In [ ]:

# M3-P3 workflow validation - edit-lint-sync-execute cycle verified

# M3-P3 workflow validation - edit-lint-sync-execute cycle verified

Activity Tutorial¶

This tutorial provides a comprehensive introduction to computing chemical activity in aerosol particles using Particula's activity strategies. We'll cover ideal activity (Raoult's Law), non-ideal activity using the BAT model, kappa parameter activity for hygroscopic growth, and integration with equilibria calculations.

What is Activity?¶

Chemical activity is a measure of the "effective concentration" of a species that determines its thermodynamic behavior. In aerosol systems:

• Activity controls partitioning: Species with higher activity in the condensed phase tend to evaporate
• Water activity determines hygroscopic growth: Low water activity drives water uptake from the gas phase
• Non-ideality matters: Real mixtures deviate from ideal behavior, especially organic-water systems

Notebook Structure¶

1. Ideal Activity - Raoult's Law and ideal mixing
2. Non-Ideal Activity (BAT) - Binary Activity Thermodynamic model
3. Kappa Hygroscopic Parameter - Water activity from kappa values
4. Integration with Equilibria - Liquid-vapor partitioning

Note: This tutorial complements the existing Activity Tutorial which demonstrates Strategy, Builder, and Factory patterns in detail.

In [ ]:

# Install particula if needed (uncomment for Colab)
# !pip install particula --quiet

import matplotlib.pyplot as plt
import numpy as np
import particula as par

# Set plot style
plt.style.use("seaborn-v0_8-whitegrid")

# Install particula if needed (uncomment for Colab) # !pip install particula --quiet import matplotlib.pyplot as plt import numpy as np import particula as par # Set plot style plt.style.use("seaborn-v0_8-whitegrid")

---

1. Ideal Activity (Raoult's Law)¶

For ideal solutions, activity equals the mole fraction of the species. This is known as Raoult's Law:

$$a_i = x_i$$

where $a_i$ is the activity and $x_i$ is the mole fraction of species $i$.

The partial pressure is:

$$p_i = a_i \cdot p_i^{\circ} = x_i \cdot p_i^{\circ}$$

1.1 Creating an Ideal Activity Strategy¶

In [ ]:

# Define species: water and organic
molar_mass = np.array([18.015e-3, 200.0e-3])  # kg/mol

# Create ideal molar activity strategy
ideal_strategy = par.particles.ActivityIdealMolar(
    molar_mass=molar_mass,
)

print(f"Strategy: {type(ideal_strategy).__name__}")
print(f"Molar masses: {ideal_strategy.molar_mass * 1e3} g/mol")

# Define species: water and organic molar_mass = np.array([18.015e-3, 200.0e-3]) # kg/mol # Create ideal molar activity strategy ideal_strategy = par.particles.ActivityIdealMolar( molar_mass=molar_mass, ) print(f"Strategy: {type(ideal_strategy).__name__}") print(f"Molar masses: {ideal_strategy.molar_mass * 1e3} g/mol")

1.2 Computing Activity from Mass Concentrations¶

In [ ]:

# Define mass concentrations (50% water, 50% organic by mass)
mass = np.array([0.5e-9, 0.5e-9])  # kg/m^3

# Compute activity
activity = ideal_strategy.activity(mass_concentration=mass)

print(f"Mass concentrations: {mass * 1e9} ng/m^3")
print(f"Activity values: water={activity[0]:.4f}, organic={activity[1]:.4f}")

# Verify activity equals mole fraction
moles = mass / molar_mass
mole_fractions = moles / np.sum(moles)
print(
    f"Mole fractions: water={mole_fractions[0]:.4f}, organic={mole_fractions[1]:.4f}"
)

# Define mass concentrations (50% water, 50% organic by mass) mass = np.array([0.5e-9, 0.5e-9]) # kg/m^3 # Compute activity activity = ideal_strategy.activity(mass_concentration=mass) print(f"Mass concentrations: {mass * 1e9} ng/m^3") print(f"Activity values: water={activity[0]:.4f}, organic={activity[1]:.4f}") # Verify activity equals mole fraction moles = mass / molar_mass mole_fractions = moles / np.sum(moles) print( f"Mole fractions: water={mole_fractions[0]:.4f}, organic={mole_fractions[1]:.4f}" )

1.3 Visualization: Activity vs Composition¶

In [ ]:

