Chemical formalisms: toward a semiotic typology

3.1 Field

This paper will use two theoretical tools from SFL: the register variable field, and its understanding of types of grammatical structure. In common sense terms, field can be broadly understood as organizing the content meanings of language or semiosis. More technically, it is a resource for organizing the ideational meaning of a semiotic system (Martin 1992). Under an evolving model of field proposed by Doran and Martin (2021: 108), field can be described as a resource for construing phenomena statically as relations among items or dynamically as unfolding events (known as activities) oriented to some global institutional purpose.

From a static perspective, field can be viewed in terms of two main types of relation between items: classification and composition. Classification is the relation between items in terms of class and sub-class. For example, chemistry distinguishes between two types of ion: cations and anions. The items “cation” and “anion” are thus sub-classes in relation to the more general item “ion.” Composition, on the other hand, is the part-whole relations among items. For example, the explanation of atomic structure depends on multiple levels of composition: an atom is composed of one nucleus and at least one electron, and a nucleus is in turn composed of neutrons and protons.

From a dynamic perspective, field can view phenomena as activities that organize events and changes. Activities may be cyclical, where an event can recur indefinitely, such as in, “electrons orbit the nucleus,” or they can be linear where a single event occurs and eventually ends, for example, “a neutron strikes a nucleus” (Doran and Martin 2021).

In addition, each of these items and activities may have certain properties that may be graded and/or measured numerically. Properties can be understood as qualities or positions of both items and activities that often enable a rich description of phenomena. For example, properties may occur on items, as in “ice is hard,” or on activities as in “ice melts into liquid water rapidly under heating.” There are two main types of properties relevant to this study of chemical formalisms: qualitative properties that give qualities of an item or activity such as “electrons are negatively charged” and spatio-temporal properties that indicate the positions of the item or activity in time or space, such as “electrons orbit around the nucleus.”

These options in field – static relations between items in terms of classification or composition, dynamic unfoldings of cyclical or linear activities, and gradable arrays of qualitative or spatio-temporal properties – offer a useful set of resources for viewing different meanings realized by different chemical formalisms. Figure 2 presents a system network with the aspects of field important for this study. This figure says that there are two main perspectives on field – a dynamic (activity) perspective or a static (item) perspective. If dynamic is chosen, the activities can be either cyclical or linear, or if static is chosen, the taxonomies produced can be of classification or composition. It also says there may be two types of properties added to the activities or items, qualitative properties and spatio-temporal properties.

Figure 2:

Aspects of field.

3.2 Types of structure

Complementing the view from field, this paper will also explore chemical formalisms in terms of the types of structure they show in their grammar. This will help give a general sense of how the various formalisms are organized and how they combine and arrange their meanings. SFL theory construes a rich array of types of structure for language and other semiotic resources (e.g., Halliday 1979). Within this array, two structure types that are particularly relevant for understanding chemical formalisms are known as multivariate and univariate structures (Halliday 1981 [1965]).

Multivariate structures involve structures where there are multiple functions that can each occur only once. An example of this is the transitivity structure of the English clause (Halliday and Matthiessen 2014; see also the example from Liu in (5) above), as illustrated by (12):

In this example, there are three Elements performing three distinct functions: electrons functions as a Carrier, are functions as a Process and negatively charged functions as an Attribute. These functions are distinct from each other, as they have different grammatical possibilities and they can occur only once in a clause (Halliday and Matthiessen 2014). For example, we could not add in an additional Process and Attribute, to say something like:

*Electrons are negatively charged are leptons.^[3]

By contrast, a univariate structure consists of only one type of function, but this function can typically be repeated or iterated. An example of a univariate structure in English is the complexing of words. In the example atoms, molecules, and ions, each word plays a similar role in relation to the others in the sense that they all have very similar grammatical possibilities. In addition, there may be an indefinite number of words, as shown by (13) and (14). By convention, this structure is presented in SFL with numbers ‘1 ^ 2 ^ 3’ (or in other cases through Greek letters).

These two types of structure are summarized as Table 1.

As we will see, these two types of structure provide a useful means of distinguishing the different organizations of each type of chemical formalism. Combined with an interpretation of their meanings through field, we will be able to see not only what meanings they construe but also how they construe these meanings.

