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Molecular Weights, Polymers, & Polymer Solutions adhunter/Teaching/Chem5861/Chemistry5861.Notes.2...Molecular Weights, Polymers, & Polymer Solutions (Part I ... Some Important Methods

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  • Chemistry 5861 - Polymer Chemistry 1

    Molecular Weights, Polymers, & Polymer Solutions (Part I - Chapter 2 in Stevens)1

    I Number and Weight Average Molecular Weight - An Introduction

    Importance of MW and MW Distribution A)

    1)

    a)

    2)

    a)

    b)

    3)

    a)

    b)

    Optimum MW, MW Distribution, etc.

    depends upon application via processing and performance tradeoffs

    Typical MW values for commercial polymers

    Vinyl polymers in the 105 and 106 range

    Strongly H-bonding polymers in the 104 range

    i)

    i)

    ii)

    iii)

    iv)

    v)

    vi)

    e.g., 15,000 - 20,000 for Nylon

    MW Determinations (many more details later in chapter)

    We wish to determine both average values of MW and information about MW

    distribution

    Some Important Methods

    Gel Permeation Chromatography, GPC

    Light Scattering

    Viscometry

    Mass Spectroscopy

    End Group Analysis (Chemical & Spectroscopic)

    Colligative Properties (P-Chem Methods)

    Boiling Point Elevation

    Freezing Depression (Cryoscopy)

    1 The graphics in these notes indicated by Figure/Table/Equation/Etc., x.x in Stevens are taken from our lecture text: Polymer Chemistry: An Introduction - 3rd Edition Malcolm P. Stevens (Oxford University Press, New York,

    2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry

  • Chemistry 5861 - Polymer Chemistry 2

    B)

    Osmometry, etc.

    Number Average Molecular Weight, Mn bar

    1)

    a)

    2)

    3)

    a)

    C)

    This term is very sensitive to the total number of molecules in solution and hence is

    especially sensitive to the low molecular weight monomers and oligomers

    Determined by End Group Analysis and Colligative Properties

    Mn bar = NiMi / Ni

    Example

    9 moles of MW = 30,000 and 5 moles of MW = 50,000 Mn bar 37,000

    Weight Average Molecular Weight, Mw bar

    1)

    a)

    2)

    3)

    a)

    4)

    This term is sensitive to the mass of the molecules in solution and hence is especially

    sensitive to the very highest MW species present in the system

    Determined by Light Scattering and Ultracentrifugation

    Mw bar = WiMi / Wi = NiMi2 / NiMi

    Example

    9 moles of MW = 30,000 and 5 moles of MW = 50,000 Mw bar 40,000

    Note:

    a)

    b)

    c)

    Mw bar Mn bar (Draw MW distribution chart)

    Mw bar/Mn bar = Polydispersity Index

    Mw bar/Mn bar = 1, Mw bar = Mn bar for a sample having a single MW

    (Monodisperse)

    1999).

    2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry

  • Chemistry 5861 - Polymer Chemistry 3

    d)

    D)

    Mw bar/Mn bar 1 is Polydisperse

    General Molecular Weight Expression & Mz bar and Mv bar

    1)

    2)

    a)

    3)

    a)

    b)

    II

    M bar = NiMi(a+1) / NiMia

    A Higher Order MW, called the Z average, is closely related to processing

    characteristics a = 2

    Mz bar = NiMi(2+1) / NiMi2 = NiMi3) / NiMi2

    A viscosity based MW, Mv bar, has 0 a 1 and closer to 1 (i.e., to Mw bar)

    MV bar = NiMi(1.x) / NiMi0.x

    i)

    ii)

    i)

    ii)

    iii)

    Where x is typically close to 1 and 1.x is typically close to 2

    MV bar = NiMi(1.9) / NiMi0.9 in a typical case

    Mz bar Mw bar Mv bar Mn bar

    Polymer Solutions

    Steps Dissolving a Discrete Molecule and a Polymer A)

    1)

    a)

    2)

    a)

    Discrete Molecule Dissolution Steps for a Crystalline Sample

    Polymer Dissolution Steps

    solvent diffusion

    solvation & swelling

    Gel formation

    network polymers stop at this stage, degree of swelling correlated with

    crosslink density

    2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry

  • Chemistry 5861 - Polymer Chemistry 4

    b)

    B)

    True dissolution

    i)

    ii)

    untangling of chains

    very slow process and may not occur on timescale of real world

    Thermodynamics of Polymer Dissolution

    1)

    a)

    b)

