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Effects of solvent-particle interaction kinetics on microstructure formation during three-dimensional printing.


Three-dimensional printing {3DP) fabricates complex structures by ink-jet printing liquid binder onto loose, fine powder in a laminated printing fashion (1, 2). The printing pattern is derived from computer-aided-design (CAD) models. A large number of material combinations can be processed because the liquid and powder phases can have different compositions. The relevant machine components are shown in Fig. 1. The computerized X-Y positioning system directs the 2D horizontal motion of the printhead, which delivers the liquid binder droplets. Binding occurs only where binder droplets contact the powder material below, The local composition can be manipulated by specifying the appropriate printhead to deposit a predetermined volume of binder. The local microstructure can be controlled by either modulating the binder composition (3). or by altering the printing parameters during component construction (4).

These features make 3D Printing an attractive manufacturing technology for biomedical devices. Dense, defect-free structures are required for most drug delivery devices in which uncontrolled defects may lead to adverse complications. Highly dense structures are also necessary for many orthopedic fixation devices in which random defects can deteriorate mechanical integrity and result in premature clinical failures. Highly porous matrices with interconnected microporosity and controlled channel dimensions are critical for successful engineering of thick tissues. The ability to control feature size, or optimize print resolution, is critical for all types of devices. The common theme for controlling feature size, microstructure, and spatial distribution of printed matter is to understand the fundamental binding mechanisms during 3D Printing.

The predominant binding mechanism for lactone based absorbable polyesters is dissolution-reprecipitation, in which four stages have been identified: droplet impact, binder imbibition and drainage, particle dissolution/swelling, and re-precipitation {5). The four stages are diagrammed in Fig. 2. In the 3DP process, droplets impact the loose powder bed at typical speeds of 10 m/s, creating a crater and an initial core of binder-powder mixture. Binder imbibition/drainage commences as the liquid in the initial core migrates away from the saturated pores, and drains into surrounding empty pores. Smaller pores tend to exert larger capillary forces for the binder, while larger pores tend to offer less resistance against binder drainage. Neighboring loose particles are partially or completely dissolved by the solvent droplets, and 3D structures are produced by re-precipitation of the solvent-polymer gel-mix as a result of solvent evaporation.

Ballistic impact has been studied to determine its effects on surface finish of 3DP parts. The timescale for ballistic impact was observed with high speed photography to be on the order of milliseconds (6). Binder migration was studied to determine its effects on printed feature size. Simple capillary models and high speed photography have determined the timescale for imbibition/drainage to be on the order of 10 to 100 milliseconds (6, 7). Dissolution/swelling and reprecipitation during 3DP have not been studied, and the timescales for these processes are unknown. The relative timescales between these binding stages have important implications on printing strategy and resultant microstructure. The migrating liquid is expected to become increasingly viscous during imbibition/drainage if dissolution is rapid. This would result in improved print resolution. The liquid viscosity is unaffected if insignificant dissolution occurs prior to migration arrest. Dense microstructure and smooth surfaces are expected if the timescale for dissolution is shorter than that for evaporation. Random defects and granular surfaces are expected if dissolution rate is slower than that for solvent evaporation. It is, therefore, important to determine the actual timescale for particle dissolution and reprecipitation.


Particle Dissolution

A dissolution cell was designed and constructed as shown in Fig. 3. The holder assembly, which contains the main housing, top metal block, and three tightening screws, was fabricated by modifying a commercial FTIR sample cell (Beckman Quick-mount Multicell, Columbia, Ohio). Two 1-mm-thick glass plates (1.5 cm x 3 cm) were cut from a microscope slide to fit into the main housing. One glass plate was used to form the "bottom" of the dissolution cell. Two holes (2 mm diameter) were drilled into the second glass plate to form the "top" boundary of the dissolution cell. The holes were positioned to correspond with the solvent inlet and outlet ports of the metal block above. A thin Teflon (DuPont) spacer was placed between the two 1-mm-thick glass plates to control the interplate distance and maintain the seal for the dissolution cell. The various components of the dissolution cell are depicted in Fig. 4.