4.1 Chemical formulas

Chemical formulas are a means of representing chemical substances that are used from early secondary school. In chemical formulas, the core symbols represent the elements that constitute a chemical substance. Each symbol is one or two letters taken from the Latin name of the substance (Berzelius 1814: 51). For example, in the chemical formula CO (carbon monoxide), C is taken from ‘carbon’ and O from ‘oxygen’. These symbols may or may not have subscript numbers, depicting the quantity of the atoms. For example, the chemical formula CO₂ (carbon dioxide) contrasts with CO (carbon monoxide) by virtue of the subscript ‘2’ attached to the symbol O, which indicates that there are two oxygen atoms for every carbon atom.

Focusing first on the grammatical structure illustrated by chemical formulas, we can see that a key feature is their capability for including an indefinite number of chemical symbols, which allows them to represent increasingly complex chemical compounds. Chemical formulas may have only one chemical symbol to represent a single substance, for example, hydrogen gas (H) in (15):

Or they can include two chemical symbols to represent a compound, such as for water (H, O):

Or they can include three chemical symbols to represent a more complex compound, such as for hypochlorous acid (H, Cl, O):

Indeed in principle, chemical formalisms can include indefinitely more symbols, so long as the represented chemical species exists.^[4] For example, the formula for amidephrine in (18) involves five symbols (C, H, N, O, S; most of which additionally have subscripts).

In terms of the structure of the overall chemical formula, each symbol plays the same role. That is, there is no “central element” within the formula that all the others are dependent on (as O’Halloran 2005 also argues for mathematical symbolism). This can be seen by virtue of the fact that no individual element must occur for any others to occur – they are relatively freely combinable (presuming the chemical molecule exists). Thus, from the perspective of grammatical structure introduced above, the fact that chemical symbols can be iterated indefinitely and perform the same grammatical function indicates that chemical formulas are organized through a univariate structure.^[5] This structure enables chemical formulas to represent an indefinitely wide range of chemical elements within any individual substance, which enables it to be malleable to any particular chemical compound. Univariate structures are common in academic formalisms, as they allow an indefinite number of elements to be related at once, which helps build the highly intricate sets of technical meaning needed in science (Doran 2019).

To complement this view of chemical formulas from the perspective of their grammatical structure, we can also consider them in terms of the general content meanings they realize. In terms of the model of field introduced above, chemical formulas primarily realize a compositional (part-whole) relation. For example, H₂O comprises a two-level compositional taxonomy, where the whole is the water molecule itself, and the parts are the two hydrogen atoms and one oxygen. Similarly, HClO represents hypochlorous acid as the whole, with its component parts being one hydrogen, one chlorine, and one oxygen atom.^[6]

Combined with the iterative structure of the grammar, this interpretation from field means that chemical formulas can realize indefinitely expandable composition taxonomies. This expansion occurs in terms of the breadth of the compositional taxonomy: every added chemical symbol is part of the molecule at “the same level” as all the others. Elements are all “parts” of the whole molecule, rather than showing new molecules or parts of the elements themselves – the electrons, protons, and neutrons that make up the elements (i.e., they do not allow for expanding the depth of the compositional taxonomy).^[7]

The relation between the grammatical organization and field-specific meanings realized in chemical formulas can be summarized as Table 2.

The indefinite expansion of the compositional taxonomy in chemical formulas enables a relatively efficient view of the overarching composition of substances. As we will see, structural formulas offer similar meanings but additionally add a spatial layout.

4.2 Structural formulas

As noted above, structural formulas show how atoms are bonded to one another in molecules (Ebbing and Gammon 2008: 57). They consist of two main components: chemical symbols representing atoms, and lines representing covalent bonds. For example, Figure 3 presents a structural formula of hydrogen chloride. The symbols ‘H’ and ‘Cl’ represent hydrogen and chlorine atoms, and the line between the symbols denotes a single covalent bond.

Figure 3:

The structural formula of hydrogen chloride.

One of the key differences between structural formulas and chemical formulas is that structural formulas can present different types of covalent bonds, while chemical formulas cannot. For example, the structural formula of hydrogen cyanide, shown in Figure 4, includes two different lines, representing two types of covalent bonds: the single line between H and C indicates a single bond, and the three lines between C and N indicate a triple bond.

Figure 4:

The structural formula of hydrogen cyanide.

The second key difference between structural formulas and chemical formulas is that structural formulas can arrange symbols along multiple spatial dimensions. This was illustrated in Figure 1 above where the hydrogen symbols were positioned in diagonal directions in relation to the oxygen symbol. The relative locations of the symbols in the two-dimensional space depict the shape of how the atoms are bonded in water molecules. This means that structural formulas present in some sense the geometry of molecules.