# Calculate activity across composition range
water_fractions = np.linspace(0.01, 0.99, 50)
water_activities = []
organic_activities = []

for wf in water_fractions:
    mass = np.array([wf, 1.0 - wf]) * 1e-9
    activity = ideal_strategy.activity(mass_concentration=mass)
    water_activities.append(activity[0])
    organic_activities.append(activity[1])

# Plot
fig, ax = plt.subplots(figsize=(8, 5))
ax.plot(water_fractions, water_activities, "b-", linewidth=2, label="Water")
ax.plot(water_fractions, organic_activities, "r-", linewidth=2, label="Organic")
ax.set_xlabel("Water Mass Fraction", fontsize=12)
ax.set_ylabel("Activity", fontsize=12)
ax.set_title("Ideal Activity (Raoult's Law)", fontsize=14)
ax.legend(fontsize=11)
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
plt.tight_layout()
plt.show()

# Calculate activity across composition range water_fractions = np.linspace(0.01, 0.99, 50) water_activities = [] organic_activities = [] for wf in water_fractions: mass = np.array([wf, 1.0 - wf]) * 1e-9 activity = ideal_strategy.activity(mass_concentration=mass) water_activities.append(activity[0]) organic_activities.append(activity[1]) # Plot fig, ax = plt.subplots(figsize=(8, 5)) ax.plot(water_fractions, water_activities, "b-", linewidth=2, label="Water") ax.plot(water_fractions, organic_activities, "r-", linewidth=2, label="Organic") ax.set_xlabel("Water Mass Fraction", fontsize=12) ax.set_ylabel("Activity", fontsize=12) ax.set_title("Ideal Activity (Raoult's Law)", fontsize=14) ax.legend(fontsize=11) ax.set_xlim(0, 1) ax.set_ylim(0, 1) plt.tight_layout() plt.show()

Note that water activity is not linear with mass fraction due to the different molar masses. Even at 50% water by mass, water activity is high (~0.92) because water has many more moles than the heavy organic.

---

2. Non-Ideal Activity (BAT Model)¶

The Binary Activity Thermodynamic (BAT) model accounts for non-ideal interactions between water and organic species. The model uses the organic's oxygen-to-carbon (O:C) ratio to predict activity coefficients.

For non-ideal mixtures:

$$a_i = \gamma_i \cdot x_i$$

where $\gamma_i$ is the activity coefficient (deviates from 1 for non-ideal behavior).

2.1 Creating a BAT Activity Strategy¶

In [ ]:

# Create non-ideal activity strategy using builder
bat_strategy = (
    par.particles.ActivityNonIdealBinaryBuilder()
    .set_molar_mass(200.0, "g/mol")  # automatic unit conversion
    .set_oxygen2carbon(0.4)  # O:C ratio
    .set_density(1200.0, "kg/m^3")
    .build()
)

print(f"Strategy: {type(bat_strategy).__name__}")
print(f"Organic O:C ratio: {bat_strategy.oxygen2carbon}")

# Create non-ideal activity strategy using builder bat_strategy = ( par.particles.ActivityNonIdealBinaryBuilder() .set_molar_mass(200.0, "g/mol") # automatic unit conversion .set_oxygen2carbon(0.4) # O:C ratio .set_density(1200.0, "kg/m^3") .build() ) print(f"Strategy: {type(bat_strategy).__name__}") print(f"Organic O:C ratio: {bat_strategy.oxygen2carbon}")

2.2 Comparing Ideal vs Non-Ideal Activity¶

In [ ]:

# Compute activities at 50% water
mass = np.array([0.5, 0.5]) * 1e-9  # kg/m^3

ideal_activity = ideal_strategy.activity(mass_concentration=mass)
# Note: BAT model returns only organic activity (scalar)
bat_organic_activity = bat_strategy.activity(mass_concentration=mass)

print("At 50% water by mass:")
print(
    f"  Ideal activity:     water={ideal_activity[0]:.4f}, organic={ideal_activity[1]:.4f}"
)
print(f"  Non-ideal (BAT):    organic={bat_organic_activity:.4f}")

# Compute activity coefficient for organic
moles = mass / np.array([18.015e-3, 200.0e-3])
mole_frac = moles / np.sum(moles)
gamma_organic = bat_organic_activity / mole_frac[1]
print(f"\n  Organic activity coefficient: gamma={gamma_organic:.4f}")