Polymer particles were placed in between the glass plates within the confines of the thin Teflon spacer. The three screws shown in Fig. 3 were tightened slightly in order to secure the various components together and prevent leakage during the experiment. Cracking of the top glass plate was prevented by cushioning with a thin Teflon spacer between the glass plate and top metal block. Another thin Teflon spacer was placed between the bottom glass plate and the Teflon block for similar purposes. The entire assembly was placed under an objective lens of an optical microscope (Olympus BH-2, Japan) outfitted with a color CCD video camera (Toshiba Image Master SIK-636S, Japan). A monochromatic light source (512 nm wafer QC lamp, American Scientific Products, McGaw Park, Ill.) was directed at the dissolution cell at [approximately]20 [degrees] angle. This angle was determined in preliminary experiments to provide the best viewing contrast during dissolution. Solvent was introduced at time zero at 0.1 cc/min into the dissolution cell through the metal block in-port. Particle dissolution was observed on a 20-inch monitor (Toshiba CM1900A, Japan) in real time, and captured on a video cassette recorder (JVC BR-S600U, Japan) at 30 frames/sec for later analyses.

Evaporation From Powder Bed

Polylactide-co-glycolide (PLGA 85:15 100,000 MW) pellets were cryogenically milled and dried in vacuum for 72 hours. NaCl crystals were cold milled and similarly dried. Both powder types were classified into the following particle size ranges: [less than] 45 [[micro]meter], 45-75 [[micro]meter], and 75-150 [[micro]meter]. The classified particles were manually spread to uniform 200 [[micro]meter] thick layers on a stainless steel plate by first leveling the plate with the piston roller guides and then lowering the piston actuator by the desired distance. The plate was then placed on an analytical balance and connected to a computer via a data communication module. A stainless steel stencil with a rectangular opening was placed over the plate, exposing the salt particles below. The bottom side of the stencil had a milled recess around the stencil opening so as to avoid contact with the particles during the experiments. A LabView VI was activated at this point to establish the baseline weight. The quantity 200 [[micro]liter] chloroform was deposited through the stencil and directly onto the particles. Data was collected from the balance at a rate of 1 sample per second. Five samples were tested for each size range.

Specimen Preparation

The combined effects of particle dissolution and evaporation kinetics on microstructure formation can be evaluated by comparing the results from the above experiments with microstructural analysis of actual 3DP samples. Saltpolymer mixtures, were 60:40 v/v, were prepared from the classified PLGA and NaCl powder. A new supply of pure chloroform was used to print thin strips (5 mm wide, 50 mm long, 1.5 mm thick) with each polymer-salt mixture. Two print speeds (75 cm/sec and 150 cm/s) were tested to determine the effects of print speed. More binder is expected to be deposited per unit line length under slower print speed conditions, assuming that the volumetric binder flow rate through the nozzle is kept constant. Freshly printed strips were placed into N2 glove box for 48 hours, and into vacuum for 48 hours. Additional post processing steps to reduce residual chloroform to below regulatory specifications were not performed for these samples since they will not be implanted. The salt particles were selectively removed by immersing the strips into individual vials of deionized water for 2 hours in an automated shaker rotating at 200 rpm. The strips were subsequently placed into a desiccator for 48 hours, and vacuumed for 48 hours. The dried samples were sectioned, sputter coated, and prepared for microstructural analysis by scanning electron microscopy.


Particle Dissolution

Highly soluble polymer-solvent systems tend to exhibit gel formation during dissolution. The interaction begins with solvent penetration into the polymer particle. The external polymer layer undergoes rapid transformation from the solid state to the gel state when a critical solvent concentration in the polymer is reached. The gel state is characterized as the swollen mass of entangled polymer chains. The diagram in Fig. 5 describes this mode of particle dissolution. Two distinct interfaces are identifiable during the initial stages of dissolution. An internal solid-gel interface divides the inner solid (low solvent volume fraction) and gel layer. An external gel-solvent interface separates the gel layer from the surrounding solvent (low polymer volume fraction).

