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.
Why is molar mass distribution required?
In many instances, average molar masses and their ratios (i.e. molar mass dispersities) are insufficient to describe the properties of a polymer, and more complete information on the molar mass distribution (MMD) is required. This is particularly important for polymers that have MMDs which are broad, non-uniform (e.g. having low or high molar mass shoulders) and/or multimodal. Even for polymers with relatively simple MMDs, there is advantage in knowing the complete MMD. Furthermore, any molar mass average can be calculated from the moments of the distribution curve.
What are the equations for the different average molar mases using their MDD
Check written notes pt3
What is the process of gel permeation chromatography (GPC)
In GPC a dilute polymer solution is injected into a solvent stream, which then flows through a column packed with beads of a porous gel. The porosity of the gel is of critical importance and typically is in the range 5–10^5 nm. The small solvent molecules pass both through and around the beads, carrying the polymer molecules with them where possible. The smallest polymer molecules are able to pass through most of the pores in the beads and so have a relatively long flow-path through the column.
However, the largest polymer molecules are excluded from all but the largest of the pores because of their greater molecular size and consequently have a much shorter flow-path. Thus GPC is a form of size-exclusion chromatography in which the polymer molecules elute from the chromatography column in order of decreasing molecular size in solution.
How is GPC then used to find the qualitive indication of MMD
The concentration of polymer that elutes from the GPC is monitored continuously and the chromatogram obtained is a plot of concentration against elution volume, which provides a qualitative indication of the MMD. The chromatogram also can reveal the presence of low molar mass additives (e.g. plasticizers), since they appear as separate peaks at large elution volumes
How can the qualitive indication of MMD be converted into the real MMD
Written notes pt 3
What is universal calibration and why is it used?
Universal calibration is a concept that provides a calibration curve universal calibration that applies to all polymers analysed using a given GPC system.
This is used since (with the
exception of the more common polymers) standard samples suitable for calibration are not available
for most polymers. Thus the concept of a universal calibrationuniversal calibration that applies to all polymers analysed
using a given GPC system is very attractive.
Figure 14.8 found in digital notes shows a calibration curve.
How can we find the Molar mass of a polymer with an unknown calbration curve? i.e using the universal calibration curve
now form my understaniding a plot of ([η]M) or log([η]M) aggaint the elution volume would lead to a calbration curve that is approximentaly linear and indpedent of the polymer under concetration.
Then from using the Mark-Houwink-sakurada equation we can find the molar mass of the polymer as shown in notes
What are the GPC coloumn packing most commonly used with organic solvents?
rigid porous beads of either crosslinked polystyrene or surface-treated silica gel
For aqueous GPC separations, What are the coloumn packing most commonly used with organic solvents?
porous beads of water-swellable crosslinked polymers (e.g. crosslinked polyacrylamide gels), glass or silica are employed.
The ability to resolve the different molar mass species present in a polymer sample depend upon what factors?
- an appropriate range of gel porosities is required to obtain the necessary resolution and is obtained by using either a connected series of shorter columns each of which is packed with a gel of different porosity, or one long column packed with mixed gels (See figure 14.6 in digital notes)
- The Resolution increases approximately with l^1/2 where l is the total column
length, and also with (1/d^2) where d is the bead diameter
What is high-throughput GPC
It is GPC where some resolution is sacrificed in the drive to achieve very fast analyses (10–15 min) for which low-volume, monolithic porous columns have been developed.
What is the effect of eluetent choice in GPC
The choice of eluant is of considerable importance because it can have a significant influence upon the contribution of secondary modes of separation. For example, adsorption of polymer molecules to the walls of the pores will retard their movement through the column, causing Ve to increase beyond its value for size exclusion alone. Such effects are more probable if the solvency conditions are poor, and so a good solvent for the polymer should be used as the eluant. The most common eluants are toluene and tetrahydrofuran for non-polar and moderately-polar polymers that are soluble at room temperature, dimethylacetamide for more polar polymers that do not dissolve in tetrahydrofuran, 1,2-dichlorobenzene at about 130 °C for crystalline polyolefins, and 2-chlorophenol at aboutv90 °C for crystalline polyesters and polyamides.
What are the essentail components of a GPC apparatus?
(i) a solvent pump: High-quality solvent pumps which give pulse-free constant volumetric flow rates Q are essential for GPC because it is more accurate to record elution times te rather than measure elution volumes
(=Qte) due to the relatively small values of V0+Vi (typically 30–40 cm)
Also, the pump must generate high pressures to force the solvent through the columns (of tightly packed
small-diameter beads of gel) at the usual flow rate of about 1 cm3 min−1. To facilitate adjustment for
any slight fluctuations in flow rate from one run to another it is normal to include a flow marker in the polymer solution, typically a small inert organic compound (e.g. decalin) that elutes at the full
permeation limit.
