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“Reverse Kendrick Mass Defect Analysis”: Rotating Mass Defect Graphs to Determine Oligomer Compositions for Homopolymers Robert Bernard Cody, and Thierry Fouquet Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b03413 • Publication Date (Web): 09 Oct 2018 Downloaded from http://pubs.acs.org on October 16, 2018
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Analytical Chemistry
1.
“Reverse Kendrick Mass Defect Analysis”: Rotating Mass Defect Graphs to Determine Oligomer Compositions for Homopolymers Robert B. Cody1* and Thierry Fouquet2 1
JEOL USA, Inc. 11 Dearborn Rd., Peabody MA 01960 USA, 2 Research Institute for Sustainable Chemistry, National Institute for Advanced Industrial Science and Technology (AIST), Tsukuba 305-8565, Japan. ABSTRACT: A new approach to determining the repeat unit compositions of homopolymers is reported in which a mass defect graph is rotated to zero slope to give a graph identical to a Kendrick mass defect graph. Because the Kendrick mass defect is directly related to the elemental composition of the base unit, the process can be reversed. A mass defect graph (fractional m/z plotted against exact m/z) of a homopolymer can be rotated until the slope of the data points is zero. This is equivalent to finding a new constant factor by which the measured exact masses would have to be multiplied to create a Kendrick mass defect graph with zero slope. The elemental composition of the repeat unit can be determined by matching the new factor against the calculated factors for candidate compositions. This approach provides some benefits over simply looking for pairs of peaks corresponding to oligomer units. The primary benefit is to assist in visualization of the data. Rotating the data points corresponding to polymer masses to zero slope makes it easier to visualize the polymer data, and it facilitates the graphical isolation of polymer masses from background interferences. The repeat unit composition is determined not from a single pair of peaks, but from multiple data points, and systematic errors in mass assignment can be visualized as deviations from linearity. Resolution-enhanced KMD graphs can be constructed for the calculated repeat unit composition by using fractional base units.
For the classical Kendrick mass defect with a CH2 repeat unit, the exact mass of the repeat unit is 14.01565 and
Introduction Edward Kendrick introduced a mass scale based on CH2 = 14.0000 in 1963 as a method for simplifying the data analysis of high-resolution mass spectra of petrochemicals1. Kendrick mass analysis was originally applied to families of compounds having a common core structure but differing only in the degree of alkylation. However, the method can be extended for application to any high-resolution mass spectra containing families of compounds with varying numbers of a common substructure or repeat unit. Kendrick mass analysis is particularly well suited for use with high-resolution mass spectra of polymers2-10. Mass defect graphs are a useful way to view high-resolution mass spectra of complex mixtures. The mass defect is defined as the difference between the exact mass and the integer mass. An IUPAC mass defect graph displays the mass defect on the y-axis against the exact mass on the x-axis. A Kendrick mass defect graph rotates the slope of a mass defect graph by multiplying each measured mass by a constant factor. The Kendrick mass KM is calculated by multiplying the measured IUPAC mass-to-charge ratio m/z by a factor k KM = k(m/z) Where the multiplicative factor k is calculated by dividing the nominal (nearest integer) mass for a given repeating (base) unit by the exact mass for the base unit: k = Nominal base unit mass / IUPAC base unit mass The factor k is strongly dependent on the elemental composition of the repeat unit.