# Compute activities at 50% water mass = np.array([0.5, 0.5]) * 1e-9 # kg/m^3 ideal_activity = ideal_strategy.activity(mass_concentration=mass) # Note: BAT model returns only organic activity (scalar) bat_organic_activity = bat_strategy.activity(mass_concentration=mass) print("At 50% water by mass:") print( f" Ideal activity: water={ideal_activity[0]:.4f}, organic={ideal_activity[1]:.4f}" ) print(f" Non-ideal (BAT): organic={bat_organic_activity:.4f}") # Compute activity coefficient for organic moles = mass / np.array([18.015e-3, 200.0e-3]) mole_frac = moles / np.sum(moles) gamma_organic = bat_organic_activity / mole_frac[1] print(f"\n Organic activity coefficient: gamma={gamma_organic:.4f}")

2.3 Visualization: Ideal vs Non-Ideal Comparison¶

In [ ]:

# Calculate activities across composition range
water_fractions = np.linspace(0.1, 0.9, 40)

ideal_water = []
bat_organic = []

for wf in water_fractions:
    mass = np.array([wf, 1.0 - wf]) * 1e-9
    ideal_water.append(ideal_strategy.activity(mass_concentration=mass)[0])
    # BAT returns organic activity (scalar), not water activity
    bat_organic.append(float(bat_strategy.activity(mass_concentration=mass)))

# Plot
fig, ax = plt.subplots(figsize=(8, 5))
ax.plot(
    water_fractions,
    ideal_water,
    "b--",
    linewidth=2,
    label="Ideal Water Activity",
)
ax.plot(
    water_fractions,
    bat_organic,
    "r-",
    linewidth=2,
    label="Non-Ideal Organic Activity (BAT, O:C=0.4)",
)
ax.set_xlabel("Water Mass Fraction", fontsize=12)
ax.set_ylabel("Activity", fontsize=12)
ax.set_title("Activity: Ideal vs Non-Ideal (BAT)", fontsize=14)
ax.legend(fontsize=11)
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
plt.tight_layout()
plt.show()

# Calculate activities across composition range water_fractions = np.linspace(0.1, 0.9, 40) ideal_water = [] bat_organic = [] for wf in water_fractions: mass = np.array([wf, 1.0 - wf]) * 1e-9 ideal_water.append(ideal_strategy.activity(mass_concentration=mass)[0]) # BAT returns organic activity (scalar), not water activity bat_organic.append(float(bat_strategy.activity(mass_concentration=mass))) # Plot fig, ax = plt.subplots(figsize=(8, 5)) ax.plot( water_fractions, ideal_water, "b--", linewidth=2, label="Ideal Water Activity", ) ax.plot( water_fractions, bat_organic, "r-", linewidth=2, label="Non-Ideal Organic Activity (BAT, O:C=0.4)", ) ax.set_xlabel("Water Mass Fraction", fontsize=12) ax.set_ylabel("Activity", fontsize=12) ax.set_title("Activity: Ideal vs Non-Ideal (BAT)", fontsize=14) ax.legend(fontsize=11) ax.set_xlim(0, 1) ax.set_ylim(0, 1) plt.tight_layout() plt.show()

2.4 Effect of O:C Ratio on Non-Ideality¶

In [ ]:

# Test different O:C ratios
o2c_values = [0.1, 0.3, 0.5, 0.7]
water_fractions = np.linspace(0.1, 0.9, 40)

fig, ax = plt.subplots(figsize=(8, 5))

# Ideal reference (organic activity)
ideal_organic = [
    ideal_strategy.activity(mass_concentration=np.array([wf, 1 - wf]) * 1e-9)[1]
    for wf in water_fractions
]
ax.plot(water_fractions, ideal_organic, "k--", linewidth=1.5, label="Ideal")

# BAT at different O:C ratios (returns organic activity)
colors = plt.cm.get_cmap("viridis")(np.linspace(0.2, 0.8, len(o2c_values)))
for o2c, color in zip(o2c_values, colors):
    strat = (
        par.particles.ActivityNonIdealBinaryBuilder()
        .set_molar_mass(200.0, "g/mol")
        .set_oxygen2carbon(o2c)
        .set_density(1200.0, "kg/m^3")
        .build()
    )
    bat_organic = [
        float(strat.activity(mass_concentration=np.array([wf, 1 - wf]) * 1e-9))
        for wf in water_fractions
    ]
    ax.plot(
        water_fractions,
        bat_organic,
        "-",
        color=color,
        linewidth=2,
        label=f"O:C={o2c}",
    )

ax.set_xlabel("Water Mass Fraction", fontsize=12)
ax.set_ylabel("Organic Activity", fontsize=12)
ax.set_title("Effect of O:C Ratio on Organic Activity (BAT Model)", fontsize=14)
ax.legend(fontsize=10, loc="lower right")
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
plt.tight_layout()
plt.show()

