Nevertheless, a deeper understanding of the relationship between molecular structure properties is needed to make polymers with tailored structures. He was the first recipient of the Macromolecular Science and Engineering Award from the Chemical Institute of Canada in 1989.
Repeating Unit
The concept of a simple identifiable repeating unit loses some of its utility with polymers that are highly branched, with species consisting of interconnected branches, or with those macromolecules that are synthesized from more than a few different precursor monomers. little ones. Any deficiency in the general application of the term is not serious, since the concept of a repeating unit is actually used only when such groups of atoms are readily apparent.
Representations of Polymer Structures
This limitation of the definition will become clearer in context when some of these polymer types, such as alkyds (section 1.6), are discussed later in the text. Formula (b) would not normally be written because the nominal break is in the middle of an —OCH2CH2O— unit, which is the residue of one of the precursors (HOCH2CH2OH) actually used in syntheses of this polymer by the reaction:.
End Groups
Degree of Polymerization
Creating a new word for one of these concepts may make this book clearer, but may confuse the reader's understanding of the general literature, where the single term degree of polymerization is unfortunately used in both contexts.) . The relationship between the degree of polymerization and the molecular weight, M, of the same macromolecule is given by.
Polymerization and Functionality
Polymerization
This number will be equal to that in the definition mentioned above if the repeating unit is a single monomer residue. We use the abbreviation DP for the degree of polymerization defined here and X for the term explained later.
Functionality
If the ana-functional monomer reacts with the ab-functional monomer in a non-chain reaction, the functionality of the product molecule is a1b22. The use of the term functionality here is not the same as in organic chemistry where a carbon double bond, for example, is classified as a single functional group.
Latent Functionality
In this reaction the functionality of the bisphenol Aepichlorohydrin prepolymer will be 1-20 2 since hydroxyl groups are not involved and the functionality of each epoxide group is one. However, when the curing reaction involves cationic polymerization induced by a Lewis acid, the functionality of each epoxy group is 2 and that of structure 1-20 is 4. The general curing reaction is shown in Eq.
Why Are Synthetic Polymers Useful? [3]
1.1, where a mechanical property is plotted against the average number of repeating units in the polymer. "Zero-strength" molecular sizes will be inversely related to the strength of intermolecular forces of attraction, as shown in the figure.
Copolymers
- Random Copolymer
- Alternating Copolymer
- Graft Copolymer
- Block Copolymer
When styrene is polymerized by free-radical initiation, it reacts by adding double bonds of other styrene and rubber units, and the resulting product contains polystyrene grafts on the rubber as well as ungrafted rubber and polystyrene molecules. In this case, the rubber in a polybutadiene-in-water emulsion is swollen with a mixture of styrene and acrylonitrile monomers, which is then copolymerized in situ under the influence of a water-soluble free radical initiator.
Molecular Architecture
An example of the first type is the polymer made from, for example, glycerol, phthalic anhydride and linseed oil. The molecular weight of the polymer is not actually infinite, even if all the rubber in the tire is part of a single molecule (this is possible, at least in theory), since the size of the tire is limited.
Thermoplastics and Thermosets
This polymer is practically as resistant to high temperatures and high-energy radiation as pyrolytic graphite. The main advantage of this crosslinking is increased dimensional stability under loads and elevated temperatures.
Elastomers, Fibers, and Plastics
The mechanical properties of commercial synthetic fibers change in the temperature range between The intermolecular forces in polyolefins such as polyethylene (1-3) are quite small, but the structure of the polymer is so symmetrical and regular that the segments of the polymer in the molten state are not completely random.
Miscellaneous Terms
Not all plastics can form practical fibers, however, because the intermolecular forces or the tendency to crystallize may be too weak to achieve useful stable fibers. This excludes chemical species in which intermolecular forces are strong at the temperature of use or which crystallize rapidly.
Polymer Nomenclature
Some polymers have names based on the repeating unit without reference to the parent monomer. Polymers that can be made from amino acids are called nylon-x, where x is the number of carbon atoms in the repeating unit.