(ii) an injection valve: A dilute solution (e.g. 2 g dm−3) of the polymer to be analysed is transferred by syringe to the
injection loop of the injection valve. In the normal valve position, the solvent stream passes directly through the valve, but when it is switched to the injection position, the flow path is changed to pass around the injection loop thus carrying the polymer solution from the loop towards the columns. The injection valve is then moved back to its normal position so that another polymer solution can be placed in the injection loop ready for the next analysis
(iii) a column (or series of columns) packed with beads of porous gel: The GPC columns usually are placed inside an oven so that their temperature can be kept constant; this also enables higher temperatures to be used for solvents that are too viscous to pump at room temperature or for polymers that dissolve only at higher temperatures
(iv) a detector:
Since only about 0.1 mg of polymer is injected, highly sensitive detectors are needed. UV absorption detectors are ideal, but they can only be used if the polymer absorbs UV light at wavelengths where the solvent does not. For polymers that do not absorb UV light, IR detectors are more suitable, although they are more expensive.
Evaporative light scattering (ELS) detectors work by evaporating the solvent and detecting the remaining solute particles through light scattering. The most commonly used detectors are differential refractometers (RI), which measure the difference between the refractive index of the eluate and the pure solvent. Responses from UV, IR, RI, and ELS detectors are proportional to polymer concentration.
More advanced detectors can measure the polymer’s molar mass continuously. The key ones are capillary-bridge differential viscometers and low-angle laser light scattering (LALLS) detectors. By using a combination of RI, viscometer, and LALLS detectors in series, a triple-detector GPC system allows direct measurement of polymer concentration, intrinsic viscosity, and molar mass. This system eliminates the need for calibration and directly provides the molecular mass distribution (MMD). Multi-angle laser light scattering (MALLS) detectors, which measure light scattering at different angles, can also be used to measure both molar mass and molecular size continuously.
(v) a computer for data analysis: The signal from the detector(s) is analogue and so is converted to digital before being stored
in the memory of a computer which then is used to perform the necessary data manipulation. In this way, the MMD and the molar mass averages can be obtained soon after the sample has eluted. Where more than one detector is used in series, the detectors need to be synchronized using
the signals from the flow marker.
(see Figure 14.9 in digital notes)
What are some issues that GPC faces?
When analyzing very high molar mass polymers by GPC, care is needed to check for polymer degradation. The high shear rates in the columns can break the largest chains, especially those above 1,000,000 g/mol. Additionally, GPC struggles to resolve very high molar mass chains, making it less suitable for polymers with a significant proportion above this molar mass
What are preparative GPC systems?
A natural development from analytical GPC systems is the creation of larger preparative GPC systems for polymer fractionation. These systems are about 10 times larger and can fractionate 10–25 mg of polymer in a single run, taking about the same time as an analytical GPC analysis. The eluate is collected in portions corresponding to specific molar mass ranges, and the different polymer fractions are recovered by removing the solvent. If more of each fraction is needed, the process can be repeated. Preparative GPC offers significant advantages over traditional fractionation methods.
How is GPC used in copolymers?
GPC of copolymers is complicated by the overlap of molecular size and composition distributions. To address this, it’s best to use complementary detectors in series (like RI+UV or RI+IR). This allows the RI detector to show the full molecular mass distribution (MMD) and the UV or IR detector to reveal the copolymer composition at each point. This helps determine how evenly UV- or IR-active units are distributed across copolymer chains with different molar masses, which can be linked to synthesis conditions.
A more advanced method, chromatographic cross-fractionation, offers a better way to characterize copolymers. It separates molecules first by size (using GPC) and then by composition (using another column system based on solubility or adsorption). This provides both the molecular size and composition distributions.
What is the problem associated with analyzing a polymer molar mass via MS, and how can it be fixed?
During MS the molecules
usually undergo significant fragmentation into smaller species (of lower m/z), which is not an issue for analysis of small molecules of unique molar mass, but for polymers is a serious issue because, even when the MMD is narrow, they comprise chains with different molar masses (e.g. if fragmentation occurred, it would not be possible to know whether signals at lower m/z were from whole polymer chains or from chain fragments).
In order to solve this new approaches (Such as MALDI and ESI (electrospray ionization)) to soft ionization were developed. Where we are able to generate and vaporize molecular ions from polymers without causing fragmentation.
What is unique about the mass spectra of polymers
Polymer chains have molar masses that are multiples of the repeat unit mass (ignoring end groups), and unlike other methods, mass spectrometry (MS) has high enough resolution to show this discrete pattern. This is evident in the MALDI mass spectra of low molar mass polystyrene samples, where the strength of the signal indicates the number of molecular ions with a specific m/z value. The insets in the spectra show that the spacing between molecular ion peaks matches the repeat unit mass of polystyrene (104 Da). This regular spacing can be used to determine the repeat unit molar mass, helping to identify or confirm a polymer’s structure. This is shown in Figure 14.3 and slide 55.
