The 2022 Emerging Leader in Molecular Spectroscopy Award

A Different Kind of Art Analysis

A Survey of Basic Instrument Components Used in Spectroscopy

Agilent Technologies (Santa Clara, California) is launching a partnership with Delaware State University (DSU) (Dover, Delaware), a prominent historically Black university, to increase the share of underrepresented students entering science, technology, engineering, and math (STEM) fields. This goal is a fundamental mission of the company’s philanthropic work through the Agilent Foundation.

Agilent will donate $1 million along with new laboratory instrumentation to help DSU expand educational opportunities and advance research in applied chemistry, biological sciences, food science, molecular, and cellular neuroscience, and related disciplines. The company’s support will also contribute to building research capacity of a consortium of historically Black colleges and universities (HBCUs) in the mid-Atlantic region, led by Delaware State.

“DSU has a tremendous pool of talented STEM students,” Agilent President and CEO Mike McMullen said in a statement. “This partnership will help us provide direct support to these students and encourage more scholars at HBCUs across the mid-Atlantic to consider opportunities at Agilent and within the broader life sciences sector.”

Agilent’s donation arrives as DSU breaks ground on a new 24,000-square-foot building for its College of Agriculture Science and Technology (CAST), which includes space for new laboratories.

“Many believe that this is a renaissance moment for HBCUs. It’s not,” DSU President Dr. Tony Allen said in a statement, “We’ve been doing the work for 175 years—building the most useful pipeline for African Americans to the American middle class and breaking new ground in every field of human endeavor.” He praised Agilent for understanding the work being done and connecting with DSU’s system, which he said produces 25% of all the Black STEM graduates in the United States. 

Agilent’s donation will fully fund 21 graduate and undergraduate students pursuing STEM degrees. The company is also providing analytical laboratory instrumentation, supplies, services, and other infrastructure to equip CAST’s new laboratory space. Additionally, Agilent will provide mentorship opportunities for DSU students with Agilent scientists, engineers, and researchers and will help fund DSU’s summer internship program for STEM students.

Articles

Agilent Technologies (Santa Clara, California) is launching a partnership with Delaware State University (DSU) (Dover, Delaware), a prominent historically Black university, to increase the share of underrepresented students entering science, technology, engineering, and math (STEM) fields.

Partnership between Agilent and Delaware State University Promotes Diversity in Science, Technology, Engineering, and Math (STEM) Fields

Trace elements can be taken up by crops and animals from the air, water, soil, and food during growth, or introduced during food processing. Although some of these elements are essential macronutrients, others are toxic. Through food consumption, humans are exposed to toxic elements with the risk increasing proportionately to the amount consumed, which can have neurological-, endocrine-, and exocrine-disrupting properties, as well as being potentially genotoxic or carcinogenic. As a result, the contamination of food and water by toxic elements is of great concern because concentrations can be present at trace to ultra-trace levels, requiring sensitive and reliable analytical techniques for accurate measurement. Inductively coupled plasma mass spectrometry (ICP-MS) is a powerful elemental analysis technique with multi-element detection capabilities, low detection limits, high speed of analysis, and wide linear dynamic range. However, it is also susceptible to interfering species, leading to the formation of polyatomic and doubly charged ions. Here, we evaluate the performance characteristics of ICP-MS to carry out the validation procedures and QC requirements defined in AOAC Method 2015.01.

Polyatomic interferences are generated by the reaction of matrix ions and plasma-based elements, such as Ar, C, N, O, and H, which can overlap target ions. Examples of such polyatomic interferences relevant to toxic-element analysis include 

, and so forth. Doubly-charged ions are formed by the secondary ionization of elements with low second-ionization potentials, such as rare earth elements (REEs). For example, the doubly-charged ions from 

As, resulting in a false overestimation of the result. Rare earth elements are not usually present in significant amounts in food samples, but with increased industrialization and globalization, food products can be sourced from geological regions with high REEs. As such, rare earth elements present in some food products should not be overlooked in elemental analyses.

All commercially available single quadrupole inductively coupled plasma–mass spectrometry (ICP-MS) systems are fitted with a collision/reaction cell (CRC) or collision/reaction interface (CRI), which either utilizes collision mode with kinetic energy discrimination (KED) or reaction mode with dynamic bandpass tuning (DBT) to mitigate interferences from polyatomic ions. The collision mode typically involves colliding both the analytes and interferences with an inert gas, usually helium. Because polyatomic interferences have a larger cross-sectional diameter than elemental ions at the same mass (for example, 

), they undergo more collisions and lose more energy. Therefore, they cannot pass the energy barrier at the exit of the collision/reaction cell and are rejected from the ion beam. However, interferences from doubly-charged ions and isobars cannot be effectively resolved using collision mode. A few techniques have been developed to correct for these interferences, which can be either through post-analysis mathematical corrections or via the use of reaction gases. For doubly-charged ions, mathematical corrections using the half-mass approach (such as correction equations at higher resolution) are often not preferred because this comes at the expense of analyte sensitivity. A more effective means of removing these interferences is to use reaction gases where, in the case of As, it reacts with oxygen to form 

 at mass 91. Moving the analyte away by +16 amu from the respective doubly-charged interferents results in a lower detection limit without compromising analyte sensitivity.

The Association of Official Analytical Collaboration (AOAC) International elemental analytical method AOAC 2015.01 (1) describes the analysis of toxic elements in food samples using ICP-MS. In this work, the analysis of toxic elements As, Cd, Hg, Pb, and Sb in various food matrices following AOAC 2015.01 was validated using the NexION ICP-MS (PerkinElmer Inc.) instrument fitted with a universal cell using both collision and reaction modes. The instrument was also equipped with a high throughput system (HTS) that utilized flow injection technology to deliver the sample to the plasma during the data acquisition stage and diverted the sample to the waste for the rest of the time. This reduces the total sample load on the plasma and results in less maintenance and downtime. Because the sample loading and loop wash were enabled by the vacuum pump, HTS can perform the wash procedure more efficiently than conventional sample introduction. Sample digestion was performed using a Titan MPS microwave digestion system (PerkinElmer Inc.). The instrument components and operating conditions used for the analysis are shown in Table I.

Instrument Optimization and Method Development

The elements being determined, their respective isotopes, and the mode of analysis used for each element in this method are listed in Table II. Cobalt, Mo, Zr, and W were monitored for interference evaluation. Among the analytes, As was measured as AsO in reaction (DRC) mode using oxygen as the cell gas, and the rest of the analytes were measured in collision (KED) mode using helium as the cell gas.

Ultrapure water (UPW; 18.2 MΩ.cm) and high-purity acids (Tamapure, Tama Chemicals) were used throughout this work. The calibration standards were prepared by the dilution of ICP-MS grade multi-element standards in a diluent made of 5% HNO

 spiked with 200 ppb of Au to aid the mobility of Hg. This diluent was also used as the calibration blank and carrier solution. The concentrations of the calibration standards are shown in Table III. Standard 4 was also used as a continuing calibration verification (CCV) standard.

