Lecture 2 Flashcards
Molar mass and DP equations
Shown in notes page 1!
Molar Mass Distrubution
With very few exceptions, polymers consist of macromolecules (or network chains) with a range of molar masses. Since the molar mass changes in intervals of M0, the distribution of molar mass is discontinuous. However, for most polymers, these intervals are extremely small in comparison to the total range of molar mass and the distribution can be assumed to be continuous, as exemplified in Figure 1.4 (shown in digital notes)
Molar Mass Averages
Whilst a knowledge of the complete molar mass distribution is essential in many uses of polymers, it is convenient to characterize the distribution in terms of molar mass averages. These usually are defined by considering the discontinuous nature of the distribution in which the macromolecules exist in discrete fractions ‘i’ containing Ni molecules of molar mass M….Check written notes
What is the polydispersity index?
The ratio Mw/Mn must by definition be greater than unity for a polydisperse polymer and is known as the polydispersity or heterogeneity index (often referred to as PDI). Its value often is used as a measure of the breadth of the molar mass distribution, though it is a poor substitute for knowledge of the complete distribution curve. Typically Mw/M n is in the range 1.5−2.0, though there are many polymers which have smaller or very much larger values of polydispersity index. A perfectly monodisperse polymer would have Mw/Mn=1.00.
Note that IUPAC has recommended that a polymer
sample composed of a single macromolecular species should be called a uniform polymer (instead of monodisperse) and a polymer sample composed of macromolecular species of differing molar masses a non-uniform polymer (instead of polydisperse). They further recommended that polydispersity should be replaced by a new term, dispersity (given the symbol Ð), such that ÐM is the molar mass dispersity (= Mw/Mn), ÐX is the degree-of-polymerization dispersity (= xw/xn) and for most polymers Ð=ÐM =ÐX.
What is the key concept of Dilute Solution Viscometry?
Dilute Solution Viscometry lies around the key concept that a dilute polymer solution viscosity is considerably higher than that of either the pure solvent or similarly dilute solutions of small molecules. This arises because of the large differences in size between polymer and solvent molecules, and the magnitude of the viscosity increase is related to the dimensions of the polymer molecules in solution. Therefore, measurements of the viscosities of dilute polymer solutions can be used to provide information concerning the effects upon chain dimensions of polymer structure (chemical and skeletal), molecular shape, degree of polymerization (hence molar mass) and polymer−solvent interactions. Most commonly, however, such measurements are used to determine the molar mass of a polymer.
The quantities required, and terminology used, in dilute solution viscometry are summarised in Table 13.1 found in the digital notes.
What is the intrinsic viscosity [η]?
The quantity for the purpose of polymer characterisation. it relates to the intrinsic ability of a polymer to increase the viscosity of a particular solvent at a given temperature
What are the equations for specific, reduced, and inherent viscosity?
Found in written notes pt2
Interpretation of Intrinsic Viscosity Data
The intrinsic viscosity [η] of a polymer is related to its viscosity-average molar mass Mv by the Mark−Houwink Sakurada equation (shown in notes).
In the equation K and a are characteristic constants for a given polymer/solvent/temperature system and are known as the Mark–Houwink–Sakurada constants (or often simply as the Mark–Houwink constants). For Gaussian coils, it was shown that a=0.5 under theta conditions, and that a increases to a limiting
value of 0.8 with coil expansion (typically a>0.7 for polymers in good solvents). The value of K tends to decrease as a increases and for flexible chains it is typically in the range 10−3–10−1 cm3 g−1 (g mol−1)−a.
How can the viscosity-average molar mass Mv be deduced?
Lit so confused?
Check the written notes
How can you evaluate Mv from [η] using the Mark-Houwink-Sakurada equation?
In order to evaluate Mv from [η] using the Mark–Houwink–Sakurada equation, it is necessary to know the values of K and a for the system under study. These values most commonly are determined from measurements of [η] for a series of polymer samples with known Mn or Mw. Ideally, the samples should have narrow molar mass distributions so that Mn ≈ Mv ≈ Mw; if this is not the case,
then provided that their molar mass distributions are of the same functional form (e.g. most probable distribution), the calibration is valid and yields equations that are similar to Mark-Houwink-Sakurada equations
v is replaced by Mn or Mw. Generally a plot of log[η] against log M is fitted to a straight line from which K and a are determined.