What is something important to note when looking at MMD from MALDI MS
the MMD of MALDI MS is given as abundance vs the m/z ration while MMD from other techniques are given as weight fraction of species against molar mass. This needs to be borne in mind when comparing MMDs from MALDI MS with those measured by the other methods
What causes peak broadening in MALDI MS
Peak broadening in mass spectrometry can be caused by both the instrument’s resolution limits and the presence of different isotopes of elements. For example, carbon has an isotope,
13C, with about 1.1% abundance. In a polymer with a long chain of carbon atoms, some of these carbons will be
13C instead of the more common 12C. This means that polymers of the same size can have different masses depending on how many 13C atoms they contain. These variations in mass cause the peaks in the mass spectrum to broaden because the mass spectrometer can’t always distinguish between them, especially as the polymer size increases.
What are all the details involving MALDI
MALDI (Matrix-Assisted Laser Desorption/Ionization) works by vaporizing a solid mixture of a polymer, a metal salt, and a low-mass crystalline matrix. The polymer is present in a low concentration (0.01–1%) within this matrix. A high-energy UV laser (usually 337 nm wavelength) vaporizes the sample in a short pulse, causing each polymer molecule to associate with a metal ion and enter the vapor phase. After a brief delay, the ions are sent to the mass detector.
MALDI is preferred over other techniques like ESI (Electrospray Ionization) for polymer analysis because it typically produces singly-charged ions, which simplifies data interpretation for polymers with varying molecular masses. The choice of matrix material is crucial for reliable results, as it must absorb the laser energy and vaporize quickly. The matrix must also form a uniform mixture with the polymer and metal salt, with its solubility matching that of the polymer.
The metal salt used for ionization depends on the polymer’s structure. Polymers with heteroatoms (e.g., polyethers, polyesters) work well with alkali metal salts like Na+, which simplify mass spectrum interpretation since sodium has a single isotope. However, non-polar polymers, like polyethylene, are difficult to analyze using MALDI. For polymers like polystyrene, transition metal ions (like Ag+) are used, which bind to π-bonds in the polymer.
Sample preparation often involves mixing the polymer, matrix, and metal salt in a solution, then rapidly evaporating the solvent to ensure a uniform distribution of components.
What is Time Of Flight detection and why is it employed?
In time-of-flight (ToF) detection, all molecular ions follow exactly the same path to the detector, irrespective of m/z, and are separated simply by differences in the time taken to reach the detector. Thus, in ToF MS, all the molecular ions generated are captured by the detector, greatly improving sensitivity and facilitating easy detection of
molecular ions with high m/z values. For this reason, most ESI and MALDI mass spectrometers available nowadays employ ToF detection.
What happens in MALDI ToF spec?
In MALDI ToF (Time-of-Flight) mass spectrometers, molecular ions generated from the MALDI plate are accelerated by applying a high voltage (15–35 kV) between the plate and a grounded extractor plate. These ions then enter a long drift tube (1–2 meters), where they travel towards the detector at speeds that depend on their mass-to-charge ratio (m/z). As a result, ions with different m/z values arrive at the detector at different times, allowing for separation and detection. The process happens very quickly, in less than 100 microseconds.
To improve resolution and detect heavier ions, many MALDI ToF systems use a reflectron. This device reflects the ions back along a new path to another detector, enhancing the accuracy of measurements for higher mass molecules.
What are the uncertainties associated with MALDI ToF MS
As MALDI MS developed in the 1990s, there was hope it could provide accurate molecular mass distributions (MMDs), but several uncertainties make this challenging. Incomplete ionization of larger molecules, unknown fragmentation of polymer chains during ionization, and limitations in detector sensitivity at higher mass-to-charge (m/z) values are key issues. Additionally, the detector can become less responsive to high m/z ions because lower m/z ions reach it first, and fewer large molecules hit the detector even if they make up a large portion of the sample. These factors cause MALDI MS to skew MMD results toward lower molar masses, especially for higher mass polymers.
ToF mass spectra also present data with a non-linear m/z axis, meaning the spacing between peaks increases as m/z increases, which can distort the true appearance of the MMD.
What is the comparison between GPC vs Maldi
Several comparisons have been made between MMDs (molecular mass distributions) obtained by GPC and MALDI MS for the same polymer samples. MALDI MS provides accurate molar mass measurements but has uncertainty in determining the number and weight fraction of each species, especially for higher molar mass polymers. GPC, on the other hand, has more uncertainty in molar mass measurements but is highly reliable in measuring the weight fraction of each species.
For low molar mass polymers with narrow MMDs, MALDI MS gives accurate results if the sample preparation and settings are correct. However, for moderate to high molar mass polymers or those with broad MMDs, MALDI MS is less reliable, and the data should be carefully evaluated. While modern MALDI MS instruments can analyze polymers up to 1000 kg/mol, it is best suited for polymers with MMDs up to around 50,000 g/mol. MALDI MS is particularly useful for determining both MMD and molecular structure
OTHER INFO (VERY IMPORTANT)
Digital slides
also sorry this was very very hard to do even more hard than you learning it now…i was sick