The internal standard solution was comprised of 40 ppb of Rh and Ir in a solution of 1% HNO

 and 4% isopropanol (IPA) and spiked with 200 ppb of Au. Isopropanol was added to compensate for the difference in the carbon content in the standards and the samples and among samples to address the carbon-induced signal enhancement effects on As (2,3). The internal standard was introduced into the designated port of the HTS valve and mixed online with the sample. The wash solution consisted of 1.5% HCl (v/v), 1.5% HNO

 (v/v), and 5% IPA, and it was spiked with 200 ppb Au where IPA was used to facilitate the washout of organic materials.

was evaluated using a series of single-element standard solutions of Co, Zr, Mo, and W, which were prepared in 3% HNO

 with concentrations of 10, 50, and 100 ppb each.

Three food certified reference materials—SRM 1568b (rice flour) and SRM 2976 (mussel tissues), purchased from the National Institute of Science and Technology (NIST), and DORM-5 (fish protein) purchased from National Research Council Canada—were used to validate the accuracy of the method. They were also used to evaluate the method precision (via method duplicates) and matrix spikes, in which the samples were spiked with multi-element standards to the concentrations of 1 ppb for As, Cd, Sb, and Pb, and 0.1 for Hg in the analytical solutions. For all food samples, lutetium (Lu) was added before digestion to assess the potential loss during digestion, as specified in AOAC 2015.01. Three method blanks were included in each digestion batch. The blanks were treated the same as the samples and went through all the preparative steps.

The digestion vessel was pre-wet by adding a few drops of ultrapure water (UPW). Food samples of ca. 0.5 g were accurately weighed, and then transferred into 75 mL microwave digestion vessels. Then, 1 mL of UPW was added, followed by 8 mL HNO

, and 0.1 mL of 100 mg/L Au and 100 mg/L Lu. The method blanks, samples, and matrix spikes were digested in the same batch using the built-in rice flour method. Microwave digestion parameters are shown in Table IV.

After digestion, the samples were decanted into the pre-weighed centrifuge tubes and brought up to the 40 mL mark with UPW to obtain the intermediate sample solution, and the weights were recorded. An aliquot of the intermediate sample solution (10 mL) was pipetted into a pre-weighed 50 mL centrifuge tube before UPW was added to the 40 mL mark, and then the weights were recorded. A total dilution factor of ca. 320 was achieved and the samples were ready for ICP-MS analysis.

Evaluation of the Interference Mitigation/Removal

The effectiveness of the interference mitigation/removal was evaluated by the background equivalent concentrations (BECs) of the target elements in the interference removal checking solutions. The results are shown in Table V. For As, which is analyzed as AsO, the background is at ppt/sub-ppt levels with Zr and Co at concentrations up to 100 ppb; for Hg and Cd, the background is ≤10 ppt with W and Mo at concentrations up to 50 ppb. In all cases, the concentrations tested for the interfering elements were much higher than can be expected in normal food materials. For this reason, the interfering elements were monitored in this study to cover extreme analytical scenarios.

Recoveries higher than 85% were achieved for all digested samples, including matrix spikes, blanks, and blank spikes, meeting the acceptance criteria (≥ 75%) as recommended in AOAC Table 2015.01F (2).

The limit of quantification (LOQ) was calculated as 10 times the standard deviation of 10 replicated measurements of the method blank multiplied by the dilution factor.

A comparison of the LOQs achieved in this work and those provided in AOAC 2015.01 is shown in Figure 1. For all the target elements, the LOQs obtained in this work were lower than those of different food types published in AOAC Table 2015.01H.

FIGURE 1: Comparison of limits of quantification (LOQs) achieved in this work with those captured in AOAC Table 2015.01H (2).

The accuracy was verified by evaluating the recoveries of various analytes achieved for the SRMs: NIST 1568b (rice flour), NIST 2976 (mussel tissues), CRM DORM-5 (fish protein), and the matrix spikes.

The CRMs and matrix spikes were prepared in duplicates, and each preparation was measured three times. The mean recoveries of the duplicates are shown in Figure 2. Recoveries between 85% and 114% were obtained for the certified elements, falling well within the QC criteria of 75–125% as provided in AOAC Table 2015.01F.

FIGURE 2: Recoveries for the certified elements in the CRMs.

Matrix spikes were performed on three CRMs. Duplicates were prepared for each spiked sample. The mean recoveries are shown in Figure 3. Recoveries between 75% and 113% were obtained for all target elements, meeting the QC acceptance criteria of 70–130% as specified in AOAC Table 2015.01F.

FIGURE 3: Spike recoveries for the tested CRMs. *The recoveries of As for NIST 2976 and DORM-5 were not reported. The spike level in this case was too low (<5% of the intrinsic amount), resulting in higher errors.

The precision was evaluated by the relative percent difference (RPD) of duplicated sample analysis. The duplicated samples were separately digested and went through the same sample preparation process as individual samples. These tests were performed on three CRMs. In all cases, the RPDs were within the QC acceptance criteria of <30% as specified in AOAC Table 2015.01F for all target elements, as shown in Table VI.

To validate the stability of the method, various food samples were measured repeatedly over 8 h , and the CCV recoveries were checked over this period. CCV was measured every 10–15 samples. All CCV recoveries were normalized to Standard 4 (Table III), and were well within ± 10% of the original reading, as shown in Figure 4, meeting the QC acceptance criteria of 85– 115% as specified in AOAC Table 2015.01F.

FIGURE 4: CCV recoveries over an 8-h run of food samples.

The method outlined in AOAC 2015.01 was validated with a commercially available ICP-MS instrument using both collision and reaction cell modes, automated sampling procedure, and microwave digestion system for the determination of the toxic elements As, Cd, Hg, Pb, and Sb in various food matrices. The study was evaluated for the LOQ, accuracy, precision, and stability. All the QC criteria were met or exceeded, showing the method suitability of this equipment in a routine laboratory environment.

(1) AOAC Official Method 2015.01; “Determination of Heavy Metals in Food by Inductively Coupled Plasma-Mass Spectrometry First Action” (2015).

 is with PerkinElmer Inc., in Woodbridge, Ontario, Canada. She holds a Ph.D. in Analytical Chemistry and has specialized in elemental and isotope analysis using ICP-MS. Liyan is currently a national committee member of the Canadian Society for Analytical Sciences and Spectroscopy (CSASS) and the editor of the Society’s newsletter since 2019.

, the editor of the “Atomic Perspectives” column, is the principal of Scientific Solutions, a consulting company that serves the educational and writing needs of the trace element analysis user community. Rob has worked in the field of atomic spectroscopy and mass spectrometry for more than 45 years, including 24 years for a manufacturer of atomic spectroscopic instrumentation. He has authored more than 100 scientific publications, including a 15-part tutorial series, “A Beginners Guide to ICP-MS.” In addition, he has authored five textbooks on the fundamentals and applications of ICP-MS. His most recent book, a paperback edition of 

Measuring Heavy Metal Contaminants in Cannabis and Hemp

 was published in December 2021. Rob has an advanced degree in analytical chemistry from the University of Wales, UK, and is a Fellow of the Royal Society of Chemistry (FRSC) and a Chartered Chemist (CChem). Direct correspondence to 

Is ICP-MS instrumentation ready to handle the requirements of AOAC Method 2015.01 for the determination of toxic elements in food—including dealing with interferences? We ran this study to check.

