**3. Stereolithography**

Stereolithography (SLA) is a widely used additive manufacturing technique in the field of polymers, as well as ceramics (**Figure 7**). Here, a monomer resin is polymerised by a laser, layer-by-layer, until a 3D print is fabricated. Hence it differs from fused deposition modelling and other additive manufacturing techniques as it does not involve the use of a nozzle. Such light-curable resins are referred to as photopolymers. In its simplest form, the resin will include the photopolymer and a photoinitiator: the compounds needed to initiate crosslinking of the monomers. However, other additives can be incorporated to modify the properties, such as modifying the mechanical properties of the final product, or the viscosity of the pre-cured resin [51]. Additionally, the resin is a suitable binder for fashioning metal, ceramic and glass materials; and in conjunction with the spatial resolution obtainable, makes SLA an attractive technique for fabricating complex three-dimensional structures.

The viscosity measurement is achieved by performing a steady-shear rate test on the resin free from curable light source(s). The test can be performed at the SLA's functioning shear rate, whether it be 30 s−1, 100 s−1 or any other value, and ensuring the viscosity is below the effec-

**Figure 7.** Representative schematic of a stereolithography printer. The figure includes the components that comprise the

information can be attained. Alternatively, a repeated cycle of LAOS and SAOS can be used; whereby LAOS for reflecting the deformation imparted during the submergence and withdrawal (**Figure 8**); and SAOS to investigate the viscoelastic recovery [57]. At the initial position during SLA printing, the build platform is lowered until submersion thereof is achieved. The platform is thereafter withdrawn, before being submerged again. During withdrawal, the resin should possess a low viscosity to attain complete recoating. Otherwise, a resin with high viscosity, the platform will be lowered with an incomplete recoating. A repeated cycle of LAOS and SAOS can be informative as to whether the structure can recover following defor-

Measuring the viscosity over a range of shear rates rather than at a single point would be of particular interest to those formulating a UV-curable suspension, as parameters such as degree of shear-thinning and yield stress are of importance. The yield stress is correlated to the stability

If working with a commercial printer whose supplier produces their own photopolymer resin, then one can measure the

; but the test is more commonly performed at a wider shear rate range as more

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tive threshold<sup>5</sup>

printer, and the rheological facet of interest.

5

mation by the submersion of the build platform.

viscosity thereof, and attempt to closely match it.

SLA has been used in the field of structural, tissue engineering, electronics and pneumatically-actuated soft robots [52, 53], and ergo, demonstrating its wide applicability. There are many advantages to this technique over FDM, including printing can be achieved without high temperatures, higher spatial resolution, and nozzle clogging is not of concern. SLA is predominantly Couette flow, thus only rotational rheometry is pertinent here. Furthermore, the dynamic aspect of rotational rheometers can be used for photorheology, which will be described in Section 3.2.

#### **3.1. Viscosity measurements**

In comparison to FDM, both the operating viscosity and shear rates are considerably smaller. The viscosity of the photopolymer should be under 5 Pa.s at 30 s−1 [54, 55], which ensures that the photopolymer is free-flowing, and capable of forming a new layer (i.e. recoating) ready for polymerisation. However, this value depends on the SLA printer, as others require, for example, a viscosity below 10 Pa.s at 100 s−1 [56]. This will ultimately depend on the settings of the SLA printer, but nonetheless, one should consider the maximum operable viscosity prior to printing.

**3. Stereolithography**

52 Polymer Rheology

formed the better the adhesion between adjacent layers.

described in Section 3.2.

prior to printing.

**3.1. Viscosity measurements**

Stereolithography (SLA) is a widely used additive manufacturing technique in the field of polymers, as well as ceramics (**Figure 7**). Here, a monomer resin is polymerised by a laser, layer-by-layer, until a 3D print is fabricated. Hence it differs from fused deposition modelling and other additive manufacturing techniques as it does not involve the use of a nozzle. Such light-curable resins are referred to as photopolymers. In its simplest form, the resin will include the photopolymer and a photoinitiator: the compounds needed to initiate crosslinking of the monomers. However, other additives can be incorporated to modify the properties, such as modifying the mechanical properties of the final product, or the viscosity of the pre-cured resin [51]. Additionally, the resin is a suitable binder for fashioning metal, ceramic and glass materials; and in conjunction with the spatial resolution obtainable, makes SLA an