Constitutional Isomerism
Positional Isomerism
It has been suggested that the tail-to-tail linkages in vinyl polymers may constitute weak points at which thermal degradation can initiate more easily than in the dominant head-to-tail structures. Each isomer shown in reaction (1-17) can also exist in head-to-tail or head-to-tail, tail-to-tail forms, and thus six are possible.
Branching
An example is the use of divinylbenzene (1-62) in the polymerization of butadiene with butyl lithium (Section 12.2). This technique has great potential when bands in polymer spectra can be unambiguously determined.
Configurational Isomerism
Geometrical Isomerism
Stereoisomerism
The configurational nature of a vinyl polymer has profound effects on its physical properties when the configurations of the pseudo-asymmetric carbons are regular and the polymer is crystallizable. The importance of stereoregularity in vinyl polymers lies in its effect on the crystallisability of the material.
Polymer Conformation
It can be predicted from knowledge of the polymer configuration and the van der Waals radii of the chain substituents. This is the basis of ideal elastic behavior, which is described in more detail in Section 4.5.
Molecular Dimensions in the Amorphous State
Radius of Gyration and End-to-End Distance of Flexible Macromolecules
The end-to-end distance is not directly observable and has no meaning for branched species that have more than two points. -23) The end-to-end distance is more easily visualized than the radius of gyration and is more directly applicable in the molecular explanation of rubber elasticity.
Root Mean Square End-to-End Distance of Flexible Macromolecules
The root mean square (rms) end-to-end distance will be lσ1/2 from the above equation. When some conformations are favored over others (for example, in Figure 1.6), the chain sizes are further extended relative to those calculated, and Eq.
PROBLEMS
What is the fundamental difference in the state of the polymer in these two different applications. What is the functionality of the diglycidyl ether of bisphenol A(1) in a curing reaction with diethylenetriamine (2).
CHAPTER
Importance of Molecular Weight Control
Poly(vinyl chloride) (PVC) production is controlled by the viscosity of a solution of arbitrary concentration relative to that of the pure solvent. However, it is not often possible to recognize and use such parallels, unless the molecular weight distribution parameters in different cases are measured in the same units.
Plan of This Chapter
Many technical problems that can be encountered, e.g. with a new thermoplastic, will already be met and solved with polymers such as rubber that have been on the market for a relatively long time. This results in much unnecessary rediscovery of "old" answers, and the engineer or scientist who can interpret both "Mooney" and "melt index" values in terms of statistical parameters of the molecular weight distributions of the respective rubber and thermoplastic can save considerable time and effort.
Arithmetic Mean
- Number Distribution, M n
- Weight Distribution, M w
The unit of the ordinate is therefore mole fractions and extends from 0 to 1; the integral distribution is now said to be normalized. The proportion of the sample of size Mi is expressed in the present case as the corresponding weight fraction.
Molecular Weight Averages as Ratios of Moments
- Moments in Statistics and Mechanics
- Dimensions
- Arithmetic Mean as a Ratio of Moments
- Extension to Other Molecular Weight Averages
In general, the ratio of the first moment to the zeroth moment of any distribution defines the arithmetic mean. M3ini5Mz11 (2-24) We can generally define a mean as the ratio of successive moments of the distribution.
Breadth of the Distribution
If the MwandMn of a polymer sample is known, we have information about the standard deviation sn and the variance of the number distribution. The skewness of different distributions is most easily compared by relating skewness to the width of the distribution.
Summarizing the Molecular Weight Distribution
The method most directly applicable to polymers uses the third moment of the distribution around the mean. Note that Mn and Mw can be measured directly without knowing the distribution, but it has not been easy to obtain Mz from synthetic polymers as a direct measurement of a sample property.
Integral and Summative Expressions
The number part of the distribution with molecular weights in the range M to M1dM is dx(M)5x(M)dM and the corresponding weight fraction is dw(M)5 w(M)dM. The results are equivalent to those presented here for molecular weight distributions because negative values of the variable are physically impossible.
