Effect of Solute Core Curvature on Solubility

Luz Teresa PadróApril 26, 2004.

Introduction Aerosols are composed of:

Inorganic and organic matter

Implications of organics in cloud condensation nuclei (CCN) activity

Composition, structure and surface affect activation diameters at different supersaturations

Raymond and Pandis [2002] Studied cloud activation of single

component aerosol particles at 0.3% and 1% supersaturation 15 compounds

Hygroscopic secondary organics Hydrophobic primary organics

Compared results with classical Köhler theory and one that takes into account solubility

Results Theoretical and experimental

values do not agree Attributing this to the particles

solubility in water

More solute is being dissolved than that calculated by solubility studies Is the organic completely soluble?

0.3% Supersaturation

1% Supersaturation

Modification of Results

Assumed everything dissolved No core present

Theoretical and experimental values have better agreement Low solubility compounds activation

may be determined by the curvature or Kelvin effect alone

Complete Solubility Assumption

Köhler Theory

3

lnpp

o

pw

D

B

D

A

p

Dp

w

ws

w

ww

MnB

RT

MA

6

4

where:

pw(Dp) - water vapor pressure over the droplet diameter Dp

po - water vapor pressure over a flat surface at the same temperature

Mw - molecular weight of water

σw - surface tension of water

R - ideal gas constant

T – temperature

ρw - density of water

ns - moles of solute

Köhler Curves

Critical Parameters Dpc and Sc

Critical Droplet Diameter, Dpc

Critical Saturation, Sc

21

3

A

BDpc

21

3

27

4ln

B

ASc

Sc : Accounting for Solute

s

sss M

dn

6

3

21

3

3

27

4ln

sws

swc dM

MAS

where:

ν - van’t Hoff factor

ds - dry particle diameter

ρs - density of the solute

Ms - molecular weight of the solute

Compounds Studied Adipic acid Glutamic acid Glutaric acid Norpinic acid Pinic acid Pinonic acid

Method

Theory calculations: ns required by theory Dpc required for ns

mass of water in Dpc

nsolubility in mass of water

Ratio of ns/nsolubility for each compound

Theory to Solubility

ns/nA ns/nGR ns/nGM ns/nN ns/nPI ns/nPO

a 0.500 0.007 1.321 0.229 0.137 1.703

b 18.317 0.245 48.422 8.379 5.035 62.432

where:

A – adipic acid

GR – glutaric acid

GM – glutamic acid

N – norpinic acid

PI – pinic acid

PO – pinonic acid

Table 1. Theory to solubility ratio for (a) 0.3% supersaturation and (b) 1% supersaturation.

Method II Experimental Calculations:

nexperimental

Core diameters

Kelvin effect greater than 1? curvature enhanced-solubility

Theory to Experimental

ns/nA ns/nGR ns/nGM ns/nN ns/nPI ns/nPO

a 0.137 0.902 1.554 2.164 0.002 0.000

b 0.054 0.677 1.083 0.002 0.003 0.001

Table 2. Theory to experimental ratio for (a) 0.3% supersaturation and (b) 1% supersaturation.

Core diameter

dwA (cm) dwGR (cm) dwGM (cm) dwN (cm) dwPI (cm) dwPO (cm)

a1.57E-05 -4.56E-05 -4.21E-06 -1.79E-05 9.15E-05 1.14E-03

b1.06E-05 -1.43E-05 3.46E-06 4.20E-05 3.79E-05 5.00E-05

Table 3. Dry core diameter for (a) 0.3% supersaturation and (b) 1% supersaturation.

Mass Balance31

3 6

s

ssw

mdd

where:

dw – core diameter

ds – dry particle diameter

ms – mass of solute

Kelvin effect

Ccurved surface

/Cflat surfaceA

Ccurved surface

/Cflat surfaceGM

Ccurved surface

/Cflat surfaceN

Ccurved surface

/Cflat surfacePI

Ccurved surface

/Cflat surfacePO

a 1.0021  -  - 1.0009 1.0001

b 1.0032 1.0180 1.0019 1.0021 1.0017

Table 4. Kelvin effect of compounds that have a core for (a) 0.3% supersaturation and (b) 1% supersaturation.

Summary of Results

Solubility shows no activation: at both supersaturations

glutamic acid and pinonic acid at 1% supersaturation

adipic acid, glutaric acid, norpinic acid and pinic acid

Summary of Results II Experiments shows no activation:

At both supersaturations glutamic acid

At 0.3% supersaturation norpinic acid

Kelvin effect > 1 Shows possibility of curvature-enhanced

solubility Will be studied using a dissolution kinetics model

Thank you!