KCH2 = 14.00000 / 14.01565 = 0.998883 For an ethylene oxide (C2H4O) homopolymer, kC2H4O = 44.00000/ 44.02621 = 0.999405 For a poly(dimethylsiloxane) with repeat unit composition C3H6SiO, kC3H6SiO = 74.00000 / 74.01879 = 0.999746 The Kendrick mass defect KMD is calculated by subtracting the Kendrick mass from the nominal Kendrick mass NKM: KMD = NKM - KM The KMD graph for a homopolymer constructed by using the monomer composition as the base unit is a straight line with zero slope, and the y-intercept is equal to the Kendrick mass defect. Given a mass spectrum of an unknown homopolymer, the IUPAC mass defect graph will show a series of points that fall along a straight line with a given slope. The slope will be nonzero except for the special case of ions that differ only in the number of carbons (e.g. carbon clusters or PAH’s). By finding a value of the multiplicative constant k that results in rotating the points to fall along a zero slope, the y-intercept will be the Kendrick mass defect for the unknown repeat series. Given an IUPAC mass defect graph with initial slope m, the value of k that will rotate that graph to zero slope is: k=1–m
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This can be extended to any non-IUPAC mass defect graph created by using an initial multiplicative factor k0 so that the new value k that will rotate the graph to zero slope is simply k = k0 - m The multiplicative factor determined by rotating the slope of a mass defect graph to zero can then be searched against the calculated multiplicative factors for common oligomers. Alternatively, the measured multiplicative factor can be used to calculate repeat unit elemental compositions that would have calculated multiplicative factor values within a given error tolerance. The calculated KMD values are not used to determine the repeat unit composition because these values are dependent on the terminal group composition.
Experimental Mass spectra were obtained by using an AccuTOF-DART 4G (JEOL USA, Inc., Peabody MA USA) reflectron time-of-flight mass spectrometer equipped with a DART-SVP Direct Analysis in real Time (DART) ion source (IonSense LLC, Saugus MA USA) and a prototype paper spray ion source. Mass spectra were acquired in positive-ion mode with a resolving power of >10,000 (FWHM definition). JEOL “msAxel” software was used for instrument control, data acquisition, mass calibration, spectral averaging and peak centroiding. Kendrick mass defect analysis was carried out using Mass Mountaineer software (RBC Software, Portsmouth NH USA, available from massmountaineer.com) for the centroided mass spectra. Functions were added to the software to permit interactive rotation of mass defect plots, allow cursor selection of polymer data points to eliminate background interferences, to zero the slope of a mass defect graph to determine the Kendrick multiplicative factor k, and to determine candidate repeat unit compositions from the k value. Jeffamine M-600 was purchased from the Huntsman Corporation (The Woodlands, TX, USA). The gasoline sample was obtained from the pumps at a local convenience store. Silicone oil (linear poly(dimethylsiloxane) with a viscosity of 5 cSt) was purchased from Sigma-Aldrich (St. Louis MO USA). DART mass spectra of Jeffamine M-600 and gasoline were obtained by applying approximately 1-2 L of neat liquid onto the sealed end of a 2 mm OD Pyrex melting point tube and dangling the tip of the tube in the DART gas stream approximately 1-2 mm from the ceramic insulator of the DART ion source. The gas heater was set to 400°C for the helium DART gas and the DART exit electrode was set to 150V. The DART was positioned on its linear rail so that the tip of the ceramic insulator was approximately 1 cm from the apex of the sampling orifice (designated “orifice 1”) of the mass spectrometer atmospheric pressure interface. No additional interface hardware was required for DART operation on the AccuTOF mass spectrometer. The remaining DART parameters (gas flow rate and discharge electrode voltage) were determined by the DART-SVP hardware and were not under operator control. For DART analysis, the mass spectrometer operating parameters were: orifice 1 = 20V, ring lens and orifice 2 = 5V, RF ion guide = 500V, orifice 1 temperature = 120°C, spectral storage rate = 1 spectrum s-1 , acquired m/z range = 50 - 1000. Isotactic poly(methyl methacrylate), abbreviated as PMMA, was obtained from Polysciences Inc. (Washington, PA USA). A small particle of the polymer was suspended in the DART
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gas stream using forceps with the DART operated in positiveion mode with helium gas and a gas heater temperature of 350°C. The DART mass spectrum of poly(lactic acid), abbreviated as PLA, was obtained by depositing a few micrograms of plastic cut from feedstock for a 3D printer onto the copper sample holder of a thermal desorption and pyrolysis attachment for the AccuTOF-DART (“ionRocket” from Biochromato, San Diego CA USA). The temperature program started at 50°C with a 0.5 minute hold time, followed by a temperature program of 100°C to 600°C at a heating rate of 100°C min-1. The paper spray mass spectrum of poly(dimethylsiloxane), abbreviated as PDMS, was obtained by using a prototype paper spray ion source. The source and experimental parameters for polymer analysis were described in a previous publication 5 to which the reader is referred for details.