Structural formulas can in fact represent spatial organization in three dimensions. In Figure 5, for example, the solid wedge () linking N with H indicates an arrangement out of the page, while the dashed wedge () linking N with H indicates an arrangement into the page.

Figure 5:

A structural formula showing a three-dimensional arrangement.

This spatial arrangement uses the affordances that arise from its imagic organization, in contrast to the symbolic arrangement of chemical formulas. But to generalize structural formulas as “images,” with a presumption that this involves similar grammatical structures to other images (described by, say, Kress and van Leeuwen 2021 or O’Toole 1994), is to miss the highly specialized and tightly constrained grammar they show. Indeed, in many respects, structural formulas show a more similar grammatical organization to the chemical formulas discussed above than to other types of images.

To see this, we will once again begin by viewing structural formulas in terms of their predominant grammatical structure. Like chemical formulas, a key feature of structural formulas is the possibility of iterating chemical symbols and connectors. For example, an expansion of the formulas shown in Figures 1, 3, 4, and 5 above is given in Figure 6, where a polyethene molecule is realized by an indefinite number of symbols and connectors.

Figure 6:

The structural formula of polyethene.

Similarly, like chemical formulas, structural formulas do not involve any “central” element upon which the rest depends. Each symbol performs the same function as the others, grammatically speaking. Thus, just like chemical formulas, the possibility for indefinite repetition of symbols with each performing the same function indicates that structural formulas are best modelled as univariate structures. However, in contrast to chemical formulas that involve linear iteration of symbols, structural formulas allow symbols to be iterated in different directions in two-dimensional space, as shown in Figure 7.^[8]

Figure 7:

The structural formula of hexane.

In terms of field, again like chemical formulas, structural formulas realize a composition taxonomy. The symbols and connectors (the lines between symbols) indicate parts of the molecule as a whole. This means that, like chemical formulas, the univariate structure in structural formulas also expands the breadth of composition taxonomy. But it does more than this. The spatial arrangement additionally allows for two dimensions of expanding compositional breadth. Thus, structural formulas add a spatial property to the compositional taxonomy that allows two avenues for expanding the breadth of its compositional taxonomy. This means the elements within structural formulas are not just specified as unordered components of a molecule but are also ordered in relation to each other.

These spatial arrangements of symbols, to some extent, reflect how chemistry conceives of a molecule’s actual structure. This gives structural formulas its seemingly “mixed” feature of being “half-symbolic and half-iconic” (Hoffmann and Laszlo 1991: 10). The importance of this spatial property is that it plays a significant role in making explicit molecules’ chemical properties for those who understand the formalism. For example, the different spatial arrangements of ‘ –O–H’ (circled red) shown in Figure 8 form two distinct molecules, known as butan-1-ol and butan-2-ol, with different physical and chemical properties (Chan et al. 2019: 286). However, this difference is perceivable only in structural formulas. The compositional makeup of the molecules is the same, which means the two molecules are not distinguished in chemical formulas – they both share the formula C₄H₁₀O. But by adding in the spatial organization in structural formulas they can be distinguished as in Figure 8.

Figure 8:

The structural formulas of butan-1-ol (left) and butan-2-ol (right).

Synthesizing the description of structural formulas, we can say that the field-specific meanings realized by structural formulas include two main components, a composition taxonomy and its spatial properties, and their grammar is organized primarily around a univariate structure, which works to expand the breadth of the composition taxonomy along multiple dimensions. The relation between the grammatical organization and the field-specific meanings realized is summarised in Table 3.

Here it is worth re-emphasizing that despite chemical formulas being primarily “symbolic” and structural formulas being “imagic,” they display a remarkably similar structure and overlap considerably in terms of the ideational meanings they show. This illustrates the benefit of taking a typological approach to regions of semiosis, as we are doing here, as it allows us to move beyond common-sense distinctions such as “images” and “symbols.” As noted above, structural formulas display many more similarities to their symbolic counterparts than with other types of images. The comparison so far also suggests a significance of the internal structure of substances for the discipline of chemistry. Indeed, as we will see, although in many respects chemical equations are quite distinct from the formulas above, they do in fact include chemical formulas as one of their components, thus also presenting the composition of substances. This emphasis on composition contrasts with disciplines such as physics that heavily rely on mathematics, where the interdependency of properties is paramount, rather than compositional structure (Doran 2021).

