Oxygen Transmission Rate Calculation

Calculate and understand the oxygen permeability of materials.

OTR Calculation Tool

Enter the required parameters to calculate the Oxygen Transmission Rate (OTR).

What is Oxygen Transmission Rate (OTR)?

Oxygen Transmission Rate (OTR) is a critical material property that quantifies the rate at which oxygen gas passes through a specific material per unit area, over a given time, under a defined pressure differential. It's a key indicator of a material's barrier performance against oxygen ingress, essential for industries like food packaging, pharmaceuticals, electronics, and medical devices where maintaining specific atmospheric conditions is vital for product integrity, shelf life, and efficacy.

Understanding OTR helps manufacturers select the appropriate packaging materials to protect sensitive products from oxidative degradation. For instance, fresh produce requires packaging with a moderate OTR to allow respiration, while highly perishable items or sensitive electronics demand very low OTR to prevent spoilage or damage. Common misunderstandings often arise from the variety of units used to express OTR, making direct comparisons difficult without proper conversion and context.

Who should use this OTR calculator?

• Packaging engineers
• Material scientists
• Product developers
• Quality control specialists
• Researchers
• Anyone involved in selecting or testing barrier materials.

OTR Formula and Explanation

The fundamental calculation for Oxygen Transmission Rate (OTR) is derived from Fick's Law of Diffusion, adapted for gas permeation through a material. The most common form expresses OTR as the volume of oxygen transmitted over time, per unit area, and per unit pressure difference.

The core formula used in this calculator is:

OTR = (Oxygen Volume Transmitted / Time) / (Area * Pressure Differential)

Let's break down the variables:

Variables and Units for OTR Calculation

Variable	Meaning	Unit (Common)	Typical Range (Example)
Oxygen Volume Transmitted	The total amount of oxygen that has passed through the material sample.	cc (cubic centimeters) or g (grams)	1 – 1000 cc
Time	The duration over which the oxygen transmission was measured.	day (days) or sec (seconds)	1 – 72 hours (0.04 – 3 days)
Area	The effective surface area of the material sample exposed to oxygen.	m² (square meters) or 100 in² (hundred square inches)	0.0001 – 0.1 m²
Pressure Differential	The difference in oxygen partial pressure across the material. Often assumed to be 1 atm if one side is pure oxygen and the other is vacuum or nitrogen.	atm (atmospheres) or Pa (Pascals)	0.1 – 1 atm

Intermediate Calculations:

• Rate of Transmission: Oxygen Volume Transmitted / Time
• Oxygen Flux: (Oxygen Volume Transmitted / Time) / Area
• Permeance: Oxygen Flux / Pressure Differential

The calculator then converts these intermediate values into the selected output units.

Practical Examples of OTR

Here are a couple of scenarios illustrating OTR calculations:

Example 1: Low-Barrier Plastic Film

A manufacturer is testing a basic polyethylene film for packaging snacks. They run a test where 50 cc of oxygen permeates through a 0.05 m² sample in 24 hours, under a standard pressure differential of 1 atm. The film is intended for products needing moderate protection.

• Oxygen Volume Transmitted: 50 cc
• Time: 24 hours (1 day)
• Area: 0.05 m²
• Pressure Differential: 1 atm
• Selected Units: cc / m² / day / atm

Calculation:

OTR = (50 cc / 1 day) / (0.05 m² * 1 atm) = 1000 cc / m² / day / atm

Result: The OTR is 1000 cc/m²/day/atm. This value indicates a relatively high oxygen transmission, suitable for products that are not extremely sensitive to oxidation or have a short shelf-life requirement.

Example 2: High-Barrier Film (Unit Conversion Scenario)

A company is evaluating a specialized multi-layer film for sensitive pharmaceutical packaging. A test shows 2 cc of oxygen permeated through a 100 square inch area in 48 hours (2 days), with a pressure differential of 1 atm. They need the result in the more common metric unit (cc/m²/day/atm).

• Oxygen Volume Transmitted: 2 cc
• Time: 48 hours (2 days)
• Area: 100 in²
• Pressure Differential: 1 atm
• Selected Units: cc / m² / day / atm

First, convert the area: 100 in² * (0.0254 m/in)² ≈ 0.0645 m²

Calculation:

OTR = (2 cc / 2 days) / (0.0645 m² * 1 atm) = 1 cc / day / 0.0645 m² / atm ≈ 15.5 cc / m² / day / atm

Result: The OTR is approximately 15.5 cc/m²/day/atm. This significantly lower OTR indicates excellent barrier properties, making it suitable for long-term preservation of oxygen-sensitive pharmaceuticals.