Results and Discussion Case 1: the integer value of the repeat unit is known A mass spectrum of a simple homopolymer with few interferences will be used to illustrate the procedure for rotating mass defect plots to determine the repeat unit composition. Figure 1A shows the positive-ion DART mass spectrum of Jeffamine M-600, an amine-terminated propylene oxide homopolymer with the structure shown below.
CH3 O H3C
NH2 O
O
n
CH3
Jeffamine M-600 has been used as a mass reference standard for DART mass spectrometry11. The IUPAC mass defect graph shown in Figure 1B has a positive slope and exhibits aliasing above n=9. Figure 1C shows the rotated KMD graph with zero slope. The abundance cutoff threshold was adjusted to eliminate low-level background peaks prior to rotation to zero slope. The measured multiplicative factor k is 0.9992785 which differs from the calculated factor for C3H6O of 0.9992786 (=58.0/58.04187) by only 1x10 -7. Given a value of k = 0.9992785 and assuming a nominal mass of 58 for the repeat unit, the calculated exact mass of the repeat unit is 58.0 / 0.9992785 = 58.04187 which is exactly equal within 5 decimal places to the calculated exact mass for the monoisotopic mass of C3H6O.
Case 2: Searching a list of candidate repeat unit compositions If we do not know that the nominal mass for the repeat unit is 58, we can search a list of polymer repeat unit compositions to find a composition that has a calculated k within a specified error tolerance. Table S1 shows the results of searching for compositions with matching k values in a list of 51 common oligomer compositions. The best match is propylene oxide (C3H6O) with a difference of only 2x10-8 between the measured and calculated k values.
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Analytical Chemistry Case 3: Elemental composition determination for the repeat unit A different approach is to use the measured k value to determine an elemental composition. The strategy is analogous to the method for determining elemental compositions for an exact mass. In the traditional approach, the operator provides a set of elements that may be present and the minimum and maximum values that may be present. The program calculates the monoisotopic exact mass for each combination of atoms and only reports those compositions with a calculated exact mass that falls within the specified error tolerances. Additional constraints may be applied, such as unsaturation limits, ion type, isotopic accuracy, etc. To determine the elemental composition for a repeating unit from the zero-slope mass defect graph, we follow the same procedure, except that the Kendrick factor k calculated for each candidate composition is substituted for the monoisotopic exact mass. For each matching composition, the number of mass pairs n that differ by the calculated composition is counted.
However, there is a less abundant series of points in Figure 2A that fall along a line with a positive slope. Although these peaks have a very low relative abundance, we can follow a similar procedure by rotating the mass defect graph and using the cursor to isolate the most abundant peaks in this series.
Table S2 shows the elemental compositions calculated using the measured k value of 0.9992785, an abundance threshold of 1% for counting mass pairs, and a limit ensuring that the absolute value of the difference between calculated and measured k values is ≤1 .0x10-5. Although it can be argued that more than one pair of masses is required to define a repeat unit, values that have one or more pairs of masses that differ by the oligomer unit are reported. Two compositions have the smallest difference between calculated and measured k: C3H6O and C6H12O2. The correct composition has n=36 pairs of masses identified with the mass difference corresponding to the monoisotopic mass of C3H6O. The number n includes isotope peaks and all peaks above 1% relative abundance. The other composition corresponds to the C3H6O dimer, and only n=31 pairs of masses are found with a mass difference corresponding to the composition C6H12O2. Therefore, the correct composition is C3H6O. The positive-ion mass spectrum of a partially evaporated gasoline sample in Figure 2A provides a more complex example. The base peak at m/z 547.3998 corresponds to trioctyl trimellitate, a lead scavenger. In addition to additives such as dimethylaminopropylamine (DMAPA, m/z 103.1222) and octylamine (m/z 130.1609), a series of polymer peaks are observed over the range from approximately m/z 400-1200. By inspection, one can determine that the repeat unit is C4H8 corresponding to poly(isobutylene) abbreviated as PIB. Polyisobutylene fuel additives are used to prevent and remove engine deposits. Figure 2B shows the corresponding mass defect graph rotated to zero the slope for the PIB polymer. By adjusting the relative abundance threshold and using the cursor, one can select the PIB peak series, zero their slope (Figure 2C), and use the calculated k to determine the repeat unit composition as C4H8, as expected (Table S3). This example was chosen to illustrate the importance of counting the number of peak pairs that differ by a candidate repeat unit composition. All of the calculated compositions are multiples of CH2, yet the correct composition has 71 pairs of peaks with a relative abundance > 2% that differ by C4H8. If the threshold is lowered to 1% difference in the number of pairs is diminished between correct and incorrect compositions because chemical background peaks contribute to the count (Table S4).