**Figure 6.** Schematic depicting the evolution of neck size during polymer sintering. The larger the sintering neck size

SLA has been used in the field of structural, tissue engineering, electronics and pneumatically-actuated soft robots [52, 53], and ergo, demonstrating its wide applicability. There are many advantages to this technique over FDM, including printing can be achieved without high temperatures, higher spatial resolution, and nozzle clogging is not of concern. SLA is predominantly Couette flow, thus only rotational rheometry is pertinent here. Furthermore, the dynamic aspect of rotational rheometers can be used for photorheology, which will be

In comparison to FDM, both the operating viscosity and shear rates are considerably smaller. The viscosity of the photopolymer should be under 5 Pa.s at 30 s−1 [54, 55], which ensures that the photopolymer is free-flowing, and capable of forming a new layer (i.e. recoating) ready for polymerisation. However, this value depends on the SLA printer, as others require, for example, a viscosity below 10 Pa.s at 100 s−1 [56]. This will ultimately depend on the settings of the SLA printer, but nonetheless, one should consider the maximum operable viscosity

attractive technique for fabricating complex three-dimensional structures.

**Figure 7.** Representative schematic of a stereolithography printer. The figure includes the components that comprise the printer, and the rheological facet of interest.

The viscosity measurement is achieved by performing a steady-shear rate test on the resin free from curable light source(s). The test can be performed at the SLA's functioning shear rate, whether it be 30 s−1, 100 s−1 or any other value, and ensuring the viscosity is below the effective threshold<sup>5</sup> ; but the test is more commonly performed at a wider shear rate range as more information can be attained. Alternatively, a repeated cycle of LAOS and SAOS can be used; whereby LAOS for reflecting the deformation imparted during the submergence and withdrawal (**Figure 8**); and SAOS to investigate the viscoelastic recovery [57]. At the initial position during SLA printing, the build platform is lowered until submersion thereof is achieved. The platform is thereafter withdrawn, before being submerged again. During withdrawal, the resin should possess a low viscosity to attain complete recoating. Otherwise, a resin with high viscosity, the platform will be lowered with an incomplete recoating. A repeated cycle of LAOS and SAOS can be informative as to whether the structure can recover following deformation by the submersion of the build platform.

Measuring the viscosity over a range of shear rates rather than at a single point would be of particular interest to those formulating a UV-curable suspension, as parameters such as degree of shear-thinning and yield stress are of importance. The yield stress is correlated to the stability

<sup>5</sup> If working with a commercial printer whose supplier produces their own photopolymer resin, then one can measure the viscosity thereof, and attempt to closely match it.

formulate a solvent-free photopolymer comprising of polycaprolactone, in which heating was needed to achieve the operable viscosity [62]. If such an approach is pursued, then performing a temperature ramp will help to identify the minimum temperature without needing to use

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Aside from viscosity measurement, a rheometer is an indispensable tool for SLA as it can be used to measure the cross-linking characteristic of the resin. As mentioned, the monomer transforms from a liquid to a solid upon UV contact, which can be measured by a rotational rheometer. The transition from resin to solid manifest itself in a tremendous increase to both the storage and loss modulus, with values such as a curing time and material stiffness extracted. This entails the use of an oscillatory time ramp, whereby both the storage and loss modulus are recorded over time (**Figure 9**). The test is allowed to run until a baseline value for the resin is obtained, whereafter a UV source is activated, and the solidification behaviour is observed. Both the time to achieving solidification and the shear modulus of the solid can be quantified. The former is necessary to predict the scanning speed of the UV laser needed to achieve a solid structure; whereas the latter provides a strong correlation to the mechanical properties of the 3D print, namely Young's Modulus [63]. Such a test saves

**Figure 9.** Representative dynamic mechanical analysis curve for measuring the crosslinking characteristics of a

an unnecessarily high value.

both time and cost.

UV-curable formulation.

**3.2. Photorheology: dynamic mechanical analysis**

**Figure 8.** Illustration depicting SLA sequence of events.

of the suspension, which would provide insight into the stability of the suspension over time, and the tendency of the particles to sediment. Particle sedimentation is indeed undesirable as it results in an inhomogeneous print. Other rheological analysis performed to elucidate the degree of sedimentation in suspensions include determining the tan δ from oscillatory tests, creep-recovery tests and stress relaxation tests [58]. Note that if suspensions are to be measured using a rotational rheometer, then one has to use a plate-plate geometry configuration as a cone-plate configuration is susceptible to erroneous measurement due to the particles.