Determination of Toxic Elements in Food by ICP-MS Using AOAC Method 2015.01

The dichotomy created by the advent of computers and brought up by the title of this column was a major quandary in the early days of the computer revolution, causing major controversy in both the academic and commercial communities involved in the development of modern computer architectures. Even though the controversy was eventually decided (in favor of binary representation; all commercially available computers use a binary internal architecture), echoes of that controversy still affect computer usage today by creating errors when data is transferred between computers, especially in the chemometric world. A close examination of the consequences reveals a previously unexpected error source.

Howard Mark serves on the Editorial Advisory Board of 

 and runs a consulting service, Mark Electronics that provides assistance, training, and consultation in near-IR spectroscopy as well as custom hardware and software design and development.

So what’s the cause for all the furor? Basically, it’s because the “natural” smallest piece of internal hardware of a computer (a “bit”—contraction of a 

) has two states: “on” and “off.” The literature assigns various name pairs to those states: on/off; high/ low; true/false, or one of the various others depending on the application. The name pair of special interest to us here is “1/0.” Conceptually, the 1/0 dichotomy can be used to implement several different underlying concepts, including Boolean logic states and numbers. Regardless of this interpretation, the state of the circuit is represented by an actual voltage at the output of the circuit. Typically, the state “0” would correspond to an actual zero voltage at the output, whereas a “1” state would represent some non-zero voltage; five volts is the common value. Actual hardware can transiently have intermediate values while changing from one state to another. As an example, when analyzing the function the hardware performs, intermediate voltages are considered disallowed; in actual hardware, intermediate voltages only occur briefly during a change of state.

Hardware can be devised to create basic Boolean logic functions such as “AND,” “OR,” and “NOT.” Combinations of those basic functions can be, and are, used to create more complicated logic functions, and they can also perform functions George Boole never conceived of as long as the output signal of the hardware is a voltage that corresponds to either a “zero” or a “one.”

So much for interpreting 1/0 as logic. What we want to know is how that same concept is used to represent numbers. It is very straightforward; it’s done the same way that we do with decimal numbers. We call our usual number system “decimal,” which is also called base-10 because it consists of 10 digits: “0,” “1,” “2,” “3,” “4,” “5,” “6,” “7,” “8,” and “9” (10 different symbols representing the 10 digits). In contrast, binary (base-2) numbers are only allowed two states, with symbols representing the two states, the zero and one described above. As a short aside, mathematicians have described number systems with different numbers of states (and corresponding symbols). For example, in a ternary number system, a digit can have three states (“0”, “1”, and “2”), although the issue with this system is that it is not so easily implemented in hardware. That’s one reason you never see it in day-to-day use. Donald Knuth discusses some of the more exotic number systems mathematicians have devised in his masterwork (see section 1.2.2 of [1]), such as number systems with fractional and even irrational bases (“There is a real number, denoted by 

 = 2.718281828459045..., for which the logarithms have simpler properties” (see page 23 in [1]). That means that 

, a number that is not only irrational, but transcendental, can be the base of a number system. But we won’t go there today.).

In fact, some of the alternative number systems are sometimes seen in computer applications. In particular, the octal (base-8) and the hexadecimal (base-16) number systems are sometimes used in special computer applications and for pedagogical purposes in instructional texts. Octal- and hexadecimal systems are particularly well-suited to being used for representing numbers in computers by virtue of the fact that they are both powers of two. Thus, they can easily be converted to or from their binary representation. Octal numbers can be expressed simply by taking the bits of a binary number in groups of three, and hexadecimal numbers can be expressed by taking the bits of a binary number in groups of four. Conversion to other bases is more complicated and we leave that for another time.

Sometimes, we need to accommodate another limitation of the number systems we use. For example, all number systems have one and the same limitation—the number of symbols that are used to represent numbers is finite and limited. So how do we represent numbers higher than those that can be represented with a single symbol?

For example, the binary system only allows for two states, so how can we count to values higher than 1? Again, the answer is in a similar fashion to how we do it in the decimal number system. And how is that? The answer is that we use positional information to enable counting beyond the limit of the number of symbols available. When we’ve “used up” all the symbols available to us in one place of the number, we add another place, and in it we put the number of times we’ve “run through” all the available symbols in the next lower place.

Regardless of the number system, another limitation is that there are only a finite number of symbols to represent the digits, so how can we keep counting to higher numbers when we’ve “used up” the available symbols? Of all the number systems we’ve mentioned, one of them encounters this problem—the hexadecimal system, which requires 16 different symbols, six more than our usual numbers do. The solution generally applied is to co-opt some of the alphabetic characters as numerical digits; typically the letters a–f are used to represent digits with values of 10 to 15.

To see how this all works, Table I shows how the first 20 numbers (plus zero) are represented in each of these various number systems. Online utilities are available to convert from one number base to another (an example is in the literature [2]). It is obvious that there is danger of confusion because the same symbol combination could represent different numbers depending on which number system it is being used in. In cases where such confusion could arise, the number system is indicated with a subscript after the number. Thus, for example, 100

 (read as: “one-oh-oh in base two equals four in base ten”), whereas 100

 (read as “one-oh-oh in base three equals nine in base 10,” as we can see from Table I), and the subscripts tell us which is which. How do we then interpret the subscripts? Those are decimal!

Once they are constructed, computers have no problem dealing with any of those systems of numbers, although some are more complicated for engineers to set up than others. However, people have problems with them. For example, consider one very simple question: “is ef7da1

 greater or less than 1100101110101000010

?” I’m sure that any of our readers could, with enough time and effort, work out the answer to that question, but the point is that it doesn’t come easily; certainly, it’s not as easy as answering the similar question “Is 5

We’re used to working with decimal numbers. At the beginning of the computer revolution and even in the times before then when “computers” meant multi-million-dollar devices attended by “high priests” (as they were perceived at the time), the question of how to represent numbers inside a computer arose, and it was an important question. Back then, computers were used to perform calculations involving multi-million-dollar business transactions (at a time when a million dollars was worth something!), and the results needed to be checked to ensure that the computers were working properly and providing correct answers. Only people could do that, and they had to do it using decimal representation. That created a strong incentive to have the computers also use decimal representation so that the computers’ internal numbers could easily and directly be compared with the manual computations.

Eventually, the need for people to comprehend what the computers were doing was addressed with a hybrid approach called 

. Numerical information was maintained internally as decimal values, where each digit 0–9 was expressed individually in binary. This process required only four bits per digit, just like hexadecimal, but only 10 of the 16 possible combinations were allowed to be expressed. This process allowed combinations to be put into a one-to-one correspondence with the ten decimal digits. This scheme made it easier for humans to interpret, but it carried some disadvantages: 1) it increased the complexity of each digit’s circuitry to prevent it from entering a disallowed state, which made computers more expensive to construct and more subject to breakdowns; 2) arithmetic circuits were also more complicated to enable decimal instead of binary operations; and 3) the circuitry for all four bits for each digit had to be present for every decimal digit throughout the computer, even though only 10 of the possible 16 combinations of those four bits were used.

As a result, it was a very inefficient use of the hardware. To represent numbers of up to (say) 100,000

, all components, wiring, controls, memory, and interconnects required 6 x 4 = 24 bits of (more complicated) hardware for BCD numbers compared to only 17 bits for binary numbers. The discrepancy increased as the magnitude of the numbers that needed to be accommodated increased. In the days before large-scale integration techniques were available, that allowed an entire computer to be fabricated on a single silicon chip, which imposed a substantial cost penalty on computer manufacturing because the extra bits had to be included in the control, processing, memory, and every other part of the computer. Some “tricks” were available to reduce this BCD penalty, but the “tricks” often had the side-effect of exchanging higher hardware cost for slower computation speed, and it was still more expensive to build a computer for BCD numbers than for binary numbers.

