14 Rates

Microwave-assisted acid digestion

The conversion of solid samples into representative solutions is the first step for the analytical procedure. By using microwave technology it is possible to heat up the sample solution extremely fast and perform digestions at high pressures and temperatures, due to the applied pressure vessels even far above the boiling point of the used acids. The possibility to perform digestions at higher temperatures reduces the digestion time down to only a few minutes. This rate acceleration is based on the Arrhenius Law, which states as a rule of thumb that the digestion speed is doubled when increasing the reaction temperature by 10°C.

Acid digestion

Acid digestion is the most often used wet-chemical sample preparation technique. By using concentrated acids or mixtures thereof, the matrices of organic as well as inorganic samples can be totally destroyed or dissolved, and the whole sample can be brought into solution. Subsequently, concentration of elements or species can be determined with an adequate analytical technique.

Find below the most commonly used acids for acid digestion and their typical concentrations:

  • Nitric acid, HNO3 (65 %)
  • Hydrochloric acid, HCl (30-37 %)
  • Hydrofluoric acid, HF (40-48 %)
  • Sulfuric acid, H2SO4 (95-98 %)
  • Perchloric acid, HClO4 (70-72 %)
  • Phosphoric acid, H3PO4 (85 %)
  • Hydrogen peroxide, H2O2 (30 %)
  • Aqua regia, HCl + HNO3 (volume ratio 3:1)
  • Reverse aqua regia, HCl + HNO3 (volume ratio 1:3)
  • Boric acid, H3BO3 (approx. 5 %)

Acid leaching

Acid leaching is similar to acid digestion, but without completely destroying or dissolving the sample matrix. As determination of the (bio-) availability of elements is an important question, acid leaching is also a typical environmental application. For leaching of species from the sample matrix acids with different strengths – preferably a (diluted) mixture of HCl and HNO3 (3:1, aqua regia) – will be used.

Basic digestion chemistry

Depending on the sample material which has to be digested, combinations of the following chemical reactions take place:

Organic materials:

Organic matter + nitric acid gaseous products + water
(CH2)n + 2n HNO3 n CO2(g) + 2n NO(g) + 2n H2O


Metal + acids metal ions + gaseous products + water
3 Me + 6 H+ + 2 HNO3 3 Me2+ + 2 NO(g) + 4 H2O
2 Me + 6 H+ 2 Me3+ + 3 H2(g)

Geological samples:

Silicate + acid gaseous products + water
SiO2 + 4 HF SiF4(g) + 2 H2O

During all reactions listed above gaseous products are formed. This means that a higher sample weight will result in more gaseous products. While this parameter is of less importance with open vessel digestion, it is crucial for closed vessel digestion since the pressure inside the vessel will increase.

Open vs. closed vessel digestion

Open vessel digestion

Influence of temperature on residual carbon content

Figure 1: Influence of temperature on residual carbon content

Conventional open digestion methods (e.g. hot plate, hot block) show several advantages, but also suffer from severe drawbacks:


  • Low investment costs
  • Simple equipment, easy to handle
  • High (sample) throughput
  • Large sample weight – all gaseous by-products are released without any pressure build-up


  • High reagent consumption – important cost factor
  • High reagent blank – evaporation of reagents requires regular restocking of acids
  • Increased risk of contamination (e.g. airborne particles)
  • Risk of analyte loss due to evaporation
  • Limited temperature – depends on the reagent mixture
  • Long digestion time – due to the limited temperature

Increasing the reaction temperature does not only speed up the digestion process, but also decreases the residual carbon content in the final digested solution (see Figure 1). For open vessel digestion, addition of high-boiling reagents (e.g. sulfuric acid) does also increase the maximum achievable temperature, but may affect the subsequent analysis.

Closed vessel digestion

Closed vessel digestion can overcome the disadvantages of open digestion.