If a UV-curable emulsion has been formulated, and syneresis (i.e. phase separation between the two solvents) is of concern, then a frequency sweep is advisable. Using this test, a storage modulus *G'* of comparable magnitude, or superior, to the loss modulus *G"*, at the low frequency (i.e. longer periods) suggests the emulsion is less likely to exhibit syneresis. In other words, a high tan δ indicates a higher tendency to exhibit syneresis [59].

A minimum viscosity limit on the other hand appears to be less discussed, as this is less problematic for most researchers. One author inferred a minimum of 2 Pa.s [55], albeit successful SLA prints were achieved with a viscosity between 0.1 and 1 Pa.s [53, 60].

The low viscosities make SLA desirable as a binder for powder metallurgy, as more of the inorganic powder can be suspended therein. Both metal and ceramic structures have been fabricated using SLA, wherein the inorganic particles are suspended therein; cured into the desirable 3D structure, and subsequently thermally de-bound, leaving behind only the inorganic material [61] elbadawi et al. The material is then sintered to achieve permanence. To achieve a green body that is mechanically sound, at least 40 vol% solids loading is needed, and as expected, this produces a substantial increase in viscosity, above the operating range. However, through the incorporation of dispersants and diluents, the viscosity can be lowered, and hence rheological analysis is key to identifying the minimum dispersant concentration needed to produce a suitable resin.

If working with a photopolymer resin that is not liquid at room temperature, then a viscosity test of importance will be to perform a temperature ramp. Elomaa et al. (2011) opted to formulate a solvent-free photopolymer comprising of polycaprolactone, in which heating was needed to achieve the operable viscosity [62]. If such an approach is pursued, then performing a temperature ramp will help to identify the minimum temperature without needing to use an unnecessarily high value.

#### **3.2. Photorheology: dynamic mechanical analysis**

of the suspension, which would provide insight into the stability of the suspension over time, and the tendency of the particles to sediment. Particle sedimentation is indeed undesirable as it results in an inhomogeneous print. Other rheological analysis performed to elucidate the degree of sedimentation in suspensions include determining the tan δ from oscillatory tests, creep-recovery tests and stress relaxation tests [58]. Note that if suspensions are to be measured using a rotational rheometer, then one has to use a plate-plate geometry configuration as a

If a UV-curable emulsion has been formulated, and syneresis (i.e. phase separation between the two solvents) is of concern, then a frequency sweep is advisable. Using this test, a storage modulus *G'* of comparable magnitude, or superior, to the loss modulus *G"*, at the low frequency (i.e. longer periods) suggests the emulsion is less likely to exhibit syneresis. In other

A minimum viscosity limit on the other hand appears to be less discussed, as this is less problematic for most researchers. One author inferred a minimum of 2 Pa.s [55], albeit successful

The low viscosities make SLA desirable as a binder for powder metallurgy, as more of the inorganic powder can be suspended therein. Both metal and ceramic structures have been fabricated using SLA, wherein the inorganic particles are suspended therein; cured into the desirable 3D structure, and subsequently thermally de-bound, leaving behind only the inorganic material [61] elbadawi et al. The material is then sintered to achieve permanence. To achieve a green body that is mechanically sound, at least 40 vol% solids loading is needed, and as expected, this produces a substantial increase in viscosity, above the operating range. However, through the incorporation of dispersants and diluents, the viscosity can be lowered, and hence rheological analysis is key to identifying the minimum dispersant concentration

If working with a photopolymer resin that is not liquid at room temperature, then a viscosity test of importance will be to perform a temperature ramp. Elomaa et al. (2011) opted to

cone-plate configuration is susceptible to erroneous measurement due to the particles.

words, a high tan δ indicates a higher tendency to exhibit syneresis [59].

SLA prints were achieved with a viscosity between 0.1 and 1 Pa.s [53, 60].

needed to produce a suitable resin.