Chloroform is one of the most common solvents used in 3DP for the lactone based absorbable polyesters. Dissolution of a polycaprolactone (PCL 30,000) particle in chloroform is shown in Fig. 6. A gel layer can be observed shortly after solvent flow, and grows to appreciable size after only 1 second. The solid-gel interface moves radially inwards. The gel-solvent interface expands to almost twice the initial particle diameter after only 5 seconds, while the solid-gel interface continues to shrink. The gel-solvent interface remains visible after 15 seconds, beyond which time the solid-gel interface converges to the center of the particle. No solid polymer remains at that point. Polylactide-co-glycolides (PLGA 85:15 108,000) also exhibited gel layer formation during dissolution in chloroform.

One interesting finding with polymer-solvent systems that dissolve with gel formation is the existence of a "minimal" dissolution time and an optimal particle size. The dissolution time of 50 PLGA (85:15 108,000) particles in chloroform is plotted against their initial particle dimensions, which are idealized for spherical particles in Fig. 7. Two dissolution regimes can be observed, suggesting a change in controlling mechanism. In the first regime, the dissolution time of larger particles decreases with decreasing particle size. In the second regime, the dissolution time becomes independent of particle dimension for particles below 75 [[micro]meter]. This critical dissolution time ([t.sub.min] = 1.25 sec) may represent the "minimal" time required for the dissolution of small PLGA (85:15 108,000) particles.

Evaporation From Powder Bed

A typical mass loss profile during chloroform evaporation from a powder bed of [less than] 45 [[micro]meter] salt is shown in Fig. 8. Two regimes are clearly discernible after the solvent peak. A linear regime, labeled "constant rate period" in Fig. 8, can be seen immediately after solvent deposition. A nonlinear regime can be seen at longer times. The timescale for transition from the constant rate period to the nonlinear period was found to be on the order of 100 seconds for chloroform and salt particles.

The extent of the linear region was determined by using linear regression analysis and identifying the limits where [r.sup.2] [greater than] 0.99. The slope value as determined in this manner was converted into evaporation rate, expressed as [micro]mole/[s.sup.*][cm.sup.2]. Evaporation rates for all samples were determined similarly, and the averages and standard deviations are plotted in Fig. 9. It can be seen that solvent evaporation from a particulate surface is three times faster than that from a planar, smooth surface. The data also seem to suggest that particle size has minimal effects on the kinetics of chloroform evaporation from a thin layer of nondissolving powder, This may be attributed to the cubic crystalline structure of the salt particles, for which variations in particle size do not result in changes in radii of curvature. The salt particles were prepared by mechanical milling, which tend to produce particles with fiat surfaces.


At least five distinct phenomena are involved during dissolution of PLGA in chloroform: 1) solvent ingression into the polymer particle, 2) particle swelling, 3) chain disentanglement, or reptation, 4) chain disengagement from the solvent-gel interface, and 5) chain diffusion across the liquid boundary layer. Repration is the process by which individual polymeric chains "free" themselves from the entangled swollen polymer network. Ranade and Mashelkar developed a two-dimensional transport model to describe the dissolution of a spherical polymer particle under a uniform solvent convective field (8). Analytical approximations of the model showed that the dissolution process is reptation controlled if the particles are small, and the disentaglement rate is much slower than that for disengagement and mass transfer. The dissolution time is simply the reptation time this case. Similar analytical arguments showed that for larger particles, dissolution time scales with initial particle radius to the 5/3 power if the process is mass transferred controlled.

Brochard and de Gennes (9) analyzed the dissolution of a semidilute polymer solution of various droplet sizes and reported the existence of a critical droplet size, below which the dissolution time is droplet size independent. This minimum dissolution time termed the reptation time, [t.sub.rep], was dependent on the molecular weight and structure of the polymer. The critical droplet size was found to be on the order of [-square root of [][t.sub.rep]], where [] is the cooperative diffusion coefficient. Devotta et al. (10) extended the analysis to solid particles, and found that dissolution time of polymeric particles also becomes size-independent for particles smaller than a critical size. This finding is in marked contrast with the dissolution behavior of nonpolymeric solid particles and low molecular weight particles, which are primarily mass transfer limited, and are strongly dependent on particle size. Nonpolymeric particles shrink continually during dissolution, while polymeric particles first swell, and then shrink, during dissolution. The particle size dependence for the dissolution of monodispersed, nonpolymeric particles can be described by the Hixon-Crowell equation (11, 12):