In fact, remnants of BCD number representations still persist in the form of any device that has a built-in numeric display. Typically, those consist of a seven-segment LED (or other electro-optical technology) are arranged so that activating appropriate segments allow any numeral from zero to nine to be displayed. Although often combined into a single circuit, that requires conceptually two stages of decoding to implement. For each digit displayed, four binary bits are decoded to one of the 10 decimal digits, then each of those is decoded to determine which of the LED segments needed to be activated.

In modern times, computers are based on micro-controllers that often include, as mentioned above, an entire computer on the silicon integrated circuit (the “chip”). Because the “fab” needed to construct such a computer costs several millions of dollars, efficiency in using silicon “real estate” is of paramount importance, so modern computers use binary numbers for their internal operations, whereas input (accepting data), and output (providing results), both of which involve human interaction, are done using decimal. With the increases in computer speed and reliability achieved over the years, the conversions between the two domains is performed via the software, bypassing the older problems previously encountered.

However, we’re not out of the woods yet! We have not yet accounted for all the numbers and types of numbers we expect our computers to deal with. In particular, ordinary scientific measurements need to deal with very small (for example, the size of a proton is 8 x 10

 meters) and very large quantities (the universe is (as of this writing) known to be roughly 92 billion (9.2 x 10

) light years in diameter and 14 billion (1.4 x 10

 atoms, and so forth). Ordinary numbers were insufficient to deal with the need to represent these very small and very large quantities. As a result, scientific notation was devised to help us express these extreme quantities, as I just did at the beginning of this paragraph.

There is a similar problem in computer expression of numbers—how to deal with very large and very small numbers. A separate but related problem is how to represent fractions; note that the examples and number systems described above all deal with integers. However, computers used in the “real world” have to deal with fractional values as well as very large and small ones. The computer community has dealt with that problem by devising a solution analogous to scientific notation. Computers generally recognize two types of numbers, maintained by the software and independent of the number base used by the hardware. These are designated “integers” and “floating point” numbers. All the number systems we’ve discussed above, regardless of the number base, are integers. Although a mathematician might disagree with this definition, for our purposes here we consider “integers” to mean the counting numbers (as in Table I). Integers are generally limited to values from zero to a maximum determined by the number of bits in a computer “word” (which is hardware-dependent) and their negatives, regardless of the number base. Table I tells us (almost) everything else we need to know right now about integers.

The other type of numbers, which are recognized and used internally by computers, is analogous to scientific notation and called “floating point” numbers. Floating point numbers come in a variety of implementations, which are designated Float-16, Float-32, Float-64, and so forth, depending on how many bits of memory are allocated by the computer software to each “floating point” number. Generally, that is a small multiple of the size of a computer “word,” which is the number of bits, determined by the hardware, that the computer can handle simultaneously (and not incidentally, usually also determines the maximum size of an integer). Generally, each number is divided into four parts: an exponent; a mantissa; sign of the exponent; and sign of the mantissa.

Because different manufacturers could split up the parts of a floating point number in a variety of ways, this scheme could—and did—lead to chaos and incompatibility problems in the industry, until the Institute of Electrical and Electronic Engineers (IEEE), a standards-setting organization for engineering disciplines, stepped in (3). Comparable to the American Society for Testing and Materials (ASTM) (4,5), IEEE created a standard (see IEEE-754) (6) for the formats of numbers used inside computers. The standard defines two types of floating point numbers, single precision and double precision. Each is defined by splitting a number into two main parts, an exponent and a mantissa. Per the standard, the 32 bits of a single-precision number allocate 23 bits for the mantissa of the number, which gives a precision equivalent to 6–9 decimal digits depending on the magnitude of the number. Double precision uses 64 bits to represent a number and actually provides more than double that of single precision, the 52-bit mantissa of an IEEE double-precision number is equivalent to a precision of approximately 16 decimal digits.

However, we’re still not out of the woods. There’s no flexibility in the binary representation of data in the computer, especially if they are, in fact, IEEE single-precision numbers, but a problem arises when someone is careless when changing the representation to decimal for external use, such as transferring the data to another computer, displaying it for people to read, or performing computations on it after conversion to decimal. It doesn’t matter what the data is; it’s a fundamental problem of number representations. Converting the internal values in your computer to a format with an insufficient number of decimal digits is the underlying source of a problem, and that will affect the results of any further calculation performed on that data.

The IEEE specifications include the following proviso: if a decimal string with at most six significant digits is converted to IEEE 754 single-precision representation and then converted back to a decimal string with the same number of digits, the final result should match the original string. Similarly, if an IEEE 754 single-precision number is converted to a decimal string with at least nine significant digits, and then converted back to single-precision representation, the final result must match the original number (3). So when you write out your data to a file and the data is written as decimal numbers, the data stored in the file will have an insufficient number of decimal digits of precision, and contain neither the six-and-a-half digits worth that the internal binary representation of the data contains nor the nine that is recommended. When that data is read into another computer, the binary number generated in the second computer is not the same as the original binary number that gave rise to it. Performing computations, such as a derivative or other processing, does not fix the problem, because the new data will also be subject to the same limitations. Thus, transferring data to a different computer so that a different program can work on it may not give the same results as performing the same computations on the original data.

This discussion is pertinent to some data-transfer standards. For example, JCAMP-DX (7) is a popular format for computer exchange of spectral data. The JCAMP-DX standard does not address the question of the precision of the data being handled; it permits data to be stored using an arbitrary number of digits to represent the original data. Therefore, an unwary user of JCAMP-DX may use an insufficient number of decimal digits to store spectral data in a JCAMP-DX file and later be surprised by the results obtained after the data has been transferred.

For example, if the data is to be used for chemometric calibration purposes (for example, multiple linear regression [MLR] or principal component regression [PCR]), different results will be obtained from data after it has been transferred to a second computer than if it was obtained from the original data in the original computer.

How can this be fixed? As per the discussion above, any external decimal representation of the data must be formatted as a decimal string of at least nine decimal digits. Currently, examples of JCAMP-DX files I’ve seen sometimes use as few as five decimal digits. I have seen JCAMP-DX files written by current software packages that wrote the spectral data using as few as six or seven decimal digits, which is better but still short of the nine required. I am not completely convinced that nine digits is sufficient, although at least it errs on the side of safety. The reasons for my doubt are explained in the appendix below. Therefore, rewriting the code you use to export the data, so that it writes the data out with nine significant digits, is a minimal requirement on what needs to be done. Any other programs that read in that data file must also accept and properly convert those digits.

The below is a demonstration of the need for sufficient digits in the decimal representation of numbers converted from internal binary to decimal.

As in any number system, numbers are represented by the sum of various powers of the base of the number system. In a binary system as used in computers, the base is 2. Integers (counting numbers ≥1) are represented as the sum of powers of 2 with positive exponents: 

 + ...In the binary system, the multiplier, 

, can only have values of 0 or 1; the corresponding power of two is then either in or not in the representation of the number.