**Figure 8.** Illustration depicting SLA sequence of events.

54 Polymer Rheology

Aside from viscosity measurement, a rheometer is an indispensable tool for SLA as it can be used to measure the cross-linking characteristic of the resin. As mentioned, the monomer transforms from a liquid to a solid upon UV contact, which can be measured by a rotational rheometer. The transition from resin to solid manifest itself in a tremendous increase to both the storage and loss modulus, with values such as a curing time and material stiffness extracted. This entails the use of an oscillatory time ramp, whereby both the storage and loss modulus are recorded over time (**Figure 9**). The test is allowed to run until a baseline value for the resin is obtained, whereafter a UV source is activated, and the solidification behaviour is observed. Both the time to achieving solidification and the shear modulus of the solid can be quantified. The former is necessary to predict the scanning speed of the UV laser needed to achieve a solid structure; whereas the latter provides a strong correlation to the mechanical properties of the 3D print, namely Young's Modulus [63]. Such a test saves both time and cost.

**Figure 9.** Representative dynamic mechanical analysis curve for measuring the crosslinking characteristics of a UV-curable formulation.

The shrinkage of the material can also be measured by exploiting the rheometer's<sup>6</sup> axial movement, and the upper plate geometry can be adjusted to move in-line with the shrinkage that occurs with cross-linking. As **Figure 10** demonstrates, a minimum compressive force is applied to the sample during oscillatory measurements, which if not registered will cause the upper plate to move until the compressive force is re-established. Therefore, in addition to measuring the crosslinking properties of the photopolymers, a rotational rheometer can be

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Given the success and ubiquity of FDM, similar extrusion-based additive manufacturing techniques exists. Examples include bioprinters, where hydrogels and cells are extruded; robocasting, where a ceramic, metallic, or glass powder enveloped by a polymeric binder is extruded; and inkjet printing, where polymeric inks are ejected. Said techniques differ to FDM with respect to their printing conditions. For example, bioprinters and robocasting can be performed at room temperature, and hence high-temperature rheology is of less interest. Another example is the solidification process post-extrusion: where FDM relies in cooling for the material post-extrusion to maintain its structural integrity, cold-extrusion techniques require shear-thinning materials that can rapidly restore their structural integrity following shearing [63]. Moreover, each of the aforementioned techniques have their unique desirable rheological properties, with respect to viscosity ranges, flow characteristics and dynamic mechanical properties. These are just a few of the common extrusion-based AM techniques, and as the field progresses, alternative derivatives are anticipated. Hence, the desirable rheological properties will evolve accordingly, and it is for this reason, that rheology will need to

A brief mention of selective laser sintering (SLS) is merited. Distinctly different from other techniques, SLS utilises a laser to sinter adjacent polymer powders laterally, such as nylon, and subsequently layer-by-layer to fashion a 3D print. After each layer is fully sintered, a new powder layer is deposited, prior to sintering. The ability of the powder to flow, as well as its packing performance and distribution behaviour, are of interest; and where powder rheology can be employed for elucidation thereof. Measurements performed using a powder rheometer include powder flow, particle-particle interaction during flow, compressibility, and adhesivity. Furthermore, the sintering behaviour discussed in Section 2.3 are applicable herein. Thus, despite SLS possessing a dissimilar mode of operation, rheology is still a relevant technique.

The chapter has demonstrated the necessity and utility of rheological characterisation techniques for polymer-based additive manufacturing, irrespective of the technique. For fused deposition modelling, rheologically characterisation are performed to obtain the true shear rate at the nozzle wall, the ideal viscosity for material flow, the critical buckling stress, extrudate swelling and sintering characteristics. For stereolithography, a contrasting AM technique, rheology is a requisite for ensuring the resin possesses the ideal viscosity, as well as attaining information regarding the curing characteristics and mechanical properties of the cured resin.

incorporated to offer insight into the material's shrinkage characteristics.

be a habitual characterisation technique in polymer AM fabrication.

**4. Other techniques**

**5. Concluding remarks**

**Figure 10.** Schematic illustrating the events occurring when measuring shrinkage due to UV-curing. (a) at first the rheometer plate establishes a baseline by applying a prescribed axial force (0.1 N). As the sample is cured it shrinks (b) causing a decrease in the force, and subsequently the rheometer moves axially until the prescribed force is re-established (c). Such movements allow the simultaneous measurement of the gap decrease(Δh).

<sup>6</sup> For Example TA Instruments Discovery Hybrid Series rheometers, which can measure both tensile and compressive forces up to 50 N.

applied to the sample during oscillatory measurements, which if not registered will cause the upper plate to move until the compressive force is re-established. Therefore, in addition to measuring the crosslinking properties of the photopolymers, a rotational rheometer can be incorporated to offer insight into the material's shrinkage characteristics.
