14.1 Public Perception of the Safety of Nanoproducts

One issue that has not so far received much prominence is that of safety, especially regarding nanoparticles in products brought into contact with the skin, if not actually ingested. Compared with the furore over genetically modified food crops, leading to widespread prohibition of their cultivation, at least in Europe, nanoparticle-containing products have generally had a favorable reception, perhaps because of the considerable care taken by the industry to inform members of the public about the technological developments that led to them.

Nevertheless, there is no doubt that nanoparticles have significant biological effects. An extensive literature already exists [2]. A member of the public might wish to take the following widely known facts into account:

This list could be prolonged, but the point is made that no coherent policy can be discerned at present; the situation is full of paradoxes. Items 1 and 2 can doubtless be resolved by recalling Paracelsus' dictum “The poison is in the dose” [3], but in other cases doubtless economic and political factors took precedence over scientific and medical ones. The British government now seems to be resolved to bring some order into this chaos, and has commissioned a report prescribing how studies to determine the biological hazards of nanoparticles ought to be carried out [4]. The dispassionate observer of the field will find it remarkable that despite decades of investigations, most reported studies have failed to carry out requisite controls, or are deficient in other regards. A very great difficulty of the field is the extremely long incubation time (decades) of some of the diseases associated with exposure to particles. The effects of long-term chronic exposure might be particularly difficult to establish. At the same time, ever since the time of Prometheus man has been exposed to smoke, an almost inevitable accompaniment to fire, and doubtless our immune system has developed the ability to cope with many kinds of particles [5].

The most appropriate response is to make good the deficiencies of previous work, as recommended by Tran et al. [4,6]. The question remains, what are we to do meanwhile, since it might be many years before reasonably definitive answers are available. Most suppliers of nanomaterials would, naturally enough, prefer the status quo to continue until there is clear evidence for acting otherwise; “pressure groups” are active in promulgating the opposite extreme, advocating application of the precautionary (or “White Queen”) principle (do nothing unless it is demonstrably safe) and an innovation-stifling regulatory régime (cf. Chapter 15). The latter is anyway supported by governments (probably, even doing the research required to establish the safety or otherwise of nanoparticles contravenes existing health and safety legislation) and supergovernmental organizations such as the European Commission.

Hence, the most sensible course that can be taken by the individual consumer is to apply the time-honored principle of caveat emptor. But, the consumer will say, we are not experts, how can we judge? But, the expert may respond, we all live in a technologically advanced society, and we all have a corresponding responsibility to acquaint ourselves with the common fund of knowledge about our world in order to ensure a long and healthy life. Naturally we have a right to demand that this knowledge is available in accessible and intelligible form.

The only rational way to proceed is to build up knowledge that can then be applied to calculate the risks and weigh them against the possible benefits. Provided the knowledge is there, this can be done objectively and reliably (see Section 14.11), but gaining the knowledge is likely to be a laborious task, especially when it comes to assessing the chronic effects resulting from many years of low-level exposure. There is particular anxiety regarding the addition of small metallic or metal oxide nanoparticles to food. Although a lot about their biological effects is indeed already known [2], the matter is complex enough for the ultimate fates of such particles in human bodies to be still rather poorly understood [7], and new types of nanoparticles are being made all the time [8]. On the other hand, it is also worth bearing in mind that some kinds of nanoparticles have been around for a long time—volcanoes and forest fires generate vast quantities of dust and smoke, virus particles are generally within the nanorange, comestible biological fluids such as milk contain soft nanoparticles, and so forth, merely considering natural sources. Anthropogenic sources include combustion in many forms, ranging from candles, oil lamps, tallow dips and the like used for indoor lighting, internal combustion engines—this is a major source of nanoparticle pollution in cities, along with the dust generated from demolishing buildings—cooking operations, and recreational smoking. The occupational hazards from certain industries, especially mining and mineral processing (silicosis, asbestosis), are well recognized, and the physicochemical and immunological aspects of the hazards of the nanoparticles are reasonably well understood [9].