Floating point numbers (for example, IEEE-754 single precision) are represented by binary fractions; that is, numbers less than 1 that consist of the sum of powers of 2 with negative exponents (for example, A

 can only have values of 0 or 1. When we convert this representation to decimal, each binary digit contributes to the final result an amount equal to its individual value. Table II presents a list of the exact decimal values corresponding to each binary bit. In Table II, these decimal values are an exact representation of the corresponding binary bit. If a conversion of a number from binary to decimal does not include sufficient digits in the representation, then it does not accurately represent the binary number. When the number is converted back to binary in the receiving computer, that number will not be the same as the corresponding number in the original. We discuss this point further below.

Numbers greater than 1 are represented by multiplying the mantissa (from Table II) by an appropriate power of two, which is available as the “exponent” of the IEEE-754 representation of the number. You should be careful when decoding the exponent because there are a couple of “gotchas” that you might run into; those are explained in the official standard (available as a PDF file online), in discussions of the standard, and in the literature (8) that provide details for creating and decoding the exponent, as well as the binary number comprising the mantissa.

There are several takeaways from Table II: first, we see that the number of decimal digits needed to exactly express the value of the number (including the leading ze- roes) equals the power to which 2 is raised. We also see a repeating pattern: beyond 2 , the last three digits of the decimal number repeat the sequence ...125, ...625, ...125.... From Table II, we also see that the statement “single precision corresponds to (roughly) 6.5 digits” (as derived from the IEEE-754 standard [3]) means that by virtue of the leading string of zeros in the decimal-conversion value, any bits beyond the 23rd bit will not affect the value of the decimal number to which binary representation is converted. Table II demonstrates that property because all of the first seven digits of the decimal equivalent are zero at and beyond the 24th bit. Therefore, when added into the 6-decimal-digit equivalent of the binary representation, the sum would not be affected.

At any stage, the exact decimal representation of a binary number requires exactly the same number of decimal digits to represent the corresponding binary fraction as the exponent of that binary digit. One point of this exercise was to demonstrate that because these representations of the binary digits are what must be added to give an exact representation of the original binary number, it therefore requires as many decimal digits to represent the binary number as there are bits in that binary number.

Above, we alluded to the fact that floating-point numbers are inexact, and that the degree to which they are inexact depends on the number base. For example, the decimal number 0.310 cannot easily be represented in the binary system. 2

 = 0.25 is too small. We can add smaller increments to approach 0.3 more closely. For example, 0.011

 is again too small. We’re closing in on 0.3

, but clearly it’s not simple. Using an online decimal-to-binary converter (2) reveals that 0.01001100110011...

 is the unending binary approximation to 0.3

 but any finite-length binary approximation is inevitably still in error. Different number bases are not always easily compatible.

This issue becomes particularly acute when converting numbers from the binary base inside a computer to a decimal base for transferring data to another computer, and then back again. Ideally, the binary value received and stored by the recipient computer should be identical to the binary value sent by the initial computer. For some data transfer protocols, for example, JCAMP-DX allows for varying precision of the decimal numbers used by the transfer. In Table III, we present the results of a computer experiment that emulates this process while examining the effect of truncating the decimal number used in the transfer (perhaps because of insufficient numbers of decimal digits being specified as the format). We picked a single number to represent the numbers that might be transferred and expressed it in decimal and hexadecimal numbers; the hex number represents the internal number of the transmitting computer. The decimal number was successively truncated to emulate the effect of different precision during the transfer and the truncated value used, to learn what the receiving computer receives (the value recovered). The test number we used for this experiment was pi—a nice round number! We used Matlab to convert decimal digits to hexadecimal representation. Unfortunately, Matlab has no provision to allow entry of hexadecimal numbers, so an on-line hex-to-decimal software program was used to implement the hex-to-decimal conversions.

The results in Table III are enlightening. Most users of JCAMP software packages (and probably other spectrum-handling software as well) do not provide enough decimal digits in the representation of the spectral data that is transferred to ensure that spectra transferred from one to computer to another are identical on both computers. Therefore, any further computations the computers execute will give different answers because of the use of different data values, which is particularly pernicious in the case of “derivatives,” where the computation inherently provides the results of small differences between large values. This pushes the (normally negligible) errors of the computation into the more significant figures of the results.

(2) D. Wolff, Base Convert: The Simple Floating Base Converter (accessed September 2022). 

IEEE Standard for Floating-Point Arithmetic, IEEE Std 754TM-2008

https://irem.univreunion.fr/IMG/pdf/ieee-754-2008.pdf

 serves on the Editorial Advisory Board of Spectroscopy, and runs a consulting service, Mark Electronics, in Suffern, New York. Direct correspondence to: 

 serves on the Editorial Advisory Board of 

. He is also a Certified Core Adjunct Professor at U.S. National University in La Jolla, California. He was formerly the Executive Vice President of Research and Engineering for Unity Scientific and Process Sensors Corporation. ●

The past decision to use binary representation in computer architectures affects the results of chemometric-based outputs, especially if different data values are used.

Decimal Versus Binary Representation of Numbers in Computers

Color is something that most people take for granted. A key assumption in color science is that our perceptions are similar and individual differences are small. Predictable rules, such as additive color mixing, make color modeling possible so that we can describe the richness of color in relatively low-dimensional spaces like red, green, and blue (RGB). Here, we look at how scientists define and calibrate color, various color measurement methods, and issues that arise when attempting to accurately measure and quantify color.

, is the General Manager of the Applied Systems business at Ocean Insight, an affiliate associate professor at the University of Washington, and has started and advised numerous companies in spectroscopy and in applications of machine learning. He has approximately 40 peer-reviewed publications and 6 patents. His work in practical optical spectroscopy, such as LIBS, Raman, and TDL spectroscopy, dovetails with the coverage in this column, which reviews methods (new and old) in laser-based spectroscopy and optical sensing.

Spectroscopy can be defined as “the interaction of light with matter,” and typically involves judgments about the matter based on light absorption or emission. Hence, spectroscopists deal with the electromagnetic spectrum regularly, and we’re particularly interested in emission or absorption of particular wavelengths of light. The initial modern study of matter with light may be traced to the flame spectroscope devised by Bunsen and Kirchoff in the 1800s in Heidelberg, which allowed them to identify elements by their emission spectrum when they were injected into the eponymous Bunsen burner. The motivation for this occurrence was almost certainly the addition of a common salt such as table salt, which generated the intense emission of the sodium “D” lines at 589.0 and 589.6 nm. The pair went on to discover two new elements, cesium and rubidium, with their spectroscope.

Although spectroscopists work continuously with light of various wavelengths, we are typically thinking of discrete wavelengths corresponding with emission or absorption. Few of us have had a formal introduction to color science, and how the perception of “color” is derived from viewing either continuous sources (like a tungsten filament or other hot source emitting blackbody radiation) or a combination of discrete sources with narrower wavelength emissions.

Here, we cover some of the basics of color science with my colleague, Ethan Montag, who is an expert in color science. I had the opportunity to ask him a number of questions about color. Hopefully, the discussion of how color is parameterized and how we make accurate color measurements serves as a good introduction that piques your interest!

There are lots of ways to describe color, known as color spaces. Most readers of Spectroscopy are probably familiar with the red, green, blue (RGB) color system, whereby the three primary colors can be additively combined to make any other color. Could you describe any other color systems? For example, what is the purpose and origin of the International Commission on Illumination Laboratory (CIELAB)? 