[Mathematical Expression Omitted] (1)


[m.sub.o] = initial mass of a particle

m = remaining mass at time t

[D.sub.o] = initial particle diameter

k = reaction rate constant

The Hixon-Crowell equation suggests that a plot of dissolution time of nonpolymer and low molecular weight polymers vs. particle size should consist of a straight line passing through the origin ([D.sub.o] [varies] f). A similar plot for polymeric particles, as shown in Fig. 7, intercepts the temporal axis at a finite minimum dissolution time. Devotta et al. (10) added 60 mg of polymer particles of known "average" particle size into a beaker containing 80 ml solvent and used a stopwatch to determine the dissolution time according to visual observation. The authors reported that the readings were reproducible to within [+ or -]5 sec. The experimental setup described in this report offers a finer time resolution. This time resolution can be further improved, if necessary, by simply upgrading the setup with a high-speed video recorder.

The existence of a "minimum" dissolution time and an "optimal" particle size has important implications for 3DP. Powder processing for polymeric materials is inefficient at best, particularly for very fine powder. A 75 [[micro]meter] "optimal" particle size for this polymer implies that there is no need to expand great efforts in producing sub-45 micron powder from this polymer, since no improvement in particle dissolution will be achieved. The use of sub-45 micron powder of this polymer may also cause powder spreading problems due to electrostatic charging, resulting in poor powder bed uniformity.

The problem of solvent evaporation from nondissolving 3DP powder beds is analogous to the problem of drying from a porous substrate. The latter process is frequently encountered in sol-gel processing, tape casting, and many coating applications. Briefly, three drying stages have been described. The initial drying stage is termed "constant rate period," in which the evaporation process is similar to that observed with pure liquid layers. Evaporation rate is expected to be higher from a powder bed because of increased surface area as the surface liquids conform to the particle morphology. The planar, nontextured surface of the pure liquid case has less surface area, but equal evaporation flux. The curvature of the liquid may also contribute to the increased evaporation rate. The additional thermal mass of the salt particles may also help to maintain the solvent temperature at constant levels, hence maintaining evaporation rate. Solvent molecules in both cases vaporize from the liquid-vapor interface, diffuse across a boundary layer, and mix with ambient gases. This stage is controlled by external diffusion across the boundary layer, and is expected to dominate the process if the boundary layer is large. As the initial surface liquid layer is depleted, a constant evaporation rate can be maintained by redistributing liquid from the interior of the porous body to replenish the surface liquid. Liquid redistribution is expected to be a minimal effect for thin powder layers, especially if the particle dimensions are on the same order of magnitude as the layer thickness. Isolated dry regions develop on the exterior surface as drying continues, but constant rate may still be maintained initially by lateral diffusion of vapor molecules within the boundary layer. This is particularly true if lateral diffusivity within the boundary is much faster than that through the boundary. The constant rate period for chloroform evaporation from a powder bed is labeled in Fig. 8. The second stage of drying commences when the evaporated volume is no longer replenished adequately by capillary migration of liquid from the interior to the surface, or when lateral diffusion inside the boundary layer is insufficient to compensate for the loss in surface area. The second drying stage is termed "first falling rate period," and the evaporation process is controlled by the capillary migration kinetics of bulk liquid to the surface. The final stage of drying is termed "second falling rate period." This stage is characterized by solvent vapor diffusion from isolated wet pores to the surface through the interconnected dried pores. Pathways in thin powder layers for vapor diffusion are expected to be more straightforward than those in thick granular structures.