14.2 Evaluating Risk

The fundamental equation describing the risk derived from coming into contact with substances is commonly presented as:

$\begin{array}{cc}\hfill \text{Risk (from the substance)}& =\text{Exposure (to the substance)}\hfill \\ \hfill & \times \text{Hazard (from the substance)}.\hfill \end{array}$

The fact that we can write such an equation implies that all the terms can be quantified. Unfortunately “exposure” is ambiguously defined. In everyday language, we might simply say that we have been “exposed to light”, or “exposed to a chemical”, but as soon as the exposure is quantified it is clear that it is the integral of the irradiance (for light) or partial pressure (for a vapor) over the (time) interval during which the exposure takes place. Irradiance being expressed in the number of photons falling on unit area per unit time, given the exposure interval one can precisely calculate the number of photons falling on a photographic plate, for example. Chemicals pose more difficult challenges; indeed the case for an “exposure science” has recently been put forward [10]. The official “Workplace Exposure Limits” (WELs) [11] are defined as “concentrations of hazardous substances in the air, averaged over a specified period of time referred to as the time-weighted average (TWA)”. Knowing the average rate of human respiration (expressed as a certain volume of air per unit time), this can immediately be expressed as a certain mass of silica, which is the actual dose received by the exposed subject.

Hazard may be expressed in various ways. Very often, laboratory animals are given increasing doses of a (suspected) poison under controlled conditions and the proportion of animals dying within an appropriate interval following administration of poison is recorded. From this data a dose–response curve can be constructed. Thus, hazard (with respect to lethality) is expressed as the probability of lethality per dose, multiplying with which according to equation (14.1) gives risk as the probability of lethality. The information provided by the dose–response curve is sometimes compressed into a single number, such as the lethal dose for 50% of the animals, commonly represented as LD₅₀. If the curve rises very steeply at around the LD₅₀, it might be appropriate to express the risk in binary fashion; for a dose less than LD₅₀, the risk is zero and above it, one. Instead of lethality, the hazard can be expressed as the probability of contracting a certain disease. In general, though, it seems to be satisfactory to convolute an actual exposure, fluctuating, possibly quite significantly, during the interval under consideration with the dose–response curve. This is more sophisticated than the approach recommended in [11], which also takes no account of the body's ability to eliminate toxins with which it has been dosed. That, in turn, depends on other factors including the subject's genetic constitution, recent dietary intake, bodily activity, general level of fitness, exposure to other toxins, etc. All of these could be incorporated into an expanded equation (14.1), but such sophistication is scarcely justified by the present level of knowledge of the toxicity of nanomaterials. Here, we merely aim to characterize the hazards from nanomaterials qualitatively, while pointing out how it could be done more quantitatively. Likely exposures will be estimated for the general public and in the factory and will be compared with natural exposures to nanomaterials.

The WEL approach is rooted in the concept of “no observed adverse effect level” (NOAEL) or “lowest observed adverse effect level” (LOAEL) [11], which implies a threshold exposure level (i.e., concentration in the atmosphere), below which there is no hazard no matter how long exposure continues. It is, however, recognized that there are substances for which there may be no threshold, in particular DNA-reactive chemicals, exposure to which at any level may ultimately cause cancer, although only decades after exposure, hence causation is very difficult to demonstrate. In general, therefore, there is no threshold, from which it follows that the only way to eliminate risk is for exposure to be zero.

14.3 Evaluating the Toxicity of Nanomaterials

It seems to be easy enough to carry out an investigation of some nanomaterial X, especially if it is conveniently available in powder form. One simply sets up an experiment in which large numbers of animals are given increasing doses of X under controlled conditions, and one observes the response. Such experiments are very familiar to the chemical and pharmaceutical industries. Unfortunately, it is as if this very ease of investigation has led to an overwhelming plethora of reported results with nanomaterials, based on experiments that have often been carried out with every appearance of haste, and usually with massive doses far exceeding anything that would be encountered in an occupational or other context. At best, a huge work is now required in order to assess all this data for reliability and consistency. The OECD Working Party on Nanomaterials (WPNM) is attempting to do that, although it is doubtful whether it will be able to keep up with the flood of new results. At worst, much of this data is essentially worthless. An egregious (and, unfortunately, not untypical) example is the study by Poland and nine co-workers entitled “Carbon nanotubes introduced into the abdominal cavity of mice show asbestos-like pathology in a pilot study” [12]. Massive doses of the carbon nanotubes were injected directly into the lungs of the animals, of which there were only four, and only two reacted. The work was widely publicized and appeared to be aimed at promoting the popular perception that carbon nanotubes cause mesothelioma. There are, actually, good theoretical reasons for believing that they can [9] but it has been pointed out that due to its poor quality the work would probably never be admissible as evidence in a court of law [13]; the paper's existence might even (if it were accorded any serious attention) make it harder to establish a causal link between (say) occupational exposure and disease because of the weakness of its apparent underpinning of such a link. A rather comprehensive discussion of the inadequacies of the present state of nanotoxicology—which can be defined as the toxicology of nanomaterials—has been given by Hunt and Riediker [7].