4.3 Chemical equations

Chemical equations show reactions that different substances undergo to form products. For example in (19), methane, represented by CH₄, and oxygen gas, represented by O₂, react to form two new substances, carbon dioxide (CO₂) and water (H₂O):

In comparison to chemical formulas and structural formulas, chemical equations display a considerably more complex grammar, and so we will discuss them in terms of their different levels – what in SFL is called ranks. There are three main ranks we will deal with: the equation, the term, and the formula.^[9] The equation rank (relabelled from Liu’s “clause” rank, so as to more closely align with chemistry terminology) refers to the highest level in a chemical equation. For example, the entirety of (19) comprises the rank of equation. The main constituents of an equation include the whole set of symbols on the left side of the arrow, known as the reactants CH₄(g) + 2O₂(g), the arrow →, and the set of symbols on the right side of the arrow, known as the products CO₂(g) + 2H₂O(l).

Within the reactants and products are the terms. In (19) above, the terms are the sets of symbols related by a plus sign +: CH₄(g), 2O₂(g), CO₂(g), and 2H₂O(l) (Taber 2009: 88). Within each term is a chemical formula (such as H₂O in 2H₂O[l]), which follows the same organization as the chemical formulas above, as well as a numerical coefficient (the first 2 in 2H₂O[l]) indicating the quantity of the chemical species in the reaction, and a symbol giving the state ([l] for liquid in 2H₂O[l]). These three levels are summarized in Table 4.

To understand the overarching organization of chemical equations and the meanings they realize, we will step through each level in turn.

In terms of the predominant grammatical structure of chemical equations, at the equation rank, Equation (19) is composed of three parts that can be accounted for through three distinct functions shown in (20):

The left and right sides are labelled differently as Reactant and Product as they perform distinct functions. This is illustrated by the fact that the two sides cannot be swapped without changing the ideational meaning of the equation. By swapping the sides in (19), the initial starting point of the reaction and its result are different – i.e., their ideational meaning changes. In addition, none of the elements in chemical equations are iterative at the equation rank as it is not possible to add another arrow and iterate the terms. For example, Equation (21) does not occur (* indicates an example that is not well-formed):^[10]

As the two sides of the equation perform distinct functions and are not iterative, chemical equations can be considered a multivariate structure (Halliday 1981 [1965]). In some sense, this multivariate structure is determined by the arrow’s directionality, which strictly defines the roles of the two surrounding sides, with the left being reactants and the right being products. However, there is another type of reaction arrow in chemical equations that occurs in what is called “reversible equations” (Brown et al. 2012: 613). As indicated by its name, a reversible equation represents a reaction that can go forward and backward. For example, (22) represents a reversible reaction between nitrogen gas (N₂) and hydrogen gas (H₂), and liquid ammonia (NH₃). It denotes that nitrogen gas first reacts with hydrogen gas to form ammonia liquid, which then decomposes back into nitrogen gas and hydrogen gas.

The double arrow indicates there is a sequential order between the forward reaction – nitrogen gas first reacts with hydrogen gas to form ammonia liquid – that comes first, and the reverse reaction – ammonia liquid decomposes into nitrogen and hydrogen gas – that follows. That is, for both irreversible equations using ‘→’ and reversible equations using ‘⇆’, chemical reactions always start from the left. Although the reaction itself goes back and forth (what we will call a cyclical activity below), grammatically speaking, elements within reversible equations still cannot be iterated. That is, constructions like (23), with multiple arrows and a third set of terms, do not occur:

The back and forth in reversible reactions occur until they reach “an equilibrium state” (Taber 2009: 96), where the concentrations of reactants and products no longer change with time. This means that although grammatically speaking reversible equations share the same structural configuration as irreversible equations of “Reactant ^ Relator ^ Product,” they realize slightly different types of activities in terms of field. Irreversible equations realize linear activities and reversible equations realize cyclical activities. Importantly, however, neither of these activities can be iterated due to the equations’ multivariate structure.

At the rank below, terms are usually composed of three components: coefficients, chemical formulas, and state symbols (Ebbing and Gammon 2008: 73). For example, in 2H₂O(l), ‘2’ is the coefficient that specifies the number of units of the molecule, ‘H₂O’ is the chemical formula that indicates the chemical species and ‘(l)’ is the state symbol which indicates the physical state (liquid). ‘2H₂O(l)’ thus indicates that there are two units of water molecules in liquid state. With respect to the term’s functional structure, once again, none of the elements are iterative and they all perform distinct functions. Thus, we also treat terms as a multivariate structure, as in (24).