The evaporation rates obtained from the previous sections can he used to estimate the time scale for complete solvent evaporation from typical 3DP features. The binder per unit line length (BPULL) is the volume delivered to print a 1-cm-long line:

BPULL = f/v [cc/cm] (2)


f = volumetric flowrate of binder solution [cc/sec]

v = printspeed [cm/sec]

The time scale for solvent to evaporate from the top surface of a printed line is:

[[Tau].sub.evap = [Epsilon] [multiplied by] BPULL [multiplied by] [10.sup.6]/[J.sub.evap] [multiplied by] A = [Epsilon] [multiplied by] f [multiplied by] [10.sup.6]/[J.sub.evap [multiplied by] v [multiplied by] A [s] (3)


[Epsilon] = correction factor accounting for evaporation in flight

A = area of top surface of printed line [[cm.sup.2]]

The correction factor for chloroform evaporation in flight was determined in preliminary experiments to be 0.9. The [10.sup.6] is for unit conversion from nl to ml. Typical 3DP lines range from 300 to 500 [[micro]meter], depending on packing density and extent of capillary migration. The timescale can be estimated by using representative operational flow rates of 0.8 cc/min, and experimentally obtained chloroform evaporation rates.

The unvented evaporation timescales for three line widths are plotted in Fig. 10. It can be seen that the timescale of evaporation is not significantly affected by changes in print speed for speeds above 60 cm/s, and is highly sensitive to printspeed below 30 cm/s. Widths of the printed lines, hence evaporating surface area, appear to have more influence on evaporation timescale than print speed under typical 3DP operational conditions. The plot shows that even at the maximum print speed (lowest saturation), the minimum evaporation time is approximately 17 seconds. The typical 3DP print speed is chosen based on a number of parameters. One important parameter is print resolution, which can be adversely affected there is more liquid volume deposited than the available pore volume within the local region. Flooding occurs when the liquid volume oversaturates the pore volume. The saturation print speed can be determined based on volume conservation:

[v.sub.s] = f/60 (1 - [[Rho].sub.p][Pi][r.sup.2] (4)


[v.sub.s] = print speed below which oversaturation occurs [cm/sec]

f = volumetric binder flow rate [cc/min]

[[Rho].sub.p] = powder packing density

r = radius of printed line [cm]

The saturation printspeed is 33.7 cm/sec, for example, based on typical binder flow rate of 1 cc/min, packing density of 0.30, and 300 [[micro]meter] wide line.

The vented evaporation time scale is expected to be significantly shorter. The vented evaporation timescales for three typical line widths are plotted in Fig. 11. It can be seen that the timescale of evaporation is not significantly affected by changes in print speed for speeds above 30 cm/s, and is highly sensitive to print speed below 15 cm/s. Less dependence on primitive dimension is also observed. Figure 11 shows that even at the lowest saturation, the minimum evaporation time is approximately 3 seconds. This is within the timescale for PLGA particle dissolution, as shown in Fig. 6. It should be emphasized that the plots in and Figs. 10 and 11 are based on calculations that do not account for capillary migration of the solvent into adjacent pores, and become unavailable for particle dissolution. An additional assumption is that evaporation occurs only from the top surface, but in reality some evaporation is expected along portions of other surfaces. The evaporation rates used to generate Figs. 10 and 11 were measured from solvent evaporation from a large area. The plots were based on evaporation from thin lines, which have larger surface area to volume ratio. The combined effect of these conditions is that the evaporation timescales predicted in Figs. 10 and 11 represent upper limits.

The effects of ventilation on evaporation timescale can be better appreciated by combining the two previous Figures, as shown in Fig. 12. Significant reduction in timescale is achieved with ventilation. It should be noted that although the plot shows that approximately 3 seconds are needed for complete evaporation, it does not suggest that 3 seconds are available for dissolution. The solvent-polymer gel mixture becomes increasingly polymer-rich during initial evaporation and dissolution. Dissolution may cease when enough chloroform has evaporated, or enough polymer has dissolved, to exceed the solubility limit for PLGA (85:15 108,000) in chloroform. The actual time available for particle dissolution is expected to be less than predicted by the evaporation timescales. The previous three plots showed a dramatic dependence of timescale on print speed for the low print speed regimes. It should be emphasized that those extremely low printspeeds are not practical in 3DP, as they tend to deteriorate print resolution. A better approach to maximize particle dissolution is to decrease line spacing between adjacent lines, but preserve print resolution by staying on the high print speed regime.