    2)

    a)

    b)

    c)

    3)

    a)

    b)

    c)

    4)

    5)

    C)

    Choosing a Solvent for Polymers

    Polymer Handbook!!!!! lists solvents and nonsolvents for common polymers

    Rule of Thumb: Like dissolves Like

    G = H - TS

    G must be negative for spontaneous (but not necessarily fast) dissolution

    S will be positive because of greater mobility in solution

    need H to be negative or at least not too positive

    Hmix (1 - 2)2

    Hmix is the Enthalpy of mixing (dissolution)

    1 is the Solubility Parameter of one component

    2 is the Solubility Parameter of the other component

    In practice, H is seldom negative and we simply try to keep it from getting too

    positive

    we see that we want the polymer and the solvent to have as similar of Solubility

    Parameters as possible

    Solubility Parameters,

    1) The Parameters is related to the heat of vaporization of the sample

    2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry

  • Chemistry 5861 - Polymer Chemistry 5

    2)

    3)

    a)

    4)

    a)

    For small molecules these can be measured experimentally

    the Parameters of solvents are tabulated

    multiple parameter expressions can also be used for more precision

    For conventional polymers these can be estimated using tables

    Group Molar Attraction Constants

    b)

    c)

    D)

    Table 2.1 in Stevens

    = d G / M

    i)

    ii)

    iii)

    G = the individual Group Molar Attraction Constants of each structural

    fragment

    d = density

    M = molecular weight

    Hydrodynamic Volume in Solution

    1)

    2)

    The apparent size of the polymer in solution

    Reflects both the polymer chain itself and the solvating molecules in inner and outer

    spheres

    3)

    4)

    a)

    b)

    Figure 2.1 in Stevens

    Hydrodynamic Volume is related to an

    Expansion Factor,

    = 1 is the value for the non-expanded polymer in the ideal statistical coil

    having the smallest possible size

    as increases, so does the Hydrodynamic Volume of the sample

    2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry

  • Chemistry 5861 - Polymer Chemistry 6

    E) The Theta State ()

    1)

    2)

    3)

    4)

    F)

    Solubility varies with temperature and the nature of the solvent

    there will be a minimal dissolution temperature call the Theta Temperature and at

    that point the solvent is said to be the Theta Solvent

    The Theta State at this point is the one in which the last of the polymer is about to

    precipitate

    Compilations of Theta Temperatures & Solvents are available in the literature

    Intrinsic Viscosity & Molecular Weight

    1)

    2)

    a)

    b)

    c)

    III

    [] = Intrinsic Viscosity (i.e., the viscosity in an Ideal Solution)

    Mark- Houwink-Sakurada Equation

    [] = K (Mv bar)a

    K and a are characteristic of the particular solvent/polymer combination (more

    later)

    Mv bar = the Viscosity Average Molecular Weight

    Measurement of Number Average Molecular Weight

    A) General Considerations

    1)

    a)

    Ideal Instrument

    Gives full information on the molecular weight distributions for sample

    i)

    ii)

    Reliable for all species in sample from monomers to crosslinked polymers

    From this MW distribution can be extracted mathematically for the

    various types of MW averages (Mw bar, Mn bar, Mv bar, etc.)

    2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry

  • Chemistry 5861 - Polymer Chemistry 7

    iii)

    iv)

    i)

    i)

    ii)

    iii)

    i)

    i)

    Highly sensitive so can use small & very dilute samples

    Data quality

    b)

    c)

    2)

    a)

    b)

    c)

    d)

    e)

    f)

    B)

    highly accurate

    highly precise

    Requires no calibration

    Neither at the start of each run nor for different types of samples

    Cost and convenience

    low cost to buy and maintain

    highly reliable/robust

    easy to operate

    Real Instruments

    Most methods give only averages

    exceptions are: GPC, Light Scattering, & MS

    Most methods results vary depending on the structure of the sample

    need to calibrate each sample and/or know some structural information

    such as branching

    Most methods have limited sensitivities and/or linear ranges

    Most methods require expensive instrumentation

    There can be substantial disagreements between the results of different techniques

    However, many methods are improving in these areas rapidly

    End-Group Analysis

    1) Basic principles

    2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry

  • Chemistry 5861 - Polymer Chemistry 8

    a)

    b)

    c)

    2)

    a)

    b)

    c)

    3)

    a)

    b)

    c)

    The structures of the end groups must be different from that of the bulk repeating

    units (e.g., CH3 vs. CH2 in an ideal polyethylene)

    If you detect the concentra

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