# Test different O:C ratios o2c_values = [0.1, 0.3, 0.5, 0.7] water_fractions = np.linspace(0.1, 0.9, 40) fig, ax = plt.subplots(figsize=(8, 5)) # Ideal reference (organic activity) ideal_organic = [ ideal_strategy.activity(mass_concentration=np.array([wf, 1 - wf]) * 1e-9)[1] for wf in water_fractions ] ax.plot(water_fractions, ideal_organic, "k--", linewidth=1.5, label="Ideal") # BAT at different O:C ratios (returns organic activity) colors = plt.cm.get_cmap("viridis")(np.linspace(0.2, 0.8, len(o2c_values))) for o2c, color in zip(o2c_values, colors): strat = ( par.particles.ActivityNonIdealBinaryBuilder() .set_molar_mass(200.0, "g/mol") .set_oxygen2carbon(o2c) .set_density(1200.0, "kg/m^3") .build() ) bat_organic = [ float(strat.activity(mass_concentration=np.array([wf, 1 - wf]) * 1e-9)) for wf in water_fractions ] ax.plot( water_fractions, bat_organic, "-", color=color, linewidth=2, label=f"O:C={o2c}", ) ax.set_xlabel("Water Mass Fraction", fontsize=12) ax.set_ylabel("Organic Activity", fontsize=12) ax.set_title("Effect of O:C Ratio on Organic Activity (BAT Model)", fontsize=14) ax.legend(fontsize=10, loc="lower right") ax.set_xlim(0, 1) ax.set_ylim(0, 1) plt.tight_layout() plt.show()

Higher O:C ratios (more polar organics) show behavior closer to ideal, while low O:C ratios (hydrophobic organics) show stronger non-ideality.

---

3. Kappa Hygroscopic Parameter¶

The kappa parameter ($\kappa$) provides a single-parameter representation of hygroscopicity from the Kohler equation. It relates the dry particle volume to water activity:

$$a_w = \frac{V_w}{V_w + \kappa V_s}$$

where $V_w$ is water volume and $V_s$ is solute volume.

Common kappa values:

• Ammonium sulfate: $\kappa \approx 0.61$
• Sodium chloride: $\kappa \approx 1.28$
• Organics: $\kappa \approx 0.1$ (variable)

3.1 Creating a Kappa Parameter Strategy¶

In [ ]:

# Water + ammonium sulfate system
kappa_strategy = par.particles.ActivityKappaParameter(
    kappa=np.array([0.0, 0.61]),  # water, (NH4)2SO4
    density=np.array([1000.0, 1770.0]),  # kg/m^3
    molar_mass=np.array([18.015e-3, 132.14e-3]),  # kg/mol
    water_index=0,
)

print(f"Strategy: {type(kappa_strategy).__name__}")
print(f"Kappa values: {kappa_strategy.kappa}")

# Water + ammonium sulfate system kappa_strategy = par.particles.ActivityKappaParameter( kappa=np.array([0.0, 0.61]), # water, (NH4)2SO4 density=np.array([1000.0, 1770.0]), # kg/m^3 molar_mass=np.array([18.015e-3, 132.14e-3]), # kg/mol water_index=0, ) print(f"Strategy: {type(kappa_strategy).__name__}") print(f"Kappa values: {kappa_strategy.kappa}")

3.2 Water Activity at Different Compositions¶

In [ ]:

# Compute water activity at different water contents
print("Water Activity for Water + Ammonium Sulfate:")
print("Water Fraction | Water Activity")
print("-" * 35)

for water_frac in [0.3, 0.5, 0.7, 0.9]:
    mass = np.array([water_frac, 1.0 - water_frac]) * 1e-9
    activity = kappa_strategy.activity(mass_concentration=mass)
    print(f"    {water_frac:.1f}        |     {activity[0]:.4f}")

# Compute water activity at different water contents print("Water Activity for Water + Ammonium Sulfate:") print("Water Fraction | Water Activity") print("-" * 35) for water_frac in [0.3, 0.5, 0.7, 0.9]: mass = np.array([water_frac, 1.0 - water_frac]) * 1e-9 activity = kappa_strategy.activity(mass_concentration=mass) print(f" {water_frac:.1f} | {activity[0]:.4f}")

3.3 Visualization: Kappa Activity vs Composition¶

In [ ]:

# Compare different kappa values
kappa_values = [0.1, 0.3, 0.61, 1.0]
water_fractions = np.linspace(0.2, 0.95, 40)

fig, ax = plt.subplots(figsize=(8, 5))

colors = plt.cm.get_cmap("plasma")(np.linspace(0.2, 0.8, len(kappa_values)))
for kappa, color in zip(kappa_values, colors):
    strat = par.particles.ActivityKappaParameter(
        kappa=np.array([0.0, kappa]),
        density=np.array([1000.0, 1500.0]),
        molar_mass=np.array([18.015e-3, 100.0e-3]),
        water_index=0,
    )
    water_activities = [
        strat.activity(mass_concentration=np.array([wf, 1 - wf]) * 1e-9)[0]
        for wf in water_fractions
    ]
    ax.plot(
        water_fractions,
        water_activities,
        "-",
        color=color,
        linewidth=2,
        label=f"$\\kappa$={kappa}",
    )

ax.set_xlabel("Water Mass Fraction", fontsize=12)
ax.set_ylabel("Water Activity", fontsize=12)
ax.set_title("Effect of Kappa on Water Activity", fontsize=14)
ax.legend(fontsize=11)
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
plt.tight_layout()
plt.show()

# Compare different kappa values kappa_values = [0.1, 0.3, 0.61, 1.0] water_fractions = np.linspace(0.2, 0.95, 40) fig, ax = plt.subplots(figsize=(8, 5)) colors = plt.cm.get_cmap("plasma")(np.linspace(0.2, 0.8, len(kappa_values))) for kappa, color in zip(kappa_values, colors): strat = par.particles.ActivityKappaParameter( kappa=np.array([0.0, kappa]), density=np.array([1000.0, 1500.0]), molar_mass=np.array([18.015e-3, 100.0e-3]), water_index=0, ) water_activities = [ strat.activity(mass_concentration=np.array([wf, 1 - wf]) * 1e-9)[0] for wf in water_fractions ] ax.plot( water_fractions, water_activities, "-", color=color, linewidth=2, label=f"$\\kappa$={kappa}", ) ax.set_xlabel("Water Mass Fraction", fontsize=12) ax.set_ylabel("Water Activity", fontsize=12) ax.set_title("Effect of Kappa on Water Activity", fontsize=14) ax.legend(fontsize=11) ax.set_xlim(0, 1) ax.set_ylim(0, 1) plt.tight_layout() plt.show()

Higher kappa values (more hygroscopic) result in lower water activity at the same water content, driving more water uptake to reach equilibrium.

---

4. Integration with Equilibria¶

Activity calculations integrate with liquid-vapor partitioning to determine how organic species distribute between gas and particle phases.

4.1 Liquid-Vapor Partitioning Strategy¶

In [ ]:

# Create partitioning strategy at 75% RH
partitioning = par.equilibria.LiquidVaporPartitioningStrategy(
    water_activity=0.75,
)

print(f"Strategy: {type(partitioning).__name__}")
print(f"Target water activity: {partitioning.water_activity}")

# Create partitioning strategy at 75% RH partitioning = par.equilibria.LiquidVaporPartitioningStrategy( water_activity=0.75, ) print(f"Strategy: {type(partitioning).__name__}") print(f"Target water activity: {partitioning.water_activity}")

4.2 Solving for Equilibrium¶

In [ ]:

# Define organic species (3 volatility classes)
c_star_j_dry = np.array([1e-6, 1e-4, 1e-2])  # saturation conc (ug/m^3)
concentration_organic = np.array([1.0, 5.0, 10.0])  # ug/m^3
molar_mass = np.array([200.0, 200.0, 200.0])  # g/mol
o2c_ratio = np.array([0.2, 0.3, 0.5])
density = np.array([1200.0, 1200.0, 1200.0])  # kg/m^3

# Solve for equilibrium
result = partitioning.solve(
    c_star_j_dry=c_star_j_dry,
    concentration_organic_matter=concentration_organic,
    molar_mass=molar_mass,
    oxygen2carbon=o2c_ratio,
    density=density,
)

print("=== Equilibrium Results ===")
print(f"Partition coefficients: {result.partition_coefficients}")
print(f"Alpha phase water: {result.alpha_phase.water_concentration:.2f} ug/m^3")
print(f"Optimization error: {result.error:.2e}")