An approximate dissolution time([[Tau].sub.D]) curve can be constructed from Fig. 7 to describe the dissolution of PLGA (85:15 108,000) particles in chloroform, and superimposed onto the evaporation curves from Fig. 12 to illustrate the combined influence of dissolution-evaporation on microstructure formation [ILLUSTRATION FOR FIGURE 13 OMITTED]. The shaded circle in the dissolution-evaporation (DE) plot in Fig. 13 represent the evaporation time for a line printed at 150 cm/s. The dotted horizontal line shows that at 150 cm/s, the evaporation time is greater than that required for complete dissolution of [less than]90 [[micro]meter] particles.

The micrographs (SEM's #1-3) in Fig. 13 represent actual 3DP samples of various PLGA particle sizes, printed at 150 cm/s. It should be emphasized that these samples were prepared by printing into a bed of salt/polymer mixture. The samples were then sectioned for SEM analysis after particulate leaching. This approach greatly reduced the occurrence of sectioning artifacts such as smearing and scratching, and allowed the observation of the as-printed polymer surfaces. It can be readily seen that complete dissolution is achieved for [less than] 45 [[micro]meter] PLGA particles (SEM #1), and 45-75 PLGA particles (SEM #2). SEM #3 shows that although some large particles are connected to each other, many remain undissolved. This is not surprising, since the dissolution-evaporation plot shows that the timescale for dissolution of [greater than] 90 [[micro]meter] particles under these printing conditions is much greater than that for evaporation. The dissolution-evaporation plot suggests that complete dissolution of the large particles can be achieved by turning off the ventilation, or by decreasing the print speed. SEM #4 shows that the particle dissolution was indeed enhanced by decreasing the print speed by 50%, which effectively doubles the volume of solvent available for dissolution (shaded square). The micrograph shows that some particles still remained undissolved, as predicted by the DE plot. The DE plot suggests that 150 [[micro]meter] particles can be completely dissolved at very low printspeed (20 cm/s). Such slow print speeds are 'impractical for 3DP since they deteriorate feature resolution. An alternative strategy to extend the evaporation time is to print repeatedly over the same layer, such that the Large particles become progressively smaller and smaller until dissolution is completed. This approach is superior to the slow print speed method because it provides the additional time required for dissolution without adversely affecting print resolution. Another approach is to decrease the ventilation rate to increase the evaporation timescale.


An experimental setup was devised to determine the timescale for particle dissolution. This timescale was found to be particle size independent for small particles, but particle size dependent for larger particles. The kinetics of chloroform evaporation from a typical 3DP powder bed were determined experimentally. The timescales for these processes were found to be on the same order of magnitude. Dissolution-evaporation (DE) plots were constructed to illustrate the relationship between evaporation timescale, dissolution timescale, particle size, printing conditions, and external mass transfer conditions. The DE plot provides a good estimate of the necessary printing conditions under which the evaporation time is sufficient for particle dissolution for a given particle dimension. Microstructural analysis of the printed structures confirmed the importance of the relative timescales.


This project was funded in part by NIH (DE0027505) and Therics, Inc.


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3. J. Yoo, M. J. Cima, E, Sachs, and S. Suresh, in Ceramics Eng. and Sci. Proceedings, G.N. Pfendt, ed., ACS, Westerville, Ohio (1995).

4. B. M. Wu, S. W. Borland, R. A. Giordano, L. G. Cima, E. M. Sachs, and M. J. Cima, J. Controlled Release, 40, 77 (1996).

5. B. M, Wu, PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts (1997).

6. T. L. Fan, PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts (1995).

7. J. F. Bredt, PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts (1996).

8. V. V, Ranade and R. A. Mashelkar, A/ChE J., 41, 666 (1995).

9. F. Brochard and P. G. de Gennes, PhysicoChem. Hydrodynamics, 4. 313 (1983).

10. I. Devotta, V. D. Ambeskar, A. B. Mandhare, and R. A. Mashelkar, Chem. Eng. Sci., 49, 645 (1994).

11. A. Hixon and J. Crowell, J. Ind. Eng. Chem, 23, 923 (1931).

12. M. Otsuka and Y. Matsuda, J. Pharmaceutical Sci., 85, 112 (1996).
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Author:Wu, Benjamin M.; Cima, Michael J.
Publication:Polymer Engineering and Science
Date:Feb 1, 1999
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