  • High reaction temperature – fast method
  • Complete digestion – minimized interferences with analysis
  • Low amount of reagents required
  • Simplified chemistry – no need to add high-boiling reagents
  • No loss of analytes
  • Minimized risk of contamination
  • Reproducibility
  • Documentation


  • Limited sample amount – due to formation of gaseous by-products (not with closed vessels with venting capability)
  • Need for pressure resistant vessels
  • Addition of reagents during a run not possible – two-step procedure required
  • Higher investment costs

Arrhenius Law

Reachable temperatures of a liquid with a boiling point of 120 °C in open and closed vessels

Figure 2: Reachable temperatures of a liquid with a boiling point of 120 °C in open and closed vessels

Classical chemical reactions often take quite a long time. Since nowadays time equals money, it is of high interest to find ways for accelerating those processes.

The key to acceleration is the Arrhenius law. It states as a rule of thumb that increasing the temperature by 10 °C doubles the speed of a reaction process, so that the respective digestion reaction can be finished much faster (e.g. a temperature increase of only 20 °C reduces the digestion time to a quarter of the original demand).

Only if a vessel is pressurized temperatures beyond the boiling point can be reached. Figure 2 visualizes this fact with a liquid which boils at approx. 120 °C. The blue curve shows that the temperature at ambient pressure (open vessel) does not increase anymore once it has reached the solvent’s boiling point. If the vessel is closed and pressurized, higher temperatures can be reached (pink curve).

A very important factor to consider with closed-vessel digestion systems is the limited sample weight, as during digestion reactions usually gaseous by-products are formed. A higher sample weight produces more pressure, which means that it reaches the pressure limit faster during heating. As a consequence, the final digestion temperature will decrease with higher sample weight.

Closed vessels with venting capability

Figure 3: Schematic representation of a venting vessel

A smart way to overcome one limitation of closed vessels (increasing the sample weight will decrease the final digestion temperature) is the use of closed vessels with venting capability (see Figure 3).

The main component of such a vessel is a screw cap that allows short and controlled opening of the vessel at a defined pressure level. If the pressure level in the vessel goes below this limit again, the vessel will be resealed.

That way gaseous products are released during a digestion run in a controlled manner. As a consequence, the reaction temperature can be maintained at a high level independent of the sample amount.

There are certain benefits related to closed vessels with venting capability:

  • Higher (organic) sample amounts are applicable than in closed vessels without venting capability with same specifications
  • Digestion vessels can be smaller, simpler and more budget-friendly
  • Less sensitive against sample overload
  • Digestion of different sample types in one run is possible


  • Acid losses when the acid vapor pressure exceeds the venting pressure of the vessel

Microwave vs. Conventional Heating

During classical oil bath heating the reaction mixture is heated in a conductive way: the hotplate heats the oil bath, the oil bath heats the vessel container (flask) and the hot vessel container heats the reaction mixture (heating from the outside to the inside, see Figure 4, entry a).

In contrast, microwave irradiation results in energy efficient internal heating by direct coupling of microwave energy with dipoles and/or ions that are present in the reaction mixture. Microwaves pass through the (almost) microwave-transparent vessel wall and heat the reaction mixture on a molecular basis – by direct interaction with the molecules. Due to this direct “in-core” heating (no initial heating of the vessel surface), microwave irradiation results in inverted temperature gradients as compared to a conventionally heated system (see Figure 4, entry b).

The conversion of electromagnetic energy into heat energy works highly efficiently and results in extremely fast heating rates – not reproducible with conventional heating. Additionally, no direct contact to a heating core is necessary, enabling the heating of different vessel sizes, shapes and amounts with the same microwave.

Figure 4: Simplified schemes of the heat distribution in a conventionally heated reaction mixture (a), and in a microwave heated reaction mixture (b). While conventionally the heat comes from the outside and goes into the reaction mixture by convection currents (resulting in a very hot vessel wall), microwaves go through the almost microwave-transparent vessel wall and directly heat the reaction mixture on a molecular basis.

Basics of Microwave Heating

Microwaves are electromagnetic waves in the range of 300 MHz (0.3 GHz) to 300 GHz, with a typical frequency of 2.450 MHz for both domestic microwave ovens and laboratory equipment (see Figure 5).

Figure 5: The spectrum of electromagnetic waves

There are basically three different ways how materials can interact with microwaves (see Figure 6):

  • Reflection: Conducting materials (like metals) do not absorb, but reflect microwaves. Heating does not occur.
  • Absorption: Dielectric materials (i.e. which can be polarized by an electric field) absorb microwaves, and therefore become hot. Typical examples are water, acids or polar organic solvents.
  • Transmission: Insulating materials (like polymers, quartz or ceramics) are transparent to microwaves. Heating does not occur.