Except in cases of wholesale destruction, such as the devastation caused by an earthquake, or a fire, shelling and bombing in warfare, or deliberate demolition, once nano-objects are incorporated into a matrix (e.g., an organic polymer) their rate of release into the environment generally becomes negligible. Hence, nanostructured materials are, in general, a negligible source of exposure. It might be that the most common source of damage to nanocomposites is presently accidental collisions between motor-cars. If, however, the collision is serious enough for a significant quantity of nanoparticles to be released from automotive nanocomposite components such as bumpers, it is likely that the occupants of the motor-car have suffered other, more serious, bodily injuries. Quantifying the balance of risk in such cases is nontrivial and will not be attempted here. We shall, therefore, confine our attention to exposure to nano-objects: particles, nanotubes, nanoplatelets, and the like. Because of their small size, they can readily penetrate into the human body, whereas artifacts made from nanocomposites are usually large and cannot. Unless there has been significant degradation of the matrix (e.g., due to weathering), the nano-objects embedded in it will not normally be released and even contact with the artifact will not usually pose any risk.

Whereas with most of the molecular (chemical) toxins listed in EH40 [11] and similar compilations it can be assumed that if the substance is present in the ambient air it will be taken up by the body, in the case of nano-objects the relationship between presence and uptake is rarely so simple. In fact, the WELs attempt to capture the complexities of what we can call penetrability in a rudimentary way by specifying different exposure limits depending on the particle size; for example, in EH40 silica has three entries, “amorphous inhalable dust and respirable dust”, “respirable crystalline” and “fused respirable dust” with successively decreasing limits (by about an order of magnitude each time). It may be more useful to use an elaborated form of equation (14.1) that explicitly takes account of penetrability:

$\begin{array}{cc}\hfill \text{Risk (from the substance)}& =\text{Exposure (to the substance)}\hfill \\ \hfill & \times \text{Penetrability}\times \text{Hazard (from the substance)}.\hfill \end{array}$

The penetrability (Section 14.6) could be quantified as the probability that a nano-object arriving at the boundary of the organism is taken up by it in a biologically active form. If one suspects that collective effects affect penetrability (e.g., a group of nano-objects arriving roughly simultaneously within a small area can penetrate more readily than particles arriving in isolation both temporally and spacially) then convolution rather than simple multiplication may, again, be a more appropriate way of combining the factors on the right-hand side.

14.4 Characteristic Features of Nano-Objects

A nano-object could be unambiguously specified as a list of its atoms giving their identities and positions. Perhaps in the future that is how they will be specified, but for the present it is impracticable for all but the smallest clusters, hence a somewhat coarse-grained description is usually adopted.

Geometry. The type of object is determined by the number of dimensions in the nanoscale: 1, 2 or 3 (fractal dimensions are not usually considered), named nanoplatelet, nanofiber (further subdivided into tubes (hollow), rods (rigid) and wires (conducting)), and nanoparticle, respectively.

All of the object's dimensions should be specified. A rod 3 nm in diameter and 70 nm long would, apparently, be called a nanoparticle despite having an aspect ratio of over 20, since its lengths in all three orthogonal directions are below 100 nm. If both shape and dimensions are specified, there should be no ambiguity. A particle does not have to be spherical; far more elaborate shapes have been synthesized, often called nanoflowers (e.g., [14]), which defy a standardized description.

Most production processes do not produce batches of nano-objects in which all have identical size (and other parameters). The dimensions are distributed and the distribution should be considered part of the specification. If the objects are of irregular shape, there may also be a distribution of shape; which in some cases can be quantitatively characterized from the dimensions (e.g., the shape distribution of ellipsoidal nanoparticles is the distribution of aspect ratio).

Atomic arrangement. The crystal structure (or lack of it) should be specified. If particles have been made by a “top–down” method, it is often assumed that they have the same crystal structure as the bulk material, but this should be confirmed or otherwise by measurements on the particles themselves, for example by selected area electron diffraction. Anomalous atomic arrangements with no bulk equivalent are known to exist in nanoparticles [15].