# Define organic species (3 volatility classes) c_star_j_dry = np.array([1e-6, 1e-4, 1e-2]) # saturation conc (ug/m^3) concentration_organic = np.array([1.0, 5.0, 10.0]) # ug/m^3 molar_mass = np.array([200.0, 200.0, 200.0]) # g/mol o2c_ratio = np.array([0.2, 0.3, 0.5]) density = np.array([1200.0, 1200.0, 1200.0]) # kg/m^3 # Solve for equilibrium result = partitioning.solve( c_star_j_dry=c_star_j_dry, concentration_organic_matter=concentration_organic, molar_mass=molar_mass, oxygen2carbon=o2c_ratio, density=density, ) print("=== Equilibrium Results ===") print(f"Partition coefficients: {result.partition_coefficients}") print(f"Alpha phase water: {result.alpha_phase.water_concentration:.2f} ug/m^3") print(f"Optimization error: {result.error:.2e}")

4.3 Effect of RH on Partitioning¶

In [ ]:

# Calculate partitioning at different RH values
rh_values = np.linspace(0.3, 0.95, 20)
mean_partitions = []
water_contents = []

for rh in rh_values:
    strat = par.equilibria.LiquidVaporPartitioningStrategy(water_activity=rh)
    res = strat.solve(
        c_star_j_dry=c_star_j_dry,
        concentration_organic_matter=concentration_organic,
        molar_mass=molar_mass,
        oxygen2carbon=o2c_ratio,
        density=density,
    )
    mean_partitions.append(np.mean(res.partition_coefficients))
    water_contents.append(res.alpha_phase.water_concentration)

# Plot
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4.5))

ax1.plot(rh_values * 100, mean_partitions, "b-", linewidth=2)
ax1.set_xlabel("Relative Humidity (%)", fontsize=12)
ax1.set_ylabel("Mean Partition Coefficient", fontsize=12)
ax1.set_title("Partitioning vs RH", fontsize=14)
ax1.set_xlim(30, 100)

ax2.plot(rh_values * 100, water_contents, "g-", linewidth=2)
ax2.set_xlabel("Relative Humidity (%)", fontsize=12)
ax2.set_ylabel("Water Content ($\\mu$g/m$^3$)", fontsize=12)
ax2.set_title("Water Uptake vs RH", fontsize=14)
ax2.set_xlim(30, 100)

plt.tight_layout()
plt.show()

# Calculate partitioning at different RH values rh_values = np.linspace(0.3, 0.95, 20) mean_partitions = [] water_contents = [] for rh in rh_values: strat = par.equilibria.LiquidVaporPartitioningStrategy(water_activity=rh) res = strat.solve( c_star_j_dry=c_star_j_dry, concentration_organic_matter=concentration_organic, molar_mass=molar_mass, oxygen2carbon=o2c_ratio, density=density, ) mean_partitions.append(np.mean(res.partition_coefficients)) water_contents.append(res.alpha_phase.water_concentration) # Plot fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4.5)) ax1.plot(rh_values * 100, mean_partitions, "b-", linewidth=2) ax1.set_xlabel("Relative Humidity (%)", fontsize=12) ax1.set_ylabel("Mean Partition Coefficient", fontsize=12) ax1.set_title("Partitioning vs RH", fontsize=14) ax1.set_xlim(30, 100) ax2.plot(rh_values * 100, water_contents, "g-", linewidth=2) ax2.set_xlabel("Relative Humidity (%)", fontsize=12) ax2.set_ylabel("Water Content ($\\mu$g/m$^3$)", fontsize=12) ax2.set_title("Water Uptake vs RH", fontsize=14) ax2.set_xlim(30, 100) plt.tight_layout() plt.show()

---

Summary¶

In this tutorial, we covered:

1. Ideal Activity (Raoult's Law): Activity equals mole fraction for ideal mixtures
2. Non-Ideal Activity (BAT): Activity coefficients deviate from 1, especially for low O:C organics
3. Kappa Parameter: Single-parameter representation of hygroscopicity for water activity
4. Equilibria Integration: Activity determines gas-particle partitioning

Key Takeaways¶

• Choose your activity model based on your system:
  • Simple mixtures: ActivityIdealMolar
  • Hygroscopic aerosols: ActivityKappaParameter
  • Organic-water mixtures: ActivityNonIdealBinary (BAT)
• Non-ideality is important for accurate aerosol thermodynamics
• Higher RH increases water uptake and organic partitioning

Next Steps¶

• Activity Theory - Mathematical foundations
• Equilibria Theory - Partitioning equations
• Activity System Feature Guide - Full API documentation