Figure 1. (A) Positive-ion DART-TOF mass spectrum of Jeffamine M-600. (B) mass defect plot for the same sample and (C) the mass defect plot in (B) with the abundance threshold raised to eliminate small background peaks and rotated to zero slope (indicated by the red horizontal line).
By finding the k value that zeroes the slope for these peaks, the repeat unit composition is determined to be C 3H6O (propylene oxide) and this series of peaks represents trace low molecular weight poly(propylene oxide) [HO-(C3H6O)n-H + H]+. The origin or purpose of this is unclear because unmodified polyethers are not commonly known to be used as a fuel additive, and unmodified poly(propylene oxide) is not used as a mass reference standard in our laboratory.
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Figure 2. (A) Positive-ion DART-TOF mass spectrum of additives in a partially evaporated gasoline sample (B) mass defect graph showing two polymeric series, rotated so that the more abundant series has near-zero slope (C) series A rotated to zero slope following selection with the mouse cursor and adjustment of the abundance cutoff threshold (D) data points from series B rotated to zero slope following cursor selection and adjustment of the abundance cutoff threshold.
The pyrolysis-DART mass spectrum of poly(methyl methacrylate) provides an example of a case where it is not trivial to find the repeat unit by visual inspection (Figure 3A). The base peak at m/z 100.062 corresponds to the protonated methyl methacrylate (MMA) monomer with composition C5H8O2+, but it is difficult to see a clear series of peaks differing by MMA in the low-abundance fragment ions at higher m/z. However, the mass defect plot shows a series of data points that fall along a line with positive slope (Figure 3B). Selecting these peaks and rotating them to zero slope produces the graph shown in Figure 3C. Calculating the composition of the repeat group from the measured k value results in the correct composition C 5H8O2 having the smallest difference between measured and calculated k values, and the largest number (15) of mass pairs differing by the exact mass of methyl methacrylate (Table S5). Knowing the correct repeat unit composition, we can construct a resolution-enhanced KMD graph9 (Figure 3D) that shows several different series of pyrolysis fragment peaks with MMA repeat units. The most abundant series (designated series “A”) consists of peaks at nominal m/z 315, 415, 515, … 815 with compositions [C14H15O2 + C5H8O2)n]+. A second series of peaks (series “B”) consists of peaks with nominal m/z 187, 287, 387 .. 887 with compositions [C13H15O + C5H8O2)n]+. A third series (series “C”) has nominal m/z 355 … 855 with compositions [C17H19O2 + C5H8O2)n]+. The structures and origins of these DART pyrolysis fragments are unknown and their identification is beyond the scope of this work. Other minor
fragment series can be identified in the resolution-enhanced that differ by the exact mass of MMA but are not labeled in Figure 3D. The rotating mass defect approach was also applied to a positive-ion DART mass spectrum of poly(lactic acid) or “PLA” (Figure 4A) and a paper spray mass spectrum of poly(dimethylsiloxane) or “PDMS” (Figure 4B). The repeat unit in Figure 4A was determined (Table S6) to be C3H4O2 for a measured k=0.9996975. The major series of pyrolysis fragments observed is protonated cyclic PLA [C3H4O2 + H]+ at nominal m/z 433, 505, 577 etc. with smaller series observed for the ammonium adducts [C3H4O2 + NH4]+ and linear PLA [C3H4O2 + H3O]+. The repeat unit was determined (Table S7) from the paper spray mass spectrum of PDMS to be C 2H6SiO for k=0.9997500. The major peak series corresponds to sodium adducts with the composition [C6H18Si2O + (C2H6SiO)n + Na]+ for linear PDMS having the structure shown below.