Color is a perception. It is not a property of an object, but the effect of light emitted or reflected from objects impinging on the eye and interpreted by the nervous system. The ability to describe color using different color spaces all derive from the fact that there are three independent channels for conveying color information from the eye to the brain. The process of distinguishing color begins in the retina, where there are three types of cone receptors, each sensitive to a different, but overlapping, region of the visible spectrum. My thesis advisor, Robert M. Boynton, liked to point out that the Young-Helmholtz Theory of Trichromacy is the only theory in psychology to be experimentally confirmed.

There are many different types of color spaces that are used for different purposes. There are device-dependent color spaces (for example, cyan, magenta, yellow, key [CMYK] and RGB) that are used to specify the pro- duction of color by subtractive (dyes and pigments) or additive (displays) mixing of primary colors. Then, there are device-independent color spaces (for example, standard RGB [sRGB] and Pantone) used for color communication and specifying colors between devices. For example, profiles can be made that can transform the RGB of a particular calibrated display to sRGB and then back to the RGB of a different, calibrated display so that the two displays match.

In color metrology, we use the device-independent color spaces adopted by the CIE based on color matching experiments performed in the last century. These include the CIE 1931 2° XYZ color space and the CIE 1964 10° supplementary XYZ color space. These color spaces are based on linear transforms of specific RGB primaries used in color-matching experiments. Because of trichromacy, these XYZ primaries are linear transforms of the actual cone response in the eye. Because the curves describing the sensitivity of cones to the visible spectrum overlap, it was impossible to measure them directly when the system of colorimetry was being developed. Vision researchers now have excellent values for the long-, medium-, and short-wavelength sensitive cones (abbreviated as LWS, MWS, and SWS, respectively), but the color science community has been slow to adopt these physiologically based primaries.

These primary-based color spaces are actually “color blind.” That is, they tell you whether two color patches match (to the ideal observer) under specific geometric illumination and viewing conditions, but they do not tell you what the color looks like. An empirically derived color space, CIELAB, converts XYZ color coordinates to a three-dimensional (3D) color space where Euclidian distances (ΔE*ab) are meant to be correlated with perceived color differences. A unit distance between the [L*, a*, b*] coordinates of two colors represents a noticeable differ- ence between the colors. This space allows for the setting of color tolerances for color reproduction. Over the years, the use of this space has been refined by replacing the Euclidian distance with more complicated color difference equations using the same coordinate system. Although often represented as a color appearance space, CIELAB is more of an intermediate stage between the CIE XYZ and appearance.

There are color spaces, such as the physical Munsell Book of Colors and various color appearance models (CAMs), that attempt to organize colors based on perceptual attributes such as lightness, hue, and chroma (colorfulness). The opponent processing of color is built into these spaces. The appearance of color is based on two opponent channels, red–green and blue–yellow. These dimensions are typically part of an appearance space. However, the appearance of a color is difficult to quantify because it depends on the observer’s state of adaptation, the context of the colored area being viewed (its complex surroundings), and both the conscious and subconscious expectations of the observer.

What are some of the challenges in making standardized color measure- ments? How does one “normalize” illumination in the computation of color values?

As mentioned in the last answer, colorimetry is based on an ideal (theoretical) observer’s response derived from a limited set of human observers making real color-matching judgments of isolated color patches. Briefly, the color of a reflective surface is calculated by integrating over the visible spectrum the product of the illuminant spectral power, the reflectance factor of the surface, and each of the standard observer’s color matching functions (x, y, and z) to get tristimulus values (X, Y, and Z). The system was designed so that the color matching functions are all positive and 

 is directly proportional to luminance. Therefore, they do not look like any real primaries you might see in a display. A non-spectroscopic form of color measurement uses a colorimeter that has three sensors, each with a sensitivity close to the color matching functions (or a linear transform of them). You might notice that when we do this calculation, the reflectance of the object is lost. This observation might be surprising to spectroscopists unfamiliar with color measurement.

A consequence of this occurrence is color metamerism. 

 is the change in the color of an object because of a change in the illumination. Two surfaces might match under one illuminant but appear different under another. The ramifications of this for color inspection is that the desired illuminant must be specified. The quantification and evaluation of the effects of illumination metamerism is part of the portfolio of the field of illumination engineering.

 is the mismatch between colors because of changes in the observer. Two people may have slightly different spectral sensitivities in their LWS cones, so a match for one of them does not hold for the other. In the extreme, this issue is manifested by color-blindness, dichromacy, a missing cone type, or anomalous trichromacy where LWS or MWS cones have sensitivities shifted closer to each other. In the normal color population, there are differences between people because of slight wavelength shifts in the LWS and MWS cone types. Pre-retinal pigments can also contribute to observer metamerism. As one ages, changes in the densities of optical structures in the eye can cause spectrally selective changes as well, so that you can make different color matches than your younger self.

A controversial topic in color vision is tetrachromacy. It has been observed that multiple MWS and LWS cone pigments with slightly different peaks can be expressed in the cones. A small percentage of biological females have four cone types where the additional cone has a shifted SWS or LWS cone pigment. Although this trait is rare in biological females, it influences color matching behavior and discrimination (they’re better than us!). The consensus understanding is that the neural pathways to the brain are still trichromatic, meaning that these individuals do not have any additional dimensions of color sensations. An analogous effect is that under mesopic conditions, illumination levels where the rod photoreceptors and the cones both can respond. The color-matching behavior is different than under photopic illumination where only the cones contribute because the rod response is saturated. We are all monochromats under scotopic (low-light) illumination where only the rods are functional.

This information leads to the questions that people often ask about color: Do colors look alike to everyone? Is it possible that my “red” is perceived as “green” to you? Because the physiology, color-matching behavior, and color-opponency of color-normal humans is, to within close limits, the same, I tend to believe, based on transitive relationships, that colors “look alike” to normal trichromats.

However, it is important to note that it doesn’t mean that cultural and personal aspects of the “meaning” of color do not affect how we see color in a more expansive definition of what perception is (as opposed to sensation). The association of pink for girls and blue for boys is a cultural imposition, which actually flipped the convention from the early 1900s. It is very difficult to control for the cultural influence of color meaning when trying to study whether different colors have emotional or physiological effects. I refer you to the literature on Baker-Miller Pink, or the question of why we don’t have yellow fire engines if you want to enter the morass I try to avoid.

Why do we measure color? Are there particular benefits from using one or another of the structured color sys- tems? How are color measurements calibrated?

Why do we measure color? Before I attempt to answer this, we should address what color is used for. I can list three purposes of color: identification; quality assessment; and aesthetics. Color is perhaps the first tool we use to help us identify objects in the world. Think of a bookshelf in your home. If you want to find a particular one, you might typically think of the color of the object and narrow your search by focusing only on the books with that color. Likewise, when you try to find your car in a crowded parking lot, color is what you use to search efficiently. Camouflage is a nice example of how color helps us in identification.

There is a theory that color vision may have evolved to aid in the identification of ripe fruit in a background of leaves. Although it may be problematic to apply a teleologic explanation to the development of a biological characteristic, it is hardly controversial to say that color vision aids us in functions that help us maintain our species. Although we can see the shape of a fruit without color, we use color to assess its quality. Likewise, we use color to assess other aspects of fitness and health.

