Weight Average Molecular Weight Calculator

Weight Average Molecular Weight Formula:

\[ M_w = \frac{\sum (w_i \times M_i^2)}{\sum (w_i \times M_i)} \]

Weight Average Molecular Weight (M_w):

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1. What is Weight Average Molecular Weight?

The weight average molecular weight (M_w) is a way to characterize the molecular weight distribution of a polymer sample. It gives more weight to the heavier molecules in the distribution, making it particularly sensitive to the presence of high molecular weight species.

2. How Does the Calculator Work?

The calculator uses the weight average molecular weight formula:

\[ M_w = \frac{\sum (w_i \times M_i^2)}{\sum (w_i \times M_i)} \]

Where:

\( M_w \) — Weight average molecular weight (g/mol)
\( w_i \) — Weight fraction of component i (unitless)
\( M_i \) — Molecular weight of component i (g/mol)

Explanation: The weight average molecular weight is calculated by summing the products of each component's weight fraction and the square of its molecular weight, divided by the sum of the products of each component's weight fraction and its molecular weight.

3. Importance of M_w Calculation

Details: The weight average molecular weight is particularly important in polymer science as it strongly influences the mechanical properties of polymers. It's more sensitive to high molecular weight fractions than the number average molecular weight (M_n).

4. Using the Calculator

Tips:

Enter the number of components in your mixture
For each component, enter its weight fraction (between 0 and 1) and molecular weight
Ensure the sum of all weight fractions equals 1 for accurate results
Click "Calculate" to get the weight average molecular weight

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between M_w and M_n?
A: M_n (number average) gives equal weight to each molecule, while M_w (weight average) gives more weight to heavier molecules. M_w ≥ M_n, with equality only for monodisperse samples.

Q2: What does the polydispersity index (PDI) indicate?
A: PDI = M_w/M_n. A PDI of 1 indicates a monodisperse sample, while higher values indicate broader molecular weight distributions.

Q3: When is M_w more important than M_n?
A: M_w is more relevant for properties influenced by the heavier fractions, like melt viscosity and mechanical strength.

Q4: How do I determine weight fractions experimentally?
A: Weight fractions can be determined by techniques like gel permeation chromatography (GPC) or mass spectrometry.

Q5: Can this calculator be used for copolymers?
A: Yes, as long as you can define the weight fractions and molecular weights of the different components.