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Analytical Chemistry create a Kendrick mass defect plot using the fractional base unit corresponding to PDMS/72 where
k=
74.01879 ) 72 = 0.9727259 74.01879 72
𝑅𝑜𝑢𝑛𝑑(
Figure 5 shows the rotated mass defect graph for the paper spray mass spectrum of polydimethylsiloxane (Figure 4B) rotated until k = 0.972725. This graph is identical to the graph created by using the fractional base unit corresponding to PDMS/72 with separation of the individual isotope peaks for each of the PDMS sodium adducts.
Case 4: Finding the repeat unit mass by extended rotation For a generic mass spectrum with R the exact mass of the unknown repeating unit, the first multiplication factor leading to a zero-slope KMD plot is defined as: k1 =
round(R) R
Considering the relationship between the rotating plot and the fractional base units R/X with X being a positive integer (previous section), additional zero-slope KMD plots are computed with other multiplication factors kn generically defined as
kn =
round(R⁄X) R⁄ X
A recommended range of divisors X has been defined 12. as X=round(2/3R,…,2R) based on the founding principle round(R/X)=1. Typical values of X are defined as X=round(R)+n with n being a positive or negative integer (e.g. DMS/72, round(DMS)=74, n=-2, vide supra). Replacing X by its recommended definition: Figure 3. (A) Pyrolysis DART mass spectrum of isotactic poly methyl(methacrylate), (B) mass defect graph for PMMA, (C) mass defect graph for the minor pyrolysis fragments rotated to zero slope and (D) resolution-enhanced KMD graph using a fractional base unit corresponding to MMA/99.
Relationship between rotated mass defect graph and fractional base unit graph Resolution-enhanced Kendrick mass defect graphs are created by using a fractional base unit9. A Kendrick mass defect graph created with a fractional base unit is equivalent to changing the multiplication factor k. Therefore, if we continue to rotate a mass defect plot through all possible values of k, we will pass through the k value for every possible fractional base unit. Taking the paper spray mass spectrum of polydimethylsiloxane (monoisotopic exact mass = 74.01879) as an example, we can
round(R⁄(round(R) + n)) round(R) + n kn = = R⁄ R (round(R) + n) Subtracting k1 from kn provides a direct relationship between the exact mass of the repeating unit R and the multiplication factors:
k n − k1 =
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round(R) + n round(R) n − = R R R R=
n k n − k1
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Figure 4. (A) Positive-ion DART mass spectrum of poly(lactic acid) from a 3D printer feedstock, (B) paper spray mass spectrum of poly(dimethylsiloxane) (C,D) mass defect plots of cursor-selected data from (A,B) rotated to zero slope (grey dots: k=1).
Figure 5. (A)-(G) Rotating mass defect graphs from the paper spray mass spectrum of poly(dimethylsiloxane) with decreasing multiplication factors k from the first zero-slope case (k=0.99975) to the second zero-slope case with k=0.98624. This last graph is identical to the resolution-enhanced Kendrick mass defect graph created by using the fractional base unit DMS/73 for the same sample. (H) Rotating mass defect graph with k=0.97273 identical to the resolution-enhanced Kendrick mass defect graph created by using the fractional base unit DMS/72.
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Analytical Chemistry R can thus be computed by rotating the KMD plot until two zero-slope cases are reached with n=+/-1 if consecutively (n=+1 if increasing k>1, n=-1 if decreasing k