Chemical composition. Even in the simplest case of a nano-object constituted from a single element, the reactivity of the atoms depends on geometry. Considering nanocubes as an example, atoms on the edges are more reactive than atoms on the plane, and the corner atoms are more reactive still. The situation is considerably more complicated in the case of a binary compound MX. If it is crystalline, depending on the indices of the faces, their chemical constitution may be very different (e.g., all M or all X or equal numbers of both types of atoms). Nano-objects made from compounds are likely to be nonstoicheiometric (i.e., berthollides rather than daltonides). Atoms of the surface cannot fully bond with their partners-in-compound (the carbon nano-objects graphene, nanotubes and the fullerenes are exceptions) and nano-objects have a very high proportion of surface to bulk atoms. The unsatisfied chemical bonding capabilities of the surface atoms are usually satisfied either by scavenging other atoms or molecules from the environment or by deliberately coating the nanoparticle with some other compound, often in order to increase stability with respect to agglomeration. A particularly extreme example is the protein “corona” that forms when blood, which is very rich in proteins, comes into contact with a foreign surface [16]. The corona is defined as proteins adsorbed to a nonbiological particle and/or sufficiently strongly attracted to it to move together with the particle [17]. These surface-associated proteins are likely to become denatured [18], making them foreign in the sight of the immune system, which therefore promptly marks them for elimination. Especially in view of the fact that the substances bound to the surface are likely to constitute an appreciable proportion of the total mass of the nano-object, they need to be included in its description. If the substances are macromolecules, conformational information should also be given.

The complexity of the chemical composition increases further in the case of ternary and more elaborate compounds (including substances in which X is a multi-atom entity such as an oxy anion), and in the case of objects with deliberately engineered internal structure, such as a “core-shell” particle with chemically different core and shell.

Agglomeration. Nano-objects are often produced in agglomerated form, either deliberately as a final step in production or because the balance of surface forces makes them agglomerate. When the medium in which the objects are dispersed changes, the agglomerate may also change. Typically agglomerates are less harmful than dispersed primary particles.

All of these features will influence penetrability and hazard (e.g., [19]); it cannot be asserted that there is a generic kind of nanoparticle that can be used to assess the risk from exposure (Sction 14.5).

14.5 Exposure

Apart from direct injection into the bloodstream, inhalation (of an aerosol) is by far the most effective route of entry of foreign substances into the body. We shall, therefore, neglect the other two routes usually considered, dermal and oral. Assuming that the duration of contact with the aerosol is well defined, the main metrology problem is, therefore, the determination of the number of nano-objects per unit volume of the ambient air. The number (or number of moles) of nano-objects is more useful and relevant than the total mass of exposure (note that the molecular weight of a nanoparticle may well be considerably smaller than that of a typical blood protein). Knowing the mean size, one can quickly estimate the corresponding number of surface atoms. The most common approach is to collect the objects by causing them to pass over or through an adhesive or entangling surface under defined conditions for a defined interval and then subsequently analyzing the surface [20,21]; online sensors capable of real time continuous monitoring are also available [20,21]. Exposure assessment continues to be an active field of research [22–24].

14.6 Penetrability and clearance

Penetrability has been introduced above, in equation (14.2) as “the probability that a nano-object arriving at the boundary of the organism is taken up by it in a biologically active form”. “Is taken up in a biologically active form” could be construed to mean “taken up by the target organ”, which could even be a cell or an organelle within a cell. Penetrability corresponds to the adsorption and distribution phases that precede drug metabolism, part of the ADME framework used in pharmacokinetics. The last phase of ADME is excretion, which corresponds to what is often called clearance of a nano-object from the body. It can be thought of as negative penetrability and subsumed into the same parameter, which gives the net availability of the nano-object at the site of action.

Penetration is generally a multistep process. We have assumed that it begins by inhalation; see [29] for details of the pulmonary interactions of nano-objects. From the lungs they can readily pass to the bloodstream and thence into individual cells. The epithelium of the lung (the primary organ) is exposed to the highest concentration; the exposure suffered by secondary organs may be two or more orders of magnitude lower. “Pinocytosis is the primary process by which an exogenous entity enters the cell, goes to the specific organelle of the cell and there manifests its cellular function” [30,32]. Phagocytosis is the process of engulfment of foreign objects by an immune cell [31], and should therefore be considered as part of the clearance process (cf. [33]), which ends with excretion.