Typical Molecular Weight Distributions
What is the polydispersity index and the standard deviation of the number distribution of molecular weight of the mixture. -13 Given that the number distribution of the molecular weight of a polymer (fN(M)) is given by the following expression:.
M n Methods
- Ideal Solutions [1]
- Osmotic Pressure
- Osmotic Pressure Measures, M n
- Virial Equations and Virial Coefficients
- Membrane Osmometry
- Vapor Phase Osmometry
- Ebulliometry
- Cryoscopy (Freezing Point Depression)
- End-Group Determinations
The second virial coefficient decreases with increasing molecular weight of the solute and with increased branching. The lower limit depends on the permeability of the membrane to low molecular weight polymers.
Light Scattering
- Terminology
- Effect of Polydispersity
- Scattering from Large Particles
- Light-Scattering Instrumentation
- Light Scattering from Copolymers [2]
- Radius of Gyration from Light-Scattering Data
Since the square of the specific refractive index increment (dn/dc) appears in the light scattering equations, this value must be known exactly to measure Mw: (An error of x% in dn/dc will result in a corresponding error of 2x% in Mw :). An average radius of gyration can be determined from the angular dependence of the intensities of scattered light.
Dilute Solution Viscometry
- Viscosity Average Molecular Weight M v
- Calibration of the Mark Houwink Sakurada Equation
- Measurement of Intrinsic Viscosity
- Single-Point Intrinsic Viscosities
- Solution Viscosity Terminology
- Solution Viscosities in Polymer Quality Control
- Copolymers and Branched Polymers
3-82) Note that Mv is a function of the solvent (through exponents) as well as of the molecular weight distribution of the polymer. Its size can be related to the width of the molecular weight distribution or branching of the solute.
Size Exclusion Chromatography
- Experimental Arrangement
- Data Interpretation
- Universal Calibration for Linear Homopolymers
- Branched Polymers
- Aqueous SEC
- Inhomogeneous Polymers
- MALDI-MS [27]
Polystyrene calibration curve for GPC, where is the molecular weight of the anionic polystyrene standard samples. where the subscript refers to the polymer type. Express the intrinsic viscosity (in deciliters per gram) as a function of the apparent specific volume (reciprocal density) of the solute.
Introduction
Thermal Transitions
During a short temperature interval corresponding to the EF interval, the thermal expansion coefficient of the substance changes, but there is no break in the volume temperature curve. With semicrystalline thermoplastics, the beginning of the melting range defines the upper service temperature.
Crystallization of Polymers
- Degree of Crystallinity
- Microstructure of Semicrystalline Polymers
The crystal density can be calculated from the dimensions of the unit cell in the crystal lattice as determined by X-ray analysis. This phenomenon, known as secondary crystallization, will cause a gradual increase in the average crystallinity of the sample.
The Glass Transition
- Modulus Temperature Relations
- Effect of Polymer Structure on T g
- Correlations between T m and T g
- Measurement of T g
In this case, TgA and TgB refer to the glass transition temperature of the corresponding homopolymers. These two methods reflect changes in the specific heat of the polymer as it transitions from glass to rubber.
Rubber Elasticity
- Qualitative Description of Elastomer Behavior
- Rubber as an Entropy Spring
The internal energy of an ideal gas does not change when it expands at constant temperature. In an ideal gas, we considered the relationships between the thermodynamic properties S and U on the other hand and the state variables P, V and T of the substance.
Rodlike Macromolecules
The entanglements will be more unstable at higher temperatures, where the molecular chains are more flexible, with a net decrease in the number of effective intermolecular anchor points, an increase in Mc, and a decrease in the attractive force, according to Eq.
Polymer Viscoelasticity
- Phenomenological Viscoelasticity
- Linear Viscoelasticity
In a dynamic experiment, the stress will be directly proportional to the strain if the magnitude of the strain is small enough. When the stress is decomposed into two components, the ratio between the stress in phase and the strain amplitude (γa, maximum strain) is called the storage modulus.