Figure 6: Interaction of different materials with microwaves: electrical conductors (e.g. metals), absorbing materials (e.g. polar solvents or acids) and insulation materials (e.g. Teflon, quartz).

The fundament of microwave chemistry is the efficient heating of materials by dielectric heating effects. Dielectric heating works with two main mechanisms (see Figure 7):

  • Dipolar polarizationy
    Substances that are dipoles are able to generate heat when irradiated with microwaves. That means their molecular structure must be charged partly negatively and partly positively. Because the microwave field is oscillating, the dipoles in the field align to the oscillating field. This process causes rotation, which results in friction and ultimately in heat energy.
  • Ionic conduction
    During ionic conduction, dissolved charged particles (usually ions) oscillate back and forth when irradiated with microwaves. Due to this oscillation the charged particles collide with neighboring molecules or atoms, which ultimately create heat energy. For example: if the same amount of distilled water and tap water is heated by microwave irradiation, the tap water will heat more rapidly because of its ionic content in addition to the dipolar rotation of water molecules.

Microwave heating of gases and solids…
… is hardly possible. Gases cannot be heated with microwaves because the distance between the rotating molecules is too far. Similarly, solid materials like ice are (almost) microwave transparent as the water dipoles have a fixed position in the crystal lattice and cannot move as freely as in the liquid state. However, some conductive solid materials, like silicon carbide, with freely moving electrons, are excellent microwave absorbers and therefore heat very fast.

Figure 7: Schematic illustration of the two main dielectric heating mechanisms: dipolar polarization (dipoles align in the microwave field) and ionic conduction (ions move in the microwave field).

With dielectric heating, electric energy is converted into kinetic energy which is ultimately converted into heat.

Microwave Reactors

The cavity is the part of a microwave reactor where the reaction container is placed and irradiated. There are different irradiation modes depending on the design of the instrument:

Monomode Microwave Reactors

The microwave energy is created by a single magnetron and directed through a waveguide to the reaction mixture (see Figure 8). This results in a “standing wave” and the reaction vessel is located in a hot spot where efficient heating of small volumes is possible. The instruments can have a space saving design but only one sample can be digested at once.

Figure 8: Schematic illustration of a monomode cavity with a small sample.

Multimode Microwave Reactors

One or two magnetrons create microwave irradiation, which is directed into the cavity through a waveguide and distributed by a mode stirrer (see Figure 9). Microwaves are reflected from the walls thus interacting with the reaction mixture in a chaotic manner. Additional rotation of the reaction vessel in the cavity prevents temperature inhomogeneity and formation of hot spots.

This mode allows for heating larger volumes (>20 mL) of reaction mixtures and of heating several samples simultaneously (up to 64 samples). To enable homogenous heating of several samples the multimode reactors need to have a bigger footprint compared to monomode reactors.

Figure 9: Schematic illustration of a multimode cavity

DMC Directed Multimode Cavity

The DMC Directed Multimode Cavity combines the benefits of monomode and multimode reactors. Like in a monomode system, the microwaves are directed to the samples providing highly efficient heating in a small footprint system, but like in a multimode system, more than one sample (up to 12 samples) can be digested in a single run (see Figure 10). 

Figure 10: Schematic illustration of a DMC (Directed Multimode Cavity)

Pressurized Digestion Cavity (PDC)

The microwave energy is created by one magnetron and is directed to the pressurized digestion cavity. The microwaves are splitted and directed upwards in a circle to the cavity. Due to this splitting the spot in the middle of the PDC can be used for a temperature sensor and/or stirring device. Prior to heating, the cavity is pressurized with an inert gas (e.g. nitrogen or argon), which will avoid boiling and evaporation of the reagent mixture. The pressure in the cavity is sealing the vials.

The cavity is additionally filled with a load solution which is heated together with the reaction media to create a counter pressure and to optimize the temperature distribution. This enables the use of one or up to 24 thin-walled vials (made of quartz, glass, or fluoropolymer) closed with plug-on caps.

Figure 11: Schematic illustration of a Pressurized Digestion Chamber (PDC)