Theoretically, this plot should not be linear over a wide range of M, so that K and a values should not be used for polymers with M outside the range defined by the calibration samples. However, in practice, such plots are essentially linear over wide ranges of M, though curvature at low M often is observed due to the non-Gaussian character of short flexible chains.
How is the expansion parameter α(η) for the hydrodynamic chain dimensions given?
Check written notes
Interpatation: Thus the corresponding [η] and M data obtained for evaluation of Mark–Houwink–Sakurada constants from calibration samples with narrow molar mass distributions, also can be plotted as [η]/M1/2 against M1/2 to give Kθ as the intercept at [η]/M1/2=0. The
value of Kθ can then be used to evaluate for the polymer to which it relates: (i) s (i.e. unperturbed dimensions) for any M by assuming a theoretical value for Φ, and (ii) αη for a given pair of corresponding [η] and M values by using the Flory–Fox Equation.
Whar will the effect of branching have on the viscosity and the Hydrodynamic volume?
The effect of branching is to increase the segment density within the molecular coil. Thus a branched polymer molecule has a smaller hydrodynamic volume and a lower intrinsic viscosity than a similar linear polymer of the same molar mass.
How does viscosity differ for copolymers with the same molar mass
For copolymers of the same molar mass, [η] will differ according to the composition, composition distribution, sequence distribution of the different repeat units, interactions between unlike repeat units, and degree of preferential interaction of solvent molecules with one of the different types of repeat unit.
How can we generally measure a solutions viscosity?
The viscosities of dilute polymer solutions most commonly are measured using capillary viscometers of which there are two general classes, namely, U-tube viscometers and suspended-level viscometers (see Figure 13.2 look at digital notes). A common feature of these viscometers is that a measuring bulb, with upper and lower etched marks, is attached directly above the capillary tube. The solution is either drawn or forced into the measuring bulb from a reservoir bulb attached to the bottom of the capillary tube, and the time required for it to flow back between the two etched marks is recorded.
What does the pressure head depend on in U-tube viscometers?
In U-tube viscometers, the pressure head giving rise to flow depends upon the volume of solution contained in the viscometer, and so it is essential that this volume is exactly the same for each measurement. This normally is achieved after temperature equilibration by carefully adjusting the liquid level to an etched mark just above the reservoir bulb.
What does the pressure head depend on in suspended-level viscometers?
Most suspended-level viscometers are based upon the design due to Ubbelohde, the important feature of which is the additional tube attached just below the capillary tube. This ensures that during measurement, the solution is suspended in the measuring bulb and capillary tube, with atmospheric pressure acting both above and below the flowing column of liquid. Thus, the pressure head depends only upon the volume of solution in and above the capillary, and so is independent of the total volume of solution contained in the viscometer. This feature is particularly useful because it enables solutions to be diluted in the viscometer by adding more solvent. While When U-tube viscometers are used, they must be emptied, cleaned, dried and refilled with the new solution each time the concentration is changed.
What is the specific procedure for measuring the viscocity using viscometers?
Before use, it is essential to ensure that the viscometer is thoroughly clean and that the solvent and solutions are freed from dust by filtration, otherwise incorrect and erratic flow times can be
anticipated.
The viscometer is first placed in a thermostatted water (or
oil) bath with temperature control of ±0.01 °C or better because viscosity generally changes rapidly with temperature. After allowing sufficient time for temperature equilibration of the solution, several measurements of flow time are made and should be reproducible to ±0.1% when measured visually using a stopwatch. When analysing polyelectrolyte solutions, it is important to suppress the polyelectrolyte effect by using an aqueous solution (typically about 0.1 moldm−3) of an inert electrolyte (e.g. NaCl) as the solvent.
Under conditions of steady laminar Newtonian flow, the volume V of liquid which flows in time t through a capillary of length l and radius r is related to both the pressure difference P across them capillary and the viscosity η of the liquid by Poiseuille’s equation (shown on written notes pt 3)
note that Poiseuille’s equation does not take into account the energy dissipated in imparting kinetic energy to the liquid, but is satisfactory for most viscometers provided that the flow times exceed about 180 s.
Absolute measurements of viscosity are not required in dilute solution viscometry since it is only necessary to determine the viscosity of a polymer solution relative to that of the pure solvent.