There is uncertainty over whether nano-objects can pass into the brain. The blood–brain barrier may be robust but nerve cells may offer channels for conduction [34,35].

The dependence of penetrability on nano-object characteristics (Section 14.4, especially size) is stronger than that of exposure [36,37]. As a general rule, the smaller the objects, the easier they can penetrate the various barriers such as the epithelium and the endothelium (whence the general suspicion concerning nano-objects [38]); at the same time, the easier they can be phagocytosed and eliminated. This implies that there is an intermediate, doubtless shape-dependent [39], size where the net penetrability is maximal.

14.7 Hazard

Nano-objects that have penetrated inside the human body can subsequently act in a number of ways [2], which can be grouped into three. The first group comprises what might be called (bio)physicochemical effects: phenomena that do not depend on what might be called a living response, and which could be readily observed in vitro in the absence of living cells. The second group comprises effects consequent on the dissolution of the nano-object, following which the nanoparticulate origin of the dissolved substances is of no significance and the effects are covered by classical toxicology [40]; examples would be nanoparticles of strychnine, potassium cyanide or cadmium selenide. The third group comprises effects only observable within a living organism. These may in turn be divided into single-cell or subcellular responses and responses involving one of the complex subsystems inside the body, notably the immune system.

Group 1: (Bio)physicochemical effects

Group 3: Effects on cellular machinery

1. 4.  persistent attempted phagocytosis: if two dimensions of a nano-object are smaller than the diameter of a macrophage, and one is much greater (i.e., a fiber), the macrophage will attempt to ingest the object but will be unable to do so (Figure 14.1). The result is inflammation and the release of reactive oxygen species (note that certain nanoparticles can generate reactive oxygen species themselves, e.g. [44]), which can damage biomolecules;

2. 5.  platelet activation leading to thrombus formation [45];
3. 6.  suppression of the immune system [46–48];
4. 7.  genotoxicity (DNA damage) [49].

Broadly speaking, Group 1 will influence Group 3, which in turn will influence higher level physiological functions, such as lung performance [50]. In summary of the above list, it should be emphasized that it only gives a very incomplete picture of the situation. In 2006 Revell wrote “relatively little is known of the biological consequences of exposure to nanoparticles” [2]; seven years later little appeared to have changed since Treuel et al. commented that “the fundamental interactions of nanomaterials with biomatter remain incompletely understood” [51].

Nano-objects penetrating into the body may serve as carriers for toxins that they have picked up on their surfaces while in the external environment. For example, a poisonous vapor might be present in the workplace, but below the WEL. If nanoparticles are also present in the atmosphere, the vapor may condense on them and thereby be transported into the lungs yielding an exposure well in excess of the WEL. There is a wider scenario of multiple effects, such as simultaneous exposure to different nanoparticles, that has barely been investigated. Furthermore, exposure to purportedly a single kind of nanoparticle may actually be exposure to a mixture if the preparation contains a variety of sizes and shapes. If the preparation is merely characterized by its mean size and other features, this variety may be unsuspected. It is important to be aware that whereas exposure is only weakly dependent on nano-object characteristics (Section 14.4) the hazards are strongly dependent. The chemical constitution of the surface of the objects is, obviously, expected to be of particular importance since it constitutes the “nano” side of the bio/nano interface. Nanoparticles incorporated into a product may have surface characteristics considerably different from those of the nanomaterial prior to its incorporation.

14.8 Variability of Individual Response

It is salutary to remember that, just as individuals vary enormously in their response to medicinal drugs, they may also show differentiated responses to nano-objects. We still know too little about the detailed pathways of ADME in order to be able to pinpoint particular features of, say, genetic constitution as responsible for hypersensitivity to a particular nano-object, for example (cf. Section 14.2). The NOAEL approach is supposed to ensure that no individual is subjected to adverse conditions, but we do not even know how variable the response of a population is. Even individual cells show a variable response [52]! Consideration of these aspects also leads to caution in accepting toxicological tests carried out on nonhuman species for determining NOAELs or other input into WELs.