Therefore, it is conceivable that aesthetics plays the biggest role in our use of color. Because of this, color measurement becomes important so that we can ensure the faithful and consistent reproduction of objects we use in the world. Unlike other aspects of spectroscopy, color measurement is rarely used to assess the physical characteristics of objects. Surface reflectance in the visible spectrum does not give us much information about material properties. We leave this to other regions of the spectrum or high energy applications such as Raman or laser-induced breakdown spectroscopy (LIBS).

Therefore, colorimetry is primarily used to ensure visual consistency of the color of an object. For example, if your company produces widgets, the process in which they are colored may be susceptible to changes over time because of changes in the formulation or other process changes. You may want to measure a few of your widgets coming from a new batch to make sure they are the right color. If your widgets are made up of multiple parts joined together, you may want to bin your parts based on their color so that you join matched parts together. In some industries, there is a need for an 100% inspection of color for quality control (QC). If you buy paint, you want the color to match from one can to the next. If you buy floor tiles, you want all the tiles to match.

However, even the measurement of surface reflectance is complicated. To ensure that our color measurements are not misinterpreted, the method in which they are made are also specified.

To fully describe the reflectance of an object, one would need to measure the bidirectional reflectance distribution function (BRDF). The BDRF describes the ratio of reflected light to incident light at every angle of incidence and reflectance. A perfectly diffuse surface reflects light equally in all directions. A perfect mirror reflects light only in the specular direction. In between these extremes are materials with various degrees of gloss. There may also be a change in reflectance that is wavelength-dependent as seen in iridescent and pearlescent materials.

Generally, it is too expensive and time-consuming to make goniometric measurements of a surface. Instead, there are standard geometries that are typically used with spectrophotometers for color measurement. For example, we use integrating spheres to gather light at all angles to get an estimate of the overall reflectance factor. We describe the illumination as diffuse if it enters the side of the sphere and then specify the angle from the normal at which the spectrometer measures the sample, as shown in Figure 1. We define this geometry as d/8°. Because of Helmholtz reciprocity, this geometry is equivalent to 8°/d where we switch the positions of the detector and the illumination. In this sphere configuration, all the light reflected from the surface is measured, including the specular reflectance that is reflected off the surface at -8°. We call this configuration specular component included (SCI). We can put a hole (a light trap) in the sphere at -8° so that the specular component of the reflectance leaves the sphere, which we call the specular component excluded (SCE).

FIGURE 1: Schematic of a d/8° sphere geometry for spectrophotometry.

Another common configuration is to illuminate the surface of the sample at 45° and measure at 0°. Typically, a ring of lights is positioned at the 45° angle for this 45°/0° configuration (in this scenario, there is no specular component contributing to the measurement). Custom configurations can be used, but the measurement geometry must be specified in the reporting of the measurement. Different instruments have been developed for multi-angle measurement. For example, multi-angle instruments are used in the automotive paint industry because of the complex nature of the coatings used on cars. In addition to the illumination and measurement geometry, the size of the measured area must also be considered. For example, if you are measuring a surface with texture or a printed surface with a halftone pattern, you must ensure that you are measuring a large enough area to integrate over the local nonuniformities.

Let’s get into the weeds a bit to describe color measurement. What we are measuring with these different geometries is the spectral reflectance factor. This is the fraction of light reflected off the sample relative to a perfectly diffuse reflector. We calibrate the spectrophotometer with a calibrated plaque with a known reflectance factor. In its simplest form, the reflectance factor is calculating using this equation:

 is the calculated reflectance factor of sample, 

is the spectrometer response from the sample; 

 is the spectrometer response from the calibration plaque, and 

 is the reflectance factor of the calibration plaque. In practice, correction factors may need to be applied.

Once we have measured the reflectance, we can use CIE colorimetry to calculate the [

] tristimulus values for any illuminant, which map to the RGB coordinates. The CIE has tabulated a variety of standard illuminants and the American Standards of Testing and Materials (ASTM) has standards for calculating tristimulus values as well.

Now that we have calculated the tristimulus values of a sample, we may want to find out how different they are from the color we want to achieve. As mentioned above, this is where CIELAB may be used. The CIELAB calculation uses a white point to normalize its coordinate system The white point is the tristimulus values of the perfect diffuse reflector (a reflectance value of one at all wavelengths). Now we can calculate the color coordinates in CIELAB space of the sample and the standard and use a color difference equation to determine if the sample is within the desired tolerance.

Setting these tolerance limits is a science within itself. There are different techniques that can be used including performing visual experiments to find tolerance limits and adjusting coefficients in color difference equations. The goal is to choose the proper geometry that produces measurements that correlate with the perceptual assessments for the samples you are measuring.

Are there any other interesting facts about color and color science you would like to share?

I focused mainly on the practical aspect of simple color measurement and inspection in the last answer. But this is only a small part of color science and the study of color vision. There are too many interesting topics to choose from. It was fun when “the dress” picture (1) went viral in 2015, and I still get asked about this. Even regarding basic color measurement, we encounter interesting phenomena such as the changes in surface color that can be caused by changes in temperature and humidity. As a multidisciplinary field, there are surprises around every corner.

Thanks to Ethan for an interesting and entertaining introduction to color science and perception. I certainly learned a lot of new vocabulary and gained some new understanding through working with him on this article, which is entirely the point of the “Lasers and Optics” column in 

 magazine. I will note here that this article concludes nearly 7 years of my contributions to this column—allowing you, dear readers, some new and fresh perspectives. It has been a pleasure to write for the wonderful staff at Spectroscopy, and you will no doubt hear more from me occasionally in this magazine and on other channels. I hope that these columns have been useful to you, and I wish each of you continued fun in your explorations of the interactions of light and matter!

(1) Wikipedia, The dress (accessed September 2022). 

 is the General Manager of the Applied Systems business at Ocean Insight, an affiliate associate professor at the University of Washington, and has started and advised numerous companies in spectroscopy and in applications of machine learning. He has approximately 40 peer-reviewed publications and 6 patents. His work in practical optical spectroscopy, such as LIBS, Raman, and TDL spectroscopy, dovetails with the coverage in this column, which reviews methods (new and old) in laser-based spectroscopy and optical sensing. Direct correspondence to: 

 is a Senior Scientist at Ocean Insight working in the Applied Systems group in Rochester, New York. He received his Ph.D. in Experimental Psychology at the University of California, San Diego studying human color vision. He served as an Assistant Professor at the Munsell Color Science Laboratory at the Rochester Institute of Technology. Subsequently he worked in machine vision before moving to FluxData, Inc. which is now part of Ocean Insight. He has published numerous papers in vision and color science. In addition to color metrology, he works on developing and evaluating optical and spectroscopic solutions for industry. ●

Accurately measuring and quantifying the perception of color is an ongoing challenge for scientists, but understanding spectroscopic techniques can help standardize color measurements.

Where Perception Meets Reality: The Science of Measuring Color

In the last column, we reviewed the spectroscopy of the carbonyl group and that of ketones. We then analyzed our first C=O containing polymer. In this column, we continue to study C=O containing polymers by first reviewing the spectroscopy of the ester functional group and then analyzing the spectra of several important polyesters. Among the spectra we study is that of polyethylene terephthalate (PET), one of the most economically important polymers in the world.