There are two primary reasons for proposing this multivariate structure. One is that the sequence of the elements is strictly defined and does not allow variations. It is not possible to place a coefficient in between a chemical formula and a state symbol, (e.g.*H₂O2(l)), or place a state symbol in the middle (*2(l)H₂O). This suggests they perform distinct functions. The other reason for proposing a multivariate structure is that none of the elements are iterative. It is not possible to repeat coefficients, chemical formulas, or state symbols. Thus, being non-iterative, elements in a term are best modelled as multivariate.^[11]

However, in contrast to the multivariate structure of the broader equations that realize activities, the multivariate structure of terms construes two types of property. The function Quantity specifies the number of units of a chemical species, construing what Doran and Martin (2021) refer to as a gauged property. This property allows chemical equations to establish quantitative relations of reactions (Simon 1926: 1306). More specifically, it specifies the molar ratios in which the chemical species react and are formed. For example, in the chemical equation CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), methane gas (CH₄) and oxygen gas (O₂) molecules react in a ratio of one to two, and carbon dioxide (CO₂) and water molecules (H₂O) are formed in the same ratio.

In addition to gauged properties, terms realize another type of property – qualitative properties, construed by the function of State. For example, the ‘(l)’ in 2H₂O(l) represents that the water is in liquid state. Whereas the gauged property given by the numerical coefficient enables chemical equations to describe the quantitative relations of a reaction at the microscopic level (the molecule level), the qualitative property given by the state symbol allows for construing chemical reactions at the macroscopic level (the material world that can be sensed), i.e., it describes the physical states of chemical species observed in chemical reactions. Viewed in terms of a well-known conceptualization of chemistry knowledge called Johnstone’s (1991) chemical triplet, the two field properties thus bridge two levels of chemistry knowledge: the macroscopic and microscopic, all the while construing these in terms of Johnstone’s third level called symbolic knowledge.

Looking further, although the internal organization of terms displays a multivariate structure, there can be an indefinite number of terms within any Reactant or Product. Each term is separated by a ‘+’. For example, (25)–(27) illustrate that on either side of a chemical equation, there can be one term as in the right side of (25), two terms as in the left side of (25), three terms as in the right side of (26), and four terms as in the right side of (27):

Theoretically, there can be no limit to the number of terms that can occur within either side of a chemical equation. This means that terms are indefinitely iterative and thus best modelled as a univariate structure.

In terms of field, each side of a chemical equation and the terms within it form a whole-part relation within the reactants or products – a composition taxonomy. For example, the left side of (28) shows that reactants (left-side) for the chemical reaction consist of two chemical species, methane (CH₄) and oxygen gas (O₂), while the products (right side) are composed of carbon dioxide (CO₂) and water (H₂O).

The iterative structure means that term complexes can indefinitely expand the breadth of the composition taxonomy and allow chemical equations to construe chemical reactions that involve as many reactants or products as possible, enabling them to represent extremely complex reactions.

As the constituents of terms are chemical formulas (discussed in Section 3.1 above), this provides another layer of composition given in chemical equations, as described above. Together, chemical equations construe three levels of composition taxonomies, two of which can expand indefinitely through a univariate structure. The highest level of the composition taxonomy on each side of the arrow is the reactants and products. At the next level within each of these are the substances indicated by the terms. And finally at the lowest level are the atoms within the substances, given by the chemical symbols within chemical formulas. This is illustrated for the right side of CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) in Figure 9.

Figure 9:

Composition taxonomy of reactants.

Viewed together with the equation rank (realizing an activity), we can view the full equation as an activity oriented toward changing the compositional taxonomy, as illustrated in Figure 10 for the entire equation (17):^[12]

Figure 10:

Change in composition through an equation.

Overall, viewed in relation to structural formulas and chemical formulas, chemical equations thus show deeper composition taxonomies than the other two formalisms, as well as changing composition. Bringing this all together, we can view the various types of meaning being made in chemical equations as in Table 5.

Table 5:

The grammatical organization and field-specific meanings realized in chemical equations.

Grammatical organization	Field-specific meanings realized	Examples
Multivariate structure at the equation rank	activities
Multivariate structure at the term rank	properties (quantities and physical states) of substances
Univariate structure at the term rank	breadth of composition taxonomy of chemical substances involved in a chemical reaction
Univariate structure at the formula rank	breadth of composition taxonomy of elements within chemical substances