥❡ ●■❳❘❉✱ ❳✲r❛② ✢✉♦r❡s❝❡♥❝❡ ❡①♣❡r✐♠❡♥ts

✭✜♥❡ ❞❡t❡r♠✐♥❛t✐♦♥ ♦❢ ❧❛t❡r❛❧ ❝r②st❛❧❧✐♥❡ str✉❝t✉r❡✮❀

P❤♦s♣❤♦❧✐♣✐❞ ♠✐①t✉r❡s ❛♥❞ ✐♥✲s✐t✉ ✈❛r✐❛t✐♦♥ ♦❢ s✉❜str❛t❡ ❝♦♠♣♦s✐t✐♦♥❀ ❚❤❡♦r❡t✐❝❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ s♣♦♥t❛♥❡♦✉s ❧✐♣✐❞ str❛t✐✜❝❛t✐♦♥ ♣r♦❝❡ss

✭❜✐♦♣❤②s✐❝✐st ♥❡❡❞❡❞✮❀

■♥ s✐t✉ ♠❡♠❜r❛♥❡✲♣r♦t❡✐♥ ❝♦♥❢♦r♠❛t✐♦♥ ♣r♦❝❡ss❡s❀ P❤♦s♣❤♦❧✐♣✐❞ ❧❛②❡rs ❛t ❧✐q✉✐❞✴❧✐q✉✐❞ ✐♥t❡r❢❛❝❡✳

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✷✵ ✴ ✷✶

❚❍❆◆❑ ❨❖❯ ❋❖❘ ❨❖❯❘ ❆❚❚❊◆❚■❖◆✦

❱♦❧❦♦✈✱ ❚✐❦❤♦♥♦✈ ❡t ❛❧✳ ✭■❈ ❘❆❙✮ ❙❚❘❯❈❚❯❘❆▲ P❆❘❆▼❊❚❊❘❙ ❖❋ ▼❆❈❘❖❙❈❖P■❈❆▲▲❨ ❋▲❆❚ ▲■P■❉ ▼❯▲❚■▲❆❨❊❘❙ ❖◆ ❆ ❙■▲■❈❆ ❙❖▲ ❙❯❇❙❚❘❆❚❊❙ ❙❋❘✲✷✵✶✻✱ ◆♦✈♦s✐❜✐rs❦ ✷✶ ✴ ✷✶