#5 Molecular Weight & Distribution | Polymers Concepts, Properties, Uses & Sustainability

Name: #5 Molecular Weight & Distribution | Polymers Concepts, Properties, Uses & Sustainability
Uploaded: 2020-09-28T05:29:22.000Z
Duration: 1 h 14 min 29 s

Introduction to Molecular Weight in Polymers

Overview of the Lecture

This lecture introduces molecular weight and its distribution, focusing on polymers and their unique features. The course aims to explore various aspects from concepts to properties, applications, and sustainability.

Key Questions Addressed

The primary questions include: What are polymers? What are their unique features? The focus is on estimation, quantification, and properties related to molecular weight.

Influence of Molecular Weight on Properties

Effect on Melting Point

Higher molecular weight typically leads to higher melting temperatures due to increased thermal energy required for mobility. This relationship is exemplified by comparing sugar molecules like fructose, glucose, and sucrose.

Viscosity Considerations

The viscosity of alkanes (e.g., pentane, hexane) at 25°C is influenced by molecular weight; expectations suggest that higher molecular weights result in higher viscosities. Students are encouraged to verify this through research.

Diffusion Coefficient in Proteins

Importance of Molecular Size

In biological contexts, the diffusion coefficient determines how proteins move within cells; larger proteins generally have lower diffusion coefficients due to size constraints affecting movement. Flux is defined as the product of diffusion coefficient and concentration gradient.

Variability in Macromolecules

Unlike specific proteins with fixed molecular weights, biopolymers like starch exhibit a range of molecular weights depending on species and location within an organism (e.g., collagen tissue). This variability impacts their functional roles significantly.

Experimental Data on Diffusion Coefficients

Trends Observed

Experimental data shows a clear trend: as protein size increases (molecular weight), the diffusion coefficient decreases significantly across a wide range (10^4 to 10^7). This trend highlights the inverse relationship between size and diffusivity in macromolecules.

Quantitative Analysis

Understanding Protein Diffusion and Molecular Weight

The Nature of Protein Movement in Water

Discussion on how proteins are surrounded by water and the importance of understanding their diffusion coefficient.

Explanation of protein shape (spherical or cylindrical) and its impact on diffusion in a water medium.

Molecular Weight and Polymerization Theories

Introduction to two theories regarding molecular weight: ideal chain (radius proportional to N^0.5) and expanded chain (radius proportional to N^0.6), where N is the degree of polymerization.

Emphasis on the significance of molecular size in defining macromolecular properties, including considerations for linear versus branched macromolecules.

Macromolecular Architecture

Overview of block copolymers, specifically diblock copolymers, highlighting the need to specify block types and lengths.

Example provided with polyethylene and polypropylene blocks, illustrating how to denote different block lengths in a copolymer structure.

Cross-Linking Systems

Importance of quantifying cross-link density per unit volume or segment length between cross-link points for understanding macromolecule behavior.

Molar Mass Distribution in Polymers

Clarification on terminology: "molecular weight" vs. "molar mass," with an emphasis on scientific accuracy versus common usage.

Description of polydisperse polymers containing macromolecules with varying molar masses compared to monodisperse polymers that have uniform molar mass.

Biological Implications of Polymerization

Proteins as examples of monodisperse polymers due to their specific tasks linked to precise structures determined by molecular weight.

Contrast drawn between proteins and polysaccharides regarding uniformity in molecular weight distribution during biological processes.

Understanding Molar Mass Distribution

Introduction to measuring relative distribution using polydispersity index; distinction made between discrete and continuous molar mass distributions.

Understanding Macromolecular Distribution

Introduction to Macromolecules

The course begins with the application of mathematical equations and principles to derive important results for understanding macromolecules, focusing primarily on discrete variables.

Key Variables in Macromolecular Samples

The variable i represents the number of repeating units in a macromolecule, which can vary significantly among different samples (e.g., 400 or 405 units).

N_i denotes the number of macromolecules that contain i repeating units, allowing for a complete specification of distribution when both i and N_i are known.

Mass Calculations in Macromolecules

The mass of molecules with i repeating units is calculated as i times M_0 , where M_0 is the molar mass of a single repeating unit.

To find the total mass of macromolecules with i repeating units, multiply N_i (the count of such molecules) by their individual mass iM_0 .

Distribution and Averages

A distribution plot can be created showing the number of repeating units against corresponding counts, providing insight into molar mass distributions within a sample.

Continuous distributions are introduced through probability density functions (PDF), where P(m)dM describes the distribution similar to traditional PDFs.

Polymerization Methods and Their Impact

The method used for polymerization significantly influences molar mass distribution; examples will be discussed in future lectures regarding step-growth polymerization.

Calculating Average Molar Masses

To calculate average masses, one must sum all masses from macromolecules containing various numbers of repeating units using defined quantities like N_i .

The overall mass can be derived from summing products of N_i times M_i , leading to insights about total sample weight.

Defining Number and Weight Average Molar Masses

Two common methods for defining average molar mass include:

Number average: Total weight divided by total number ( W_T/N_T ).

Weight average: Incorporates weighting factors based on molar masses raised to different powers.

Understanding Molar Mass and Its Distribution in Macromolecules

Key Concepts of Molar Mass

The concept of molar mass is defined through variables like mean, standard deviation, and mean square. The number average molecular weight (mean) is the summation of individual molecular weights (M_i), while the mean square relates to M_i squared.

Number average molar mass correlates with mechanical properties, while weight average molar mass is crucial for understanding material behavior. Different definitions exist based on measurement techniques and applications.

Importance of Molar Mass Distribution

The distribution of molar masses in macromolecules significantly impacts their application-specific properties. Identifying which fraction contributes most to a property can be challenging due to this distribution.

Various types of average molar masses are defined: number average, weight average, viscosity average, and z-average. Each type serves different purposes in correlating engineering properties with polymer characteristics.

Mark-Houwink Relation

The parameter aMH indicates polymer-solvent interactions and solution behavior. This relationship will be explored further in future lectures, specifically regarding intrinsic viscosity.

The Mark-Houwink equation acknowledges contributions from multiple scientists and provides insights into how different fractions affect flowability and mechanical strength.

Polydispersity Index

Average molar mass alone does not suffice; understanding the distribution is essential. The polydispersity index (D), defined as the ratio of weight average to number average molar mass, quantifies this distribution effectively.

D values are always greater than or equal to 1; when D equals 1, it indicates uniform or monodisperse polymers. This measure helps assess the diversity within a polymer sample's molecular weights.

Practical Application in Calculations

An example problem illustrates calculating the polydispersity index using given macromolecule masses instead of repeating units. Understanding notation is critical for accurate calculations.

Clarification on notation used for counting molecules with varying repeating units emphasizes careful consideration when determining quantities related to molecular distributions.

Understanding Probability Density Functions

Theoretical Foundations of Probability Density

The concept of p(M)dM represents the probability of locating a macromolecule with a molar mass between M and M + dM . This foundational idea is crucial for understanding distributions in statistical mechanics.

When summing probabilities from the smallest to the largest macromolecule, the total must equal 1. This principle illustrates the normalization requirement for probability density functions.

The term "normalization" refers to ensuring that the area under the probability density function equals one, confirming that it is a valid representation of probabilities across all possible values.

For educational purposes, focusing on discrete molar mass distribution and average quantities derived from it suffices, rather than delving into more complex continuous distributions.