How to Use This OTR Calculator

Using the Oxygen Transmission Rate calculator is straightforward:

1. Input Oxygen Volume: Enter the measured volume of oxygen that passed through the material sample. Use consistent units (e.g., cubic centimeters, grams).
2. Input Time: Specify the duration of the test in days or seconds, depending on the material's permeability and the chosen unit system.
3. Input Area: Enter the surface area of the material sample. Ensure units align with your selected output (e.g., square meters, square inches).
4. Input Pressure Differential: Enter the difference in oxygen partial pressure across the material. This is often 1 atm for standard tests but can vary.
5. Select Units: Choose the desired output unit for OTR from the dropdown menu. Common units include metric (cc/m²/day/atm) and imperial (cc/100in²/day/atm).
6. Calculate: Click the "Calculate OTR" button.

Interpreting Results: The calculator will display the calculated OTR value, along with intermediate values like rate, flux, and permeance. A lower OTR value signifies better oxygen barrier performance.

Resetting: Click the "Reset" button to clear all fields and return to default values.

Copying Results: Use the "Copy Results" button to quickly copy the calculated OTR, intermediate values, and unit assumptions to your clipboard for reports or further analysis.

Key Factors That Affect Oxygen Transmission Rate

Several factors influence the OTR of a material, impacting its effectiveness as an oxygen barrier:

1. Material Type: Different polymers have inherently different molecular structures and densities, affecting their gas permeability. For example, PET and EVOH are known for good OTR, while LDPE is less effective.
2. Material Thickness: Generally, a thicker material will have a lower OTR, as oxygen has a longer path to diffuse through. However, the relationship isn't always linear and depends on the material's specific permeation properties.
3. Temperature: Higher temperatures increase the kinetic energy of gas molecules and can increase the free volume within the polymer matrix, leading to higher OTR. This is a critical factor for products stored under varying temperature conditions.
4. Humidity: For some materials, particularly polar polymers like nylon or cellulosic films, absorbed moisture can plasticize the material, increasing chain mobility and thus increasing OTR.
5. Pressure Differential: A higher pressure difference of oxygen across the material will drive a higher rate of transmission, as per Fick's Law.
6. Chemical Structure & Morphology: Crystallinity, presence of fillers, orientation, and the specific chemical bonds within a polymer significantly affect gas diffusion pathways and rates.
7. Multi-layer Structures: Co-extruded or laminated films often combine layers with different barrier properties (e.g., a barrier layer like EVOH sandwiched between structural layers like PE or PP) to achieve a very low overall OTR.

FAQ: Oxygen Transmission Rate

What are the standard units for OTR?

Common units include cc/(m²·day·atm) (metric) and cc/(100in²·day·atm) (imperial). Other units like g/(m²·day·atm) or mol/(m²·s·Pa) are also used, especially in scientific contexts. This calculator supports conversion between several common units.

How does OTR relate to water vapor transmission rate (WVTR)?

OTR measures oxygen permeation, while WVTR measures water vapor permeation. Both are critical barrier properties, but they are distinct. A material might have excellent OTR but poor WVTR, or vice versa. Both need to be considered based on the product's requirements.

Is a lower OTR always better?

Not necessarily. For products like fresh produce that respire, a specific OTR is needed to allow gas exchange. For highly oxygen-sensitive products (e.g., certain pharmaceuticals, fats, oils), a lower OTR is indeed crucial for extending shelf life and maintaining quality.

How is OTR typically measured?

OTR is usually measured using coulometric or infrared sensor-based instruments (like MOCON/AMETEK or Illinois Instruments testers) under controlled temperature and humidity conditions, following standardized test methods (e.g., ASTM D3985, ISO 15105-1).

Can OTR change over time?

Yes. For some materials, OTR can change due to factors like long-term exposure to UV light, oxidation of the material itself, or changes in morphology. Also, the barrier properties of some films (like EVOH) can degrade significantly if humidity is not controlled.

What is the difference between Permeability, Permeance, and Flux?

Permeability (P): An intrinsic property of the material itself, independent of thickness. Units: (Volume * Thickness) / (Area * Time * Pressure Difference).
Permeance (P_p): The overall ease with which a gas permeates a *specific* film of a given thickness. Units: Permeability / Thickness.
Flux (J): The rate of permeation per unit area. Units: (Volume / Time) / Area.

How do I convert OTR units manually?

Conversions require careful application of conversion factors for volume (e.g., cc to g based on oxygen density), area (m² to in²), time (days to seconds), and pressure (atm to Pa). For example, 1 atm ≈ 101325 Pa. 1 m² ≈ 1550 in². Ensure consistency in all units during conversion.

What is a typical OTR range for food packaging?

It varies widely. For items needing respiration (fresh salads), OTR might be 1000-10000 cc/m²/day/atm. For snacks or baked goods needing protection from staleness, 50-500 cc/m²/day/atm is common. For highly sensitive foods or long-shelf-life products, OTR below 10 cc/m²/day/atm is often desired.