14.9 Risks to Vital Ecosystems

If risk over the entire lifecycle of a nanomaterial is to be considered, then we must inquire into the fate of the artifact in which it is incorporated after the use for which it was fabricated has ceased. In comparison with the large volume of data that has been accumulated on toxic effects in humans (and surrogate laboratory mammals), very little has been done to investigate the effects of nanoparticles on other organisms. Deleterious effects of particular nanoparticles have been observed in zebrafish [53], Daphnia [54] and even bacteria [55] (apart from intentional bactericidal activity), to give just a few examples. It has also been found that plants are able to take up nanoparticles [56]. The soil in particular is a very complex, still poorly understood ecosystem [57], full of microörganisms, and there is plenty of potential for unexpected effects of unnatural nanoparticles to occur. In the face of such ignorance, caution is advised. Recently it has become popular to impregnate socks and other garments with nanoscale silver particles in order to inhibit the growth of bacteria. These particles are fairly fugitive and liable to be released in significant numbers when the textile is laundered. Given the rather trivial nature of the application, it should be deprecated since the risks to vital ecosystems appear to outweigh the benefits to human quality of life.

14.10 “Natural” Exposure to Nanoparticles

Small particles have been present in the air long before mankind appeared on Earth, chiefly in the form of wind-borne mineral dusts, organic aerosols from forests, and carbon from fires. Civilization has enormously increased exposure. People are increasingly concentrated in cities, where their particle-generating activities are also concentrated, sometimes with dire results. Many of these activities are related to combustion, including the internal combustion engine powering motor vehicles and other engines [58] and pyrometallurgy. The mean particle size of smokes from combustion (including recreational tobacco smoking [59]) tends to be in the micrometer range, with only the tail of the distribution falling below 100 nm (similarly with the products of milling, such as flour). Given that the control of fire for cooking and heating apparently long predates the emergence of H. sapiens [60], humans are presumably adapted to protect themselves (to some extent) against deleterious effects of fine particle exposure. Many natural waters, which until relatively recently were often drunk untreated, contain nanoparticles in abundance (e.g., [61]). At any rate, the health effects of airborne particulate matter have been well studied [62]. Nevertheless, the products of the nano industry will increasingly be smaller objects of compositions not previously encountered, and the question then arises, how rapidly can humans adapt to cope with them (possibly faster than one might think [63])? An additional problem is distinguishing manufactured nanoparticles from the natural background [64].

14.11 A Rational Basis for Safety Measures

The rationale behind any measure designed to increase safety is the prolongation of life expectancy, but it must do so sufficiently to prevent life quality falling as a result of loss of income.

This provides the basis for a quantitative assessment of the value of safety measures, expressed as the judgment (J)-value [65], defined as the quotient of the actual cost S of the safety measure and the maximum amount that can be spent before the life quality index falls.

The life quality index Q is rooted, unexceptionably, in income (G, income per person, most conveniently taken to be GDP per head) and life expectancy X, and defined as [66]:

$Q=G^{1-\epsilon }X$

where ε is risk aversion (specifically associated with actions that extend life expectancy); it is estimated as 0.91 for the UK and assumed to be the same in other industrialized countries [66].

An individual may choose to divert a portion of his income δG into a safety measure that will prolong his life by an amount δX. Assuming δG and δX are small, expanding equation (14.3) and neglecting higher powers and cross-product terms yields

$\delta Q=\frac{\partial Q}{\partial G}\times (-\delta G)+\frac{\partial Q}{\partial X}\times (\delta X)=-(1-\epsilon )G^{-\epsilon }X\delta G+G^{1-\epsilon }\delta X.$

Dividing by equation (14.3) yields:

$\frac{\delta Q}{Q}=-(1-\epsilon )\frac{\delta G}{G}+\frac{\delta X}{X}.$

It makes no sense to spend more on safety than the equivalent benefit in terms of life prolongation; the greatest rational expenditure on a safety scheme therefore occurs when $\delta Q=0$, and for $Q>0$ this will occur when

$\frac{\delta X}{X}=(1-\epsilon )\frac{\delta G}{G}.$

If the overall cost of a safety measure is S, then the per capita cost is $\hat{S}=S/N$, where N is the size of the population contributing to the measure. The Judgment or J-value is then defined as

$J=\hat{S}/\delta G.$

Equation (14.7) is shown graphically in Figure 14.2. Whether to proceed with a safety measure can therefore be decided on the basis of the J-value: if it is greater than 1, the expenditure S cannot be justified (see [68] for some examples).

14.12 Bow Tie Diagrams

The bow tie diagram is essentially a visual, qualitative representation of a hazard and the associated preventive measures and consequences. It seems to have originated in the oil and gas industry and is becoming popular in the chemical industry. It is likely to be useful for the nanotechnology industry. An example is shown in Figure 14.3.