, is the founder and CEO of Big Sur Scientific, a maker of portable mid-infrared cannabis analyzers. He has over 30 years experience as an industrial infrared spectroscopist, has published numerous peer-reviewed papers, and has written three books on spectroscopy. As a trainer, he has helped thousands of people around the world improve their infrared analyses. In addition to writing for Spectroscopy, Dr. Smith writes a regular column for its sister publication Cannabis Science and Technology and sits on its editorial board. He earned his PhD in physical chemistry from Dartmouth College.

Recall (1) that if an alcohol and a carboxylic acid are reacted, a functional group called an 

 is synthesized, and the reaction is called 

. The molecular framework of the ester functional group is shown in Figure 1.

FIGURE 1: The molecular framework of the ester functional group.

In the figure, the carbon in the C=O group is called the 

, the carbon to the left of the carbonyl carbon is called the 

, and the oxygen to the right is called the 

. If the alpha carbon is saturated, it gives a saturated ester, whereas if the alpha carbon is aromatic, we have an 

. Esters are commonly found in food and generally taste good. For example, isoamyl acetate is what gives a banana some of its flavor, and ethyl acetate gives cherries some of their flavor. Polyesters are important polymeric materials being made into beverage bottles, fabric, and clothing and hence are worth studying.

The Infrared (IR) Spectroscopy of Esters: A Review

Note from Figure 1 that ester groups contain a carbonyl bond and two C-O bonds. We have already studied the IR spectroscopy of these bonds, so we can take a stab at predicting what their spectra might look like. Recall (2–7) that carbonyl stretching peaks are strong and generally occur between 1800 and 1600 cm

 (assume all peak positions noted in this article will be in cm

 units, even if not explicitly stated). We also know (6) that C-O stretches are intense peaks typically seen between 1300 and 1000. Because one of the C-O bonds in the ester group is attached to the carbonyl carbon and the other is not, we might expect them to be chemically distinct, have different force constants, and hence give rise to two separate peaks between 1300 and 1000.

As it turns out, our predictions are correct. Esters have a memorable pattern of three intense peaks at ~1700, ~1200, and ~1100 from the C=O and two C-O stretches, and hence follow what I call the “Rule of Three” (1). The first of these peaks is the C=O stretch, which we know from previous experience (7) will be an intense peak in the vicinity of 1700. We also learned last time that carbonyl stretches for aromatic carbonyl groups tend to be 30 cm

 lower than for saturated carbonyl groups because of conjugation (7). Thus, for saturated esters, the C=O stretch falls from 1755 to 1735. Note that this is a little higher than some other saturated C=O groups, and if you see a C=O stretch around 1750, one of your first thoughts should be saturated ester.

For aromatic esters, the C=O stretch falls from 1730 to 1715. This is a tricky peak position because several other functional groups, including saturated ketones (7), have C=O stretching peak positions in this range. This is why, as is typical for carbonyl spectra, we will be dependent upon other peaks besides the C=O stretch to identify the carbonyl functional group present in a sample.

The first C-O single bond stretch of esters and the second of the Rule of Three peaks involves the asymmetric stretching of the alpha carbon, carbonyl carbon, and carbonyl oxygen as seen in Figure 2. I call this the “ester C-C-O stretch (8).”

FIGURE 2: The C-C-O stretch of the ester functional group. This vibration is responsible for the second of the “Rule of Three” peaks.

This vibration is reminiscent of the C-C-C stretch of ketones (7), except that, of course, esters contain a C-C-O linkage instead of a C-C-C linkage. In general, for saturated esters, this peak falls from 1210 to 1160, whereas for aromatic esters, it falls from 1310 to 1250.

The third of our rule of three peaks involves the asymmetric stretch of the ester oxygen and the one or two carbons attached to its right. This is called the “O-C-C stretch (8),” as illustrated in Figure 3.

FIGURE 3: The O-C-C stretch of the ester functional group. This vibration is responsible for the third of the “Rule of Three” peaks.

For saturated esters in general, the O-C-C stretch appears from 1100 to 1030, and from 1130 to 1100 for aromatic esters. A summary of the group wavenumbers for saturated esters is found in Table I.

Note in Table I that there are six separate wavenumber ranges listed because each type of ester, saturated and aromatic, follows its own rule of three. This is because the peak position of all three ester peaks are sensitive as to whether the ester is saturated or aromatic. This means that any of the ester Rule of Three peaks can be used to distinguish saturated from aromatic esters, and, if a sample contains both a saturated and aromatic ester, it will have six ester peaks total.

 is a polymer where the ester group is found in the backbone of the polymer chain. A ubiquitous polymer in our modern society is polyethylene terephthalate (PET), otherwise known as soda bottles and polyester clothing. The chemical structure and spectrum of PET are seen in Figure 4.

FIGURE 4: The IR spectrum of polyethylene terephthalate (PET).

Note that the ester group is in the backbone of PET, and that it is also an aromatic ester. The Rule of Three peaks in Figure 4 are labeled A, B, and C. Note how these three peaks stick up out of the spectrum like the index, middle, and ring fingers of your hand, and these peaks are often times the three most intense peaks in the spectrum of an ester. In the spectrum of PET, the C=O stretch is at 1721, the C-C-O stretch is at 1245, and the O-C-C stretch is at 1100.

The spectrum of another polyester, polybutylene terephthalate (PET), is seen in Figure 5. The Rule of Three peaks are labeled A, B, and C. The C=O stretch for this polymer is seen at 1730, the C-C-O stretch is at 1286, and the O-C-C stretch falls at 1133. Note that the third of the Rule of Three peaks is smaller than the other two as expected.

The only chemical difference between PET and polybutylene terephthalate is that the former has two methylene groups in a row, whereas the latter has four CH

s in a row. Recall (9) that when an alkyl chain has four or more methylenes in a row, the CH2 rocking peak falls around 730. In Figure 5, this peak is found at 742 and labeled D.

A common biodegradable polymer that you might not think of as being a polyester actually is one. Polylactic acid, which is found in sour milk (among other things), does have a saturated ester group in its backbone, as you can see from its structure in Figure 6. This polymer is becoming increasingly important because it is made from readily available biological materials and will biodegrade, alleviating somewhat the worldwide problem of plastic pollution (10). For example, it is made into biodegradable cutlery (10). Polylactic acid is made from the condensation reaction (splitting off of water) of lactic acid. The structure and spectrum of lactic acid are seen in the top of Figure 6, whereas the structure and spectrum of polylactic acid are seen in the bottom of the figure.

FIGURE 6: (a) The structure and IR spectrum of lactic acid and (b) the structure and IR spectrum of polyactic acid.

Note that lactic acid is a carboxylic acid, whose spectra we have studied previously (11).

Briefly, the spectra of carboxylic acids are characterized by a broad and intense O-H stretching envelope because of hydrogen bonding from 3500 to 2500, a carbonyl stretch around 1700, and a C-O stretch around 1250. These peaks for lactic acid are labeled A, B, and C in Figure 6.

An exploration of polyethylene terephthalate (PET), one of the most important polymers, is presented.

Featured Content

The 2022 Emerging Leader in Molecular Spectroscopy Award

A Different Kind of Art Analysis

A Survey of Basic Instrument Components Used in Spectroscopy